Kinetic Theory Approach Research Articles

Chemical nonequilibrium for interacting bosons: Applications to the pion gas

We consider an interacting pion gas in a stage of the system evolution where thermal but not chemical equilibrium has been reached, i.e., for temperatures between thermal and chemical freeze-out T(ther) < T < T(chem) reached in relativistic heavy-ion collisions. Approximate particle number conservation is implemented by a nonvanishing pion number chemical potential mu(pi) within a diagrammatic thermal field-theory approach, valid in principle for any bosonic field theory in this regime. The resulting Feynman rules are derived here and applied within the context of chiral perturbation theory to discuss thermodynamical quantities of interest for the pion gas such as the free energy, the quark condensate, and thermal self-energy. In particular, we derive the mu(pi) not equal 0 generalization of Luscher and Gell-Mann-Oakes-Renner-type relations. We pay special attention to the comparison with the conventional kinetic theory approach in the dilute regime, which allows for a check of consistency of our approach. Several phenomenological applications are discussed, concerning chiral symmetry restoration, freeze-out conditions, and Bose-Einstein pion condensation.

Study into laser short-pulse heating of a layered structure

Laser short-pulse heating of a lead—silicon—gold-layered structure is considered and non-equilibrium equation in the lattice and electron subsystems is formulated using the electron kinetic theory approach. The Seebeck coefficient in the metallic and silicon layers is also formulated. Electron and lattice site temperature rise in the subsystems and the Seebeck coefficients are computed for time exponentially decaying pulse. The study is extended to include the influence of the first layer (lead layer) thickness on temperature rise and the Seebeck coefficients. It is found that the lattice site temperature across the interface of the lead and silicon layers increases sharply. The Seebeck coefficient predicted in the silicon layer is higher than in the metallic layers in the structure.

Modelling of dense and complex granular flow in high shear mixer granulator—A CFD approach

In the aspect of granulation process control, the numerical simulations appear to be a cost-effective and flexible tool to investigate the flow structure of granular materials in mixer granulators of various configurations and operating conditions. Computational fluid dynamics (CFD) is used in this study to model the granular flow in a vertical high shear mixer granulator. The simulation is based on the continuum model of dense-gas kinetic theory [Gidaspow, D., Bezburuah, R., Ding, J., 1992. Hydrodynamics of circulating fluidized beds, kinetic theory approach. In: Fluidization, vol. VII, Proceedings of the 7th Engineering Foundation Conference on Fluidization, Brisbane, Australia, pp. 75–82] with consideration of inter-particle friction force at dense condition [Schaeffer, D.G., 1987. Instability in the evolution equations describing incompressible granular flow. Journal of Differential Equations 66 (1), 19–50]. This study aims to verify this numerical method in modelling dense and complex granular flows, where the solids motion obtained from the simulation is validated against the experimental results of positron emission particle tracking (PEPT) technique [Ng, B.H., Kwan, C.C., Ding, Y.L., Ghadiri, M., Fan, X.F., 2007. Solids motion of calcium carbonate particles in a high shear mixer granulator: a comparison between dry and wet conditions. Powder Technology 177 (1), 1–11]. In general, the Eulerian based continuum model captures the main features of solids motion in high shear mixer granulator including the bed height and dominating flow direction (the tangential velocity). However, the continuum based kinetic-frictional model is not capable of capturing the complex vertical swirl pattern. Quantitative comparison shows over-predictions in the tangential velocity and stiff drops of the tangential velocity at the wall region. These results demonstrate the deficiency in transmitting forces in the bed of granular materials which indicate the necessity to improve the constitutive relations of dense granular materials as a continuum.

Entropy generation analysis for the free surface turbulent flow during laser material processing

PurposeThe purpose of this paper is to carry out a systematic energy analysis for predicting the first and second law efficiencies and the entropy generation during a laser surface alloying (LSA) process.Design/methodology/approachA three‐dimensional transient macroscopic numerical model is developed to describe the turbulent transport phenomena during a typical LSA process and subsequently, the energy analysis is carried out to predict the entropy generation as well as the first and second law efficiencies. A modified k–ε model is used to address turbulent molten metal‐pool convection. The phase change aspects are addressed using a modified enthalpy‐porosity technique. A kinetic theory approach is adopted for modelling evaporation from the top surface of the molten pool.FindingsIt is found that the heat transfer due to the strong temperature gradient is mainly responsible for the irreversible degradation of energy in the form of entropy production and the flow and mass transfer effects are less important for this type of phase change problem. The first and second law efficiencies are found to increase with effective heat input and remain independent of the powder feed rate. With the scanning speed, the first law efficiency increases whereas the second law efficiency decreases.Research limitations/implicationsThe top surface undulations are not taken care of in this model which is a reasonable approximation.Practical implicationsThe results obtained will eventually lead to an optimized estimation of laser parameters (such as laser power, scanning speed, etc.), which in turn improves the process control and reduces the cost substantially.Originality/valueThis paper provides essential information for modelling solid–liquid phase transition as well as a systematic analysis for entropy generation prediction.

