Related papers: Schr\"{o}dinger Diffusion for Shape Analysis with …
Numerical simulation of steady-state heat conduction is common for thermal engineering. The simulation process usually involves mathematical formulation, numerical discretization and iteration of discretized ordinary or partial differential…
The crystallographic texture of metallic materials is a key microstructural feature that is responsible for the anisotropic behavior, e.g., important in forming operations. In materials science, crystallographic texture is commonly…
We introduce the notion of strip complex. A strip complex is a special type of complex obtained by gluing "strips" along their natural boundaries according to a given graph structure. The most familiar example is the one dimensional complex…
In the present paper, we prove that the $C_{0}$-semigroup generated by a Schr\"odinger operator with drift on a complete Riemannian manifold is approximated by the discrete semigroups associated with a family of discrete time random walks…
We propose a structure-preserving parametric finite element method (SP-PFEM) for discretizing the surface diffusion of a closed curve in two dimensions (2D) or surface in three dimensions (3D). Here the "structure-preserving" refers to…
We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Schr\"odinger and wave equations. In particular, we improve upon previous works and weaken the conditions on the potentials. To this end we also provide…
Regions of stellar and planetary interiors that are unstable according to the Schwarzschild criterion, but stable according to the Ledoux criterion, are subject to a form of oscillatory double-diffusive (ODD) convection often called…
We introduce a technique based on infrared thermal emission, termed depth thermography, that can remotely measure the temperature distribution beneath the surface of certain objects. Depth thermography utilizes the thermal-emission spectrum…
In this paper, we describe ongoing work to investigate the properties of the heat spreader, and its implication on architecture research. In specific, we conduct two experiments to quantify the heat distribution across the surface of a…
Network theory provides a principled abstraction of the human brain: reducing a complex system into a simpler representation from which to investigate brain organisation. Recent advancement in the neuroimaging field are towards representing…
We are interested in the kernel of one-dimensional diffusion equations with continuous coefficients as evaluated by means of explicit discretization schemes of uniform step $h>0$ in the limit as $h\to0$. We consider both semidiscrete…
Classical and non classical Besov and Triebel-Lizorkin spaces with complete range of indices are developed in the general setting of Dirichlet space with a doubling measure and local scale-invariant Poincar\'e inequality. This leads to Heat…
A set of interpolating functions of the type f(v)={(sin[v pi/2])/(v pi/2)}^n is analyzed in the context of the smoothed-particle hydrodynamics (SPH) technique. The behaviour of these kernels for several values of the parameter n has been…
This work presents an efficient numerical method to evaluate the free energy density and associated thermodynamic quantities of (quasi) one-dimensional classical systems, by combining the transfer operator approach with a numerical…
In this paper, we propose a new construction for the Mexican hat wavelets on shapes with applications to partial shape matching. Our approach takes its main inspiration from the well-established methodology of diffusion wavelets. This novel…
Recently, the theory of diffusion maps was extended to a large class of local kernels with exponential decay which were shown to represent various Riemannian geometries on a data set sampled from a manifold embedded in Euclidean space.…
We study the diffusion of tangential tensor-valued data on curved surfaces. For this purpose, several finite-element-based numerical methods are collected and used to solve a tangential surface n-tensor heat flow problem. These methods…
In this paper, we propose Complex Diffusion Maps (CDM), a novel diffusion mapping framework that aims to reveal the dominant complex harmonics of high-dimensional data. Inspired by the local Gaussian kernel relevant to the heat equation and…
We study long-time behaviors for branching-diffusion process corresponding to the drifted Schr\"odinger operator $\mathcal{L} = \frac{1}{2} \Delta + \langle \nabla V,\nabla \rangle - K$, where $K$ represents the reduction rate of a…
A novel numerical method called the Thermal Discrete Dipole Approximation (T-DDA) is proposed for modeling near-field radiative heat transfer in three-dimensional arbitrary geometries. The T-DDA is conceptually similar to the Discrete…