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We investigate the instabilities of low winding number electroweak strings using standard numerical techniques of linear algebra. For strings of unit winding we are able to confirm and extend existing calculations of the unstable region in…
In this article we discuss the numerical analysis for the finite difference scheme of the one-dimensional nonlinear wave equations with dynamic boundary conditions. From the viewpoint of the discrete variational derivative method we propose…
As a complementary tool to laboratory experiments, discrete numerical simulation, applied to granular materials, provides valuable information on the grain and contact scale microstructure, thereby enabling one to better understand the…
In this paper, we study the nonlinear stability of the composite wave consisting of planar rarefaction and planar contact waves for viscous conservation laws with degenerate flux under multi-dimensional periodic perturbations. To the level…
Many modern engineering structures exhibit nonlinear vibration. Characterizing such vibrations efficiently is critical to optimizing designs for reliability and performance. For linear systems, steady-state vibration occurs only at the…
Using dimensionally reduced models for the numerical simulation of thin objects is highly attractive as this reduces the computational work substantially. The case of narrow thin elastic bands is considered and a convergent finite element…
We discuss semiclassical quantization of circular pulsating strings in AdS3 x S3 background with and without the Neveu-Schwarz- Neveu-Schwarz (NS-NS) flux. We find the equations of motion corresponding to the quadratic action in bosonic…
Non-linear dynamical systems represent a compact, flexible, and robust tool for reactive motion generation. The effectiveness of dynamical systems relies on their ability to accurately represent stable motions. Several approaches have been…
Several cases of the explanation of the phenomenon of standing waves in strings, there are few experimental measurement tools when demonstrating this phenomenon in a classroom, it is for this reason that we have implemented different forms…
Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic…
In the following, we discuss nonlinear simulations of nonlinear dynamical systems, which are applied in technical and biological models. We deal with different ideas to overcome the treatment of the nonlinearities and discuss a novel…
Well-defined non-perturbative formulations of the physics of string theories, sometimes with D-branes present, were identified over a decade ago, from a careful study of double scaled matrix models. Following recent work which recasts some…
In this work, we develop novel structure-preserving numerical schemes for a class of nonlinear Fokker--Planck equations with nonlocal interactions. Such equations can cover many cases of importance, such as porous medium equations with…
The concept of nonlinear modes is useful for the dynamical characterization of nonlinear mechanical systems. While efficient and broadly applicable methods are now available for the computation of nonlinear modes, nonlinear modal testing is…
We present a stability theory for kink propagation in chains of coupled oscillators and a new algorithm for the numerical study of kink dynamics. The numerical solutions are computed using an equivalent integral equation instead of a system…
Dynamical theories of speech use computational models of articulatory control to generate quantitative predictions and advance understanding of speech dynamics. The addition of a nonlinear restoring force to task dynamic models is a…
Kinetic numerical simulations of the evolution of the Weibel instability during the full nonlinear regime are presented. The formation of strong distortions in the electron distribution function resulting in formation of strong peaks in it…
Control of complex turbulent dynamical systems involving strong nonlinearity and high degrees of internal instability is an important topic in practice. Different from traditional methods for controlling individual trajectories, controlling…
Dynamic perturbation equations are derived for a generic stationary state of an elastic string model -- of the kind appropriate for representing a superconducting cosmic string -- in a flat background. In the case of a circular equilibrium…
Stability of dynamical systems is a central topic with applications in widespread areas such as economy, biology, physics and mechanical engineering. The dynamics of nonlinear systems may completely change due to perturbations forcing the…