Algorithms for Brownian first-passage-time estimation

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2009-09-01

A class of algorithms in discrete space and continuous time for Brownian first-passage-time estimation is considered. A simple algorithm is derived that yields exact mean first-passage times (MFPTs) for linear potentials in one dimension, regardless of the lattice spacing. When applied to nonlinear potentials and/or higher spatial dimensions, numerical evidence suggests that this algorithm yields MFPT estimates that either outperform or rival Langevin-based (discrete time and continuous space) estimates.

Modeling 2D and 3D diffusion.

PubMed

Saxton, Michael J

2007-01-01

Modeling obstructed diffusion is essential to the understanding of diffusion-mediated processes in the crowded cellular environment. Simple Monte Carlo techniques for modeling obstructed random walks are explained and related to Brownian dynamics and more complicated Monte Carlo methods. Random number generation is reviewed in the context of random walk simulations. Programming techniques and event-driven algorithms are discussed as ways to speed simulations.

Brownian cluster dynamics with short range patchy interactions: Its application to polymers and step-growth polymerization

NASA Astrophysics Data System (ADS)

Prabhu, A.; Babu, S. B.; Dolado, J. S.; Gimel, J.-C.

2014-07-01

We present a novel simulation technique derived from Brownian cluster dynamics used so far to study the isotropic colloidal aggregation. It now implements the classical Kern-Frenkel potential to describe patchy interactions between particles. This technique gives access to static properties, dynamics and kinetics of the system, even far from the equilibrium. Particle thermal motions are modeled using billions of independent small random translations and rotations, constrained by the excluded volume and the connectivity. This algorithm, applied to a single polymer chain leads to correct static and dynamic properties, in the framework where hydrodynamic interactions are ignored. By varying patch angles, various local chain flexibilities can be obtained. We have used this new algorithm to model step-growth polymerization under various solvent qualities. The polymerization reaction is modeled by an irreversible aggregation between patches while an isotropic finite square-well potential is superimposed to mimic the solvent quality. In bad solvent conditions, a competition between a phase separation (due to the isotropic interaction) and polymerization (due to patches) occurs. Surprisingly, an arrested network with a very peculiar structure appears. It is made of strands and nodes. Strands gather few stretched chains that dip into entangled globular nodes. These nodes act as reticulation points between the strands. The system is kinetically driven and we observe a trapped arrested structure. That demonstrates one of the strengths of this new simulation technique. It can give valuable insights about mechanisms that could be involved in the formation of stranded gels.

ML-Space: Hybrid Spatial Gillespie and Particle Simulation of Multi-Level Rule-Based Models in Cell Biology.

PubMed

Bittig, Arne T; Uhrmacher, Adelinde M

2017-01-01

Spatio-temporal dynamics of cellular processes can be simulated at different levels of detail, from (deterministic) partial differential equations via the spatial Stochastic Simulation algorithm to tracking Brownian trajectories of individual particles. We present a spatial simulation approach for multi-level rule-based models, which includes dynamically hierarchically nested cellular compartments and entities. Our approach ML-Space combines discrete compartmental dynamics, stochastic spatial approaches in discrete space, and particles moving in continuous space. The rule-based specification language of ML-Space supports concise and compact descriptions of models and to adapt the spatial resolution of models easily.

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)).

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 cost of computing Brownian displacements comparable to the cost of computing deterministic displacements in BD simulations. A high-performance implementation employing non-uniform fast Fourier transforms implemented on graphics processing units and integrated with the software package HOOMD-blue is used for benchmarking.

Markov Chain Monte Carlo in the Analysis of Single-Molecule Experimental Data

NASA Astrophysics Data System (ADS)

Kou, S. C.; Xie, X. Sunney; Liu, Jun S.

2003-11-01

This article provides a Bayesian analysis of the single-molecule fluorescence lifetime experiment designed to probe the conformational dynamics of a single DNA hairpin molecule. The DNA hairpin's conformational change is initially modeled as a two-state Markov chain, which is not observable and has to be indirectly inferred. The Brownian diffusion of the single molecule, in addition to the hidden Markov structure, further complicates the matter. We show that the analytical form of the likelihood function can be obtained in the simplest case and a Metropolis-Hastings algorithm can be designed to sample from the posterior distribution of the parameters of interest and to compute desired estiamtes. To cope with the molecular diffusion process and the potentially oscillating energy barrier between the two states of the DNA hairpin, we introduce a data augmentation technique to handle both the Brownian diffusion and the hidden Ornstein-Uhlenbeck process associated with the fluctuating energy barrier, and design a more sophisticated Metropolis-type algorithm. Our method not only increases the estimating resolution by several folds but also proves to be successful for model discrimination.

Computationally efficient algorithms for Brownian dynamics simulation of long flexible macromolecules modeled as bead-rod chains

NASA Astrophysics Data System (ADS)

Moghani, Mahdy Malekzadeh; Khomami, Bamin

2017-02-01

The computational efficiency of Brownian dynamics (BD) simulation of the constrained model of a polymeric chain (bead-rod) with n beads and in the presence of hydrodynamic interaction (HI) is reduced to the order of n2 via an efficient algorithm which utilizes the conjugate-gradient (CG) method within a Picard iteration scheme. Moreover, the utility of the Barnes and Hut (BH) multipole method in BD simulation of polymeric solutions in the presence of HI, with regard to computational cost, scaling, and accuracy, is discussed. Overall, it is determined that this approach leads to a scaling of O (n1.2) . Furthermore, a stress algorithm is developed which accurately captures the transient stress growth in the startup of flow for the bead-rod model with HI and excluded volume (EV) interaction. Rheological properties of the chains up to n =350 in the presence of EV and HI are computed via the former algorithm. The result depicts qualitative differences in shear thinning behavior of the polymeric solutions in the intermediate values of the Weissenburg number (10

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

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.

A Method for Molecular Dynamics on Curved Surfaces

PubMed Central

Paquay, Stefan; Kusters, Remy

2016-01-01

Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in the field of diffusive transport have focused on solving the diffusion equation on curved surfaces, for which it is not tractable to incorporate particle interactions even though these play a crucial role in crowded systems. We show here that it is possible to take such interactions into account by combining standard constraint algorithms with the classical velocity Verlet scheme to perform molecular dynamics simulations of particles constrained to an arbitrarily curved surface. Furthermore, unlike Brownian dynamics schemes in local coordinates, our method is based on Cartesian coordinates, allowing for the reuse of many other standard tools without modifications, including parallelization through domain decomposition. We show that by applying the schemes to the Langevin equation for various surfaces, we obtain confined Brownian motion, which has direct applications to many biological and physical problems. Finally we present two practical examples that highlight the applicability of the method: 1) the influence of crowding and shape on the lateral diffusion of proteins in curved membranes; and 2) the self-assembly of a coarse-grained virus capsid protein model. PMID:27028633

A Method for Molecular Dynamics on Curved Surfaces

NASA Astrophysics Data System (ADS)

Paquay, Stefan; Kusters, Remy

2016-03-01

Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in the field of diffusive transport have focussed on solving the diffusion equation on curved surfaces, for which it is not tractable to incorporate particle interactions even though these play a crucial role in crowded systems. We show here that it is possible to combine standard constraint algorithms with the classical velocity Verlet scheme to perform molecular dynamics simulations of particles constrained to an arbitrarily curved surface, in which such interactions can be taken into account. Furthermore, unlike Brownian dynamics schemes in local coordinates, our method is based on Cartesian coordinates allowing for the reuse of many other standard tools without modifications, including parallelisation through domain decomposition. We show that by applying the schemes to the Langevin equation for various surfaces, confined Brownian motion is obtained, which has direct applications to many biological and physical problems. Finally we present two practical examples that highlight the applicability of the method: (i) the influence of crowding and shape on the lateral diffusion of proteins in curved membranes and (ii) the self-assembly of a coarse-grained virus capsid protein model.

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

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.

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 in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.« less

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 particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.

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 in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.« less

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.

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.

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.

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.

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.

Stochastic Simulation of Complex Fluid Flows

DTIC Science & Technology

The PI has developed novel numerical algorithms and computational codes to simulate the Brownian motion of rigidparticles immersed in a viscous fluid...processes and to the design of novel nanofluid materials. Therandom Brownian motion of particles in fluid can be accounted for in fluid-structure

Applications of Density Functional Theory in Soft Condensed Matter

NASA Astrophysics Data System (ADS)

Löwen, Hartmut

Applications of classical density functional theory (DFT) to soft matter systems like colloids, liquid crystals and polymer solutions are discussed with a focus on the freezing transition and on nonequilibrium Brownian dynamics. First, after a brief reminder of equilibrium density functional theory, DFT is applied to the freezing transition of liquids into crystalline lattices. In particular, spherical particles with radially symmetric pair potentials will be treated (like hard spheres, the classical one-component plasma or Gaussian-core particles). Second, the DFT will be generalized towards Brownian dynamics in order to tackle nonequilibrium problems. After a general introduction to Brownian dynamics using the complementary Smoluchowski and Langevin pictures appropriate for the dynamics of colloidal suspensions, the dynamical density functional theory (DDFT) will be derived from the Smoluchowski equation. This will be done first for spherical particles (e.g. hard spheres or Gaussian-cores) without hydrodynamic interactions. Then we show how to incorporate hydrodynamic interactions between the colloidal particles into the DDFT framework and compare to Brownian dynamics computer simulations. Third orientational degrees of freedom (rod-like particles) will be considered as well. In the latter case, the stability of intermediate liquid crystalline phases (isotropic, nematic, smectic-A, plastic crystals etc) can be predicted. Finally, the corresponding dynamical extension of density functional theory towards orientational degrees of freedom is proposed and the collective behaviour of "active" (self-propelled) Brownian particles is briefly discussed.

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.

Universal Algorithm for Identification of Fractional Brownian Motion. A Case of Telomere Subdiffusion

PubMed Central

Burnecki, Krzysztof; Kepten, Eldad; Janczura, Joanna; Bronshtein, Irena; Garini, Yuval; Weron, Aleksander

2012-01-01

We present a systematic statistical analysis of the recently measured individual trajectories of fluorescently labeled telomeres in the nucleus of living human cells. The experiments were performed in the U2OS cancer cell line. We propose an algorithm for identification of the telomere motion. By expanding the previously published data set, we are able to explore the dynamics in six time orders, a task not possible earlier. As a result, we establish a rigorous mathematical characterization of the stochastic process and identify the basic mathematical mechanisms behind the telomere motion. We find that the increments of the motion are stationary, Gaussian, ergodic, and even more chaotic—mixing. Moreover, the obtained memory parameter estimates, as well as the ensemble average mean square displacement reveal subdiffusive behavior at all time spans. All these findings statistically prove a fractional Brownian motion for the telomere trajectories, which is confirmed by a generalized p-variation test. Taking into account the biophysical nature of telomeres as monomers in the chromatin chain, we suggest polymer dynamics as a sufficient framework for their motion with no influence of other models. In addition, these results shed light on other studies of telomere motion and the alternative telomere lengthening mechanism. We hope that identification of these mechanisms will allow the development of a proper physical and biological model for telomere subdynamics. This array of tests can be easily implemented to other data sets to enable quick and accurate analysis of their statistical characteristics. PMID:23199912

Pseudochemotaxis in inhomogeneous active Brownian systems

NASA Astrophysics Data System (ADS)

Vuijk, Hidde D.; Sharma, Abhinav; Mondal, Debasish; Sommer, Jens-Uwe; Merlitz, Holger

2018-04-01

We study dynamical properties of confined, self-propelled Brownian particles in an inhomogeneous activity profile. Using Brownian dynamics simulations, we calculate the probability to reach a fixed target and the mean first passage time to the target of an active particle. We show that both these quantities are strongly influenced by the inhomogeneous activity. When the activity is distributed such that high-activity zone is located between the target and the starting location, the target finding probability is increased and the passage time is decreased in comparison to a uniformly active system. Moreover, for a continuously distributed profile, the activity gradient results in a drift of active particle up the gradient bearing resemblance to chemotaxis. Integrating out the orientational degrees of freedom, we derive an approximate Fokker-Planck equation and show that the theoretical predictions are in very good agreement with the Brownian dynamics simulations.

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.

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.

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.

From samples to populations in retinex models

NASA Astrophysics Data System (ADS)

Gianini, Gabriele

2017-05-01

Some spatial color algorithms, such as Brownian Milano retinex (MI-retinex) and random spray retinex (RSR), are based on sampling. In Brownian MI-retinex, memoryless random walks (MRWs) explore the neighborhood of a pixel and are then used to compute its output. Considering the relative redundancy and inefficiency of MRW exploration, the algorithm RSR replaced the walks by samples of points (the sprays). Recent works point to the fact that a mapping from the sampling formulation to the probabilistic formulation of the corresponding sampling process can offer useful insights into the models, at the same time featuring intrinsically noise-free outputs. The paper continues the development of this concept and shows that the population-based versions of RSR and Brownian MI-retinex can be used to obtain analytical expressions for the outputs of some test images. The comparison of the two analytic expressions from RSR and from Brownian MI-retinex demonstrates not only that the two outputs are, in general, different but also that they depend in a qualitatively different way upon the features of the image.

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.

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.

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%.

A CONTINUUM HARD-SPHERE MODEL OF PROTEIN ADSORPTION

PubMed Central

Finch, Craig; Clarke, Thomas; Hickman, James J.

2012-01-01

Protein adsorption plays a significant role in biological phenomena such as cell-surface interactions and the coagulation of blood. Two-dimensional random sequential adsorption (RSA) models are widely used to model the adsorption of proteins on solid surfaces. Continuum equations have been developed so that the results of RSA simulations can be used to predict the kinetics of adsorption. Recently, Brownian dynamics simulations have become popular for modeling protein adsorption. In this work a continuum model was developed to allow the results from a Brownian dynamics simulation to be used as the boundary condition in a computational fluid dynamics (CFD) simulation. Brownian dynamics simulations were used to model the diffusive transport of hard-sphere particles in a liquid and the adsorption of the particles onto a solid surface. The configuration of the adsorbed particles was analyzed to quantify the chemical potential near the surface, which was found to be a function of the distance from the surface and the fractional surface coverage. The near-surface chemical potential was used to derive a continuum model of adsorption that incorporates the results from the Brownian dynamics simulations. The equations of the continuum model were discretized and coupled to a CFD simulation of diffusive transport to the surface. The kinetics of adsorption predicted by the continuum model closely matched the results from the Brownian dynamics simulation. This new model allows the results from mesoscale simulations to be incorporated into micro- or macro-scale CFD transport simulations of protein adsorption in practical devices. PMID:23729843

CNT based thermal Brownian motor to pump water in nanodevices

NASA Astrophysics Data System (ADS)

Oyarzua, Elton; Zambrano, Harvey; Walther, J. H.

2016-11-01

Brownian molecular motors are nanoscale machines that exploit thermal fluctuations for directional motion by employing mechanisms such as the Feynman-Smoluchowski ratchet. In this study, using Non Equilibrium Molecular Dynamics, we propose a novel thermal Brownian motor for pumping water through Carbon Nanotubes (CNTs). To achieve this we impose a thermal gradient along the axis of a CNT filled with water and impose, in addition, a spatial asymmetry by fixing specific zones on the CNT in order to modify the vibrational modes of the CNT. We find that the temperature gradient and imposed spatial asymmetry drive the water flow in a preferential direction. We systematically modified the magnitude of the applied thermal gradient and the axial position of the fixed points. The analysis involves measurement of the vibrational modes in the CNTs using a Fast Fourier Transform (FFT) algorithm. We observed water flow in CNTs of 0.94, 1.4 and 2.0 nm in diameter, reaching a maximum velocity of 5 m/s for a thermal gradient of 3.3 K/nm. The proposed thermal motor is capable of delivering a continuous flow throughout a CNT, providing a useful tool for driving liquids in nanofluidic devices by exploiting thermal gradients. We aknowledge partial support from Fondecyt project 11130559.

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

Dynamic simulation of concentrated macromolecular solutions with screened long-range hydrodynamic interactions: Algorithm and limitations

PubMed Central

Ando, Tadashi; Chow, Edmond; Skolnick, Jeffrey

2013-01-01

Hydrodynamic interactions exert a critical effect on the dynamics of macromolecules. As the concentration of macromolecules increases, by analogy to the behavior of semidilute polymer solutions or the flow in porous media, one might expect hydrodynamic screening to occur. Hydrodynamic screening would have implications both for the understanding of macromolecular dynamics as well as practical implications for the simulation of concentrated macromolecular solutions, e.g., in cells. Stokesian dynamics (SD) is one of the most accurate methods for simulating the motions of N particles suspended in a viscous fluid at low Reynolds number, in that it considers both far-field and near-field hydrodynamic interactions. This algorithm traditionally involves an O(N3) operation to compute Brownian forces at each time step, although asymptotically faster but more complex SD methods are now available. Motivated by the idea of hydrodynamic screening, the far-field part of the hydrodynamic matrix in SD may be approximated by a diagonal matrix, which is equivalent to assuming that long range hydrodynamic interactions are completely screened. This approximation allows sparse matrix methods to be used, which can reduce the apparent computational scaling to O(N). Previously there were several simulation studies using this approximation for monodisperse suspensions. Here, we employ newly designed preconditioned iterative methods for both the computation of Brownian forces and the solution of linear systems, and consider the validity of this approximation in polydisperse suspensions. We evaluate the accuracy of the diagonal approximation method using an intracellular-like suspension. The diffusivities of particles obtained with this approximation are close to those with the original method. However, this approximation underestimates intermolecular correlated motions, which is a trade-off between accuracy and computing efficiency. The new method makes it possible to perform large-scale and long-time simulation with an approximate accounting of hydrodynamic interactions. PMID:24089734

Comparison of Brownian-dynamics-based estimates of polymer tension with direct force measurements.

PubMed

Arsenault, Mark E; Purohit, Prashant K; Goldman, Yale E; Shuman, Henry; Bau, Haim H

2010-11-01

With the aid of brownian dynamics models, it is possible to estimate polymer tension by monitoring polymers' transverse thermal fluctuations. To assess the precision of the approach, brownian dynamics-based tension estimates were compared with the force applied to rhodamine-phalloidin labeled actin filaments bound to polymer beads and suspended between two optical traps. The transverse thermal fluctuations of each filament were monitored with a CCD camera, and the images were analyzed to obtain the filament's transverse displacement variance as a function of position along the filament, the filament's tension, and the camera's exposure time. A linear Brownian dynamics model was used to estimate the filament's tension. The estimated force was compared and agreed within 30% (when the tension <0.1 pN ) and 70% (when the tension <1 pN ) with the applied trap force. In addition, the paper presents concise asymptotic expressions for the mechanical compliance of a system consisting of a filament attached tangentially to bead handles (dumbbell system). The techniques described here can be used for noncontact estimates of polymers' and fibers' tension.

Browndye: A software package for Brownian dynamics

NASA Astrophysics Data System (ADS)

Huber, Gary A.; McCammon, J. Andrew

2010-11-01

A new software package, Browndye, is presented for simulating the diffusional encounter of two large biological molecules. It can be used to estimate second-order rate constants and encounter probabilities, and to explore reaction trajectories. Browndye builds upon previous knowledge and algorithms from software packages such as UHBD, SDA, and Macrodox, while implementing algorithms that scale to larger systems. Program summaryProgram title: Browndye Catalogue identifier: AEGT_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGT_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: MIT license, included in distribution No. of lines in distributed program, including test data, etc.: 143 618 No. of bytes in distributed program, including test data, etc.: 1 067 861 Distribution format: tar.gz Programming language: C++, OCaml ( http://caml.inria.fr/) Computer: PC, Workstation, Cluster Operating system: Linux Has the code been vectorised or parallelized?: Yes. Runs on multiple processors with shared memory using pthreads RAM: Depends linearly on size of physical system Classification: 3 External routines: uses the output of APBS [1] ( http://www.poissonboltzmann.org/apbs/) as input. APBS must be obtained and installed separately. Expat 2.0.1, CLAPACK, ocaml-expat, Mersenne Twister. These are included in the Browndye distribution. Nature of problem: Exploration and determination of rate constants of bimolecular interactions involving large biological molecules. Solution method: Brownian dynamics with electrostatic, excluded volume, van der Waals, and desolvation forces. Running time: Depends linearly on size of physical system and quadratically on precision of results. The included example executes in a few minutes.

Universal algorithm for identification of fractional Brownian motion. A case of telomere subdiffusion.

PubMed

Burnecki, Krzysztof; Kepten, Eldad; Janczura, Joanna; Bronshtein, Irena; Garini, Yuval; Weron, Aleksander

2012-11-07

We present a systematic statistical analysis of the recently measured individual trajectories of fluorescently labeled telomeres in the nucleus of living human cells. The experiments were performed in the U2OS cancer cell line. We propose an algorithm for identification of the telomere motion. By expanding the previously published data set, we are able to explore the dynamics in six time orders, a task not possible earlier. As a result, we establish a rigorous mathematical characterization of the stochastic process and identify the basic mathematical mechanisms behind the telomere motion. We find that the increments of the motion are stationary, Gaussian, ergodic, and even more chaotic--mixing. Moreover, the obtained memory parameter estimates, as well as the ensemble average mean square displacement reveal subdiffusive behavior at all time spans. All these findings statistically prove a fractional Brownian motion for the telomere trajectories, which is confirmed by a generalized p-variation test. Taking into account the biophysical nature of telomeres as monomers in the chromatin chain, we suggest polymer dynamics as a sufficient framework for their motion with no influence of other models. In addition, these results shed light on other studies of telomere motion and the alternative telomere lengthening mechanism. We hope that identification of these mechanisms will allow the development of a proper physical and biological model for telomere subdynamics. This array of tests can be easily implemented to other data sets to enable quick and accurate analysis of their statistical characteristics. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

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.

Local collective motion analysis for multi-probe dynamic imaging and microrheology

NASA Astrophysics Data System (ADS)

Khan, Manas; Mason, Thomas G.

2016-08-01

Dynamical artifacts, such as mechanical drift, advection, and hydrodynamic flow, can adversely affect multi-probe dynamic imaging and passive particle-tracking microrheology experiments. Alternatively, active driving by molecular motors can cause interesting non-Brownian motion of probes in local regions. Existing drift-correction techniques, which require large ensembles of probes or fast temporal sampling, are inadequate for handling complex spatio-temporal drifts and non-Brownian motion of localized domains containing relatively few probes. Here, we report an analytical method based on local collective motion (LCM) analysis of as few as two probes for detecting the presence of non-Brownian motion and for accurately eliminating it to reveal the underlying Brownian motion. By calculating an ensemble-average, time-dependent, LCM mean square displacement (MSD) of two or more localized probes and comparing this MSD to constituent single-probe MSDs, we can identify temporal regimes during which either thermal or athermal motion dominates. Single-probe motion, when referenced relative to the moving frame attached to the multi-probe LCM trajectory, provides a true Brownian MSD after scaling by an appropriate correction factor that depends on the number of probes used in LCM analysis. We show that LCM analysis can be used to correct many different dynamical artifacts, including spatially varying drifts, gradient flows, cell motion, time-dependent drift, and temporally varying oscillatory advection, thereby offering a significant improvement over existing approaches.

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 concentrations of our model linear polymer solutions. The results show that the polymers and the fluid are coupled very well with each other, showing no lag between their velocities. Furthermore, our results show non-Newtonian shear thinning and the characteristic flattening of the Poiseuille flow profile typically observed for polymer solutions.

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 concentrations of our model linear polymer solutions. The results show that the polymers and the fluid are coupled very well with each other, showing no lag between their velocities. Furthermore, our results show non-Newtonian shear thinning and the characteristic flattening of the Poiseuille flow profile typically observed for polymer solutions.

Brownian dynamics simulation of protein diffusion in crowded environments

NASA Astrophysics Data System (ADS)

Mereghetti, Paolo; Wade, Rebecca C.

2013-02-01

High macromolecular concentrations are a distinguishing feature of living organisms. Understanding how the high concentration of solutes affects the dynamic properties of biological macromolecules is fundamental for the comprehension of biological processes in living systems. We first describe the development of a Brownian dynamics simulation methodology to investigate the dynamic and structural properties of protein solutions using atomic-detail protein structures. We then discuss insights obtained from applying this approach to simulation of solutions of a range of types of proteins.

Field dynamics inference via spectral density estimation

NASA Astrophysics Data System (ADS)

Frank, Philipp; Steininger, Theo; Enßlin, Torsten A.

2017-11-01

Stochastic differential equations are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to solve, e.g., when modeling Brownian motion. In some cases, the equations governing the dynamics of a physical system on macroscopic scales occur to be unknown since they typically cannot be deduced from general principles. In this work, we describe how the underlying laws of a stochastic process can be approximated by the spectral density of the corresponding process. Furthermore, we show how the density can be inferred from possibly very noisy and incomplete measurements of the dynamical field. Generally, inverse problems like these can be tackled with the help of Information Field Theory. For now, we restrict to linear and autonomous processes. To demonstrate its applicability, we employ our reconstruction algorithm on a time-series and spatiotemporal processes.

Field dynamics inference via spectral density estimation.

PubMed

Frank, Philipp; Steininger, Theo; Enßlin, Torsten A

2017-11-01

Stochastic differential equations are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to solve, e.g., when modeling Brownian motion. In some cases, the equations governing the dynamics of a physical system on macroscopic scales occur to be unknown since they typically cannot be deduced from general principles. In this work, we describe how the underlying laws of a stochastic process can be approximated by the spectral density of the corresponding process. Furthermore, we show how the density can be inferred from possibly very noisy and incomplete measurements of the dynamical field. Generally, inverse problems like these can be tackled with the help of Information Field Theory. For now, we restrict to linear and autonomous processes. To demonstrate its applicability, we employ our reconstruction algorithm on a time-series and spatiotemporal processes.

Velocity Gradient Power Functional for Brownian Dynamics.

PubMed

de Las Heras, Daniel; Schmidt, Matthias

2018-01-12

We present an explicit and simple approximation for the superadiabatic excess (over ideal gas) free power functional, admitting the study of the nonequilibrium dynamics of overdamped Brownian many-body systems. The functional depends on the local velocity gradient and is systematically obtained from treating the microscopic stress distribution as a conjugate field. The resulting superadiabatic forces are beyond dynamical density functional theory and are of a viscous nature. Their high accuracy is demonstrated by comparison to simulation results.

Velocity Gradient Power Functional for Brownian Dynamics

NASA Astrophysics Data System (ADS)

de las Heras, Daniel; Schmidt, Matthias

2018-01-01

We present an explicit and simple approximation for the superadiabatic excess (over ideal gas) free power functional, admitting the study of the nonequilibrium dynamics of overdamped Brownian many-body systems. The functional depends on the local velocity gradient and is systematically obtained from treating the microscopic stress distribution as a conjugate field. The resulting superadiabatic forces are beyond dynamical density functional theory and are of a viscous nature. Their high accuracy is demonstrated by comparison to simulation results.

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

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.

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.

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.

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.

Mapping migratory flyways in Asia using dynamic Brownian bridge movement models

USGS Publications Warehouse

Palm, E.C.; Newman, S.H.; Prosser, Diann J.; Xiao, Xiangming; Luo, Ze; Batbayar, Nyambayar; Balachandran, Sivananinthaperumal; Takekawa, John Y.

2015-01-01

The dynamic Brownian bridge movement model improves our understanding of flyways by estimating relative use of regions in the flyway while providing detailed, quantitative information on migration timing and population connectivity including uncertainty between locations. This model effectively quantifies the relative importance of different migration corridors and stopover sites and may help prioritize specific areas in flyways for conservation of waterbird populations.

Hydrodynamic interactions induce movement against an external load in a ratchet dimer Brownian motor.

PubMed

Fornés, José A

2010-01-15

We use the Brownian dynamics with hydrodynamic interactions simulation in order to describe the movement of a elastically coupled dimer Brownian motor in a ratchet potential. The only external forces considered in our system were the load, the random thermal noise and an unbiased thermal fluctuation. For a given set of parameters we observe direct movement against the load force if hydrodynamic interactions were considered.

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

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 dynamics simulations of a flexible polymer chain which includes continuous resistance and multibody hydrodynamic interactions

NASA Astrophysics Data System (ADS)

Butler, Jason E.; Shaqfeh, Eric S. G.

2005-01-01

Using methods adapted from the simulation of suspension dynamics, we have developed a Brownian dynamics algorithm with multibody hydrodynamic interactions for simulating the dynamics of polymer molecules. The polymer molecule is modeled as a chain composed of a series of inextensible, rigid rods with constraints at each joint to ensure continuity of the chain. The linear and rotational velocities of each segment of the polymer chain are described by the slender-body theory of Batchelor [J. Fluid Mech. 44, 419 (1970)]. To include hydrodynamic interactions between the segments of the chain, the line distribution of forces on each segment is approximated by making a Legendre polynomial expansion of the disturbance velocity on the segment, where the first two terms of the expansion are retained in the calculation. Thus, the resulting linear force distribution is specified by a center of mass force, couple, and stresslet on each segment. This method for calculating the hydrodynamic interactions has been successfully used to simulate the dynamics of noncolloidal suspensions of rigid fibers [O. G. Harlen, R. R. Sundararajakumar, and D. L. Koch, J. Fluid Mech. 388, 355 (1999); J. E. Butler and E. S. G. Shaqfeh, J. Fluid Mech. 468, 204 (2002)]. The longest relaxation time and center of mass diffusivity are among the quantities calculated with the simulation technique. Comparisons are made for different levels of approximation of the hydrodynamic interactions, including multibody interactions, two-body interactions, and the "freely draining" case with no interactions. For the short polymer chains studied in this paper, the results indicate a difference in the apparent scaling of diffusivity with polymer length for the multibody versus two-body level of approximation for the hydrodynamic interactions.

Brownian dynamics simulations of a flexible polymer chain which includes continuous resistance and multibody hydrodynamic interactions.

PubMed

Butler, Jason E; Shaqfeh, Eric S G

2005-01-01

Using methods adapted from the simulation of suspension dynamics, we have developed a Brownian dynamics algorithm with multibody hydrodynamic interactions for simulating the dynamics of polymer molecules. The polymer molecule is modeled as a chain composed of a series of inextensible, rigid rods with constraints at each joint to ensure continuity of the chain. The linear and rotational velocities of each segment of the polymer chain are described by the slender-body theory of Batchelor [J. Fluid Mech. 44, 419 (1970)]. To include hydrodynamic interactions between the segments of the chain, the line distribution of forces on each segment is approximated by making a Legendre polynomial expansion of the disturbance velocity on the segment, where the first two terms of the expansion are retained in the calculation. Thus, the resulting linear force distribution is specified by a center of mass force, couple, and stresslet on each segment. This method for calculating the hydrodynamic interactions has been successfully used to simulate the dynamics of noncolloidal suspensions of rigid fibers [O. G. Harlen, R. R. Sundararajakumar, and D. L. Koch, J. Fluid Mech. 388, 355 (1999); J. E. Butler and E. S. G. Shaqfeh, J. Fluid Mech. 468, 204 (2002)]. The longest relaxation time and center of mass diffusivity are among the quantities calculated with the simulation technique. Comparisons are made for different levels of approximation of the hydrodynamic interactions, including multibody interactions, two-body interactions, and the "freely draining" case with no interactions. For the short polymer chains studied in this paper, the results indicate a difference in the apparent scaling of diffusivity with polymer length for the multibody versus two-body level of approximation for the hydrodynamic interactions. (c) 2005 American Institute of Physics.

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.

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

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

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.

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.

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

Exact and approximate stochastic simulation of intracellular calcium dynamics.

PubMed

Wieder, Nicolas; Fink, Rainer H A; Wegner, Frederic von

2011-01-01

In simulations of chemical systems, the main task is to find an exact or approximate solution of the chemical master equation (CME) that satisfies certain constraints with respect to computation time and accuracy. While Brownian motion simulations of single molecules are often too time consuming to represent the mesoscopic level, the classical Gillespie algorithm is a stochastically exact algorithm that provides satisfying results in the representation of calcium microdomains. Gillespie's algorithm can be approximated via the tau-leap method and the chemical Langevin equation (CLE). Both methods lead to a substantial acceleration in computation time and a relatively small decrease in accuracy. Elimination of the noise terms leads to the classical, deterministic reaction rate equations (RRE). For complex multiscale systems, hybrid simulations are increasingly proposed to combine the advantages of stochastic and deterministic algorithms. An often used exemplary cell type in this context are striated muscle cells (e.g., cardiac and skeletal muscle cells). The properties of these cells are well described and they express many common calcium-dependent signaling pathways. The purpose of the present paper is to provide an overview of the aforementioned simulation approaches and their mutual relationships in the spectrum ranging from stochastic to deterministic algorithms.

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.

Ergodicity convergence test suggests telomere motion obeys fractional dynamics

NASA Astrophysics Data System (ADS)

Kepten, E.; Bronshtein, I.; Garini, Y.

2011-04-01

Anomalous diffusion, observed in many biological processes, is a generalized description of a wide variety of processes, all obeying the same law of mean-square displacement. Identifying the basic mechanisms of these observations is important for deducing the nature of the biophysical systems measured. We implement a previously suggested method for distinguishing between fractional Langevin dynamics, fractional Brownian motion, and continuous time random walk based on the ergodic nature of the data. We apply the method together with the recently suggested P-variation test and the displacement correlation to the lately measured dynamics of telomeres in the nucleus of mammalian cells and find strong evidence that the telomeres motion obeys fractional dynamics. The ergodic dynamics are observed experimentally to fit fractional Brownian or Langevin dynamics.

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.

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.

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.

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.

Hybrid finite element and Brownian dynamics method for diffusion-controlled reactions.

PubMed

Bauler, Patricia; Huber, Gary A; McCammon, J Andrew

2012-04-28

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. This paper proposes a new hybrid diffusion method that couples the strengths of each of these two methods. The method is derived for a general multidimensional system, and is presented using a basic test case for 1D linear and radially symmetric diffusion systems.

Brownian dynamics simulations with stiff finitely extensible nonlinear elastic-Fraenkel springs as approximations to rods in bead-rod models.

PubMed

Hsieh, Chih-Chen; Jain, Semant; Larson, Ronald G

2006-01-28

A very stiff finitely extensible nonlinear elastic (FENE)-Fraenkel spring is proposed to replace the rigid rod in the bead-rod model. This allows the adoption of a fast predictor-corrector method so that large time steps can be taken in Brownian dynamics (BD) simulations without over- or understretching the stiff springs. In contrast to the simple bead-rod model, BD simulations with beads and FENE-Fraenkel (FF) springs yield a random-walk configuration at equilibrium. We compare the simulation results of the free-draining bead-FF-spring model with those for the bead-rod model in relaxation, start-up of uniaxial extensional, and simple shear flows, and find that both methods generate nearly identical results. The computational cost per time step for a free-draining BD simulation with the proposed bead-FF-spring model is about twice as high as the traditional bead-rod model with the midpoint algorithm of Liu [J. Chem. Phys. 90, 5826 (1989)]. Nevertheless, computations with the bead-FF-spring model are as efficient as those with the bead-rod model in extensional flow because the former allows larger time steps. Moreover, the Brownian contribution to the stress for the bead-FF-spring model is isotropic and therefore simplifies the calculation of the polymer stresses. In addition, hydrodynamic interaction can more easily be incorporated into the bead-FF-spring model than into the bead-rod model since the metric force arising from the non-Cartesian coordinates used in bead-rod simulations is absent from bead-spring simulations. Finally, with our newly developed bead-FF-spring model, existing computer codes for the bead-spring models can trivially be converted to ones for effective bead-rod simulations merely by replacing the usual FENE or Cohen spring law with a FENE-Fraenkel law, and this convertibility provides a very convenient way to perform multiscale BD simulations.

Brownian dynamics simulations with stiff finitely extensible nonlinear elastic-Fraenkel springs as approximations to rods in bead-rod models

NASA Astrophysics Data System (ADS)

Hsieh, Chih-Chen; Jain, Semant; Larson, Ronald G.

