arXiv subjects

Yufeng Wei

Publications and source records attributed to Yufeng Wei.

18 recordsLinked to original sources

arXiv2026

A unified gas-kinetic wave-particle method for multiscale gas-mixture flow with an elementary chemical reaction

Hypersonic flows in the near space often couple continuum-rarefied multiscale effect with finite-rate chemistry. This paper extends the UGKWP method to multiscale gas mixture flows with a single elementary reaction. In the UGKWP method, hydrodynamic waves are employed to describe near-equilibrium distribution functions, and numerical particles are used for the evolution of nonequilibrium ones. The adaptive conversion between waves and particles, guided by the characteristic integral solution, together with the introduction of dt into the flux as an observation scale, has enabled the UGKWP method to succeed in many multiscale problems involving complex physics. In this work, rather than relying on a comprehensive reactive kinetic model for the entire distribution function, chemical source terms are first evaluated at the macroscopic level and then incorporated into the wave-particle update, while free-transport particles are kept chemically inactive in the monatomic setting considered here. This approach leverages the modeling advantages of wave-particle decoupling, facilitating extension to more complex chemical reactions. Moreover, an approximate extension of an advanced multispecies kinetic model is developed in this work for multispecies effect with species number larger than two. The present UGKWP method is assessed for the Zeldovich-type reaction O2+N=NO+O through hypersonic cylinder flows over a wide Knudsen number range, covering chemically inert, forward exothermic, forward endothermic and dE=0 conditions, and through shock structures with hot upstream/downstream equilibrium states. Agreement with DSMC is obtained for gas mixture flow fields, species mole fractions and wall quantities. A three-dimensional side jet flow over a blunt cone is further simulated to demonstrate the three-dimensional capability of the present code.

physics.comp-ph↗

arXiv2026

An Implicit Time-Domain Harmonic Balance Method for Radio-Frequency Capacitively Coupled Plasma Simulations

Fast and accurate fluid simulation of radio-frequency capacitively coupled plasmas (RF CCPs) is of great importance for the iterative design and parameter optimization of modern plasma reactors. This study presents the first successful extension of the time-domain harmonic balance (HB) method to a fully coupled drift-diffusion-Poisson system with complete electron-energy transport for RF plasma simulations. To resolve the severe numerical stiffness arising from highly nonlinear energy-dependent kinetics and dense phase-coupling, a highly efficient spatiotemporal operator-splitting strategy is employed. By sequentially executing a spatial implicit relaxation and a cell-local temporal inversion, this strategy entirely avoids the memory-intensive assembly of global Jacobians while preserving robust numerical stability. The proposed method is rigorously validated against a standard parallel-plate argon CCP benchmark. Evaluated across all discrete temporal collocation points, the HB solution demonstrates that retaining eight harmonics perfectly resolves both the quasi-steady bulk plasma and the highly nonlinear transient sheath dynamics, yielding macroscopic relative errors strictly below 0.3% compared to conventional dual-time stepping (DTS) solutions. Beyond its high physical fidelity, the time-domain HB method completely bypasses the prohibitive physical transients required by conventional time-marching methods. Evaluated on a purely sequential single-core execution, the HB method delivers a greater than 10-fold speedup over fully converged DTS baselines and remains over 5 times faster than the coarsest time-marching configurations. These results establish the time-domain HB framework as a physically rigorous, memory-efficient, and highly accelerated paradigm for practical RF plasma simulations.

physics.plasm-ph↗

arXiv2026

A Low-Storage Implicit Dual-Time Finite-Volume Framework for Radio-Frequency Capacitively Coupled Plasma Fluid Simulations

