Background The phenomenon where excessive activation of branched-chain amino acid(BCAA)degrading enzymes caused by high concentrations of leucine(Leu)leads to a decrease in the overall concentration of BCAA[including ...Background The phenomenon where excessive activation of branched-chain amino acid(BCAA)degrading enzymes caused by high concentrations of leucine(Leu)leads to a decrease in the overall concentration of BCAA[including isoleucine(Ile)and valine(Val)]is called BCAA antagonism.Although this phenomenon has long been widely studied,the specific mechanism of its occurrence is still poorly understood.In this study,we investigated the specific mechanism by which Val and Ile alleviate the antagonistic effect caused by high concentrations of Leu through influencing insulin function.First,the ratios of Ile and Val in the low-protein diet were adjusted up and down by 15%to observe the metabolic status of broilers at the end of the experiment(the experiment period was from 0 to 42 d).Subsequently,the physiological and biochemical changes related to antagonism were determined using transcriptome and lipid metabolome analyses.Results When fed with a high concentration of Leu,restricting Ile or supplementing Val can effectively alleviate antagonism.Under conditions of excessive dietary Val supplementation,insulin levels remained stable,whereas blood glucose levels increased(P<0.05),and liver fat accumulated predominantly as ceramides rather than triglycerides,thereby disrupting the insulin-mediated phosphatidylinositol 3-kinase/protein kinase B signaling pathway(P<0.05).Excessive dietary Ile promoted liver inflammation and interleukin-6 release(P<0.05),which acted on the pancreas to enhance insulin secretion.Additionally,the glucagon content in the pancreas decreased(P<0.05),while insulin and glucagon-like peptide-1 levels increased(P<0.05).Conclusion Supplementation of Val or restriction of Ile in low-protein diets could alleviate the BCAA antagonism caused by high Leu,which mainly achieved by influencing insulin function.These findings provide new insights in revealing the BCAA antagonism.展开更多
Background Research on low-protein-level diets has indicated that even though the profiles of essential amino acids(EAAs)follow the recommendation for a normal-protein-level diet,broilers fed low-protein diets failed ...Background Research on low-protein-level diets has indicated that even though the profiles of essential amino acids(EAAs)follow the recommendation for a normal-protein-level diet,broilers fed low-protein diets failed to achieve pro-ductive performance compared to those fed normal diets.Therefore,it is imperative to reassess the optimum profile of EAAs in low-protein diets and establish a new ideal pattern for amino acid balance.Furthermore,identifying novel sensitive biomarkers for assessing amino acid balance will greatly facilitate the development of amino acid nutrition and application technology.In this study,12 dietary treatments[Con(+),Con(-),L&A(-),L&A(+),M&C(-),M&C(+),BCAA(-),BCAA(+),Thr(-),Thr(+),Trp(-)and Trp(+)]were established by combining different EAAs including lysine and argi-nine,methionine and cysteine,branched-chain amino acid(BCAA),threonine,and tryptophan to observe the growth and development of the broiler chickens fed with low-protein-level diets.Based on the biochemical parameters and untargeted metabolomic analysis of animals subjected to different treatments,biomarkers associated with opti-mal and suboptimal amino acid balance were identified.Results Growth performance,carcass characteristics,hepatic enzyme activity,serum biochemical parameters,and breast muscle mRNA expression differed significantly between male and female broilers under different dietary amino acid patterns.Male broilers exhibited higher sensitivity to the adjustment of amino acid patterns than female broilers.For the low-protein diet,the dietary concentrations of lysine,arginine,and tryptophan,but not of methionine,cystine,or threonine,needed to be increased.Therefore,further research on individual BCAA is required.For untar-geted metabolomic analysis,Con(+)was selected as a normal diet(NP)while Con(-)represented a low-protein diet(LP).L&A(+)denotes a low-protein amino acid balanced diet(LPAB)and Thr(+)represents a low-protein amino acid imbalance diet(LPAI).The metabolites oxypurinol,pantothenic acid,and D-octopine in birds were significantly influ-enced by different dietary amino acid patterns.Conclusion Adjusting the amino acid profile of low-protein diets is required to achieve normal growth performance in broiler chickens fed normal-protein diets.Oxypurinol,pantothenic acid,and D-octopine have been identified as potentially sensitive biomarkers for assessing amino acid balance.展开更多
We propose a high-performance path planning algorithm for automatic target tracking in the applications of real-time simulation and visualization of large-scale terrain datasets, with a large number of moving objects ...We propose a high-performance path planning algorithm for automatic target tracking in the applications of real-time simulation and visualization of large-scale terrain datasets, with a large number of moving objects （such as vehicles） tracking multiple moving targets. By using a modified Dijkstra＇s algorithm, an optimal path between each vehicle-target pair over a weighted grid-presented terrain is computed and updated to eliminate the problem of local minima and losing of tracking. Then, a dynamic path re-planning strategy using multi-resolution representation of a dynamic updating region is proposed to achieve high-performance by trading-off precision for efficiency, while guaranteeing accuracy. Primary experimental results showed that our algorithm successfully achieved l0 to 96 frames per second interactive path-replanning rates during a terrain simulation scenario with 10 to 100 vehicles and multiple moving targets.展开更多
