Kinetic Theory Approach Research Articles

Dissipative properties of hot and dense hadronic matter in an excluded-volume hadron resonance gas model

We estimate dissipative properties viz: shear and bulk viscosities of hadronic matter using relativistic Boltzmann equation in relaxation time approximation within ambit of excluded volume hadron resonance gas (EHRG) model. We find that at zero baryon chemical potential the shear viscosity to entropy ratio ($\eta/s$) decreases with temperature while at finite baryon chemical potential this ratio shows same behavior as a function of temperature but reaches close to Kovtun-Son-Starinets (KSS) bound. Further along chemical freezout curve, ratio $\eta/s$ is almost constant apart from small initial monotonic rise. This observation may have some relevance to the experimental finding that the differential elliptic flow of charged hadrons does not change considerably at lower center of mass energy. We further find that bulk viscosity to entropy density ($\zeta/s$) decreases with temperature while this ratio has higher value at finite baryon chemical potential at higher temperature. Along freezout curve $\zeta/s$ decreases monotonically at lower center of mass energy and then saturates.

Kinetic theory of dust ion acoustic waves in a kappa-distributed plasma

Using a kinetic theory approach, dust ion acoustic (DIA) waves are investigated in an unmagnetized collisionless plasma with kappa-distributed electrons and ions, and Maxwellian dust grains of constant charge. Both analytical and numerical results, the latter following from the full solution of the associated dispersion relation, are presented, and a comparison is made. The effects of the ion and electron spectral indices, as well as the species' density (ne/ni) and temperature (Te/Ti) ratios, on the dispersion and damping of the waves are considered. In the long wavelength regime, increases in both the electron spectral index (κe) and the dust density fraction (reduced f=ne/ni) lead to an increase in phase velocity. The range in wavelength over which modes are weakly damped increases with an increase in Te/Ti. However, the ion spectral index, κi, does not have a significant effect on the dispersion or damping of DIA waves.

Medium effects on the transport coefficients of a hot pion gas

The study of transport properties of strongly interacting matter has captured much attention in recent times. The interpretation of experimentally measured elliptic flow of hadrons in RHIC, by nearly ideal hydrodynamics with a small value of η/s, close to the quantum bound 1/4π, provides much interest towards the transport coefficients, which characterize the response of an out of equilibrium system to certain disturbances. Our aim is to determine the shear and bulk viscous coefficients and as well as the thermal conductivity for an interacting pion gas by solving relativistic transport equation in kinetic theory approach. For the dynamical input we need to construct a medium dependent ππ cross-section which gives noticeable effects on the temperature of viscous coefficients and thermal conductivity.

Parameters identification in the mathematical model of immune competition cells

Abstract This paper deals with the problem of identifying parameters in the mathematical model of immune competition developed in [Modelling Complex Biological Systems: A Kinetic Theory Approach, Birkhäuser, Boston, 2006]. More precisely, we use the approach called inverse problem to identify the parameters of the model, and we investigate the identifiability as well as the stability of the inverse problem. In numerical analysis, the inverse problem is reformulated as an optimization problem where the variables are the estimated parameters in the model. In our study, the regularized least-squares cost function and the adjoint technique to compute the gradient of the cost function are used. Finally, some numerical tests for parameters identification using synthetic data are presented.

A fully-discrete-state kinetic theory approach to traffic flow on road networks

This paper presents a new approach to the modeling of vehicular traffic flows on road networks based on kinetic equations. While in the literature the problem has been extensively studied by means of macroscopic hydrodynamic models, to date there are still not, to the authors' knowledge, contributions tackling it from a genuine statistical mechanics point of view. Probably one of the reasons is the higher technical complexity of kinetic traffic models, further increased in case of several interconnected roads. Here such difficulties of the theory are overcome by taking advantage of a discrete structure of the space of microscopic states of the vehicles, which is also significant in view of including the intrinsic microscopic granularity of the system in the mesoscopic representation.

Thermal stress analysis and entropy generation rate due to laser short pulse heating of a metallic surface

An analytical solution is developed for thermal stress in exponentially time decaying laser short-pulse heating of a metallic surface. Because the heating duration is short, a nonequilibrium heating model incorporating the electron kinetic theory approach is used to formulate the temperature distribution during the laser heating pulse. Thermomechanical coupling is introduced in the analysis to formulate the thermal stress field. Thermodynamic irreversibility is considered and the entropy generation rate due to heat transfer and thermal stress field is formulated during the heating process. It is found that temperature decays gradually in the surface region and becomes sharp as the distance increases towards the solid bulk. Thermal stress is compressive in the irradiated region. Thermodynamic irreversibility due to heat transfer dominates thermodynamic irreversibility because of the thermal stress field.