Radio-frequency (RF) capacitively coupled plasmas (CCPs) are widely utilized in semiconductor manufacturing. Efficiently and accurately solving the underlying fluid governing equations to resolve the complex multi-physics fields is crucial for optimizing plasma reactor designs and process control. To overcome the severe numerical stiffness and prohibitive time-step constraints inherent in low-temperature plasma modeling, we present a robust, low-storage implicit dual-time finite-volume framework for RF CCP simulations, establishing a highly efficient and memory-friendly pathway for the predictive modeling of multi-dimensional low-temperature plasmas. In this approach, the physical time advancement is strictly decoupled from explicit stability limits through a backward-difference formula (BDF), while the resulting nonlinear system is efficiently solved using pseudo-time iterations. A localized block-implicit relaxation method is employed to handle the stiff transport and chemical source terms at the cell level, effectively circumventing the massive memory overhead typical of conventional fully implicit solvers. Concurrently, a semi-implicit treatment of Poisson's equation is integrated to accelerate the electrostatic coupling. The framework is first verified against a standard one-dimensional argon discharge benchmark, demonstrating that a highly accurate periodic state can be achieved with satisfactory computational efficiency through the optimal selection of the physical time step, pseudo-CFL number, and inner iteration step. To further demonstrate the multidimensional applicability of the proposed method, the solver is extended to genuine two-dimensional configurations. The numerical results show the multi-dimensional distortion of the electrostatic potential and localized electron heating zones induced by the transverse boundaries.

physics.flu-dyn↗

arXiv2026

RCLUPPr: a new randomized CholeskyQR with LU preconditioning

In this work, we present the comprehensive rounding error analysis of RCLUPPr proposed in \cite{RCLUPP}, which is a novel randomized CholeskyQR-type algorithm performing LU decomposition with partial pivoting (LUPP decomposition) directly on the tall-skinny $X\in\mathbb{R}^{m\times n}$ with $m \ge n$ and $\mbox{rank}(X)=n$. In contrast to the existing RCLUPP in \cite{RCLUPP}, which applies matrix sketching before LUPP decomposition, RCLUPPr places LUPP decomposition as a preconditioning step first, significantly reducing error propagation. Our analysis rigorously proves that RCLUPPr enjoys markedly better applicability to the ill-conditioned matrices than the existing CholeskyQR-type algorithms and remains stable and accurate in the mixed-precision arithmetic. We further propose practical acceleration strategies in the real implementations of RCLUPPr. Extensive numerical experiments on the real-world problems confirm the theoretical results in this work, demonstrating the robustness and practicality of RCLUPPr in the single, double, and the mixed-precision architecture.

math.NA↗

arXiv2026

A unified gas-kinetic wave-particle method for multiscale binary-species gas mixtures

This paper presents a unified gas-kinetic wave-particle (UGKWP) method for simulating multiscale binary-species gas mixtures. Benefiting from direct modeling in a discretized space, the UGKWP method enables the automatic decomposition of the gas distribution function into analytical hydrodynamic waves and discrete particles, which respectively describe its near-equilibrium and non-equilibrium parts. This approach offers significant advantages for simulating various multiscale physical phenomena, such as hypersonic flows, plasma transport, and radiation transport. In this study, we employ the model proposed by Groppi et al. [EPL, 96 (2011) 64002] to calculate the macroscopic velocity and temperature of the local target equilibrium distribution function, thereby recovering the correct viscosity and diffusion coefficients in the continuum flow regime. To address the heat conduction coefficient, the Shakhov model is incorporated to correct the Prandtl number. Diffusion effects are accounted for not only in the source term via an operator-splitting method, but also in the flux evolution through the characteristic integral solution, while strictly maintaining consistency between the wave and particle descriptions. Furthermore, the microscopic model for high-speed particles is improved by utilizing a physically corrected collision time to determine their free-transport time. Through a series of numerical tests spanning the continuum to rarefied regimes, the proposed UGKWP method is shown to accurately capture the differences in velocity and temperature between different species. Notably, for hypersonic flows, the predicted wall pressure, shear stress, and heat flux coefficients agree well with DSMC results.

physics.flu-dyn↗

arXiv2026

A Time-Domain Harmonic Balance Unified Gas-Kinetic Scheme for Temporally Periodic Flows Across all Knudsen Regimes

This paper introduces a time-domain harmonic balance unified gas-kinetic scheme (HB-UGKS) designed to simulate temporally periodic flows across all Knudsen regimes. The harmonic balance approach reformulates the periodic problem into a block-coupled, quasi-steady system via a time-spectral source term. This allows for pseudo-time marching, local time-stepping, and the concurrent resolution of all sub-time levels, drastically reducing wall-clock time. Coupled with the UGKS-which maintains essential transport-collision coupling in its flux evaluations--the framework ensures multiscale validity across the entire Knudsen number range. The method is validated against two representative cavity flows. For a shear-driven oscillatory cavity under small-amplitude excitation, the fundamental harmonic alone accurately resolves the flow dynamics across various Knudsen and Strouhal numbers, successfully capturing the anti-resonance phenomenon and matching hydrodynamic damping predictions from linearized Boltzmann analyses. For a thermally driven cavity with large temperature modulations, higher-order harmonics prove essential to capture strong nonlinear waveform distortions and rarefaction effects. Beyond its physical fidelity, the HB-UGKS demonstrates substantial computational efficiency over explicit time-domain methods. This advantage peaks in high-frequency regimes, achieving speedup factors of 9.0 and 8.26 for the shear-driven and thermally driven cases, respectively.

