相关论文: Stochastic Continuum Models for High--Entropy Allo…

We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of…

We investigate transport properties of topologically disordered, three-dimensional, one-particle, tight binding models, featuring site distance dependent hopping terms. We start from entirely disordered systems into which we gradually…

High entropy alloys (HEAs) are a new class of metals that exhibit unique mechanical performance. Among HEAs, additively manufactured eutectic high entropy alloys (AM-EHEAs) have recently emerged as candidate materials for use in extreme…

A long-standing, though ill-understood problem in rocket dynamics, rocket response to random, altitude-dependent nozzle side-loads, is investigated. Side loads arise during low altitude flight due to random, asymmetric, shock-induced…

This chapter presents an innovative framework for the application of machine learning and data analytics for the identification of alloys or composites exhibiting certain desired properties of interest. The main focus is on alloys and…

Electronic-structure methods based on density-functional theory (DFT) were used to directly quantify the effect of chemical short-range order (SRO) on thermodynamic, structural, and electronic properties of archetypal face-centered-cubic…

In this paper, we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with uncertainties. The new approach is realized in the semi-discrete finite-volume framework and is based…

We consider discrete random Schr\"odinger operators on $\ell^2 (\mathbb{Z}^d)$ with a potential of discrete alloy-type structure. That is, the potential at lattice site $x \in \mathbb{Z}^d$ is given by a linear combination of independent…

The metallurgy and materials communities have long known and exploited fundamental links between chemical and structural ordering in metallic solids and their mechanical properties. The highest reported strength achievable through the…

Reduced order models of nonlinear conservation laws in fluid dynamics do not typically inherit stability properties of the full order model. We introduce projection-based hyper-reduced models of nonlinear conservation laws which are…

We present a new equation of state (EOS) for dense hydrogen/helium mixtures which covers a range of densities from $10^{-8}$ to $10^6$ g.cm$^{-3}$, pressures from $10^{-9}$ to $10^{13}$ GPa and temperatures from $10^{2}$ to $10^{8}$ K. The…

In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…

This article develops a stochastic differential equation (SDE) for modeling the temporal evolution of queue length dynamics at signalized intersections. Inspired by the observed quasiperiodic and self-similar characteristics of the queue…

We propose a method of neural evolution structures (NESs) combining artificial neural networks (ANNs) and evolutionary algorithms (EAs) to generate High Entropy Alloys (HEAs) structures. Our inverse design approach is based on pair…

The Ornstein-Uhlenbeck (OU) process describes the dynamics of Brownian particles in a confining harmonic potential, thereby constituting the paradigmatic model of overdamped, mean-reverting Langevin dynamics. Despite its widespread…

An analytical expression for the self-energy of the infinite-dimensional Hubbard model is proposed that interpolates between different exactly solvable limits. We profit by the combination of two recent approaches that are based on the…

Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…

Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction…

We study an atomistic model that describes the microscopic formation of material voids inside elastically stressed solids under an additional curvature regularization at the discrete level. Using a discrete-to-continuum analysis, by means…

We develop here a stochastic framework for modeling and segmenting transient spindle-like oscillatory bursts in electroencephalogram (EEG) signals. At the modeling level, individual spindles are represented as path realizations of a…