arXiv subjects

Y. Shang

Publications and source records attributed to Y. Shang.

4 recordsLinked to original sources

arXiv2025

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs

We present approximation results and numerical experiments for the use of randomized neural networks within physics-informed extreme learning machines to efficiently solve high-dimensional PDEs, demonstrating both high accuracy and low computational cost. Specifically, we prove that RaNNs can approximate certain classes of functions, including Sobolev functions, in the $H^2$-norm at dimension-independent convergence rates, thereby alleviating the curse of dimensionality. Numerical experiments are provided for the high-dimensional heat equation, the Black-Scholes model, and the Heston model, demonstrating the accuracy and efficiency of randomized neural networks.

math.NA↗

arXiv2013

Preliminary design of laser accelerator beam line

A Compact laser plasma accelerator (CLAPA) is being built in Peking University, which is based on RPA-PSA mechanism or other acceleration mechanisms. According to the beam parameters from preparatory experiments and theoretical simulations, the beam line is preliminarily designed. The beam line is mainly constituted by common transport elements to deliver proton beam with the energy of 1~50MeV, energy spread of 0~1% and current of 0~108 proton per pulse to satisfy the requirement of different experiments. The simulation result of 15MeV proton beam with an energy spread of 1%, current of 1x108 proton per pulse and final spot radius of 9mm is presented in this paper.

physics.acc-ph↗

arXiv2010

SrRietveld: A program for automating Rietveld refinements for high throughput powder diffraction studies

SrRietveld is a highly automated software toolkit for Rietveld refinement. Compared to traditional refinement programs, it is more efficient to use and easier to learn. It is designed for modern high throughput diffractometers and capable of processing large numbers of data-sets with minimal effort. The new software currently uses conventional Rietveld refinement engines, automating GSAS and FullProf refinements. However, as well as automating and extending many tasks associated with these programs, it is designed in a flexible and extensible way so that in the future these engines can be replaced with new refinement engines as they become available. SrRietveld is an open source software package developed in Python.

cond-mat.mtrl-sci↗

arXiv2005

Pressure as a Source of Gravity

The active mass density in Einstein's theory of gravitation in the analog of Poisson's equation in a local inertial system is proportional to $ρ+3p/c^2$. Here $ρ$ is the density of energy and $p$ its pressure for a perfect fluid. By using exact solutions of Einstein's field equations in the static case we study whether the pressure term contributes towards the mass.

gr-qc↗