This research focuses on tin whisker growth under two different environmental conditions namely hygrothermal and a salt solution. Tin coated brass coupons were used for this study to analyze the growth of tin whiskers...This research focuses on tin whisker growth under two different environmental conditions namely hygrothermal and a salt solution. Tin coated brass coupons were used for this study to analyze the growth of tin whiskers over time. Their growth rates were examined periodically using optical and scanning electron microscopy. The physical characteristics of the tin whiskers were identified for each environmental condition. It was discovered that submersion of tin coated brass substrates in 5% salt solution considerably increased the density (number of whiskers per unit area), and the length of the whiskers. In addition, it was found that the geometry and aspect ratio of tin whiskers were different for each environment.展开更多
It is well-known that equilibrium density profiles of gases and fluids in gravitational potentials have an r−1 dependence, where r is the radius. This is found in both astronomical observations and detailed ...It is well-known that equilibrium density profiles of gases and fluids in gravitational potentials have an r−1 dependence, where r is the radius. This is found in both astronomical observations and detailed simulations in spherically-symmetric geometries. It is also well-known that the standard equation for hydrostatic equilibrium does not produce such solutions. This paper utilizes a Lagrangian formulation that produces a closed-form r−1 solution and identifies the needed terms to be added to the standard equation for hydrostatic equilibrium to obtain such a solution. Variants of the r−1 solution avoid a density singularity at the origin and a total-enclosed mass singularity at infinity. The resulting solutions are shown to be in good agreement with well-established density profiles of ordinary matter in galaxies, dark matter haloes, and the atmosphere of earth. Comparisons are made to solutions based on the standard hydrostatic equation, including solutions based on the Lane-Emden equation. The origins of differences are explained.展开更多
Concepts of precision engineering design process for optimal design where engineering sciences contribute in the successful good design are elaborated in this paper.Scientific theory and practicality are discussed in ...Concepts of precision engineering design process for optimal design where engineering sciences contribute in the successful good design are elaborated in this paper.Scientific theory and practicality are discussed in this paper.Factors necessary for a complete product or systems design are detailed and application of mathematical design optimization in producing a good design are shown.Many applicable engineering design examples are itemized to show relevancy of the optimal design theory to engineering design.Future trends of optimal design with respect to the 4th industrial revolution of digitization are presented.Paper sets to elaborate that most of the engineering and scientific design problems can be optimized to a good design based on many new/advanced optimization techniques.展开更多
The objective of this research is to provide an explanation of galactic haloes using established particles and forces using recent theoretical developments. Light fermions, with masses on the order of 1 eV/c<sup>...The objective of this research is to provide an explanation of galactic haloes using established particles and forces using recent theoretical developments. Light fermions, with masses on the order of 1 eV/c<sup>2</sup>, are not a leading candidate for dark matter because of their large free-streaming scale length and their violation of the Tremaine-Gunn bound. With a self-interaction of fermions, the free-streaming scaling length is reduced, and the tenets of the Tremaine-Gunn bound are not applicable. Binding of neutrinos via a feeble SU(3) force is considered as a model for such interactions. The assumed sum of masses of the three neutrino flavors is 0.07 eV/c<sup>2</sup>. The resulting form of matter for such bound neutrinos is found to be a degenerate Fermi fluid. Pressure-equilibrium approaches applied to this fluid provide cuspy solutions and match observationally-inferred profiles for galactic haloes. Such approaches also match the observed total enclosed mass for galaxies similar to the Milky Way. The computed structures are found to be stable. The hypothesis is considered in view of observationally-inferred halo-halo interactions and gives results that are consistent with the observed Bullet cluster halo interaction. The theory gives agreement with observationally-inferred properties of dark matter near earth. Questions related to interaction rates, consistency with SN1987a data, the cosmic microwave background, the issue of SU(3) interactions between neutrinos and quarks, free-streaming after neutrino decoupling, and dark-matter abundance are addressed in a companion paper.展开更多
