Distribution Of Particle Displacements Research Articles

An exactly solvable model for non-Fickian transport in dynamically heterogeneous media

Abstract Diffusion, observed in various condensed phases, finds its theoretical background in Einstein’s theory of Brownian motion, characterized by the linear time-dependence of mean square displacement (MSD) denoting Fickian behavior and the Gaussian distribution of particle displacement. Nevertheless, diverse systems exhibit either non-linear, non-Fickian time-dependence of the MSD or non-Gaussian displacement distribution. Montroll and Weiss’s continuous-time random walk (CTRW) model and the stochastic diffusivity (SD) model have provided insights into anomalous diffusion phenomena and Fickian-yet-non-Gaussian transport in dynamically heterogeneous environments, respectively. Building upon these approaches, Song et al developed a generalized transport equation with an environment-dependent diffusion kernel, providing a quantitative explanation for non-Fickian MSD and non-Gaussian displacement distribution. Based on the generalized transport equation, this study introduces an exactly solvable model for a non-Gaussian displacement distribution, accommodating arbitrary time profiles in its MSD, including both Fickian and non-Fickian behaviors. Our findings confirm the model’s capability in describing such transport processes. Furthermore, the proposed model unifies the CTRW model under fast environmental fluctuations and the SD model under Fickian time dependencies, making it suitable for understanding tracer particle motion within explicit solvent or complex media.

DEM evaluation of the mobilization of mechanisms governing the geogrid-aggregate interaction

Pullout tests of geogrids embedded in a single clean aggregate type were conducted and subsequently simulated to investigate the geogrid-aggregate interaction mechanisms. The Discrete Element Method (DEM) model, which was carefully calibrated and validated against the experimental results, was adopted for the simulations. The three-dimensional deformation behavior of geogrids and the shear behavior of aggregates with complex particle shapes were successfully predicted. Analysis of the particle displacement distribution and contact force distribution allowed determination of the particle-scale interaction mechanisms of the geogrid-aggregate system. In particular, the mobilization of pullout resistance components was tracked based on the contact identification method and the influence of geogrid stiffness on the mobilization of pullout resistance components could be evaluated. The results indicate that the activation of the different geogrid resistance components that develop during pullout are not synchronized. During the pullout process, DEM predictions indicate that the frictional resistance of the geogrid is activated first, peaking rapidly and being followed by the development of passive resistance of the transverse ribs. Also, an increased geogrid stiffness was found to enhance the passive resistance of the transverse ribs but to influence only negligibly the frictional resistance.

A new macro- and micro- coupling model of barrier dam soil

Barrier dams are widely distributed worldwide. It is highly important to accurately evaluate the safety and emergency response of barrier dams. However, the stressstrain relationship of barrier dam soil, which is an important issue for the safety evaluation of barrier dams, has not been elucidated clearly because of its complex composition and wide particle gradation. Based on the proposed macro- and micro- coupling modeling scheme, a series of CT triaxial tests were carried out on barrier dam soil to observe the macroscopic and microscopic behavior. Based on the particle displacement distribution, a fabric evolution rate was proposed as an index to describe the evolution of fabric behaviors. A significant correlation was detected between the shear band fabric evolution rate and the macroscopic mechanical properties of the soil. The fabric evolution equation, modulus evolution equation and Poisson's ratio evolution equation were proposed to set up a new macro- and micro- coupling model for barrier dam soil. The model has only five parameters that have definite physical meanings and can be easily determined by a series of triaxial tests. The validity of the proposed model was verified by different types of tests of barrier dam soil and soilrock mixtures. The model can reasonably describe the fundamental properties of barrier dam soil with wide particle gradation. The proposed model established by macro- and micro- coupling modeling considers the relationship between macroscopic mechanical properties and microscopic fabric behavior, which is suitable for barrier dam soils with wide particle gradations.

Non-Gaussian Displacements in Active Transport on a Carpet of Motile Cells.

We study the dynamics of micron-sized particles on a layer of motile cells. This cell carpet acts as an active bath that propels passive tracer particles via direct mechanical contact. The resulting nonequilibrium transport shows a crossover from superdiffusive to normal-diffusive dynamics. The particle displacement distribution is distinctly non-Gaussian even at macroscopic timescales exceeding the measurement time. We obtain the distribution of diffusion coefficients from the experimental data and introduce a model for the displacement distribution that matches the experimentally observed non-Gaussian statistics. We argue why similar transport properties are expected for many composite active matter systems.

