Related papers: Variational principle for non-linear wave propagat…
In this work, we are concerned with a nonlinear wave equation with variable exponents. A distributive delay is imposed into the damping term with variable exponents nonlinearity. Firstly, we show that the global nonexistence time can be…
Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional…
Initially straight slender elastic rods with geometrically constrained ends buckle and form stable two-dimensional shapes when compressed by bringing the ends together. It is also known that beyond a critical value of the pre-stress,…
The dynamics of a viscous accretion disc subject to a slowly varying warp of large amplitude is considered. Attention is restricted to discs in which self-gravitation is negligible, and to the generic case in which the resonant wave…
{The problem of laser beam concentration in a focal spot via wavefront variations is formulated as a maximization of the $beam$ $propagation$ $functional$ defined as the light power passing through aperture of an arbitrary shape located in…
The article presents a novel variational calculus to analyze the stability and the propagation of chaos properties of nonlinear and interacting diffusions. This differential methodology combines gradient flow estimates with backward…
Nonreciprocal wave propagation allows for directional energy transport. In this work, we systematically investigate wave dynamics in an elastic lattice that combines nonreciprocal stiffness with viscous damping. After establishing how…
We introduce a dissipative particle dynamics scheme for the dynamics of non-ideal fluids. Given a free-energy density that determines the thermodynamics of the system, we derive consistent conservative forces. The use of these effective,…
A new category of front propagation problems is proposed in which a spreading instability evolves through a singular configuration before saturating. We examine the nature of this front for the viscous Rayleigh instability of a column of…
Acoustic waves in a linear time-invariant medium are generally reciprocal; however, reciprocity can break down in a time-variant system. In this Letter, we report on an experimental demonstration of nonreciprocity in a dynamic…
A formal methodology for developing variational principles corresponding to a given nonlinear PDE system is discussed. The scheme is demonstrated in the context of the incompressible Navier-Stokes equations, systems of first-order…
Nonlinear diffusion is studied in the presence of multiplicative noise. The nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing field. A dynamic phase transition occurs when the system ``unbinds'' from the wall.…
We study wave propagation in strongly nonlinear 1D diatomic granular crystals under an impact load. Depending on the mass ratio of the `light' to `heavy' beads, this system exhibits rich wave dynamics from highly localized traveling waves…
Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is…
The data of simultaneous measurements of the surface displacement produced by propagating planar waves in experimental flume and of the dynamic pressure beneath the waves are compared with the theoretical predictions based on different…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
The structure of spiral waves is investigated in super-excitable reaction-diffusion systems where the local dynamics exhibits multi-looped phase space trajectories. It is shown that such systems support stable spiral waves with broken…
Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…
The propagation of nonlinear waves in one dimensional space, unsteady and compressible flow in Darcy-type porous media is analyzed. It is assumed that the weak discontinuity propagate long the characteristic path using the characteristics…
Dynamic modulation of material properties in space and time enables powerful control over wave propagation, yet existing theories largely rely on idealized, nondispersive models. In realistic media, frequency dispersion can strongly reshape…