Currently,flight delays are common and they propagate from an originating flight to connecting flights,leading to large disruptions in the overall schedule.These disruptions cause massive economic losses,affect airli...Currently,flight delays are common and they propagate from an originating flight to connecting flights,leading to large disruptions in the overall schedule.These disruptions cause massive economic losses,affect airlines’reputations,waste passengers’time and money,and directly impact the environment.This study adopts a network science approach for solving the delay propagation problem by modeling and analyzing the flight schedules and historical operational data of an airline.We aim to determine the most disruptive airports,flights,flightconnections,and connection types in an airline network.Disruptive elements are influential or critical entities in an airline network.They are the elements that can either cause(airline schedules)or have caused(historical data)the largest disturbances in the network.An airline can improve its operations by avoiding delays caused by the most disruptive elements.The proposed network science approach for disruptive element analysis was validated using a case study of an operating airline.The analysis indicates that potential disruptive elements in a schedule of an airline are also actual disruptive elements in the historical data and they should be considered to improve operations.The airline network exhibits small-world effects and delays can propagate to any part of the network with a minimum of four delayed flights.Finally,we observed that passenger connections between flights are the most disruptive connection type.Therefore,the proposed methodology provides a tool for airlines to build robust flight schedules that reduce delays and propagation.展开更多
The texture-based volume rendering is a memory-intensive algorithm.Its performance relies heavily on the performance of the texture cache.However,most existing texture-based volume rendering methods blindly map comput...The texture-based volume rendering is a memory-intensive algorithm.Its performance relies heavily on the performance of the texture cache.However,most existing texture-based volume rendering methods blindly map computational resources to texture memory and result in incoherent memory access patterns,causing low cache hit rates in certain cases.The distance between samples taken by threads of an atomic scheduling unit(e.g.a warp of 32 threads in CUDA)of the GPU is a crucial factor that affects the texture cache performance.Based on this fact,we present a new sampling strategy,called Warp Marching,for the ray-casting algorithm of texture-based volume rendering.The effects of different sample organizations and different thread-pixel mappings in the ray-casting algorithm are thoroughly analyzed.Also,a pipeline manner color blending approach is introduced and the power of warp-level GPU operations is leveraged to improve the efficiency of parallel executions on the GPU.In addition,the rendering performance of the Warp Marching is view-independent,and it outperforms existing empty space skipping techniques in scenarios that need to render large dynamic volumes in a low resolution image.Through a series of micro-benchmarking and real-life data experiments,we rigorously analyze our sampling strategies and demonstrate significant performance enhancements over existing sampling methods.展开更多
Blockchains have been around for more than ten years,and since 2015,a plethora of systems have been launched to target more flexible use cases.More recently,several enterprise blockchain systems,such as Consensys Quor...Blockchains have been around for more than ten years,and since 2015,a plethora of systems have been launched to target more flexible use cases.More recently,several enterprise blockchain systems,such as Consensys Quorum and Hyperledger Fabric,have been launched to make blockchain simpler to apply in complex organizational configurations.In this paper,we identify a specific Department of Defense use case,extrapolate requirements,and perform a thorough assessment of the different layers of the blockchain stack to identify the existing state of the art and undertake a gap analysis of the technology for this context.We describe a platform that meets many of these challenges and show how we architected,designed,and implemented a solution for this use case for deployment at NAVAIR.This solution connects transactions from two separate blockchain systems,Consensys Quorum and Hyperledger Fabric,by using a graph-based approach that preserves privacy while enabling full transparency across the military and supplier networks.展开更多
Hypersonic flows about space vehicles produce flowfields in thermodynamic non-equilibrium with the local Knudsen numbers Kn which may lie in all the three regimes:continuum,transition and rarefied.Continuum flows can ...Hypersonic flows about space vehicles produce flowfields in thermodynamic non-equilibrium with the local Knudsen numbers Kn which may lie in all the three regimes:continuum,transition and rarefied.Continuum flows can be modeled accurately by solving the Navier–Stokes(NS)equations;however,the flows in transition and rarefied regimes require a kinetic approach such as the direct simulation Monte Carlo(DSMC)method or the solution of the Boltzmann equation.The Boltzmann equation and the general solution approach,using the splitting method,will be introduced in this paper.Details of the method used for solving both the classical Boltzmann equation(CBE)and the generalized Boltzmann equation(GBE)are also provided.The gas mixture discussed in this paper may consist of both monoatomic and diatomic gases.In particular,the method is applied to simulate two of the three primary constituents of air(N_(2),O_(2),and Ar)in a binary mixture at 1:1 density ratio at Mach 2 and 5,with gases in translational,rotational and vibrational non-equilibrium.展开更多
