Stochastic Particle Transport Research Articles

LAST – a Library And Stochastic Transport tool

A new stochastic particle transport tool named LAST has been developed to allow seamless integral data assimilation on nuclear reaction model parameters during the evaluation process of nuclear data. The present work demonstrates its capability to perform actuate once-through information propagation from pre-processed application library to integral multiplication factor. Exact perturbation on reactivity is the starting point of the integral feedback on nuclear reaction model parameters. Its implementation in LAST is also shown.

Stochastic particle transport by deep-water irregular breaking waves

Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results by Deike et al. (J. Fluid Mech., vol. 829, 2017, pp. 364–391) and Pizzo et al. (J. Phys. Oceanogr., vol. 49, no. 4, 2019, pp. 983–992) have indicated transport by deep-water breaking waves is enhanced compared with non-breaking waves. To model particle transport in irregular waves, some of which break, we develop a stochastic differential equation describing both mean particle transport and its uncertainty. The equation combines a Brownian motion, which captures non-breaking drift-diffusion effects, and a compound Poisson process, which captures jumps in particle positions due to breaking. From the corresponding Fokker–Planck equation for the evolution of the probability density function for particle position, we obtain closed-form expressions for its first three moments. We corroborate these predictions with new experiments, in which we track large numbers of particles in irregular breaking waves. For breaking and non-breaking wave fields, our experiments confirm that the variance of the particle position grows linearly with time, in accordance with Taylor's single-particle dispersion theory. For wave fields that include breaking, the compound Poisson process increases the linear growth rate of the mean and variance and introduces a finite skewness of the particle position distribution.

Tensor-network approaches to counting statistics for the current in a boundary-driven diffusive system

We apply tensor networks to counting statistics for the stochastic particle transport in an out-of-equilibrium diffusive system. This system is composed of a one-dimensional channel in contact with two particle reservoirs at the ends. Two tensor-network algorithms, namely, density matrix renormalization group and time evolving block decimation, are respectively implemented. The cumulant generating function for the current is numerically calculated and then compared with the analytical solution. Excellent agreement is found, manifesting the validity of these approaches in such an application. Moreover, the fluctuation theorem for the current is shown to hold.

Universal and Non-Universal Features in the Random Shear Model

The stochastic transport of particles in a disordered two-dimensional layered medium, driven by correlated y-dependent random velocity fields is usually referred to as random shear model. This model exhibits a superdiffusive behavior in the x direction ascribable to the statistical properties of the disorder advection field. By introducing layered random amplitude with a power-law discrete spectrum, the analytical expressions for the space and time velocity correlation functions, together with those of the position moments, are derived by means of two distinct averaging procedures. In the case of quenched disorder, the average is performed over an ensemble of uniformly spaced initial conditions: albeit the strong sample-to-sample fluctuations, and universality appears in the time scaling of the even moments. Such universality is exhibited in the scaling of the moments averaged over the disorder configurations. The non-universal scaling form of the no-disorder symmetric or asymmetric advection fields is also derived.

On the dynamic role of energy in underdamped particle motion

In his seminal work on stochastic particle transport in periodic potentials [1], claims that the overall energy, in underdamped conditions, plays the role of a slow dynamic variable, compared to position and velocity. The scope of this communication is to show that this claim is incorrect and that the conditions for the existence of a slow-invariant manifold fail in the low-friction limit. Nevertheless, the energy-based analysis developed by Risken to predict particle mobility remains substantially correct.

Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest Times

We introduce a persistent random walk model for the stochastic transport of particles involving self-reinforcement and a rest state with Mittag–Leffler distributed residence times. The model involves a system of hyperbolic partial differential equations with a non-local switching term described by the Riemann–Liouville derivative. From Monte Carlo simulations, we found that this model generates superdiffusion at intermediate times but reverts to subdiffusion in the long time asymptotic limit. To confirm this result, we derived the equation for the second moment and find that it is subdiffusive in the long time limit. Analyses of two simpler models are also included, which demonstrate the dominance of the Mittag–Leffler rest state leading to subdiffusion. The observation that transient superdiffusion occurs in an eventually subdiffusive system is a useful feature for applications in stochastic biological transport.

Stochastic impedance

The concept of impedance, which characterises the current response to a periodical driving, is introduced in the context of stochastic transport. In particular, we calculate the impedance for an exactly solvable model, namely the stochastic transport of particles through a single-level quantum dot.