A kinetic theory approach to the dynamics of crowd evacuation from bounded domains

A mathematical model of the evacuation of a crowd from bounded domains is derived by a hybrid approach with kinetic and macro-features. Interactions at the micro-scale, which modify the velocity direction, are modeled by using tools of game theory and are transferred to the dynamics of collective behaviors. The velocity modulus is assumed to depend on the local density. The modeling approach considers dynamics caused by interactions of pedestrians not only with all the other pedestrians, but also with the geometry of the domain, such as walls and exits. Interactions with the boundary of the domain are non-local and described by games. Numerical simulations are developed to study evacuation time depending on the size of the exit zone, on the initial distribution of the crowd and on a parameter which weighs the unconscious attraction of the stream and the search for less crowded walking directions.

An improved kinetic theory approach for calculating the thermal conductivity of polyatomic gases

A new kinetic theory approach for calculating the thermal conductivity of a dilute polyatomic gas from the intermolecular pair potential is presented. The contributions due to internal degrees of freedom have been separated into a classical rotational and a quantum-mechanical vibrational part. Assuming that the vibrational states of the molecules do not significantly influence the collision trajectories, and that vibrationally inelastic and vibrationally resonant collisions are rare, we have obtained a simple self-diffusion mechanism for the vibrational contribution to the thermal conductivity. For non-polar gases like methane or nitrogen, the new approach yields thermal conductivity values that are very close to those obtained with the previously used kinetic theory approach. However, for polar gases like hydrogen sulphide and water vapour, the values obtained with the new scheme are much closer to the most accurate experimental data.

Universal short-time response and formation of correlations after quantum quenches

The short-time evolutions of two distinct systems, the pump and probe experiments with a semiconductor and the sudden quench of cold atoms in an optical lattice, are found to be described by the same universal response function. This analytic formula at short time scales is derived from the quantum kinetic-theory approach observing that correlations need time to form. The demand of density conservation leads to a reduction of the relaxation time by a factor of 4 in quench setups. The influence of the finite-trapping potential is derived and discussed along with Singwi-Sj\o{}lander local-field corrections including the proof of sum rules.

On the derivation of angiogenesis tissue models: From the micro-scale to the macro-scale

This paper deals with the derivation of mathematical models at the macroscale of biological tissues corresponding to angiogenesis phenomena. The derivation is obtained by mathematical description delivered at the microscale of cells using a kinetic theory approach. A classical Chapman–Enskog expansion properly truncated is used to obtain the desired result. It is shown that the approach is general enough to describe a broad variety of different angiogenesis models corresponding to well-defined assumptions on interactions at the cellular scale.

A Combined Multifluid-Population Balance Model Applied to Dispersed Gas–Liquid Flows

The two-phase bubble columns are widely used for carrying out gas–liquid reactions in a variety of industrial applications. The optimal operation of many of the processes carried out in the bubble columns depends on the bubble size distribution, which determines the interfacial momentum, mass, and heat transfer fluxes through the contact area between the liquid and gas phases. In this context, the population balance equation is relevant as it can be used to quantify the amount of bubbles of different sizes present at different locations in the bubble column. The combined multifluid-population balance models use mass and momentum equations coupled with population balances for the dispersed phase, whereas the continuum mechanical equations of the two-fluid or multifluid models are used for the liquid phase. The most rigorous description is based on a kinetic theory approach with size resolution (KTAWSR). In this study, the KTAWSR model is applied to simulate bubbly flows under complex conditions, that is, significant change in the Sauter mean diameter along the axial direction of the bubble column. The model is solved using the spectral orthogonal collocation method. Both sensitivity analyzes and comparison to experimental data from the literature are used to assess the potential of the model. Fair agreement between the experimental data and model prediction is achieved. It is concluded that the model adds as a valuable tool with good potentials for the population balance community, considering both the level of details resolved with this model and its possible use in developing future breakage and coalescence models.