基金financially supported by the National Key R&D Program of China(2021YFD1300404)Shenyang Governmental Science and Technology Program(Project No.22-316-2-02)+1 种基金China Agriculture Research System program(CARS-41)China Association for Science and Technology(CAST)Youth Talent Lifting Project–Special Program for Doctoral Candidates(2024)。
文摘Background The phenomenon where excessive activation of branched-chain amino acid(BCAA)degrading enzymes caused by high concentrations of leucine(Leu)leads to a decrease in the overall concentration of BCAA[including isoleucine(Ile)and valine(Val)]is called BCAA antagonism.Although this phenomenon has long been widely studied,the specific mechanism of its occurrence is still poorly understood.In this study,we investigated the specific mechanism by which Val and Ile alleviate the antagonistic effect caused by high concentrations of Leu through influencing insulin function.First,the ratios of Ile and Val in the low-protein diet were adjusted up and down by 15%to observe the metabolic status of broilers at the end of the experiment(the experiment period was from 0 to 42 d).Subsequently,the physiological and biochemical changes related to antagonism were determined using transcriptome and lipid metabolome analyses.Results When fed with a high concentration of Leu,restricting Ile or supplementing Val can effectively alleviate antagonism.Under conditions of excessive dietary Val supplementation,insulin levels remained stable,whereas blood glucose levels increased(P<0.05),and liver fat accumulated predominantly as ceramides rather than triglycerides,thereby disrupting the insulin-mediated phosphatidylinositol 3-kinase/protein kinase B signaling pathway(P<0.05).Excessive dietary Ile promoted liver inflammation and interleukin-6 release(P<0.05),which acted on the pancreas to enhance insulin secretion.Additionally,the glucagon content in the pancreas decreased(P<0.05),while insulin and glucagon-like peptide-1 levels increased(P<0.05).Conclusion Supplementation of Val or restriction of Ile in low-protein diets could alleviate the BCAA antagonism caused by high Leu,which mainly achieved by influencing insulin function.These findings provide new insights in revealing the BCAA antagonism.
基金Shenyang Governmental Science and Technology Program(Project No.22-316-2-02)China Agriculture Research System Program(Project No.CARS-41-G04).
文摘Background Research on low-protein-level diets has indicated that even though the profiles of essential amino acids(EAAs)follow the recommendation for a normal-protein-level diet,broilers fed low-protein diets failed to achieve pro-ductive performance compared to those fed normal diets.Therefore,it is imperative to reassess the optimum profile of EAAs in low-protein diets and establish a new ideal pattern for amino acid balance.Furthermore,identifying novel sensitive biomarkers for assessing amino acid balance will greatly facilitate the development of amino acid nutrition and application technology.In this study,12 dietary treatments[Con(+),Con(-),L&A(-),L&A(+),M&C(-),M&C(+),BCAA(-),BCAA(+),Thr(-),Thr(+),Trp(-)and Trp(+)]were established by combining different EAAs including lysine and argi-nine,methionine and cysteine,branched-chain amino acid(BCAA),threonine,and tryptophan to observe the growth and development of the broiler chickens fed with low-protein-level diets.Based on the biochemical parameters and untargeted metabolomic analysis of animals subjected to different treatments,biomarkers associated with opti-mal and suboptimal amino acid balance were identified.Results Growth performance,carcass characteristics,hepatic enzyme activity,serum biochemical parameters,and breast muscle mRNA expression differed significantly between male and female broilers under different dietary amino acid patterns.Male broilers exhibited higher sensitivity to the adjustment of amino acid patterns than female broilers.For the low-protein diet,the dietary concentrations of lysine,arginine,and tryptophan,but not of methionine,cystine,or threonine,needed to be increased.Therefore,further research on individual BCAA is required.For untar-geted metabolomic analysis,Con(+)was selected as a normal diet(NP)while Con(-)represented a low-protein diet(LP).L&A(+)denotes a low-protein amino acid balanced diet(LPAB)and Thr(+)represents a low-protein amino acid imbalance diet(LPAI).The metabolites oxypurinol,pantothenic acid,and D-octopine in birds were significantly influ-enced by different dietary amino acid patterns.Conclusion Adjusting the amino acid profile of low-protein diets is required to achieve normal growth performance in broiler chickens fed normal-protein diets.Oxypurinol,pantothenic acid,and D-octopine have been identified as potentially sensitive biomarkers for assessing amino acid balance.
