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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

LigninGraphs: lignin structure determination with multiscale graph modeling

Lignin is an aromatic biopolymer found in ubiquitous sources of woody biomass. Designing and optimizing lignin valorization processes requires a fundamental understanding of lignin structures. Experimental characterization techniques, such as 2D-heteronuclear single quantum coherence (HSQC) nuclear magnetic resonance (NMR) spectra, could elucidate the global properties of the polymer molecules. Computer models could extend the resolution of experiments by representing structures at the molecular and atomistic scales. We introduce a graph-based multiscale modeling framework for lignin structure generation and visualization. The framework employs accelerated rejection-free polymerization and hierarchical Metropolis Monte Carlo optimization algorithms. We obtain structure libraries for various lignin feedstocks based on literature and new experimental NMR data for poplar wood, pinewood, and herbaceous lignin. The framework could guide researchers towards feasible lignin structures, efficient space exploration, and future kinetics modeling. Its software implementation in Python, LigninGraphs, is open-source and available on GitHub.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Universal Tripartite Entanglement in One-Dimensional Many-Body Systems

Motivated by conjectures in holography relating the entanglement of purification and reflected entropy to the entanglement wedge cross section, we introduce two related non-negative measures of tripartite entanglement g and h. We prove structure theorems which show that states with nonzero g or h have nontrivial tripartite entanglement. We then establish that in one dimension these tripartite entanglement measures are universal quantities that depend only on the emergent low-energy theory. For a gapped system, we argue that either g≠0 and h=0 or g=h=0, depending on whether the ground state has long-range order. For a critical system, we develop a numerical algorithm for computing g and h from a lattice model. We compute g and h for various CFTs and show that h depends only on the central charge whereas g depends on the whole operator content.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Bridging paradigms: Designing for HPC-Quantum convergence

Here, this paper presents a comprehensive software stack architecture for integrating quantum computing (QC) capabilities with High-Performance Computing (HPC) environments. While quantum computers show promise as specialized accelerators for scientific computing, their effective integration with classical HPC systems presents significant technical challenges. We propose a hardware-agnostic software framework that supports both current noisy intermediate-scale quantum devices and future fault-tolerant quantum computers, while maintaining compatibility with existing HPC workflows. The architecture includes a quantum gateway interface, standardized APIs for resource management, and robust scheduling mechanisms to handle both simultaneous and interleaved quantum–classical workloads. Key innovations include: (1) a unified resource management system that efficiently coordinates quantum and classical resources, (2) a flexible quantum programming interface that abstracts hardware-specific details, (3) A Quantum Platform Manager API that simplifies the integration of various quantum hardware systems, and (4) a comprehensive tool chain for quantum circuit optimization and execution. We demonstrate our architecture through implementation of quantum–classical algorithms, including the variational quantum linear solver, showcasing the framework’s ability to handle complex hybrid workflows while maximizing resource utilization. This work provides a foundational blueprint for integrating QC capabilities into existing HPC infrastructures, addressing critical challenges in resource management, job scheduling, and efficient data movement between classical and quantum resources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Numerical methods for high-dimensional probability density function equations

In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker–Planck and Dostupov–Pugachev equations), random wave theory (Malakhov–Saichev equations) and coarse-grained stochastic systems (Mori–Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Finite-temperature many-body perturbation theory for anharmonic vibrations: Recursions, algebraic reduction, second-quantized reduction, diagrammatic rules, linked-diagram theorem, finite-temperature self-consistent field, and general-order algorithm

