A non-Maxwellian collision kernel is employed to study the evolution of wealth distribution in a multi-agent society.The collision kernel divides agents into two different groups under certain conditions. Applying the...A non-Maxwellian collision kernel is employed to study the evolution of wealth distribution in a multi-agent society.The collision kernel divides agents into two different groups under certain conditions. Applying the kinetic theory of rarefied gases, we construct a two-group kinetic model for the evolution of wealth distribution. Under the continuous trading limit, the Fokker–Planck equation is derived and its steady-state solution is obtained. For the non-Maxwellian collision kernel, we find a suitable redistribution operator to match the taxation. Our results illustrate that taxation and redistribution have the property to change the Pareto index.展开更多
A Maxwellian electron energy distribution function （EEDF） is often assumed when using the optical emission line-ratio method to determine the electron temperature in low- temperature plasmas. However, in many cases,...A Maxwellian electron energy distribution function （EEDF） is often assumed when using the optical emission line-ratio method to determine the electron temperature in low- temperature plasmas. However, in many cases, non-Maxwellian EEDFs can be formed due to the non-local electron heating or the inelastic-collisional energy loss processes. In this work, with a collisional-radiative model, we propose an approach to obtain the non-Maxwellian EEDF with a ＇two-temperature structure＇ from the emission line-ratios of Paschen 2p levels of argon and kryp- ton atoms. For applications of this approach in reactive gas （CF4, O2, etc） discharges that contain argon and krypton, recommendations of some specific emission line-ratios are provided, according to their sensitivities to the EEDF variation. The kinetic processes of the relevant excited atoms are also discussed in detail.展开更多
In many physical situations where a laser or electron beam passes through a dense plasma,hot low-density electron populations can be generated,resulting in a particle distribution function consisting of a dense cold p...In many physical situations where a laser or electron beam passes through a dense plasma,hot low-density electron populations can be generated,resulting in a particle distribution function consisting of a dense cold population and a small hot population.Presence of such low-density electron distributions can alter the wave damping rate.A kinetic model is employed to study the Landau damping of Langmuir waves when a small hot electron population is present in the dense cold electron population with non-Maxwellian distribution functions.Departure of plasma from Maxwellian distributions significantly alters the damping rates as compared to the Maxwellian plasma.Strong damping is found for highly nonMaxwellian distributions as well as plasmas with a higher density and hot electron population.Existence of weak damping is also established when the distribution contains broadened flat tops at the low energies or tends to be Maxwellian.These results may be applied in both experimental and space physics regimes.展开更多
In this paper, a new method to derive the Fokker-Planck coefficients defined by a non-Maxwellian velocity distribution function for the field particles is presented. The three- fold integral and the new Debye cutoff p...In this paper, a new method to derive the Fokker-Planck coefficients defined by a non-Maxwellian velocity distribution function for the field particles is presented. The three- fold integral and the new Debye cutoff parameter, which were introduced by CHANG and LI, are applied. Therefore, divergence difficulties and the customary replacement of relative velocity g by thermal velocity vth are naturally avoided. The probability function P（v, Av） for non- Maxwellian scattering is derived by the method of choosing velocity transfer Av, which is a true measure of collision intensity, as an independent variable. The method enables the difference between small-angle scattering and small-momentum-transfer collisions of the inverse-square force to be well clarified. With the help of the probability function, the Fokker-Planck coefficients are obtained by a normal original Fokker-Planck approach. The friction and diffusion coefficients of the Fokker-Planck equation are modified for non-Maxwellian scattering and are used to investigate the relaxation processes for the weakly coupled plasma. The profiles of the relaxation rates show that the slowing down and deflection processes are weakened in the conditions of non-Maxwellian scattering.展开更多
In this paper, a solution to the Fokker-Planck equation is presented, which is extended to the field particles＇ high-energy-tail non-Maxwellian velocity distribution function in transport theory. Based on the correct...In this paper, a solution to the Fokker-Planck equation is presented, which is extended to the field particles＇ high-energy-tail non-Maxwellian velocity distribution function in transport theory. Based on the correct physical concept of collision intensity, introduced by CHANG and LI, the electrical conductivities for like-particles collisions are obtained in different conditions. The modified Fokker-Planck coefficients for non-Maxwellian scattering are applied in the study. It is found that the parallel part of the collision operator plays an important role. The non-Maxwellian scattering will stimulate the transport processes in various degrees with mutative deviation parameters.展开更多
Space plasmas often possess non-Maxwellian distribution functions which have a significant effect on the plasma waves. When a laser or electron beam passes through a dense plasma, hot low density electron populations ...Space plasmas often possess non-Maxwellian distribution functions which have a significant effect on the plasma waves. When a laser or electron beam passes through a dense plasma, hot low density electron populations can be generated to alter the wave damping/growth rate. In this paper, we present theoretical analysis of the nonlinear Landau damping for Langmuir waves in a plasma where two electron populations are found. The results show a marked difference between the Maxwellian and non-Maxwellian instantaneous damping rates when we employ a non-Maxwellian distribution function called the generalized （r, q） distribution function, which is the generalized form of the kappa and Maxwellian distribution functions. In the limiting case of r = 0 and q→∞, it reduces to the classical Maxwellian distribution function, and when r = 0 and q→k ＋1, it reduces to the kappa distribution function.展开更多
