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Many materials, processes, and structures in science and engineering have important features at multiple scales of time and/or space; examples include biological tissues, active matter, oceans, networks, and images. Explicitly extracting,…
We consider the one-dimensional propagation of electromagnetic waves in a weakly nonlinear and low-contrast spatially inhomogeneous medium with no energy dissipation. We focus on the case of a periodic medium, in which dispersion enters…
Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part, assuming a sinusoidal field variation, we consider the…
This paper is the first part of a two-fold study of mixing, i.e. the formation of layers and upwelling of buoyancy, in axially stratified Taylor--Couette flow, with fixed outer cylinder. Using linear analysis and direct numerical…
We study in detail the role of covariant Lyapunov vectors and their respective angles for detecting transitions between metastable states in dynamical systems, as recently discussed in several atmospheric science applications. The…
We consider the Vlasov-Poisson system in a cosmological setting and prove nonlinear stability of homogeneous solutions against small, spatially periodic perturbations in the sup-norm of the spatial mass density. This result is connected…
In this thesis, we construct and classify planar noncommutative phase spaces by the coadjoint orbit method on the anisotropic and absolute time kinematical groups. We show that noncommutative symplectic structures can be generated in the…
We consider the relativistic Vlasov-Maxwell system (RVM) on a general axisymmetric spatial domain with perfect conducting boundary which reflects particles specularly, assuming axisymmetry in the problem. We construct continuous global…
Variational inference (VI) has become a widely used approach for scalable Bayesian inference, but its performance strongly depends on the flexibility of the chosen variational family. In this work, we propose a novel variational family that…
The use of the isoconfigurational ensemble to explore structure-dynamic correlations in supercooled liquids is examined. The statistical error of the dynamic propensity and its spatial distribution are determined. The authors present the…
We suggest and implement an approach for the bottom-up description of systems undergoing large-scale structural changes and chemical transformations from dynamic atomically resolved imaging data, where only partial or uncertain data on…
Jamming is a phenomenon shared by a wide variety of systems, such as granular materials, foams, and glasses in their high density regime. This has motivated the development of a theoretical framework capable of explaining many of their…
A deep latent variable model is a powerful method for capturing complex distributions. These models assume that underlying structures, but unobserved, are present within the data. In this dissertation, we explore high-dimensional problems…
Slender beam-like structures frequently occur in engineering applications and often interact at discrete locations through joints or connectors. Accurate modeling of such interactions is particularly challenging when different numerical…
Cyclic pursuit frameworks, which are built upon pursuit interactions between neighboring agents in a cycle graph, provide an efficient way to create useful global behaviors in a collective of autonomous robots. Previous work had considered…
In this work, we derive reduced interface models for hydroelastic water waves coupled to a nonlinear viscoelastic plate. In a weakly nonlinear small-steepness regime we obtain bidirectional nonlocal evolution equations capturing the…
We show that the semi-implicit time discretization approaches previously introduced for multilayer shallow water models for the barotropic case can be also applied to the variable density case with Boussinesq approximation. Furthermore,…
Three geometric formulations of the Hamiltonian structure of the macroscopic Maxwell equations are given: one in terms of the double de Rham complex, one in terms of L2 duality, and one utilizing an abstract notion of duality. The final of…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…