Improved formulation of electron kinetic theory approach for laser shortpulse heating: Thermal stress consideration

Nonequilibrium energy transport between excited electrons and lattice site is re-formulated after considering the ballistic contribution of the electron energy to the energy transport process. The improved formulation of the electron kinetic theory predictions are compared with the previously obtained electron kinetic and two-equation models. Thermal stress developed in the region irradiated by a laser beam is formulated during the heating pulse. Copper with variable properties is used in the simulations. It is found that improved electron kinetic theory model predicts less temperature rise than that corresponding to previously formulated electron kinetic theory and two equation models in the surface region; in this case, electron temperature attains high values. Thermal stress developed is compressive and attains the maximum at some depth below the surface. The thermal stress level is well below the yielding limit of the substrate material.

Double milling in self-propelled swarms from kinetic theory

We present a kinetic theory for swarming systems of interacting, self-propelled discrete particles. Starting from the Liouville equation for the many-body problem we derive a kinetic equation for the single particle probability distribution function and the related macroscopic hydrodynamic equations. General solutions include flocks of constant density and fixed velocity and other non-trivial morphologies such as compactly supported rotating mills. The kinetic theory approach leads us to the identification of macroscopic structures otherwise not recognized as solutions of the hydrodynamic equations, such as double mills of two superimposed flows. We find the conditions allowing for the existence of such solutions and compare to the case of single mills.

Comparing 2-nt 3' overhangs against blunt-ended siRNAs: a systems biology based study

In this study, we formulate a computational reaction model following a chemical kinetic theory approach to predict the binding rate constant for the siRNA-RISC complex formation reaction. The model allowed us to study the potency difference between 2-nt 3' overhangs against blunt-ended siRNA molecules in an RNA interference (RNAi) system. The rate constant predicted by this model was fed into a stochastic simulation of the RNAi system (using the Gillespie stochastic simulator) to study the overall potency effect. We observed that the stochasticity in the transcription/translation machinery has no observable effects in the RNAi pathway. Sustained gene silencing using siRNAs can be achieved only if there is a way to replenish the dsRNA molecules in the cell. Initial findings show about 1.5 times more blunt-ended molecules will be required to keep the mRNA at the same reduced level compared to the 2-nt overhang siRNAs. However, the mRNA levels jump back to saturation after a longer time when blunt-ended siRNAs are used. We found that the siRNA-RISC complex formation reaction rate was 2 times slower when blunt-ended molecules were used pointing to the fact that the presence of the 2-nt overhangs has a greater effect on the reaction in which the bound RISC complex cleaves the mRNA.

A kinetic theory approach to capturing interneuronal correlation: the feed-forward case

We present an approach for using kinetic theory to capture first and second order statistics of neuronal activity. We coarse grain neuronal networks into populations of neurons and calculate the population average firing rate and output cross-correlation in response to time varying correlated input. We derive coupling equations for the populations based on first and second order statistics of the network connectivity. This coupling scheme is based on the hypothesis that second order statistics of the network connectivity are sufficient to determine second order statistics of neuronal activity. We implement a kinetic theory representation of a simple feed-forward network and demonstrate that the kinetic theory model captures key aspects of the emergence and propagation of correlations in the network, as long as the correlations do not become too strong. By analyzing the correlated activity of feed-forward networks with a variety of connectivity patterns, we provide evidence supporting our hypothesis of the sufficiency of second order connectivity statistics.

Analytical solution for non-equilibrium energy transfer in gold: Influence of ballistic contribution of electrons on energy transfer

The analytical solution for non-equilibrium energy transfers in gold substrate and ballistic contribution of electrons to the energy transfer mechanism is examined. The non-equilibrium energy equation including the ballistic contribution of electrons is obtained using the electron kinetic theory approach. The analytical solution using the perturbation method is introduced to formulate lattice and electron temperature distributions in the film. A numerical method using the finite difference scheme is employed to predict and compare electron and lattice site temperatures to those obtained from the analytical solution. It is found that temperature remains high in the surface region of the gold film due to the cases: (i) accounting for the ballistic contribution of electrons to non-equilibrium energy transfer, and (ii) excluding the ballistic contribution to the non-equilibrium energy transfer. This is true for electron and lattice temperatures.

