Journal articles on the topic 'Kinetic theory, active particle, Nonlinear diffusion'

An epidemic spreading model is presented in the framework of the kinetic theory of active particles. The model is characterized by the influence of risk perception which can reduce the diffusion of infection. The evolution of the system is modeled through nonlinear interactions, whose output is described by stochastic games. The results of numerical simulations are discussed for different initial conditions.

This paper deals with a micro–macro derivation of a variety of cross-diffusion models for a large system of active particles. Some of the models at the macroscopic scale can be viewed as developments of the classical Keller–Segel model. The first part of the presentation focuses on a survey and a critical analysis of some phenomenological models known in the literature. The second part is devoted to the design of the micro–macro general framework, where methods of the kinetic theory are used to model the dynamics of the system including the case of coupling with a fluid. The third part deals with the derivation of macroscopic models from the underlying description, delivered within a general framework of the kinetic theory.

Abstract Kinetic and hydrodynamic theories are widely employed for describing the collective behavior of active matter systems. At the fluctuating level, these have been obtained from explicit coarse-graining procedures in the limit where each particle interacts weakly with many others, so that the total forces and torques exerted on each of them is of order unity at all times. Such limit is however not relevant for dilute systems that mostly interact via alignment; there, collisions are rare and make the self-propulsion direction to change abruptly. We derive a fluctuating kinetic theory, and the corresponding fluctuating hydrodynamics, for aligning self-propelled particles in the limit of dilute systems. We discover that fluctuations at kinetic level are not Gaussian and depend on the interactions among particles, but that only their Gaussian part survives in the hydrodynamic limit. At variance with fluctuating hydrodynamics for weakly interacting particles, we find that the noise variance at hydrodynamic level depends on the interaction rules among particles and is proportional to the square of the density, reflecting the binary nature of the aligning process. The results of this paper, which are derived for polar self-propelled particles with polar alignment, could be straightforwardly extended to polar particles with nematic alignment or to fully nematic systems.

Abstract We investigate the first passage statistics of active continuous time random walks with Poissonian waiting time distribution on a one dimensional infinite lattice and a two dimensional infinite square lattice. We study the small and large time properties of the probability of the first return to the origin as well as the probability of the first passage to an arbitrary lattice site. It is well known that the occupation probabilities of an active particle resemble that of an ordinary Brownian motion with an effective diffusion constant at large times. Interestingly, we demonstrate that even at the leading order, the first passage probabilities are not given by a simple effective diffusion constant. We demonstrate that at late times, activity enhances the probability of the first return to the origin and the probabilities of the first passage to lattice sites close enough to the origin, which we quantify in terms of the Péclet number. Additionally, we derive the first passage probabilities of a symmetric random walker and a biased random walker without activity as limiting cases. We verify our analytic results by performing kinetic Monte Carlo simulations of an active random walker in one and two dimensions.

Abstract High brightness-temperature radiation is observed in various astrophysical sources: active galactic nuclei, pulsars, interstellar masers, and flaring stars; the discovery of fast radio bursts renewed interest in the nonlinear interaction of intense radiation with plasma. In astronomical systems, the radiation frequency is typically well above the plasma frequency and its spectrum is broad, so nonlinear processes differ considerably from those typically studied in laboratory plasma. This paper is the first in a series devoted to the numerical study of nonlinear interactions of electromagnetic waves with plasma. We start with nonmagnetized pair plasmas, where the primary processes are induced (Compton) scattering and filamentation instability. In this paper, we consider waves in which electron oscillations are nonrelativistic. Here, the numerical results can be compared to analytical theory, facilitating the development of appropriate numerical tools and framework. We distill the analytic theory, reconciling the plasma and radiative transfer pictures of induced scattering and developing in detail the kinetic theory of modulation/filamentation instability. We carry out homogeneous numerical simulations using the particle-in-cell codes EPOCH and Tristan-MP for both monochromatic waves and wave packets. We show that simulations of both processes are consistent with theoretical predictions, setting the stage for analyzing the highly nonlinear regime.