2006-01-01

A very stiff finitely extensible nonlinear elastic (FENE)-Fraenkel spring is proposed to replace the rigid rod in the bead-rod model. This allows the adoption of a fast predictor-corrector method so that large time steps can be taken in Brownian dynamics (BD) simulations without over- or understretching the stiff springs. In contrast to the simple bead-rod model, BD simulations with beads and FENE-Fraenkel (FF) springs yield a random-walk configuration at equilibrium. We compare the simulation results of the free-draining bead-FF-spring model with those for the bead-rod model in relaxation, start-up of uniaxial extensional, and simple shear flows, and find that both methods generate nearly identical results. The computational cost per time step for a free-draining BD simulation with the proposed bead-FF-spring model is about twice as high as the traditional bead-rod model with the midpoint algorithm of Liu [J. Chem. Phys. 90, 5826 (1989)]. Nevertheless, computations with the bead-FF-spring model are as efficient as those with the bead-rod model in extensional flow because the former allows larger time steps. Moreover, the Brownian contribution to the stress for the bead-FF-spring model is isotropic and therefore simplifies the calculation of the polymer stresses. In addition, hydrodynamic interaction can more easily be incorporated into the bead-FF-spring model than into the bead-rod model since the metric force arising from the non-Cartesian coordinates used in bead-rod simulations is absent from bead-spring simulations. Finally, with our newly developed bead-FF-spring model, existing computer codes for the bead-spring models can trivially be converted to ones for effective bead-rod simulations merely by replacing the usual FENE or Cohen spring law with a FENE-Fraenkel law, and this convertibility provides a very convenient way to perform multiscale BD simulations.

Single-molecule dynamics in nanofabricated traps

NASA Astrophysics Data System (ADS)

Cohen, Adam

2009-03-01

The Anti-Brownian Electrokinetic trap (ABEL trap) provides a means to immobilize a single fluorescent molecule in solution, without surface attachment chemistry. The ABEL trap works by tracking the Brownian motion of a single molecule, and applying feedback electric fields to induce an electrokinetic motion that approximately cancels the Brownian motion. We present a new design for the ABEL trap that allows smaller molecules to be trapped and more information to be extracted from the dynamics of a single molecule than was previously possible. In particular, we present strategies for extracting dynamically fluctuating mobilities and diffusion coefficients, as a means to probe dynamic changes in molecular charge and shape. If one trapped molecule is good, many trapped molecules are better. An array of single molecules in solution, each immobilized without surface attachment chemistry, provides an ideal test-bed for single-molecule analyses of intramolecular dynamics and intermolecular interactions. We present a technology for creating such an array, using a fused silica plate with nanofabricated dimples and a removable cover for sealing single molecules within the dimples. With this device one can watch the shape fluctuations of single molecules of DNA or study cooperative interactions in weakly associating protein complexes.

Coupling all-atom molecular dynamics simulations of ions in water with Brownian dynamics.

PubMed

Erban, Radek

2016-02-01

Molecular dynamics (MD) simulations of ions (K + , Na + , Ca 2+ and Cl - ) in aqueous solutions are investigated. Water is described using the SPC/E model. A stochastic coarse-grained description for ion behaviour is presented and parametrized using MD simulations. It is given as a system of coupled stochastic and ordinary differential equations, describing the ion position, velocity and acceleration. The stochastic coarse-grained model provides an intermediate description between all-atom MD simulations and Brownian dynamics (BD) models. It is used to develop a multiscale method which uses all-atom MD simulations in parts of the computational domain and (less detailed) BD simulations in the remainder of the domain.

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.

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.

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.

The wave-equivalent of the Black-Scholes option price: an interpretation

NASA Astrophysics Data System (ADS)

Haven, Emmanuel

2004-12-01

We propose an interpretation of the wave-equivalent of the Black-Scholes option price. We consider Nelson's version of the Brownian motion (Dynamical Theories of Brownian Motion, Princeton University Press, Princeton, NJ, 1967) and we use this specific motion as an input to produce a Black-Scholes PDE with a risk premium.

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.

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.

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

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.

Kramers problem in evolutionary strategies

NASA Astrophysics Data System (ADS)

Dunkel, J.; Ebeling, W.; Schimansky-Geier, L.; Hänggi, P.

2003-06-01

We calculate the escape rates of different dynamical processes for the case of a one-dimensional symmetric double-well potential. In particular, we compare the escape rates of a Smoluchowski process, i.e., a corresponding overdamped Brownian motion dynamics in a metastable potential landscape, with the escape rates obtained for a biologically motivated model known as the Fisher-Eigen process. The main difference between the two models is that the dynamics of the Smoluchowski process is determined by local quantities, whereas the Fisher-Eigen process is based on a global coupling (nonlocal interaction). If considered in the context of numerical optimization algorithms, both processes can be interpreted as archetypes of physically or biologically inspired evolutionary strategies. In this sense, the results discussed in this work are utile in order to evaluate the efficiency of such strategies with regard to the problem of surmounting various barriers. We find that a combination of both scenarios, starting with the Fisher-Eigen strategy, provides a most effective evolutionary strategy.

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.

Structure Analysis of Jungle-Gym-Type Gels by Brownian Dynamics Simulation

NASA Astrophysics Data System (ADS)

Ohta, Noriyoshi; Ono, Kohki; Takasu, Masako; Furukawa, Hidemitsu

2008-02-01

We investigated the structure and the formation process of two kinds of gels by Brownian dynamics simulation. The effect of flexibility of main chain oligomer was studied. From our results, hard gel with rigid main chain forms more homogeneous network structure than soft gel with flexible main chain. In soft gel, many small loops are formed, and clusters tend to shrink. This heterogeneous network structure may be caused by microgels. In the low density case, soft gel shows more heterogeneity than the high density case.

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 fluctuation, surfactant, etc.

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.

Ion Move Brownian Dynamics (IMBD)--simulations of ion transport.

PubMed

Kurczynska, Monika; Kotulska, Malgorzata

2014-01-01

Comparison of the computed characteristics and physiological measurement of ion transport through transmembrane proteins could be a useful method to assess the quality of protein structures. Simulations of ion transport should be detailed but also timeefficient. The most accurate method could be Molecular Dynamics (MD), which is very time-consuming, hence is not used for this purpose. The model which includes ion-ion interactions and reduces the simulation time by excluding water, protein and lipid molecules is Brownian Dynamics (BD). In this paper a new computer program for BD simulation of the ion transport is presented. We evaluate two methods for calculating the pore accessibility (round and irregular shape) and two representations of ion sizes (van der Waals diameter and one voxel). Ion Move Brownian Dynamics (IMBD) was tested with two nanopores: alpha-hemolysin and potassium channel KcsA. In both cases during the simulation an ion passed through the pore in less than 32 ns. Although two types of ions were in solution (potassium and chloride), only ions which agreed with the selectivity properties of the channels passed through the pores. IMBD is a new tool for the ion transport modelling, which can be used in the simulations of wide and narrow pores.

Brownian motion of a circle swimmer in a harmonic trap

NASA Astrophysics Data System (ADS)

Jahanshahi, Soudeh; Löwen, Hartmut; ten Hagen, Borge

2017-02-01

We study the dynamics of a Brownian circle swimmer with a time-dependent self-propulsion velocity in an external temporally varying harmonic potential. For several situations, the noise-free swimming paths, the noise-averaged mean trajectories, and the mean-square displacements are calculated analytically or by computer simulation. Based on our results, we discuss optimal swimming strategies in order to explore a maximum spatial range around the trap center. In particular, we find a resonance situation for the maximum escape distance as a function of the various frequencies in the system. Moreover, the influence of the Brownian noise is analyzed by comparing noise-free trajectories at zero temperature with the corresponding noise-averaged trajectories at finite temperature. The latter reveal various complex self-similar spiral or rosette-like patterns. Our predictions can be tested in experiments on artificial and biological microswimmers under dynamical external confinement.

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 smooth particle-mesh Ewald algorithm for Stokes suspension simulations: The sedimentation of fibers

NASA Astrophysics Data System (ADS)

Saintillan, David; Darve, Eric; Shaqfeh, Eric S. G.

2005-03-01

Large-scale simulations of non-Brownian rigid fibers sedimenting under gravity at zero Reynolds number have been performed using a fast algorithm. The mathematical formulation follows the previous simulations by Butler and Shaqfeh ["Dynamic simulations of the inhomogeneous sedimentation of rigid fibres," J. Fluid Mech. 468, 205 (2002)]. The motion of the fibers is described using slender-body theory, and the line distribution of point forces along their lengths is approximated by a Legendre polynomial in which only the total force, torque, and particle stresslet are retained. Periodic boundary conditions are used to simulate an infinite suspension, and both far-field hydrodynamic interactions and short-range lubrication forces are considered in all simulations. The calculation of the hydrodynamic interactions, which is typically the bottleneck for large systems with periodic boundary conditions, is accelerated using a smooth particle-mesh Ewald (SPME) algorithm previously used in molecular dynamics simulations. In SPME the slowly decaying Green's function is split into two fast-converging sums: the first involves the distribution of point forces and accounts for the singular short-range part of the interactions, while the second is expressed in terms of the Fourier transform of the force distribution and accounts for the smooth and long-range part. Because of its smoothness, the second sum can be computed efficiently on an underlying grid using the fast Fourier transform algorithm, resulting in a significant speed-up of the calculations. Systems of up to 512 fibers were simulated on a single-processor workstation, providing a different insight into the formation, structure, and dynamics of the inhomogeneities that occur in sedimenting fiber suspensions.

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.

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.

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.

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.

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.

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.

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.

Mesoscopic Simulations of Crosslinked Polymer Networks

NASA Astrophysics Data System (ADS)

Megariotis, Grigorios; Vogiatzis, Georgios G.; Schneider, Ludwig; Müller, Marcus; Theodorou, Doros N.

2016-08-01

A new methodology and the corresponding C++ code for mesoscopic simulations of elastomers are presented. The test system, crosslinked ds-1’4-polyisoprene’ is simulated with a Brownian Dynamics/kinetic Monte Carlo algorithm as a dense liquid of soft, coarse-grained beads, each representing 5-10 Kuhn segments. From the thermodynamic point of view, the system is described by a Helmholtz free-energy containing contributions from entropic springs between successive beads along a chain, slip-springs representing entanglements between beads on different chains, and non-bonded interactions. The methodology is employed for the calculation of the stress relaxation function from simulations of several microseconds at equilibrium, as well as for the prediction of stress-strain curves of crosslinked polymer networks under deformation.

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.

Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement

NASA Astrophysics Data System (ADS)

Roldán, Édgar; Gupta, Shamik

2017-08-01

We study the dynamics of overdamped Brownian particles diffusing in conservative force fields and undergoing stochastic resetting to a given location at a generic space-dependent rate of resetting. We present a systematic approach involving path integrals and elements of renewal theory that allows us to derive analytical expressions for a variety of statistics of the dynamics such as (i) the propagator prior to first reset, (ii) the distribution of the first-reset time, and (iii) the spatial distribution of the particle at long times. We apply our approach to several representative and hitherto unexplored examples of resetting dynamics. A particularly interesting example for which we find analytical expressions for the statistics of resetting is that of a Brownian particle trapped in a harmonic potential with a rate of resetting that depends on the instantaneous energy of the particle. We find that using energy-dependent resetting processes is more effective in achieving spatial confinement of Brownian particles on a faster time scale than performing quenches of parameters of the harmonic potential.

Swarming behavior of gradient-responsive Brownian particles in a porous medium.

PubMed

Grančič, Peter; Štěpánek, František

2012-07-01

Active targeting by Brownian particles in a fluid-filled porous environment is investigated by computer simulation. The random motion of the particles is enhanced by diffusiophoresis with respect to concentration gradients of chemical signals released by the particles in the proximity of a target. The mathematical model, based on a combination of the Brownian dynamics method and a diffusion problem is formulated in terms of key parameters that include the particle diffusiophoretic mobility and the signaling threshold (the distance from the target at which the particles release their chemical signals). The results demonstrate that even a relatively simple chemical signaling scheme can lead to a complex collective behavior of the particles and can be a very efficient way of guiding a swarm of Brownian particles towards a target, similarly to the way colonies of living cells communicate via secondary messengers.

Brownian dynamics simulation of fission yeast mitotic spindle formation

NASA Astrophysics Data System (ADS)

Edelmaier, Christopher

2014-03-01

The mitotic spindle segregates chromosomes during mitosis. The dynamics that establish bipolar spindle formation are not well understood. We have developed a computational model of fission-yeast mitotic spindle formation using Brownian dynamics and kinetic Monte Carlo methods. Our model includes rigid, dynamic microtubules, a spherical nuclear envelope, spindle pole bodies anchored in the nuclear envelope, and crosslinkers and crosslinking motor proteins. Crosslinkers and crosslinking motor proteins attach and detach in a grand canonical ensemble, and exert forces and torques on the attached microtubules. We have modeled increased affinity for crosslinking motor attachment to antiparallel microtubule pairs, and stabilization of microtubules in the interpolar bundle. We study parameters controlling the stability of the interpolar bundle and assembly of a bipolar spindle from initially adjacent spindle-pole bodies.

Statistical mechanical theory for steady state systems. II. Reciprocal relations and the second entropy.

PubMed

Attard, Phil

2005-04-15

The concept of second entropy is introduced for the dynamic transitions between macrostates. It is used to develop a theory for fluctuations in velocity, and is exemplified by deriving Onsager reciprocal relations for Brownian motion. The cases of free, driven, and pinned Brownian particles are treated in turn, and Stokes' law is derived. The second entropy analysis is applied to the general case of thermodynamic fluctuations, and the Onsager reciprocal relations for these are derived using the method. The Green-Kubo formulas for the transport coefficients emerge from the analysis, as do Langevin dynamics.

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.

Relaxation dynamics of internal segments of DNA chains in nanochannels

NASA Astrophysics Data System (ADS)

Jain, Aashish; Muralidhar, Abhiram; Dorfman, Kevin; Dorfman Group Team

We will present relaxation dynamics of internal segments of a DNA chain confined in nanochannel. The results have direct application in genome mapping technology, where long DNA molecules containing sequence-specific fluorescent probes are passed through an array of nanochannels to linearize them, and then the distances between these probes (the so-called ``DNA barcode'') are measured. The relaxation dynamics of internal segments set the experimental error due to dynamic fluctuations. We developed a multi-scale simulation algorithm, combining a Pruned-Enriched Rosenbluth Method (PERM) simulation of a discrete wormlike chain model with hard spheres with Brownian dynamics (BD) simulations of a bead-spring chain. Realistic parameters such as the bead friction coefficient and spring force law parameters are obtained from PERM simulations and then mapped onto the bead-spring model. The BD simulations are carried out to obtain the extension autocorrelation functions of various segments, which furnish their relaxation times. Interestingly, we find that (i) corner segments relax faster than the center segments and (ii) relaxation times of corner segments do not depend on the contour length of DNA chain, whereas the relaxation times of center segments increase linearly with DNA chain size.

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.

Effect of molecular topology on the transport properties of dendrimers in dilute solution at Θ temperature: A Brownian dynamics study

NASA Astrophysics Data System (ADS)

Bosko, Jaroslaw T.; Ravi Prakash, J.

2008-01-01

Structure and transport properties of dendrimers in dilute solution are studied with the aid of Brownian dynamics simulations. To investigate the effect of molecular topology on the properties, linear chain, star, and dendrimer molecules of comparable molecular weights are studied. A bead-spring chain model with finitely extensible springs and fluctuating hydrodynamic interactions is used to represent polymer molecules under Θ conditions. Structural properties as well as the diffusivity and zero-shear-rate intrinsic viscosity of polymers with varied degrees of branching are analyzed. Results for the free-draining case are compared to and found in very good agreement with the Rouse model predictions. Translational diffusivity is evaluated and the difference between the short-time and long-time behavior due to dynamic correlations is observed. Incorporation of hydrodynamic interactions is found to be sufficient to reproduce the maximum in the intrinsic viscosity versus molecular weight observed experimentally for dendrimers. Results of the nonequilibrium Brownian dynamics simulations of dendrimers and linear chain polymers subjected to a planar shear flow in a wide range of strain rates are also reported. The flow-induced molecular deformation of molecules is found to decrease hydrodynamic interactions and lead to the appearance of shear thickening. Further, branching is found to suppress flow-induced molecular alignment and deformation.

Multifractal detrending moving-average cross-correlation analysis

NASA Astrophysics Data System (ADS)

Jiang, Zhi-Qiang; Zhou, Wei-Xing

2011-07-01

There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross correlations. The multifractal detrended cross-correlation analysis (MFDCCA) approaches can be used to quantify such cross correlations, such as the MFDCCA based on the detrended fluctuation analysis (MFXDFA) method. We develop in this work a class of MFDCCA algorithms based on the detrending moving-average analysis, called MFXDMA. The performances of the proposed MFXDMA algorithms are compared with the MFXDFA method by extensive numerical experiments on pairs of time series generated from bivariate fractional Brownian motions, two-component autoregressive fractionally integrated moving-average processes, and binomial measures, which have theoretical expressions of the multifractal nature. In all cases, the scaling exponents hxy extracted from the MFXDMA and MFXDFA algorithms are very close to the theoretical values. For bivariate fractional Brownian motions, the scaling exponent of the cross correlation is independent of the cross-correlation coefficient between two time series, and the MFXDFA and centered MFXDMA algorithms have comparative performances, which outperform the forward and backward MFXDMA algorithms. For two-component autoregressive fractionally integrated moving-average processes, we also find that the MFXDFA and centered MFXDMA algorithms have comparative performances, while the forward and backward MFXDMA algorithms perform slightly worse. For binomial measures, the forward MFXDMA algorithm exhibits the best performance, the centered MFXDMA algorithms performs worst, and the backward MFXDMA algorithm outperforms the MFXDFA algorithm when the moment order q<0 and underperforms when q>0. We apply these algorithms to the return time series of two stock market indexes and to their volatilities. For the returns, the centered MFXDMA algorithm gives the best estimates of hxy(q) since its hxy(2) is closest to 0.5, as expected, and the MFXDFA algorithm has the second best performance. For the volatilities, the forward and backward MFXDMA algorithms give similar results, while the centered MFXDMA and the MFXDFA algorithms fail to extract rational multifractal nature.

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.

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 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.

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.

A Numerical Method for the Simulation of Skew Brownian Motion and its Application to Diffusive Shock Acceleration of Charged Particles

NASA Astrophysics Data System (ADS)

McEvoy, Erica L.

Stochastic differential equations are becoming a popular tool for modeling the transport and acceleration of cosmic rays in the heliosphere. In diffusive shock acceleration, cosmic rays diffuse across a region of discontinuity where the up- stream diffusion coefficient abruptly changes to the downstream value. Because the method of stochastic integration has not yet been developed to handle these types of discontinuities, I utilize methods and ideas from probability theory to develop a conceptual framework for the treatment of such discontinuities. Using this framework, I then produce some simple numerical algorithms that allow one to incorporate and simulate a variety of discontinuities (or boundary conditions) using stochastic integration. These algorithms were then modified to create a new algorithm which incorporates the discontinuous change in diffusion coefficient found in shock acceleration (known as Skew Brownian Motion). The originality of this algorithm lies in the fact that it is the first of its kind to be statistically exact, so that one obtains accuracy without the use of approximations (other than the machine precision error). I then apply this algorithm to model the problem of diffusive shock acceleration, modifying it to incorporate the additional effect of the discontinuous flow speed profile found at the shock. A steady-state solution is obtained that accurately simulates this phenomenon. This result represents a significant improvement over previous approximation algorithms, and will be useful for the simulation of discontinuous diffusion processes in other fields, such as biology and finance.

Continuum theory of phase separation kinetics for active Brownian particles.

PubMed

Stenhammar, Joakim; Tiribocchi, Adriano; Allen, Rosalind J; Marenduzzo, Davide; Cates, Michael E

2013-10-04

Active Brownian particles (ABPs), when subject to purely repulsive interactions, are known to undergo activity-induced phase separation broadly resembling an equilibrium (attraction-induced) gas-liquid coexistence. Here we present an accurate continuum theory for the dynamics of phase-separating ABPs, derived by direct coarse graining, capturing leading-order density gradient terms alongside an effective bulk free energy. Such gradient terms do not obey detailed balance; yet we find coarsening dynamics closely resembling that of equilibrium phase separation. Our continuum theory is numerically compared to large-scale direct simulations of ABPs and accurately accounts for domain growth kinetics, domain topologies, and coexistence densities.

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.

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.

An analogy of the charge distribution on Julia sets with the Brownian motion

NASA Astrophysics Data System (ADS)

Lopes, Artur O.

1989-09-01

A way to compute the entropy of an invariant measure of a hyperbolic rational map from the information given by a Ruelle-Perron-Frobenius operator of a generic Holder-continuous function will be shown. This result was motivated by an analogy of the Brownian motion with the dynamical system given by a rational map and the maximal measure. In the case the rational map is a polynomial, then the maximal measure is the charge distribution in the Julia set. The main theorem of this paper can be seen as a large deviation result. It is a kind of Donsker-Varadhan formula for dynamical systems.

Control of dynamical self-assembly of strongly Brownian nanoparticles through convective forces induced by ultrafast laser

NASA Astrophysics Data System (ADS)

Ilday, Serim; Akguc, Gursoy B.; Tokel, Onur; Makey, Ghaith; Yavuz, Ozgun; Yavuz, Koray; Pavlov, Ihor; Ilday, F. Omer; Gulseren, Oguz

We report a new dynamical self-assembly mechanism, where judicious use of convective and strong Brownian forces enables effective patterning of colloidal nanoparticles that are almost two orders of magnitude smaller than the laser beam. Optical trapping or tweezing effects are not involved, but the laser is used to create steep thermal gradients through multi-photon absorption, and thereby guide the colloids through convective forces. Convective forces can be thought as a positive feedback mechanism that helps to form and reinforce pattern, while Brownian motion act as a competing negative feedback mechanism to limit the growth of the pattern, as well as to increase the possibilities of bifurcation into different patterns, analogous to the competition observed in reaction-diffusion systems. By steering stochastic processes through these forces, we are able to gain control over the emergent pattern such as to form-deform-reform of a pattern, to change its shape and transport it spatially within seconds. This enables us to dynamically initiate and control large patterns comprised of hundreds of colloids. Further, by not relying on any specific chemical, optical or magnetic interaction, this new method is, in principle, completely independent of the material type being assembled.

Dynamics of a magnetic active Brownian particle under a uniform magnetic field.

PubMed

Vidal-Urquiza, Glenn C; Córdova-Figueroa, Ubaldo M

2017-11-01

The dynamics of a magnetic active Brownian particle undergoing three-dimensional Brownian motion, both translation and rotation, under the influence of a uniform magnetic field is investigated. The particle self-propels at a constant speed along its magnetic dipole moment, which reorients due to the interplay between Brownian and magnetic torques, quantified by the Langevin parameter α. In this work, the time-dependent active diffusivity and the crossover time (τ^{cross})-from ballistic to diffusive regimes-are calculated through the time-dependent correlation function of the fluctuations of the propulsion direction. The results reveal that, for any value of α, the particle undergoes a directional (or ballistic) propulsive motion at very short times (t≪τ^{cross}). In this regime, the correlation function decreases linearly with time, and the active diffusivity increases with it. It the opposite time limit (t≫τ^{cross}), the particle moves in a purely diffusive regime with a correlation function that decays asymptotically to zero and an active diffusivity that reaches a constant value equal to the long-time active diffusivity of the particle. As expected in the absence of a magnetic field (α=0), the crossover time is equal to the characteristic time scale for rotational diffusion, τ_{rot}. In the presence of a magnetic field (α>0), the correlation function, the active diffusivity, and the crossover time decrease with increasing α. The magnetic field regulates the regimes of propulsion of the particle. Here, the field reduces the period of time at which the active particle undergoes a directional motion. Consequently, the active particle rapidly reaches a diffusive regime at τ^{cross}≪τ_{rot}. In the limit of weak fields (α≪1), the crossover time decreases quadratically with α, while in the limit of strong fields (α≫1) it decays asymptotically as α^{-1}. The results are in excellent agreement with those obtained by Brownian dynamics simulations.

Dynamics of a magnetic active Brownian particle under a uniform magnetic field

NASA Astrophysics Data System (ADS)

Vidal-Urquiza, Glenn C.; Córdova-Figueroa, Ubaldo M.

2017-11-01

The dynamics of a magnetic active Brownian particle undergoing three-dimensional Brownian motion, both translation and rotation, under the influence of a uniform magnetic field is investigated. The particle self-propels at a constant speed along its magnetic dipole moment, which reorients due to the interplay between Brownian and magnetic torques, quantified by the Langevin parameter α . In this work, the time-dependent active diffusivity and the crossover time (τcross)—from ballistic to diffusive regimes—are calculated through the time-dependent correlation function of the fluctuations of the propulsion direction. The results reveal that, for any value of α , the particle undergoes a directional (or ballistic) propulsive motion at very short times (t ≪τcross ). In this regime, the correlation function decreases linearly with time, and the active diffusivity increases with it. It the opposite time limit (t ≫τcross ), the particle moves in a purely diffusive regime with a correlation function that decays asymptotically to zero and an active diffusivity that reaches a constant value equal to the long-time active diffusivity of the particle. As expected in the absence of a magnetic field (α =0 ), the crossover time is equal to the characteristic time scale for rotational diffusion, τrot. In the presence of a magnetic field (α >0 ), the correlation function, the active diffusivity, and the crossover time decrease with increasing α . The magnetic field regulates the regimes of propulsion of the particle. Here, the field reduces the period of time at which the active particle undergoes a directional motion. Consequently, the active particle rapidly reaches a diffusive regime at τcross≪τrot . In the limit of weak fields (α ≪1 ), the crossover time decreases quadratically with α , while in the limit of strong fields (α ≫1 ) it decays asymptotically as α-1. The results are in excellent agreement with those obtained by Brownian dynamics simulations.

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.

Random Matrix Theory in molecular dynamics analysis.

PubMed

Palese, Luigi Leonardo

2015-01-01

It is well known that, in some situations, principal component analysis (PCA) carried out on molecular dynamics data results in the appearance of cosine-shaped low index projections. Because this is reminiscent of the results obtained by performing PCA on a multidimensional Brownian dynamics, it has been suggested that short-time protein dynamics is essentially nothing more than a noisy signal. Here we use Random Matrix Theory to analyze a series of short-time molecular dynamics experiments which are specifically designed to be simulations with high cosine content. We use as a model system the protein apoCox17, a mitochondrial copper chaperone. Spectral analysis on correlation matrices allows to easily differentiate random correlations, simply deriving from the finite length of the process, from non-random signals reflecting the intrinsic system properties. Our results clearly show that protein dynamics is not really Brownian also in presence of the cosine-shaped low index projections on principal axes. Copyright © 2014 Elsevier B.V. All rights reserved.

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.

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 and Molecular Dynamics Study of the Association between Hydrogenase and Ferredoxin from Chlamydomonas reinhardtii

PubMed Central

Long, Hai; Chang, Christopher H.; King, Paul W.; Ghirardi, Maria L.; Kim, Kwiseon

2008-01-01

The [FeFe] hydrogenase from the green alga Chlamydomonas reinhardtii can catalyze the reduction of protons to hydrogen gas using electrons supplied from photosystem I and transferred via ferredoxin. To better understand the association of the hydrogenase and the ferredoxin, we have simulated the process over multiple timescales. A Brownian dynamics simulation method gave an initial thorough sampling of the rigid-body translational and rotational phase spaces, and the resulting trajectories were used to compute the occupancy and free-energy landscapes. Several important hydrogenase-ferredoxin encounter complexes were identified from this analysis, which were then individually simulated using atomistic molecular dynamics to provide more details of the hydrogenase and ferredoxin interaction. The ferredoxin appeared to form reasonable complexes with the hydrogenase in multiple orientations, some of which were good candidates for inclusion in a transition state ensemble of configurations for electron transfer. PMID:18621810

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

Fractional Brownian motion and the critical dynamics of zipping polymers.

PubMed

Walter, J-C; Ferrantini, A; Carlon, E; Vanderzande, C

2012-03-01

We consider two complementary polymer strands of length L attached by a common-end monomer. The two strands bind through complementary monomers and at low temperatures form a double-stranded conformation (zipping), while at high temperature they dissociate (unzipping). This is a simple model of DNA (or RNA) hairpin formation. Here we investigate the dynamics of the strands at the equilibrium critical temperature T=T(c) using Monte Carlo Rouse dynamics. We find that the dynamics is anomalous, with a characteristic time scaling as τ∼L(2.26(2)), exceeding the Rouse time ∼L(2.18). We investigate the probability distribution function, velocity autocorrelation function, survival probability, and boundary behavior of the underlying stochastic process. These quantities scale as expected from a fractional Brownian motion with a Hurst exponent H=0.44(1). We discuss similarities to and differences from unbiased polymer translocation.

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 explicit inclusion of the solvent in the description of Brownian motion allows us to better understand the behaviour of the memory kernel at those thermodynamic states near the critical region without any further approximation. This information is useful to elaborate more realistic descriptions of Brownian motion that take into account the particular details of the host medium.

Linear response approach to active Brownian particles in time-varying activity fields

NASA Astrophysics Data System (ADS)

Merlitz, Holger; Vuijk, Hidde D.; Brader, Joseph; Sharma, Abhinav; Sommer, Jens-Uwe

2018-05-01

In a theoretical and simulation study, active Brownian particles (ABPs) in three-dimensional bulk systems are exposed to time-varying sinusoidal activity waves that are running through the system. A linear response (Green-Kubo) formalism is applied to derive fully analytical expressions for the torque-free polarization profiles of non-interacting particles. The activity waves induce fluxes that strongly depend on the particle size and may be employed to de-mix mixtures of ABPs or to drive the particles into selected areas of the system. Three-dimensional Langevin dynamics simulations are carried out to verify the accuracy of the linear response formalism, which is shown to work best when the particles are small (i.e., highly Brownian) or operating at low activity levels.

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

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.

Quantum State Diffusion

NASA Astrophysics Data System (ADS)

Percival, Ian

2005-10-01

1. Introduction; 2. Brownian motion and Itô calculus; 3. Open quantum systems; 4. Quantum state diffusion; 5. Localisation; 6. Numerical methods and examples; 7. Quantum foundations; 8. Primary state diffusion; 9. Classical dynamics of quantum localisation; 10. Semiclassical theory and linear dynamics.

Nanoparticles and nonlinear thermal radiation properties in the rheology of polymeric material

NASA Astrophysics Data System (ADS)

Awais, M.; Hayat, T.; Muqaddass, N.; Ali, A.; Aqsa; Awan, Saeed Ehsan

2018-03-01

The present analysis is related to the dynamics of polymeric liquids (Oldroyd-B model) with the presence of nanoparticles. The rheological system is considered under the application of nonlinear thermal radiations. Energy and concentration equations are presented when thermophoresis and Brownian motion effects are present. Bidirectional form of stretching is considered to interpret the three-dimensional flow dynamics of polymeric liquid. Making use of the similarity transformations, problem is reduced into ordinary differential system which is approximated by using HAM. Influence of physical parameters including Deborah number, thermophoresis and Brownian motion on velocity, temperature and mass fraction expressions are plotted and analyzed. Numerical values for local Sherwood and Nusselt numbers are presented and discussed.

Quantum Darwinism in Quantum Brownian Motion

NASA Astrophysics Data System (ADS)

Blume-Kohout, Robin; Zurek, Wojciech H.

2008-12-01

Quantum Darwinism—the redundant encoding of information about a decohering system in its environment—was proposed to reconcile the quantum nature of our Universe with apparent classicality. We report the first study of the dynamics of quantum Darwinism in a realistic model of decoherence, quantum Brownian motion. Prepared in a highly squeezed state—a macroscopic superposition—the system leaves records whose redundancy increases rapidly with initial delocalization. Redundancy appears rapidly (on the decoherence time scale) and persists for a long time.

Quantum Darwinism in quantum Brownian motion.

PubMed

Blume-Kohout, Robin; Zurek, Wojciech H

2008-12-12

Quantum Darwinism--the redundant encoding of information about a decohering system in its environment--was proposed to reconcile the quantum nature of our Universe with apparent classicality. We report the first study of the dynamics of quantum Darwinism in a realistic model of decoherence, quantum Brownian motion. Prepared in a highly squeezed state--a macroscopic superposition--the system leaves records whose redundancy increases rapidly with initial delocalization. Redundancy appears rapidly (on the decoherence time scale) and persists for a long time.

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.

The special theory of Brownian relativity: equivalence principle for dynamic and static random paths and uncertainty relation for diffusion.

PubMed

Mezzasalma, Stefano A

2007-03-15

The theoretical basis of a recent theory of Brownian relativity for polymer solutions is deepened and reexamined. After the problem of relative diffusion in polymer solutions is addressed, its two postulates are formulated in all generality. The former builds a statistical equivalence between (uncorrelated) timelike and shapelike reference frames, that is, among dynamical trajectories of liquid molecules and static configurations of polymer chains. The latter defines the "diffusive horizon" as the invariant quantity to work with in the special version of the theory. Particularly, the concept of universality in polymer physics corresponds in Brownian relativity to that of covariance in the Einstein formulation. Here, a "universal" law consists of a privileged observation, performed from the laboratory rest frame and agreeing with any diffusive reference system. From the joint lack of covariance and simultaneity implied by the Brownian Lorentz-Poincaré transforms, a relative uncertainty arises, in a certain analogy with quantum mechanics. It is driven by the difference between local diffusion coefficients in the liquid solution. The same transformation class can be used to infer Fick's second law of diffusion, playing here the role of a gauge invariance preserving covariance of the spacetime increments. An overall, noteworthy conclusion emerging from this view concerns the statistics of (i) static macromolecular configurations and (ii) the motion of liquid molecules, which would be much more related than expected.

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.

Random functions via Dyson Brownian Motion: progress and problems

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

Wang, Gaoyuan; Battefeld, Thorsten

2016-09-05

We develope a computationally efficient extension of the Dyson Brownian Motion (DBM) algorithm to generate random function in C{sup 2} locally. We further explain that random functions generated via DBM show an unstable growth as the traversed distance increases. This feature restricts the use of such functions considerably if they are to be used to model globally defined ones. The latter is the case if one uses random functions to model landscapes in string theory. We provide a concrete example, based on a simple axionic potential often used in cosmology, to highlight this problem and also offer an ad hocmore » modification of DBM that suppresses this growth to some degree.« less

First passage Brownian functional properties of snowmelt dynamics

NASA Astrophysics Data System (ADS)

Dubey, Ashutosh; Bandyopadhyay, Malay

2018-04-01

In this paper, we model snow-melt dynamics in terms of a Brownian motion (BM) with purely time dependent drift and difusion and examine its first passage properties by suggesting and examining several Brownian functionals which characterize the lifetime and reactivity of such stochastic processes. We introduce several probability distribution functions (PDFs) associated with such time dependent BMs. For instance, for a BM with initial starting point x0, we derive analytical expressions for : (i) the PDF P(tf|x0) of the first passage time tf which specify the lifetime of such stochastic process, (ii) the PDF P(A|x0) of the area A till the first passage time and it provides us numerous valuable information about the total fresh water availability during melting, (iii) the PDF P(M) associated with the maximum size M of the BM process before the first passage time, and (iv) the joint PDF P(M; tm) of the maximum size M and its occurrence time tm before the first passage time. These P(M) and P(M; tm) are useful in determining the time of maximum fresh water availability and in calculating the total maximum amount of available fresh water. These PDFs are examined for the power law time dependent drift and diffusion which matches quite well with the available data of snowmelt dynamics.

Diffusion in the presence of a local attracting factor: Theory and interdisciplinary applications.

PubMed

Veermäe, Hardi; Patriarca, Marco

2017-06-01

In many complex diffusion processes the drift of random walkers is not caused by an external force, as in the case of Brownian motion, but by local variations of fitness perceived by the random walkers. In this paper, a simple but general framework is presented that describes such a type of random motion and may be of relevance in different problems, such as opinion dynamics, cultural spreading, and animal movement. To this aim, we study the problem of a random walker in d dimensions moving in the presence of a local heterogeneous attracting factor expressed in terms of an assigned position-dependent "attractiveness function." At variance with standard Brownian motion, the attractiveness function introduced here regulates both the advection and diffusion of the random walker, thus providing testable predictions for a specific form of fluctuation-relations. We discuss the relation between the drift-diffusion equation based on the attractiveness function and that describing standard Brownian motion, and we provide some explicit examples illustrating its relevance in different fields, such as animal movement, chemotactic diffusion, and social dynamics.

