Kinetic Theory Approach Research Articles

Multicomponent fluid model for two-temperature plasmas derived from kinetic theory : application to magnetic reconnection

This contribution deals with the fluid modeling of multicomponent magnetized plasmas in thermo-chemical non-equilibrium from the partially- to fully-ionized collisional regimes, aiming at the predictive simulation of magnetic reconnection in Sun chromosphere conditions. Such fluid models are required for large-scale simulations by relying on high performance computing. The fluid model is derived from a kinetic theory approach, yielding a rigorous description of the dissipative and non-equilibrium effects and a well-identified mathematical structure. We start from a general system of equations that is obtained by means of a multiscale Chapman-Enskog method, based on a non-dimensional analysis accounting for the mass disparity between the electrons and heavy particles, including the influence of the electromagnetic field and transport properties. The latter are computed by using a spectral Galerkin method based on a converged Laguerre-Sonine polynomial approximation. Then, in the limit of small Debye length with respect to the characteristic scale in the Sun chromosphere, we derive a two-temperature single-momentum multicomponent diffusion model coupled to Maxwell’s equations, which is able to describe fully- and partially-ionized plasmas, beyond the multi-fluid model of Braginskii, valid for the whole range of the Sun chromosphere conditions. The second contribution is the development and verification of an accurate and robust numerical strategy that is based on CanoP, a massively parallel code with adaptive mesh refinement capability, which is able to cope with the full spectrum of scales of the magnetic reconnection process, without additional constraint on the time steps compared to single-fluid Magnetohydrodynamics (MHD) models. The final contribution is a study of the physics of magnetic reconnection in collaboration with the heliophysics team of NASA Ames Research Center. We show that the model and methods allow us to retrieve the results of usual single-fluid MHD models in the highly collisional case at equilibrium, while achieving a more detailed physics description relevant to such applications in the weakly collisional case, where non-equilibrium effects become important.

Phonon-electron coupling and nonlocal heat transport in Bi2Te3 nanowires

A hydrodynamical model of heat transfer with phonons and electrons is applied to infer the steady-state temperature profile in a Bi2Te3 nanowire. Our analysis is concerned with systems which allow for different temperatures of phonons and electrons. Along with the approach of kinetic theory, the phonons and the electrons are regarded as a gas-like mixture flowing through the crystal lattice. The coupling between phonons and electrons is taken into account by an additional term in the partial balances of energy of the components of the mixture. The compatibility of the model with the second law of thermodynamics is investigated in view of the requirement of positive entropy production, and of a nonlocal constitutive equation for the entropy flux.

Effective two-dimensional model for granular matter with phase separation.

Granular systems confined in vertically vibrated shallow horizontal boxes (quasi-two-dimensional geometry) present a liquid-to-solid phase transition when the frequency of the periodic forcing is increased. An effective model, where grains move and collide in two-dimensions is presented, which reproduces the aforementioned phase transition. The key element is that besides the two-dimensional degrees of freedom, each grain has an additional variable ɛ that accounts for the kinetic energy stored in the vertical motion in the real quasi-two-dimensional motion. This energy grows monotonically during free flight, mimicking the energy gained by collisions with the vibrating walls and, at collisions, this energy is instantaneously transferred to the horizontal degrees of freedom. As a result, the average values of ɛ and the kinetic temperature are decreasing functions of the local density, giving rise to an effective pressure that can present van der Waals loops. A kinetic theory approach predicts the conditions that must satisfy the energy growth function to obtain the phase separation, which are verified with molecular dynamics simulations. Notably, the effective equation of state and the critical points computed considering the velocity-time-of-flight correlations differ only slightly from those obtained by simple kinetic theory calculations that neglect those correlations.