The collision frequencies of electron-neutral-particle in weakly ionized complex plasmas with the non-Maxwellian velocity distributions are studied.The average collision frequencies of electron-neutral-particle in pla...The collision frequencies of electron-neutral-particle in weakly ionized complex plasmas with the non-Maxwellian velocity distributions are studied.The average collision frequencies of electron-neutral-particle in plasmas are accurately derived.We find that these collision frequencies are significantly dependent on the power-law spectral indices of non-Maxwellian distribution functions and so they are generally different from the collision frequencies in plasmas with a Maxwellian velocity distribution,which will affect the transport properties of the charged particles in plasmas.Numerically analyses are made to show the roles of the spectral indices in the average collision frequencies respectively.展开更多
A sixteen moment approximation based on a bi-Maxwellian that contains the stress tensor and the heat flow vector is applied to describe the ion velocity distribution which influences the incoherent scatter spectra. A ...A sixteen moment approximation based on a bi-Maxwellian that contains the stress tensor and the heat flow vector is applied to describe the ion velocity distribution which influences the incoherent scatter spectra. A discussion is made about the effects on the incoherent scatter spectra caused by different values of the normalized perpendicular drift velocity D, aspect angle Φ between the magnetic field and the line-of-sight direction, and the ratio α of the ion-neutral collision to ion cyclotron frequency. Numerical results show that the shifting and asymmetry of incoherent scatter spectra appear parallel to E × B and E as the normalized perpendicular drift velocity D increases due to the ion drift velocity, the stress tensor and the heat flow vector respectively. However, the spectrum is always typically double-humped Maxwellian parallel to B. The ion velocity distribution is more distorted from the Maxwellian as the aspect angle Φ increases from 0° to 90°, and consequently the incoherent scatter spectra is no longer typically double-humped Maxwellian. Asαincreases, the ion velocity distribution becomes Maxwellian and the incoherent scatter spectra become typically double-humped Maxwellian even with a large value of the normalized perpendicular drift velocity D. It is reasonable to use the sixteen-moment approximation to describe the non-Maxwellian plasma characterized by the large temperature anisotropy.展开更多
The law of mass action, based on maxwellian statistics, cannot explain recent epicatalysis experiments but does when generalized to non-maxwellian statistics. Challenges to the second law are traced to statistical het...The law of mass action, based on maxwellian statistics, cannot explain recent epicatalysis experiments but does when generalized to non-maxwellian statistics. Challenges to the second law are traced to statistical heterogeneity that falls outside assumptions of homogeneity and indistinguishability made by Boltzmann, Gibbs, Tolman and Von Neumann in their H-Theorems. Epicatalysis operates outside these assumptions. Hence, H-Theorems do not apply to it and the second law is bypassed, not broken. There is no contradiction with correctly understood established physics. Other phenomena also based on heterogeneous statistics include non-maxwellian adsorption, the field-induced thermoelectric effect and the reciprocal Hall effect. Elementary particles have well known distributions such as Fermi-Dirac and Bose Einstein, but composite particles such as those involved in chemical reactions, have complex intractable statistics not necessarily maxwellian and best determined by quantum modeling methods. A step by step solution for finding the quantum thermodynamic properties of a quantum composite gas, that avoids the computational requirement of modeling a large number of composite particles includes 1) quantum molecular modeling of a few particles, 2) determining their available microstates, 3) producing their partition function, 4) generating their statistics, and 5) producing the epicatalytic parameter for the generalized law of mass action.展开更多
A Faraday isolator is shown to develop a temperature difference between its input and output, but still complies with the second law when all the heat carriers, in this case, photons are homogeneous and indistinguisha...A Faraday isolator is shown to develop a temperature difference between its input and output, but still complies with the second law when all the heat carriers, in this case, photons are homogeneous and indistinguishable. This result is a consequence of the H-theorem which assumes homogeneity and indistinguishability of particles. However, when a thermal feedback path is added, in which heat carriers have physical properties different from the photons in the isolator, then a heterogeneous system is formed not covered by the H-theorem, and the second law is violated.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11471263)the Natural Science Foundation of Xinjiang Uygur Autonomous Region,China(Grant No.2021D01B09)+1 种基金the Initial Research Foundation of Kashi University(Grant No.022024076)“Mathematics and Finance Research Centre Funding Project”,Dazhou Social Science Federation(Grant No.SCMF202305)。
文摘A non-Maxwellian collision kernel is employed to study the evolution of wealth distribution in a multi-agent society.The collision kernel divides agents into two different groups under certain conditions. Applying the kinetic theory of rarefied gases, we construct a two-group kinetic model for the evolution of wealth distribution. Under the continuous trading limit, the Fokker–Planck equation is derived and its steady-state solution is obtained. For the non-Maxwellian collision kernel, we find a suitable redistribution operator to match the taxation. Our results illustrate that taxation and redistribution have the property to change the Pareto index.
