6 citations · 25 across the 10 of their papers we have counts for
10 papers
Gauss--Hermite Quadrature for Gaussian-Mixture Entropy with an Action-Space Hermite Surrogate
Jae Wan Shim
Gaussian distributions are used to model uncertainty in signals and states, and Gaussian mixtures are often used when the underlying distribution is multimodal. Unlike a single Gau…
Parameter-Space Heat Flow, Gaussian Density Ratios, and Sharp Hermite Truncation Rates
Jae Wan Shim
We reinterpret the classical Hermite generating function as a Gaussian density ratio: relative to the unit Gaussian reference, it is the density ratio of a Gaussian with shifted me…
Conductive Heat Flux Driven by a Pressure Gradient in Non-Maxwellian Reference States
Jae Wan Shim
Standard Navier--Stokes--Fourier theory and Maxwellian-based Grad 13-moment closures yield no independent pressure-gradient driving of the conductive heat flux in an isothermal, si…
Entropy formula of N-body system
Jae Wan Shim
We prove a proposition that the entropy of the system composed of finite molecules of ideal gas is the -entropy or Havrda-Charvát-Tsallis entropy, which is also known as Tsa…
Parametric Lattice Boltzmann Method
Jae Wan Shim
The discretized equilibrium distributions of the lattice Boltzmann method are presented by using the coefficients of the Lagrange interpolating polynomials that pass through the po…
Multidimensional On-lattice Higher-order Models in the Thermal Lattice Boltzmann Theory
Jae Wan Shim
We present a set of uniform polynomial equations that provides multidimensional on-lattice higher-order models of the lattice Boltzmann theory, while keeping compact the number of…
Generalized Entropy Approach for Conserved Systems with Finite vs Infinite Entities: Insights into Non-Gaussian and Non-Chi-Square Distributions using Havrda-Charvát-Tsallis Entropy vs Gaussian Distributions via Boltzmann-Shannon Entropy
Jae Wan Shim
We demonstrate that the most probable state of a conserved system with a limited number of entities or molecules is the state where non-Gaussian and non-chi-square distributions go…
Minimal number of discrete velocities for a flow description and internal structural evolution of a shock wave
Jae Wan Shim
A fluid flow is described by fictitious particles hopping on homogeneously distributed nodes with a given finite set of discrete velocities. We emphasize that the existence of a fi…
Uniform Polynomial Equations Providing Higher-order Multi-dimensional Models in Lattice Boltzmann Theory
Jae Wan Shim
We present a set of polynomial equations that provides models of the lattice Boltzmann theory for any required level of accuracy and for any dimensional space in a general form. We…
Univariate Polynomial Equation Providing Models of Thermal Lattice Boltzmann Theory
Jae Wan Shim
A univariate polynomial equation is presented. It provides models of the thermal lattice Boltzmann equation. The models can be accurate up to any required level and can be applied…