In this thesis, we present various models of distributed computation and algorithms for these models. The underlying theme is to come up with fast algorithms that can tolerate faults in the underlying network. We begin with the classical message-passing model of computation, surveying many known results. We give a new, universally optimal, edge-biconnectivity algorithm for the classical model. ...

This thesis analyzes the collective modes of a Bose-Einstein condensate trapped in a harmonic cylindrically symmetric potential well. We use the Gross-Pitaeskii equation to evaluate the mean-field ground state, and the Bogoliubov-De Gennes formalism to compute normal modes. We solve both problems numerically by means of a newly developed code based on standard numerical techniques. In particula...

We consider the recovery of smooth 3D region boundaries with piecewise constant coefficients in Optical Tomography (OT). The method is based on a parametrisation of the closed boundaries of the regions by spherical harmonic coefficients, and a Newton type optimisation process. A boundary integral formulation is used for the forward modelling. An advantage of the proposed method is the implicit ...

A generalization of canonical quantization which maps a dynamical operator to a dynamical superoperator is suggested. Weyl quantization of dynamical operator, which cannot be represented as Poisson bracket with some function, is considered. The usual Weyl quantization of observables is a specific case of suggested quantization. This approach allows to define consistent quantization procedure fo...

RF integrated circuit designers make extensive use of simulation tools which perform nonlinear periodic steady-state analysis and its extensions. However, the computational costs of these simulation tools have restricted users from examining the detailed behavior of complete RF subsystems. Recent algorithmic developments , based on matrix-implicit iterative methods, is rapidly changing this sit...

In this work, we compare different mesh moving techniques for monolithically-coupled fluid-structure interactions in arbitrary Lagrangian–Eulerian coordinates. The mesh movement is realized by solving an additional partial differential equation of harmonic, linear-elastic, or biharmonic type. We examine an implementation of time discretization that is designed with finite differences. Spatial d...

We studied a dynamical model for the motion of the large scales of proteins in water. The model was obtained by projecting the (averaged) Newton equations onto some set of harmonic modes. We compared the statistics of the so-obtained trajectories with those obtained by standard techniques, and concluded that our dynamical model is able to fairly reproduce the average properties of the large-sca...

This paper presents and analyzes a new dynamic element matching technique for low-harmonic distortion digitalto-analog conversion. The benefit of this technique over the prior art is a significantly reduced hardware complexity with no reduction in performance. It is particularly appropriate for applications such as direct digital synthesis (DDS) in wireless communications systems, where low har...