Brownian Dynamics Simulations Research Articles

Spontaneous velocity alignment of Brownian particles with feedback-induced propulsion (a)

Based on Brownian dynamics simulations we study the collective behavior of a two-dimensional system of repulsively interacting colloidal particles, where each particle is propelled by a repulsive feedback force with time delay τ. Although the pair interactions are purely isotropic we observe a spontaneous, large-scale alignment of the velocity vectors. This phenomenon persists for long times and occurs in the absence of steady-state clustering. We explain our observations by a combination of the effect of steric interactions yielding local velocity ordering, and the effect of time delay, that generates cluster dissolution, velocity persistence and velocity alignment over large distances. Overall, the behavior reveals intriguing similarities, but also differences, with that observed in models of active matter, such as active Brownian particles and the Vicsek model.

Superadiabatic dynamical density functional study of Brownian hard-spheres in time-dependent external potentials.

Superadiabatic dynamical density functional theory (superadiabatic-DDFT), a first-principles approach based on inhomogeneous two-body correlation functions, is employed to investigate the response of interacting Brownian particles to time-dependent external driving. Predictions for the superadiabatic dynamics of the one-body density are made directly from the underlying interparticle interactions without the need for either adjustable fit parameters or simulation input. The external potentials we investigate have been chosen to probe distinct aspects of structural relaxation in dense, strongly interacting liquid states. Nonequilibrium density profiles predicted by the superadiabatic theory are compared with those obtained from both adiabatic DDFT and event-driven Brownian dynamics simulation. Our findings show that superadiabatic-DDFT accurately predicts the time-evolution of the one-body density.

Dual hydrodynamic trap based on coupled stagnation point flows

Recent advancements in science and engineering have allowed for trapping and manipulation of individual particles and macromolecules within an aqueous medium using a flow-based confinement method. In this work, we demonstrate the feasibility of trapping and manipulating two particles using coupled planar extensional flows. Using Brownian dynamics simulations and a proportional feedback control algorithm, we show that two micro/nanoscale particles can be simultaneously confined and manipulated at the stagnation points of a pair of interconnected planar extensional flows. We specifically studied the effect of strain rate, particle size, and feedback control parameters on particle confinement. We also demonstrate precise control of the interparticle distance by manipulating the strain rates at both junctions and particle position at one of the junctions. We further discuss the advantages and limitations of the dual hydrodynamic trap in comparison to existing colloidal particle confinement methods and outline some potential applications in polymer science and biology. Our results demonstrate the versatility of flow-based confinement and further our understanding of feedback-controlled particle manipulation.

Active particles with delayed attractions form quaking crystallites (a)

Perception-reaction delays have experimentally been found to cause a spontaneous circling of microswimmers around a fixed target particle. Here we investigate a many-body version of such an experiment with Brownian-dynamics simulations of active particles in a plane. For short delays, they form a hexagonal crystallite around the target. The bifurcation to a chiral dynamical phase, seen for longer delays, maps onto that for a single active particle. Different angular velocities at different distances from the target induce shear stresses that grow with increasing delay. By exciting shear bands, they shake and intermittently break the rotating crystallite. For long delays, it detaches from the target to circle around it near the preferred single-particle orbit as a compact spinning satellite, trembling from what could be called tidal quakes.

Portable Bulk-Water Disinfection by Live Capture of Bacteria with Divergently Branched Porous Graphite in Electric Fields.

Easy access to clean water is essential to functioning and development of modern society. However, it remains arduous to develop energy-efficient, facile, and portable water treatment systems for point-of-use (POU) applications, which is particularly imperative for the safety and resilience of society during extreme weather and critical situations. Here, we propose and validate a meritorious working scheme for water disinfection via directly capturing and removing pathogen cells from bulk water using strategically designed three-dimensional (3D) porous dendritic graphite foams (PDGFs) in a high-frequency AC field. The prototype, integrated in a 3D-printed portable water-purification module, can reproducibly remove 99.997% E. coli bacteria in bulk water at a few voltages with among the lowest energy consumption at 435.5 J·L-1. The PDGFs, costing $1.47 per piece, can robustly operate at least 20 times for more than 8 h in total without functional degradation. Furthermore, we successfully unravel the involved disinfection mechanism with one-dimensional Brownian dynamics simulation. The system is practically applied that brings natural water in Waller Creek at UT Austin to the safe drinking level. This research, including the working mechanism based on dendritically porous graphite and the design scheme, could inspire a future device paradigm for POU water treatment.

