Related papers: Construction of a minimum energy path for the VT f…
This paper addresses a class of robust stochastic optimal control problems. Its main contribution lies in the introduction of a general optimization model with variance penalization and an associated solution algorithm that improves…
Deeply embedded systems often have the tightest constraints on energy consumption, requiring that they consume tiny amounts of current and run on batteries for years. However, they typically execute code directly from flash, instead of the…
We propose and analyze a second-order Strang splitting method for a class of stiff matrix differential equations with Sylvester-type structure. The method splits the dynamics into a stiff linear part, treated exactly via matrix…
Conventional explicit electromagnetic particle-in-cell (PIC) algorithms do not conserve discrete energy exactly. Time-centered fully implicit PIC algorithms can conserve discrete energy exactly, but may introduce large dispersion errors in…
In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional. For the non-stochastic case, we…
In this paper, we propose a robust low-order stabilization-free virtual element method on quadrilateral meshes for linear elasticity that is based on the stress-hybrid principle. We refer to this approach as the Stress-Hybrid Virtual…
We introduce and analyze a new mixed finite element method with reduced symmetry for the standard linear model in viscoelasticity. Following a previous approach employed for linear elastodynamics, the present problem is formulated as a…
Many problems of practical interest rely on Continuous-time Markov chains~(CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible…
The task of finding the smallest energy needed to bring a solid to its onset of mechanical instability arises in many problems in materials science, from the determination of the elasticity limit to the consistent assignment of free…
We consider the second-order in time Strang-splitting approximation for vector-valued and matrix-valued Allen-Cahn equations. Both the linear propagator and the nonlinear propagator are computed explicitly. For the vector-valued case, we…
Molecular dynamics is a powerful tool for studying the thermodynamics and kinetics of complex molecular events. However, these simulations can rarely sample the required time scales in practice. Transition path sampling overcomes this…
The Alpha version of the Fermi-Pasta-Ulam problem is revisited through direct numerical simulations and an application of weak turbulence theory. The energy spectrum, initialized with a large scale excitation, is traced through a series of…
Stochastic electronic structure theories, e.g., Quantum Monte Carlo methods, enable highly accurate total energy calculations which in principle can be used to construct highly accurate potential energy surfaces. However, their stochastic…
The engineering of the optical response of materials is a paradigm that demands microscopic-level accuracy and reliable predictive theoretical tools. Here we compare and contrast the dispersive permittivity tensor, using both a low-energy…
In this paper, we develop an asymptotic-preserving dynamical low-rank method for the multiscale linear kinetic transport equation. The proposed scheme is unconditionally stable in the diffusive regime while preserving the correct asymptotic…
In this paper, we consider numerical approximations for the viscous Cahn-Hilliard equation with hyperbolic relaxation. This type of equations processes energy-dissipative structure. The main challenge in solving such a diffusive system…
We propose a method for constructing sparse high-frequency volatility estimators that are robust against change points in the spot volatility process. The estimators we propose are $\ell_1$-regularized versions of existing volatility…
This research rigorously investigates the convergence of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in elastic solids. We specifically examine a novel Ambrosio-Tortorelli (AT1)…
Drift-diffusion models that account for the motion of both electronic and ionic charges are important tools for explaining the hysteretic behaviour and guiding the development of metal halide perovskite solar cells. Furnishing numerical…
We present a novel physics-informed system identification method to construct a passive linear time-invariant system. In more detail, for a given quadratic energy functional, measurements of the input, state, and output of a system in the…