Confined active Brownian particles: theoretical description of propulsion-induced accumulation

NASA Astrophysics Data System (ADS)

Das, Shibananda; Gompper, Gerhard; Winkler, Roland G.

2018-01-01

The stationary-state distribution function of confined active Brownian particles (ABPs) is analyzed by computer simulations and analytical calculations. We consider a radial harmonic as well as an anharmonic confinement potential. In the simulations, the ABP is propelled with a prescribed velocity along a body-fixed direction, which is changing in a diffusive manner. For the analytical approach, the Cartesian components of the propulsion velocity are assumed to change independently; active Ornstein-Uhlenbeck particle (AOUP). This results in very different velocity distribution functions. The analytical solution of the Fokker-Planck equation for an AOUP in a harmonic potential is presented and a conditional distribution function is provided for the radial particle distribution at a given magnitude of the propulsion velocity. This conditional probability distribution facilitates the description of the coupling of the spatial coordinate and propulsion, which yields activity-induced accumulation of particles. For the anharmonic potential, a probability distribution function is derived within the unified colored noise approximation. The comparison of the simulation results with theoretical predictions yields good agreement for large rotational diffusion coefficients, e.g. due to tumbling, even for large propulsion velocities (Péclet numbers). However, we find significant deviations already for moderate Péclet number, when the rotational diffusion coefficient is on the order of the thermal one.

Static structure of active Brownian hard disks

NASA Astrophysics Data System (ADS)

de Macedo Biniossek, N.; Löwen, H.; Voigtmann, Th; Smallenburg, F.

2018-02-01

We explore the changes in static structure of a two-dimensional system of active Brownian particles (ABP) with hard-disk interactions, using event-driven Brownian dynamics simulations. In particular, the effect of the self-propulsion velocity and the rotational diffusivity on the orientationally-averaged fluid structure factor is discussed. Typically activity increases structural ordering and generates a structure factor peak at zero wave vector which is a precursor of motility-induced phase separation. Our results provide reference data to test future statistical theories for the fluid structure of active Brownian systems. This manuscript was submitted for the special issue of the Journal of Physics: Condensed Matter associated with the Liquid Matter Conference 2017.

Brownian Motion with Active Fluctuations

NASA Astrophysics Data System (ADS)

Romanczuk, Pawel; Schimansky-Geier, Lutz

2011-06-01

We study the effect of different types of fluctuation on the motion of self-propelled particles in two spatial dimensions. We distinguish between passive and active fluctuations. Passive fluctuations (e.g., thermal fluctuations) are independent of the orientation of the particle. In contrast, active ones point parallel or perpendicular to the time dependent orientation of the particle. We derive analytical expressions for the speed and velocity probability density for a generic model of active Brownian particles, which yields an increased probability of low speeds in the presence of active fluctuations in comparison to the case of purely passive fluctuations. As a consequence, we predict sharply peaked Cartesian velocity probability densities at the origin. Finally, we show that such a behavior may also occur in non-Gaussian active fluctuations and discuss briefly correlations of the fluctuating stochastic forces.

Separation of superparamagnetic particles through ratcheted Brownian motion and periodically switching magnetic fields.

PubMed

Liu, Fan; Jiang, Li; Tan, Huei Ming; Yadav, Ashutosh; Biswas, Preetika; van der Maarel, Johan R C; Nijhuis, Christian A; van Kan, Jeroen A

2016-11-01

Brownian ratchet based particle separation systems for application in lab on chip devices have drawn interest and are subject to ongoing theoretical and experimental investigations. We demonstrate a compact microfluidic particle separation chip, which implements an extended on-off Brownian ratchet scheme that actively separates and sorts particles using periodically switching magnetic fields, asymmetric sawtooth channel sidewalls, and Brownian motion. The microfluidic chip was made with Polydimethylsiloxane (PDMS) soft lithography of SU-8 molds, which in turn was fabricated using Proton Beam Writing. After bonding of the PDMS chip to a glass substrate through surface activation by oxygen plasma treatment, embedded electromagnets were cofabricated by the injection of InSn metal into electrode channels. This fabrication process enables rapid production of high resolution and high aspect ratio features, which results in parallel electrodes accurately aligned with respect to the separation channel. The PDMS devices were tested with mixtures of 1.51  μ m, 2.47  μ m, and 2.60  μ m superparamagnetic particles suspended in water. Experimental results show that the current device design has potential for separating particles with a size difference around 130 nm. Based on the promising results, we will be working towards extending this design for the separation of cells or biomolecules.

Separation of superparamagnetic particles through ratcheted Brownian motion and periodically switching magnetic fields

PubMed Central

Liu, Fan; Jiang, Li; Tan, Huei Ming; Yadav, Ashutosh; Biswas, Preetika; van der Maarel, Johan R. C.; Nijhuis, Christian A.; van Kan, Jeroen A.

2016-01-01

Brownian ratchet based particle separation systems for application in lab on chip devices have drawn interest and are subject to ongoing theoretical and experimental investigations. We demonstrate a compact microfluidic particle separation chip, which implements an extended on-off Brownian ratchet scheme that actively separates and sorts particles using periodically switching magnetic fields, asymmetric sawtooth channel sidewalls, and Brownian motion. The microfluidic chip was made with Polydimethylsiloxane (PDMS) soft lithography of SU-8 molds, which in turn was fabricated using Proton Beam Writing. After bonding of the PDMS chip to a glass substrate through surface activation by oxygen plasma treatment, embedded electromagnets were cofabricated by the injection of InSn metal into electrode channels. This fabrication process enables rapid production of high resolution and high aspect ratio features, which results in parallel electrodes accurately aligned with respect to the separation channel. The PDMS devices were tested with mixtures of 1.51 μm, 2.47 μm, and 2.60 μm superparamagnetic particles suspended in water. Experimental results show that the current device design has potential for separating particles with a size difference around 130 nm. Based on the promising results, we will be working towards extending this design for the separation of cells or biomolecules. PMID:27917252

Beating of grafted chains induced by active Brownian particles

NASA Astrophysics Data System (ADS)

Yang, Qiu-song; Fan, Qing-wei; Shen, Zhuang-lin; Xia, Yi-qi; Tian, Wen-de; Chen, Kang

2018-06-01

We study the interplay between active Brownian particles (ABPs) and a "hairy" surface in two-dimensional geometry. We find that the increase of propelling force leads to and enhances inhomogeneous accumulation of ABPs inside the brush region. Oscillation of chain bundles (beating like cilia) is found in company with the formation and disassembly of a dynamic cluster of ABPs at large propelling forces. Meanwhile chains are stretched and pushed down due to the effective shear force by ABPs. The decrease of the average brush thickness with propelling force reflects the growth of the beating amplitude of chain bundles. Furthermore, the beating phenomenon is investigated in a simple single-chain system. We find that the chain swings regularly with a major oscillatory period, which increases with chain length and decreases with the increase of propelling force. We build a theory to describe the phenomenon and the predictions on the relationship between the period and amplitude for various chain lengths, and propelling forces agree very well with simulation data.

New weight factor for Brownian force exerted on micro/nano-particles in air flow

NASA Astrophysics Data System (ADS)

Zhang, Peijie; Lin, Jianzhong; Ku, Xiaoke

2018-05-01

In order to effectively describe the effect of Brownian force exerted on the micro/nano-particles in air flow, a new weight factor, which is defined as the ratio of the characteristic velocity of the Brownian motion to the macroscopic velocity, is proposed and applied to the particle settlement under gravity. Results show that the weight factor can quantitatively evaluate the effect of Brownian force on the particle motion. Moreover, the value of the weight factor can also be used to judge the particle motion pattern and determine whether the Brownian force should be taken into account.

Intermediate scattering function of an anisotropic active Brownian particle

PubMed Central

Kurzthaler, Christina; Leitmann, Sebastian; Franosch, Thomas

2016-01-01

Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations. PMID:27830719

Intermediate scattering function of an anisotropic active Brownian particle.

PubMed

Kurzthaler, Christina; Leitmann, Sebastian; Franosch, Thomas

2016-10-10

Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations.

Intermediate scattering function of an anisotropic active Brownian particle

NASA Astrophysics Data System (ADS)

Kurzthaler, Christina; Leitmann, Sebastian; Franosch, Thomas

2016-10-01

Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations.

Brownian motion of arbitrarily shaped particles in two dimensions.

PubMed

Chakrabarty, Ayan; Konya, Andrew; Wang, Feng; Selinger, Jonathan V; Sun, Kai; Wei, Qi-Huo

2014-11-25

We implement microfabricated boomerang particles with unequal arm lengths as a model for nonsymmetric particles and study their Brownian motion in a quasi-two-dimensional geometry by using high-precision single-particle motion tracking. We show that because of the coupling between translation and rotation, the mean squared displacements of a single asymmetric boomerang particle exhibit a nonlinear crossover from short-time faster to long-time slower diffusion, and the mean displacements for fixed initial orientation are nonzero and saturate out at long times. The measured anisotropic diffusion coefficients versus the tracking point position indicate that there exists one unique point, i.e., the center of hydrodynamic stress (CoH), at which all coupled diffusion coefficients vanish. This implies that in contrast to motion in three dimensions where the CoH exists only for high-symmetry particles, the CoH always exists for Brownian motion in two dimensions. We develop an analytical model based on Langevin theory to explain the experimental results and show that among the six anisotropic diffusion coefficients only five are independent because the translation-translation coupling originates from the translation-rotation coupling. Finally, we classify the behavior of two-dimensional Brownian motion of arbitrarily shaped particles into four groups based on the particle shape symmetry group and discussed potential applications of the CoH in simplifying understanding of the circular motions of microswimmers.

Achieving swift equilibration of a Brownian particle using flow-fields

NASA Astrophysics Data System (ADS)

Patra, Ayoti; Jarzynski, Christopher

Can a system be driven to a targeted equilibrium state on a timescale that is much shorter than its natural equilibration time? In a recent experiment, the swift equilibration of an overdamped Brownian particle was achieved by use of an appropriately designed, time-dependent optical trap potential. Motivated by these results, we develop a general theoretical approach for guiding an ensemble of Brownian particles to track the instantaneous equilibrium distribution of a desired potential U (q , t) . In our approach, we use flow-fields associated with the parametric evolution of the targeted equilibrium state to construct an auxiliary potential U (q , t) , such that dynamics under the composite potential U (t) + U (t) achieves the desired evolution. Our results establish a close connection between the swift equilibration of Brownian particles, quantum shortcuts to adiabaticity, and the dissipationless driving of a classical, Hamiltonian system.

Lagrangian dynamics for classical, Brownian, and quantum mechanical particles

NASA Astrophysics Data System (ADS)

Pavon, Michele

1996-07-01

In the framework of Nelson's stochastic mechanics [E. Nelson, Dynamical Theories of Brownian Motion (Princeton University, Princeton, 1967); F. Guerra, Phys. Rep. 77, 263 (1981); E. Nelson, Quantum Fluctuations (Princeton University, Princeton, 1985)] we seek to develop the particle counterpart of the hydrodynamic results of M. Pavon [J. Math. Phys. 36, 6774 (1995); Phys. Lett. A 209, 143 (1995)]. In particular, a first form of Hamilton's principle is established. We show that this variational principle leads to the correct equations of motion for the classical particle, the Brownian particle in thermodynamical equilibrium, and the quantum particle. In the latter case, the critical process q satisfies a stochastic Newton law. We then introduce the momentum process p, and show that the pair (q,p) satisfies canonical-like equations.

Large scale Brownian dynamics of confined suspensions of rigid particles

NASA Astrophysics Data System (ADS)

Sprinkle, Brennan; Balboa Usabiaga, Florencio; Patankar, Neelesh A.; Donev, Aleksandar

2017-12-01

We introduce methods for large-scale Brownian Dynamics (BD) simulation of many rigid particles of arbitrary shape suspended in a fluctuating fluid. Our method adds Brownian motion to the rigid multiblob method [F. Balboa Usabiaga et al., Commun. Appl. Math. Comput. Sci. 11(2), 217-296 (2016)] at a cost comparable to the cost of deterministic simulations. We demonstrate that we can efficiently generate deterministic and random displacements for many particles using preconditioned Krylov iterative methods, if kernel methods to efficiently compute the action of the Rotne-Prager-Yamakawa (RPY) mobility matrix and its "square" root are available for the given boundary conditions. These kernel operations can be computed with near linear scaling for periodic domains using the positively split Ewald method. Here we study particles partially confined by gravity above a no-slip bottom wall using a graphical processing unit implementation of the mobility matrix-vector product, combined with a preconditioned Lanczos iteration for generating Brownian displacements. We address a major challenge in large-scale BD simulations, capturing the stochastic drift term that arises because of the configuration-dependent mobility. Unlike the widely used Fixman midpoint scheme, our methods utilize random finite differences and do not require the solution of resistance problems or the computation of the action of the inverse square root of the RPY mobility matrix. We construct two temporal schemes which are viable for large-scale simulations, an Euler-Maruyama traction scheme and a trapezoidal slip scheme, which minimize the number of mobility problems to be solved per time step while capturing the required stochastic drift terms. We validate and compare these schemes numerically by modeling suspensions of boomerang-shaped particles sedimented near a bottom wall. Using the trapezoidal scheme, we investigate the steady-state active motion in dense suspensions of confined microrollers, whose

Financial Brownian Particle in the Layered Order-Book Fluid and Fluctuation-Dissipation Relations

NASA Astrophysics Data System (ADS)

Yura, Yoshihiro; Takayasu, Hideki; Sornette, Didier; Takayasu, Misako

2014-03-01

We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of comprehensive market data enables us to identify all motions of the fluid particles. Correlations between the motions of the Brownian particle and its surrounding fluid particles reflect specific layering interactions; in the inner layer the correlation is strong and with short memory, while in the outer layer it is weaker and with long memory. By interpreting and estimating the contribution from the outer layer as a drag resistance, we demonstrate the validity of the fluctuation-dissipation relation in this nonmaterial Brownian motion process.

Financial Brownian particle in the layered order-book fluid and fluctuation-dissipation relations.

PubMed

Yura, Yoshihiro; Takayasu, Hideki; Sornette, Didier; Takayasu, Misako

2014-03-07

We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of comprehensive market data enables us to identify all motions of the fluid particles. Correlations between the motions of the Brownian particle and its surrounding fluid particles reflect specific layering interactions; in the inner layer the correlation is strong and with short memory, while in the outer layer it is weaker and with long memory. By interpreting and estimating the contribution from the outer layer as a drag resistance, we demonstrate the validity of the fluctuation-dissipation relation in this nonmaterial Brownian motion process.

Large Scale Brownian Dynamics of Confined Suspensions of Rigid Particles

NASA Astrophysics Data System (ADS)

Donev, Aleksandar; Sprinkle, Brennan; Balboa, Florencio; Patankar, Neelesh

2017-11-01

We introduce new numerical methods for simulating the dynamics of passive and active Brownian colloidal suspensions of particles of arbitrary shape sedimented near a bottom wall. The methods also apply for periodic (bulk) suspensions. Our methods scale linearly in the number of particles, and enable previously unprecedented simulations of tens to hundreds of thousands of particles. We demonstrate the accuracy and efficiency of our methods on a suspension of boomerang-shaped colloids. We also model recent experiments on active dynamics of uniform suspensions of spherical microrollers. This work was supported in part by the National Science Foundation under award DMS-1418706, and by the U.S. Department of Energy under award DE-SC0008271.

A modified Brownian force for ultrafine particle penetration through building crack modeling

NASA Astrophysics Data System (ADS)

Chen, Chen; Zhao, Bin

2017-12-01

Combustion processes related to industry, traffic, agriculture, and waste treatment and disposal increase the amount of outdoor ultrafine particles (UFPs), which have adverse effects on human health. Given that people spend the majority of their time indoors, it is critical to understand the penetration of outdoor UFPs through building cracks in order to estimate human exposure to outdoor-originated UFPs. Lagrangian tracking is an efficient approach for modeling particle penetration. However, the Brownian motion for Lagrangian tracking in ANSYS Fluent®, a widely used software for particle dispersion modeling, is not able to model UFP dispersion accurately. In this study, we modified the Brownian force by rewriting the Brownian diffusion coefficient and particle integration time step with a user-defined function in ANSYS Fluent® to model particle penetration through building cracks. The results obtained using the modified model agree much better with the experimental results, with the averaged relative error less than 14% for the smooth crack cases and 21% for the rough crack case. We expect the modified Brownian force model proposed herein to be applied for UFP dispersion modeling in more indoor air quality studies.

Ratcheted electrophoresis of Brownian particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kowalik, Mikołaj; Bishop, Kyle J. M., E-mail: kjmbishop@engr.psu.edu

2016-05-16

The realization of nanoscale machines requires efficient methods by which to rectify unbiased perturbations to perform useful functions in the presence of significant thermal noise. The performance of such Brownian motors often depends sensitively on their operating conditions—in particular, on the relative rates of diffusive and deterministic motions. In this letter, we present a type of Brownian motor that uses contact charge electrophoresis of a colloidal particle within a ratcheted channel to achieve directed transport or perform useful work against an applied load. We analyze the stochastic dynamics of this model ratchet to show that it functions under any operatingmore » condition—even in the limit of strong thermal noise and in contrast to existing ratchets. The theoretical results presented here suggest that ratcheted electrophoresis could provide a basis for electrochemically powered, nanoscale machines capable of transport and actuation of nanoscale components.« less

Brownian escape and force-driven transport through entropic barriers: Particle size effect.

PubMed

Cheng, Kuang-Ling; Sheng, Yu-Jane; Tsao, Heng-Kwong

2008-11-14

Brownian escape from a spherical cavity through small holes and force-driven transport through periodic spherical cavities for finite-size particles have been investigated by Brownian dynamic simulations and scaling analysis. The mean first passage time and force-driven mobility are obtained as a function of particle diameter a, hole radius R(H), cavity radius R(C), and external field strength. In the absence of external field, the escape rate is proportional to the exit effect, (R(H)R(C))(1-a2R(H))(32). In weak fields, Brownian diffusion is still dominant and the migration is controlled by the exit effect. Therefore, smaller particles migrate faster than larger ones. In this limit the relation between Brownian escape and force-driven transport can be established by the generalized Einstein-Smoluchowski relation. As the field strength is strong enough, the mobility becomes field dependent and grows with increasing field strength. As a result, the size selectivity diminishes.

An elementary singularity-free Rotational Brownian Dynamics algorithm for anisotropic particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ilie, Ioana M.; Briels, Wim J.; MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede

2015-03-21

Brownian Dynamics is the designated technique to simulate the collective dynamics of colloidal particles suspended in a solution, e.g., the self-assembly of patchy particles. Simulating the rotational dynamics of anisotropic particles by a first-order Langevin equation, however, gives rise to a number of complications, ranging from singularities when using a set of three rotational coordinates to subtle metric and drift corrections. Here, we derive and numerically validate a quaternion-based Rotational Brownian Dynamics algorithm that handles these complications in a simple and elegant way. The extension to hydrodynamic interactions is also discussed.

Relation between cooperative molecular motors and active Brownian particles.

PubMed

Touya, Clément; Schwalger, Tilo; Lindner, Benjamin

2011-05-01

Active Brownian particles (ABPs), obeying a nonlinear Langevin equation with speed-dependent drift and noise amplitude, are well-known models used to describe self-propelled motion in biology. In this paper we study a model describing the stochastic dynamics of a group of coupled molecular motors (CMMs). Using two independent numerical methods, one based on the stationary velocity distribution of the motors and the other one on the local increments (also known as the Kramers-Moyal coefficients) of the velocity, we establish a connection between the CMM and the ABP models. The parameters extracted for the ABP via the two methods show good agreement for both symmetric and asymmetric cases and are independent of N, the number of motors, provided that N is not too small. This indicates that one can indeed describe the CMM problem with a simpler ABP model. However, the power spectrum of velocity fluctuations in the CMM model reveals a peak at a finite frequency, a peak which is absent in the velocity spectrum of the ABP model. This implies richer dynamic features of the CMM model which cannot be captured by an ABP model.

Relation between cooperative molecular motors and active Brownian particles

NASA Astrophysics Data System (ADS)

Touya, Clément; Schwalger, Tilo; Lindner, Benjamin

2011-05-01

Active Brownian particles (ABPs), obeying a nonlinear Langevin equation with speed-dependent drift and noise amplitude, are well-known models used to describe self-propelled motion in biology. In this paper we study a model describing the stochastic dynamics of a group of coupled molecular motors (CMMs). Using two independent numerical methods, one based on the stationary velocity distribution of the motors and the other one on the local increments (also known as the Kramers-Moyal coefficients) of the velocity, we establish a connection between the CMM and the ABP models. The parameters extracted for the ABP via the two methods show good agreement for both symmetric and asymmetric cases and are independent of N, the number of motors, provided that N is not too small. This indicates that one can indeed describe the CMM problem with a simpler ABP model. However, the power spectrum of velocity fluctuations in the CMM model reveals a peak at a finite frequency, a peak which is absent in the velocity spectrum of the ABP model. This implies richer dynamic features of the CMM model which cannot be captured by an ABP model.

Brownian systems with spatially inhomogeneous activity

NASA Astrophysics Data System (ADS)

Sharma, A.; Brader, J. M.

2017-09-01

We generalize the Green-Kubo approach, previously applied to bulk systems of spherically symmetric active particles [J. Chem. Phys. 145, 161101 (2016), 10.1063/1.4966153], to include spatially inhomogeneous activity. The method is applied to predict the spatial dependence of the average orientation per particle and the density. The average orientation is given by an integral over the self part of the Van Hove function and a simple Gaussian approximation to this quantity yields an accurate analytical expression. Taking this analytical result as input to a dynamic density functional theory approximates the spatial dependence of the density in good agreement with simulation data. All theoretical predictions are validated using Brownian dynamics simulations.

Stochastically gated local and occupation times of a Brownian particle

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.

2017-01-01

We generalize the Feynman-Kac formula to analyze the local and occupation times of a Brownian particle moving in a stochastically gated one-dimensional domain. (i) The gated local time is defined as the amount of time spent by the particle in the neighborhood of a point in space where there is some target that only receives resources from (or detects) the particle when the gate is open; the target does not interfere with the motion of the Brownian particle. (ii) The gated occupation time is defined as the amount of time spent by the particle in the positive half of the real line, given that it can only cross the origin when a gate placed at the origin is open; in the closed state the particle is reflected. In both scenarios, the gate randomly switches between the open and closed states according to a two-state Markov process. We derive a stochastic, backward Fokker-Planck equation (FPE) for the moment-generating function of the two types of gated Brownian functional, given a particular realization of the stochastic gate, and analyze the resulting stochastic FPE using a moments method recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment-generating function, averaged with respect to realizations of the stochastic gate.

Simultaneous sizing and electrophoretic mobility measurement of sub-micron particles using Brownian motion

PubMed Central

Palanisami, Akilan; Miller, John H.

2011-01-01

The size and surface chemistry of micron scale particles are of fundamental importance in studies of biology and air particulate pollution. However, typical electrophoretic measurements of these and other sub-micron scale particles (300 nm – 1 μm) cannot resolve size information within heterogeneous mixtures unambiguously. Using optical microscopy, we monitor electrophoretic motion together with the Brownian velocity fluctuations—using the latter to measure size by either the Green-Kubo relation or by calibration from known size standards. Particle diameters are resolved to ±12% with 95% confidence. Strikingly, the size resolution improves as particle size decreases due to the increased Brownian motion. The sizing ability of the Brownian assessed electrophoresis method described here complements the electrophoretic mobility resolution of traditional capillary electrophoresis. PMID:20882556

Ellipsoidal Brownian self-driven particles in a magnetic field

NASA Astrophysics Data System (ADS)

Fan, Wai-Tong Louis; Pak, On Shun; Sandoval, Mario

2017-03-01

We study the two-dimensional Brownian dynamics of an ellipsoidal paramagnetic microswimmer moving at a low Reynolds number and subject to a magnetic field. Its corresponding mean-square displacement, showing the effect of a particles's shape, activity, and magnetic field on the microswimmer's diffusion, is analytically obtained. Comparison between analytical and computational results shows good agreement. In addition, the effect of self-propulsion on the transition time from anisotropic to isotropic diffusion of the ellipse is investigated.

Active Brownian motion models and applications to ratchets

NASA Astrophysics Data System (ADS)

Fiasconaro, A.; Ebeling, W.; Gudowska-Nowak, E.

2008-10-01

We give an overview over recent studies on the model of Active Brownian Motion (ABM) coupled to reservoirs providing free energy which may be converted into kinetic energy of motion. First, we present an introduction to a general concept of active Brownian particles which are capable to take up energy from the source and transform part of it in order to perform various activities. In the second part of our presentation we consider applications of ABM to ratchet systems with different forms of differentiable potentials. Both analytical and numerical evaluations are discussed for three cases of sinusoidal, staircaselike and Mateos ratchet potentials, also with the additional loads modelled by tilted potential structure. In addition, stochastic character of the kinetics is investigated by considering perturbation by Gaussian white noise which is shown to be responsible for driving the directionality of the asymptotic flux in the ratchet. This stochastically driven directionality effect is visualized as a strong nonmonotonic dependence of the statistics of the right versus left trajectories of motion leading to a net current of particles. Possible applications of the ratchet systems to molecular motors are also briefly discussed.

Communication: translational Brownian motion for particles of arbitrary shape.

PubMed

Cichocki, Bogdan; Ekiel-Jeżewska, Maria L; Wajnryb, Eligiusz

2012-02-21

A single Brownian particle of arbitrary shape is considered. The time-dependent translational mean square displacement W(t) of a reference point at this particle is evaluated from the Smoluchowski equation. It is shown that at times larger than the characteristic time scale of the rotational Brownian relaxation, the slope of W(t) becomes independent of the choice of a reference point. Moreover, it is proved that in the long-time limit, the slope of W(t) is determined uniquely by the trace of the translational-translational mobility matrix μ(tt) evaluated with respect to the hydrodynamic center of mobility. The result is applicable to dynamic light scattering measurements, which indeed are performed in the long-time limit. © 2012 American Institute of Physics

Ellipsoidal Brownian self-driven particles in a magnetic field

NASA Astrophysics Data System (ADS)

Sandoval, Mario; Wai-Tong, Fan; Shun Pak, On

We study the two-dimensional Brownian dynamics of an ellipsoidal paramagnetic microswimmer moving at low Reynolds number and subject to a magnetic field. Its corresponding mean-square displacement showing the effect of particles's shape, activity, and magnetic field on the microswimmer's diffusion is analytically obtained. A comparison among analytical and computational results is also made and we obtain good agreement. Additionally, the effect of self-propulsion on the transition time from anisotropic to isotropic diffusion of the ellipse is also elucidated. CONACYT GRANT: CB 2014/237848.

Turning Passive Brownian Motion Into Active Motion

NASA Astrophysics Data System (ADS)

Sevilla, Francisco J.; VáSquez-Arzola, Alejandro; Puga-Cital, Enrique

We consider out-of-equilibrium phenomena, specifically, the pattern of motion of active particles. These particles absorb energy from the environment and transform it into self-locomotion, generally, through complex mechanisms. Though the out-of-equilibrium nature of on the motion of these systems is well recognized, is generally difficult to pinpoint how far from equilibrium these systems are. In this work we elucidate the out-of-equilibrium nature of non-interacting, trapped, active particles, whose pattern of motion is described by a run-and-tumble dynamics. We show that the stationary distributions of these run-and-tumble particles, moving under the effects of an external potential, is equivalent to the stationary distribution of non-interacting, passive Brownian particles moving in the same potential but in an inhomogeneous source of heat. The interest in this topic has recently regrown due to the experimental possibility to design man-made active particles that emulate the ones that exist in the biological realm. F.J.S kindly acknowledges support from Grant UNAM-DGAPA-PAPIIT-IN113114.

Brownian self-propelled particles on a sphere

NASA Astrophysics Data System (ADS)

Apaza-Pilco, Leonardo Felix; Sandoval, Mario

We present the dynamics of a Brownian self-propelled particle at low Reynolds number moving on the surface of a sphere. The effects of curvature and self-propulsion on the diffusion of the particle are elucidated by determining (numerically) the mean-square displacement of the particle's angular (azimuthal and polar) coordinates. The results show that the long time behavior of its angular mean-square displacement is linear in time. We also see that the slope of the angular MSD is proportional to the propulsion velocity and inverse to the curvature of the sphere. The angular probability distribution function (PDF) of the particle is also obtained by numerically solving its respective Smoluchowski equation.

Study of Submicron Particle Size Distributions by Laser Doppler Measurement of Brownian Motion.

DTIC Science & Technology

1984-10-29

o ..... . 5-1 A.S *6NEW DISCOVERIES OR INVENTIONS .. o......... ......... 6-1 APPENDIX: COMPUTER SIMULATION OF THE BROWNIAN MOTION SENSOR SIGNALS...scattering regime by analysis of the scattered light intensity and particle mass (size) obtained using the Brownian motion sensor . 9 Task V - By application...of the Brownian motion sensor in a flat-flame burner, the contractor shall assess the application of this technique for In-situ sizing of submicron

Displacements Of Brownian Particles In Terms Of Marian Von Smoluchowski's Heuristic Model

ERIC Educational Resources Information Center

Klein, Hermann; Woermann, Dietrich

2005-01-01

Albert Einstein's theory of the Brownian motion, Marian von Smoluchowski's heuristic model, and Perrin's experimental results helped to bring the concept of molecules from a state of being a useful hypothesis in chemistry to objects existing in reality. Central to the theory of Brownian motion is the relation between mean particle displacement and…

Velocity persistence of Brownian particles generated in a glow discharge

NASA Astrophysics Data System (ADS)

Hurd, Alan J.; Ho, Pauline

1989-06-01

Quasielastic light scattering from Brownian particles in the rarefied environment of a glow discharge exhibits Gaussianlike intensity correlation functions owing to the long mean free paths of the particles. The shape of the correlation function depends on the particles' average thermal velocity and friction coefficient, which can be related to aggregate mass and structure, and indicates a crossover from kinetic to hydrodynamic behavior.

Experimental Studies of the Brownian Diffusion of Boomerang Colloidal Particle in a Confined Geometry

NASA Astrophysics Data System (ADS)

Chakrabarty, Ayan; Wang, Feng; Joshi, Bhuwan; Wei, Qi-Huo

2011-03-01

Recent studies shows that the boomerang shaped molecules can form various kinds of liquid crystalline phases. One debated topic related to boomerang molecules is the existence of biaxial nematic liquid crystalline phase. Developing and optical microscopic studies of colloidal systems of boomerang particles would allow us to gain better understanding of orientation ordering and dynamics at ``single molecule'' level. Here we report the fabrication and experimental studies of the Brownian motion of individual boomerang colloidal particles confined between two glass plates. We used dark-field optical microscopy to directly visualize the Brownian motion of the single colloidal particles in a quasi two dimensional geometry. An EMCCD was used to capture the motion in real time. An indigenously developed imaging processing algorithm based on MatLab program was used to precisely track the position and orientation of the particles with sub-pixel accuracy. The experimental finding of the Brownian diffusion of a single boomerang colloidal particle will be discussed.

Suspended particle transport through constriction channel with Brownian motion

NASA Astrophysics Data System (ADS)

Hanasaki, Itsuo; Walther, Jens H.

2017-08-01

It is well known that translocation events of a polymer or rod through pores or narrower parts of micro- and nanochannels have a stochastic nature due to the Brownian motion. However, it is not clear whether the objects of interest need to have a larger size than the entrance to exhibit the deviation from the dynamics of the surrounding fluid. We show by numerical analysis that the particle injection into the narrower part of the channel is affected by thermal fluctuation, where the particles have spherical symmetry and are smaller than the height of the constriction. The Péclet number (Pe) is the order parameter that governs the phenomena, which clarifies the spatio-temporal significance of Brownian motion compared to hydrodynamics. Furthermore, we find that there exists an optimal condition of Pe to attain the highest flow rate of particles relative to the dispersant fluid flow. Our finding is important in science and technology from nanopore DNA sequencers and lab-on-a-chip devices to filtration by porous materials and chromatography.

Suspended particle transport through constriction channel with Brownian motion.

PubMed

Hanasaki, Itsuo; Walther, Jens H

2017-08-01

It is well known that translocation events of a polymer or rod through pores or narrower parts of micro- and nanochannels have a stochastic nature due to the Brownian motion. However, it is not clear whether the objects of interest need to have a larger size than the entrance to exhibit the deviation from the dynamics of the surrounding fluid. We show by numerical analysis that the particle injection into the narrower part of the channel is affected by thermal fluctuation, where the particles have spherical symmetry and are smaller than the height of the constriction. The Péclet number (Pe) is the order parameter that governs the phenomena, which clarifies the spatio-temporal significance of Brownian motion compared to hydrodynamics. Furthermore, we find that there exists an optimal condition of Pe to attain the highest flow rate of particles relative to the dispersant fluid flow. Our finding is important in science and technology from nanopore DNA sequencers and lab-on-a-chip devices to filtration by porous materials and chromatography.

Brownian self-driven particles on the surface of a sphere

NASA Astrophysics Data System (ADS)

Apaza, Leonardo; Sandoval, Mario

2017-08-01

We present the dynamics of overdamped Brownian self-propelled particles moving on the surface of a sphere. The effect of self-propulsion on the diffusion of these particles is elucidated by determining their angular (azimuthal and polar) mean-square displacement. Short- and long-times analytical expressions for their angular mean-square displacement are offered. Finally, the particles' steady marginal angular probability density functions are also elucidated.

Derivation of diffusion coefficient of a Brownian particle in tilted periodic potential from the coordinate moments

NASA Astrophysics Data System (ADS)

Zhang, Yunxin

2009-07-01

In this research, diffusion of an overdamped Brownian particle in the tilted periodic potential is investigated. Using the one-dimensional hopping model, the formulations of the mean velocity V and effective diffusion coefficient D of the Brownian particle have been obtained [B. Derrida, J. Stat. Phys. 31 (1983) 433]. Based on the relation between the effective diffusion coefficient and the moments of the mean first passage time, the formulation of effective diffusion coefficient D of the Brownian particle also has been obtained [P. Reimann, et al., Phys. Rev. E 65 (2002) 031104]. In this research, we'll give another analytical expression of the effective diffusion coefficient D from the moments of the particle's coordinate.

Equilibrium stochastic dynamics of a Brownian particle in inhomogeneous space: Derivation of an alternative model

NASA Astrophysics Data System (ADS)

Bhattacharyay, A.

2018-03-01

An alternative equilibrium stochastic dynamics for a Brownian particle in inhomogeneous space is derived. Such a dynamics can model the motion of a complex molecule in its conformation space when in equilibrium with a uniform heat bath. The derivation is done by a simple generalization of the formulation due to Zwanzig for a Brownian particle in homogeneous heat bath. We show that, if the system couples to different number of bath degrees of freedom at different conformations then the alternative model gets derived. We discuss results of an experiment by Faucheux and Libchaber which probably has indicated possible limitation of the Boltzmann distribution as equilibrium distribution of a Brownian particle in inhomogeneous space and propose experimental verification of the present theory using similar methods.

Hybrid particle-continuum simulations coupling Brownian dynamics and local dynamic density functional theory.

PubMed

Qi, Shuanhu; Schmid, Friederike

2017-11-08

We present a multiscale hybrid particle-field scheme for the simulation of relaxation and diffusion behavior of soft condensed matter systems. It combines particle-based Brownian dynamics and field-based local dynamics in an adaptive sense such that particles can switch their level of resolution on the fly. The switching of resolution is controlled by a tuning function which can be chosen at will according to the geometry of the system. As an application, the hybrid scheme is used to study the kinetics of interfacial broadening of a polymer blend, and is validated by comparing the results to the predictions from pure Brownian dynamics and pure local dynamics calculations.

Light scattering and dynamics of interacting Brownian particles

NASA Technical Reports Server (NTRS)

Tsang, T.; Tang, H. T.

1982-01-01

The relative motions of interacting Brownian particles in liquids may be described as radial diffusion in an effective potential of the mean force. By using a harmonic approximation for the effective potential, the intermediate scattering function may also be evaluated. For polystyrene spheres of 250 A mean radius in aqueous environment at 0.00125 g/cu cm concentration, the results for the calculated mean square displacement are in qualitative agreement with experimental data from photon correlation spectroscopy. Because of the interactions, the functions deviate considerably from the exponential forms for the free particles.

Dispersion of aerosol particles undergoing Brownian motion

NASA Astrophysics Data System (ADS)

Alonso, Manuel; Endo, Yoshiyuki

2001-12-01

The variance of the position distribution for a Brownian particle is derived in the general case where the particle is suspended in a flowing medium and, at the same time, is acted upon by an external field of force. It is shown that, for uniform force and flow fields, the variance is equal to that for a free particle. When the force field is not uniform but depends on spatial location, the variance can be larger or smaller than that for a free particle depending on whether the average motion of the particles takes place toward, respectively, increasing or decreasing absolute values of the field strength. A few examples concerning aerosol particles are discussed, with especial attention paid to the mobility classification of charged aerosols by a non-uniform electric field. As a practical application of these ideas, a new design of particle-size electrostatic classifier differential mobility analyser (DMA) is proposed in which the aerosol particles migrate between the electrodes in a direction opposite to that for a conventional DMA, thereby improving the resolution power of the instrument.

Brownian motion of boomerang colloidal particles.

PubMed

Chakrabarty, Ayan; Konya, Andrew; Wang, Feng; Selinger, Jonathan V; Sun, Kai; Wei, Qi-Huo

2013-10-18

We investigate the Brownian motion of boomerang colloidal particles confined between two glass plates. Our experimental observations show that the mean displacements are biased towards the center of hydrodynamic stress (CoH), and that the mean-square displacements exhibit a crossover from short-time faster to long-time slower diffusion with the short-time diffusion coefficients dependent on the points used for tracking. A model based on Langevin theory elucidates that these behaviors are ascribed to the superposition of two diffusive modes: the ellipsoidal motion of the CoH and the rotational motion of the tracking point with respect to the CoH.

Brownian Motion of Boomerang Colloidal Particles

NASA Astrophysics Data System (ADS)

Chakrabarty, Ayan; Konya, Andrew; Wang, Feng; Selinger, Jonathan V.; Sun, Kai; Wei, Qi-Huo

2013-10-01

We investigate the Brownian motion of boomerang colloidal particles confined between two glass plates. Our experimental observations show that the mean displacements are biased towards the center of hydrodynamic stress (CoH), and that the mean-square displacements exhibit a crossover from short-time faster to long-time slower diffusion with the short-time diffusion coefficients dependent on the points used for tracking. A model based on Langevin theory elucidates that these behaviors are ascribed to the superposition of two diffusive modes: the ellipsoidal motion of the CoH and the rotational motion of the tracking point with respect to the CoH.

Brownian trail rectified

NASA Astrophysics Data System (ADS)

Hurd, Alan J.; Ho, Pauline

The experiments described here indicate when one of Nature's best fractals -- the Brownian trail -- becomes nonfractal. In most ambient fluids, the trail of a Brownian particle is self-similar over many decades of length. For example, the trail of a submicron particle suspended in an ordinary liquid, recorded at equal time intervals, exhibits apparently discontinuous changes in velocity from macroscopic lengths down to molecular lengths: the trail is a random walk with no velocity memory from one step to the next. In ideal Brownian motion, the kinks in the trail persist to infinitesimal time intervals, i.e., it is a curve without tangents. Even in real Brownian motion in a liquid, the time interval must be shortened to approximately 10(-8) s before the velocity appears continuous. In sufficiently rarefied environments, this time resolution at which a Brownian trail is rectified from a curve without tangents to a smoothly varying trajectory is greatly lengthened, making it possible to study the kinetic regime by dynamic light scattering. Our recent experiments with particles in a plasma have demonstrated this capability. In this regime, the particle velocity persists over a finite step length allowing an analogy to an ideal gas with Maxwell-Boltzmann velocities; the particle mass could be obtained from equipartition. The crossover from ballistic flight to hydrodynamic diffusion was also seen.

Two-temperature Brownian dynamics of a particle in a confining potential

NASA Astrophysics Data System (ADS)

Mancois, Vincent; Marcos, Bruno; Viot, Pascal; Wilkowski, David

2018-05-01

We consider the two-dimensional motion of a particle in a confining potential, subject to Brownian orthogonal forces associated with two different temperatures. Exact solutions are obtained for an asymmetric harmonic potential in the overdamped and underdamped regimes. For more general confining potentials, a perturbative approach shows that the stationary state exhibits some universal properties. The nonequilibrium stationary state is characterized with a nonzero orthoradial mean current, corresponding to a global rotation of the particle around the center. The rotation is due to two broken symmetries: two different temperatures and a mismatch between the principal axes of the confining asymmetric potential and the temperature axes. We confirm our predictions by performing a Brownian dynamics simulation. Finally, we propose to observe this effect on a laser-cooled atomic gas.

Stochastic heating of a single Brownian particle by charge fluctuations in a radio-frequency produced plasma sheath

NASA Astrophysics Data System (ADS)

Schmidt, Christian; Piel, Alexander

2015-10-01

The Brownian motion of a single particle in the plasma sheath is studied to separate the effect of stochastic heating by charge fluctuations from heating by collective effects. By measuring the particle velocities in the ballistic regime and by carefully determining the particle mass from the Epstein drag it is shown that for a pressure of 10 Pa, which is typical of many experiments, the proper kinetic temperature of the Brownian particle remains close to the gas temperature and rises only slightly with particle size. This weak effect is confirmed by a detailed model for charging and charge fluctuations in the sheath. A substantial temperature rise is found for decreasing pressure, which approximately shows the expected scaling with p-2. The system under study is an example for non-equilibrium Brownian motion under the influence of white noise without corresponding dissipation.

Brownian Motion of Boomerang Colloidal Particles

NASA Astrophysics Data System (ADS)

Wei, Qi-Huo; Konya, Andrew; Wang, Feng; Selinger, Jonathan V.; Sun, Kai; Chakrabarty, Ayan

2014-03-01

We present experimental and theoretical studies on the Brownian motion of boomerang colloidal particles confined between two glass plates. Our experimental observations show that the mean displacements are biased towards the center of hydrodynamic stress (CoH), and that the mean-square displacements exhibit a crossover from short-time faster to long-time slower diffusion with the short-time diffusion coefficients dependent on the points used for tracking. A model based on Langevin theory elucidates that these behaviors are ascribed to the superposition of two diffusive modes: the ellipsoidal motion of the CoH and the rotational motion of the tracking point with respect to the CoH.

Swimming path statistics of an active Brownian particle with time-dependent self-propulsion

NASA Astrophysics Data System (ADS)

Babel, S.; ten Hagen, B.; Löwen, H.

2014-02-01

Typically, in the description of active Brownian particles, a constant effective propulsion force is assumed, which is then subjected to fluctuations in orientation and translation, leading to a persistent random walk with an enlarged long-time diffusion coefficient. Here, we generalize previous results for the swimming path statistics to a time-dependent, and thus in many situations more realistic, propulsion which is a prescribed input. We analytically calculate both the noise-free and the noise-averaged trajectories for time-periodic propulsion under the action of an additional torque. In the deterministic case, such an oscillatory microswimmer moves on closed paths that can be much more complicated than the commonly observed straight lines and circles. When exposed to random fluctuations, the mean trajectories turn out to be self-similar curves which bear the characteristics of their noise-free counterparts. Furthermore, we consider a propulsion force which scales in time t as ∝tα (with α = 0,1,2, …) and analyze the resulting superdiffusive behavior. Our predictions are verifiable for diffusiophoretic artificial microswimmers with prescribed propulsion protocols.

Extreme fluctuations of active Brownian motion

NASA Astrophysics Data System (ADS)

Pietzonka, Patrick; Kleinbeck, Kevin; Seifert, Udo

2016-05-01

In active Brownian motion, an internal propulsion mechanism interacts with translational and rotational thermal noise and other internal fluctuations to produce directed motion. We derive the distribution of its extreme fluctuations and identify its universal properties using large deviation theory. The limits of slow and fast internal dynamics give rise to a kink-like and parabolic behavior of the corresponding rate functions, respectively. For dipolar Janus particles in two- and three-dimensions interacting with a field, we predict a novel symmetry akin to, but different from, the one related to entropy production. Measurements of these extreme fluctuations could thus be used to infer properties of the underlying, often hidden, network of states.

A Mechanical Model of Brownian Motion for One Massive Particle Including Slow Light Particles

NASA Astrophysics Data System (ADS)

Liang, Song

2018-01-01

We provide a connection between Brownian motion and a classical mechanical system. Precisely, we consider a system of one massive particle interacting with an ideal gas, evolved according to non-random mechanical principles, via interaction potentials, without any assumption requiring that the initial velocities of the environmental particles should be restricted to be "fast enough". We prove the convergence of the (position, velocity)-process of the massive particle under a certain scaling limit, such that the mass of the environmental particles converges to 0 while the density and the velocities of them go to infinity, and give the precise expression of the limiting process, a diffusion process.

Development of a semiclassical method to compute mobility and diffusion coefficient of a Brownian particle in a nonequilibrium environment.

PubMed

Shit, Anindita; Ghosh, Pradipta; Chattopadhyay, Sudip; Chaudhuri, Jyotipratim Ray

2011-03-01

We explore the issue of a quantum-noise-induced directed transport of an overdamped Brownian particle that is allowed to move in a spatially periodic potential. The established system-reservoir model has been employed here to study the quantum-noise-induced transport of a Brownian particle in a periodic potential, where the reservoir is being modulated externally by a Gaussian-colored noise. The mobility of the Brownian particle in the linear response regime has been calculated. Then, using Einstein's relation, the analytical expression for the diffusion rate is evaluated for any arbitrary periodic potential for the high-temperature quantum regime.

Self-propelled colloidal particle near a planar wall: A Brownian dynamics study

NASA Astrophysics Data System (ADS)

Mozaffari, Ali; Sharifi-Mood, Nima; Koplik, Joel; Maldarelli, Charles

2018-01-01

Miniaturized, self-propelled locomotors use chemo-mechanical transduction mechanisms to convert fuel in the environment to autonomous motion. Recent experimental and theoretical studies demonstrate that these autonomous engines can passively follow the contours of solid boundaries they encounter. Boundary guidance, however, is not necessarily stable: Mechanical disturbances can cause the motor to hydrodynamically depart from the passively guided pathway. Furthermore, given the scaled-down size of micromotors (typically 100 nm to10 μ m ), Brownian thermal fluctuation forces are necessarily important, and these stochastic forces can randomize passively steered trajectories. Here we examine theoretically the stability of boundary-guided motion of micromotors along infinite planar walls to mechanical disturbances and to Brownian forces. Our aim is to understand under what conditions this passively guided motion is stable. We choose a locomotor design in which spherical colloids are partially coated with a catalytic cap that reacts with solute to produce a product. The product is repelled from the particle surface, causing the particle to move with the inert face at the front (autonomous motion via self-diffusiophoresis). When propelled towards a planar wall, deterministic hydrodynamic studies demonstrate that these locomotors can exhibit, for large enough cap sizes, steady trajectories in which the particle either skims unidirectionally along the surface at a constant distance from the wall or becomes stationary. We first investigate the linear hydrodynamic stability of these states by expanding the equations of motion about the states, and we find that linear perturbations decay exponentially in time. We then study the effects of thermal fluctuations by formulating a Langevin equation for the particle motion which includes the Brownian stochastic force. The Péclet number scales the ratio of deterministic to Brownian forces, where Pe =π μ a2v˜c/kBT and a denotes

Upside/Downside statistical mechanics of nonequilibrium Brownian motion. I. Distributions, moments, and correlation functions of a free particle.

PubMed

Craven, Galen T; Nitzan, Abraham

2018-01-28

Statistical properties of Brownian motion that arise by analyzing, separately, trajectories over which the system energy increases (upside) or decreases (downside) with respect to a threshold energy level are derived. This selective analysis is applied to examine transport properties of a nonequilibrium Brownian process that is coupled to multiple thermal sources characterized by different temperatures. Distributions, moments, and correlation functions of a free particle that occur during upside and downside events are investigated for energy activation and energy relaxation processes and also for positive and negative energy fluctuations from the average energy. The presented results are sufficiently general and can be applied without modification to the standard Brownian motion. This article focuses on the mathematical basis of this selective analysis. In subsequent articles in this series, we apply this general formalism to processes in which heat transfer between thermal reservoirs is mediated by activated rate processes that take place in a system bridging them.

Upside/Downside statistical mechanics of nonequilibrium Brownian motion. I. Distributions, moments, and correlation functions of a free particle

NASA Astrophysics Data System (ADS)

Craven, Galen T.; Nitzan, Abraham

2018-01-01

Statistical properties of Brownian motion that arise by analyzing, separately, trajectories over which the system energy increases (upside) or decreases (downside) with respect to a threshold energy level are derived. This selective analysis is applied to examine transport properties of a nonequilibrium Brownian process that is coupled to multiple thermal sources characterized by different temperatures. Distributions, moments, and correlation functions of a free particle that occur during upside and downside events are investigated for energy activation and energy relaxation processes and also for positive and negative energy fluctuations from the average energy. The presented results are sufficiently general and can be applied without modification to the standard Brownian motion. This article focuses on the mathematical basis of this selective analysis. In subsequent articles in this series, we apply this general formalism to processes in which heat transfer between thermal reservoirs is mediated by activated rate processes that take place in a system bridging them.

Broadband boundary effects on Brownian motion.

PubMed

Mo, Jianyong; Simha, Akarsh; Raizen, Mark G

2015-12-01

Brownian motion of particles in confined fluids is important for many applications, yet the effects of the boundary over a wide range of time scales are still not well understood. We report high-bandwidth, comprehensive measurements of Brownian motion of an optically trapped micrometer-sized silica sphere in water near an approximately flat wall. At short distances we observe anisotropic Brownian motion with respect to the wall. We find that surface confinement not only occurs in the long time scale diffusive regime but also in the short time scale ballistic regime, and the velocity autocorrelation function of the Brownian particle decays faster than that of a particle in bulk fluid. Furthermore, at low frequencies the thermal force loses its color due to the reflected flow from the no-slip boundary. The power spectrum of the thermal force on the particle near a no-slip boundary becomes flat at low frequencies. This detailed understanding of boundary effects on Brownian motion opens a door to developing a 3D microscope using particles as remote sensors.

Escape rate of Brownian particles from a metastable potential well under time derivative Ornstein-Uhlenbeck noise

NASA Astrophysics Data System (ADS)

Bai, Zhan-Wu; Wang, Ping

2016-03-01

We investigate the escape rate of Brownian particles that move in a cubic metastable potential subjected to an internal time derivative Ornstein-Uhlenbeck noise (DOUN). This noise can induce the ballistic diffusion of force-free Brownian particles. Some new features are found. The escape rate for DOUN shows qualitative different dependence on potential well width compared with OUN which induces normal diffusion. As the potential barrier height decreases, the escape rate of DOUN deviates from Arrhenius law considerably earlier than that of Ornstein-Uhlenbeck noise (OUN). The Brownian particles escape faster under DOUN than that under OUN. A quasi-periodic oscillation occurs in transient state. A solvable case is presented to demonstrate the significant cancellation behavior in the barrier region that governs most of these phenomena. The physical mechanism of the findings can be clarified by the noise features. These characteristics should be common for internal noises that induce superdiffusion, especially the ballistic diffusion.

Emergence of Collective Motion in a Model of Interacting Brownian Particles.

