相关论文: Comparative Study of Different Discretizations of …
Fluid-structure interaction models involve parameters that describe the solid and the fluid behavior. In simulations, there often is a need to vary these parameters to examine the behavior of a fluid-structure interaction model for…
We analyze the propagation properties of the numerical versions of one and two-dimensional wave equations, semi-discretized in space by finite difference schemes. We focus on high-frequency solutions whose propagation can be described, both…
The properties of the phi^4 scalar field theory on a fuzzy sphere are studied numerically. The fuzzy sphere is a discretization of the sphere through matrices in which the symmetries of the space are preserved. This model presents three…
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…
A spinor theory on a space with linear Lie type noncommutativity among spatial coordinates is presented. The model is based on the Fourier space corresponding to spatial coordinates, as this Fourier space is commutative. When the group is…
We modify the recently proposed model of Speight and Ward to make it possess time dependent solutions. We find that for each lattice spacing and for each velocity of the sine Gordon kink we can find a modification of the model for which…
We investigate the role that quasinormal modes can play in kink-antikink collisions, via an example based on a perturbation of the $\phi^4$ model. We find that narrow quasinormal modes can store energy during collision processes and return…
We study final states in the scattering of kinks and antikinks of the $\varphi^8$ field-theoretic model. We use the initial conditions in the form of two, three or four static or moving kinks. In the numerical experiments we observe a…
In this Letter, we address the {long-range interaction} between kinks and antikinks, as well as kinks and kinks, in $\varphi^{2n+4}$ field theories for $n>1$. The kink-antikink interaction is generically attractive, while the kink-kink…
We study effects of Kac-Baker long-range dispersive interaction (LRI) between particles on kink properties in the discrete sine-Gordon model. We show that the kink width increases indefinitely as the range of LRI grows only in the case of…
The peridynamic model of a solid does not involve spatial gradients of the displacement field and is therefore well suited for studying defect propagation. Here, bond-based peridynamic theory is used to study the equilibrium and steady…
We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discretization, i.e., there exists a difference equation whose…
We consider self-affine tilings in the Euclidean space and the associated tiling dynamical systems, namely, the translation action on the orbit closure of the given tiling. We investigate the spectral properties of the system. It turns out…
A first order equation for a static ${\phi}^4$ kink in the presence of an impurity is extended into an iterative scheme. At the first iteration, the solution is the standard kink, but at the second iteration the kink impurity generates a…
In this paper we analyze the scattering process in a two-field model in $(1+1)$-dimensions, with the special property to have several topological solutions: i) one with higher rest mass, characterized by a nested defect (lump inside a…
The utility of lattice discretization technique is demonstrated for solving nonrelativistic quantum scattering problems and specially for the treatment of ultraviolet divergences in these problems with some potentials singular at the origin…
This paper reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, but where continuity in derivatives is replaced by (a…
Finite volume multiple-particle interaction is studied in a two-dimensional complex $\phi^4$ lattice model. The existence of analytical solutions to the $\phi^4$ model in two-dimensional space and time makes it a perfect model for the…
This work is devoted to the study of relaxation--dissipation processes in systems described by Quantum Field Theory. In the first part, I focus on the phi^4 scalar quantum field theory in finite volume in the large N limit. I find that the…
We present a review of our recent works directed towards discovery of a periodic, kink-like and soliton-like travelling wave solutions within the models of transport phenomena and the mathematical biology. Analytical description of these…