Distribution Of Particle Displacements Research Articles

Micro-mechanical analysis of caisson foundation in sand using DEM

Caisson foundation has been widely used for offshore structures. The micro-mechanical analysis of the behaviors of a caisson foundation during its installation, operation and failure is important but not currently available. The goal of this study is to improve the understanding of the micro-mechanisms in the installation, operation and progressive failure processes of caisson foundation and provide guidance on the design. For this, the discrete element method (DEM) is adopted to investigate the interaction of caisson foundation and sand. The DEM model is first validated by comparing the results of DEM simulations and experiments, in which similar trends are found in various load-displacement curves. With the validated model, the micro-mechanical response of soils induced by the installation process is studied firstly. Then the behavior of soils during the failure of the caisson foundation, including particle displacement, rotation, and stress distribution, are investigated for cases of different loading combinations. In addition, the fabric, including contact orientation, normal contact force, and shear contact force, and its evolution are studied by dividing the soils into four different zones based on their positions and failure mechanisms. At last, the effect of dimensionally homogenous moment to horizontal load ratio (M/(DH)) is discussed.

Statistics of Colloidal Suspensions Stirred by Microswimmers.

We present a statistical analysis of the experimental trajectories of colloids in a dilute suspension of the green algae Chlamydomonas reinhardtii. The measured probability density function (pdf) of the displacements of colloids covers 7 orders of magnitude. The pdfs are characterized by non-Gaussian tails for intermediate time intervals, but nevertheless they collapse when scaled with their standard deviation. This diffusive scaling breaks down for longer time intervals and the pdf becomes Gaussian. However, the mean squared displacements of tracer positions are linear over the complete measurement time interval. Experiments are performed for various tracer diameters, swimmer concentrations, and mean swimmer velocities. This allows a rigorous comparison with several theoretical models. We can exclude a description based on an effective temperature and other mean field approaches that describe the irregular motion as a sum of the fluctuating far field of many microswimmers. The data are best described by the microscopic model by J.-L. Thiffeault, Distribution of particle displacements due to swimming microorganisms, Phys. Rev. E 92, 023023 (2015)PRESCM1539-375510.1103/PhysRevE.92.023023.

Discrete element modelling of the mechanical behaviour of a sand-rubber mixture containing large rubber particles

Sand-rubber mixtures (SRMs) are newly developed geomaterials that have been widely applied in geotechnical engineering. However, the precise particle-level mechanical properties of SRMs are not yet fully understood. The present study conducted numerical simulations of triaxial tests of SRM samples containing large rubber particles employing the discrete-element method. This method allows the tracking of many important microstructural quantities, including the distribution of contact normal orientations, coordination number, particle displacement, particle sliding, and rolling during shearing. Numerical simulations showed that the contact normal anisotropy along the loading direction is clearly weakened by the addition of rubber particles. Rubber-rubber contacts are found to mainly participate in weak force networks. With an increase in the rubber content, rubber particles gradually participate in strong force chains, resulting in a more homogeneous magnitude of contact forces in the SRM. It is also observed that the rubber inclusions obviously change the pattern of strain localisation in the displacement field, indicating that rubber particles can prevent the formation of shear bands. The addition of rubbers also restrains the particle rearrangement effect by restricting interparticle rolling and sliding motion on a microscale. These findings expand the current understanding of the mechanical behaviours of SRMs.

First passage statistics for diffusing diffusivity

A rapidly increasing number of systems is identified in which the stochastic motion of tracer particles follows the Brownian law yet the distribution of particle displacements is strongly non-Gaussian. A central approach to describe this effect is the diffusing diffusivity (DD) model in which the diffusion coefficient itself is a stochastic quantity, mimicking heterogeneities of the environment encountered by the tracer particle on its path. We here quantify in terms of analytical and numerical approaches the first passage behaviour of the DD model. We observe significant modifications compared to Brownian–Gaussian diffusion, in particular that the DD model may have a faster first passage dynamics. Moreover we find a universal crossover point of the survival probability independent of the initial condition.