Kinetic nanofriction: a mechanism transition from quasi-continuous to ballistic-like Brownian regime

PubMed Central

2012-01-01

Surface diffusion of mobile adsorbates is not only the key to control the rate of dynamical processes on solid surfaces, e.g. epitaxial growth, but also of fundamental importance for recent technological applications, such as nanoscale electro-mechanical, tribological, and surface probing devices. Though several possible regimes of surface diffusion have been suggested, the nanoscale surface Brownian motion, especially in the technologically important low friction regimes, remains largely unexplored. Using molecular dynamics simulations, we show for the first time, that a C60 admolecule on a graphene substrate exhibits two distinct regimes of nanoscale Brownian motion: a quasi-continuous and a ballistic-like. A crossover between these two regimes is realized by changing the temperature of the system. We reveal that the underlying physical origin for this crossover is a mechanism transition of kinetic nanofriction arising from distinctive ways of interaction between the admolecule and the graphene substrate in these two regimes due to the temperature change. Our findings provide insight into surface mass transport and kinetic friction control at the nanoscale. PMID:22353343

Diffusion in the presence of a local attracting factor: Theory and interdisciplinary applications

NASA Astrophysics Data System (ADS)

Veermäe, Hardi; Patriarca, Marco

2017-06-01

In many complex diffusion processes the drift of random walkers is not caused by an external force, as in the case of Brownian motion, but by local variations of fitness perceived by the random walkers. In this paper, a simple but general framework is presented that describes such a type of random motion and may be of relevance in different problems, such as opinion dynamics, cultural spreading, and animal movement. To this aim, we study the problem of a random walker in d dimensions moving in the presence of a local heterogeneous attracting factor expressed in terms of an assigned position-dependent "attractiveness function." At variance with standard Brownian motion, the attractiveness function introduced here regulates both the advection and diffusion of the random walker, thus providing testable predictions for a specific form of fluctuation-relations. We discuss the relation between the drift-diffusion equation based on the attractiveness function and that describing standard Brownian motion, and we provide some explicit examples illustrating its relevance in different fields, such as animal movement, chemotactic diffusion, and social dynamics.

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.

Measuring the self-similarity exponent in Lévy stable processes of financial time series

NASA Astrophysics Data System (ADS)

Fernández-Martínez, M.; Sánchez-Granero, M. A.; Trinidad Segovia, J. E.

2013-11-01

Geometric method-based procedures, which will be called GM algorithms herein, were introduced in [M.A. Sánchez Granero, J.E. Trinidad Segovia, J. García Pérez, Some comments on Hurst exponent and the long memory processes on capital markets, Phys. A 387 (2008) 5543-5551], to efficiently calculate the self-similarity exponent of a time series. In that paper, the authors showed empirically that these algorithms, based on a geometrical approach, are more accurate than the classical algorithms, especially with short length time series. The authors checked that GM algorithms are good when working with (fractional) Brownian motions. Moreover, in [J.E. Trinidad Segovia, M. Fernández-Martínez, M.A. Sánchez-Granero, A note on geometric method-based procedures to calculate the Hurst exponent, Phys. A 391 (2012) 2209-2214], a mathematical background for the validity of such procedures to estimate the self-similarity index of any random process with stationary and self-affine increments was provided. In particular, they proved theoretically that GM algorithms are also valid to explore long-memory in (fractional) Lévy stable motions. In this paper, we prove empirically by Monte Carlo simulation that GM algorithms are able to calculate accurately the self-similarity index in Lévy stable motions and find empirical evidence that they are more precise than the absolute value exponent (denoted by AVE onwards) and the multifractal detrended fluctuation analysis (MF-DFA) algorithms, especially with a short length time series. We also compare them with the generalized Hurst exponent (GHE) algorithm and conclude that both GM2 and GHE algorithms are the most accurate to study financial series. In addition to that, we provide empirical evidence, based on the accuracy of GM algorithms to estimate the self-similarity index in Lévy motions, that the evolution of the stocks of some international market indices, such as U.S. Small Cap and Nasdaq100, cannot be modelized by means of a Brownian motion.

An iterative method for hydrodynamic interactions in Brownian dynamics simulations of polymer dynamics

NASA Astrophysics Data System (ADS)

Miao, Linling; Young, Charles D.; Sing, Charles E.

2017-07-01

Brownian Dynamics (BD) simulations are a standard tool for understanding the dynamics of polymers in and out of equilibrium. Quantitative comparison can be made to rheological measurements of dilute polymer solutions, as well as direct visual observations of fluorescently labeled DNA. The primary computational challenge with BD is the expensive calculation of hydrodynamic interactions (HI), which are necessary to capture physically realistic dynamics. The full HI calculation, performed via a Cholesky decomposition every time step, scales with the length of the polymer as O(N3). This limits the calculation to a few hundred simulated particles. A number of approximations in the literature can lower this scaling to O(N2 - N2.25), and explicit solvent methods scale as O(N); however both incur a significant constant per-time step computational cost. Despite this progress, there remains a need for new or alternative methods of calculating hydrodynamic interactions; large polymer chains or semidilute polymer solutions remain computationally expensive. In this paper, we introduce an alternative method for calculating approximate hydrodynamic interactions. Our method relies on an iterative scheme to establish self-consistency between a hydrodynamic matrix that is averaged over simulation and the hydrodynamic matrix used to run the simulation. Comparison to standard BD simulation and polymer theory results demonstrates that this method quantitatively captures both equilibrium and steady-state dynamics after only a few iterations. The use of an averaged hydrodynamic matrix allows the computationally expensive Brownian noise calculation to be performed infrequently, so that it is no longer the bottleneck of the simulation calculations. We also investigate limitations of this conformational averaging approach in ring polymers.

Brownian dynamics simulation of sickle hemoglobin bundle formation

NASA Astrophysics Data System (ADS)

Liu, Ya; Gunton, James; Chakrabarti, Amit

2010-03-01

The physical properties of biopolymer fibers, such as their stability and degree of aggregation, are implicated in many diseases, including sickle cell anemia. The natural chirality of protofilaments plays a crucial role in the formation of sickle hemoglobin fiber which leads to the permanent blockage of microvessels. We use Brownian dynamics to investigate the kinetics of fiber aggregation. The geometrical helical structure and chirality of the filaments are modeled by anisotropic patch-like interactions. We present the kinetics of fiber formation and study the possibility of a finite critical fiber bundle size. We compare our results with various experimental and theoretical results. This work is supported by grants from the NSF and the G. Harold and Leila Y. Mathers Foundation.

Modeling the electrophoretic separation of short biological molecules in nanofluidic devices

NASA Astrophysics Data System (ADS)

Fayad, Ghassan; Hadjiconstantinou, Nicolas

2010-11-01

Via comparisons with Brownian Dynamics simulations of the worm-like-chain and rigid-rod models, and the experimental results of Fu et al. [Phys. Rev. Lett., 97, 018103 (2006)], we demonstrate that, for the purposes of low-to-medium field electrophoretic separation in periodic nanofilter arrays, sufficiently short biomolecules can be modeled as point particles, with their orientational degrees of freedom accounted for using partition coefficients. This observation is used in the present work to build a particularly simple and efficient Brownian Dynamics simulation method. Particular attention is paid to the model's ability to quantitatively capture experimental results using realistic values of all physical parameters. A variance-reduction method is developed for efficiently simulating arbitrarily small forcing electric fields.

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 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.

Adaptive two-regime method: Application to front propagation

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

Robinson, Martin, E-mail: martin.robinson@maths.ox.ac.uk; Erban, Radek, E-mail: erban@maths.ox.ac.uk; Flegg, Mark, E-mail: mark.flegg@monash.edu

2014-03-28

The Adaptive Two-Regime Method (ATRM) is developed for hybrid (multiscale) stochastic simulation of reaction-diffusion problems. It efficiently couples detailed Brownian dynamics simulations with coarser lattice-based models. The ATRM is a generalization of the previously developed Two-Regime Method [Flegg et al., J. R. Soc., Interface 9, 859 (2012)] to multiscale problems which require a dynamic selection of regions where detailed Brownian dynamics simulation is used. Typical applications include a front propagation or spatio-temporal oscillations. In this paper, the ATRM is used for an in-depth study of front propagation in a stochastic reaction-diffusion system which has its mean-field model given in termsmore » of the Fisher equation [R. Fisher, Ann. Eugen. 7, 355 (1937)]. It exhibits a travelling reaction front which is sensitive to stochastic fluctuations at the leading edge of the wavefront. Previous studies into stochastic effects on the Fisher wave propagation speed have focused on lattice-based models, but there has been limited progress using off-lattice (Brownian dynamics) models, which suffer due to their high computational cost, particularly at the high molecular numbers that are necessary to approach the Fisher mean-field model. By modelling only the wavefront itself with the off-lattice model, it is shown that the ATRM leads to the same Fisher wave results as purely off-lattice models, but at a fraction of the computational cost. The error analysis of the ATRM is also presented for a morphogen gradient model.« less

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.

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.

Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders.

PubMed

Kanazawa, Kiyoshi; Sueshige, Takumi; Takayasu, Hideki; Takayasu, Misako

2018-03-30

A microscopic model is established for financial Brownian motion from the direct observation of the dynamics of high-frequency traders (HFTs) in a foreign exchange market. Furthermore, a theoretical framework parallel to molecular kinetic theory is developed for the systematic description of the financial market from microscopic dynamics of HFTs. We report first on a microscopic empirical law of traders' trend-following behavior by tracking the trajectories of all individuals, which quantifies the collective motion of HFTs but has not been captured in conventional order-book models. We next introduce the corresponding microscopic model of HFTs and present its theoretical solution paralleling molecular kinetic theory: Boltzmann-like and Langevin-like equations are derived from the microscopic dynamics via the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. Our model is the first microscopic model that has been directly validated through data analysis of the microscopic dynamics, exhibiting quantitative agreements with mesoscopic and macroscopic empirical results.

Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders

NASA Astrophysics Data System (ADS)

Kanazawa, Kiyoshi; Sueshige, Takumi; Takayasu, Hideki; Takayasu, Misako

2018-03-01

A microscopic model is established for financial Brownian motion from the direct observation of the dynamics of high-frequency traders (HFTs) in a foreign exchange market. Furthermore, a theoretical framework parallel to molecular kinetic theory is developed for the systematic description of the financial market from microscopic dynamics of HFTs. We report first on a microscopic empirical law of traders' trend-following behavior by tracking the trajectories of all individuals, which quantifies the collective motion of HFTs but has not been captured in conventional order-book models. We next introduce the corresponding microscopic model of HFTs and present its theoretical solution paralleling molecular kinetic theory: Boltzmann-like and Langevin-like equations are derived from the microscopic dynamics via the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. Our model is the first microscopic model that has been directly validated through data analysis of the microscopic dynamics, exhibiting quantitative agreements with mesoscopic and macroscopic empirical results.

Random walks of colloidal probes in viscoelastic materials

NASA Astrophysics Data System (ADS)

Khan, Manas; Mason, Thomas G.

2014-04-01

To overcome limitations of using a single fixed time step in random walk simulations, such as those that rely on the classic Wiener approach, we have developed an algorithm for exploring random walks based on random temporal steps that are uniformly distributed in logarithmic time. This improvement enables us to generate random-walk trajectories of probe particles that span a highly extended dynamic range in time, thereby facilitating the exploration of probe motion in soft viscoelastic materials. By combining this faster approach with a Maxwell-Voigt model (MVM) of linear viscoelasticity, based on a slowly diffusing harmonically bound Brownian particle, we rapidly create trajectories of spherical probes in soft viscoelastic materials over more than 12 orders of magnitude in time. Appropriate windowing of these trajectories over different time intervals demonstrates that random walk for the MVM is neither self-similar nor self-affine, even if the viscoelastic material is isotropic. We extend this approach to spatially anisotropic viscoelastic materials, using binning to calculate the anisotropic mean square displacements and creep compliances along different orthogonal directions. The elimination of a fixed time step in simulations of random processes, including random walks, opens up interesting possibilities for modeling dynamics and response over a highly extended temporal dynamic range.

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.

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.

On-chip Brownian relaxation measurements of magnetic nanobeads in the time domain

NASA Astrophysics Data System (ADS)

Østerberg, Frederik Westergaard; Rizzi, Giovanni; Hansen, Mikkel Fougt

2013-06-01

We present and demonstrate a new method for on-chip Brownian relaxation measurements on magnetic nanobeads in the time domain using magnetoresistive sensors. The beads are being magnetized by the sensor self-field arising from the bias current passed through the sensors and thus no external magnetic fields are needed. First, the method is demonstrated on Brownian relaxation measurements of beads with nominal sizes of 40, 80, 130, and 250 nm. The results are found to compare well to those obtained by an already established measurement technique in the frequency domain. Next, we demonstrate the time and frequency domain methods on Brownian relaxation detection of clustering of streptavidin coated magnetic beads in the presence of different concentrations of biotin-conjugated bovine serum albumin and obtain comparable results. In the time domain, a measurement is carried out in less than 30 s, which is about six times faster than in the frequency domain. This substantial reduction of the measurement time allows for continuous monitoring of the bead dynamics vs. time and opens for time-resolved studies, e.g., of binding kinetics.

Atomic detail brownian dynamics simulations of concentrated protein solutions with a mean field treatment of hydrodynamic interactions.

PubMed

Mereghetti, Paolo; Wade, Rebecca C

2012-07-26

High macromolecular concentrations are a distinguishing feature of living organisms. Understanding how the high concentration of solutes affects the dynamic properties of biological macromolecules is fundamental for the comprehension of biological processes in living systems. In this paper, we describe the implementation of mean field models of translational and rotational hydrodynamic interactions into an atomically detailed many-protein brownian dynamics simulation method. Concentrated solutions (30-40% volume fraction) of myoglobin, hemoglobin A, and sickle cell hemoglobin S were simulated, and static structure factors, oligomer formation, and translational and rotational self-diffusion coefficients were computed. Good agreement of computed properties with available experimental data was obtained. The results show the importance of both solvent mediated interactions and weak protein-protein interactions for accurately describing the dynamics and the association properties of concentrated protein solutions. Specifically, they show a qualitative difference in the translational and rotational dynamics of the systems studied. Although the translational diffusion coefficient is controlled by macromolecular shape and hydrodynamic interactions, the rotational diffusion coefficient is affected by macromolecular shape, direct intermolecular interactions, and both translational and rotational hydrodynamic interactions.

Homology Model of the GABAA Receptor Examined Using Brownian Dynamics

PubMed Central

O'Mara, Megan; Cromer, Brett; Parker, Michael; Chung, Shin-Ho

2005-01-01

We have developed a homology model of the GABAA receptor, using the subunit combination of α1β2γ2, the most prevalent type in the mammalian brain. The model is produced in two parts: the membrane-embedded channel domain and the extracellular N-terminal domain. The pentameric transmembrane domain model is built by modeling each subunit by homology with the equivalent subunit of the heteropentameric acetylcholine receptor transmembrane domain. This segment is then joined with the extracellular domain built by homology with the acetylcholine binding protein. The all-atom model forms a wide extracellular vestibule that is connected to an oval chamber near the external surface of the membrane. A narrow, cylindrical transmembrane channel links the outer segment of the pore to a shallow intracellular vestibule. The physiological properties of the model so constructed are examined using electrostatic calculations and Brownian dynamics simulations. A deep energy well of ∼80 kT accommodates three Cl− ions in the narrow transmembrane channel and seven Cl− ions in the external vestibule. Inward permeation takes place when one of the ions queued in the external vestibule enters the narrow segment and ejects the innermost ion. The model, when incorporated into Brownian dynamics, reproduces key experimental features, such as the single-channel current-voltage-concentration profiles. Finally, we simulate the γ2 K289M epilepsy inducing mutation and examine Cl− ion permeation through the mutant receptor. PMID:15749776

Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning.

PubMed

Hellander, Stefan; Hellander, Andreas; Petzold, Linda

2017-12-21

The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian dynamics or Green's function reaction dynamics, the RDME can be orders of magnitude faster if the lattice spacing can be chosen coarse enough. However, strongly diffusion-controlled reactions mandate a very fine mesh resolution for acceptable accuracy. It is common that reactions in the same model differ in their degree of diffusion control and therefore require different degrees of mesh resolution. This renders mesoscopic simulation inefficient for systems with multiscale properties. Mesoscopic-microscopic hybrid methods address this problem by resolving the most challenging reactions with a microscale, off-lattice simulation. However, all methods to date require manual partitioning of a system, effectively limiting their usefulness as "black-box" simulation codes. In this paper, we propose a hybrid simulation algorithm with automatic system partitioning based on indirect a priori error estimates. We demonstrate the accuracy and efficiency of the method on models of diffusion-controlled networks in 3D.

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.

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.

Communication: Dominance of extreme statistics in a prototype many-body Brownian ratchet.

PubMed

Hohlfeld, Evan; Geissler, Phillip L

2014-10-28

Many forms of cell motility rely on Brownian ratchet mechanisms that involve multiple stochastic processes. We present a computational and theoretical study of the nonequilibrium statistical dynamics of such a many-body ratchet, in the specific form of a growing polymer gel that pushes a diffusing obstacle. We find that oft-neglected correlations among constituent filaments impact steady-state kinetics and significantly deplete the gel's density within molecular distances of its leading edge. These behaviors are captured quantitatively by a self-consistent theory for extreme fluctuations in filaments' spatial distribution.

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.

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

Force-velocity relation for actin-polymerization-driven motility from Brownian dynamics simulations.

PubMed

Lee, Kun-Chun; Liu, Andrea J

2009-09-02

We report numerical simulation results for the force-velocity relation for actin-polymerization-driven motility. We use Brownian dynamics to solve a physically consistent formulation of the dendritic nucleation model with semiflexible filaments that self-assemble and push a disk. We find that at small loads, the disk speed is independent of load, whereas at high loads, the speed decreases and vanishes at a characteristic stall pressure. Our results demonstrate that at small loads, the velocity is controlled by the reaction rates, whereas at high loads the stall pressure is determined by the mechanical properties of the branched actin network. The behavior is consistent with experiments and with our recently proposed self-diffusiophoretic mechanism for actin-polymerization-driven motility. New in vitro experiments to measure the force-velocity relation are proposed.

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.

Mapping migratory flyways in Asia using dynamic Brownian bridge movement models.

PubMed

Palm, Eric C; Newman, Scott H; Prosser, Diann J; Xiao, Xiangming; Ze, Luo; Batbayar, Nyambayar; Balachandran, Sivananinthaperumal; Takekawa, John Y

2015-01-01

Identifying movement routes and stopover sites is necessary for developing effective management and conservation strategies for migratory animals. In the case of migratory birds, a collection of migration routes, known as a flyway, is often hundreds to thousands of kilometers long and can extend across political boundaries. Flyways encompass the entire geographic range between the breeding and non-breeding areas of a population, species, or a group of species, and they provide spatial frameworks for management and conservation across international borders. Existing flyway maps are largely qualitative accounts based on band returns and survey data rather than observed movement routes. In this study, we use satellite and GPS telemetry data and dynamic Brownian bridge movement models to build upon existing maps and describe waterfowl space use probabilistically in the Central Asian and East Asian-Australasian Flyways. Our approach provided new information on migratory routes that was not easily attainable with existing methods to describe flyways. Utilization distributions from dynamic Brownian bridge movement models identified key staging and stopover sites, migration corridors and general flyway outlines in the Central Asian and East Asian-Australasian Flyways. A map of space use from ruddy shelducks depicted two separate movement corridors within the Central Asian Flyway, likely representing two distinct populations that show relatively strong connectivity between breeding and wintering areas. Bar-headed geese marked at seven locations in the Central Asian Flyway showed heaviest use at several stopover sites in the same general region of high-elevation lakes along the eastern Qinghai-Tibetan Plateau. Our analysis of data from multiple Anatidae species marked at sites throughout Asia highlighted major movement corridors across species and confirmed that the Central Asian and East Asian-Australasian Flyways were spatially distinct. The dynamic Brownian bridge movement model improves our understanding of flyways by estimating relative use of regions in the flyway while providing detailed, quantitative information on migration timing and population connectivity including uncertainty between locations. This model effectively quantifies the relative importance of different migration corridors and stopover sites and may help prioritize specific areas in flyways for conservation of waterbird populations.

A novel model for the chaotic dynamics of superdiffusion

NASA Astrophysics Data System (ADS)

Cushman, J. H.; Park, M.; O'Malley, D.

2009-04-01

Previously we've shown that by modeling the convective velocity in a turbulent flow field as Brownian, one obtains Richardson super diffusion where the expected distance between pairs of particles scales with time cubed. By proving generalized central limit type theorems it's possible to show that modeling the velocity or the acceleration as α-stable Levy gives rise to more general scaling laws that can easily explain other super diffusive regimes. The problem with this latter approach is that the mean square displacement of a particle is infinite. Here we provide an alternate approach that gives a power law mean square displacement of any desired order. We do so by constructing compressed and stretched extensions to Brownian motion. The finite size Lyapunov exponent, the underlying stochastic differential equation and its corresponding Fokker-Planck equations are derived. The fractal dimension of these processes turns out to be the same as that of classical Brownian motion.

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

A comment on measuring the Hurst exponent of financial time series

NASA Astrophysics Data System (ADS)

Couillard, Michel; Davison, Matt

2005-03-01

A fundamental hypothesis of quantitative finance is that stock price variations are independent and can be modeled using Brownian motion. In recent years, it was proposed to use rescaled range analysis and its characteristic value, the Hurst exponent, to test for independence in financial time series. Theoretically, independent time series should be characterized by a Hurst exponent of 1/2. However, finite Brownian motion data sets will always give a value of the Hurst exponent larger than 1/2 and without an appropriate statistical test such a value can mistakenly be interpreted as evidence of long term memory. We obtain a more precise statistical significance test for the Hurst exponent and apply it to real financial data sets. Our empirical analysis shows no long-term memory in some financial returns, suggesting that Brownian motion cannot be rejected as a model for price dynamics.

Microsecond Simulations of DNA and Ion Transport in Nanopores with Novel Ion-Ion and Ion-Nucleotides Effective Potentials

PubMed Central

De Biase, Pablo M.; Markosyan, Suren; Noskov, Sergei

2014-01-01

We developed a novel scheme based on the Grand-Canonical Monte-Carlo/Brownian Dynamics (GCMC/BD) simulations and have extended it to studies of ion currents across three nanopores with the potential for ssDNA sequencing: solid-state nanopore Si3N4, α-hemolysin, and E111N/M113Y/K147N mutant. To describe nucleotide-specific ion dynamics compatible with ssDNA coarse-grained model, we used the Inverse Monte-Carlo protocol, which maps the relevant ion-nucleotide distribution functions from an all-atom MD simulations. Combined with the previously developed simulation platform for Brownian Dynamic (BD) simulations of ion transport, it allows for microsecond- and millisecond-long simulations of ssDNA dynamics in nanopore with a conductance computation accuracy that equals or exceeds that of all-atom MD simulations. In spite of the simplifications, the protocol produces results that agree with the results of previous studies on ion conductance across open channels and provide direct correlations with experimentally measured blockade currents and ion conductances that have been estimated from all-atom MD simulations. PMID:24738152

Computational Models for Nanoscale Fluid Dynamics and Transport Inspired by Nonequilibrium Thermodynamics1

PubMed Central

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

2017-01-01

Traditionally, the numerical computation of particle motion in a fluid is resolved through computational fluid dynamics (CFD). However, resolving the motion of nanoparticles poses additional challenges due to the coupling between the Brownian and hydrodynamic forces. Here, we focus on the Brownian motion of a nanoparticle coupled to adhesive interactions and confining-wall-mediated hydrodynamic interactions. We discuss several techniques that are founded on the basis of combining CFD methods with the theory of nonequilibrium statistical mechanics in order to simultaneously conserve thermal equipartition and to show correct hydrodynamic correlations. These include the fluctuating hydrodynamics (FHD) method, the generalized Langevin method, the hybrid method, and the deterministic method. Through the examples discussed, we also show a top-down multiscale progression of temporal dynamics from the colloidal scales to the molecular scales, and the associated fluctuations, hydrodynamic correlations. While the motivation and the examples discussed here pertain to nanoscale fluid dynamics and mass transport, the methodologies presented are rather general and can be easily adopted to applications in convective heat transfer. PMID:28035168

Emergence of nonwhite noise in Langevin dynamics with magnetic Lorentz force

NASA Astrophysics Data System (ADS)

Chun, Hyun-Myung; Durang, Xavier; Noh, Jae Dong

2018-03-01

We investigate the low mass limit of Langevin dynamics for a charged Brownian particle driven by a magnetic Lorentz force. In the low mass limit, velocity variables relaxing quickly are coarse-grained out to yield effective dynamics for position variables. Without the Lorentz force, the low mass limit is equivalent to the high friction limit. Both cases share the same Langevin equation that is obtained by setting the mass to zero. The equivalence breaks down in the presence of the Lorentz force. The low mass limit cannot be achieved by setting the mass to zero. The limit is also distinct from the large friction limit. We derive the effective equations of motion in the low mass limit. The resulting stochastic differential equation involves a nonwhite noise whose correlation matrix has antisymmetric components. We demonstrate the importance of the nonwhite noise by investigating the heat dissipation by a driven Brownian particle, where the emergent nonwhite noise has a physically measurable effect.

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

Multi-Dielectric Brownian Dynamics and Design-Space-Exploration Studies of Permeation in Ion Channels.

PubMed

Siksik, May; Krishnamurthy, Vikram

2017-09-01

This paper proposes a multi-dielectric Brownian dynamics simulation framework for design-space-exploration (DSE) studies of ion-channel permeation. The goal of such DSE studies is to estimate the channel modeling-parameters that minimize the mean-squared error between the simulated and expected "permeation characteristics." To address this computational challenge, we use a methodology based on statistical inference that utilizes the knowledge of channel structure to prune the design space. We demonstrate the proposed framework and DSE methodology using a case study based on the KcsA ion channel, in which the design space is successfully reduced from a 6-D space to a 2-D space. Our results show that the channel dielectric map computed using the framework matches with that computed directly using molecular dynamics with an error of 7%. Finally, the scalability and resolution of the model used are explored, and it is shown that the memory requirements needed for DSE remain constant as the number of parameters (degree of heterogeneity) increases.

Near Wall Dynamics in Colloidal Suspensions Studied by Evansescent Wave Dynamic Light Scattering

NASA Astrophysics Data System (ADS)

Lang, Peter R.

2011-03-01

The dynamics of dispersed colloidal particles is slowed down, and becomes anisotropic in the ultimate vicinity of a flat wall due to the wall drag effect. Although theoretically predicted in the early 20th century, experimental verification of this effect for Brownian particles became possible only in the late 80s. Since then a variety of experimental investigations on near wall Brownian dynamics by evanescent wave dynamic light scattering (EWDLS) has been published. In this contribution the method of EWDLS will be briefly introduced, experiments at low and high colloid concentration for hard-sphere suspensions, and the theoretical prediction for measured initial slopes of correlation functions will be discussed. On increasing the particle concentration the influence of the wall drag effect is found to diminishes gradually, until it becomes negligible at volume fractions above ϕ 0.35. The effect that a wall exerts on the orientational dynamics was investigated for different kinds of colloids. Experiments, simulations and a virial expansion theory show that rotational dynamics is slowed down as well. However, the effect is prominent in EWDLS only if the particles' short axis is of the order of the evanescent wave penetration depth. The author acknowledges financial support from the EU through FP7, project Nanodirect (Grant 395 No. NMP4-SL-2008-213948).

Molecular Dynamics Simulations of Orai Reveal How the Third Transmembrane Segment Contributes to Hydration and Ca2+ Selectivity in Calcium Release-Activated Calcium Channels.

PubMed

Alavizargar, Azadeh; Berti, Claudio; Ejtehadi, Mohammad Reza; Furini, Simone

2018-04-26

Calcium release-activated calcium (CRAC) channels open upon depletion of Ca 2+ from the endoplasmic reticulum, and when open, they are permeable to a selective flux of calcium ions. The atomic structure of Orai, the pore domain of CRAC channels, from Drosophila melanogaster has revealed many details about conduction and selectivity in this family of ion channels. However, it is still unclear how residues on the third transmembrane helix can affect the conduction properties of the channel. Here, molecular dynamics and Brownian dynamics simulations were employed to analyze how a conserved glutamate residue on the third transmembrane helix (E262) contributes to selectivity. The comparison between the wild-type and mutated channels revealed a severe impact of the mutation on the hydration pattern of the pore domain and on the dynamics of residues K270, and Brownian dynamics simulations proved that the altered configuration of residues K270 in the mutated channel impairs selectivity to Ca 2+ over Na + . The crevices of water molecules, revealed by molecular dynamics simulations, are perfectly located to contribute to the dynamics of the hydrophobic gate and the basic gate, suggesting a possible role in channel opening and in selectivity function.

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.

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.

A Huygens principle for diffusion and anomalous diffusion in spatially extended systems

PubMed Central

Gottwald, Georg A.; Melbourne, Ian

2013-01-01

We present a universal view on diffusive behavior in chaotic spatially extended systems for anisotropic and isotropic media. For anisotropic systems, strong chaos leads to diffusive behavior (Brownian motion with drift) and weak chaos leads to superdiffusive behavior (Lévy processes with drift). For isotropic systems, the drift term vanishes and strong chaos again leads to Brownian motion. We establish the existence of a nonlinear Huygens principle for weakly chaotic systems in isotropic media whereby the dynamics behaves diffusively in even space dimension and exhibits superdiffusive behavior in odd space dimensions. PMID:23653481

Molecular motors that digest their track to rectify Brownian motion: processive movement of exonuclease enzymes.

PubMed

Xie, Ping

2009-09-16

A general model is presented for the processive movement of molecular motors such as λ-exonuclease, RecJ and exonuclease I that use digestion of a DNA track to rectify Brownian motion along this track. Using this model, the translocation dynamics of these molecular motors is studied. The sequence-dependent pausing of λ-exonuclease, which results from a site-specific high affinity DNA interaction, is also studied. The theoretical results are consistent with available experimental data. Moreover, the model is used to predict the lifetime distribution and force dependence of these paused states.

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.

Smoldyn on graphics processing units: massively parallel Brownian dynamics simulations.

PubMed

Dematté, Lorenzo

2012-01-01

Space is a very important aspect in the simulation of biochemical systems; recently, the need for simulation algorithms able to cope with space is becoming more and more compelling. Complex and detailed models of biochemical systems need to deal with the movement of single molecules and particles, taking into consideration localized fluctuations, transportation phenomena, and diffusion. A common drawback of spatial models lies in their complexity: models can become very large, and their simulation could be time consuming, especially if we want to capture the systems behavior in a reliable way using stochastic methods in conjunction with a high spatial resolution. In order to deliver the promise done by systems biology to be able to understand a system as whole, we need to scale up the size of models we are able to simulate, moving from sequential to parallel simulation algorithms. In this paper, we analyze Smoldyn, a widely diffused algorithm for stochastic simulation of chemical reactions with spatial resolution and single molecule detail, and we propose an alternative, innovative implementation that exploits the parallelism of Graphics Processing Units (GPUs). The implementation executes the most computational demanding steps (computation of diffusion, unimolecular, and bimolecular reaction, as well as the most common cases of molecule-surface interaction) on the GPU, computing them in parallel on each molecule of the system. The implementation offers good speed-ups and real time, high quality graphics output

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

Dynamical stability of the one-dimensional rigid Brownian rotator: the role of the rotator’s spatial size and shape

NASA Astrophysics Data System (ADS)

Jeknić-Dugić, Jasmina; Petrović, Igor; Arsenijević, Momir; Dugić, Miroljub

2018-05-01

We investigate dynamical stability of a single propeller-like shaped molecular cogwheel modelled as the fixed-axis rigid rotator. In the realistic situations, rotation of the finite-size cogwheel is subject to the environmentally-induced Brownian-motion effect that we describe by utilizing the quantum Caldeira-Leggett master equation. Assuming the initially narrow (classical-like) standard deviations for the angle and the angular momentum of the rotator, we investigate the dynamics of the first and second moments depending on the size, i.e. on the number of blades of both the free rotator as well as of the rotator in the external harmonic field. The larger the standard deviations, the less stable (i.e. less predictable) rotation. We detect the absence of the simple and straightforward rules for utilizing the rotator’s stability. Instead, a number of the size-related criteria appear whose combinations may provide the optimal rules for the rotator dynamical stability and possibly control. In the realistic situations, the quantum-mechanical corrections, albeit individually small, may effectively prove non-negligible, and also revealing subtlety of the transition from the quantum to the classical dynamics of the rotator. As to the latter, we detect a strong size-dependence of the transition to the classical dynamics beyond the quantum decoherence process.

Multiscale modeling and simulation of microtubule-motor-protein assemblies

NASA Astrophysics Data System (ADS)

Gao, Tong; Blackwell, Robert; Glaser, Matthew A.; Betterton, M. D.; Shelley, Michael J.

2015-12-01

Microtubules and motor proteins self-organize into biologically important assemblies including the mitotic spindle and the centrosomal microtubule array. Outside of cells, microtubule-motor mixtures can form novel active liquid-crystalline materials driven out of equilibrium by adenosine triphosphate-consuming motor proteins. Microscopic motor activity causes polarity-dependent interactions between motor proteins and microtubules, but how these interactions yield larger-scale dynamical behavior such as complex flows and defect dynamics is not well understood. We develop a multiscale theory for microtubule-motor systems in which Brownian dynamics simulations of polar microtubules driven by motors are used to study microscopic organization and stresses created by motor-mediated microtubule interactions. We identify polarity-sorting and crosslink tether relaxation as two polar-specific sources of active destabilizing stress. We then develop a continuum Doi-Onsager model that captures polarity sorting and the hydrodynamic flows generated by these polar-specific active stresses. In simulations of active nematic flows on immersed surfaces, the active stresses drive turbulent flow dynamics and continuous generation and annihilation of disclination defects. The dynamics follow from two instabilities, and accounting for the immersed nature of the experiment yields unambiguous characteristic length and time scales. When turning off the hydrodynamics in the Doi-Onsager model, we capture formation of polar lanes as observed in the Brownian dynamics simulation.

Multiscale modeling and simulation of microtubule-motor-protein assemblies.

PubMed

Gao, Tong; Blackwell, Robert; Glaser, Matthew A; Betterton, M D; Shelley, Michael J

2015-01-01

Microtubules and motor proteins self-organize into biologically important assemblies including the mitotic spindle and the centrosomal microtubule array. Outside of cells, microtubule-motor mixtures can form novel active liquid-crystalline materials driven out of equilibrium by adenosine triphosphate-consuming motor proteins. Microscopic motor activity causes polarity-dependent interactions between motor proteins and microtubules, but how these interactions yield larger-scale dynamical behavior such as complex flows and defect dynamics is not well understood. We develop a multiscale theory for microtubule-motor systems in which Brownian dynamics simulations of polar microtubules driven by motors are used to study microscopic organization and stresses created by motor-mediated microtubule interactions. We identify polarity-sorting and crosslink tether relaxation as two polar-specific sources of active destabilizing stress. We then develop a continuum Doi-Onsager model that captures polarity sorting and the hydrodynamic flows generated by these polar-specific active stresses. In simulations of active nematic flows on immersed surfaces, the active stresses drive turbulent flow dynamics and continuous generation and annihilation of disclination defects. The dynamics follow from two instabilities, and accounting for the immersed nature of the experiment yields unambiguous characteristic length and time scales. When turning off the hydrodynamics in the Doi-Onsager model, we capture formation of polar lanes as observed in the Brownian dynamics simulation.

Multiscale modeling and simulation of microtubule–motor-protein assemblies

PubMed Central

Gao, Tong; Blackwell, Robert; Glaser, Matthew A.; Betterton, M. D.; Shelley, Michael J.

