Expanding selfsimilar solutions of a crystalline flow with applications to contour figure analysis

A numerical method for obtaining a crystalline flow starting from a general polygon is presented. A crystalline flow is a polygonal flow and can be regarded as a discrete version of a classical curvature flow. In some cases, new facets may be created instantaneously and their facet lengths are governed by a system of singular ordinary differential equations(ODEs). The proposed method solves the system of the ODEs numerically by using expanding selfsimilar solutions for newly created facets. The computation method is applied to a multi-scale analysis of a contour figure

Expanding selfsimilar solutions of a crystalline flow with applications to contour figure analysis

AbstractA numerical method for obtaining a crystalline flow starting from a general polygon is presented. A crystalline flow is a polygonal flow and can be regarded as a discrete version of a classical curvature flow. In some cases, new facets may be created instantaneously and their facet lengths are governed by a system of singular ordinary differential equations (ODEs). The proposed method solves the system of the ODEs numerically by using expanding selfsimilar solutions for newly created facets. The computation method is applied to a multi-scale analysis of a contour figure

On the role of kinetic and interfacial anisotropy in the crystal growth theory

A planar anisotropic curvature flow equation with constant driving force term is considered when the interfacial energy is crystalline. The driving force term is given so that a closed convex set grows if it is sufficiently large. If initial shape is convex, it is shown that a flat part called a facet (with admissible orientation) is instantaneously formed. Moreover, if the initial shape is convex and slightly bigger than the critical size, the shape becomes fully faceted in a finite time provided that the Frank diagram of interfacial energy density is a regular polygon centered at the origin. The proofs of these statements are based on approximation by crystalline algorithm whose foundation was established a decade ago. Our results indicate that the anisotropy of intefacial energy plays a key role when crystal is small in the theory of crystal growth. In particular, our theorems explain a reason why snow crystal forms a hexagonal prism when it is very small

Asymptotic behavior of solutions to an area-preserving motion by crystalline curvature

summary:Asymptotic behavior of solutions of an area-preserving crystalline curvature flow equation is investigated. In this equation, the area enclosed by the solution polygon is preserved, while its total interfacial crystalline energy keeps on decreasing. In the case where the initial polygon is essentially admissible and convex, if the maximal existence time is finite, then vanishing edges are essentially admissible edges. This is a contrast to the case where the initial polygon is admissible and convex: a solution polygon converges to the boundary of the Wulff shape without vanishing edges as time tends to infinity

Expanding selfsimilar solutions of a crystalline flow with applications to contour figure analysis

A numerical method for obtaining a crystalline flow starting from a general polygon is presented. A crystalline flow is a polygonal flow and can be regarded as a discrete version of a classical curvature flow. In some cases, new facets may be created instantaneously and their facet lengths are governed by a system of singular ordinary differential equations(ODEs). The proposed method solves the system of the ODEs numerically by using expanding selfsimilar solutions for newly created facets. The computation method is applied to a multi-scale analysis of a contour figure

Microstructural Analysis for Dynamic Pulverization and Asymmetric Damage at the Base of Seismogenic Strike-slip Faults

Although the mechanics of continental, seismogenic strike-slip faults have been primarily studied around active faults near Earth’s surface, large earthquakes on these faults commonly extend to depths between 10 and 20 km. At the base of seismogenic strike-slip faults, interaction and feedback between coseismic brittle fracturing and post- and interseismic viscous flow affect transient and long-term changes in stress cycling, fluid and heat transport, fault strength, and associated strain localization and deformation mechanisms. A primary goal of my dissertation is to explore the deeper structures of damage zones near the base of the seismogenic zone and to better understand the influence of the damaged rocks on rupture dynamics, by examining microstructures of exhumed fault rocks. My study area, the Sandhill Corner shear zone that is the longest strand of the Paleozoic Norumbega fault system in Maine, USA, represents large-displacement, seismogenic strike-slip faults at frictional-to-viscous transition depths (corresponding to temperatures of ~400–500 °C). The shear zone contains mutually overprinting pseudotachylyte and mylonite, and juxtaposes quartzofeldspathic mylonites and mica-rich schists. I analyzed fractured and fragmented garnet grains using particle size distributions, microfracture patterns, and electron backscatter diffraction fabrics. Microstructural studies of fragmented garnets reveal asymmetric distribution of dynamic pulverization with a width of ~70 m in the Sandhill Corner shear zone, and these results imply that the same damage processes observed around active seismogenic strike-slip faults operate at the base of the seismogenic zone. Garnet microstructures formed during earthquake cycles at the frictional-viscous transition can also provide evidence for dynamic pulverization even though the particle size distribution is modified by quasi-static fragmentation during post- and interseismic shearing. Elastic and seismic properties of the quartzofeldspathic rock and the mica-rich schist are quantified using the Thermo-Elastic and Seismic Analysis (TESA) numerical toolbox. The results illustrate how elastic contrast across bimaterial faults separating two different anisotropic materials affects preferred rupture propagation and asymmetric damage distribution. Strong anisotropy occurs in fault zones where preferentially aligned phyllosilicate minerals are a major component of the modal mineralogy. My findings suggest that the orientation and proportion of preferentially aligned phyllosilicates, or other highly anisotropic minerals, should be considered when investigating fault ruptures in anisotropic rocks

Nineteenth International Cosmic Ray Conference. OG Sessions, Volume 3

Papers submitted for presentation at the 19th International Cosmic Ray Conference are compiled. This volume addresses cosmic ray sources and acceleration, interstellar propagation and nuclear interactions, and detection techniques and instrumentation