Mean Square Displacement Of Particle Research Articles

Brownian particle diffusion in generalized polynomial shear flows.

This study presents a mathematical framework for calculating the diffusion of Brownian particles in generalized shear flows. By solving the Langevin equationsusing stochastic instead of classical calculus, we propose a mathematical formulation that resolves the particle mean-square displacement (MSD) at all timescales for any two-dimensional parallel shear flow described by a polynomial velocity profile. We show that at long timescales, the polynomial order of time of the particle MSD is n+2, where n is the polynomial order of the transverse coordinate of the velocity profile. We generalize the method to resolve particle diffusion in any polynomial shear flow at all timescales, including the order of particle relaxation timescale, which is unresolved in current theories. Particle diffusion at all timescales is then studied for the cases of Couette and plane Poiseuille flows and a polynomial approximation of a hyperbolic tangent flow while neglecting the boundary effects. We observe three main stages of particle diffusion along the timeline for Couette and plane Poiseuille flows and four main stages for hyperbolic tangent flow. The particle MSD is distinctly different across these stages due to different dominant physical mechanisms. Thus, higher temporal and spatial resolution for diffusion processes in shear flows may be realized, suggesting a more accurate analytical approach for the diffusion of Brownian particles.

A Simulation of the Mechanical Testing of the Cell Membrane and Cytoskeleton.

Cell models play a crucial role in analyzing the mechanical response of cells and quantifying cellular damage incurred during micromanipulation. While traditional models can capture the overall mechanical behavior of cells, they often lack the ability to discern among distinct cellular components. Consequently, by employing dissipative particle dynamics, this study constructed a triangular network-like representation of the cell membrane along with cross-linked cytoskeletal chains. The mechanical properties of both the membrane and cytoskeleton were then analyzed through a series of simulated mechanical tests, validated against real-world experiments. The investigation utilized particle-tracking rheology to monitor changes in the mean square displacements of membrane particles over time, facilitating the analysis of the membrane's storage and loss moduli. Additionally, the cytoskeletal network's storage and loss moduli were examined via a double-plate oscillatory shear experiment. The simulation results revealed that both the membrane and cytoskeleton exhibit viscoelastic behavior, as evidenced by the power-law dependency of their storage and loss moduli on frequency. Furthermore, indentation and microinjection simulations were conducted to examine the overall mechanical properties of cells. In the indentation experiments, an increase in the shear modulus of the membrane's WLCs correlated with a higher Young's modulus for the entire cell. Regarding the microinjection experiment, augmenting the microinjection speed resulted in reduced deformation of the cell at the point of membrane rupture and a lower percentage of high strain.

Modeling of anomalous thermal conduction in thermoelectric magnetohydrodynamics: Couette formulation with a multiphase pressure gradient

A metal/liquid-metal junction is a practical thermoelectric cell causing heat absorption or release according to the direction of electric current and temperature gradient. During thermoelectric processes, the possibility of activating the anomalous heat transfer is considered in this work based on adopting a fractional version of Jeffreys equation with three fractional parameters. Because of the connection between the mean-squared displacement of diffusive hot particles and the thermal conductivity, the fractional Jeffreys law is employed to simulate the low thermal conductivity with crossovers; accelerated or retarded transition, and the transition from high (superconductivity—above the Fourier heat conduction) to low (subconductivity—below the Fourier heat conduction) thermal conductivity. The Couette formulation describing a pressure-driven flow of a viscous thick liquid-metal layer bounded by two similar metallic plates, in the presence of a constant transverse magnetic field, is investigated. A triple-phase pressure gradient, consisting of the phases: (i) ramp-up, (ii) dwell, and (iii) exponential decay, is applied as a real-life flow cause and compared with the classical constant pressure gradient and the impulsive pressure gradient case. The velocity and temperature are obtained in the Laplace domain, and then a suitable numerical technique based on the Fourier series approximation is used to recover the solutions in the real domain. It is found that the retarded crossover of low thermal conduction shows “ultraslow” temperature propagation within the thick layer, which indicates to a case of ultralow heat conduction. As well as the strong correlation between the pressure gradient type (constant, impulsive, or three-phase) and direction (favorable or adverse) and its induced velocity, the temperature gradient between the two plates plays a key role in the determination of the velocity direction and magnitude.

