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One of my student researchers is likely falsifying some results/data. What are the consequences?
Relevant info and background:
I'm an engineering Post Doc at an American university.  One of my roles is to basically function as a 'project manager' for a couple projects that have a number of Graduate-level RAs working on them.   I have a good relationship with all the RAs and all are hard-working.
I'm convinced that one of the graduate RAs is falsifying computational results/data (also called "rigging data" by many) in some cases.  Note that the individual appears to be doing this for only some cases, not all.  I have many reasons to believe this, but here is a few: (1) inability to replicate various results, (2) finishing the work at a pace I think is not feasible, (3) finishing his work at home where he surely does not have the software environment to actually complete the work.  There are also other reasons I believe this to be the case, but you get the point.  I'm also convinced this has occurred for over 1 semester, so I probably need to report this since I am responsible for overseeing all the work.  However, the student in general is a good person and hard worker. He has passed the preliminary exams and is finished with all classes - I'd hate to see him expelled from the university since he's this far into the program.
I have some questions:

What do you think could be the maximum punishment for this grad student/researcher?  I'd feel terrible if it resulted in expulsion.  I would think that you would have to receive at least one warning from the university before an expulsion, except in very extreme cases.  I'd be fine if this resulted in suspension, and even losing funding, but for anything more I'd feel bad.  What is the standard maximum punishment for these cases?  Also, what is the most likely punishment?
What is the punishment for me if I don't  report this problem?  For instance, say I just pretended ignorance.  It is extremely unlikely I would do this, but it's worth asking.
How common is this?  I would think this happens once in a while - a grad student decides to be lazy and fabricate a small portion of the overall results to avoid working the weekend or something.  An experienced professional would know this is seriously wrong, but not necessarily a mid-level PhD student.

Any advice from people with experience in this, professors, grad students, principle investigators, etc would be great

This is a very serious issue. If you are confident the student is falsifying data, you have an ethical and professional obligation to report them, even if it ruins their career. Frankly, if they are falsifying data, the worst possible thing would be for them to continue into an academic career: at some point, their deception will be found out, and then all of their work since they received their degree will be discredited and they will probably be permanently ostracized from the academic community. The consequences they would receive if reported now, however severe, would be less damaging.

@Kevin and it will backfire on whoever failed to see through the fraud.

...Thinking about your question some more, though, it looks to me like while you have good reason to be concerned about the student's behavior, you don't have strong proof that the student is in fact falsifying data. I would move forward cautiously. I'm not very experienced (I only have my terminal masters degree), so I'm not entirely sure what to recommend doing. Perhaps you could meet with a more experienced researcher in your lab to discuss your concerns and get advice on what steps forward you should take?

The "finishing his work at home" thing doesn't read as very strong evidence to me, unless there's more to the situation that's not apparent. Lots of work can be done by remote access, using tools like SSH, remote desktop, VNC, LogMeIn, etc. I even know physical laboratory experimentalists that have full remote access to their equipment and sensors. Unless there's some unique resource necessary for this work, that's strictly inaccessible over a network, you would need to rule out actual use of such mechanisms.

This is really three questions in one. You ask what are the consequences (to them? to you, if you take no action? to you, if you take action? to the supervisor?). But you're also kind of asking us to give a guess on whether your suspicion is accurate, which is impossible. The low-key middle-ground tactic would be to tell them "I tried to replicate XYZ results and was unable", hint to them you're onto them without making accusations, and see if they knock it off.

@smci I also like this approach because the student may have an explanation for these inconsistencies that the OP simply isn't aware of.

Only the "inability to replicate various results" is a possible sign that the student is doing something suspicious. The other two could very well be lack of knowledge on your side. So have the student replicate some results under your supervision.

You should probably address the non-reproducible results before anything else. The most common reason people make non-reproducible results is honest mistakes, but even if the mistake is honest, once you're aware something is wrong it's not really honest to publish the data as if you think it's true. Even if he's not intentionally falsifying results this is a problem in itself.

I will be the devil advocate here but why not just going to see the student and explain to him what you think about his work, he will maybe say that he cheated because of pressure and so on, then (it's a student, remember) you will explain him why it is not correct, what are the consequences and you will (because you are a good teacher) try to fix that without crushing his career. I think a student can make mistake... Even those really really bad one.

Assign another student, or even two (who you are completely trustfully, grad or MSc)  to work with this student for a short time, and supervise/look through all the steps of analyzing data. It will take time, but you will have a certainty in the end.

Even if (1), (2) and (3) are correct, I would first assume (without knowing more specifics) that the student is working honestly but incorrectly (in line with @Owen's comment).  Students, and even faculty, make mistakes all the time.  I would express my concerns to the student about the correctness of their work, and discuss in detail what they did to figure out what exactly went on.

If the student has been cheating and falsifying data and it is proven, usually there is a pattern of behavior. I doubt he started this Spring semester. Who know how long he's been doing it, and the bigger question is did he earn his way to RA or did he cheat his way there?

At some extent, we need to be strict for the case like this, considering the "butterfly effect" that will be happened in the future. Besides, it is very important to bring the education to the next level. As long as you can prove it, not based on your opinion, actually there is nothing to decide here but not to accept that. As a well-educated person, it's very important to learn about the fallacies and how it can affect our decision.

Doesn't your institution have explicit guidelines about how to handle falsification of data? I though they would have.

For 3), how can you be sure he does not have software needed? To be blunt, he may not have licence, but not having legal right to have software is not a proof he does not have software. And if it's cracked software, it may have bugs legal one does not - that would explain 1) pretty well.

https://en.wikipedia.org/wiki/Schön_scandal

Why are you so worried about the negative consequences to the student? It sounds like your moral algebra has this equation in it: "If the student is guilty, but the punishment is more severe than I really feel comfortable with, it's better to let him get away with it." That's really what you're thinking? It should never be about the effects of the consequences on the person who engaged in the wrong act (as if those should mitigate punishment), it should be about the consequences on others, on society, on how serious that is.

If they are falsifying data, and have been for at least a semester, how are they a hard worker?

Is it possible to have student reproduce experiment (entire process from beginning to end, including any software used and settings changed) in front of your eyes?

When he presents data to you, why dont you ask for handover of the scripts? Then check if they reproduce the data. A lot of students are poorly organized so 1-3 are not hard evidence (in my opinion).

You have suspicions, but the evidence, as you sketch it here, is circumstantial. You need hard proof. Then you can (and must) act.
Falsifying data is a capital crime in academia. It wastes time, possibly years of other people's work. Don't let it get through. This person, if they indeed falsified data and would come through with this, will taint anybody and anything they had to do with - you, your group, your department, your university. Their results will be worthless, and so will be the degree you bestow on them.
You would feel sorry for that person if expulsed; but how sorry would you feel for a person who for 2 years will try to reproduce this grad student's results and fail for no fault of their own? How about their life and career? An honest mistake is one thing, but faking data? You are feeling sorry for the wrong person here; you'll spare the guilty and will let the innocent being impaled? A grad student is sufficiently mature to know better than to produce "synthetic" data.
How about the person abetting such a fabrication? Frankly, if caught, depending on the power structure that person may get away with a milder penalty "for not knowing what was going on", but in principle they should get the same, if not a harsher penalty, because they certainly cannot claim they didn't know that this is wrong; and they know the repercussions.
How common is it? Hard to say, but there were a number of large scandals (Jan Hendrik Schoen comes to mind), there is probably a halo of minor such attempts. From my own anecdotal stock: I once heard the conspiracy theory that spectroscopists would intentionally introduce "innocent" wrong factors into published formulas that could be interpreted as honest mistakes to prevent competitors from progressing. I didn't believe it, however, once I had to use such a formula from a paper, and to be satisfied I rederived it and some of its "brothers" myself in a tortuous process taking several weeks; lo and behold: I found that one of them had an integer factor wrong. It goes without saying that I have no real reason to assume it was intentional, but the conspiracy theory still lodges in the back of the mind.
Bottom line: if he really fakes data, letting this happen is not an option; but the evidence must be carefully and (important for fairness to the accused) confidentially vetted to establish whether this is indeed the case.

Great answer, but I disagree with "you must have incontrovertible proof". It is perfectly fine and indeed desirable to report strong suspicions based on less-than-solid proof to the PI, the dept. chair, or anyone else who has the ability to investigate the case and determine if misconduct occurred. Of course, in that case, when reporting suspicions the OP would make clear that they are suspicions and may turn out to be wrong. My point is that when suspicions are strong enough there is an ethical duty to report them, just like there is a duty to report a strongly suspected crime to the police.