PubMed

Dossetti, Victor; Sevilla, Francisco J

2015-07-31

By studying a system of Brownian particles that interact among themselves only through a local velocity-alignment force that does not affect their speed, we show that self-propulsion is not a necessary feature for the flocking transition to take place as long as underdamped particle dynamics can be guaranteed. Moreover, the system transits from stationary phases close to thermal equilibrium, with no net flux of particles, to far-from-equilibrium ones exhibiting collective motion, phase coexistence, long-range order, and giant number fluctuations, features typically associated with ordered phases of models where self-propelled particles with overdamped dynamics are considered.

Lock-and-key dimerization in dense Brownian systems of hard annular sector particles

NASA Astrophysics Data System (ADS)

Hodson, Wade D.; Mason, Thomas G.

2016-08-01

We develop a translational-rotational cage model that describes the behavior of dense two-dimensional (2D) Brownian systems of hard annular sector particles (ASPs), resembling C shapes. At high particle densities, pairs of ASPs can form mutually interdigitating lock-and-key dimers. This cage model considers either one or two mobile central ASPs which can translate and rotate within a static cage of surrounding ASPs that mimics the system's average local structure and density. By comparing with recent measurements made on dispersions of microscale lithographic ASPs [P. Y. Wang and T. G. Mason, J. Am. Chem. Soc. 137, 15308 (2015), 10.1021/jacs.5b10549], we show that mobile two-particle predictions of the probability of dimerization Pdimer, equilibrium constant K , and 2D osmotic pressure Π2 D as a function of the particle area fraction ϕA correspond closely to these experiments. By contrast, predictions based on only a single mobile particle do not agree well with either the two-particle predictions or the experimental data. Thus, we show that collective entropy can play an essential role in the behavior of dense Brownian systems composed of nontrivial hard shapes, such as ASPs.

Work fluctuations for a Brownian particle between two thermostats

NASA Astrophysics Data System (ADS)

Visco, Paolo

2006-06-01

We explicitly determine the large deviation function of the energy flow of a Brownian particle coupled to two heat baths at different temperatures. This toy model, initially introduced by Derrida and Brunet (2005, Einstein aujourd'hui (Les Ulis: EDP Sciences)), not only allows us to sort out the influence of initial conditions on large deviation functions but also allows us to pinpoint various restrictions bearing upon the range of validity of the Fluctuation Relation.

Active particles in complex and crowded environments

DOE PAGES

Bechinger, Clemens; Di Leonardo, Roberto; Löwen, Hartmut; ...

2016-11-23

Differently from passive Brownian particles, active particles, also known as self-propelled Brownian particles or microswimmers and nanoswimmers, are capable of taking up energy from their environment and converting it into directed motion. Because of this constant flow of energy, their behavior can be explained and understood only within the framework of nonequilibrium physics. In the biological realm, many cells perform directed motion, for example, as a way to browse for nutrients or to avoid toxins. Inspired by these motile microorganisms, researchers have been developing artificial particles that feature similar swimming behaviors based on different mechanisms. These man-made micromachines and nanomachinesmore » hold a great potential as autonomous agents for health care, sustainability, and security applications. Finally, with a focus on the basic physical features of the interactions of self-propelled Brownian particles with a crowded and complex environment, this comprehensive review will provide a guided tour through its basic principles, the development of artificial self-propelling microparticles and nanoparticles, and their application to the study of nonequilibrium phenomena, as well as the open challenges that the field is currently facing.« less

Large-displacement statistics of the rightmost particle of the one-dimensional branching Brownian motion.

PubMed

Derrida, Bernard; Meerson, Baruch; Sasorov, Pavel V

2016-04-01

Consider a one-dimensional branching Brownian motion and rescale the coordinate and time so that the rates of branching and diffusion are both equal to 1. If X_{1}(t) is the position of the rightmost particle of the branching Brownian motion at time t, the empirical velocity c of this rightmost particle is defined as c=X_{1}(t)/t. Using the Fisher-Kolmogorov-Petrovsky-Piscounov equation, we evaluate the probability distribution P(c,t) of this empirical velocity c in the long-time t limit for c>2. It is already known that, for a single seed particle, P(c,t)∼exp[-(c^{2}/4-1)t] up to a prefactor that can depend on c and t. Here we show how to determine this prefactor. The result can be easily generalized to the case of multiple seed particles and to branching random walks associated with other traveling-wave equations.

Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Speck, Thomas; Menzel, Andreas M.; Bialké, Julian

2015-06-14

Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation ontomore » that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.« less

Brownian dynamics simulation of rigid particles of arbitrary shape in external fields.

PubMed

Fernandes, Miguel X; de la Torre, José García

2002-12-01

We have developed a Brownian dynamics simulation algorithm to generate Brownian trajectories of an isolated, rigid particle of arbitrary shape in the presence of electric fields or any other external agents. Starting from the generalized diffusion tensor, which can be calculated with the existing HYDRO software, the new program BROWNRIG (including a case-specific subprogram for the external agent) carries out a simulation that is analyzed later to extract the observable dynamic properties. We provide a variety of examples of utilization of this method, which serve as tests of its performance, and also illustrate its applicability. Examples include free diffusion, transport in an electric field, and diffusion in a restricting environment.

111 years of Brownian motion.

PubMed

Bian, Xin; Kim, Changho; Karniadakis, George Em

2016-08-14

We consider the Brownian motion of a particle and present a tutorial review over the last 111 years since Einstein's paper in 1905. We describe Einstein's model, Langevin's model and the hydrodynamic models, with increasing sophistication on the hydrodynamic interactions between the particle and the fluid. In recent years, the effects of interfaces on the nearby Brownian motion have been the focus of several investigations. We summarize various results and discuss some of the controversies associated with new findings about the changes in Brownian motion induced by the interface.

111 years of Brownian motion

PubMed Central

Kim, Changho

2017-01-01

We consider the Brownian motion of a particle and present a tutorial review over the last 111 years since Einstein’s paper in 1905. We describe Einstein’s model, Langevin’s model and the hydrodynamic models, with increasing sophistication on the hydrodynamic interactions between the particle and the fluid. In recent years, the effects of interfaces on the nearby Brownian motion have been the focus of several investigations. We summarize various results and discuss some of the controversies associated with new findings about the changes in Brownian motion induced by the interface. PMID:27396746

Diffusion mechanism of non-interacting Brownian particles through a deformed substrate

NASA Astrophysics Data System (ADS)

Arfa, Lahcen; Ouahmane, Mehdi; El Arroum, Lahcen

2018-02-01

We study the diffusion mechanism of non-interacting Brownian particles through a deformed substrate. The study is done at low temperature for different values of the friction. The deformed substrate is represented by a periodic Remoissenet-Peyrard potential with deformability parameter s. In this potential, the particles (impurity, adatoms…) can diffuse. We ignore the interactions between these mobile particles consider them merely as non-interacting Brownian particles and this system is described by a Fokker-Planck equation. We solve this equation numerically using the matrix continued fraction method to calculate the dynamic structure factor S(q , ω) . From S(q , ω) some relevant correlation functions are also calculated. In particular, we determine the half-width line λ(q) of the peak of the quasi-elastic dynamic structure factor S(q , ω) and the diffusion coefficient D. Our numerical results show that the diffusion mechanism is described, depending on the structure of the potential, either by a simple jump diffusion process with jump length close to the lattice constant a or by a combination of a jump diffusion model with jump length close to lattice constant a and a liquid-like motion inside the unit cell. It shows also that, for different friction regimes and various potential shapes, the friction attenuates the diffusion mechanism. It is found that, in the high friction regime, the diffusion process is more important through a deformed substrate than through a non-deformed one.

Noise enhanced stability of a metastable state containing coupled Brownian particles

NASA Astrophysics Data System (ADS)

Singh, R. K.

2017-05-01

Dynamics of coupled Brownian particles with color correlated additive Gaussian colored noises in a metastable state is analyzed to study the phenomenon of noise enhanced stability. The lifetime of such a metastable state is found to depend on the noise correlations and initial conditions. Dynamics of the slow variable is analyzed using the method of adiabatic elimination in the weak color limit.

Fabrication and characterization of non-Brownian particle-based crystals.

PubMed

Lash, Melissa H; Fedorchak, Morgan V; Little, Steven R; McCarthy, Joseph J

2015-01-27

Particle-based crystals have been explored in the literature for applications in molecular electronics, photonics, sensors, and drug delivery. However, much of the research on these crystals has been focused on particles of nano- and submicrometer dimensions (so-called colloidal crystals) with limited attention directed toward building blocks with dimensions ranging from tens to hundreds of micrometers. This can be attributed, in part, to the fact that the underlying thermal effects in these larger systems typically cannot naturally overcome kinetic barriers at the meso- and macroscales so that many of the methods used for nanoscale particle assembly cannot be directly applied to larger components, as they become kinetically arrested in nonequilibrium states. In this work, ultrasonic agitation is being explored as a means of allowing large, non-Brownian microparticles (18-750 μm) to overcome the kinetic barriers to packing in the creation of close-packed, highly ordered, crystalline structures. In addition, we study how the energy input affects bulk particle behavior and describe several new ways to characterize particle-based crystals made from microparticles.

Detection of weak signals through nonlinear relaxation times for a Brownian particle in an electromagnetic field.

PubMed

Jiménez-Aquino, J I; Romero-Bastida, M

2011-07-01

The detection of weak signals through nonlinear relaxation times for a Brownian particle in an electromagnetic field is studied in the dynamical relaxation of the unstable state, characterized by a two-dimensional bistable potential. The detection process depends on a dimensionless quantity referred to as the receiver output, calculated as a function of the nonlinear relaxation time and being a characteristic time scale of our system. The latter characterizes the complete dynamical relaxation of the Brownian particle as it relaxes from the initial unstable state of the bistable potential to its corresponding steady state. The one-dimensional problem is also studied to complement the description.

Brownian microhydrodynamics of active filaments.

PubMed

Laskar, Abhrajit; Adhikari, R

2015-12-21

Slender bodies capable of spontaneous motion in the absence of external actuation in an otherwise quiescent fluid are common in biological, physical and technological contexts. The interplay between the spontaneous fluid flow, Brownian motion, and the elasticity of the body presents a challenging fluid-structure interaction problem. Here, we model this problem by approximating the slender body as an elastic filament that can impose non-equilibrium velocities or stresses at the fluid-structure interface. We derive equations of motion for such an active filament by enforcing momentum conservation in the fluid-structure interaction and assuming slow viscous flow in the fluid. The fluid-structure interaction is obtained, to any desired degree of accuracy, through the solution of an integral equation. A simplified form of the equations of motion, which allows for efficient numerical solutions, is obtained by applying the Kirkwood-Riseman superposition approximation to the integral equation. We use this form of equation of motion to study dynamical steady states in free and hinged minimally active filaments. Our model provides the foundation to study collective phenomena in momentum-conserving, Brownian, active filament suspensions.

Stochastic dynamics of coupled active particles in an overdamped limit

NASA Astrophysics Data System (ADS)

Ann, Minjung; Lee, Kong-Ju-Bock; Park, Pyeong Jun

2015-10-01

We introduce a model for Brownian dynamics of coupled active particles in an overdamped limit. Our system consists of several identical active particles and one passive particle. Each active particle is elastically coupled to the passive particle and there is no direct coupling among the active particles. We investigate the dynamics of the system with respect to the number of active particles, viscous friction, and coupling between the active and passive particles. For this purpose, we consider an intracellular transport process as an application of our model and perform a Brownian dynamics simulation using realistic parameters for processive molecular motors such as kinesin-1. We determine an adequate energy conversion function for molecular motors and study the dynamics of intracellular transport by multiple motors. The results show that the average velocity of the coupled system is not affected by the number of active motors and that the stall force increases linearly as the number of motors increases. Our results are consistent with well-known experimental observations. We also examine the effects of coupling between the motors and the cargo, as well as of the spatial distribution of the motors around the cargo. Our model might provide a physical explanation of the cooperation among active motors in the cellular transport processes.

Diffusion in different models of active Brownian motion

NASA Astrophysics Data System (ADS)

Lindner, B.; Nicola, E. M.

2008-04-01

Active Brownian particles (ABP) have served as phenomenological models of self-propelled motion in biology. We study the effective diffusion coefficient of two one-dimensional ABP models (simplified depot model and Rayleigh-Helmholtz model) differing in their nonlinear friction functions. Depending on the choice of the friction function the diffusion coefficient does or does not attain a minimum as a function of noise intensity. We furthermore discuss the case of an additional bias breaking the left-right symmetry of the system. We show that this bias induces a drift and that it generally reduces the diffusion coefficient. For a finite range of values of the bias, both models can exhibit a maximum in the diffusion coefficient vs. noise intensity.

Estimate of blow-up and relaxation time for self-gravitating Brownian particles and bacterial populations.

PubMed

Chavanis, P-H; Sire, C

2004-08-01

We determine an exact asymptotic expression of the blow-up time t(coll) for self-gravitating Brownian particles or bacterial populations (chemotaxis) close to the critical point in d=3. We show that t(coll) = t(*) (eta- eta(c) )(-1/2) with t(*) =0.917 677 02..., where eta represents the inverse temperature (for Brownian particles) or the mass (for bacterial colonies), and eta(c) is the critical value of eta above which the system blows up. This result is in perfect agreement with the numerical solution of the Smoluchowski-Poisson system. We also determine the exact asymptotic expression of the relaxation time close to but above the critical temperature and derive a large time asymptotic expansion for the density profile exactly at the critical point.

Hybrid finite element and Brownian dynamics method for charged particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huber, Gary A., E-mail: ghuber@ucsd.edu; Miao, Yinglong; Zhou, Shenggao

2016-04-28

Diffusion is often the rate-determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. A previous study introduced a new hybrid diffusion method that couples the strengths of each of these two methods, but was limited by the lack of interactions among the particles; the force on each particle had to be from an external field. This study further develops the method to allow charged particles. The method is derived for a general multidimensional system and is presented usingmore » a basic test case for a one-dimensional linear system with one charged species and a radially symmetric system with three charged species.« less

Brownian Motion.

ERIC Educational Resources Information Center

Lavenda, Bernard H.

1985-01-01

Explains the phenomenon of Brownian motion, which serves as a mathematical model for random processes. Topics addressed include kinetic theory, Einstein's theory, particle displacement, and others. Points out that observations of the random course of a particle suspended in fluid led to the first accurate measurement of atomic mass. (DH)

Brownian motion on random dynamical landscapes

NASA Astrophysics Data System (ADS)

Suñé Simon, Marc; Sancho, José María; Lindenberg, Katja

2016-03-01

We present a study of overdamped Brownian particles moving on a random landscape of dynamic and deformable obstacles (spatio-temporal disorder). The obstacles move randomly, assemble, and dissociate following their own dynamics. This landscape may account for a soft matter or liquid environment in which large obstacles, such as macromolecules and organelles in the cytoplasm of a living cell, or colloids or polymers in a liquid, move slowly leading to crowding effects. This representation also constitutes a novel approach to the macroscopic dynamics exhibited by active matter media. We present numerical results on the transport and diffusion properties of Brownian particles under this disorder biased by a constant external force. The landscape dynamics are characterized by a Gaussian spatio-temporal correlation, with fixed time and spatial scales, and controlled obstacle concentrations.

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

NASA Astrophysics Data System (ADS)

Romanczuk, P.; Bär, M.; Ebeling, W.; Lindner, B.; Schimansky-Geier, L.

2012-03-01

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.

Irreversible Brownian Heat Engine

NASA Astrophysics Data System (ADS)

Taye, Mesfin Asfaw

2017-10-01

We model a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a linearly decreasing background temperature. We show that the efficiency of such Brownian heat engine approaches the efficiency of endoreversible engine η =1-√{{Tc/Th}} [23]. On the other hand, the maximum power efficiency of the engine approaches η ^{MAX}=1-({Tc/Th})^{1\\over 4}. It is shown that the optimized efficiency always lies between the efficiency at quasistatic limit and the efficiency at maximum power while the efficiency at maximum power is always less than the optimized efficiency since the fast motion of the particle comes at the expense of the energy cost. If the heat exchange at the boundary of the heat baths is included, we show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature. The role of time on the performance of the motor is also explored via numerical simulations. Our numerical results depict that the time t and the external load dictate the direction of the particle velocity. Moreover, the performance of the heat engine improves with time. At large t (steady state), the velocity, the efficiency and the coefficient of performance of the refrigerator attain their maximum value. Furthermore, we study the effect of temperature by considering a viscous friction that decreases exponentially as the background temperature increases. Our result depicts that the Brownian particle exhibits a fast unidirectional motion when the viscous friction is temperature dependent than that of constant viscous friction. Moreover, the efficiency of this motor is considerably enhanced when the viscous friction is temperature dependent. On the hand, the motor exhibits a higher performance of the refrigerator when the viscous friction is taken to be constant.

Brownian motion of a nano-colloidal particle: the role of the solvent.

PubMed

Torres-Carbajal, Alexis; Herrera-Velarde, Salvador; Castañeda-Priego, Ramón

2015-07-15

Brownian motion is a feature of colloidal particles immersed in a liquid-like environment. Usually, it can be described by means of the generalised Langevin equation (GLE) within the framework of the Mori theory. In principle, all quantities that appear in the GLE can be calculated from the molecular information of the whole system, i.e., colloids and solvent molecules. In this work, by means of extensive Molecular Dynamics simulations, we study the effects of the microscopic details and the thermodynamic state of the solvent on the movement of a single nano-colloid. In particular, we consider a two-dimensional model system in which the mass and size of the colloid are two and one orders of magnitude, respectively, larger than the ones associated with the solvent molecules. The latter ones interact via a Lennard-Jones-type potential to tune the nature of the solvent, i.e., it can be either repulsive or attractive. We choose the linear momentum of the Brownian particle as the observable of interest in order to fully describe the Brownian motion within the Mori framework. We particularly focus on the colloid diffusion at different solvent densities and two temperature regimes: high and low (near the critical point) temperatures. To reach our goal, we have rewritten the GLE as a second kind Volterra integral in order to compute the memory kernel in real space. With this kernel, we evaluate the momentum-fluctuating force correlation function, which is of particular relevance since it allows us to establish when the stationarity condition has been reached. Our findings show that even at high temperatures, the details of the attractive interaction potential among solvent molecules induce important changes in the colloid dynamics. Additionally, near the critical point, the dynamical scenario becomes more complex; all the correlation functions decay slowly in an extended time window, however, the memory kernel seems to be only a function of the solvent density. Thus, the

The stochastic thermodynamics of a rotating Brownian particle in a gradient flow

PubMed Central

Lan, Yueheng; Aurell, Erik

2015-01-01

We compute the entropy production engendered in the environment from a single Brownian particle which moves in a gradient flow, and show that it corresponds in expectation to classical near-equilibrium entropy production in the surrounding fluid with specific mesoscopic transport coefficients. With temperature gradient, extra terms are found which result from the nonlinear interaction between the particle and the non-equilibrated environment. The calculations are based on the fluctuation relations which relate entropy production to the probabilities of stochastic paths and carried out in a multi-time formalism. PMID:26194015

Correlational approach to study interactions between dust Brownian particles in a plasma

NASA Astrophysics Data System (ADS)

Lisin, E. A.; Vaulina, O. S.; Petrov, O. F.

2018-01-01

A general approach to the correlational analysis of Brownian motion of strongly coupled particles in open dissipative systems is described. This approach can be applied to the theoretical description of various non-ideal statistically equilibrium systems (including non-Hamiltonian systems), as well as for the analysis of experimental data. In this paper, we consider an application of the correlational approach to the problem of experimental exploring the wake-mediated nonreciprocal interactions in complex plasmas. We derive simple analytic equations, which allows one to calculate the gradients of forces acting on a microparticle due to each of other particles as well as the gradients of external field, knowing only the information on time-averaged correlations of particles displacements and velocities. We show the importance of taking dissipative and random processes into account, without which consideration of a system with a nonreciprocal interparticle interaction as linearly coupled oscillators leads to significant errors in determining the characteristic frequencies in a system. In the examples of numerical simulations, we demonstrate that the proposed original approach could be an effective instrument in exploring the longitudinal wake structure of a microparticle in a plasma. Unlike the previous attempts to study the wake-mediated interactions in complex plasmas, our method does not require any external perturbations and is based on Brownian motion analysis only.

Slow kinetics of Brownian maxima.

PubMed

Ben-Naim, E; Krapivsky, P L

2014-07-18

We study extreme-value statistics of Brownian trajectories in one dimension. We define the maximum as the largest position to date and compare maxima of two particles undergoing independent Brownian motion. We focus on the probability P(t) that the two maxima remain ordered up to time t and find the algebraic decay P ∼ t(-β) with exponent β = 1/4. When the two particles have diffusion constants D(1) and D(2), the exponent depends on the mobilities, β = (1/π) arctan sqrt[D(2)/D(1)]. We also use numerical simulations to investigate maxima of multiple particles in one dimension and the largest extension of particles in higher dimensions.

Rotational Brownian Dynamics simulations of clathrin cage formation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ilie, Ioana M.; Briels, Wim J.; MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede

2014-08-14

The self-assembly of nearly rigid proteins into ordered aggregates is well suited for modeling by the patchy particle approach. Patchy particles are traditionally simulated using Monte Carlo methods, to study the phase diagram, while Brownian Dynamics simulations would reveal insights into the assembly dynamics. However, Brownian Dynamics of rotating anisotropic particles gives rise to a number of complications not encountered in translational Brownian Dynamics. We thoroughly test the Rotational Brownian Dynamics scheme proposed by Naess and Elsgaeter [Macromol. Theory Simul. 13, 419 (2004); Naess and Elsgaeter Macromol. Theory Simul. 14, 300 (2005)], confirming its validity. We then apply the algorithmmore » to simulate a patchy particle model of clathrin, a three-legged protein involved in vesicle production from lipid membranes during endocytosis. Using this algorithm we recover time scales for cage assembly comparable to those from experiments. We also briefly discuss the undulatory dynamics of the polyhedral cage.« less

Inertial effects of a small Brownian particle cause a colored power spectral density of thermal noise.

PubMed

Jannasch, Anita; Mahamdeh, Mohammed; Schäffer, Erik

2011-11-25

The random thermal force acting on Brownian particles is often approximated in Langevin models by a "white-noise" process. However, fluid entrainment results in a frequency dependence of this thermal force giving it a "color." While theoretically well understood, direct experimental evidence for this colored nature of the noise term and how it is influenced by a nearby wall is lacking. Here, we directly measured the color of the thermal noise intensity by tracking a particle strongly confined in an ultrastable optical trap. All our measurements are in quantitative agreement with the theoretical predictions. Since Brownian motion is important for microscopic, in particular, biological systems, the colored nature of the noise and its distance dependence to nearby objects need to be accounted for and may even be utilized for advanced sensor applications.

Antiswarming: Structure and dynamics of repulsive chemically active particles

NASA Astrophysics Data System (ADS)

Yan, Wen; Brady, John F.

2017-12-01

Chemically active Brownian particles with surface catalytic reactions may repel each other due to diffusiophoretic interactions in the reaction and product concentration fields. The system behavior can be described by a "chemical" coupling parameter Γc that compares the strength of diffusiophoretic repulsion to Brownian motion, and by a mapping to the classical electrostatic one component plasma (OCP) system. When confined to a constant-volume domain, body-centered cubic (bcc) crystals spontaneously form from random initial configurations when the repulsion is strong enough to overcome Brownian motion. Face-centered cubic (fcc) crystals may also be stable. The "melting point" of the "liquid-to-crystal transition" occurs at Γc≈140 for both bcc and fcc lattices.

Dynamic properties of polydisperse colloidal particles in the presence of thermal gradient studied by a modified Brownian dynamic model

NASA Astrophysics Data System (ADS)

Song, Dongxing; Jin, Hui; Jing, Dengwei; Wang, Xin

2018-03-01

Aggregation and migration of colloidal particles under the thermal gradient widely exists in nature and many industrial processes. In this study, dynamic properties of polydisperse colloidal particles in the presence of thermal gradient were studied by a modified Brownian dynamic model. Other than the traditional forces on colloidal particles, including Brownian force, hydrodynamic force, and electrostatic force from other particles, the electrostatic force from the asymmetric ionic diffusion layer under a thermal gradient has been considered and introduced into the Brownian dynamic model. The aggregation ratio of particles (R A), the balance time (t B) indicating the time threshold when {{R}A} becomes constant, the porosity ({{P}BA} ), fractal dimension (D f) and distributions of concentration (DISC) and aggregation (DISA) for the aggregated particles were discussed based on this model. The aggregated structures formed by polydisperse particles are less dense and the particles therein are loosely bonded. Also it showed a quite large compressibility as the increases of concentration and interparticle potential can significantly increase the fractal dimension. The thermal gradient can induce two competitive factors leading to a two-stage migration of particles. When t<{{t}B} , the unsynchronized aggregation is dominant and the particles slightly migrate along the thermal gradient. When t>{{t}B} , the thermophoresis becomes dominant thus the migrations of particles are against the thermal gradient. The effect of thermophoresis on the aggregate structures was found to be similar to the effect of increasing particle concentration. This study demonstrates how the thermal gradient affects the aggregation of monodisperse and polydisperse particles and can be a guide for the biomimetics and precise control of colloid system under the thermal gradient. Moreover, our model can be easily extended to other more complex colloidal systems considering shear, temperature

Quantum Brownian motion with inhomogeneous damping and diffusion

NASA Astrophysics Data System (ADS)

Massignan, Pietro; Lampo, Aniello; Wehr, Jan; Lewenstein, Maciej

2015-03-01

We analyze the microscopic model of quantum Brownian motion, describing a Brownian particle interacting with a bosonic bath through a coupling which is linear in the creation and annihilation operators of the bath, but may be a nonlinear function of the position of the particle. Physically, this corresponds to a configuration in which damping and diffusion are spatially inhomogeneous. We derive systematically the quantum master equation for the Brownian particle in the Born-Markov approximation and we discuss the appearance of additional terms, for various polynomials forms of the coupling. We discuss the cases of linear and quadratic coupling in great detail and we derive, using Wigner function techniques, the stationary solutions of the master equation for a Brownian particle in a harmonic trapping potential. We predict quite generally Gaussian stationary states, and we compute the aspect ratio and the spread of the distributions. In particular, we find that these solutions may be squeezed (superlocalized) with respect to the position of the Brownian particle. We analyze various restrictions to the validity of our theory posed by non-Markovian effects and by the Heisenberg principle. We further study the dynamical stability of the system, by applying a Gaussian approximation to the time-dependent Wigner function, and we compute the decoherence rates of coherent quantum superpositions in position space. Finally, we propose a possible experimental realization of the physics discussed here, by considering an impurity particle embedded in a degenerate quantum gas.

Brownian Dynamics of Colloidal Particles in Lyotropic Chromonic Liquid Crystals

NASA Astrophysics Data System (ADS)

Martinez, Angel; Collings, Peter J.; Yodh, Arjun G.

We employ video microscopy to study the Brownian dynamics of colloidal particles in the nematic phase of lyotropic chromonic liquid crystals (LCLCs). These LCLCs (in this case, DSCG) are water soluble, and their nematic phases are characterized by an unusually large elastic anisotropy. Our preliminary measurements of particle mean-square displacement for polystyrene colloidal particles (~5 micron-diameter) show diffusive and sub-diffusive behaviors moving parallel and perpendicular to the nematic director, respectively. In order to understand these motions, we are developing models that incorporate the relaxation of elastic distortions of the surrounding nematic field. Further experiments to confirm these preliminary results and to determine the origin of these deviations compared to simple diffusion theory are ongoing; our results will also be compared to previous diffusion experiments in nematic liquid crystals. We gratefully acknowledge financial support through NSF DMR12-05463, MRSEC DMR11-20901, and NASA NNX08AO0G.

A theory for the phase behavior of mixtures of active particles.

PubMed

Takatori, Sho C; Brady, John F

2015-10-28

Systems at equilibrium like molecular or colloidal suspensions have a well-defined thermal energy kBT that quantifies the particles' kinetic energy and gauges how "hot" or "cold" the system is. For systems far from equilibrium, such as active matter, it is unclear whether the concept of a "temperature" exists and whether self-propelled entities are capable of thermally equilibrating like passive Brownian suspensions. Here we develop a simple mechanical theory to study the phase behavior and "temperature" of a mixture of self-propelled particles. A mixture of active swimmers and passive Brownian particles is an ideal system for discovery of the temperature of active matter and the quantities that get shared upon particle collisions. We derive an explicit equation of state for the active/passive mixture to compute a phase diagram and to generalize thermodynamic concepts like the chemical potential and free energy for a mixture of nonequilibrium species. We find that different stability criteria predict in general different phase boundaries, facilitating considerations in simulations and experiments about which ensemble of variables are held fixed and varied.

Brownian motion as a new probe of wettability.

PubMed

Mo, Jianyong; Simha, Akarsh; Raizen, Mark G

2017-04-07

Understanding wettability is crucial for optimizing oil recovery, semiconductor manufacturing, pharmaceutical industry, and electrowetting. In this letter, we study the effects of wettability on Brownian motion. We consider the cases of a sphere in an unbounded fluid medium, as well as a sphere placed in the vicinity of a plane wall. For the first case, we show the effects of wettability on the statistical properties of the particles' motion, such as velocity autocorrelation, velocity, and thermal force power spectra over a large range of time scales. We also propose a new method to measure wettability based on the particles' Brownian motion. In addition, we compare the boundary effects on Brownian motion imposed by both no-slip and perfect-slip flat walls. We emphasize the surprising boundary effects on Brownian motion imposed by a perfect-slip wall in the parallel direction, such as a higher particle mobility parallel to a perfect flat wall compared to that in the absence of the wall, as well as compared to a particle near a no-slip flat wall.

Anti-Brownian ELectrokinetic (ABEL) Trapping of Single High Density Lipoprotein (HDL) Particles

NASA Astrophysics Data System (ADS)

Bockenhauer, Samuel; Furstenberg, Alexandre; Wang, Quan; Devree, Brian; Jie Yao, Xiao; Bokoch, Michael; Kobilka, Brian; Sunahara, Roger; Moerner, W. E.

2010-03-01

The ABEL trap is a novel device for trapping single biomolecules in solution for extended observation. The trap estimates the position of a fluorescently-labeled object as small as ˜10 nm in solution and then applies a feedback electrokinetic drift every 20 us to trap the object by canceling its Brownian motion. We use the ABEL trap to study HDL particles at the single-copy level. HDL particles, essential in regulation of ``good'' cholesterol in humans, comprise a small (˜10 nm) lipid bilayer disc bounded by a belt of apolipoproteins. By engineering HDL particles with single fluorescent donor/acceptor probes and varying lipid compositions, we are working to study lipid diffusion on small length scales. We also use HDL particles as hosts for single transmembrane receptors, which should enable study of receptor conformational dynamics on long timescales.

Active Brownian rods

NASA Astrophysics Data System (ADS)

Peruani, Fernando

2016-11-01

Bacteria, chemically-driven rods, and motility assays are examples of active (i.e. self-propelled) Brownian rods (ABR). The physics of ABR, despite their ubiquity in experimental systems, remains still poorly understood. Here, we review the large-scale properties of collections of ABR moving in a dissipative medium. We address the problem by presenting three different models, of decreasing complexity, which we refer to as model I, II, and III, respectively. Comparing model I, II, and III, we disentangle the role of activity and interactions. In particular, we learn that in two dimensions by ignoring steric or volume exclusion effects, large-scale nematic order seems to be possible, while steric interactions prevent the formation of orientational order at large scales. The macroscopic behavior of ABR results from the interplay between active stresses and local alignment. ABR exhibit, depending on where we locate ourselves in parameter space, a zoology of macroscopic patterns that ranges from polar and nematic bands to dynamic aggregates.

Brownian Emitters

NASA Astrophysics Data System (ADS)

Tsekov, Roumen

2016-06-01

A Brownian harmonic oscillator, which dissipates energy either by friction or via emission of electromagnetic radiation, is considered. This Brownian emitter is driven by the surrounding thermo-quantum fluctuations, which are theoretically described by the fluctuation-dissipation theorem. It is shown how the Abraham-Lorentz force leads to dependence of the half-width on the peak frequency of the oscillator amplitude spectral density. It is found that for the case of a charged particle moving in vacuum at zero temperature, its root-mean-square velocity fluctuation is a universal constant, equal to roughly 1/18 of the speed of light. The relevant Fokker-Planck and Smoluchowski equations are also derived.

Optimum analysis of a Brownian refrigerator.

PubMed

Luo, X G; Liu, N; He, J Z

2013-02-01

A Brownian refrigerator with the cold and hot reservoirs alternating along a space coordinate is established. The heat flux couples with the movement of the Brownian particles due to an external force in the spatially asymmetric but periodic potential. After using the Arrhenius factor to describe the behaviors of the forward and backward jumps of the particles, the expressions for coefficient of performance (COP) and cooling rate are derived analytically. Then, through maximizing the product of conversion efficiency and heat flux flowing out, a new upper bound only depending on the temperature ratio of the cold and hot reservoirs is found numerically in the reversible situation, and it is a little larger than the so-called Curzon and Ahlborn COP ε(CA)=(1/√[1-τ])-1. After considering the irreversible factor owing to the kinetic energy change of the moving particles, we find the optimized COP is smaller than ε(CA) and the external force even does negative work on the Brownian particles when they jump from a cold to hot reservoir.

Local characterization of hindered Brownian motion by using digital video microscopy and 3D particle tracking

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dettmer, Simon L.; Keyser, Ulrich F.; Pagliara, Stefano

In this article we present methods for measuring hindered Brownian motion in the confinement of complex 3D geometries using digital video microscopy. Here we discuss essential features of automated 3D particle tracking as well as diffusion data analysis. By introducing local mean squared displacement-vs-time curves, we are able to simultaneously measure the spatial dependence of diffusion coefficients, tracking accuracies and drift velocities. Such local measurements allow a more detailed and appropriate description of strongly heterogeneous systems as opposed to global measurements. Finite size effects of the tracking region on measuring mean squared displacements are also discussed. The use of thesemore » methods was crucial for the measurement of the diffusive behavior of spherical polystyrene particles (505 nm diameter) in a microfluidic chip. The particles explored an array of parallel channels with different cross sections as well as the bulk reservoirs. For this experiment we present the measurement of local tracking accuracies in all three axial directions as well as the diffusivity parallel to the channel axis while we observed no significant flow but purely Brownian motion. Finally, the presented algorithm is suitable also for tracking of fluorescently labeled particles and particles driven by an external force, e.g., electrokinetic or dielectrophoretic forces.« less

Experimental Study of Short-Time Brownian Motion

NASA Astrophysics Data System (ADS)

Mo, Jianyong; Simha, Akarsh; Riegler, David; Raizen, Mark

2015-03-01

We report our progress on the study of short-time Brownian motion of optically-trapped microspheres. In earlier work, we observed the instantaneous velocity of microspheres in gas and in liquid, verifying a prediction by Albert Einstein from 1907. We now report a more accurate test of the energy equipartition theorem for a particle in liquid. We also observe boundary effects on Brownian motion in liquid by setting a wall near the trapped particle, which changes the dynamics of the motion. We find that the velocity autocorrelation of the particle decreases faster as the particle gets closer to the wall.

Thermophoresis of a Brownian particle driven by inhomogeneous thermal fluctuation

NASA Astrophysics Data System (ADS)

Tsuji, Tetsuro; Saita, Sho; Kawano, Satoyuki

2018-03-01

Brownian motion of a spherical particle induced by the interaction with surrounding molecules is considered. If the particle is larger than the molecules and the temperature of surrounding media is spatially non-uniform, the interaction between an individual molecule and the particle is also position-dependent. That is, the particle is subject to inhomogeneous thermal fluctuation. In this paper, we investigate the contribution of the inhomogeneous thermal fluctuation to the thermophoresis, i.e., the Soret coefficient or thermal diffusion factor. The problem is simplified by assuming a hard-sphere potential between the particle and the surrounding molecules and is investigated using the kinetic theory, namely, we consider a linear Boltzmann-type equation for the velocity distribution function of the particle. Using the perturbation analysis with respect to the square root of mass ratio between the molecule and the particle, the drift-diffusion equation of the particle is derived. It is found that the Soret coefficient, or thermal diffusion factor, is dependent on the mass ratio and the excluded volume of the particle. In particular, when the ratio of the mass density of the particle to that of the surrounding media decreases, the Soret coefficient also decreases and may take negative value. The present result well describes the mass-dependency of thermal diffusion factor obtained by the molecular dynamics simulation carried out in an existing study and the one in the present study, where soft potentials of Lennard-Jones-type are used instead of hard-sphere potential.

Negative mobility of a Brownian particle: Strong damping regime

NASA Astrophysics Data System (ADS)

Słapik, A.; Łuczka, J.; Spiechowicz, J.

2018-02-01

We study impact of inertia on directed transport of a Brownian particle under non-equilibrium conditions: the particle moves in a one-dimensional periodic and symmetric potential, is driven by both an unbiased time-periodic force and a constant force, and is coupled to a thermostat of temperature T. Within selected parameter regimes this system exhibits negative mobility, which means that the particle moves in the direction opposite to the direction of the constant force. It is known that in such a setup the inertial term is essential for the emergence of negative mobility and it cannot be detected in the limiting case of overdamped dynamics. We analyse inertial effects and show that negative mobility can be observed even in the strong damping regime. We determine the optimal dimensionless mass for the presence of negative mobility and reveal three mechanisms standing behind this anomaly: deterministic chaotic, thermal noise induced and deterministic non-chaotic. The last origin has never been reported. It may provide guidance to the possibility of observation of negative mobility for strongly damped dynamics which is of fundamental importance from the point of view of biological systems, all of which in situ operate in fluctuating environments.

Channeling by Proximity: The Catalytic Advantages of Active Site Colocalization Using Brownian Dynamics.

PubMed

Bauler, Patricia; Huber, Gary; Leyh, Thomas; McCammon, J Andrew

2010-05-06

Nature often colocalizes successive steps in a metabolic pathway. Such organization is predicted to increase the effective concentration of pathway intermediates near their recipient active sites and to enhance catalytic efficiency. Here, the pathway of a two-step reaction is modeled using a simple spherical approximation for the enzymes and substrate particles. Brownian dynamics are used to simulate the trajectory of a substrate particle as it diffuses between the active site zones of two different enzyme spheres. The results approximate distances for the most effective reaction pathways, indicating that the most effective reaction pathway is one in which the active sites are closely aligned. However, when the active sites are too close, the ability of the substrate to react with the first enzyme was hindered, suggesting that even the most efficient orientations can be improved for a system that is allowed to rotate or change orientation to optimize the likelihood of reaction at both sites.

Effect of interfaces on the nearby Brownian motion

PubMed Central

Huang, Kai; Szlufarska, Izabela

2015-01-01

Near-boundary Brownian motion is a classic hydrodynamic problem of great importance in a variety of fields, from biophysics to micro-/nanofluidics. However, owing to challenges in experimental measurements of near-boundary dynamics, the effect of interfaces on Brownian motion has remained elusive. Here we report a computational study of this effect using μs-long large-scale molecular dynamics simulations and our newly developed Green–Kubo relation for friction at the liquid–solid interface. Our computer experiment unambiguously reveals that the t−3/2 long-time decay of the velocity autocorrelation function of a Brownian particle in bulk liquid is replaced by a t−5/2 decay near a boundary. We discover a general breakdown of traditional no-slip boundary condition at short time scales and we show that this breakdown has a profound impact on the near-boundary Brownian motion. Our results demonstrate the potential of Brownian-particle-based micro-/nanosonar to probe the local wettability of liquid–solid interfaces. PMID:26438034

Effect of interfaces on the nearby Brownian motion.

PubMed

Huang, Kai; Szlufarska, Izabela

2015-10-06

Near-boundary Brownian motion is a classic hydrodynamic problem of great importance in a variety of fields, from biophysics to micro-/nanofluidics. However, owing to challenges in experimental measurements of near-boundary dynamics, the effect of interfaces on Brownian motion has remained elusive. Here we report a computational study of this effect using μs-long large-scale molecular dynamics simulations and our newly developed Green-Kubo relation for friction at the liquid-solid interface. Our computer experiment unambiguously reveals that the t(-3/2) long-time decay of the velocity autocorrelation function of a Brownian particle in bulk liquid is replaced by a t(-5/2) decay near a boundary. We discover a general breakdown of traditional no-slip boundary condition at short time scales and we show that this breakdown has a profound impact on the near-boundary Brownian motion. Our results demonstrate the potential of Brownian-particle-based micro-/nanosonar to probe the local wettability of liquid-solid interfaces.

The Bumper Boats Effect: Effect of Inertia on Self Propelled Active Particles Systems

NASA Astrophysics Data System (ADS)

Dai, Chengyu; Bruss, Isaac; Glotzer, Sharon

Active matter has been well studied using the standard Brownian dynamics model, which assumes that the self-propelled particles have no inertia. However, many examples of active systems, such as sub-millimeter bacteria and colloids, have non-negligible inertia. Using particle-based Langevin Dynamics simulation with HOOMD-blue, we study the role of particle inertia on the collective emergent behavior of self-propelled particles. We find that inertia hinders motility-induced phase separation. This is because the effective speed of particles is reduced due to particle-particle collisions-\\x9Dmuch like bumper boats, which take time to reach terminal velocity after a crash. We are able to fully account for this effect by tracking a particle's average rather than terminal velocity, allowing us to extend the standard Brownian dynamics model to account for the effects of momentum. This study aims to inform experimental systems where the inertia of the active particles is non-negligible. We acknowledge the funding support from the Center for Bio-Inspired Energy Science (CBES), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award # DE-SC0000989.

Diffusion of active chiral particles

NASA Astrophysics Data System (ADS)

Sevilla, Francisco J.

2016-12-01

The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position x and moving along the direction v ̂ at time t , and numerically, by the use of Langevin dynamics simulations. The analysis is focused on the marginal probability density of finding a particle at a given location and at a given time (independently of its direction of motion), which is found from an infinite hierarchy of differential-recurrence relations for the coefficients that appear in the multipole expansion of the probability distribution, which contains the whole kinematic information. This approach allows the explicit calculation of the time dependence of the mean-squared displacement and the time dependence of the kurtosis of the marginal probability distribution, quantities from which the effective diffusion coefficient and the "shape" of the positions distribution are examined. Oscillations between two characteristic values were found in the time evolution of the kurtosis, namely, between the value that corresponds to a Gaussian and the one that corresponds to a distribution of spherical shell shape. In the case of an ensemble of particles, each one rotating around a uniformly distributed random axis, evidence is found of the so-called effect "anomalous, yet Brownian, diffusion," for which particles follow a non-Gaussian distribution for the positions yet the mean-squared displacement is a linear function of time.

Scaling of the space-time correlation function of particle currents in a suspension of hard-sphere-like particles: exposing when the motion of particles is Brownian.

PubMed

van Megen, W; Martinez, V A; Bryant, G

2009-12-18

The current correlation function is determined from dynamic light scattering measurements of a suspension of particles with hard spherelike interactions. For suspensions in thermodynamic equilibrium we find scaling of the space and time variables of the current correlation function. This finding supports the notion that the movement of suspended particles can be described in terms of uncorrelated Brownian encounters. However, in the metastable fluid, at volume fractions above freezing, this scaling fails.

Mathematical interpretation of Brownian motor model: Limit cycles and directed transport phenomena

NASA Astrophysics Data System (ADS)

Yang, Jianqiang; Ma, Hong; Zhong, Suchuang

2018-03-01

In this article, we first suggest that the attractor of Brownian motor model is one of the reasons for the directed transport phenomenon of Brownian particle. We take the classical Smoluchowski-Feynman (SF) ratchet model as an example to investigate the relationship between limit cycles and directed transport phenomenon of the Brownian particle. We study the existence and variation rule of limit cycles of SF ratchet model at changing parameters through mathematical methods. The influences of these parameters on the directed transport phenomenon of a Brownian particle are then analyzed through numerical simulations. Reasonable mathematical explanations for the directed transport phenomenon of Brownian particle in SF ratchet model are also formulated on the basis of the existence and variation rule of the limit cycles and numerical simulations. These mathematical explanations provide a theoretical basis for applying these theories in physics, biology, chemistry, and engineering.

Triplet correlation in sheared suspensions of Brownian particles

NASA Astrophysics Data System (ADS)

Yurkovetsky, Yevgeny; Morris, Jeffrey F.

2006-05-01

Triplet microstructure of sheared concentrated suspensions of Brownian monodisperse spherical particles is studied by sampling realizations of a three-dimensional unit cell subject to periodic boundary conditions obtained in accelerated Stokesian dynamics simulations. Triplets are regarded as a bridge between particle pairs and many-particle clusters thought responsible for shear thickening. Triplet-correlation data for weakly sheared near-equilibrium systems display an excluded volume effect of accumulated correlation for equilateral contacting triplets. As the Péclet number increases, there is a change in the preferred contacting isosceles triplet configuration, away from the "closed" triplet where the particles lie at the vertices of an equilateral triangle and toward the fully extended rod-like linear arrangement termed the "open" triplet. This transition is most pronounced for triplets lying in the plane of shear, where the open triplets' angular orientation with respect to the flow is very similar to that of a contacting pair. The correlation of suspension rheology to observed structure signals onset of larger clusters. An investigation of the predictive ability of Kirkwood's superposition approximation (KSA) provides valuable insights into the relationship between the pair and triplet probability distributions and helps achieve a better and more detailed understanding of the interplay of the pair and triplet dynamics. The KSA is seen more successfully to predict the shape of isosceles contacting triplet nonequilibrium distributions in the plane of shear than for similar configurations in equilibrium hard-sphere systems; in the sheared case, the discrepancies in magnitudes of distribution peaks are attributable to two interaction effects when pair average trajectories and locations of particles change in response to real, or "hard," and probabilistically favored ("soft") neighboring excluded volumes and, in the case of open triplets, due to changes in the

Transport of nano-objects in narrow channels: influence of Brownian diffusion, confinement and particle nature

NASA Astrophysics Data System (ADS)

Liot, O.; Socol, M.; Garcia, L.; Thiéry, J.; Figarol, A.; Mingotaud, A. F.; Joseph, P.

2018-06-01

This paper presents experimental results about transport of dilute suspensions of nano-objects in silicon-glass micrometric and sub-micrometric channels. Two kinds of objects are used: solid, rigid latex beads and spherical capsule-shaped, soft polymersomes. They are tracked using fluorescence microscopy. Three aspects are studied: confinement (ratio between particle diameter and channel depth), Brownian diffusion and particle nature. The aim of this work is to understand how these different aspects affect the transport of suspensions in narrow channels and to understand the different mechanisms at play. Concerning the solid beads we observe the appearance of two regimes, one where the experimental mean velocity is close to the expected one and another where this velocity is lower. This is directly related to a competition between confinement, Brownian diffusion and advection. These two regimes are shown to be linked to the inhomogeneity of particles distribution in the channel depth, which we experimentally deduce from velocity distributions. This inhomogeneity appears during the entrance process into the sub-micrometric channels, as for hydrodynamic separation or deterministic lateral displacement. Concerning the nature of the particles we observed a shift of transition towards the second regime likely due to the relationships between shear stress and polymersomes mechanical properties which could reduce the inhomogeneity imposed by the geometry of our device.

Transport of nano-objects in narrow channels: influence of Brownian diffusion, confinement and particle nature.

PubMed

Liot, O; Socol, M; Garcia, L; Thiéry, J; Figarol, A; Mingotaud, A F; Joseph, P

2018-06-13

This paper presents experimental results about transport of dilute suspensions of nano-objects in silicon-glass micrometric and sub-micrometric channels. Two kinds of objects are used: solid, rigid latex beads and spherical capsule-shaped, soft polymersomes. They are tracked using fluorescence microscopy. Three aspects are studied: confinement (ratio between particle diameter and channel depth), Brownian diffusion and particle nature. The aim of this work is to understand how these different aspects affect the transport of suspensions in narrow channels and to understand the different mechanisms at play. Concerning the solid beads we observe the appearance of two regimes, one where the experimental mean velocity is close to the expected one and another where this velocity is lower. This is directly related to a competition between confinement, Brownian diffusion and advection. These two regimes are shown to be linked to the inhomogeneity of particles distribution in the channel depth, which we experimentally deduce from velocity distributions. This inhomogeneity appears during the entrance process into the sub-micrometric channels, as for hydrodynamic separation or deterministic lateral displacement. Concerning the nature of the particles we observed a shift of transition towards the second regime likely due to the relationships between shear stress and polymersomes mechanical properties which could reduce the inhomogeneity imposed by the geometry of our device.

Nonisothermal fluctuating hydrodynamics and Brownian motion

NASA Astrophysics Data System (ADS)

Falasco, G.; Kroy, K.

2016-03-01

The classical theory of Brownian dynamics follows from coarse graining the underlying linearized fluctuating hydrodynamics of the solvent. We extend this procedure to globally nonisothermal conditions, requiring only a local thermal equilibration of the solvent. Starting from the conservation laws, we establish the stochastic equations of motion for the fluid momentum fluctuations in the presence of a suspended Brownian particle. These are then contracted to the nonisothermal generalized Langevin description of the suspended particle alone, for which the coupling to stochastic temperature fluctuations is found to be negligible under typical experimental conditions.

O'Connell's process as a vicious Brownian motion.

PubMed

Katori, Makoto

2011-12-01

Vicious Brownian motion is a diffusion scaling limit of Fisher's vicious walk model, which is a system of Brownian particles in one dimension such that if two motions meet they kill each other. We consider the vicious Brownian motions conditioned never to collide with each other and call it noncolliding Brownian motion. This conditional diffusion process is equivalent to the eigenvalue process of the Hermitian-matrix-valued Brownian motion studied by Dyson [J. Math. Phys. 3, 1191 (1962)]. Recently, O'Connell [Ann. Probab. (to be published)] introduced a generalization of the noncolliding Brownian motion by using the eigenfunctions (the Whittaker functions) of the quantum Toda lattice in order to analyze a directed polymer model in 1 + 1 dimensions. We consider a system of one-dimensional Brownian motions with a long-ranged killing term as a generalization of the vicious Brownian motion and construct the O'Connell process as a conditional process of the killing Brownian motions to survive forever.

O'Connell's process as a vicious Brownian motion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Katori, Makoto

Vicious Brownian motion is a diffusion scaling limit of Fisher's vicious walk model, which is a system of Brownian particles in one dimension such that if two motions meet they kill each other. We consider the vicious Brownian motions conditioned never to collide with each other and call it noncolliding Brownian motion. This conditional diffusion process is equivalent to the eigenvalue process of the Hermitian-matrix-valued Brownian motion studied by Dyson [J. Math. Phys. 3, 1191 (1962)]. Recently, O'Connell [Ann. Probab. (to be published)] introduced a generalization of the noncolliding Brownian motion by using the eigenfunctions (the Whittaker functions) of themore » quantum Toda lattice in order to analyze a directed polymer model in 1 + 1 dimensions. We consider a system of one-dimensional Brownian motions with a long-ranged killing term as a generalization of the vicious Brownian motion and construct the O'Connell process as a conditional process of the killing Brownian motions to survive forever.« less

Limitations of differential electrophoresis for measuring colloidal forces: a Brownian dynamics study.