Computer-aided generation and lung deposition modeling of nano-scale particle aggregates

The study sets its main focus on the introduction of a random-walk-based model for the generation of variably shaped particle aggregates consisting of a predefined number of spherical components. With the help of a well-defined algorithm, the user is enabled to select between isodimensional, chain-like and platelet-like aggregates, for which related aerodynamic parameters (dynamic shape factors, volume-equivalent diameters, aerodynamic diameters) are determined automatically. The theoretical approach for random aggregate construction is directly connected with the previously developed stochastic particle transport and deposition model. Thereby, individually shaped aggregates may be provided for each random-walk scenario taking place in the almost realistic lung structure. Preliminary application of the aggregate generation model was carried out by assuming single components with a constant diameter of 1 nm and unit-density (1 g cm−3) and variably shaped aggregates consisting of 10, 100 and 1000 components. Inhalation of the aggregate-loaded aerosol into lungs of average size (FRC = 3300 mL) was supposed to take place under sitting, light-exercise and heavy-exercise conditions. Results obtained from deposition modeling clearly show that, independent of aggregate geometry, total deposition declines with increasing number of components included in the particulate construct, but experiences a continuous enhancement with rising inhalation flow rate. Among the predefined geometric categories, platelet-like aggregates are distinguished by lowest deposition and isodimensional clusters by highest. While isodimensional aggregates preferentially deposit in the extrathoracic and bronchial airways, chain-like and platelet-like aggregates exhibit a significantly increased tendency to hit the alveolar walls.

Phase transitions in Brownian pumps.

We study stochastic particle transport between two reservoirs along a channel, where the particles are pumped against a bias by a traveling wave potential. It is shown that phase transitions of period-averaged densities or currents occur inside the channel when exclusion interactions between the particles are taken into account. These transitions reflect those known for the asymmetric simple exclusion process. We argue that their occurrence is a generic feature of Brownian motors operating in open systems.

Simulation of Nanotube Deposition in the Human Respiratory Tract

The study investigates the behavior of singlewalled carbon nanotubes (SWCNT) and multiwalled carbon nanotubes (MWCNT) in the human respiratory tract. Particle geometries were modeled by assuming different dynamic shape factors for nanotubes oriented parallel and nanotubes oriented perpendicular to the air stream. Based upon these assumptions, particle-specific aerodynamic diameters were computed. Mathematical approaches to particle geometry were implemented into a stochastic particle transport and deposition model which is founded on the Monte Carlo concept for the generation of high numbers of particle trajectories through the lung airways. Nanotube deposition was simulated for sitting breathing conditions and heavywork breathing conditions. According to the results obtained from the model, SWCNT are characterized by significantly higher total deposition than MWCNT. With increasing respiratory flow rate and aspect ratio, total deposition of both types of nanotubes is slightly reduced. MWCNT have the tendency to be deposited in more distal lung regions than SWCNT. Hygienic consequences of this deposition behavior are discussed.

Stochastic transport of particles across single barriers

Transport phenomena of interacting particles are of high interest for many applications in biology and mesoscopic systems. Here we present measurements on colloidal particles, which are confined in narrow channels on a substrate and interact with a barrier, which impedes the motion along the channel. The substrate of the particle is tilted in order for the particles to be driven towards the barrier and, if the energy gained by the tilt is large enough, surpass the barrier by thermal activation. We therefore study the influence of this barrier as well as the influence of particle interaction on the particle transport through such systems. All experiments are supported with Brownian dynamics simulations in order to complement the experiments with tests of a large range of parameter space which cannot be accessed in experiments.

The geometry of inertial particle mixing in urban flows, from deterministic and random displacement models

We use Lagrangian measures, depicted by finite-time Lyapunov exponents, to characterize transport patterns of inertial pollutant particles formed in urban flows. Motivated by actual events we focus on flows in realistic urban geometry. Both deterministic and stochastic particle transport patterns have been identified, as inertial Lagrangian coherent structures. For the deterministic case, the organizing structures are well-defined and we extract them at different hours of a day to reveal the variability of coherent patterns. For the stochastic case, we use a random displacement model for fluid particles and derive the governing equation for inertial particles to examine the change in organizing structures due to “zeroth-order” random noise. We find that, (1) the Langevin equation for inertial particles can be reduced to a random displacement model; (2) using random noise based on inhomogeneous turbulence, whose diffusivity is derived from k − ε models, major coherent structures survive to organize local flow patterns and weaker structures are smoothed out due to random motion.

Stochastic transport of particles in straining flows

Important features associated with the segregration of particles in turbulent flow are investigated by considering the statistical distribution (phase-space number density) of particles subject to the combined effects of straining flow and stochastic forcing. A Fokker-Planck model is used to obtain results for the phase-space distributions of particles that are entrained into straining flow fields. The analysis shows that, in marked contrast to the zero strain case, nonsingular steady-state distributions are generated, and also confirms that the diffusional effect resulting from stochastic forcing is sufficient to offset the otherwise singular distributions that would result from the indefinite accumulation of particles along stagnation lines. The influence of particle inertia (Stokes number) on the form of the resulting distributions is considered and several significant results are observed. The influence of strain rate on the attenuation of particle kinetic stresses is quantified and explained. The development of large third-order velocity moments is observed for Stokes numbers above a critical value. The mechanism underlying this phenomenon is seen to be a generic feature of particle transport in flows where vortex structures induce local counterflows of particles. The system therefore provides an ideal test for closure models for third-order moments of particle velocities, and here the standard Chapman-Enskog approximation is assessed.