Fickian yet non-Gaussian diffusion of a quasi-2D colloidal system in an optical speckle field: experiment and simulations

We investigate a quasi-2D suspension of Brownian particles in an optical speckle field produced by holographic manipulation of a laser wavefront. This system was developed to study, in a systematic and controllable way, a distinctive instance of diffusion, called Fickian yet Non Gaussian diffusion (FnGD), observed, during the last decade, for colloidal particles in a variety of complex and biological fluids. Our setup generates an optical speckle field that behaves like a disordered set of optical traps. First, we describe the experimental setup and the dynamics of the particles, focusing on mean square displacements, displacement distributions and kurtosis. Then, we present Brownian Dynamics simulations of point-like particles in a complex energy landscape, mimicking that generated by the optical speckle field. We show that our simulations can capture the salient features of the experimental results, including the emergence of FnGD, also covering times longer than the ones so far achieved in experiments. Some deviations are observed at long time only, with the Gaussian restoring being slower in simulations than in experiments. Overall, the introduced numerical model might be exploited to guide the design of upcoming experiments targeted, for example, to fully monitor the recovery of Gaussianity.

Characterizing the information transmission of inverse stochastic resonance and noise-induced activity amplification in neuronal systems.

Purkinje cells exhibit a reduction of the mean firing rate at intermediate-noise intensities, which is somewhat reminiscent of the response enhancement known as "stochastic resonance" (SR). Although the comparison with the stochastic resonance ends here, the current phenomenon has been given the name "inverse stochastic resonance" (ISR). Recent research has demonstrated that the ISR effect, like its close relative "nonstandard SR" [or, more correctly, noise-induced activity amplification (NIAA)], has been shown to stem from the weak-noise quenching of the initial distribution, in bistable regimes where the metastable state has a larger attraction basin than the global minimum. To understand the underlying mechanism of the ISR and NIAA phenomena, we study the probability distribution function of a one-dimensional system subjected to a bistable potential that has the property of symmetry, i.e., if we change the sign of one of its parameters, we can obtain both phenomena with the same properties in the depth of the wells and the width of their basins of attraction subjected to Gaussian white noise with variable intensity. Previous work has shown that one can theoretically determine the probability distribution function using the convex sum between the behavior at small and high noise intensities. To determine the probability distribution function more precisely, we resort to the "weighted ensemble Brownian dynamics simulation" model, which provides an accurate estimate of the probability distribution function for both low and high noise intensities and, most importantly, for the transition of both behaviors. In this way, on the one hand, we show that both phenomena emerge from a metastable system where, in the case of ISR, the global minimum of the system is in a state of lower activity, while in the case of NIAA, the global minimum is in a state of increased activity, the importance of which does not depend on the width of the basins of attraction. On the other hand, we see that quantifiers such as Fisher information, statistical complexity, and especially Shannon entropy fail to distinguish them, but they show the existence of the mentioned phenomena. Thus, noise management may well be a mechanism by which Purkinje cells find an efficient way to transmit information in the cerebral cortex.

Swirling transition with social interactions: Analyzed by a sixth-order Landau-type model (a)

Swirling groups of animals or bacteria are a common phenomenon in nature. It is thought that this collective organization occurs in the vicinity of a continuous transition between dynamic states to ensure robust group cohesion while allowing for high sensitivity to outside stimuli like predators. Here, we present Brownian dynamics simulations of active particles with social interactions which can form stable swirls. We observe a transition between swarming and swirling states and analyze these using a sixth-order Landau-type model. Our results suggest that the transition is weakly discontinuous. However, by lowering the rotational diffusion coefficient, it becomes continuous.

