Related papers: Asymptotic-Preserving Schemes for Multiscale Physi…
We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix…
A closed set of equations for the evolution of linear perturbations of homogeneous, isotropic cosmological models can be obtained in various ways. The simplest approach is to assume a macroscopic equation of state, e.g.\ that of a perfect…
Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms ``critical transition'' or ``tipping point'' have been used to describe this situation. Critical transitions have been…
In this work, we propose some numerical schemes for linear kinetic equations in the diffusion and anomalous diffusion limit. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate…
Coarse-grained, mesoscale simulations are invaluable for studying soft condensed matter because of their ability to model systems in which a background solvent plays a significant role but is not the primary interest. Such methods generally…
This paper develops a conceptual extension of the Kinetic Theory of Active Particles, building upon the framework introduced in [2]. Living systems cannot be adequately described within classical single-scale paradigms, even when refined.…
Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we…
Recent advances in (scanning) transmission electron microscopy have enabled routine generation of large volumes of high-veracity structural data on 2D and 3D materials, naturally offering the challenge of using these as starting inputs for…
The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at…
Employing physically-consistent numerical methods is an important step towards attaining robust and accurate numerical simulations. When addressing compressible flows, in addition to preserving kinetic energy at a discrete level, as done in…
The present paper is devoted to the convergence analysis of an asymptotic preserving particle scheme designed to serve as a particle pusher in a Particle-In-Cell (PIC) method for the Vlasov equation with a strong inhomogeneous magnetic…
The method of asymptotic expansions is used to build an approximation scheme relevant to celestial mechanics in relativistic theories of gravitation. A scalar theory is considered, both as a simple example and for its own sake. This theory…
Surface hopping algorithms, as an important class of quantum dynamics simulation algorithms for non-adiabatic dynamics, are typically performed in the adiabatic representation, which can break down in the presence of ill-defined adiabatic…
Variational algorithms have particular relevance for near-term quantum computers but require non-trivial parameter optimisations. Here we propose Analytic Descent: Given that the energy landscape must have a certain simple form in the local…
The Riemann problem is one of the basic building blocks for numerical methods in computational fluid mechanics. Nonetheless, there are still open questions and gaps in theory and modelling for situations with complex thermodynamic behavior.…
A multiscale asymptotic homogenization method for periodic microstructured materials in presence of thermoelasticity with periodic spatially dependent one relaxation time is introduced. The asymptotic expansions of the micro-displacement…
We propose a class of numerical schemes for mixed optimal stopping and control of processes with infinite activity jumps and where the objective is evaluated by a nonlinear expectation. Exploiting an approximation by switching systems,…
Scientists and engineers often create accurate, trustworthy, computational simulation schemes - but all too often these are too computationally expensive to execute over the time or spatial domain of interest. The equation-free approach is…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…
Integrated task and motion planning problems describe a multi-modal state space, which is often abstracted as a set of smooth manifolds that are connected via sets of transitions states. One approach to solving such problems is to sample…