AbstractIt is well-known that in a dense, gravity-driven flow, large particles typically rise to the top relative to smaller equal-density particles. In dense flows, this has historically been attributed to gravity alone. However, recently kinetic stress gradients have been shown to segregate large particles to regions with higher granular temperature, in contrast to sparse energetic granular mixtures where the large particles segregate to regions with lower granular temperature. We present a segregation theory for dense gravity-driven granular flows that explicitly accounts for the effects of both gravity and kinetic stress gradients involving a separate partitioning of contact and kinetic stresses among the mixture constituents. We use discrete-element-method (DEM) simulations of different-sized particles in a rotated drum to validate the model and determine diffusion, drag, and stress partition coefficients. The model and simulations together indicate, surprisingly, that gravity-driven kinetic sieving is not active in these flows. Rather, a gradient in kinetic stress is the key segregation driving mechanism, while gravity plays primarily an implicit role through the kinetic stress gradients. Finally, we demonstrate that this framework captures the experimentally observed segregation reversal of larger particles downward in particle mixtures where the larger particles are sufficiently denser than their smaller counterparts.

The hydrodynamics of the dense granular flow of rough inelastic particles down an inclined plane is analysed using constitutive relations derived from kinetic theory. The basic equations are the momentum and energy conservation equations, and the granular energy conservation equation contains a term which represents the dissipation of energy due to inelastic collisions. A fundamental length scale in the flow is the ‘conduction length’ δ=(d/(1-en)1/2), which is the length over which the rate of conduction of energy is comparable to the rate of dissipation. Here, d is the particle diameter and en is the normal coefficient of restitution. For a thick granular layer with height h ≫ δ, the flow in the bulk is analysed using an asymptotic analysis in the small parameter δ/h. In the leading approximation, the rate of conduction of energy is small compared to the rates of production and dissipation, and there is a balance between the rate of production due to mean shear and the rate of dissipation due to inelastic collisions. A direct consequence of this is that the volume fraction in the bulk is a constant in the leading approximation. The first correction due to the conduction of energy is determined using asymptotic analysis, and is found to be O(δ/h)2 smaller than the leading-order volume fraction. The numerical value of this correction is found to be negligible for systems of practical interest, resulting in a lack of variation of volume fraction with height in the bulk.The flow in the ‘conduction boundary layers’ of thickness comparable to the conduction length at the bottom and top is analysed. Asymptotic analysis is used to simplify the governing equations to a second-order differential equation in the scaled cross-stream coordinate, and the resulting equation has the form of a diffusion equation. However, depending on the parameters in the constitutive model, it is found that the diffusion coefficient could be positive or negative. Domains in the parameter space where the diffusion coefficients are positive and negative are identified, and analytical solutions for the boundary layer equations, subject to appropriate boundary conditions, are obtained when the diffusion coefficient is positive. There is no boundary layer solution that matches the solution in the bulk for parameter regions where the diffusion coefficient is negative, indicating that a steady solution does not exist. An analytical result is derived showing that a boundary layer solution exists (diffusion coefficient is positive) if, and only if, the numerical values of the viscometric coefficients are such that volume fraction in the bulk decreases as the angle of inclination increases. If the numerical values of the viscometric coefficients are such that the volume fraction in the bulk increases as the angle of inclination increases, a boundary layer solution does not exist.The results are extended to dense flows in thin layers using asymptotic analysis. Use is made of the fact that the pair distribution function is numerically large for dense flows, and the inverse of the pair distribution function is used as a small parameter. This approximation results in a nonlinear second-order differential equation for the pair distribution function, which is solved subject to boundary conditions. For a dissipative base, it is found that a flowing solution exists only when the height is larger than a critical value, whereas the temperature decreases to zero and the flow stops when the height becomes smaller than this critical value. This is because the dissipation at the base becomes a larger fraction of the total dissipation as the height is decreased, and there is a minimum height below which the rate of production due to shear is not sufficient to compensate for the rate of dissipation at the base. The scaling of the minimum height with dissipation in the base, the bulk volume fraction and the parameters in the constitutive relations are determined. From this, the variation of the minimum height on the angle of inclination is obtained, and this is found to be in qualitative agreement with previous experiments and simulations.

The local mobility of particles in highly supercooled liquids is demonstrated to be spatially heterogeneous on time scales comparable to the structural relaxation time τα. The particle motions in the active regions dominantly contribute to the mean square displacement, giving rise to a diffusion constant systematically larger than the Stokes–Einstein value. The diffusion process eventually becomes homogeneous on time scales longer than the life time of the heterogeneity structure (~ 3τα). The heterogeneity structure in the local mobility is very analogous to the critical fluctuation in Ising spin systems with their structure factor being excellently fitted to the Ornstein–Zernike form.