@DanRomik In principle, I agree with you: "incontrovertible" may be too strong. Still, the evidence must be carefully and - initially - confidentially vetted and should be sufficiently close to certainty - more than anywhere, reputation is central in science. And even if one is wrongly accused and thus wrongly perceived as falsifying data, that person's career will take a dive, whether deservedly or not. I think this is the case one needs to worry about, not about harshly treating someone who has provably falsified. The knife cuts both ways.

why not talk to the student and communicate your concerns with him? Based on the OP's question, it seems like he does have very legitimate cause for concern. However, going over his head and getting the administration involved would be a step I would take AFTER communicating with the student and letting him know that his methods "don't seem as rigorous as expected." If he ignores OP's admonishment/advice, then OP has to do what he has to do. But OP is, in fact, the superior directly in charge.

@CaptainEmacs thanks for agreeing. I agree that "the evidence must be carefully and initially vetted". That is the point of having an investigation, which is what will happen before the student can be punished and certainly before any misconduct is made public (if indeed it ever is). US universities have well-oiled machinery for carrying out such processes, so I see no reason for the vetting of the evidence to be done by OP. OP will of course aid in the investigation by providing information and expertise, but acting as an investigator is way beyond the scope of a postdoc's job.

To summarize, I suggest changing or removing the last sentence of your answer to make your otherwise great answer more precise.

@DanRomik Modified according to your request. I did not state how the procedures should look like as they may depend on country.

In US research universities, there will be detailed policies in place to manage potential research misconduct complaints, both establishing if research misconduct has taken place and the committee who will determine what will happen. If I were you, with what you have described, I would advise checking your university's responsible conduct of research  webpages to find who is that person and make an appointment to see them.

This misconduct is considered the ultimate misconduct in the research community. The offender is often stripped of his credentials and because of the tight knit nature of the scientific community, even if the credentials are not stripped the researcher may never find work as a researcher again. It will impact the ability to secure funding in the future.
If you are aware of it, as you claim to be, you can also be affected, ESPECIALLY if your name is on or associated with the paper. Additionally, if you are the one who secured the grant, this could backfire for you trying to secure grants in the future.
This is not common or uncommon, some people purposefully falsify data to support their hypothesis, but it is not always inaccurate. Sometimes researchers choose to only highlight some information and not other so that their hypothesis is supported and this is a more grey area.
BOTTOM LINE: If you know your student is falsifying data, then don't allow them to do so, for their career and for yours.

Communicate with the student.  Let the student know your concerns.
The question seems rigged to determine what penalty may be appropriate, and how to kindly dish out the pain.
However, if we show good faith, then maybe we don't need to be quite as secretive.  Say, "This resembles trouble.  Here are the concerns."  Then, if the student is innocent, the student may be able to explain things, and learn importance of proactively make things more clear so that suspicions don't grow into bigger problems than warranted.
If the student did do something wrong, maybe the student can correct things before they get further out of hand.  The situation may be more correctable before more resources (including time) get spent on a road that may be wrong.
In education, the goal is often to help people do better.  A common assumption is that people are typically inexperienced, and mistakes may be made.  The goal isn't to try to maximize penalty for people who may be struggling with new skills.  The goal is to try to get people in a good situation, including experience doing things desirably (including doing things properly, and successfully).
So, to re-cap this quite simply:

if you're absolutely convinced that something is completely wrong, then go through the formal steps of handling such problems (reporting the issue, and whatever consequences follow through).
If you're not, then communicate the observations that bring concern.

(If this communication results in more trouble being discovered, be ready to shift over to the first bullet point, as needed.)

My concern here is that if the student has falsified data, your suggestion is to give them a heads up. This will enable them to adjust their methods to avoid being found out in future. Falsifying data is not a teachable moment or a mistake. It is deliberate and deeply immoral, and should quite rightly permanently taint a researcher who does it.

"I cannot reproduce the results you obtained. Please write down your methods and provide to me all tools required to reproduce." is not giving him a heads up to adjust his methods to avoid being found out in the future. It is either bringing him back on the right track (not falsifying data anymore, for fear of being found out), or it won't change a thing, and then you can still decide to go to the chair/dean/whatever.

@MJeffryes : Giving them a heads up is completely intentional.  Attempting to keep actions secretive would be a more adversarial move, and I don't recommend that until you start to determine that adversarial actions are required.  At this point, I'm recommending to take the friendly approach.  The intended goal is helping to correct an apparent problem.  If you declare enemies too quickly, you can eliminate some potential opportunities to still resolve things while on more friendly terms.  Don't try to begin the punishment process before non-speculatively knowing the penalty is warranted.

I wonder why none of the other more voted answers opt for this. Why isn't talking with the student the first option? Somehow it's implicitly assumed that whatever he's done he'll continue doing regardless...

What do you think could be the maximum punishment for this grad student/researcher?

Whatever the maximum punishment is, that punishment has been decided by the people running the university. If you consider your university to be a reasonably well-functioning institution (and I would hope you feel this way about the place where you have decided to spend several years of your career), you need to remember that the people making such decisions have much, much more experience than you in handling all different kinds of academic misconduct. Thus, the punishment is likely to have been well-calibrated over many years and based on a large amount of cumulative experience. What makes you think that your personal judgment on this question is more wise or likely to be correct than such a body of accumulated knowledge and experience?
By not reporting your suspicions, you would essentially be saying "I know better than everyone else what needs to happen to this student, so I will usurp the institution's right to properly bring the student to account for his actions and just act based on my own gut feeling to save myself from the feeling of guilt over the punishment that the student would receive (even though any such punishment would be 100% the student's fault)." This line of thinking is simply wrong. The punishment is not, and shouldn't be, your decision. You have a duty to report the misconduct, and by not doing so you would be making yourself complicit in all its many potentially harmful consequences, which were described quite well in the other answers.

+1 for "I usurp the institutions' rights to bring the student to account".

Completely disagree: rules on the institution level are indeed built on accumulated experience, but not necessarily with the interest of either science or the PI. Rather based on maximizing the interest of the institution under their legal, financial and political constraints (which can be opposite to the interest and values of the OP).

@Dilworth in principle you may be right, which is why I added the caveat "If you consider your university to be a reasonably well-functioning institution ...". If OP has serious cause for concern that the university is staffed with incompetent or corrupt people, that might call for extra caution. However, the default assumption should be that large US universities have well-tested and reasonable procedures for handling misconduct. Thinking that one knows better than everyone else is a common human cognitive bias; in this case it would almost certainly be an incorrect assumption to make.

Even large US universities have interests that may directly oppose the interests of the OP. It is not a case where the OP and the university have both the same goal, in which it is correct to assume that the university knows better than him how to act. It is about the possibility of completely contradicting goals.

You don't need to kick up a big fuss about it.
While it is definitely the case that any case of data fabrication is worthy of the levels of punishment it incurs in academia, it is not very clear that this is actually happening here. And in any case, the repercussions of scientific falsification should be very clear at any level, even for undergraduate students.
Inability to replicate results is extremely common in all scientific fields, and the overarching likelihood is that the analysis or experiments were carried out incorrectly for some reason. In the vast majority of cases, that is all there is to the story.
Simply deal with this problem as you would with any other inexplicable scientific result. Walk through the entire protocol, troubleshooting all potential issue spots, and exclude variables as required. In the extremely unlikely case that you find that the student was actually falsifying data, you must report it, but it seems unlikely to me that it is going to be the case.

If this person is falsifying data now, this person will continue to do so later as a PI. While you're sure to feel bad about it, science as a whole requires you to address the situation. When the public loses faith in science, we all suffer.
There are many ways to address this in a discreet manner (to ensure your intuition is accurate). Why not have this person walk you through the data/analysis step by step from ground zero?

How do you know the person will continue to do so later?

You don't know in any absolute sense, but it is the least assumption.

So it is not known after all. In this specific case where one has the questioner's personal experience to rely on, what is the point in making such assumptions? Why not just ask the questioner whether, per his/her judgement, this student is likely to repeat such behavior throughout their career, and then base the answer off of that?

@Jin It is expensive to verify results (people do not get funds to reproduce known results); therefore, trust is absolutely central in science. If someone falsifies data once, he cannot be trusted anymore. Everything that person claims to find out, especially an expensive to produce result, needs to be independently verified anyway; their testimony is unreliable; so why waste attention and grants on them ever again? A person once caught taking a bit of money out of the cash register showed a "fluid" morals once, they won't be let handling the cash again.

@CaptainEmacs This is perhaps the correct procedure from an external position, yes, but the question being posed is case-specific and internally framed, and the answer should reflect that. I don't see much point in brandishing out general multi-purpose guidelines (which the OP could find anywhere easily, rather than going through the hassle of writing up his/her question in search of a tailored answer). You may not ever trust the student in question, but the OP may, and he/she is our only window into this specific case, and it is through their lens that any decision should be measured.

Unless, of course, you think that anybody who commits such fraud should never be trusted by anyone, which I feel is a bit too grim view on the world.