Fickian yet non-Gaussian diffusion is not ubiquitous in soft matter

Recent studies unveiled the Fickian yet non-Gaussian (FNG) dynamics of many soft matter systems and suggested this phenomenon as a general characteristic of the diffusion in complex fluids. In particular, it was shown that the distribution of particle displacements in Fickian diffusion is not necessarily Gaussian, and thus the Einstein and Smoluchowski theory describing the Brownian motion of individual objects in a fluid would not be applicable. In this Letter, we investigate whether the FNG dynamics so far reported in gels, granular materials, biological and active matter systems, is also a distinctive feature of colloidal liquid crystals. To this end, we perform Brownian Dynamics simulations of oblate and prolate colloidal particles in the nematic phase. We detect a normal and Gaussian dynamics at short and long time scales, whereas, at intermediate time scales, a non-Fickian and non-Gaussian dynamics is found. Additionally, we revisit the nature of the decay of the self-van Hove correlation function, $G_s(r,t)$, which is here approximated with an ellipsoidal, rather than spherical, Gaussian distribution. The new expression that we propose is able to correctly assess the Gaussian dynamics in inherently anisotropic systems, like liquid crystals, where the standard Gaussian approximation of $G_s(r,t)$ would fail.

(Invited) Elucidating the Micro Phase-Separation of Mixed Kappa and Iota Carrageenan Gels Using Multiple Particle Tracking

Carrageenan is a family of linear sulfated polysaccharides extracted from seaweeds. Among the different types of carrageenan, kappa carrageenan (KC) and iota carrageenan (IC) are widely used in industries due to its gelling behavior. Because of its importance in industries, KC and IC as well as its mixtures have been extensively studied using different methods. However, it is still unclear whether mixed KC:IC undergo a phase separated network structure of IC-rich and KC-rich or interpenetrated network structure. In this report, the network structure and gelation mechanism of KC, IC and its mixture were elucidated using multiple particle tracking. Sodium-type κ- and ι- carrageenan powder was purchased from Tokyo Chemical Industry Co., Ltd. (Tokyo, Japan). All samples were dialyzed against NaCl solution and subsequently against deionized water, to obtain Na+ type carrageenan solutions. Samples were prepared by diluting carrageenan and KCl solutions and heated for 30 min at 70 °C under vigorous stirring. The prepared solutions were mixed using vortex to obtain 1.5% w/w carrageenan with 10 mM KCl and heated at 90 °C for 20 min. Fluorescently labelled 0.1 μm particles (Green, ThermoScientific) were added at a concentration of ~0.01% (v/w) at 90 °C and stirred for another 5 min to assure homogenous dispersion. Mixture of KC and IC was prepared at different volume fraction of IC. Movies of the diffusing particles were recorded at a frame rate of 7.5 frames per second for 110 seconds. In cooling experiments, particle tracking was performed at different sample temperatures from 50 °C to 10 °C. In storage experiments, hot solutions of carrageenan were cooled down from 50 °C to 5 °C at a rate of 1 °C/min in a temperature-controlled incubator to form a gel. The gelled sample was stored at 5 °C prior to experiment and particle tracking was performed at 5 °C. Particle tacking was implemented in Mathematica 10 (Wolfram Research, Inc., USA). The temperature dependence of the mean square displacement (MSD) of particles in KC, IC and mixed KC:IC gels were carried out to quantify the dynamics of the evolving network structure on cooling as shown in Figure 1. In mixed KC:IC, a two-step decrease in MSD was observed. The onset of the observed decrease is close to the decrease in pure KC and IC gels. This trend is consistent with the observed increase in the viscoelastic modulus in dynamic viscoelasticity measurements. The decrease in the MSD with decreasing temperature is due to the steric hindrance created by the formation of clusters of IC and KC chain aggregates. This suggests that KC and IC chains formed aggregates independently on cooling. In pure carrageenan, IC gels formed weak entanglement among clusters of IC chain that allowed diffusion of particles through crevices of the entangled clusters while KC gels rapidly formed thick aggregates of interconnected clusters that confined the particles. On the other hand, in mixed KC:IC, the presence of IC clusters decreased the mobility of KC chains at low temperature thus slowed the formation of stable clusters of KC. With storage time, a broad distribution of MSD was observed for the mixed gels. This suggests that an inhomogeneous solution was formed as KC and IC clusters continue to rearrange to form a stable network. The degree of heterogeneity in the mixed gels is reflected in the corresponding van Hove distribution of particle displacement and the distribution of MSD as a function of slope. In the van Hove distribution, a bimodal Gaussian form with a broad and narrow Gaussian width fit well on the distribution suggests a mobile and immobile fraction of particle at each mixing ratios. In the distribution of MSD as a function of slope, the mobile and immobile particles were identified and clustered accordingly. This suggests that the presence of mobile particles was due to the existence of IC-rich domains that allowed diffusion of particles and the immobile particles was due to the confinement of particles in KC-rich domains as shown in the graphical representation in Figure 1. This is consistent with the proposed gelation mechanism of a local phase separation into IC-rich and KC-rich domains. As the volume fraction of IC was increased, the number of mobile particles increased consequently and suggests a phase transition from a sea-island (80%KC:20%IC) to a bi-continuous (50%KC:50%IC) to an island-sea (30%KC:70%IC) network structure is likely to occur. Figure 1