We study the influence of hydrodynamic, thermodynamic and interparticle forces on the diffusive motion of a Brownian probe driven by a constant external force through a dilute colloidal dispersion. The influence of these microscopic forces on equilibrium self-diffusivity (passive microrheology) is well known: all three act to hinder the short- and long-time self-diffusion. Here, via pair-Smoluchowski theory, we explore their influence on self-diffusion in a flowing suspension, where particles and fluid have been set into motion by an externally forced probe (active microrheology), giving rise to non-equilibrium flow-induced diffusion. The probe’s motion entrains background particles as it travels through the bath, deforming the equilibrium suspension microstructure. The shape and extent of microstructural distortion is set by the relative strength of the external force $F^{\mathit{ext}}$ to the entropic restoring force $kT/a_{\mathit{th}}$ of the bath particles, defining a Péclet number $\mathit{Pe}\equiv F^{\mathit{ext}}/(2kT/a_{\mathit{th}})$; and also by the strength of hydrodynamic interactions, set by the range of interparticle repulsion ${\it\kappa}=(a_{\mathit{th}}-a)/a$, where $kT$ is the thermal energy and $a_{\mathit{th}}$ and $a$ are the thermodynamic and hydrodynamic sizes of the particles, respectively. We find that in the presence of flow, the same forces that hinder equilibrium diffusion now enhance it, with diffusive anisotropy set by the range of interparticle repulsion ${\it\kappa}$. A transition from hindered to enhanced diffusion occurs when diffusive and advective forces balance, $\mathit{Pe}\sim 1$, where the exact value is a sensitive function of the strength of hydrodynamics, ${\it\kappa}$. We find that the hindered to enhanced transition straddles two transport regimes: in hindered diffusion, stochastic forces in the presence of other bath particles produce deterministic displacements (Brownian drift) at the expense of a maximal random walk. In enhanced diffusion, driving the probe with a deterministic force through an initially random suspension leads to fluctuations in the duration of probe–bath particle entrainment, giving rise to enhanced, flow-induced diffusion. The force-induced diffusion is anisotropic for all $\mathit{Pe}$, scaling as $D\sim \mathit{Pe}^{2}$ in all directions for weak forcing, regardless of the strength of hydrodynamic interactions. When probe forcing is strong, $D\sim \mathit{Pe}$ in all directions in the absence of hydrodynamic interactions, but the picture changes qualitatively as hydrodynamic interactions grow strong. In this nonlinear regime, microstructural asymmetry weakens while the anisotropy of the force-induced diffusion tensor increases dramatically. This behaviour owes its origins to the approach toward Stokes flow reversibility, where diffusion along the direction of probe force scales advectively while transverse diffusion must vanish.

Climate change, population growth, and rising fossil fuel prices have encouraged governments and scientists for alternate energy resources. This energy transition requires a high-performance energy storage device to satisfy the high energy and power demand and lithium-ion battery (LIB) is one of the promising one. The performance of these batteries ultimately relies on the properties of their components. In this regard, to meet the high-power demand in high-power applications (such as electric vehicles (EVs) and hybrid EVs), materials with rapid lithium transport are required. Lithium Nickel Manganese Cobalt Oxide (NMC) has attracted scientists’ attentions due to its outstanding performance as a cathode material. Therefore, understanding the effect of various factors on lithium diffusivity in NMC is critical to develop high-performance LIBs for high-power applications. Electrochemical methods such as potentiostatic and galvanostatic intermittent titration techniques (PITT and GITT) have been frequently utilized to experimentally quantify lithium diffusivity in NMC. These techniques need the knowledge of electrode particle shape and dimension, and uncertainty about these parameters leads to substantial errors in predicting the diffusion coefficient. In addition, because these techniques consider the response of the whole electrochemical cell, it is hard to distinguish the effect of different structural factors on Li diffusivity in a single NMC active material. Therefore, an appropriate method still needs to be developed to capture the structural effects on lithium diffusivity in NMC. For this purpose, a multi-level modelling from Density Functional Theory (DFT) to kinetic Monte Carlo (KMC) should be implemented. In this study, we will use DFT to find the ground state energy of NMC at different lithium concentrations and configurations. Also, the minimum energy path of lithium migration and the related activation barrier will be found by Climbing Image-Nudge Elastic Band (CI-NEB) method. Then by implementing the configurational dependent activation barrier into the KMC simulation, the lithium diffusivity will be studied. This atomistic simulation gives insight about the structural effects on lithium diffusivity in NMC to further develop this cathode material for high performance LIBs.