Laser short-pulse heating of metallic surface: Consideration of Seebeck effect

In the present study, laser short-pulse heating is formulated using an electron kinetic theory approach. Temperature predictions are compared with that obtained from two-equation model. Seebeck effect is considered during the heating process. The predicted Seebeck coefficients are compared with the results based on the early formulation. Electron excess energy loss due to Seebeck effect is compared with electron mean energy. It is found that Seebeck coefficient decays sharply in the surface region due to sharp decay of electron temperature in this region. Seebeck coefficient obtained from the present study is in agreement with the predictions based on the early formulation, provided electron temperature is used in the previous formulation. However, Seebeck coefficient differs significantly once the lattice site temperature is used in the previous formulation. Electron excess energy loss due to Seebeck effect is considerably less than electron mean energy, i.e. the ratio is in the order of 10−5.

Jet-induced gauge field instabilities in the quark-gluon plasma: A kinetic theory approach

We discuss the properties of the collective modes of a system composed by a thermalized quark-gluon plasma traversed by a relativistic jet of partons. The transport equations obeyed by the components of the plasma and of the jet are studied in the Vlasov approximation. Assuming that the partons in the jet can be described with a tsunamilike distribution function we derive the expressions of the dispersion law of the collective modes. Then the behavior of the unstable gauge modes of the system is analyzed for various values of the velocity of the jet, of the momentum of the collective modes and of the angle between these two quantities. We find that the most unstable modes are those with momentum orthogonal to the velocity of the jet and that these instabilities appear when the velocity of the jet is higher than a threshold value, which depends on the plasma and jet frequencies. The results obtained within the Vlasov approximation are compared with the corresponding results obtained using a chromohydrodynamical approach. The effect we discuss here suggests a possible collective mechanism for the description of the jet quenching phenomena in heavy-ion collisions.

Microstructure evolution during liquid–liquid laminar mixing: a kinetic theory approach

Many material forming processes involve liquid–liquid mixing, and in general the induced properties are strongly dependent on the resulting microstructure. Microstructure during liquid–liquid mixing exhibits a morphology characterized by a length scale usually much smaller that the one associated with the macroscopic flow. In this context a microstructure description allowing to characterize the microscopic morphology, its characteristic size, shape and orientation as well as the time evolution of the specific interface area, seems to be necessary in order to qualify and even quantify, the ability of flows to perform mixing, leading to the definition of optimal flows to maximize some desired criteria. The approach based on the definition of area tensor is a promising description of such phenomena, being its main drawback the necessity of introducing a closure relation to derive the equation governing its time evolution, whose impact on the computed solution can be in some cases significant. In this paper we propose a new description which considers the area tensor description as starting point, but defines its evolution in a kinetic theory framework, avoiding the introduction of any closure relation.

Topology optimization of fluid domains: kinetic theory approach

AbstractWe consider the problem of optimal design of flow domains for Navier–Stokes flows in order to minimize a given performance functional. We attack the problem using topology optimization techniques, or control in coefficients, which are widely known in structural optimization of elastic solids and structures for their flexibility, generality, yet ease of use, and integration with existing FEM software. We use a simple kinetic model to approximate the Navier–Stokes system. Arguably, we take a rather unconventional path in the kinetic theory, using it only to gain insight about the Navier–Stokes‐related system of hydrodynamical equations, which we take as our starting point. Thus all the modifications we make to the kinetic models are “hydrodynamically” inspired and we seek no particular physical explanation for them; the only requirement for us is the convergence (at least, formal) of the kinetic equations towards the correct hydrodynamical limit. We formally compute the hydrodynamical limit of the proposed kinetic system, and rigorously establish the existence of flow solutions and their continuous dependence on the design parameters. Optimal controls are shown to belong to a special class (0–1 solutions) for a popular power dissipation minimization problem for viscous fluids.

Cascade damage evolution: rate theory versus kinetic Monte Carlo simulations

The thermal evolution of defects produced by ion irradiation is studied by kinetic Monte Carlo and Rate Theory approaches. An isochronal annealing is simulated to evidence the different thermally activated mechanisms that govern defect evolution. KMC simulations show that in the case of ion irradiation, additional recovery peaks should be expected, in comparison to electron irradiation conditions. A comparison between kMC and RT results indicates that some of these peaks are due to spatially – correlated recombinations that occur at low temperature. Therefore kMC and RT approaches differ at low temperature. However, at higher temperature results obtained by both models are in near perfect agreement. In addition, we studied the influence of vacancy cluster mobility on the evolution of damage. KMC simulations show that the mobility of V2, V3 and V4 clusters does not significantly affect the evolution of defects and can be neglected in these conditions.