Molecular dynamics simulation of geminal dicationic ionic liquids [Cn(mim)2][NTf2]2 - structural and dynamical properties.

In this work, the structural and dynamical properties of two imidazolium-based geminal dicationic ionic liquids (GDILs), i.e. [Cn(mim)2][NTf2]2 with n = 3 and 5, have been studied to obtain a fundamental understanding of the molecular basis of the macroscopic and microscopic properties of the bulk liquid phase. To achieve this purpose, molecular dynamics (MD) simulation, density functional theory (DFT) and atoms in molecule (AIM) methods were used. Interaction energies, charge transfers and hydrogen bonds between the cation and anions of each studied GDIL were investigated by DFT calculations and also AIM. The mean square displacement (MSD), self-diffusion coefficient, and transference number of the cation and anions, and also the density, viscosity and electrical conductivity of the studied GDILs, were computed at 333.15 K and at 1 atm. The simulated values were in good agreement with the experimental data. The effect of linkage alkyl chain length on the thermodynamic, transport and structural properties of these GDILs has been investigated. The structural features of these GDILs were characterized by calculating the partial site-site radial distribution functions (RDFs) and spatial distribution functions (SDFs). The heterogeneity order parameter (HOP) has been used to describe the spatial structures of these GDILs and the distribution of the angles formed between two cation heads and the middle carbon atom of the linkage alkyl chain was analyzed in these ILs. To investigate the temporal heterogeneity of the studied GDILs, the deviation of the self-part of the van Hove correlation function, Gs(r[combining right harpoon above],t), from the Gaussian distribution of particle displacement and also the second-order non-Gaussian parameter, α2(t), were used. Since, the transport and interfacial properties and ionic characteristics of these GDILs were studied experimentally in our previous studies as a function of linkage chain length and temperature, in this work, we try to give a better perspective of the structure and dynamics of these systems at a molecular level.

Novel discrete element modeling coupled with finite element method for investigating ballasted railway track dynamics

A quadruple discrete element method (QDEM) was developed for viscoelastic multi-body dynamics. The sleeper motion modeled using QDEM was coupled with the rail motion modeled using a finite element method (FEM). The traffic impact response of a ballast particle and a sleeper was analyzed. The three-dimensional spatial distribution of ballast particle displacement was clearly revealed. Moreover, the ballast layer absorbed the low frequency vibration of the sleeper more effectively than its high frequency vibration. This study suggests that the proposed QDEM-FEM can provide greater insight into the impact response of ballasted railway tracks.