Lithium-ion batteries (LIBs) become an essential part of many portable devices and even electric vehicles than ever before. Among the various cathode materials, Ni rich layered cathode material has big attention because it has higher specific capacity and energy density. However, at a delithiated state, unstable Ni4+ leads to oxygen release and structural degradation and as a result, irreversible phase transition from R3m to electrochemical inactive Fm3m is observed. So, various strategy is applying to overcome this limitation like three-component system (NCM) or surface coating. However, NCM still cannot solve that problem perfectly and surface coating makes a problem like reducing specific capacity caused by insulating coating material (Al2O3, MnO2...etc) And also, this day, Co free structure of Ni rich cathode material has received more great attention as an alternative to NCM because of its hazardous toxicity and increasing price of Co. At this perspective, many studies have demonstrated Core-Shell or FCG (Full Concentration Gradient) structure can make better structural stability without Co metal than surface coating, which has insulated coating materials. In addition, core shell structure is easier to control the composition than FCG structure. However, in Core-Shell structure, interdiffusion of shell metal to core deteriorate the stability of Core-Shell material, so it needs very delicate heat treatment. And generally, to prevent interdiffusion from traditional core-shell structure, lower synthesis temperature or high valence metal dopant would be needed and that leads lower initial specific capacity or additional doped metal. So, we prevent the Mn interdiffusion by changing valence state of Mn in precursor through simple convection drying process not vacuum drying without decreasing synthesis temperature and additional dopant. Atomic interdiffusion in layered metal oxide structures follows the atomic migration through octahedral and tetrahedral sites. In case of various stated Mn, higher valence state Mn has higher energy barrier to migrate between each Oh and Td sites. Based on this theory, surface Mn rich shell can be oxidized easily under convection oven drying and highly oxidized Mn will be remained better than lower state Mn during high temperature calcination. These more remained Mn in shell can protect the particle surface from electrolyte attack and also higher valence state Mn makes slightly more Ni2+ due to thermodynamic stability and charge balance of Mn on the surface. And that Ni2+ in Li slab (Cation mixing) acts as a pillar to suppress irreversible phase transition of Ni rich materials. Through this surface passivation, phase transition (layered to rock salt ) propagation surface to bulk can be blocked. Furthermore, mechanical pulverization of secondary particle is also prevented because of less permeating electrolyte into bulk structure. Therefore, Li ion diffusion will not be sluggish after cycling as observed by GITT. In addition, more clear Ni rich core assure high specific capacity and faster electrochemical reaction kinetic without severe capacity fading. And also, in Full cell test (using graphite as anode), convection oven dried sample has better structure stability and that means our strategy for core-shell LiNi0.97Mn0.03O2 sample can be good candidate to alternate conventional cathode active material for Lithium ion battery practically. As prepared materials, atomic distribution was observed by EDS and XPS analysis. This study suggests useless of vacuum drying and more cost effective way to prepare Co free Core Shell LiNi0.97Mn0.03O2 cathode material for Lithium Ion Batteries.

The results obtained by the plasma physics community for the validation and the prediction of turbulence and transport in magnetized plasmas come mainly from the use of very central processing unit (CPU)-consuming particle-in-cell or (gyro)kinetic codes which naturally include non-Maxwellian kinetic effects. To date, fluid codes are not considered to be relevant for the description of these kinetic effects. Here, after revisiting the limitations of the current fluid theory developed in the 19th century, we generalize the fluid theory including kinetic effects such as non-Maxwellian super-thermal tails with as few fluid equations as possible. The collisionless and collisional fluid closures from the nonlinear Landau Fokker–Planck collision operator are shown for an arbitrary collisionality. Indeed, the first fluid models associated with two examples of collisionless fluid closures are obtained by assuming an analytic non-Maxwellian distribution function (e.g. the INMDF (Izacard, O. 2016b Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas. Phys. Plasmas 23, 082504) that stands for interpreted non-Maxwellian distribution function). One of the main differences with the literature is our analytic representation of the distribution function in the velocity phase space with as few hidden variables as possible thanks to the use of non-orthogonal basis sets. These new non-Maxwellian fluid equations could initiate the next generation of fluid codes including kinetic effects and can be expanded to other scientific disciplines such as astrophysics, condensed matter or hydrodynamics. As a validation test, we perform a numerical simulation based on a minimal reduced INMDF fluid model. The result of this test is the discovery of the origin of particle and heat diffusion. The diffusion is due to the competition between a growing INMDF on short time scales due to spatial gradients and the thermalization on longer time scales. The results shown here could provide the insights to break some of the unsolved puzzles of turbulence.