基金supported by National Natural Science Foundation of China （Nos. 11075093 and 10935006） and the China Postdoctoral Science Foundation （No. 20100480327）
文摘A Maxwellian electron energy distribution function （EEDF） is often assumed when using the optical emission line-ratio method to determine the electron temperature in low- temperature plasmas. However, in many cases, non-Maxwellian EEDFs can be formed due to the non-local electron heating or the inelastic-collisional energy loss processes. In this work, with a collisional-radiative model, we propose an approach to obtain the non-Maxwellian EEDF with a ＇two-temperature structure＇ from the emission line-ratios of Paschen 2p levels of argon and kryp- ton atoms. For applications of this approach in reactive gas （CF4, O2, etc） discharges that contain argon and krypton, recommendations of some specific emission line-ratios are provided, according to their sensitivities to the EEDF variation. The kinetic processes of the relevant excited atoms are also discussed in detail.
基金Project supported by the National Natural Science Foundation of China (Grant No. 40931054)the National Basic Research Program of China (Grant No. 2011CB811404)the Higher Education Commission of China (Grant No. 20-1886/R&D/10)
文摘In many physical situations where a laser or electron beam passes through a dense plasma,hot low-density electron populations can be generated,resulting in a particle distribution function consisting of a dense cold population and a small hot population.Presence of such low-density electron distributions can alter the wave damping rate.A kinetic model is employed to study the Landau damping of Langmuir waves when a small hot electron population is present in the dense cold electron population with non-Maxwellian distribution functions.Departure of plasma from Maxwellian distributions significantly alters the damping rates as compared to the Maxwellian plasma.Strong damping is found for highly nonMaxwellian distributions as well as plasmas with a higher density and hot electron population.Existence of weak damping is also established when the distribution contains broadened flat tops at the low energies or tends to be Maxwellian.These results may be applied in both experimental and space physics regimes.
基金National High-Tech ICF(Inertial Confinement Fusion)Committee in ChinaNational Natural Science Foundation of China(Nos.10475076,10505021,40336052,and 10175065)
文摘In this paper, a new method to derive the Fokker-Planck coefficients defined by a non-Maxwellian velocity distribution function for the field particles is presented. The three- fold integral and the new Debye cutoff parameter, which were introduced by CHANG and LI, are applied. Therefore, divergence difficulties and the customary replacement of relative velocity g by thermal velocity vth are naturally avoided. The probability function P（v, Av） for non- Maxwellian scattering is derived by the method of choosing velocity transfer Av, which is a true measure of collision intensity, as an independent variable. The method enables the difference between small-angle scattering and small-momentum-transfer collisions of the inverse-square force to be well clarified. With the help of the probability function, the Fokker-Planck coefficients are obtained by a normal original Fokker-Planck approach. The friction and diffusion coefficients of the Fokker-Planck equation are modified for non-Maxwellian scattering and are used to investigate the relaxation processes for the weakly coupled plasma. The profiles of the relaxation rates show that the slowing down and deflection processes are weakened in the conditions of non-Maxwellian scattering.
基金supported by National High-Tech ICF Committee in ChinaNational Natural Science Foundation of China(Nos.10475076,10505021,40336052,and 10175065)
文摘In this paper, a solution to the Fokker-Planck equation is presented, which is extended to the field particles＇ high-energy-tail non-Maxwellian velocity distribution function in transport theory. Based on the correct physical concept of collision intensity, introduced by CHANG and LI, the electrical conductivities for like-particles collisions are obtained in different conditions. The modified Fokker-Planck coefficients for non-Maxwellian scattering are applied in the study. It is found that the parallel part of the collision operator plays an important role. The non-Maxwellian scattering will stimulate the transport processes in various degrees with mutative deviation parameters.