Time–space fractional governing equations of one‐dimensional unsteady open channel flow process: Numerical solution and exploration

AbstractAlthough fractional integration and differentiation have found many applications in various fields of science, such as physics, finance, bioengineering, continuum mechanics, and hydrology, their engineering applications, especially in the field of fluid flow processes, are rather limited. In this study, a finite difference numerical approach is proposed to solve the time–space fractional governing equations of 1‐dimensional unsteady/non‐uniform open channel flow process. By numerical simulations, results of the proposed fractional governing equations of the open channel flow process were compared with those of the standard Saint‐Venant equations. Numerical simulations showed that flow discharge and water depth can exhibit heavier tails in downstream locations as space and time fractional derivative powers decrease from 1. The fractional governing equations under consideration are generalizations of the well‐known Saint‐Venant equations, which are written in the integer differentiation framework. The new governing equations in the fractional‐order differentiation framework have the capability of modelling nonlocal flow processes both in time and in space by taking the global correlations into consideration. Furthermore, the generalized flow process may possibly shed light on understanding the theory of the anomalous transport processes and observed heavy‐tailed distributions of particle displacements in transport processes.

Lévy flight with absorption: A model for diffusing diffusivity with long tails.

We consider diffusion of a particle in rearranging environment, so that the diffusivity of the particle is a stochastic function of time. In our previous model of "diffusing diffusivity" [Jain and Sebastian, J. Phys. Chem. B 120, 3988 (2016)JPCBFK1520-610610.1021/acs.jpcb.6b01527], it was shown that the mean square displacement of particle remains Fickian, i.e., 〈x^{2}(T)〉∝T at all times, but the probability distribution of particle displacement is not Gaussian at all times. It is exponential at short times and crosses over to become Gaussian only in a large time limit in the case where the distribution of D in that model has a steady state limit which is exponential, i.e., π_{e}(D)∼e^{-D/D_{0}}. In the present study, we model the diffusivity of a particle as a Lévy flight process so that D has a power-law tailed distribution, viz., π_{e}(D)∼D^{-1-α} with 0<α<1. We find that in the short time limit, the width of displacement distribution is proportional to sqrt[T], implying that the diffusion is Fickian. But for long times, the width is proportional to T^{1/2α} which is a characteristic of anomalous diffusion. The distribution function for the displacement of the particle is found to be a symmetric stable distribution with a stability index 2α which preserves its shape at all times.

Theoretical Study of Monolayer and Double-Layer Waveguide Love Wave Sensors for Achieving High Sensitivity.

Love wave sensors have been widely used for sensing applications. In this work, we introduce the theoretical analysis of the monolayer and double-layer waveguide Love wave sensors. The velocity, particle displacement and energy distribution of Love waves were analyzed. Using the variations of the energy repartition, the sensitivity coefficients of Love wave sensors were calculated. To achieve a higher sensitivity coefficient, a thin gold layer was added as the second waveguide on top of the silicon dioxide (SiO2) waveguide–based, 36 degree–rotated, Y-cut, X-propagating lithium tantalate (36° YX LiTaO3) Love wave sensor. The Love wave velocity was significantly reduced by the added gold layer, and the flow of wave energy into the waveguide layer from the substrate was enhanced. By using the double-layer structure, almost a 72-fold enhancement in the sensitivity coefficient was achieved compared to the monolayer structure. Additionally, the thickness of the SiO2 layer was also reduced with the application of the gold layer, resulting in easier device fabrication. This study allows for the possibility of designing and realizing robust Love wave sensors with high sensitivity and a low limit of detection.

Anomalous dynamical responses in a driven system

The interplay between structure and dynamics in non-equilibrium steady-state is far from understood. We address this issue by tracking Brownian Dynamics trajectories of particles in a binary colloid of opposite charges in an external electric field. The particles show crossover from homogeneous to lane state, a prototype of heterogeneous structure formation in non-equilibrium systems. We show that the length scale of structural correlations controls heterogeneity in diffusion and consequent anomalous dynamic responses, like the exponential tail in the probability distributions of particle displacements and stretched exponential structural relaxation. We generalise our observations using equations for steady-state density which may help to understand the microscopic basis of heterogeneous diffusion in condensed matter systems.

