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We develop a cubic scaling approach to excited-state-specific second order perturbation theory in which the completeness of a local correlation treatment is carefully matched between the ground and excited state. With this matching, the…
We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into…
We consider the accuracy of slender body theory in approximating the force exerted by a thin fiber on the surrounding viscous fluid when the fiber velocity is prescribed. We term this the slender body inverse problem, as it is known that…
We present a two-dimensional theoretical model for the slow chemical corrosion of a thin film of a disordered solid by suitable etching solutions. This model explain different experimental results showing that the corrosion stops…
We present a perturbative method for constructing approximate invariants of motion directly from the equations of discrete-time symplectic systems. This framework offers a natural nonlinear extension of the classic Courant-Snyder (CS)…
Sticky diffusion models a Markovian particle experiencing reflection and temporary adhesion phenomena at the boundary. Numerous numerical schemes exist for approximating stopped or reflected stochastic differential equations (SDEs), but…
The smoothed particle hydrodynamics (SPH) method has been widely used to simulate incompressible and slightly compressible fluid flows. Adaptive refinement strategies to dynamically increase the resolution of the particles to capture sharp…
Two new families of self-consistent axisymmetric truncated equilibrium models for the description of quasi-relaxed rotating stellar systems are presented. The first extends the spherical King models to the case of solid-body rotation. The…
There is a vast amount of literature concerning the appropriateness of various perturbation parameters for the standard quasi-steady state approximation in the Michaelis-Menten reaction mechanism, and also concerning the relevance of these…
Using a particle model of Physarum displaying emer- gent morphological adaptation behaviour we demonstrate how a minimal approach to collective material computation may be used to transform and summarise properties of spatially represented…
This dissertation studies the statistics and modeling of a quantum system probed by a coherent laser field. We focus on an ensemble of qubits dispersively coupled to a traveling wave light field. The first research topic explores the…
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…
In an effort to generalize the self-consistent Ornstein-Zernike approximation (SCOZA) -- an accurate liquid-state theory that has been restricted so far to hard-core systems -- to arbitrary soft-core systems we study a combination of SCOZA…
In this paper, we extend the previous method for solving inverse problems for steady-state equations using the Generalized Collage Theorem by searching for an approximation that not only minimizes the collage error but also maximizes the…
The periodic s-d(f) exchange model is characterized by a wide variety of interesting applications, a simple mathematical structure and a limited number of reliable approximations which take care of the quantum nature of the participating…
In this work we have proposed some spherically symmetric, static spacetimes in a theory of gravity which permits non-minimal coupling (NMC) between curvature of spacetime and fluid variables. It is shown that these non-minimally coupled…
We present new convergence analyses for parallel subspace correction methods for unconstrained semicoercive and nearly semicoercive convex optimization problems, generalizing the theory of singular and nearly singular linear problems to a…
We consider a kinetic model, which describes the sedimentation of rod-like particles in dilute suspensions under the influence of gravity. This model has recently been derived by Helzel and Tzavaras in \cite{HT2015}. Here we restrict our…
This paper addresses the problem of obtaining low-order models of fluid flows for the purpose of designing robust feedback controllers. This is challenging since whilst many flows are governed by a set of nonlinear, partial…
Sequencing batch reactors (SBRs) are devices widely used in wastewater treatment, chemical engineering, and other areas. They allow for the sedimentation and compression of solid particles of biomass simultaneously with biochemical…