Motion and twisting of magnetic particles ingested by alveolar macrophages in non-smokers and smokers: Implementation of viscoelasticity

Ferrimagnetic iron oxide particles were inhaled by 17 healthy volunteers (9 non-smokers, 8 smokers), and the retained particles were magnetized and detected by a SQUID. Stochastic particle transport due to cytoskeletal reorganizations within macrophages (relaxation) and directed particle motion in a weak magnetic twisting field were investigated with respect to viscous and elastic properties of the cytoskeleton. Relaxation and cytoskeletal stiffness were not influenced by cigarette smoking. Relaxation and particle twisting revealed a non-Newtonian viscosity with a pure viscous and a viscoelastic compartment. Viscous and elastic data obtained from relaxation correlated with particle twisting, indicating that the proposed simple model is a reasonable approximation of cytoskeletal mechanical properties.

Turbulent transport of ions with large Larmor radii

The stochastic transport of particles with large Larmor radii is studied using the decorrelation trajectory method, which is able to describe the nonlinear process of intrinsic trajectory trapping. The diffusion coefficient is determined for wide ranges of the parameters in order to provide a quantitative description of the possible effects that the turbulence can have on large Larmor radius particles.

Relativistic quasilinear diffusion in axisymmetric magnetic geometry for arbitrary-frequency electromagnetic fluctuations

A relativistic bounce-averaged quasilinear diffusion equation is derived to describe stochastic particle transport associated with arbitrary-frequency electromagnetic fluctuations in a nonuniform magnetized plasma. Expressions for the elements of a relativistic quasilinear diffusion tensor are calculated explicitly for magnetically trapped particle distributions in axisymmetric magnetic geometry in terms of gyro-drift-bounce wave-particle resonances. The resonances can destroy any one of the three invariants of the unperturbed guiding-center Hamiltonian dynamics.

Relativistic bounce-averaged quasilinear diffusion equation for low-frequency electromagnetic fluctuations

A relativistic bounce-averaged quasilinear diffusion equation is derived to describe stochastic particle transport associated with low-frequency electromagnetic fluctuations in a nonuniform magnetized plasma. Expressions for the relativistic quasilinear diffusion coefficients are calculated explicitly for magnetically-trapped particle distributions in axisymmetric magnetic geometry in terms of drift-bounce resonant contributions associated with low-frequency fluctuations which conserve the first adiabatic invariant.

The Backward Theory of Stochastic Particle Transport withMultiple Emission Sources

The backward theory of stochastic transport is elaborated for thecase of subcritical systems with a source that emits more than oneparticle in each source emission event. Examples of such sources arespontaneous fission sources, such as 252Cf, and, moreimportant, spallation sources. Possible forms of the sourcedistribution describing e.g. a spallation source in a thin target arediscussed. The essence of the theory is the generalization of aformula due to Bartlett, connecting the probability distribution dueto a single particle, with that due to a continuous source, to thecase of multiple emission sources. From this formula, expressions arederived for first and second order moments of the particledistribution (or the detector count), induced by a multiple source,expressed as integrals over similar moments of the single-particleinduced distribution. These expressions are suitable for thecalculation of the Feynmann-alpha and Rossi-alpha formulae formultiple emission sources.

Stochastic particle transport in a magnetic island due to electrostatic drift waves

The effect of poloidally mode coupled, ballooning type electrostatic drift waves on a magnetic island has been studied both analytically and numerically. It has been shown quantitatively that particle orbits become stochastic and their behavior can be a possible candidate for the radial plasma transport across a magnetic island of a tokamak. The transport is significant in that it takes place even when the flux surface is not destroyed. The mechanism of the stochasticity generation is understood as an overlapping of secondary islands caused by resonance between periodic particle motions in the magnetic island and Fourier modes of E×B drift due to the electrostatic drift waves. The diffusion process perpendicular to magnetic surface has been analyzed by approximating the distribution to the Gaussian type. In addition, local diffusion process in the vicinity of Kolmogorov, Arnold, and Moser surfaces has been discussed.

Magnetic fluctuation induced transport in MST (abstract)a)

We made local measurements of the magnetic fluctuation induced transport of particles and energy in the outer region (r/a≳0.75) of the MST reversed field pinch plasma. These measurements allow comparison with the Rochester–Rosenbluth stochastic diffusion coefficients. An electrostatic electron energy analyzer and fast pyrobolometer were employed in combination with magnetic pickup coils to directly measure the correlated products 〈J̃θB̃r〉 and 〈q̃∥B̃r〉, respectively. Magnetic fluctuation induced transport of both particles and energy is negligible at the extreme edge of MST (r/a≳0.9), but increases to a level consistent with estimates of the entire particle and energy flux as the core is approached (5×1021 m−2 s−1 and 105 W m−2). Stochastic particle transport is limited by an apparent ambipolar electric field to the ion stochastic diffusion rate (D=50 m2 s−1), the electron transport being dominated by the energetic component of the distribution (E≳50 eV). The measured heat transport is consistent with the convective energy transport carried by the fast electron component (Teffective=100 eV).