2016-01-01

Microtubules and motor proteins self-organize into biologically important assemblies including the mitotic spindle and the centrosomal microtubule array. Outside of cells, microtubule-motor mixtures can form novel active liquid-crystalline materials driven out of equilibrium by adenosine triphosphate–consuming motor proteins. Microscopic motor activity causes polarity-dependent interactions between motor proteins and microtubules, but how these interactions yield larger-scale dynamical behavior such as complex flows and defect dynamics is not well understood. We develop a multiscale theory for microtubule-motor systems in which Brownian dynamics simulations of polar microtubules driven by motors are used to study microscopic organization and stresses created by motor-mediated microtubule interactions. We identify polarity-sorting and crosslink tether relaxation as two polar-specific sources of active destabilizing stress. We then develop a continuum Doi-Onsager model that captures polarity sorting and the hydrodynamic flows generated by these polar-specific active stresses. In simulations of active nematic flows on immersed surfaces, the active stresses drive turbulent flow dynamics and continuous generation and annihilation of disclination defects. The dynamics follow from two instabilities, and accounting for the immersed nature of the experiment yields unambiguous characteristic length and time scales. When turning off the hydrodynamics in the Doi-Onsager model, we capture formation of polar lanes as observed in the Brownian dynamics simulation. PMID:26764729

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

Predicting protein interactions by Brownian dynamics simulations.

PubMed

Meng, Xuan-Yu; Xu, Yu; Zhang, Hong-Xing; Mezei, Mihaly; Cui, Meng

2012-01-01

We present a newly adapted Brownian-Dynamics (BD)-based protein docking method for predicting native protein complexes. The approach includes global BD conformational sampling, compact complex selection, and local energy minimization. In order to reduce the computational costs for energy evaluations, a shell-based grid force field was developed to represent the receptor protein and solvation effects. The performance of this BD protein docking approach has been evaluated on a test set of 24 crystal protein complexes. Reproduction of experimental structures in the test set indicates the adequate conformational sampling and accurate scoring of this BD protein docking approach. Furthermore, we have developed an approach to account for the flexibility of proteins, which has been successfully applied to reproduce the experimental complex structure from the structure of two unbounded proteins. These results indicate that this adapted BD protein docking approach can be useful for the prediction of protein-protein interactions.

Brownian motion and entropic torque driven motion of domain walls in antiferromagnets

NASA Astrophysics Data System (ADS)

Yan, Zhengren; Chen, Zhiyuan; Qin, Minghui; Lu, Xubing; Gao, Xingsen; Liu, Junming

2018-02-01

We study the spin dynamics in antiferromagnetic nanowire under an applied temperature gradient using micromagnetic simulations on a classical spin model with a uniaxial anisotropy. The entropic torque driven domain-wall motion and the Brownian motion are discussed in detail, and their competition determines the antiferromagnetic wall motion towards the hotter or colder region. Furthermore, the spin dynamics in an antiferromagnet can be well tuned by the anisotropy and the temperature gradient. Thus, this paper not only strengthens the main conclusions obtained in earlier works [Kim et al., Phys. Rev. B 92, 020402(R) (2015), 10.1103/PhysRevB.92.020402; Selzer et al., Phys. Rev. Lett. 117, 107201 (2016), 10.1103/PhysRevLett.117.107201], but more importantly gives the concrete conditions under which these conclusions apply, respectively. Our results may provide useful information on the antiferromagnetic spintronics for future experiments and storage device design.

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.

Elastic moduli of a Brownian colloidal glass former

NASA Astrophysics Data System (ADS)

Fritschi, S.; Fuchs, M.

2018-01-01

The static, dynamic and flow-dependent shear moduli of a binary mixture of Brownian hard disks are studied by an event-driven molecular dynamics simulation. Thereby, the emergence of rigidity close to the glass transition encoded in the static shear modulus G_∞ is accessed by three methods. Results from shear stress auto-correlation functions, elastic dispersion relations, and the elastic response to strain deformations upon the start-up of shear flow are compared. This enables one to sample the time-dependent shear modulus G(t) consistently over several decades in time. By that a very precise specification of the glass transition point and of G_∞ is feasible. Predictions by mode coupling theory of a finite shear modulus at the glass transition, of α-scaling in fluid states close to the transition, and of shear induced decay in yielding glass states are tested and broadly verified.

Dynamic heterogeneity and non-Gaussian statistics for acetylcholine receptors on live cell membrane

NASA Astrophysics Data System (ADS)

He, W.; Song, H.; Su, Y.; Geng, L.; Ackerson, B. J.; Peng, H. B.; Tong, P.

2016-05-01

The Brownian motion of molecules at thermal equilibrium usually has a finite correlation time and will eventually be randomized after a long delay time, so that their displacement follows the Gaussian statistics. This is true even when the molecules have experienced a complex environment with a finite correlation time. Here, we report that the lateral motion of the acetylcholine receptors on live muscle cell membranes does not follow the Gaussian statistics for normal Brownian diffusion. From a careful analysis of a large volume of the protein trajectories obtained over a wide range of sampling rates and long durations, we find that the normalized histogram of the protein displacements shows an exponential tail, which is robust and universal for cells under different conditions. The experiment indicates that the observed non-Gaussian statistics and dynamic heterogeneity are inherently linked to the slow-active remodelling of the underlying cortical actin network.

Momentum conserving Brownian dynamics propagator for complex soft matter fluids

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

Padding, J. T.; Briels, W. J.

2014-12-28

We present a Galilean invariant, momentum conserving first order Brownian dynamics scheme for coarse-grained simulations of highly frictional soft matter systems. Friction forces are taken to be with respect to moving background material. The motion of the background material is described by locally averaged velocities in the neighborhood of the dissolved coarse coordinates. The velocity variables are updated by a momentum conserving scheme. The properties of the stochastic updates are derived through the Chapman-Kolmogorov and Fokker-Planck equations for the evolution of the probability distribution of coarse-grained position and velocity variables, by requiring the equilibrium distribution to be a stationary solution.more » We test our new scheme on concentrated star polymer solutions and find that the transverse current and velocity time auto-correlation functions behave as expected from hydrodynamics. In particular, the velocity auto-correlation functions display a long time tail in complete agreement with hydrodynamics.« less

Exact probability distribution functions for Parrondo's games

NASA Astrophysics Data System (ADS)

Zadourian, Rubina; Saakian, David B.; Klümper, Andreas

2016-12-01

We study the discrete time dynamics of Brownian ratchet models and Parrondo's games. Using the Fourier transform, we calculate the exact probability distribution functions for both the capital dependent and history dependent Parrondo's games. In certain cases we find strong oscillations near the maximum of the probability distribution with two limiting distributions for odd and even number of rounds of the game. Indications of such oscillations first appeared in the analysis of real financial data, but now we have found this phenomenon in model systems and a theoretical understanding of the phenomenon. The method of our work can be applied to Brownian ratchets, molecular motors, and portfolio optimization.

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.

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.

Diffusion limit of Lévy-Lorentz gas is Brownian motion

NASA Astrophysics Data System (ADS)

Magdziarz, Marcin; Szczotka, Wladyslaw

2018-07-01

In this paper we analyze asymptotic behaviour of a stochastic process called Lévy-Lorentz gas. This process is aspecial kind of continuous-time random walk in which walker moves in the fixed environment composed of scattering points. Upon each collision the walker performs a flight to the nearest scattering point. This type of dynamics is observed in Lévy glasses or long quenched polymers. We show that the diffusion limit of Lévy-Lorentz gas with finite mean distance between scattering centers is the standard Brownian motion. Thus, for long times the behaviour of the Lévy-Lorentz gas is close to the diffusive regime.

Exact probability distribution functions for Parrondo's games.

PubMed

Zadourian, Rubina; Saakian, David B; Klümper, Andreas

2016-12-01

We study the discrete time dynamics of Brownian ratchet models and Parrondo's games. Using the Fourier transform, we calculate the exact probability distribution functions for both the capital dependent and history dependent Parrondo's games. In certain cases we find strong oscillations near the maximum of the probability distribution with two limiting distributions for odd and even number of rounds of the game. Indications of such oscillations first appeared in the analysis of real financial data, but now we have found this phenomenon in model systems and a theoretical understanding of the phenomenon. The method of our work can be applied to Brownian ratchets, molecular motors, and portfolio optimization.

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.

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.

Brownian motion of a self-propelled particle.

PubMed

ten Hagen, B; van Teeffelen, S; Löwen, H

2011-05-18

Overdamped Brownian motion of a self-propelled particle is studied by solving the Langevin equation analytically. On top of translational and rotational diffusion, in the context of the presented model, the 'active' particle is driven along its internal orientation axis. We calculate the first four moments of the probability distribution function for displacements as a function of time for a spherical particle with isotropic translational diffusion, as well as for an anisotropic ellipsoidal particle. In both cases the translational and rotational motion is either unconfined or confined to one or two dimensions. A significant non-Gaussian behaviour at finite times t is signalled by a non-vanishing kurtosis γ(t). To delimit the super-diffusive regime, which occurs at intermediate times, two timescales are identified. For certain model situations a characteristic t(3) behaviour of the mean-square displacement is observed. Comparing the dynamics of real and artificial microswimmers, like bacteria or catalytically driven Janus particles, to our analytical expressions reveals whether their motion is Brownian or not.

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.

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.

Comparative study of cluster Ag17Cu2 by instantaneous normal mode analysis and by isothermal Brownian-type molecular dynamics simulation.

PubMed

Tang, Ping-Han; Wu, Ten-Ming; Yen, Tsung-Wen; Lai, S K; Hsu, P J

2011-09-07

We perform isothermal Brownian-type molecular dynamics simulations to obtain the velocity autocorrelation function and its time Fourier-transformed power spectral density for the metallic cluster Ag(17)Cu(2). The temperature dependences of these dynamical quantities from T = 0 to 1500 K were examined and across this temperature range the cluster melting temperature T(m), which we define to be the principal maximum position of the specific heat is determined. The instantaneous normal mode analysis is then used to dissect the cluster dynamics by calculating the vibrational instantaneous normal mode density of states and hence its frequency integrated value I(j) which is an ensemble average of all vibrational projection operators for the jth atom in the cluster. In addition to comparing the results with simulation data, we look more closely at the entities I(j) of all atoms using the point group symmetry and diagnose their temperature variations. We find that I(j) exhibit features that may be used to deduce T(m), which turns out to agree very well with those inferred from the power spectral density and specific heat. © 2011 American Institute of Physics

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.

Markov switching of the electricity supply curve and power prices dynamics

NASA Astrophysics Data System (ADS)

Mari, Carlo; Cananà, Lucianna

2012-02-01

Regime-switching models seem to well capture the main features of power prices behavior in deregulated markets. In a recent paper, we have proposed an equilibrium methodology to derive electricity prices dynamics from the interplay between supply and demand in a stochastic environment. In particular, assuming that the supply function is described by a power law where the exponent is a two-state strictly positive Markov process, we derived a regime switching dynamics of power prices in which regime switches are induced by transitions between Markov states. In this paper, we provide a dynamical model to describe the random behavior of power prices where the only non-Brownian component of the motion is endogenously introduced by Markov transitions in the exponent of the electricity supply curve. In this context, the stochastic process driving the switching mechanism becomes observable, and we will show that the non-Brownian component of the dynamics induced by transitions from Markov states is responsible for jumps and spikes of very high magnitude. The empirical analysis performed on three Australian markets confirms that the proposed approach seems quite flexible and capable of incorporating the main features of power prices time-series, thus reproducing the first four moments of log-returns empirical distributions in a satisfactory way.

Chromosomal locus tracking with proper accounting of static and dynamic errors

PubMed Central

Backlund, Mikael P.; Joyner, Ryan; Moerner, W. E.

2015-01-01

The mean-squared displacement (MSD) and velocity autocorrelation (VAC) of tracked single particles or molecules are ubiquitous metrics for extracting parameters that describe the object’s motion, but they are both corrupted by experimental errors that hinder the quantitative extraction of underlying parameters. For the simple case of pure Brownian motion, the effects of localization error due to photon statistics (“static error”) and motion blur due to finite exposure time (“dynamic error”) on the MSD and VAC are already routinely treated. However, particles moving through complex environments such as cells, nuclei, or polymers often exhibit anomalous diffusion, for which the effects of these errors are less often sufficiently treated. We present data from tracked chromosomal loci in yeast that demonstrate the necessity of properly accounting for both static and dynamic error in the context of an anomalous diffusion that is consistent with a fractional Brownian motion (FBM). We compare these data to analytical forms of the expected values of the MSD and VAC for a general FBM in the presence of these errors. PMID:26172745

How fast do stock prices adjust to market efficiency? Evidence from a detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Reboredo, Juan C.; Rivera-Castro, Miguel A.; Miranda, José G. V.; García-Rubio, Raquel

2013-04-01

In this paper we analyse price fluctuations with the aim of measuring how long the market takes to adjust prices to weak-form efficiency, i.e., how long it takes for prices to adjust to a fractional Brownian motion with a Hurst exponent of 0.5. The Hurst exponent is estimated for different time horizons using detrended fluctuation analysis-a method suitable for non-stationary series with trends-in order to identify at which time scale the Hurst exponent is consistent with the efficient market hypothesis. Using high-frequency share price, exchange rate and stock data, we show how price dynamics exhibited important deviations from efficiency for time periods of up to 15 min; thereafter, price dynamics was consistent with a geometric Brownian motion. The intraday behaviour of the series also indicated that price dynamics at trade opening and close was hardly consistent with efficiency, which would enable investors to exploit price deviations from fundamental values. This result is consistent with intraday volume, volatility and transaction time duration patterns.

Bulk dynamics of Brownian hard disks: Dynamical density functional theory versus experiments on two-dimensional colloidal hard spheres

NASA Astrophysics Data System (ADS)

Stopper, Daniel; Thorneywork, Alice L.; Dullens, Roel P. A.; Roth, Roland

2018-03-01

Using dynamical density functional theory (DDFT), we theoretically study Brownian self-diffusion and structural relaxation of hard disks and compare to experimental results on quasi two-dimensional colloidal hard spheres. To this end, we calculate the self-van Hove correlation function and distinct van Hove correlation function by extending a recently proposed DDFT-approach for three-dimensional systems to two dimensions. We find that the theoretical results for both self-part and distinct part of the van Hove function are in very good quantitative agreement with the experiments up to relatively high fluid packing fractions of roughly 0.60. However, at even higher densities, deviations between the experiment and the theoretical approach become clearly visible. Upon increasing packing fraction, in experiments, the short-time self-diffusive behavior is strongly affected by hydrodynamic effects and leads to a significant decrease in the respective mean-squared displacement. By contrast, and in accordance with previous simulation studies, the present DDFT, which neglects hydrodynamic effects, shows no dependence on the particle density for this quantity.

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

Visibility graph analysis on quarterly macroeconomic series of China based on complex network theory

NASA Astrophysics Data System (ADS)

Wang, Na; Li, Dong; Wang, Qiwen

2012-12-01

The visibility graph approach and complex network theory provide a new insight into time series analysis. The inheritance of the visibility graph from the original time series was further explored in the paper. We found that degree distributions of visibility graphs extracted from Pseudo Brownian Motion series obtained by the Frequency Domain algorithm exhibit exponential behaviors, in which the exponential exponent is a binomial function of the Hurst index inherited in the time series. Our simulations presented that the quantitative relations between the Hurst indexes and the exponents of degree distribution function are different for different series and the visibility graph inherits some important features of the original time series. Further, we convert some quarterly macroeconomic series including the growth rates of value-added of three industry series and the growth rates of Gross Domestic Product series of China to graphs by the visibility algorithm and explore the topological properties of graphs associated from the four macroeconomic series, namely, the degree distribution and correlations, the clustering coefficient, the average path length, and community structure. Based on complex network analysis we find degree distributions of associated networks from the growth rates of value-added of three industry series are almost exponential and the degree distributions of associated networks from the growth rates of GDP series are scale free. We also discussed the assortativity and disassortativity of the four associated networks as they are related to the evolutionary process of the original macroeconomic series. All the constructed networks have “small-world” features. The community structures of associated networks suggest dynamic changes of the original macroeconomic series. We also detected the relationship among government policy changes, community structures of associated networks and macroeconomic dynamics. We find great influences of government policies in China on the changes of dynamics of GDP and the three industries adjustment. The work in our paper provides a new way to understand the dynamics of economic development.

Exact symmetries in the velocity fluctuations of a hot Brownian swimmer

NASA Astrophysics Data System (ADS)

Falasco, Gianmaria; Pfaller, Richard; Bregulla, Andreas P.; Cichos, Frank; Kroy, Klaus

2016-09-01

Symmetries constrain dynamics. We test this fundamental physical principle, experimentally and by molecular dynamics simulations, for a hot Janus swimmer operating far from thermal equilibrium. Our results establish scalar and vectorial steady-state fluctuation theorems and a thermodynamic uncertainty relation that link the fluctuating particle current to its entropy production at an effective temperature. A Markovian minimal model elucidates the underlying nonequilibrium physics.

Ultrafast image-based dynamic light scattering for nanoparticle sizing

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

Zhou, Wu; Zhang, Jie; Liu, Lili

An ultrafast sizing method for nanoparticles is proposed, called as UIDLS (Ultrafast Image-based Dynamic Light Scattering). This method makes use of the intensity fluctuation of scattered light from nanoparticles in Brownian motion, which is similar to the conventional DLS method. The difference in the experimental system is that the scattered light by nanoparticles is received by an image sensor instead of a photomultiplier tube. A novel data processing algorithm is proposed to directly get correlation coefficient between two images at a certain time interval (from microseconds to milliseconds) by employing a two-dimensional image correlation algorithm. This coefficient has been provedmore » to be a monotonic function of the particle diameter. Samples of standard latex particles (79/100/352/482/948 nm) were measured for validation of the proposed method. The measurement accuracy of higher than 90% was found with standard deviations less than 3%. A sample of nanosilver particle with nominal size of 20 ± 2 nm and a sample of polymethyl methacrylate emulsion with unknown size were also tested using UIDLS method. The measured results were 23.2 ± 3.0 nm and 246.1 ± 6.3 nm, respectively, which is substantially consistent with the transmission electron microscope results. Since the time for acquisition of two successive images has been reduced to less than 1 ms and the data processing time in about 10 ms, the total measuring time can be dramatically reduced from hundreds seconds to tens of milliseconds, which provides the potential for real-time and in situ nanoparticle sizing.« less

A generic signature of a fluctuating magnetic field: An additional turnover prior to the Kramers' one

NASA Astrophysics Data System (ADS)

Mondal, Shrabani; Baura, Alendu; Das, Sudip; Bag, Bidhan Chandra

2018-07-01

In this paper we have presented the dynamics of a Brownian particle which is coupled to a thermal bath in the presence of a fluctuating magnetic field (FMF). By virtue of the FMF the Brownian particle experiences a time dependent damping strength for the x -direction motion even in the presence of a stationary Markovian thermal bath. There is a transition state along this direction. The time dependent damping strength leads to appear a bi-turnover phenomenon in the variation of the barrier crossing rate as a function of the thermal bath induced damping strength. It is a generic signature of the fluctuating magnetic field.

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.

Clustering Multiple Sclerosis Subgroups with Multifractal Methods and Self-Organizing Map Algorithm

NASA Astrophysics Data System (ADS)

Karaca, Yeliz; Cattani, Carlo

Magnetic resonance imaging (MRI) is the most sensitive method to detect chronic nervous system diseases such as multiple sclerosis (MS). In this paper, Brownian motion Hölder regularity functions (polynomial, periodic (sine), exponential) for 2D image, such as multifractal methods were applied to MR brain images, aiming to easily identify distressed regions, in MS patients. With these regions, we have proposed an MS classification based on the multifractal method by using the Self-Organizing Map (SOM) algorithm. Thus, we obtained a cluster analysis by identifying pixels from distressed regions in MR images through multifractal methods and by diagnosing subgroups of MS patients through artificial neural networks.

Mobility and settling rate of agglomerates of polydisperse nanoparticles.

PubMed

Spyrogianni, Anastasia; Karadima, Katerina S; Goudeli, Eirini; Mavrantzas, Vlasis G; Pratsinis, Sotiris E

2018-02-14

Agglomerate settling impacts nanotoxicology and nanomedicine as well as the stability of engineered nanofluids. Here, the mobility of nanostructured fractal-like SiO 2 agglomerates in water is investigated and their settling rate in infinitely dilute suspensions is calculated by a Brownian dynamics algorithm tracking the agglomerate translational and rotational motion. The corresponding friction matrices are obtained using the HYDRO++ algorithm [J. G. de la Torre, G. del Rio Echenique, and A. Ortega, J. Phys. Chem. B 111, 955 (2007)] from the Kirkwood-Riseman theory accounting for hydrodynamic interactions of primary particles (PPs) through the Rotne-Prager-Yamakawa tensor, properly modified for polydisperse PPs. Agglomerates are generated by an event-driven method and have constant mass fractal dimension but varying PP size distribution, mass, and relative shape anisotropy. The calculated diffusion coefficient from HYDRO++ is used to obtain the agglomerate mobility diameter d m and is compared with that from scaling laws for fractal-like agglomerates. The ratio d m /d g of the mobility diameter to the gyration diameter of the agglomerate decreases with increasing relative shape anisotropy. For constant d m and mean d p , the agglomerate settling rate, u s , increases with increasing PP geometric standard deviation σ p,g (polydispersity). A linear relationship between u s and agglomerate mass to d m ratio, m/d m , is revealed and attributed to the fast Brownian rotation of such small and light nanoparticle agglomerates. An analytical expression for the u s of agglomerates consisting of polydisperse PPs is then derived, u s =1-ρ f ρ p g3πμmd m (ρ f is the density of the fluid, ρ p is the density of PPs, μ is the viscosity of the fluid, and g is the acceleration of gravity), valid for agglomerates for which the characteristic rotational time is considerably shorter than their settling time. Our calculations demonstrate that the commonly made assumption of monodisperse PPs underestimates u s by a fraction depending on σ p,g and agglomerate mass mobility exponent. Simulations are in excellent agreement with deposition rate measurements of fumed SiO 2 agglomerates in water.

Mobility and settling rate of agglomerates of polydisperse nanoparticles

NASA Astrophysics Data System (ADS)

Spyrogianni, Anastasia; Karadima, Katerina S.; Goudeli, Eirini; Mavrantzas, Vlasis G.; Pratsinis, Sotiris E.

2018-02-01

Agglomerate settling impacts nanotoxicology and nanomedicine as well as the stability of engineered nanofluids. Here, the mobility of nanostructured fractal-like SiO2 agglomerates in water is investigated and their settling rate in infinitely dilute suspensions is calculated by a Brownian dynamics algorithm tracking the agglomerate translational and rotational motion. The corresponding friction matrices are obtained using the HYDRO++ algorithm [J. G. de la Torre, G. del Rio Echenique, and A. Ortega, J. Phys. Chem. B 111, 955 (2007)] from the Kirkwood-Riseman theory accounting for hydrodynamic interactions of primary particles (PPs) through the Rotne-Prager-Yamakawa tensor, properly modified for polydisperse PPs. Agglomerates are generated by an event-driven method and have constant mass fractal dimension but varying PP size distribution, mass, and relative shape anisotropy. The calculated diffusion coefficient from HYDRO++ is used to obtain the agglomerate mobility diameter dm and is compared with that from scaling laws for fractal-like agglomerates. The ratio dm/dg of the mobility diameter to the gyration diameter of the agglomerate decreases with increasing relative shape anisotropy. For constant dm and mean dp, the agglomerate settling rate, us, increases with increasing PP geometric standard deviation σp,g (polydispersity). A linear relationship between us and agglomerate mass to dm ratio, m/dm, is revealed and attributed to the fast Brownian rotation of such small and light nanoparticle agglomerates. An analytical expression for the us of agglomerates consisting of polydisperse PPs is then derived, us=(1/-{ρf/ρp})g 3 π μ m/dm (ρf is the density of the fluid, ρp is the density of PPs, μ is the viscosity of the fluid, and g is the acceleration of gravity), valid for agglomerates for which the characteristic rotational time is considerably shorter than their settling time. Our calculations demonstrate that the commonly made assumption of monodisperse PPs underestimates us by a fraction depending on σp,g and agglomerate mass mobility exponent. Simulations are in excellent agreement with deposition rate measurements of fumed SiO2 agglomerates in water.

The Lattice Dynamics of Colloidal Crystals.

NASA Astrophysics Data System (ADS)

Hurd, Alan James

Colloidal crystals are ordered arrays of highly charged microspheres in water that exhibit spectacular optical diffraction effects by virtue of a large lattice parameter. The microspheres perform Brownian motion that is influenced by the interparticle and fluid forces. The purpose of this study was to understand the nature of the collective motions in colloidal crystals in terms of classical lattice dynamics. In the theoretical analysis, the particle displacements due to Brownian motion were formally decomposed into phonon -like lattice disturbances analogous to the phonons in atomic and molecular solids except that they are heavily damped. The analysis was based on a harmonic solid model with special attention paid to the hydrodynamic interaction between particles. A hydrodynamic model using the Oseen interaction was worked for a three-dimensional lattice but it failed in two important respects: it overestimated the friction factor for long wavelength modes and did not predict a previously observed propagating transverse mode. Both of these failures were corrected by a hydrodynamic model based on periodic solutions to the Stokes equation. In addition, the effects of fluid inertia and constraining walls were considered. Intensity autocorrelation spectroscopy was used to probe the lattice dynamics by measuring the phonon dispersion curves. A thin-film cell was used to reduce multiple scattering to acceptable levels. An experiment to measure wall effects on Brownian motion was necessary to determine the decrease in diffusion rate inherent in the thin-film geometry. The wall effects were found to agree with macroscopic hydrodynamics. An additional experiment measured the elastic anisotropy of the crystal lattice from the thermal diffuse scattering. The theoretical dispersion curves were found to agree well with the measured curves.

Analysis of Ligand-Receptor Association and Intermediate Transfer Rates in Multienzyme Nanostructures with All-Atom Brownian Dynamics Simulations.

PubMed

Roberts, Christopher C; Chang, Chia-En A

2016-08-25

We present the second-generation GeomBD Brownian dynamics software for determining interenzyme intermediate transfer rates and substrate association rates in biomolecular complexes. Substrate and intermediate association rates for a series of enzymes or biomolecules can be compared between the freely diffusing disorganized configuration and various colocalized or complexed arrangements for kinetic investigation of enhanced intermediate transfer. In addition, enzyme engineering techniques, such as synthetic protein conjugation, can be computationally modeled and analyzed to better understand changes in substrate association relative to native enzymes. Tools are provided to determine nonspecific ligand-receptor association residence times, and to visualize common sites of nonspecific association of substrates on receptor surfaces. To demonstrate features of the software, interenzyme intermediate substrate transfer rate constants are calculated and compared for all-atom models of DNA origami scaffold-bound bienzyme systems of glucose oxidase and horseradish peroxidase. Also, a DNA conjugated horseradish peroxidase enzyme was analyzed for its propensity to increase substrate association rates and substrate local residence times relative to the unmodified enzyme. We also demonstrate the rapid determination and visualization of common sites of nonspecific ligand-receptor association by using HIV-1 protease and an inhibitor, XK263. GeomBD2 accelerates simulations by precomputing van der Waals potential energy grids and electrostatic potential grid maps, and has a flexible and extensible support for all-atom and coarse-grained force fields. Simulation software is written in C++ and utilizes modern parallelization techniques for potential grid preparation and Brownian dynamics simulation processes. Analysis scripts, written in the Python scripting language, are provided for quantitative simulation analysis. GeomBD2 is applicable to the fields of biophysics, bioengineering, and enzymology in both predictive and explanatory roles.

Species and Scale Dependence of Bacterial Motion Dynamics

NASA Astrophysics Data System (ADS)

Sund, N. L.; Yang, X.; Parashar, R.; Plymale, A.; Hu, D.; Kelly, R.; Scheibe, T. D.

2017-12-01

Many metal reducing bacteria are motile with their motion characteristics described by run-and-tumble behavior exhibiting series of flights (jumps) and waiting (residence) time spanning a wide range of values. Accurate models of motility allow for improved design and evaluation of in-situ bioremediation in the subsurface. While many bioremediation models neglect the motion of the bacteria, others treat motility using an advection dispersion equation, which assumes that the motion of the bacteria is Brownian.The assumption of Brownian motion to describe motility has enormous implications on predictive capabilities of bioremediation models, yet experimental evidence of this assumption is mixed [1][2][3]. We hypothesize that this is due to the species and scale dependence of the motion dynamics. We test our hypothesis by analyzing videos of motile bacteria of five different species in open domains. Trajectories of individual cells ranging from several seconds to few minutes in duration are extracted in neutral conditions (in the absence of any chemical gradient). The density of the bacteria is kept low so that the interaction between the bacteria is minimal. Preliminary results show a transition from Fickian (Brownian) to non-Fickian behavior for one species of bacteria (Pelosinus) and persistent Fickian behavior of another species (Geobacter).Figure: Video frames of motile bacteria with the last 10 seconds of their trajectories drawn in red. (left) Pelosinus and (right) Geobacter.[1] Ariel, Gil, et al. "Swarming bacteria migrate by Lévy Walk." Nature Communications 6 (2015).[2] Saragosti, Jonathan, Pascal Silberzan, and Axel Buguin. "Modeling E. coli tumbles by rotational diffusion. Implications for chemotaxis." PloS one 7.4 (2012): e35412.[3] Wu, Mingming, et al. "Collective bacterial dynamics revealed using a three-dimensional population-scale defocused particle tracking technique." Applied and Environmental Microbiology 72.7 (2006): 4987-4994.

Translocation of a polymer through a nanopore across a viscosity gradient.

PubMed

de Haan, Hendrick W; Slater, Gary W

2013-04-01

The translocation of a polymer through a pore in a membrane separating fluids of different viscosities is studied via several computational approaches. Starting with the polymer halfway, we find that as a viscosity difference across the pore is introduced, translocation will predominately occur towards one side of the membrane. These results suggest an intrinsic pumping mechanism for translocation across cell walls which could arise whenever the fluid across the membrane is inhomogeneous. Somewhat surprisingly, the sign of the preferred direction of translocation is found to be strongly dependent on the simulation algorithm: for Langevin dynamics (LD) simulations, a bias towards the low viscosity side is found while for Brownian dynamics (BD), a bias towards the high viscosity is found. Examining the translocation dynamics in detail across a wide range of viscosity gradients and developing a simple force model to estimate the magnitude of the bias, the LD results are demonstrated to be more physically realistic. The LD results are also compared to those generated from a simple, one-dimensional random walk model of translocation to investigate the role of the internal degrees of freedom of the polymer and the entropic barrier. To conclude, the scaling of the results across different polymer lengths demonstrates the saturation of the directional preference with polymer length and the nontrivial location of the maximum in the exponent corresponding to the scaling of the translocation time with polymer length.

Bivariate Gaussian bridges: directional factorization of diffusion in Brownian bridge models.

PubMed

Kranstauber, Bart; Safi, Kamran; Bartumeus, Frederic

2014-01-01

In recent years high resolution animal tracking data has become the standard in movement ecology. The Brownian Bridge Movement Model (BBMM) is a widely adopted approach to describe animal space use from such high resolution tracks. One of the underlying assumptions of the BBMM is isotropic diffusive motion between consecutive locations, i.e. invariant with respect to the direction. Here we propose to relax this often unrealistic assumption by separating the Brownian motion variance into two directional components, one parallel and one orthogonal to the direction of the motion. Our new model, the Bivariate Gaussian bridge (BGB), tracks movement heterogeneity across time. Using the BGB and identifying directed and non-directed movement within a trajectory resulted in more accurate utilisation distributions compared to dynamic Brownian bridges, especially for trajectories with a non-isotropic diffusion, such as directed movement or Lévy like movements. We evaluated our model with simulated trajectories and observed tracks, demonstrating that the improvement of our model scales with the directional correlation of a correlated random walk. We find that many of the animal trajectories do not adhere to the assumptions of the BBMM. The proposed model improves accuracy when describing the space use both in simulated correlated random walks as well as observed animal tracks. Our novel approach is implemented and available within the "move" package for R.

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.

BROMOC suite: Monte Carlo/Brownian dynamics suite for studies of ion permeation and DNA transport in biological and artificial pores with effective potentials.

PubMed

De Biase, Pablo M; Markosyan, Suren; Noskov, Sergei

2015-02-05

The transport of ions and solutes by biological pores is central for cellular processes and has a variety of applications in modern biotechnology. The time scale involved in the polymer transport across a nanopore is beyond the accessibility of conventional MD simulations. Moreover, experimental studies lack sufficient resolution to provide details on the molecular underpinning of the transport mechanisms. BROMOC, the code presented herein, performs Brownian dynamics simulations, both serial and parallel, up to several milliseconds long. BROMOC can be used to model large biological systems. IMC-MACRO software allows for the development of effective potentials for solute-ion interactions based on radial distribution function from all-atom MD. BROMOC Suite also provides a versatile set of tools to do a wide variety of preprocessing and postsimulation analysis. We illustrate a potential application with ion and ssDNA transport in MspA nanopore. © 2014 Wiley Periodicals, Inc.

Orientation of chain molecules in ionotropic gels: a Brownian dynamics model

NASA Astrophysics Data System (ADS)

Woelki, Stefan; Kohler, Hans-Helmut

2003-09-01

As is known from birefringence measurements, polysaccharide molecules of ionotropic gels are preferentially orientated normal to the direction of gel growth. In this paper the orientation effect is investigated by means of an off-lattice Brownian dynamics model simulating the gel formation process. The model describes the integration of a single coarse grained phantom chain into the growing gel. The equations of motion of the chain are derived. The computer simulations show that, during the process of integration, the chain is contracting normal to the direction of gel growth. A scaling relation is obtained for the degree of contraction as a function of the length parameters of the chain, the velocity of the gel formation front and the rate constant of the crosslinking reaction. It is shown that the scaling relation, if applied to the example of ionotropic copper alginate gel, leads to reasonable predictions of the time course of the degree of contraction of the alginate chains.

Laser light scattering review

NASA Technical Reports Server (NTRS)

Schaetzel, Klaus

1989-01-01

Since the development of laser light sources and fast digital electronics for signal processing, the classical discipline of light scattering on liquid systems experienced a strong revival plus an enormous expansion, mainly due to new dynamic light scattering techniques. While a large number of liquid systems can be investigated, ranging from pure liquids to multicomponent microemulsions, this review is largely restricted to applications on Brownian particles, typically in the submicron range. Static light scattering, the careful recording of the angular dependence of scattered light, is a valuable tool for the analysis of particle size and shape, or of their spatial ordering due to mutual interactions. Dynamic techniques, most notably photon correlation spectroscopy, give direct access to particle motion. This may be Brownian motion, which allows the determination of particle size, or some collective motion, e.g., electrophoresis, which yields particle mobility data. Suitable optical systems as well as the necessary data processing schemes are presented in some detail. Special attention is devoted to topics of current interest, like correlation over very large lag time ranges or multiple scattering.

Brownian dynamics of a protein-polymer chain complex in a solid-state nanopore

NASA Astrophysics Data System (ADS)

Wells, Craig C.; Melnikov, Dmitriy V.; Gracheva, Maria E.

2017-08-01

We study the movement of a polymer attached to a large protein inside a nanopore in a thin silicon dioxide membrane submerged in an electrolyte solution. We use Brownian dynamics to describe the motion of a negatively charged polymer chain of varying lengths attached to a neutral protein modeled as a spherical bead with a radius larger than that of the nanopore, allowing the chain to thread the nanopore but preventing it from translocating. The motion of the protein-polymer complex within the pore is also compared to that of a freely translocating polymer. Our results show that the free polymer's standard deviations in the direction normal to the pore axis is greater than that of the protein-polymer complex. We find that restrictions imposed by the protein, bias, and neighboring chain segments aid in controlling the position of the chain in the pore. Understanding the behavior of the protein-polymer chain complex may lead to methods that improve molecule identification by increasing the resolution of ionic current measurements.

Brownian dynamics of a protein-polymer chain complex in a solid-state nanopore.