Development of calculation model for designing temperature characteristics of double-layered thickness-shear resonator

A calculation model for predicting the temperature characteristics of the double-layered resonator (DRL) was developed by using the total strain ratio including the influence of the waves reflected at the bonding boundary. The validity of the model proposed was examined from the comparison between the measured and calculated results for a DRL specimen consisting of 129.55°Y- and 0°Y-quartz substrates. The calculation results of the model proposed demonstrated that it is possible to predict the trends of changes in experimental values of temperature characteristics not only in the 1st-order mode but also in the higher-order modes. In addition, the changes in the particle displacement distribution and temperature characteristics of the DLR obtained by the model proposed were also in good agreement with the results of finite element method analysis. The proposed model is expected to greatly contribute to the design of DLRs with high excitation efficiency and excellent temperature characteristics.

Particle dispersion through porous media with heterogeneous attractions.

Porous media used in many practical applications contain natural spatial variations in composition and surface charge that lead to heterogeneous physicochemical attractions between the media and transported particles. We performed Stokesian dynamics (SD) simulations to examine the effects of heterogeneous attractions on quiescent diffusion and hydrodynamic dispersion of particles within geometrically ordered arrays of nanoposts. We find that transport under quiescent conditions occurs by two mechanisms, diffusion through the void space and intermittent hopping between the attractive wells of different nanoposts. As the attraction heterogeneity increases, the latter mechanism becomes dominant, resulting in an increase in the particle trajectory tortuosity, deviations from Gaussian behavior in the particle displacement distributions, and a decrease in the long-time particle diffusivity. Similarly, under flow conditions corresponding to low Péclet number (Pe), increased attraction heterogeneity leads to transient localization near the nanoposts, resulting in a broadening of the particle distribution and enhanced longitudinal dispersion in the direction of flow. At high Pe where advection strongly dominates, however, the longitudinal dispersion coefficient is insensitive to attraction heterogeneity and exhibits Taylor-Aris dispersion behavior. Our findings provide insight into how heterogeneous interactions may influence particle transport in complex 3-D porous media.

Dynamical crossovers and correlations in a harmonic chain of active particles.

We explore the dynamics of a tracer in an active particle harmonic chain, investigating the influence of interactions. Our analysis involves calculating mean-squared displacements (MSDs) and space-time correlations through Green's function techniques and numerical simulations. Depending on chain characteristics, i.e., different time scales determined by interaction stiffness and persistence of activity, tagged-particle MSDs exhibit ballistic, diffusive, and single-file diffusion (SFD) scaling over time, with crossovers explained by our analytic expressions. Our results reveal transitions in bulk particle displacement distributions from an early-time bimodal to late-time Gaussian, passing through regimes of unimodal distributions with finite support and negative excess kurtosis and longer-tailed distributions with positive excess kurtosis. The distributions exhibit data collapse, aligning with ballistic, diffusive, and SFD scaling in the appropriate time regimes. However, at much longer times, the distributions become Gaussian. Finally, we derive analytic expressions for steady-state static and dynamic two-point displacement correlations. We verify these from simulations and highlight the differences from the equilibrium results.

Different glassy characteristics are related to either caging or dynamical heterogeneity.

Despite the enormous theoretical and application interests, a fundamental understanding of the glassy dynamics remains elusive. The static properties of glassy and ordinary liquids are similar, but their dynamics are dramatically different. What leads to this difference is the central puzzle of the field. Even the primary defining glassy characteristics, their implications, and if they are related to a single mechanism remain unclear. This lack of clarity is a severe hindrance to theoretical progress. Here, we combine analytical arguments and simulations of various systems in different dimensions and address these questions. Our results suggest that the myriad of glassy features are manifestations of two distinct mechanisms. Particle caging controls the mean, and coexisting slow- and fast-moving regions govern the distribution of particle displacements. All the other glassy characteristics are manifestations of these two mechanisms; thus, the Fickian yet non-Gaussian nature of glassy liquids is not surprising. We discover a crossover, from stretched exponential to a power law, in the behavior of the overlap function. This crossover is prominent in simulation data and forms the basis of our analyses. Our results have crucial implications on how the glassy dynamics data are analyzed, challenge some recent suggestions on the mechanisms governing glassy dynamics, and impose strict constraints that a correct theory of glasses must have.