A unified theory is presented for finite-temperature many-body perturbation expansions of the anharmonic vibrational contributions to thermodynamic functions, i.e., the free energy, internal energy, and entropy. The theory is diagrammatically size-consistent at any order, as ensured by the linked-diagram theorem proved in this study, and, thus, applicable to molecular gases and solids on an equal footing. It is also a basis-set-free formalism, just like its underlying Bose–Einstein theory, capable of summing anharmonic effects over an infinite number of states analytically. It is formulated by the Rayleigh–Schrödinger-style recursions, generating sum-over-states formulas for the perturbation series, which unambiguously converges at the finite-temperature vibrational full-configuration-interaction limits. Two strategies are introduced to reduce these sum-over-states formulas into compact sum-over-modes analytical formulas. One is a purely algebraic method that factorizes each many-mode thermal average into a product of one-mode thermal averages, which are then evaluated by the thermal Born–Huang rules. Canonical forms of these rules are proposed, dramatically expediting the reduction process. The other is finite-temperature normal-ordered second quantization, which is fully developed in this study, including a proof of thermal Wick’s theorem and the derivation of a normal-ordered vibrational Hamiltonian at finite temperature. The latter naturally defines a finite-temperature extension of size-extensive vibrational self-consistent field theory. These reduced formulas can be represented graphically as Feynman diagrams with resolvent lines, which include anomalous and renormalization diagrams. Two order-by-order and one general-order algorithms of computing these perturbation corrections are implemented and applied up to the eighth order. The results show no signs of Kohn–Luttinger-type nonconvergence.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Reinforcement learning pulses for transmon qubit entangling gates

The utility of a quantum computer is highly dependent on the ability to reliably perform accurate quantum logic operations. For finding optimal control solutions, it is of particular interest to explore model-free approaches, since their quality is not constrained by the limited accuracy of theoretical models for the quantum processor—in contrast to many established gate implementation strategies. In this work, we utilize a continuous control reinforcement learning algorithm to design entangling two-qubit gates for superconducting qubits; specifically, our agent constructs cross-resonance and CNOT gates without any prior information about the physical system. Using a simulated environment of fixed-frequency fixed-coupling transmon qubits, we demonstrate the capability to generate novel pulse sequences that outperform the standard cross-resonance gates in both fidelity and gate duration, while maintaining a comparable susceptibility to stochastic unitary noise. We further showcase an augmentation in training and input information that allows our agent to adapt its pulse design abilities to drifting hardware characteristics, importantly, with little to no additional optimization. Our results exhibit clearly the advantages of unbiased adaptive-feedback learning-based optimization methods for transmon gate design.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Basic Research Needs for Microelectronics: Report of the Office of Science Workshop on Basic Research Needs for Microelectronics, October 23 – 25, 2018

Moore’s Law — realized via a combination of device physics advances, technology investments, and economic returns— allowed the number of transistors on a chip to double roughly every two years for over five decades. During those five decades, the cost of a unit of computing dropped by eight orders of magnitude. Those declines and the associated computing advances have dramatically affected every aspect of society, from science and technology through business and health to national security. Today, further computing advances are limited by the economics of chip fabrication and the physical limits on transistors, electrical interconnects, and memory elements at the nanoscale. If we are to evolve new generations of computing systems over the next decades that are both faster and more energy efficient, a complete reorganization of the science and technology underlying computing is needed. Within the Department of Energy’s (DOE’s) mission, which includes a pivotal and historical role in the evolution of computing, the needs are critical as well. Advanced computing and simulation underpin all aspects of DOE missions in energy, the environment, and national security, requiring energy-efficient computing beyond the exascale range. Edge computing, low-power computing technologies, and computers optimized for artificial intelligence are key to next-generation scientific facilities for high-energy physics research, as well as neutron and x-ray facilities. Finally, microelectronics will also play a major role in reshaping the U.S. electricity grid: from its current state to one that is cleaner, more efficient, cyber-secure, and resilient to widespread events, both natural and manmade. Realizing this vision will require advancements in both system architecture and power electronics. To enable continued advances in computing technologies, a fundamental rethinking is needed of the science behind the materials, synthesis and placement technologies, architectures, and algorithms. This cannot be modular and linear, as it has been in the past. Rather, these advances must be developed collectively, in a spirit of co-design, where each scientific discipline informs and engages the other to achieve orders of magnitude improvements in system-level performance. To explore these challenges, the Office of Science convened a Basic Research Needs Workshop for Microelectronics in October 2018 and charged workshop participants to conduct a thorough assessment of the scientific issues associated with advanced microelectronics technologies for applications relevant to the DOE mission. The workshop examined research relevant to the extension of complementary metal oxide semiconductor (CMOS) and beyond CMOS technologies; however, topics of direct relevance to quantum information science and quantum computing were outside the scope of this workshop.