@Jin The only question is whether the OP has hard proof that the person falsified in the past. It is irrelevant whether they will do later - for which I explained the reason above. Also, usually universities will have procedures in place to punish such transgressions, but what the precise consequences are, will depend on the uni and cannot be answered on SE. But you asked "How one knows that the person will do it later?" - and what I am trying to say is: it's not relevant whether they will really continue this or not - only that the costs for everybody in the future will be as if they do.

Surely that's only the case if the person is ever actually caught. If the OP doesn't reveal what he knows, then nobody knows that this person falsified data, and then they won't treat this person as if they will falsify data again. That brings us back to the essential question of whether OP will reveal it or not, and my point has all along been that this decision depends (or, should depend) on whether OP personally thinks this person will continue to falsify data even after the OP has confronted them with it. But the answer we are commenting does not reflect this nuance. I'm stopping here.

@Jin Confronting the offender may help if the warning is dire enough, ok.

@Jin - seriously??  So it's ok if I steal money from you now, as long as I might not do it again later?

@HEITZ Where did I say it was "ok"? You sound confused.

@HEITZ Let me reformulate your example slightly: Jack steals money from Jin in the past. Will Jin leave the wallet out again when Jack is around in the future?

If I trust Jack anyways, I will leave the wallet out, and if he steals from me again, I will cut all ties and report him to the relevant authorities. If I don't trust Jack anymore, I will cut all ties, and depending on the severity of the crime, I may or may not report him as well. But what is certain in all of this is that if I were unsure of how to handle the situation, I would be fully unappreciative of lazy one-dimensional answers like "report him! lynch him! Jack can never be trusted, ever!". Hope this analogy makes my point clear.

@Jin I would agree if it were just about you and Jack; but it's not. I thus fine-tune my example: Jack has stolen from you. You give him a dire warning. People know he has handled your money in the past (you didn't mention anything to them) and thus think he is honest. They leave their wallets lying on the table. Jack is around. Do you warn them off?

In terms of immediate authority, I assume you and the student in question both ultimately report to a professor. I expect that professor is one or more of the PI on the supporting grant, the student's thesis advisor, and your supervisor. I really hope you have a strong, trusting relationship with this professor, for a few reasons:

they will be the first line of investigation and response in dealing with this situation, and likely carry more personal/reputational and institutional responsibility for it than you do
the student has likely worked with them longer than you have (postdoc there maybe 1-2 years, vs ABD student)

Basically, you don't want to end up in a position where your actions lead the professor to hold this against you. That could lead to withdrawn/non-renewed funding for you, withheld or weakened recommendations for future positions, and so forth. You really need the professor on board with the suspicions before any wheels of process start moving.
If there's some administrator responsible for this sort of issue that you know and trust not to jump the gun, you could potentially speak to them first to get your concerns on record before bringing them to the professor, to avoid the risk of the professor trying to sweep them under the rug and/or throw you under the bus.
Edit to add 1:
Ultimately, though, resolving this situation now, while the student is still pre-PhD, is in their best interest. If they aren't doing anything wrong, then they'll learn how to conduct their work in a more traceable, transparent, supportable, and reproducible manner. If they are, there's at least a chance that they can get straight without a permanent black mark on their career. Once they've gotten that degree, any such allegation could lead to it being revoked, grants they've received being suspended or cancelled, etc. This is the last point in their career where they can learn appropriate boundaries and reasonably hope to rehabilitate themselves.

I think three statements that you make are just your impressions and as you know that these are your impressions, you are not completly sure that student in question falsifies the data. Otherwise, I think you would not have asked the question here.
The best thing to do in order to be sure 100 % is to replicate all results with this student in your office on your computer. Otherwise, I think your statements are just your own impressions, without any solid evidence.
If you see that data is falsified, then you should report it.

+1 This answer addresses an important aspect of the question. Whereas in the lab sciences the experiments are never 100% reproducible due to inevitable small environmental factors, in the computational realm everything, if properly documented, should be able to be verified and reproduced. Even random algorithms like Monte-Carlo can be exactly reproduced, especially in the testing stage, by seeding the pseudo-RNG with the same seed everytime. So if you want to make sure the student is doing his work: just get the code from him and run it on your own computer.

@Willie Wong, Fully agree. The code that uses student would be useful to understand if there is any falsifaction. As in programming stuff, it is more difficult to understand the code of others than writing its own, I think it is better to reproduce all results with the student. By doing this, OP can understand also the methodology used and can verify the data used.
Unfortunately, in some fields like economics, most of papers are not reproducible ;
https://www.timeshighereducation.com/news/papers-in-economics-not-reproducible

@WillieWong, I have the impression that computational experiments are also prone to variation due to hard-to-control environmental factors, including software versions and initial states of random number generators. Avoiding these pitfalls should be possible, as you say, but it doesn't seem straightforward to me (http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1003285).

@Vectornaut: initial states of random number generators can be controlled by properly seeding it as I wrote. See, for example, the documentation for the Julia language. Software versions can be documented; and if open-source software is used, the older versions can usually be tracked down in the appropriate repositories. Avoiding these pitfalls is in fact quite straightforward (and in fact the rules in your linked article make it even more so). Compare to the laboratory sciences the amount of documentation...

... is not more than what would be expected to go into a lab notebook keeping track of the conditions underwhich experiments are run etc. The fact that some individuals find it "hard" is more an indication that some computational scientists are not given the appropriate data management training that typical laboratory scientists would be given. In this day and age it should be the responsibility of the head of the lab (either the professor or the lab manager) to hold the students accountable for good data management practices.

@WillieWong—Whoops, I didn't see that you'd mentioned seeding in your original comment! That Julia documentation may come in handy for me, since I've been using Julia more and more; thank you for sharing it.

@WillieWong, since I didn't say it explicitly in my previous comment: I apologize for my careless reading.

@Vectornaut: no apologies was ever needed! Thank you for the sentiment.

@Vectornaut if the RA cannot make results reproducible for his supervisor, how will he make them reproducible for anyone else in his community? It is his problem, and he has to find a way to demonstrate that his research is indeed reproducible.

@xmp125a, I had the mistaken impression that standards for reproducibility in computational science are currently not much higher than in laboratory sciences. I got this impression from things like [ https://reproduciblescience.org/who-we-are/ ] [ https://khinsen.wordpress.com/2015/01/07/why-bitwise-reproducibility-matters/ ] [ http://ivory.idyll.org/blog/2014-myths-of-computational-reproducibility.html ]. Fortunately, as WillieWong says, reproducibility stadards are now much higher than I thought.

@Vectornaut the reproducibility standards across the field are pretty poor indeed, but there is no reason that OP would not demand reproducibility inside his own group. At least, this is much easier to achieve due to (probably) far more uniform resources inside one lab than across the field in general (same software, same hardware).

I agree with Captain Emacs's answer, but there is something missing that I feel is important, namely:

Ask the RA directly whether he is fabricating any data, and while asking tell him why it is wrong to do so, and also that if he really does it and anyone finds out he can be expelled. At the same time tell him that at this juncture the best thing to do now is to redo all tests properly, meaning that he records all the random seeds used so that his data is completely reproducible.

After that it is likely that the problem will be resolved more or less satisfactorily, because it is generally difficult to write a program that looks normal and yet find a special random seed that causes it to have special behaviour. (It is possible but increasingly improbable for larger-scale tests.)

Tell the student that this doubt exists but in a one-on-one situation
To clear this doubt, ask him to make his results fully reproducible. It is in his own interest to show that he did not falsify anything. Show him that there is "immediate danger" that this gets investigated.
If he did not falsify anything (and your doubts were wrong), then this is a viable route. It requires some effort, but of course it can be done (and should be done, anyway). Then no damage is done, you only force him to work more transparently.
Allow him to redact work, if no harm has been done yet
This is the only "easy way out" that is in my opinion acceptable. In particular if nothing has been published outside of the university, you can allow him to redact falsified material, in order to replace it with real work. This may be punishment enough at this stage: It may set him back half a year towards graduation! But it may also require additional measures, depending on the severity.
He may then learn a key lesson here: while you may get away in highschool and maybe even undergrad, once the work gets more closely reviewed, misbehavior, copypasting and data fabrication is likely to be discovered, and this is not a good way of working. A backlash could come any time, and may ruin his reputation.
In the case that he admits cheating on this project, I would consider also reviewing earlier work, too.
If harm has been done, you want to redact anyway
If anything of this has been published yet, your name or your professors name is likely to appear on it, or at least be associated with it. In this case, you really will want to have this resolved...
At this point, it may be necessary for your own reputation to trigger a formal investigation; partially to clear yourself from any responsibility.

