Related papers: Shock propagation in a granular chain
Large scale networks delineating collective dynamics often exhibit cascading failures across nodes leading to a system-wide collapse. Prominent examples of such phenomena would include collapse on financial and economic networks.…
Instead of the infinitesimal extrinsic and intrinsic perturbations on strings, considered so far, we discuss the evolution and propagation of finite-amplitude perturbations. Those intrinsic perturbations may result in appearance of stable…
We experimentally investigate the interplay between spatial shock waves and the degree of disorder during nonlinear optical propagation in a thermal defocusing medium. We characterize the way the shock point is affected by the amount of…
An analytical solution to the problem of formation and propagation of large amplitude shock electromagnetic waves in strip transmission line (TL) based on the distributed semiconductor diode was obtained. This solution correctly takes into…
We investigate the effect of non-paraxiality in the dynamics of dispersive shock waves in the defocusing nonlinear Schroedinger equation. We show that the problem can be described in terms of a relativistic particle moving in a potential.…
The mechanics of lower dimensional elastic structures depends strongly on the geometry of their stress-free state. Elastic deformations separate into in-plane stretching and lower energy out-of-plane bending deformations. For elastic…
We develop and study a 1D model for the acoustic wave propagation with two-phase physics and irreversible elastoplastic deformations in the rock matrix. We address the effect of the P-wave energy attenuation due to pore-scale plastic…
We experimentally study linear and nonlinear waves on the surface of a fluid covered by an elastic sheet where both tension and flexural waves take place. An optical method is used to obtain the full space-time wave field, and the…
Asymptotic decay laws for planar and nonplanar shock waves and the first order associated discontinuities that catch up with the shock from behind are obtained using four different approximation methods. The singular surface theory is used…
We review various methods for the analysis of initial-value problems for integrable dispersive equations in the weak-dispersion or semiclassical regime. Some methods are sufficiently powerful to rigorously explain the generation of…
Pulse propagation in nonlinear arrays continues to be of interest because it provides a possible mechanism for energy transfer with little dispersion. Here we show that common measures of pulse dispersion might be misleading; in strongly…
Non-linear sound is an extreme phenomenon typically observed in solids after violent explosions. But granular media are different. Right when they jam, these fragile and disordered solids exhibit a vanishing rigidity and sound speed, so…
We investigate how forces spread through frictionless granular packs at the jamming transition. Previous work has indicated that such packs are isostatic, and thus obey a null stress law which, independent of the packing history, causes…
We report on the strongly nonlinear dynamics of an array of weakly coupled, non-compressed, parallel granular chains subject to a local initial impulse. The motion of the granules in each chain is constrained to be in one direction which…
The evolution of effective force chains percolating through a compressed granular system is investigated. We performed experiments by compressing an ensemble of spherical particles in a cylindrical container monitoring the macroscopic…
We are concerned with rigorous mathematical analysis of shock diffraction by two-dimensional convex cornered wedges in compressible fluid flow governed by the nonlinear wave system. This shock diffraction problem can be formulated as a…
In this work we present a mathematical model for the propagation of the shock waves that occur in graded density profiles. These waves can occur in a wide range of astrophysical events, such as collisions in planetary and stellar…
Experiments on isotropic compression of a granular assembly of spheres show that the shear and bulk moduli vary with the confining pressure faster than the 1/3 power law predicted by Hertz-Mindlin effective medium theories (EMT) of contact…
A minimal model for studying the mechanical properties of amorphous solids is a disordered network of point masses connected by unbreakable springs. At a critical value of its mean connectivity, such a network becomes fragile: it undergoes…
We present a phenomenological approach to dispersion in nonlinear elasticity. A simple, thermomechanically sound, constitutive model is proposed to describe the (non-dissipative) properties of a hyperelastic dispersive solid, without…