On the streaming model for redshift-space distortions

The streaming model describes the mapping between real and redshift space for 2-point clustering statistics. Its key element is the probability density function (PDF) of line-of-sight pairwise peculiar velocities. Following a kinetic-theory approach, we derive the fundamental equations of the streaming model for ordered and unordered pairs. In the first case, we recover the classic equation while we demonstrate that modifications are necessary for unordered pairs. We then discuss several statistical properties of the pairwise velocities for DM particles and haloes by using a suite of high-resolution $N$-body simulations. We test the often used Gaussian ansatz for the PDF of pairwise velocities and discuss its limitations. Finally, we introduce a mixture of Gaussians which is known in statistics as the generalised hyperbolic distribution and show that it provides an accurate fit to the PDF. Once inserted in the streaming equation, the fit yields an excellent description of redshift-space correlations at all scales that vastly outperforms the Gaussian and exponential approximations. Using a principal-component analysis, we reduce the complexity of our model for large redshift-space separations. Our results increase the robustness of studies of anisotropic galaxy clustering and are useful for extending them towards smaller scales in order to test theories of gravity and interacting dark-energy models.

Mean-field kinetic theory approach to evaporation of a binary liquid into vacuum

Evaporation of a binary liquid into near vacuum conditions has been studied using numerical solutions of a system of two coupled Enskog-Vlasov equations. Liquidvapor coexistence curves have been mapped out for different liquid compositions. The evaporation process has been investigated at a range of liquid temperatures sufficiently lower than the critical one for the vapor not to significantly deviate from the ideal behaviour. It is found that the shape of the distribution functions of evaporating atoms is well approximated by an anisotropic Maxwellian distribution with different characteristic temperatures for velocity components normal and parallel to the liquid-vapor interface. The anisotropy reduces as the evaporation temperature decreases. Evaporation coefficients are computed based on the separation temperature and the maximum concentration of the less volatile component close to the liquid-vapor interface. This choice leads to values which are almost constant in the simulation conditions.

Kinetic theory for strongly coupled Coulomb systems.

The calculation of dynamical properties for matter under extreme conditions is a challenging task. The popular Kubo-Greenwood model exploits elements from equilibrium density-functional theory (DFT) that allow a detailed treatment of electron correlations, but its origin is largely phenomenological; traditional kinetic theories have a more secure foundation but are limited to weak ion-electron interactions. The objective here is to show how a combination of the two evolves naturally from the short-time limit for the generator of the effective single-electron dynamics governing time correlation functions without such limitations. This provides a theoretical context for the current DFT-related approach, the Kubo-Greenwood model, while showing the nature of its corrections. The method is to calculate the short-time dynamics in the single-electron subspace for a given configuration of the ions. This differs from the usual kinetic theory approach in which an average over the ions is performed as well. In this way the effective ion-electron interaction includes strong Coulomb coupling and is shown to be determined from DFT. The correlation functions have the form of the random-phase approximation for an inhomogeneous system but with renormalized ion-electron and electron-electron potentials. The dynamic structure function, density response function, and electrical conductivity are calculated as examples. The static local field corrections in the dielectric function are identified in this way. The current analysis is limited to semiclassical electrons (quantum statistical potentials), so important quantum conditions are excluded. However, a quantization of the kinetic theory is identified for broader application while awaiting its detailed derivation.

An advanced kinetic theory for morphing continuum with inner structures

Advanced kinetic theory with the Boltzmann-Curtiss equation provides a promising tool for polyatomic gas flows, especially for fluid flows containing inner structures, such as turbulence, polyatomic gas flows and others. Although a Hamiltonian-based distribution function was proposed for diatomic gas flow, a general distribution function for the generalized Boltzmann-Curtiss equations and polyatomic gas flow is still out of reach. With assistance from Boltzmann's entropy principle, a generalized Boltzmann-Curtiss distribution for polyatomic gas flow is introduced. The corresponding governing equations at equilibrium state are derived and compared with Eringen's morphing (micropolar) continuum theory derived under the framework of rational continuum thermomechanics. Although rational continuum thermomechanics has the advantages of mathematical rigor and simplicity, the presented statistical kinetic theory approach provides a clear physical picture for what the governing equations represent.