In a nutshell,
1) you must get a decent proof of misconduct, and
2) if/when you get it, you should report it immediately, even if this means the definite end of his career
Falsifying data is a cardinal sin for a scientist, and as many others remarked, it may waste years of work for other scientists try to replicate (and possibly improve) the faulty results. I was once caught in a situation where my student was trying to replicate somebody else's results, and it seriously impacted her PhD work, since the original authors' selective reporting (they later found that their solution works only in very limited cases, but did not share that finding until much later).
Now, before you rush to your superiors, I would advise you to talk to student about his methodology. Explain him that as (de-facto) project leader you have responsibility to guarantee that all results conform to scientific standards and that after you went through his work, you suspect there might be a problem with his results, as a result of unintentional mistakes or inexperience on his part. Start with this - if he made unintentional mistake (or even multiple mistakes), he will probably more than glad to learn from them and work hard to correct them. For a PhD student, this is sufficiently vague and yet serious that, if he is honest, he will work really hard to correct the problems (and redo the experiments). In that case it is your decision whether you trust him enough to have him on the team, and if you don't want, you should simply explain to your superiors that he does not fulfill your criteria, since he makes too many mistakes, and you do not need such people on the project, period.
I understand that this is a very difficult task for you, since you will have to waste your own time to go through his work and make sense of it, and probably you have your hands full with other work.
On the other hand, it may be pretty easy to spot if he is really dishonest or trying to hide something, because if he took a shortcut the first time by falsifying the results, I very much doubt he will "waste" his time correcting them - more likely he will try to weasel out or start making excuses, which then really means a red flag, and gives you a really good grounds to either confront him directly (usually it won't be necessary, as he will probably start digging his hole deeper and deeper) or just go and report him to the superiors. Because, if his mistakes were unintentional or result of carelessness but he does not feel he needs to correct them, he still deserves to be reported and sanctioned - refusing to learn from mistakes that others point out and refusing to correct them is almost as bad as falsifying data.
I do advise against going to superiors based only on a hunch, because an accusation of falsifying data may ruin his career even if he is not guilty, and further graduate students may become reluctant to work with you, fearing the same treatment (and some may even interpret your actions in a way that you got rid of competition down the road, which is the last thing you need).
And, since you are his superior, you are guilty if you do nothing, and the problems get discovered in his further career. You must act.

Falsifying data is a big no-no. It's on par with (and possibly worse than) plagiarism. It can ruin careers, and can lead to a whole host of huge problems (we don't need any more Andrew Wakefields). So if the student is doing this, you absolutely must report it and cannot feel bad.
That said, from the information you provided, there really isn't strong evidence. If I were on that jury, I would acquit without a second thought.
1) Working from home: Can he connect to a network to access the needed software? Can he run the program in the lab, get the raw data (say in a text file, or spreadsheet) take it home and do post processing/analysis there?
2) Not replicating data: I've written programs and ran simulations that performed beautifully and satisfied all the tests. But when I get to the group meeting, it fails. Why? Because I changed something that "wouldn't affect the results or the existing tests" (Ha!) between the time I originally got it working and the meeting. Or maybe an initial guess was changed. It might only take a few minutes to fix on my own, but in a meeting/high pressure environment I can't fix it right there. To me, that seems like a plausible explanation. (And I'm assuming there's no randomization in the code, I've had Monte Carlo approaches give significantly different results depending on the seed used).
3) Working faster than you expect: I see two possible explanations for this: a) The student is better than you think. b) The student is worse than you think. For (a), perhaps the student is able to crank out code fast, when he hits his stride and has a good mental map of where to go and how things should fit together (this "gunslinger" approach can be effective, but also can let bugs show up that make data replication difficult). Or he has written scripts to run several computations simultaneously or overnight. For (b), perhaps the student "hacks" everything in the code. Hardcodes things that should not be hardcoded, for example. Messes with things that shouldn't be messed with. This can give the illusion of working fast, but results in unmaintainable or inconsistent code, essentially borrowing time from the future.
Obviously, you have access to more information than we do, so perhaps these explanations don't apply. I would suggest talking to the student about the results, though not in an accusing way. Ask him to explain the results, explain what he did, and how he did it. Look through the code that he uses with him, make sure you both understand it. Perhaps there's honest mistakes to be corrected. Maybe there isn't a problem. If he seems to have no idea what he did or can't explain the procedure, then you probably want to bring up your concerns with the PI. But, under no circumstances can you let data falsification continue.


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How do you cite an image no longer found on the internet
I have been working on this report and I saved and downloaded certain images off the internet to put in my paper. When I was going back to cite them later, I reverse google searched the images by uploading the images to have the search engine find them on the internet. Some of these images could no longer be found. How do I cite the images I can no longer find the sources for? Or should I just find different images?

In addition to citation, you probably also need to ensure that the images have a license that allows you to use them in your report, if that's what you plan to do.

What scientific domain is your report about? That should go into your question

If you can't find the source at all, you should choose a different image. You can't simply put a citation like:

Image. Found on the internet, source unknown.

Even though it would be nice to be able to do that, that defeats the purpose of having a citation at all, which is so that people can see where you got it.
You might find the following questions useful:

This question that was pointed out in the comments seems to be a case similar to yours, with good advice. Basically you need to somehow track down the source; once you have tracked it down, the specific citation text is not such a big deal, as long as you are listing the source.
This question is also relevant. Unfortunately or not, the culture is extremely pervasive in academia to just go pasting images from the internet without citations (especially Google images, and especially in presentations rather than published papers). This is not completely ethical, but it is common practice.

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Some co-authors unresponsive when I asked for consent for submission to biorXiv
In short - wrote an article, sent the manuscript to all co-authors and asked for consent for submission and for feedback, if any. After most of the co-authors replied, I made some small tweaks to the manuscript that improved it, but I'm still waiting for consent from 2 co-authors. I sent the e-mail 2 weeks ago, and that should be enough time for them to at least acknowledge they received it, right? All other co-authors replied within a few days.
What makes this especially interesting is the fact that the 2 co-authors that didn't respond were the ones not actually super involved in the experiments, they just provided the transgenic model that I experimented on. I included them as authors on the first (published in a journal) paper because my PI told me we should include them because of that and ok. But now they aren't responding at all, so I'm wondering how to move forward. Remind them? When? Just submit without their consent? Remove them from the author block (and risk a clash with the PI)? I want to submit this, but have no idea what to do.

Ethically you can't submit a paper without the consent of all named contributors. Cutting them out of authorship might be another ethical issue. Editors don't like to see it happen. Let your PI serve as intermediary. Don't let frustration lead you to bad practice. And "just provided the transgenic model" doesn't seem like a minor thing.

This is another reason why models, code, data and such should just be citations to give people credit, rather than giving everyone authorship

It is the final exam period at many US universities, and between that and the pandemic it's an unusually chaotic time for many. You might find out when the final exam period is for the unresponsive coauthors; if it's now, you might send a reminder email immediately after it's over.

Also, you might read this to get a sense for their possible perspective: https://www.scottaaronson.com/blog/?p=388

@Joe Citations to what if the paper is the first mention of models, code and data?

@CaptainEmacs : If they're using someone's data who's not part of the research, then there needs to be some sort of citeable record for that data to uncouple it from the article.   (see the Joint Declaration of Data Citation Principles and the Software Citation Principles )

2 weeks is a fair amount of time, so yes, remind them. You could also write something like "If I don't hear from you by [time] I'll assume you consent to submission", or "I'll submit this by [time], if you have any objections please let me know before then".
That said if you have a PI, you might as well ask them what to do. There's no reason not to, especially for contentious decisions that might lead to bad feelings.

+1 Setting an explicit deadline is definitely the way to go.

Assuming someone has given you permission when they have not is unethical. Sorry. You have no idea why they haven't responded. No. Don't do this. But seeking advice from the PI is good advice.

Actually, since you've been an editor, I'd expect you to know better than to advise this.

Do a little due-diligence. Double check email addresses are correct  and if mulitple emails are floating around, try to send to the others. (or check if there are other ways to contact them to remind them that you are simply waiting on their acknowledgement.  e.g., if you know a cell phone to text).

I used my (ex)PI as an intermediary; he told me that he would contact them and let me know about the result as soon as possible, but it's been 2 weeks since then. Plus 2 weeks since I contacted the co-authors directly, which makes it a total of a month. Any other ideas? I'm applying for post-doc positions and not having this published at least on bioRxiv hurts my chances. :/

Sadly, until you get the positive agreement of all participants you are just stuck. It is frustrating, but necessary that everyone agree to things published in their name. You can't assume they agree if they don't make it explicit.
Any ethical publisher would require the agreement of all authors and most (all?) require it for those mentioned by name in acknowledgements. You don't need it for citations, of course, but you do for direct contributions.
Dropping them from authorship, if authorship is warranted, is even worse and leaves you open to charges of plagiarism.
I don't know if you could "sneak it by" an editor, but you will have the worst of all outcomes if one of the people whose agreement is needed later objects. Or worse, if a charge of plagiarism is made.
What you can, do, is to keep trying to contact them. There may be reasons that their reply is not forthcoming. Anything from medical reasons to the possibility that they just don't want to work with you or have their name associated with you. Hundreds of other possibilities.
You can also seek to use an intermediary. If there is someone with authority over everyone, then a request made through them might be more likely to receive a response. And a plea from them might be more likely to receive a positive reply.
But, don't let your frustration lead you to unethical behavior. There are outcomes worse than just burying the work. I'm sorry you are stuck. But don't make it worse.