Diffusion in multicomponent granular mixtures.

We investigate diffusion in polydisperse granular media. We derive the mean-squared displacement of granular particles in a polydisperse granular gas in a homogeneous cooling state, containing an arbitrary amount of species of different sizes and masses. We investigate both models of constant and time-dependent restitution coefficients and obtain a universal law for the size dependence of the mean-squared displacement for steep size distributions.

The distinguishable-particle lattice model of glasses in three dimensions.

The nature of glassy states in realistic finite dimensions is still under fierce debate. Lattice models can offer valuable insights and facilitate deeper theoretical understanding. Recently, a disordered-interacting lattice model with distinguishable particles in two dimensions (2D) has been shown to produce a wide range of dynamical properties of structural glasses, including the slow and heterogeneous characteristics of the glassy dynamics, various fragility behaviors of glasses, and so on. These findings support the usefulness of this model for modeling structural glasses. An important question is whether such properties still hold in the more realistic three dimensions. In this study, we aim to extend the distinguishable-particle lattice model (DPLM) to three dimensions (3D) and explore the corresponding glassy dynamics. Through extensive kinetic Monte Carlo simulations, we found that the 3D DPLM exhibits many typical glassy behaviors, such as plateaus in the mean square displacement of particles and the self-intermediate scattering function, dynamic heterogeneity, variability of glass fragilities, and so on, validating the effectiveness of the DPLM in a broader realistic setting. The observed glassy behaviors of the 3D DPLM appear similar to those of its 2D counterpart, in accordance with recent findings in molecular models of glasses. We further investigate the role of void-induced motions in dynamical relaxations and discuss their relation to dynamic facilitation. As lattice models tend to keep the minimal but important modeling elements, they are typically much more amenable to analysis. Therefore, we envisage that the DPLM will benefit future theoretical developments, such as the configuration tree theory, towards a more comprehensive understanding of structural glasses.

Impact of Evanescence Process on Three-Dimensional Sub-Diffusion based Molecular Communication Channel.

In most of the existing works of molecular communication (MC), the standard diffusion environment is taken into account where the mean square displacement (MSD) of an information molecule (IM) scales linearly with time. On the contrary, this work considers the sub-diffusion motion that appears in crowded and complex (porous or fractal) environments (movement of the particles in the living cells) where the particle's MSD scales as a fractional order power law in time. Moreover, we examine an additional evanescence process resulting from which the molecules can degrade before hitting the boundary of the receiver (RX). Thus, in this work, we present a 3D MC system with a point transmitter (TX) and the spherical RX with the sub-diffusive behavior of an IM along with its evanescence. Furthermore, an IM's closed-form expressions for the arrival probability and the first passage time density (FPTD) are emulated in the above context. Additionally, we investigate the performance of MC by using the concentration-based modulation technique in a sub-diffusion channel. Finally, the considered MC channel is exploited in terms of the probability of detection, probability of false alarm, and probability of error for different parameters such as the reaction rate, fractional power, and radius of the RX.

Approach to hyperuniformity in a metallic glass-forming material exhibiting a fragile to strong glass transition

We investigate a metallic glass-forming (GF) material (Al90Sm10) exhibiting a fragile-strong (FS) glass-formation by molecular dynamics simulation to better understand this highly distinctive pattern of glass-formation in which many of the usual phenomenological relations describing relaxation times and diffusion of ordinary GF liquids no longer apply, and where instead genuine thermodynamic features are observed in response functions and little thermodynamic signature is exhibited at the glass transition temperature, Tg. Given the many unexpected similarities between the thermodynamics and dynamics of this metallic GF material with water, we first focus on the anomalous static scattering in this liquid, following recent studies on water, silicon and other FS GF liquids. We quantify the “hyperuniformity index” H of our liquid, which provides a quantitative measure of molecular “jamming”. To gain insight into the T-dependence and magnitude of H, we also estimate another more familiar measure of particle localization, the Debye–Waller parameter 〈u2〉 describing the mean-square particle displacement on a timescale on the order of the fast relaxation time, and we also calculate H and 〈u2〉 for heated crystalline Cu. This comparative analysis between H and 〈u2〉 for crystalline and metallic glass materials allows us to understand the critical value of H on the order of 10–3 as being analogous to the Lindemann criterion for both the melting of crystals and the “softening” of glasses. We further interpret the emergence of FS GF and liquid–liquid phase separation in this class of liquids to arise from a cooperative self-assembly process in the GF liquid.Graphical abstract

The influence of KCl concentration on the gelation of myofibrillar protein giant squid (Dosidicus gigas) due to molecular conformation change.

