A Computational Model for Martensitic Thin Films With Compositional Fluctuation

We develop a computational model for the martensitic first-order structural phase transformation in a single crystal thin film, and we use this model to study the effect of spatial compositional fluctuation, spatial temporal noise, and the loss of stability of the metastable phase at temperatures sufficiently far from the transformation temperature

Computational Modeling of Softening in a Structural Phase Transformation

We develop a free energy density to model a structural first-order phase transformation from a high-temperature cubic phase to a low-temperature tetragonal phase. The free energy density models the softening of the elastic modulus controlling the low-energy path from the cubic to the tetragonal lattice, the loss of stability of the tetragonal phase at high temperatures and the loss of stability of the cubic phase at low temperatures, and the effect of compositional fluctuation on the transformation temperature. Numerical experiments are given for the quasi-static cooling and heating of a single crystal thin film through the transformation. Tweed-like oscillations are obtained as precursors to the structural phase transformation

Analysis of Economic Indicators of a Selected Company Using Statistical Methods.

Tato bakalářská práce se zabývá analýzou ekonomických ukazatelů vybrané společnosti. Zdrojem informací pro analýzu jsou podklady z účetnictví firmy. Práce je rozdělena na část teoretickou a část praktickou. Teoretická část se věnuje popisu metod finanční analýzy a statistickým metodám. V části praktické již analyzuji účetní výkazy a vybrané ukazatele finanční analýzou a následně aplikuji analýzu časových řad na ekonomické ukazatele.This bachelor thesis deals with analysis of economical indexes of selected company. The source of information for analysis is documentation from accounting firm. Thesis is divided to teoretical and practical part. Teoretical part describes financial and statistical methods. In practical part are already analysed accounting reports and chosen indexes by financial analyse. Then I apply analysis of time series to economical indexes.

On the numerical modeling of deformations of pressurized martensitic thin films

We propose, analyze, and compare several numerical methods for the computation of the deformation of a pressurized martensitic thin film. Numerical results have been obtained for the hysteresis of the deformation as the film transforms reversibly from austenite to martensite

On the Dynamics of Laguerre’s Iteration Method for Finding the nth Roots of Unity

Previous analyses of Laguerre’s iteration method have provided results on the behavior of this popular method when applied to the polynomials () = − 1, ∈ N. In this paper, we summarize known analytical results and provide new results. In particular, we study symmetry properties of the Laguerre iteration function and clarify the dynamics of the method. We show analytically and demonstrate computationally that for each ≥ 5 the basin of attraction to the roots is a subset of an annulus that contains the unit circle and whose Lebesgue measure shrinks to zero as → ∞. We obtain a good estimate of the size of the bounding annulus. We show that the boundary of the basin of convergence exhibits fractal nature and quasi self-similarity. We also discuss the connectedness of the basin for large values of . We also numerically nd some short nite cycles on the boundary of the basin of convergence for = 5, ..., 8. Finally, we demonstrate that when using the oating point arithmetic and the general formulation of the method, convergence occurs even from starting values outside of the basin of convergence due to the loss of signi cance during the evaluation of the iteration function

Applications of vortex gas models to tornadogenesis and maintenance

Processes related to the production of vorticity in the forward and rear flank downdrafts and their interaction with the boundary layer are thought to play a role in tornadogenesis. We argue that an inverse energy cascade is a plausible mechanism for tornadogenesis and tornado maintenance and provide supporting evidence which is both numerical and observational. We apply a three-dimensional vortex gas model to supercritical vortices produced at the surface boundary layer possibly due to interactions of vortices brought to the surface by the rear flank downdraft and also to those related to the forward flank downdraft. Two-dimensional and three-dimensional vortex gas models are discussed, and the three-dimensional vortex gas model of Chorin, developed further by Flandoli and Gubinelli, is proposed as a model for intense small- scale subvortices found in tornadoes and in recent numerical studies by Orf et al. In this paper, the smaller scales are represented by intense, supercritical vortices, which transfer energy to the larger-scale tornadic flows (inverse energy cascade). We address the formation of these vortices as a result of the interaction of the flow with the surface and a boundary layer.Comment: 20 pages, 6 figure

Fractal powers in Serrin\u27s swirling vortex solutions

We consider a modification of the fluid flow model for a tornado-like swirling vortex developed by Serrin [Phil. Trans. Roy. Soc. London, Series A, Math & Phys. Sci. 271(1214) (1972), 325–360], where velocity decreases as the reciprocal of the distance from the vortex axis. Recent studies, based on radar data of selected severe weather events [Mon. Wea. Rev. 133(9) (2005), 2535–2551; Mon. Wea. Rev. 128(7) (2000), 2135–2164; Mon. Wea. Rev. 133(1) (2005), 97–119], indicate that the angular momentum in a tornado may not be constant with the radius, and thus suggest a different scaling of the velocity/radial distance dependence. Motivated by this suggestion, we consider Serrin\u27s approach with the assumption that the velocity decreases as the reciprocal of the distance from the vortex axis to the power b with a general b\u3e0. This leads to a boundary-value problem for a system of nonlinear differential equations. We analyze this problem for particular cases, both with nonzero and zero viscosity, discuss the question of existence of solutions, and use numerical techniques to describe those solutions that we cannot obtain analytically