PubMed

Wells, Craig C; Melnikov, Dmitriy V; Gracheva, Maria E

2017-08-07

We study the movement of a polymer attached to a large protein inside a nanopore in a thin silicon dioxide membrane submerged in an electrolyte solution. We use Brownian dynamics to describe the motion of a negatively charged polymer chain of varying lengths attached to a neutral protein modeled as a spherical bead with a radius larger than that of the nanopore, allowing the chain to thread the nanopore but preventing it from translocating. The motion of the protein-polymer complex within the pore is also compared to that of a freely translocating polymer. Our results show that the free polymer's standard deviations in the direction normal to the pore axis is greater than that of the protein-polymer complex. We find that restrictions imposed by the protein, bias, and neighboring chain segments aid in controlling the position of the chain in the pore. Understanding the behavior of the protein-polymer chain complex may lead to methods that improve molecule identification by increasing the resolution of ionic current measurements.

Swimming in external fields

NASA Astrophysics Data System (ADS)

Stark, Holger

2016-11-01

Microswimmers move autonomously but are subject to external fields, which influence their swimming path and their collective dynamics. With three concrete examples we illustrate swimming in external fields and explain the methodology to treat it. First, an active Brownian particle shows a conventional sedimentation profile in a gravitational field but with increased sedimentation length and some polar order along the vertical. Bottom-heavy swimmers are able to invert the sedimentation profile. Second, active Brownian particles interacting by hydrodynamic flow fields in a three-dimensional harmonic trap can spontaneously break the isotropic symmetry. They develop polar order, which one can describe by mean-field theory reminiscent to Weiss theory of ferromagnetism, and thereby pump fluid. Third, a single microswimmer shows interesting non-linear dynamics in Poiseuille flow including swinging and tumbling trajectories. For pushers, hydrodynamic interactions with bounding surfaces stabilize either straight swimming against the flow or tumbling close to the channel wall, while pushers always move on a swinging trajectory with a specific amplitude as limit cycle.

Systemic risk and causality dynamics of the world international shipping market

NASA Astrophysics Data System (ADS)

Zhang, Xin; Podobnik, Boris; Kenett, Dror Y.; Eugene Stanley, H.

2014-12-01

Various studies have reported that many economic systems have been exhibiting an increase in the correlation between different market sectors, a factor that exacerbates the level of systemic risk. We measure this systemic risk of three major world shipping markets, (i) the new ship market, (ii) the second-hand ship market, and (iii) the freight market, as well as the shipping stock market. Based on correlation networks during three time periods, that prior to the financial crisis, during the crisis, and after the crisis, minimal spanning trees (MSTs) and hierarchical trees (HTs) both exhibit complex dynamics, i.e., different market sectors tend to be more closely linked during financial crisis. Brownian distance correlation and Granger causality test both can be used to explore the directional interconnectedness of market sectors, while Brownian distance correlation captures more dependent relationships, which are not observed in the Granger causality test. These two measures can also identify and quantify market regression periods, implying that they contain predictive power for the current crisis.

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.

Watching Single Enzymes and Fluorescent Proteins in Action in Solution Using a Microfluidic Trap

NASA Astrophysics Data System (ADS)

Goldsmith, Randall

2012-02-01

Observation of dynamics of single biomolecules over a prolonged time without altering the biomolecule via immobilization is achieved with a specialized microfluidic device. This device, the Anti-Brownian ELectrokinetic (ABEL) Trap, uses real-time electrokinetic feedback to cancel Brownian motion of single objects in solution. First, we use the ABEL Trap to study Allophycocyanin (APC), a photosynthetic antenna-protein and popular fluorescent probe. A complex relationship between fluorescence intensity and lifetime is observed, suggesting light-induced conformational changes and radiative and non-radiative rate fluctuations. Second, we apply the ABEL Trap to single molecules of the multi-copper enzyme blue Nitrite Reductase where a fluorescent label reports on the oxidation state of the Type I Copper. Redox cycling is observed and kinetic analysis allows extraction of the microscopic rate constants in the kinetic scheme. Evidence of a substrate-induced shift of the intramolecular electron transfer rate is seen. Taken together, these observations provide windows of unprecedented detail into the dynamics of solution-phase biomolecules.

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.

Dynamic Decision Making under Uncertainty and Partial Information

DTIC Science & Technology

2013-11-14

integral under the natural filtration generated by the Brownian motions . This compact expression potentially enables us to design sub- optimal penalties...bounds on bermudan option price under jump diffusion processes. Quantitative Finance , 2013. Under review, available at http://arxiv.org/abs/1305.4321... Finance , 19:53 – 71, 2009. [3] D.P. Bertsekas. Dynamic Programming and Optimal Control. Athena Scientific, 4th edition, 2012. [4] D.B. Brown and J.E

Brownian dynamics simulation of amphiphilic block copolymers with different tail lengths, comparison with theory and comicelles.

PubMed

Hafezi, Mohammad-Javad; Sharif, Farhad

2015-11-01

Study on the effect of amphiphilic copolymers structure on their self assembly is an interesting subject, with important applications in the area of drug delivery and biological system treatments. Brownian dynamics simulations were performed to study self-assembly of the linear amphiphilic block copolymers with the same hydrophilic head, but hydrophobic tails of different lengths. Critical micelle concentration (CMC), gyration radius distribution, micelle size distribution, density profiles of micelles, shape anisotropy, and dynamics of micellization were investigated as a function of tail length. Simulation results were compared with predictions from theory and simulation for mixed systems of block copolymers with long and short hydrophobic tail, reported in our previous work. Interestingly, the equilibrium structural and dynamic parameters of pure and mixed block copolymers were similarly dependant on the intrinsic/apparent hydrophobic block length. Log (CMC) was, however; proportional to the tail length and had a different behavior compared to the mixed system. The power law scaling relation of equilibrium structural parameters for amphiphilic block copolymers predicts the same dependence for similar hydrophobic tail lengths, but the power law prediction of CMC is different, which is due to its simplifying assumptions as discussed here. Copyright © 2015 Elsevier Inc. All rights reserved.

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.

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.

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

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

From quantum stochastic differential equations to Gisin-Percival state diffusion

NASA Astrophysics Data System (ADS)

Parthasarathy, K. R.; Usha Devi, A. R.

2017-08-01

Starting from the quantum stochastic differential equations of Hudson and Parthasarathy [Commun. Math. Phys. 93, 301 (1984)] and exploiting the Wiener-Itô-Segal isomorphism between the boson Fock reservoir space Γ (L2(R+ ) ⊗(Cn⊕Cn ) ) and the Hilbert space L2(μ ) , where μ is the Wiener probability measure of a complex n-dimensional vector-valued standard Brownian motion {B (t ) ,t ≥0 } , we derive a non-linear stochastic Schrödinger equation describing a classical diffusion of states of a quantum system, driven by the Brownian motion B. Changing this Brownian motion by an appropriate Girsanov transformation, we arrive at the Gisin-Percival state diffusion equation [N. Gisin and J. Percival, J. Phys. A 167, 315 (1992)]. This approach also yields an explicit solution of the Gisin-Percival equation, in terms of the Hudson-Parthasarathy unitary process and a randomized Weyl displacement process. Irreversible dynamics of system density operators described by the well-known Gorini-Kossakowski-Sudarshan-Lindblad master equation is unraveled by coarse-graining over the Gisin-Percival quantum state trajectories.

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.

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.

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

Kinetic theory of dark solitons with tunable friction.

PubMed

Hurst, Hilary M; Efimkin, Dmitry K; Spielman, I B; Galitski, Victor

2017-05-01

We study controllable friction in a system consisting of a dark soliton in a one-dimensional Bose-Einstein condensate coupled to a noninteracting Fermi gas. The fermions act as impurity atoms, not part of the original condensate, that scatter off of the soliton. We study semiclassical dynamics of the dark soliton, a particlelike object with negative mass, and calculate its friction coefficient. Surprisingly, it depends periodically on the ratio of interspecies (impurity-condensate) to intraspecies (condensate-condensate) interaction strengths. By tuning this ratio, one can access a regime where the friction coefficient vanishes. We develop a general theory of stochastic dynamics for negative-mass objects and find that their dynamics are drastically different from their positive-mass counterparts: they do not undergo Brownian motion. From the exact phase-space probability distribution function (i.e., in position and velocity), we find that both the trajectory and lifetime of the soliton are altered by friction, and the soliton can undergo Brownian motion only in the presence of friction and a confining potential. These results agree qualitatively with experimental observations by Aycock et al. [Proc. Natl. Acad. Sci. USA 114 , 2503 (2017)] in a similar system with bosonic impurity scatterers.

Cooperativity of self-organized Brownian motors pulling on soft cargoes.

PubMed

Orlandi, Javier G; Blanch-Mercader, Carles; Brugués, Jan; Casademunt, Jaume

2010-12-01

We study the cooperative dynamics of Brownian motors moving along a one-dimensional track when an external load is applied to the leading motor, mimicking molecular motors pulling on membrane-bound cargoes in intracellular traffic. Due to the asymmetric loading, self-organized motor clusters form spontaneously. We model the motors with a two-state noise-driven ratchet formulation and study analytically and numerically the collective velocity-force and efficiency-force curves resulting from mutual interactions, mostly hard-core repulsion and weak (nonbinding) attraction. We analyze different parameter regimes including the limits of weak noise, mean-field behavior, rigid coupling, and large numbers of motors, for the different interactions. We present a general framework to classify and quantify cooperativity. We show that asymmetric loading leads generically to enhanced cooperativity beyond the simple superposition of the effects of individual motors. For weakly attracting interactions, the cooperativity is mostly enhanced, including highly coordinated motion of motors and complex nonmonotonic velocity-force curves, leading to self-regulated clusters. The dynamical scenario is enriched by resonances associated to commensurability of different length scales. Large clusters exhibit synchronized dynamics and bidirectional motion. Biological implications are discussed.

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.

Kinetic theory of dark solitons with tunable friction

PubMed Central

Hurst, Hilary M.; Efimkin, Dmitry K.; Spielman, I. B.; Galitski, Victor

2018-01-01

We study controllable friction in a system consisting of a dark soliton in a one-dimensional Bose-Einstein condensate coupled to a noninteracting Fermi gas. The fermions act as impurity atoms, not part of the original condensate, that scatter off of the soliton. We study semiclassical dynamics of the dark soliton, a particlelike object with negative mass, and calculate its friction coefficient. Surprisingly, it depends periodically on the ratio of interspecies (impurity-condensate) to intraspecies (condensate-condensate) interaction strengths. By tuning this ratio, one can access a regime where the friction coefficient vanishes. We develop a general theory of stochastic dynamics for negative-mass objects and find that their dynamics are drastically different from their positive-mass counterparts: they do not undergo Brownian motion. From the exact phase-space probability distribution function (i.e., in position and velocity), we find that both the trajectory and lifetime of the soliton are altered by friction, and the soliton can undergo Brownian motion only in the presence of friction and a confining potential. These results agree qualitatively with experimental observations by Aycock et al. [Proc. Natl. Acad. Sci. USA 114, 2503 (2017)] in a similar system with bosonic impurity scatterers. PMID:29744482

Cooperativity of self-organized Brownian motors pulling on soft cargoes

NASA Astrophysics Data System (ADS)

Orlandi, Javier G.; Blanch-Mercader, Carles; Brugués, Jan; Casademunt, Jaume

2010-12-01

We study the cooperative dynamics of Brownian motors moving along a one-dimensional track when an external load is applied to the leading motor, mimicking molecular motors pulling on membrane-bound cargoes in intracellular traffic. Due to the asymmetric loading, self-organized motor clusters form spontaneously. We model the motors with a two-state noise-driven ratchet formulation and study analytically and numerically the collective velocity-force and efficiency-force curves resulting from mutual interactions, mostly hard-core repulsion and weak (nonbinding) attraction. We analyze different parameter regimes including the limits of weak noise, mean-field behavior, rigid coupling, and large numbers of motors, for the different interactions. We present a general framework to classify and quantify cooperativity. We show that asymmetric loading leads generically to enhanced cooperativity beyond the simple superposition of the effects of individual motors. For weakly attracting interactions, the cooperativity is mostly enhanced, including highly coordinated motion of motors and complex nonmonotonic velocity-force curves, leading to self-regulated clusters. The dynamical scenario is enriched by resonances associated to commensurability of different length scales. Large clusters exhibit synchronized dynamics and bidirectional motion. Biological implications are discussed.

Rectified Brownian movement in molecular and cell biology

NASA Astrophysics Data System (ADS)

Fox, Ronald F.

1998-02-01

A unified model is presented for rectified Brownian movement as the mechanism for a variety of putatively chemomechanical energy conversions in molecular and cell biology. The model is established by a detailed analysis of ubiquinone transport in electron transport chains and of allosteric conformation changes in proteins. It is applied to P-type ATPase ion transporters and to a variety of rotary arm enzyme complexes. It provides a basis for the dynamics of actin-myosin cross-bridges in muscle fibers. In this model, metabolic free energy does no work directly, but instead biases boundary conditions for thermal diffusion. All work is done by thermal energy, which is harnessed at the expense of metabolic free energy through the establishment of the asymmetric boundary conditions.

Normal versus anomalous self-diffusion in two-dimensional fluids: memory function approach and generalized asymptotic Einstein relation.

PubMed

Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun

2014-12-07

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.

Normal versus anomalous self-diffusion in two-dimensional fluids: Memory function approach and generalized asymptotic Einstein relation

NASA Astrophysics Data System (ADS)

Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun

2014-12-01

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.

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

Computer simulations of polymer chain structure and dynamics on a hypersphere in four-space

NASA Astrophysics Data System (ADS)

Râsmark, Per Johan; Ekholm, Tobias; Elvingson, Christer

2005-05-01

There is a rapidly growing interest in performing computer simulations in a closed space, avoiding periodic boundary conditions. To extend the range of potential systems to include also macromolecules, we describe an algorithm for computer simulations of polymer chain molecules on S3, a hypersphere in four dimensions. In particular, we show how to generate initial conformations with a bond angle distribution given by the persistence length of the chain and how to calculate the bending forces for a molecule moving on S3. Furthermore, we discuss how to describe the shape of a macromolecule on S3, by deriving the radius of gyration tensor in this non-Euclidean space. The results from both Monte Carlo and Brownian dynamics simulations in the infinite dilution limit show that the results on S3 and in R3 coincide, both with respect to the size and shape as well as for the diffusion coefficient. All data on S3 can also be described by master curves by suitable scaling by the corresponding values in R3. We thus show how to extend the use of spherical boundary conditions, which are most effective for calculating electrostatic forces, to polymer chain molecules, making it possible to perform simulations on S3 also for polyelectrolyte systems.

Stochastic Modeling of the Persistence of HIV: Early Population Dynamics

DTIC Science & Technology

2013-05-10

fluid, Brownian motion is named after the botanist Robert Brown. In the late nineteenth century, he observed that pollen floating in water appeared...to move about in a random manner. When he replaced the pollen with inorganic material, he noticed that the motion persisted. Upon plotting the motion

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.

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.

Tempo and mode of performance evolution across multiple independent origins of adhesive toe pads in lizards.

PubMed

Hagey, Travis J; Uyeda, Josef C; Crandell, Kristen E; Cheney, Jorn A; Autumn, Kellar; Harmon, Luke J

2017-10-01

Understanding macroevolutionary dynamics of trait evolution is an important endeavor in evolutionary biology. Ecological opportunity can liberate a trait as it diversifies through trait space, while genetic and selective constraints can limit diversification. While many studies have examined the dynamics of morphological traits, diverse morphological traits may yield the same or similar performance and as performance is often more proximately the target of selection, examining only morphology may give an incomplete understanding of evolutionary dynamics. Here, we ask whether convergent evolution of pad-bearing lizards has followed similar evolutionary dynamics, or whether independent origins are accompanied by unique constraints and selective pressures over macroevolutionary time. We hypothesized that geckos and anoles each have unique evolutionary tempos and modes. Using performance data from 59 species, we modified Brownian motion (BM) and Ornstein-Uhlenbeck (OU) models to account for repeated origins estimated using Bayesian ancestral state reconstructions. We discovered that adhesive performance in geckos evolved in a fashion consistent with Brownian motion with a trend, whereas anoles evolved in bounded performance space consistent with more constrained evolution (an Ornstein-Uhlenbeck model). Our results suggest that convergent phenotypes can have quite distinctive evolutionary patterns, likely as a result of idiosyncratic constraints or ecological opportunities. © 2017 The Author(s). Evolution © 2017 The Society for the Study of Evolution.

A Dynamical Model Reveals Gene Co-Localizations in Nucleus

PubMed Central

Yao, Ye; Lin, Wei; Hennessy, Conor; Fraser, Peter; Feng, Jianfeng

2011-01-01

Co-localization of networks of genes in the nucleus is thought to play an important role in determining gene expression patterns. Based upon experimental data, we built a dynamical model to test whether pure diffusion could account for the observed co-localization of genes within a defined subnuclear region. A simple standard Brownian motion model in two and three dimensions shows that preferential co-localization is possible for co-regulated genes without any direct interaction, and suggests the occurrence may be due to a limitation in the number of available transcription factors. Experimental data of chromatin movements demonstrates that fractional rather than standard Brownian motion is more appropriate to model gene mobilizations, and we tested our dynamical model against recent static experimental data, using a sub-diffusion process by which the genes tend to colocalize more easily. Moreover, in order to compare our model with recently obtained experimental data, we studied the association level between genes and factors, and presented data supporting the validation of this dynamic model. As further applications of our model, we applied it to test against more biological observations. We found that increasing transcription factor number, rather than factory number and nucleus size, might be the reason for decreasing gene co-localization. In the scenario of frequency- or amplitude-modulation of transcription factors, our model predicted that frequency-modulation may increase the co-localization between its targeted genes. PMID:21760760

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.

Inchworm movement of two rings switching onto a thread by biased Brownian diffusion represent a three-body problem.

PubMed

Benson, Christopher R; Maffeo, Christopher; Fatila, Elisabeth M; Liu, Yun; Sheetz, Edward G; Aksimentiev, Aleksei; Singharoy, Abhishek; Flood, Amar H

2018-05-07

The coordinated motion of many individual components underpins the operation of all machines. However, despite generations of experience in engineering, understanding the motion of three or more coupled components remains a challenge, known since the time of Newton as the "three-body problem." Here, we describe, quantify, and simulate a molecular three-body problem of threading two molecular rings onto a linear molecular thread. Specifically, we use voltage-triggered reduction of a tetrazine-based thread to capture two cyanostar macrocycles and form a [3]pseudorotaxane product. As a consequence of the noncovalent coupling between the cyanostar rings, we find the threading occurs by an unexpected and rare inchworm-like motion where one ring follows the other. The mechanism was derived from controls, analysis of cyclic voltammetry (CV) traces, and Brownian dynamics simulations. CVs from two noncovalently interacting rings match that of two covalently linked rings designed to thread via the inchworm pathway, and they deviate considerably from the CV of a macrocycle designed to thread via a stepwise pathway. Time-dependent electrochemistry provides estimates of rate constants for threading. Experimentally derived parameters (energy wells, barriers, diffusion coefficients) helped determine likely pathways of motion with rate-kinetics and Brownian dynamics simulations. Simulations verified intercomponent coupling could be separated into ring-thread interactions for kinetics, and ring-ring interactions for thermodynamics to reduce the three-body problem to a two-body one. Our findings provide a basis for high-throughput design of molecular machinery with multiple components undergoing coupled motion.

On extreme events for non-spatial and spatial branching Brownian motions

NASA Astrophysics Data System (ADS)

Avan, Jean; Grosjean, Nicolas; Huillet, Thierry

2015-04-01

We study the impact of having a non-spatial branching mechanism with infinite variance on some parameters (height, width and first hitting time) of an underlying Bienaymé-Galton-Watson branching process. Aiming at providing a comparative study of the spread of an epidemics whose dynamics is given by the modulus of a branching Brownian motion (BBM) we then consider spatial branching processes in dimension d, not necessarily integer. The underlying branching mechanism is either a binary branching model or one presenting infinite variance. In particular we evaluate the chance p(x) of being hit if the epidemics started away at distance x. We compute the large x tail probabilities of this event, both when the branching mechanism is regular and when it exhibits very large fluctuations.

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.

Model of the initiation of signal transduction by ligands in a cell culture: Simulation of molecules near a plane membrane comprising receptors

NASA Astrophysics Data System (ADS)

Plante, Ianik; Cucinotta, Francis A.

2011-11-01

Cell communication is a key mechanism in tissue responses to radiation. Several molecules are implicated in radiation-induced signaling between cells, but their contributions to radiation risk are poorly understood. Meanwhile, Green's functions for diffusion-influenced reactions have appeared in the literature, which are applied to describe the diffusion of molecules near a plane membrane comprising bound receptors with the possibility of reversible binding of a ligand and activation of signal transduction proteins by the ligand-receptor complex. We have developed Brownian dynamics algorithms to simulate particle histories in this system which can accurately reproduce the theoretical distribution of distances of a ligand from the membrane, the number of reversibly bound particles, and the number of receptor complexes activating signaling proteins as a function of time, regardless of the number of time steps used for the simulation. These simulations will be of great importance to model interactions at low doses where stochastic effects induced by a small number of molecules or interactions come into play.

Optimizing Likelihood Models for Particle Trajectory Segmentation in Multi-State Systems.

PubMed

Young, Dylan Christopher; Scrimgeour, Jan

2018-06-19

Particle tracking offers significant insight into the molecular mechanics that govern the behav- ior of living cells. The analysis of molecular trajectories that transition between different motive states, such as diffusive, driven and tethered modes, is of considerable importance, with even single trajectories containing significant amounts of information about a molecule's environment and its interactions with cellular structures. Hidden Markov models (HMM) have been widely adopted to perform the segmentation of such complex tracks. In this paper, we show that extensive analysis of hidden Markov model outputs using data derived from multi-state Brownian dynamics simulations can be used both for the optimization of the likelihood models used to describe the states of the system and for characterization of the technique's failure mechanisms. This analysis was made pos- sible by the implementation of parallelized adaptive direct search algorithm on a Nvidia graphics processing unit. This approach provides critical information for the visualization of HMM failure and successful design of particle tracking experiments where trajectories contain multiple mobile states. © 2018 IOP Publishing Ltd.

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.

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.

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.

Sliding of proteins non-specifically bound to DNA: Brownian dynamics studies with coarse-grained protein and DNA models.

PubMed

Ando, Tadashi; Skolnick, Jeffrey

2014-12-01

DNA binding proteins efficiently search for their cognitive sites on long genomic DNA by combining 3D diffusion and 1D diffusion (sliding) along the DNA. Recent experimental results and theoretical analyses revealed that the proteins show a rotation-coupled sliding along DNA helical pitch. Here, we performed Brownian dynamics simulations using newly developed coarse-grained protein and DNA models for evaluating how hydrodynamic interactions between the protein and DNA molecules, binding affinity of the protein to DNA, and DNA fluctuations affect the one dimensional diffusion of the protein on the DNA. Our results indicate that intermolecular hydrodynamic interactions reduce 1D diffusivity by 30%. On the other hand, structural fluctuations of DNA give rise to steric collisions between the CG-proteins and DNA, resulting in faster 1D sliding of the protein. Proteins with low binding affinities consistent with experimental estimates of non-specific DNA binding show hopping along the CG-DNA. This hopping significantly increases sliding speed. These simulation studies provide additional insights into the mechanism of how DNA binding proteins find their target sites on the genome.

Brownian dynamics simulations of insulin microspheres formation

NASA Astrophysics Data System (ADS)

Li, Wei; Chakrabarti, Amit; Gunton, James

2010-03-01

Recent experiments have indicated a novel, aqueous process of microsphere insulin fabrication based on controlled phase separation of protein from water-soluble polymers. We investigate the insulin microsphere crystal formation from insulin-PEG-water systems via 3D Brownian Dynamics simulations. We use the two component Asakura-Oosawa model to simulate the kinetics of this colloid polymer mixture. We first perform a deep quench below the liquid-crystal boundary that leads to fractal formation. We next heat the system to obtain a break-up of the fractal clusters and subsequently cool the system to obtain a spherical aggregation of droplets with a relatively narrow size distribution. We analyze the structure factor S(q) to identify the cluster dimension. S(q) crosses over from a power law q dependence of 1.8 (in agreement with DLCA) to 4 as q increases, which shows the evolution from fractal to spherical clusters. By studying the bond-order parameters, we find the phase transition from liquid-like droplets to crystals which exhibit local HCP and FCC order. This work is supported by grants from the NSF and Mathers Foundation.

Revealing nonergodic dynamics in living cells from a single particle trajectory

NASA Astrophysics Data System (ADS)

Lanoiselée, Yann; Grebenkov, Denis S.

2016-05-01

We propose the improved ergodicity and mixing estimators to identify nonergodic dynamics from a single particle trajectory. The estimators are based on the time-averaged characteristic function of the increments and can thus capture additional information on the process as compared to the conventional time-averaged mean-square displacement. The estimators are first investigated and validated for several models of anomalous diffusion, such as ergodic fractional Brownian motion and diffusion on percolating clusters, and nonergodic continuous-time random walks and scaled Brownian motion. The estimators are then applied to two sets of earlier published trajectories of mRNA molecules inside live Escherichia coli cells and of Kv2.1 potassium channels in the plasma membrane. These statistical tests did not reveal nonergodic features in the former set, while some trajectories of the latter set could be classified as nonergodic. Time averages along such trajectories are thus not representative and may be strongly misleading. Since the estimators do not rely on ensemble averages, the nonergodic features can be revealed separately for each trajectory, providing a more flexible and reliable analysis of single-particle tracking experiments in microbiology.

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.

Self-assembled clusters of spheres related to spherical codes.

PubMed

Phillips, Carolyn L; Jankowski, Eric; Marval, Michelle; Glotzer, Sharon C

2012-10-01

We consider the thermodynamically driven self-assembly of spheres onto the surface of a central sphere. This assembly process forms self-limiting, or terminal, anisotropic clusters (N-clusters) with well-defined structures. We use Brownian dynamics to model the assembly of N-clusters varying in size from two to twelve outer spheres and free energy calculations to predict the expected cluster sizes and shapes as a function of temperature and inner particle diameter. We show that the arrangements of outer spheres at finite temperatures are related to spherical codes, an ideal mathematical sequence of points corresponding to the densest possible sphere packings. We demonstrate that temperature and the ratio of the diameters of the inner and outer spheres dictate cluster morphology. We present a surprising result for the equilibrium structure of a 5-cluster, for which the square pyramid arrangement is preferred over a more symmetric structure. We show this result using Brownian dynamics, a Monte Carlo simulation, and a free energy approximation. Our results suggest a promising way to assemble anisotropic building blocks from constituent colloidal spheres.

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.

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

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

Temperature and chain length dependence of ultrafast vibrational dynamics of thiocyanate in alkylimidazolium ionic liquids: A random walk on a rugged energy landscape.

PubMed

Brinzer, Thomas; Garrett-Roe, Sean

2017-11-21

Ultrafast two-dimensional infrared spectroscopy of a thiocyanate vibrational probe (SCN - ) was used to investigate local dynamics in alkylimidazolium bis-[trifluoromethylsulfonyl]imide ionic liquids ([Im n,1 ][Tf 2 N], n = 2, 4, 6) at temperatures from 5 to 80 °C. The rate of frequency fluctuations reported by SCN - increases with increasing temperature and decreasing alkyl chain length. Temperature-dependent correlation times scale proportionally to temperature-dependent bulk viscosities of each ionic liquid studied. A multimode Brownian oscillator model demonstrates that very low frequency (<10 cm -1 ) modes primarily drive the observed spectral diffusion and that these modes broaden and blue shift on average with increasing temperature. An Arrhenius analysis shows activation barriers for local motions around the probe between 5.5 and 6.5 kcal/mol that are very similar to those for translational diffusion of ions. [Im 6,1 ][Tf 2 N] shows an unexpected decrease in activation energy compared to [Im 4,1 ][Tf 2 N] that may be related to mesoscopically ordered polar and nonpolar domains. A model of dynamics on a rugged potential energy landscape provides a unifying description of the observed Arrhenius behavior and the Brownian oscillator model of the low frequency modes.

Mode-coupling theory for active Brownian particles

NASA Astrophysics Data System (ADS)

Liluashvili, Alexander; Ónody, Jonathan; Voigtmann, Thomas

2017-12-01

We present a mode-coupling theory (MCT) for the slow dynamics of two-dimensional spherical active Brownian particles (ABPs). The ABPs are characterized by a self-propulsion velocity v0 and by their translational and rotational diffusion coefficients Dt and Dr, respectively. Based on the integration-through-transients formalism, the theory requires as input only the equilibrium static structure factors of the passive system (where v0=0 ). It predicts a nontrivial idealized-glass-transition diagram in the three-dimensional parameter space of density, self-propulsion velocity, and rotational diffusivity that arise because at high densities, the persistence length of active swimming ℓp=v0/Dr interferes with the interaction length ℓc set by the caging of particles. While the low-density dynamics of ABPs is characterized by a single Péclet number Pe=v02/DrDt , close to the glass transition the dynamics is found to depend on Pe and ℓp separately. At fixed density, increasing the self-propulsion velocity causes structural relaxation to speed up, while decreasing the persistence length slows down the relaxation. The active-MCT glass is a nonergodic state that is qualitatively different from the passive glass. In it, correlations of initial density fluctuations never fully decay, but also an infinite memory of initial orientational fluctuations is retained in the positions.

Brownian dynamics study of ion transport in the vestibule of membrane channels.

PubMed

Li, S C; Hoyles, M; Kuyucak, S; Chung, S H

1998-01-01

Brownian dynamics simulations have been carried out to study the transport of ions in a vestibular geometry, which offers a more realistic shape for membrane channels than cylindrical tubes. Specifically, we consider a torus-shaped channel, for which the analytical solution of Poisson's equation is possible. The system is composed of the toroidal channel, with length and radius of the constricted region of 80 A and 4 A, respectively, and two reservoirs containing 50 sodium ions and 50 chloride ions. The positions of each of these ions executing Brownian motion under the influence of a stochastic force and a systematic electric force are determined at discrete time steps of 50 fs for up to 2.5 ns. All of the systematic forces acting on an ion due to the other ions, an external electric field, fixed charges in the channel protein, and the image charges induced at the water-protein boundary are explicitly included in the calculations. We find that the repulsive dielectric force arising from the induced surface charges plays a dominant role in channel dynamics. It expels an ion from the vestibule when it is deliberately put in it. Even in the presence of an applied electric potential of 100 mV, an ion cannot overcome this repulsive force and permeate the channel. Only when dipoles of a favorable orientation are placed along the sides of the transmembrane segment can an ion traverse the channel under the influence of a membrane potential. When the strength of the dipoles is further increased, an ion becomes detained in a potential well, and the driving force provided by the applied field is not sufficient to drive the ion out of the well. The trajectory of an ion navigating across the channel mostly remains close to the central axis of the pore lumen. Finally, we discuss the implications of these findings for the transport of ions across the membrane.

Currency target-zone modeling: An interplay between physics and economics.

PubMed

Lera, Sandro Claudio; Sornette, Didier

2015-12-01

We study the performance of the euro-Swiss franc exchange rate in the extraordinary period from September 6, 2011 to January 15, 2015 when the Swiss National Bank enforced a minimum exchange rate of 1.20 Swiss francs per euro. Within the general framework built on geometric Brownian motions and based on the analogy between Brownian motion in finance and physics, the first-order effect of such a steric constraint would enter a priori in the form of a repulsive entropic force associated with the paths crossing the barrier that are forbidden. Nonparametric empirical estimates of drift and volatility show that the predicted first-order analogy between economics and physics is incorrect. The clue is to realize that the random-walk nature of financial prices results from the continuous anticipation of traders about future opportunities, whose aggregate actions translate into an approximate efficient market with almost no arbitrage opportunities. With the Swiss National Bank's stated commitment to enforce the barrier, traders' anticipation of this action leads to a vanishing drift together with a volatility of the exchange rate that depends on the distance to the barrier. This effect is described by Krugman's model [P. R. Krugman, Target zones and exchange rate dynamics, Q. J. Econ. 106, 669 (1991)]. We present direct quantitative empirical evidence that Krugman's theoretical model provides an accurate description of the euro-Swiss franc target zone. Motivated by the insights from the economic model, we revise the initial economics-physics analogy and show that, within the context of hindered diffusion, the two systems can be described with the same mathematics after all. Using a recently proposed extended analogy in terms of a colloidal Brownian particle embedded in a fluid of molecules associated with the underlying order book, we derive that, close to the restricting boundary, the dynamics of both systems is described by a stochastic differential equation with a very small constant drift and a linear diffusion coefficient. As a side result, we present a simplified derivation of the linear hydrodynamic diffusion coefficient of a Brownian particle close to a wall.

Currency target-zone modeling: An interplay between physics and economics

NASA Astrophysics Data System (ADS)

Lera, Sandro Claudio; Sornette, Didier

2015-12-01

We study the performance of the euro-Swiss franc exchange rate in the extraordinary period from September 6, 2011 to January 15, 2015 when the Swiss National Bank enforced a minimum exchange rate of 1.20 Swiss francs per euro. Within the general framework built on geometric Brownian motions and based on the analogy between Brownian motion in finance and physics, the first-order effect of such a steric constraint would enter a priori in the form of a repulsive entropic force associated with the paths crossing the barrier that are forbidden. Nonparametric empirical estimates of drift and volatility show that the predicted first-order analogy between economics and physics is incorrect. The clue is to realize that the random-walk nature of financial prices results from the continuous anticipation of traders about future opportunities, whose aggregate actions translate into an approximate efficient market with almost no arbitrage opportunities. With the Swiss National Bank's stated commitment to enforce the barrier, traders' anticipation of this action leads to a vanishing drift together with a volatility of the exchange rate that depends on the distance to the barrier. This effect is described by Krugman's model [P. R. Krugman, Target zones and exchange rate dynamics, Q. J. Econ. 106, 669 (1991), 10.2307/2937922]. We present direct quantitative empirical evidence that Krugman's theoretical model provides an accurate description of the euro-Swiss franc target zone. Motivated by the insights from the economic model, we revise the initial economics-physics analogy and show that, within the context of hindered diffusion, the two systems can be described with the same mathematics after all. Using a recently proposed extended analogy in terms of a colloidal Brownian particle embedded in a fluid of molecules associated with the underlying order book, we derive that, close to the restricting boundary, the dynamics of both systems is described by a stochastic differential equation with a very small constant drift and a linear diffusion coefficient. As a side result, we present a simplified derivation of the linear hydrodynamic diffusion coefficient of a Brownian particle close to a wall.

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 height above the wall is set by a combination of thermal noise and active flows. We find the existence of two populations of active particles, slower ones closer to the bottom and faster ones above them, and demonstrate that our method provides quantitative accuracy even with relatively coarse resolutions of the particle geometry.

Conduction at the onset of chaos

NASA Astrophysics Data System (ADS)

Baldovin, Fulvio

2017-02-01

After a general discussion of the thermodynamics of conductive processes, we introduce specific observables enabling the connection of the diffusive transport properties with the microscopic dynamics. We solve the case of Brownian particles, both analytically and numerically, and address then whether aspects of the classic Onsager's picture generalize to the non-local non-reversible dynamics described by logistic map iterates. While in the chaotic case numerical evidence of a monotonic relaxation is found, at the onset of chaos complex relaxation patterns emerge.

Experimental investigation of granular dynamics close to the jamming transition

NASA Astrophysics Data System (ADS)

Caballero, G.; Kolb, E.; Lindner, A.; Lanuza, J.; Clément, E.

2005-06-01

We present different experiments on dense granular assemblies with the aim of clarifying the notion of 'jamming transition' for these assemblies of non-Brownian particles. The experimental set-ups differ in the way in which external perturbations are applied in order to unjam the systems. The first experiment monitors the response to a locally applied deformation of a model packing at rest. The two other experiments study local and collective dynamics in a granular assembly weakly excited by vibration.

Models for twistable elastic polymers in Brownian dynamics, and their implementation for LAMMPS.

