Related papers: Sparse random matrices and vibrational spectra of …
The averaged dynamics of various two-phase systems in a high-frequency vibration field is studied theoretically. The continuum approach is applied to describe such systems as solid particle suspensions, emulsions, bubbly fluids, when the…
A sparse random block matrix model suggested by the Hessian matrix used in the study of elastic vibrational modes of amorphous solids is presented and analyzed. By evaluating some moments, benchmarked against numerics, differences in the…
A matrix method is formulated in a Lagrangian representation for the solution of the characteristic value problem governing modes of oscillation and instability in a collisionless stellar system. The underlying perturbation equations govern…
In an absorptive system the Wigner reaction $K-$matrix (directly related to the impedance matrix in acoustic or electromagnetic wave scattering) is non-selfadjoint, hence its eigenvalues are complex. The most interesting regime arises when…
We show that viscoelastic effects play a crucial role in the damping of vibrational modes in harmonic amorphous solids. The relaxation of a given plane wave is described by a memory function of a semi-infinite one-dimensions mass-spring…
Given $A_n:=\frac{1}{\sqrt{n}}(a_{ij})$ an $n\times n$ symmetric random matrix, with elements above the diagonal given by i.i.d. random variables having mean zero and unit variance. It is known that when…
We show through simulations of amorphous solids prepared in open boundary conditions that they possess significantly fewer low-frequency vibrational modes compared to their periodic boundary counterparts. Specifically, using measurements of…
Pattern formation of a thin layer of vertically agitated wet granular matter is investigated experimentally. Due to the strong cohesion arising from the capillary bridges formed between adjacent particles, agitated wet granular matter…
We present a practical method to compute the vibrational resonant Raman spectra in solids with delocalized excitations. We apply this approach to the study of tetrahedrous amorphous carbon. We determine the vibrational eigenmodes and…
Non-Hermitian random matrices with statistical spectral characteristics beyond the standard Ginibre ensembles have recently emerged in the description of dissipative quantum many-body systems as well as in non-ergodic wave transport in…
We consider random hermitian matrices made of complex blocks. The symmetries of these matrices force them to have pairs of opposite real eigenvalues, so that the average density of eigenvalues must vanish at the origin. These densities are…
Jamming is a phenomenon shared by a wide variety of systems, such as granular materials, foams, and glasses in their high density regime. This has motivated the development of a theoretical framework capable of explaining many of their…
Granular materials are defined as collections of macroscopic dissipative particles. Although these systems are ubiquitous in our lives, the nature and the causes of their non-trivial collective dynamics still remain elusive and have…
We consider a particle that is subject to a constant force and scatters inelastically on a vibrating periodically corrugated floor. At small friction and small radius of the circular scatterers the dynamics is dominated by resonances…
Glasses have a large excess of low-frequency vibrational modes in comparison with most crystalline solids. We show that such a feature is a necessary consequence of the weak connectivity of the solid, and that the frequency of modes in…
The low-frequency range of vibrational spectra is sensitive to collective vibrations of the lattice. In molecular crystals, it can be decisive to identify the structure of different polymorphs, and in addition, it plays an important role on…
We discuss recent work on the static and dynamical properties of the asymmetric exclusion process, generalized to include the effect of disorder. We study in turn: random disorder in the properties of particles; disorder in the spatial…
Disordered mechanical systems with high connectivity represent a limit opposite to the more familiar case of disordered crystals. Individual ions in a crystal are subjected essentially to nearest-neighbor interactions. In contrast, the…
Suspended graphene waveguides were deposited on micron-scale periodic metal (plasmonic) structures. Raman scattering of test molecules (B. Megaterium), deposited on the waveguides' surface, exhibited azimuthal cycles upon rotation: at these…
Fractional models and their parameters are sensitive to changes in the intrinsic micro-structures of anomalous materials. We investigate how such physics-informed models propagate the evolving anomalous rheology to the nonlinear dynamics of…