Related papers: Quantitative approximation schemes for glasses
When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…
Most camera lens systems are designed in isolation, separately from downstream computer vision methods. Recently, joint optimization approaches that design lenses alongside other components of the image acquisition and processing pipeline…
The richness of the mean-field solution of simple glasses leaves many of its features challenging to interpret. A minimal model that illuminates glass physics the same way the random energy model clarifies spin glass behavior would…
Solutions of initial-boundary value problems for systems of conservation laws depend on the underlying viscous mechanism, namely different viscosity operators lead to different limit solutions. Standard numerical schemes for approximating…
The validity of dilute gas approximation is explored by making use of the large-sized instanton in quantum mechanical model. It is shown that the Euclidean probability amplitude derived through a dilute gas approximation not only cannot…
Understanding the mechanical properties of glasses remains elusive since the glass transition itself is not fully understood, even in well studied examples of glass formers in two dimensions. In this context we demonstrate here: (i) a…
We show that the dynamics of soft-sphere systems with purely repulsive interactions can be described by introducing an effective hard-sphere diameter determined using the Andersen-Weeks-Chandler approximation. We find that this…
Approximate group analysis technique, that is, the technique combining the methodology of group analysis and theory of small perturbations, is applied to finite-difference equations approximating ordinary differential equations.…
Amorphous solids exhibit quasi-universal low-temperature anomalies whose origin has been ascribed to localized tunneling defects. Using an advanced Monte Carlo procedure, we create {\it in silico} glasses spanning from hyperquenched to…
A classical model for water-gas flows in porous media is considered. The degenerate coupled system of equations obtained by mass conservation is usually approximated by finite volume schemes in the oil reservoir simulations. The convergence…
We present a method for computing the topological entropy of one-dimensional maps. As an approximation scheme, the algorithm converges rapidly and provides both upper and lower bounds.
The perimeter and area generating functions of exactly solvable polygon models satisfy q-functional equations, where q is the area variable. The behaviour in the vicinity of the point where the perimeter generating function diverges can…
We propose a novel computational strategy to study the glass transition of molecular fluids. Our approach combines the construction of simple yet realistic models with the development of Monte Carlo algorithms to accelerate equilibration…
Many models require integrals of high-dimensional functions: for instance, to obtain marginal likelihoods. Such integrals may be intractable, or too expensive to compute numerically. Instead, we can use the Laplace approximation (LA). The…
We propose a first principle computation of the thermodynamics of simple fragile glasses starting from the two body interatomic potential. A replica formulation translates this problem into that of a gas of interacting molecules, each…
Data depth is a concept in multivariate statistics that measures the centrality of a point in a given data cloud in $\IR^d$. If the depth of a point can be represented as the minimum of the depths with respect to all one-dimensional…
Glass formation is one of the most interesting phenomena in the condensed matter field. Considerable effort has gone into understanding and predicting the glass formability. However, the previous prediction requires the glass first made…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Diffusivity, a measure for how rapidly a fluid self-mixes, shows an intimate, but seemingly fragmented, connection to thermodynamics. On one hand, the "configurational" contribution to entropy (related to the number of mechanically-stable…
A method is presented, which allows to sample directly low-temperature configurations of glassy systems, like spin glasses. The basic idea is to generate ground states and low lying excited configurations using a heuristic algorithm. Then,…