Protein gelation process is of importance in food industry. The objective of this study is to investigate the influence of salt concentration variation, which induced protein conformation change, on protein's intermolecular interactions and its gelation process. Paramyosin has been separated and purified from myofibrillar protein extracted from giant squid. Then Giant squid's paramyosin molecular mass and intermolecular interactions were quantified by means of light scattering techniques. Finally, the micro-rheology study via diffusing wave spectroscopy (DWS) technique revealed that this conformation change dramatically affected myofibrillar protein gelation process. The obtained apparent molecular weight (ca 2 × 105 g/mol) suggested that protein molecules existed as dimers, while the second virial coefficient A2 significantly reduced from -3.98456 × 10-5 to -5.07575 × 10-4 ml mol/g2 when KCl concentrated from 0.15 to 1 mol/L. Light scattering data also suggest that paramyosin dimers are stiff, with a persistence length of 120 nm, almost the length of a molecule and independent of salt concentration. Mean-square displacement (MSD) of tracer particles at 5 temperatures with 4 salt concentrations displayed that this conformation change had dramatic effect. Therefore, G' and G" were remarkably altered with at least one order of magnitude difference owing to this event occurrence. Paramyosin conformation change due to KCl concentrated enhances attractive interactions with apparent molecular mass increase, which resulted in majority paramyosin molecules (> 99%) in dimeric form and promoted aggregates formation. DWS technique revealed that the conformation change dramatic affected this process characterized by the correlation functions, MSD, and G' and G". This study brings forward data on understanding the effect of a major salt supplement, KCl, on the chemical physics of a major muscle protein.

Effects of dust particle number on the structure and dynamics in a binary complex plasma system by Langevin dynamics simulation

In this paper, Langevin dynamics simulation is used to study the influence of particle number on the structures and dynamics of a binary complex plasma, in which two kinds of particles with different masses are considered. The structures of the binary system are characterized by particle distribution, nearest-neighbor, and pair correlation function. The dynamics of the system are characterized by the evolution of average speed and kinetic energy as time, the mean square displacement (MSD) and self-diffusion coefficient of the binary particles. The lattice structures and the dynamics evolution of binary particles versus the particle number are investigated in detail in this paper. The space distribution shows that the binary particles easily fully separate themselves for a small particle number. The dynamics evolutions indicate that small particles reach the system center first, and then are pushed out by the later reached large particles. As the number of particles increases, the system becomes more ordered and the kinetic energy difference between the two kinds of particles becomes smaller. This study shows that the structure and dynamics of a binary complex plasma can be affected by dust particle number.

Isomorph Invariance in the Liquid and Plastic-Crystal Phases of Asymmetric-Dumbbell Models

We present a numerical study of the asymmetric dumbbell model consisting of “molecules” constructed as two different-sized Lennard-Jones spheres connected by a rigid bond. In terms of the largest (A) particle radius, we report data for the structure and dynamics of the liquid phase for the bond lengths 0.05, 0.1, 0.2, and 0.5, and analogous data for the plastic-crystal phase for the bond lengths 0.05, 0.1, 0.2, and 0.3. Structure is probed by means of the AA, AB, and BB radial distribution functions. Dynamics is probed via the A and B particle mean-square displacement as functions of time and via the rotational time-autocorrelation function. Consistent with the systems’ strong virial potential-energy correlations, the structure and dynamics are found to be isomorph invariant to a good approximation in reduced units, while they generally vary considerably along isotherms of the same (20%) density variation. Even the rotational time-autocorrelation function, which due to the constant bond length is not predicted to be isomorph invariant, varies more along isotherms than along isomorphs. Our findings provide the first validation of isomorph-theory predictions for plastic crystals for which isomorph invariance, in fact, is found to apply better than in the liquid phase of asymmetric-dumbbell models.

