Related papers: Strength-Duration Relationship in an Excitable Med…
Molecular dynamic simulations for systems with $D=2,3$ Lennard-Jones-like interactions are studied. In the model, we assume that, at long distances, the two-body attractive potential decays as $r^{-\alpha}$. Thermodynamic extensivity…
We obtain an expression for the energy of the density wave propagating in a multicomponent gravitating medium in the form well known from electrodynamics. Using the above, the possibility of "triple production" of the quasi-particles, or…
Kinematic Simulations of turbulent pair diffusion in planar turbulence with a -5/3 energy spectrum reproduce the results of the laboratory measurements of Jullien Phys. Rev. Lett. 82, 2872 (1999), in particular the stretched exponential…
Starting from a simple definition of stationary regime in first-order relaxation processes, we obtain that experimental results are to be fitted to a power-law when approaching the stationary limit. On the basis of this result we propose a…
I derive a temporally propagated uni-directional optical pulse equation valid in the few cycle limit. Temporal propagation is advantageous because it naturally preserves causality, unlike the competing spatially propagated models. The exact…
Spatially dispersive (also known as non-local) electromagnetic media are considered where the parameters defining the permittivity relation vary periodically. Maxwell's equations give rise to a difference equation corresponding to the…
The solutions of the reduced Maxwell-Bloch equations for an anisotropic two-level medium, which describe the propagation of electromagnetic pulses having a duration from a few field oscillations, are studied. An influence of the permanent…
We analyse dissipative boundary conditions for nonlinear hyperbolic systems in one space dimension. We show that a previous known sufficient condition for exponential stability with respect to the C^1-norm is optimal. In particular a known…
Spiral waves are a ubiquitous feature of the nonequilibrium dynamics of a great variety of excitable systems. In the limit of a large separation in timescale between fast excitation and slow recovery, one can reduce the spiral problem to…
We derive exact expressions for effective elastodynamic properties of two-phase composites in the long-wavelength (quasistatic) regime via homogenized constitutive relations that are local in space. This is accomplished by extending the…
We investigate the instabilities and bifurcations of traveling pulses in a model excitable medium; in particular we discuss three different scenarios for the loss of stability resp. the disappearance of stable pulses. In numerical…
We analyze the force-extension curve for a general class of systems, which are described at the mesoscopic level by a free energy depending on the extension of its components. Similarly to what is done in real experiments, the total length…
We propose thermodynamically consistent models for viscoelastic fluids with a stress diffusion term. In particular, we derive variants of compressible/incompressible Maxwell/Oldroyd-B models with a stress diffusion term in the evolution…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
Stretched exponential distributions and relaxation responses are encountered in a wide range of physical systems such as glasses, polymers and spin glasses. As found recently, this type of behavior occurs also for the distribution function…
We present an extension of the canonical coupled mode theory of electromagnetic waves to the case of pulses and spatio-temporal perturbations in complex media. Unlike previous attempts to derive such a model, our approach involves no…
We consider the problem of initiation of propagating wave in a one-dimensional excitable fiber. In the FitzHugh-Nagumo theory, the key role is played by ``critical nucleus'' and ``critical pulse'' solutions whose (center-)stable manifold is…
This study investigates the effect of a Maxwellian fluid on the propagation of waves in poroelastic media. Based on a fractional derivative stress-strain relation, a viscous dissipation function is obtained to measure the viscoelastic…
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…
We present an effective medium description of time-modulated dielectric media. By taking the averaged fields over one modulation period, the relationship between them is derived, defining therefore the different constitutive parameters. In…