Twisted modes instability of electron–positron shell interacted with moving ion background

AbstractIn this paper, the instability of electrostatic twisted modes carrying orbital angular momentum in the moving electron–positron–ion plasma is investigated. In the kinetic theory approach, the general dispersion relation of twisted modes is derived by using Laguerre–Gaussian perturbed distribution function and electrostatic potential in the paraxial limit. Utilizing the obtained general dispersion relation for a specific case of electron–positron (e–p) shell with temperature anisotropy interacted with moving ion background, the effects of angular mode number, electrons and positrons temperature, and positron concentration on the group velocity and instability growth rate of twisted waves are illustrated, numerically. The results of the present investigation will greatly attribute to the understanding of e–p jet dynamic in astrophysical environments and laboratory experiments where the twisted modes can play a central role as a perturbed term.

Impact of grain boundary characteristics on lattice thermal conductivity: A kinetic theory study on ZnO

Grain boundaries are natural interfaces present in polycrystalline materials and have an important role in transport properties. In this work, the impact of grain boundary crystallographic mismatch, local impurity modulation, and spacing on lattice thermal conductivity is examined from the kinetic theory approach, with ZnO as a case study. We employ a dislocation-based model to describe the grain boundary scatterings of phonons, in which structural characteristics of grain boundaries are explicitly built-in and grain boundary scattering time depends on phonon frequency. This is in contrast to the gray model or the commonly used Casimir limit, which is blind to both grain boundary features and phonon frequency. We show that the lattice thermal conductivity generally decreases with grain boundary misorientation angle, and this dependence is significant for small grain boundary spacing while it tends to diminish for a large one. Intriguingly, our results show that local grain boundary chemistry can affect even more substantially than the crystallographic misfit on phonon relaxation time and interfacial thermal (Kapitza) resistance. Our results suggest new opportunities in tuning lattice thermal conductivity besides the nanostructure engineering approach, and demonstrates the synergetic effects of grain boundary characteristics on phonon conduction in polycrystals.

Hilbert method toward a multiscale analysis from kinetic to macroscopic models for active particles

This paper develops a Hilbert type method to derive models at the macroscopic scale for large systems of several interacting living entities whose statistical dynamics at the microscopic scale is delivered by kinetic theory methods. The presentation is in three steps, where the first one presents the structures of the kinetic theory approach used toward the aforementioned analysis; the second step presents the mathematical method; while the third step provides a number of specific applications. The approach is focused on a simple system and with a binary mixture, where different time-space scalings are used. Namely, parabolic, hyperbolic, and mixed in the case of a mixture.

Density-functional calculations of transport properties in the nondegenerate limit and the role of electron-electron scattering.

We compute electrical and thermal conductivities of hydrogen plasmas in the nondegenerate regime using Kohn-Sham density functional theory (DFT) and an application of the Kubo-Greenwood response formula, and demonstrate that for thermal conductivity, the mean-field treatment of the electron-electron (e-e) interaction therein is insufficient to reproduce the weak-coupling limit obtained by plasma kinetic theories. An explicit e-e scattering correction to the DFT is posited by appealing to Matthiessen's Rule and the results of our computations of conductivities with the quantum Lenard-Balescu (QLB) equation. Further motivation of our correction is provided by an argument arising from the Zubarev quantum kinetic theory approach. Significant emphasis is placed on our efforts to produce properly converged results for plasma transport using Kohn-Sham DFT, so that an accurate assessment of the importance and efficacy of our e-e scattering corrections to the thermal conductivity can be made.

Gradient expansion for anisotropic hydrodynamics

We compute the gradient expansion for anisotropic hydrodynamics. The results are compared with the corresponding expansion of the underlying kinetic-theory model with the collision term treated in the relaxation time approximation. We find that a recent formulation of anisotropic hydrodynamics based on an anisotropic matching principle yields the first three terms of the gradient expansion in agreement with those obtained for the kinetic theory. This gives further support for this particular hydrodynamic model as a good approximation of the kinetic-theory approach. We further find that the gradient expansion of anisotropic hydrodynamics is an asymptotic series, and the singularities of the analytic continuation of its Borel transform indicate the presence of non-hydrodynamic modes.