Bubble Coalescence Modeling in the Population Balance Framework

In the churn-turbulent bubbly flow regime with highly nonuniform bubble size distributions, bubble breakage and coalescence are important processes because they govern the bubble size distribution and consequently directly affect the interfacial mass, momentum, and heat transfer fluxes through the renewal bubble surfaces. At present, accurate prediction of bubble size distributions of dispersed gas–liquid flows by use of the population balance (PB) equation is a difficult task. The modeling of bubble breakup and coalescence rates is very complex and is based on the knowledge of collision and breakup frequencies, breakage daughter size distributions, and probability of coalescence. In this work, we focus on the coalescence phenomenon. The coalescence models are still on an empirical level and the mechanisms are not fully understood. This motivates the analysis of the suitability of the coalescence closures for the prediction of experimental data obtained from coalescence dominated gas–liquid flows. For this task, a cross-sectional averaged combined multifluid-PB model is adopted. Based on different theories for the coalescence efficiency, the simulation results show a similar trend in the prediction of the experimental data. Good prediction of the Sauter mean diameter is achieved although the shape of the bubble size distribution is not completely reproduced. The second aim of this work is to review the PB framework. Here, focus is placed on the coalescence term and the combined multifluid-PB model based on kinetic theory approach.

Transport coefficients of Quark-Gluon Plasma in a Kinetic Theory approach

One of the main results of heavy ions collision at relativistic energy experiments is the very small shear viscosity to entropy density ratio of the Quark-Gluon Plasma, close to the conjectured lower bound η/s = 1/4π for systems in the infinite coupling limit. Transport coefficients like shear viscosity are responsible of non-equilibrium properties of a system: Green- Kubo relations give us an exact expression to compute these coefficients. We computed shear viscosity numerically using Green-Kubo relation in the framework of Kinetic Theory solving the relativistic transport Boltzmann equation in a finite box with periodic boundary conditions. We investigated different cases of particles, for one component system (gluon matter), interacting via isotropic or anisotropic cross-section in the range of temperature of interest for HIC. Green-Kubo results are in agreement with Chapman-Enskog approximation while Relaxation Time approximation can underestimates the viscosity of a factor 2. Another transport coefficient of interest is the electric conductivity σel which determines the response of QGP to the electromagnetic fields present in the early stage of the collision. We study the σel dependence on microscopic details of interaction and we find also in this case that Relaxation Time Approximation is a good approximation only for isotropic cross-section.

Flow of granular materials with slip boundary condition: A continuum–kinetic theory approach

We study the steady fully developed flow of granular materials between two horizontal flat plates, subject to slip at the walls. The constitutive model for the stress tensor is based on ideas in continuum mechanics and kinetic theory. The constitutive equation used in our study is a model proposed by Rajagopal et al. (1994) [24], and the material properties such as viscosity and the normal stress coefficients are derived using the kinetic theory approximation proposed by Boyle and Massoudi (1990) [2] which includes the effect of the gradient of volume fraction. The slip boundary condition is based on the particle dynamics simulation results of Rosato and Kim (1994) [30]. The governing equations are non-dimensionalized, and the resulting system of non-linear differential equations is solved numerically. The results for the velocity profiles and the volume fraction profiles are presented.

Shear viscosity of the normal phase of a unitary Fermi gas from theɛexpansion

Using the $\ensuremath{\varepsilon}$-expansion technique, we compute $\ensuremath{\eta}/s$, where $\ensuremath{\eta}$ is the shear viscosity and $s$ is the entropy density of the normal phase of unitary Fermi gas in $d=4\ensuremath{-}\ensuremath{\varepsilon}$ dimensions to leading order (LO) in $\ensuremath{\varepsilon}$. We use the kinetic theory approach and solve transport equations for a medium perturbed by a shear hydrodynamic flow. The collision integrals are calculated to ${\ensuremath{\varepsilon}}^{2}$, which is LO. The LO result is temperature independent with $\ensuremath{\eta}/s\ensuremath{\simeq}(0.11/{\ensuremath{\varepsilon}}^{2})(\ensuremath{\hbar}/{k}_{B})$. The $d=3$ prediction for $\ensuremath{\eta}/s$ exceeds the $\ensuremath{\hbar}/4\ensuremath{\pi}{k}_{B}$ bound by a factor of about $1.4$.

Anisotropic Flow from Non-equilibrium Initial Condition with a Saturation Scale

A current goal of relativistic heavy ion collisions experiments is to understand the impact of initial non-equilibrium on final observables. A Color Glass Condensate (CGC) as the limiting state of QCD matter at very high density implies initial non-thermal distribution at least for momenta below the saturation scale. In viscous hydrodynamics simulations, a standard Glauber initial condition leads to estimate 4= s 1, while em- ploying the Kharzeev-Levin-Nardi (KLN) modeling of the CGC leads to at least a factor of 2 larger = s. Within a kinetic theory approach based on a relativistic Boltzmann-like transport simulation, our main result is that the out-of-equilibrium initial distribution in p-space reduces the e ciency in building-up the elliptic flow. At RHIC energy we find the available data onv2 are in agreement with a 4= s 1 also for KLN initial conditions.