42 ENGINEERING↗
DOE OSTI2020

Optimal control of coupled quantum systems based on the first-order Magnus expansion: Application to multiple dipole-dipole-coupled molecular rotors

This paper presents a method for performing approximate optimal control simulations for quantum systems with multiple coupled degrees of freedom. In this work, the time evolution is simulated using the first-order Magnus expansion in the interaction picture, where the couplings between different degrees of freedom are treated as the perturbation. A numerical implementation procedure is presented that leverages upon pairwise couplings and the separability of the zeroth-order time evolution operator to achieve a reduced computational cost, which is analyzed with respect to the number of degrees of freedom. The formulation is compatible with gradient-free methods to optimize the control field, and a stochastic hill climbing algorithm is adopted for this purpose. As illustrations, optimal control simulations are performed for systems of two and three dipole-dipole-coupled molecular rotors under the influence of a control field. For the two-rotor system, the field is optimized to achieve either orientation or entanglement objectives. For the three-rotor system, the field is optimized either to orient all three rotors in the same direction or to orient one rotor in a particular direction while the other two rotors point in the opposite direction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Transmon qubit readout fidelity at the threshold for quantum error correction without a quantum-limited amplifier

Abstract High-fidelity and rapid readout of a qubit state is key to quantum computing and communication, and it is a prerequisite for quantum error correction. We present a readout scheme for superconducting qubits that combines two microwave techniques: applying a shelving technique to the qubit that reduces the contribution of decay error during readout, and a two-tone excitation of the readout resonator to distinguish among qubit populations in higher energy levels. Using a machine-learning algorithm to post-process the two-tone measurement results further improves the qubit-state assignment fidelity. We perform single-shot frequency-multiplexed qubit readout, with a 140 ns readout time, and demonstrate 99.5% assignment fidelity for two-state readout and 96.9% for three-state readout–without using a quantum-limited amplifier.

Chen, Liangyu (ORCID:0000000250722445)↗
DOE OSTI2026

Quantum-classical embedding via ghost Gutzwiller approximation for enhanced simulations of correlated electron systems

Simulating correlated materials on present-day quantum hardware remains challenging due to limited quantum resources. Quantum embedding methods offer a promising route by reducing computational complexity through the mapping of bulk systems onto effective impurity models, allowing more feasible simulations on pre- and early-fault-tolerant quantum devices. Here, this work develops a quantum-classical embedding framework based on the ghost Gutzwiller approximation to enable quantum-enhanced simulations of ground-state properties and spectral functions of correlated electron systems. Circuit complexity is analyzed using an adaptive variational quantum algorithm on a statevector simulator, applied to the infinite-dimensional Hubbard model with increasing ghost mode numbers from 3 to 5, resulting in circuit depths growing from 16 to 104. Noise effects are examined using a realistic error model, revealing significant impact on the spectral weight of the Hubbard bands. To mitigate these effects, the Iceberg quantum error detection code is employed, achieving up to 40% error reduction in simulations. Finally, the accuracy of the density matrix estimation and the derived spectral function is benchmarked on IBM and Quantinuum quantum hardware, featuring distinct qubit-connectivity and employing multiple levels of error mitigation techniques.