PubMed

Holtzer, Gretchen L; Velegol, Darrell

2005-10-25

Differential electrophoresis experiments are often used to measure subpiconewton forces between two spheres of a heterodoublet. The experiments have been interpreted by solving the electrokinetic equations to obtain a simple Stokes law-type equation. However, for nanocolloids, the effects of Brownian motion alter the interpretation: (1) Brownian translation changes the rate of axial separation. (2) Brownian rotation reduces the alignment of the doublet with the applied electric field. (3) Particles can reaggregate by Brownian motion after they break, forming either heterodoublets or homodoublets, and because homodoublets cannot be broken by differential electrophoresis, this effectively terminates the experiment. We tackle points 1 and 2 using Brownian dynamics simulations (BDS) with electrophoresis as an external force, accounting for convective translation and rotation as well as Brownian translation and rotation. Our simulations identify the lower particle size limit of differential electrophoresis to be about 1 microm for desired statistical accuracy. Furthermore, our simulations predict that particles around 10 nm in size and at ambient conditions will break primarily by Brownian motion, with a negligible effect due to the electric field.

Entropic forces in Brownian motion

NASA Astrophysics Data System (ADS)

Roos, Nico

2014-12-01

Interest in the concept of entropic forces has risen considerably since Verlinde proposed in 2011 to interpret the force in Newton's second law and gravity as entropic forces. Brownian motion—the motion of a small particle (pollen) driven by random impulses from the surrounding molecules—may be the first example of a stochastic process in which such forces are expected to emerge. In this article, it is shown that at least two types of entropic force can be identified in three-dimensional Brownian motion. This analysis yields simple derivations of known results of Brownian motion, Hooke's law, and—applying an external (non-radial) force—Curie's law and the Langevin-Debye equation.

Enhancement of Brownian motion for a chain of particles in a periodic potential

NASA Astrophysics Data System (ADS)

Dessup, Tommy; Coste, Christophe; Saint Jean, Michel

2018-02-01

The transport of particles in very confined channels in which single file diffusion occurs has been largely studied in systems where the transverse confining potential is smooth. However, in actual physical systems, this potential may exhibit both static corrugations and time fluctuations. Some recent results suggest the important role played by this nonsmoothness of the confining potential. In particular, quite surprisingly, an enhancement of the Brownian motion of the particles has been evidenced in these kinds of systems. We show that this enhancement results from the commensurate effects induced by the underlying potential on the vibrational spectra of the chain of particles, and from the effective temperature associated with its time fluctuations. We will restrict our derivation to the case of low temperatures for which the mean squared displacement of the particles remains smaller than the potential period.

Entropy production of a Brownian ellipsoid in the overdamped limit.

PubMed

Marino, Raffaele; Eichhorn, Ralf; Aurell, Erik

2016-01-01

We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called "anomalous" contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the "anomalous" entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the "anomalous entropy" for prolate and oblate spheroids and for near-spherical Brownian particles.

The Effects of the Interplay between Motor and Brownian Forces on the Rheology of Active Gels.

PubMed

Córdoba, Andrés

2018-04-19

Active gels perform key mechanical roles inside the cell, such as cell division, motion, and force sensing. The unique mechanical properties required to perform such functions arise from the interactions between molecular motors and semiflexible polymeric filaments. Molecular motors can convert the energy released in the hydrolysis of ATP into forces of up to piconewton magnitudes. Moreover, the polymeric filaments that form active gels are flexible enough to respond to Brownian forces but also stiff enough to support the large tensions induced by the motor-generated forces. Brownian forces are expected to have a significant effect especially at motor activities at which stable noncontractile in vitro active gels are prepared for rheological measurements. Here, a microscopic mean-field theory of active gels originally formulated in the limit of motor-dominated dynamics is extended to include Brownian forces. In the model presented here, Brownian forces are included accurately, at real room temperature, even in systems with high motor activity. It is shown that a subtle interplay, or competition, between motor-generated forces and Brownian forces has an important impact on the mass transport and rheological properties of active gels. The model predictions show that at low frequencies the dynamic modulus of active gels is determined mostly by motor protein dynamics. However, Brownian forces significantly increase the breadth of the relaxation spectrum and can affect the shape of the dynamic modulus over a wide frequency range even for ratios of motor to Brownian forces of more than a hundred. Since the ratio between motor and Brownian forces is sensitive to ATP concentration, the results presented here shed some light on how the transient mechanical response of active gels changes with varying ATP concentration.

Tested Demonstrations. Brownian Motion: A Classroom Demonstration and Student Experiment.

ERIC Educational Resources Information Center

Kirksey, H. Graden; Jones, Richard F.

1988-01-01

Shows how video recordings of the Brownian motion of tiny particles may be made. Describes a classroom demonstration and cites a reported experiment designed to show the random nature of Brownian motion. Suggests a student experiment to discover the distance a tiny particle travels as a function of time. (MVL)

Microscopic theory of Brownian motion revisited: The Rayleigh model

NASA Astrophysics Data System (ADS)

Kim, Changho; Karniadakis, George Em

2013-03-01

We investigate three force autocorrelation functions , , and and the friction coefficient γ for the Rayleigh model (a massive particle in an ideal gas) by analytic methods and molecular-dynamics (MD) simulations. Here, F and F+ are the total force and the Mori fluctuating force, respectively, whereas F0 is the force on the Brownian particle under the frozen dynamics, where the Brownian particle is held fixed and the solvent particles move under the external potential due to the presence of the Brownian particle. By using ensemble averaging and the ray representation approach, we obtain two expressions for in terms of the one-particle trajectory and corresponding expressions for γ by the time integration of these expressions. Performing MD simulations of the near-Brownian-limit (NBL) regime, we investigate the convergence of and and compare them with . We show that for a purely repulsive potential between the Brownian particle and a solvent particle, both expressions for produce in the NBL regime. On the other hand, for a potential containing an attractive component, the ray representation expression produces only the contribution of the nontrapped solvent particles. However, we show that the net contribution of the trapped particles to γ disappears, and hence we confirm that both the ensemble-averaged expression and the ray representation expression for γ are valid even if the potential contains an attractive component. We also obtain a closed-form expression of γ for the square-well potential. Finally, we discuss theoretical and practical aspects for the evaluation of and γ.

Brownian dynamics without Green's functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Delong, Steven; Donev, Aleksandar, E-mail: donev@courant.nyu.edu; Usabiaga, Florencio Balboa

2014-04-07

We develop a Fluctuating Immersed Boundary (FIB) method for performing Brownian dynamics simulations of confined particle suspensions. Unlike traditional methods which employ analytical Green's functions for Stokes flow in the confined geometry, the FIB method uses a fluctuating finite-volume Stokes solver to generate the action of the response functions “on the fly.” Importantly, we demonstrate that both the deterministic terms necessary to capture the hydrodynamic interactions among the suspended particles, as well as the stochastic terms necessary to generate the hydrodynamically correlated Brownian motion, can be generated by solving the steady Stokes equations numerically only once per time step. Thismore » is accomplished by including a stochastic contribution to the stress tensor in the fluid equations consistent with fluctuating hydrodynamics. We develop novel temporal integrators that account for the multiplicative nature of the noise in the equations of Brownian dynamics and the strong dependence of the mobility on the configuration for confined systems. Notably, we propose a random finite difference approach to approximating the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. Through comparisons with analytical and existing computational results, we numerically demonstrate the ability of the FIB method to accurately capture both the static (equilibrium) and dynamic properties of interacting particles in flow.« less

Recovery of mechanical pressure in a gas of underdamped active dumbbells with Brownian noise

NASA Astrophysics Data System (ADS)

Joyeux, Marc

2017-05-01

In contrast with a gas at thermodynamic equilibrium, the mean force exerted on a wall by a gas of active particles usually depends on the confining potential, thereby preventing a proper definition of mechanical pressure. In this paper, we investigate numerically the properties of a gas of underdamped self-propelled dumbbells subject to Brownian noise of increasing intensity, in order to understand how the notion of pressure is recovered as noise progressively masks the effects of self-propulsion and the system approaches thermodynamic equilibrium. The simulations performed for a mobile asymmetric wall separating two chambers containing an equal number of active dumbbells highlight some subtle and unexpected properties of the system. First, Brownian noise of moderate intensity is sufficient to let mean forces equilibrate for small values of the damping coefficient, while much stronger noise is required for larger values of the damping coefficient. Moreover, the displacement of the mean position of the wall upon increase of the intensity of the noise is not necessarily monotonous and may instead display changes of direction. Both facts actually reflect the existence of several mechanisms leading to the rupture of force balance, which tend to displace the mean position of the wall towards different directions and display different robustness against an increase of the intensity of Brownian noise. This work therefore provides a clear illustration of the fact that driving an autonomous system towards (or away from) thermodynamic equilibrium may not be a straightforward process, but may instead proceed through the variations of the relative weights of several conflicting mechanisms.

Transport properties of active Brownian particles in a modified energy-depot model driven by correlated noises

NASA Astrophysics Data System (ADS)

Guan, Lin; Fang, Yuwen; Li, Kongzhai; Zeng, Chunhua; Yang, Fengzao

2018-09-01

In this paper, we investigate the role of correlated multiplicative (κ1) and additive (κ2) noises in a modified energy conversion depot model, at which it is added a linear term in the conversion of internal energy of active Brownian particles (ABPs). The linear term (a1 ≠ 0 . 0) in energy conversion model breaks the symmetry of the potential to generate motion of the ABPs with a net transport velocity. Adopt a nonlinear Langevin approach, the transport properties of the ABPs have been discussed, and our results show that: (i) the transport velocity <υ1 > of the ABPs are always positive whether the correlation intensity λ = 0 . 0 or not; (ii) for a small value of the multiplicative noise intensity κ1, the variation of <υ1 > with λ shows a minimum, there exists an optimal value of the correlation intensity λ at which the <υ1 > of the ABPs is minimized. But for a large value of κ1, the <υ1 > monotonically decreases; (iii) the transport velocity <υ1 > increases with the increase of the κ1 or κ2, i.e., the multiplicative or additive noise can facilitate the transport of the ABPs; and (iv) the effective diffusion increases with the increase of a1, namely, the linear term in modified energy conversion model of the ABPs can enhance the diffusion of the ABPs.

Deposition and reentrainment of Brownian particles in porous media under unfavorable chemical conditions: some concepts and applications.

PubMed

Hahn, Melinda W; O'Meliae, Charles R

2004-01-01

The deposition and reentrainment of particles in porous media have been examined theoretically and experimentally. A Brownian Dynamics/Monte Carlo (MC/BD) model has been developed that simulates the movement of Brownian particles near a collector under "unfavorable" chemical conditions and allows deposition in primary and secondary minima. A simple Maxwell approach has been used to estimate particle attachment efficiency by assuming deposition in the secondary minimum and calculating the probability of reentrainment. The MC/BD simulations and the Maxwell calculations support an alternative view of the deposition and reentrainment of Brownian particles under unfavorable chemical conditions. These calculations indicate that deposition into and subsequent release from secondary minima can explain reported discrepancies between classic model predictions that assume irreversible deposition in a primary well and experimentally determined deposition efficiencies that are orders of magnitude larger than Interaction Force Boundary Layer (IFBL) predictions. The commonly used IFBL model, for example, is based on the notion of transport over an energy barrier into the primary well and does not address contributions of secondary minimum deposition. A simple Maxwell model based on deposition into and reentrainment from secondary minima is much more accurate in predicting deposition rates for column experiments at low ionic strengths. It also greatly reduces the substantial particle size effects inherent in IFBL models, wherein particle attachment rates are predicted to decrease significantly with increasing particle size. This view is consistent with recent work by others addressing the composition and structure of the first few nanometers at solid-water interfaces including research on modeling water at solid-liquid interfaces, surface speciation, interfacial force measurements, and the rheological properties of concentrated suspensions. It follows that deposition under these

Meandering Brownian Donkeys

NASA Astrophysics Data System (ADS)

Eichhorn, R.; Reimann, P.

2004-04-01

We consider a Brownian particle whose motion is confined to a ``meandering'' pathway and which is driven away from thermal equilibrium by an alternating external force. This system exhibits absolute negative mobility, i.e. when an external static force is applied the particle moves in the direction opposite to that force. We reveal the physical mechanism behind this ``donkey-like'' behavior, and derive analytical approximations that are in excellent agreement with numerical results.

Simulations of magnetic nanoparticle Brownian motion

PubMed Central

Reeves, Daniel B.; Weaver, John B.

2012-01-01

Magnetic nanoparticles are useful in many medical applications because they interact with biology on a cellular level thus allowing microenvironmental investigation. An enhanced understanding of the dynamics of magnetic particles may lead to advances in imaging directly in magnetic particle imaging or through enhanced MRI contrast and is essential for nanoparticle sensing as in magnetic spectroscopy of Brownian motion. Moreover, therapeutic techniques like hyperthermia require information about particle dynamics for effective, safe, and reliable use in the clinic. To that end, we have developed and validated a stochastic dynamical model of rotating Brownian nanoparticles from a Langevin equation approach. With no field, the relaxation time toward equilibrium matches Einstein's model of Brownian motion. In a static field, the equilibrium magnetization agrees with the Langevin function. For high frequency or low amplitude driving fields, behavior characteristic of the linearized Debye approximation is reproduced. In a higher field regime where magnetic saturation occurs, the magnetization and its harmonics compare well with the effective field model. On another level, the model has been benchmarked against experimental results, successfully demonstrating that harmonics of the magnetization carry enough information to infer environmental parameters like viscosity and temperature. PMID:23319830

Effective diffusion of confined active Brownian swimmers.

PubMed

Sandoval, Mario; Dagdug, Leornardo

2014-12-01

We theoretically find the effect of confinement and thermal fluctuations on the diffusivity of a spherical active swimmer moving inside a two-dimensional narrow cavity of general shape. The explicit formulas for the effective diffusion coefficient of a swimmer moving inside two particular cavities are presented. We also compare our analytical results with Brownian dynamics simulations and we obtain excellent agreement.

High-precision tracking of brownian boomerang colloidal particles confined in quasi two dimensions.

PubMed

Chakrabarty, Ayan; Wang, Feng; Fan, Chun-Zhen; Sun, Kai; Wei, Qi-Huo

2013-11-26

In this article, we present a high-precision image-processing algorithm for tracking the translational and rotational Brownian motion of boomerang-shaped colloidal particles confined in quasi-two-dimensional geometry. By measuring mean square displacements of an immobilized particle, we demonstrate that the positional and angular precision of our imaging and image-processing system can achieve 13 nm and 0.004 rad, respectively. By analyzing computer-simulated images, we demonstrate that the positional and angular accuracies of our image-processing algorithm can achieve 32 nm and 0.006 rad. Because of zero correlations between the displacements in neighboring time intervals, trajectories of different videos of the same particle can be merged into a very long time trajectory, allowing for long-time averaging of different physical variables. We apply this image-processing algorithm to measure the diffusion coefficients of boomerang particles of three different apex angles and discuss the angle dependence of these diffusion coefficients.

Resonances arising from hydrodynamic memory in Brownian motion.

PubMed

Franosch, Thomas; Grimm, Matthias; Belushkin, Maxim; Mor, Flavio M; Foffi, Giuseppe; Forró, László; Jeney, Sylvia

2011-10-05

Observation of the Brownian motion of a small probe interacting with its environment provides one of the main strategies for characterizing soft matter. Essentially, two counteracting forces govern the motion of the Brownian particle. First, the particle is driven by rapid collisions with the surrounding solvent molecules, referred to as thermal noise. Second, the friction between the particle and the viscous solvent damps its motion. Conventionally, the thermal force is assumed to be random and characterized by a Gaussian white noise spectrum. The friction is assumed to be given by the Stokes drag, suggesting that motion is overdamped at long times in particle tracking experiments, when inertia becomes negligible. However, as the particle receives momentum from the fluctuating fluid molecules, it also displaces the fluid in its immediate vicinity. The entrained fluid acts back on the particle and gives rise to long-range correlations. This hydrodynamic 'memory' translates to thermal forces, which have a coloured, that is, non-white, noise spectrum. One hundred years after Perrin's pioneering experiments on Brownian motion, direct experimental observation of this colour is still elusive. Here we measure the spectrum of thermal noise by confining the Brownian fluctuations of a microsphere in a strong optical trap. We show that hydrodynamic correlations result in a resonant peak in the power spectral density of the sphere's positional fluctuations, in strong contrast to overdamped systems. Furthermore, we demonstrate different strategies to achieve peak amplification. By analogy with microcantilever-based sensors, our results reveal that the particle-fluid-trap system can be considered a nanomechanical resonator in which the intrinsic hydrodynamic backflow enhances resonance. Therefore, instead of being treated as a disturbance, details in thermal noise could be exploited for the development of new types of sensor and particle-based assay in lab

Diffusion of torqued active particles

NASA Astrophysics Data System (ADS)

Sandoval, Mario; Lauga, Eric

2012-11-01

Motivated by swimming microorganisms whose trajectories are affected by the presence of an external torque, we calculate the diffusivity of an active particle subject to an external torque and in a fluctuating environment. The analytical results are compared with Brownian dynamics simulations showing excellent agreement between theory and numerical experiments. This work was funded in part by the Consejo Nacional de Ciencia y Tecnologia of Mexico (Conacyt postdoctoral fellowship to M. S.) and the US National Science Foundation (Grant CBET-0746285 to E.L.).

Near-Field, On-Chip Optical Brownian Ratchets.

PubMed

Wu, Shao-Hua; Huang, Ningfeng; Jaquay, Eric; Povinelli, Michelle L

2016-08-10

Nanoparticles in aqueous solution are subject to collisions with solvent molecules, resulting in random, Brownian motion. By breaking the spatiotemporal symmetry of the system, the motion can be rectified. In nature, Brownian ratchets leverage thermal fluctuations to provide directional motion of proteins and enzymes. In man-made systems, Brownian ratchets have been used for nanoparticle sorting and manipulation. Implementations based on optical traps provide a high degree of tunability along with precise spatiotemporal control. Here, we demonstrate an optical Brownian ratchet based on the near-field traps of an asymmetrically patterned photonic crystal. The system yields over 25 times greater trap stiffness than conventional optical tweezers. Our technique opens up new possibilities for particle manipulation in a microfluidic, lab-on-chip environment.

Efficiency of Brownian heat engines.

PubMed

Derényi, I; Astumian, R D

1999-06-01

We study the efficiency of one-dimensional thermally driven Brownian ratchets or heat engines. We identify and compare the three basic setups characterized by the type of the connection between the Brownian particle and the two heat reservoirs: (i) simultaneous, (ii) alternating in time, and (iii) position dependent. We make a clear distinction between the heat flow via the kinetic and the potential energy of the particle, and show that the former is always irreversible and it is only the third setup where the latter is reversible when the engine works quasistatically. We also show that in the third setup the heat flow via the kinetic energy can be reduced arbitrarily, proving that even for microscopic heat engines there is no fundamental limit of the efficiency lower than that of a Carnot cycle.

Brownian dynamics of self-regulated particles with additional degrees of freedom: Symmetry breaking and homochirality

NASA Astrophysics Data System (ADS)

Bhattacharyya, Debankur; Paul, Shibashis; Ghosh, Shyamolina; Ray, Deb Shankar

2018-04-01

We consider the Brownian motion of a collection of particles each with an additional degree of freedom. The degree of freedom of a particle (or, in general, a molecule) can assume distinct values corresponding to certain states or conformations. The time evolution of the additional degree of freedom of a particle is guided by those of its neighbors as well as the temperature of the system. We show that the local averaging over these degrees of freedom results in emergence of a collective order in the dynamics in the form of selection or dominance of one of the isomers leading to a symmetry-broken state. Our statistical model captures the basic features of homochirality, e.g., autocatalysis and chiral inhibition.

Two-dimensional nature of the active Brownian motion of catalytic microswimmers at solid and liquid interfaces

NASA Astrophysics Data System (ADS)

Dietrich, Kilian; Renggli, Damian; Zanini, Michele; Volpe, Giovanni; Buttinoni, Ivo; Isa, Lucio

2017-06-01

Colloidal particles equipped with platinum patches can establish chemical gradients in H2O2-enriched solutions and undergo self-propulsion due to local diffusiophoretic migration. In bulk (3D), this class of active particles swim in the direction of the surface heterogeneities introduced by the patches and consequently reorient with the characteristic rotational diffusion time of the colloids. In this article, we present experimental and numerical evidence that planar 2D confinements defy this simple picture. Instead, the motion of active particles both on solid substrates and at flat liquid-liquid interfaces is captured by a 2D active Brownian motion model, in which rotational and translational motion are constrained in the xy-plane. This leads to an active motion that does not follow the direction of the surface heterogeneities and to timescales of reorientation that do not match the free rotational diffusion times. Furthermore, 2D-confinement at fluid-fluid interfaces gives rise to a unique distribution of swimming velocities: the patchy colloids uptake two main orientations leading to two particle populations with velocities that differ up to one order of magnitude. Our results shed new light on the behavior of active colloids in 2D, which is of interest for modeling and applications where confinements are present.

Non-Markovian quantum Brownian motion in one dimension in electric fields

NASA Astrophysics Data System (ADS)

Shen, H. Z.; Su, S. L.; Zhou, Y. H.; Yi, X. X.

2018-04-01

Quantum Brownian motion is the random motion of quantum particles suspended in a field (or an effective field) resulting from their collision with fast-moving modes in the field. It provides us with a fundamental model to understand various physical features concerning open systems in chemistry, condensed-matter physics, biophysics, and optomechanics. In this paper, without either the Born-Markovian or rotating-wave approximation, we derive a master equation for a charged-Brownian particle in one dimension coupled with a thermal reservoir in electric fields. The effect of the reservoir and the electric fields is manifested as time-dependent coefficients and coherent terms, respectively, in the master equation. The two-photon correlation between the Brownian particle and the reservoir can induce nontrivial squeezing dynamics to the particle. We derive a current equation including the source from the driving fields, transient current from the system flowing into the environment, and the two-photon current caused by the non-rotating-wave term. The presented results then are compared with that given by the rotating-wave approximation in the weak-coupling limit, and these results are extended to a more general quantum network involving an arbitrary number of coupled-Brownian particles. The presented formalism might open a way to better understand exactly the non-Markovian quantum network.

Optimal tuning of a confined Brownian information engine.

PubMed

Park, Jong-Min; Lee, Jae Sung; Noh, Jae Dong

2016-03-01

A Brownian information engine is a device extracting mechanical work from a single heat bath by exploiting the information on the state of a Brownian particle immersed in the bath. As for engines, it is important to find the optimal operating condition that yields the maximum extracted work or power. The optimal condition for a Brownian information engine with a finite cycle time τ has been rarely studied because of the difficulty in finding the nonequilibrium steady state. In this study, we introduce a model for the Brownian information engine and develop an analytic formalism for its steady-state distribution for any τ. We find that the extracted work per engine cycle is maximum when τ approaches infinity, while the power is maximum when τ approaches zero.

Manipulating freely diffusing single 20-nm particles in an Anti-Brownian Electrokinetic Trap (ABELtrap)

NASA Astrophysics Data System (ADS)

Zarrabi, Nawid; Clausen, Caterina; Düser, Monika G.; Börsch, Michael

2013-02-01

Conformational changes of individual fluorescently labeled proteins can be followed in solution using a confocal microscope. Two fluorophores attached to selected domains of the protein report fluctuating conformations. Based on Förster resonance energy transfer (FRET) between these fluorophores on a single protein, sequential distance changes between the dyes provide the real time trajectories of protein conformations. However, observation times are limited for freely diffusing biomolecules by Brownian motion through the confocal detection volume. A. E. Cohen and W. E. Moerner have invented and built microfluidic devices with 4 electrodes for an Anti-Brownian Electrokinetic Trap (ABELtrap). Here we present an ABELtrap based on a laser focus pattern generated by a pair of acousto-optical beam deflectors and controlled by a programmable FPGA chip. Fluorescent 20-nm beads in solution were used to mimic freely diffusing large proteins like solubilized FoF1-ATP synthase. The ABELtrap could hold these nanobeads for about 10 seconds at the given position. Thereby, observation times of a single particle were increased by a factor of 1000.

Brownian relaxation of an inelastic sphere in air

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bird, G. A., E-mail: gab@gab.com.au

2016-06-15

The procedures that are used to calculate the forces and moments on an aerodynamic body in the rarefied gas of the upper atmosphere are applied to a small sphere of the size of an aerosol particle at sea level. While the gas-surface interaction model that provides accurate results for macroscopic bodies may not be appropriate for bodies that are comprised of only about a thousand atoms, it provides a limiting case that is more realistic than the elastic model. The paper concentrates on the transfer of energy from the air to an initially stationary sphere as it acquires Brownian motion.more » Individual particle trajectories vary wildly, but a clear relaxation process emerges from an ensemble average over tens of thousands of trajectories. The translational and rotational energies in equilibrium Brownian motion are determined. Empirical relationships are obtained for the mean translational and rotational relaxation times, the mean initial power input to the particle, the mean rates of energy transfer between the particle and air, and the diffusivity. These relationships are functions of the ratio of the particle mass to an average air molecule mass and the Knudsen number, which is the ratio of the mean free path in the air to the particle diameter. The ratio of the molecular radius to the particle radius also enters as a correction factor. The implications of Brownian relaxation for the second law of thermodynamics are discussed.« less

Entropic Approach to Brownian Movement.

ERIC Educational Resources Information Center

Neumann, Richard M.

1980-01-01

A diffusional driving force, called the radial force, which is responsible for the increase with time of the scalar separation between a fixed point and a particle undergoing three-dimensional Brownian motion, is derived using Boltzmann's equation. (Author/HM)

The Diffusion Process in Small Particles and Brownian Motion

NASA Astrophysics Data System (ADS)

Khoshnevisan, M.

Albert Einstein in 1926 published his book entitled ''INVESTIGATIONS ON THE THEORY OF THE BROWNIAN MOVEMENT''. He investigated the process of diffusion in an undissociated dilute solution. The diffusion process is subject to Brownian motion. Furthermore, he elucidated the fact that the heat content of a substance will change the position of the single molecules in an irregular fashion. In this paper, I have shown that in order for the displacement of the single molecules to be proportional to the square root of the time, and for v/2 - v 1 Δ =dv/dx , (where v1 and v2 are the concentrations in two cross sections that are separated by a very small distance), ∫ - ∞ ∞ Φ (Δ) dΔ = I and I/τ ∫ - ∞ ∞Δ2/2 Φ (Δ) dΔ = D conditions to hold, then equation (7a) D =√{ 2 D }√{ τ} must be changed to Δ =√{ 2 D }√{ τ} . I have concluded that D =√{ 2 D }√{ τ} is an unintended error, and it has not been amended for almost 90 years in INVESTIGATIONS ON THE THEORY OF THE BROWNIAN MOVEMENT, 1926 publication.

The van Hove distribution function for Brownian hard spheres: Dynamical test particle theory and computer simulations for bulk dynamics

NASA Astrophysics Data System (ADS)

Hopkins, Paul; Fortini, Andrea; Archer, Andrew J.; Schmidt, Matthias

2010-12-01

We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the "self " component having only one particle, the "distinct" component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities.

Brownian motion probe for water-ethanol inhomogeneous mixtures

NASA Astrophysics Data System (ADS)

Furukawa, Kazuki; Judai, Ken

2017-12-01

Brownian motion provides information regarding the microscopic geometry and motion of molecules, insofar as it occurs as a result of molecular collisions with a colloid particle. We found that the mobility of polystyrene beads from the Brownian motion in a water-ethanol mixture is larger than that predicted from the liquid shear viscosity. This indicates that mixing water and ethanol is inhomogeneous in micron-sized probe beads. The discrepancy between the mobility of Brownian motion and liquid mobility can be explained by the way the rotation of the beads in an inhomogeneous viscous solvent converts the translational movement.

Brownian motion probe for water-ethanol inhomogeneous mixtures.

PubMed

Furukawa, Kazuki; Judai, Ken

2017-12-28

Brownian motion provides information regarding the microscopic geometry and motion of molecules, insofar as it occurs as a result of molecular collisions with a colloid particle. We found that the mobility of polystyrene beads from the Brownian motion in a water-ethanol mixture is larger than that predicted from the liquid shear viscosity. This indicates that mixing water and ethanol is inhomogeneous in micron-sized probe beads. The discrepancy between the mobility of Brownian motion and liquid mobility can be explained by the way the rotation of the beads in an inhomogeneous viscous solvent converts the translational movement.

Two-dimensional motion of Brownian swimmers in linear flows.

PubMed

Sandoval, Mario; Jimenez, Alonso

2016-03-01

The motion of viruses and bacteria and even synthetic microswimmers can be affected by thermal fluctuations and by external flows. In this work, we study the effect of linear external flows and thermal fluctuations on the diffusion of those swimmers modeled as spherical active (self-propelled) particles moving in two dimensions. General formulae for their mean-square displacement under a general linear flow are presented. We also provide, at short and long times, explicit expressions for the mean-square displacement of a swimmer immersed in three canonical flows, namely, solid-body rotation, shear and extensional flows. These expressions can now be used to estimate the effect of external flows on the displacement of Brownian microswimmers. Finally, our theoretical results are validated by using Brownian dynamics simulations.

Mixing and demixing of binary mixtures of polar chiral active particles.

PubMed

Ai, Bao-Quan; Shao, Zhi-Gang; Zhong, Wei-Rong

2018-05-17

We study a binary mixture of polar chiral (counterclockwise or clockwise) active particles in a two-dimensional box with periodic boundary conditions. Besides the excluded volume interactions between particles, the particles are also subjected to the polar velocity alignment. From the extensive Brownian dynamics simulations, it is found that the particle configuration (mixing or demixing) is determined by the competition between the chirality difference and the polar velocity alignment. When the chirality difference competes with the polar velocity alignment, the clockwise particles aggregate in one cluster and the counterclockwise particles aggregate in the other cluster; thus, the particles are demixed and can be separated. However, when the chirality difference or the polar velocity alignment is dominant, the particles are mixed. Our findings could be used for the experimental pursuit of the separation of binary mixtures of chiral active particles.

Effective temperatures of hot Brownian motion.

PubMed

Falasco, G; Gnann, M V; Rings, D; Kroy, K

2014-09-01

We derive generalized Langevin equations for the translational and rotational motion of a heated Brownian particle from the fluctuating hydrodynamics of its nonisothermal solvent. The temperature gradient around the particle couples to the hydrodynamic modes excited by the particle itself so that the resulting noise spectrum is governed by a frequency-dependent temperature. We show how the effective temperatures at which the particle coordinates and (angular) velocities appear to be thermalized emerge from this central quantity.

Rectified brownian transport in corrugated channels: Fractional brownian motion and Lévy flights.

PubMed

Ai, Bao-quan; Shao, Zhi-gang; Zhong, Wei-rong

2012-11-07

We study fractional brownian motion and Lévy flights in periodic corrugated channels without any external driving forces. From numerical simulations, we find that both fractional gaussian noise and Lévy-stable noise in asymmetric corrugated channels can break thermodynamical equilibrium and induce directed transport. The rectified mechanisms for fractional brownian motion and Lévy flights are different. The former is caused by non-uniform spectral distribution (low or high frequencies) of fractional gaussian noise, while the latter is due to the nonthermal character (occasional long jumps) of the Lévy-stable noise. For fractional brownian motion, average velocity increases with the Hurst exponent for the persistent case, while for the antipersistent case there exists an optimal value of Hurst exponent at which average velocity takes its maximal value. For Lévy flights, the group velocity decreases monotonically as the Lévy index increases. In addition, for both cases, the optimized periodicity and radius at the bottleneck can facilitate the directed transport. Our results could be implemented in constrained structures with narrow channels and pores where the particles undergo anomalous diffusion.

Nanoparticle Brownian motion and hydrodynamic interactions in the presence of flow fields

PubMed Central

Uma, B.; Swaminathan, T. N.; Radhakrishnan, R.; Eckmann, D. M.; Ayyaswamy, P. S.

2011-01-01

We consider the Brownian motion of a nanoparticle in an incompressible Newtonian fluid medium (quiescent or fully developed Poiseuille flow) with the fluctuating hydrodynamics approach. The formalism considers situations where both the Brownian motion and the hydrodynamic interactions are important. The flow results have been modified to account for compressibility effects. Different nanoparticle sizes and nearly neutrally buoyant particle densities are also considered. Tracked particles are initially located at various distances from the bounding wall to delineate wall effects. The results for thermal equilibrium are validated by comparing the predictions for the temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical and experimental results where available. The equipartition theorem for a Brownian particle in Poiseuille flow is verified for a range of low Reynolds numbers. Numerical predictions of wall interactions with the particle in terms of particle diffusivities are consistent with results, where available. PMID:21918592

The tug-of-war behavior of a Brownian particle in an asymmetric double optical trap with stochastic fluctuations

NASA Astrophysics Data System (ADS)

Long, Fei; Zhu, Jia-Pei

2018-07-01

A Brownian particle optically trapped in an asymmetric double potential surrounded by a thermal bath was simulated. Under the cooperative action of the resultant deterministic optical force and the stochastic fluctuations of the thermal bath, the confined particle undergoes Kramers transition, and oscillates between the two traps with a probability of trap occupancy that is asymmetrically distributed about the midpoint. The simulation results obtained at different temperatures indicate that the oscillation behavior of the particle can be treated as the result of a tug-of-war game played between the resultant deterministic force and the random force. We also employ a bistable model to explain the observed phenomena.

Suppressing Brownian motion of individual biomolecules in solution

PubMed Central

Cohen, Adam E.; Moerner, W. E.

2006-01-01

Single biomolecules in free solution have long been of interest for detailed study by optical methods, but Brownian motion prevents the observation of one single molecule for extended periods. We have used an anti-Brownian electrokinetic (ABEL) trap to trap individual protein molecules in free solution, under ambient conditions, without requiring any attachment to beads or surfaces. We also demonstrate trapping and manipulation of single virus particles, lipid vesicles, and fluorescent semiconductor nanocrystals. PMID:16537418

Non-equilibrium surface tension of the vapour-liquid interface of active Lennard-Jones particles

NASA Astrophysics Data System (ADS)

Paliwal, Siddharth; Prymidis, Vasileios; Filion, Laura; Dijkstra, Marjolein

2017-08-01

We study a three-dimensional system of self-propelled Brownian particles interacting via the Lennard-Jones potential. Using Brownian dynamics simulations in an elongated simulation box, we investigate the steady states of vapour-liquid phase coexistence of active Lennard-Jones particles with planar interfaces. We measure the normal and tangential components of the pressure tensor along the direction perpendicular to the interface and verify mechanical equilibrium of the two coexisting phases. In addition, we determine the non-equilibrium interfacial tension by integrating the difference of the normal and tangential components of the pressure tensor and show that the surface tension as a function of strength of particle attractions is well fitted by simple power laws. Finally, we measure the interfacial stiffness using capillary wave theory and the equipartition theorem and find a simple linear relation between surface tension and interfacial stiffness with a proportionality constant characterized by an effective temperature.

Shear-induced reaction-limited aggregation kinetics of Brownian particles at arbitrary concentrations

NASA Astrophysics Data System (ADS)

Zaccone, Alessio; Gentili, Daniele; Wu, Hua; Morbidelli, Massimo

2010-04-01

The aggregation of interacting Brownian particles in sheared concentrated suspensions is an important issue in colloid and soft matter science per se. Also, it serves as a model to understand biochemical reactions occurring in vivo where both crowding and shear play an important role. We present an effective medium approach within the Smoluchowski equation with shear which allows one to calculate the encounter kinetics through a potential barrier under shear at arbitrary colloid concentrations. Experiments on a model colloidal system in simple shear flow support the validity of the model in the concentration range considered. By generalizing Kramers' rate theory to the presence of shear and collective hydrodynamics, our model explains the significant increase in the shear-induced reaction-limited aggregation kinetics upon increasing the colloid concentration.

Brownian versus Newtonian devitrification of hard-sphere glasses

NASA Astrophysics Data System (ADS)

Montero de Hijes, Pablo; Rosales-Pelaez, Pablo; Valeriani, Chantal; Pusey, Peter N.; Sanz, Eduardo

2017-08-01

In a recent molecular dynamics simulation work it has been shown that glasses composed of hard spheres crystallize via cooperative, stochastic particle displacements called avalanches [E. Sanz et al., Proc. Natl. Acad. Sci. USA 111, 75 (2014), 10.1073/pnas.1308338110]. In this Rapid Communication we investigate if such a devitrification mechanism is also present when the dynamics is Brownian rather than Newtonian. The research is motivated in part by the fact that colloidal suspensions, an experimental realization of hard-sphere systems, undergo Brownian motion. We find that Brownian hard-sphere glasses do crystallize via avalanches with very similar characteristics to those found in the Newtonian case. We briefly discuss the implications of these findings for experiments on colloids.

Communication: Memory effects and active Brownian diffusion

NASA Astrophysics Data System (ADS)

Ghosh, Pulak K.; Li, Yunyun; Marchegiani, Giampiero; Marchesoni, Fabio

2015-12-01

A self-propelled artificial microswimmer is often modeled as a ballistic Brownian particle moving with constant speed aligned along one of its axis, but changing direction due to random collisions with the environment. Similarly to thermal noise, its angular randomization is described as a memoryless stochastic process. Here, we speculate that finite-time correlations in the orientational dynamics can affect the swimmer's diffusivity. To this purpose, we propose and solve two alternative models. In the first one, we simply assume that the environmental fluctuations governing the swimmer's propulsion are exponentially correlated in time, whereas in the second one, we account for possible damped fluctuations of the propulsion velocity around the swimmer's axis. The corresponding swimmer's diffusion constants are predicted to get, respectively, enhanced or suppressed upon increasing the model memory time. Possible consequences of this effect on the interpretation of the experimental data are discussed.

Biased and flow driven Brownian motion in periodic channels

NASA Astrophysics Data System (ADS)

Martens, S.; Straube, A.; Schmid, G.; Schimansky-Geier, L.; Hänggi, P.

2012-02-01

In this talk we will present an expansion of the common Fick-Jacobs approximation to hydrodynamically as well as by external forces driven Brownian transport in two-dimensional channels exhibiting smoothly varying periodic cross-section. We employ an asymptotic analysis to the components of the flow field and to stationary probability density for finding the particles within the channel in a geometric parameter. We demonstrate that the problem of biased Brownian dynamics in a confined 2D geometry can be replaced by Brownian motion in an effective periodic one-dimensional potential ψ(x) which takes the external bias, the change of the local channel width, and the flow velocity component in longitudinal direction into account. In addition, we study the influence of the external force magnitude, respectively, the pressure drop of the fluid on the particle transport quantities like the averaged velocity and the effective diffusion coefficient. The critical ratio between the external force and pressure drop where the average velocity equals zero is identified and the dependence of the latter on the channel geometry is derived. Analytic findings are confirmed by numerical simulations of the particle dynamics in a reflection symmetric sinusoidal channel.

The Brownian mean field model

NASA Astrophysics Data System (ADS)

Chavanis, Pierre-Henri

2014-05-01

We discuss the dynamics and thermodynamics of the Brownian mean field (BMF) model which is a system of N Brownian particles moving on a circle and interacting via a cosine potential. It can be viewed as the canonical version of the Hamiltonian mean field (HMF) model. The BMF model displays a second order phase transition from a homogeneous phase to an inhomogeneous phase below a critical temperature T c = 1 / 2. We first complete the description of this model in the mean field approximation valid for N → +∞. In the strong friction limit, the evolution of the density towards the mean field Boltzmann distribution is governed by the mean field Smoluchowski equation. For T < T c , this equation describes a process of self-organization from a non-magnetized (homogeneous) phase to a magnetized (inhomogeneous) phase. We obtain an analytical expression for the temporal evolution of the magnetization close to T c . Then, we take fluctuations (finite N effects) into account. The evolution of the density is governed by the stochastic Smoluchowski equation. From this equation, we derive a stochastic equation for the magnetization and study its properties both in the homogenous and inhomogeneous phase. We show that the fluctuations diverge at the critical point so that the mean field approximation ceases to be valid. Actually, the limits N → +∞ and T → T c do not commute. The validity of the mean field approximation requires N( T - T c ) → +∞ so that N must be larger and larger as T approaches T c . We show that the direction of the magnetization changes rapidly close to T c while its amplitude takes a long time to relax. We also indicate that, for systems with long-range interactions, the lifetime of metastable states scales as e N except close to a critical point. The BMF model shares many analogies with other systems of Brownian particles with long-range interactions such as self-gravitating Brownian particles, the Keller-Segel model describing the chemotaxis

Current and efficiency of Brownian particles under oscillating forces in entropic barriers

NASA Astrophysics Data System (ADS)

Nutku, Ferhat; Aydιner, Ekrem

2015-04-01

In this study, considering the temporarily unbiased force and different forms of oscillating forces, we investigate the current and efficiency of Brownian particles in an entropic tube structure and present the numerically obtained results. We show that different force forms give rise to different current and efficiency profiles in different optimized parameter intervals. We find that an unbiased oscillating force and an unbiased temporal force lead to the current and efficiency, which are dependent on these parameters. We also observe that the current and efficiency caused by temporal and different oscillating forces have maximum and minimum values in different parameter intervals. We conclude that the current or efficiency can be controlled dynamically by adjusting the parameters of entropic barriers and applied force. Project supported by the Funds from Istanbul University (Grant No. 45662).

Directed motion of a Brownian motor in a temperature gradient

NASA Astrophysics Data System (ADS)

Liu, Yibing; Nie, Wenjie; Lan, Yueheng

2017-05-01

Directed motion of mesoscopic systems in a non-equilibrium environment is of great interest to both scientists and engineers. Here, the translation and rotation of a Brownian motor is investigated under non-equilibrium conditions. An anomalous directed translation is found if the two heads of the Brownian motor are immersed in baths with different particle masses, which is hinted in the analytic computation and confirmed by the numerical simulation. Similar consideration is also used to find the directed movement in the single rotational and translational degree of freedom of the Brownian motor when residing in one thermal bath with a temperature gradient.

Theory of relativistic Brownian motion: the (1+3) -dimensional case.

PubMed

Dunkel, Jörn; Hänggi, Peter

2005-09-01

A theory for (1+3) -dimensional relativistic Brownian motion under the influence of external force fields is put forward. Starting out from a set of relativistically covariant, but multiplicative Langevin equations we describe the relativistic stochastic dynamics of a forced Brownian particle. The corresponding Fokker-Planck equations are studied in the laboratory frame coordinates. In particular, the stochastic integration prescription--i.e., the discretization rule dilemma--is elucidated (prepoint discretization rule versus midpoint discretization rule versus postpoint discretization rule). Remarkably, within our relativistic scheme we find that the postpoint rule (or the transport form) yields the only Fokker-Planck dynamics from which the relativistic Maxwell-Boltzmann statistics is recovered as the stationary solution. The relativistic velocity effects become distinctly more pronounced by going from one to three spatial dimensions. Moreover, we present numerical results for the asymptotic mean-square displacement of a free relativistic Brownian particle moving in 1+3 dimensions.

Communication: Memory effects and active Brownian diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Pulak K.; Li, Yunyun, E-mail: yunyunli@tongji.edu.cn; Marchegiani, Giampiero

A self-propelled artificial microswimmer is often modeled as a ballistic Brownian particle moving with constant speed aligned along one of its axis, but changing direction due to random collisions with the environment. Similarly to thermal noise, its angular randomization is described as a memoryless stochastic process. Here, we speculate that finite-time correlations in the orientational dynamics can affect the swimmer’s diffusivity. To this purpose, we propose and solve two alternative models. In the first one, we simply assume that the environmental fluctuations governing the swimmer’s propulsion are exponentially correlated in time, whereas in the second one, we account for possiblemore » damped fluctuations of the propulsion velocity around the swimmer’s axis. The corresponding swimmer’s diffusion constants are predicted to get, respectively, enhanced or suppressed upon increasing the model memory time. Possible consequences of this effect on the interpretation of the experimental data are discussed.« less

Model Experiment of Two-Dimentional Brownian Motion by Microcomputer.

ERIC Educational Resources Information Center

Mishima, Nobuhiko; And Others

1980-01-01

Describes the use of a microcomputer in studying a model experiment (Brownian particles colliding with thermal particles). A flow chart and program for the experiment are provided. Suggests that this experiment may foster a deepened understanding through mutual dialog between the student and computer. (SK)

Fractional Brownian motion with a reflecting wall.

PubMed

Wada, Alexander H O; Vojta, Thomas

2018-02-01

Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of Monte Carlo simulations. Whereas the mean-square displacement of the particle shows the expected anomalous diffusion behavior 〈x^{2}〉∼t^{α}, the interplay between the geometric confinement and the long-time memory leads to a highly non-Gaussian probability density function with a power-law singularity at the barrier. In the superdiffusive case α>1, the particles accumulate at the barrier leading to a divergence of the probability density. For subdiffusion α<1, in contrast, the probability density is depleted close to the barrier. We discuss implications of these findings, in particular, for applications that are dominated by rare events.

Fractional Brownian motion with a reflecting wall

NASA Astrophysics Data System (ADS)

Wada, Alexander H. O.; Vojta, Thomas

2018-02-01

Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of Monte Carlo simulations. Whereas the mean-square displacement of the particle shows the expected anomalous diffusion behavior ˜tα , the interplay between the geometric confinement and the long-time memory leads to a highly non-Gaussian probability density function with a power-law singularity at the barrier. In the superdiffusive case α >1 , the particles accumulate at the barrier leading to a divergence of the probability density. For subdiffusion α <1 , in contrast, the probability density is depleted close to the barrier. We discuss implications of these findings, in particular, for applications that are dominated by rare events.

Brownian Motion in a Speckle Light Field: Tunable Anomalous Diffusion and Selective Optical Manipulation

PubMed Central

Volpe, Giorgio; Volpe, Giovanni; Gigan, Sylvain

2014-01-01

The motion of particles in random potentials occurs in several natural phenomena ranging from the mobility of organelles within a biological cell to the diffusion of stars within a galaxy. A Brownian particle moving in the random optical potential associated to a speckle pattern, i.e., a complex interference pattern generated by the scattering of coherent light by a random medium, provides an ideal model system to study such phenomena. Here, we derive a theory for the motion of a Brownian particle in a speckle field and, in particular, we identify its universal characteristic timescale. Based on this theoretical insight, we show how speckle light fields can be used to control the anomalous diffusion of a Brownian particle and to perform some basic optical manipulation tasks such as guiding and sorting. Our results might broaden the perspectives of optical manipulation for real-life applications. PMID:24496461

Nonlinear-drifted Brownian motion with multiple hidden states for remaining useful life prediction of rechargeable batteries

NASA Astrophysics Data System (ADS)

Wang, Dong; Zhao, Yang; Yang, Fangfang; Tsui, Kwok-Leung

2017-09-01

Brownian motion with adaptive drift has attracted much attention in prognostics because its first hitting time is highly relevant to remaining useful life prediction and it follows the inverse Gaussian distribution. Besides linear degradation modeling, nonlinear-drifted Brownian motion has been developed to model nonlinear degradation. Moreover, the first hitting time distribution of the nonlinear-drifted Brownian motion has been approximated by time-space transformation. In the previous studies, the drift coefficient is the only hidden state used in state space modeling of the nonlinear-drifted Brownian motion. Besides the drift coefficient, parameters of a nonlinear function used in the nonlinear-drifted Brownian motion should be treated as additional hidden states of state space modeling to make the nonlinear-drifted Brownian motion more flexible. In this paper, a prognostic method based on nonlinear-drifted Brownian motion with multiple hidden states is proposed and then it is applied to predict remaining useful life of rechargeable batteries. 26 sets of rechargeable battery degradation samples are analyzed to validate the effectiveness of the proposed prognostic method. Moreover, some comparisons with a standard particle filter based prognostic method, a spherical cubature particle filter based prognostic method and two classic Bayesian prognostic methods are conducted to highlight the superiority of the proposed prognostic method. Results show that the proposed prognostic method has lower average prediction errors than the particle filter based prognostic methods and the classic Bayesian prognostic methods for battery remaining useful life prediction.

Simulations of shear-thinning frictional non-Brownian suspensions

NASA Astrophysics Data System (ADS)

Lemaire, Elisabeth; Lobry, Laurent; Blanc, Frederic; Peters, Francois; RSC Team

2017-11-01

Most non-Brownian suspensions exhibit non-Newtonian behaviours such as anisotropic normal stresses, shear-thickening or shear-thinning. The later is still largely an open question. Acrivos wet al. (JoR 1994) proposed that particle resuspension is responsible for the apparent shear-thinning behavior in a cylindrical Couette rheometer. Another explanation has been suggested by Vasquez-Quesada et al. (PRL 2017), who noticed that some polymeric suspending liquids themselves are shear-thinning for the high shear-rate values involved in the narrow gaps between particles. Here we propose that the shear-thinning behaviour is directly connected to the solid contact between particles that has been shown to play a crucial role in the rheological behaviour of concentrated non-Brownian suspensions. In particular, it has been recently shown that frictional contact between particles greatly enhances the viscosity. Even though the friction coefficient between macroscopic surfaces does not depend on the load, it may be not the case at the scale of the low load contact between particles in suspensions. Here, we present discrete numerical simulations where the friction coefficient decreases with the interparticle forces. The obtained shear-thinning behaviour is in good agreement with our experiments.

Nucleation theory in Langevin's approach and lifetime of a Brownian particle in potential wells.

PubMed

Alekseechkin, N V

2008-07-14

The multivariable theory of nucleation suggested by Alekseechkin [J. Chem. Phys. 124, 124512 (2006)] is further developed in the context of Langevin's approach. The use of this approach essentially enhances the capability of the nucleation theory, because it makes possible to consider the cases of small friction which are not taken into account by the classical Zel'dovich-Frenkel theory and its multivariable extensions. The procedure for the phenomenological determination of the nucleation parameters is described. Using the similarity of the Kramers model with that of nucleation, the lifetime of a Brownian particle in potential wells in various dimensionalities is calculated with the help of the expression for the steady state nucleation rate.

Size-Resolved Ultrafine Particle Deposition and Brownian Coagulation from Gasoline Vehicle Exhaust in an Environmental Test Chamber.

PubMed

Zhao, Yu; Wang, Fang; Zhao, Jianing

2015-10-20

Size-resolved deposition rates and Brownian coagulation of particles between 20 and 900 nm (mobility diameter) were estimated in a well-mixed environmental chamber from a gasoline vehicle exhaust with a total peak particle concentration of 10(5)-10(6) particles/cm(3) at 12.24-25.22 °C. A deposition theory with modified friction velocity and coagulation model was also employed to predict particle concentration decay. Initially during particle decay, approximately 85% or more of the particles had diameters of <100 nm. Particle deposition rates with standard deviations were highly dependent on particle size ranges, and varied from 0.012 ± 0.003 to 0.48 ± 0.02 h(-1). In the experiment, the friction velocity obtained was in the range 1.5-2.5 cm/s. The most explainable fractal dimension and Hamaker constant in coagulation model were 2.5-3 and 20 kT, respectively, and the contribution from coagulation dominated the total particle decay during the first 1 h of decay. It is considered that the modified friction velocity and best fitted fractal dimension and Hamaker constants could be further used to analyze gasoline vehicle exhaust particle dynamics and assess human exposure to vehicle particle pollutants in urban areas, tunnels, and underground parking lots.

Rapid sampling of stochastic displacements in Brownian dynamics simulations with stresslet constraints.