PubMed

Brackley, C A; Morozov, A N; Marenduzzo, D

2014-04-07

An elastic rod model for semi-flexible polymers is presented. Theory for a continuum rod is reviewed, and it is shown that a popular discretised model used in numerical simulations gives the correct continuum limit. Correlation functions relating to both bending and twisting of the rod are derived for both continuous and discrete cases, and results are compared with numerical simulations. Finally, two possible implementations of the discretised model in the multi-purpose molecular dynamics software package LAMMPS are described.

Instantaneous and dynamical decoherence

NASA Astrophysics Data System (ADS)

Polonyi, Janos

2018-04-01

Two manifestations of decoherence, called instantaneous and dynamical, are investigated. The former reflects the suppression of the interference between the components of the current state while the latter reflects that within the initial state. These types of decoherence are computed in the case of the Brownian motion and the harmonic and anharmonic oscillators within the semiclassical approximation. A remarkable phenomenon, namely the opposite orientation of the time arrow of the dynamical variables compared to that of the quantum fluctuations generates a double exponential time dependence of the dynamical decoherence in the presence of a harmonic force. For the weakly anharmonic oscillator the dynamical decoherence is found to depend in a singular way on the amount of the anharmonicity.

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).

Double-temperature ratchet model and current reversal of coupled Brownian motors

NASA Astrophysics Data System (ADS)

Li, Chen-Pu; Chen, Hong-Bin; Zheng, Zhi-Gang

2017-12-01

On the basis of the transport features and experimental phenomena observed in studies of molecular motors, we propose a double-temperature ratchet model of coupled motors to reveal the dynamical mechanism of cooperative transport of motors with two heads, where the interactions and asynchrony between two motor heads are taken into account. We investigate the collective unidirectional transport of coupled system and find that the direction of motion can be reversed under certain conditions. Reverse motion can be achieved by modulating the coupling strength, coupling free length, and asymmetric coefficient of the periodic potential, which is understood in terms of the effective potential theory. The dependence of the directed current on various parameters is studied systematically. Directed transport of coupled Brownian motors can be manipulated and optimized by adjusting the pulsation period or the phase shift of the pulsation temperature.

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.

Simulation of Molecular Transport in Systems Containing Mobile Obstacles.

PubMed

Polanowski, Piotr; Sikorski, Andrzej

2016-08-04

In this paper, we investigate the movement of molecules in crowded environments with obstacles undergoing Brownian motion by means of extensive Monte Carlo simulations. Our investigations were performed using the dynamic lattice liquid model, which was based on the cooperative movement concept and allowed to mimic systems at high densities where the motion of all elements (obstacles as well as moving particles) were highly correlated. The crowded environments are modeled on a two-dimensional triangular lattice containing obstacles (particles whose mobility was significantly reduced) moving by a Brownian motion. The subdiffusive motion of both elements in the system was analyzed. It was shown that the percolation transition does not exist in such systems in spite of the cooperative character of the particles' motion. The reduction of the obstacle mobility leads to the longer caging of liquid particles by mobile obstacles.

Quasi-steady-state analysis of coupled flashing ratchets.

PubMed

Levien, Ethan; Bressloff, Paul C

2015-10-01

We perform a quasi-steady-state (QSS) reduction of a flashing ratchet to obtain a Brownian particle in an effective potential. The resulting system is analytically tractable and yet preserves essential dynamical features of the full model. We first use the QSS reduction to derive an explicit expression for the velocity of a simple two-state flashing ratchet. In particular, we determine the relationship between perturbations from detailed balance, which are encoded in the transitions rates of the flashing ratchet, and a tilted-periodic potential. We then perform a QSS analysis of a pair of elastically coupled flashing ratchets, which reduces to a Brownian particle moving in a two-dimensional vector field. We suggest that the fixed points of this vector field accurately approximate the metastable spatial locations of the coupled ratchets, which are, in general, impossible to identify from the full system.

Stochastic description of quantum Brownian dynamics

NASA Astrophysics Data System (ADS)

Yan, Yun-An; Shao, Jiushu

2016-08-01

Classical Brownian motion has well been investigated since the pioneering work of Einstein, which inspired mathematicians to lay the theoretical foundation of stochastic processes. A stochastic formulation for quantum dynamics of dissipative systems described by the system-plus-bath model has been developed and found many applications in chemical dynamics, spectroscopy, quantum transport, and other fields. This article provides a tutorial review of the stochastic formulation for quantum dissipative dynamics. The key idea is to decouple the interaction between the system and the bath by virtue of the Hubbard-Stratonovich transformation or Itô calculus so that the system and the bath are not directly entangled during evolution, rather they are correlated due to the complex white noises introduced. The influence of the bath on the system is thereby defined by an induced stochastic field, which leads to the stochastic Liouville equation for the system. The exact reduced density matrix can be calculated as the stochastic average in the presence of bath-induced fields. In general, the plain implementation of the stochastic formulation is only useful for short-time dynamics, but not efficient for long-time dynamics as the statistical errors go very fast. For linear and other specific systems, the stochastic Liouville equation is a good starting point to derive the master equation. For general systems with decomposable bath-induced processes, the hierarchical approach in the form of a set of deterministic equations of motion is derived based on the stochastic formulation and provides an effective means for simulating the dissipative dynamics. A combination of the stochastic simulation and the hierarchical approach is suggested to solve the zero-temperature dynamics of the spin-boson model. This scheme correctly describes the coherent-incoherent transition (Toulouse limit) at moderate dissipation and predicts a rate dynamics in the overdamped regime. Challenging problems such as the dynamical description of quantum phase transition (local- ization) and the numerical stability of the trace-conserving, nonlinear stochastic Liouville equation are outlined.

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.

Long-range correlations, geometrical structure, and transport properties of macromolecular solutions. The equivalence of configurational statistics and geometrodynamics of large molecules.

PubMed

Mezzasalma, Stefano A

2007-12-04

A special theory of Brownian relativity was previously proposed to describe the universal picture arising in ideal polymer solutions. In brief, it redefines a Gaussian macromolecule in a 4-dimensional diffusive spacetime, establishing a (weak) Lorentz-Poincaré invariance between liquid and polymer Einstein's laws for Brownian movement. Here, aimed at inquiring into the effect of correlations, we deepen the extension of the special theory to a general formulation. The previous statistical equivalence, for dynamic trajectories of liquid molecules and static configurations of macromolecules, and rather obvious in uncorrelated systems, is enlarged by a more general principle of equivalence, for configurational statistics and geometrodynamics. Accordingly, the three geodesic motion, continuity, and field equations could be rewritten, and a number of scaling behaviors were recovered in a spacetime endowed with general static isotropic metric (i.e., for equilibrium polymer solutions). We also dealt with universality in the volume fraction and, unexpectedly, found that a hyperscaling relation of the form, (average size) x (diffusivity) x (viscosity)1/2 ~f(N0, phi0) is fulfilled in several regimes, both in the chain monomer number (N) and polymer volume fraction (phi). Entangled macromolecular dynamics was treated as a geodesic light deflection, entaglements acting in close analogy to the field generated by a spherically symmetric mass source, where length fluctuations of the chain primitive path behave as azimuth fluctuations of its shape. Finally, the general transformation rule for translational and diffusive frames gives a coordinate gauge invariance, suggesting a widened Lorentz-Poincaré symmetry for Brownian statistics. We expect this approach to find effective applications to solutions of arbitrarily large molecules displaying a variety of structures, where the effect of geometry is more explicit and significant in itself (e.g., surfactants, lipids, proteins).

Arbitrage with fractional Gaussian processes

NASA Astrophysics Data System (ADS)

Zhang, Xili; Xiao, Weilin

2017-04-01

While the arbitrage opportunity in the Black-Scholes model driven by fractional Brownian motion has a long history, the arbitrage strategy in the Black-Scholes model driven by general fractional Gaussian processes is in its infancy. The development of stochastic calculus with respect to fractional Gaussian processes allowed us to study such models. In this paper, following the idea of Shiryaev (1998), an arbitrage strategy is constructed for the Black-Scholes model driven by fractional Gaussian processes, when the stochastic integral is interpreted in the Riemann-Stieltjes sense. Arbitrage opportunities in some fractional Gaussian processes, including fractional Brownian motion, sub-fractional Brownian motion, bi-fractional Brownian motion, weighted-fractional Brownian motion and tempered fractional Brownian motion, are also investigated.

Stochastic driven systems far from equilibrium

NASA Astrophysics Data System (ADS)

Kim, Kyung Hyuk

We study the dynamics and steady states of two systems far from equilibrium: a 1-D driven lattice gas and a driven Brownian particle with inertia. (1) We investigate the dynamical scaling behavior of a 1-D driven lattice gas model with two species of particles hopping in opposite directions. We confirm numerically that the dynamic exponent is equal to z = 1.5. We show analytically that a quasi-particle representation relates all phase points to a special phase line directly related to the single-species asymmetric simple exclusion process. Quasi-particle two-point correlations decay exponentially, and in such a manner that quasi-particles of opposite charge dynamically screen each other with a special balance. The balance encompasses all over the phase space. These results indicate that the model belongs to the Kardar-Parisi-Zhang (KPZ) universality class. (2) We investigate the non-equilibrium thermodynamics of a Brownian particle with inertia under feedback control of its inertia. We find such open systems can act as a molecular refrigerator due to an entropy pumping mechanism. We extend the fluctuation theorems to the refrigerator. The entropy pumping modifies both the Jarzynski equality and the fluctuation theorems. We discover that the entropy pumping has a dual role of work and heat. We also investigate the thermodynamics of the particle under a hydrodynamic interaction described by a Langevin equation with a multiplicative noise. The Stratonovich stochastic integration prescription involved in the definition of heat is shown to be the unique physical choice.

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.

Brownian aggregation rate of colloid particles with several active sites

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

Nekrasov, Vyacheslav M.; Yurkin, Maxim A.; Chernyshev, Andrei V., E-mail: chern@ns.kinetics.nsc.ru

2014-08-14

We theoretically analyze the aggregation kinetics of colloid particles with several active sites. Such particles (so-called “patchy particles”) are well known as chemically anisotropic reactants, but the corresponding rate constant of their aggregation has not yet been established in a convenient analytical form. Using kinematic approximation for the diffusion problem, we derived an analytical formula for the diffusion-controlled reaction rate constant between two colloid particles (or clusters) with several small active sites under the following assumptions: the relative translational motion is Brownian diffusion, and the isotropic stochastic reorientation of each particle is Markovian and arbitrarily correlated. This formula was shownmore » to produce accurate results in comparison with more sophisticated approaches. Also, to account for the case of a low number of active sites per particle we used Monte Carlo stochastic algorithm based on Gillespie method. Simulations showed that such discrete model is required when this number is less than 10. Finally, we applied the developed approach to the simulation of immunoagglutination, assuming that the formed clusters have fractal structure.« less

Neutral biogeography and the evolution of climatic niches.

PubMed

Boucher, Florian C; Thuiller, Wilfried; Davies, T Jonathan; Lavergne, Sébastien

2014-05-01

Recent debate on whether climatic niches are conserved through time has focused on how phylogenetic niche conservatism can be measured by deviations from a Brownian motion model of evolutionary change. However, there has been no evaluation of this methodological approach. In particular, the fact that climatic niches are usually obtained from distribution data and are thus heavily influenced by biogeographic factors has largely been overlooked. Our main objective here was to test whether patterns of climatic niche evolution that are frequently observed might arise from neutral dynamics rather than from adaptive scenarios. We developed a model inspired by neutral biodiversity theory, where individuals disperse, compete, and undergo speciation independently of climate. We then sampled the climatic niches of species according to their geographic position and showed that even when species evolve independently of climate, their niches can nonetheless exhibit evolutionary patterns strongly differing from Brownian motion. Indeed, climatic niche evolution is better captured by a model of punctuated evolution with constraints due to landscape boundaries, two features that are traditionally interpreted as evidence for selective processes acting on the niche. We therefore suggest that deviation from Brownian motion alone should not be used as evidence for phylogenetic niche conservatism but that information on phenotypic traits directly linked to physiology is required to demonstrate that climatic niches have been conserved through time.

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

Neutral biogeography and the evolution of climatic niches

PubMed Central

Boucher, Florian C.; Thuiller, Wilfried; Davies, T. Jonathan; Lavergne, Sébastien

2014-01-01

Recent debate on whether climatic niches are conserved through time has focused on how phylogenetic niche conservatism can be measured by deviations from a Brownian motion model of evolutionary change. However, there has been no evaluation of this methodological approach. In particular, the fact that climatic niches are usually obtained from distribution data and are thus heavily influenced by biogeographic factors has largely been overlooked. Our main objective here was to test whether patterns of climatic niche evolution that are frequently observed might arise from neutral dynamics rather than adaptive scenarios. We develop a model inspired by Neutral Biodiversity Theory, where individuals disperse, compete, and undergo speciation independently of climate. We then sample the climatic niches of species according to their geographic position and show that even when species evolved independently of climate, their niches can nonetheless exhibit evolutionary patterns strongly differing from Brownian motion. Indeed, climatic niche evolution is better captured by a model of punctuated evolution with constraints due to landscape boundaries, two features that are traditionally interpreted as evidence for selective processes acting on the niche. We therefore suggest that deviation from Brownian motion alone should not be used as evidence for phylogenetic niche conservatism, but that information on phenotypic traits directly linked to physiology is required to demonstrate that climatic niches have been conserved through time. PMID:24739191

Active Brownian particles with velocity-alignment and active fluctuations

NASA Astrophysics Data System (ADS)

Großmann, R.; Schimansky-Geier, L.; Romanczuk, P.

2012-07-01

We consider a model of active Brownian particles (ABPs) with velocity alignment in two spatial dimensions with passive and active fluctuations. Here, active fluctuations refers to purely non-equilibrium stochastic forces correlated with the heading of an individual active particle. In the simplest case studied here, they are assumed to be independent stochastic forces parallel (speed noise) and perpendicular (angular noise) to the velocity of the particle. On the other hand, passive fluctuations are defined by a noise vector independent of the direction of motion of a particle, and may account, for example, for thermal fluctuations. We derive a macroscopic description of the ABP gas with velocity-alignment interaction. Here, we start from the individual-based description in terms of stochastic differential equations (Langevin equations) and derive equations of motion for the coarse-grained kinetic variables (density, velocity and temperature) via a moment expansion of the corresponding probability density function. We focus here on the different impact of active and passive fluctuations on onset of collective motion and show how active fluctuations in the active Brownian dynamics can change the phase-transition behaviour of the system. In particular, we show that active angular fluctuations lead to an earlier breakdown of collective motion and to the emergence of a new bistable regime in the mean-field case.

Active Polymers — Emergent Conformational and Dynamical Properties: A Brief Review

NASA Astrophysics Data System (ADS)

Winkler, Roland G.; Elgeti, Jens; Gompper, Gerhard

2017-10-01

Active matter exhibits a wealth of emerging nonequilibrium behaviours. A paradigmatic example is the interior of cells, where active components, such as the cytoskeleton, are responsible for its structural organization and the dynamics of the various components. Of particular interest are the properties of polymers and filaments. The intimate coupling of thermal and active noise, hydrodynamic interactions, and polymer conformations implies the emergence of novel structural and dynamical features. In this article, we review recent theoretical and simulation developments and results for the structural and dynamical properties of polymers exposed to activity. Two- and three-dimensional filaments are considered propelled by different mechanisms such as active Brownian particles or hydrodynamically-coupled force dipoles.

Dynamic Forces Between Two Deformable Oil Droplets in Water

NASA Astrophysics Data System (ADS)

Dagastine, Raymond R.; Manica, Rogério; Carnie, Steven L.; Chan, D. Y. C.; Stevens, Geoffrey W.; Grieser, Franz

2006-07-01

The understanding of static interactions in colloidal suspensions is well established, whereas dynamic interactions more relevant to biological and other suspended soft-matter systems are less well understood. We present the direct force measurement and quantitative theoretical description for dynamic forces for liquid droplets in another immiscible fluid. Analysis of this system demonstrates the strong link between interfacial deformation, static surface forces, and hydrodynamic drainage, which govern dynamic droplet-droplet interactions over the length scale of nanometers and over the time scales of Brownian collisions. The results and analysis have direct bearing on the control and manipulation of suspended droplets in soft-matter systems ranging from the emulsions in shampoo to cellular interactions.

Fractal based curves in musical creativity: A critical annotation

NASA Astrophysics Data System (ADS)

Georgaki, Anastasia; Tsolakis, Christos

In this article we examine fractal curves and synthesis algorithms in musical composition and research. First we trace the evolution of different approaches for the use of fractals in music since the 80's by a literature review. Furthermore, we review representative fractal algorithms and platforms that implement them. Properties such as self-similarity (pink noise), correlation, memory (related to the notion of Brownian motion) or non correlation at multiple levels (white noise), can be used to develop hierarchy of criteria for analyzing different layers of musical structure. L-systems can be applied in the modelling of melody in different musical cultures as well as in the investigation of musical perception principles. Finally, we propose a critical investigation approach for the use of artificial or natural fractal curves in systematic musicology.

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.

Internal friction and nonequilibrium unfolding of polymeric globules.

PubMed

Alexander-Katz, Alfredo; Wada, Hirofumi; Netz, Roland R

2009-07-10

The stretching response of a single collapsed homopolymer is studied using Brownian dynamic simulations. The irreversibly dissipated work is found to be dominated by internal friction effects below the collapse temperature, and the internal viscosity grows exponentially with the effective cohesive strength between monomers. These results explain friction effects of globular DNA and are relevant for dissipation at intermediate stages of protein folding.

Poissonian steady states: from stationary densities to stationary intensities.

PubMed

Eliazar, Iddo

2012-10-01

Markov dynamics are the most elemental and omnipresent form of stochastic dynamics in the sciences, with applications ranging from physics to chemistry, from biology to evolution, and from economics to finance. Markov dynamics can be either stationary or nonstationary. Stationary Markov dynamics represent statistical steady states and are quantified by stationary densities. In this paper, we generalize the notion of steady state to the case of general Markov dynamics. Considering an ensemble of independent motions governed by common Markov dynamics, we establish that the entire ensemble attains Poissonian steady states which are quantified by stationary Poissonian intensities and which hold valid also in the case of nonstationary Markov dynamics. The methodology is applied to a host of Markov dynamics, including Brownian motion, birth-death processes, random walks, geometric random walks, renewal processes, growth-collapse dynamics, decay-surge dynamics, Ito diffusions, and Langevin dynamics.

Poissonian steady states: From stationary densities to stationary intensities

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2012-10-01

Markov dynamics are the most elemental and omnipresent form of stochastic dynamics in the sciences, with applications ranging from physics to chemistry, from biology to evolution, and from economics to finance. Markov dynamics can be either stationary or nonstationary. Stationary Markov dynamics represent statistical steady states and are quantified by stationary densities. In this paper, we generalize the notion of steady state to the case of general Markov dynamics. Considering an ensemble of independent motions governed by common Markov dynamics, we establish that the entire ensemble attains Poissonian steady states which are quantified by stationary Poissonian intensities and which hold valid also in the case of nonstationary Markov dynamics. The methodology is applied to a host of Markov dynamics, including Brownian motion, birth-death processes, random walks, geometric random walks, renewal processes, growth-collapse dynamics, decay-surge dynamics, Ito diffusions, and Langevin dynamics.

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.

Two-Point Microrheology of Phase-Separated Domains in Lipid Bilayers

PubMed Central

Hormel, Tristan T.; Reyer, Matthew A.; Parthasarathy, Raghuveer

2015-01-01

Though the importance of membrane fluidity for cellular function has been well established for decades, methods for measuring lipid bilayer viscosity remain challenging to devise and implement. Recently, approaches based on characterizing the Brownian dynamics of individual tracers such as colloidal particles or lipid domains have provided insights into bilayer viscosity. For fluids in general, however, methods based on single-particle trajectories provide a limited view of hydrodynamic response. The technique of two-point microrheology, in which correlations between the Brownian dynamics of pairs of tracers report on the properties of the intervening medium, characterizes viscosity at length-scales that are larger than that of individual tracers and has less sensitivity to tracer-induced distortions, but has never been applied to lipid membranes. We present, to our knowledge, the first two-point microrheological study of lipid bilayers, examining the correlated motion of domains in phase-separated lipid vesicles and comparing one- and two-point results. We measure two-point correlation functions in excellent agreement with the forms predicted by two-dimensional hydrodynamic models, analysis of which reveals a viscosity intermediate between those of the two lipid phases, indicative of global fluid properties rather than the viscosity of the local neighborhood of the tracer. PMID:26287625

Confinement of active systems: trapping, swim pressure, and explosions

NASA Astrophysics Data System (ADS)

Takatori, Sho; de Dier, Raf; Vermant, Jan; Brady, John

2015-11-01

We analyze the run-and-tumble dynamics and motion of living bacteria and self-propelled Janus motors confined in an acoustic trap. Since standard optical tweezers are far too weak, we developed an acoustic trap strong enough to confine swimmers over distances large compared to the swimmers' size and run length. The external trap behaves as an ``osmotic barrier'' that confines the swimmers inside the trapping region, analogous to semipermeable membranes that confine passive Brownian particles inside a boundary. From the swimmers' restricted motion inside the trap, we calculate the unique swim pressure generated by active systems originating from the force required to confine them by boundaries. We apply a strong trap to collect the swimmers into a close-packed active crystal and then turn off the trap which causes the crystal to ``explode'' due to an imbalance of the active pressure. We corroborate all experimental results with Brownian dynamics simulations and analytical theory. ST is supported by a Gates Millennium Scholars fellowship and a NSF Fellowship No. DGE-1144469. RDD is supported by a doctoral fellowship of the fund for scientific research (FWO-Vlaanderen). This work is also supported by NSF Grant CBET 1437570.

Brownian dynamics simulation of a polymer chain in a solid-state nanopore attached to a molecular stop

NASA Astrophysics Data System (ADS)

Wells, Craig; Hulings, Zachery; Melnikov, Dmitriy; Gracheva, Maria

We study a nanopore inside a silicon dioxide membrane submerged in a KCl solution with a negatively charged polymer chain of varying lengths whose movement is described using Brownian dynamics. The polymer is attached to a molecule with a radius larger than that of the nanopore's which acts as a molecular stop, allowing the chain to thread the nanopore but preventing it from translocating. We found that the polymer chain's variation of movement along the nanopore decreased when increasing applied biases and chain lengths for portions of the chain closest to the molecular stop. The chain displacement within the pore is also compared to a freely translocating polymer where preliminary results show the free polymer having a greater variation in the radial direction. Overall, our preliminary results indicate that the radial direction of the polymer chain is dominated by the confinement in the narrow nanopore with restrictions imposed by the molecular stop and bias playing a lesser role. Understanding the interaction behavior of the polymer chain-stop molecule may lead to methods that decrease movement variation, facilitating an improvement on characterizing and identification of molecules. NSF DMR and CBET Grant No. 1352218.

Modeling of enhanced catalysis in multienzyme nanostructures: effect of molecular scaffolds, spatial organization, and concentration.

PubMed

Roberts, Christopher C; Chang, Chia-en A

2015-01-13

Colocalized multistep enzymatic reaction pathways within biological catabolic and metabolic processes occur with high yield and specificity. Spatial organization on membranes or surfaces may be associated with increased efficiency of intermediate substrate transfer. Using a new Brownian dynamics package, GeomBD, we explored the geometric features of a surface-anchored enzyme system by parallel coarse-grained Brownian dynamics simulations of substrate diffusion over microsecond (μs) to millisecond (ms) time scales. We focused on a recently developed glucose oxidase (GOx), horseradish peroxidase (HRP), and DNA origami-scaffold enzyme system, where the H2O2 substrate of HRP is produced by GOx. The results revealed and explained a significant advantage in catalytic enhancement by optimizing interenzyme distance and orientation in the presence of the scaffold model. The planar scaffold colocalized the enzymes and provided a diffusive barrier that enhanced substrate transfer probability, becoming more relevant with increasing interenzyme distance. The results highlight the importance of protein geometry in the proper assessment of distance and orientation dependence on the probability of substrate transfer. They shed light on strategies for engineering multienzyme complexes and further investigation of enhanced catalytic efficiency for substrate diffusion between membrane-anchoring proteins.

A dynamic Brownian bridge movement model to estimate utilization distributions for heterogeneous animal movement.

PubMed

Kranstauber, Bart; Kays, Roland; Lapoint, Scott D; Wikelski, Martin; Safi, Kamran

2012-07-01

1. The recently developed Brownian bridge movement model (BBMM) has advantages over traditional methods because it quantifies the utilization distribution of an animal based on its movement path rather than individual points and accounts for temporal autocorrelation and high data volumes. However, the BBMM assumes unrealistic homogeneous movement behaviour across all data. 2. Accurate quantification of the utilization distribution is important for identifying the way animals use the landscape. 3. We improve the BBMM by allowing for changes in behaviour, using likelihood statistics to determine change points along the animal's movement path. 4. This novel extension, outperforms the current BBMM as indicated by simulations and examples of a territorial mammal and a migratory bird. The unique ability of our model to work with tracks that are not sampled regularly is especially important for GPS tags that have frequent failed fixes or dynamic sampling schedules. Moreover, our model extension provides a useful one-dimensional measure of behavioural change along animal tracks. 5. This new method provides a more accurate utilization distribution that better describes the space use of realistic, behaviourally heterogeneous tracks. © 2012 The Authors. Journal of Animal Ecology © 2012 British Ecological Society.

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.

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.

Brownian dynamics of wall tethered polymers in shear flow

NASA Astrophysics Data System (ADS)

Lin, Tiras Y.; Saadat, Amir; Kushwaha, Amit; Shaqfeh, Eric S. G.

2017-11-01

The dynamics of a wall tethered polymer in shear flow is studied using Brownian dynamics. Simulations are performed with bead-spring chains, and the effect of hydrodynamic interactions (HI) is incorporated through Blake's tensor with a finite size bead correction. We characterize the configuration of the polymer as a function of the Weissenberg number by investigating the regions the polymer explores in both the flow-gradient and flow-vorticity planes. The fractional extension in the flow direction, the width in the vorticity direction, and the thickness in the gradient direction are reported as well, and these quantities are found to compare favorably with the experimental data of the literature. The cyclic motion of the polymer is demonstrated through analysis of the mean velocity field of the end bead. We characterize the collision process of each bead with the wall as a Poisson process and extract an average wall collision rate, which in general varies along the backbone of the chain. The inclusion of HI with the wall for a tethered polymer is found to reduce the average wall collision rate. We anticipate that results from this work will be directly applicable to, e.g., the design of polymer brushes or the use of DNA for making nanowires in molecular electronics. T.Y.L. is supported by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.

Brownian Dynamics Simulations of Ion Transport through the VDAC

PubMed Central

Lee, Kyu Il; Rui, Huan; Pastor, Richard W.; Im, Wonpil

2011-01-01

It is important to gain a physical understanding of ion transport through the voltage-dependent anion channel (VDAC) because this channel provides primary permeation pathways for metabolites and electrolytes between the cytosol and mitochondria. We performed grand canonical Monte Carlo/Brownian dynamics (GCMC/BD) simulations to explore the ion transport properties of human VDAC isoform 1 (hVDAC1; PDB:2K4T) embedded in an implicit membrane. When the MD-derived, space-dependent diffusion constant was used in the GCMC/BD simulations, the current-voltage characteristics and ion number profiles inside the pore showed excellent agreement with those calculated from all-atom molecular-dynamics (MD) simulations, thereby validating the GCMC/BD approach. Of the 20 NMR models of hVDAC1 currently available, the third one (NMR03) best reproduces both experimental single-channel conductance and ion selectivity (i.e., the reversal potential). In addition, detailed analyses of the ion trajectories, one-dimensional multi-ion potential of mean force, and protein charge distribution reveal that electrostatic interactions play an important role in the channel structure and ion transport relationship. Finally, the GCMC/BD simulations of various mutants based on NMR03 show good agreement with experimental ion selectivity. The difference in ion selectivity between the wild-type and the mutants is the result of altered potential of mean force profiles that are dominated by the electrostatic interactions. PMID:21281575

Better Than Counting: Density Profiles from Force Sampling

NASA Astrophysics Data System (ADS)

de las Heras, Daniel; Schmidt, Matthias

2018-05-01

Calculating one-body density profiles in equilibrium via particle-based simulation methods involves counting of events of particle occurrences at (histogram-resolved) space points. Here, we investigate an alternative method based on a histogram of the local force density. Via an exact sum rule, the density profile is obtained with a simple spatial integration. The method circumvents the inherent ideal gas fluctuations. We have tested the method in Monte Carlo, Brownian dynamics, and molecular dynamics simulations. The results carry a statistical uncertainty smaller than that of the standard counting method, reducing therefore the computation time.

Cycles, scaling and crossover phenomenon in length of the day (LOD) time series

NASA Astrophysics Data System (ADS)

Telesca, Luciano

2007-06-01

The dynamics of the temporal fluctuations of the length of the day (LOD) time series from January 1, 1962 to November 2, 2006 were investigated. The power spectrum of the whole time series has revealed annual, semi-annual, decadal and daily oscillatory behaviors, correlated with oceanic-atmospheric processes and interactions. The scaling behavior was analyzed by using the detrended fluctuation analysis (DFA), which has revealed two different scaling regimes, separated by a crossover timescale at approximately 23 days. Flicker-noise process can describe the dynamics of the LOD time regime involving intermediate and long timescales, while Brownian dynamics characterizes the LOD time series for small timescales.

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.

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

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.

Fast antibody fragment motion: flexible linkers act as entropic spring

PubMed Central

Stingaciu, Laura R.; Ivanova, Oxana; Ohl, Michael; Biehl, Ralf; Richter, Dieter

2016-01-01

A flexible linker region between three fragments allows antibodies to adjust their binding sites to an antigen or receptor. Using Neutron Spin Echo Spectroscopy we observed fragment motion on a timescale of 7 ns with motional amplitudes of about 1 nm relative to each other. The mechanistic complexity of the linker region can be described by a spring model with Brownian motion of the fragments in a harmonic potential. Displacements, timescale, friction and force constant of the underlying dynamics are accessed. The force constant exhibits a similar strength to an entropic spring, with friction of the fragment matching the unbound state. The observed fast motions are fluctuations in pre-existing equilibrium configurations. The Brownian motion of domains in a harmonic potential is the appropriate model to examine functional hinge motions dependent on the structural topology and highlights the role of internal forces and friction to function. PMID:27020739

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.

Self-induced polar order of active Brownian particles in a harmonic trap.

PubMed

Hennes, Marc; Wolff, Katrin; Stark, Holger

2014-06-13

Hydrodynamically interacting active particles in an external harmonic potential form a self-assembled fluid pump at large enough Péclet numbers. Here, we give a quantitative criterion for the formation of the pump and show that particle orientations align in the self-induced flow field in surprising analogy to ferromagnetic order where the active Péclet number plays the role of inverse temperature. The particle orientations follow a Boltzmann distribution Φ(p) ∼ exp(Ap(z)) where the ordering mean field A scales with the active Péclet number and polar order parameter. The mean flow field in which the particles' swimming directions align corresponds to a regularized Stokeslet with strength proportional to swimming speed. Analytic mean-field results are compared with results from Brownian dynamics simulations with hydrodynamic interactions included and are found to capture the self-induced alignment very well.

Fast antibody fragment motion: flexible linkers act as entropic spring

DOE PAGES

Stingaciu, Laura R.; Ivanova, Oxana; Ohl, Michael; ...

2016-03-29

A flexible linker region between three fragments allows antibodies to adjust their binding sites to an antigen or receptor. Using Neutron Spin Echo Spectroscopy we observed fragment motion on a timescale of 7 ns with motional amplitudes of about 1 nm relative to each other. The mechanistic complexity of the linker region can be described by a spring model with Brownian motion of the fragments in a harmonic potential. Displacements, timescale, friction and force constant of the underlying dynamics are accessed. The force constant exhibits a similar strength to an entropic spring, with friction of the fragment matching the unboundmore » state. The observed fast motions are fluctuations in pre-existing equilibrium configurations. In conclusion, the Brownian motion of domains in a harmonic potential is the appropriate model to examine functional hinge motions dependent on the structural topology and highlights the role of internal forces and friction to function.« less

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.

Fast antibody fragment motion: flexible linkers act as entropic spring.

PubMed

Stingaciu, Laura R; Ivanova, Oxana; Ohl, Michael; Biehl, Ralf; Richter, Dieter

2016-03-29

A flexible linker region between three fragments allows antibodies to adjust their binding sites to an antigen or receptor. Using Neutron Spin Echo Spectroscopy we observed fragment motion on a timescale of 7 ns with motional amplitudes of about 1 nm relative to each other. The mechanistic complexity of the linker region can be described by a spring model with Brownian motion of the fragments in a harmonic potential. Displacements, timescale, friction and force constant of the underlying dynamics are accessed. The force constant exhibits a similar strength to an entropic spring, with friction of the fragment matching the unbound state. The observed fast motions are fluctuations in pre-existing equilibrium configurations. The Brownian motion of domains in a harmonic potential is the appropriate model to examine functional hinge motions dependent on the structural topology and highlights the role of internal forces and friction to function.

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.

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 of bacterial populations, the Kuramoto model describing the collective synchronization of coupled oscillators, the Desai-Zwanzig model, and the models describing the collective motion of social organisms such as bird flocks or fish schools.

Biophysical Discovery through the Lens of a Computational Microscope

NASA Astrophysics Data System (ADS)

Amaro, Rommie

With exascale computing power on the horizon, improvements in the underlying algorithms and available structural experimental data are enabling new paradigms for chemical discovery. My work has provided key insights for the systematic incorporation of structural information resulting from state-of-the-art biophysical simulations into protocols for inhibitor and drug discovery. We have shown that many disease targets have druggable pockets that are otherwise ``hidden'' in high resolution x-ray structures, and that this is a common theme across a wide range of targets in different disease areas. We continue to push the limits of computational biophysical modeling by expanding the time and length scales accessible to molecular simulation. My sights are set on, ultimately, the development of detailed physical models of cells, as the fundamental unit of life, and two recent achievements highlight our efforts in this arena. First is the development of a molecular and Brownian dynamics multi-scale modeling framework, which allows us to investigate drug binding kinetics in addition to thermodynamics. In parallel, we have made significant progress developing new tools to extend molecular structure to cellular environments. Collectively, these achievements are enabling the investigation of the chemical and biophysical nature of cells at unprecedented scales.

Swarms with canonical active Brownian motion.

PubMed

Glück, Alexander; Hüffel, Helmuth; Ilijić, Saša

2011-05-01

We present a swarm model of Brownian particles with harmonic interactions, where the individuals undergo canonical active Brownian motion, i.e., each Brownian particle can convert internal energy to mechanical energy of motion. We assume the existence of a single global internal energy of the system. Numerical simulations show amorphous swarming behavior as well as static configurations. Analytic understanding of the system is provided by studying stability properties of equilibria.

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

Clustering of Magnetic Swimmers in a Poiseuille Flow

NASA Astrophysics Data System (ADS)

Meng, Fanlong; Matsunaga, Daiki; Golestanian, Ramin

2018-05-01

We investigate the collective behavior of magnetic swimmers, which are suspended in a Poiseuille flow and placed under an external magnetic field, using analytical techniques and Brownian dynamics simulations. We find that the interplay between intrinsic activity, external alignment, and magnetic dipole-dipole interactions leads to longitudinal structure formation. Our work sheds light on a recent experimental observation of a clustering instability in this system.

Path integral analysis of Jarzynski's equality: Analytical results

NASA Astrophysics Data System (ADS)

Minh, David D. L.; Adib, Artur B.

2009-02-01

We apply path integrals to study nonequilibrium work theorems in the context of Brownian dynamics, deriving in particular the equations of motion governing the most typical and most dominant trajectories. For the analytically soluble cases of a moving harmonic potential and a harmonic oscillator with a time-dependent natural frequency, we find such trajectories, evaluate the work-weighted propagators, and validate Jarzynski’s equality.

