Related papers: Basis functions on the grain boundary space: Theor…
We construct a boundary integral formula for harmonic functions on open, smoothly-bordered subdomains of Riemann surfaces embeddable into $\C\P^2$. The formula may be considered as an analogue of the Green's formula for domains in $\C$.
Many technologically useful materials are polycrystals composed of small monocrystalline grains that are separated by grain boundaries of crystallites with different lattice orientations. The energetics and connectivities of the grain…
A threshold dynamics model of grain growth that accounts for the anisotropy in the grain boundary energy has been used to simulate experimentally observed grain growth of polycrystalline Ni. The simulation reproduces several aspects of the…
The material properties of polycrystals are strongly affected by the evolution and coarsening of their internal grain structures. Yet, studying this process is challenging due to the complex interactions within grain boundary networks.…
We study the constraints of crossing symmetry and unitarity for conformal field theories in the presence of a boundary, with a focus on the Ising model in various dimensions. We show that an analytic approach to the bootstrap is feasible…
The existence of kinematic formulas for area measures with respect to any connected, closed subgroup of the orthogonal group acting transitively on the unit sphere is established. In particular, the kinematic operator for area measures is…
We study orthogonal polynomials for a weight function defined over a domain of revolution, where the domain is formed from rotating a two-dimensional region and goes beyond the quadratic domains. Explicit constructions of orthogonal bases…
The properties of interstellar grains can now be defined by a rapidly growing wealth of observational data. We rely upon models to combine these data with unobserved properties such as the size distribution of grains, their structure and…
Grain boundary (GB) energy is a fundamental property that affects the form of grain boundary and plays an important role to unveil the behavior of polycrystalline materials. With a better understanding of grain boundary energy distribution…
Polycrystalline materials undergoing coarsening can be represented as evolving networks of grain boundaries, whose statistical characteristics determine macroscopic materials properties. The process of formation of various statistical…
Coarse graining enables the investigation of molecular dynamics for larger systems and at longer timescales than is possible at atomic resolution. However, a coarse graining model must be formulated such that the conclusions we draw from it…
Spatial statistics is concerned with the analysis of data that have spatial locations associated with them, and those locations are used to model statistical dependence between the data. The spatial data are treated as a single realisation…
Recent grain growth experiments have revealed that the same type of grain boundary can have very different mobilities depending on its local microstructure. In this work, we use molecular dynamics simulations to quantify uncertainty in the…
We present a construction of harmonic functions on bounded domains for the spectral fractional Laplacian operator and we classify them in terms of their divergent profile at the boundary. This is used to establish and solve boundary value…
A numerical investigation of grain-boundary grooving by means of a Level Set method is carried out. An idealized polygranular interconnect which consists of grains separated by parallel grain boundaries aligned normal to the average…
This contribution reports on numerical simulations of 2D granular flows on erodible beds. The broad aim is to investigate whether simple flows of model granular matter exhibits spontaneous oscillatory motion in generic flow conditions, and…
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…
Grain microstructures are crucial to the mechanical properties, performance, and often lifetime of metallic components. Hence, the prediction of grain microstructures emerging from solidification processes at relevant macroscopic scale is…
The grain boundary network of nanocrystalline Cu foils was modified by the systematic application of cyclic loadings and elevated temperatures having a range of magnitudes. Most broadly, the changes to the boundary network were directly…
Boundary conformal field theory (BCFT) is the study of conformal field theory (CFT) on manifolds with a boundary. We can use conformal symmetry to constrain correlation functions of conformal invariant fields. We compute two-point and…