In-medium viscous coefficients of a hot hadronic gas mixture

We estimate the shear and the bulk viscous coefficients for a hot hadronic gas mixture constituting of pions and nucleons. The viscosities are evaluated in the relativistic kinetic theory approach by solving the transport equation in the relaxation time approximation for binary collisions ($\pi\pi$,$\pi N$ and $NN$). Instead of vacuum cross-sections usually used in the literature we employ in-medium scattering amplitudes in the estimation of the relaxation times. The modified cross-sections for $\pi\pi$ and $\pi N$ scattering are obtained using one-loop modified thermal propagators for $\rho$, $\sigma$ and $\Delta$ in the scattering amplitudes which are calculated using effective interactions. The resulting suppression of the cross sections at finite temperature and baryon density is observed to significantly affect the $T$ and $\mu_N$ dependence of the viscosities of the system.

Polymer Fluid Dynamics: Continuum and Molecular Approaches.

To solve problems in polymer fluid dynamics, one needs the equations of continuity, motion, and energy. The last two equations contain the stress tensor and the heat-flux vector for the material. There are two ways to formulate the stress tensor: (a) One can write a continuum expression for the stress tensor in terms of kinematic tensors, or (b) one can select a molecular model that represents the polymer molecule and then develop an expression for the stress tensor from kinetic theory. The advantage of the kinetic theory approach is that one gets information about the relation between the molecular structure of the polymers and the rheological properties. We restrict the discussion primarily to the simplest stress tensor expressions or constitutive equations containing from two to four adjustable parameters, although we do indicate how these formulations may be extended to give more complicated expressions. We also explore how these simplest expressions are recovered as special cases of a more general framework, the Oldroyd 8-constant model. Studying the simplest models allows us to discover which types of empiricisms or molecular models seem to be worth investigating further. We also explore equivalences between continuum and molecular approaches. We restrict the discussion to several types of simple flows, such as shearing flows and extensional flows, which are of greatest importance in industrial operations. Furthermore, if these simple flows cannot be well described by continuum or molecular models, then it is not necessary to lavish time and energy to apply them to more complex flow problems.

Numerical analysis of electrostatic ion cyclotron instability in an electron-positron-ion plasma

This paper presents a theoretical study of the effects of positron density on the electrostatic ion cyclotron instability in an electron-positron-ion plasma using the kinetic theory approach. It is supposed that positrons and electrons can drift parallel to the magnetic field either in the same or the opposite directions. The dispersion relation for the electrostatic ion cyclotron waves in an electron-positron-ion plasma is derived, and the numerical results are investigated. It is found that an increase in positron concentration increases the critical drift velocity for excitation of the instability in both configurations. It is also found that as the positron concentration increases the growth rate of instability decreases. In addition, it is shown that at low velocities the maximum instability growth rate for the unidirectional case is higher than the counter-streaming case; however, after a certain velocity, the maximum growth rate in the counter-streaming case dominates that of the unidirectional case.

Calculation of the thermal conductivity of low-density CH4-N2 gas mixtures using an improved kinetic theory approach.

