Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Ultrametricity property of energy landscapes of multidisperse packing problems
2009
We consider the problem of finding the densest closed packing of hard disks with proposed different radii in a circular environment, such that the radius of the circumcircle is minimal. The subspace of the quasioptimum configurations of this problem exhibits the property of ultrametricity.
Exact dark soliton solutions for a family ofNcoupled nonlinear Schrödinger equations in optical fiber media
2001
We consider a family of N coupled nonlinear Schr\"odinger equations which govern the simultaneous propagation of N fields in the normal dispersion regime of an optical fiber with various important physical effects. The linear eigenvalue problem associated with the integrable form of all the equations is constructed with the help of the Ablowitz-Kaup-Newell-Segur method. Using the Hirota bilinear method, exact dark soliton solutions are explicitly derived.
Introduction: Signals and Transforms
2015
In this chapter we outline some well known facts about periodic signals and transforms, which are needed throughout the book. For details we refer to the classical textbook Oppenheim and Schafer [2].
Analysis of oscillations in discontinuous Lurie systems via LPRS method
2019
We discuss advantages and limitations of the harmonic balance method and the locus of a perturbed relay system (LPRS) method in the problem of finding periodic oscillations. In this paper we present the results of using harmonic balance method and LPRS method while investigating a 3rd order dynamic system in Lurie form. In this system a symmetric periodic oscillation is found, while other two asymmetric periodic motions are not found using both methods.
Finite size effects at thermally-driven first order phase transitions: A phenomenological theory of the order parameter distribution
1993
We consider the rounding and shifting of a firstorder transition in a finited-dimensional hypercubicL d geometry,L being the linear dimension of the system, and surface effects are avoided by periodic boundary conditions. We assume that upon lowering the temperature the system discontinuously goes to one ofq ordered states, such as it e.g. happens for the Potts model ind=3 forq≧3, with the correlation length ξ of order parameter fluctuation staying finite at the transition. We then describe each of theseq ordered phases and the disordered phase forL≫ξ by a properly weighted Gaussian. From this phenomenological ansatz for the total distribution of the order parameter, all moments of interest…
Bloch analysis of finite periodic microring chains
2005
We apply Bloch analysis to the study of finite periodic cascading of microring resonators. Diagonalization of the standard transfer matrix approach not only allows to find an exact analytic expression for transmission and reflection, but also to derive a closed form solution for the field in every point of the structure. To give more physical insight we analyze the main features of the transmission resonances in a finite chain and we give some hints for their experimental verification
EnCurv: Simple Technique of Maintaining Global Membrane Curvature in Molecular Dynamics Simulations.
2021
The EnCurv method for maintaining membrane curvature in molecular dynamics simulations is introduced. The method allows maintaining any desired curvature in a sector of lipid membrane bent in a single plane without adding any unphysical interactions into the system and without restrictions on lateral and transversal lipid diffusion and distribution. The current implementation is limited to the membranes curved in a single plane but generalization to arbitrary curvature and membrane topology is possible. The method is simple, easy to implement, and scales linearly with the system size. EnCurv is agnostic to the force field, simulation parameters, and membrane composition. The proof of princi…
T-model field equations: the general solution
2021
We analyze the field equations for the perfect fluid solutions admitting a group G$_3$ of isometries acting on orbits S$_2$ whose curvature has a gradient that is tangent to the fluid flow (T-models). We propose several methods to integrate the field equations and we present the general solution without the need to calculate any integral.
self-consistent approach to describe unit-cell-parameter and volume variations with pressure and temperature
2021
A method is presented for the self-consistent description of the variations of unit-cell parameters of crystals with pressure and temperature.
High Reynolds number Navier-Stokes solutions and boundary layer separation induced by a rectilinear vortex array
2008
Numerical solutions of Prandtl’s equation and Navier Stokes equations are considered for the two dimensional flow induced by an array of periodic rec- tilinear vortices interacting with an infinite plane. We show how this initial datum develops a separation singularity for Prandtl equation. We investigate the asymptotic validity of boundary layer theory considering numerical solu- tions for the full Navier Stokes equations at high Reynolds numbers.