Effects of particle breakage on the mechanical characteristics of geogrid-reinforced granular soils under triaxial shear: A DEM investigation

A series of numerically triaxial shear tests on crushable and uncrushable granular soils reinforced by geogrid were conducted using 3-Dimension Particle Flow Code. The macroscopic behaviors of crushable and uncrushable granular soil during shearing were compared. Also, the underlying macro–micro linkages were explored. The main findings are as follows: Particle breakage decreases the contact forces between soil particles to reduce the shear strength of granular soils; The reinforcement effect of geogrids on the shear strength of granular soils can be attributed to the increase in fabric and force anisotropies; The particle displacement distribution of crushable soil samples is more uniform than that of uncrushable samples, and the shear band of crushable samples is not obvious; The reinforcement effect of geogrid with the aperture size ratio of 4.4 is the highest among the samples because the number of crushed particles and the deformation of geogrids reaches a balance.

Three-dimensional FEM–DEM coupling simulation for analysis of asphalt mixture responses under rolling tire loads

As traffic grows by leaps and bounds, deterioration of asphalt surface layers emerges as the primary cause of road network costs. A deep understanding of the tire–pavement interaction is essential for optimizing the surface design of asphalt pavements in the context of aging infrastructure and limited maintenance resources. Most of the current tire–pavement interaction studies have been conducted in the continuum mechanics framework using Finite Element Methods (FEM), which shows limitations in modeling the discontinuity nature of asphalt mixtures. Discrete Element Methods (DEM) offer a promising way to examine the mechanical properties of asphalt mixtures at the particle level, but it is inadequate for modeling deformable tire structure and capturing realistic tire contact forces on the pavement surface. In this study, a FEM–DEM coupling strategy was developed for the modeling of tire–pavement interaction by implementing a DEM model of asphalt mixtures with rolling tire loads from a FEM model. Based on simulations with realistic rolling tire load conditions, this coupling algorithm allows the investigation of particle force chain network evolution, particle displacement and velocity distributions, movements of individual particles, and particle contact force characteristics inside an asphalt mixture. This study offers an enriching expansion of both continuum and discrete mechanics methods for analyzing asphalt mixture responses under rolling tire loads, which can provide insight into pavement surface design.

Quantum uncertainty effects in the dynamics of supercooled liquids: A molecular dynamics study.

Dynamics of density fluctuations in quantum supercooled liquids is analyzed using molecular dynamics simulations. In contrast to the classical case, the uncertainty in the particle position (delocalization of quantum particle in space) leads to significant differences in the dynamics of quantum liquids, both in the short- and long-time limits. The effect of uncertainty is found to be significant for length scales smaller than the uncertainty itself, and diminishes as the length scale grows. The dynamic heterogeneity of the system at short times is enhanced due to uncertainty. In the intermediate (β-relaxation) time regime, the heterogeneity tends to get suppressed due to quantum uncertainty. The probability distribution of particle displacements shows highly nonclassical behavior with double-peak structure at short timescales.

A combined QTAIM, DFT and molecular dynamics study on the nanoscale dynamical and structural organization of imidazolium-based dicationic ionic liquids

In this work, the effects of linkage alkyl chain length on the dynamical and structural micro-heterogeneities of some imidazolium-based dicationic ionic liquids (DILs) i.e. [Cn(mim)2][BF4]2, (n = 3, 6, 9, and 12) were studied via quantum mechanical calculations and also classical molecular dynamics (MD) simulations. Hydrogen bondings and also the interaction energies between the studied ions have been calculated using the density functional theory (DFT) calculations and also the quantum theory of atoms in molecules (QTAIM) method. The results showed that with increasing the linkage alkyl chain length of DILs, the interaction energies and electron densities are decreased, because the electrostatic interactions in DILs are weakened with increasing the –CH2 groups in the linkage chain. Different kinds of combined distribution functions (CDFs) were computed to better understand the orientations of ions in the studied DILs. Although, two rings of cation are almost perpendicular with respect to each other in all studied DILs, the orientation of linkage chain with respect to the rings is different in short- and long-linkage chain DILs. To understand the arrangement of the nearest neighboring ions, neighborhood analysis and spatial distribution functions (SDFs) of ions were analyzed. Furthermore, the mean square displacement (MSD), non-Gaussian parameter, van Hove correlation of cation and anions and also the ion pair, ion cage, hydrogen bond and reorientation dynamics were computed. DILs with longer alkyl chain length have more deviation in non-Gaussian parameter and Gaussian behavior of distribution of particle displacements, probably due to weakening the electrostatic interactions. Also, they have higher ion cage/ion pair stabilities than DILs with shorter linkage chain. Altogether, the linkage chain length in DILs has significant influences on their organizations in such a way that with increasing linkage chain length, their dynamical and structural micro-heterogeneities increase.