Microrheological study of single chain dynamics in semidilute entangled flexible polymer solutions: Crossover from Rouse to Zimm modes

The dynamics of polymer chains in entangled semidilute solution have been of theoretical and experimental interest. Among a number of characteristic lengths and times of the polymer in solution, those of the correlation blob are the key to understand the applicability of the Rouse and Zimm models to rheology of the semidilute solution. Direct rheological measurements of Rouse and Zimm modes are limited as the corresponding time scale is out of the range of classical rheological techniques. We investigated the single chain dynamics of entangled poly(ethylene oxide) in semidilute aqueous solutions by high-frequency micro-rheology based on diffusing-wave spectroscopy compared to classical shear macro-rheology. Concentration dependence of the three characteristic times of the entangled polymer chains, reptation time, entanglement time, and correlation time, was studied with the help of the time-concentration superposition. At the low frequency range, dynamic moduli measured by macro-rheology and micro-rheology showed a good agreement without adjustable parameters. At the higher frequency range, we found the Rouse regime in the mean square displacement of the probe particles and in the magnitude of the complex specific viscosity of the solution. We propose a simple method to estimate the boundary of the Rouse regime. Finally, at the high frequency range, we demonstrate that the contribution of the solvent to the solution viscosity needs to be subtracted to observe the power-law behavior of the Zimm mode.

Power-law frictional landscapes induce anomalous diffusion

Particle motion often exhibits anomalous diffusion arising from spatial inhomogeneity in the complex structures of soft materials. Spatial inhomogeneity induces a power-law frictional landscape for the mean-squared displacement of particles in a force-free environment; expressly, 〈x2(t)〉∼tα (i.e., 0<α≤2). We calculate analytically and numerically this mean-squared displacement. By comparing with a XY system in a logarithmic potential, for which anomalous diffusion transitions occur in regimes from normal diffusion to confinement, we investigated the diffusive dynamics of a realistic system away from its equilibrium state. Spatial nonlocal processes were found to be equivalent to time nonlocal ones (i.e., non-Ohmic memory); specifically, the weaker the effective friction produced, the stronger is the diffusion induced. This overcomes the difficulty encountered when evaluating memory effects in experiments. Aided by the generalized Green–Kubo formula, our model is also compared with diffusion processes obeying the scaling behavior of the velocity correlation function. The present study on anomalous diffusion in inhomogeneous environments is helpful because the phenomenon appears in soft, solid and biological matter.

Emergent collective behavior of active Brownian particles with visual perception.

Systems comprised of self-steering active Brownian particles are studied via simulations for a minimal cognitive flocking model. The dynamics of the active Brownian particles is extended by an orientational response with limited maneuverability to an instantaneous visual input of the positions of neighbors within a vision cone and a cut-off radius. The system exhibits large-scale self-organized structures, which depend on selected parameter values, and, in particular, the presence of excluded-volume interactions. The emergent structures in two dimensions, such as worms, worm-aggregate coexistence, and hexagonally close-packed structures, are analysed and phase diagrams are constructed. The analysis of the particle's mean-square displacement shows ABP-like dynamics for dilute systems and the worm phase. In the limit of densely packed structures, the active diffusion coefficient is significantly smaller and depends on the number of particles in the cluster. Our analysis of the cluster-growth dynamics shows distinct differences to processes in systems of short-range attractive colloids in equilibrium. Specifically, the characteristic time for the growth and decay of clusters of a particular size is longer than that of isotropically attractive colloids, which we attribute to the non-reciprocal nature of the directed visual perception. Our simulations reveal a strong interplay between ABP-characteristic interactions, such as volume exclusion and rotational diffusion, and cognitive-based interactions and navigation.

Motion of a self-propelled particle with rotational inertia.