I recognize that biorXiv isn't a traditional publisher. But, still, it is your reputation at stake here.

I used my (ex)PI as an intermediary; he told me that he would contact them and let me know about the result as soon as possible, but it's been 2 weeks since then. Plus 2 weeks since I contacted the co-authors directly, which makes it a total of a month. Any other ideas? I'm applying for post-doc positions and not having this published at least on bioRxiv hurts my chances. :/

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PhD in theoretical physics: good or bad for engineering jobs?
I'm a student who is currently undertaking a Master of Physics (coursework & research) at the University of Western Australia. I have also previously completed two Bachelor's degrees: one in physics and one in electrical engineering (with honours). Next year, I am hoping to start a PhD in high-energy physics (HEP) somewhere in Australia, doing a highly theoretical topic (such as supersymmetry, string theory, etc.) with the long term goal of following an academic path in this area of research.
From my understanding though, it is VERY hard finding academic jobs relevant to this particular field. I've heard through the grapevine that you have more chance of becoming a professional athlete than becoming a professor in theoretical HEP which is honestly quite dejecting.
However, understanding physics beyond the standard model is undoubtedly my passion so I would really like to pursue a PhD in it to determine whether or not it can become more than just a hobby. I've heard of theoretical HEP PhD's going into finance, etc. when finding an academic position proved fruitless, but if I'm being honest, that doesn't sound all that appealing to me. If the academic path didn't work out, I have always had a super keen interest in areas such as signal processing, control theory and data analysis. Which leads me to my main question:
In case I can't find an academic position in theoretical HEP, do you think my EE degree and MPhys (both of which involved experimental research projects highly focused on signal processing and data analysis) would be sufficient credentials to land a job in engineering/signal processing/data analysis? Or perhaps if I'm lucky, even some area of industry research (if so, what areas)?
Further, do you think having a PhD in theoretical HEP, in addition to my other credentials, would be a benefit or a hindrance in securing these types of jobs?
Some potentially relevant information:
I have 3 months of work experience at an electrical engineering company
My EE research project involved analyzing audio signals using a DSP to achieve desired acoustic properties
My MPhys research project is about detecting gravitational waves which involves heavy signal processing and manipulating large sets of data (100GB+) using python
By the end of this year my MPhys research should produce at least 1 or 2 papers in the Physical Review Letters journal

Note: I originally posted this in the electrical engineering stackexchange but was instructed to post it here instead since it was apparently off topic.

If you have 2 PRL papers befor you even start your PhD I'd say you have a better chance of making it in academia than most.

If you have a PhD in physics, it will be very easy for you to find a job in industry. It may be quite hard for you to find a job you like, or specifically one that you find engaging and challenging, but I don't think you'll have any problems getting an engineering job in some sort of signal processing or data analysis area. I don't think you'll find anything comparable in scope or ambition to theoretical HEP research in industry, but you could easily get a job as some sort of industry research scientist, data scientist, etc. if you want.

You might do well to check with folks in industry for their opinions in addition to academics. I'm guessing from your description a government lab might be a better fit for you.

I would say that strongly depends on what you do in the HEP PhD.
If it is more like pen and paper theory I would say this is not very interesting for industry. Perhaps even in the contrary as you might seem too "academic". Pen and paper theory jobs do not really exist in industry.
It is more the big data processing and computer simulation related skills what is relevant. The tools (python and methods) you use in your MPhys research sounds exactly what some companies are also using internally.
Industry considers hiring people from adjacent fields, when demand is much higher than the supply for certain jobs. Currently I see that this is the case for "data scientists". So I would say now your chances are good to find a job there as many companies are now exploring big data applications. They are scared by the success of Google, Facebook, etc.. and do not want them to take over an important part of their business. So many are investing here. Industry also has these jobs so it is not just finance. It is very diverse. One gains some feeling for it when one looks at current job offers (which is what I did, so I have no deeper experience than that). However, you have to keep in mind that the situation may be different is in a few years when you might have to give up your academic career (hopefully not).
A PhD is liked for certain types of jobs even in industry. As the PhD is teaching more a generic mindset (-> how to work scientifically,/thoroughly, know how to tackle big, unsolved problems) this is considered useful in some industrial jobs. Appropriate job descriptions would perhaps have names with "scientist" in it, like "data scientist", "research scientist" and so, not so much the "engineer" type of jobs. Sometimes PhDs are also found in sales/marketing, when a product needs deep explanation, training (and the customers are themselves PhDs) or must be customized to the users needs (and this is not straightforward).
Note: Even though I have worked in the US, I a most familiar with the German system. Nevertheless I hope the answer helps somehow.

You can probably do OK, but it is likely a  diversion from just going into the specific engineering field.

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Career prospects in theoretical physics after nightmare PhD
I will try to keep this as short and concise as possible.
I am a 3rd year PhD student in theoretical physics (condensed matter theory) in a US university. I worked for a certain professor for a year and things seemed to be going well, until he announced one day that he could not continue working with me because his grant application fell through. So I was forced to look for another advisor after I had already started my third year. Nobody else in the condensed matter group wanted to take me because they all claimed not to have funding (this turned out to be a lie, as I later found out). I was finally forced to work for a professor who is 76 years old and does not do research anymore. He has an incomplete project he hasn't worked on for 20 years and I am trying to complete it. I do NOT mind working on an old project. The problem is that whenever I ask him a question or ask for feedback, he ignores me. He does not have any ideas and when I ask for feedback and suggestions on my own ideas and work, he says he doesn't know and I can do whatever I want. I have tried approaching other professors in the department for help, but they refuse to meet/talk to me, saying that they are busy. I am worried that I will never be able to come up with a decent thesis without any sort of guidance, and will almost certainly not have any publications.
My question is: Is there any way I can minimize the damage to my career that this is causing? Is it possible to get a post-doc in theoretical physics without a publication/ with a sub-standard thesis? I am an international student and there are no physics jobs in my country, so any kind of advice on how to proceed would be welcome.
If anyone wants more detailed information, I am happy to provide it.

Are you sure the advisor(s) are the core of your problem here? Did you not accomplish anything all year, perhaps spending too much time on courses? (I had an officemate back in school that I didn't know existed for a year, because he never showed till his adviser apparently got tired of funding the guy for nothing and dumped him). At productive departments they generally expect students to be go-getters with independent initiative. Did you ace the other professors' classes? That always gets their interest in my experience.

I think you should consider applying or transfering to chemsitry department, they have also solid state chem groups that will be interest, Physics are not the only one

@ASimpleAlgorithm: Yes, I am sure I'm not the problem here. I did do productive work all year and the only reason I lost my first advisor was due to funds. I also have very good grades and aced the qualifying exam. I am continuing to do work on my own, but I do feel like my advisor has a certain responsibility to guide me. Comments such as this are not useful and have completely missed the point of the question.

Extension: there should be a reason, why you got that old project. An unsuccessful, decades old project is forgotten, if they give it to you, it should have some special reason. A PhD student costs a lot of money, and the department is responsible to use the money of the Uni effectively. If they wouldn't see a reasonable chance for your PhD, they would fire you. It is sure, that this project was selected for you by the old prof. Beware him, he knows you much better as you would think! He probably feels your dislike of this project, and this is the reason, why he became so  uncooperative.

He probably sees some important, some useful in that project. This is why he selected it for you! Find it! If you find the reason, and you show interest, he will support you with all his influence!

@ss1508 Identifying the source of the problem is always useful if you want to turn it around. The fact is it will be extremely difficult to get a postdoc without any publications or an adviser who provides references for you. Further in such a job, you will be expected to work much more independently and maintain a publication rate around 1-2 per year or whatever is typical in your field. How else do you expect to get your work from here to there if you are already writing this phase off as a failure?

You can never have too many condensed matter theorists. Problems only arise when two condensed matter theorists attempt to occupy the same space, at the same time.

I find it extremely unlikely that good students of a well-regarded supervisor would be let down by a university in the manner described above.   Thus, there is a problem with either: the supervisor, the student, or the university, or some combination of the above.

@Strawberry that would be a truly repulsive situation.

The reason why he does not give you hints could be because he does not want to risk leading you to any of the wrong paths he took in trying to solve the problem.

Many people here agree the thing you really need to answer is "Nobody else in the condensed matter group wanted to take me [and lied to me]". Was it your visibility, work style, personality, reputation? Whatever that reason was, the current PhD is just a consequence of it.

@Strawberry You've pinpointed a big problem: These matter theorists tend to condense.

