Related papers: Transition fronts and their universality classes
Collision process between breather and moving kink-soliton is investigated both analytically and numerically in Fermi-Pasta-Ulam (FPU) chains. As it is shown by both analytical and numerical consideration low amplitude breathers and soft…
The Fermi-Pasta-Ulam-Tsingou (FPUT) problem addresses fundamental questions in statistical physics, and attempts to understand the origin of recurrences in the system have led to many great advances in nonlinear dynamics and mathematical…
Self-sustained dynamical phases of living matter can exhibit remarkable similarities over a wide range of scales, from mesoscopic vortex structures in microbial suspensions and motility assays of biopolymers to turbulent large-scale…
We establish nonlinear stability of fronts that describe the creation of a periodic pattern through the invasion of an unstable state. Our results concern pushed fronts, that is, fronts whose propagation is driven by a localized mode at the…
Pinning and depinning of wavefronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators…
The pioneering computer simulations of the energy relaxation mechanisms performed by Fermi, Pasta and Ulam can be considered as the first attempt of understanding energy relaxation and thus heat conduction in lattices of nonlinear…
We study numerically time evolution of a system which consists of two attractors connected by Fermi-Pasta-Ulam (FPU) chain. It is found that after sufficiently long time there exits self-consistent large scale structure in the system. The…
In this paper we construct a higher order expansion of the manifold of quasi unidirectional waves in the Fermi-Pasta-Ulam (FPU) chain. We also approximate the dynamics on this manifold. As perturbation parameter we use $h^2=1/n^2$, where…
The diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) lattice is an infinite chain of alternating particles connected by identical nonlinear springs. We prove the existence of micropteron traveling waves in the diatomic FPUT lattice in the limit as…
Some exact solutions and multi-mode invariant submanifolds were found for the Fermi-Pasta-Ulam (FPU) beta-model by Poggi and Ruffo in Phys. D 103 (1997) 251. In the present paper we demonstrate how results of such a type can be obtained for…
Phase transitions are a fundamental concept in science describing diverse phenomena ranging from, e.g., the freezing of water to Bose-Einstein condensation. While the concept is well-established in equilibrium, similarly fundamental…
We study atomic chains with nonlinear nearest neighbour interactions and prove the existence of fronts (heteroclinic travelling waves with constant asymptotic states). Generalizing recent results of Herrmann and Rademacher we allow for…
After a brief review of the Fermi-Pasta-Ulam (FPU) conservative system of N nonlinearly coupled oscillators, this paper addresses two problems: first, comparing two indicators for the equipartition, showing that the results are essentially…
This paper is concerned with the existence and uniqueness of transition fronts of a general reaction-diffusion-advection equation in domains with multiple branches. In this paper, every branch in the domain is not necessary to be straight…
We investigate the connection between local and global dynamics of two N-degree of freedom Hamiltonian systems with different origins describing one-dimensional nonlinear lattices: The Fermi-Pasta-Ulam (FPU) model and a discretized version…
We consider a class of either fermionic or bosonic noninteracting open quantum chains driven by dissipative interactions at the boundaries and study the interplay of coherent transport and dissipative processes, such as bulk dephasing and…
We consider a system of particles performing a one-dimensional dyadic branching Brownian motion with space-dependent branching rate, negative drift $-\mu$ and killed upon reaching $0$, starting with $N$ particles. More precisely, particles…
We establish sharp nonlinear stability results for fronts that describe the creation of a periodic pattern through the invasion of an unstable state. The fronts we consider are critical, in the sense that they are expected to mediate…
In this paper we study the invasion fronts of spatially periodic monotone reaction-diffusion systems in a multi-dimensional setting. We study the pulsating traveling waves that connect the trivial equilibrium, for which all components of…
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…