Numerical approach on dynamic self-assembly of colloidal particles

NASA Astrophysics Data System (ADS)

Ibrahimi, Muhamet; Ilday, Serim; Makey, Ghaith; Pavlov, Ihor; Yavuz, Özgàn; Gulseren, Oguz; Ilday, Fatih Omer

Far from equilibrium systems of artificial ensembles are crucial for understanding many intelligent features in self-organized natural systems. However, the lack of established theory underlies a need for numerical implementations. Inspired by a novel work, we simulate a solution-suspended colloidal system that dynamically self assembles due to convective forces generated in the solvent when heated by a laser. In order to incorporate with random fluctuations of particles and continuously changing flow, we exploit a random-walk based Brownian motion model and a fluid dynamics solver prepared for games, respectively. Simulation results manage to fit to experiments and show many quantitative features of a non equilibrium dynamic self assembly, including phase space compression and an ensemble-energy input feedback loop.

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.

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.

Rapid Brownian Motion Primes Ultrafast Reconstruction of Intrinsically Disordered Phe-Gly Repeats Inside the Nuclear Pore Complex.

PubMed

Moussavi-Baygi, R; Mofrad, M R K

2016-07-29

Conformational behavior of intrinsically disordered proteins, such as Phe-Gly repeat domains, alters drastically when they are confined in, and tethered to, nan channels. This has challenged our understanding of how they serve to selectively facilitate translocation of nuclear transport receptor (NTR)-bearing macromolecules. Heterogeneous FG-repeats, tethered to the NPC interior, nonuniformly fill the channel in a diameter-dependent manner and adopt a rapid Brownian motion, thereby forming a porous and highly dynamic polymeric meshwork that percolates in radial and axial directions and features two distinguishable zones: a dense hydrophobic rod-like zone located in the center, and a peripheral low-density shell-like zone. The FG-meshwork is locally disrupted upon interacting with NTR-bearing macromolecules, but immediately reconstructs itself between 0.44 μs and 7.0 μs, depending on cargo size and shape. This confers a perpetually-sealed state to the NPC, and is solely due to rapid Brownian motion of FG-repeats, not FG-repeat hydrophobic bonds. Elongated-shaped macromolecules, both in the presence and absence of NTRs, penetrate more readily into the FG-meshwork compared to their globular counterparts of identical volume and surface chemistry, highlighting the importance of the shape effects in nucleocytoplasmic transport. These results can help our understanding of geometrical effects in, and the design of, intelligent and responsive biopolymer-based materials in nanofiltration and artificial nanopores.

Probability distribution of financial returns in a model of multiplicative Brownian motion with stochastic diffusion coefficient

NASA Astrophysics Data System (ADS)

Silva, Antonio

2005-03-01

It is well-known that the mathematical theory of Brownian motion was first developed in the Ph. D. thesis of Louis Bachelier for the French stock market before Einstein [1]. In Ref. [2] we studied the so-called Heston model, where the stock-price dynamics is governed by multiplicative Brownian motion with stochastic diffusion coefficient. We solved the corresponding Fokker-Planck equation exactly and found an analytic formula for the time-dependent probability distribution of stock price changes (returns). The formula interpolates between the exponential (tent-shaped) distribution for short time lags and the Gaussian (parabolic) distribution for long time lags. The theoretical formula agrees very well with the actual stock-market data ranging from the Dow-Jones index [2] to individual companies [3], such as Microsoft, Intel, etc. [] [1] Louis Bachelier, ``Th'eorie de la sp'eculation,'' Annales Scientifiques de l''Ecole Normale Sup'erieure, III-17:21-86 (1900).[] [2] A. A. Dragulescu and V. M. Yakovenko, ``Probability distribution of returns in the Heston model with stochastic volatility,'' Quantitative Finance 2, 443--453 (2002); Erratum 3, C15 (2003). [cond-mat/0203046] [] [3] A. C. Silva, R. E. Prange, and V. M. Yakovenko, ``Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact,'' Physica A 344, 227--235 (2004). [cond-mat/0401225

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

Dark field differential dynamic microscopy enables accurate characterization of the roto-translational dynamics of bacteria and colloidal clusters

NASA Astrophysics Data System (ADS)

Cerbino, Roberto; Piotti, Davide; Buscaglia, Marco; Giavazzi, Fabio

2018-01-01

Micro- and nanoscale objects with anisotropic shape are key components of a variety of biological systems and inert complex materials, and represent fundamental building blocks of novel self-assembly strategies. The time scale of their thermal motion is set by their translational and rotational diffusion coefficients, whose measurement may become difficult for relatively large particles with small optical contrast. Here we show that dark field differential dynamic microscopy is the ideal tool for probing the roto-translational Brownian motion of anisotropic shaped particles. We demonstrate our approach by successful application to aqueous dispersions of non-motile bacteria and of colloidal aggregates of spherical particles.

Volumetric bioimaging based on light field microscopy with temporal focusing illumination

NASA Astrophysics Data System (ADS)

Hsu, Feng-Chun; Sie, Yong Da; Lai, Feng-Jie; Chen, Shean-Jen

2018-02-01

Light field technique at a single shot can get the whole volume image of observed sample. Therefore, the original frame rate of the optical system can be taken as the volumetric image rate. For dynamically imaging whole micron-scale biosample, a light field microscope with temporal focusing illumination has been developed. In the light field microscope, the f-number of the microlens array (MLA) is adopted to match that of the objective; hence, the subimages via adjacent lenslets do not overlay each other. A three-dimensional (3D) deconvolution algorithm is utilized to deblur the out-of-focusing part. Conventional light field microscopy (LFM) illuminates whole volume sample even noninteresting parts; nevertheless, whole volume excitation causes even more damage on bio-sample and also increase the background noise from the out of range. Therefore, temporal focusing is integrated into the light field microscope for selecting the illumination volume. Herein, a slit on the back focal plane of the objective is utilized to control the axial excitation confinement for selecting the illumination volume. As a result, the developed light field microscope with the temporal focusing multiphoton illumination (TFMPI) can reconstruct 3D images within the selected volume, and the lateral resolution approaches to the theoretical value. Furthermore, the 3D Brownian motion of two-micron fluorescent beads is observed as the criterion of dynamic sample. With superior signal-to-noise ratio and less damage to tissue, the microscope is potential to provide volumetric imaging for vivo sample.

A computational kinetic model of diffusion for molecular systems.

PubMed

Teo, Ivan; Schulten, Klaus

2013-09-28

Regulation of biomolecular transport in cells involves intra-protein steps like gating and passage through channels, but these steps are preceded by extra-protein steps, namely, diffusive approach and admittance of solutes. The extra-protein steps develop over a 10-100 nm length scale typically in a highly particular environment, characterized through the protein's geometry, surrounding electrostatic field, and location. In order to account for solute energetics and mobility of solutes in this environment at a relevant resolution, we propose a particle-based kinetic model of diffusion based on a Markov State Model framework. Prerequisite input data consist of diffusion coefficient and potential of mean force maps generated from extensive molecular dynamics simulations of proteins and their environment that sample multi-nanosecond durations. The suggested diffusion model can describe transport processes beyond microsecond duration, relevant for biological function and beyond the realm of molecular dynamics simulation. For this purpose the systems are represented by a discrete set of states specified by the positions, volumes, and surface elements of Voronoi grid cells distributed according to a density function resolving the often intricate relevant diffusion space. Validation tests carried out for generic diffusion spaces show that the model and the associated Brownian motion algorithm are viable over a large range of parameter values such as time step, diffusion coefficient, and grid density. A concrete application of the method is demonstrated for ion diffusion around and through the Eschericia coli mechanosensitive channel of small conductance ecMscS.

Dynamical continuous time random Lévy flights

NASA Astrophysics Data System (ADS)

Liu, Jian; Chen, Xiaosong

2016-03-01

The Lévy flights' diffusive behavior is studied within the framework of the dynamical continuous time random walk (DCTRW) method, while the nonlinear friction is introduced in each step. Through the DCTRW method, Lévy random walker in each step flies by obeying the Newton's Second Law while the nonlinear friction f(v) = - γ0v - γ2v3 being considered instead of Stokes friction. It is shown that after introducing the nonlinear friction, the superdiffusive Lévy flights converges, behaves localization phenomenon with long time limit, but for the Lévy index μ = 2 case, it is still Brownian motion.

Application of dynamic light scattering for studying the evolution of micro- and nano-droplets

NASA Astrophysics Data System (ADS)

Derkachov, G.; Jakubczyk, D.; Kolwas, K.; Shopa, Y.; Woźniak, M.; Wojciechowski, T.

2018-01-01

The dynamic light scattering (DLS) technique was used for studying the processes of aggregation of spherical SiO2 particles in various diethylene glycol (DEG) suspensions. The suspensions were studied in a cuvette, in a millimeter-sized droplet and in a micrometer-sized droplet. For the first time DLS signals for droplets of picolitre volume, levitated in an electrodynamic quadrupole trap, were obtained. It is shown that the correlation analysis of light scattered from a micro-droplet allows monitoring the changes of its internal structure, as well as its motions: trap-constricted Brownian motions and random rotations.

The hydrogen diffusion in liquid aluminum alloys from ab initio molecular dynamics

NASA Astrophysics Data System (ADS)

Jakse, N.; Pasturel, A.

2014-09-01

We study the hydrogen diffusion in liquid aluminum alloys through extensive ab initio molecular dynamics simulations. At the microscopic scale, we show that the hydrogen motion is characterized by a broad distribution of spatial jumps that does not correspond to a Brownian motion. To determine the self-diffusion coefficient of hydrogen in liquid aluminum alloys, we use a generalized continuous time random walk model recently developed to describe the hydrogen diffusion in pure aluminum. In particular, we show that the model successfully accounts the effects of alloying elements on the hydrogen diffusion in agreement with experimental features.

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.

Dynamic Control of Topological Defects in Artificial Colloidal Ice

DOE PAGES

Libál, A.; Nisoli, C.; Reichhardt, C.; ...

2017-04-05

We demonstrate the use of an external field to stabilize and control defect lines connecting topological monopoles in spin ice. For definiteness we perform Brownian dynamics simulations with realistic units mimicking experimentally realized artificial colloidal spin ice systems, and show how defect lines can grow, shrink or move under the action of direct and alternating fields. Asymmetric alternating biasing forces can cause the defect line to ratchet in either direction, making it possible to precisely position the line at a desired location. Such manipulation could be employed to achieve mobile information storage in these metamaterials.

Microstructural Dynamics and Rheology of Suspensions of Rigid Fibers

NASA Astrophysics Data System (ADS)

Butler, Jason E.; Snook, Braden

2018-01-01

The dynamics and rheology of suspensions of rigid, non-Brownian fibers in Newtonian fluids are reviewed. Experiments, theories, and computer simulations are considered, with an emphasis on suspensions at semidilute and concentrated conditions. In these suspensions, interactions between the particles strongly influence the microstructure and rheological properties of the suspension. The interactions can arise from hydrodynamic disturbances, giving multibody interactions at long ranges and pairwise lubrication forces over short distances. For concentrated suspensions, additional interactions due to excluded volume (contacts) and adhesive forces are addressed. The relative importance of the various interactions as a function of fiber concentration is assessed.

Molten Salts and Isotope Separation

NASA Astrophysics Data System (ADS)

Lantelme, Frédéric

2013-02-01

The work on molten salts and isotope separation performed over the years at Université Pierre et Marie Curie and at Collège de France is critically reviewed. This research, closely related to A. Klemm's pioneering contributions, leads among other things to the discovery of the effect now called the `Chemla effect', after the late Professor Marius Chemla. These studies of ionic motions in melts, and liquids in general, have greatly benefitted from recent advances in molecular simulations. Some recent results of such simulations - molecular dynamics (MD) and Brownian dynamics (BD) - as well as of related theoretical work are discussed.

Dynamic Control of Topological Defects in Artificial Colloidal Ice

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

Libál, A.; Nisoli, C.; Reichhardt, C.

We demonstrate the use of an external field to stabilize and control defect lines connecting topological monopoles in spin ice. For definiteness we perform Brownian dynamics simulations with realistic units mimicking experimentally realized artificial colloidal spin ice systems, and show how defect lines can grow, shrink or move under the action of direct and alternating fields. Asymmetric alternating biasing forces can cause the defect line to ratchet in either direction, making it possible to precisely position the line at a desired location. Such manipulation could be employed to achieve mobile information storage in these metamaterials.

Brownian Dynamics Simulation of Nucleocytoplasmic Transport: A Coarse-Grained Model for the Functional State of the Nuclear Pore Complex

PubMed Central

Moussavi-Baygi, Ruhollah; Jamali, Yousef; Karimi, Reza; Mofrad, Mohammad R. K.

2011-01-01

The nuclear pore complex (NPC) regulates molecular traffic across the nuclear envelope (NE). Selective transport happens on the order of milliseconds and the length scale of tens of nanometers; however, the transport mechanism remains elusive. Central to the transport process is the hydrophobic interactions between karyopherins (kaps) and Phe-Gly (FG) repeat domains. Taking into account the polymeric nature of FG-repeats grafted on the elastic structure of the NPC, and the kap-FG hydrophobic affinity, we have established a coarse-grained model of the NPC structure that mimics nucleocytoplasmic transport. To establish a foundation for future works, the methodology and biophysical rationale behind the model is explained in details. The model predicts that the first-passage time of a 15 nm cargo-complex is about 2.6±0.13 ms with an inverse Gaussian distribution for statistically adequate number of independent Brownian dynamics simulations. Moreover, the cargo-complex is primarily attached to the channel wall where it interacts with the FG-layer as it passes through the central channel. The kap-FG hydrophobic interaction is highly dynamic and fast, which ensures an efficient translocation through the NPC. Further, almost all eight hydrophobic binding spots on kap-β are occupied simultaneously during transport. Finally, as opposed to intact NPCs, cytoplasmic filaments-deficient NPCs show a high degree of permeability to inert cargos, implying the defining role of cytoplasmic filaments in the selectivity barrier. PMID:21673865

Web interface for Brownian dynamics simulation of ion transport and its applications to beta-barrel pores.

PubMed

Lee, Kyu Il; Jo, Sunhwan; Rui, Huan; Egwolf, Bernhard; Roux, Benoît; Pastor, Richard W; Im, Wonpil

2012-01-30

Brownian dynamics (BD) based on accurate potential of mean force is an efficient and accurate method for simulating ion transport through wide ion channels. Here, a web-based graphical user interface (GUI) is presented for carrying out grand canonical Monte Carlo (GCMC) BD simulations of channel proteins: http://www.charmm-gui.org/input/gcmcbd. The webserver is designed to help users avoid most of the technical difficulties and issues encountered in setting up and simulating complex pore systems. GCMC/BD simulation results for three proteins, the voltage dependent anion channel (VDAC), α-Hemolysin (α-HL), and the protective antigen pore of the anthrax toxin (PA), are presented to illustrate the system setup, input preparation, and typical output (conductance, ion density profile, ion selectivity, and ion asymmetry). Two models for the input diffusion constants for potassium and chloride ions in the pore are compared: scaling of the bulk diffusion constants by 0.5, as deduced from previous all-atom molecular dynamics simulations of VDAC, and a hydrodynamics based model (HD) of diffusion through a tube. The HD model yields excellent agreement with experimental conductances for VDAC and α-HL, while scaling bulk diffusion constants by 0.5 leads to underestimates of 10-20%. For PA, simulated ion conduction values overestimate experimental values by a factor of 1.5-7 (depending on His protonation state and the transmembrane potential), implying that the currently available computational model of this protein requires further structural refinement. Copyright © 2011 Wiley Periodicals, Inc.

Web Interface for Brownian Dynamics Simulation of Ion Transport and Its Applications to Beta-Barrel Pores

PubMed Central

Lee, Kyu Il; Jo, Sunhwan; Rui, Huan; Egwolf, Bernhard; Roux, Benoît; Pastor, Richard W.; Im, Wonpil

2011-01-01

Brownian dynamics (BD) in a suitably constructed potential of mean force is an efficient and accurate method for simulating ion transport through wide ion channels. Here, a web-based graphical user interface (GUI) is presented for grand canonical Monte Carlo (GCMC) BD simulations of channel proteins: http://www.charmm-gui.org/input/gcmcbd. The webserver is designed to help users avoid most of the technical difficulties and issues encountered in setting up and simulating complex pore systems. GCMC/BD simulation results for three proteins, the voltage dependent anion channel (VDAC), α-Hemolysin, and the protective antigen pore of the anthrax toxin (PA), are presented to illustrate system setup, input preparation, and typical output (conductance, ion density profile, ion selectivity, and ion asymmetry). Two models for the input diffusion constants for potassium and chloride ions in the pore are compared: scaling of the bulk diffusion constants by 0.5, as deduced from previous all-atom molecular dynamics simulations of VDAC; and a hydrodynamics based model (HD) of diffusion through a tube. The HD model yields excellent agreement with experimental conductances for VDAC and α-Hemolysin, while scaling bulk diffusion constants by 0.5 leads to underestimates of 10–20%. For PA, simulated ion conduction values overestimate experimental values by a factor of 1.5 to 7 (depending on His protonation state and the transmembrane potential), implying that the currently available computational model of this protein requires further structural refinement. PMID:22102176

Thermal fluctuations of haemoglobin from different species: adaptation to temperature via conformational dynamics

PubMed Central

Stadler, A. M.; Garvey, C. J.; Bocahut, A.; Sacquin-Mora, S.; Digel, I.; Schneider, G. J.; Natali, F.; Artmann, G. M.; Zaccai, G.

2012-01-01

Thermodynamic stability, configurational motions and internal forces of haemoglobin (Hb) of three endotherms (platypus, Ornithorhynchus anatinus; domestic chicken, Gallus gallus domesticus and human, Homo sapiens) and an ectotherm (salt water crocodile, Crocodylus porosus) were investigated using circular dichroism, incoherent elastic neutron scattering and coarse-grained Brownian dynamics simulations. The experimental results from Hb solutions revealed a direct correlation between protein resilience, melting temperature and average body temperature of the different species on the 0.1 ns time scale. Molecular forces appeared to be adapted to permit conformational fluctuations with a root mean square displacement close to 1.2 Å at the corresponding average body temperature of the endotherms. Strong forces within crocodile Hb maintain the amplitudes of motion within a narrow limit over the entire temperature range in which the animal lives. In fully hydrated powder samples of human and chicken, Hb mean square displacements and effective force constants on the 1 ns time scale showed no differences over the whole temperature range from 10 to 300 K, in contrast to the solution case. A complementary result of the study, therefore, is that one hydration layer is not sufficient to activate all conformational fluctuations of Hb in the pico- to nanosecond time scale which might be relevant for biological function. Coarse-grained Brownian dynamics simulations permitted to explore residue-specific effects. They indicated that temperature sensing of human and chicken Hb occurs mainly at residues lining internal cavities in the β-subunits. PMID:22696485

Thermal fluctuations of haemoglobin from different species: adaptation to temperature via conformational dynamics.

PubMed

Stadler, A M; Garvey, C J; Bocahut, A; Sacquin-Mora, S; Digel, I; Schneider, G J; Natali, F; Artmann, G M; Zaccai, G

2012-11-07

Thermodynamic stability, configurational motions and internal forces of haemoglobin (Hb) of three endotherms (platypus, Ornithorhynchus anatinus; domestic chicken, Gallus gallus domesticus and human, Homo sapiens) and an ectotherm (salt water crocodile, Crocodylus porosus) were investigated using circular dichroism, incoherent elastic neutron scattering and coarse-grained Brownian dynamics simulations. The experimental results from Hb solutions revealed a direct correlation between protein resilience, melting temperature and average body temperature of the different species on the 0.1 ns time scale. Molecular forces appeared to be adapted to permit conformational fluctuations with a root mean square displacement close to 1.2 Å at the corresponding average body temperature of the endotherms. Strong forces within crocodile Hb maintain the amplitudes of motion within a narrow limit over the entire temperature range in which the animal lives. In fully hydrated powder samples of human and chicken, Hb mean square displacements and effective force constants on the 1 ns time scale showed no differences over the whole temperature range from 10 to 300 K, in contrast to the solution case. A complementary result of the study, therefore, is that one hydration layer is not sufficient to activate all conformational fluctuations of Hb in the pico- to nanosecond time scale which might be relevant for biological function. Coarse-grained Brownian dynamics simulations permitted to explore residue-specific effects. They indicated that temperature sensing of human and chicken Hb occurs mainly at residues lining internal cavities in the β-subunits.

Simple wealth distribution model causing inequality-induced crisis without external shocks

NASA Astrophysics Data System (ADS)

Benisty, Henri

2017-05-01

We address the issue of the dynamics of wealth accumulation and economic crisis triggered by extreme inequality, attempting to stick to most possibly intrinsic assumptions. Our general framework is that of pure or modified multiplicative processes, basically geometric Brownian motions. In contrast with the usual approach of injecting into such stochastic agent models either specific, idiosyncratic internal nonlinear interaction patterns or macroscopic disruptive features, we propose a dynamic inequality model where the attainment of a sizable fraction of the total wealth by very few agents induces a crisis regime with strong intermittency, the explicit coupling between the richest and the rest being a mere normalization mechanism, hence with minimal extrinsic assumptions. The model thus harnesses the recognized lack of ergodicity of geometric Brownian motions. It also provides a statistical intuition to the consequences of Thomas Piketty's recent "r >g " (return rate > growth rate) paradigmatic analysis of very-long-term wealth trends. We suggest that the "water-divide" of wealth flow may define effective classes, making an objective entry point to calibrate the model. Consistently, we check that a tax mechanism associated to a few percent relative bias on elementary daily transactions is able to slow or stop the build-up of large wealth. When extreme fluctuations are tamed down to a stationary regime with sizable but steadier inequalities, it should still offer opportunities to study the dynamics of crisis and the inner effective classes induced through external or internal factors.

Finite element formulation of fluctuating hydrodynamics for fluids filled with rigid particles using boundary fitted meshes

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

De Corato, M., E-mail: marco.decorato@unina.it; Slot, J.J.M., E-mail: j.j.m.slot@tue.nl; Hütter, M., E-mail: m.huetter@tue.nl

In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementation fulfills the fluctuation–dissipation theorem exactly at the discrete level. Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements. Brownian motion of arbitrarily shaped particles in complex confinements can be considered withinmore » the present formulation. A multi-step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation (SDE) describing the evolution of the positions of the particles. The proposed approach is validated by simulating the Brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity. The time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential.« less

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

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.

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.

ERRATUM: A reduced model for shock and detonation waves. I. The inert case

NASA Astrophysics Data System (ADS)

Stoltz, G.

2007-02-01

In the computation of the variations of depsii, a factor d is missing in the Itô term (since the Brownian motion is d-dimensional). Besides, the fluctuation-dissipation determining σij is not written correctly. The dynamics (3) should be replaced by \\begin{eqnarray*} \\left \\{ \\begin{array}{@{}rcl} dq_i = \\displaystyle \\frac{p_i}{m_i} \\, dt, \\\\ [9pt] dp_i = \\displaystyle \\sum_{j, \\, j \

A Dynamic Model for Forecasting New Cloud Development

DTIC Science & Technology

1988-12-19

Fourseand Vefor cay 2,or at our0 LT~ Z7 :rZ198 -’ut l o b o u d r f ro m sh o we a ct v t na o t h o t he a lm i 13 in di c at ed Or-& I W PFA ,.M...nucleation model includes: sorption /deposition, contact nucleation by Brownian collision plus thermophoresis plus diffusiophoresis, secondary ice

Anti-Brownian ELectrokinetic (ABEL) trapping of single β2-adrenergic receptors in the absence and presence of agonist

NASA Astrophysics Data System (ADS)

Bockenhauer, Samuel; Fuerstenberg, Alexandre; Yao, Xiao Jie; Kobilka, Brian K.; Moerner, W. E.

2012-02-01

The ABEL trap allows trapping of single biomolecules in solution for extended observation without immobilization. The essential idea combines fluorescence-based position estimation with fast electrokinetic feedback in a microfluidic geometry to counter the Brownian motion of a single nanoscale object, hence maintaining its position in the field of view for hundreds of milliseconds to seconds. Such prolonged observation of single proteins allows access to slow dynamics, as probed by any available photophysical observables. We have used the ABEL trap to study conformational dynamics of the β2-adrenergic receptor, a key G-protein coupled receptor and drug target, in the absence and presence of agonist. A single environment-sensitive dye reports on the receptor microenvironment, providing a real-time readout of conformational change for each trapped receptor. The focus of this paper will be a quantitative comparison of the ligandfree and agonist-bound receptor data from our ABEL trap experiments. We observe a small but clearly detectable shift in conformational equilibria and a lengthening of fluctuation timescales upon binding of agonist. In order to quantify the shift in state distributions and timescales, we apply nonparametric statistical tests to place error bounds on the resulting single-molecule distributions.

Dynamics of hard sphere colloidal dispersions

NASA Technical Reports Server (NTRS)

Zhu, J. X.; Chaikin, Paul M.; Phan, S.-E.; Russel, W. B.

1994-01-01

Our objective is to perform on homogeneous, fully equilibrated dispersions the full set of experiments characterizing the transition from fluid to solid and the properties of the crystalline and glassy solid. These include measurements quantifying the nucleation and growth of crystallites, the structure of the initial fluid and the fully crystalline solid, and Brownian motion of particles within the crystal, and the elasticity of the crystal and the glass. Experiments are being built and tested for ideal microgravity environment. Here we describe the ground based effort, which exploits a fluidized bed to create a homogeneous, steady dispersion for the studies. The differences between the microgravity environment and the fluidized bed is gauged by the Peclet number Pe, which measures the rate of convection/sedimentation relative to Brownian motion. We have designed our experiment to accomplish three types of measurements on hard sphere suspensions in a fluidized bed: the static scattering intensity as a function of angle to determine the structure factor, the temporal autocorrelation function at all scattering angles to probe the dynamics, and the amplitude of the response to an oscillatory forcing to deduce the low frequency viscoelasticity. Thus the scattering instrument and the colloidal dispersion were chosen such as that the important features of each physical property lie within the detectable range for each measurement.

Testing the Applicability of Nernst-Planck Theory in Ion Channels: Comparisons with Brownian Dynamics Simulations

PubMed Central

Song, Chen; Corry, Ben

2011-01-01

The macroscopic Nernst-Planck (NP) theory has often been used for predicting ion channel currents in recent years, but the validity of this theory at the microscopic scale has not been tested. In this study we systematically tested the ability of the NP theory to accurately predict channel currents by combining and comparing the results with those of Brownian dynamics (BD) simulations. To thoroughly test the theory in a range of situations, calculations were made in a series of simplified cylindrical channels with radii ranging from 3 to 15 Å, in a more complex ‘catenary’ channel, and in a realistic model of the mechanosensitive channel MscS. The extensive tests indicate that the NP equation is applicable in narrow ion channels provided that accurate concentrations and potentials can be input as the currents obtained from the combination of BD and NP match well with those obtained directly from BD simulations, although some discrepancies are seen when the ion concentrations are not radially uniform. This finding opens a door to utilising the results of microscopic simulations in continuum theory, something that is likely to be useful in the investigation of a range of biophysical and nano-scale applications and should stimulate further studies in this direction. PMID:21731672

Testing the applicability of Nernst-Planck theory in ion channels: comparisons with Brownian dynamics simulations.

PubMed

Song, Chen; Corry, Ben

2011-01-01

The macroscopic Nernst-Planck (NP) theory has often been used for predicting ion channel currents in recent years, but the validity of this theory at the microscopic scale has not been tested. In this study we systematically tested the ability of the NP theory to accurately predict channel currents by combining and comparing the results with those of Brownian dynamics (BD) simulations. To thoroughly test the theory in a range of situations, calculations were made in a series of simplified cylindrical channels with radii ranging from 3 to 15 Å, in a more complex 'catenary' channel, and in a realistic model of the mechanosensitive channel MscS. The extensive tests indicate that the NP equation is applicable in narrow ion channels provided that accurate concentrations and potentials can be input as the currents obtained from the combination of BD and NP match well with those obtained directly from BD simulations, although some discrepancies are seen when the ion concentrations are not radially uniform. This finding opens a door to utilising the results of microscopic simulations in continuum theory, something that is likely to be useful in the investigation of a range of biophysical and nano-scale applications and should stimulate further studies in this direction.

Coarse-grained Brownian dynamics simulations of protein translocation through nanopores

NASA Astrophysics Data System (ADS)

Lee, Po-Hsien; Helms, Volkhard; Geyer, Tihamér

2012-10-01

A crucial process in biological cells is the translocation of newly synthesized proteins across cell membranes via integral membrane protein pores termed translocons. Recent improved techniques now allow producing artificial membranes with pores of similar dimensions of a few nm as the translocon system. For the translocon system, the protein has to be unfolded, whereas the artificial pores are wide enough so that small proteins can pass through even when folded. To study how proteins permeate through such membrane pores, we used coarse-grained Brownian dynamics simulations where the proteins were modeled as single beads or bead-spring polymers for both folded and unfolded states. The pores were modeled as cylindrical holes through the membrane with various radii and lengths. Diffusion was driven by a concentration gradient created across the porous membrane. Our results for both folded and unfolded configurations show the expected reciprocal relation between the flow rate and the pore length in agreement with an analytical solution derived by Brunn et al. [Q. J. Mech. Appl. Math. 37, 311 (1984)], 10.1093/qjmam/37.2.311. Furthermore, we find that the geometric constriction by the narrow pore leads to an accumulation of proteins at the pore entrance, which in turn compensates for the reduced diffusivity of the proteins inside the pore.

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.

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.

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.

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.

Brownian motion of a particle with arbitrary shape.

PubMed

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

2015-06-07

Brownian motion of a particle with an arbitrary shape is investigated theoretically. Analytical expressions for the time-dependent cross-correlations of the Brownian translational and rotational displacements are derived from the Smoluchowski equation. The role of the particle mobility center is determined and discussed.

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.

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

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

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.

Role of hydrodynamic interactions in dynamics of semi-flexible polyelectrolytes

NASA Astrophysics Data System (ADS)

Kekre, Rahul

Experiments have shown that DNA molecules in capillary electrophoresis migrate across field lines if a pressure gradient is applied simultaneously. We suggest that this migration results from an electrically driven flow field around the polyelectrolyte, which generates additional contributions to the center-of-mass velocity if the overall polymer conformation is asymmetric. Numerical simulations and experiments have demonstrated that confined polymers migrate towards the center of the channel in response to both external forces and uniaxial flows. Yet, migration towards the walls has been observed with combinations of external force and flow. In this work, the kinetic theory for an elastic dumbbell developed by Ma and Graham [Phys. Fluids 17, 083103 (2005)] has been extended to account for the effects of an external body force. Further modifications account for counterion screening within a Debye-Huckel approximation for the specific case of applied electric field. The theory qualitatively reproduces results of both experiments for the migration of neutral polymers and polyelectrolytes. The favorable comparison supports the contention [Long et al., Phys. Rev. Lett. 76, 3858 (1996)] that the hydrodynamic interactions in polyelectrolytes decay algebraically, as 1/r 3, rather than exponentially. A coarse-grained polymer model, without explicit charges, is developed and integrated using Brownian-dynamics simulations in analogy with the kinetic theory. The novel feature of the simulations is the inclusion of hydrodynamic interactions induced by the electric field. This model quantitatively captures experimental observations [Zheng and Yeung, Anal. Chem. 75, 3675 (2003)] of DNA migration under combined electric and pressure-driven flow fields in absence of any adjusted parameters. In addition the model predicts dependence of electrophoretic velocity on the instantaneous length of the polyelectrolyte which has been verified by experiments of Lee et. al. [Electrophoresis 31, 2813 (2010)]. The model also predicts phenomenons that are yet to be verified experimentally. These include decrease in diffusivity and increase in radius of gyration of the polyelectrolyte in high electric fields due to internal dispersion. The resulting change in orientation distribution at high electric fields decreases the extent of migration. Preliminary results from microfluidic experiments are presented in this dissertation demonstrating the saturation of migration. This dissertation also includes comparison of results from lattice-Boltzmann and Brownian dynamics simulations of a linear bead-spring model of DNA for two cases; infinite dilution and confinement. We have systematically varied the parameters that may affect the accuracy of the lattice-Boltzmann simulations, including grid resolution, temperature, polymer mass, periodic boundary size and fluid viscosity. For the case of a single chain Lattice-Boltzmann results for the diffusion coefficient and Rouse mode relaxation times were within 1--2% from those obtained from Brownian-dynamics. Results from both methods are also compared for polymer migration in confined flows driven by a uniform shear or pressure gradient. Center-of-mass distribution obtained from Lattice-Boltzmann simulations agrees quantitatively with Brownian-dynamics results, contradicting previously published results. The mobility matrix for a confined polymer was derived by applying Faxen's correction to the flow-field generated by a point force bounded by two parallel plates. This formulation of the mobility matrix is symmetric and positive-definite for all physically accessible configurations of the polymer.

Dynamics of a fluctuating semi-flexible membrane

NASA Astrophysics Data System (ADS)

Tukdarian, Nathaniel; Huang, Aiqun; Adhikari, Ramesh; Bhattacharya, Aniket

2015-03-01

We report our preliminary studies of conformations and dynamics of a fluctuating semi-flexible membrane. Our model of membrane with linear dimension L consists of N2 (L = Nbl) excluded volume beads connected by anharmonic springs. The stiffness of the membrane is controlled by adjusting the strength κb of the bending potential Ubend =κb(1-n̂i .n̂j) between adjacent elementary plaquettes consisting of three beads at the corners connected by bonds and characterized by normal unit vectors n̂i and n̂j. We study the conformations and dynamic fluctuations of the membrane using Brownian dynamics simulation. We show how the radius of gyration scales with N and κb, and study characteristics of the transverse fluctuations, the root-mean-square displacement of the center of mass, and the dynamics of the end monomers at each corner.

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.

Contributions of microtubule rotation and dynamic instability to kinetochore capture

NASA Astrophysics Data System (ADS)

Sweezy-Schindler, Oliver; Edelmaier, Christopher; Blackwell, Robert; Glaser, Matt; Betterton, Meredith

2014-03-01

The capture of lost kinetochores (KCs) by microtubules (MTs) is a crucial part of prometaphase during mitosis. Microtubule dynamic instability has been considered the primary mechanism of KC capture, but recent work discovered that lateral KC attachment to pivoting MTs enabled rapid capture even with significantly reduced MT dynamics. We aim to understand the relative contributions of MT rotational diffusion and dynamic instability to KC capture, as well as KC capture through end-on and/or lateral attachment. Our model consists of rigid MTs and a spherical KC, which are allowed to diffuse inside a spherical nuclear envelope consistent with the geometry of fission yeast. For simplicity, we include a single spindle pole body, which is anchored to the nuclear membrane, and its associated polar MTs. Brownian dynamics treats the diffusion of the MTs and KC and kinetic Monte Carlo models stochastic processes such as dynamic instability. NSF 1546021.

Molecular dynamics and brownian dynamics investigation of ion permeation and anesthetic halothane effects on a proton-gated ion channel.

PubMed

Cheng, Mary Hongying; Coalson, Rob D; Tang, Pei

2010-11-24

Bacterial Gloeobacter violaceus pentameric ligand-gated ion channel (GLIC) is activated to cation permeation upon lowering the solution pH. Its function can be modulated by anesthetic halothane. In the present work, we integrate molecular dynamics (MD) and Brownian dynamics (BD) simulations to elucidate the ion conduction, charge selectivity, and halothane modulation mechanisms in GLIC, based on recently resolved X-ray crystal structures of the open-channel GLIC. MD calculations of the potential of mean force (PMF) for a Na(+) revealed two energy barriers in the extracellular domain (R109 and K38) and at the hydrophobic gate of transmembrane domain (I233), respectively. An energy well for Na(+) was near the intracellular entrance: the depth of this energy well was modulated strongly by the protonation state of E222. The energy barrier for Cl(-) was found to be 3-4 times higher than that for Na(+). Ion permeation characteristics were determined through BD simulations using a hybrid MD/continuum electrostatics approach to evaluate the energy profiles governing the ion movement. The resultant channel conductance and a near-zero permeability ratio (P(Cl)/P(Na)) were comparable to experimental data. On the basis of these calculations, we suggest that a ring of five E222 residues may act as an electrostatic gate. In addition, the hydrophobic gate region may play a role in charge selectivity due to a higher dehydration energy barrier for Cl(-) ions. The effect of halothane on the Na(+) PMF was also evaluated. Halothane was found to perturb salt bridges in GLIC that may be crucial for channel gating and open-channel stability, but had no significant impact on the single ion PMF profiles.

