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We identify `minimal seeds' for turbulence, i.e. initial conditions of the smallest possible total perturbation energy density $E_c$ that trigger turbulence from the laminar state, in stably stratified plane Couette flow using the…
This paper is concerned with developing and analyzing two novel implicit temporal discretization methods for the stochastic semilinear wave equations with multiplicative noise. The proposed methods are natural extensions of well-known…
A local search algorithm solving an NP-complete optimisation problem can be viewed as a stochastic process moving in an 'energy landscape' towards eventually finding an optimal solution. For the random 3-satisfiability problem, the…
In this paper, we study the linear stability of Couette flow for 2D compressible Navier-Stokes-Poisson system at high Reynolds number in the domain $\mathbb{T}\times\mathbb{R}$ with initial perturbation in Sobolev spaces. We establish the…
The solution to an optimal power flow (OPF) problem provides a minimum cost operating point for an electric power system. The performance of OPF solution techniques strongly depends on the problem's feasible space. This paper presents an…
We study the optimal power flow problem with switching (or, equivalently, the line expansion problem) under demand uncertainty. Specifically, we consider the line-use variables at the first stage and the current- or power-flow at the second…
High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The…
Fine scale elastic structures are widespread in nature, for instances in plants or bones, whenever stiffness and low weight are required. These patterns frequently refine towards a Dirichlet boundary to ensure an effective load transfer.…
State-specific approximations can provide an accurate representation of challenging electronic excitations by enabling relaxation of the electron density. While state-specific wave functions are known to be local minima or saddle points of…
Solving the optimal power flow problem is one of the main objectives in electrical power systems analysis and design. The modern optimization algorithms such as the evolutionary algorithms are also adopted to solve this problem, especially…
The phenomenon of bursting, in which streaks in turbulent boundary layers oscillate and then eject low speed fluid away from the wall, has been studied experimentally, theoretically, and computationally for more than 50 years because of its…
A recently developed high-order implicit shock tracking (HOIST) framework for resolving discontinuous solutions of inviscid, steady conservation laws [41, 43] is extended to the unsteady case. Central to the framework is an optimization…
Consider a species whose population density solves the steady diffusive logistic equation in a heterogeneous environment modeled with the help of a spatially non constant coefficient standing for a resources distribution in a given box. We…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
Linear fixed point equations in Hilbert spaces arise in a variety of settings, including reinforcement learning, and computational methods for solving differential and integral equations. We study methods that use a collection of random…
In computational inverse problems, the optimal experimental design (OED) problem seeks the best locations in time and space at which to take measurements. We investigate the nonlinear OED problem in the context of continuously-indexed…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
Topology optimization has emerged as a powerful and increasingly relevant strategy for enhancing the flexibility and efficiency of power system operations. However, solving these problems is computationally demanding due to their…
We propose a new approach to solve optimal stopping problems via simulation. Working within the backward dynamic programming/Snell envelope framework, we augment the methodology of Longstaff-Schwartz that focuses on approximating the…
Supersonic shear layers experience instabilities that generate significant adverse effects; in complex configurations, these instabilities have global impacts as they foster compounding complications with other independent flow features. We…