Chen, I-Chi [Ames Laboratory (AMES), Ames, IA (Uni↗
DOE OSTI2014

Calculation of exact vibrational spectra for P{sub 2}O and CH{sub 2}NH using a phase space wavelet basis

‘‘Exact” quantum dynamics calculations of vibrational spectra are performed for two molecular systems of widely varying dimensionality (P{sub 2}O and CH{sub 2}NH), using a momentum-symmetrized Gaussian basis. This basis has been previously shown to defeat exponential scaling of computational cost with system dimensionality. The calculations were performed using the new “SWITCHBLADE” black-box code, which utilizes both dimensionally independent algorithms and massive parallelization to compute very large numbers of eigenstates for any fourth-order force field potential, in a single calculation. For both molecules considered here, many thousands of vibrationally excited states were computed, to at least an “intermediate” level of accuracy (tens of wavenumbers). Future modifications to increase the accuracy to “spectroscopic” levels, along with other potential future improvements of the new code, are also discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Computing an Optimal Entanglement Path with Throughput and Fidelity Considerations

Entanglement distribution is a core function of quantum networks essential for operations including teleportation, distributed quantum sensing, and multisite computation. Entanglement throughput and fidelity are two critical performance measures that depend on the quantum transmission along the links and swapping operations at the repeaters along the path. We study the problem of computing a end-to-end entanglement path that satisfies both fidelity and throughput requirements, leveraging qubit buffers at the nodes and considering the sequential swapping order. We show that the general problem of simultaneously satisfying both metrics to be NP-hard, and develop an algorithm to maximize throughput subject to a given fidelity threshold. We introduce the concepts of entanglement probability distribution and path domination and exploit them in the design of our algorithm. Extensive numerical results show that our algorithm can find optimal solutions in networks with thousands of nodes in less than a second. We also describe practical and possible implementation aspects of this algorithm in terms of devices and architecture support.

Xue, Guoliang [Arizona State University]↗
DOE OSTI2013

Dynamic Stochastic Superresolution of sparsely observed turbulent systems

Real-time capture of the relevant features of the unresolved turbulent dynamics of complex natural systems from sparse noisy observations and imperfect models is a notoriously difficult problem. The resulting lack of observational resolution and statistical accuracy in estimating the important turbulent processes, which intermittently send significant energy to the large-scale fluctuations, hinders efficient parameterization and real-time prediction using discretized PDE models. This issue is particularly subtle and important when dealing with turbulent geophysical systems with an vast range of interacting spatio-temporal scales and rough energy spectra near the mesh scale of numerical models. Here, we introduce and study a suite of general Dynamic Stochastic Superresolution (DSS) algorithms and show that, by appropriately filtering sparse regular observations with the help of cheap stochastic exactly solvable models, one can derive stochastically ‘superresolved’ velocity fields and gain insight into the important characteristics of the unresolved dynamics, including the detection of the so-called black swans. The DSS algorithms operate in Fourier domain and exploit the fact that the coarse observation network aliases high-wavenumber information into the resolved waveband. It is shown that these cheap algorithms are robust and have significant skill on a test bed of turbulent solutions from realistic nonlinear turbulent spatially extended systems in the presence of a significant model error. In particular, the DSS algorithms are capable of successfully capturing time-localized extreme events in the unresolved modes, and they provide good and robust skill for recovery of the unresolved processes in terms of pattern correlation. Moreover, we show that DSS improves the skill for recovering the primary modes associated with the sparse observation mesh which is equally important in applications. The skill of the various DSS algorithms depends on the energy spectrum of the turbulent signal and the observation time relative to the decorrelation time of the turbulence at a given spatial scale in a fashion elucidated here. The DSS technique exploiting a simple Gaussian closure of the nonlinear stochastic forecast model emerges as the most suitable trade-off between the superresolution skill and computational complexity associated with estimating the cross-correlations between the aliasing modes of the sparsely observed turbulent signal. Such techniques offer a promising and efficient approach to constraining unresolved turbulent fluxes through stochastic superparameterization and a subsequent improvement in coarse-grained filtering and prediction of the next generation atmosphere–ocean system (AOS) models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Synthesis of the unmanned aerial vehicle remote control augmentation system

