Related papers: Variational principle for non-linear wave propagat…
When waves impinge on a disordered material they are back-scattered and form a highly complex interference pattern. Suppressing any such distortions in the free propagation of a wave is a challenging task with many applications in a number…
The topological pressure is defined for subadditive sequence of potentials in bundle random dynamical systems. A variational principle for the topological pressure is set up in a very weak condition. The result may have some applications in…
The notion of dissipative dynamical systems provides a formal description of processes that cannot generate energy internally. For these systems, changes in energy can only occur due to an external energy supply or dissipation effects.…
A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
Stability criterion for the surface gravity capillary waves in a flowing two-layered fluid system with viscous dissipation is investigated. It is seen that the dissipative instability of negative energy waves is absent,- contrary to what…
We show that the contact dynamics obtained from the Herglotz variational principle can be described as a constrained nonholonomic or vakonomic ordinary Lagrangian system depending on a dissipative variable with an adequate choice of one…
We study the dynamics of fronts when both inertial effects and external fluctuations are taken into account. Stochastic fluctuations are introduced as multiplicative noise arising from a control parameter of the system. Contrary to the…
We study numerically and analytically the dynamics of particles on the Galton board, a regular lattice of disc scatters, in the presence of a constant external force and friction. It is shown that under certain conditions friction leads to…
Significant amplitude-independent and passive non-reciprocal wave motion can be achieved in a one dimensional (1D) discrete chain of masses and springs with bilinear elastic stiffness. Some fundamental asymmetric spatial modulations of the…
This paper is devoted to study the wave propagation and its stability for a class of two-component discrete diffusive systems. We first establish the existence of positive monotone monostable traveling wave fronts. Then, applying the…
Patterns on curved surfaces are ubiquitous, yet the influence of surface geometry on pattern dynamics remains elusive. We recently reported a new mechanism of pattern propagation in which a static pattern on a flat plane becomes a…
Wave front pinning and propagation in damped chains of coupled oscillators are studied. There are two important thresholds for an applied constant stress $F$: for $|F|<F_{cd}$ (dynamic Peierls stress), wave fronts fail to propagate, for…
In this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable…
Time-varying media, characterized by dynamic or spacetime-modulated constitutive parameters such as permittivity and permeability, have recently emerged as a transformative paradigm for advanced wave control, transcending the constraints…
Locally broken symmetries are used across fields to transport matter, particles and information in preferential directions. Beyond local mechanisms, spatially distributed nonlinearities in crystalline media have enabled non-reciprocal…
In this paper we consider a layer of incompressible viscous fluid lying above a flat periodic surface in a uniform gravitational field. The upper boundary of the fluid is free and evolves in time. We assume that a mass of surfactants…
Propagation of acoustic waves in an one-dimensional water duct containing many air filled blocks is studied by the transfer matrix formalism. Energy distribution and interface vibration of the air blocks are computed. For periodic…
We study theoretically the spatial evolution of optical beams inside a graded-index fiber exhibiting saturable nonlinearity. Utilizing an approach based on the variational principle, we identify the existence of bistable spatial solitons…
Flow networks are fundamental for understanding systems such as animal and plant vasculature or power distribution grids. These networks can encode, transmit, and transform information embodied in the spatial and temporal distribution of…