The thermal conductivity of low-density CH4-N2 gas mixtures has been calculated by means of the classical trajectory method using state-of-the-art intermolecular potential energy surfaces for the CH4-CH4, N2-N2, and CH4-N2 interactions. Results are reported in the temperature range from 70 K to 1200 K. Since the thermal conductivity is influenced by the vibrational degrees of freedom of the molecules, which are not included in the rigid-rotor classical trajectory computations, a new correction scheme to account for vibrational degrees of freedom in a dilute gas mixture is presented. The calculations show that the vibrational contribution at the highest temperature studied amounts to 46% of the total thermal conductivity of an equimolar mixture compared to 13% for pure nitrogen and 58% for pure methane. The agreement with the available experimental thermal conductivity data at room temperature is good, within ±1.4%, whereas at higher temperatures, larger deviations up to 4.5% are observed, which can be tentatively attributed to deteriorating performance of the measuring technique employed. Results are also reported for the magnitude and temperature dependence of the rotational collision number, Z(rot), for CH4 relaxing in collisions with N2 and for N2 relaxing in collisions with CH4. Both collision numbers increase with temperature, with the former being consistently about twice the value of the latter.

KAOS: A Kinetic Theory Tool for Modeling Complex Social Systems

The kinetic theory approach is successfully used to model complex phenomena related to social systems, allowing to predict the dynamics and emergent behavior of large populations of agents. In particular, kinetic theory for active particles (KTAP) models are usually analyzed by numerically solving the underlying Boltzmann-type differential equations through ad-hoc implementations. In this paper, we present KAOS: a kinetic theory of active particles modeling and analysis software tool. To the best of our knowledge, KAOS represents the first attempt to design and implement a comprehensive tool that assists the user in all the steps of the modeling process in the framework of the kinetic theories, from the model definition to the representation of transient solutions. To show the KAOS features, we present a new model capturing the competition/cooperation dynamics of a socio-economic system with welfare dynamics, in different socio-political conditions

Schwinger effect at modern laser facilities

The theoretical and experimental investigation of physical processes in strong fields of different nature (electromagnetic, gravitational, etc.) is one of the important directions of modern physics. Particular interest is devoted to the area of extremely strong fields, in which qualitatively new effects become important due to the restructuring of the physical vacuum which accompanies the creation of matter from the vacuum at modern laser facilities. Such kind of time-dependent strong field vacuum effects can be appropriately described within a kinetic theory approach as an effective instrument of theoretical investigations. A short review of recent achievements in the direction of the dynamical Schwinger effect is given in this contribution.

Non-equilibrium kinetics, diffusion and heat transfer in shock heated flows of N2/N and O2/O mixtures

In this paper, the influence of vibrational and dissociation kinetics on heat transfer and diffusion in non-equilibrium flows of N2/N and O2/O mixtures in the relaxation zone behind shock waves is studied on the basis of the state-to-state and one-temperature kinetic theory approaches. The results of calculations of vibrational level populations ni, gas temperature T, total energy flux q, diffusion velocities of molecules at different vibrational states Vi and atoms Va in the relaxation zone behind a shock front are presented for the free stream Mach numbers M=18, 15, 10. The contribution of different dissipative processes to the total energy flux is evaluated for various flow conditions. Characteristic features of non-equilibrium kinetics, diffusion and energy transfer in two considered mixtures are discussed. The impact of vibrational excitation of N2 and O2 molecules in the free stream on a relaxation zone structure and transport properties behind a shock is shown.

Bubble expansion and the viability of singlet-driven electroweak baryogenesis

The standard picture of electroweak baryogenesis requires slowly expanding bubbles. This can be difficult to achieve if the vacuum expectation value of a gauge singlet scalar field changes appreciably during the electroweak phase transition. It is important to determine the bubble wall velocity in this case, since the predicted baryon asymmetry can depend sensitively on its value. Here, this calculation is discussed and illustrated in the real singlet extension of the Standard Model. The friction on the bubble wall is computed using a kinetic theory approach and including hydrodynamic effects. Wall velocities are found to be rather large ($v_w \gtrsim 0.2$) but compatible with electroweak baryogenesis in some portions of the parameter space. If the phase transition is strong enough, however, a subsonic solution may not exist, precluding non-local electroweak baryogenesis altogether. The results presented here can be used in calculating the baryon asymmetry in various singlet-driven scenarios, as well as other features related to cosmological phase transitions in the early Universe, such as the resulting spectrum of gravitational radiation.