@mathreadler If the adviser is aware of wrong paths, he should tell the student about the paths and why they're wrong.

I think you should consider transferring to another grad school. Certainly prospects on the post-doc market won't be good without any publications, interesting work, or a strong letter of recommendation. On the other hand, your advisor's grant expiring and no one else being able to take you gives you a very good reason to want to change grad schools.
Your former advisor's letter will be crucial. If he confirms your story about the grant falling through and no one else being able to take you, you should be able to transfer no problem. If he hints that your conduct contributed to your situation, you could be in a pickle. Good luck!

@cag51: I assure you that it was not my conduct. We parted amiably and he said he was satisfied with my work. The problem is that I have now spent one more year working for this new advisor, who refuses to guide me. Other professors in the department are too "busy" to respond to emails or to meet. If I choose to transfer, I will have to explain why things didn't work out with this new advisor and I don't know how to do that.

@ss1508 "they all claimed not to have funding (this turned out to be a lie, as I later found out)" hints potentially at your conduct, in some way. If there was "nothing wrong with you" and they did have the resources, why not take you over? Yes, grand conspiracy/evil department could be one answer, but Occam's razor suggests differently.

@ss1508 - thanks for info. Still, I think the first step for you is to decide what you want to do. If you decide that you do want to transfer, then the second step will be writing an essay that concisely and optimistically describes your situation. I think this will be eminently do-able given your circumstances. Academia.SE has some existing questions asking exactly about this, or you can post a new question asking for writing advice when the time comes.

@FooBar Or a misunderstanding on the part of the OP, e.g., having funding for other grad students is not in conflict with having funding for you.

20 years is not so much. If that project was useful 20 years ago, you should understand it.
Based on what you said, we have no way to know, what is in the background. A possible explanation: the professor is practically retired, is not hungry for more publications, and was nice enough to take on a student who needed help.
The important thing is: you don't need this knowledge for your optimal strategy.
"he says he doesn't know and I can do whatever I want" <-- You have free hands.
Check that 20 years old work, and check what relevance it has today. And then, follow what the old prof said: "do whatever you want".
You may have got a "window seat"1, but you've also got the possibility to get your PhD and work freely. The prof is probably a honored member of that department, his protegee won't be simply fired on some cloudy reason. You surely hadn't got this option if they would want to expel you. Also the workplace world is full with such situations. Typically, you know what are the decisions about your position, but you have only a few fragments, why. The important thing is, if they would think you need these infos, they had said it for you. There are no safe positions, if you get a gift, there is no reason to reject it.
1Slang in the Japanese government for out-of-favor people not being fired, but not getting real work tasks any more.

I think this answer is somehow missing that the OP seems to need at least some minimal guidance for his PhD and he's asking for that.
So just telling him: "Work on yourself" is not so helpful imho.

@suntoch I think it depends on, what are his later plans with his PhD. The old prof clearly abstains to advice, but also to influence him. Others are doing likely the same, because they won't violate the old prof's authority. If I would be in the (in my opinion, lucky) position of the OP, I would "creatively re-interpret" that old project on the way, that "making it final" would essentially mean, what I really want to do. Being a 20 yr old project cut short, should be "finalized" today, I don't think that even major changes would be really expostulated ever by anybody.

@suntoch If the prof goes really into retirement, he will have his department having to do something with the papers of the prof, and with the protegee of the prof. Thus, I would also check, what the other groups / researchers are doing. I think being a young PhD student improving the work of the old, retired Prof X, is a likely way to become once the follower of Prof X. Of course only if he is doing his tasks well. But these two long comments are all only assumptions, because nothing more can be said. What can be said: the OP is not only neglected, he has also freedom which is now a gift.

An unrelated note about old projects: Brian May, lead guitarist of the band Queen, studied for a PhD in the seventies, which he eventually abandoned due to the band. However, in 2006 he re-enrolled and finished the work. If the old project has not been solved in the meantime, and it carries still some significance; it may be worthwhile working on it.

There is one aspect missed by other answers and commenters: you were admitted to PhD program to succeed and there are people who are interested in that happening. Namely, you should set up a meeting with your departmental graduate advisor. That is a person who's job is to help students and guide them through grad school policies and possible help fix arising issues.
Your next point of contact will probably be department chair. It is their job to make sure that students are busy and professors are doing their job.
One advice: when meeting with these people, stick to the facts and explain what outcome you hope for. Remember, that there might be cultural differences between where you came from and US (it is definitely true in my case). There are many possible outcomes, for example:

your current "old" prof will be advised to help you more
you will be advised to work more on your own
you will be teamed up with another prof or postdoc in or outside of your department
you will be advised and helped to transfer
you will be asked to work with prof X on topic that you both enjoy, while you get paid by teaching, not just research
and definitely few other things can happen

Just remember that you have made significant investment in your current position, and school has made same thing.
Good luck.
PS: i am 5ish year international phd student ready to graduate from biomedical engineering program in US

this answer assumes that there is a good outcome. I'm not sure there is one -- the original advisor has no money, the new advisor is in over his head, and the department can't force other advisors to take a student they don't want. The department may have done the best they could by assigning the elderly prof rather than kicking OP out. From the information given, OP's options seem to be (a) stick it out with the current advisor, or (b) transfer

@cag51 i assume uni knows what they doing. and that there are options apart from quitting, although it might be best option. Mainly it seems that OP didn't seek enough help

Have you spoken to your department, which has a responsibility to make sure the necessary elements are in place in order for you to complete your degree?
If your department wants to leave you high and dry, then I suggest you consider: Your current advisor, who has one foot in the grave, seems willing to fund you without caring how much meaningful work you do on his project.
So why not spend 40% of your time on his project and 60% of your time on the project you were working on up until a year ago?  And get some informal help from your former advisor?  (These proportions could be adjusted, as needed.)
Alternatively, perhaps you could support yourself in the most common way -- as a teaching assistant.
But we need to explore a couple of things you wrote that suggest there might be more to your situation than meets the eye:

They all claimed not to have funding (this turned out to be a lie, as I later found out).

What possible explanations of this have you been able to work out?  What objective corroboration, if any, exists for some or all of the possible explanations?  Is what you described part of a larger pattern, or was it an isolated negative incident?

I have tried approaching other professors in the department for help, but they refuse to meet/talk to me, saying that they are busy.

What do you think about this?  Do you suspect the "busy" excuse is a lame attempt on their part to distance themselves from you?  If so, what do you think is the underlying reason for this?  Has this avoidance pattern always been the case?  If not, why the change?

Some very good points and suggestions here. +1.

The other answers had good advice, imo.
I'm about to suggest a few things.  Please forgive me if you've tried all of this.  However, please give it some thought to make sure you're not missing something.

whenever I ask him a question or ask for feedback, he ignores me

Very few people ignore me in person.  So I'll assume you're not asking him in person.  Make sure you're asking in person!  I immediately switch to phone or in person if electronic communication isn't going as intended.
Next, make sure your attitude toward him is correct (It might be but I thought it was worth mentioning).  If you're upset or angry with him, that will likely come through when you interact with him.  Sure, he isn't doing his job properly.  And it could severely harm your career and future.  You have a serious problem here and it's perfectly valid to feel angry and upset.  However if you feel that way, it won't help your situation.  What will help your situation the most is to be the bigger person.  Chances are he's partially to completely oblivious to what he's doing and how he's making you feel.  Give him the benefit of the doubt to overcome your emotion (that could be you one day!).
Make sure you are taking his interests into account.  Do you know what he wants?  One thing to do, too, would be to ask him what his goals/aspirations are.  Also ask him how you can help him achieve those (and do it).  If your attitude is to support him without false pretense, that will shine through.  He is much more likely to reciprocate.
I can also recommend being vulnerable and totally honest:

I'm really worried about my future here.  I need more advice and criticism to make it.  It's my dream to pursue research in physics.  I can't and won't give up.  However I'm stuck.  I don't know what to do to move forward.  How can I get the advice and criticism I need?  What do I need to change?

I'd actually recommend recommend pursuing all options at once (although I'd recommend approach him before others at the university - I think it's better to make every effort handle things with the person before escalating).  So do this while also preparing to possibly transfer, etc.
You've made it this far.  There is a path to move forward.  You just have to find it.  In fact, you've already started down the right now by coming here for help.  Don't give up!

