Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analog simulator of integro-differential equations with classical
  memristors   An analog computer makes use of continuously changeable quantities of a
system, such as its electrical, mechanical, or hydraulic properties, to solve a
given problem. While these devices are usually computationally more powerful
than their digital counterparts, they suffer from analog noise which does not
allow for error control. We will focus on analog computers based on active
electrical networks comprised of resistors, capacitors, and operational
amplifiers which are capable of simulating any linear ordinary differential
equation. However, the class of nonlinear dynamics they can solve is limited.
In this work, by adding memristors to the electrical network, we show that the
analog computer can simulate a large variety of linear and nonlinear
integro-differential equations by carefully choosing the conductance and the
dynamics of the memristor state variable. To the best of our knowledge, this is
the first time that circuits based on memristors are proposed for simulations.
We study the performance of these analog computers by simulating
integro-differential models related to fluid dynamics, nonlinear Volterra
equations for population growth, and quantum models describing non-Markovian
memory effects, among others. Finally, we perform stability tests by
considering imperfect analog components, obtaining robust solutions with up to
$13\%$ relative error for relevant timescales.

0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph