Diffusive Transport Of Particles Research Articles

Flat Spectra of Energetic Particles in Interplanetary Shock Precursors

The observed energy spectra of accelerated particles at interplanetary shocks often do not match the diffusive shock acceleration (DSA) theory predictions. In some cases, the particle flux forms a plateau over a wide range of energies, extending upstream of the shock for up to seven flux e-folds before submerging into the background spectrum. Remarkably, at and downstream of the shock we have studied in detail, the flux falls off in energy as ϵ −1, consistent with the DSA prediction for a strong shock. The upstream plateau suggests a particle transport mechanism different from those traditionally employed in DSA models. We show that a standard (linear) DSA solution based on a widely accepted diffusive particle transport with an underlying resonant wave–particle interaction is inconsistent with the plateau in the particle flux. To resolve this contradiction, we modify the DSA theory in two ways. First, we include a dependence of the particle diffusivity κ on the particle flux F (nonlinear particle transport). Second, we invoke short-scale magnetic perturbations that are self-consistently generated by, but not resonant with, accelerated particles. They lead to the particle diffusivity increasing with the particle energy as ∝ϵ 3/2 that simultaneously decreases with the particle flux as 1/F. The combination of these two trends results in the flat spectrum upstream. We speculate that nonmonotonic spatial variations of the upstream spectrum, apart from being time-dependent, may also result from non-DSA acceleration mechanisms at work upstream, such as stochastic Fermi or magnetic pumping acceleration.

Modelling diffusive transport of particles interacting with slit nanopore walls: The case of fullerenes in toluene filled alumina pores

Accurate modeling of diffusive transport of nanoparticles across nanopores is a particularly challenging problem. The reason is that for such narrow pores the large surface-to-volume ratio amplifies the relevance of the nanoscopic details and of the effective interactions at the interface with pore walls. Close to the pore wall, there is no clear separation between the length scales associated with molecular interactions, layering of the solvent at the interface with the pore and the particle size. Therefore, the standard hydrodynamic arguments may not apply and alternative solutions to determining average transport coefficients need to be developed. We here address this problem by offering a multiscale ansatz that uses effective potentials determined from molecular dynamics simulations to parametrise a four state stochastic model for the positional configuration of the particle in the pore. This is in turn combined with diffusivities in the centre of the pore and at the pore wall to calculate the average diffusion constant. We apply this model to the diffusion of fullerenes in a toluene filled slit nanopore and calculate the mean diffusion coefficient as a function of the pore size. We show that the accuracy of our model is affected by the partial slip of the toluene on the pore wall.

Analysis of a Hidden-Memory Variably Distributed-Order Time-Fractional Diffusion Equation

We analyze the well-posedness and regularity of a variably distributed-order time-fractional diffusion equation (tFDE) with a hidden-memory fractional derivative, which provide a competitive means to describe the anomalously diffusive transport of particles in heterogeneous media. We prove that the solution of a variably distributed-order tFDE has weak singularity at the initial time t=0 which depends on the upper bound of a distributed order α¯(0).

Analysis and numerical approximation to time-fractional diffusion equation with a general time-dependent variable order

Variable-order time-fractional diffusion equations (tFDEs), in which the variable fractional order accommodates the fractal dimension change of the surrounding medium via the Hurst index, provide a competitive instrument to describe anomalously diffusive transport of particles through deformable heterogeneous materials. We analyze the mapping properties of the fractional integral with a general time-dependent variable order, based on which we prove the well-posedness and smoothing properties of corresponding variable-order tFDE model in multiple space dimensions. We then derive and analyze a fully discretized finite element approximation, in which we develop a novel decomposition of L-1 discretization coefficients to prove an optimal-order error estimate of the numerical scheme based only on the regularity assumptions on the data. Numerical experiments are performed to substantiate the theoretical findings.

Enhanced diffusion by reversible binding to active polymers.

Cells are known to use reversible binding to active biopolymer networks to allow diffusive transport of particles in an otherwise impenetrable mesh. We here determine the motion of a particle that experiences random forces during binding and unbinding events while being constrained by attached polymers. Using Monte-Carlo simulations and a statistical mechanics model, we find that enhanced diffusion is possible with active polymers. However, this is possible only under optimum conditions that has to do with the relative length of the chains to that of the plate. For example, in systems where the plate is shorter than the chains, diffusion is maximum when many chains have the potential to bind but few remain bound at any one time. Interestingly, if the chains are shorter than the plate, we find that diffusion is maximized when more active chains remain transiently bound. The model provides insight into these findings by elucidating the mechanisms for binding-mediated diffusion in biology and design rules for macromolecular transport in transient synthetic polymers.

Bayesian analysis of turbulent transport coefficients in 2D interchange dominated ExB turbulence involving flow shear

While turbulent transport is known to dominate the radial particle and energy transport in the plasma edge, a self-consistent description of turbulent transport in mean-field transport codes remains lacking. Mean-field closure models based on the turbulent kinetic energy (k ⊥) and turbulent enstrophy (ζ⊥) have recently been proposed to self-consistently model this transport. This contribution analyses the diffusive particle transport relations of these models by means of the Bayesian framework for parameter estimation and model comparison. The reference data includes a set of isothermal simulations that not only include the scrape-off layer (SOL) but also the outer core region (in which a drift wave-like model is activated) and a set of anisothermal SOL simulations, both obtained with the TOKAM2D turbulence code. This analysis shows that the k ⊥(–ζ⊥) model does not appropriately capture the diffusion coefficients for these new data sets, presumably due to the strong flows in the diamagnetic direction that appear in these new cases. While flow shear is expected to quench the turbulence and the turbulent transport, its effect was not explicitly taken into account in the earlier k ⊥(–ζ⊥) transport models. As flow shear provides a new mechanism for the decorrelation of the turbulence, we propose to introduce an additional time scale in the diffusive transport relation as . Inspiration is drawn from shear decorrelation times reported in literature to propose several new candidate models, which are then analysed in a Bayesian setting. This allowed identifying irrelevant terms for certain models and to rank all models according to the Bayesian evidence. While the new models accounting for shear do improve the match to the data, significant errors still remain. Also, no single model could be identified that performs best for all data sets.

Capacities and Optimal Input Distributions for Particle-Intensity Channels

This work introduces the particle-intensity channel (PIC) as a new model for molecular communication systems that includes imperfections at both transmitter and receiver and provides a new characterization of the capacity limits as well as properties of the optimal (capacity-achieving) input distributions for such channels. In the PIC, the transmitter encodes information, in symbols of a given duration, based on the probability of particle release, and the receiver detects and decodes the message based on the number of particles detected during the symbol interval. In this channel, the transmitter may be unable to control precisely the probability of particle release, and the receiver may not detect all the particles that arrive. We model this channel using a generalization of the binomial channel and show that the capacity-achieving input distribution for this channel always has mass points at probabilities of particle release of zero and one. To find the capacity-achieving input distributions, we develop a novel and efficient algorithm we call dynamic assignment Blahut-Arimoto (DAB). For diffusive particle transport, we also derive the conditions under which the input with two mass points is capacity-achieving.

Roles of Magnetospheric Convection on Nonlinear Drift Resonance Between Electrons and ULF Waves

AbstractIn the Earth's inner magnetosphere, charged particles can be accelerated and transported by ultralow frequency (ULF) waves via drift resonance. We investigate the effects of magnetospheric convection on the nonlinear drift resonance process, which provides an inhomogeneity factor S to externally drive the pendulum equation that describes the particle motion in the ULF wave field. The S factor, defined as the ratio of the driving amplitude to the square of the pendulum trapping frequency, is found to vary with magnetic local time and, as a consequence, oscillates quasi‐periodically at the particle drift frequency ωd. To better understand the particle behavior governed by the driven pendulum equation, we carry out simulations to obtain the evolution of electron distribution functions in energy and L‐shell phase space. We find that resonant electrons can remain phase trapped by the low‐m ULF waves under strong convection electric field, whereas for high‐m ULF waves, the electrons trajectories can be significantly modified. More interestingly, the electron drift frequency ωd is close to the nonlinear trapping frequency ωtr for intermediate‐m ULF waves, which corresponds to chaotic motion of resonant electrons. These findings shed new light on the nature of coherent and diffusive particle transport in the inner magnetosphere.

Biased diffusion in periodic potentials: Three types of force dependence of effective diffusivity and generalized Lifson-Jackson formula.

Diffusive transport of particles in a biased periodic potential is characterized by the effective drift velocity and diffusivity, which are functions of the biasing force. We derive a simple exact expression for the effective diffusivity and use it to show that the force dependence of this quantity may be a nonmonotonic function with a maximum [as shown in the work of Reimann et al. Phys. Rev. Lett. 87, 010602 (2001) for periodic sinusoidal potential] or with a minimum, or a monotonic function. The shape of the dependence is determined by the shape of the periodic potential.

A nonlinear energetic particle diffusion model with a variable source

We investigate analytically and numerically the effect of a time-dependent source in a nonlinear model of diffusive particle transport, based on the p-Laplacian equation. The equation has been used to explain the observed cosmic-ray distributions and it appears in fluid dynamics and other areas of applied mathematics. We derive self-similar solutions for a class of the particle source functions and develop approximate analytical solutions, based on an integral method. We also use the fundamental solution to obtain an asymptotic description of an evolving particle density profile, and we use numerical simulations to investigate the accuracy of the analytical approximations.

Anomalously slow transport in single-file diffusion with slow binding kinetics

We computationally study the effects of binding kinetics to the channel wall, leading to transient immobility, on the diffusive transport of particles within narrow channels, that exhibit single-file diffusion (SFD). We find that slow binding kinetics leads to an anomalously slow diffusive transport. Remarkably, the scaled diffusivity D[over ̂] characterizing transport exhibits scaling collapse with respect to the occupation fraction p of sites along the channel. We present a simple "cage-physics" picture that captures the characteristic occupation fraction p_{scale} and the asymptotic 1/p^{2} behavior for p/p_{scale}≳1. We confirm that subdiffusive behavior of tracer particles is controlled by the same D[over ̂] as particle transport.

Comparing Eddy‐Permitting Ocean Model Parameterizations via Lagrangian Particle Statistics in a Quasigeostrophic Setting

AbstractThis paper uses Lagrangian statistics—absolute dispersion, pair dispersion, and particle forecasting—to compare four eddy‐permitting models of idealized mesoscale ocean dynamics. The baseline model uses scale‐selective biharmonic damping of momentum to keep the velocity field smooth at the grid scale without overly smearing the partially resolved eddies. The second model uses a nonlinear space‐ and time‐varying Leith viscosity to absorb enstrophy near the grid scale without dissipating too much energy. The last two models use a strong biharmonic damping of momentum to keep the velocity field smooth at the grid scale; this dissipates an unrealistically large amount of kinetic energy, and the models add either deterministic or stochastic forcing to reinject this energy at larger scales. These models are called Jansen and Held models after Jansen and Held (2014, https://doi.org/10.1016/j.ocemod.2014.06.002). All four models correctly model the diffusive transport of particles over time scales more than a few weeks, as measured by the Lagrangian absolute dispersion, showing that all models correctly reproduce the large scales of coherent eddies. The Lagrangian relative dispersion (or pair dispersion) is more sensitive to structure at smaller scales in the velocity field. The Leith model has the least‐accurate relative dispersion, while the two Jansen and Held models have the most accurate. In initialized forecast experiments, there is very little difference in performance between the models.

Convective and diffusive particle transport in channels of periodic cross-section: comparison with experiment

This paper compares the results of a theoretical model with published experimental data investigating the potential use of a drift ratchet as a particle transport device. The drift ratchet of interest here involves the oscillation of a particle-laden fluid through a periodically shaped tube, combined with an exploitation of the Brownian motion of the small particles. Our theoretical results support the experimental evidence that, at these scales, the ratchet effect is not the predominant mechanism for facilitating particle transport. Rather, the tube geometry (but not orientation) and the form of the applied oscillating pressure gradient are the primary characteristics which determine the effectiveness of a device for particle transport. In particular, we find that transport is enhanced in a saw-tooth tube in comparison with a straight, cylindrical tube.

Diffusion tensor optical coherence tomography

In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.

Diffusion in pulsar wind nebulae: an investigation using magnetohydrodynamic and particle transport models

We study the transport of high-energy particles in pulsar wind nebulae (PWN) using three-dimensional MHD (see Porth et al. (2014) for details) and test-particle simulations, as well as a Fokker-Planck particle transport model. The latter includes radiative and adiabatic losses, diffusion, and advection on the background flow of the simulated MHD nebula. By combining the models, the spatial evolution of flux and photon index of the X-ray synchrotron emission is modelled for the three nebulae G21.5-0.9, the inner regions of Vela, and 3C 58, thereby allowing us to derive governing parameters: the magnetic field strength, average flow velocity and spatial diffusion coefficient. For comparison, the nebulae are also modelled with the semi-analytic Kennel & Coroniti (1984) model but the Porth et al. (2014) model generally yields better fits to the observational data. We find that high velocity fluctuations in the turbulent nebula (downstream of the termination shock) give rise to efficient diffusive transport of particles, with average P\'eclet number close to unity, indicating that both advection and diffusion play an important role in particle transport. We find that the diffusive transport coefficient of the order of $\sim2\times 10^{27} (L_{\rm s}/0.42\rm Ly) cm^{2}s^{-1}$ ($L_{\rm s}$ is the size of the termination shock) is independent of energy up to extreme particle Lorentz factors of $\gamma_{p}\sim10^{10}$.

Particle transport analysis of the density build-up after the L–H transition in ASDEX Upgrade

Predictive-iterative modelling has been performed to investigate the role of convective and diffusive particle transport in the edge during the density build-up after the L–H transition. For the time-dependent modelling, the 1.5D radial transport code ASTRA has been used. The convective velocity, diffusion coefficient and the particle source profiles have been parameterized. Their parameters were varied until the best match of the modelling to the density measurements was found. The extensive parameter scans show that the density build-up can be reproduced by assuming only a diffusive edge transport barrier (ETB) with reduced diffusion coefficient at the edge with respect to the core values. Moreover, the replacement of the diffusive ETB by a strong inwards directed convective velocity at the edge (edge pinch) did not succeed in describing the data. This indicates that a diffusive ETB is required to explain the density build-up. However, the addition of an edge pinch to the diffusive ETB barrier slightly enhances the agreement between modelling and experiment. The best agreement was found with an edge diffusion coefficient of 0.031 m2 s−1 and an edge convective velocity of −0.5 m s−1. Because of the large uncertainties in the source, it is not possible to pin down the exact value for the additional edge pinch. An upper limit for a possible edge convective velocity of −5 m s−1 was estimated. These findings could also be confirmed by analysing H-mode phases of a collisionality scan, in which the normalized collisionality varied from 3.5 to 5.5 at the pedestal top.

Inertial Particle Deposition in a 90° Laminar Flow Bend: An Eulerian Fluid Particle Approach

A numerical model for the simulation of aerosol flows via an Eulerian–Eulerian, one-way coupled, two-phase flow description is presented. An in-house computational fluid dynamics code is used to simulate the gaseous (continuous) phase, whereas a modified convective diffusion equation models particle transport. The convective diffusion equation, which includes inertial, gravitational, and diffusive particle transport, is solved by computational fluid dynamics techniques. The model is validated by comparing the calculated laminar fluid flow and particle deposition fractions to analytical and experimentally studied aerosol flows in a laminar flow 90° bend of circular cross section available in the literature. Model predictions are also compared with numerical predictions of Eulerian-Lagrangian models. Particle concentration profiles at different cross sections are calculated, and deposition sites on the wall boundary are indicated. For the range of studied particle diameters, the Eulerian–Eulerian model predicts deposition fractions satisfactorily, being in good agreement with the experimental data.

Artificial Brownian motors: Controlling transport on the nanoscale

In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with unbiased external input signals, deterministic and random alike, can assist directed motion of particles at submicron scales. In such cases, one speaks of ``Brownian motors.'' In this review the constructive role of Brownian motion is exemplified for various physical and technological setups, which are inspired by the cellular molecular machinery: the working principles and characteristics of stylized devices are discussed to show how fluctuations, either thermal or extrinsic, can be used to control diffusive particle transport. Recent experimental demonstrations of this concept are surveyed with particular attention to transport in artificial, i.e., nonbiological, nanopores, lithographic tracks, and optical traps, where single-particle currents were first measured. Much emphasis is given to two- and three-dimensional devices containing many interacting particles of one or more species; for this class of artificial motors, noise rectification results also from the interplay of particle Brownian motion and geometric constraints. Recently, selective control and optimization of the transport of interacting colloidal particles and magnetic vortices have been successfully achieved, thus leading to the new generation of microfluidic and superconducting devices presented here. The field has recently been enriched with impressive experimental achievements in building artificial Brownian motor devices that even operate within the quantum domain by harvesting quantum Brownian motion. Sundry akin topics include activities aimed at noise-assisted shuttling other degrees of freedom such as charge, spin, or even heat and the assembly of chemical synthetic molecular motors. This review ends with a perspective for future pathways and potential new applications.

A Co-Condensation Model for In-Flight Synthesis of Metal-Carbide Nanoparticles in Thermal Plasma Jet

We present a theoretical analysis of the formation, growth, and transport of two-component nanoparticles in thermal plasma jet. The approach of the aerosol science and the idea of multicomponent co-condensation are employed for the analysis. The processes of homogeneous nucleation, heterogeneous growth, and coagulations due to Brownian collisions are considered in combination with the convective and diffusive transport of particles and the reacting gases within an axisymmetric domain. As a particular example, the authors study multicomponent co-condensation of metal-carbide nanoparticles from various precursors in a DC plasma gun operating in an argon atmosphere.

Modelling of the in-flight synthesis of TaC nanoparticles from liquid precursor in thermal plasma jet

A simple and efficient numerical model describing the processes of nucleation, growth and transport of multi-component nanoparticles is developed. The approach is conceptually similar to the classical method of moments but can be applied to co-condensation of several substances. The processes of homogeneous nucleation, heterogeneous growth, and coagulations due to Brownian collisions are considered in combination with the convective and diffusive transport of particles and reacting gases within multi-dimensional geometries. The model is applied to the analysis of multi-component co-condensation of TaC nanoparticles within a dc plasma reactor.