On the multiscale modeling of vehicular traffic: From kinetic to hydrodynamics

This paper deals with the multiscale modeling of vehicular traffic according to a kinetictheory approach, where the microscopic state of vehicles is described by position, velocityand activity, namely a variable suitable to model the quality of the driver-vehicle micro-system. Interactions at the microscopic scale are modeled by methods of game theory, thus leading to the derivation of mathematical models within the framework of the kinetic theory. Macroscopic equations are derived by asymptotic limits from the underlying description at the lower scale. This approach shows the hypothesis under which macroscopic models known in the literature can be derived and how new models can be developed.

Elliptic flow from non-equilibrium initial condition with a saturation scale

A current goal of relativistic heavy-ion collisions experiments is the search for a Color Glass Condensate (CGC) as the limiting state of QCD matter at very high density. In viscous hydrodynamics simulations, a standard Glauber initial condition leads to estimate 4πη/s∼1, while employing the Kharzeev–Levin–Nardi (KLN) modeling of the glasma leads to at least a factor of 2 larger η/s. Within a kinetic theory approach based on a relativistic Boltzmann-like transport simulation, our main result is that the out-of-equilibrium initial distribution reduces the efficiency in building-up the elliptic flow. At RHIC energy we find the available data on v2 are in agreement with a 4πη/s∼1 also for KLN initial conditions. More generally, our study shows that the initial non-equilibrium in p-space can have a significant impact on the build-up of anisotropic flow.

Induced diffusion of tracers in a bacterial suspension: theory and experiments

AbstractThe induced diffusion of tracers in a bacterial suspension is studied theoretically and experimentally at low bacterial concentrations. Considering the swimmer–tracer hydrodynamic interactions at low Reynolds number and using a kinetic theory approach, it is shown that the induced diffusion coefficient is proportional to the swimmer concentration, their mean velocity and a coefficient$\beta $, as observed experimentally. This paper shows that$\beta $increases as a result of the interaction with solid surfaces. The coefficient$\beta $scales as the tracer–swimmer cross-section times the mean square displacement produced by single scattering events, which depends on the swimmer propulsion forces. Considering simple swimmer models (acting on the fluid as two monopoles or as a force dipole), it is shown that$\beta $increases for decreasing swimming efficiencies. Close to solid surfaces, the swimming efficiency degrades and, consequently, the induced diffusion increases. Experiments on wild-typeEscherichia coliin a Hele-Shaw cell, under buoyant conditions, are performed to measure the induced diffusion on tracers near surfaces. The modification of the suspension pH varies the swimmers’ velocity over a wide range, allowing the$\beta $coefficient to be extracted with precision. It is found that solid surfaces modify the induced diffusion: decreasing the confinement height of the cell,$\beta $increases by a factor of 4. The theoretical model reproduces this increase, although there are quantitative differences, probably attributed to the simplicity of the swimmer models and to the estimates for the parameters that modelE. coli.

Ion–Aerosol Flux Coefficients and the Steady-State Charge Distribution of Aerosols in a Bipolar Ion Environment

Fuchs’ theory, as corrected by Hoppel and Frick, is widely used to compute flux coefficients of ions to aerosol particles and the resultant charge distribution. We have identified approximations made in previous works that limit the theory's accuracy. Hoppel and Frick used two characteristic speeds or kinetic energies to calculate the flux coefficients of ions to aerosol particles in lieu of an average of the flux coefficients over the Maxwell–Boltzmann distribution of ion speeds. In the present work, we show that this approximation artificially reduces the number of multiply charged particles. Ion capture may be enhanced by three-body trapping, a process wherein an ion has a collision with a neutral gas molecule and loses sufficient kinetic energy to be captured by the particle. The gas kinetic theory approach to three-body trapping has been refined to better account for the collision between the ion and a neutral gas molecule within the potential presented by the particle. Approximations to the calculation of energy losses and the probability of ion capture have been relaxed. The possibility that an image charge may be induced on the ion as well as on the particle is allowed. While the previous work was limited to electrically conductive particles, both the ion and the particle are allowed to have any dielectric constant in the present work, and the finite size of the ions is taken into account when calculating minimum capture radii for the ion–particle interactions. The resulting ion flux coefficients differ from previous results both in the low nanometer regime and in the continuum regime. We explore the influence of key parameters on the charge distribution, including dielectric constant, temperature, and pressure, to understand how operating conditions may affect the interpretation of differential mobility analyzer measurements of particle size distributions. Finally, an empirical expression for the new charge distribution is given to facilitate rapid calculations. © 2013 American Association for Aerosol Research