Protein motors induced enhanced diffusion in intracellular transport

Diffusion of transported particles in the intracellular medium is described by means of a generalized diffusion equation containing forces due to the cytoskeleton network and to the protein motors. We find that the enhanced diffusion observed in experiments depends on the nature of the force exerted by the protein motors and on parameters characterizing the intracellular medium which is described in terms of a generalized Debye spectrum for the noise density of states.     

Hurst exponents for interacting random walkers obeying nonlinear Fokker-Planck equations

Anomalous diffusion of random walks has been extensively studied for the case of non-interacting particles. Here we study the evolution of nonlinear partial differential equations by interpreting them as Fokker-Planck equations arising from interactions among random walkers. We extend the formalism of generalized Hurst exponents to the study of nonlinear evolution equations and apply it to several illustrative examples. They include an analytically solvable case of a nonlinear diffusion constant and three nonlinear equations which are not analytically solvable: the usual Fisher equation which contains a quadratic nonlinearity, a generalization of the Fisher equation with density-dependent diffusion constant, and the Nagumo equation which incorporates a cubic rather than a quadratic nonlinearity. We estimate the generalized Hurst exponents.     

On the depolarized Rayleigh scattering from macromolecular and colloidal solutions — Anisotropy of the diffusional broadening

The width of the depolarized Rayleigh line for the light scattered from a solution of non-spherical particles is calculated from a generalized diffusion equation. Due to the correlation between the translational motion and the orientation of the particles, the diffusional contribution to the width is anisotropic, i.e. the relevant effective diffusion coefficient depends on the scattering angle and on the polarization vectors. This anisotropy is related to the shape of the particles.     

Diffusion of thermonuclear alpha particles under the influence of intense LH waves

Recently, a new mechanism was proposed by Fisch and Rax which should lead to amplification of lower hybrid (LH) waves at the expense of alpha particles energy, improving thus the LH current drive efficiency. The present contribution investigates the possibility of achieving the conditions on which this mechanism — based on the spatial diffusion of fusion alpha particles — could become operative. The analysis performed shows that in reactor grade tokamaks, the penetration of LH waves into the plasma column is very poor due to the intense electron Landau damping and the complicated geometry of the equilibrium magnetic fields. Consequently, at acceptable LHW input power levels, the waves do not reach the regions where fusion alpha particle power could reasonably compensate the losses of LHW energy due to the damping by electrons. The model of Fisch and Rax is based on special features of the induced diffusion of alpha particles in the energy-configuration space. Using suitable Hamiltonian formalism, the LHW induced radial diffusion of alpha particles and the energy transport between LHW and alpha particles in the frame of generalized quasilinear lines of diffusion constraint is also investigated. A rather strong change ofk of LHW along the ray trace can contribute to the change of energy transport between LHW and alpha particles as well.The authors are indebted to Dr. R. Klíma for valuable discussions.     

Directional region control of the thermal fractal diffusion of a space body

We present a directional region control(DRC) model of thermal diffusion fractal growth with active heat diffusion in three-dimensional space. This model can be applied to predict the space body heat fractal growth and study its directional region control. When the nonlinear interference term and the inner heat source term are generalized functions, the relationship between the particle aggregation probability and the interference terms can be obtained using the norm theory. We can then predict the aggregation form of particles in different regions. When the nonlinear interference terms in the model are expressed as a trigonometric function and its composite function, our simulations show that the DRC method of thermal fractal diffusion is effective and has reference value for the directional control of actual fractal growth systems.     

Modelling of anisotropic sintering in crystalline ceramics

We present a model that describes anisotropic shrinkage during sintering in a powder compact of aligned, elongated particles by deriving the anisotropic sintering stress and the anisotropic generalized viscosity as a function of material and geometric parameters. The powder compact consists of elongated particles, which are perfectly aligned and simply packed with elliptical pores at all the quadra-junctions between the particles. The model considers mass transport by grain boundary diffusion and surface diffusion. Shrinkage rates are calculated for a variety of geometries and are compared to kinetic Monte Carlo simulations.     

Diffusion-induced bistability of driven nanomechanical resonators

We study nanomechanical resonators with frequency fluctuations due to diffusion of absorbed particles. The diffusion depends on the vibration amplitude through inertial effect. We find that, if the diffusion coefficient D is sufficiently large, the resonator response to periodic driving displays bistability. The lifetime of the coexisting vibrational states exponentially increases with increasing D and displays a scaling dependence on the parameters close to bifurcation points.     

Generalized Green Functions and Current Correlations in the TASEP

We study correlation functions of the totally asymmetric simple exclusion process (TASEP) in discrete time with backward sequential update. We prove a determinantal formula for the generalized Green function which describes transitions between positions of particles at different individual time moments. In particular, the generalized Green function defines a probability measure at staircase lines on the space-time plane. The marginals of this measure are the TASEP correlation functions in the space-time region not covered by the standard Green function approach. As an example, we calculate the current correlation function that is the joint probability distribution of times taken by selected particles to travel given distance. An asymptotic analysis shows that current fluctuations converge to the Airy₂ process.     

Particle Transport through Scattering Regions with Clear Layers and Inclusions

This paper introduces generalized diffusion models for the transport of particles in scattering media with nonscattering inclusions. Classical diffusion is known as a good approximation of transport only in scattering media. Based on asymptotic expansions and the coupling of transport and diffusion models, generalized diffusion equations with nonlocal interface conditions are proposed which offer a computationally cheap, yet accurate, alternative to solving the full phase-space transport equations. The paper shows which computational model should be used depending on the size and shape of the nonscattering inclusions in the simplified setting of two space dimensions. An important application is the treatment of clear layers in near-infrared (NIR) spectroscopy, an imaging technique based on the propagation of NIR photons in human tissues.     

Interacting Brownian motion in a periodic potential

We study transport properties of a system composed of Brownian particles immersed in a periodic potential. Interaction among the Brownian particles is treated perturbationally in a framework of a generalized Fokker-Planck equation, which due to the interaction contains a renormalized periodic potential and an extra mean field term. We solve the kinetic equation numerically and discuss effects of the (repulsive) interaction on dynamic response functions and transport coefficients.     

Exact diffusion constant of a one-dimensional asymmetric exclusion model with open boundaries

For the 1D fully asymmetric exclusion model with open boundary conditions, we calculate exactly the fluctuations of the current of particles. The method used is an extension of a matrix technique developed recently to describe the equatime steady-state properties for open boundary conditions and the diffusion constant for particles on a ring. We show how the fluctuations of the current are related to non-equal-time correlations. In the thermodynamic limit, our results agree with recent results of Ferrari and Fontes obtained by working directly in the infinite system. We also show that the fluctuations of the current become singular when the system undergoes a phase transition with discontinuities along the first-order transition line.     

Structure of the magnetic reconnection diffusion region from four-spacecraft observations

Magnetic reconnection leads to energy conversion in large volumes in space but is initiated in small diffusion regions. Because of the small sizes of the diffusion regions, their crossings by spacecraft are rare. We report four-spacecraft observations of a diffusion region encounter at the Earth's magnetopause that allow us to reliably distinguish spatial from temporal features. We find that the diffusion region is stable on ion time and length scales in agreement with numerical simulations. The electric field normal to the current sheet is balanced by the Hall term in the generalized Ohm's law, E(n) approximately jxB/ne.n, thus establishing that Hall physics is dominating inside the diffusion region. The reconnection rate is fast, approximately 0.1. We show that strong parallel currents flow along the separatrices; they are correlated with observations of high-frequency Langmuir/upper hybrid waves.     

Segregation instabilities of moving interfaces

The segregation of solute particles on a moving interface leads to the appearance of two types of instabilities near competing velocity thresholds. This behavior is shown to occur in a variety of exactly solvable models where the interface motion is coupled to a diffusion process of the solute particles. These models directly apply to the propagation of internal domain walls, but can also be generalized to surfaces of growing crystals in the kinetics-limited regime.     

各向异性扩散DLA集团的豪斯道夫维数与标度性质

讨论了DLA集团的各向异性扩散效应.计算机模拟证实了具有各向异性扩散规则的DLA集团有严格的菱形结构.导出了一个粒子的各向异性扩散的新方程，计算了各向异性扩散DLA集团的豪斯道夫维数，结果表明，有效外半角β_eff=min(β_ix,β_iy).讨论了各向异性扩散DLA集团的广义维数，使用修改的楔模型得到了广义维数D_q的表达式. 关键词：     

Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations

We study a general class of nonlinear mean field Fokker-Planck equations in relation with an effective generalized thermodynamical (E.G.T.) formalism. We show that these equations describe several physical systems such as: chemotaxis of bacterial populations, Bose-Einstein condensation in the canonical ensemble, porous media, generalized Cahn-Hilliard equations, Kuramoto model, BMF model, Burgers equation, Smoluchowski-Poisson system for self-gravitating Brownian particles, Debye-Hückel theory of electrolytes, two-dimensional turbulence... In particular, we show that nonlinear mean field Fokker-Planck equations can provide generalized Keller-Segel models for the chemotaxis of biological populations. As an example, we introduce a new model of chemotaxis incorporating both effects of anomalous diffusion and exclusion principle (volume filling). Therefore, the notion of generalized thermodynamics can have applications for concrete physical systems. We also consider nonlinear mean field Fokker-Planck equations in phase space and show the passage from the generalized Kramers equation to the generalized Smoluchowski equation in a strong friction limit. Our formalism is simple and illustrated by several explicit examples corresponding to Boltzmann, Tsallis, Fermi-Dirac and Bose-Einstein entropies among others.     

