A physically-plausible simulation of snow is a challenging task. The method we analyze in this thesis is a Material Point Method (MPM), that has been adjusted to accommodate both the fluid-like and the granular properties of snow. We analyze the simulation in four aspects. One, the noise generated from problems in numerical stability. Two, we analyze the domain in which simulation parameters pe...

In this paper, we study numerically the existence and stability of some special solutions of the nonlinear beam equation: utt +uxxxx +u− |u|p−1u = 0 when p = 3 and p = 5. First we show the existence and the orbital stability of the standing wave solutions: u(x, t) = eφω(x). Next, we study the existence and linear stability of the traveling wave solutions: u(x, t) = φ(x + ct). For both types of ...

Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is widely used to compute eigenvalues of large sparse symmetric matrices. The algorithm can suffer from numerical instability if it is not implemented with care. This is especially problematic when the number of eigenpairs to be computed is relatively large. We present a number of techniques to improve the robustness and efficienc...

In this paper we characterize the set of all restrictions on the behaviour of a plant that shape the characteristic polynomial of the closed-loop system. These control laws include both classical feedback laws and singular feedback laws. One of the results is the behavioural version of the Youla-Jabr-BongiornoKuEera-parameterization of all stabilizing control laws for a given plant. We also stu...

The aim of this paper is to study the Bounded Input Bounded Output (BIBO) stability of bilinear systems. The stability of linear systems can be studied by computing their transfer function. In this paper, we use the generating series (generalization of the transfer function) as a tool for analysing the stability of bilinear systems. In fact, the generating series G of a bilinear system is a for...

We construct curve counting invariants for a Calabi-Yau threefold Y equipped with a dominant birational morphism π : Y → X. Our invariants generalize the stable pair invariants of Pandharipande and Thomas which occur for the case when π : Y → Y is the identity. Our main result is a PT/DT-type formula relating the partition function of our invariants to the Donaldson-Thomas partition function in...

In this paper we study the exponential and uniform exponential stability problem for linear discrete time-varying systems with independent stochastic perturbations. We give two representations of the solutions of the discussed systems and we use them to obtain necessary and sufficient conditions for the two types of stability. A deterministic characterization of the uniform exponential stabilit...

The stability of electric currents in multifilamentary superconducting composites against flux jumps is discussed in detail. The normal procedure for such a quantitative stability investigation is carried out. In some particular cases the stability criteria are found and analysed.

We compute the stable reduction of some Galois covers of the projective line branched at three points. These covers are constructed using Hurwitz spaces parameterizing metacyclic covers. The reduction is determined by a certain hypergeometric differential equation. This generalizes the result of Deligne and Rapoport on the reduction of the modular curve X (p).

In this paper we propose a necessary condition for the existence of chaos in delay differential equations of fractional order. To explain the proposed theory, we discuss fractional order Liu system and financial system involving delay. Keywords—Caputo derivative, delay, stability, chaos.