PubMed

Fiore, Andrew M; Swan, James W

2018-01-28

Brownian Dynamics simulations are an important tool for modeling the dynamics of soft matter. However, accurate and rapid computations of the hydrodynamic interactions between suspended, microscopic components in a soft material are a significant computational challenge. Here, we present a new method for Brownian dynamics simulations of suspended colloidal scale particles such as colloids, polymers, surfactants, and proteins subject to a particular and important class of hydrodynamic constraints. The total computational cost of the algorithm is practically linear with the number of particles modeled and can be further optimized when the characteristic mass fractal dimension of the suspended particles is known. Specifically, we consider the so-called "stresslet" constraint for which suspended particles resist local deformation. This acts to produce a symmetric force dipole in the fluid and imparts rigidity to the particles. The presented method is an extension of the recently reported positively split formulation for Ewald summation of the Rotne-Prager-Yamakawa mobility tensor to higher order terms in the hydrodynamic scattering series accounting for force dipoles [A. M. Fiore et al., J. Chem. Phys. 146(12), 124116 (2017)]. The hydrodynamic mobility tensor, which is proportional to the covariance of particle Brownian displacements, is constructed as an Ewald sum in a novel way which guarantees that the real-space and wave-space contributions to the sum are independently symmetric and positive-definite for all possible particle configurations. This property of the Ewald sum is leveraged to rapidly sample the Brownian displacements from a superposition of statistically independent processes with the wave-space and real-space contributions as respective covariances. The cost of computing the Brownian displacements in this way is comparable to the cost of computing the deterministic displacements. The addition of a stresslet constraint to the over-damped particle

Rapid sampling of stochastic displacements in Brownian dynamics simulations with stresslet constraints

NASA Astrophysics Data System (ADS)

Fiore, Andrew M.; Swan, James W.

2018-01-01

Brownian Dynamics simulations are an important tool for modeling the dynamics of soft matter. However, accurate and rapid computations of the hydrodynamic interactions between suspended, microscopic components in a soft material are a significant computational challenge. Here, we present a new method for Brownian dynamics simulations of suspended colloidal scale particles such as colloids, polymers, surfactants, and proteins subject to a particular and important class of hydrodynamic constraints. The total computational cost of the algorithm is practically linear with the number of particles modeled and can be further optimized when the characteristic mass fractal dimension of the suspended particles is known. Specifically, we consider the so-called "stresslet" constraint for which suspended particles resist local deformation. This acts to produce a symmetric force dipole in the fluid and imparts rigidity to the particles. The presented method is an extension of the recently reported positively split formulation for Ewald summation of the Rotne-Prager-Yamakawa mobility tensor to higher order terms in the hydrodynamic scattering series accounting for force dipoles [A. M. Fiore et al., J. Chem. Phys. 146(12), 124116 (2017)]. The hydrodynamic mobility tensor, which is proportional to the covariance of particle Brownian displacements, is constructed as an Ewald sum in a novel way which guarantees that the real-space and wave-space contributions to the sum are independently symmetric and positive-definite for all possible particle configurations. This property of the Ewald sum is leveraged to rapidly sample the Brownian displacements from a superposition of statistically independent processes with the wave-space and real-space contributions as respective covariances. The cost of computing the Brownian displacements in this way is comparable to the cost of computing the deterministic displacements. The addition of a stresslet constraint to the over-damped particle

Nanofluidic rocking Brownian motors

NASA Astrophysics Data System (ADS)

Skaug, Michael J.; Schwemmer, Christian; Fringes, Stefan; Rawlings, Colin D.; Knoll, Armin W.

2018-03-01

Control and transport of nanoscale objects in fluids is challenging because of the unfavorable scaling of most interaction mechanisms to small length scales. We designed energy landscapes for nanoparticles by accurately shaping the geometry of a nanofluidic slit and exploiting the electrostatic interaction between like-charged particles and walls. Directed transport was performed by combining asymmetric potentials with an oscillating electric field to achieve a rocking Brownian motor. Using gold spheres 60 nanometers in diameter, we investigated the physics of the motor with high spatiotemporal resolution, enabling a parameter-free comparison with theory. We fabricated a sorting device that separates 60- and 100-nanometer particles in opposing directions within seconds. Modeling suggests that the device separates particles with a radial difference of 1 nanometer.

Effective diffusion of confined active Brownian swimmers

NASA Astrophysics Data System (ADS)

Sandoval, Mario; Dagdug, Leonardo

2014-11-01

We find theoretically the effect of confinement and thermal fluctuations, on the diffusivity of a spherical active swimmer moving inside a two-dimensional narrow cavity of general shape. The explicit formulas for the effective diffusion coefficient of a swimmer moving inside two particular cavities are presented. We also compare our analytical results with Brownian Dynamics simulations and we obtain excellent agreement. L.D. thanks Consejo Nacional de Ciencia y Tecnologia (CONACyT) Mexico, for partial support by Grant No. 176452. M. S. thanks CONACyT and Programa de Mejoramiento de Profesorado (PROMEP) for partially funding this work under Grant No. 103.5/13/6732.

Heat, temperature and Clausius inequality in a model for active Brownian particles

PubMed Central

Marconi, Umberto Marini Bettolo; Puglisi, Andrea; Maggi, Claudio

2017-01-01

Methods of stochastic thermodynamics and hydrodynamics are applied to a recently introduced model of active particles. The model consists of an overdamped particle subject to Gaussian coloured noise. Inspired by stochastic thermodynamics, we derive from the system’s Fokker-Planck equation the average exchanges of heat and work with the active bath and the associated entropy production. We show that a Clausius inequality holds, with the local (non-uniform) temperature of the active bath replacing the uniform temperature usually encountered in equilibrium systems. Furthermore, by restricting the dynamical space to the first velocity moments of the local distribution function we derive a hydrodynamic description where local pressure, kinetic temperature and internal heat fluxes appear and are consistent with the previous thermodynamic analysis. The procedure also shows under which conditions one obtains the unified coloured noise approximation (UCNA): such an approximation neglects the fast relaxation to the active bath and therefore yields detailed balance and zero entropy production. In the last part, by using multiple time-scale analysis, we provide a constructive method (alternative to UCNA) to determine the solution of the Kramers equation and go beyond the detailed balance condition determining negative entropy production. PMID:28429787

Heat, temperature and Clausius inequality in a model for active Brownian particles.

PubMed

Marconi, Umberto Marini Bettolo; Puglisi, Andrea; Maggi, Claudio

2017-04-21

Methods of stochastic thermodynamics and hydrodynamics are applied to a recently introduced model of active particles. The model consists of an overdamped particle subject to Gaussian coloured noise. Inspired by stochastic thermodynamics, we derive from the system's Fokker-Planck equation the average exchanges of heat and work with the active bath and the associated entropy production. We show that a Clausius inequality holds, with the local (non-uniform) temperature of the active bath replacing the uniform temperature usually encountered in equilibrium systems. Furthermore, by restricting the dynamical space to the first velocity moments of the local distribution function we derive a hydrodynamic description where local pressure, kinetic temperature and internal heat fluxes appear and are consistent with the previous thermodynamic analysis. The procedure also shows under which conditions one obtains the unified coloured noise approximation (UCNA): such an approximation neglects the fast relaxation to the active bath and therefore yields detailed balance and zero entropy production. In the last part, by using multiple time-scale analysis, we provide a constructive method (alternative to UCNA) to determine the solution of the Kramers equation and go beyond the detailed balance condition determining negative entropy production.

Wavelet Monte Carlo dynamics: A new algorithm for simulating the hydrodynamics of interacting Brownian particles

NASA Astrophysics Data System (ADS)

Dyer, Oliver T.; Ball, Robin C.

2017-03-01

We develop a new algorithm for the Brownian dynamics of soft matter systems that evolves time by spatially correlated Monte Carlo moves. The algorithm uses vector wavelets as its basic moves and produces hydrodynamics in the low Reynolds number regime propagated according to the Oseen tensor. When small moves are removed, the correlations closely approximate the Rotne-Prager tensor, itself widely used to correct for deficiencies in Oseen. We also include plane wave moves to provide the longest range correlations, which we detail for both infinite and periodic systems. The computational cost of the algorithm scales competitively with the number of particles simulated, N, scaling as N In N in homogeneous systems and as N in dilute systems. In comparisons to established lattice Boltzmann and Brownian dynamics algorithms, the wavelet method was found to be only a factor of order 1 times more expensive than the cheaper lattice Boltzmann algorithm in marginally semi-dilute simulations, while it is significantly faster than both algorithms at large N in dilute simulations. We also validate the algorithm by checking that it reproduces the correct dynamics and equilibrium properties of simple single polymer systems, as well as verifying the effect of periodicity on the mobility tensor.

Transport behaviors of locally fractional coupled Brownian motors with fluctuating interactions

NASA Astrophysics Data System (ADS)

Wang, Huiqi; Ni, Feixiang; Lin, Lifeng; Lv, Wangyong; Zhu, Hongqiang

2018-09-01

In some complex viscoelastic mediums, it is ubiquitous that absorbing and desorbing surrounding Brownian particles randomly occur in coupled systems. The conventional method is to model a variable-mass system driven by both multiplicative and additive noises. In this paper, an improved mathematical model is created based on generalized Langevin equations (GLE) to characterize the random interaction with locally fluctuating number of coupled particles in the elastically coupled factional Brownian motors (FBM). By the numerical simulations, the effect of fluctuating interactions on collective transport behaviors is investigated, and some abnormal phenomena, such as cooperative behaviors, stochastic resonance (SR) and anomalous transport, are observed in the regime of sub-diffusion.

Flagellar dynamics of a connected chain of active, polar, Brownian particles.

PubMed

Chelakkot, Raghunath; Gopinath, Arvind; Mahadevan, L; Hagan, Michael F

2014-03-06

We show that active, self-propelled particles that are connected together to form a single chain that is anchored at one end can produce the graceful beating motions of flagella. Changing the boundary condition from a clamp to a pivot at the anchor leads to steadily rotating tight coils. Strong noise in the system disrupts the regularity of the oscillations. We use a combination of detailed numerical simulations, mean-field scaling analysis and first passage time theory to characterize the phase diagram as a function of the filament length, passive elasticity, propulsion force and noise. Our study suggests minimal experimental tests for the onset of oscillations in an active polar chain.

Flagellar dynamics of a connected chain of active, polar, Brownian particles

PubMed Central

Chelakkot, Raghunath; Gopinath, Arvind; Mahadevan, L.; Hagan, Michael F.

2014-01-01

We show that active, self-propelled particles that are connected together to form a single chain that is anchored at one end can produce the graceful beating motions of flagella. Changing the boundary condition from a clamp to a pivot at the anchor leads to steadily rotating tight coils. Strong noise in the system disrupts the regularity of the oscillations. We use a combination of detailed numerical simulations, mean-field scaling analysis and first passage time theory to characterize the phase diagram as a function of the filament length, passive elasticity, propulsion force and noise. Our study suggests minimal experimental tests for the onset of oscillations in an active polar chain. PMID:24352670

Active Brownian particles near straight or curved walls: Pressure and boundary layers

NASA Astrophysics Data System (ADS)

Duzgun, Ayhan; Selinger, Jonathan V.

2018-03-01

Unlike equilibrium systems, active matter is not governed by the conventional laws of thermodynamics. Through a series of analytic calculations and Langevin dynamics simulations, we explore how systems cross over from equilibrium to active behavior as the activity is increased. In particular, we calculate the profiles of density and orientational order near straight or circular walls and show the characteristic width of the boundary layers. We find a simple relationship between the enhancements of density and pressure near a wall. Based on these results, we determine how the pressure depends on wall curvature and hence make approximate analytic predictions for the motion of curved tracers, as well as the rectification of active particles around small openings in confined geometries.

Quantum Brownian motion model for the stock market

NASA Astrophysics Data System (ADS)

Meng, Xiangyi; Zhang, Jian-Wei; Guo, Hong

2016-06-01

It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysical framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system-a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenberg's uncertainty relationship of quantum mechanics in an analogous manner. We analyze real stock data of Shanghai Stock Exchange of China and investigate fat-tail phenomena and non-Markovian behaviors of the stock index with the assistance of the quantum Brownian motion model, thereby interpreting and studying the limitations of the classical Brownian motion model for the efficient market hypothesis from a new perspective of quantum open system dynamics.

Brownian Dynamics simulations of model colloids in channel geometries and external fields

NASA Astrophysics Data System (ADS)

Siems, Ullrich; Nielaba, Peter

2018-04-01

We review the results of Brownian Dynamics simulations of colloidal particles in external fields confined in channels. Super-paramagnetic Brownian particles are well suited two- dimensional model systems for a variety of problems on different length scales, ranging from pedestrian walking through a bottleneck to ions passing ion-channels in living cells. In such systems confinement into channels can have a great influence on the diffusion and transport properties. Especially we will discuss the crossover from single file diffusion in a narrow channel to the diffusion in the extended two-dimensional system. Therefore a new algorithm for computing the mean square displacement (MSD) on logarithmic time scales is presented. In a different study interacting colloidal particles were dragged over a washboard potential and are additionally confined in a two-dimensional micro-channel. In this system kink and anti-kink solitons determine the depinning process of the particles from the periodic potential.

Self-Consistent Simulation of the Brownian Stage of Dust Growth

NASA Technical Reports Server (NTRS)

Kempf, S.; Pfalzner, S.; Henning, Th.

1996-01-01

It is a widely accepted view that in proto-planetary accretion disks the collision and following sticking of dust particles embedded in the gas eventually leads to the formation of planetesimals (coagulation). For the smallest dust grains, Brownian motion is assumed to be the dominant source of their relative velocities leading to collisions between these dust grains. As the dust grains grow they eventually couple to the turbulent motion of the gas which then drives the coagulation much more efficiently. Many numerical coagulation simulations have been carried out to calculate the fractal dimension of the aggregates, which determines the duration of the ineffective Brownian stage of growth. Predominantly on-lattice and off-lattice methods were used. However, both methods require simplification of the astrophysical conditions. The aggregates found by those methods had a fractal dimension of approximately 2 which is equivalent to a constant, mass-independent friction time. If this value were valid for the conditions in an accretion disk, this would mean that the coagulation process would finally 'freeze out' and the growth of a planetesimal would be impossible within the lifetime of an accretion disk. In order to investigate whether this fractal dimension is model independent, we simulate self-consistently the Brownian stage of the coagulation by an N-particle code. This method has the advantage that no further assumptions about homogeneity of the dust have to be made. In our model, the dust grains are considered as aggregates built up of spheres. The equation of motion of the dust grains is based on the probability density for the diffusive transport within the gas atmosphere. Because of the very low number density of the dust grains, only 2-body-collisions have to be considered. As the Brownian stage of growth is very inefficient, the system is to be simulated over long periods of time. In order to find close particle pairs of the system which are most likely to

Aging underdamped scaled Brownian motion: Ensemble- and time-averaged particle displacements, nonergodicity, and the failure of the overdamping approximation.

PubMed

Safdari, Hadiseh; Cherstvy, Andrey G; Chechkin, Aleksei V; Bodrova, Anna; Metzler, Ralf

2017-01-01

We investigate both analytically and by computer simulations the ensemble- and time-averaged, nonergodic, and aging properties of massive particles diffusing in a medium with a time dependent diffusivity. We call this stochastic diffusion process the (aging) underdamped scaled Brownian motion (UDSBM). We demonstrate how the mean squared displacement (MSD) and the time-averaged MSD of UDSBM are affected by the inertial term in the Langevin equation, both at short, intermediate, and even long diffusion times. In particular, we quantify the ballistic regime for the MSD and the time-averaged MSD as well as the spread of individual time-averaged MSD trajectories. One of the main effects we observe is that, both for the MSD and the time-averaged MSD, for superdiffusive UDSBM the ballistic regime is much shorter than for ordinary Brownian motion. In contrast, for subdiffusive UDSBM, the ballistic region extends to much longer diffusion times. Therefore, particular care needs to be taken under what conditions the overdamped limit indeed provides a correct description, even in the long time limit. We also analyze to what extent ergodicity in the Boltzmann-Khinchin sense in this nonstationary system is broken, both for subdiffusive and superdiffusive UDSBM. Finally, the limiting case of ultraslow UDSBM is considered, with a mixed logarithmic and power-law dependence of the ensemble- and time-averaged MSDs of the particles. In the limit of strong aging, remarkably, the ordinary UDSBM and the ultraslow UDSBM behave similarly in the short time ballistic limit. The approaches developed here open ways for considering other stochastic processes under physically important conditions when a finite particle mass and aging in the system cannot be neglected.

Aging underdamped scaled Brownian motion: Ensemble- and time-averaged particle displacements, nonergodicity, and the failure of the overdamping approximation

NASA Astrophysics Data System (ADS)

Safdari, Hadiseh; Cherstvy, Andrey G.; Chechkin, Aleksei V.; Bodrova, Anna; Metzler, Ralf

2017-01-01

We investigate both analytically and by computer simulations the ensemble- and time-averaged, nonergodic, and aging properties of massive particles diffusing in a medium with a time dependent diffusivity. We call this stochastic diffusion process the (aging) underdamped scaled Brownian motion (UDSBM). We demonstrate how the mean squared displacement (MSD) and the time-averaged MSD of UDSBM are affected by the inertial term in the Langevin equation, both at short, intermediate, and even long diffusion times. In particular, we quantify the ballistic regime for the MSD and the time-averaged MSD as well as the spread of individual time-averaged MSD trajectories. One of the main effects we observe is that, both for the MSD and the time-averaged MSD, for superdiffusive UDSBM the ballistic regime is much shorter than for ordinary Brownian motion. In contrast, for subdiffusive UDSBM, the ballistic region extends to much longer diffusion times. Therefore, particular care needs to be taken under what conditions the overdamped limit indeed provides a correct description, even in the long time limit. We also analyze to what extent ergodicity in the Boltzmann-Khinchin sense in this nonstationary system is broken, both for subdiffusive and superdiffusive UDSBM. Finally, the limiting case of ultraslow UDSBM is considered, with a mixed logarithmic and power-law dependence of the ensemble- and time-averaged MSDs of the particles. In the limit of strong aging, remarkably, the ordinary UDSBM and the ultraslow UDSBM behave similarly in the short time ballistic limit. The approaches developed here open ways for considering other stochastic processes under physically important conditions when a finite particle mass and aging in the system cannot be neglected.

Nanofluidic rocking Brownian motors.

PubMed

Skaug, Michael J; Schwemmer, Christian; Fringes, Stefan; Rawlings, Colin D; Knoll, Armin W

2018-03-30

Control and transport of nanoscale objects in fluids is challenging because of the unfavorable scaling of most interaction mechanisms to small length scales. We designed energy landscapes for nanoparticles by accurately shaping the geometry of a nanofluidic slit and exploiting the electrostatic interaction between like-charged particles and walls. Directed transport was performed by combining asymmetric potentials with an oscillating electric field to achieve a rocking Brownian motor. Using gold spheres 60 nanometers in diameter, we investigated the physics of the motor with high spatiotemporal resolution, enabling a parameter-free comparison with theory. We fabricated a sorting device that separates 60- and 100-nanometer particles in opposing directions within seconds. Modeling suggests that the device separates particles with a radial difference of 1 nanometer. Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.

Reversible Quantum Brownian Heat Engines for Electrons

NASA Astrophysics Data System (ADS)

Humphrey, T. E.; Newbury, R.; Taylor, R. P.; Linke, H.

2002-08-01

Brownian heat engines use local temperature gradients in asymmetric potentials to move particles against an external force. The energy efficiency of such machines is generally limited by irreversible heat flow carried by particles that make contact with different heat baths. Here we show that, by using a suitably chosen energy filter, electrons can be transferred reversibly between reservoirs that have different temperatures and electrochemical potentials. We apply this result to propose heat engines based on mesoscopic semiconductor ratchets, which can quasistatically operate arbitrarily close to Carnot efficiency.

Self-propelled Brownian spinning top: dynamics of a biaxial swimmer at low Reynolds numbers.

PubMed

Wittkowski, Raphael; Löwen, Hartmut

2012-02-01

Recently the Brownian dynamics of self-propelled (active) rodlike particles was explored to model the motion of colloidal microswimmers, catalytically driven nanorods, and bacteria. Here we generalize this description to biaxial particles with arbitrary shape and derive the corresponding Langevin equation for a self-propelled Brownian spinning top. The biaxial swimmer is exposed to a hydrodynamic Stokes friction force at low Reynolds numbers, to fluctuating random forces and torques as well as to an external and an internal (effective) force and torque. The latter quantities control its self-propulsion. Due to biaxiality and hydrodynamic translational-rotational coupling, the Langevin equation can only be solved numerically. In the special case of an orthotropic particle in the absence of external forces and torques, the noise-free (zero-temperature) trajectory is analytically found to be a circular helix. This trajectory is confirmed numerically to be more complex in the general case of an arbitrarily shaped particle under the influence of arbitrary forces and torques involving a transient irregular motion before ending up in a simple periodic motion. By contrast, if the external force vanishes, no transient regime is found, and the particle moves on a superhelical trajectory. For orthotropic particles, the noise-averaged trajectory is a generalized concho-spiral. We furthermore study the reduction of the model to two spatial dimensions and classify the noise-free trajectories completely finding circles, straight lines with and without transients, as well as cycloids and arbitrary periodic trajectories. © 2012 American Physical Society

Rate laws of the self-induced aggregation kinetics of Brownian particles

NASA Astrophysics Data System (ADS)

Mondal, Shrabani; Sen, Monoj Kumar; Baura, Alendu; Bag, Bidhan Chandra

2016-03-01

In this paper we have studied the self induced aggregation kinetics of Brownian particles in the presence of both multiplicative and additive noises. In addition to the drift due to the self aggregation process, the environment may induce a drift term in the presence of a multiplicative noise. Then there would be an interplay between the two drift terms. It may account qualitatively the appearance of the different laws of aggregation process. At low strength of white multiplicative noise, the cluster number decreases as a Gaussian function of time. If the noise strength becomes appreciably large then the variation of cluster number with time is fitted well by the mono exponentially decaying function of time. For additive noise driven case, the decrease of cluster number can be described by the power law. But in case of multiplicative colored driven process, cluster number decays multi exponentially. However, we have explored how the rate constant (in the mono exponentially cluster number decaying case) depends on strength of interference of the noises and their intensity. We have also explored how the structure factor at long time depends on the strength of the cross correlation (CC) between the additive and the multiplicative noises.

Controlling Brownian motion of single protein molecules and single fluorophores in aqueous buffer.

PubMed

Cohen, Adam E; Moerner, W E

2008-05-12

We present an Anti-Brownian Electrokinetic trap (ABEL trap) capable of trapping individual fluorescently labeled protein molecules in aqueous buffer. The ABEL trap operates by tracking the Brownian motion of a single fluorescent particle in solution, and applying a time-dependent electric field designed to induce an electrokinetic drift that cancels the Brownian motion. The trapping strength of the ABEL trap is limited by the latency of the feedback loop. In previous versions of the trap, this latency was set by the finite frame rate of the camera used for video-tracking. In the present system, the motion of the particle is tracked entirely in hardware (without a camera or image-processing software) using a rapidly rotating laser focus and lock-in detection. The feedback latency is set by the finite rate of arrival of photons. We demonstrate trapping of individual molecules of the protein GroEL in buffer, and we show confinement of single fluorophores of the dye Cy3 in water.

Effects of non-Gaussian Brownian motion on direct force optical tweezers measurements of the electrostatic forces between pairs of colloidal particles.

PubMed

Raudsepp, Allan; A K Williams, Martin; B Hall, Simon

2016-07-01

Measurements of the electrostatic force with separation between a fixed and an optically trapped colloidal particle are examined with experiment, simulation and analytical calculation. Non-Gaussian Brownian motion is observed in the position of the optically trapped particle when particles are close and traps weak. As a consequence of this motion, a simple least squares parameterization of direct force measurements, in which force is inferred from the displacement of an optically trapped particle as separation is gradually decreased, contains forces generated by the rectification of thermal fluctuations in addition to those originating directly from the electrostatic interaction between the particles. Thus, when particles are close and traps weak, simply fitting the measured direct force measurement to DLVO theory extracts parameters with modified meanings when compared to the original formulation. In such cases, however, physically meaningful DLVO parameters can be recovered by comparing the measured non-Gaussian statistics to those predicted by solutions to Smoluchowski's equation for diffusion in a potential.

Current Reversals of an Underdamped Brownian Particle in an Asymmetric Deformable Potential

NASA Astrophysics Data System (ADS)

Cai, Chun-Chun; Liu, Jian-Li; Chen, Hao; Li, Feng-Guo

2018-03-01

Transport of an underdamped Brownian particle in a one-dimensional asymmetric deformable potential is investigated in the presence of both an ac force and a static force, respectively. From numerical simulations, we obtain the current average velocity. The current reversals and the absolute negative mobility are presented. The increasing of the deformation of the potential can cause the absolute negative mobility to be suppressed and even disappear. When the static force is small, the increase of the potential deformation suppresses the absolute negative mobility. When the force is large, the absolute negative mobility disappears. In particular, when the potential deformation is equal to 0.015, the two current reversals present with the increasing of the force. Remarkably, when the potential deformation is small, there are three current reversals with the increasing of the friction coefficient and the average velocity presents a oscillation behavior. Supported in part by the National Natural Science Foundation of China under Grant Nos. 11575064 and 11175067, and the Natural Science Foundation of Guangdong Province under Grant No. 2016A030313433

The effective temperature for the thermal fluctuations in hot Brownian motion

NASA Astrophysics Data System (ADS)

Srivastava, Mayank; Chakraborty, Dipanjan

2018-05-01

We revisit the effective parameter description of hot Brownian motion—a scenario where a colloidal particle is kept at an elevated temperature than the ambient fluid. Due to the time scale separation between heat diffusion and particle motion, a stationary halo of hot fluid is carried along with the particle resulting in a spatially varying comoving temperature and viscosity profile. The resultant Brownian motion in the overdamped limit can be well described by a Langevin equation with effective parameters such as effective temperature THBM and friction coefficient ζHBM that quantifies the thermal fluctuations and the diffusivity of the particle. These parameters can exactly be calculated using the framework of fluctuating hydrodynamics and require the knowledge of the complete flow field and the temperature field around the particle. Additionally, it was also observed that configurational and kinetic degrees of freedom admit to different effective temperatures, THB M x and THB M v, respectively, with the former predicted accurately from fluctuating hydrodynamics. A more rigorous calculation by Falasco et al. [Phys. Rev. E 90, 032131-10 (2014)] extends the overdamped description to a generalized Langevin equation where the effective temperature becomes frequency dependent and consequently, for any temperature measurement from a Brownian trajectory requires the knowledge of this frequency dependence. We use this framework to expand on the earlier work and look at the first order correction to the limiting values in the hydrodynamic limit and the kinetic limit. We use the linearized Stokes equation and a constant viscosity approximation to calculate the dissipation function in the fluid. The effective temperature is calculated from the weighted average of the temperature field with the dissipation function. Further, we provide a closed form analytical result for effective temperature in the small as well as high frequency limit. Since hot Brownian motion can be

Shear thickening regimes of dense non-Brownian suspensions.

PubMed

Ness, Christopher; Sun, Jin

2016-01-21

We propose a unifying rheological framework for dense suspensions of non-Brownian spheres, predicting the onsets of particle friction and particle inertia as distinct shear thickening mechanisms, while capturing quasistatic and soft particle rheology at high volume fractions and shear rates respectively. Discrete element method simulations that take suitable account of hydrodynamic and particle-contact interactions corroborate the model predictions, demonstrating both mechanisms of shear thickening, and showing that they can occur concurrently with carefully selected particle surface properties under certain flow conditions. Microstructural transitions associated with frictional shear thickening are presented. We find very distinctive divergences of both microstructural and dynamic variables with respect to volume fraction in the thickened and non-thickened states.

Rapid sampling of stochastic displacements in Brownian dynamics simulations

NASA Astrophysics Data System (ADS)

Fiore, Andrew M.; Balboa Usabiaga, Florencio; Donev, Aleksandar; Swan, James W.

2017-03-01

We present a new method for sampling stochastic displacements in Brownian Dynamics (BD) simulations of colloidal scale particles. The method relies on a new formulation for Ewald summation of the Rotne-Prager-Yamakawa (RPY) tensor, which guarantees that the real-space and wave-space contributions to the tensor are independently symmetric and positive-definite for all possible particle configurations. Brownian displacements are drawn from a superposition of two independent samples: a wave-space (far-field or long-ranged) contribution, computed using techniques from fluctuating hydrodynamics and non-uniform fast Fourier transforms; and a real-space (near-field or short-ranged) correction, computed using a Krylov subspace method. The combined computational complexity of drawing these two independent samples scales linearly with the number of particles. The proposed method circumvents the super-linear scaling exhibited by all known iterative sampling methods applied directly to the RPY tensor that results from the power law growth of the condition number of tensor with the number of particles. For geometrically dense microstructures (fractal dimension equal three), the performance is independent of volume fraction, while for tenuous microstructures (fractal dimension less than three), such as gels and polymer solutions, the performance improves with decreasing volume fraction. This is in stark contrast with other related linear-scaling methods such as the force coupling method and the fluctuating immersed boundary method, for which performance degrades with decreasing volume fraction. Calculations for hard sphere dispersions and colloidal gels are illustrated and used to explore the role of microstructure on performance of the algorithm. In practice, the logarithmic part of the predicted scaling is not observed and the algorithm scales linearly for up to 4 ×106 particles, obtaining speed ups of over an order of magnitude over existing iterative methods, and making the

Krylov subspace methods for computing hydrodynamic interactions in Brownian dynamics simulations

PubMed Central

Ando, Tadashi; Chow, Edmond; Saad, Yousef; Skolnick, Jeffrey

2012-01-01

Hydrodynamic interactions play an important role in the dynamics of macromolecules. The most common way to take into account hydrodynamic effects in molecular simulations is in the context of a Brownian dynamics simulation. However, the calculation of correlated Brownian noise vectors in these simulations is computationally very demanding and alternative methods are desirable. This paper studies methods based on Krylov subspaces for computing Brownian noise vectors. These methods are related to Chebyshev polynomial approximations, but do not require eigenvalue estimates. We show that only low accuracy is required in the Brownian noise vectors to accurately compute values of dynamic and static properties of polymer and monodisperse suspension models. With this level of accuracy, the computational time of Krylov subspace methods scales very nearly as O(N2) for the number of particles N up to 10 000, which was the limit tested. The performance of the Krylov subspace methods, especially the “block” version, is slightly better than that of the Chebyshev method, even without taking into account the additional cost of eigenvalue estimates required by the latter. Furthermore, at N = 10 000, the Krylov subspace method is 13 times faster than the exact Cholesky method. Thus, Krylov subspace methods are recommended for performing large-scale Brownian dynamics simulations with hydrodynamic interactions. PMID:22897254

Fractional Brownian motion and motion governed by the fractional Langevin equation in confined geometries.

PubMed

Jeon, Jae-Hyung; Metzler, Ralf

2010-02-01

Motivated by subdiffusive motion of biomolecules observed in living cells, we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time-averaged mean-squared displacement and displacement correlation) are affected by spatial confinement and dimensionality. In particular, we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain. The general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality. We define the displacement correlation function and find that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single-particle trajectory data.

Lossless Brownian Information Engine

NASA Astrophysics Data System (ADS)

Paneru, Govind; Lee, Dong Yun; Tlusty, Tsvi; Pak, Hyuk Kyu

2018-01-01

We report on a lossless information engine that converts nearly all available information from an error-free feedback protocol into mechanical work. Combining high-precision detection at a resolution of 1 nm with ultrafast feedback control, the engine is tuned to extract the maximum work from information on the position of a Brownian particle. We show that the work produced by the engine achieves a bound set by a generalized second law of thermodynamics, demonstrating for the first time the sharpness of this bound. We validate a generalized Jarzynski equality for error-free feedback-controlled information engines.

Lossless Brownian Information Engine.

PubMed

Paneru, Govind; Lee, Dong Yun; Tlusty, Tsvi; Pak, Hyuk Kyu

2018-01-12

We report on a lossless information engine that converts nearly all available information from an error-free feedback protocol into mechanical work. Combining high-precision detection at a resolution of 1 nm with ultrafast feedback control, the engine is tuned to extract the maximum work from information on the position of a Brownian particle. We show that the work produced by the engine achieves a bound set by a generalized second law of thermodynamics, demonstrating for the first time the sharpness of this bound. We validate a generalized Jarzynski equality for error-free feedback-controlled information engines.

Brownian motion of tethered nanowires.

PubMed

Ota, Sadao; Li, Tongcang; Li, Yimin; Ye, Ziliang; Labno, Anna; Yin, Xiaobo; Alam, Mohammad-Reza; Zhang, Xiang

2014-05-01

Brownian motion of slender particles near a boundary is ubiquitous in biological systems and in nanomaterial assembly, but the complex hydrodynamic interaction in those systems is still poorly understood. Here, we report experimental and computational studies of the Brownian motion of silicon nanowires tethered on a substrate. An optical interference method enabled direct observation of microscopic rotations of the slender bodies in three dimensions with high angular and temporal resolutions. This quantitative observation revealed anisotropic and angle-dependent hydrodynamic wall effects: rotational diffusivity in inclined and azimuth directions follows different power laws as a function of the length, ∼ L(-2.5) and ∼ L(-3), respectively, and is more hindered for smaller inclined angles. In parallel, we developed an implicit simulation technique that takes the complex wire-wall hydrodynamic interactions into account efficiently, the result of which agreed well with the experimentally observed angle-dependent diffusion. The demonstrated techniques provide a platform for studying the microrheology of soft condensed matters, such as colloidal and biological systems near interfaces, and exploring the optimal self-assembly conditions of nanostructures.

Magnetic microstructures for regulating Brownian motion

NASA Astrophysics Data System (ADS)

Sooryakumar, Ratnasingham

2013-03-01

Nature has proven that it is possible to engineer complex nanoscale machines in the presence of thermal fluctuations. These biological complexes, which harness random thermal energy to provide functionality, yield a framework to develop related artificial, i.e., nonbiological, phenomena and devices. A major challenge to achieving positional control of fluid-borne submicron sized objects is regulating their Brownian fluctuations. In this talk a magnetic-field-based trap that regulates the thermal fluctuations of superparamagnetic beads in suspension will be presented. Local domain-wall fields originating from patterned magnetic wires, whose strength and profile are tuned by weak external fields, enable bead trajectories within the trap to be managed and easily varied between strong confinements and delocalized spatial excursions. Moreover, the frequency spectrum of the trapped bead responds to fields as a power-law function with a tunable, non-integer exponent. When extended to a cluster of particles, the trapping landscape preferentially stabilizes them into formations of 5-fold symmetry, while their Brownian fluctuations result in frequent transitions between different cluster configurations. The quantitative understanding of the Brownian dynamics together with the ability to tune the extent of the fluctuations enables the wire-based platform to serve as a model system to investigate the competition between random and deterministic forces. Funding from the U.S. Army Research Office under contract W911NF-10-1-0353 is acknowledged.

Boltzmann distribution in a nonequilibrium steady state: measuring local potential by granular Brownian particles.

PubMed

To, Kiwing

2014-06-01

We investigate experimentally the steady state motion of a millimeter-sized granular polyhedral object on vertically vibrating platforms of flat, conical, and parabolic surfaces. We find that the position distribution of the granular object is related to the shape of the platform, just like that of a Brownian particle trapped in a potential at equilibrium, even though the granular object is intrinsically not at equilibrium due to inelastic collisions with the platform. From the collision dynamics, we derive the Langevin equation which describes the motion of the object under an effective potential that equals the gravitational potential along the platform surface. The potential energy is found to agree with the equilibrium equipartition theorem while the kinetic energy does not. Furthermore, the granular temperature is found to be higher than the effective temperature associated with the average potential energy, suggesting the presence of heat transfer from the kinetic part to the potential part of the granular object.

Boltzmann distribution in a nonequilibrium steady state: Measuring local potential by granular Brownian particles

NASA Astrophysics Data System (ADS)

To, Kiwing

2014-06-01

We investigate experimentally the steady state motion of a millimeter-sized granular polyhedral object on vertically vibrating platforms of flat, conical, and parabolic surfaces. We find that the position distribution of the granular object is related to the shape of the platform, just like that of a Brownian particle trapped in a potential at equilibrium, even though the granular object is intrinsically not at equilibrium due to inelastic collisions with the platform. From the collision dynamics, we derive the Langevin equation which describes the motion of the object under an effective potential that equals the gravitational potential along the platform surface. The potential energy is found to agree with the equilibrium equipartition theorem while the kinetic energy does not. Furthermore, the granular temperature is found to be higher than the effective temperature associated with the average potential energy, suggesting the presence of heat transfer from the kinetic part to the potential part of the granular object.

One-Dimensional Brownian Motion of Charged Nanoparticles along Microtubules: A Model System for Weak Binding Interactions

PubMed Central

Minoura, Itsushi; Katayama, Eisaku; Sekimoto, Ken; Muto, Etsuko

2010-01-01

Abstract Various proteins are known to exhibit one-dimensional Brownian motion along charged rodlike polymers, such as microtubules (MTs), actin, and DNA. The electrostatic interaction between the proteins and the rodlike polymers appears to be crucial for one-dimensional Brownian motion, although the underlying mechanism has not been fully clarified. We examined the interactions of positively-charged nanoparticles composed of polyacrylamide gels with MTs. These hydrophilic nanoparticles bound to MTs and displayed one-dimensional Brownian motion in a charge-dependent manner, which indicates that nonspecific electrostatic interaction is sufficient for one-dimensional Brownian motion. The diffusion coefficient decreased exponentially with an increasing particle charge (with the exponent being 0.10 kBT per charge), whereas the duration of the interaction increased exponentially (exponent of 0.22 kBT per charge). These results can be explained semiquantitatively if one assumes that a particle repeats a cycle of binding to and movement along an MT until it finally dissociates from the MT. During the movement, a particle is still electrostatically constrained in the potential valley surrounding the MT. This entire process can be described by a three-state model analogous to the Michaelis-Menten scheme, in which the two parameters of the equilibrium constant between binding and movement, and the rate of dissociation from the MT, are derived as a function of the particle charge density. This study highlights the possibility that the weak binding interactions between proteins and rodlike polymers, e.g., MTs, are mediated by a similar, nonspecific charge-dependent mechanism. PMID:20409479

One-dimensional Brownian motion of charged nanoparticles along microtubules: a model system for weak binding interactions.

PubMed

Minoura, Itsushi; Katayama, Eisaku; Sekimoto, Ken; Muto, Etsuko

2010-04-21

Various proteins are known to exhibit one-dimensional Brownian motion along charged rodlike polymers, such as microtubules (MTs), actin, and DNA. The electrostatic interaction between the proteins and the rodlike polymers appears to be crucial for one-dimensional Brownian motion, although the underlying mechanism has not been fully clarified. We examined the interactions of positively-charged nanoparticles composed of polyacrylamide gels with MTs. These hydrophilic nanoparticles bound to MTs and displayed one-dimensional Brownian motion in a charge-dependent manner, which indicates that nonspecific electrostatic interaction is sufficient for one-dimensional Brownian motion. The diffusion coefficient decreased exponentially with an increasing particle charge (with the exponent being 0.10 kBT per charge), whereas the duration of the interaction increased exponentially (exponent of 0.22 kBT per charge). These results can be explained semiquantitatively if one assumes that a particle repeats a cycle of binding to and movement along an MT until it finally dissociates from the MT. During the movement, a particle is still electrostatically constrained in the potential valley surrounding the MT. This entire process can be described by a three-state model analogous to the Michaelis-Menten scheme, in which the two parameters of the equilibrium constant between binding and movement, and the rate of dissociation from the MT, are derived as a function of the particle charge density. This study highlights the possibility that the weak binding interactions between proteins and rodlike polymers, e.g., MTs, are mediated by a similar, nonspecific charge-dependent mechanism. Copyright 2010 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Observation of Brownian motion in liquids at short times: instantaneous velocity and memory loss.

PubMed

Kheifets, Simon; Simha, Akarsh; Melin, Kevin; Li, Tongcang; Raizen, Mark G

2014-03-28

Measurement of the instantaneous velocity of Brownian motion of suspended particles in liquid probes the microscopic foundations of statistical mechanics in soft condensed matter. However, instantaneous velocity has eluded experimental observation for more than a century since Einstein's prediction of the small length and time scales involved. We report shot-noise-limited, high-bandwidth measurements of Brownian motion of micrometer-sized beads suspended in water and acetone by an optical tweezer. We observe the hydrodynamic instantaneous velocity of Brownian motion in a liquid, which follows a modified energy equipartition theorem that accounts for the kinetic energy of the fluid displaced by the moving bead. We also observe an anticorrelated thermal force, which is conventionally assumed to be uncorrelated.

Two-dimensional dynamics of a trapped active Brownian particle in a shear flow

NASA Astrophysics Data System (ADS)

Li, Yunyun; Marchesoni, Fabio; Debnath, Tanwi; Ghosh, Pulak K.

2017-12-01

We model the two-dimensional dynamics of a pointlike artificial microswimmer diffusing in a harmonic trap subject to the shear flow of a highly viscous medium. The particle is driven simultaneously by the linear restoring force of the trap, the drag force exerted by the flow, and the torque due to the shear gradient. For a Couette flow, elliptical orbits in the noiseless regime, and the correlation functions between the particle's displacements parallel and orthogonal to the flow are computed analytically. The effects of thermal fluctuations (translational) and self-propulsion fluctuations (angular) are treated separately. Finally, we discuss how to extend our approach to the diffusion of a microswimmer in a Poiseuille flow. These results provide an accurate reference solution to investigate, both numerically and experimentally, hydrodynamics corrections to the diffusion of active matter in confined geometries.

Exact Green's functions for a Brownian particle reversibly binding to a fixed target in a finite, two-dimensional, circular domain

NASA Astrophysics Data System (ADS)

Kalay, Ziya

2012-06-01

Despite the apparent need to study reversible reactions between molecules confined to a two-dimensional space such as the cell membrane, exact Green’s functions for this case have not been reported. Here we present exact analytical Green’s functions for a Brownian particle reversibly reacting with a fixed reaction center in a finite two-dimensional circular region with reflecting or absorbing boundaries, considering either a spherically symmetric initial distribution or a particle that is initially bound. We show that Green’s function can be used to predict the effect of measurement uncertainties on the outcome of single-particle/molecule-tracking experiments in which molecular interactions are investigated. Hence, we bridge the gap between previously known solutions in one dimension (Agmon 1984 J. Chem. Phys. 81 2811) and three dimensions (Kim and Shin 1999 Phys. Rev. Lett. 82 1578), and provide an example of how the knowledge of Green’s function can be used to predict experimentally accessible quantities.

Clustering and phase behaviour of attractive active particles with hydrodynamics.

PubMed

Navarro, Ricard Matas; Fielding, Suzanne M

2015-10-14

We simulate clustering, phase separation and hexatic ordering in a monolayered suspension of active squirming disks subject to an attractive Lennard-Jones-like pairwise interaction potential, taking hydrodynamic interactions between the particles fully into account. By comparing the hydrodynamic case with counterpart simulations for passive and active Brownian particles, we elucidate the relative roles of self-propulsion, interparticle attraction, and hydrodynamic interactions in determining clustering and phase behaviour. Even in the presence of an attractive potential, we find that hydrodynamic interactions strongly suppress the motility induced phase separation that might a priori have been expected in a highly active suspension. Instead, we find only a weak tendency for the particles to form stringlike clusters in this regime. At lower activities we demonstrate phase behaviour that is broadly equivalent to that of the counterpart passive system at low temperatures, characterized by regimes of gas-liquid, gas-solid and liquid-solid phase coexistence. In this way, we suggest that a dimensionless quantity representing the level of activity relative to the strength of attraction plays the role of something like an effective non-equilibrium temperature, counterpart to the (dimensionless) true thermodynamic temperature in the passive system. However there are also some important differences from the equilibrium case, most notably with regards the degree of hexatic ordering, which we discuss carefully.

Diffusion of Brownian particles in a tilted periodic potential under the influence of an external Ornstein-Uhlenbeck noise

NASA Astrophysics Data System (ADS)

Bai, Zhan-Wu; Zhang, Wei

2018-01-01

The diffusion behaviors of Brownian particles in a tilted periodic potential under the influence of an internal white noise and an external Ornstein-Uhlenbeck noise are investigated through numerical simulation. In contrast to the case when the bias force is smaller or absent, the diffusion coefficient exhibits a nonmonotonic dependence on the correlation time of the external noise when bias force is large. A mechanism different from locked-to-running transition theory is presented for the diffusion enhancement by a bias force in intermediate to large damping. In the underdamped regime and the presence of external noise, the diffusion coefficient is a monotonically decreasing function of low temperature rather than a nonmonotonic function when external noise is absent. The diffusive process undergoes four regimes when bias force approaches but is less than its critical value and noises intensities are small. These behaviors can be attributed to the locked-to-running transition of particles.

Mixed analytical-stochastic simulation method for the recovery of a Brownian gradient source from probability fluxes to small windows.

PubMed

Dobramysl, U; Holcman, D

2018-02-15

Is it possible to recover the position of a source from the steady-state fluxes of Brownian particles to small absorbing windows located on the boundary of a domain? To address this question, we develop a numerical procedure to avoid tracking Brownian trajectories in the entire infinite space. Instead, we generate particles near the absorbing windows, computed from the analytical expression of the exit probability. When the Brownian particles are generated by a steady-state gradient at a single point, we compute asymptotically the fluxes to small absorbing holes distributed on the boundary of half-space and on a disk in two dimensions, which agree with stochastic simulations. We also derive an expression for the splitting probability between small windows using the matched asymptotic method. Finally, when there are more than two small absorbing windows, we show how to reconstruct the position of the source from the diffusion fluxes. The present approach provides a computational first principle for the mechanism of sensing a gradient of diffusing particles, a ubiquitous problem in cell biology.

Fractional Brownian motion of an Al nanosphere in liquid Al-Si alloy under electron-beam irradiation

NASA Astrophysics Data System (ADS)

Yokota, Takeshi; Howe, J. M.; Jesser, W. A.; Murayama, M.

2004-05-01

Fractional forces and Brownian motion are expected to govern the behavior of nanoscale metallic solids in liquids, but such systems have not been studied. We investigated the motion of a crystalline Al nanosphere inside a partially molten Al-Si alloy particle, using an electron beam to both stimulate and observe the motion of the nanosphere. The irregular motion observed was quantified as antipersistant fractional Brownian motion. Analysis of possible phenomena contributing to the motion demonstrates that the incident electrons provide the fractional force that moves the Al nanosphere and that gravity and the oxide shell on the partially molten particle cause the antipersistant behavior.

Thermodynamic laws and equipartition theorem in relativistic Brownian motion.

PubMed

Koide, T; Kodama, T

2011-06-01

We extend the stochastic energetics to a relativistic system. The thermodynamic laws and equipartition theorem are discussed for a relativistic Brownian particle and the first and the second law of thermodynamics in this formalism are derived. The relation between the relativistic equipartition relation and the rate of heat transfer is discussed in the relativistic case together with the nature of the noise term.

Theory of relativistic Brownian motion in the presence of electromagnetic field in (1+1) dimension

NASA Astrophysics Data System (ADS)

Mukhopadhyay, Annesh; Bandyopadhyay, M.; Bhamidipati, C.

2018-04-01

In this work, we consider the relativistic generalization of the theory of Brownian motion for the (1+1) dimensional case, which is again consistent with Einstein's special theory of relativity and reduces to standard Brownian motion in the Newtonian limit. All the generalizations are made considering Special theory of relativity into account. The particle under consideration has a velocity close to the speed of light and is a free Brownian particle suspended in a heat bath. With this generalization the velocity probability density functions are also obtained using Ito, Stratonovich and Hanggi-Klimontovich approach of pre-point, mid-point and post-point discretization rule. Subsequently, in our work, we have obtained the relativistic Langevin equations in the presence of an electromagnetic field. Finally, taking a special case of a constant vector potential and a constant electric field into account the Langevin equations are solved for the momentum and subsequently the velocity of the particle. Using a similar approach to the Fokker-planck equations of motion, the velocity distributions are also obtained in the presence of a constant vector potential and are plotted, which shows essential deviations from the one obtained without a potential. Our constant potential model can be realized in an optical potential.

The flashing Brownian ratchet and Parrondo's paradox.

PubMed

Ethier, S N; Lee, Jiyeon

2018-01-01

A Brownian ratchet is a one-dimensional diffusion process that drifts towards a minimum of a periodic asymmetric sawtooth potential. A flashing Brownian ratchet is a process that alternates between two regimes, a one-dimensional Brownian motion and a Brownian ratchet, producing directed motion. These processes have been of interest to physicists and biologists for nearly 25 years. The flashing Brownian ratchet is the process that motivated Parrondo's paradox, in which two fair games of chance, when alternated, produce a winning game. Parrondo's games are relatively simple, being discrete in time and space. The flashing Brownian ratchet is rather more complicated. We show how one can study the latter process numerically using a random walk approximation.

Local times for grey Brownian motion

NASA Astrophysics Data System (ADS)

da Silva, J. L.

2015-01-01

In this paper we study the grey Brownian motion, namely its representation and local time. First it is shown that grey Brownian motion may be represented in terms of a standard Brownian motion and then using a criterium of S. Berman, Trans. Amer. Math. Soc., 137, 277-299 (1969), we show that grey Brownian motion admits a λ-square integrable local time almost surely (λ denotes the Lebesgue measure). As a consequence we obtain the occupation formula and state possible generalizations of these results.

Brownian motion of massive black hole binaries and the final parsec problem

NASA Astrophysics Data System (ADS)

Bortolas, E.; Gualandris, A.; Dotti, M.; Spera, M.; Mapelli, M.

2016-09-01

Massive black hole binaries (BHBs) are expected to be one of the most powerful sources of gravitational waves in the frequency range of the pulsar timing array and of forthcoming space-borne detectors. They are believed to form in the final stages of galaxy mergers, and then harden by slingshot ejections of passing stars. However, evolution via the slingshot mechanism may be ineffective if the reservoir of interacting stars is not readily replenished, and the binary shrinking may come to a halt at roughly a parsec separation. Recent simulations suggest that the departure from spherical symmetry, naturally produced in merger remnants, leads to efficient loss cone refilling, preventing the binary from stalling. However, current N-body simulations able to accurately follow the evolution of BHBs are limited to very modest particle numbers. Brownian motion may artificially enhance the loss cone refilling rate in low-N simulations, where the binary encounters a larger population of stars due its random motion. Here we study the significance of Brownian motion of BHBs in merger remnants in the context of the final parsec problem. We simulate mergers with various particle numbers (from 8k to 1M) and with several density profiles. Moreover, we compare simulations where the BHB is fixed at the centre of the merger remnant with simulations where the BHB is free to random walk. We find that Brownian motion does not significantly affect the evolution of BHBs in simulations with particle numbers in excess of one million, and that the hardening measured in merger simulations is due to collisionless loss cone refilling.

Transient aging in fractional Brownian and Langevin-equation motion.

