相关论文: An Approximate Analytical Solution to Knudsen Laye…
Ab initio thermodynamics is a widespread, computationally efficient approach to predict the stable configuration of a surface in contact with a surrounding (gas or liquid) environment. In a prevalent realization of this approach, this…
We present a relativistic Shakhov-type generalization of the Anderson-Witting relaxation time model for the Boltzmann collision integral to modify the ratio of momentum diffusivity to thermal diffusivity. This is achieved by modifying the…
Spectral methods, thanks to the high accuracy and the possibility of using fast algorithms, represent an effective way to approximate collisional kinetic equations in kinetic theory. On the other hand, the loss of some local invariants can…
Atomic layer deposition allows for precise control over film thickness and conformality. It is a critical enabler of high aspect ratio structures, such as 3D NAND memory, since its self-limiting behavior enables higher conformality than…
Since the first optimality proofs for adaptive mesh refinement algorithms in the early 2000s, the theory of optimal mesh refinement for PDEs was inherently limited to stationary problems. The reason for this is that time-dependent problems…
We introduce new multilevel methods for solving large-scale unconstrained optimization problems. Specifically, the philosophy of multilevel methods is applied to Newton-type methods that regularize the Newton sub-problem using second order…
We report a novel hybrid method of simultaneous atomistic simulation of solids in critical regions (contacts surfaces, cracks areas, etc.), along with continuum modeling of other parts. The continuum is treated in terms of quasi-atoms of…
The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural…
We develop a highly accurate analytic approximation for small-scale non-cold relic perturbations by solving the collisionless Boltzmann equation in the quasi-stationary regime. The approximation is implemented in CLASSIER (CLASS Integral…
Precise temperature measurements on systems of few ultracold atoms is of paramount importance in quantum technologies, but can be very resource-intensive. Here, we put forward an adaptive Bayesian framework that substantially boosts the…
Within the theoretical framework of a recently introduced approach to approximate Lie symmetries of differential equations containing small terms, which is consistent with the principles of perturbative analysis, we define accordingly…
We present a modified simulated annealing method with a dynamical choice of the cooling temperature. The latter is determined via a closed-loop control and is proven to yield exponential decay of the entropy of the particle system. The…
The goal of this paper is to accurately describe the metastable dynamics of the solutions to the hyperbolic relaxation of the Cahn-Hilliard equation in a bounded interval of the real line, subject to homogeneous Neumann boundary conditions.…
We analyze a large number of high-order discrete velocity models for solving the Boltzmann-BGK equation for finite Knudsen number flows. Using the Chapman-Enskog formalism, we prove for isothermal flows a relation identifying the resolved…
We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. We prove the solution can be approximated in $L^{\infty}$ by the sum of interior solution which satisfies steady incompressible…
We develop a method to approximate the moments of a discrete-time stochastic polynomial system. Our method is built upon Carleman linearization with truncation. Specifically, we take a stochastic polynomial system with finitely many states…
We establish the hydrodynamic limit of the one-dimensional Boltzmann equation with hard-sphere collisions toward Riemann solutions of the compressible Euler system. The Riemann solutions covered by our result include generic superpositions…
Tackling the low-temperature fate of supercooled liquids is challenging due to the immense timescales involved, which prevent equilibration and lead to the operational glass transition. Relating glassy behaviour to an underlying,…
In this paper, we consider a class of nonlinear reaction-hyperbolic systems with relaxation terms as models for axonal transport in neuroscience. We show the Kruzkov entropy-satisfying BV-solutions of the systems converge towards the…
Maximum-entropy moment methods allow for the modelling of gases from the continuum regime to strongly rarefied conditions. The development of approximated solutions to the entropy maximization problem has made these methods computationally…