If you can slip into the right frame of mind, your situation is really fortuitous.
In order to make the case you're qualified for a faculty position, you need to show a high level of independence.  Yes you're being forced into this situation by your current advising arrangement, but you'd probably be anyway if any school were to hire you as a faculty member.  Why not develop your own research program that you can potentially take with you?
Independence doesn't mean working on things all by yourself.  What it means is soliciting the right collaborations, both within and outside the standard support system offered by your university and grants.
Since you have a sponsor, assuming you have a good relationship with your old advisor you could probably go back to your old advisor's project.  Or you could find the other people in your new advisor's field and work on his project.  Your call about which could lead to more important work and which makes the most sense given your situation - or, as another answer suggested, you could do a bit of both.  But all else being equal, you're probably better off establishing yourself in a single field.
There is a third option.  Really take advantage of your freedom.  Find the collaboration you would most want to be part of, and figure out how to contribute.  If you think you could contribute you have no reason not to choose a top university, a Nobel laureate, or the project of your dreams.  In the Internet era, with more types of long-distance communication possible, it's become easier to do this.  You can enter a collaboration slowly - start by reading and corresponding and if you like what you're getting back, gradually put in more.  This might be the riskiest path and might mean you need to be a visiting student somewhere or switch advisors/departments/schools again, but it always "looks good" to have a respected name or group among your collaborators.
P.S.  You might be too demoralized or worried to do any of the above properly.  If you are, take a leave of absence.  You might also want to read about my namesake La-comadreja, the weasel.  The weasel is small and cute and so good at slipping through small openings in space and time, it doesn't fit into anyone's idea of what a small animal should and shouldn't be capable of doing.  Here is one of the things a weasel can accomplish.  It's lightning fast and took advantage of a tiny, ephemeral vulnerability in rabbit defense.  Another one of the weasel family's achievements is weaseling their way to a life in the sea (sea otters are in the weasel family).

(This is basically an extended comment, but a bit long for a comment.)
Sorry about your unpleasant situation. I generally agree that moving to another place is (probably) the best idea from the information you have given, but try to make sure that whatever issues you had in your old place don't recur. For example, check your department and possible advisers out throughly. Make sure funding is available. Though are teaching assistantships not available at your university? From everything I know, if your PhD is of poor quality, you are basically screwed. It's brutal out there. So you need to do everything you can to ensure that your PhD is of good quality. At the end of the day, the quality of your results will affect you more than anyone else, by a long way. In theory it can reflect poorly on your adviser if his students do badly, but in practice nobody cares, unless your adviser is up for tenure or something.
At the risk of stating the obvious, some departments can be in very poor shape, but it's not so obvious from the outside. So, do your homework/due diligence. Talking to current and past graduate students can be helpful. For relevant faculty, check their past students and where they are now. And also, of course, check their publications. Obviously, you will also need to visit the campus and meet with faculty and students, but that isn't sufficient by itself. Another thing to check is whether you will be able to transfer any credit from your current university, or whether you will have to start from scratch.
Other people have suggested in their answers that the situation may be salvageable at your current university. Of course, this is hard to say, but from your description, it does not sound promising. Also, did you check out your current department properly before joining it?


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Writing a series of papers
I'm writing a series of three papers. Each paper I'm writing contains two parts (part A + part X), where part A is a new technology and part X is the field of applying it. Part A is common in all the three papers while part X (the field) is variable according to the field the paper discusses.
Can I use the resources of part A in the same arrangement (but with different paraphrasing) in all three papers, or should I get different resources for the same information in part A for all of them?
my question here represent my intention to understand the scientific logic not to suggest bad solution because i am a beginner still .

Your question is stated in too abstract a way for good advice, I think. Anyone could answer in just about any way, which won't help you. Do something that seems to make sense to you.

Do you have a supervisor, a research mentor or a more experienced colleague, who can take a look at your paper drafts/plans and give you perhaps a more specific advice?

Is your concern that your later papers will have less credibility because you'll be citing yourself?

Clearly on-topic IMHO, despite appearing as off-topic in the close queue. What the asker is proposing to do is a bad idea, but that's not a reason to close the question!

@DmitrySavostyanov i will search for but for the moment i dont , i was just thinking in loud voice but unfortunately many people think in aggressive way toward the beginner questions

@candied_orange  yes beside thinking that re use the same sources will give a less value to the work although re paraphrasing it

@Flyto i am just searching for any suggestion and seeking for advice from the more experienced academic to improve my academic logic ,

@RainMan I do not think the problem is that this is a beginner's question, but more that there is not enough details in your question to provide a useful and well-informed answer. Academic work is complicated and often does not fit in tweet-size or elevator-pitch format.

It sounds to me like you are trying to game the system by publishing Part A three times simultaneously with revisions to the wording to claim it is not self-plagiarized.
Assuming Part A is important, which it seems to be because you are describing it as a new technology, you seem to be trying to get three journals to think they are each the first to publish that new technology, when in fact they are not. This is unethical.
If all the applications are relevant, you should publish whichever your favorite one is with Part A, and then submit separate papers citing that paper that show the results with the other applications. These works will likely repeat some of Part A, but only as much as is needed to explain it for that application.
However, this is something best discussed with your academic advisor.

my intentions is not to gaming any one nor publishing in three different journals, its the same journal i would like to publish in it  ,its just because that the technology i am concerned with is  still new and have application in many fields . the third section of your kind answer is a good advice . many thanks

@RainMan Okay that's good to hear, hopefully you will also take my first advice not as an offense but realize that others might have the same concern. Finally, the last sentence I write is probably the most important and I strongly encourage you to get advice from a senior person close to you.

Thanks alot sir , unfortunately many people think in aggressive way towards the beginners questions while my objectives is to understand the logic of papers publishing , this is my second try and that is why i am facing many questions , thanks for all your answer parts not meaning to underestimate your answer in any way

@RainMan The aggression towards novices, at least from me and I assume from others, always comes from a perspective of caring. If you are a parent, you should not usually yell at your children (or dog), but if a child is about to fall of a cliff, you need to yell to get their attention to save them. Similarly, sometimes it's important to point out dangers in an attention-grabbing way, especially if you can do so before the mistake is made. Afterwards it isn't much use.

some times it will prevent people from asking especially the beginners , in some places in our worlds young students are beaten by their teachers in their schools when they do mistakes to let them ( as teachers suppose) do matters correct , the result is that they left the schools .. understanding and supposing good intentions  in my opinion is more helpful

There is no reason to self-plagiarize. All it takes is cross citations of the papers.

In general, the best way to approach this specific type of problem is to consult with your advisor and review the standards of the place (journal?) to where you are submitting this work.
As practical writing advice goes, arbitrarily changing sources will not help your readers. If you got your information from Source Z, you should cite Source Z instead of arbitrarily citing Source Q, even if the information is largely the same between both of them.
You may make your research better if you try to rework part A as each field (part X) changes. Many of your resources will largely be the same between the three papers, but part A will cater more closely to the specific topic this way. A reader of one of your individual papers is likely better served this way too.

Thanks a lot sir for your kind answer

I thought that if you got the information from source Z, you should try to trace the idea to the earliest source A, and cite A, to acknowledge the original author, not an arbitrary guy who used this idea later.

@DmitrySavostyanov I agree with this. I was trying to say that if Source Z talks about something like how rainbows are formed, and Source Q also mentions stuff on how rainbows are formed, you should cite Source Z instead of Source Q because you got your information from Source Z and would be citing Source Q for the sake of having an arbitrarily different source on how rainbows are formed. Of course, you should do your due diligence and trace Source Z back to A where this was a novel discovery.


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Career change for a mathematician - from academia to ...?
I'm looking for good hints for my professional life.
I am a mathematician (32 years old) who worked up to now in academia in Europe.
My short CV: PhD + three and a half years of postdoctoral fellowships.
Domain of expertise: dynamical systems / ergodic theory (no applied math).
It's been some time that I have been losing progressively motivation for research, I do not manage to obtain a permanent position and I start wondering what I could do elsewhere with my expertise (besides teaching, which is of course a possibility).
However I fear that I'm too "specialized" in my domain and I don't feel adapted for the industry. I have some programming skills, but not enough in my opinion to work in a big data company.
Do you know some examples of mathematicians who found their way in industry with a 100% academic CV like mine? And where? In which areas? Do companies hire mathematicians with no experience outside academics? Do they invest in people with pure-theoretical background and competences?

The last paragraph (at least part of it) of your question risks a flag for it being a "shopping question" (off topic for this site). I would advise you to remove the "asking for lists of mathematicians in industry or for companies hiring them" and replace it with a more generic question.

@skymningen done

Related: https://academia.stackexchange.com/questions/12239/career-for-a-mathematician-outside-academia?rq=1

Rumors say that the financial industry hires Ph.D.s in math and physics, having found that those guys are smart in ways that matter there.
In the US, the largest non-academic employer of Ph.D. mathematicians is the National Security Agency.  But they hire US citizens only.  I do not know if there are similar opportunities in Europe.

alright, but that's only rumors or are we allowed to be more precise?

the countries of Europe definitely have signals intelligence departments within their security agencies, and are known to employ mathematicians as analysts. And similarly to the NSA they don't tend to employ non-citizens (as in it's not enough to have EU citizenship, you need to meet specific national citizenship requirements).