Overdamped active Brownian motion of self-propelled particles in a liquid has been fairly well studied. However, there are a variety of situations in which the overdamped approximation is not justified, for instance, when self-propelled particles move in a low-viscosity medium or when their rotational diffusivity is enhanced by internal active processes or external control. Examples of various origins include biofilaments driven by molecular motors, living and artificial microflyers and interfacial surfers, field-controlled and superfluid microswimmers, vibration-driven granular particles and autonomous mini-robots with sensorial delays, etc. All of them extend active Brownian motion to the underdamped case, i.e., to active Langevin motion, which takes into account inertia. Despite a rich experimental background, there is a gap in the theory in the field where rotational inertia significantly affects the random walk of active particles on all time scales. In particular, although the well-known models of active Brownian and Ornstein-Uhlenbeck particles include a memory effect of the direction of motion, they are not applicable in the underdamped case, because the rotational inertia, which they do not account for, can partially prevent "memory loss" with increasing rotational diffusion. We describe the two-dimensional motion of a self-propelled particle with both translational and rotational inertia and velocity fluctuations. The proposed generalized analytical equations for the mean kinetic energy, mean-square displacement and noise-averaged trajectory of the self-propelled particle are confirmed by numerical simulations in a wide range of self-propulsion velocities, moments of inertia, rotational diffusivities, medium viscosities and observation times.

Interparticle Adhesion Regulates the Surface Roughness of Growing Dense Three-Dimensional Active Particle Aggregates.

Activity and self-generated motion are fundamental features observed in many living and nonliving systems. Given that interparticle adhesive forces can regulate particle dynamics, we investigate how interparticle adhesion strength controls the boundary growth and roughness of active particle aggregates. Using particle based simulations incorporating both activity (birth, death, and growth) and systematic physical interactions (elasticity and adhesion), we establish that interparticle adhesion strength (fad) controls the surface roughness of a densely packed three-dimensional(3D) active particle aggregate expanding into a highly viscous medium. We discover that the surface roughness of a 3D active particle aggregate increases in proportion to the interparticle adhesion strength (fad) and show that asymmetry in the radial and transverse active particle mean-squared displacement (MSD) suppresses 3D surface roughness at lower adhesion strengths. By analyzing the statistical properties of particle displacements at the aggregate periphery, we determine that the 3D surface roughness is driven by the movement of active particle toward the core at high interparticle adhesion strengths. Our results elucidate the physics controlling the expansion of adhesive 3D active particle collectives into a highly viscous medium, with implications into understanding stochastic interface growth in active matter systems characterized by self-generation of particles.

Gelation and network structure of acidified milk gel investigated at different length scales with and without addition of iota-carrageenan

This work investigated the formation of acid milk gel at different length scales with and without the addition of iota-carrageenan (IC) (0.5% w/w) during incubation at 30 °C, using bulk rheology and syringe compression test at the macroscopic level, passive particle tracking (particle diameter 0.3 μm and 1.0 μm) at the microscopic level and pulsed field gradient (PFG)-NMR with poly(ethylene oxide) (PEO) at the molecular level. IC induced the early formation of the gel network in the sample as demonstrated by the progressive G′ and G″ increase (where G′ > G″) in the macroscopic measurement. When repeatedly compressed at the developing stage, the formed gel network in the IC sample reassociated into non-native colloidal structures unable to contain the serum phase, which also occurred without IC but at later incubation stage. The increased PEO diffusion at 30 min in PFG-NMR reflected the emerging casein-casein network and its extensive rearrangement occurring at the molecular level in both samples. This corresponded with the mean square displacement of the probe particles with IC at 30 min but not without IC, indicating that IC altered the length scale of the network rearrangements occurring at the molecular level to be detected at the microscopic level in the particle tracking. The size-dependent particle behaviors in the particle tracking demonstrated a high degree of IC-induced network heterogeneity that continued to develop even at late incubation stage, on contrary to the drastic compaction of the formed network observed in the sample without IC.