基金Project partially supported by NSF (No. CCR0306438) and theBoeing Company, USA
文摘We propose a high-performance path planning algorithm for automatic target tracking in the applications of real-time simulation and visualization of large-scale terrain datasets, with a large number of moving objects （such as vehicles） tracking multiple moving targets. By using a modified Dijkstra＇s algorithm, an optimal path between each vehicle-target pair over a weighted grid-presented terrain is computed and updated to eliminate the problem of local minima and losing of tracking. Then, a dynamic path re-planning strategy using multi-resolution representation of a dynamic updating region is proposed to achieve high-performance by trading-off precision for efficiency, while guaranteeing accuracy. Primary experimental results showed that our algorithm successfully achieved l0 to 96 frames per second interactive path-replanning rates during a terrain simulation scenario with 10 to 100 vehicles and multiple moving targets.
文摘This research focuses on tin whisker growth under two different environmental conditions namely hygrothermal and a salt solution. Tin coated brass coupons were used for this study to analyze the growth of tin whiskers over time. Their growth rates were examined periodically using optical and scanning electron microscopy. The physical characteristics of the tin whiskers were identified for each environmental condition. It was discovered that submersion of tin coated brass substrates in 5% salt solution considerably increased the density (number of whiskers per unit area), and the length of the whiskers. In addition, it was found that the geometry and aspect ratio of tin whiskers were different for each environment.
文摘It is well-known that equilibrium density profiles of gases and fluids in gravitational potentials have an r−1 dependence, where r is the radius. This is found in both astronomical observations and detailed simulations in spherically-symmetric geometries. It is also well-known that the standard equation for hydrostatic equilibrium does not produce such solutions. This paper utilizes a Lagrangian formulation that produces a closed-form r−1 solution and identifies the needed terms to be added to the standard equation for hydrostatic equilibrium to obtain such a solution. Variants of the r−1 solution avoid a density singularity at the origin and a total-enclosed mass singularity at infinity. The resulting solutions are shown to be in good agreement with well-established density profiles of ordinary matter in galaxies, dark matter haloes, and the atmosphere of earth. Comparisons are made to solutions based on the standard hydrostatic equation, including solutions based on the Lane-Emden equation. The origins of differences are explained.
文摘Concepts of precision engineering design process for optimal design where engineering sciences contribute in the successful good design are elaborated in this paper.Scientific theory and practicality are discussed in this paper.Factors necessary for a complete product or systems design are detailed and application of mathematical design optimization in producing a good design are shown.Many applicable engineering design examples are itemized to show relevancy of the optimal design theory to engineering design.Future trends of optimal design with respect to the 4th industrial revolution of digitization are presented.Paper sets to elaborate that most of the engineering and scientific design problems can be optimized to a good design based on many new/advanced optimization techniques.
文摘The objective of this research is to provide an explanation of galactic haloes using established particles and forces using recent theoretical developments. Light fermions, with masses on the order of 1 eV/c<sup>2</sup>, are not a leading candidate for dark matter because of their large free-streaming scale length and their violation of the Tremaine-Gunn bound. With a self-interaction of fermions, the free-streaming scaling length is reduced, and the tenets of the Tremaine-Gunn bound are not applicable. Binding of neutrinos via a feeble SU(3) force is considered as a model for such interactions. The assumed sum of masses of the three neutrino flavors is 0.07 eV/c<sup>2</sup>. The resulting form of matter for such bound neutrinos is found to be a degenerate Fermi fluid. Pressure-equilibrium approaches applied to this fluid provide cuspy solutions and match observationally-inferred profiles for galactic haloes. Such approaches also match the observed total enclosed mass for galaxies similar to the Milky Way. The computed structures are found to be stable. The hypothesis is considered in view of observationally-inferred halo-halo interactions and gives results that are consistent with the observed Bullet cluster halo interaction. The theory gives agreement with observationally-inferred properties of dark matter near earth. Questions related to interaction rates, consistency with SN1987a data, the cosmic microwave background, the issue of SU(3) interactions between neutrinos and quarks, free-streaming after neutrino decoupling, and dark-matter abundance are addressed in a companion paper.