physics.flu-dyn↗

arXiv2025

Adaptive criterion and modification of wave-particle decomposition in UGKWP method for high-speed flow simulation

Benefitting from the direct modeling of physical laws in a discretized space and the automatic decomposition of hydrodynamic waves and particles, the unified gas-kinetic wave-particle (UGKWP) method offers notable advantages in various multiscale physics, such as hypersonic flow, plasma transport and radiation transport. Aiming at achieving a more suitable and efficient wave-particle decomposition in high-speed flow simulation and enhancing the performance in the drastic scale variation region, in this work, the scale adaptive criterion is studied and the flux evolution of UGKWP method is modified. Specifically, besides the perspective of time which is naturally considered in the time-dependent distribution function of UGKWP method, two more criteria from views of space and gradient are utilized to identify the local scale, and to reduce the computational consumption of particles on describing the near-equilibrium microscopic gas distribution function. Moreover, corresponding to the coefficients in the time integration flux of unified gas-kinetic scheme (UGKS), the evolution of hydrodynamic wave is modified to be more consistent with particles, which is essential when the scale changes intensely in different cells. A variety of test cases are conducted to validate the performance of the adaptive UGKWP method, including hypersonic flows around a cylinder at multiple inflow Knudsen numbers, hypersonic flow over a slender cavity, side-jet impingement on hypersonic flow and three-dimensional hypersonic flows over a $70^{\circ}$ blunted cone with a cylindrical sting.

physics.comp-ph↗

arXiv2025

Radiative hydrodynamic equations with nonequilibrium radiative transfer

This paper presents a kinetic model for the coupled evolution of radiation, electrons, and ions in a radiation plasma system. The model is solved using two methods. The gas-kinetic scheme (GKS) for electron and ion hydrodynamics and the unified gas-kinetic scheme (UGKS) for non-equilibrium radiative transfer. The UGKS accurately captures multiscale photon transport from free streaming to diffusion across varying fluid opacities. This approach enables the scheme to model equilibrium plasma with non-equilibrium radiation transport. The model is validated through several test cases, including radiative transfer in kinetic and diffusion regimes, Marshak wave, Radiative shock, 3T(three-temperature) double lax shock tube problem, two-dimensional Sedov blast wave, and two-dimensional tophat based problem. These tests demonstrate the current scheme's capability to handle diverse radiation plasma scenarios.

physics.comp-ph↗

arXiv2024

Unified gas-kinetic scheme for reactive flow with multi-scale transport and chemical non-equilibrium

Reactive flows for rarefied gas mixtures involve a multi-scale transport characterized by particle collisions and free streaming, and non-equilibrium physics containing multi-species interactions, and chemical non-equilibrium. These flows are pivotal in aerospace engineering and semiconductor manufacturing, impacting spacecraft control and thermal protection in near-space flight, and plasma etching for chip processing. Therefore, the simulation of these multi-scale and non-equilibrium flow is of scientific and industrial significance. Following the methodology of direct modeling, the unified gas-kinetic scheme (UGKS) is constructed to describe the multi-scale transport of gas molecules across all flow regimes. This study extends the UGKS to the reactive flows with chemical non-equilibrium for the capture of more complex flow physics. Test cases, including shock structures, hypersonic flows around a two-dimensional cylinder and the three-dimensional re-entry and space vehicle, and nozzle plume flow into a vacuum, are used to validate the UGKS through the comparison with the direct simulation Monte Carlo method. The study shows that the methodology of direct modeling and the extended UGKS have great potential for simulating multi-scale flows with complex non-equilibrium physics.

physics.flu-dyn↗

arXiv2024

An efficiency and memory-saving programming paradigm for the unified gas-kinetic scheme