Study on the heterogeneity in mixture carrageenan gels viewed by long time particle tracking

The network structure of mixed κ- (KC) and ι- (IC) carrageenan gels were investigated using particle tracking in a long time observation. The Brownian motion of 100 nm particles tracked for ~1400 s was utilized to probe the microenvironment in the mixed gels. The individual mean square displacement (msd) of particles in different mixing ratios of KC/IC showed a broad distribution, indicating spatial heterogeneity in the particle diffusion, suggesting the phase-separated network structure with KC-rich and IC-rich domains. The broad distribution of msd further suggests fast-moving particles in IC-rich and slow-moving particles in KC-rich domains. The distribution of displacement for each of the fast-moving particles showed a non-Gaussian distribution indicating the heterogeneous diffusion behavior. The time-course of the radius of gyration in a sliding time window with a duration time for the mobile particles revealed multiple confinement events. These were attributed to the sterical hindrance or the interaction with the surface of the KC-rich domain, which tolerates the breakaway from the confinement by the Brownian motion. Simulation of particle diffusion was performed to understand the interaction that causes the confinement period. Results revealed that the confinement was caused by the interaction between the particle and the KC-rich domain covered with KC chains. The KC chains have the negatively charged sulfonic group, but salt ions of KCl should satisfyingly shield the repulsive interaction by the sulfonic group to have cohesive interaction with the particle.

On the evolution of the exclusion zone produced by hydrophilic surfaces: A contracted description.

After exciting scientific debates about its nature, the development of the exclusion zone, a region near hydrophilic surfaces from which charged colloidal particles are strongly expelled, has been finally traced back to the diffusiophoresis produced by unbalanced ion gradients. This was done by numerically solving the coupled Poisson equation for electrostatics, the two stationary Stokes equations for low Reynolds numbers in incompressible fluids, and the Nernst-Planck equation for mass transport. Recently, it has also been claimed that the leading mechanism behind the diffusiophoretic phenomenon is electrophoresis [Esplandiu et al., Soft Matter 16, 3717 (2020)]. In this paper, we analyze the evolution of the exclusion zone based on a one-component interaction model at the Langevin equation level, which leads to simple analytical expressions instead of the complex numerical scheme of previous works, yet being consistent with it. We manage to reproduce the evolution of the exclusion zone width and the mean-square displacements of colloidal particles we measure near Nafion, a perfluorinated polymer membrane material, along with all characteristic time regimes, in a unified way. Our findings are also strongly supported by complementary experiments using two parallel planar conductors kept at a fixed voltage, mimicking the hydrophilic surfaces, and some computer simulations.

Extended space and time correlations in strongly magnetized plasmas

Molecular dynamics simulations are used to show that strong magnetization significantly increases the space and time scales associated with interparticle correlations. The physical mechanism responsible is a channeling effect whereby particles are confined to move along narrow cylinders with a width characterized by the gyroradius and a length characterized by the collision mean free path. The predominant interactions are the 180° collisions at the ends of the collision cylinders, resulting in a long-range correlation parallel to the magnetic field. Its influence is demonstrated via the dependence of the velocity autocorrelation functions and self-diffusion coefficients on the domain size and run time in simulations of the one-component plasma. A very large number of particles, and therefore domain size, must be used to resolve the long-range correlations, suggesting that the number of charged particles in the collection must increase in order to constitute a plasma. Correspondingly, this effect significantly delays the time it takes to reach a diffusive regime, in which the mean square displacement of particles increases linearly in time. This result presents challenges for connecting measurements in non-neutral and ultracold neutral plasma experiments, as well as molecular dynamics simulations, with fluid transport properties due to their finite size.

Entropic Effects of Interacting Particles Diffusing on Spherical Surfaces

We present a molecular dynamics and theoretical study on the diffusion of interacting particles embedded on the surface of a sphere. By proposing five different interaction potentials among particles, we perform molecular dynamics simulations and calculate the mean square displacement (MSD) of tracer particles under a crowded regime of high surface density. Results for all the potentials show four different behaviors passing from ballistic and transitory at very short times, to sub-diffusive and saturation behaviors at intermediary and long times. Making use of irreversible thermodynamics theory, we also model the last two stages showing that the crowding induces a sub-diffusion process similar to that caused by particles trapped in cages, and that the saturation of the MSD is due to the existence of an entropic potential that limits the number of accessible states to the particles. By discussing the convenience of projecting the motions of the particles over a plane of observation, consistent with experimental capabilities, we compare the predictions of our theoretical model with the simulations showing that these stages are remarkably well described in qualitative and quantitative terms.