PubMed

Kursawe, Jochen; Schulz, Johannes; Metzler, Ralf

2013-12-01

Stochastic processes driven by stationary fractional Gaussian noise, that is, fractional Brownian motion and fractional Langevin-equation motion, are usually considered to be ergodic in the sense that, after an algebraic relaxation, time and ensemble averages of physical observables coincide. Recently it was demonstrated that fractional Brownian motion and fractional Langevin-equation motion under external confinement are transiently nonergodic-time and ensemble averages behave differently-from the moment when the particle starts to sense the confinement. Here we show that these processes also exhibit transient aging, that is, physical observables such as the time-averaged mean-squared displacement depend on the time lag between the initiation of the system at time t=0 and the start of the measurement at the aging time t(a). In particular, it turns out that for fractional Langevin-equation motion the aging dependence on t(a) is different between the cases of free and confined motion. We obtain explicit analytical expressions for the aged moments of the particle position as well as the time-averaged mean-squared displacement and present a numerical analysis of this transient aging phenomenon.

Coherent random lasing controlled by Brownian motion of the active scatterer

NASA Astrophysics Data System (ADS)

Liang, Shuofeng; Yin, Leicheng; Zhang, ZhenZhen; Xia, Jiangying; Xie, Kang; Zou, Gang; Hu, Zhijia; Zhang, Qijin

2018-05-01

The stability of the scattering loop is fundamental for coherent random lasing in a dynamic scattering system. In this work, fluorescence of DPP (N, N-di [3-(isobutyl polyhedral oligomeric silsesquioxanes) propyl] perylene diimide) is scattered to produce RL and we realize the transition from incoherent RL to coherent RL by controlling the Brownian motion of the scatterers (dimer aggregates of DPP) and the stability of scattering loop. To produce coherent random lasers, the loop needs to maintain a stable state within the loop-stable time, which can be determined through controlled Brownian motion of scatterers in the scattering system. The result shows that the loop-stable time is within 5.83 × 10‑5 s to 1.61 × 10‑4 s based on the transition from coherent to incoherent random lasing. The time range could be tuned by finely controlling the viscosity of the solution. This work not only develops a method to predict the loop-stable time, but also develops the study between Brownian motion and random lasers, which opens the road to a variety of novel interdisciplinary investigations involving modern statistical mechanics and disordered photonics.

Dependence of Brownian and Néel relaxation times on magnetic field strength

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deissler, Robert J., E-mail: rjd42@case.edu; Wu, Yong; Martens, Michael A.

2014-01-15

Purpose: In magnetic particle imaging (MPI) and magnetic particle spectroscopy (MPS) the relaxation time of the magnetization in response to externally applied magnetic fields is determined by the Brownian and Néel relaxation mechanisms. Here the authors investigate the dependence of the relaxation times on the magnetic field strength and the implications for MPI and MPS. Methods: The Fokker–Planck equation with Brownian relaxation and the Fokker–Planck equation with Néel relaxation are solved numerically for a time-varying externally applied magnetic field, including a step-function, a sinusoidally varying, and a linearly ramped magnetic field. For magnetic fields that are applied as a stepmore » function, an eigenvalue approach is used to directly calculate both the Brownian and Néel relaxation times for a range of magnetic field strengths. For Néel relaxation, the eigenvalue calculations are compared to Brown's high-barrier approximation formula. Results: The relaxation times due to the Brownian or Néel mechanisms depend on the magnitude of the applied magnetic field. In particular, the Néel relaxation time is sensitive to the magnetic field strength, and varies by many orders of magnitude for nanoparticle properties and magnetic field strengths relevant for MPI and MPS. Therefore, the well-known zero-field relaxation times underestimate the actual relaxation times and, in particular, can underestimate the Néel relaxation time by many orders of magnitude. When only Néel relaxation is present—if the particles are embedded in a solid for instance—the authors found that there can be a strong magnetization response to a sinusoidal driving field, even if the period is much less than the zero-field relaxation time. For a ferrofluid in which both Brownian and Néel relaxation are present, only one relaxation mechanism may dominate depending on the magnetic field strength, the driving frequency (or ramp time), and the phase of the magnetization

Internal dynamics of semiflexible polymers with active noise

NASA Astrophysics Data System (ADS)

Eisenstecken, Thomas; Gompper, Gerhard; Winkler, Roland G.

2017-04-01

The intramolecular dynamics of flexible and semiflexible polymers in response to active noise is studied theoretically. The active noise may either originate from interactions of a passive polymer with a bath of active Brownian particles or the polymer itself is comprised of active Brownian particles. We describe the polymer by the continuous Gaussian semiflexible-polymer model, taking into account the finite polymer extensibility. Our analytical calculations predict a strong dependence of the polymer dynamics on the activity. In particular, active semiflexible polymers exhibit a crossover from a bending elasticity-dominated dynamics at weak activity to that of flexible polymers at strong activity. The end-to-end vector correlation function decays exponentially for times longer than the longest polymer relaxation time. Thereby, the polymer relaxation determines the decay of the correlation function for long and flexible polymers. For shorter and stiffer polymers, the relaxation behavior of individual active Brownian particles dominates the decay above a certain activity. The diffusive dynamics of a polymer is substantially enhanced by the activity. Three regimes can be identified in the mean square displacement for sufficiently strong activities: an activity-induced ballistic regime at short times, followed by a Rouse-type polymer-specific regime for any polymer stiffness, and free diffusion at long times, again determined by the activity.

A Brownian dynamics study on ferrofluid colloidal dispersions using an iterative constraint method to satisfy Maxwell’s equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dubina, Sean Hyun, E-mail: sdubin2@uic.edu; Wedgewood, Lewis Edward, E-mail: wedge@uic.edu

2016-07-15

Ferrofluids are often favored for their ability to be remotely positioned via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally simulated using the Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely, Maxwell’s equations. An iterative constraint method was developed to satisfy Maxwell’s equations when a uniform magnetic field is imposed on ferrofluids in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters in a mesoscale particle collection. This was accomplished bymore » allowing a particulate system in a simple shear flow to advance by a time step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint method applied over sub-volume length scales until Maxwell’s equations were satisfied. The resultant ferrofluid model with constraints demonstrates that the magnetoviscosity contribution is not as substantial when compared to homogeneous simulations that assume the material’s magnetism is a direct response to the external magnetic field. This was detected across varying intensities of particle-particle interaction, Brownian motion, and shear flow. Ferroparticle aggregation was still extensively present but less so than typically observed.« less

Shear thinning in non-Brownian suspensions.

PubMed

Chatté, Guillaume; Comtet, Jean; Niguès, Antoine; Bocquet, Lydéric; Siria, Alessandro; Ducouret, Guylaine; Lequeux, François; Lenoir, Nicolas; Ovarlez, Guillaume; Colin, Annie

2018-02-14

We study the flow of suspensions of non-Brownian particles dispersed into a Newtonian solvent. Combining capillary rheometry and conventional rheometry, we evidence a succession of two shear thinning regimes separated by a shear thickening one. Through X-ray radiography measurements, we show that during each of those regimes, the flow remains homogeneous and does not involve particle migration. Using a quartz-tuning fork based atomic force microscope, we measure the repulsive force profile and the microscopic friction coefficient μ between two particles immersed into the solvent, as a function of normal load. Coupling measurements from those three techniques, we propose that (1) the first shear-thinning regime at low shear rates occurs for a lubricated rheology and can be interpreted as a decrease of the effective volume fraction under increasing particle pressures, due to short-ranged repulsive forces and (2) the second shear thinning regime after the shear-thickening transition occurs for a frictional rheology and can be interpreted as stemming from a decrease of the microscopic friction coefficient at large normal load.

Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion

PubMed Central

Bodrova, Anna S.; Chechkin, Aleksei V.; Cherstvy, Andrey G.; Safdari, Hadiseh; Sokolov, Igor M.; Metzler, Ralf

2016-01-01

It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases. PMID:27462008

Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion.

PubMed

Bodrova, Anna S; Chechkin, Aleksei V; Cherstvy, Andrey G; Safdari, Hadiseh; Sokolov, Igor M; Metzler, Ralf

2016-07-27

It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.

Active Teaching of Diffusion through History of Science, Computer Animation and Role Playing

ERIC Educational Resources Information Center

Krajsek, Simona Strgulc; Vilhar, Barbara

2010-01-01

We developed and tested a lesson plan for active teaching of diffusion in secondary schools (grades 10-13), which stimulates understanding of the thermal (Brownian) motion of particles as the principle underlying diffusion. During the lesson, students actively explore the Brownian motion through microscope observations of irregularly moving small…

Multiscale modeling of particle in suspension with smoothed dissipative particle dynamics

NASA Astrophysics Data System (ADS)

Bian, Xin; Litvinov, Sergey; Qian, Rui; Ellero, Marco; Adams, Nikolaus A.

2012-01-01

We apply smoothed dissipative particle dynamics (SDPD) [Español and Revenga, Phys. Rev. E 67, 026705 (2003)] to model solid particles in suspension. SDPD is a thermodynamically consistent version of smoothed particle hydrodynamics (SPH) and can be interpreted as a multiscale particle framework linking the macroscopic SPH to the mesoscopic dissipative particle dynamics (DPD) method. Rigid structures of arbitrary shape embedded in the fluid are modeled by frozen particles on which artificial velocities are assigned in order to satisfy exactly the no-slip boundary condition on the solid-liquid interface. The dynamics of the rigid structures is decoupled from the solvent by solving extra equations for the rigid body translational/angular velocities derived from the total drag/torque exerted by the surrounding liquid. The correct scaling of the SDPD thermal fluctuations with the fluid-particle size allows us to describe the behavior of the particle suspension on spatial scales ranging continuously from the diffusion-dominated regime typical of sub-micron-sized objects towards the non-Brownian regime characterizing macro-continuum flow conditions. Extensive tests of the method are performed for the case of two/three dimensional bulk particle-system both in Brownian/ non-Brownian environment showing numerical convergence and excellent agreement with analytical theories. Finally, to illustrate the ability of the model to couple with external boundary geometries, the effect of confinement on the diffusional properties of a single sphere within a micro-channel is considered, and the dependence of the diffusion coefficient on the wall-separation distance is evaluated and compared with available analytical results.

Coupled Brownian motors: Anomalous hysteresis and zero-bias negative conductance

NASA Astrophysics Data System (ADS)

Reimann, P.; Kawai, R.; Van den Broeck, C.; Hänggi, P.

1999-03-01

We introduce a model of interacting Brownian particles in a symmetric, periodic potential that undergoes a noise-induced non-equilibrium phase transition. The associated spontaneous symmetry breaking entails a ratchet-like transport mechanism. In response to an external force we identify several novel features; among the most prominent being a zero-bias negative conductance and a prima facie counterintuitive, anomalous hysteresis.

Comparisons of characteristic timescales and approximate models for Brownian magnetic nanoparticle rotations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reeves, Daniel B., E-mail: dbr@Dartmouth.edu; Weaver, John B.

2015-06-21

Magnetic nanoparticles are promising tools for a host of therapeutic and diagnostic medical applications. The dynamics of rotating magnetic nanoparticles in applied magnetic fields depend strongly on the type and strength of the field applied. There are two possible rotation mechanisms and the decision for the dominant mechanism is often made by comparing the equilibrium relaxation times. This is a problem when particles are driven with high-amplitude fields because they are not necessarily at equilibrium at all. Instead, it is more appropriate to consider the “characteristic timescales” that arise in various applied fields. Approximate forms for the characteristic time ofmore » Brownian particle rotations do exist and we show agreement between several analytical and phenomenological-fit models to simulated data from a stochastic Langevin equation approach. We also compare several approximate models with solutions of the Fokker-Planck equation to determine their range of validity for general fields and relaxation times. The effective field model is an excellent approximation, while the linear response solution is only useful for very low fields and frequencies for realistic Brownian particle rotations.« less

Brownian motion under dynamic disorder: effects of memory on the decay of the non-Gaussianity parameter

NASA Astrophysics Data System (ADS)

Tyagi, Neha; Cherayil, Binny J.

2018-03-01

The increasingly widespread occurrence in complex fluids of particle motion that is both Brownian and non-Gaussian has recently been found to be successfully modeled by a process (frequently referred to as ‘diffusing diffusivity’) in which the white noise that governs Brownian diffusion is itself stochastically modulated by either Ornstein–Uhlenbeck dynamics or by two-state noise. But the model has so far not been able to account for an aspect of non-Gaussian Brownian motion that is also commonly observed: a non-monotonic decay of the parameter that quantifies the extent of deviation from Gaussian behavior. In this paper, we show that the inclusion of memory effects in the model—via a generalized Langevin equation—can rationalise this phenomenon.

Hydrodynamically Coupled Brownian Dynamics: A coarse-grain particle-based Brownian dynamics technique with hydrodynamic interactions for modeling self-developing flow of polymer solutions

NASA Astrophysics Data System (ADS)

Ahuja, V. R.; van der Gucht, J.; Briels, W. J.

2018-01-01

We present a novel coarse-grain particle-based simulation technique for modeling self-developing flow of dilute and semi-dilute polymer solutions. The central idea in this paper is the two-way coupling between a mesoscopic polymer model and a phenomenological fluid model. As our polymer model, we choose Responsive Particle Dynamics (RaPiD), a Brownian dynamics method, which formulates the so-called "conservative" and "transient" pair-potentials through which the polymers interact besides experiencing random forces in accordance with the fluctuation dissipation theorem. In addition to these interactions, our polymer blobs are also influenced by the background solvent velocity field, which we calculate by solving the Navier-Stokes equation discretized on a moving grid of fluid blobs using the Smoothed Particle Hydrodynamics (SPH) technique. While the polymers experience this frictional force opposing their motion relative to the background flow field, our fluid blobs also in turn are influenced by the motion of the polymers through an interaction term. This makes our technique a two-way coupling algorithm. We have constructed this interaction term in such a way that momentum is conserved locally, thereby preserving long range hydrodynamics. Furthermore, we have derived pairwise fluctuation terms for the velocities of the fluid blobs using the Fokker-Planck equation, which have been alternatively derived using the General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) approach in Smoothed Dissipative Particle Dynamics (SDPD) literature. These velocity fluctuations for the fluid may be incorporated into the velocity updates for our fluid blobs to obtain a thermodynamically consistent distribution of velocities. In cases where these fluctuations are insignificant, however, these additional terms may well be dropped out as they are in a standard SPH simulation. We have applied our technique to study the rheology of two different

Hydrodynamically Coupled Brownian Dynamics: A coarse-grain particle-based Brownian dynamics technique with hydrodynamic interactions for modeling self-developing flow of polymer solutions.

PubMed

Ahuja, V R; van der Gucht, J; Briels, W J

2018-01-21

We present a novel coarse-grain particle-based simulation technique for modeling self-developing flow of dilute and semi-dilute polymer solutions. The central idea in this paper is the two-way coupling between a mesoscopic polymer model and a phenomenological fluid model. As our polymer model, we choose Responsive Particle Dynamics (RaPiD), a Brownian dynamics method, which formulates the so-called "conservative" and "transient" pair-potentials through which the polymers interact besides experiencing random forces in accordance with the fluctuation dissipation theorem. In addition to these interactions, our polymer blobs are also influenced by the background solvent velocity field, which we calculate by solving the Navier-Stokes equation discretized on a moving grid of fluid blobs using the Smoothed Particle Hydrodynamics (SPH) technique. While the polymers experience this frictional force opposing their motion relative to the background flow field, our fluid blobs also in turn are influenced by the motion of the polymers through an interaction term. This makes our technique a two-way coupling algorithm. We have constructed this interaction term in such a way that momentum is conserved locally, thereby preserving long range hydrodynamics. Furthermore, we have derived pairwise fluctuation terms for the velocities of the fluid blobs using the Fokker-Planck equation, which have been alternatively derived using the General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) approach in Smoothed Dissipative Particle Dynamics (SDPD) literature. These velocity fluctuations for the fluid may be incorporated into the velocity updates for our fluid blobs to obtain a thermodynamically consistent distribution of velocities. In cases where these fluctuations are insignificant, however, these additional terms may well be dropped out as they are in a standard SPH simulation. We have applied our technique to study the rheology of two different

The Fluctuation-Dissipation Theorem of Colloidal Particle's energy on 2D Periodic Substrates: A Monte Carlo Study of thermal noise-like fluctuation and diffusion like Brownian motion

NASA Astrophysics Data System (ADS)

Najafi, Amin

2014-05-01

Using the Monte Carlo simulations, we have calculated mean-square fluctuations in statistical mechanics, such as those for colloids energy configuration are set on square 2D periodic substrates interacting via a long range screened Coulomb potential on any specific and fixed substrate. Random fluctuations with small deviations from the state of thermodynamic equilibrium arise from the granular structure of them and appear as thermal diffusion with Gaussian distribution structure as well. The variations are showing linear form of the Fluctuation-Dissipation Theorem on the energy of particles constitutive a canonical ensemble with continuous diffusion process of colloidal particle systems. The noise-like variation of the energy per particle and the order parameter versus the Brownian displacement of sum of large number of random steps of particles at low temperatures phase are presenting a markovian process on colloidal particles configuration, too.

Ergodicity breaking and ageing of underdamped Brownian dynamics with quenched disorder

NASA Astrophysics Data System (ADS)

Guo, Wei; Li, Yong; Song, Wen-Hua; Du, Lu-Chun

2018-03-01

The dynamics of an underdamped Brownian particle moving in one-dimensional quenched disorder under the action of an external force is investigated. Within the tailored parameter regime, the transiently anomalous diffusion and ergodicity breaking, spanning several orders of magnitude in time, have been obtained. The ageing nature of the system weakens as the dissipation of the system increases for other given parameters. Its origin is ascribed to the highly local heterogeneity of the disorder. Two kinds of approximations (in the stationary state), respectively, for large bias and large damping are derived. These results may be helpful in further understanding the nontrivial response of nonlinear dynamics, and also have potential applications to experiments and activities of biological processes.

The flashing Brownian ratchet and Parrondo’s paradox

PubMed Central

Ethier, S. N.

2018-01-01

A Brownian ratchet is a one-dimensional diffusion process that drifts towards a minimum of a periodic asymmetric sawtooth potential. A flashing Brownian ratchet is a process that alternates between two regimes, a one-dimensional Brownian motion and a Brownian ratchet, producing directed motion. These processes have been of interest to physicists and biologists for nearly 25 years. The flashing Brownian ratchet is the process that motivated Parrondo’s paradox, in which two fair games of chance, when alternated, produce a winning game. Parrondo’s games are relatively simple, being discrete in time and space. The flashing Brownian ratchet is rather more complicated. We show how one can study the latter process numerically using a random walk approximation. PMID:29410868

Reconfigurable paramagnetic microswimmers: Brownian motion affects non-reciprocal actuation.

PubMed

Du, Di; Hilou, Elaa; Biswal, Sibani Lisa

2018-05-09

Swimming at low Reynolds number is typically dominated by a large viscous drag, therefore microscale swimmers require non-reciprocal body deformation to generate locomotion. Purcell described a simple mechanical swimmer at the microscale consisting of three rigid components connected together with two hinges. Here we present a simple microswimmer consisting of two rigid paramagnetic particles with different sizes. When placed in an eccentric magnetic field, this simple microswimmer exhibits non-reciprocal body motion and its swimming locomotion can be directed in a controllable manner. Additional components can be added to create a multibody microswimmer, whereby the particles act cooperatively and translate in a given direction. For some multibody swimmers, the stochastic thermal forces fragment the arm, which therefore modifies the swimming strokes and changes the locomotive speed. This work offers insight into directing the motion of active systems with novel time-varying magnetic fields. It also reveals that Brownian motion not only affects the locomotion of reciprocal swimmers that are subject to the Scallop theorem, but also affects that of non-reciprocal swimmers.

Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion.

PubMed

Jeon, Jae-Hyung; Chechkin, Aleksei V; Metzler, Ralf

2014-08-14

Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is 〈x(2)(t)〉 ≃ 2K(t)t with K(t) ≃ t(α-1) for 0 < α < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion, for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely, we demonstrate that under confinement, the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments, in particular, under confinement inside cellular compartments or when optical tweezers tracking methods are used.

Observing conformations of single FoF1-ATP synthases in a fast anti-Brownian electrokinetic trap

NASA Astrophysics Data System (ADS)

Su, Bertram; Düser, Monika G.; Zarrabi, Nawid; Heitkamp, Thomas; Starke, Ilka; Börsch, Michael

2015-03-01

To monitor conformational changes of individual membrane transporters in liposomes in real time, we attach two fluorophores to selected domains of a protein. Sequential distance changes between the dyes are recorded and analyzed by Förster resonance energy transfer (FRET). Using freely diffusing membrane proteins reconstituted in liposomes, observation times are limited by Brownian motion through the confocal detection volume. A. E. Cohen and W. E. Moerner have invented and built microfluidic devices to actively counteract Brownian motion of single nanoparticles in electrokinetic traps (ABELtrap). Here we present a version of an ABELtrap with a laser focus pattern generated by electro-optical beam deflectors and controlled by a programmable FPGA. This ABELtrap could hold single fluorescent nanobeads for more than 100 seconds, increasing the observation times of a single particle more than 1000-fold. Conformational changes of single FRET-labeled membrane enzymes FoF1-ATP synthase can be detected in the ABELtrap.

Brownian motion of graphene.

PubMed

Maragó, Onofrio M; Bonaccorso, Francesco; Saija, Rosalba; Privitera, Giulia; Gucciardi, Pietro G; Iatì, Maria Antonia; Calogero, Giuseppe; Jones, Philip H; Borghese, Ferdinando; Denti, Paolo; Nicolosi, Valeria; Ferrari, Andrea C

2010-12-28

Brownian motion is a manifestation of the fluctuation-dissipation theorem of statistical mechanics. It regulates systems in physics, biology, chemistry, and finance. We use graphene as prototype material to unravel the consequences of the fluctuation-dissipation theorem in two dimensions, by studying the Brownian motion of optically trapped graphene flakes. These orient orthogonal to the light polarization, due to the optical constants anisotropy. We explain the flake dynamics in the optical trap and measure force and torque constants from the correlation functions of the tracking signals, as well as comparing experiments with a full electromagnetic theory of optical trapping. The understanding of optical trapping of two-dimensional nanostructures gained through our Brownian motion analysis paves the way to light-controlled manipulation and all-optical sorting of biological membranes and anisotropic macromolecules.

STOCHASTIC INTEGRATION FOR TEMPERED FRACTIONAL BROWNIAN MOTION.

PubMed

Meerschaert, Mark M; Sabzikar, Farzad

2014-07-01

Tempered fractional Brownian motion is obtained when the power law kernel in the moving average representation of a fractional Brownian motion is multiplied by an exponential tempering factor. This paper develops the theory of stochastic integrals for tempered fractional Brownian motion. Along the way, we develop some basic results on tempered fractional calculus.

Stochastic interactions of two Brownian hard spheres in the presence of depletants

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karzar-Jeddi, Mehdi; Fan, Tai-Hsi, E-mail: thfan@engr.uconn.edu; Tuinier, Remco

2014-06-07

A quantitative analysis is presented for the stochastic interactions of a pair of Brownian hard spheres in non-adsorbing polymer solutions. The hard spheres are hypothetically trapped by optical tweezers and allowed for random motion near the trapped positions. The investigation focuses on the long-time correlated Brownian motion. The mobility tensor altered by the polymer depletion effect is computed by the boundary integral method, and the corresponding random displacement is determined by the fluctuation-dissipation theorem. From our computations it follows that the presence of depletion layers around the hard spheres has a significant effect on the hydrodynamic interactions and particle dynamicsmore » as compared to pure solvent and uniform polymer solution cases. The probability distribution functions of random walks of the two interacting hard spheres that are trapped clearly shift due to the polymer depletion effect. The results show that the reduction of the viscosity in the depletion layers around the spheres and the entropic force due to the overlapping of depletion zones have a significant influence on the correlated Brownian interactions.« less

Morphology of clusters of attractive dry and wet self-propelled spherical particle suspensions.

PubMed

Alarcón, Francisco; Valeriani, Chantal; Pagonabarraga, Ignacio

2017-01-25

In order to assess the effect of hydrodynamics in the assembly of active attractive spheres, we simulate a semi-dilute suspension of attractive self-propelled spherical particles in a quasi-two dimensional geometry comparing the case with and without hydrodynamics interactions. To start with, independent of the presence of hydrodynamics, we observe that depending on the ratio between attraction and propulsion, particles either coarsen or aggregate forming finite-size clusters. Focusing on the clustering regime, we characterize two different cluster parameters, i.e. their morphology and orientational order, and compare the case when active particles behave either as pushers or pullers (always in the regime where inter-particle attractions compete with self-propulsion). Studying cluster phases for squirmers with respect to those obtained for active Brownian disks (indicated as ABPs), we have shown that hydrodynamics alone can sustain a cluster phase of active swimmers (pullers), while ABPs form cluster phases due to the competition between attraction and self-propulsion. The structural properties of the cluster phases of squirmers and ABPs are similar, although squirmers show sensitivity to active stresses. Active Brownian disks resemble weakly pusher squirmer suspensions in terms of cluster size distribution, structure of the radius of gyration on the cluster size and degree of cluster polarity.

A bound particle coupled to two thermostats

NASA Astrophysics Data System (ADS)

Fogedby, Hans C.; Imparato, Alberto

2011-05-01

We consider a harmonically bound Brownian particle coupled to two distinct heat reservoirs at different temperatures. We show that the presence of a harmonic trap does not change the large deviation function from the case of a free Brownian particle discussed by Derrida and Brunet and Visco. Likewise, the Gallavotti-Cohen fluctuation theorem related to the entropy production at the heat sources remains in force. We support the analytical results with numerical simulations.

Nonisothermal Brownian motion: Thermophoresis as the macroscopic manifestation of thermally biased molecular motion.

PubMed

Brenner, Howard

2005-12-01

A quiescent single-component gravity-free gas subject to a small steady uniform temperature gradient T, despite being at rest, is shown to experience a drift velocity UD=-D* gradient ln T, where D* is the gas's nonisothermal self-diffusion coefficient. D* is identified as being the gas's thermometric diffusivity alpha. The latter differs from the gas's isothermal isotopic self-diffusion coefficient D, albeit only slightly. Two independent derivations are given of this drift velocity formula, one kinematical and the other dynamical, both derivations being strictly macroscopic in nature. Within modest experimental and theoretical uncertainties, this virtual drift velocity UD=-alpha gradient ln T is shown to be constitutively and phenomenologically indistinguishable from the well-known experimental and theoretical formulas for the thermophoretic velocity U of a macroscopic (i.e., non-Brownian) non-heat-conducting particle moving under the influence of a uniform temperature gradient through an otherwise quiescent single-component rarefied gas continuum at small Knudsen numbers. Coupled with the size independence of the particle's thermophoretic velocity, the empirically observed equality, U=UD, leads naturally to the hypothesis that these two velocities, the former real and the latter virtual, are, in fact, simply manifestations of the same underlying molecular phenomenon, namely the gas's Brownian movement, albeit biased by the temperature gradient. This purely hydrodynamic continuum-mechanical equality is confirmed by theoretical calculations effected at the kinetic-molecular level on the basis of an existing solution of the Boltzmann equation for a quasi-Lorentzian gas, modulo small uncertainties pertaining to the choice of collision model. Explicitly, this asymptotically valid molecular model allows the virtual drift velocity UD of the light gas and the thermophoretic velocity U of the massive, effectively non-Brownian, particle, now regarded as the tracer particle

Parsing anomalous versus normal diffusive behavior of bedload sediment particles

USGS Publications Warehouse

Fathel, Siobhan; Furbish, David; Schmeeckle, Mark

2016-01-01

Bedload sediment transport is the basic physical ingredient of river evolution. Formulae exist for estimating transport rates, but the diffusive contribution to the sediment flux, and the associated spreading rate of tracer particles, are not clearly understood. The start-and-stop motions of sediment particles transported as bedload on a streambed mimic aspects of the Einstein–Smoluchowski description of the random-walk motions of Brownian particles. Using this touchstone description, recent work suggests the presence of anomalous diffusion, where the particle spreading rate differs from the linear dependence with time of Brownian behavior. We demonstrate that conventional measures of particle spreading reveal different attributes of bedload particle behavior depending on details of the calculation. When we view particle motions over start-and-stop timescales obtained from high-speed (250 Hz) imaging of coarse-sand particles, high-resolution measurements reveal ballistic-like behavior at the shortest (10−2 s) timescale, followed by apparent anomalous behavior due to correlated random walks in transition to normal diffusion (>10−1 s) – similar to Brownian particle behavior but involving distinctly different physics. However, when treated as a ‘virtual plume’ over this timescale range, particles exhibit inhomogeneous diffusive behavior because both the mean and the variance of particle travel distances increase nonlinearly with increasing travel times, a behavior that is unrelated to anomalous diffusion or to Brownian-like behavior. Our results indicate that care is needed in suggesting anomalous behavior when appealing to conventional measures of diffusion formulated for ideal particle systems.

Theoretical Investigation on Particle Brownian Motion on Micro-air-bubble Characteristic in H2O Solvent

NASA Astrophysics Data System (ADS)

Eka Putri, Irana; Gita Redhyka, Grace

2017-07-01

Micro-air-bubble has a high potential contribution in waste water, farming, and fishery treatment. In this research, submicron scale of micro-air-bubble was observed to determine its stability in H2O solvent. By increasing its stability, it can be used for several applications, such as bio-preservative for medical and food transport. The micro-air-bubble was assumed in spherical shape that in incompressible gas boundary condition. So, the random motion of particle (Brownian motion) can be solved by using Stokes-Einstein approximation. But, Hadamard and Rybczynski equation is promoted to solve for larger bubble (micro scale). While, the effect of physical properties (e.g. diffusion coefficient, density, and flow rate) have taken important role in its characteristics in water. According to the theoretical investigation that have been done, decreasing of bubble velocity indicates that the bubble dissolves away or shrinking to the surface. To obtain longevity bubble in pure water medium, it is recomended to apply some surfactant molecules (e.g. NaCl) in micro-air-bubble medium.

Brownian motion from Boltzmann's equation.

NASA Technical Reports Server (NTRS)

Montgomery, D.

1971-01-01

Two apparently disparate lines of inquiry in kinetic theory are shown to be equivalent: (1) Brownian motion as treated by the (stochastic) Langevin equation and Fokker-Planck equation; and (2) Boltzmann's equation. The method is to derive the kinetic equation for Brownian motion from the Boltzmann equation for a two-component neutral gas by a simultaneous expansion in the density and mass ratios.

Fractional Brownian motion run with a multi-scaling clock mimics diffusion of spherical colloids in microstructural fluids.

PubMed

Park, Moongyu; Cushman, John Howard; O'Malley, Dan

2014-09-30

The collective molecular reorientations within a nematic liquid crystal fluid bathing a spherical colloid cause the colloid to diffuse anomalously on a short time scale (i.e., as a non-Brownian particle). The deformations and fluctuations of long-range orientational order in the liquid crystal profoundly influence the transient diffusive regimes. Here we show that an anisotropic fractional Brownian process run with a nonlinear multiscaling clock effectively mimics this collective and transient phenomenon. This novel process has memory, Gaussian increments, and a multiscale mean square displacement that can be chosen independently from the fractal dimension of a particle trajectory. The process is capable of modeling multiscale sub-, super-, or classical diffusion. The finite-size Lyapunov exponents for this multiscaling process are defined for future analysis of related mixing processes.

Representation of Reserves Through a Brownian Motion Model

NASA Astrophysics Data System (ADS)

Andrade, M.; Ferreira, M. A. M.; Filipe, J. A.

2012-11-01

The Brownian Motion is commonly used as an approximation for some Random Walks and also for the Classic Risk Process. As the Random Walks and the Classic Risk Process are used frequently as stochastic models to represent reserves, it is natural to consider the Brownian Motion with the same purpose. In this study a model, based on the Brownian Motion, is presented to represent reserves. The Brownian Motion is used in this study to estimate the ruin probability of a fund. This kind of models is considered often in the study of pensions funds.

Minimum-variance Brownian motion control of an optically trapped probe.

PubMed

Huang, Yanan; Zhang, Zhipeng; Menq, Chia-Hsiang

2009-10-20

This paper presents a theoretical and experimental investigation of the Brownian motion control of an optically trapped probe. The Langevin equation is employed to describe the motion of the probe experiencing random thermal force and optical trapping force. Since active feedback control is applied to suppress the probe's Brownian motion, actuator dynamics and measurement delay are included in the equation. The equation of motion is simplified to a first-order linear differential equation and transformed to a discrete model for the purpose of controller design and data analysis. The derived model is experimentally verified by comparing the model prediction to the measured response of a 1.87 microm trapped probe subject to proportional control. It is then employed to design the optimal controller that minimizes the variance of the probe's Brownian motion. Theoretical analysis is derived to evaluate the control performance of a specific optical trap. Both experiment and simulation are used to validate the design as well as theoretical analysis, and to illustrate the performance envelope of the active control. Moreover, adaptive minimum variance control is implemented to maintain the optimal performance in the case in which the system is time varying when operating the actively controlled optical trap in a complex environment.

FAST TRACK COMMUNICATION: Semiclassical Klein Kramers and Smoluchowski equations for the Brownian motion of a particle in an external potential

NASA Astrophysics Data System (ADS)

Coffey, W. T.; Kalmykov, Yu P.; Titov, S. V.; Mulligan, B. P.

2007-01-01

The quantum Brownian motion of a particle in an external potential V(x) is treated using the master equation for the Wigner distribution function W(x, p, t) in phase space (x, p). A heuristic method of determination of diffusion coefficients in the master equation is proposed. The time evolution equation so obtained contains explicit quantum correction terms up to o(planck4) and in the classical limit, planck → 0, reduces to the Klein-Kramers equation. For a quantum oscillator, the method yields an evolution equation for W(x, p, t) coinciding with that of Agarwal (1971 Phys. Rev. A 4 739). In the non-inertial regime, by applying the Brinkman expansion of the momentum distribution in Weber functions (Brinkman 1956 Physica 22 29), the corresponding semiclassical Smoluchowski equation is derived.

Parallel O(N) Stokes’ solver towards scalable Brownian dynamics of hydrodynamically interacting objects in general geometries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Xujun; Li, Jiyuan; Jiang, Xikai

An efficient parallel Stokes’s solver is developed towards the complete inclusion of hydrodynamic interactions of Brownian particles in any geometry. A Langevin description of the particle dynamics is adopted, where the long-range interactions are included using a Green’s function formalism. We present a scalable parallel computational approach, where the general geometry Stokeslet is calculated following a matrix-free algorithm using the General geometry Ewald-like method. Our approach employs a highly-efficient iterative finite element Stokes’ solver for the accurate treatment of long-range hydrodynamic interactions within arbitrary confined geometries. A combination of mid-point time integration of the Brownian stochastic differential equation, the parallelmore » Stokes’ solver, and a Chebyshev polynomial approximation for the fluctuation-dissipation theorem result in an O(N) parallel algorithm. We also illustrate the new algorithm in the context of the dynamics of confined polymer solutions in equilibrium and non-equilibrium conditions. Our method is extended to treat suspended finite size particles of arbitrary shape in any geometry using an Immersed Boundary approach.« less

Parallel O(N) Stokes’ solver towards scalable Brownian dynamics of hydrodynamically interacting objects in general geometries

DOE PAGES

Zhao, Xujun; Li, Jiyuan; Jiang, Xikai; ...

2017-06-29

An efficient parallel Stokes’s solver is developed towards the complete inclusion of hydrodynamic interactions of Brownian particles in any geometry. A Langevin description of the particle dynamics is adopted, where the long-range interactions are included using a Green’s function formalism. We present a scalable parallel computational approach, where the general geometry Stokeslet is calculated following a matrix-free algorithm using the General geometry Ewald-like method. Our approach employs a highly-efficient iterative finite element Stokes’ solver for the accurate treatment of long-range hydrodynamic interactions within arbitrary confined geometries. A combination of mid-point time integration of the Brownian stochastic differential equation, the parallelmore » Stokes’ solver, and a Chebyshev polynomial approximation for the fluctuation-dissipation theorem result in an O(N) parallel algorithm. We also illustrate the new algorithm in the context of the dynamics of confined polymer solutions in equilibrium and non-equilibrium conditions. Our method is extended to treat suspended finite size particles of arbitrary shape in any geometry using an Immersed Boundary approach.« less

Unsteady sedimentation of flocculating non-Brownian suspensions

NASA Astrophysics Data System (ADS)

Zinchenko, Alexander

2017-11-01

Microstructural evolution and temporal dynamics of the sedimentation rate U(t) are studied for a monodisperse suspension of non-Brownian spherical particles subject to van der Waals attraction and electrostatic repulsion in the realistic range of colloidal parameters (Hamaker constant, surface potential, double layer thickness etc.). A novel economical high-order multipole algorithm is used to fully resolve hydrodynamical interactions in the dynamical simulations with up to 500 spheres in a periodic box and O(106) time steps, combined with geometry perturbation to incorporate lubrication and extend the solution to arbitrarily small particle separations. The total colloidal force near the secondary minimum often greatly exceeds the effective gravity/buoyancy force, resulting in the formation of strong but flexible bonds and large clusters as the suspension evolves from an initial well-mixed state of non-aggregated spheres. Ensemble averaging over many initial configurations is used to predict U(t) for particle volume fractions between 0.1 and 0.25. The results are fully convergent, system-size independent and cover a 2-2.5 fold growth of U(t) after a latency time.

Differential dynamic microscopy to characterize Brownian motion and bacteria motility

NASA Astrophysics Data System (ADS)

Germain, David; Leocmach, Mathieu; Gibaud, Thomas

2016-03-01

We have developed a lab module for undergraduate students, which involves the process of quantifying the dynamics of a suspension of microscopic particles using Differential Dynamic Microscopy (DDM). DDM is a relatively new technique that constitutes an alternative method to more classical techniques such as dynamic light scattering (DLS) or video particle tracking (VPT). The technique consists of imaging a particle dispersion with a standard light microscope and a camera and analyzing the images using a digital Fourier transform to obtain the intermediate scattering function, an autocorrelation function that characterizes the dynamics of the dispersion. We first illustrate DDM in the textbook case of colloids under Brownian motion, where we measure the diffusion coefficient. Then we show that DDM is a pertinent tool to characterize biological systems such as motile bacteria.

Three-dimensional nanoscale imaging by plasmonic Brownian microscopy

NASA Astrophysics Data System (ADS)

Labno, Anna; Gladden, Christopher; Kim, Jeongmin; Lu, Dylan; Yin, Xiaobo; Wang, Yuan; Liu, Zhaowei; Zhang, Xiang

2017-12-01

Three-dimensional (3D) imaging at the nanoscale is a key to understanding of nanomaterials and complex systems. While scanning probe microscopy (SPM) has been the workhorse of nanoscale metrology, its slow scanning speed by a single probe tip can limit the application of SPM to wide-field imaging of 3D complex nanostructures. Both electron microscopy and optical tomography allow 3D imaging, but are limited to the use in vacuum environment due to electron scattering and to optical resolution in micron scales, respectively. Here we demonstrate plasmonic Brownian microscopy (PBM) as a way to improve the imaging speed of SPM. Unlike photonic force microscopy where a single trapped particle is used for a serial scanning, PBM utilizes a massive number of plasmonic nanoparticles (NPs) under Brownian diffusion in solution to scan in parallel around the unlabeled sample object. The motion of NPs under an evanescent field is three-dimensionally localized to reconstruct the super-resolution topology of 3D dielectric objects. Our method allows high throughput imaging of complex 3D structures over a large field of view, even with internal structures such as cavities that cannot be accessed by conventional mechanical tips in SPM.

High-resolution detection of Brownian motion for quantitative optical tweezers experiments.

PubMed

Grimm, Matthias; Franosch, Thomas; Jeney, Sylvia

2012-08-01

We have developed an in situ method to calibrate optical tweezers experiments and simultaneously measure the size of the trapped particle or the viscosity of the surrounding fluid. The positional fluctuations of the trapped particle are recorded with a high-bandwidth photodetector. We compute the mean-square displacement, as well as the velocity autocorrelation function of the sphere, and compare it to the theory of Brownian motion including hydrodynamic memory effects. A careful measurement and analysis of the time scales characterizing the dynamics of the harmonically bound sphere fluctuating in a viscous medium directly yields all relevant parameters. Finally, we test the method for different optical trap strengths, with different bead sizes and in different fluids, and we find excellent agreement with the values provided by the manufacturers. The proposed approach overcomes the most commonly encountered limitations in precision when analyzing the power spectrum of position fluctuations in the region around the corner frequency. These low frequencies are usually prone to errors due to drift, limitations in the detection, and trap linearity as well as short acquisition times resulting in poor statistics. Furthermore, the strategy can be generalized to Brownian motion in more complex environments, provided the adequate theories are available.

Instantaneous ballistic velocity of suspended Brownian nanocrystals measured by upconversion nanothermometry

NASA Astrophysics Data System (ADS)

Brites, Carlos D. S.; Xie, Xiaoji; Debasu, Mengistie L.; Qin, Xian; Chen, Runfeng; Huang, Wei; Rocha, João; Liu, Xiaogang; Carlos, Luís D.

2016-10-01

Brownian motion is one of the most fascinating phenomena in nature. Its conceptual implications have a profound impact in almost every field of science and even economics, from dissipative processes in thermodynamic systems, gene therapy in biomedical research, artificial motors and galaxy formation to the behaviour of stock prices. However, despite extensive experimental investigations, the basic microscopic knowledge of prototypical systems such as colloidal particles in a fluid is still far from being complete. This is particularly the case for the measurement of the particles' instantaneous velocities, elusive due to the rapid random movements on extremely short timescales. Here, we report the measurement of the instantaneous ballistic velocity of Brownian nanocrystals suspended in both aqueous and organic solvents. To achieve this, we develop a technique based on upconversion nanothermometry. We find that the population of excited electronic states in NaYF4:Yb/Er nanocrystals at thermal equilibrium can be used for temperature mapping of the nanofluid with great thermal sensitivity (1.15% K-1 at 296 K) and a high spatial resolution (<1 μm). A distinct correlation between the heat flux in the nanofluid and the temporal evolution of Er3+ emission allows us to measure the instantaneous velocity of nanocrystals with different sizes and shapes.

Brownian motion in time-dependent logarithmic potential: Exact results for dynamics and first-passage properties.

PubMed

Ryabov, Artem; Berestneva, Ekaterina; Holubec, Viktor

2015-09-21

The paper addresses Brownian motion in the logarithmic potential with time-dependent strength, U(x, t) = g(t)log(x), subject to the absorbing boundary at the origin of coordinates. Such model can represent kinetics of diffusion-controlled reactions of charged molecules or escape of Brownian particles over a time-dependent entropic barrier at the end of a biological pore. We present a simple asymptotic theory which yields the long-time behavior of both the survival probability (first-passage properties) and the moments of the particle position (dynamics). The asymptotic survival probability, i.e., the probability that the particle will not hit the origin before a given time, is a functional of the potential strength. As such, it exhibits a rather varied behavior for different functions g(t). The latter can be grouped into three classes according to the regime of the asymptotic decay of the survival probability. We distinguish 1. the regular (power-law decay), 2. the marginal (power law times a slow function of time), and 3. the regime of enhanced absorption (decay faster than the power law, e.g., exponential). Results of the asymptotic theory show good agreement with numerical simulations.

Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion

NASA Astrophysics Data System (ADS)

Sposini, Vittoria; Chechkin, Aleksei V.; Seno, Flavio; Pagnini, Gianni; Metzler, Ralf

2018-04-01

A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential (Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time-dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.

Optimal estimates of the diffusion coefficient of a single Brownian trajectory.

PubMed

Boyer, Denis; Dean, David S; Mejía-Monasterio, Carlos; Oshanin, Gleb

2012-03-01

Modern developments in microscopy and image processing are revolutionizing areas of physics, chemistry, and biology as nanoscale objects can be tracked with unprecedented accuracy. The goal of single-particle tracking is to determine the interaction between the particle and its environment. The price paid for having a direct visualization of a single particle is a consequent lack of statistics. Here we address the optimal way to extract diffusion constants from single trajectories for pure Brownian motion. It is shown that the maximum likelihood estimator is much more efficient than the commonly used least-squares estimate. Furthermore, we investigate the effect of disorder on the distribution of estimated diffusion constants and show that it increases the probability of observing estimates much smaller than the true (average) value.

Brownian dynamics and dynamic Monte Carlo simulations of isotropic and liquid crystal phases of anisotropic colloidal particles: a comparative study.

PubMed

Patti, Alessandro; Cuetos, Alejandro

2012-07-01

We report on the diffusion of purely repulsive and freely rotating colloidal rods in the isotropic, nematic, and smectic liquid crystal phases to probe the agreement between Brownian and Monte Carlo dynamics under the most general conditions. By properly rescaling the Monte Carlo time step, being related to any elementary move via the corresponding self-diffusion coefficient, with the acceptance rate of simultaneous trial displacements and rotations, we demonstrate the existence of a unique Monte Carlo time scale that allows for a direct comparison between Monte Carlo and Brownian dynamics simulations. To estimate the validity of our theoretical approach, we compare the mean square displacement of rods, their orientational autocorrelation function, and the self-intermediate scattering function, as obtained from Brownian dynamics and Monte Carlo simulations. The agreement between the results of these two approaches, even under the condition of heterogeneous dynamics generally observed in liquid crystalline phases, is excellent.

Extreme-value statistics of fractional Brownian motion bridges.

PubMed

Delorme, Mathieu; Wiese, Kay Jörg

2016-11-01

Fractional Brownian motion is a self-affine, non-Markovian, and translationally invariant generalization of Brownian motion, depending on the Hurst exponent H. Here we investigate fractional Brownian motion where both the starting and the end point are zero, commonly referred to as bridge processes. Observables are the time t_{+} the process is positive, the maximum m it achieves, and the time t_{max} when this maximum is taken. Using a perturbative expansion around Brownian motion (H=1/2), we give the first-order result for the probability distribution of these three variables and the joint distribution of m and t_{max}. Our analytical results are tested and found to be in excellent agreement, with extensive numerical simulations for both H>1/2 and H<1/2. This precision is achieved by sampling processes with a free end point and then converting each realization to a bridge process, in generalization to what is usually done for Brownian motion.

Diffusion of passive particles in active suspensions

NASA Astrophysics Data System (ADS)

Mussler, Matthias; Rafai, Salima; John, Thomas; Peyla, Philippe; Wagner, Christian

2013-11-01

We study how an active suspension consisting of a definite volume fraction of the microswimmer Chlamydomonas Reinhardtii modifies the Brownian movement of small to medium size microspheres. We present measurements and simulations of trajectories of microspheres with a diameter of 20 μm in suspensions of Chlamydomonas Reinhardtii, a so called ``puller,'' and show that the mean squared displacement of such trajectories consist of parabolic and a linear part. The linear part is due to the hydrodynamic noise of the microswimmers while the parabolic part is a consequence of directed motion events that occur randomly, when a microsphere is transported by a microswimmer on a timescale that is in higher order of magnitude than the Brownian like hydrodynamic interaction. In addition, we theoretically describe this effect with a dimensional analysis that takes the force dipole model used to describe ``puller'' like Chlamydomonas Reinhardtii into account.

Efficient Brownian Dynamics of rigid colloids in linear flow fields based on the grand mobility matrix

NASA Astrophysics Data System (ADS)

Palanisamy, Duraivelan; den Otter, Wouter K.

2018-05-01

We present an efficient general method to simulate in the Stokesian limit the coupled translational and rotational dynamics of arbitrarily shaped colloids subject to external potential forces and torques, linear flow fields, and Brownian motion. The colloid's surface is represented by a collection of spherical primary particles. The hydrodynamic interactions between these particles, here approximated at the Rotne-Prager-Yamakawa level, are evaluated only once to generate the body's (11 × 11) grand mobility matrix. The constancy of this matrix in the body frame, combined with the convenient properties of quaternions in rotational Brownian Dynamics, enables an efficient simulation of the body's motion. Simulations in quiescent fluids yield correct translational and rotational diffusion behaviour and sample Boltzmann's equilibrium distribution. Simulations of ellipsoids and spherical caps under shear, in the absence of thermal fluctuations, yield periodic orbits in excellent agreement with the theories by Jeffery and Dorrepaal. The time-varying stress tensors provide the Einstein coefficient and viscosity of dilute suspensions of these bodies.

Quantum Brownian motion and its conflict with the second law

NASA Astrophysics Data System (ADS)

Nieuwenhuizen, Theo M.; Allahverdyan, Armen E.

2002-11-01

The Brownian motion of a harmonically bound quantum particle and coupled to a harmonic quantum bath is exactly solvable. At low enough temperatures the stationary state is non-Gibbsian due to an entanglement with the bath. This happens when a cloud of bath modes around the particle is formed. Equilibrium thermodynamics for particle plus bath together, does not imply standard thermodynamics for the particle itself at low T. Various formulations of the second law are then invalid. First, the Clausius inequality can be violated. Second, when the width of the confining potential is suddenly changed, there occurs a relaxation to equilibrium during which the rate of entropy production is partly negative. Third, for non-adiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Conditions are put forward under which perpetuum mobile of the second kind, having several work extraction cycles, enter the realm of condensed matter physics.

Conformal correlation functions in the Brownian loop soup

NASA Astrophysics Data System (ADS)

Camia, Federico; Gandolfi, Alberto; Kleban, Matthew

2016-01-01

We define and study a set of operators that compute statistical properties of the Brownian loop soup, a conformally invariant gas of random Brownian loops (Brownian paths constrained to begin and end at the same point) in two dimensions. We prove that the correlation functions of these operators have many of the properties of conformal primaries in a conformal field theory, and compute their conformal dimension. The dimensions are real and positive, but have the novel feature that they vary continuously as a periodic function of a real parameter. We comment on the relation of the Brownian loop soup to the free field, and use this relation to establish that the central charge of the loop soup is twice its intensity.

Geometric Brownian Motion with Tempered Stable Waiting Times

NASA Astrophysics Data System (ADS)

Gajda, Janusz; Wyłomańska, Agnieszka

2012-08-01

One of the earliest system that was used to asset prices description is Black-Scholes model. It is based on geometric Brownian motion and was used as a tool for pricing various financial instruments. However, when it comes to data description, geometric Brownian motion is not capable to capture many properties of present financial markets. One can name here for instance periods of constant values. Therefore we propose an alternative approach based on subordinated tempered stable geometric Brownian motion which is a combination of the popular geometric Brownian motion and inverse tempered stable subordinator. In this paper we introduce the mentioned process and present its main properties. We propose also the estimation procedure and calibrate the analyzed system to real data.

Composite generalized Langevin equation for Brownian motion in different hydrodynamic and adhesion regimes.

PubMed

Yu, Hsiu-Yu; Eckmann, David M; Ayyaswamy, Portonovo S; Radhakrishnan, Ravi

2015-05-01

We present a composite generalized Langevin equation as a unified framework for bridging the hydrodynamic, Brownian, and adhesive spring forces associated with a nanoparticle at different positions from a wall, namely, a bulklike regime, a near-wall regime, and a lubrication regime. The particle velocity autocorrelation function dictates the dynamical interplay between the aforementioned forces, and our proposed methodology successfully captures the well-known hydrodynamic long-time tail with context-dependent scaling exponents and oscillatory behavior due to the binding interaction. Employing the reactive flux formalism, we analyze the effect of hydrodynamic variables on the particle trajectory and characterize the transient kinetics of a particle crossing a predefined milestone. The results suggest that both wall-hydrodynamic interactions and adhesion strength impact the particle kinetics.

