Related papers: (A note on) self-similarity in granular media
We consider the wave propagation in media with step-like inhomogeneities. We choose two different protocols: (I) a step-like spatial dependence of the coupling constant that physically corresponds to the junction of two systems and (II) the…
Pour sand into a container and only the grains near the top surface move. The collective motion associated with the translational and rotational energy of the grains in a thin flowing layer is quickly dissipated as friction through…
Discrete-element simulations are used to monitor several micro-scale characteristics within a granular material, demonstrating their convergence during loading toward the critical state, their stationarity at the critical state, and the…
The top of the attractor $A$ of a hyperbolic iterated function system $\left\{ f_{i}:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}|i=1,2,\dots,M\right\} $ is defined and used to extend self-similar tilings to overlapping systems. The theory…
The generalization ability of kernel interpolation in large dimensions (i.e., $n \asymp d^{\gamma}$ for some $\gamma>0$) might be one of the most interesting problems in the recent renaissance of kernel regression, since it may help us…
In this paper, we introduce the notion of spectral genus $\widetilde{p}_{g}$ of a germ of an isolated hypersurface singularity $(\mathbb{C}^{n+1}, 0) \to (\mathbb{C}, 0)$, defined as a sum of small exponents of monodromy eigenvalues. The…
Light-scattering in the terahertz region is demonstrated for granular matter. A quantum-cascade laser is used in a benchtop setup to determine the angle-dependent scattering of spherical grains as well as coffee powder and sugar grains. For…
The nature of long-range interactions between dust grains in plasma is discussed. The dust grain interaction potential within a cell model of dusty plasma is introduced. The attractive part of intergrain potential is described by multipole…
We analyze in the framework of the space group theory the change of the dispersion law in grapenein the vicinity of the (former) Dirac points due to application of supercell potential with the $\sqrt{3}\times\sqrt{3}$ space periodicity and…
Linear superposition of gravitational fields is shown to be possible for a large class of spacetimes, in some specific coordinates. Explicit examples are presented.
Motivated by the application problem of sensor fusion the author introduced the concept of graded set. It is reasoned that in classification problem arising in an information system (represented by information table), a novel set called…
We study theoretically nonlinear propagation of light in a graphene monolayer. We show that the large intrinsic nonlinearity of graphene at optical frequencies enables the formation of quasi one-dimensional self-guided beams (spatial…
It has been recently pointed out that local volume fluctuations in granular packings follow remarkably well a shifted and rescaled Gamma distribution named the kGamma distribution [T. Aste, T. Di Matteo, Phys. Rev. E 77 (2008) 021309]. In…
Odd elasticity describes the unusual elastic response of solids whose stress-strain relationship is not compatible with an elastic potential. Here, we present a study of odd elasticity in a driven granular matter system composed of grains…
Recently, Yang, Yuan and Zhang [Doubling properties of self-similar measures and Bernoulli measures on self-affine Sierpinski sponges, Indiana Univ. Math. J., 73 (2024), 475-492] characterized when a self-similar measure satisfying the open…
Modularity is a quantity which has been introduced in the context of complex networks in order to quantify how close a network is to an ideal modular network in which the nodes form small interconnected communities that are joined together…
The properties of optical solitons in periodic nonlinear media are reviewed. The emphasis is on solitons in periodically refractive media (Bragg gratings) incorporating a periodic set of thin layers of two-level systems resonantly…
Total internal reflection occurs for large angles of incidence, when light is incident from a high-refractive-index medium onto a low-index medium. We consider the situation where the low-index medium is active. By invoking causality in its…
We derive some equalities for relations on the algebra A, under the assumption that every subalgebra of A $\times$ A is congruence modular.
A polycrystalline graphene consists of perfect domains tilted at angle {\alpha} to each other and separated by the grain boundaries (GB). These nearly one-dimensional regions consist in turn of elementary topological defects, 5-pentagons…