Search results for "2 dimensions"
showing 4 items of 4 documents
Memristors in Nonlinear Network : Application to Information (Signal and Image) Processing
2021
Memristor is a two-terminal nonlinear dynamic electronic device. Typically, it is a passive nano-device whose conductivity is controlled by the flux, time-integral of the voltage across its terminals, or by the charge, time-integral of the current flowing through it, and it presents interesting features for versatile applications. This thesis considers memristor use as a neighborhood connection for 2D cellular nonlinear or neural network (CNN), essentially for information (image and signal) processing and electronic prosthesis. We develop a model of the memristor based 2D cellular nonlinear networks CNNs compatible to image applications by incorporating memristor in the adjacent neighborhoo…
Finite size spectrum of SU(N) principal chiral field from discrete Hirota dynamics
2016
Using recently proposed method of discrete Hirota dynamics for integrable (1+1)D quantum field theories on a finite space circle of length L, we derive and test numerically a finite system of nonlinear integral equations for the exact spectrum of energies of SU(N)xSU(N) principal chiral field model as functions of m L, where m is the mass scale. We propose a determinant solution of the underlying Y-system, or Hirota equation, in terms of determinants (Wronskians) of NxN matrices parameterized by N-1 functions of the spectral parameter, with the known analytical properties at finite L. Although the method works in principle for any state, the explicit equations are written for states in the …
Spectral approach to D-bar problems
2017
We present the first numerical approach to D-bar problems having spectral convergence for real analytic, rapidly decreasing potentials. The proposed method starts from a formulation of the problem in terms of an integral equation that is numerically solved with Fourier techniques. The singular integrand is regularized analytically. The resulting integral equation is approximated via a discrete system that is solved with Krylov methods. As an example, the D-bar problem for the Davey-Stewartson II equations is considered. The result is used to test direct numerical solutions of the PDE.© 2017 Wiley Periodicals, Inc.
Field-induced ordering phenomena and non-local elastic compliance in two-dimensional colloidal crystals
2008
Ordering phenomena in colloidal dispersions exposed to external one-dimensional, periodic fields or under confinement are studied systematically by Monte Carlo computer simulations. Such systems are useful models for the study of monolayers on a substrate. We find that the interaction with a substrate potential completely changes the miscibility of a binary, hard disc mixture at low external field amplitudes. The underlying ordering mechanisms leading to this laser-induced de-mixing differ, depending on which components interact with the substrate potential. Generic effects of confinement on crystalline order in two dimensions are studied in a model system of point particles interacting via…