基金Project supported by the Pakistan Science Foundation Project No.PSF/Res/P-GCU/Phys.(143)the National Natural Science Foundation of China(Grant Nos.41074114 and 41274146)the Specialized Research Fund for State Key Laboratories of China
文摘Space plasmas often possess non-Maxwellian distribution functions which have a significant effect on the plasma waves. When a laser or electron beam passes through a dense plasma, hot low density electron populations can be generated to alter the wave damping/growth rate. In this paper, we present theoretical analysis of the nonlinear Landau damping for Langmuir waves in a plasma where two electron populations are found. The results show a marked difference between the Maxwellian and non-Maxwellian instantaneous damping rates when we employ a non-Maxwellian distribution function called the generalized （r, q） distribution function, which is the generalized form of the kappa and Maxwellian distribution functions. In the limiting case of r = 0 and q→∞, it reduces to the classical Maxwellian distribution function, and when r = 0 and q→k ＋1, it reduces to the kappa distribution function.
基金supported by the National Natural science foundation of China under Grant No.11775156.
文摘The collision frequencies of electron-neutral-particle in weakly ionized complex plasmas with the non-Maxwellian velocity distributions are studied.The average collision frequencies of electron-neutral-particle in plasmas are accurately derived.We find that these collision frequencies are significantly dependent on the power-law spectral indices of non-Maxwellian distribution functions and so they are generally different from the collision frequencies in plasmas with a Maxwellian velocity distribution,which will affect the transport properties of the charged particles in plasmas.Numerically analyses are made to show the roles of the spectral indices in the average collision frequencies respectively.
基金supported by the Foundation of National Key Laboratory of Electromagnetic EnvironmentNational Natural Science Foundation of China (No. 40310223)
文摘A sixteen moment approximation based on a bi-Maxwellian that contains the stress tensor and the heat flow vector is applied to describe the ion velocity distribution which influences the incoherent scatter spectra. A discussion is made about the effects on the incoherent scatter spectra caused by different values of the normalized perpendicular drift velocity D, aspect angle Φ between the magnetic field and the line-of-sight direction, and the ratio α of the ion-neutral collision to ion cyclotron frequency. Numerical results show that the shifting and asymmetry of incoherent scatter spectra appear parallel to E × B and E as the normalized perpendicular drift velocity D increases due to the ion drift velocity, the stress tensor and the heat flow vector respectively. However, the spectrum is always typically double-humped Maxwellian parallel to B. The ion velocity distribution is more distorted from the Maxwellian as the aspect angle Φ increases from 0° to 90°, and consequently the incoherent scatter spectra is no longer typically double-humped Maxwellian. Asαincreases, the ion velocity distribution becomes Maxwellian and the incoherent scatter spectra become typically double-humped Maxwellian even with a large value of the normalized perpendicular drift velocity D. It is reasonable to use the sixteen-moment approximation to describe the non-Maxwellian plasma characterized by the large temperature anisotropy.
文摘The law of mass action, based on maxwellian statistics, cannot explain recent epicatalysis experiments but does when generalized to non-maxwellian statistics. Challenges to the second law are traced to statistical heterogeneity that falls outside assumptions of homogeneity and indistinguishability made by Boltzmann, Gibbs, Tolman and Von Neumann in their H-Theorems. Epicatalysis operates outside these assumptions. Hence, H-Theorems do not apply to it and the second law is bypassed, not broken. There is no contradiction with correctly understood established physics. Other phenomena also based on heterogeneous statistics include non-maxwellian adsorption, the field-induced thermoelectric effect and the reciprocal Hall effect. Elementary particles have well known distributions such as Fermi-Dirac and Bose Einstein, but composite particles such as those involved in chemical reactions, have complex intractable statistics not necessarily maxwellian and best determined by quantum modeling methods. A step by step solution for finding the quantum thermodynamic properties of a quantum composite gas, that avoids the computational requirement of modeling a large number of composite particles includes 1) quantum molecular modeling of a few particles, 2) determining their available microstates, 3) producing their partition function, 4) generating their statistics, and 5) producing the epicatalytic parameter for the generalized law of mass action.
文摘A Faraday isolator is shown to develop a temperature difference between its input and output, but still complies with the second law when all the heat carriers, in this case, photons are homogeneous and indistinguishable. This result is a consequence of the H-theorem which assumes homogeneity and indistinguishability of particles. However, when a thermal feedback path is added, in which heat carriers have physical properties different from the photons in the isolator, then a heterogeneous system is formed not covered by the H-theorem, and the second law is violated.