Brownian Motion of Asymmetric Boomerang Colloidal Particles

NASA Astrophysics Data System (ADS)

Chakrabarty, Ayan; Konya, Andrew; Wang, Feng; Selinger, Jonathan; Sun, Kai; Wei, Qi-Huo

2014-03-01

We used video microscopy and single particle tracking to study the diffusion and local behaviors of asymmetric boomerang particles in a quasi-two dimensional geometry. The motion is biased towards the center of hydrodynamic stress (CoH) and the mean square displacements of the particles are linear at short and long times with different diffusion coefficients and in the crossover regime it is sub-diffusive. Our model based on Langevin theory shows that these behaviors arise from the non-coincidence of the CoH with the center of the body. Since asymmetric boomerangs represent a class of rigid bodies of more generals shape, therefore our findings are generic and true for any non-skewed particle in two dimensions. Both experimental and theoretical results will be discussed.

Diffuse correlation tomography in the transport regime: A theoretical study of the sensitivity to Brownian motion.

PubMed

Tricoli, Ugo; Macdonald, Callum M; Durduran, Turgut; Da Silva, Anabela; Markel, Vadim A

2018-02-01

Diffuse correlation tomography (DCT) uses the electric-field temporal autocorrelation function to measure the mean-square displacement of light-scattering particles in a turbid medium over a given exposure time. The movement of blood particles is here estimated through a Brownian-motion-like model in contrast to ordered motion as in blood flow. The sensitivity kernel relating the measurable field correlation function to the mean-square displacement of the particles can be derived by applying a perturbative analysis to the correlation transport equation (CTE). We derive an analytical expression for the CTE sensitivity kernel in terms of the Green's function of the radiative transport equation, which describes the propagation of the intensity. We then evaluate the kernel numerically. The simulations demonstrate that, in the transport regime, the sensitivity kernel provides sharper spatial information about the medium as compared with the correlation diffusion approximation. Also, the use of the CTE allows one to explore some additional degrees of freedom in the data such as the collimation direction of sources and detectors. Our results can be used to improve the spatial resolution of DCT, in particular, with applications to blood flow imaging in regions where the Brownian motion is dominant.

Diffuse correlation tomography in the transport regime: A theoretical study of the sensitivity to Brownian motion

NASA Astrophysics Data System (ADS)

Tricoli, Ugo; Macdonald, Callum M.; Durduran, Turgut; Da Silva, Anabela; Markel, Vadim A.

2018-02-01

Diffuse correlation tomography (DCT) uses the electric-field temporal autocorrelation function to measure the mean-square displacement of light-scattering particles in a turbid medium over a given exposure time. The movement of blood particles is here estimated through a Brownian-motion-like model in contrast to ordered motion as in blood flow. The sensitivity kernel relating the measurable field correlation function to the mean-square displacement of the particles can be derived by applying a perturbative analysis to the correlation transport equation (CTE). We derive an analytical expression for the CTE sensitivity kernel in terms of the Green's function of the radiative transport equation, which describes the propagation of the intensity. We then evaluate the kernel numerically. The simulations demonstrate that, in the transport regime, the sensitivity kernel provides sharper spatial information about the medium as compared with the correlation diffusion approximation. Also, the use of the CTE allows one to explore some additional degrees of freedom in the data such as the collimation direction of sources and detectors. Our results can be used to improve the spatial resolution of DCT, in particular, with applications to blood flow imaging in regions where the Brownian motion is dominant.

Generalized Arcsine Laws for Fractional Brownian Motion.

PubMed

Sadhu, Tridib; Delorme, Mathieu; Wiese, Kay Jörg

2018-01-26

The three arcsine laws for Brownian motion are a cornerstone of extreme-value statistics. For a Brownian B_{t} starting from the origin, and evolving during time T, one considers the following three observables: (i) the duration t_{+} the process is positive, (ii) the time t_{last} the process last visits the origin, and (iii) the time t_{max} when it achieves its maximum (or minimum). All three observables have the same cumulative probability distribution expressed as an arcsine function, thus the name arcsine laws. We show how these laws change for fractional Brownian motion X_{t}, a non-Markovian Gaussian process indexed by the Hurst exponent H. It generalizes standard Brownian motion (i.e., H=1/2). We obtain the three probabilities using a perturbative expansion in ϵ=H-1/2. While all three probabilities are different, this distinction can only be made at second order in ϵ. Our results are confirmed to high precision by extensive numerical simulations.

Myosin V is a biological Brownian machine.

PubMed

Fujita, Keisuke; Iwaki, Mitsuhiro

2014-01-01

Myosin V is a vesicle transporter that unidirectionally walks along cytoskeletal actin filaments by converting the chemical energy of ATP into mechanical work. Recently, it was found that myosin V force generation is a composition of two processes: a lever-arm swing, which involves a conformational change in the myosin molecule, and a Brownian search-and-catch, which involves a diffusive "search" by the motor domain that is followed by an asymmetric "catch" in the forward actin target such that Brownian motion is rectified. Here we developed a system that combines optical tweezers with DNA nano-material to show that the Brownian search-and-catch mechanism is the energetically dominant process at near stall force, providing 13 kBT of work compared to just 3 kBT by the lever-arm swing. Our result significantly reconsiders the lever-arm swinging model, which assumes the swing dominantly produces work (>10 kBT), and sheds light on the Brownian search-and-catch as a driving process.

Generalized Arcsine Laws for Fractional Brownian Motion

NASA Astrophysics Data System (ADS)

Sadhu, Tridib; Delorme, Mathieu; Wiese, Kay Jörg

2018-01-01

The three arcsine laws for Brownian motion are a cornerstone of extreme-value statistics. For a Brownian Bt starting from the origin, and evolving during time T , one considers the following three observables: (i) the duration t+ the process is positive, (ii) the time tlast the process last visits the origin, and (iii) the time tmax when it achieves its maximum (or minimum). All three observables have the same cumulative probability distribution expressed as an arcsine function, thus the name arcsine laws. We show how these laws change for fractional Brownian motion Xt, a non-Markovian Gaussian process indexed by the Hurst exponent H . It generalizes standard Brownian motion (i.e., H =1/2 ). We obtain the three probabilities using a perturbative expansion in ɛ =H -1/2 . While all three probabilities are different, this distinction can only be made at second order in ɛ . Our results are confirmed to high precision by extensive numerical simulations.

Influence of internal viscoelastic modes on the Brownian motion of a λ-DNA coated colloid.

PubMed

Yanagishima, Taiki; Laohakunakorn, Nadanai; Keyser, Ulrich F; Eiser, Erika; Tanaka, Hajime

2014-03-21

We study the influence of grafted polymers on the diffusive behaviour of a colloidal particle. Our work demonstrates how such additional degrees of freedom influence the Brownian motion of the particle, focusing on internal viscoelastic coupling between the polymer and colloid. Specifically, we study the mean-squared displacements (MSDs) of λ-DNA grafted colloids using Brownian dynamics simulation. Our simulations reveal the non-trivial effect of internal modes, which gives rise to a crossover from the short-time viscoelastic to long-time diffusional behaviour. We also show that basic features can be captured by a simple theoretical model considering the relative motion of a colloid to a part of the polymer corona. This model describes well a MSD calculated from an extremely long trajectory of a single λ-DNA coated colloid from experiment and allows characterisation of the λ-DNA hairs. Our study suggests that the access to the internal relaxation modes via the colloid trajectory offers a novel method for the characterisation of soft attachments to a colloid.

First passage times for a tracer particle in single file diffusion and fractional Brownian motion.

PubMed

Sanders, Lloyd P; Ambjörnsson, Tobias

2012-05-07

We investigate the full functional form of the first passage time density (FPTD) of a tracer particle in a single-file diffusion (SFD) system whose population is: (i) homogeneous, i.e., all particles having the same diffusion constant and (ii) heterogeneous, with diffusion constants drawn from a heavy-tailed power-law distribution. In parallel, the full FPTD for fractional Brownian motion [fBm-defined by the Hurst parameter, H ∈ (0, 1)] is studied, of interest here as fBm and SFD systems belong to the same universality class. Extensive stochastic (non-Markovian) SFD and fBm simulations are performed and compared to two analytical Markovian techniques: the method of images approximation (MIA) and the Willemski-Fixman approximation (WFA). We find that the MIA cannot approximate well any temporal scale of the SFD FPTD. Our exact inversion of the Willemski-Fixman integral equation captures the long-time power-law exponent, when H ≥ 1/3, as predicted by Molchan [Commun. Math. Phys. 205, 97 (1999)] for fBm. When H < 1/3, which includes homogeneous SFD (H = 1/4), and heterogeneous SFD (H < 1/4), the WFA fails to agree with any temporal scale of the simulations and Molchan's long-time result. SFD systems are compared to their fBm counter parts; and in the homogeneous system both scaled FPTDs agree on all temporal scales including also, the result by Molchan, thus affirming that SFD and fBm dynamics belong to the same universality class. In the heterogeneous case SFD and fBm results for heterogeneity-averaged FPTDs agree in the asymptotic time limit. The non-averaged heterogeneous SFD systems display a lack of self-averaging. An exponential with a power-law argument, multiplied by a power-law pre-factor is shown to describe well the FPTD for all times for homogeneous SFD and sub-diffusive fBm systems.

Myosin V is a biological Brownian machine

PubMed Central

Fujita, Keisuke; Iwaki, Mitsuhiro

2014-01-01

Myosin V is a vesicle transporter that unidirectionally walks along cytoskeletal actin filaments by converting the chemical energy of ATP into mechanical work. Recently, it was found that myosin V force generation is a composition of two processes: a lever-arm swing, which involves a conformational change in the myosin molecule, and a Brownian search-and-catch, which involves a diffusive “search” by the motor domain that is followed by an asymmetric “catch” in the forward actin target such that Brownian motion is rectified. Here we developed a system that combines optical tweezers with DNA nano-material to show that the Brownian search-and-catch mechanism is the energetically dominant process at near stall force, providing 13 kBT of work compared to just 3 kBT by the lever-arm swing. Our result significantly reconsiders the lever-arm swinging model, which assumes the swing dominantly produces work (>10 kBT), and sheds light on the Brownian search-and-catch as a driving process. PMID:27493501

Detection of Brownian Torque in a Magnetically-Driven Rotating Microsystem

PubMed Central

Romodina, Maria N.; Lyubin, Evgeny V.; Fedyanin, Andrey A.

2016-01-01

Thermal fluctuations significantly affect the behavior of microscale systems rotating in shear flow, such as microvortexes, microbubbles, rotating micromotors, microactuators and other elements of lab-on-a-chip devices. The influence of Brownian torque on the motion of individual magnetic microparticles in a rotating magnetic field is experimentally determined using optical tweezers. Rotational Brownian motion induces the flattening of the breakdown transition between the synchronous and asynchronous modes of microparticle rotation. The experimental findings regarding microparticle rotation in the presence of Brownian torque are compared with the results of numerical Brownian dynamics simulations. PMID:26876334

Brownian Carnot engine

PubMed Central

Dinis, L.; Petrov, D.; Parrondo, J. M. R.; Rica, R. A.

2016-01-01

The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths1. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors2 and some artificial micro-engines3–5 operate. As described by stochastic thermodynamics6,7, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit8. Here we report an experimental realization of a Carnot engine with a single optically trapped Brownian particle as the working substance. We present an exhaustive study of the energetics of the engine and analyse the fluctuations of the finite-time efficiency, showing that the Carnot bound can be surpassed for a small number of non-equilibrium cycles. As its macroscopic counterpart, the energetics of our Carnot device exhibits basic properties that one would expect to observe in any microscopic energy transducer operating with baths at different temperatures9–11. Our results characterize the sources of irreversibility in the engine and the statistical properties of the efficiency—an insight that could inspire new strategies in the design of efficient nano-motors. PMID:27330541

Stock price prediction using geometric Brownian motion

NASA Astrophysics Data System (ADS)

Farida Agustini, W.; Restu Affianti, Ika; Putri, Endah RM

2018-03-01

Geometric Brownian motion is a mathematical model for predicting the future price of stock. The phase that done before stock price prediction is determine stock expected price formulation and determine the confidence level of 95%. On stock price prediction using geometric Brownian Motion model, the algorithm starts from calculating the value of return, followed by estimating value of volatility and drift, obtain the stock price forecast, calculating the forecast MAPE, calculating the stock expected price and calculating the confidence level of 95%. Based on the research, the output analysis shows that geometric Brownian motion model is the prediction technique with high rate of accuracy. It is proven with forecast MAPE value ≤ 20%.

Small particle transport across turbulent nonisothermal boundary layers

NASA Technical Reports Server (NTRS)

Rosner, D. E.; Fernandez De La Mora, J.

1982-01-01

The interaction between turbulent diffusion, Brownian diffusion, and particle thermophoresis in the limit of vanishing particle inertial effects is quantitatively modeled for applications in gas turbines. The model is initiated with consideration of the particle phase mass conservation equation for a two-dimensional boundary layer, including the thermophoretic flux term directed toward the cold wall. A formalism of a turbulent flow near a flat plate in a heat transfer problem is adopted, and variable property effects are neglected. Attention is given to the limit of very large Schmidt numbers and the particle concentration depletion outside of the Brownian sublayer. It is concluded that, in the parameter range of interest, thermophoresis augments the high Schmidt number mass-transfer coefficient by a factor equal to the product of the outer sink and the thermophoretic suction.

Monte Carlo algorithms for Brownian phylogenetic models.

PubMed

Horvilleur, Benjamin; Lartillot, Nicolas

2014-11-01

Brownian models have been introduced in phylogenetics for describing variation in substitution rates through time, with applications to molecular dating or to the comparative analysis of variation in substitution patterns among lineages. Thus far, however, the Monte Carlo implementations of these models have relied on crude approximations, in which the Brownian process is sampled only at the internal nodes of the phylogeny or at the midpoints along each branch, and the unknown trajectory between these sampled points is summarized by simple branchwise average substitution rates. A more accurate Monte Carlo approach is introduced, explicitly sampling a fine-grained discretization of the trajectory of the (potentially multivariate) Brownian process along the phylogeny. Generic Monte Carlo resampling algorithms are proposed for updating the Brownian paths along and across branches. Specific computational strategies are developed for efficient integration of the finite-time substitution probabilities across branches induced by the Brownian trajectory. The mixing properties and the computational complexity of the resulting Markov chain Monte Carlo sampler scale reasonably with the discretization level, allowing practical applications with up to a few hundred discretization points along the entire depth of the tree. The method can be generalized to other Markovian stochastic processes, making it possible to implement a wide range of time-dependent substitution models with well-controlled computational precision. The program is freely available at www.phylobayes.org. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Single-particle tracking: applications to membrane dynamics.

PubMed

Saxton, M J; Jacobson, K

1997-01-01

Measurements of trajectories of individual proteins or lipids in the plasma membrane of cells show a variety of types of motion. Brownian motion is observed, but many of the particles undergo non-Brownian motion, including directed motion, confined motion, and anomalous diffusion. The variety of motion leads to significant effects on the kinetics of reactions among membrane-bound species and requires a revision of existing views of membrane structure and dynamics.

Regime of aggregate structures and magneto-rheological characteristics of a magnetic rod-like particle suspension: Monte Carlo and Brownian dynamics simulations

NASA Astrophysics Data System (ADS)

Okada, Kazuya; Satoh, Akira

2017-09-01

In the present study, we address a suspension composed ferromagnetic rod-like particles to elucidate a regime change in the aggregate structures and the magneto-rheological characteristics. Monte Carlo simulations have been employed for investigating the aggregate structures in thermodynamic equilibrium, and Brownian dynamics simulations for magneto-rheological features in a simple shear flow. The main results obtained here are summarized as follows. For the case of thermodynamic equilibrium, the rod-like particles aggregate to form thick chain-like clusters and the neighboring clusters incline in opposite directions. If the external magnetic field is increased, the thick chain-like clusters in the magnetic field direction grow thicker by adsorbing the neighboring clusters that incline in the opposite direction. Hence, a significant phase change in the particle aggregates is not induced by an increase in the magnetic field strength. For the case of a simple shear flow, even a weak shear flow induces a significant regime change from the thick chain-like clusters of thermodynamic equilibrium into wall-like aggregates composed of short raft-like clusters. A strong external magnetic field drastically changes these aggregates into wall-like aggregates composed of thick chain-like clusters rather than the short raft-like clusters. The internal structure of these aggregates is not strongly influenced by a shear flow, and the formation of the short raft-like clusters is maintained inside the aggregates. The main contribution to the net viscosity is the viscosity component due to magnetic particle-particle interaction forces in relation to the present volumetric fraction. Hence, a larger magnetic interaction strength and also a stronger external magnetic field give rise to a larger magneto-rheological effect. However, the dependence of the viscosity on these factors is governed in a complex manner by whether or not the wall-like aggregates are composed mainly of short raft

On Certain Functionals of the Maximum of Brownian Motion and Their Applications

NASA Astrophysics Data System (ADS)

Perret, Anthony; Comtet, Alain; Majumdar, Satya N.; Schehr, Grégory

2015-12-01

We consider a Brownian motion (BM) x(τ ) and its maximal value x_{max } = max _{0 ≤ τ ≤ t} x(τ ) on a fixed time interval [0, t]. We study functionals of the maximum of the BM, of the form {O}_{max }(t)=int _0^t V(x_{max } - x(τ )) {d}τ where V( x) can be any arbitrary function and develop various analytical tools to compute their statistical properties. These tools rely in particular on (i) a "counting paths" method and (ii) a path-integral approach. In particular, we focus on the case where V(x) = δ (x-r), with r a real parameter, which is relevant to study the density of near-extreme values of the BM (the so called density of states), ρ (r,t), which is the local time of the BM spent at given distance r from the maximum. We also provide a thorough analysis of the family of functionals {T}_{α }(t)=int _0^t (x_{max } - x(τ ))^α {{d}}τ corresponding to V(x) = x^α with α real. As α is varied, T_α (t) interpolates between different interesting observables. For instance, for α =1, T_{α = 1}(t) is a random variable of the "area", or "Airy", type while for α =-1/2 it corresponds to the maximum time spent by a ballistic particle through a Brownian random potential. On the other hand, for α = -1, it corresponds to the cost of the optimal algorithm to find the maximum of a discrete random walk, proposed by Odlyzko. We revisit here, using tools of theoretical physics, the statistical properties of this algorithm which had been studied before using probabilistic methods. Finally, we extend our methods to constrained BM, including in particular the Brownian bridge, i.e., the Brownian motion starting and ending at the origin.

Transport properties of elastically coupled fractional Brownian motors

NASA Astrophysics Data System (ADS)

Lv, Wangyong; Wang, Huiqi; Lin, Lifeng; Wang, Fei; Zhong, Suchuan

2015-11-01

Under the background of anomalous diffusion, which is characterized by the sub-linear or super-linear mean-square displacement in time, we proposed the coupled fractional Brownian motors, in which the asymmetrical periodic potential as ratchet is coupled mutually with elastic springs, and the driving source is the external harmonic force and internal thermal fluctuations. The transport mechanism of coupled particles in the overdamped limit is investigated as the function of the temperature of baths, coupling constant and natural length of the spring, the amplitude and frequency of driving force, and the asymmetry of ratchet potential by numerical stimulations. The results indicate that the damping force involving the information of historical velocity leads to the nonlocal memory property and blocks the traditional dissipative motion behaviors, and it even plays a cooperative role of driving force in drift motion of the coupled particles. Thus, we observe various non-monotonic resonance-like behaviors of collective directed transport in the mediums with different diffusion exponents.

Robustness of multidimensional Brownian ratchets as directed transport mechanisms.

PubMed

González-Candela, Ernesto; Romero-Rochín, Víctor; Del Río, Fernando

2011-08-07

Brownian ratchets have recently been considered as models to describe the ability of certain systems to locate very specific states in multidimensional configuration spaces. This directional process has particularly been proposed as an alternative explanation for the protein folding problem, in which the polypeptide is driven toward the native state by a multidimensional Brownian ratchet. Recognizing the relevance of robustness in biological systems, in this work we analyze such a property of Brownian ratchets by pushing to the limits all the properties considered essential to produce directed transport. Based on the results presented here, we can state that Brownian ratchets are able to deliver current and locate funnel structures under a wide range of conditions. As a result, they represent a simple model that solves the Levinthal's paradox with great robustness and flexibility and without requiring any ad hoc biased transition probability. The behavior of Brownian ratchets shown in this article considerably enhances the plausibility of the model for at least part of the structural mechanism behind protein folding process.

Brownian motion in inhomogeneous suspensions.

PubMed

Yang, Mingcheng; Ripoll, Marisol

2013-06-01

The Langevin description of Brownian motion in inhomogeneous suspensions is here revisited. Inhomogeneous suspensions are characterized by a position-dependent friction coefficient, which can significantly influence the dynamics of the suspended particles. Outstanding examples are suspensions in confinement or in the presence of a temperature gradient. The Langevin approach in inhomogeneous systems encounters a fundamental difficulty related to the interpretation of the multiplicative noise induced by the position-dependent friction. We show that the so-called Ito-Stratonovich dilemma is originated by the violation of the macroscopic force balance condition in the traditional procedure of eliminating the fast variables. Repairing this deficit, we rederive the extended overdamped Langevin equation directly from the infradamped Langevin equation. This is without invoking the Fokker-Planck formalism, such that the self-completeness of the Langevin framework is restored. Furthermore, we derive the generalized forms of the drift-force relation and the Smoluchowski equation for inhomogeneous suspensions in a straightforward manner.

Three-body correlations and conditional forces in suspensions of active hard disks

NASA Astrophysics Data System (ADS)

Härtel, Andreas; Richard, David; Speck, Thomas

2018-01-01

Self-propelled Brownian particles show rich out-of-equilibrium physics, for instance, the motility-induced phase separation (MIPS). While decades of studying the structure of liquids have established a deep understanding of passive systems, not much is known about correlations in active suspensions. In this work we derive an approximate analytic theory for three-body correlations and forces in systems of active Brownian disks starting from the many-body Smoluchowski equation. We use our theory to predict the conditional forces that act on a tagged particle and their dependence on the propulsion speed of self-propelled disks. We identify preferred directions of these forces in relation to the direction of propulsion and the positions of the surrounding particles. We further relate our theory to the effective swimming speed of the active disks, which is relevant for the physics of MIPS. To test and validate our theory, we additionally run particle-resolved computer simulations, for which we explicitly calculate the three-body forces. In this context, we discuss the modeling of active Brownian swimmers with nearly hard interaction potentials. We find very good agreement between our simulations and numerical solutions of our theory, especially for the nonequilibrium pair-distribution function. For our analytical results, we carefully discuss their range of validity in the context of the different levels of approximation we applied. This discussion allows us to study the individual contribution of particles to three-body forces and to the emerging structure. Thus, our work sheds light on the collective behavior, provides the basis for further studies of correlations in active suspensions, and makes a step towards an emerging liquid state theory.

Synergic co-activation of muscles in elbow flexion via fractional Brownian motion.

PubMed

Chang, Shyang; Hsyu, Ming-Chun; Cheng, Hsiu-Yao; Hsieh, Sheng-Hwu

2008-12-31

In reflex and volitional actions, co-activations of agonist and antagonist muscles are believed to be present. Recent studies indicate that such co-activations can be either synergic or dyssynergic. The aim of this paper is to investigate if the co-activations of biceps brachii, brachialis, and triceps brachii during volitional elbow flexion are in the synergic or dyssynergic state. In this study, two groups with each containing six healthy male volunteers participated. Each person of the first group performed 30 trials of volitional elbow flexion while each of the second group performed 30 trials of passive elbow flexion as control experiments. Based on the model of fractional Brownian motion, the intensity and frequency information of the surface electromyograms (EMGs) could be extracted simultaneously. No statistically significant changes were found in the control group. As to the other group, results indicated that the surface EMGs of all five muscle groups were temporally synchronized in frequencies with persistent intensities during each elbow flexion. In addition, the mean values of fractal dimensions for rest and volitional flexion states revealed significant differences with P < 0.01. The obtained positive results suggest that these muscle groups work together synergically to facilitate elbow flexion during the co-activations.

Theory of molecular crowding in Brownian hard-sphere liquids.

PubMed

Zaccone, Alessio; Terentjev, Eugene M

2012-06-01

We derive an analytical pair potential of mean force for Brownian molecules in the liquid state. Our approach accounts for many-particle correlations of crowding particles of the liquid and for diffusive transport across the spatially modulated local density of crowders in the dense environment. Focusing on the limit of equal-size particles, we show that this diffusive transport leads to additional density- and structure-dependent terms in the interaction potential and to a much stronger attraction (by a factor of ≈4 at average volume fraction of crowders φ{0}=0.25) than in the standard depletion interaction where the diffusive effects are neglected. As an illustration of the theory, we use it to study the size of a polymer chain in a solution of inert crowders. Even in the case of an athermal background solvent, when a classical chain should be fully swollen, we find a sharp coil-globule transition of the ideal chain collapsing at a critical value of the crowder volume fraction φ{c}≈0.145.

Brownian motion in non-equilibrium systems and the Ornstein-Uhlenbeck stochastic process.

PubMed

Donado, F; Moctezuma, R E; López-Flores, L; Medina-Noyola, M; Arauz-Lara, J L

2017-10-03

The Ornstein-Uhlenbeck stochastic process is an exact mathematical model providing accurate representations of many real dynamic processes in systems in a stationary state. When applied to the description of random motion of particles such as that of Brownian particles, it provides exact predictions coinciding with those of the Langevin equation but not restricted to systems in thermal equilibrium but only conditioned to be stationary. Here, we investigate experimentally single particle motion in a two-dimensional granular system in a stationary state, consisting of 1 mm stainless balls on a plane circular surface. The motion of the particles is produced by an alternating magnetic field applied perpendicular to the surface of the container. The mean square displacement of the particles is measured for a range of low concentrations and it is found that following an appropriate scaling of length and time, the short-time experimental curves conform a master curve covering the range of particle motion from ballistic to diffusive in accordance with the description of the Ornstein-Uhlenbeck model.

Fractional Brownian motion and long term clinical trial recruitment

PubMed Central

Zhang, Qiang; Lai, Dejian

2015-01-01

Prediction of recruitment in clinical trials has been a challenging task. Many methods have been studied, including models based on Poisson process and its large sample approximation by Brownian motion (BM), however, when the independent incremental structure is violated for BM model, we could use fractional Brownian motion to model and approximate the underlying Poisson processes with random rates. In this paper, fractional Brownian motion (FBM) is considered for such conditions and compared to BM model with illustrated examples from different trials and simulations. PMID:26347306

Fractional Brownian motion and long term clinical trial recruitment.

PubMed

Zhang, Qiang; Lai, Dejian

2011-05-01

Prediction of recruitment in clinical trials has been a challenging task. Many methods have been studied, including models based on Poisson process and its large sample approximation by Brownian motion (BM), however, when the independent incremental structure is violated for BM model, we could use fractional Brownian motion to model and approximate the underlying Poisson processes with random rates. In this paper, fractional Brownian motion (FBM) is considered for such conditions and compared to BM model with illustrated examples from different trials and simulations.

Electrostatic channeling in P. falciparum DHFR-TS: Brownian dynamics and Smoluchowski modeling.

PubMed

Metzger, Vincent T; Eun, Changsun; Kekenes-Huskey, Peter M; Huber, Gary; McCammon, J Andrew

2014-11-18

We perform Brownian dynamics simulations and Smoluchowski continuum modeling of the bifunctional Plasmodium falciparum dihydrofolate reductase-thymidylate synthase (P. falciparum DHFR-TS) with the objective of understanding the electrostatic channeling of dihydrofolate generated at the TS active site to the DHFR active site. The results of Brownian dynamics simulations and Smoluchowski continuum modeling suggest that compared to Leishmania major DHFR-TS, P. falciparum DHFR-TS has a lower but significant electrostatic-mediated channeling efficiency (?15-25%) at physiological pH (7.0) and ionic strength (150 mM). We also find that removing the electric charges from key basic residues located between the DHFR and TS active sites significantly reduces the channeling efficiency of P. falciparum DHFR-TS. Although several protozoan DHFR-TS enzymes are known to have similar tertiary and quaternary structure, subtle differences in structure, active-site geometry, and charge distribution appear to influence both electrostatic-mediated and proximity-based substrate channeling.

Amplified effect of Brownian motion in bacterial near-surface swimming

PubMed Central

Li, Guanglai; Tam, Lick-Kong; Tang, Jay X.

2008-01-01

Brownian motion influences bacterial swimming by randomizing displacement and direction. Here, we report that the influence of Brownian motion is amplified when it is coupled to hydrodynamic interaction. We examine swimming trajectories of the singly flagellated bacterium Caulobacter crescentus near a glass surface with total internal reflection fluorescence microscopy and observe large fluctuations over time in the distance of the cell from the solid surface caused by Brownian motion. The observation is compared with computer simulation based on analysis of relevant physical factors, including electrostatics, van der Waals force, hydrodynamics, and Brownian motion. The simulation reproduces the experimental findings and reveals contribution from fluctuations of the cell orientation beyond the resolution of present observation. Coupled with hydrodynamic interaction between the bacterium and the boundary surface, the fluctuations in distance and orientation subsequently lead to variation of the swimming speed and local radius of curvature of swimming trajectory. These results shed light on the fundamental roles of Brownian motion in microbial motility, nutrient uptake, and adhesion. PMID:19015518

Optimal Control of Stochastic Systems Driven by Fractional Brownian Motions

DTIC Science & Technology

2014-10-09

problems for stochastic partial differential equations driven by fractional Brownian motions are explicitly solved. For the control of a continuous time...linear systems with Brownian motion or a discrete time linear system with a white Gaussian noise and costs 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 stochastic optimal control, fractional Brownian motion , stochastic

[Brownian dynamics simulations of protein-protein interactions in photosynthetic electron transport chain].

PubMed

Khruschev, S S; Abaturova, A M; Diakonova, A N; Fedorov, V A; Ustinin, D M; Kovalenko, I B; Riznichenko, G Yu; Rubin, A B

2015-01-01

The application of Brownian dynamics for simulation of transient protein-protein interactions is reviewed. The review focuses on theoretical basics of Brownian dynamics method, its particular implementations, advantages and drawbacks of the method. The outlook for future development of Brownian dynamics-based simulation techniques is discussed. Special attention is given to analysis of Brownian dynamics trajectories. The second part of the review is dedicated to the role of Brownian dynamics simulations in studying photosynthetic electron transport. Interactions of mobile electron carriers (plastocyanin, cytochrome c6, and ferredoxin) with their reaction partners (cytochrome b6f complex, photosystem I, ferredoxin:NADP-reductase, and hydrogenase) are considered.

Efficient reactive Brownian dynamics

DOE PAGES

Donev, Aleksandar; Yang, Chiao-Yu; Kim, Changho

2018-01-21

We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and dissociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently processmore » reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as reaction-diffusion master equation algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction-limited and diffusion-limited irreversible association in three dimensions and compare to existing theoretical predictions at low and moderate densities. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium and compare to recent theoretical predictions. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. Our studies reinforce the common finding that microscopic mechanisms and correlations matter for diffusion-limited systems, making continuum and even mesoscopic modeling of such systems difficult or impossible. We also find that for models

Efficient reactive Brownian dynamics

NASA Astrophysics Data System (ADS)

Donev, Aleksandar; Yang, Chiao-Yu; Kim, Changho

2018-01-01

We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and dissociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently process reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as reaction-diffusion master equation algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction-limited and diffusion-limited irreversible association in three dimensions and compare to existing theoretical predictions at low and moderate densities. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium and compare to recent theoretical predictions. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. Our studies reinforce the common finding that microscopic mechanisms and correlations matter for diffusion-limited systems, making continuum and even mesoscopic modeling of such systems difficult or impossible. We also find that for models in which

Efficient reactive Brownian dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Donev, Aleksandar; Yang, Chiao-Yu; Kim, Changho

We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and dissociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently processmore » reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as reaction-diffusion master equation algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction-limited and diffusion-limited irreversible association in three dimensions and compare to existing theoretical predictions at low and moderate densities. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium and compare to recent theoretical predictions. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. Our studies reinforce the common finding that microscopic mechanisms and correlations matter for diffusion-limited systems, making continuum and even mesoscopic modeling of such systems difficult or impossible. We also find that for models

Biased Brownian dynamics for rate constant calculation.

PubMed

Zou, G; Skeel, R D; Subramaniam, S

2000-08-01

An enhanced sampling method-biased Brownian dynamics-is developed for the calculation of diffusion-limited biomolecular association reaction rates with high energy or entropy barriers. Biased Brownian dynamics introduces a biasing force in addition to the electrostatic force between the reactants, and it associates a probability weight with each trajectory. A simulation loses weight when movement is along the biasing force and gains weight when movement is against the biasing force. The sampling of trajectories is then biased, but the sampling is unbiased when the trajectory outcomes are multiplied by their weights. With a suitable choice of the biasing force, more reacted trajectories are sampled. As a consequence, the variance of the estimate is reduced. In our test case, biased Brownian dynamics gives a sevenfold improvement in central processing unit (CPU) time with the choice of a simple centripetal biasing force.

Langevin Theory of Anomalous Brownian Motion Made Simple

ERIC Educational Resources Information Center

Tothova, Jana; Vasziova, Gabriela; Glod, Lukas; Lisy, Vladimir

2011-01-01

During the century from the publication of the work by Einstein (1905 "Ann. Phys." 17 549) Brownian motion has become an important paradigm in many fields of modern science. An essential impulse for the development of Brownian motion theory was given by the work of Langevin (1908 "C. R. Acad. Sci.", Paris 146 530), in which he proposed an…

Entropic stochastic resonance of a self-propelled Janus particle

NASA Astrophysics Data System (ADS)

Liu, Zhenzhen; Du, Luchun; Guo, Wei; Mei, Dong-Cheng

2016-10-01

Entropic stochastic resonance is investigated when a self-propelled Janus particle moves in a double-cavity container. Numerical simulation results indicate the entropic stochastic resonance can survive even if there is no symmetry breaking in any direction. This is the essential distinction between the property of a self-propelled Janus particle and that of a passive Brownian particle, for the symmetry breaking is necessary for the entropic stochastic resonance of a passive Brownian particle. With the rotational noise intensity growing at small fixed noise intensity of translational motion, the signal power amplification increases monotonically towards saturation which also can be regarded as a kind of stochastic resonance effect. Besides, the increase in the natural frequency of the periodic driving depresses the degree of the stochastic resonance, whereas the rise in its amplitude enhances and then suppresses the behavior.

Analyzing animal movements using Brownian bridges.

PubMed

Horne, Jon S; Garton, Edward O; Krone, Stephen M; Lewis, Jesse S

2007-09-01

By studying animal movements, researchers can gain insight into many of the ecological characteristics and processes important for understanding population-level dynamics. We developed a Brownian bridge movement model (BBMM) for estimating the expected movement path of an animal, using discrete location data obtained at relatively short time intervals. The BBMM is based on the properties of a conditional random walk between successive pairs of locations, dependent on the time between locations, the distance between locations, and the Brownian motion variance that is related to the animal's mobility. We describe two critical developments that enable widespread use of the BBMM, including a derivation of the model when location data are measured with error and a maximum likelihood approach for estimating the Brownian motion variance. After the BBMM is fitted to location data, an estimate of the animal's probability of occurrence can be generated for an area during the time of observation. To illustrate potential applications, we provide three examples: estimating animal home ranges, estimating animal migration routes, and evaluating the influence of fine-scale resource selection on animal movement patterns.

Translocation by T7 RNA polymerase: a sensitively poised Brownian ratchet.

PubMed

Guo, Qing; Sousa, Rui

2006-04-21

Studies of halted T7 RNA polymerase (T7RNAP) elongation complexes (ECs) or of T7RNAP transcription against roadblocks due to DNA-bound proteins indicate that T7RNAP translocates via a passive Brownian ratchet mechanism. Crystal structures of T7RNAP ECs suggest that translocation involves an active power-stroke. However, neither solution studies of halted or slowed T7RNAP ECs, nor crystal structures of static complexes, are necessarily relevant to how T7RNAP translocates during rapid elongation. A recent single molecule study of actively elongating T7RNAPs provides support for the Brownian ratchet mechanism. Here, we obtain additional evidence for the existence of a Brownian ratchet during active T7RNAP elongation by showing that both rapidly elongating and halted complexes are equally sensitive to pyrophosphate. Using chemical nucleases tethered to the polymerase we achieve sub-ångström resolution in measuring the average position of halted T7RNAP ECs and find that the positional equilibrium of the EC is sensitively poised between pre-translocated and post-translocated states. This may be important in maximizing the sensitivity of the polymerase to sequences that cause pausing or termination. We also confirm that a crystallographically observed disorder to order transition in a loop formed by residues 589-612 also occurs in solution and is coupled to pyrophosphate or NTP release. This transition allows the loop to make interactions with the DNA that help stabilize the laterally mobile, ligand-free EC against dissociation.

A simple microviscometric approach based on Brownian motion tracking.

PubMed

Hnyluchová, Zuzana; Bjalončíková, Petra; Karas, Pavel; Mravec, Filip; Halasová, Tereza; Pekař, Miloslav; Kubala, Lukáš; Víteček, Jan

2015-02-01

Viscosity-an integral property of a liquid-is traditionally determined by mechanical instruments. The most pronounced disadvantage of such an approach is the requirement of a large sample volume, which poses a serious obstacle, particularly in biology and biophysics when working with limited samples. Scaling down the required volume by means of microviscometry based on tracking the Brownian motion of particles can provide a reasonable alternative. In this paper, we report a simple microviscometric approach which can be conducted with common laboratory equipment. The core of this approach consists in a freely available standalone script to process particle trajectory data based on a Newtonian model. In our study, this setup allowed the sample to be scaled down to 10 μl. The utility of the approach was demonstrated using model solutions of glycerine, hyaluronate, and mouse blood plasma. Therefore, this microviscometric approach based on a newly developed freely available script can be suggested for determination of the viscosity of small biological samples (e.g., body fluids).

How superdiffusion gets arrested: ecological encounters explain shift from Lévy to Brownian movement

PubMed Central

de Jager, Monique; Bartumeus, Frederic; Kölzsch, Andrea; Weissing, Franz J.; Hengeveld, Geerten M.; Nolet, Bart A.; Herman, Peter M. J.; van de Koppel, Johan

2014-01-01

Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when foraging in resource-poor environments. Yet, empirical studies reveal animals moving in a Brownian fashion when resources are abundant. We demonstrate that Einstein's original theory of collision-induced Brownian motion in physics provides a parsimonious, mechanistic explanation for these observations. Here, Brownian motion results from frequent encounters between organisms in dense environments. In density-controlled experiments, movement patterns of mussels shifted from Lévy towards Brownian motion with increasing density. When the analysis was restricted to moves not truncated by encounters, this shift did not occur. Using a theoretical argument, we explain that any movement pattern approximates Brownian motion at high-resource densities, provided that movement is interrupted upon encounters. Hence, the observed shift to Brownian motion does not indicate a density-dependent change in movement strategy but rather results from frequent collisions. Our results emphasize the need for a more mechanistic use of Brownian motion in ecology, highlighting that especially in rich environments, Brownian motion emerges from ecological interactions, rather than being a default movement pattern. PMID:24225464

How superdiffusion gets arrested: ecological encounters explain shift from Lévy to Brownian movement.

PubMed

de Jager, Monique; Bartumeus, Frederic; Kölzsch, Andrea; Weissing, Franz J; Hengeveld, Geerten M; Nolet, Bart A; Herman, Peter M J; van de Koppel, Johan

2014-01-07

Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when foraging in resource-poor environments. Yet, empirical studies reveal animals moving in a Brownian fashion when resources are abundant. We demonstrate that Einstein's original theory of collision-induced Brownian motion in physics provides a parsimonious, mechanistic explanation for these observations. Here, Brownian motion results from frequent encounters between organisms in dense environments. In density-controlled experiments, movement patterns of mussels shifted from Lévy towards Brownian motion with increasing density. When the analysis was restricted to moves not truncated by encounters, this shift did not occur. Using a theoretical argument, we explain that any movement pattern approximates Brownian motion at high-resource densities, provided that movement is interrupted upon encounters. Hence, the observed shift to Brownian motion does not indicate a density-dependent change in movement strategy but rather results from frequent collisions. Our results emphasize the need for a more mechanistic use of Brownian motion in ecology, highlighting that especially in rich environments, Brownian motion emerges from ecological interactions, rather than being a default movement pattern.

Coiled to diffuse: Brownian motion of a helical bacterium.

PubMed

Butenko, Alexander V; Mogilko, Emma; Amitai, Lee; Pokroy, Boaz; Sloutskin, Eli

2012-09-11

We employ real-time three-dimensional confocal microscopy to follow the Brownian motion of a fixed helically shaped Leptospira interrogans (LI) bacterium. We extract from our measurements the translational and the rotational diffusion coefficients of this bacterium. A simple theoretical model is suggested, perfectly reproducing the experimental diffusion coefficients, with no tunable parameters. An older theoretical model, where edge effects are neglected, dramatically underestimates the observed rates of translation. Interestingly, the coiling of LI increases its rotational diffusion coefficient by a factor of 5, compared to a (hypothetical) rectified bacterium of the same contour length. Moreover, the translational diffusion coefficients would have decreased by a factor of ~1.5, if LI were rectified. This suggests that the spiral shape of the spirochaete bacteria, in addition to being employed for their active twisting motion, may also increase the ability of these bacteria to explore the surrounding fluid by passive Brownian diffusion.

Computer simulation on the collision-sticking dynamics of two colloidal particles in an optical trap.

PubMed

Xu, Shenghua; Sun, Zhiwei

2007-04-14

Collisions of a particle pair induced by optical tweezers have been employed to study colloidal stability. In order to deepen insights regarding the collision-sticking dynamics of a particle pair in the optical trap that were observed in experimental approaches at the particle level, the authors carry out a Brownian dynamics simulation. In the simulation, various contributing factors, including the Derjaguin-Landau-Verwey-Overbeek interaction of particles, hydrodynamic interactions, optical trapping forces on the two particles, and the Brownian motion, were all taken into account. The simulation reproduces the tendencies of the accumulated sticking probability during the trapping duration for the trapped particle pair described in our previous study and provides an explanation for why the two entangled particles in the trap experience two different statuses.

Brownian Motion and the Temperament of Living Cells

NASA Astrophysics Data System (ADS)

Tsekov, Roumen; Lensen, Marga C.

2013-07-01

The migration of living cells usually obeys the laws of Brownian motion. While the latter is due to the thermal motion of the surrounding matter, the locomotion of cells is generally associated with their vitality. We study what drives cell migration and how to model memory effects in the Brownian motion of cells. The concept of temperament is introduced as an effective biophysical parameter driving the motion of living biological entities in analogy with the physical parameter of temperature, which dictates the movement of lifeless physical objects. The locomemory of cells is also studied via the generalized Langevin equation. We explore the possibility of describing cell locomemory via the Brownian self-similarity concept. An heuristic expression for the diffusion coefficient of cells on structured surfaces is derived.

NMR signals within the generalized Langevin model for fractional Brownian motion

NASA Astrophysics Data System (ADS)

Lisý, Vladimír; Tóthová, Jana

2018-03-01

The methods of Nuclear Magnetic Resonance belong to the best developed and often used tools for studying random motion of particles in different systems, including soft biological tissues. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard memoryless Langevin description of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spin-bearing particles in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in an exceedingly simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues. The effect of the trap is demonstrated by introducing a simple model for the generalized diffusion coefficient of the particle.

Survival of Near-Critical Branching Brownian Motion

NASA Astrophysics Data System (ADS)

Berestycki, Julien; Berestycki, Nathanaël; Schweinsberg, Jason

2011-06-01

Consider a system of particles performing branching Brownian motion with negative drift μ= sqrt{2 - \\varepsilon} and killed upon hitting zero. Initially there is one particle at x>0. Kesten (Stoch. Process. Appl. 7:9-47, 1978) showed that the process survives with positive probability if and only if ɛ>0. Here we are interested in the asymptotics as ɛ→0 of the survival probability Q μ ( x). It is proved that if L=π/sqrt{\\varepsilon} then for all x∈ℝ, lim ɛ→0 Q μ ( L+ x)= θ( x)∈(0,1) exists and is a traveling wave solution of the Fisher-KPP equation. Furthermore, we obtain sharp asymptotics of the survival probability when x< L and L- x→∞. The proofs rely on probabilistic methods developed by the authors in (Berestycki et al. in arXiv: 1001.2337, 2010). This completes earlier work by Harris, Harris and Kyprianou (Ann. Inst. Henri Poincaré Probab. Stat. 42:125-145, 2006) and confirms predictions made by Derrida and Simon (Europhys. Lett. 78:60006, 2007), which were obtained using nonrigorous PDE methods.

Heterodyne holographic microscopy of gold particles.

PubMed

Atlan, Michael; Gross, Michel; Desbiolles, Pierre; Absil, Emilie; Tessier, Gilles; Coppey-Moisan, Maïté

2008-03-01

We report experimental results on heterodyne holographic microscopy of subwavelength-size gold particles. The apparatus uses continuous green-laser illumination of the metal beads in a total internal reflection configuration for dark-field operation. Detection of the scattered light at the illumination wavelength on a charge-coupled-device array detector enables 3D localization of brownian particles in water.

Rheology of wormlike micellar fluids from Brownian and molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Padding, J. T.; Boek, E. S.; Briels, W. J.

2005-11-01

There is a great need for understanding the link between the detailed chemistry of surfactants, forming wormlike micelles, and their macroscopic rheological properties. In this paper we show how this link may be explored through particle simulations. First we review an existing bead-spring model. We find that shear flow enhances the formation of rings at the expense of linear chains. The shear viscosity of this model is dominated by solvent contributions, however, and the link with the chemistry of the surfactants is missing. We introduce a more realistic Brownian dynamics model, the parameters of which are measured from atomistic molecular dynamics simulations.

On the use of reverse Brownian motion to accelerate hybrid simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bakarji, Joseph; Tartakovsky, Daniel M., E-mail: tartakovsky@stanford.edu

Multiscale and multiphysics simulations are two rapidly developing fields of scientific computing. Efficient coupling of continuum (deterministic or stochastic) constitutive solvers with their discrete (stochastic, particle-based) counterparts is a common challenge in both kinds of simulations. We focus on interfacial, tightly coupled simulations of diffusion that combine continuum and particle-based solvers. The latter employs the reverse Brownian motion (rBm), a Monte Carlo approach that allows one to enforce inhomogeneous Dirichlet, Neumann, or Robin boundary conditions and is trivially parallelizable. We discuss numerical approaches for improving the accuracy of rBm in the presence of inhomogeneous Neumann boundary conditions and alternative strategiesmore » for coupling the rBm solver with its continuum counterpart. Numerical experiments are used to investigate the convergence, stability, and computational efficiency of the proposed hybrid algorithm.« less

Volume fraction instability in an oscillating non-Brownian iso-dense suspension.

NASA Astrophysics Data System (ADS)

Roht, Y. L.; Gauthier, G.; Hulin, J. P.; Salin, D.; Chertcoff, R.; Auradou, H.; Ippolito, I.

2017-06-01

The instability of an iso-dense non-Brownian suspension of polystyrene beads of diameter 40 μm dispersed in a water-glycerol mixture submitted to a periodic square wave oscillating flow in a Hele-Shaw cell is studied experimentally. The instability gives rise to stationary bead concentration waves transverse to the flow. It has been observed for average particle volume fractions between 0.25 and 0.4, for periods of the square wave flow variation between 0.4 and 10 s and in finite intervals of the amplitude of the fluid displacement. The study shows that the wavelength λ increases roughly linearly with the amplitude of the oscillatory flow; on the other hand, λ is independent of the particle concentration and of the period of oscillation of the flow although the minimum threshold amplitude for observing the instability increases with the period.

The topography of the environment alters the optimal search strategy for active particles

PubMed Central

Volpe, Giovanni

2017-01-01

In environments with scarce resources, adopting the right search strategy can make the difference between succeeding and failing, even between life and death. At different scales, this applies to molecular encounters in the cell cytoplasm, to animals looking for food or mates in natural landscapes, to rescuers during search and rescue operations in disaster zones, and to genetic computer algorithms exploring parameter spaces. When looking for sparse targets in a homogeneous environment, a combination of ballistic and diffusive steps is considered optimal; in particular, more ballistic Lévy flights with exponent α≤1 are generally believed to optimize the search process. However, most search spaces present complex topographies. What is the best search strategy in these more realistic scenarios? Here, we show that the topography of the environment significantly alters the optimal search strategy toward less ballistic and more Brownian strategies. We consider an active particle performing a blind cruise search for nonregenerating sparse targets in a 2D space with steps drawn from a Lévy distribution with the exponent varying from α=1 to α=2 (Brownian). We show that, when boundaries, barriers, and obstacles are present, the optimal search strategy depends on the topography of the environment, with α assuming intermediate values in the whole range under consideration. We interpret these findings using simple scaling arguments and discuss their robustness to varying searcher’s size. Our results are relevant for search problems at different length scales from animal and human foraging to microswimmers’ taxis to biochemical rates of reaction. PMID:29073055

The topography of the environment alters the optimal search strategy for active particles

NASA Astrophysics Data System (ADS)

Volpe, Giorgio; Volpe, Giovanni

2017-10-01

In environments with scarce resources, adopting the right search strategy can make the difference between succeeding and failing, even between life and death. At different scales, this applies to molecular encounters in the cell cytoplasm, to animals looking for food or mates in natural landscapes, to rescuers during search and rescue operations in disaster zones, and to genetic computer algorithms exploring parameter spaces. When looking for sparse targets in a homogeneous environment, a combination of ballistic and diffusive steps is considered optimal; in particular, more ballistic Lévy flights with exponent α≤1 are generally believed to optimize the search process. However, most search spaces present complex topographies. What is the best search strategy in these more realistic scenarios? Here, we show that the topography of the environment significantly alters the optimal search strategy toward less ballistic and more Brownian strategies. We consider an active particle performing a blind cruise search for nonregenerating sparse targets in a 2D space with steps drawn from a Lévy distribution with the exponent varying from α=1 to α=2 (Brownian). We show that, when boundaries, barriers, and obstacles are present, the optimal search strategy depends on the topography of the environment, with α assuming intermediate values in the whole range under consideration. We interpret these findings using simple scaling arguments and discuss their robustness to varying searcher's size. Our results are relevant for search problems at different length scales from animal and human foraging to microswimmers' taxis to biochemical rates of reaction.

Fast orthogonal transforms and generation of Brownian paths

PubMed Central

Leobacher, Gunther

2012-01-01

We present a number of fast constructions of discrete Brownian paths that can be used as alternatives to principal component analysis and Brownian bridge for stratified Monte Carlo and quasi-Monte Carlo. By fast we mean that a path of length n can be generated in O(nlog(n)) floating point operations. We highlight some of the connections between the different constructions and we provide some numerical examples. PMID:23471545

Noise and diffusion of a vibrated self-propelled granular particle

NASA Astrophysics Data System (ADS)

Walsh, Lee; Wagner, Caleb G.; Schlossberg, Sarah; Olson, Christopher; Baskaran, Aparna; Menon, Narayanan

Granular materials are an important physical realization of active matter. In vibration-fluidized granular matter, both diffusion and self-propulsion derive from the same collisional forcing, unlike many other active systems where there is a clean separation between the origin of single-particle mobility and the coupling to noise. Here we present experimental studies of single-particle motion in a vibrated granular monolayer, along with theoretical analysis that compares grain motion at short and long time scales to the assumptions and predictions, respectively, of the active Brownian particle (ABP) model. The results demonstrate that despite the unique relation between noise and propulsion, granular media do show the generic features predicted by the ABP model and indicate that this is a valid framework to predict collective phenomena. Additionally, our scheme of analysis for validating the inputs and outputs of the model can be applied to other granular and non-granular systems.

Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Han Yuecai; Hu Yaozhong; Song Jian, E-mail: jsong2@math.rutgers.edu

2013-04-15

We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter H>1/2). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential equation driven by both fractional Brownian motions and the corresponding underlying standard Brownian motions. In addition to this backward equation, the maximum principle also involves the Malliavin derivatives. Our approach is to use conditioning and Malliavin calculus. To arrive at our maximum principle we need tomore » develop some new results of stochastic analysis of the controlled systems driven by fractional Brownian motions via fractional calculus. Our approach of conditioning and Malliavin calculus is also applied to classical system driven by standard Brownian motions while the controller has only partial information. As a straightforward consequence, the classical maximum principle is also deduced in this more natural and simpler way.« less

A Computational Approach to Increase Time Scales in Brownian Dynamics–Based Reaction-Diffusion Modeling

PubMed Central

Frazier, Zachary

2012-01-01

Abstract Particle-based Brownian dynamics simulations offer the opportunity to not only simulate diffusion of particles but also the reactions between them. They therefore provide an opportunity to integrate varied biological data into spatially explicit models of biological processes, such as signal transduction or mitosis. However, particle based reaction-diffusion methods often are hampered by the relatively small time step needed for accurate description of the reaction-diffusion framework. Such small time steps often prevent simulation times that are relevant for biological processes. It is therefore of great importance to develop reaction-diffusion methods that tolerate larger time steps while maintaining relatively high accuracy. Here, we provide an algorithm, which detects potential particle collisions prior to a BD-based particle displacement and at the same time rigorously obeys the detailed balance rule of equilibrium reactions. We can show that for reaction-diffusion processes of particles mimicking proteins, the method can increase the typical BD time step by an order of magnitude while maintaining similar accuracy in the reaction diffusion modelling. PMID:22697237

Measurement of Average Aggregate Density by Sedimentation and Brownian Motion Analysis.

PubMed

Cavicchi, Richard E; King, Jason; Ripple, Dean C

2018-05-01

The spatially averaged density of protein aggregates is an important parameter that can be used to relate size distributions measured by orthogonal methods, to characterize protein particles, and perhaps to estimate the amount of protein in aggregate form in a sample. We obtained a series of images of protein aggregates exhibiting Brownian diffusion while settling under the influence of gravity in a sealed capillary. The aggregates were formed by stir-stressing a monoclonal antibody (NISTmAb). Image processing yielded particle tracks, which were then examined to determine settling velocity and hydrodynamic diameter down to 1 μm based on mean square displacement analysis. Measurements on polystyrene calibration microspheres ranging in size from 1 to 5 μm showed that the mean square displacement diameter had improved accuracy over the diameter derived from imaged particle area, suggesting a future method for correcting size distributions based on imaging. Stokes' law was used to estimate the density of each particle. It was found that the aggregates were highly porous with density decreasing from 1.080 to 1.028 g/cm 3 as the size increased from 1.37 to 4.9 μm. Published by Elsevier Inc.

Anomalous versus Slowed-Down Brownian Diffusion in the Ligand-Binding Equilibrium

PubMed Central

Soula, Hédi; Caré, Bertrand; Beslon, Guillaume; Berry, Hugues

2013-01-01

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes. PMID:24209851

Undergraduate Labs for Biological Physics: Brownian Motion and Optical Trapping

NASA Astrophysics Data System (ADS)

Chu, Kelvin; Laughney, A.; Williams, J.

2006-12-01

We describe a set of case-study driven labs for an upper-division biological physics course. These labs are motivated by case-studies and consist of inquiry-driven investigations of Brownian motion and optical-trapping experiments. Each lab incorporates two innovative educational techniques to drive the process and application aspects of scientific learning. Case studies are used to encourage students to think independently and apply the scientific method to a novel lab situation. Student input from this case study is then used to decide how to best do the measurement, guide the project and ultimately evaluate the success of the program. Where appropriate, visualization and simulation using VPython is used. Direct visualization of Brownian motion allows students to directly calculate Avogadro's number or the Boltzmann constant. Following case-study driven discussion, students use video microscopy to measure the motion of latex spheres in different viscosity fluids arrive at a good approximation of NA or kB. Optical trapping (laser tweezer) experiments allow students to investigate the consequences of 100-pN forces on small particles. The case study consists of a discussion of the Boltzmann distribution and equipartition theorem followed by a consideration of the shape of the potential. Students can then use video capture to measure the distribution of bead positions to determine the shape and depth of the trap. This work supported by NSF DUE-0536773.

On the Small Mass Limit of Quantum Brownian Motion with Inhomogeneous Damping and Diffusion

NASA Astrophysics Data System (ADS)

Lim, Soon Hoe; Wehr, Jan; Lampo, Aniello; García-March, Miguel Ángel; Lewenstein, Maciej

2018-01-01

We study the small mass limit (or: the Smoluchowski-Kramers limit) of a class of quantum Brownian motions with inhomogeneous damping and diffusion. For Ohmic bath spectral density with a Lorentz-Drude cutoff, we derive the Heisenberg-Langevin equations for the particle's observables using a quantum stochastic calculus approach. We set the mass of the particle to equal m = m0 ɛ , the reduced Planck constant to equal \\hbar = ɛ and the cutoff frequency to equal Λ = E_{Λ}/ɛ , where m_0 and E_{Λ} are positive constants, so that the particle's de Broglie wavelength and the largest energy scale of the bath are fixed as ɛ → 0. We study the limit as ɛ → 0 of the rescaled model and derive a limiting equation for the (slow) particle's position variable. We find that the limiting equation contains several drift correction terms, the quantum noise-induced drifts, including terms of purely quantum nature, with no classical counterparts.

Particle image diffusometry: Resolving diffusion coefficient field from microscopy movie data without particle tracking

NASA Astrophysics Data System (ADS)

Hanasaki, Itsuo; Ooi, Yuto

2018-06-01

We propose a technique to evaluate the field of diffusion coefficient for particle dispersion where the Brownian motion is heterogeneous in space and single particle tracking (SPT) analysis is hindered by high concentration of the particles and/or their small size. We realize this "particle image diffusometry" by the principle of the differential dynamic microscopy (DDM). We extend the DDM by introducing the automated objective decision of the scaling regime itself. Label-free evaluation of spatially non-uniform diffusion coefficients without SPT is useful in the diverse applications including crystal nucleation and glass transition where non-invasive observation is desired.

Temperature measurement of a dust particle in a RF plasma GEC reference cell

NASA Astrophysics Data System (ADS)

Kong, Jie; Qiao, Ke; Matthews, Lorin S.; Hyde, Truell W.

2016-10-01

The thermal motion of a dust particle levitated in a plasma chamber is similar to that described by Brownian motion in many ways. The primary difference between a dust particle in a plasma system and a free Brownian particle is that in addition to the random collisions between the dust particle and the neutral gas atoms, there are electric field fluctuations, dust charge fluctuations, and correlated motions from the unwanted continuous signals originating within the plasma system itself. This last contribution does not include random motion and is therefore separable from the random motion in a `normal' temperature measurement. In this paper, we discuss how to separate random and coherent motions of a dust particle confined in a glass box in a Gaseous Electronic Conference (GEC) radio-frequency (RF) reference cell employing experimentally determined dust particle fluctuation data analysed using the mean square displacement technique.

Nonequilibrium Brownian Motion beyond the Effective Temperature

PubMed Central

Gnoli, Andrea; Puglisi, Andrea; Sarracino, Alessandro; Vulpiani, Angelo

2014-01-01

The condition of thermal equilibrium simplifies the theoretical treatment of fluctuations as found in the celebrated Einstein’s relation between mobility and diffusivity for Brownian motion. Several recent theories relax the hypothesis of thermal equilibrium resulting in at least two main scenarios. With well separated timescales, as in aging glassy systems, equilibrium Fluctuation-Dissipation Theorem applies at each scale with its own “effective” temperature. With mixed timescales, as for example in active or granular fluids or in turbulence, temperature is no more well-defined, the dynamical nature of fluctuations fully emerges and a Generalized Fluctuation-Dissipation Theorem (GFDT) applies. Here, we study experimentally the mixed timescale regime by studying fluctuations and linear response in the Brownian motion of a rotating intruder immersed in a vibro-fluidized granular medium. Increasing the packing fraction, the system is moved from a dilute single-timescale regime toward a denser multiple-timescale stage. Einstein’s relation holds in the former and is violated in the latter. The violation cannot be explained in terms of effective temperatures, while the GFDT is able to impute it to the emergence of a strong coupling between the intruder and the surrounding fluid. Direct experimental measurements confirm the development of spatial correlations in the system when the density is increased. PMID:24714671

Nonequilibrium Brownian motion beyond the effective temperature.

PubMed

Gnoli, Andrea; Puglisi, Andrea; Sarracino, Alessandro; Vulpiani, Angelo

2014-01-01

The condition of thermal equilibrium simplifies the theoretical treatment of fluctuations as found in the celebrated Einstein's relation between mobility and diffusivity for Brownian motion. Several recent theories relax the hypothesis of thermal equilibrium resulting in at least two main scenarios. With well separated timescales, as in aging glassy systems, equilibrium Fluctuation-Dissipation Theorem applies at each scale with its own "effective" temperature. With mixed timescales, as for example in active or granular fluids or in turbulence, temperature is no more well-defined, the dynamical nature of fluctuations fully emerges and a Generalized Fluctuation-Dissipation Theorem (GFDT) applies. Here, we study experimentally the mixed timescale regime by studying fluctuations and linear response in the Brownian motion of a rotating intruder immersed in a vibro-fluidized granular medium. Increasing the packing fraction, the system is moved from a dilute single-timescale regime toward a denser multiple-timescale stage. Einstein's relation holds in the former and is violated in the latter. The violation cannot be explained in terms of effective temperatures, while the GFDT is able to impute it to the emergence of a strong coupling between the intruder and the surrounding fluid. Direct experimental measurements confirm the development of spatial correlations in the system when the density is increased.

Brownian Motion--a Laboratory Experiment.

ERIC Educational Resources Information Center

Kruglak, Haym

1988-01-01

Introduces an experiment involving the observation of Brownian motion for college students. Describes the apparatus, experimental procedures, data analysis and results, and error analysis. Lists experimental techniques used in the experiment. Provides a circuit diagram, typical data, and graphs. (YP)

Direct observation on the Brownian coagulation of PSL particles through optical microscope in the regime near critical coagulation concentration (CCC).

PubMed

Fukasawa, Tomonori; Adachi, Yasuhisa

2010-04-15

Microscopic monitoring of floc structure, floc size distribution and the rate of coagulation was carried out for Brownian coagulation of PSL particles. Experiments were designed for the condition of salt concentration that is slightly below critical coagulation concentration (CCC). The density of the solvent was controlled by using deuterium oxide (D(2)O) to avoid sedimentation. Results are summarized as follows: (i) Near CCC, floc restructuring from the beginning stage of coagulation was evidenced, i.e., the ratio of linear triplet is found to be remarkably reduced as compared with the result obtained for the case of rapid coagulation which was implemented under sufficiently high salt concentration. (ii) The increase of fractal dimension from 1.8 in the case of rapid coagulation to 2.2 was confirmed by the analysis of mass balance using size distribution of flocs. This increment resulted in the decrease of effective excluded volume of flocs. (iii) The rate of coagulation was constant until later stage. This result contrasts to the result of rapid coagulation [T. Fukasawa, Y. Adachi, J. Colloid Interface Sci. 304 (2006) 115]. 2010 Elsevier Inc. All rights reserved.

Anomalous versus slowed-down Brownian diffusion in the ligand-binding equilibrium.

PubMed

Soula, Hédi; Caré, Bertrand; Beslon, Guillaume; Berry, Hugues

2013-11-05

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Entropy production of active particles and for particles in active baths

NASA Astrophysics Data System (ADS)

Pietzonka, Patrick; Seifert, Udo

2018-01-01

Entropy production of an active particle in an external potential is identified through a thermodynamically consistent minimal lattice model that includes the chemical reaction providing the propulsion and ordinary translational noise. In the continuum limit, a unique expression follows, comprising a direct contribution from the active process and an indirect contribution from ordinary diffusive motion. From the corresponding Langevin equation, this physical entropy production cannot be inferred through the conventional, yet here ambiguous, comparison of forward and time-reversed trajectories. Generalizations to several interacting active particles and passive particles in a bath of active ones are presented explicitly, further ones are briefly indicated.

Tracer diffusion in active suspensions

NASA Astrophysics Data System (ADS)

Burkholder, Eric W.; Brady, John F.

2017-05-01

We study the diffusion of a Brownian probe particle of size R in a dilute dispersion of active Brownian particles of size a , characteristic swim speed U0, reorientation time τR, and mechanical energy ksTs=ζaU02τR/6 , where ζa is the Stokes drag coefficient of a swimmer. The probe has a thermal diffusivity DP=kBT /ζP , where kBT is the thermal energy of the solvent and ζP is the Stokes drag coefficient for the probe. When the swimmers are inactive, collisions between the probe and the swimmers sterically hinder the probe's diffusive motion. In competition with this steric hindrance is an enhancement driven by the activity of the swimmers. The strength of swimming relative to thermal diffusion is set by Pes=U0a /DP . The active contribution to the diffusivity scales as Pes2 for weak swimming and Pes for strong swimming, but the transition between these two regimes is nonmonotonic. When fluctuations in the probe motion decay on the time scale τR, the active diffusivity scales as ksTs/ζP : the probe moves as if it were immersed in a solvent with energy ksTs rather than kBT .

Cluster growth mechanisms in Lennard-Jones fluids: A comparison between molecular dynamics and Brownian dynamics simulations

NASA Astrophysics Data System (ADS)

Jung, Jiyun; Lee, Jumin; Kim, Jun Soo

2015-03-01

We present a simulation study on the mechanisms of a phase separation in dilute fluids of Lennard-Jones (LJ) particles as a model of self-interacting molecules. Molecular dynamics (MD) and Brownian dynamics (BD) simulations of the LJ fluids are employed to model the condensation of a liquid droplet in the vapor phase and the mesoscopic aggregation in the solution phase, respectively. With emphasis on the cluster growth at late times well beyond the nucleation stage, we find that the growth mechanisms can be qualitatively different: cluster diffusion and coalescence in the MD simulations and Ostwald ripening in the BD simulations. We also show that the rates of the cluster growth have distinct scaling behaviors during cluster growth. This work suggests that in the solution phase the random Brownian nature of the solute dynamics may lead to the Ostwald ripening that is qualitatively different from the cluster coalescence in the vapor phase.

Perturbative expansion for the maximum of fractional Brownian motion.

PubMed

Delorme, Mathieu; Wiese, Kay Jörg

2016-07-01

Brownian motion is the only random process which is Gaussian, scale invariant, and Markovian. Dropping the Markovian property, i.e., allowing for memory, one obtains a class of processes called fractional Brownian motion, indexed by the Hurst exponent H. For H=1/2, Brownian motion is recovered. We develop a perturbative approach to treat the nonlocality in time in an expansion in ɛ=H-1/2. This allows us to derive analytic results beyond scaling exponents for various observables related to extreme value statistics: the maximum m of the process and the time t_{max} at which this maximum is reached, as well as their joint distribution. We test our analytical predictions with extensive numerical simulations for different values of H. They show excellent agreement, even for H far from 1/2.

Brownian motion and its descendants according to Schrödinger

NASA Astrophysics Data System (ADS)

Garbaczewski, Piotr; Vigier, Jean-Pierre

1992-08-01

We revisit Schrödinger's original suggestion of the existence of a special class of random processes, which have their origin in the Einstein-Smoluchowski theory of Brownian motion. Our principal goal is to clarify the physical nature of links connecting the realistic Brownian motion with the abstract mathematical formalism of Nelson and Bernstein diffusions.

Brownian motion and gambling: from ratchets to paradoxical games

NASA Astrophysics Data System (ADS)

Parrondo, J. M. R.; Dinís, Luis

2004-02-01

Two losing gambling games, when alternated in a periodic or random fashion, can produce a winning game. This paradox has been inspired by certain physical systems capable of rectifying fluctuations: the so-called Brownian ratchets. In this paper we review this paradox, from Brownian ratchets to the most recent studies on collective games, providing some intuitive explanations of the unexpected phenomena that we will find along the way.

Hydrodynamics of suspensions of passive and active rigid particles: a rigid multiblob approach

DOE PAGES

Usabiaga, Florencio Balboa; Kallemov, Bakytzhan; Delmotte, Blaise; ...

2016-01-12

, leading to linear scaling with the number of particles. We optimize a number of parameters in the iterative solvers and apply our method to a variety of benchmark problems to carefully assess the accuracy of the rigid multiblob approach as a function of the resolution. We also model the dynamics of colloidal particles studied in recent experiments, such as passive boomerangs in a slit channel, as well as a pair of non-Brownian active nanorods sedimented against a wall.« less

Quantum dynamical framework for Brownian heat engines

NASA Astrophysics Data System (ADS)

Agarwal, G. S.; Chaturvedi, S.

2013-07-01

We present a self-contained formalism modeled after the Brownian motion of a quantum harmonic oscillator for describing the performance of microscopic Brownian heat engines such as Carnot, Stirling, and Otto engines. Our theory, besides reproducing the standard thermodynamics results in the steady state, enables us to study the role dissipation plays in determining the efficiency of Brownian heat engines under actual laboratory conditions. In particular, we analyze in detail the dynamics associated with decoupling a system in equilibrium with one bath and recoupling it to another bath and obtain exact analytical results, which are shown to have significant ramifications on the efficiencies of engines involving such a step. We also develop a simple yet powerful technique for computing corrections to the steady state results arising from finite operation time and use it to arrive at the thermodynamic complementarity relations for various operating conditions and also to compute the efficiencies of the three engines cited above at maximum power. Some of the methods and exactly solvable models presented here are interesting in their own right and could find useful applications in other contexts as well.

Experimental investigation of particle deposition mechanisms in the lung acinus using microfluidic models.

NASA Astrophysics Data System (ADS)

Fishler, Rami; Mulligan, Molly; Dubowski, Yael; Sznitman, Josue; Sznitman Lab-department of Biomedical Engineering Team; Dubowski Lab-faculty of Civil; Environmental Engineering Team

2014-11-01

In order to experimentally investigate particle deposition mechanisms in the deep alveolated regions of the lungs, we have developed a novel microfluidic device mimicking breathing acinar flow conditions directly at the physiological scale. The model features an anatomically-inspired acinar geometry with five dichotomously branching airway generations lined with periodically expanding and contracting alveoli. Deposition patterns of airborne polystyrene microspheres (spanning 0.1 μm to 2 μm in diameter) inside the airway tree network compare well with CFD simulations and reveal the roles of gravity and Brownian motion on particle deposition sites. Furthermore, measured trajectories of incense particles (0.1-1 μm) inside the breathing device show a critical role for Brownian diffusion in determining the fate of inhaled sub-micron particles by enabling particles to cross from the acinar ducts into alveolar cavities, especially during the short time lag between inhalation and exhalation phases.

Maximum of a Fractional Brownian Motion: Analytic Results from Perturbation Theory.

PubMed

Delorme, Mathieu; Wiese, Kay Jörg

2015-11-20

Fractional Brownian motion is a non-Markovian Gaussian process X_{t}, indexed by the Hurst exponent H. It generalizes standard Brownian motion (corresponding to H=1/2). We study the probability distribution of the maximum m of the process and the time t_{max} at which the maximum is reached. They are encoded in a path integral, which we evaluate perturbatively around a Brownian, setting H=1/2+ϵ. This allows us to derive analytic results beyond the scaling exponents. Extensive numerical simulations for different values of H test these analytical predictions and show excellent agreement, even for large ϵ.

A Brownian model for recurrent earthquakes

USGS Publications Warehouse

Matthews, M.V.; Ellsworth, W.L.; Reasenberg, P.A.

2002-01-01

We construct a probability model for rupture times on a recurrent earthquake source. Adding Brownian perturbations to steady tectonic loading produces a stochastic load-state process. Rupture is assumed to occur when this process reaches a critical-failure threshold. An earthquake relaxes the load state to a characteristic ground level and begins a new failure cycle. The load-state process is a Brownian relaxation oscillator. Intervals between events have a Brownian passage-time distribution that may serve as a temporal model for time-dependent, long-term seismic forecasting. This distribution has the following noteworthy properties: (1) the probability of immediate rerupture is zero; (2) the hazard rate increases steadily from zero at t = 0 to a finite maximum near the mean recurrence time and then decreases asymptotically to a quasi-stationary level, in which the conditional probability of an event becomes time independent; and (3) the quasi-stationary failure rate is greater than, equal to, or less than the mean failure rate because the coefficient of variation is less than, equal to, or greater than 1/???2 ??? 0.707. In addition, the model provides expressions for the hazard rate and probability of rupture on faults for which only a bound can be placed on the time of the last rupture. The Brownian relaxation oscillator provides a connection between observable event times and a formal state variable that reflects the macromechanics of stress and strain accumulation. Analysis of this process reveals that the quasi-stationary distance to failure has a gamma distribution, and residual life has a related exponential distribution. It also enables calculation of "interaction" effects due to external perturbations to the state, such as stress-transfer effects from earthquakes outside the target source. The influence of interaction effects on recurrence times is transient and strongly dependent on when in the loading cycle step pertubations occur. Transient effects may

Stripes instability of an oscillating non-Brownian iso-dense suspension of spheres

NASA Astrophysics Data System (ADS)

Roht, Y. L.; Ippolito, I.; Hulin, J. P.; Salin, D.; Gauthier, G.

2018-03-01

We analyze experimentally the behavior of a non-Brownian, iso-dense suspension of spheres submitted to periodic square wave oscillations of the flow in a Hele-Shaw cell of gap H. We do observe an instability of the initially homogeneous concentration in the form of concentration variation stripes transverse to the flow. The wavelength of these regular spatial structures scales roughly as the gap of the cell and is independent of the particle concentration and of the period of oscillation. This instability requires large enough particle volume fractions φ≥ 0.25 and a gap large enough compared to the sphere diameter (H/d ≥ 8) . Mapping the domain of the existence of this instability in the space of the control parameters shows that it occurs only in a limited range of amplitudes of the fluid displacement. The analysis of the concentration distribution across the gap supports a scenario of particle migration towards the wall followed by an instability due to a particle concentration gradient with a larger concentration at the walls. In order to account for the main features of this stripes instability, we use the theory of longitudinal instability due to normal stresses difference and recent observations of a dependence of the first normal stresses difference on the particle concentration.

Active colloidal propulsion over a crystalline surface

NASA Astrophysics Data System (ADS)

Choudhury, Udit; Straube, Arthur V.; Fischer, Peer; Gibbs, John G.; Höfling, Felix

2017-12-01

We study both experimentally and theoretically the dynamics of chemically self-propelled Janus colloids moving atop a two-dimensional crystalline surface. The surface is a hexagonally close-packed monolayer of colloidal particles of the same size as the mobile one. The dynamics of the self-propelled colloid reflects the competition between hindered diffusion due to the periodic surface and enhanced diffusion due to active motion. Which contribution dominates depends on the propulsion strength, which can be systematically tuned by changing the concentration of a chemical fuel. The mean-square displacements (MSDs) obtained from the experiment exhibit enhanced diffusion at long lag times. Our experimental data are consistent with a Langevin model for the effectively two-dimensional translational motion of an active Brownian particle in a periodic potential, combining the confining effects of gravity and the crystalline surface with the free rotational diffusion of the colloid. Approximate analytical predictions are made for the MSD describing the crossover from free Brownian motion at short times to active diffusion at long times. The results are in semi-quantitative agreement with numerical results of a refined Langevin model that treats translational and rotational degrees of freedom on the same footing.

Emergent Vortex Patterns in Systems of Self-Propelled, Chiral Particles

NASA Astrophysics Data System (ADS)

Huber, Lorenz; Denk, Jonas; Reithmann, Emanuel; Frey, Erwin

Self-organization of FtsZ polymers is vital for Z-ring assembly during bacterial cell division, and has been studied using reconstituted in vitro model systems. Employing Brownian dynamics simulations and a Boltzmann approach, we model FtsZ polymers as active particles moving along chiral circular paths. With both theoretical approaches we find self-organization into vortex structures and characterize different states in parameter states. Our work demonstrates that these patterns are robust and are generic for active chiral matter. Moreover, we show that the dynamics at the onset of pattern formation is described by a generalized complex Ginzburg-Landau equation.

Aging scaled Brownian motion

NASA Astrophysics Data System (ADS)

Safdari, Hadiseh; Chechkin, Aleksei V.; Jafari, Gholamreza R.; Metzler, Ralf

2015-04-01

Scaled Brownian motion (SBM) is widely used to model anomalous diffusion of passive tracers in complex and biological systems. It is a highly nonstationary process governed by the Langevin equation for Brownian motion, however, with a power-law time dependence of the noise strength. Here we study the aging properties of SBM for both unconfined and confined motion. Specifically, we derive the ensemble and time averaged mean squared displacements and analyze their behavior in the regimes of weak, intermediate, and strong aging. A very rich behavior is revealed for confined aging SBM depending on different aging times and whether the process is sub- or superdiffusive. We demonstrate that the information on the aging factorizes with respect to the lag time and exhibits a functional form that is identical to the aging behavior of scale-free continuous time random walk processes. While SBM exhibits a disparity between ensemble and time averaged observables and is thus weakly nonergodic, strong aging is shown to effect a convergence of the ensemble and time averaged mean squared displacement. Finally, we derive the density of first passage times in the semi-infinite domain that features a crossover defined by the aging time.

Aging scaled Brownian motion.

PubMed

Safdari, Hadiseh; Chechkin, Aleksei V; Jafari, Gholamreza R; Metzler, Ralf

2015-04-01

Scaled Brownian motion (SBM) is widely used to model anomalous diffusion of passive tracers in complex and biological systems. It is a highly nonstationary process governed by the Langevin equation for Brownian motion, however, with a power-law time dependence of the noise strength. Here we study the aging properties of SBM for both unconfined and confined motion. Specifically, we derive the ensemble and time averaged mean squared displacements and analyze their behavior in the regimes of weak, intermediate, and strong aging. A very rich behavior is revealed for confined aging SBM depending on different aging times and whether the process is sub- or superdiffusive. We demonstrate that the information on the aging factorizes with respect to the lag time and exhibits a functional form that is identical to the aging behavior of scale-free continuous time random walk processes. While SBM exhibits a disparity between ensemble and time averaged observables and is thus weakly nonergodic, strong aging is shown to effect a convergence of the ensemble and time averaged mean squared displacement. Finally, we derive the density of first passage times in the semi-infinite domain that features a crossover defined by the aging time.

Binary data corruption due to a Brownian agent

NASA Astrophysics Data System (ADS)

Newman, T. J.; Triampo, Wannapong

1999-05-01

We introduce a model of binary data corruption induced by a Brownian agent (active random walker) on a d-dimensional lattice. A continuum formulation allows the exact calculation of several quantities related to the density of corrupted bits ρ, for example, the mean of ρ and the density-density correlation function. Excellent agreement is found with the results from numerical simulations. We also calculate the probability distribution of ρ in d=1, which is found to be log normal, indicating that the system is governed by extreme fluctuations.

Evaluation of Proteins' Rotational Diffusion Coefficients from Simulations of Their Free Brownian Motion in Volume-Occupied Environments.

PubMed

Długosz, Maciej; Antosiewicz, Jan M

2014-01-14

We have investigated the rotational dynamics of hen egg white lysozyme in monodisperse aqueous solutions of concentrations up to 250 mg/mL, using a rigid-body Brownian dynamics method that accurately accounts for anisotropies of diffusing objects. We have examined the validity of the free diffusion concept in the analysis of computer simulations of volume-occupied molecular solutions. We have found that, when as the only intermolecular interaction, the excluded volume effect is considered, rotational diffusion of molecules adheres to the free diffusion model. Further, we present a method based on the exact (in the case of the free diffusion) analytic forms of autocorrelation functions of particular vectors rigidly attached to diffusing objects, which allows one to obtain from results of molecular simulations the three principal rotational diffusion coefficients characterizing rotational Brownian motion of an arbitrarily shaped rigid particle for an arbitrary concentration of crowders. We have applied this approach to trajectories resulting from Brownian dynamics simulations of hen egg white lysozyme solutions. We show that the apparent anisotropy of proteins' rotational motions increases with an increasing degree of crowding. Finally, we demonstrate that even if the hydrodynamic anisotropy of molecules is neglected and molecules are simulated using their average translational and rotational diffusion coefficients, excluded volume effects still lead to their anisotropic rotational dynamics.

Ratchet Effects in Active Matter Systems

NASA Astrophysics Data System (ADS)

Reichhardt, C. J. Olson; Reichhardt, C.

2017-03-01

Ratchet effects can arise for single or collectively interacting Brownian particles on an asymmetric substrate when a net dc transport is produced by an externally applied ac driving force or by periodically flashing the substrate. Recently, a new class of active ratchet systems that do not require the application of external driving has been realized through the use of active matter; they are self-propelled units that can be biological or nonbiological in nature. When active materials such as swimming bacteria interact with an asymmetric substrate, a net dc directed motion can arise even without external driving, opening a wealth of possibilities such as sorting, cargo transport, or micromachine construction. We review the current status of active matter ratchets for swimming bacteria, cells, active colloids, and swarming models, focusing on the role of particle-substrate interactions. We describe ratchet reversals produced by collective effects and the use of active ratchets to transport passive particles. We discuss future directions including deformable substrates or particles, the role of different swimming modes, varied particle-particle interactions, and nondissipative effects.

Brownian dynamics simulations on a hypersphere in 4-space

NASA Astrophysics Data System (ADS)

Nissfolk, Jarl; Ekholm, Tobias; Elvingson, Christer

2003-10-01

We describe an algorithm for performing Brownian dynamics simulations of particles diffusing on S3, a hypersphere in four dimensions. The system is chosen due to recent interest in doing computer simulations in a closed space where periodic boundary conditions can be avoided. We specifically address the question how to generate a random walk on the 3-sphere, starting from the solution of the corresponding diffusion equation, and we also discuss an efficient implementation based on controlled approximations. Since S3 is a closed manifold (space), the average square displacement during a random walk is no longer proportional to the elapsed time, as in R3. Instead, its time rate of change is continuously decreasing, and approaches zero as time becomes large. We show, however, that the effective diffusion coefficient can still be obtained from the time dependence of the square displacement.

Nanotip analysis for dielectrophoretic concentration of nanosized viral particles.

PubMed

Yeo, Woon-Hong; Lee, Hyun-Boo; Kim, Jong-Hoon; Lee, Kyong-Hoon; Chung, Jae-Hyun

2013-05-10

Rapid and sensitive detection of low-abundance viral particles is strongly demanded in health care, environmental control, military defense, and homeland security. Current detection methods, however, lack either assay speed or sensitivity, mainly due to the nanosized viral particles. In this paper, we compare a dendritic, multi-terminal nanotip ('dendritic nanotip') with a single terminal nanotip ('single nanotip') for dielectrophoretic (DEP) concentration of viral particles. The numerical computation studies the concentration efficiency of viral particles ranging from 25 to 100 nm in radius for both nanotips. With DEP and Brownian motion considered, when the particle radius decreases by two times, the concentration time for both nanotips increases by 4-5 times. In the computational study, a dendritic nanotip shows about 1.5 times faster concentration than a single nanotip for the viral particles because the dendritic structure increases the DEP-effective area to overcome the Brownian motion. For the qualitative support of the numerical results, the comparison experiment of a dendritic nanotip and a single nanotip is conducted. Under 1 min of concentration time, a dendritic nanotip shows a higher sensitivity than a single nanotip. When the concentration time is 5 min, the sensitivity of a dendritic nanotip for T7 phage is 10(4) particles ml(-1). The dendritic nanotip-based concentrator has the potential for rapid identification of viral particles.

Nanotip analysis for dielectrophoretic concentration of nanosized viral particles

NASA Astrophysics Data System (ADS)

Yeo, Woon-Hong; Lee, Hyun-Boo; Kim, Jong-Hoon; Lee, Kyong-Hoon; Chung, Jae-Hyun

2013-05-01

Rapid and sensitive detection of low-abundance viral particles is strongly demanded in health care, environmental control, military defense, and homeland security. Current detection methods, however, lack either assay speed or sensitivity, mainly due to the nanosized viral particles. In this paper, we compare a dendritic, multi-terminal nanotip (‘dendritic nanotip’) with a single terminal nanotip (‘single nanotip’) for dielectrophoretic (DEP) concentration of viral particles. The numerical computation studies the concentration efficiency of viral particles ranging from 25 to 100 nm in radius for both nanotips. With DEP and Brownian motion considered, when the particle radius decreases by two times, the concentration time for both nanotips increases by 4-5 times. In the computational study, a dendritic nanotip shows about 1.5 times faster concentration than a single nanotip for the viral particles because the dendritic structure increases the DEP-effective area to overcome the Brownian motion. For the qualitative support of the numerical results, the comparison experiment of a dendritic nanotip and a single nanotip is conducted. Under 1 min of concentration time, a dendritic nanotip shows a higher sensitivity than a single nanotip. When the concentration time is 5 min, the sensitivity of a dendritic nanotip for T7 phage is 104 particles ml-1. The dendritic nanotip-based concentrator has the potential for rapid identification of viral particles.

Coupling of Lever Arm Swing and Biased Brownian Motion in Actomyosin

PubMed Central

Nie, Qing-Miao; Togashi, Akio; Sasaki, Takeshi N.; Takano, Mitsunori; Sasai, Masaki; Terada, Tomoki P.

2014-01-01

An important unresolved problem associated with actomyosin motors is the role of Brownian motion in the process of force generation. On the basis of structural observations of myosins and actins, the widely held lever-arm hypothesis has been proposed, in which proteins are assumed to show sequential structural changes among observed and hypothesized structures to exert mechanical force. An alternative hypothesis, the Brownian motion hypothesis, has been supported by single-molecule experiments and emphasizes more on the roles of fluctuating protein movement. In this study, we address the long-standing controversy between the lever-arm hypothesis and the Brownian motion hypothesis through in silico observations of an actomyosin system. We study a system composed of myosin II and actin filament by calculating free-energy landscapes of actin-myosin interactions using the molecular dynamics method and by simulating transitions among dynamically changing free-energy landscapes using the Monte Carlo method. The results obtained by this combined multi-scale calculation show that myosin with inorganic phosphate (Pi) and ADP weakly binds to actin and that after releasing Pi and ADP, myosin moves along the actin filament toward the strong-binding site by exhibiting the biased Brownian motion, a behavior consistent with the observed single-molecular behavior of myosin. Conformational flexibility of loops at the actin-interface of myosin and the N-terminus of actin subunit is necessary for the distinct bias in the Brownian motion. Both the 5.5–11 nm displacement due to the biased Brownian motion and the 3–5 nm displacement due to lever-arm swing contribute to the net displacement of myosin. The calculated results further suggest that the recovery stroke of the lever arm plays an important role in enhancing the displacement of myosin through multiple cycles of ATP hydrolysis, suggesting a unified movement mechanism for various members of the myosin family. PMID:24762409

Coupling of lever arm swing and biased Brownian motion in actomyosin.

PubMed

Nie, Qing-Miao; Togashi, Akio; Sasaki, Takeshi N; Takano, Mitsunori; Sasai, Masaki; Terada, Tomoki P

2014-04-01

An important unresolved problem associated with actomyosin motors is the role of Brownian motion in the process of force generation. On the basis of structural observations of myosins and actins, the widely held lever-arm hypothesis has been proposed, in which proteins are assumed to show sequential structural changes among observed and hypothesized structures to exert mechanical force. An alternative hypothesis, the Brownian motion hypothesis, has been supported by single-molecule experiments and emphasizes more on the roles of fluctuating protein movement. In this study, we address the long-standing controversy between the lever-arm hypothesis and the Brownian motion hypothesis through in silico observations of an actomyosin system. We study a system composed of myosin II and actin filament by calculating free-energy landscapes of actin-myosin interactions using the molecular dynamics method and by simulating transitions among dynamically changing free-energy landscapes using the Monte Carlo method. The results obtained by this combined multi-scale calculation show that myosin with inorganic phosphate (Pi) and ADP weakly binds to actin and that after releasing Pi and ADP, myosin moves along the actin filament toward the strong-binding site by exhibiting the biased Brownian motion, a behavior consistent with the observed single-molecular behavior of myosin. Conformational flexibility of loops at the actin-interface of myosin and the N-terminus of actin subunit is necessary for the distinct bias in the Brownian motion. Both the 5.5-11 nm displacement due to the biased Brownian motion and the 3-5 nm displacement due to lever-arm swing contribute to the net displacement of myosin. The calculated results further suggest that the recovery stroke of the lever arm plays an important role in enhancing the displacement of myosin through multiple cycles of ATP hydrolysis, suggesting a unified movement mechanism for various members of the myosin family.

Tracer diffusion in active suspensions.

PubMed

Burkholder, Eric W; Brady, John F

2017-05-01

We study the diffusion of a Brownian probe particle of size R in a dilute dispersion of active Brownian particles of size a, characteristic swim speed U_{0}, reorientation time τ_{R}, and mechanical energy k_{s}T_{s}=ζ_{a}U_{0}^{2}τ_{R}/6, where ζ_{a} is the Stokes drag coefficient of a swimmer. The probe has a thermal diffusivity D_{P}=k_{B}T/ζ_{P}, where k_{B}T is the thermal energy of the solvent and ζ_{P} is the Stokes drag coefficient for the probe. When the swimmers are inactive, collisions between the probe and the swimmers sterically hinder the probe's diffusive motion. In competition with this steric hindrance is an enhancement driven by the activity of the swimmers. The strength of swimming relative to thermal diffusion is set by Pe_{s}=U_{0}a/D_{P}. The active contribution to the diffusivity scales as Pe_{s}^{2} for weak swimming and Pe_{s} for strong swimming, but the transition between these two regimes is nonmonotonic. When fluctuations in the probe motion decay on the time scale τ_{R}, the active diffusivity scales as k_{s}T_{s}/ζ_{P}: the probe moves as if it were immersed in a solvent with energy k_{s}T_{s} rather than k_{B}T.

Transport dynamics -- one particle at a time

NASA Astrophysics Data System (ADS)

Granick, Steve

2010-03-01

By watching particles and molecules diffuse, one-by-one, the full displacement probability distribution can be measured, enabling one to see experimentally how, how fast, and with what fidelity to classical assumptions, particles and molecules diffuse through complex environments. This allows us to measuring the confining tube potential through which thin actin filaments reptate, and also some of the amazing differences in diffusion rate between colloidal particles and phospholipid vesicles of the same size. Pervasively, we find that Brownian diffusion can be non-Gaussian.

Model-based image analysis of a tethered Brownian fibre for shear stress sensing

PubMed Central

2017-01-01

The measurement of fluid dynamic shear stress acting on a biologically relevant surface is a challenging problem, particularly in the complex environment of, for example, the vasculature. While an experimental method for the direct detection of wall shear stress via the imaging of a synthetic biology nanorod has recently been developed, the data interpretation so far has been limited to phenomenological random walk modelling, small-angle approximation, and image analysis techniques which do not take into account the production of an image from a three-dimensional subject. In this report, we develop a mathematical and statistical framework to estimate shear stress from rapid imaging sequences based firstly on stochastic modelling of the dynamics of a tethered Brownian fibre in shear flow, and secondly on a novel model-based image analysis, which reconstructs fibre positions by solving the inverse problem of image formation. This framework is tested on experimental data, providing the first mechanistically rational analysis of the novel assay. What follows further develops the established theory for an untethered particle in a semi-dilute suspension, which is of relevance to, for example, the study of Brownian nanowires without flow, and presents new ideas in the field of multi-disciplinary image analysis. PMID:29212755

Equivalence of Brownian dynamics and dynamic Monte Carlo simulations in multicomponent colloidal suspensions.

PubMed

Cuetos, Alejandro; Patti, Alessandro

2015-08-01

We propose a simple but powerful theoretical framework to quantitatively compare Brownian dynamics (BD) and dynamic Monte Carlo (DMC) simulations of multicomponent colloidal suspensions. By extending our previous study focusing on monodisperse systems of rodlike colloids, here we generalize the formalism described there to multicomponent colloidal mixtures and validate it by investigating the dynamics in isotropic and liquid crystalline phases containing spherical and rodlike particles. In order to investigate the dynamics of multicomponent colloidal systems by DMC simulations, it is key to determine the elementary time step of each species and establish a unique timescale. This is crucial to consistently study the dynamics of colloidal particles with different geometry. By analyzing the mean-square displacement, the orientation autocorrelation functions, and the self part of the van Hove correlation functions, we show that DMC simulation is a very convenient and reliable technique to describe the stochastic dynamics of any multicomponent colloidal system. Our theoretical formalism can be easily extended to any colloidal system containing size and/or shape polydisperse particles.

Ratchet Effects in Active Matter Systems

DOE PAGES

Reichhardt, Cynthia Jane; Reichhardt, Charles

2016-12-21

Ratchet effects can arise for single or collectively interacting Brownian particles on an asymmetric substrate when a net dc transport is produced by an externally applied ac driving force or by periodically flashing the substrate. Recently, a new class of active ratchet systems that do not require the application of external driving has been realized through the use of active matter; they are self-propelled units that can be biological or nonbiological in nature. When active materials such as swimming bacteria interact with an asymmetric substrate, a net dc directed motion can arise even without external driving, opening a wealth ofmore » possibilities such as sorting, cargo transport, or micromachine construction. We review the current status of active matter ratchets for swimming bacteria, cells, active colloids, and swarming models, focusing on the role of particle-substrate interactions. Here, we describe ratchet reversals produced by collective effects and the use of active ratchets to transport passive particles. We discuss future directions including deformable substrates or particles, the role of different swimming modes, varied particle–particle interactions, and nondissipative effects.« less

On modeling animal movements using Brownian motion with measurement error.

PubMed

Pozdnyakov, Vladimir; Meyer, Thomas; Wang, Yu-Bo; Yan, Jun

2014-02-01

Modeling animal movements with Brownian motion (or more generally by a Gaussian process) has a long tradition in ecological studies. The recent Brownian bridge movement model (BBMM), which incorporates measurement errors, has been quickly adopted by ecologists because of its simplicity and tractability. We discuss some nontrivial properties of the discrete-time stochastic process that results from observing a Brownian motion with added normal noise at discrete times. In particular, we demonstrate that the observed sequence of random variables is not Markov. Consequently the expected occupation time between two successively observed locations does not depend on just those two observations; the whole path must be taken into account. Nonetheless, the exact likelihood function of the observed time series remains tractable; it requires only sparse matrix computations. The likelihood-based estimation procedure is described in detail and compared to the BBMM estimation.

ReaDDy - A Software for Particle-Based Reaction-Diffusion Dynamics in Crowded Cellular Environments

PubMed Central

Schöneberg, Johannes; Noé, Frank

2013-01-01

We introduce the software package ReaDDy for simulation of detailed spatiotemporal mechanisms of dynamical processes in the cell, based on reaction-diffusion dynamics with particle resolution. In contrast to other particle-based reaction kinetics programs, ReaDDy supports particle interaction potentials. This permits effects such as space exclusion, molecular crowding and aggregation to be modeled. The biomolecules simulated can be represented as a sphere, or as a more complex geometry such as a domain structure or polymer chain. ReaDDy bridges the gap between small-scale but highly detailed molecular dynamics or Brownian dynamics simulations and large-scale but little-detailed reaction kinetics simulations. ReaDDy has a modular design that enables the exchange of the computing core by efficient platform-specific implementations or dynamical models that are different from Brownian dynamics. PMID:24040218

Finite-element approach to Brownian dynamics of polymers.

PubMed

Cyron, Christian J; Wall, Wolfgang A

2009-12-01

In the last decades simulation tools for Brownian dynamics of polymers have attracted more and more interest. Such simulation tools have been applied to a large variety of problems and accelerated the scientific progress significantly. However, the currently most frequently used explicit bead models exhibit severe limitations, especially with respect to time step size, the necessity of artificial constraints and the lack of a sound mathematical foundation. Here we present a framework for simulations of Brownian polymer dynamics based on the finite-element method. This approach allows simulating a wide range of physical phenomena at a highly attractive computational cost on the basis of a far-developed mathematical background.

Narrow Escape of Interacting Diffusing Particles

NASA Astrophysics Data System (ADS)

Agranov, Tal; Meerson, Baruch

2018-03-01

The narrow escape problem deals with the calculation of the mean escape time (MET) of a Brownian particle from a bounded domain through a small hole on the domain's boundary. Here we develop a formalism which allows us to evaluate the nonescape probability of a gas of diffusing particles that may interact with each other. In some cases the nonescape probability allows us to evaluate the MET of the first particle. The formalism is based on the fluctuating hydrodynamics and the recently developed macroscopic fluctuation theory. We also uncover an unexpected connection between the narrow escape of interacting particles and thermal runaway in chemical reactors.

Local shear stress and its correlation with local volume fraction in concentrated non-Brownian suspensions: Lattice Boltzmann simulation

NASA Astrophysics Data System (ADS)

Lee, Young Ki; Ahn, Kyung Hyun; Lee, Seung Jong

2014-12-01

The local shear stress of non-Brownian suspensions was investigated using the lattice Boltzmann method coupled with the smoothed profile method. Previous studies have only focused on the bulk rheology of complex fluids because the local rheology of complex fluids was not accessible due to technical limitations. In this study, the local shear stress of two-dimensional solid particle suspensions in Couette flow was investigated with the method of planes to correlate non-Newtonian fluid behavior with the structural evolution of concentrated particle suspensions. Shear thickening was successfully captured for highly concentrated suspensions at high particle Reynolds number, and both the local rheology and local structure of the suspensions were analyzed. It was also found that the linear correlation between the local particle stress and local particle volume fraction was dramatically reduced during shear thickening. These results clearly show how the change in local structure of suspensions influences the local and bulk rheology of the suspensions.

APM_GUI: analyzing particle movement on the cell membrane and determining confinement.

PubMed

Menchón, Silvia A; Martín, Mauricio G; Dotti, Carlos G

2012-02-20

Single-particle tracking is a powerful tool for tracking individual particles with high precision. It provides useful information that allows the study of diffusion properties as well as the dynamics of movement. Changes in particle movement behavior, such as transitions between Brownian motion and temporary confinement, can reveal interesting biophysical interactions. Although useful applications exist to determine the paths of individual particles, only a few software implementations are available to analyze these data, and these implementations are generally not user-friendly and do not have a graphical interface,. Here, we present APM_GUI (Analyzing Particle Movement), which is a MatLab-implemented application with a Graphical User Interface. This user-friendly application detects confined movement considering non-random confinement when a particle remains in a region longer than a Brownian diffusant would remain. In addition, APM_GUI exports the results, which allows users to analyze this information using software that they are familiar with. APM_GUI provides an open-source tool that quantifies diffusion coefficients and determines whether trajectories have non-random confinements. It also offers a simple and user-friendly tool that can be used by individuals without programming skills.

Amoeba-inspired nanoarchitectonic computing implemented using electrical Brownian ratchets.

PubMed

Aono, M; Kasai, S; Kim, S-J; Wakabayashi, M; Miwa, H; Naruse, M

2015-06-12

In this study, we extracted the essential spatiotemporal dynamics that allow an amoeboid organism to solve a computationally demanding problem and adapt to its environment, thereby proposing a nature-inspired nanoarchitectonic computing system, which we implemented using a network of nanowire devices called 'electrical Brownian ratchets (EBRs)'. By utilizing the fluctuations generated from thermal energy in nanowire devices, we used our system to solve the satisfiability problem, which is a highly complex combinatorial problem related to a wide variety of practical applications. We evaluated the dependency of the solution search speed on its exploration parameter, which characterizes the fluctuation intensity of EBRs, using a simulation model of our system called 'AmoebaSAT-Brownian'. We found that AmoebaSAT-Brownian enhanced the solution searching speed dramatically when we imposed some constraints on the fluctuations in its time series and it outperformed a well-known stochastic local search method. These results suggest a new computing paradigm, which may allow high-speed problem solving to be implemented by interacting nanoscale devices with low power consumption.

Influence of Brownian Motion on Blood Platelet Flow Behavior and Adhesive Dynamics near a Planar Wall

PubMed Central

Mody, Nipa A.; King, Michael R.

2008-01-01

We used the Platelet Adhesive Dynamics computational method to study the influence of Brownian motion of a platelet on its flow characteristics near a surface in the creeping flow regime. Two important characterizations were done in this regard: (1) quantification of the platelet’s ability to contact the surface by virtue of the Brownian forces and torques acting on it, and (2) determination of the relative importance of Brownian motion in promoting surface encounters in the presence of shear flow. We determined the Peclet number for a platelet undergoing Brownian motion in shear flow, which could be expressed as a simple linear function of height of the platelet centroid, H from the surface Pe (platelet) = γ. · (1.56H + 0.66) for H > 0.3 μm. Our results demonstrate that at timescales relevant to shear flow in blood, Brownian motion plays an insignificant role in influencing platelet motion or creating further opportunities for platelet-surface contact. The platelet Peclet number at shear rates > 100 s-1 is large enough (> 200) to neglect platelet Brownian motion in computational modeling of flow in arteries and arterioles for most practical purposes even at very close distances from the surface. We also conducted adhesive dynamics simulations to determine the effects of platelet Brownian motion on GPIbα-vWF-A1 single-bond dissociation dynamics. Brownian motion was found to have little effect on bond lifetime and caused minimal bond stressing as bond rupture forces were calculated to be less than 0.005 pN. We conclude from our results that for the case of platelet-shaped cells, Brownian motion is not expected to play an important role in influencing flow characteristics, platelet-surface contact frequency and dissociative binding phenomena under flow at physiological shear rates (> 50 s-1). PMID:17417890

Influence of Brownian motion on blood platelet flow behavior and adhesive dynamics near a planar wall.

PubMed

Mody, Nipa A; King, Michael R

2007-05-22

We used the platelet adhesive dynamics computational method to study the influence of Brownian motion of a platelet on its flow characteristics near a surface in the creeping flow regime. Two important characterizations were done in this regard: (1) quantification of the platelet's ability to contact the surface by virtue of the Brownian forces and torques acting on it, and (2) determination of the relative importance of Brownian motion in promoting surface encounters in the presence of shear flow. We determined the Peclet number for a platelet undergoing Brownian motion in shear flow, which could be expressed as a simple linear function of height of the platelet centroid, H from the surface Pe (platelet) = . (1.56H + 0.66) for H > 0.3 microm. Our results demonstrate that at timescales relevant to shear flow in blood Brownian motion plays an insignificant role in influencing platelet motion or creating further opportunities for platelet-surface contact. The platelet Peclet number at shear rates >100 s-1 is large enough (>200) to neglect platelet Brownian motion in computational modeling of flow in arteries and arterioles for most practical purposes even at very close distances from the surface. We also conducted adhesive dynamics simulations to determine the effects of platelet Brownian motion on GPIbalpha-vWF-A1 single-bond dissociation dynamics. Brownian motion was found to have little effect on bond lifetime and caused minimal bond stressing as bond rupture forces were calculated to be less than 0.005 pN. We conclude from our results that, for the case of platelet-shaped cells, Brownian motion is not expected to play an important role in influencing flow characteristics, platelet-surface contact frequency, and dissociative binding phenomena under flow at physiological shear rates (>50 s(-1)).

