Two-Dimensional Grain Boundary Networks: Stochastic Particle Models and Kinetic Limits

Kinetic equations for grain boundary networks in two-dimensions

infinite dimensional garch models

مدلهای گارچ در فضاهای هیلبرت پایان نامه حاضر شامل دو بخش می باشد. در قسمت اول مدلهای اتورگرسیو تعمیم یافته مشروط به ناهمگنی واریانس در فضاهای هیلبرت را معرفی، مفاهیم ریاضی مورد نیاز در تحلیل این مدلها در دامنه زمان را مطرح کرده و آنها را مورد بررسی قرار می دهیم. بر اساس پیشرفتهایی که اخیرا در زمینه تئوری داده های تابعی و آماره های عملگری ایجاد شده است، فرآیندهایی که دارای مقادیر در فضاهای ...

Three-dimensional digital approximations of grain boundary networks in polycrystals

In this work, we offer a set of algorithms that convert a voxellated image to a conformal surface mesh that is targeted for polycrystalline materials containing grains with a wide range of sizes and complex shapes. More specifically, we propose a simple but effective algorithm for approximating the grain boundary networks that are implicit in three-dimensional digital images of polycrystals. Th...

Two-dimensional grain boundary percolation in alloy 304 stainless steel

An experimentally-obtained percolation threshold for high-angle random grain boundary networks in alloy 304 stainless steel is compared to thresholds predicted by percolation theory. A discrepancy occurs in the two values (0.46 experimental and 0.65 theoretical). Possible reasons for the discrepancy are explored. The grain boundary network appears to be composed of two distinct sub-networks, wi...

Grain Boundary Buckling and Spin Glass Models

A systematic investigation is presented of grain boundaries and grain boundary networks in two dimensional flexible membranes with crystalline order. An isolated grain boundary undergoes a buckling transition at a critical value of the elastic constants, but, contrary to previous findings, the shape of the buckled membrane is shown to be asymptotically flat. This is in general not true in the c...