Accurately modelling and forecasting of the dynamics of the Earth’s radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave–particle resonant interaction. Energetic electron acceleration or scattering into the Earth’s atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave–particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation.

Particle transport, acceleration and energization are phenomena of major importance for both space and laboratory plasmas. Despite years of study, an accurate theoretical description of these effects is still lacking. Validating models with self-consistent, kinetic simulations represents today a new challenge for the description of weakly collisional, turbulent plasmas. We perform simulations of steady state turbulence in the 2.5-dimensional approximation (three-dimensional fields that depend only on two-dimensional spatial directions). The chosen plasma parameters allow to span different systems, going from the solar corona to the solar wind, from the Earth’s magnetosheath to confinement devices. To describe the ion diffusion we adapted the nonlinear guiding centre (NLGC) theory to the two-dimensional case. Finally, we investigated the local influence of coherent structures on particle energization and acceleration: current sheets play an important role if the ions’ Larmor radii are of the order of the current sheet’s size. This resonance-like process leads to the violation of the magnetic moment conservation, eventually enhancing the velocity-space diffusion.

The dispersion of a chemically active solute in unidirectional laminar flow in a channel of constant cross-sectional area is considered. Adsorption/desorption of the solute at the wall or the presence of a bulk or surface chemical reaction introduce additional timescales, in addition to the diffusive and convective ones, such that, under certain conditions, the asymptotic evolution of the cross-sectional mean concentration cannot be described by a one-dimensional Taylor-Aris model. We use the centre and invariant manifold theories to establish the proper time and length scale separations necessary for the existence of an effective transport equation and to determine the dependence of the effective transport coefficients on the kinetics of adsorption/desorption and reaction. For the case of classical Taylor-Aris dispersion with no reaction, we derive the effective transport equation to infinite order in the parameter, p , representing the ratio of the characteristic time for radial molecular diffusion to that for axial convection. We show that the infinite series in the effective transport model is convergent provided p is smaller than some critical value, which depends on the initial concentration distribution. We also examine the spatial evolution of time dependent inlet conditions and show that the spatial and temporal evolutions differ at third and higher orders. It is shown that, except for slow reactions with a kinetic timescale of the same order as the transverse diffusion time, fast bulk reaction does not allow an asymptotic axial dispersion description. Slow bulk reactions do not affect dispersion but a correction to the apparent kinetics may arise due to nonlinear interaction among reaction, diffusion and convection. It is also shown that with a slow bulk reaction, steady-state dispersion due to a coupling of reaction and transverse velocity gradient can arise. Although this mechanism is distinct from the transient Taylor—Aris mechanism, the dispersion coefficient is identical to the classical unreactive Taylor—Aris coefficient. Surface reaction of any speed yields the proper asymptotic behaviour in time because the species still needs to diffuse slowly to the conduit wall. In the limit of fast surface reaction, the Taylor-Aris dispersion coefficient is reduced by a factor of 4.2, 7.1 and 4.0 for pipe, plane Poiseuille and Couette flows, respectively, as the slow-moving solutes near the wall are depleted. For the case of a linear surface reaction, we use the invariant manifold theory to derive the effective transport equation to infinite order. We also show that the radius of convergence of the invariant manifold expansion is approximately three times that of the no reaction case. We demonstrate that if adsorption/desorption is as slow as transverse diffusion an adsorption-induced dispersion, distinct from the Taylor-Aris shear dispersion, exists. While the total dispersion may increase because of the contribution of both, the Taylor-Aris component is reduced by a physical mechanism similar to surface reaction. The adsorption/desorption induced dispersion coefficient is shown to have a maximum when the adsorption equilibrium constant is exactly 2. Nonlinear Langmuir type adsorption at large concentration is shown to introduce a nonlinear drift term which causes non-Gaussian pulse responses with long tails These tails are detrimental to separation chromatography since they cause overlaps which increase with the length of the chromatograph