Medium size Unmanned Aerial Vehicle (UAV) usually flies as an autonomous aircraft including automatic take-off and landing phases. However in the case of the on-board control system failure, the remote steering is using as an emergency procedure. In this reason, remote manual control of unmanned aerial vehicle is used more often during take-of and landing phases. Depends on UAV take-off mass and speed (total energy) the potential crash can be very danger for airplane and environment. So, handling qualities of UAV is important from pilot-operator point of view. In many cases the dynamic properties of remote controlling UAV are not suitable for obtaining the desired properties of the handling qualities. In this case the control augmentation system (CAS) should be applied. Because the potential failure of the on-board control system, the better solution is that the CAS algorithms are placed on the ground station computers. The method of UAV handling qualities shaping in the case of basic control system failure is presented in this paper. The main idea of this method is that UAV reaction on the operator steering signals should be similar - almost the same - as reaction of the 'ideal' remote control aircraft. The model following method was used for controller parameters calculations. The numerical example concerns the medium size MP-02A UAV applied as an aerial observer system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Diagrammatic theories of anharmonic molecular vibrations

In this review, we summarise recent developments in our laboratory in the field of many-body quantum-mechanical calculations of the anharmonic vibrational structure of molecules. Our size-extensive vibrational self-consistent field (XVSCF) and size-extensive second-order many-body perturbation (XVMP2) methods are, unlike their parent methods (VSCF and VMP2), defined in diagram- matic formulations of the energies and Dyson self-energies, leading to manifestly size-consistent expressions for zero-point energies and anharmonic vibrational frequencies calculable with much greater efficiency. The effective one-mode potentials of XVSCF are quadratic and hence the Schrödinger equation for each mode can be solved analytically, unlike VSCF, where a basis-set expansion of wave functions on more complex one-mode potentials need to be performed; VSCF potentials and their minima (anharmonic geometry) are shown to reduce to the quadratic potentials and their minima (also given analytically) of XVSCF in the thermodynamic limit. By self-consistently solving the Dyson equation with frequency-dependent self-energies, XVMP2 has the ability to calculate anharmonic frequencies of fundamentals as well as combinations and overtones in the presence of strong anharmonic resonance without a multireference or quasi-degenerate formulation, which tends to be non-size-consistent. To eliminate the computational bottleneck of XVSCF and XVMP2, which is the high-rank force-constant evaluation, we have developed alternative algorithms in which the diagrammatic equations are recast as a small number of high-dimensional integrals and then evaluated stochastically using a Metropolis Monte Carlo (MC) method. These MC-XVSCF and MC-XVMP2 methods not only remove the need for force-constant evaluation or storage, but also take into account force constants of up to infinite order according to their importance. Furthermore, they are a new branch of quantum Monte Carlo which can calculate frequencies (excitation energies) directly without fixed-node errors.

Dyson equation↗
DOE OSTI2023

Foundations of machine learning for low-temperature plasmas: methods and case studies

Abstract Machine learning (ML) and artificial intelligence have proven to be an invaluable tool in tackling a vast array of scientific, engineering, and societal problems. The main drivers behind the recent proliferation of ML in practically all aspects of science and technology can be attributed to: (a) improved data acquisition and inexpensive data storage; (b) exponential growth in computing power; and (c) availability of open-source software and resources that have made the use of state-of-the-art ML algorithms widely accessible. The impact of ML on the field of low-temperature plasmas (LTPs) could be particularly significant in the emerging applications that involve plasma treatment of complex interfaces in areas ranging from the manufacture of microelectronics and processing of quantum materials, to the LTP-driven electrification of the chemical industry, and to medicine and biotechnology. This is primarily due to the complex and poorly-understood nature of the plasma-surface interactions in these applications that pose unique challenges to the modeling, diagnostics, and predictive control of LTPs. As the use of ML is becoming more prevalent, it is increasingly paramount for the LTP community to be able to critically analyze and assess the concepts and techniques behind data-driven approaches. To this end, the goal of this paper is to provide a tutorial overview of some of the widely-used ML methods that can be useful, amongst others, for discovering and correlating patterns in the data that may be otherwise impractical to decipher by human intuition alone, for learning multivariable nonlinear data-driven prediction models that are capable of describing the complex behavior of plasma interacting with interfaces, and for guiding the design of experiments to explore the parameter space of plasma-assisted processes in a systematic and resource-efficient manner. We illustrate the utility of various supervised, unsupervised and active learning methods using LTP datasets consisting of commonly-available, information-rich measurements (e.g. optical emission spectra, current–voltage characteristics, scanning electron microscope images, infrared surface temperature measurements, Fourier transform infrared spectra). All the ML demonstrations presented in this paper are carried out using open-source software; the datasets and codes are made publicly available. The FAIR guiding principles for scientific data management and stewardship can accelerate the adoption and development of ML in the LTP community.

