Related papers: The Glassy Solid as a Statistical Ensemble of Crys…
Frequency domain spectroscopy allows an experimenter to establish optical properties of solids in a wide frequency band including the technically challenging 10 THz region, and in other bands enables metrological comparison between…
We present a novel formalism to characterize elastic heterogeneities in amorphous solids. In particular, we derive high-order strain-energy expansions for pairwise energies under athermal quasistatic dynamics. We then use the presented…
Quasicrystals are solid structures with symmetry forbidden by crystallographic rules. Because of this some structural characteristics of quasicrystals, for instance, radial distribution function, can look similar to the ones of amorphous…
The unifying feature of glass formers (such as polymers, supercooled liquids, colloids, granulars, spin glasses, superconductors, ...) is a sluggish dynamics at low temperatures. Indeed, their dynamics is so slow that thermal equilibrium is…
There have been some interesting recent advances in understanding the notion of mechanical disorder in structural glasses and the statistical mechanics of these systems' low-energy excitations. Here we contribute to these advances by…
A stochastic method is introduced for geometric modeling aerosol surface roughness with random field and discrete differential geometry theory. Optical scattering properties are computed for randomly oriented spheroidal particles with…
Using a model Hamiltonian for a single-mode electromagnetic field interacting with a nonlinear medium, we show that quantum expectation values of subsystem observables can exhibit remarkably diverse ergodic properties even when the dynamics…
Predicting the local dynamics of supercooled liquids based purely on local structure is a key challenge in our quest for understanding glassy materials. Recent years have seen an explosion of methods for making such a prediction, often via…
We define and study statistical ensembles of matter density profiles describing spherically symmetric, virialized dark matter haloes of finite extent with a given mass and total gravitational potential energy. Our ensembles include spatial…
The average scattered intensity is determined by the optical characteristics of particles in dispersion. The normalized time auto-correlation function of the scattered light intensity $g^{(2)}(\tau) $ includes both the optical and…
From numerical minimization of a model free energy functional for a system of hard spheres, we show that the width of the local peaks of the time-averaged density field at a glassy free-energy minimum exhibits large spatial variation,…
Methods for calculating an electron density of a periodic crystal constructed using non-orthogonal localised orbitals are discussed. We demonstrate that an existing method based on the matrix expansion of the inverse of the overlap matrix…
Accurate description of crystal structures is a prerequisite for predicting the physicochemical properties of materials. However, conventional X-ray diffraction (XRD) characterization often encounters intrinsic bottlenecks when applied to…
In this paper we demonstrate that the weak temperature dependence of structure factor of supercooled liquids, a defining feature of the glass transition, is a consequence of the averaging of the scattering intensity either due to the use of…
We construct an ensemble distribution to describe steady immiscible two-phase flow of two incompressible fluids in a porous medium. The system is found to be ergodic. The distribution is used to compute macroscopic flow parameters. In…
Geodesic slice sampling, introduced in Durmus et al., 2024, is a slice sampling based Markov chain Monte Carlo method for approximate sampling from distributions on Riemannian manifolds. We prove that it is uniformly ergodic for…
In many applications, it is often necessary to sample the mean value of certain quantity with respect to a probability measure {\mu} on the level set of a smooth function $\xi: \mathbb{R}^d\rightarrow \mathbb{R}^k$, $1\le k < d$. A…
It is well-known that the dynamical spectrum of an ergodic measure dynamical system is related to the diffraction measure of a typical element of the system. This situation includes ergodic subshifts from symbolic dynamics as well as…
The diffraction of fast atoms at crystal surfaces is ideal for a detailed investigation of the surface electronic density. However, instead of sharp diffraction spots, most experiments show elongated streaks characteristic of inelastic…
Durable interest in developing a framework for the detailed structure of glassy materials has produced numerous structural descriptors that trade off between general applicability and interpretability. However, none approach the combination…