Effects of chain resolution on the configurational and rheological predictions from Brownian dynamics simulations of an isolated polymer chain in flow

Effects of chain resolution on the configurational and rheological predictions from Brownian dynamics simulations of an isolated polymer chain in flow

Shear rheology of a dilute suspension of thin rings

The rheology of suspensions of rings (tori) rotating in an unbounded low Reynolds number simple shear flow is calculated using numerical simulations at dilute particle number densities ( n ≪ 1 ). Suspensions of non-Brownian rings are studied by computing pair interactions that include hydrodynamic interactions modeled using slender body theory and particle collisions modeled using a short-range repulsive force. Particle contact and hydrodynamic interactions were found to have comparable influences on the steady-state Jeffery orbit distribution. The average tilt of the ring away from the flow-vorticity plane increased during pairwise interactions compared to the tilt associated with Jeffery rotation and the steady-state orbit distribution. Particle stresses associated with the increased tilt during the interaction were found to be comparable to the stresses induced directly by particle contact forces and the hydrodynamic velocity disturbances of other particles. The hydrodynamic diffusivity coefficients in the gradient and vorticity directions were also obtained and were found to be two orders of magnitude larger than the corresponding values in fiber suspensions at the same particle concentrations. Rotary Brownian dynamics simulations of isolated Brownian rings were used to understand the shear rate dependence of suspension rheology. The orbit distribution observed in the regime of weak Brownian motion, P e ≫ ϕ T − 3, was surprisingly similar to that obtained from pairwise interaction calculations of non-Brownian rings. Here, the Peclet number P e is the ratio of the shear rate and the rotary diffusivity of the particle and ϕ T is the effective inverse-aspect ratio of the particle (approximately equal to 2 π times the inverse of its non-dimensional Jeffery time period). Thus, the rheology results obtained from pairwise interactions should retain accuracy even for weakly Brownian rings ( n ≪ 1 and ϕ T − 3 ≪ P e ).

Pychastic: Precise Brownian dynamics using Taylor-Itō integrators in Python

In the last decade, Python-powered physics simulations ecosystem has been growing steadily, allowing greater interoperability, and becoming an important tool in numerical exploration of physical phenomena, particularly in soft matter systems. Driven by the need for fast and precise numerical integration in colloidal dynamics, here we formulate the problem of Brownian Dynamics (BD) in a mathematically consistent formalism of the Itō calculus, and develop a Python package to assist numerical computations. We show that, thanks to the automatic differentiation packages, the classical truncated Taylor-Itō integrators can be implemented without the burden of computing the derivatives of the coefficient functions beforehand. Furthermore, we show how to circumvent the difficulties of BD simulations such as calculations of the divergence of the mobility tensor in the diffusion equation and discontinuous trajectories encountered when working with dynamics on S^2S2 and SO(3)SO(3). The resulting Python package, Pychastic, is capable of performing BD simulations including hydrodynamic interactions at speeds comparable to dedicated implementations in lower-level programming languages, but with a much simpler end-user interface.

Codebase release 0.2 for Pychastic

In the last decade, Python-powered physics simulations ecosystem has been growing steadily, allowing greater interoperability, and becoming an important tool in numerical exploration of physical phenomena, particularly in soft matter systems. Driven by the need for fast and precise numerical integration in colloidal dynamics, here we formulate the problem of Brownian Dynamics (BD) in a mathematically consistent formalism of the Itō calculus, and develop a Python package to assist numerical computations. We show that, thanks to the automatic differentiation packages, the classical truncated Taylor-Itō integrators can be implemented without the burden of computing the derivatives of the coefficient functions beforehand. Furthermore, we show how to circumvent the difficulties of BD simulations such as calculations of the divergence of the mobility tensor in the diffusion equation and discontinuous trajectories encountered when working with dynamics on S^2S2 and SO(3)SO(3). The resulting Python package, Pychastic, is capable of performing BD simulations including hydrodynamic interactions at speeds comparable to dedicated implementations in lower-level programming languages, but with a much simpler end-user interface.

Magnetization relaxation dynamics in polydisperse ferrofluids.

When a ferrofluid is magnetized in a strong magnetic field, and then the field is switched off, the magnetization decays from its saturation value to zero. The dynamics of this process are controlled by the rotations of the constituent magnetic nanoparticles, and for the Brownian mechanism, the respective rotation times are strongly influenced by the particle size and the magnetic dipole-dipole interactions between the particles. In this work, the effects of polydispersity and interactions on the magnetic relaxation are studied using a combination of analytical theory and Brownian dynamics simulations. The theory is based on the Fokker-Planck-Brown equationfor Brownian rotation and includes a self-consistent, mean-field treatment of the dipole-dipole interactions. The most interesting predictions from the theory are that, at short times, the relaxation of each particle type is equal to its intrinsic Brownian rotation time, while at long times, each particle type has the same effective relaxation time, which is longer than any of the individual Brownian rotation times. Noninteracting particles, though, always relax at a rate controlled only by the Brownian rotation times. This illustrates the importance of including the effects of polydispersity and interactions when analyzing the results from magnetic relaxometry experiments on real ferrofluids, which are rarely monodisperse.

