Related papers: Solitary wave trains in granular chains: Experimen…
In this paper, we study two-dimensional traveling waves in finite-depth water that are acted upon solely by gravity. We prove that, for any supercritical Froude number (non-dimensionalized wave speed), there exists a continuous…
The study of granular crystals, metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics,…
We consider the Vlasov--Poisson system describing a two-species plasma with spatial dimension $1$ and the velocity variable in $\mathbb{R}^n$. We find the necessary and sufficient conditions for the existence of solitary waves, shock waves,…
Standing waves near the zigzag and armchair edges, and their Berry's phases are investigated. It is suggested that the Berry's phase for the standing wave near the zigzag edge is trivial, while that near the armchair edge is non-trivial. A…
Charge-stabilized colloidal spheres dispersed in weak 1:1 electrolytes are supposed to repel each other. Consequently, experimental evidence for anomalous long-ranged like-charged attractions induced by geometric confinement inspired a…
Spiral waves are striking self-organized coherent structures that organize spatio-temporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather…
We study the excitation and damping of tides in close binary systems, accounting for the leading order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct effects: three-mode nonlinear interactions…
Random packings of granular chains are presented as a model polymer system to investigate the contribution of entanglements to strain-stiffening in the absence of Brownian motion. The chain packings are sheared in triaxial compression…
Slow dynamic nonlinearity is ubiquitous amongst brittle materials, such as rocks and concrete, with cracked microstructures. A defining feature of the behavior is the logarithmic-in-time recovery of stiffness after a mechanical…
We present numerical results for the dynamics of a single chain in steady shear flow. The chain is represented by a bead-spring model, and the smoothed profile method is used to accurately account for the effects of thermal fluctuations and…
It is well known that the water-wave problem with weak surface tension has small-amplitude line solitary-wave solutions which to leading order are described by the nonlinear Schr\"odinger equation. The present paper contains an existence…
We consider the electromagnetic waves propagating in the system of coupled waveguides. One of the system components is a standard waveguide fabricated from nonlinear medium having positive refraction and another component is a waveguide…
Recent asymptotic results by the authors provided detailed information on the shape of solitary high-energy travelling waves in FPU atomic chains. In this note we use and extend the methods to understand the linearisation of the travelling…
We develop a diagrammatic theory for transport of waves in disordered media with weak nonlinearity. We first represent the solution of the nonlinear wave equation as a nonlinear Born series. From this, we construct nonlinear ladder and…
In nature, granular materials fail in abrupt avalanches, earthquakes, and other hazardous events, and also creep over time. Proposed failure mechanisms for these systems are broadly framed as friction-limited. However, mechanical…
Three fundamental segregation and pattern formation processes are known in granular mixtures in a rotating cylindrical drum: radial segregation, axial banding, and coarsening of the band pattern. While the mechanism for the first effect is…
Here we theoretically and computationally study the frequency dependence of phase speed and attenuation for marine sediments from the perspective of granular mechanics. We leverage recent theoretical insights from the granular physics…
The solitary wave naturally arises in many areas of mathematical physics, including in nonlinear optics, plasma physics, quantum field theory, and fluid mechanics. In the past few years, for an advanced nuclear energy system, a particular…
In this paper we analyze the effect of a combined pure homogeneous strain and simple shear in a principal plane of the latter on the propagation of surface waves for an incompressible isotropic elastic half-space whose boundary is normal to…
The dissipation properties of a fine sand system are investigated by a low-frequency mechanical spectroscopy. The experiments show many interesting profiles of the relative energy dissipation, which imply that some structural transition of…