In recent years, non-equilibrium flows have gained significant attention in aerospace engineering and micro-electro-mechanical systems. The unified gas-kinetic scheme (UGKS) follows the methodology of direct modeling to couple particle collisions and free transport during gas evolution. However, like other discrete-velocity-based methods, the UGKS faces challenges related to high memory requirements and computational costs, such as the possible consumption of $1.32$ TB of memory when using $512$ cores for the simulations of the hypersonic flow around an X38-like space vehicle. This paper introduces a new UGKS programming paradigm for unstructured grids, focusing on reducing memory usage and improving parallel efficiency. By optimizing the computational sequence, the current method enables each cell in physical space to store only the distribution function for the discretized velocity space, eliminating the need to retain the entire velocity space for slopes and residuals. Additionally, the parallel communication is enhanced through the use of non-blocking MPI. Numerical experiments demonstrate that the new strategy in the programming effectively simulates non-equilibrium problems while achieving high computational efficiency and low memory consumption. For the hypersonic flow around an X38-like space vehicle, the simulation, which utilizes $1,058,685$ physical mesh cells and $4,548$ discrete velocity space mesh cells, requires only $168.12$ GB of memory when executed on $512$ CPU cores. This indicates that memory consumption in the UGKS is much reduced. This new programming paradigm can serve as a reference for discrete velocity methods for solving kinetic equations.

physics.comp-ph↗

arXiv2024

Contact-interference Hybrid lithography: Toward Scalable Fabrication of cross-scale periodic micro structure and demonstration on infrared micro polarizer array

Subwavelength grating micro-polarizer arrays, as a type of focal plane division simultaneous detection method, are significantly advancing the development and practical application of polarization imaging technology. Based on the cross-scale, dual-period characteristics of the grating array, this paper proposes a fabrication method that combines laser interference lithography with contact lithography. This method constructs a complete single-layer micro-polarizer array photoresist pattern through a four-step lithography process. Compared to traditional point-by-point fabrication methods like EBL and FIB, the patterning time is reduced by 3 to 4 orders of magnitude. Additionally, by introducing a refractive index matching liquid and an alignment method based on substrate contours, the effects of gaps and splicing errors are minimized, resulting in high-quality photoresist patterns with splicing errors less than 1μm. Finally, a double-layer metal grating structure was obtained through pattern transfer. Performance tests show that the micro-polarizer array achieves a maximum transmittance of over 50% and an extinction ratio exceeding 15dB in the 3-15μm wavelength range. This exploration offers a low-cost, high-efficiency path for fabricating micro-polarizer arrays.

physics.optics↗

arXiv2024

An implicit adaptive unified gas-kinetic scheme for steady-state solutions of non-equilibrium flows

Nonequilibrium flows have been frequently encountered in various aerospace engineering applications. To understand nonequilibrium physics, multiscale effects, and the dynamics in these applications, an effective and reliable multiscale scheme for all flow regimes is required. Following the direct modeling methodology, the adaptive unified gas-kinetic scheme employs discrete velocity space (DVS) to accurately capture the non-equilibrium physics, recovering the original unified gas-kinetic scheme (UGKS), and adaptively employs continuous distribution functions based on the Chapman-Enskog expansion to achieve better efficiency. Different regions are dynamically coupled at the cell interface through the fluxes from the discrete and continuous gas distribution functions, thereby avoiding any buffer zone between them. In the current study, an implicit adaptive unified gas-kinetic scheme (IAUGKS) is constructed to further enhance the efficiency of steady-state solutions. The current scheme employs implicit macroscopic governing equations and couples them with implicit microscopic governing equations within the non-equilibrium region, resulting in high convergence efficiency in all flow regimes. A series of numerical tests were conducted for high Mach number flows around diverse geometries such as a cylinder, a sphere, an X-38-like vehicle, and a space station. The current scheme can capture the non-equilibrium physics and provide accurate predictions of surface quantities. In comparison with the original UGKS, the velocity space adaptation, unstructured DVS, and implicit iteration significantly improve the efficiency by one or two orders of magnitude. Given its exceptional efficiency and accuracy, the IAUGKS serves as an effective tool for nonequilibrium flow simulations.

physics.flu-dyn↗

arXiv2024

A Distributed Scalable Cross-chain State Channel Scheme Based on Recursive State Synchronization