Conformation of a Comb-like Chain in Solution: Effect of Backbone Rigidity.

We study the effect of backbone rigidity on the conformation of comb-like chains in dilute solution by using Brownian dynamics simulations. Our results demonstrate that the backbone rigidity can control the effect of side chains on the conformation of comb-like chains; that is, the relative strength of the excluded-volume interactions from backbone monomer-graft and graft-graft to backbone monomer-monomer gradually weakens with the increase of backbone rigidity. Only when the rigidity of the backbone tends to be flexible and the grafting density is high is the effect of excluded volume of graft-graft on the conformation of comb-like chains significant enough, and other cases can be ignored. Our results show that the radius of gyration of comb-like chains and the persistence length of the backbone are exponentially related to the stretching factor, where the power exponent exhibits an increase with the increase of the strength of bending energy. These finds provide new insights for characterizing the structure properties of comb-like chains.

Conformation and dynamics of an active filament in crowded media.

The structural and dynamical properties of active filamentous objects under macromolecular crowding have a great relevance in biology. By means of Brownian dynamics simulations, we perform a comparative study for the conformational change and diffusion dynamics of an active chain in pure solvents and in crowded media. Our result shows a robust compaction-to-swelling conformational change with the augment of the Péclet number. The presence of crowding facilitates self-trapping of monomers and, thus, reinforces the activity mediated compaction. In addition, the efficient collisions between the self-propelled monomers and crowders induce a coil-to-globulelike transition, indicated by a marked change of the Flory scaling exponent of the gyration radius. Moreover, the diffusion dynamics of the active chain in crowded solutions demonstrates activity-enhanced subdiffusion. The center of mass diffusion manifests rather new scaling relations with respect to both the chain length and Péclet number. The interplay of chain activity and medium crowding provides a new mechanism to understand the non-trivial properties of active filaments in complex environments.

Effects of direction reversals on patterns of active filaments

Active matter systems provide fascinating examples of pattern formation and collective motility without counterpart in equilibrium systems. Here, we employ Brownian dynamics simulations to study the collective motion and self-organization in systems of self-propelled semiflexible filaments, inspired by the gliding motility of filamentous Cyanobacteria. Specifically, we investigate the influence of stochastic direction reversals on the patterns. We explore pattern formation and dynamics by modulating three relevant physical parameters, the bending stiffness, the activity, and the reversal rate. In the absence of reversals, our results show rich dynamical behavior including spiral formation and collective motion of aligned clusters of various sizes, depending on the bending stiffness and self-propulsion force. The presence of reversals diminishes spiral formation and reduces the sizes of clusters or suppresses clustering entirely. This homogenizing effect of direction reversals can be understood as reversals providing an additional mechanism to either unwind spirals or to resolve clusters.

Driven particle in a two-dimensional periodic substrate: Nonmonotonic dependence of drift velocity on temperature.

Motion of a driven particle in a two-dimensional (2D) periodic potential of square symmetry is studied by means of Brownian dynamics simulations. The average drift velocity and long time diffusion coefficients are obtained as a function of driving force and temperature. For driving forces above the critical depinning force, a reduction of drift velocity is observed as temperature is increased. The drift velocity reaches a minimum for temperatures at which k_{B}T is of the order of the barrier height of the substrate potential and then increases and saturates to the value of drift velocity for the substrate free case. Depending on the driving force, the drop in drift velocity can be as large as 36% of its value at low temperatures. While this phenomenon is observed in 2D for different types of substrate potentials studied and for various drive directions, studies using the exact result show no such dip in drift velocity in one dimension (1D). As in the case of 1D, a peak is observed in the longitudinal diffusion coefficient as the driving force is varied at a fixed temperature. But unlike in 1D, the location of the peak is temperature dependent. Approximate analytical expressions for the average drift velocity and the longitudinal diffusion coefficient are formulated using the exact results in 1D by finding a temperature dependent effective 1D potential to model the motion in the presence of a 2D substrate. This approximate analysis is successful in qualitatively predicting the observations.