Spatio-temporal correlations in Coulomb clusters

The dynamical responses of Coulomb-interacting particles in two-dimensional nanoclusters are analyzed at different temperatures characterizing their solid- and liquid-like behavior. Depending on the trap symmetry, spatial correlations undergo slow, stretched exponential relaxations at long times, arising from spatially correlated motion in string-like paths. Such results stem from the combined effects of confinement and long-range repulsion, making the systems inherently heterogeneous. While particles in a “solid” flow produce dynamic heterogeneities, motion in “liquid” yields an unusually long tail in the distribution of particle displacements. A phenomenological model captures much of the subtleties of our numerical simulations.

Nanoparticle diffusion in crowded and confined media.

We identify distinct mechanisms controlling slowing of nanoparticle diffusion through complex media featuring both rigid geometrical confinement and soft mobile crowders. Towards this end, we use confocal microscopy and single particle tracking to probe the diffusion of 400 nm nanoparticles suspended in Newtonian water, in a Newtonian glycerol/water mixture, or in a non-Newtonian polymer solution through a model porous medium, a packed bed of microscale glass beads. The mobility of nanoparticles, as quantified by the long-time diffusion coefficient extracted from the particle mean-squared displacement, slows as the average pore size of the packed bed media decreases for both Newtonian and non-Newtonian solutions. The distribution of particle displacements is non-Gaussian, consistent with the spatial heterogeneity of the geometrical confinement imposed by the packed bed. The slowing of nanoparticle mobility in all solutions follows the predictions of models that describe hydrodynamic interactions with the packed bed. In non-Newtonian solutions, depletion interactions due to the polymers near the glass beads result in temporary adsorption of particles onto the bead surface, as indicated by a stretched-exponential distribution of residence times. Our results therefore suggest that the confined diffusive dynamics of nanoparticles in polymer solutions is controlled by two competing mechanisms: hydrodynamic interactions between particles and spatial obstacles, which dictate the long-time slowing of diffusion, and depletion interactions between particles and confining walls due to the macromolecules, which control transient adsorption and hence alter the statistics of the short-time motion.

Microscopic origin of temporal heterogeneities in translational dynamics of liquid water.

Liquid water is known to reorient via a combination of large angular jumps (due to exchange of hydrogen bonding (H-bond) partners) and diffusive orientations. Translation of the molecule undergoing the orientational jump and its initial and final H-bond acceptors plays a key role in the microscopic reorientation process. Here, we partition the translational dynamics into those occurring during intervals when rotating water molecules (and their initial and final H-bonding partners) undergo orientational jump and those arising when molecules wait between consecutive orientational jumps. These intervals are chosen in such a way that none of the four possible H-bonds involving the chosen water molecule undergo an exchange process within its duration. Translational dynamics is analysed in terms of the distribution of particle displacements, van Hove functions, and its moments. We observe that the translational dynamics, calculated from molecular dynamics simulations of liquid water, is fastest during the orientational jumps and slowest during periods of waiting. The translational dynamics during all temporal intervals shows an intermediate behaviour. This is the microscopic origin of temporal dynamic heterogeneity in liquid water, which is mild at 300 K and systematically increases with supercooling. Study of such partitioned dynamics in supercooled water shows increased disparity in dynamics occurring in the two different types of intervals. Nature of the distribution of particle displacements in supercooled water is investigated and it reveals signatures non-Gaussian behaviour.

Fractional Governing Equations of Diffusion Wave and Kinematic Wave Open-Channel Flow in Fractional Time-Space. II. Numerical Simulations

AbstractIn this study, finite difference numerical methods, first order accurate in time and second order accurate in space, are proposed to solve the governing equations of the one-dimensional unsteady kinematic and diffusion wave open-channel flow processes in fractional time and fractional space, which were derived in the accompanying paper. Advantages of modeling open-channel flow in a fractional time-space framework over integer time-space framework are threefold. First, the nonlocal phenomena in the open-channel flow process in either space or time can be considered by taking the global correlations into consideration. Second, the proposed governing equations of the open-channel flow process in the fractional order differentiation framework are generalization of the governing equations in the integer order differentiation framework. Third, the physics of the observed heavy tailed distributions of particle displacements in transport processes, as reported in the literature, may be explained by a flow...