Laser Short-Pulse Heating of Silver-Chromium Assembly: Improved Formulation of Electron Kinetic Theory Approach

Laser short-pulse heating of a two-layer assembly consisting of silver (40 nm thick) at the top, and chromium (800 nm) at the bottom, is considered, and the temperature field in the electron as well as electron subsystems is predicted. An improved formulation of the electron kinetic theory approach accommodating the ballistic contribution of electrons to energy transport is used when modeling the heating. In addition, electron and lattice temperatures in silver and chromium as a single substrate are predicted for comparison. It is found that the chromium layer situated below the silver layer modifies significantly the temperature rise in the silver layer. This situation is also observed for the Seebeck coefficient.

Laser Short-Pulse Heating of a Gold Surface: Comparison of Absorption and Surface Heat Flux Heating Situations

Laser irradiation of a gold surface via volumetric absorption and surface heat flux heating are examined. Electron and lattice site temperature increases are predicted and compared for two heating situations. Time-dependent pulse intensity is used to simulate the temporal variation of an actual laser pulse. Nonequilibrium energy transfer in the substrate material is considered, and the electron kinetic theory approach is accommodated when modeling the heating process. It is found that electron and lattice site temperatures attain higher values in the surface region with absorption heating than with surface heat flux heating.

Simulation of defect evolution in irradiated materials: Role of intracascade clustering and correlated recombination

The evolution of damage produced by collision cascades in Fe is studied using both kinetic Monte Carlo (kMC) and rate theory (RT) approaches. The initial damage distribution is obtained from molecular-dynamics simulations of 30 keV recoils in Fe. An isochronal annealing is simulated to identify the different thermally activated mechanisms that govern defect evolution. When clusters form during collision cascades, kMC simulations show that additional recovery peaks should be expected, in comparison to recovery curves obtained under electron irradiation conditions. Detailed kMC and RT simulations reveal that some of these recovery peaks are due to correlated recombinations at low temperature between defects. In particular, we show that under cascade-damage conditions it is possible to observe correlated recombinations between vacancies and self-interstitial clusters. These correlated recombinations cannot be reproduced with a RT model, and therefore kMC and RT differ at low temperature. However, for the conditions presented here, the contribution of correlated recombination is very small and therefore no significant differences are observed at high temperatures between these two models.

Instability of bounded gas‐particle fluidized beds

AbstractSteady flows of gas and particles in unbounded‐fluidized beds have been shown to lose stability to localized voidage disturbances. An insight is provided into the linear stability of bounded gas‐particle flows using a kinetic theory approach. The stability analysis is carried out for two illustrative sets corresponding to fluidized systems having walls acting as sinks and sources of fluctuation energy. Instabilities are characterized by computing leading eigenvalue profiles and dominant eigenfunction contour maps. Results show two types of dominant instability patterns (symmetric and antisymmetric) for flow in a vertical duct, both of which propagate through the bed in the form of traveling waves at speeds comparable to that of the solid phase. Moreover, model predictions show that increasing solids fraction and decreasing particle inelasticity will suppress the wavy disturbance. The physical mechanism of instability formation is further investigated using a term‐by‐term method of analysis. Results show that instability modes can be suppressed if solid phase inertia or inelastic particle collisions are eliminated from the momentum and pseudo‐thermal energy balance equations. Finally, the symmetric instabilities were shown to develop into bubble‐like structures while the antisymmetric instabilities develop into streamer‐like structures. © 2007 American Institute of Chemical Engineers AIChE J, 2007

On a kinetic theory approach to modelling degradation phenomena in conservation sciences

This paper deals with the modelling of degradation phenomena for works of art under the action applied by external agents. The analysis is based on a suitable development of the methods of the kinetic theory for active particles. The model consists in an evolution equation for the probability distribution of the degradation stage. The interpretation of empirical data provides the identification of the parameters of the model and a quantitative prediction of degradation events.

Laser Short-Pulse Heating of Gold–Silver Assembly: Entropy Generation Due to Heat and Electricity Flows in Electron Subsystem

ABSTRACT Laser short-pulse heating of a two-layer assembly consisting of gold–silver is considered. In the assembly, a gold layer of 3.24 × 10−8 m thickness is situated on top of a silver layer. Electron kinetic theory approach is introduced when predicting electron and lattice site temperature distributions. Seebeck coefficient is predicted and compared with values obtained from the previous formulation. Entropy generation in the electron subsystem is formulated and the Seebeck coefficient is accommodated to account for the thermoelectric effect. It is found that lattice site and electron temperature profiles decay smoothly across the gold–silver interface. The Seebeck coefficient follows electron temperature profiles and its predicted values agree well with the results obtained from the previous formulation. Entropy generation attains high values in the surface region because of the high flux term (J Q ) in this region. Entropy contribution due to Seebeck effect is smaller than that corresponding to energy flow in the electron subsystem.