Cumulant expansion with localization: A new representation of the diffusion MRI signal.

Diffusion MR is sensitive to the microstructural features of a sample. Fine-scale characteristics can be probed by employing strong diffusion gradients while the low b-value regime is determined by the cumulants of the distribution of particle displacements. A signal representation based on the cumulants, however, suffers from a finite convergence radius and cannot represent the 'localization regime' characterized by a stretched exponential decay that emerges at large gradient strengths. Here, we propose a new representation for the diffusion MR signal. Our method provides not only a robust estimate of the first three cumulants but also a meaningful extrapolation of the entire signal decay.

Microstructure evolution and densification behavior of TiC/316L composite powders during cold/warm die compaction and solid-state sintering: 3D particulate scale numerical modelling and experimental validation

To identify the microstructure evolution and densification behavior of TiC/316L composites in powder metallurgy (PM) process, 3D particulate scale numerical simulations were conducted to reproduce the cold/warm compaction and solid-state sintering of TiC/316L composite powders with corresponding physical experiments being carried out for model validation. The effects of compaction parameters and sintering temperature on the densification behavior of TiC/316L composite powders were systemically investigated. The particle deformation and morphology, stress/strain and microstructure evolutions, and grain size distribution in the whole process were characterized and compared to further illustrate the densification behavior and the underlying dynamics/mechanisms. The results show that compared with the cold compaction, the warm compaction can not only achieve higher relative density, smaller and more uniform equivalent stress, and weaker spring back effect, but also improve the friction condition among powder particles. The plastic deformation of 316L particles is the main densification mechanism during compaction. In the solid-state sintering of TiC/316L compacts, the densification is mainly indicated by shrinkage and vanishing of large residual pores along with the growth of the sintering necks, accompanied by the particle movement and growth along the boundary regions. Meanwhile, the particle displacement and grain size distribution are more uniform in the warm compacted TiC/316L component. Moreover, the equivalent (von Mises) stress in 316L particles is smaller than that in TiC particles.

Apparent anomalous diffusion and non-Gaussian distributions in a simple mobile-immobile transport model with Poissonian switching.

We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching, we unveil a rich transport dynamics including significant transient anomalous diffusion and non-Gaussian displacement distributions. Our discussion is based on experimental parameters for tau proteins in neuronal cells, but the results obtained here are expected to be of relevance for a broad class of processes in complex systems. Specifically, we obtain that, when the mean binding time is significantly longer than the mean mobile time, transient anomalous diffusion is observed at short and intermediate time scales, with a strong dependence on the fraction of initially mobile and immobile particles. We unveil a Laplace distribution of particle displacements at relevant intermediate time scales. For any initial fraction of mobile particles, the respective mean squared displacement (MSD) displays a plateau. Moreover, we demonstrate a short-time cubic time dependence of the MSD for immobile tracers when initially all particles are immobile.

Self-propulsion with speed and orientation fluctuation: Exact computation of moments and dynamical bistabilities in displacement.

We consider the influence of active speed fluctuations on the dynamics of a d-dimensional active Brownian particle performing a persistent stochastic motion. The speed fluctuation brings about a dynamical anisotropy even in the absence of shape anisotropy. We use the Laplace transform of the Fokker-Planck equationto obtain exact expressions for time-dependent dynamical moments. Our results agree with direct numerical simulations and show several dynamical crossovers determined by the activity, persistence, and speed fluctuation. The dynamical anisotropy leads to a subdiffusive scaling in the parallel component of displacement fluctuation at intermediate times. The kurtosis remains positive at short times determined by the speed fluctuation, crossing over to a negative minimum at intermediate times governed by the persistence before vanishing asymptotically. The probability distribution of particle displacement obtained from numerical simulations in two dimensions shows two crossovers between compact and extended trajectories via two bimodal distributions at intervening times. While the speed fluctuation dominates the first crossover, the second crossover is controlled by persistence like in the wormlike chain model of semiflexible polymers.

