Numerical investigation of the radial quadrupole and scissors modes in trapped gases

The analytical expressions for the frequency and damping of the radial quadrupole and scissors modes, as obtained from the method of moments, are limited to the harmonic potential. In addition, the analytical results may not be suciently accurate as an average relaxation time is used and the high-order moments are ignored. Here, we propose to numerically solve the Boltzmann model equation in the hydrodynamic, transition, and collisionless regimes to study mode frequency and damping. When the gas is trapped by the harmonic potential, we nd that the analytical expressions underestimate the damping in the transition regime. In addition, we demonstrate that the numerical simulations are able to provide reasonable predictions for the collective oscillations in the Gaussian potentials

Solving the Boltzmann equation deterministically by the fast spectral method : application to gas microflows

Based on the fast spectral approximation to the Boltzmann collision operator, we present an accurate and efficient deterministic numerical method for solving the Boltzmann equation. First, the linearised Boltzmann equation is solved for Poiseuille and thermal creep flows, where the influence of different molecular models on the mass and heat flow rates is assessed, and the Onsager-Casimir relation at the microscopic level for large Knudsen numbers is demonstrated. Recent experimental measurements of mass flow rates along a rectangular tube with large aspect ratio are compared with numerical results for the linearised Boltzmann equation. Then, a number of two-dimensional micro flows in the transition and free molecular flow regimes are simulated using the nonlinear Boltzmann equation. The influence of the molecular model is discussed, as well as the applicability of the linearised Boltzmann equation. For thermally driven flows in the free molecular regime, it is found that the magnitudes of the flow velocity are inversely proportional to the Knudsen number. The streamline patterns of thermal creep flow inside a closed rectangular channel are analysed in detail: when the Knudsen number is smaller than a critical value, the flow pattern can be predicted based on a linear superposition of the velocity profiles of linearised Poiseuille and thermal creep flows between parallel plates. For large Knudsen numbers, the flow pattern can be determined using the linearised Poiseuille and thermal creep velocity profiles at the critical Knudsen number. The critical Knudsen number is found to be related to the aspect ratio of the rectangular channel

Temperature retrieval error in Rayleigh-Brillouin scattering using Tenti’s S6 kinetic model

The Rayleigh-Brillouin spectrum of light scattered by gas density fluctuations contains information about the gas temperature. This information can be retrieved by comparing experimentally measured spectra with theoretical line shapes determined from the linearized Boltzmann equation. However, the linearized Boltzmann equation is difficult to solve so Tenti's S6 kinetic model has been widely used for several decades because of its simplicity. In this paper, the linearized Boltzmann equation is solved by the efficient fast spectral method, and the temperature retrieval error associated with the Tenti's S6 model is systematically investigated for both spontaneous and coherent Rayleigh-Brillouin scattering, for different gas rarefaction and intermolecular potentials. Our results indicate useful calibrations for laser technologies that use Rayleigh-Brillouin scattering to profile for gas temperatures with high accuracy

Fast spectral solution of the generalised Enskog equation for dense gases

We propose a fast spectral method for solving the generalized Enskog equation for dense gases. For elastic collisions, the method solves the Enskog collision operator with a computational cost of O(Md-1Nd logN), where d is the dimension of the velocity space, and Md-1 and Nd are the number of solid angle and velocity space discretizations, respectively. For inelastic collisions, the cost is N times higher. The accuracy of this fast spectral method is assessed by comparing our numerical results with analytical solutions of the spatially homogeneous relaxation of heated granular gases. We also compare our results for force driven Poiseuille flow and Fourier flow with those from molecular dynamics and Monte Carlo simulations. Although it is phenomenological, the generalized Enskog equation is capable of capturing the flow dynamics of dense granular gases, and the fast spectral method is accurate and efficient. As example applications, Fourier and Couette flows of a dense granular gas are investigated. In additional to the temperature profile, both the density and the high-energy tails in the velocity distribution functions are found to be strongly influenced by the restitution coefficient

GSIS: An efficient and accurate numerical method to obtain the apparent gas permeability of porous media

The apparent gas permeability (AGP) of a porous medium is an important parameter to predict production of unconventional gas. The Klinkenberg correlation, which states that the ratio of the AGP to the intrinsic permeability is approximately a linear function of reciprocal mean gas pressure, is one of the most popular estimations to quantify AGP. However, due to the difficulty in defining the characteristic flow length in complex porous media where the rarefied gas flow is multiscale, the slope in the Klinkenberg correlation varies significantly for different geometries such that a universal expression seems impossible. In this paper, by solving the gas kinetic equation using the general synthetic iterative scheme (GSIS), we compute the AGP in porous media that are represented by Sierpinski fractals and pore body/throat systems. With the abilities of fast convergence to steady-state solution and asymptotic preserving of Navier-Stokes limit, it is shown that GSIS is a promising tool to simulate low-speed rarefied gas flow through complex multiscale geometries. A new definition of the characteristic flow length is proposed as a function of porosity, tortuosity and intrinsic permeability of porous media, which enables to find a unique slope in the Klinkenberg correlation for all the considered geometries. This research also shows that the lattice Boltzmann method using simple wall scaling for the effective shear viscosity is not able to predict the AGP of porous media

Influence of intermolecular potentials on rarefied gas flows: fast spectral solutions of the Boltzmann equation

The Boltzmann equation with an arbitrary intermolecular potential is solved by the fast spectral method. As examples, noble gases described by the Lennard-Jones potential are considered. The accuracy of the method is assessed by comparing both transport coefficients with variational solutions and mass/heat flow rates in Poiseuille/thermal transpiration flows with results from the discrete velocity method. The fast spectral method is then applied to Fourier and Couette flows between two parallel plates, and the influence of the intermolecular potential on various flow properties is investigated. It is found that for gas flows with the same rarefaction parameter, differences in the heat flux in Fourier flow and the shear stress in Couette flow are small. However, differences in other quantities such as density, temperature, and velocity can be very large

ConDefects: A New Dataset to Address the Data Leakage Concern for LLM-based Fault Localization and Program Repair

With the growing interest on Large Language Models (LLMs) for fault localization and program repair, ensuring the integrity and generalizability of the LLM-based methods becomes paramount. The code in existing widely-adopted benchmarks for these tasks was written before the the bloom of LLMs and may be included in the training data of existing popular LLMs, thereby suffering from the threat of data leakage, leading to misleadingly optimistic performance metrics. To address this issue, we introduce "ConDefects", a novel dataset of real faults meticulously curated to eliminate such overlap. ConDefects contains 1,254 Java faulty programs and 1,625 Python faulty programs. All these programs are sourced from the online competition platform AtCoder and were produced between October 2021 and September 2023. We pair each fault with fault locations and the corresponding repaired code versions, making it tailored for in fault localization and program repair related research. We also provide interfaces for selecting subsets based on different time windows and coding task difficulties. While inspired by LLM-based tasks, ConDefects can be adopted for benchmarking ALL types of fault localization and program repair methods. The dataset is publicly available, and a demo video can be found at https://www.youtube.com/watch?v=22j15Hj5ONk.Comment: 5pages, 3 figure