相关论文: Exactly Soluble Models for Surface Partition
We extend our 2+1 dimensional discrete growth model (PRE 79, 021125 (2009)) with conserved, local exchange dynamics of octahedra, describing surface diffusion. A roughening process was realized by uphill diffusion and curvature dependence.…
We prove a division algorithm for group rings of high genus surface groups and use it to show that some $2$-complexes with surface fundamental groups are standard. We also give an application of division to cohomological dimension of…
Small- and intermediate-scale galaxy clustering can be used to establish the galaxy-halo connection to study galaxy formation and evolution and to tighten constraints on cosmological parameters. With the increasing precision of galaxy…
High-dimensional clustering analysis is a challenging problem in statistics and machine learning, with broad applications such as the analysis of microarray data and RNA-seq data. In this paper, we propose a new clustering procedure called…
The method of fundamental solutions (MFS) is known to be effective for solving 3D Laplace and Stokes Dirichlet boundary value problems in the exterior of a large collection of simple smooth objects. Here we present new scalable MFS…
Phase transition problems on curved surfaces can lead to a panopticon of fascinating patterns. In this paper we consider finite element approximations of phase field models with a spatially inhomogeneous and anisotropic surface energy…
A method for dimension reduction with clustering, classification, or discriminant analysis is introduced. This mixture model-based approach is based on fitting generalized hyperbolic mixtures on a reduced subspace within the paradigm of…
We consider clustering problems where the goal is to determine an optimal partition of a given point set in Euclidean space in terms of a collection of affine subspaces. While there is vast literature on heuristics for this kind of problem,…
Under the right circumstances, inertial particles (such as sand or dust) settling through the atmospheric boundary layer can experience a net enhancement in their average settling velocity due to their inertia. Since this enhancement arises…
The scaling properties of one-dimensional deconstructed surfaces are studied by numerical simulations of a disaggregation model. The model presented here for the disaggregation process takes into account the possibility of having quenched…
We introduce a surface finite element method for the numerical solution of Navier-Stokes equations on evolving surfaces with a prescribed deformation of the surface in normal direction. The method is based on approaches for the full surface…
We consider a system of classical particles confined in a box $\Lambda\subset\mathbb{R}^d$ with zero boundary conditions interacting via a stable and regular pair potential. Based on the validity of the cluster expansion for the canonical…
In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…
The notion of tissue surface tension has provided a physical understanding of morphogenetic phenomena such as tissue spreading or cell sorting. The measurement of tissue surface tension so far relied on strong approximations on the…
The jamming transition is ubiquitous. It is present in granular matter, colloids, glasses, and many other systems. Yet, it defines a critical point whose properties still need to be fully understood. A major breakthrough came about when the…
Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces. They are already a standard in high-end computer animation and graphics and are…
Machine learning techniques can reveal hidden structure in large data amounts and can potentially extent or even replace analytical scientific methods. In nanophotonics, modes can increase the light yield from emitters located inside the…
We present a novel method for the accurate numerical determination of the phase behavior of fluid mixtures having large particle size asymmetries. By incorporating the recently developed geometric cluster algorithm within a restricted Gibbs…
Spatially highly-resolved capacity expansion models are often simplified to a lower spatial resolution because they are computationally intensive. The simplification mixes sites with different renewable features while ignoring transmission…
In this article an upscaled model is presented, for complex networks with highly clustered regions exchanging some abstract quantities in both, microscale and macroscale level. Such an intricate system is approximated by a partitioned open…