Multiscale analysis of tire and asphalt pavement interaction via coupling FEM–DEM simulation

With the aging of roads and the lack of resources for maintenance, a thorough understanding of the interaction between tires and asphalt pavements is crucial to optimize asphalt pavement surface design. Currently, most research on this interaction system is conducted using mesh-based methods in the frame of continuum mechanics, which are insufficient to model the discontinuity behavior of asphalt mixtures during their lifespan. In this study, the Contact Dynamics method is introduced to investigate this interaction system by coupling the finite element method (FEM) and the discrete element method (DEM). FEM is utilized to model the tire and capture the resulting contact stresses on the pavement surface, while DEM is used to model the heterogeneous structure of an asphalt mixture and examine internal mixture responses at the particle scale. Analysis of contact stress distributions for free-rolling and full-braking conditions proves the tire model’s effectiveness. According to particle displacement and force distributions, particles tend to flow along the longitudinal direction and undergo a high tangential contact force under full-braking compared with those under free-rolling, resulting in mixture instability and damage initiation. This study offers an enriching supplement and expansion to mesh-based methods for analyzing pavement surface degradation under tire loads, which can provide insight into pavement surface design.

Diffusion of polymer-grafted nanoparticles with dynamical fluctuations in unentangled polymer melts.

The dynamics of polymer-grafted nanoparticles (PGNPs) in melts of unentangled linear chains were investigated by means of coarse-grained molecular dynamics simulations. The results demonstrated that the graft monomers closer to the particle surface relax more slowly than those farther away due to the constraint of the grafted surface and the confinement of the neighboring chains. Such heterogeneous relaxations of the surrounding environment would perturb the particle motion, making them fluctuating around their centers before they can diffuse through the melt. During such intermediate-time stage, the dynamics is subdiffusive while the distribution of particle displacements is Gaussian, which can be described by the popular fractional Brownian motion model. For the long-time Fickian diffusion, we found that the diffusivity D decreases with increasing grafting density Σg, grafted chain length Ng, and matrix chain length Nm. This is due to the fact that the diffusivity is controlled by the viscous drag of an effective core, consisting of the NP and the non-draining layer of graft segments, and that of the free-draining graft layer outside the "core". With increasing Σg, the PGNPs become harder with greater effective size and thinner free draining layer, resulting in a reduction in D. At extremely high Σg, the diffusivity can even be estimated by the diameter-renormalized Stokes-Einstein (SE) relation. With increasing Ng, both the effective core size and the thickness of the free-draining layer increase, leading to a reduction in diffusivity by D ∼ N-γg with 0.5 < γ < 1. Increasing Nm would lead to the enlargement of the effective core size but meanwhile result in the reduction of the free-draining layer thickness due to autophobic dewetting. The counteraction between these two opposite effects leads to only a slight reduction in the diffusivity, significantly different from the typical SE behavior where D ∼ Nm-1. These findings bear significance in unraveling the fundamental physics of the anomalous dynamics of PGNPs in various polymers, including biological and synthetic.

Length Scales in Brownian yet Non-Gaussian Dynamics

The distribution of particle displacements in certain diffusive systems takes on an unusual non-Gaussian behavior. New simulations explore how the evolution of such dynamics depends on the system's details.

Experimental and Modeling Investigation of the Mechanism for Preventing Readhesion via Zeta Potential in the Spin-Rinse Process

Adhesive particles on polished wafers are detached via, for example, scrubbing, and removed via liquid flow from the wafer while preventing readhesion by controlling the zeta potential. However, the effect of the zeta potential on the removal of detached particles in the spin-rinse process is yet to be quantitatively examined. Therefore, a physical model was constructed with some consideration of the zeta potential effect and was subsequently compared with the experimental results. According to the Derjaguin–Landau–Verwey–Overbeek theory, particle displacement in the direction normal to the wafer surface can be calculated from the energy that is mainly determined by the repulsive force depending on the zeta potential. Assuming that the particle displacement distribution takes the form of a Gaussian distribution, the ratio of particles present in the direction normal to the wafer surface can be expressed and the zeta potential effect could be incorporated into the model. Furthermore, assuming that the detached particles are removed from the wafer not only during the spin-rinse process but also during the spin-drying process, the model was in line with the experiment. It was found that the detached particles are removed from the wafer during both the spin-rinse process and the spin-drying process.