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We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in…
A method is proposed to transform any analytic solution of the Bloch equation into an analytic solution of the Landau-Lifshitz-Gilbert equation. This allows for the analytical description of the dynamics of a two level system with damping.…
The paper deals with decentralized state estimation for spatially distributed systems described by linear partial differential equations from discrete in-space-and-time noisy measurements provided by sensors deployed over the spatial domain…
We study travelling-wave spatially periodic solutions of a forced Cahn-Hilliard equation. This is a model for phase separation of a binary mixture, subject to external forcing. We look at arbitrary values of the mean mixture concentration,…
We study the existence of fixed points to a parameterized Hammertstain operator $\cH_\beta,$ $\beta\in (0,\infty],$ with sigmoid type of nonlinearity. The parameter $\beta<\infty$ indicates the steepness of the slope of a nonlinear smooth…
In this paper we extend analysis of the WaveHoltz iteration -- a time-domain iterative method for the solution of the Helmholtz equation. We expand the previous analysis of energy conserving problems and prove convergence of the WaveHoltz…
In this paper, we investigate the problem of source recovery in a dynamical system utilizing space-time samples. This is a specific issue within the broader field of dynamical sampling, which involves collecting samples from solutions to a…
Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…
Semi-discrete Galerkin formulations of transient wave equations, either with conforming or discontinuous Galerkin finite element discretizations, typically lead to large systems of ordinary differential equations. When explicit time…
Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems. We give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random…
Smoothed particle hydrodynamics (SPH) has been extensively studied in computer graphics to animate fluids with versatile effects. However, SPH still suffers from two numerical difficulties: the particle deficiency problem, which will…
The Distributed Adaptive Signal Fusion (DASF) framework is a meta-algorithm for computing data-driven spatial filters in a distributed sensing platform with limited bandwidth and computational resources, such as a wireless sensor network.…
In this paper we study the global existence of small data solutions to the Cauchy problem for the semilinear wave equation with scale-invariant damping. We obtain estimates for the solution and its energy with the same decay rate of the…
Damped wave equations have been used in many real-world fields. In this paper, we study a low-rank solution of the strongly damped wave equation with the damping term, visco-elastic damping term and mass term. Firstly, a second-order finite…
Implicit particle filtering is a sequential Monte Carlo method for data assim- ilation, designed to keep the number of particles manageable by focussing attention on regions of large probability. These regions are found by min- imizing, for…
We explore the relation between fast waves, damping and imposed noise for different scalings by considering the singularly perturbed stochastic nonlinear wave equations \nu u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on a bounded spatial domain.…
In this paper, the distributed strongly convex optimization problem is studied with spatio-temporal compressed communication and equality constraints. For the case where each agent holds an distributed local equality constraint, a…
Gradient normalization and soft clipping are two popular techniques for tackling instability issues and improving convergence of stochastic gradient descent (SGD) with momentum. In this article, we study these types of methods through the…
In this paper we study the longtime dynamics of mild solutions to retarded stochastic evolution systems driven by a Hilbert-valued Brownian motion. As a preparation for this purpose we have to show the existence and uniqueness of a cocycle…
We consider admissible weak solutions to the compressible Euler system with source terms, which include rotating shallow water system and the Euler system with damping as special examples. In the case of anti-symmetric sources such as…