As cross-chain technology continues to advance, the scale of cross-chain transactions is experiencing significant expansion. To improve scalability, researchers have turned to the study of cross-chain state channels. However, most of the existing schemes rely on trusted parties to support channel operations. To address this issue, we present Interpipe: a distributed cross-chain state channel scheme. Specifically, we propose a real-time cross-chain synchronization scheme to ensure consistent operations between two blockchains to a cross-chain state channel. Moreover, we propose a batch transaction proof scheme based on recursive SNARK to meet the cross-chain verification needs of large-scale users. Based on the above designs, Interpipe offers protocols for opening, updating, closing, and disputing operations to cross-chain state channels. Security analysis shows that Interpipe has consistency and resistance, and experimental results demonstrate that a cross-chain state channel can be nearly as efficient as an existing intra-chain state channel.

cs.NI↗

arXiv2023

Adaptive unified gas-kinetic scheme for diatomic gases with rotational and vibrational nonequilibrium

Multiscale non-equilibrium physics at large variations of local Knudsen number are encountered in applications of aerospace engineering and micro-electro-mechanical systems, such as high-speed flying vehicles and low pressure of the encapsulation. An accurate description of flow physics in all flow regimes within a single computation requires a genuinely multiscale method. The adaptive unified gas-kinetic scheme (AUGKS) is developed for such multiscale flow simulation. The AUGKS applies discretized velocity space to accurately capture the non-equilibrium physics in the multiscale UGKS, and adaptively employs continuous distribution functions following Chapman-Enskog expansion to efficiently recover near-equilibrium flow region in GKS. The UGKS and GKS are dynamically connected at the cell interface through the fluxes from the discretized and continuous gas distribution functions, which avoids any buffer zone between them. In this study, the AUGKS method with rotation and vibration non-equilibrium is developed. The real gas effect in different flow regimes has been captured. To capture aerodynamic heating accurately, the heat flux modifications are also included. Unstructured discrete particle velocity space is adopted to further improve the computational performance. Numerical tests, including Sod tube, normal shock structure, high-speed flow around the two-dimensional cylinder and three-dimensional sphere and space vehicles, and an unsteady nozzle plume flow from the continuum flow to the background vacuum, have been conducted to validate the current scheme. In comparison with the original UGKS, the current scheme speeds up the computation, reduces the memory requirement, and maintains the equivalent accuracy for multiscale flow simulation, which provides an effective tool for non-equilibrium flow simulations, especially for the flows at low and medium speed.

physics.flu-dyn↗

arXiv2023

Nonequilibrium flow simulations using unified gas-kinetic wave-particle method

Nonequilibrium flows are common in aerospace engineering, and numerical simulations are vital in understanding non-equilibrium flow dynamics in spacecraft flight. The unified gas-kinetic wave-particle (UGKWP) method has been developed for multi-scale flow simulation, which models the coupled particle transport and collision within a numerical time in the flux evaluation across a cell interface. The UGKWP balances precision and efficiency in multiscale flow simulations, particularly in high-speed flow. In this study, the UGKWP method is used to simulate supersonic flow around a sphere, hypersonic flow around a space vehicle, nozzle plume into a vacuum, and side-jet impingement on hypersonic flow. The UGKWP accurately renders the Navier-Stokes solution within the nozzle, extending to free molecular flow in the external environment, all within a singular computation. Complicated structures in flow interaction have been captured by the UGKWP method. All simulation results have been verified through experimental measurements or Direct Simulation Monte Carlo (DSMC) methods. The UGKWP method requires only 60 GiB of memory to simulate a three-dimensional space vehicle with 560593 cells under different flow conditions, making it efficient and accurate for aerospace engineering applications.

physics.flu-dyn↗

arXiv2023

Adaptive wave-particle decomposition in UGKWP method for high-speed flow simulations