Physics↗
DOE OSTI2016

SU-G-IeP2-08: Investigation On Signal Detectability in Volumetric Cone Beam CT Images with Anatomical Background

Purpose: To investigate the slice direction dependent detectability in cone beam CT images with anatomical background. Methods: We generated 3D anatomical background images using breast anatomy model. To generate 3D breast anatomy, we filtered 3D Gaussian noise with a square root of 1/f{sup 3}, and then assigned the attenuation coefficient of glandular (0.8cm{sup −1}) and adipose (0.46 cm{sup −1}) tissues based on voxel values. Projections were acquired by forward projection, and quantum noise was added to the projection data. The projection data were reconstructed by FDK algorithm. We compared the detectability of a 3 mm spherical signal in the image reconstructed from four different backprojection Methods: Hanning weighted ramp filter with linear interpolation (RECON1), Hanning weighted ramp filter with Fourier interpolation (RECON2), ramp filter with linear interpolation (RECON3), and ramp filter with Fourier interpolation (RECON4), respectively. We computed task SNR of the spherical signal in transverse and longitudinal planes using channelized Hotelling observer with Laguerre-Gauss channels. Results: Transverse plane has similar task SNR values for different backprojection methods, while longitudinal plane has a maximum task SNR value in RECON1. For all backprojection methods, longitudinal plane has higher task SNR than transverse plane. Conclusion: In this work, we investigated detectability for different slice direction in cone beam CT images with anatomical background. Longitudinal plane has a higher task SNR than transverse plane, and backprojection with hanning weighted ramp filter with linear interpolation method (i.e., RECON1) produced the highest task SNR among four different backprojection methods. This research was supported by the MSIP (Ministry of Science, ICT and Future Planning), Korea, under the IT Consilience Creative Programs(IITP-2015-R0346-15-1008) supervised by the IITP (Institute for Information & Communications Technology Promotion), Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the MSIP (2015R1C1A1A01052268) and framework of international cooperation program managed by NRF (NRF-2015K2A1A2067635).

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

An efficient particle Fokker–Planck algorithm for rarefied gas flows

This paper is devoted to the algorithmic improvement and careful analysis of the Fokker–Planck kinetic model derived by Jenny et al. [1] and Gorji et al. [2]. The motivation behind the Fokker–Planck based particle methods is to gain efficiency in low Knudsen rarefied gas flow simulations, where conventional direct simulation Monte Carlo (DSMC) becomes expensive. This can be achieved due to the fact that the resulting model equations are continuous stochastic differential equations in velocity space. Accordingly, the computational particles evolve along independent stochastic paths and thus no collision needs to be calculated. Therefore the computational cost of the solution algorithm becomes independent of the Knudsen number. In the present study, different computational improvements were persuaded in order to augment the method, including an accurate time integration scheme, local time stepping and noise reduction. For assessment of the performance, gas flow around a cylinder and lid driven cavity flow were studied. Convergence rates, accuracy and computational costs were compared with respect to DSMC for a range of Knudsen numbers (from hydrodynamic regime up to above one). In all the considered cases, the model together with the proposed scheme give rise to very efficient yet accurate solution algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