基金part of a BOEING project“Airline Performance and Disruption Management Across Extended Networks(APEMEN)”funded with research(Grant No.:46599).
文摘Currently,flight delays are common and they propagate from an originating flight to connecting flights,leading to large disruptions in the overall schedule.These disruptions cause massive economic losses,affect airlines’reputations,waste passengers’time and money,and directly impact the environment.This study adopts a network science approach for solving the delay propagation problem by modeling and analyzing the flight schedules and historical operational data of an airline.We aim to determine the most disruptive airports,flights,flightconnections,and connection types in an airline network.Disruptive elements are influential or critical entities in an airline network.They are the elements that can either cause(airline schedules)or have caused(historical data)the largest disturbances in the network.An airline can improve its operations by avoiding delays caused by the most disruptive elements.The proposed network science approach for disruptive element analysis was validated using a case study of an operating airline.The analysis indicates that potential disruptive elements in a schedule of an airline are also actual disruptive elements in the historical data and they should be considered to improve operations.The airline network exhibits small-world effects and delays can propagate to any part of the network with a minimum of four delayed flights.Finally,we observed that passenger connections between flights are the most disruptive connection type.Therefore,the proposed methodology provides a tool for airlines to build robust flight schedules that reduce delays and propagation.
文摘The texture-based volume rendering is a memory-intensive algorithm.Its performance relies heavily on the performance of the texture cache.However,most existing texture-based volume rendering methods blindly map computational resources to texture memory and result in incoherent memory access patterns,causing low cache hit rates in certain cases.The distance between samples taken by threads of an atomic scheduling unit(e.g.a warp of 32 threads in CUDA)of the GPU is a crucial factor that affects the texture cache performance.Based on this fact,we present a new sampling strategy,called Warp Marching,for the ray-casting algorithm of texture-based volume rendering.The effects of different sample organizations and different thread-pixel mappings in the ray-casting algorithm are thoroughly analyzed.Also,a pipeline manner color blending approach is introduced and the power of warp-level GPU operations is leveraged to improve the efficiency of parallel executions on the GPU.In addition,the rendering performance of the Warp Marching is view-independent,and it outperforms existing empty space skipping techniques in scenarios that need to render large dynamic volumes in a low resolution image.Through a series of micro-benchmarking and real-life data experiments,we rigorously analyze our sampling strategies and demonstrate significant performance enhancements over existing sampling methods.
基金funding from a Phase Ⅱ SBIR grant(Contract No.N68335-20-C-0302)for the VIPART project(PO,Dr Manivannan Venkat)to support NAVAIR.
文摘Blockchains have been around for more than ten years,and since 2015,a plethora of systems have been launched to target more flexible use cases.More recently,several enterprise blockchain systems,such as Consensys Quorum and Hyperledger Fabric,have been launched to make blockchain simpler to apply in complex organizational configurations.In this paper,we identify a specific Department of Defense use case,extrapolate requirements,and perform a thorough assessment of the different layers of the blockchain stack to identify the existing state of the art and undertake a gap analysis of the technology for this context.We describe a platform that meets many of these challenges and show how we architected,designed,and implemented a solution for this use case for deployment at NAVAIR.This solution connects transactions from two separate blockchain systems,Consensys Quorum and Hyperledger Fabric,by using a graph-based approach that preserves privacy while enabling full transparency across the military and supplier networks.
文摘Hypersonic flows about space vehicles produce flowfields in thermodynamic non-equilibrium with the local Knudsen numbers Kn which may lie in all the three regimes:continuum,transition and rarefied.Continuum flows can be modeled accurately by solving the Navier–Stokes(NS)equations;however,the flows in transition and rarefied regimes require a kinetic approach such as the direct simulation Monte Carlo(DSMC)method or the solution of the Boltzmann equation.The Boltzmann equation and the general solution approach,using the splitting method,will be introduced in this paper.Details of the method used for solving both the classical Boltzmann equation(CBE)and the generalized Boltzmann equation(GBE)are also provided.The gas mixture discussed in this paper may consist of both monoatomic and diatomic gases.In particular,the method is applied to simulate two of the three primary constituents of air(N_(2),O_(2),and Ar)in a binary mixture at 1:1 density ratio at Mach 2 and 5,with gases in translational,rotational and vibrational non-equilibrium.