The more quantitative hedge funds (Renaissance, Two Sigma, Tower, ...) definitively hire PhDs in Math, Physics, Stats, and CS. Source: I work for one of these hedge funds.


text:
How do I specify my affiliation/contact information when I changed institutions and fields?
I am in a situation similar to that of this question where I did some work with a former employer, I changed fields, and now something related to that work is in the process of being published.  Initial submission of the work was during my time with my former employer, but revisions are happening after leaving.  The paper is a single author paper.  Based on the responses to that question, it seems like I should be using my former employer as my affiliation, but I have a few difference in my situation that I would like to clarify.

The work in question is a discussion paper which was solicited from me by a journal.  As such, I gained the expertise necessary to write the paper working for my former employer, but the paper itself was written in my personal time so neither organization directly funded any of the work in the paper.  However I would not have been requested to write the paper if not for my work with my former employer.
If I do decide to use my former employer as my affiliation, what should my contact email be?  I would rather not use a personal email, but I don't have access to the work email from my former employer, and it seems weird for my affiliation to be Company A, but my email to be me@CompanyB.com.

In case it affects your response, the paper is in the field of quantitative forecasting and specifically on the use of machine learning for forecasting, which is what I did for my former employer.  I now work using machine learning for video processing on medical devices.

If you look at the posts with tag [tag:affiliation] you will probably find a good answer to your question. There have been several.

@Buffy Do you have a specific post in mind? I looked around in that tag for a while and I found one that was pretty similar, which I linked, but I couldn't find anything which addressed the two specific points I have listed below.  For example, most posts where work is done in personal time, the work is also unrelated to the work with their employer.  I couldn't find anything about email contacts.

The answer to this question depends on the customs in your field of study; different fields have different customs.  (I have added an item to the "Academia varies more than you think" answer on "Welcome to Academia.SE" to say this.)

@AlexanderWoo I updated to include the field of study if that helps.  If not, how do I find out the field specific answer?

@Barker - you can try asking senior people in your field who are likely to have encountered this situation (it's not that rare) before and thought about the issue.  If you don't know anyone, the editor of the journal to which you are submitting the paper is a good option.

If you have the opportunity to be clear (that is, some limited online form doesn't prevent it) explain the transition "Jon Barker, formerly of Acme Corp, now with Zypppy Inc. JB@Zypppy.com". Or something similar.
The reason for the email is so that people can contact you, so use the current one even if it seems weird. Using an obsolete mail does no one any good.
If the former employer/institution contributed funds to the project it is usually good etiquette to indicate that you were associated with them then. But for identification purposes, your current affiliation is more valuable. But if it is a paper with multiple authors, some still at Acme, then it is less important to list an old affiliation (my opinion only).
There may even be reasons that you must not imply an affiliation that no longer exists, but that is fairly rare. If you can only give a single affiliation, it is probably best in most cases to list your current one. I suspect such a rule has many possible exceptions, but I'd suggest thinking about why you think you have an exceptional case.


text:
How to reference to a whole section of other paper that my paper is heavily based on
I have a bit of a dilemma. I am writing a master thesis about a topic that I originally thought was original. It turns out that someone else has done the exact same thing, which forced me to take another perspective on the same topic. Their code and research are old, over 10 years. What I ended up doing is migrating their code to the newest version of the framework used and then evaluating the method in a real-world environment.
Now I am in a situation where I have to start writing the method section of the thesis report where I describe the method and how the original problem was solved, but I have no real theoretical background/models except for the ones that the authors of the previous articles wrote. How should I reference these things? I still want to show the logical evidence and models that they use without plagiarizing their work. Can I use the same/similar pictures/models/evidences in this section of my report and just refer these things to the original authors and their report? Should I mention it in the beginning of the section that all of the models are from the original authors?

If I understand your question correctly, your problem is that you want to write a section of your thesis and indicate that the entire section paraphrases someone else's article. I would simply add a sentence near the beginning of that section that says something like "The following discussion is taken from Watson and Crick (2016)".
Generally speaking, plagiarism not an issue if you clearly cite the other person's work. Copyright is not an issue if you only use a small bit of their text and you clearly indicate that it's a direct quotation (i.e., using quotation marks or block indentation) and cite the source.
Finally, you might need to worry about whether or not you've done enough new work to merit approval of your thesis, or to merit publication. Your advisor can tell you if you've done enough new work for your thesis. The editor of the journal you want to publish in, or the organiser of the conference you want to present at, will ultimately decide if you've made a contribution worth publication in that particular venue.

Yes that is the problem exactly. I basically have no theoretical models, since I didn't change it from the original method. Would it be okay to reference it like this? Wouldn't it be considered plagiarism?

I've expanded my answer to address your questions.

If I understand correctly, your thesis will be an application to domain A of a method that other authors had proposed for domain B. This sounds like a perfectly OK topic for research. You should of course make amply clear that the method comes originally from these other authors. If you use unpublished material (perhaps they have provided you with code in personal communication) be sure to reference that too.
Another issue is whether the translation of a method to a different domain is substantial enough to meet the requisites of your Master's program. Sometimes this kind of exercise can be very substantial, sometimes less so. This is something that you need to discuss with your supervisor.

I think you misunderstood me a little bit. The original authors created a model, and from that model a tool in a popular framework. This was more than 10 years ago, and when the company I work for proposed that I would take this old tool and migrate it to the newest version of this framework and try it out in their projects, to evaluate how much gained performance this tool implies. Said and done, now I have to write about the tool in my report and the problem comes in the method segment. How do I reference all their models, methods? mhwombat in the other comment got it right.

Well, I'm happy at least one of us got it right, then :)

You might want to take part of your comment to my answer and add it as context to your original question. Both our answers start with "if I understand..." which makes me think some more context would be helpful.

Will do, thanks for the input. :) By the way, what do you think about that proposal? Is that the way to reference a whole section, so that the readers understand that all the models etc in a section is "borrowed" from a different article?

Yes, what @mhwombat says sounds right. As an alternative, I would have probably suggested something like "This whole section borrows heavily from (Those other guys, 2018)". If you make clear elsewhere (abstract, intro, etc.) that the novelty of your contribution doesn't lie in the model, you should be fine. But, again, norms vary subtly from field to field, and you should check all of this with your supervisor.

Thanks a ton for the tips, I feel more confident now. I will definitely discuss this further with my supervisor. If I could upvote I would. Have a good day!

I am currently writing a paper in which I use an existing methodology for a new problem.  My solution is effectively the following:

Methods
We apply the method of [cite original paper] to [problem I am addressing].

I then spend the rest of the Methods section explaining the methodology I cited.
In your case, you could then proceed with something like this:

We re-implement this methodology using [whatever new frameworks etc.].  We make design decisions {A, B, C, ...} in this new implementation because [some reasons].

Later, in Results or maybe Discussion, you could discuss any performance gains your new implementation has over the original.

Thanks for the input, I will definitely use this approach in the report.

Glad it helped!

The answer by @mhwombat is excellent, but to elaborate on one of its key point: the wording of the attribution note at the start of the section should be clear and explicit about how closely you have made use of their material.
Something like “This section/discussion is taken from XYZ” gives the impression it’s close to a direct copy, in which case it’s probably best to make those portions actual direct quotes, and indicate this unmistakably by formatting them as quotes in the text.  (That way, the attribution can’t be missed by someone skimming your thesis or reading a few pages out of context.)
If you’re following their general organisation and content but have rewritten it in your own words, then something like “This section is closely follows XYZ”, “…is heavily based on…”, or similar is appropriate (along with, for any direct quotes or figures you re-use, an explicit attribution in the text at the point of use).
If you’re giving your own exposition/organisation of the discussion rather than following theirs, but essentially following them in content because their paper is the main/only source you learned the method from, then something a little weaker like “…is greatly indebted to…”, “…has been heavily informed by…” or similar makes sense (again plus specific attribution in the text for any more directly re-used material).
And, of course, in any case: check with your advisor or other experienced colleagues that whatever you write fits with conventions/expectations in your field.


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Retaking a Course in Phd that I Took During the Master
I took a course in my Master degree and I got (B). After I got my degree I applied to the Phd program in the same campus. When I started my Phd program I retook the course and got (A). I submitted my plan of study for the PhD and it was approved by my department. However, the grad school rejected my plan of study and wants me to use the old grade since it was used in the Master. They don't want me to use the new grade at all. The (B) will affect  my GPA and I'd have to take another course to meet the required GPA.
I want to know, why the grad school rejected the repeated course? and what should I do?

You need to discuss the specifics of why the school rejected the repeat course with your grad school. There may be a no repeat rule for grades above a C. You may also have an appeals process available, but we wouldn't know that.

For my specific university BOTH grades would be used for the GPA calculation. Redoing a course does not remove the previous grade. Although our institution is currently reviewing this policy. Not recognizing the new grade at all seems a bit silly in my eyes.