With wave-particle decomposition, a unified gas-kinetic wave-particle (UGKWP) method has been developed for the multiscale flow simulations. The UGKWP method captures the transport process in all flow regimes without kinetic solver's constraint on the numerical mesh size and time step being less than the particle mean free path and collision time. In the current UGKWP method, the cell's Knudsen number, defined as the ratio of collision time to numerical time step, is used to distribute the components in the wave-particle decomposition. However, the adaptation of particle in UGKWP is mainly for the capturing of the non-equilibrium transport, and the cell's Knudsen number alone is not enough to identify the non-equilibrium state. For example, in the equilibrium flow regime with a Maxwellian distribution function, even at a large cell's Knudsen number, the flow evolution can be still modelled by the Navier-Stokes solver. Therefore, to further improve the efficiency, an adaptive UGKWP (AUGKWP) method will be developed with the introduction of an additional local flow variable gradient-dependent Knudsen number. As a result, the wave-particle decomposition in UGKWP will be determined by both cell's and gradient's Knudsen numbers, and the particle in UGKWP is solely used to capture the non-equilibrium flow transport. The AUGKWP becomes much more efficient than the previous one with the cell's Knudsen number only in the determination of wave-particle composition. Many numerical tests, including Sod tube, shock structure, flow around a cylinder, flow around a reentry capsule, and an unsteady nozzle plume flow, have been conducted to validate the accuracy and efficiency of AUGKWP. Compared with the original UGKWP, the AUGKWP achieves the same accuracy but has advantages in memory reduction and computational efficiency in the simulation for the flow with the co-existing of multiple regimes.

physics.flu-dyn↗

arXiv2022

Unified gas-kinetic wave-particle methods VII: diatomic gas with rotational and vibrational nonequilibrium

Hypersonic flow around a vehicle in near space flight is associated with multiscale non-equilibrium physics at a large variation of local Knudsen number from the leading edge highly compressible flow to the trailing edge particle free transport. To accurately capture the solution in all flow regimes from the continuum Navier-Stokes solution to the rarefied gas dynamics in a single computation requires genuinely multiscale method. The unified gas-kinetic wave-particle (UGKWP) method targets on the simulation of such a multicale transport. Due to the wave-particle decomposition, the dynamics in the Navier-Stokes wave and kinetic particle transport has been unified systematically and efficiently under the unified gas-kinetic scheme (UGKS) framework. In this study, the UGKWP method with the non-equilibrium among translation, rotation and vibration modes, is developed based on a multiple temperature relaxation model. The real gas effect for high speed flow in different flow regimes has been properly captured. Numerical tests, including Sod tube, normal shock structure, hypersonic flow around two-dimensional cylinder and three-dimensional flow around a sphere and space vehicle, have been conducted to validate the UGKWP method. In comparison with the discrete velocity method (DVM)-based Boltzmann solver and particle-based direct simulation Monte Carlo (DSMC) method, the UGKWP method shows remarkable advantages in terms of computational efficiency, memory reduction, and automatic recovering of multiscale solution.

physics.flu-dyn↗

arXiv2022

UGKWP for three-dimensional simulation of gas-particle fluidized bed

The gas-solid particle two-phase flow in a fluidized bed shows complex physics. Following our previous work, the multi-scale framework based on gas-kinetic scheme (GKS) and unified gas-kinetic wave-particle method (UGKWP) for the gas-particle system is firstly extended to the three-dimensional simulation of the fluidized bed. For the solid particle evolution, different from the widely-used Eulerian and Lagrangian approaches, the UGKWP unifies the wave (dense particle region) and discrete particle (dilute particle region) formulation seamlessly according to a continuous variation of particle cell's Kundsen number ($Kn$). The GKS-UGKWP for the coupled gas-particle evolution system can automatically become an Eulerian-Eulerian (EE) method in the high particle collision regime and Eulerian-Lagrangian (EL) formulation in the collisionless particle regime. In the transition regime, the UGKWP can achieve a smooth transition between the Eulerian and Lagrangian limiting formulation. More importantly, the weights of mass distributions from analytical wave and discrete particle are related to the local $Kn$ by $\exp(-1/Kn)$ for wave and $(1-\exp(-1/Kn))$ for discrete particle. As a result, the UGKWP provides an optimal modeling for capturing the particle phase in terms of physical accuracy and numerical efficiency. In the numerical simulation, the UGKWP does not need any prior division of dilute/dense regions, which makes it suitable for the fluidized bed problem, where the dilute/transition/dense regions instantaneously coexist and are dynamically interconvertible. In this paper, based on the GKS-UGKWP formulation two lab-scale fluidization cases are simulated in 3D and the simulation results are compared with the experimental measurements. The typical heterogeneous flow features of the fluidized bed are well captured and the statistics are in good agreement with experiment data.

physics.comp-ph↗