Collective stringlike motion of semiflexible filamentous particles in columnar liquid crystalline phases

We study, by means of Brownian dynamics simulations, heterogeneous dynamics in a dense columnar phase of monodisperse hard filamentous particles, and find that in a background of barely moving particles, some particles occasionally engage in a fast coherent string-type motion similar to what is observed in glassy states of isometric particles. This fast motion is triggered by the exchange of particles between two or more columns at different positions in the columns, which leads to sudden displacement of particles between these positions. The distribution of particle displacements shows a pronounced peak at one particle length. We perform our simulations with particles of different persistence lengths and find that for more flexible particles, the number of jump events increases. As the number of particles in the columns increases with system size for a given linear fraction of particles in the columns, the peak in the distribution becomes wider and, for sufficiently large systems, the peak disappears completely. This is associated with the increase in the magnitude of fluctuations in the motion of particles as the system size increases. Our simulation results explain recent experimental observations on single-particle motion in dense columnar phases in aqueous dispersions of filamentous virus particles.

Position-displacement correlations in QELSS spectra of non-dilute colloids

This paper examines relationships between the quasielastic light scattering spectrum S(q, t) and the distribution functions for particle displacements over various times. For dilute probes in a complex, non-scattering fluid, S(q, t) is determined by the even moments <X(t)(2n)> of the one-particle displacement distribution function P(X, t). For concentrated scattering particles, S(q, t) is not determined by P(X, t). Instead, S(q, t) is determined in part by P(X, t) and in part by a spatial Fourier transform of the two particle displacement distribution function P(2)(X, t, R(12)). Here, X is the displacement of particle 1 during t, and R(12) is the component (at t = 0), parallel to the scattering vector q, of the vector from particle 1 to a second particle 2.

Theoretical analysis of direct and phase-filtered cross-correlation response to a sinusoidal displacement for PIV image processing

The response of PIV image processing routines adopting cross-correlation is commonly categorized as that of a moving average (MA) filter. This paper addresses the intrinsic response of the statistical operator to a sinusoidal displacement from a theoretical perspective. Evaluation of the derived analytical expressions for the correlation indicates the response not to behave as that of an MA filter contrary to the generally adopted simplification. Instead the inherent signal modulation is non-linear and is determined by the ratio between displacement amplitude and particle image diameter. This finding is expected to be of importance and have considerable implications for recursive image processing routines. In addition, readily available spectral filtering techniques are assessed in terms of effectiveness in minimization of correlation deterioration due to pixelization and displacement filtering inherent to particle image self-correlation. It is shown that the best possible correlation response in digital PIV is dictated by the convolution between particle image self-correlation and displacement distribution function, inevitably retaining particle image inherent amplitude modulation.

Confined glassy dynamics at grain boundaries in colloidal crystals.

Grain boundary (GB) microstructure and dynamics dictate the macroscopic properties of polycrystalline materials. Although GBs have been investigated extensively in conventional materials, it is only recently that molecular dynamics simulations have shown that GBs exhibit features similar to those of glass-forming liquids. However, current simulation techniques to probe GBs are limited to temperatures and driving forces much higher than those typically encountered in atomic experiments. Further, the short spatial and temporal scales in atomic systems preclude direct experimental access to GB dynamics. Here, we have used confocal microscopy to investigate the dynamics of high misorientation angle GBs in a three-dimensional colloidal polycrystal, with single-particle resolution, in the zero-driving force limit. We show quantitatively that glassy behavior is inherent to GBs as exemplified by the slowing down of particle dynamics due to transient cages formed by their nearest neighbors, non-Gaussian probability distribution of particle displacements and string-like cooperative rearrangements of particles. Remarkably, geometric confinement of the GB region by adjacent crystallites decreases with the misorientation angle and results in an increase in the size of cooperatively rearranging regions and hence the fragility of the glassy GBs.