Efficient and accurate multi-scale simulation for viscosity mechanism of konjac glucomannan colloids

The viscosity is a foundational parameter of biomacromolecule in the food industry. The viscosity of macroscopic colloids is closely related to the dynamical behaviors of mesoscopic biomacromolecule clusters, which are difficult to be investigated at molecular resolution by common methods. In this study, based on experimental data, multi-scale simulations combining microscopic molecular dynamics simulation, mesoscopic Brownian dynamics simulation, and macroscopic flow field construction were used to investigate the dynamical behaviors of mesoscopic clusters of konjac glucomannan (KGM) colloids (~500 nm) over a long time (~100 ms). Numerical statistical parameters of the mesoscopic simulation of macroscopic clusters were proposed and proved to represent the viscosity of colloids. Based on the intermolecular interaction and macromolecular conformation, the mechanism of the shear thinning effect was revealed as both the regular arrangement of macromolecules at low shear rates (<100 s−1) and structural collapse of macromolecules at high shear rates (>500 s−1). Then, the effect of molecular concentration, molecular weight, and temperature on the colloid viscosity and cluster structure of KGM colloids was investigated by experiments and simulations. This study provides a novel multi-scale numerical method and insight into the viscosity mechanism of biomacromolecule.

Frequency and field-dependent response of confined electrolytes from Brownian dynamics simulations.

Using Brownian dynamics simulations, we investigate the effects of confinement, adsorption on surfaces, and ion-ion interactions on the response of confined electrolyte solutions to oscillating electric fields in the direction perpendicular to the confining walls. Nonequilibrium simulations allows to characterize the transitions between linear and nonlinear regimes when varying the magnitude and frequency of the applied field, but the linear response, characterized by the frequency-dependent conductivity, is more efficiently predicted from the equilibrium current fluctuations. To that end, we (rederive and) use the Green-Kubo relation appropriate for overdamped dynamics, which differs from the standard one for Newtonian or underdamped Langevin dynamics. This expression highlights the contributions of the underlying Brownian fluctuations and of the interactions of the particles between them and with external potentials. Although already known in the literature, this relation has rarely been used to date, beyond the static limit to determine the effective diffusion coefficient or the DC conductivity. The frequency-dependent conductivity always decays from a bulk-like behavior at high frequency to a vanishing conductivity at low frequency due to the confinement of the charge carriers by the walls. We discuss the characteristic features of the crossover between the two regimes, most importantly how the crossover frequency depends on the confining distance and the salt concentration, and the fact that adsorption on the walls may lead to significant changes both at high and low frequencies. Conversely, our results illustrate the possibility to obtain information on diffusion between walls, charge relaxation, and adsorption by analyzing the frequency-dependent conductivity.

Organization of the bacterial nucleoid by DNA-bridging proteins and globular crowders.

The genomic DNA of bacteria occupies only a fraction of the cell called the nucleoid, although it is not bounded by any membrane and would occupy a volume hundreds of times larger than the cell in the absence of constraints. The two most important contributions to the compaction of the DNA coil are the cross-linking of the DNA by nucleoid proteins (like H-NS and StpA) and the demixing of DNA and other abundant globular macromolecules which do not bind to the DNA (like ribosomes). The present work deals with the interplay of DNA-bridging proteins and globular macromolecular crowders, with the goal of determining the extent to which they collaborate in organizing the nucleoid. In order to answer this question, a coarse-grained model was developed and its properties were investigated through Brownian dynamics simulations. These simulations reveal that the radius of gyration of the DNA coil decreases linearly with the effective volume ratio of globular crowders and the number of DNA bridges formed by nucleoid proteins in the whole range of physiological values. Moreover, simulations highlight the fact that the number of DNA bridges formed by nucleoid proteins depends crucially on their ability to self-associate (oligomerize). An explanation for this result is proposed in terms of the mean distance between DNA segments and the capacity of proteins to maintain DNA-bridging in spite of the thermal fluctuations of the DNA network. Finally, simulations indicate that non-associating proteins preserve a high mobility inside the nucleoid while contributing to its compaction, leading to a DNA/protein complex which looks like a liquid droplet. In contrast, self-associating proteins form a little deformable network which cross-links the DNA chain, with the consequence that the DNA/protein complex looks more like a gel.