Physical insight into the thermodynamic uncertainty relation using Brownian motion in tilted periodic potentials

NASA Astrophysics Data System (ADS)

Hyeon, Changbong; Hwang, Wonseok

2017-07-01

Using Brownian motion in periodic potentials V (x ) tilted by a force f , we provide physical insight into the thermodynamic uncertainty relation, a recently conjectured principle for statistical errors and irreversible heat dissipation in nonequilibrium steady states. According to the relation, nonequilibrium output generated from dissipative processes necessarily incurs an energetic cost or heat dissipation q , and in order to limit the output fluctuation within a relative uncertainty ɛ , at least 2 kBT /ɛ2 of heat must be dissipated. Our model shows that this bound is attained not only at near-equilibrium [f ≪V'(x ) ] but also at far-from-equilibrium [f ≫V'(x ) ] , more generally when the dissipated heat is normally distributed. Furthermore, the energetic cost is maximized near the critical force when the barrier separating the potential wells is about to vanish and the fluctuation of Brownian particles is maximized. These findings indicate that the deviation of heat distribution from Gaussianity gives rise to the inequality of the uncertainty relation, further clarifying the meaning of the uncertainty relation. Our derivation of the uncertainty relation also recognizes a bound of nonequilibrium fluctuations that the variance of dissipated heat (σq2) increases with its mean (μq), and it cannot be smaller than 2 kBT μq .

Physical insight into the thermodynamic uncertainty relation using Brownian motion in tilted periodic potentials.

PubMed

Hyeon, Changbong; Hwang, Wonseok

2017-07-01

Using Brownian motion in periodic potentials V(x) tilted by a force f, we provide physical insight into the thermodynamic uncertainty relation, a recently conjectured principle for statistical errors and irreversible heat dissipation in nonequilibrium steady states. According to the relation, nonequilibrium output generated from dissipative processes necessarily incurs an energetic cost or heat dissipation q, and in order to limit the output fluctuation within a relative uncertainty ε, at least 2k_{B}T/ε^{2} of heat must be dissipated. Our model shows that this bound is attained not only at near-equilibrium [f≪V^{'}(x)] but also at far-from-equilibrium [f≫V^{'}(x)], more generally when the dissipated heat is normally distributed. Furthermore, the energetic cost is maximized near the critical force when the barrier separating the potential wells is about to vanish and the fluctuation of Brownian particles is maximized. These findings indicate that the deviation of heat distribution from Gaussianity gives rise to the inequality of the uncertainty relation, further clarifying the meaning of the uncertainty relation. Our derivation of the uncertainty relation also recognizes a bound of nonequilibrium fluctuations that the variance of dissipated heat (σ_{q}^{2}) increases with its mean (μ_{q}), and it cannot be smaller than 2k_{B}Tμ_{q}.

Fractional Langevin Equation Model for Characterization of Anomalous Brownian Motion from NMR Signals

NASA Astrophysics Data System (ADS)

Lisý, Vladimír; Tóthová, Jana

2018-02-01

Nuclear magnetic resonance is often used to study random motion of spins in different systems. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard Langevin theory of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spins in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in a simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues.

How does a scanning ribosomal particle move along the 5'-untranslated region of eukaryotic mRNA? Brownian Ratchet model.

PubMed

Spirin, Alexander S

2009-11-17

A model of the ATP-dependent unidirectional movement of the 43S ribosomal initiation complex (=40S ribosomal subunit + eIF1 + eIF1A + eIF2.GTP.Met-tRNA(i) + eIF3) during scanning of the 5'-untranslated region of eukaryotic mRNA is proposed. The model is based on the principles of molecular Brownian ratchet machines and explains several enigmatic data concerning the scanning complex. In this model, the one-dimensional diffusion of the ribosomal initiation complex along the mRNA chain is rectified into the net-unidirectional 5'-to-3' movement by the Feynman ratchet-and-pawl mechanism. The proposed mechanism is organized by the heterotrimeric protein eIF4F (=eIF4A + eIF4E + eIF4G), attached to the scanning ribosomal particle via eIF3, and the RNA-binding protein eIF4B that is postulated to play the role of the pawl. The energy for the useful work of the ratchet-and-pawl mechanism is supplied from ATP hydrolysis induced by the eIF4A subunit: ATP binding and its hydrolysis alternately change the affinities of eIF4A for eIF4B and for mRNA, resulting in the restriction of backward diffusional sliding of the 43S ribosomal complex along the mRNA chain, while stochastic movements ahead are allowed.

Dynamics and Emergent Structures in Active Fluids

NASA Astrophysics Data System (ADS)

Baskaran, Aparna

2014-03-01

In this talk, we consider an active fluid of colloidal sized particles, with the primary manifestation of activity being a self-replenishing velocity along one body axis of the particle. This is a minimal model for varied systems such as bacterial colonies, cytoskeletal filament motility assays vibrated granular particles and self propelled diffusophoretic colloids, depending on the nature of interaction among the particles. Using microscopic Brownian dynamics simulations, coarse-graining using the tools of non-equilibrium statistical mechanics and analysis of macroscopic hydrodynamic theories, we characterize emergent structures seen in these systems, which are determined by the symmetry of the interactions among the active units, such as propagating density waves, dense stationary bands, asters and phase separated isotropic clusters. We identify a universal mechanism, termed ``self-regulation,'' as the underlying physics that leads to these structures in diverse systems. Support from NSF through DMR-1149266 and DMR-0820492.

Density profiles of granular gases studied by molecular dynamics and Brownian bridges

NASA Astrophysics Data System (ADS)

Peñuñuri, F.; Montoya, J. A.; Carvente, O.

2018-02-01

Despite the inherent frictional forces and dissipative collisions, confined granular matter can be regarded as a system in a stationary state if we inject energy continuously. Under these conditions, both the density and the granular temperature are, in general, non-monotonic variables along the height of the container. In consequence, an analytical description of a granular system is hard to conceive. Here, by using molecular dynamics simulations, we measure the packing fraction profiles for a vertically vibrating three-dimensional granular system in several gaseous-like stationary states. We show that by using the Brownian bridge concept, the determined packing fraction profiles can be reproduced accurately and give a complete description of the distribution of the particles inside the simulation box.

Brownian movement and microscopic irreversibility

NASA Astrophysics Data System (ADS)

Gordon, L. G. M.

1981-02-01

An extension of the hypothetical experiment of Szilard, which involved the action of a one-molecule gas in an isolated isothermal system, is developed to illustrate how irreversibility may arise out of Brownian motion. As this development requires a consideration of nonmolecular components such as wheels and pistons, the thought-experiment is remodeled in molecular terms and appears to function as a perpetuum mobile.

Nonclassical point of view of the Brownian motion generation via fractional deterministic model

NASA Astrophysics Data System (ADS)

Gilardi-Velázquez, H. E.; Campos-Cantón, E.

In this paper, we present a dynamical system based on the Langevin equation without stochastic term and using fractional derivatives that exhibit properties of Brownian motion, i.e. a deterministic model to generate Brownian motion is proposed. The stochastic process is replaced by considering an additional degree of freedom in the second-order Langevin equation. Thus, it is transformed into a system of three first-order linear differential equations, additionally α-fractional derivative are considered which allow us to obtain better statistical properties. Switching surfaces are established as a part of fluctuating acceleration. The final system of three α-order linear differential equations does not contain a stochastic term, so the system generates motion in a deterministic way. Nevertheless, from the time series analysis, we found that the behavior of the system exhibits statistics properties of Brownian motion, such as, a linear growth in time of mean square displacement, a Gaussian distribution. Furthermore, we use the detrended fluctuation analysis to prove the Brownian character of this motion.

The rate of collisions due to Brownian or gravitational motion of small drops

NASA Technical Reports Server (NTRS)

Zhang, Xiaoguang; Davis, Robert H.

1991-01-01

Quantitative predictions of the collision rate of two spherical drops undergoing Brownian diffusion or gravitational sedimentation are presented. The diffusion equation for relative Brownian motion of two drops is derived, and the relative motion of pairs of drops in gravitational sedimentation is traced via a trajectory analysis in order to develop theoretical models to determine the collision efficiencies, both with and without interparticle forces applied between the drops. It is concluded that finite collision rates between nondeforming fluid drops are possible for Brownian diffusion or gravitational sedimentation in the absence of attractive forces, in stark contrast to the prediction that lubrication forces prevent rigid spheres from contacting each other unless an attractive force that becomes infinite as the separation approaches zero is applied. Collision rates are shown to increase as the viscosity of the drop-phase decreases. In general, hydrodynamic interactions reduce the collision rates more for gravitational collisions than for Brownian collisions.

Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension

NASA Astrophysics Data System (ADS)

Malakar, Kanaya; Jemseena, V.; Kundu, Anupam; Vijay Kumar, K.; Sabhapandit, Sanjib; Majumdar, Satya N.; Redner, S.; Dhar, Abhishek

2018-04-01

We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite domain, this probability distribution approaches a Gaussian form in the long-time limit, as in the case of a regular Brownian particle. At intermediate times, this distribution exhibits unexpected multi-modal forms. In a finite domain, the probability distribution reaches a steady-state form with peaks at the boundaries, in contrast to a Brownian particle. We also study the relaxation to the steady-state analytically. Finally we compute the survival probability of the RTP in a semi-infinite domain with an absorbing boundary condition at the origin. In the finite interval, we compute the exit probability and the associated exit times. We provide numerical verification of our analytical results.

Active Curved Polymers Form Vortex Patterns on Membranes.

PubMed

Denk, Jonas; Huber, Lorenz; Reithmann, Emanuel; Frey, Erwin

2016-04-29

Recent in vitro experiments with FtsZ polymers show self-organization into different dynamic patterns, including structures reminiscent of the bacterial Z ring. We model FtsZ polymers as active particles moving along chiral, circular paths by Brownian dynamics simulations and a Boltzmann approach. Our two conceptually different methods point to a generic phase behavior. At intermediate particle densities, we find self-organization into vortex structures including closed rings. Moreover, we show that the dynamics at the onset of pattern formation is described by a generalized complex Ginzburg-Landau equation.

Molecular dynamics test of the Brownian description of Na(+) motion in water

NASA Technical Reports Server (NTRS)

Wilson, M. A.; Pohorille, A.; Pratt, L. R.

1985-01-01

The present paper provides the results of molecular dynamics calculations on a Na(+) ion in aqueous solution. Attention is given to the sodium-oxygen and sodium-hydrogen radial distribution functions, the velocity autocorrelation function for the Na(+) ion, the autocorrelation function of the force on the stationary ion, and the accuracy of Brownian motion assumptions which are basic to hydrodynamic models of ion dyanmics in solution. It is pointed out that the presented calculations provide accurate data for testing theories of ion dynamics in solution. The conducted tests show that it is feasible to calculate Brownian friction constants for ions in aqueous solutions. It is found that for Na(+) under the considered conditions the Brownian mobility is in error by only 60 percent.

Electrophoretic interactions and aggregation of colloidal biological particles

NASA Technical Reports Server (NTRS)

Davis, Robert H.; Nichols, Scott C.; Loewenberg, Michael; Todd, Paul

1994-01-01

The separation of cells or particles from solution has traditionally been accomplished with centrifuges or by sedimentation; however, many particles have specific densities close to unity, making buoyancy-driven motion slow or negligible, but most cells and particles carry surface charges, making them ideal for electrophoretic separation. Both buoyancy-driven and electrophoretic separation may be influenced by hydrodynamic interactions and aggregation of neighboring particles. Aggregation by electrophoresis was analyzed for two non-Brownian particles with different zeta potentials and thin double layers migrating through a viscous fluid. The results indicate that the initial rate of electrophoretically-driven aggregation may exceed that of buoyancy-driven aggregation, even under conditions in which buoyancy-driven relative motion of noninteracting particles is dominant.

Asymmetric Brownian motor driven by bubble formation in a hydrophobic channel.

PubMed

Arai, Noriyoshi; Yasuoka, Kenji; Koishi, Takahiro; Ebisuzaki, Toshikazu

2010-10-26

The "asymmetric brownian ratchet model" is a variation of Feynman's ratchet and pawl system proposed. In this model, a system consisting of a motor and a rail has two binding states. One is the random brownian state, and the other is the asymmetric potential state. When the system is alternatively switched between these states, the motor can be driven in one direction. This model is believed to explain nanomotor behavior in biological systems. The feasibility of the model has been demonstrated using electrical and magnetic forces; however, switching of these forces is unlikely to be found in biological systems. In this paper, we propose an original mechanism of transition between states by bubble formation in a nanosized channel surrounded by hydrophobic atoms. This amounts to a nanoscale motor system using bubble propulsion. The motor system consists of a hydrophobic motor and a rail on which hydrophobic patterns are printed. Potential asymmetry can be produced by using a left-right asymmetric pattern shape. Hydrophobic interactions are believed to play an important role in the binding of biomolecules and molecular recognition. The bubble formation is controlled by changing the width of the channel by an atomic distance (∼0.1 nm). Therefore, the motor is potentially more efficient than systems controlled by other forces, in which a much larger change in the motor position is necessary. We have simulated the bubble-powered motor using dissipative particle dynamics and found behavior in good agreement with that of motor proteins. Energy efficiency is as high as 60%.

Brownian excursions on combs

NASA Astrophysics Data System (ADS)

Dean, David S.; Jansons, Kalvis M.

1993-03-01

In this paper we use techniques from Ito excursion theory to analyze Brownian motion on generalized combs. Ito excursion theory is a little-known area of probability theory and we therefore present a brief introduction for the uninitiated. A general method for analyzing transport along the backbone of the comb is demonstrated and the specific case of a comb whose teeth are scaling branching trees is examined. We then present a recursive method for evaluating the distribution of the first passage times on hierarchical combs.

Brownian motion of solitons in a Bose-Einstein condensate.

PubMed

Aycock, Lauren M; Hurst, Hilary M; Efimkin, Dmitry K; Genkina, Dina; Lu, Hsin-I; Galitski, Victor M; Spielman, I B

2017-03-07

We observed and controlled the Brownian motion of solitons. We launched solitonic excitations in highly elongated [Formula: see text] Bose-Einstein condensates (BECs) and showed that a dilute background of impurity atoms in a different internal state dramatically affects the soliton. With no impurities and in one dimension (1D), these solitons would have an infinite lifetime, a consequence of integrability. In our experiment, the added impurities scatter off the much larger soliton, contributing to its Brownian motion and decreasing its lifetime. We describe the soliton's diffusive behavior using a quasi-1D scattering theory of impurity atoms interacting with a soliton, giving diffusion coefficients consistent with experiment.

Brownian motion of solitons in a Bose–Einstein condensate

PubMed Central

Aycock, Lauren M.; Hurst, Hilary M.; Efimkin, Dmitry K.; Genkina, Dina; Lu, Hsin-I; Galitski, Victor M.; Spielman, I. B.

2017-01-01

We observed and controlled the Brownian motion of solitons. We launched solitonic excitations in highly elongated Rb87 Bose–Einstein condensates (BECs) and showed that a dilute background of impurity atoms in a different internal state dramatically affects the soliton. With no impurities and in one dimension (1D), these solitons would have an infinite lifetime, a consequence of integrability. In our experiment, the added impurities scatter off the much larger soliton, contributing to its Brownian motion and decreasing its lifetime. We describe the soliton’s diffusive behavior using a quasi-1D scattering theory of impurity atoms interacting with a soliton, giving diffusion coefficients consistent with experiment. PMID:28196896

Flow induced crystallisation of penetrable particles

NASA Astrophysics Data System (ADS)

Scacchi, Alberto; Brader, Joseph M.

2018-03-01

For a system of Brownian particles interacting via a soft exponential potential we investigate the interaction between equilibrium crystallisation and spatially varying shear flow. For thermodynamic state points within the liquid part of the phase diagram, but close to the crystallisation phase boundary, we observe that imposing a Poiseuille flow can induce nonequilibrium crystalline ordering in regions of low shear gradient. The physical mechanism responsible for this phenomenon is shear-induced particle migration, which causes particles to drift preferentially towards the center of the flow channel, thus increasing the local density in the channel center. The method employed is classical dynamical density functional theory.

Flow induced crystallisation of penetrable particles.

PubMed

Scacchi, Alberto; Brader, Joseph M

2018-03-07

For a system of Brownian particles interacting via a soft exponential potential we investigate the interaction between equilibrium crystallisation and spatially varying shear flow. For thermodynamic state points within the liquid part of the phase diagram, but close to the crystallisation phase boundary, we observe that imposing a Poiseuille flow can induce nonequilibrium crystalline ordering in regions of low shear gradient. The physical mechanism responsible for this phenomenon is shear-induced particle migration, which causes particles to drift preferentially towards the center of the flow channel, thus increasing the local density in the channel center. The method employed is classical dynamical density functional theory.

Dynamics of a suspension of interacting yolk-shell particles

DOE PAGES

Sánchez Díaz, L. E.; Cortes-Morales, E. C.; Li, X.; ...

2014-12-01

In this work we study the self-diusion properties of a liquid of hollow spherical particles (shells) bearing a smaller solid sphere in their interior (yolks). We model this system using purely repulsive hard-body interactions between all (shell and yolk) particles, but assume the presence of a background ideal solvent such that all the particles execute free Brownian motion between collisions, characterized by short-time self-diusion coecients D0 s for the shells and D0 y for the yolks. Using a softened version of these interparticle potentials we perform Brownian dynamics simulations to determine the mean squared displacement and intermediate scattering function ofmore » the yolk-shell complex. These results can be understood in terms of a set of eective Langevin equations for the N interacting shell particles, pre-averaged over the yolks' degrees of freedom, from which an approximate self-consistent description of the simulated self-diusion properties can be derived. Here we compare the theoretical and simulated results between them, and with the results for the same system in the absence of yolks. We nd that the yolks, which have no eect on the shell-shell static structure, in uence the dynamic properties in a predictable manner, fully captured by the theory.« less

Brownian dynamics of sterically-stabilized colloidal suspensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

TeGrotenhuis, W.E.; Radke, C.J.; Denn, M.M.

1994-02-01

One application where microstructure plays a critical role is in the production of specialty ceramics, where colloidal suspensions act as precursors; here the microstructure influences the structural, thermal, optical and electrical properties of the ceramic products. Using Brownian dynamics, equilibrium and dynamic properties are calculated for colloidal suspensions that are stabilized through the Milner, Witten and Cates (1988) steric potential. Results are reported for osmotic pressures, radial distributions functions, static structure factors, and self-diffusion coefficients. The sterically-stabilized systems are also approximated by equivalent hard spheres, with good agreement for osmotic pressure and long-range structure. The suitability of the potential tomore » model the behavior of a real system is explored by comparing static structure factors calculated from Brownian dynamics simulations to those measured using SANS. Finally, the effects of Hamaker and hydrodynamic forces on calculated properties are investigated.« less

Generalized Scaling and the Master Variable for Brownian Magnetic Nanoparticle Dynamics

PubMed Central

Reeves, Daniel B.; Shi, Yipeng; Weaver, John B.

2016-01-01

Understanding the dynamics of magnetic particles can help to advance several biomedical nanotechnologies. Previously, scaling relationships have been used in magnetic spectroscopy of nanoparticle Brownian motion (MSB) to measure biologically relevant properties (e.g., temperature, viscosity, bound state) surrounding nanoparticles in vivo. Those scaling relationships can be generalized with the introduction of a master variable found from non-dimensionalizing the dynamical Langevin equation. The variable encapsulates the dynamical variables of the surroundings and additionally includes the particles’ size distribution and moment and the applied field’s amplitude and frequency. From an applied perspective, the master variable allows tuning to an optimal MSB biosensing sensitivity range by manipulating both frequency and field amplitude. Calculation of magnetization harmonics in an oscillating applied field is also possible with an approximate closed-form solution in terms of the master variable and a single free parameter. PMID:26959493

Cell and Particle Interactions and Aggregation During Electrophoretic Motion

NASA Technical Reports Server (NTRS)

Wang, Hua; Zeng, Shulin; Loewenberg, Michael; Todd, Paul; Davis, Robert H.

1996-01-01

The stability and pairwise aggregation rates of small spherical particles under the collective effects of buoyancy-driven motion and electrophoretic migration are analyzed. The particles are assumed to be non-Brownian, with thin double-layers and different zeta potentials. The particle aggregation rates may be enhanced or reduced, respectively, by parallel and antiparallel alignments of the buoyancy-driven and electrophoretic velocities. For antiparallel alignments, with the buoyancy-driven relative velocity exceeding the electrophoretic relative velocity between two widely-separated particles, there is a 'collision-forbidden region' in parameter space due to hydrodynamic interactions; thus, the suspension becomes stable against aggregation.

Phase separation and large deviations of lattice active matter

NASA Astrophysics Data System (ADS)

Whitelam, Stephen; Klymko, Katherine; Mandal, Dibyendu

2018-04-01

Off-lattice active Brownian particles form clusters and undergo phase separation even in the absence of attractions or velocity-alignment mechanisms. Arguments that explain this phenomenon appeal only to the ability of particles to move persistently in a direction that fluctuates, but existing lattice models of hard particles that account for this behavior do not exhibit phase separation. Here we present a lattice model of active matter that exhibits motility-induced phase separation in the absence of velocity alignment. Using direct and rare-event sampling of dynamical trajectories, we show that clustering and phase separation are accompanied by pronounced fluctuations of static and dynamic order parameters. This model provides a complement to off-lattice models for the study of motility-induced phase separation.

Numerical Solution of Dyson Brownian Motion and a Sampling Scheme for Invariant Matrix Ensembles

NASA Astrophysics Data System (ADS)

Li, Xingjie Helen; Menon, Govind

2013-12-01

The Dyson Brownian Motion (DBM) describes the stochastic evolution of N points on the line driven by an applied potential, a Coulombic repulsion and identical, independent Brownian forcing at each point. We use an explicit tamed Euler scheme to numerically solve the Dyson Brownian motion and sample the equilibrium measure for non-quadratic potentials. The Coulomb repulsion is too singular for the SDE to satisfy the hypotheses of rigorous convergence proofs for tamed Euler schemes (Hutzenthaler et al. in Ann. Appl. Probab. 22(4):1611-1641, 2012). Nevertheless, in practice the scheme is observed to be stable for time steps of O(1/ N 2) and to relax exponentially fast to the equilibrium measure with a rate constant of O(1) independent of N. Further, this convergence rate appears to improve with N in accordance with O(1/ N) relaxation of local statistics of the Dyson Brownian motion. This allows us to use the Dyson Brownian motion to sample N× N Hermitian matrices from the invariant ensembles. The computational cost of generating M independent samples is O( MN 4) with a naive scheme, and O( MN 3log N) when a fast multipole method is used to evaluate the Coulomb interaction.

Anomalous diffusion of a probe in a bath of active granular chains

NASA Astrophysics Data System (ADS)

Jerez, Michael Jade Y.; Confesor, Mark Nolan P.; Carpio-Bernido, M. Victoria; Bernido, Christopher C.

2017-08-01

We investigate the dynamics of a passive probe particle in a bath of active granular chains (AGC). The bath and the probe are enclosed in an experimental compartment with a sinusoidal boundary to prevent AGC congestion along the boundary while connected to an electrodynamic shaker. Single AGC trajectory analysis reveals a persistent type of motion compared to a purely Brownian motion as seen in its mean squared displacement (MSD). It was found that at small concentration, Φ ≤ 0.44, the MSD exhibits two dynamical regimes characterized by two different scaling exponents. For small time scales, the dynamics is superdiffusive (1.32-1.63) with the MSD scaling exponent increasing monotonically with increasing AGC concentration. On the other hand, at long time, we recover the Brownian dynamics regime, MSD = DΔt, where the mobility D ∝ Φ. We quantify the probe dynamics at short time scale by modeling it as a fractional Brownian motion. The analytical form of the MSD agrees with experimental results.

Thon rings from amorphous ice and implications of beam-induced Brownian motion in single particle electron cryo-microscopy.

PubMed

McMullan, G; Vinothkumar, K R; Henderson, R

2015-11-01

We have recorded dose-fractionated electron cryo-microscope images of thin films of pure flash-frozen amorphous ice and pre-irradiated amorphous carbon on a Falcon II direct electron detector using 300 keV electrons. We observe Thon rings [1] in both the power spectrum of the summed frames and the sum of power spectra from the individual frames. The Thon rings from amorphous carbon images are always more visible in the power spectrum of the summed frames whereas those of amorphous ice are more visible in the sum of power spectra from the individual frames. This difference indicates that while pre-irradiated carbon behaves like a solid during the exposure, amorphous ice behaves like a fluid with the individual water molecules undergoing beam-induced motion. Using the measured variation in the power spectra amplitude with number of electrons per image we deduce that water molecules are randomly displaced by a mean squared distance of ∼1.1 Å(2) for every incident 300 keV e(-)/Å(2). The induced motion leads to an optimal exposure with 300 keV electrons of 4.0 e(-)/Å(2) per image with which to observe Thon rings centred around the strong 3.7 Å scattering peak from amorphous ice. The beam-induced movement of the water molecules generates pseudo-Brownian motion of embedded macromolecules. The resulting blurring of single particle images contributes an additional term, on top of that from radiation damage, to the minimum achievable B-factor for macromolecular structure determination. Copyright © 2015 The Authors. Published by Elsevier B.V. All rights reserved.

Brownian thermal noise in functional optical surfaces

NASA Astrophysics Data System (ADS)

Kroker, S.; Dickmann, J.; Rojas Hurtado, C. B.; Heinert, D.; Nawrodt, R.; Levin, Y.; Vyatchanin, S. P.

2017-07-01

We present a formalism to compute Brownian thermal noise in functional optical surfaces such as grating reflectors, photonic crystal slabs, or complex metamaterials. Such computations are based on a specific readout variable, typically a surface integral of a dielectric interface displacement weighed by a form factor. This paper shows how to relate this form factor to Maxwell's stress tensor computed on all interfaces of the moving surface. As an example, we examine Brownian thermal noise in monolithic T-shaped grating reflectors. The previous computations by Heinert et al. [Phys. Rev. D 88, 042001 (2013), 10.1103/PhysRevD.88.042001] utilizing a simplified readout form factor produced estimates of thermal noise that are tens of percent higher than those of the exact analysis in the present paper. The relation between the form factor and Maxwell's stress tensor implies a close correlation between the optical properties of functional optical surfaces and thermal noise.

3-d brownian motion simulator for high-sensitivity nanobiotechnological applications.

PubMed

Toth, Arpád; Banky, Dániel; Grolmusz, Vince

2011-12-01

A wide variety of nanobiotechnologic applications are being developed for nanoparticle based in vitro diagnostic and imaging systems. Some of these systems make possible highly sensitive detection of molecular biomarkers. Frequently, the very low concentration of the biomarkers makes impossible the classical, partial differential equation-based mathematical simulation of the motion of the nanoparticles involved. We present a three-dimensional Brownian motion simulation tool for the prediction of the movement of nanoparticles in various thermal, viscosity, and geometric settings in a rectangular cuvette. For nonprofit users the server is freely available at the site http://brownian.pitgroup.org.

Minimization of the Renyi entropy production in the stationary states of the Brownian process with matched death and birth rates.

PubMed

Cybulski, Olgierd; Babin, Volodymyr; Hołyst, Robert

2004-01-01

We analyze the Fleming-Viot process. The system is confined in a box, whose boundaries act as a sink of Brownian particles. The death rate at the boundaries is matched by the branching (birth) rate in the system and thus the number of particles is kept constant. We show that such a process is described by the Renyi entropy whose production is minimized in the stationary state. The entropy production in this process is a monotonically decreasing function of time irrespective of the initial conditions. The first Laplacian eigenvalue is shown to be equal to the Renyi entropy production in the stationary state. As an example we simulate the process in a two-dimensional box.

Non-Brownian dynamics and strategy of amoeboid cell locomotion.

PubMed

Nishimura, Shin I; Ueda, Masahiro; Sasai, Masaki

2012-04-01

Amoeboid cells such as Dictyostelium discoideum and Madin-Darby canine kidney cells show the non-Brownian dynamics of migration characterized by the superdiffusive increase of mean-squared displacement. In order to elucidate the physical mechanism of this non-Brownian dynamics, a computational model is developed which highlights a group of inhibitory molecules for actin polymerization. Based on this model, we propose a hypothesis that inhibitory molecules are sent backward in the moving cell to accumulate at the rear of cell. The accumulated inhibitory molecules at the rear further promote cell locomotion to form a slow positive feedback loop of the whole-cell scale. The persistent straightforward migration is stabilized with this feedback mechanism, but the fluctuation in the distribution of inhibitory molecules and the cell shape deformation concurrently interrupt the persistent motion to turn the cell into a new direction. A sequence of switching behaviors between persistent motions and random turns gives rise to the superdiffusive migration in the absence of the external guidance signal. In the complex environment with obstacles, this combined process of persistent motions and random turns drives the simulated amoebae to solve the maze problem in a highly efficient way, which suggests the biological advantage for cells to bear the non-Brownian dynamics.

Theoretical Studies of Nonuniform Orientational Order in Liquid Crystals and Active Particles

NASA Astrophysics Data System (ADS)

Duzgun, Ayhan

I investigate three systems that exhibit complex patterns in orientational order, which are controlled by geometry interacting with the dynamics of phase transitions, metastability, and activity. 1. Liquid Crystal Elastomers: Liquid-crystal elastomers are remarkable materials that combine the elastic properties of cross-linked polymer networks with the anisotropy of liquid crystals. Any distortion of the polymer network affects the nematic order of the liquid crystal, and, likewise, any change in the magnitude or direction of the nematic order influences the shape of the elastomer. When elastomers are prepared without any alignment, they develop disordered polydomain structures as they are cooled into the nematic phase. To model these polydomain structures, I develop a dynamic theory for the isotropic-nematic transition in elastomers. 2. Active Brownian Particles: Unlike equilibrium systems, active matter is not governed by the conventional laws of thermodynamics. I perform Langevin dynamics simulations and analytic calculations to explore how systems cross over from equilibrium to active behavior as the activity is increased. Based on these results, I calculate how the pressure depends on wall curvature, and hence make analytic predictions for the motion of curved tracers and other effects of confinement in active matter systems. 3. Skyrmions in Liquid Crystals: Skyrmions are localized topological defects in the orientation of an order parameter field, without a singularity in the magnitude of the field. For many years, such defects have been studied in the context of chiral liquid crystals--for example, as bubbles in a confined cholesteric phase or as double-twist tubes in a blue phase. More recently, skyrmions have been investigated extensively in the context of chiral magnets. In this project, I compare skyrmions in chiral liquid crystals with the analogous magnetic defects. Through simulations based on the nematic order tensor, I model both isolated skyrmions

Spatial extent of branching Brownian motion.

PubMed

Ramola, Kabir; Majumdar, Satya N; Schehr, Grégory

2015-04-01

We study the one-dimensional branching Brownian motion starting at the origin and investigate the correlation between the rightmost (X(max)≥0) and leftmost (X(min)≤0) visited sites up to time t. At each time step the existing particles in the system either diffuse (with diffusion constant D), die (with rate a), or split into two particles (with rate b). We focus on the regime b≤a where these two extreme values X(max) and X(min) are strongly correlated. We show that at large time t, the joint probability distribution function (PDF) of the two extreme points becomes stationary P(X,Y,t→∞)→p(X,Y). Our exact results for p(X,Y) demonstrate that the correlation between X(max) and X(min) is nonzero, even in the stationary state. From this joint PDF, we compute exactly the stationary PDF p(ζ) of the (dimensionless) span ζ=(X(max)-X(min))/√[D/b], which is the distance between the rightmost and leftmost visited sites. This span distribution is characterized by a linear behavior p(ζ)∼1/2(1+Δ)ζ for small spans, with Δ=(a/b-1). In the critical case (Δ=0) this distribution has a nontrivial power law tail p(ζ)∼8π√[3]/ζ(3) for large spans. On the other hand, in the subcritical case (Δ>0), we show that the span distribution decays exponentially as p(ζ)∼(A(2)/2)ζexp(-√[Δ]ζ) for large spans, where A is a nontrivial function of Δ, which we compute exactly. We show that these asymptotic behaviors carry the signatures of the correlation between X(max) and X(min). Finally we verify our results via direct Monte Carlo simulations.

Spatial extent of branching Brownian motion

NASA Astrophysics Data System (ADS)

Ramola, Kabir; Majumdar, Satya N.; Schehr, Grégory

2015-04-01

We study the one-dimensional branching Brownian motion starting at the origin and investigate the correlation between the rightmost (Xmax≥0 ) and leftmost (Xmin≤0 ) visited sites up to time t . At each time step the existing particles in the system either diffuse (with diffusion constant D ), die (with rate a ), or split into two particles (with rate b ). We focus on the regime b ≤a where these two extreme values Xmax and Xmin are strongly correlated. We show that at large time t , the joint probability distribution function (PDF) of the two extreme points becomes stationary P (X ,Y ,t →∞ )→p (X ,Y ) . Our exact results for p (X ,Y ) demonstrate that the correlation between Xmax and Xmin is nonzero, even in the stationary state. From this joint PDF, we compute exactly the stationary PDF p (ζ ) of the (dimensionless) span ζ =(Xmax-Xmin) /√{D /b } , which is the distance between the rightmost and leftmost visited sites. This span distribution is characterized by a linear behavior p (ζ ) ˜1/2 (1 +Δ ) ζ for small spans, with Δ =(a/b -1 ) . In the critical case (Δ =0 ) this distribution has a nontrivial power law tail p (ζ ) ˜8 π √{3 }/ζ3 for large spans. On the other hand, in the subcritical case (Δ >0 ), we show that the span distribution decays exponentially as p (ζ ) ˜(A2/2 ) ζ exp(-√{Δ }ζ ) for large spans, where A is a nontrivial function of Δ , which we compute exactly. We show that these asymptotic behaviors carry the signatures of the correlation between Xmax and Xmin. Finally we verify our results via direct Monte Carlo simulations.

From Lévy to Brownian: a computational model based on biological fluctuation.

PubMed

Nurzaman, Surya G; Matsumoto, Yoshio; Nakamura, Yutaka; Shirai, Kazumichi; Koizumi, Satoshi; Ishiguro, Hiroshi

2011-02-03

Theoretical studies predict that Lévy walks maximizes the chance of encountering randomly distributed targets with a low density, but Brownian walks is favorable inside a patch of targets with high density. Recently, experimental data reports that some animals indeed show a Lévy and Brownian walk movement patterns when forage for foods in areas with low and high density. This paper presents a simple, Gaussian-noise utilizing computational model that can realize such behavior. We extend Lévy walks model of one of the simplest creature, Escherichia coli, based on biological fluctuation framework. We build a simulation of a simple, generic animal to observe whether Lévy or Brownian walks will be performed properly depends on the target density, and investigate the emergent behavior in a commonly faced patchy environment where the density alternates. Based on the model, animal behavior of choosing Lévy or Brownian walk movement patterns based on the target density is able to be generated, without changing the essence of the stochastic property in Escherichia coli physiological mechanism as explained by related researches. The emergent behavior and its benefits in a patchy environment are also discussed. The model provides a framework for further investigation on the role of internal noise in realizing adaptive and efficient foraging behavior.

Movement of particles using sequentially activated dielectrophoretic particle trapping

DOEpatents

Miles, Robin R.

2004-02-03

Manipulation of DNA and cells/spores using dielectrophoretic (DEP) forces to perform sample preparation protocols for polymerized chain reaction (PCR) based assays for various applications. This is accomplished by movement of particles using sequentially activated dielectrophoretic particle trapping. DEP forces induce a dipole in particles, and these particles can be trapped in non-uniform fields. The particles can be trapped in the high field strength region of one set of electrodes. By switching off this field and switching on an adjacent electrodes, particles can be moved down a channel with little or no flow.

Motion of particles adhering to the leading lamella of crawling cells

PubMed Central

1981-01-01

Time-lapsed films of particle motion on the leading lamella of chick heart fibroblasts and mouse peritoneal macrophages were analyzed. The particles were composed of powdered glass or powdered aminated polystyrene and were 0.5-1.0 micrometer in radius. Particle motions were described by steps in position from one frame to the time-lapse movies to the next. The statistics of the step-size distribution of the particles were consistent with a particle in Brownian motion subject to a constant force. From the Brownian movement, we have calculated the two-dimensional diffusion coefficient of different particles. These vary by more than an order of magnitude (10(-11)-10(-10) cm2/s) even for particles composed of the same material and located very close to each other on the surface of the cell. This variation was not correlated with particle size but is interpretable as a result of different numbers of adhesive bonds holding the particles to the cells. The constant component of particle movement can be interpreted as a result of a constant force acting on each particle (0.1-1.0 x 10(-8) dyn). Variations in the fractional coefficient for particles close to each other on the cell surface do not yield corresponding differences in velocity, suggesting that the frictional coefficient and the driving force vary together. This is consistent with the hypothesis that the particles are carried by flow of the membrane as a whole or by flow of some submembrane material. The utility of our methods for monitoring cell motile behavior in biologically interesting situations, such as a chemotactic gradient, is discussed. PMID:7309794

Evaluating linear response in active systems with no perturbing field

NASA Astrophysics Data System (ADS)

Szamel, Grzegorz

2017-03-01

We present a method for the evaluation of time-dependent linear response functions for systems of active particles propelled by a persistent (colored) noise from unperturbed simulations. The method is inspired by the Malliavin weights sampling method proposed by Warren and Allen (Phys. Rev. Lett., 109 (2012) 250601) for out-of-equilibrium systems of passive Brownian particles. We illustrate our method by evaluating two linear response functions for a single active particle in an external harmonic potential. As an application, we calculate the time-dependent mobility function and an effective temperature, defined through the Einstein relation between the self-diffusion and mobility coefficients, for a system of many active particles interacting via a screened Coulomb potential. We find that this effective temperature decreases with increasing persistence time of the self-propulsion. Initially, for not too large persistence times, it changes rather slowly, but then it decreases markedly when the persistence length of the self-propelled motion becomes comparable with the particle size.

How Actuated Particles Effectively Capture Biomolecular Targets

PubMed Central

2017-01-01

Because of their high surface-to-volume ratio and adaptable surface functionalization, particles are widely used in bioanalytical methods to capture molecular targets. In this article, a comprehensive study is reported of the effectiveness of protein capture by actuated magnetic particles. Association rate constants are quantified in experiments as well as in Brownian dynamics simulations for different particle actuation configurations. The data reveal how the association rate depends on the particle velocity, particle density, and particle assembly characteristics. Interestingly, single particles appear to exhibit target depletion zones near their surface, caused by the high density of capture molecules. The depletion effects are even more limiting in cases with high particle densities. The depletion effects are overcome and protein capture rates are enhanced by applying dynamic particle actuation, resulting in an increase in the association rate constants by up to 2 orders of magnitude. PMID:28192952

Optimizing photophoresis and asymmetric force fields for grading of Brownian particles.

PubMed

Neild, Adrian; Ng, Tuck Wah; Woods, Timothy

2009-12-10

We discuss a scheme that incorporates restricted spatial input location, orthogonal sort, and movement direction features, with particle sorting achieved by using an asymmetric potential cycled on and off, while movement is accomplished by photophoresis. Careful investigation has uncovered the odds of sorting between certain pairs of particle sizes to be solely dependent on radii in each phase of the process. This means that the most effective overall sorting can be achieved by maximizing the number of phases. This optimized approach is demonstrated using numerical simulation to permit grading of a range of nanometer-scale particle sizes.

Semicircular Canals Circumvent Brownian Motion Overload of Mechanoreceptor Hair Cells.

PubMed

Muller, Mees; Heeck, Kier; Elemans, Coen P H

2016-01-01

Vertebrate semicircular canals (SCC) first appeared in the vertebrates (i.e. ancestral fish) over 600 million years ago. In SCC the principal mechanoreceptors are hair cells, which as compared to cochlear hair cells are distinctly longer (70 vs. 7 μm), 10 times more compliant to bending (44 vs. 500 nN/m), and have a 100-fold higher tip displacement threshold (< 10 μm vs. <400 nm). We have developed biomechanical models of vertebrate hair cells where the bundle is approximated as a stiff, cylindrical elastic rod subject to friction and thermal agitation. Our models suggest that the above differences aid SCC hair cells in circumventing the masking effects of Brownian motion noise of about 70 nm, and thereby permit transduction of very low frequency (<10 Hz) signals. We observe that very low frequency mechanoreception requires increased stimulus amplitude, and argue that this is adaptive to circumvent Brownian motion overload at the hair bundles. We suggest that the selective advantage of detecting such low frequency stimuli may have favoured the evolution of large guiding structures such as semicircular canals and otoliths to overcome Brownian Motion noise at the level of the mechanoreceptors of the SCC.

Semicircular Canals Circumvent Brownian Motion Overload of Mechanoreceptor Hair Cells

PubMed Central

Muller, Mees; Heeck, Kier

2016-01-01

Vertebrate semicircular canals (SCC) first appeared in the vertebrates (i.e. ancestral fish) over 600 million years ago. In SCC the principal mechanoreceptors are hair cells, which as compared to cochlear hair cells are distinctly longer (70 vs. 7 μm), 10 times more compliant to bending (44 vs. 500 nN/m), and have a 100-fold higher tip displacement threshold (< 10 μm vs. <400 nm). We have developed biomechanical models of vertebrate hair cells where the bundle is approximated as a stiff, cylindrical elastic rod subject to friction and thermal agitation. Our models suggest that the above differences aid SCC hair cells in circumventing the masking effects of Brownian motion noise of about 70 nm, and thereby permit transduction of very low frequency (<10 Hz) signals. We observe that very low frequency mechanoreception requires increased stimulus amplitude, and argue that this is adaptive to circumvent Brownian motion overload at the hair bundles. We suggest that the selective advantage of detecting such low frequency stimuli may have favoured the evolution of large guiding structures such as semicircular canals and otoliths to overcome Brownian Motion noise at the level of the mechanoreceptors of the SCC. PMID:27448330

Brownian motion model with stochastic parameters for asset prices

NASA Astrophysics Data System (ADS)

Ching, Soo Huei; Hin, Pooi Ah

2013-09-01

The Brownian motion model may not be a completely realistic model for asset prices because in real asset prices the drift μ and volatility σ may change over time. Presently we consider a model in which the parameter x = (μ,σ) is such that its value x (t + Δt) at a short time Δt ahead of the present time t depends on the value of the asset price at time t + Δt as well as the present parameter value x(t) and m-1 other parameter values before time t via a conditional distribution. The Malaysian stock prices are used to compare the performance of the Brownian motion model with fixed parameter with that of the model with stochastic parameter.

Determination of the hydrodynamic friction matrix for various anisotropic particles

NASA Astrophysics Data System (ADS)

Kraft, Daniela; Wittkowksi, Raphael; Löwen, Hartmut; Pine, David

2013-03-01

The relationship between the shape of a colloidal particle and its Brownian motion can be captured by the hydrodynamic friction matrix. It fully describes the translational and rotational diffusion along the particle's main axes as well as the coupling between rotational and translational diffusion. We observed a wide variety of anisotropic colloidal particles with confocal microscopy and calculated the hydrodynamic friction matrix from the particle trajectories. We find that symmetries in the particle shape are reflected in the entries of the friction matrix. We compare our experimentally obtained results with numerical simulations and theoretical predictions. Financial support through a Rubicon grant by the Netherlands Organisation for Scientific Research.

Localization and Ballistic Diffusion for the Tempered Fractional Brownian-Langevin Motion

NASA Astrophysics Data System (ADS)

Chen, Yao; Wang, Xudong; Deng, Weihua

2017-10-01

This paper discusses the tempered fractional Brownian motion (tfBm), its ergodicity, and the derivation of the corresponding Fokker-Planck equation. Then we introduce the generalized Langevin equation with the tempered fractional Gaussian noise for a free particle, called tempered fractional Langevin equation (tfLe). While the tfBm displays localization diffusion for the long time limit and for the short time its mean squared displacement (MSD) has the asymptotic form t^{2H}, we show that the asymptotic form of the MSD of the tfLe transits from t^2 (ballistic diffusion for short time) to t^{2-2H}, and then to t^2 (again ballistic diffusion for long time). On the other hand, the overdamped tfLe has the transition of the diffusion type from t^{2-2H} to t^2 (ballistic diffusion). The tfLe with harmonic potential is also considered.

Brownian Motion and its Conditional Descendants

NASA Astrophysics Data System (ADS)

Garbaczewski, Piotr

It happened before [1] that I have concluded my publication with a special dedication to John R. Klauder. Then, the reason was John's PhD thesis [2] and the questions (perhaps outdated in the eyes of the band-wagon jumpers, albeit still retaining their full vitality [3]): (i) What are the uses of the classical (c-number, non-Grassmann) spinor fields, especially nonlinear ones, what are they for at all ? (ii) What are, if any, the classical partners for Fermi models and fields in particular ? The present dedication, even if not as conspicuously motivated as the previous one by John's research, nevertheless pertains to investigations pursued by John through the years and devoted to the analysis of random noise. Sometimes, re-reading old papers and re-analysing old, frequently forgotten ideas might prove more rewarding than racing the fashions. Following this attitude, let us take as the departure point Schrödinger's original suggestion [4] of the existence of a special class of random processes, which have their origin in the Einstein-Smoluchowski theory of the Brownian motion and its Wiener's codification. The original analysis due to Schrodinger of the probabilistic significance of the heat equation and of its time adjoint in parallel, remained unnoticed by the physics community, and since then forgotten. It reappeared however in the mathematical literature as an inspiration to generalise the concept of Markovian diffusions to the case of Bernstein stochastic processes. But, it stayed without consequences for a deeper understanding of the possible physical phenomena which might underly the corresponding abstract formalism. Schrödinger's objective was to initiate investigations of possible links between quantum theory and the theory of Brownian motion, an attempt which culminated later in the so-called Nelson's stochastic mechanics [8] and its encompassing formalism [7] in which the issue of the Brownian implementation of quantum dynamics is placed in the

Non-Brownian diffusion in lipid membranes: Experiments and simulations.

PubMed

Metzler, R; Jeon, J-H; Cherstvy, A G

2016-10-01

The dynamics of constituents and the surface response of cellular membranes-also in connection to the binding of various particles and macromolecules to the membrane-are still a matter of controversy in the membrane biophysics community, particularly with respect to crowded membranes of living biological cells. We here put into perspective recent single particle tracking experiments in the plasma membranes of living cells and supercomputing studies of lipid bilayer model membranes with and without protein crowding. Special emphasis is put on the observation of anomalous, non-Brownian diffusion of both lipid molecules and proteins embedded in the lipid bilayer. While single component, pure lipid bilayers in simulations exhibit only transient anomalous diffusion of lipid molecules on nanosecond time scales, the persistence of anomalous diffusion becomes significantly longer ranged on the addition of disorder-through the addition of cholesterol or proteins-and on passing of the membrane lipids to the gel phase. Concurrently, experiments demonstrate the anomalous diffusion of membrane embedded proteins up to macroscopic time scales in the minute time range. Particular emphasis will be put on the physical character of the anomalous diffusion, in particular, the occurrence of ageing observed in the experiments-the effective diffusivity of the measured particles is a decreasing function of time. Moreover, we present results for the time dependent local scaling exponent of the mean squared displacement of the monitored particles. Recent results finding deviations from the commonly assumed Gaussian diffusion patterns in protein crowded membranes are reported. The properties of the displacement autocorrelation function of the lipid molecules are discussed in the light of their appropriate physical anomalous diffusion models, both for non-crowded and crowded membranes. In the last part of this review we address the upcoming field of membrane distortion by elongated membrane

From Lévy to Brownian: A Computational Model Based on Biological Fluctuation

PubMed Central

Nurzaman, Surya G.; Matsumoto, Yoshio; Nakamura, Yutaka; Shirai, Kazumichi; Koizumi, Satoshi; Ishiguro, Hiroshi

2011-01-01

Background Theoretical studies predict that Lévy walks maximizes the chance of encountering randomly distributed targets with a low density, but Brownian walks is favorable inside a patch of targets with high density. Recently, experimental data reports that some animals indeed show a Lévy and Brownian walk movement patterns when forage for foods in areas with low and high density. This paper presents a simple, Gaussian-noise utilizing computational model that can realize such behavior. Methodology/Principal Findings We extend Lévy walks model of one of the simplest creature, Escherichia coli, based on biological fluctuation framework. We build a simulation of a simple, generic animal to observe whether Lévy or Brownian walks will be performed properly depends on the target density, and investigate the emergent behavior in a commonly faced patchy environment where the density alternates. Conclusions/Significance Based on the model, animal behavior of choosing Lévy or Brownian walk movement patterns based on the target density is able to be generated, without changing the essence of the stochastic property in Escherichia coli physiological mechanism as explained by related researches. The emergent behavior and its benefits in a patchy environment are also discussed. The model provides a framework for further investigation on the role of internal noise in realizing adaptive and efficient foraging behavior. PMID:21304911

Brownian Movement and Avogadro's Number: A Laboratory Experiment.

ERIC Educational Resources Information Center

Kruglak, Haym

1988-01-01

Reports an experimental procedure for studying Einstein's theory of Brownian movement using commercially available latex microspheres and a video camera. Describes how students can monitor sphere motions and determine Avogadro's number. Uses a black and white video camera, microscope, and TV. (ML)

A Simplified Treatment of Brownian Motion and Stochastic Differential Equations Arising in Financial Mathematics

ERIC Educational Resources Information Center

Parlar, Mahmut

2004-01-01

Brownian motion is an important stochastic process used in modelling the random evolution of stock prices. In their 1973 seminal paper--which led to the awarding of the 1997 Nobel prize in Economic Sciences--Fischer Black and Myron Scholes assumed that the random stock price process is described (i.e., generated) by Brownian motion. Despite its…

Active Brownian agents with concentration-dependent chemotactic sensitivity.

PubMed

Meyer, Marcel; Schimansky-Geier, Lutz; Romanczuk, Pawel

2014-02-01

We study a biologically motivated model of overdamped, autochemotactic Brownian agents with concentration-dependent chemotactic sensitivity. The agents in our model move stochastically and produce a chemical ligand at their current position. The ligand concentration obeys a reaction-diffusion equation and acts as a chemoattractant for the agents, which bias their motion towards higher concentrations of the dynamically altered chemical field. We explore the impact of concentration-dependent response to chemoattractant gradients on large-scale pattern formation, by deriving a coarse-grained macroscopic description of the individual-based model, and compare the conditions for emergence of inhomogeneous solutions for different variants of the chemotactic sensitivity. We focus primarily on the so-called receptor-law sensitivity, which models a nonlinear decrease of chemotactic sensitivity with increasing ligand concentration. Our results reveal qualitative differences between the receptor law, the constant chemotactic response, and the so-called log law, with respect to stability of the homogeneous solution, as well as the emergence of different patterns (labyrinthine structures, clusters, and bubbles) via spinodal decomposition or nucleation. We discuss two limiting cases, where the model can be reduced to the dynamics of single species: (I) the agent density governed by a density-dependent effective diffusion coefficient and (II) the ligand field with an effective bistable, time-dependent reaction rate. In the end, we turn to single clusters of agents, studying domain growth and determining mean characteristics of the stationary inhomogeneous state. Analytical results are confirmed and extended by large-scale GPU simulations of the individual based model.