Density and current response functions in strongly disordered electron systems: diffusion,electrical conductivity and Einstein relation

We study noninteracting quantum charged particles (electron gas) subject to a strong random potential and perturbed by a weak classical electromagnetic field. We examine consequences of gauge invariance and charge conservation in the space of Bloch waves. We use two specific forms of the Ward identity between the one- and two-particle averaged Green functions to establish exact relations between the density and current response functions. In particular, we find precise conditions under which we can extract the current-current from the density-density correlation functions and vice versa. We use these results to prove a formula relating the density response and the electrical conductivity in strongly disordered systems. We introduce quantum diffusion as a response function that reduces to the diffusion constant in the static limit. We then derive Ficks law, a quantum version of the Einstein relation and prove the existence of the diffusion pole in the quasistatic limit of the zero-temperature electron-hole correlation function. We show that the electrical conductivity controls the long-range spatial fluctuations of the electron-hole correlation function only in the static limit.Received: 10 June 2003, Published online: 22 September 2003PACS: 72.10.Bg General formulation of transport theory - 72.15.Eb Electrical and thermal conduction in crystalline metals and alloys - 72.15.Qm Scattering mechanisms and Kondo effect     

Multiparticle interference, Greenberger-Horne-Zeilinger entanglement, and full counting statistics

We investigate the quantum transport in a generalized N-particle Hanbury Brown-Twiss setup enclosing magnetic flux, and demonstrate that the Nth-order cumulant of current cross correlations exhibits Aharonov-Bohm oscillations, while there is no such oscillation in all the lower-order cumulants. The multiparticle interference results from the orbital Greenberger-Horne-Zeilinger entanglement of N indistinguishable particles. For sufficiently strong Aharonov-Bohm oscillations the generalized Bell inequalities may be violated, proving the N-particle quantum nonlocality.     

Knudsen Gas in a Finite Random Tube: Transport Diffusion and First Passage Properties

We consider transport diffusion in a stochastic billiard in a random tube which is elongated in the direction of the first coordinate (the tube axis). Inside the random tube, which is stationary and ergodic, non-interacting particles move straight with constant speed. Upon hitting the tube walls, they are reflected randomly, according to the cosine law: the density of the outgoing direction is proportional to the cosine of the angle between this direction and the normal vector. Steady state transport is studied by introducing an open tube segment as follows: We cut out a large finite segment of the tube with segment boundaries perpendicular to the tube axis. Particles which leave this piece through the segment boundaries disappear from the system. Through stationary injection of particles at one boundary of the segment a steady state with non-vanishing stationary particle current is maintained. We prove (i) that in the thermodynamic limit of an infinite open piece the coarse-grained density profile inside the segment is linear, and (ii) that the transport diffusion coefficient obtained from the ratio of stationary current and effective boundary density gradient equals the diffusion coefficient of a tagged particle in an infinite tube. Thus we prove Fick’s law and equality of transport diffusion and self-diffusion coefficients for quite generic rough (random) tubes. We also study some properties of the crossing time and compute the Milne extrapolation length in dependence on the shape of the random tube.     

Diffusion in inhomogeneous media

The problem is to establish the correct diffusion equation in a medium that is inhomogeneous and whose temperature also varies in space. As a special model we study particles whose phase space distribution obeys Kramers' equation with a generalized collision operator. In the usual limit of strong collisions a diffusion equation is obtained. This equation contains additional drift terms, which depend on the form of the collision operator. They cannot be expressed as a mobility and a diffusion coefficient, unless the decay law of the velocity happens to be linear. Conclusion: no universal form of the diffusion equation exists, but each system has to be studied individually.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Active colloidal suspensions exhibit polar order under gravity

Recently, the steady sedimentation profile of a dilute suspension of chemically powered colloids was studied experimentally [J. Palacci et al., Phys. Rev. Lett. 105, 088304 (2010)]. It was found that the sedimentation length increases quadratically with the swimming speed of the active Brownian particles. Here we investigate theoretically the sedimentation of self-propelled particles undergoing translational and rotational diffusion. We find that the measured increase of the sedimentation length is coupled to a partial alignment of the suspension with the mean swimming direction oriented against the gravitational field. We suggest realistic parameter values to observe this polar order. Furthermore, we find that the dynamics of the active suspension can be derived from a generalized free energy functional.