相关论文: New Use of Dimensional Continuation Illustrated by…
In this article, we prove that, on the diffusive time scale, condensing zero-range processes converge to a dimension-decaying diffusion process on the simplex \[ \Sigma = \{(x_1,\dots,x_S) : x_i \ge 0,\; \sum_{i\in S} x_i = 1\}, \] where…
In order to explain the current acceleration of the Universe, the fine tuning problem of the cosmological constant $\Lambda$ and the cosmic coincidence problem, different alternative models have been proposed in the literature. We use the…
We consider the problem of reconstructing the paths of a set of points over time, where, at each of a finite set of moments in time the current positions of points in space are only accessible through some small number of their X-rays. This…
The declustering problem is to allocate given data on parallel working storage devices in such a manner that typical requests find their data evenly distributed on the devices. Using deep results from discrepancy theory, we improve previous…
The relaxation of a weakly collisional plasma, which is of fundamental interest to laboratory and astrophysical plasmas, can be described by the Boltzmann-Poisson equations with the Lenard-Bernstein collision operator. We perform a…
We determine the drag and the momentum diffusion coefficients of heavy fermion in dense plasma. It is seen that in degenerate matter drag coefficient at the leading order mediated by transverse photon is proportional to $(E-\mu)^2$ while…
The general, multidimensional barrier crossing problem for diffusive processes under the action of conservative forces is studied with the goal of developing tractable approximations. Particular attention is given to the effect of different…
We present a simple solution to enhance the separation ability of deterministic lateral displacement (DLD) systems by expanding the two-dimensional nature of these devices and driving the particles into size-dependent, fully…
Turbulence in fluids, gases, and plasmas remains an open problem of both practical and fundamental importance. Its irreducible complexity usually cannot be tackled computationally in a brute-force style. Here, we combine Large Eddy…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
Low-dimensional embeddings (LDEs) of high-dimensional data are ubiquitous in science and engineering. They allow us to quickly understand the main properties of the data, identify outliers and processing errors, and inform the next steps of…
A $\Gamma$-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external…
In this review, we examine particle transport in strongly turbulent three-dimensional (3D) magnetized plasmas, characterized by intense (large-amplitude) magnetic field fluctuations. Such environments naturally give rise to a network of…
A discrete system constituted of particles interacting by means of a centroid-based law is numerically investigated. The elements of the system move in the plane, and the range of the interaction can be varied from a more local form…
This is the first of two lectures on a new powerful technique employed by Brown, Preston, and Singleton (BPS) to calculate transport quantities in a plasma. This exposition will be self-contained and intended for those who are not…
This article is the second of a three-part series that derives a self-consistent theoretical framework of the electromechanics of arbitrarily curved lipid membranes. Existing continuum theories commonly treat lipid membranes as strictly…
An algorithm has been developped, which makes it possible to automatically extract trajectories of a large number of particles from fast imaging data, allowing a statistical analysis of particles trajectories under various plasma…
Dimensionality plays an essential role in determining the nature and properties of a physical system. For quantum systems the impact of interactions and fluctuations is enhanced in lower dimensions, leading to a great diversity of genuine…
Contemporary materials science research is heavily conducted in silico, involving massive simulations of the atomic-scale evolution of materials. Cataloging basic patterns in the atomic displacements is key to understanding and predicting…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…