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

GPU accelerated Monte Carlo simulation of Brownian motors dynamics with CUDA

NASA Astrophysics Data System (ADS)

Spiechowicz, J.; Kostur, M.; Machura, L.

2015-06-01

This work presents an updated and extended guide on methods of a proper acceleration of the Monte Carlo integration of stochastic differential equations with the commonly available NVIDIA Graphics Processing Units using the CUDA programming environment. We outline the general aspects of the scientific computing on graphics cards and demonstrate them with two models of a well known phenomenon of the noise induced transport of Brownian motors in periodic structures. As a source of fluctuations in the considered systems we selected the three most commonly occurring noises: the Gaussian white noise, the white Poissonian noise and the dichotomous process also known as a random telegraph signal. The detailed discussion on various aspects of the applied numerical schemes is also presented. The measured speedup can be of the astonishing order of about 3000 when compared to a typical CPU. This number significantly expands the range of problems solvable by use of stochastic simulations, allowing even an interactive research in some cases.

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.

Tight-binding approach to overdamped Brownian motion on a bichromatic periodic potential.

PubMed

Nguyen, P T T; Challis, K J; Jack, M W

2016-02-01

We present a theoretical treatment of overdamped Brownian motion on a time-independent bichromatic periodic potential with spatially fast- and slow-changing components. In our approach, we generalize the Wannier basis commonly used in the analysis of periodic systems to define a basis of S states that are localized at local minima of the potential. We demonstrate that the S states are orthonormal and complete on the length scale of the periodicity of the fast-changing potential, and we use the S-state basis to transform the continuous Smoluchowski equation for the system to a discrete master equation describing hopping between local minima. We identify the parameter regime where the master equation description is valid and show that the interwell hopping rates are well approximated by Kramers' escape rate in the limit of deep potential minima. Finally, we use the master equation to explore the system dynamics and determine the drift and diffusion for the system.

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.

Estimation of time-dependent Hurst exponents with variational smoothing and application to forecasting foreign exchange rates

NASA Astrophysics Data System (ADS)

Garcin, Matthieu

2017-10-01

Hurst exponents depict the long memory of a time series. For human-dependent phenomena, as in finance, this feature may vary in the time. It justifies modelling dynamics by multifractional Brownian motions, which are consistent with time-dependent Hurst exponents. We improve the existing literature on estimating time-dependent Hurst exponents by proposing a smooth estimate obtained by variational calculus. This method is very general and not restricted to the sole Hurst framework. It is globally more accurate and easier than other existing non-parametric estimation techniques. Besides, in the field of Hurst exponents, it makes it possible to make forecasts based on the estimated multifractional Brownian motion. The application to high-frequency foreign exchange markets (GBP, CHF, SEK, USD, CAD, AUD, JPY, CNY and SGD, all against EUR) shows significantly good forecasts. When the Hurst exponent is higher than 0.5, what depicts a long-memory feature, the accuracy is higher.

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.

Non-monotonic temperature dependence of chaos-assisted diffusion in driven periodic systems

NASA Astrophysics Data System (ADS)

Spiechowicz, J.; Talkner, P.; Hänggi, P.; Łuczka, J.

2016-12-01

The spreading of a cloud of independent Brownian particles typically proceeds more effectively at higher temperatures, as it derives from the commonly known Sutherland-Einstein relation for systems in thermal equilibrium. Here, we report on a non-equilibrium situation in which the diffusion of a periodically driven Brownian particle moving in a periodic potential decreases with increasing temperature within a finite temperature window. We identify as the cause for this non-intuitive behaviour a dominant deterministic mechanism consisting of a few unstable periodic orbits embedded into a chaotic attractor together with thermal noise-induced dynamical changes upon varying temperature. The presented analysis is based on extensive numerical simulations of the corresponding Langevin equation describing the studied setup as well as on a simplified stochastic model formulated in terms of a three-state Markovian process. Because chaos exists in many natural as well as in artificial systems representing abundant areas of contemporary knowledge, the described mechanism may potentially be discovered in plentiful different contexts.

Bayesian parameter estimation for stochastic models of biological cell migration

NASA Astrophysics Data System (ADS)

Dieterich, Peter; Preuss, Roland

2013-08-01

Cell migration plays an essential role under many physiological and patho-physiological conditions. It is of major importance during embryonic development and wound healing. In contrast, it also generates negative effects during inflammation processes, the transmigration of tumors or the formation of metastases. Thus, a reliable quantification and characterization of cell paths could give insight into the dynamics of these processes. Typically stochastic models are applied where parameters are extracted by fitting models to the so-called mean square displacement of the observed cell group. We show that this approach has several disadvantages and problems. Therefore, we propose a simple procedure directly relying on the positions of the cell's trajectory and the covariance matrix of the positions. It is shown that the covariance is identical with the spatial aging correlation function for the supposed linear Gaussian models of Brownian motion with drift and fractional Brownian motion. The technique is applied and illustrated with simulated data showing a reliable parameter estimation from single cell paths.

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions.

PubMed

Banik, Suman Kumar; Bag, Bidhan Chandra; Ray, Deb Shankar

2002-05-01

Traditionally, quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasiprobability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using true probability distribution functions is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their coordinates and momenta, we derive a generalized quantum Langevin equation in c numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion, and Smoluchowski equations are the exact quantum analogs of their classical counterparts. The present work is independent of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (the Smoluchowski equation being considered in the overdamped limit).

Two-way communication between SecY and SecA suggests a Brownian ratchet mechanism for protein translocation.

PubMed

Allen, William John; Corey, Robin Adam; Oatley, Peter; Sessions, Richard Barry; Baldwin, Steve A; Radford, Sheena E; Tuma, Roman; Collinson, Ian

2016-05-16

The essential process of protein secretion is achieved by the ubiquitous Sec machinery. In prokaryotes, the drive for translocation comes from ATP hydrolysis by the cytosolic motor-protein SecA, in concert with the proton motive force (PMF). However, the mechanism through which ATP hydrolysis by SecA is coupled to directional movement through SecYEG is unclear. Here, we combine all-atom molecular dynamics (MD) simulations with single molecule FRET and biochemical assays. We show that ATP binding by SecA causes opening of the SecY-channel at long range, while substrates at the SecY-channel entrance feed back to regulate nucleotide exchange by SecA. This two-way communication suggests a new, unifying 'Brownian ratchet' mechanism, whereby ATP binding and hydrolysis bias the direction of polypeptide diffusion. The model represents a solution to the problem of transporting inherently variable substrates such as polypeptides, and may underlie mechanisms of other motors that translocate proteins and nucleic acids.

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.

Robustness of Quadratic Hedging Strategies in Finance via Backward Stochastic Differential Equations with Jumps

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

Di Nunno, Giulia, E-mail: giulian@math.uio.no; Khedher, Asma, E-mail: asma.khedher@tum.de; Vanmaele, Michèle, E-mail: michele.vanmaele@ugent.be

We consider a backward stochastic differential equation with jumps (BSDEJ) which is driven by a Brownian motion and a Poisson random measure. We present two candidate-approximations to this BSDEJ and we prove that the solution of each candidate-approximation converges to the solution of the original BSDEJ in a space which we specify. We use this result to investigate in further detail the consequences of the choice of the model to (partial) hedging in incomplete markets in finance. As an application, we consider models in which the small variations in the price dynamics are modeled with a Poisson random measure withmore » infinite activity and models in which these small variations are modeled with a Brownian motion or are cut off. Using the convergence results on BSDEJs, we show that quadratic hedging strategies are robust towards the approximation of the market prices and we derive an estimation of the model risk.« less

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.

A new coarse-grained model for E. coli cytoplasm: accurate calculation of the diffusion coefficient of proteins and observation of anomalous diffusion.

PubMed

Hasnain, Sabeeha; McClendon, Christopher L; Hsu, Monica T; Jacobson, Matthew P; Bandyopadhyay, Pradipta

2014-01-01

A new coarse-grained model of the E. coli cytoplasm is developed by describing the proteins of the cytoplasm as flexible units consisting of one or more spheres that follow Brownian dynamics (BD), with hydrodynamic interactions (HI) accounted for by a mean-field approach. Extensive BD simulations were performed to calculate the diffusion coefficients of three different proteins in the cellular environment. The results are in close agreement with experimental or previously simulated values, where available. Control simulations without HI showed that use of HI is essential to obtain accurate diffusion coefficients. Anomalous diffusion inside the crowded cellular medium was investigated with Fractional Brownian motion analysis, and found to be present in this model. By running a series of control simulations in which various forces were removed systematically, it was found that repulsive interactions (volume exclusion) are the main cause for anomalous diffusion, with a secondary contribution from HI.

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 framework of Markov-Bernstein diffusions…

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 the colloid radius, μ the continuous phase viscosity, v˜c the characteristic diffusiophoretic velocity, and kBT the thermal energy. The skimming and stationary states are found to persist for Pe above 103. At Pe below 200, the trajectory of a locomotor approaching the wall is unpredictable. We present representative individual trajectories along with probability distributions for statistical ensembles of particles, quantifying the effects of thermal fluctuations and illustrating the transition from unpredictable to passively guided motion.

Intrachain exciton dynamics in conjugated polymer chains in solution.

PubMed

Tozer, Oliver Robert; Barford, William

2015-08-28

We investigate exciton dynamics on a polymer chain in solution induced by the Brownian rotational motion of the monomers. Poly(para-phenylene) is chosen as the model system and excitons are modeled via the Frenkel exciton Hamiltonian. The Brownian fluctuations of the torsional modes were modeled via the Langevin equation. The rotation of monomers in polymer chains in solution has a number of important consequences for the excited state properties. First, the dihedral angles assume a thermal equilibrium which causes off-diagonal disorder in the Frenkel Hamiltonian. This disorder Anderson localizes the Frenkel exciton center-of-mass wavefunctions into super-localized local exciton ground states (LEGSs) and higher-energy more delocalized quasi-extended exciton states (QEESs). LEGSs correspond to chromophores on polymer chains. The second consequence of rotations-that are low-frequency-is that their coupling to the exciton wavefunction causes local planarization and the formation of an exciton-polaron. This torsional relaxation causes additional self-localization. Finally, and crucially, the torsional dynamics cause the Frenkel Hamiltonian to be time-dependent, leading to exciton dynamics. We identify two distinct types of dynamics. At low temperatures, the torsional fluctuations act as a perturbation on the polaronic nature of the exciton state. Thus, the exciton dynamics at low temperatures is a small-displacement diffusive adiabatic motion of the exciton-polaron as a whole. The temperature dependence of the diffusion constant has a linear dependence, indicating an activationless process. As the temperature increases, however, the diffusion constant increases at a faster than linear rate, indicating a second non-adiabatic dynamics mechanism begins to dominate. Excitons are thermally activated into higher energy more delocalized exciton states (i.e., LEGSs and QEESs). These states are not self-localized by local torsional planarization. During the exciton's temporary occupation of a LEGS-and particularly a quasi-band QEES-its motion is semi-ballistic with a large group velocity. After a short period of rapid transport, the exciton wavefunction collapses again into an exciton-polaron state. We present a simple model for the activated dynamics which is in agreement with the data.

Many-body dynamics of chemically propelled nanomotors

NASA Astrophysics Data System (ADS)

Colberg, Peter H.; Kapral, Raymond

2017-08-01

The collective behavior of chemically propelled sphere-dimer motors made from linked catalytic and noncatalytic spheres in a quasi-two-dimensional confined geometry is studied using a coarse-grained microscopic dynamical model. Chemical reactions at the catalytic spheres that convert fuel to product generate forces that couple to solvent degrees of freedom as a consequence of momentum conservation in the microscopic dynamics. The collective behavior of the many-body system is influenced by direct intermolecular interactions among the motors, chemotactic effects due to chemical gradients, hydrodynamic coupling, and thermal noise. Segregation into high and low density phases and globally homogeneous states with strong fluctuations are investigated as functions of the motor characteristics. Factors contributing to this behavior are discussed in the context of active Brownian models.

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)

Rapid Brownian Motion Primes Ultrafast Reconstruction of Intrinsically Disordered Phe-Gly Repeats Inside the Nuclear Pore Complex

PubMed Central

Moussavi-Baygi, R.; Mofrad, M. R. K.

2016-01-01

Conformational behavior of intrinsically disordered proteins, such as Phe-Gly repeat domains, alters drastically when they are confined in, and tethered to, nan channels. This has challenged our understanding of how they serve to selectively facilitate translocation of nuclear transport receptor (NTR)-bearing macromolecules. Heterogeneous FG-repeats, tethered to the NPC interior, nonuniformly fill the channel in a diameter-dependent manner and adopt a rapid Brownian motion, thereby forming a porous and highly dynamic polymeric meshwork that percolates in radial and axial directions and features two distinguishable zones: a dense hydrophobic rod-like zone located in the center, and a peripheral low-density shell-like zone. The FG-meshwork is locally disrupted upon interacting with NTR-bearing macromolecules, but immediately reconstructs itself between 0.44 μs and 7.0 μs, depending on cargo size and shape. This confers a perpetually-sealed state to the NPC, and is solely due to rapid Brownian motion of FG-repeats, not FG-repeat hydrophobic bonds. Elongated-shaped macromolecules, both in the presence and absence of NTRs, penetrate more readily into the FG-meshwork compared to their globular counterparts of identical volume and surface chemistry, highlighting the importance of the shape effects in nucleocytoplasmic transport. These results can help our understanding of geometrical effects in, and the design of, intelligent and responsive biopolymer-based materials in nanofiltration and artificial nanopores. PMID:27470900

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.

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.

Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise

PubMed Central

Zeng, Caibin; Yang, Qigui; Cao, Junfei

2014-01-01

This paper deals with the following type of stochastic partial differential equations (SPDEs) perturbed by an infinite dimensional fractional Brownian motion with a suitable volatility coefficient Φ: dX(t) = A(X(t))dt+Φ(t)dB H(t), where A is a nonlinear operator satisfying some monotonicity conditions. Using the variational approach, we prove the existence and uniqueness of variational solutions to such system. Moreover, we prove that this variational solution generates a random dynamical system. The main results are applied to a general type of nonlinear SPDEs and the stochastic generalized p-Laplacian equation. PMID:24574903

Spatial Stochastic Intracellular Kinetics: A Review of Modelling Approaches.

PubMed

Smith, Stephen; Grima, Ramon

2018-05-21

Models of chemical kinetics that incorporate both stochasticity and diffusion are an increasingly common tool for studying biology. The variety of competing models is vast, but two stand out by virtue of their popularity: the reaction-diffusion master equation and Brownian dynamics. In this review, we critically address a number of open questions surrounding these models: How can they be justified physically? How do they relate to each other? How do they fit into the wider landscape of chemical models, ranging from the rate equations to molecular dynamics? This review assumes no prior knowledge of modelling chemical kinetics and should be accessible to a wide range of readers.

Symmetry breaking in clogging for oppositely driven particles

NASA Astrophysics Data System (ADS)

Glanz, Tobias; Wittkowski, Raphael; Löwen, Hartmut

2016-11-01

The clogging behavior of a symmetric binary mixture of colloidal particles that are driven in opposite directions through constrictions is explored by Brownian dynamics simulations and theory. A dynamical state with a spontaneously broken symmetry occurs where one species is flowing and the other is blocked for a long time, which can be tailored by the size of the constrictions. Moreover, we find self-organized oscillations in clogging and unclogging of the two species. Apart from statistical physics, our results are of relevance for fields like biology, chemistry, and crowd management, where ions, microparticles, pedestrians, or other particles are driven in opposite directions through constrictions.

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

Dynamics of Granular Materials

NASA Technical Reports Server (NTRS)

Behringer, Robert P.

1996-01-01

Granular materials exhibit a rich variety of dynamical behavior, much of which is poorly understood. Fractal-like stress chains, convection, a variety of wave dynamics, including waves which resemble capillary waves, l/f noise, and fractional Brownian motion provide examples. Work beginning at Duke will focus on gravity driven convection, mixing and gravitational collapse. Although granular materials consist of collections of interacting particles, there are important differences between the dynamics of a collections of grains and the dynamics of a collections of molecules. In particular, the ergodic hypothesis is generally invalid for granular materials, so that ordinary statistical physics does not apply. In the absence of a steady energy input, granular materials undergo a rapid collapse which is strongly influenced by the presence of gravity. Fluctuations on laboratory scales in such quantities as the stress can be very large-as much as an order of magnitude greater than the mean.

Autonomous Agent-Based Systems and Their Applications in Fluid Dynamics, Particle Separation, and Co-evolving Networks

NASA Astrophysics Data System (ADS)

Graeser, Oliver

This thesis comprises three parts, reporting research results in Fluid Dynamics (Part I), Particle Separation (Part II) and Co-evolving Networks (Part III). Part I deals with the simulation of fluid dynamics using the lattice-Boltzmann method. Microfluidic devices often feature two-dimensional, repetitive arrays. Flows through such devices are pressure-driven and confined by solid walls. We have defined new adaptive generalised periodic boundary conditions to represent the effects of outer solid walls, and are thus able to exploit the periodicity of the array by simulating the flow through one unit cell in lieu of the entire device. The so-calculated fully developed flow describes the flow through the entire array accurately, but with computational requirements that are reduced according to the dimensions of the array. Part II discusses the problem of separating macromolecules like proteins or DNA coils. The reliable separation of such molecules is a crucial task in molecular biology. The use of Brownian ratchets as mechanisms for the separation of such particles has been proposed and discussed during the last decade. Pressure-driven flows have so far been dismissed as possible driving forces for Brownian ratchets, as they do not generate ratchet asymmetry. We propose a microfluidic design that uses pressure-driven flows to create asymmetry and hence allows particle separation. The dependence of the asymmetry on various factors of the microfluidic geometry is discussed. We further exemplify the feasibility of our approach using Brownian dynamics simulations of particles of different sizes in such a device. The results show that ratchet-based particle separation using flows as the driving force is possible. Simulation results and ratchet theory predictions are in excellent agreement. Part III deals with the co-evolution of networks and dynamic models. A group of agents occupies the nodes of a network, which defines the relationship between these agents. The evolution of the agents is defined by the rules of the dynamic model and depends on the relationship between agents, i.e., the state of the network. In return, the evolution of the network depends on the state of the dynamic model. The concept is introduced through the adaptive SIS model. We show that the previously used criterion determining the critical infected fraction, i.e., the number of infected agents required to sustain the epidemic, is inappropriate for this model. We introduce a different criterion and show that the critical infected fraction so determined is in good agreement with results obtained by numerical simulations. We further discuss the concept of co-evolving dynamics using the Snowdrift Game as a model paradigm. Co-evolution occurs through agents cutting dissatisfied links and rewiring to other agents at random. The effect of co-evolution on the emergence of cooperation is discussed using a mean-field theory and numerical simulations. A transition between a connected and a disconnected, highly cooperative state of the system is observed, and explained using the mean-field model. Quantitative deviations regarding the level of cooperation in the disconnected regime can be fully resolved through an improved mean-field theory that includes the effect of random fluctuations into its model.

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…

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.

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…

Financial Knudsen number: Breakdown of continuous price dynamics and asymmetric buy-and-sell structures confirmed by high-precision order-book information.

PubMed

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

2015-10-01

We generalize the description of the dynamics of the order book of financial markets in terms of a Brownian particle embedded in a fluid of incoming, exiting, and annihilating particles by presenting a model of the velocity on each side (buy and sell) independently. The improved model builds on the time-averaged number of particles in the inner layer and its change per unit time, where the inner layer is revealed by the correlations between price velocity and change in the number of particles (limit orders). This allows us to introduce the Knudsen number of the financial Brownian particle motion and its asymmetric version (on the buy and sell sides). Not being considered previously, the asymmetric Knudsen numbers are crucial in finance in order to detect asymmetric price changes. The Knudsen numbers allows us to characterize the conditions for the market dynamics to be correctly described by a continuous stochastic process. Not questioned until now for large liquid markets such as the USD-JPY and EUR-USD exchange rates, we show that there are regimes when the Knudsen numbers are so high that discrete particle effects dominate, such as during market stresses and crashes. We document the presence of imbalances of particles depletion rates on the buy and sell sides that are associated with high Knudsen numbers and violent directional price changes. This indicator can detect the direction of the price motion at the early stage while the usual volatility risk measure is blind to the price direction.

Financial Knudsen number: Breakdown of continuous price dynamics and asymmetric buy-and-sell structures confirmed by high-precision order-book information

NASA Astrophysics Data System (ADS)

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

2015-10-01

We generalize the description of the dynamics of the order book of financial markets in terms of a Brownian particle embedded in a fluid of incoming, exiting, and annihilating particles by presenting a model of the velocity on each side (buy and sell) independently. The improved model builds on the time-averaged number of particles in the inner layer and its change per unit time, where the inner layer is revealed by the correlations between price velocity and change in the number of particles (limit orders). This allows us to introduce the Knudsen number of the financial Brownian particle motion and its asymmetric version (on the buy and sell sides). Not being considered previously, the asymmetric Knudsen numbers are crucial in finance in order to detect asymmetric price changes. The Knudsen numbers allows us to characterize the conditions for the market dynamics to be correctly described by a continuous stochastic process. Not questioned until now for large liquid markets such as the USD-JPY and EUR-USD exchange rates, we show that there are regimes when the Knudsen numbers are so high that discrete particle effects dominate, such as during market stresses and crashes. We document the presence of imbalances of particles depletion rates on the buy and sell sides that are associated with high Knudsen numbers and violent directional price changes. This indicator can detect the direction of the price motion at the early stage while the usual volatility risk measure is blind to the price direction.

Multiscale Simulations of Reactive Transport

NASA Astrophysics Data System (ADS)

Tartakovsky, D. M.; Bakarji, J.

2014-12-01

Discrete, particle-based simulations offer distinct advantages when modeling solute transport and chemical reactions. For example, Brownian motion is often used to model diffusion in complex pore networks, and Gillespie-type algorithms allow one to handle multicomponent chemical reactions with uncertain reaction pathways. Yet such models can be computationally more intensive than their continuum-scale counterparts, e.g., advection-dispersion-reaction equations. Combining the discrete and continuum models has a potential to resolve the quantity of interest with a required degree of physicochemical granularity at acceptable computational cost. We present computational examples of such "hybrid models" and discuss the challenges associated with coupling these two levels of description.

Electrostatic and dispersion interactions during protein adsorption on topographic nanostructures.

PubMed

Elter, Patrick; Lange, Regina; Beck, Ulrich

2011-07-19

Recently, biomaterials research has focused on developing functional implant surfaces with well-defined topographic nanostructures in order to influence protein adsorption and cellular behavior. To enhance our understanding of how proteins interact with such surfaces, we analyze the adsorption of lysozyme on an oppositely charged nanostructure using a computer simulation. We present an algorithm that combines simulated Brownian dynamics with numerical field calculation methods to predict the preferred adsorption sites for arbitrarily shaped substrates. Either proteins can be immobilized at their initial adsorption sites or surface diffusion can be considered. Interactions are analyzed on the basis of Derjaguin-Landau-Verway-Overbeek (DLVO) theory, including electrostatic and London dispersion forces, and numerical solutions are derived using the Poisson-Boltzmann and Hamaker equations. Our calculations show that for a grooved nanostructure (i.e., groove and plateau width 8 nm, height 4 nm), proteins first contact the substrate primarily near convex edges because of better geometric accessibility and increased electric field strengths. Subsequently, molecules migrate by surface diffusion into grooves and concave corners, where short-range dispersion interactions are maximized. In equilibrium, this mechanism leads to an increased surface protein concentration in the grooves, demonstrating that the total amount of protein per surface area can be increased if substrates have concave nanostructures.

An improved non-Markovian degradation model with long-term dependency and item-to-item uncertainty

NASA Astrophysics Data System (ADS)

Xi, Xiaopeng; Chen, Maoyin; Zhang, Hanwen; Zhou, Donghua

2018-05-01

It is widely noted in the literature that the degradation should be simplified into a memoryless Markovian process for the purpose of predicting the remaining useful life (RUL). However, there actually exists the long-term dependency in the degradation processes of some industrial systems, including electromechanical equipments, oil tankers, and large blast furnaces. This implies the new degradation state depends not only on the current state, but also on the historical states. Such dynamic systems cannot be accurately described by traditional Markovian models. Here we present an improved non-Markovian degradation model with both the long-term dependency and the item-to-item uncertainty. As a typical non-stationary process with dependent increments, fractional Brownian motion (FBM) is utilized to simulate the fractal diffusion of practical degradations. The uncertainty among multiple items can be represented by a random variable of the drift. Based on this model, the unknown parameters are estimated through the maximum likelihood (ML) algorithm, while a closed-form solution to the RUL distribution is further derived using a weak convergence theorem. The practicability of the proposed model is fully verified by two real-world examples. The results demonstrate that the proposed method can effectively reduce the prediction error.

Calculating two-dimensional THz-Raman-THz and Raman-THz-THz signals for various molecular liquids: the samplers.

PubMed

Ito, Hironobu; Hasegawa, Taisuke; Tanimura, Yoshitaka

2014-09-28

Recently, two-dimensional (2D) THz-Raman spectroscopy has been used to investigate the intermolecular modes of liquid water. We examine such 2D spectroscopy signals by means of full molecular dynamics (MD) simulations. In this way, we carry out a detailed analysis of intermolecular interactions that play an essential role in many important chemical processes. We calculate 2D Raman-THz-THz (RTT), THz-Raman-THz (TRT), and 2D Raman signals for liquid water, methanol, formamide, acetonitrile, formaldehyde, and dimethyl sulfoxide using an equilibrium-non-equilibrium hybrid MD simulation algorithm originally developed for 2D Raman spectroscopy. These signals are briefly analyzed in terms of anharmonicity and nonlinear polarizability of vibrational modes on the basis of the 2D Raman signals calculated from a Brownian oscillator model with a nonlinear system-bath interaction. We find that the anharmonic contribution is dominant in the RTT case, while the nonlinear polarizability contribution is dominant in the TRT case. For water and methanol, we observed vibrational echo peaks of librational motion in the 2D TRT signals. The predicted signal profiles and intensities that we obtained provide valuable information that can be applied to 2D spectroscopy experiments, allowing them to be carried out more efficiently.

Model of chromosomal loci dynamics in bacteria as fractional diffusion with intermittent transport

NASA Astrophysics Data System (ADS)

Gherardi, Marco; Calabrese, Ludovico; Tamm, Mikhail; Cosentino Lagomarsino, Marco

2017-10-01

The short-time dynamics of bacterial chromosomal loci is a mixture of subdiffusive and active motion, in the form of rapid relocations with near-ballistic dynamics. While previous work has shown that such rapid motions are ubiquitous, we still have little grasp on their physical nature, and no positive model is available that describes them. Here, we propose a minimal theoretical model for loci movements as a fractional Brownian motion subject to a constant but intermittent driving force, and compare simulations and analytical calculations to data from high-resolution dynamic tracking in E. coli. This analysis yields the characteristic time scales for intermittency. Finally, we discuss the possible shortcomings of this model, and show that an increase in the effective local noise felt by the chromosome associates to the active relocations.

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.

Mean first passage time of active Brownian particle in one dimension

NASA Astrophysics Data System (ADS)

Scacchi, A.; Sharma, A.

2018-02-01

We investigate the mean first passage time of an active Brownian particle in one dimension using numerical simulations. The activity in one dimension is modelled as a two state model; the particle moves with a constant propulsion strength but its orientation switches from one state to other as in a random telegraphic process. We study the influence of a finite resetting rate r on the mean first passage time to a fixed target of a single free active Brownian particle and map this result using an effective diffusion process. As in the case of a passive Brownian particle, we can find an optimal resetting rate r* for an active Brownian particle for which the target is found with the minimum average time. In the case of the presence of an external potential, we find good agreement between the theory and numerical simulations using an effective potential approach.

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.

Rotational Dynamics of Proteins from Spin Relaxation Times and Molecular Dynamics Simulations.

PubMed

Ollila, O H Samuli; Heikkinen, Harri A; Iwaï, Hideo

2018-06-14

Conformational fluctuations and rotational tumbling of proteins can be experimentally accessed with nuclear spin relaxation experiments. However, interpretation of molecular dynamics from the experimental data is often complicated, especially for molecules with anisotropic shape. Here, we apply classical molecular dynamics simulations to interpret the conformational fluctuations and rotational tumbling of proteins with arbitrarily anisotropic shape. The direct calculation of spin relaxation times from simulation data did not reproduce the experimental data. This was successfully corrected by scaling the overall rotational diffusion coefficients around the protein inertia axes with a constant factor. The achieved good agreement with experiments allowed the interpretation of the internal and overall dynamics of proteins with significantly anisotropic shape. The overall rotational diffusion was found to be Brownian, having only a short subdiffusive region below 0.12 ns. The presented methodology can be applied to interpret rotational dynamics and conformation fluctuations of proteins with arbitrary anisotropic shape. However, a water model with more realistic dynamical properties is probably required for intrinsically disordered proteins.

3D dust clouds (Yukawa Balls) in strongly coupled dusty plasmas

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

Melzer, A.; Passvogel, M.; Miksch, T.

2010-06-16

Three-dimensional finite systems of charged dust particles confined to concentric spherical shells in a dusty plasma, so-called 'Yukawa balls', have been studied with respect to their static and dynamic properties. Here, we review the charging of particles in a dusty plasma discharge by computer simulations and the respective particle arrangements. The normal mode spectrum of Yukawa balls is measured from the 3D thermal Brownian motion of the dust particles around their equilibrium positions.

Hydrodynamic boundary condition of water on hydrophobic surfaces.

PubMed

Schaeffel, David; Yordanov, Stoyan; Schmelzeisen, Marcus; Yamamoto, Tetsuya; Kappl, Michael; Schmitz, Roman; Dünweg, Burkhard; Butt, Hans-Jürgen; Koynov, Kaloian

2013-05-01

By combining total internal reflection fluorescence cross-correlation spectroscopy with Brownian dynamics simulations, we were able to measure the hydrodynamic boundary condition of water flowing over a smooth solid surface with exceptional accuracy. We analyzed the flow of aqueous electrolytes over glass coated with a layer of poly(dimethylsiloxane) (advancing contact angle Θ = 108°) or perfluorosilane (Θ = 113°). Within an error of better than 10 nm the slip length was indistinguishable from zero on all surfaces.

Multiobjective Optimal Control Methodology for the Analysis of Certain Sociodynamic Problems

DTIC Science & Technology

2009-03-01

but less expensive in both time and memory. 137 References [1] R. Albert and A-L Barabasi. Statistical mechanics of complex networks. Reviews of Modern...Review, E(51):4282–4286, 1995. [24] D. Helbing, P. Molnar, and F. Schweitzer . Computer simulation of pedestrian dynamics and trail formation. May 1998...Patterson AFB, OH, 2001. [49] F. Schweitzer . Brownian Agents and Active Particles. Springer, Santa Fe, NM, 2003. [50] P. Sen. Complexities of social

Spatially dependent diffusion coefficient as a model for pH sensitive microgel particles in microchannels

PubMed Central

Pieprzyk, S.; Heyes, D. M.; Brańka, A. C.

2016-01-01

Solute transport and intermixing in microfluidic devices is strongly dependent on diffusional processes. Brownian Dynamics simulations of pressure-driven flow of model microgel particles in microchannels have been carried out to explore these processes and the factors that influence them. The effects of a pH-field that induces a spatial dependence of particle size and consequently the self-diffusion coefficient and system thermodynamic state were focused on. Simulations were carried out in 1D to represent some of the cross flow dependencies, and in 2D and 3D to include the effects of flow and particle concentration, with typical stripe-like diffusion coefficient spatial variations. In 1D, the mean square displacement and particle displacement probability distribution function agreed well with an analytically solvable model consisting of infinitely repulsive walls and a discontinuous pH-profile in the middle of the channel. Skew category Brownian motion and non-Gaussian dynamics were observed, which follows from correlations of step lengths in the system, and can be considered to be an example of so-called “diffusing diffusivity.” In Poiseuille flow simulations, the particles accumulated in regions of larger diffusivity and the largest particle concentration throughput was found when this region was in the middle of the channel. The trends in the calculated cross-channel diffusional behavior were found to be very similar in 2D and 3D. PMID:27795750

Absolute protein-protein association rate constants from flexible, coarse-grained Brownian dynamics simulations: the role of intermolecular hydrodynamic interactions in barnase-barstar association.

PubMed

Frembgen-Kesner, Tamara; Elcock, Adrian H

2010-11-03

Theory and computation have long been used to rationalize the experimental association rate constants of protein-protein complexes, and Brownian dynamics (BD) simulations, in particular, have been successful in reproducing the relative rate constants of wild-type and mutant protein pairs. Missing from previous BD studies of association kinetics, however, has been the description of hydrodynamic interactions (HIs) between, and within, the diffusing proteins. Here we address this issue by rigorously including HIs in BD simulations of the barnase-barstar association reaction. We first show that even very simplified representations of the proteins--involving approximately one pseudoatom for every three residues in the protein--can provide excellent reproduction of the absolute association rate constants of wild-type and mutant protein pairs. We then show that simulations that include intermolecular HIs also produce excellent estimates of association rate constants, but, for a given reaction criterion, yield values that are decreased by ∼35-80% relative to those obtained in the absence of intermolecular HIs. The neglect of intermolecular HIs in previous BD simulation studies, therefore, is likely to have contributed to the somewhat overestimated absolute rate constants previously obtained. Consequently, intermolecular HIs could be an important component to include in accurate modeling of the kinetics of macromolecular association events. Copyright © 2010 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Conduction Properties of KcsA Measured Using Brownian Dynamics with Flexible Carbonyl Groups in the Selectivity Filter

PubMed Central

Chung, Shin-Ho; Corry, Ben

2007-01-01

In the narrow segment of an ion conducting pathway, it is likely that a permeating ion influences the positions of the nearby atoms that carry partial or full electronic charges. Here we introduce a method of incorporating the motion of charged atoms lining the pore into Brownian dynamics simulations of ion conduction. The movements of the carbonyl groups in the selectivity filter of the KcsA channel are calculated explicitly, allowing their bond lengths, bond angles, and dihedral angels to change in response to the forces acting upon them. By systematically changing the coefficients of bond stretching and of angle bending, the carbon and oxygen atoms can be made to fluctuate from their fixed positions by varying mean distances. We show that incorporating carbonyl motion in this way does not alter the mechanism of ion conduction and only has a small influence on the computed current. The slope conductance of the channel increases by ∼25% when the root mean-square fluctuations of the carbonyl groups are increased from 0.01 to 0.61 Å. The energy profiles and the number of resident ions in the channel remain unchanged. The method we utilized here can be extended to allow the movement of glutamate or aspartate side chains lining the selectivity filters of other ionic channels. PMID:17434934

Brownian Dynamics Simulations of Polyelectrolyte Adsorption in Shear Flow

NASA Astrophysics Data System (ADS)

Panwar, Ajay

2005-03-01

The adsorption of polyelectrolytes onto charged surfaces often occurs in microfludic devices and can influence their operation. We employ Brownian dynamics simulations to investigate the effect of a simple shear flow on the adsorption of an isolated polyelectrolyte molecule onto an oppositely charged surface. The polyelectrolyte is modeled as a freely-jointed bead-rod chain where the total charge is distributed uniformly among all the beads, and the beads are allowed to interact with one another and the charged surface through screened Coulombic interactions. The simulations are performed by placing the chain some distance above the surface, and the adsorption behavior is studied as a function of the screening length. Specifically, we look at the components of the radius of gyration, normal and parallel to the adsorbing surface, as functions of the screening length, both in the absence and presence of the flow. We find that in the absence of flow, the chain lies flat and stretched on the adsorbing surface in the limit of weak screening, but attains free solution behavior in the limit of strong screening. In the presence of a shear flow, the chain orientation in the direction of the flow increases with increasing Weissenberg number over the entire range of screening lengths studied. We also find that increasing the strength of the shear flow leads to an increased contact of the chain with the surface compared to the case when no flow is present.

Electrostatic steering and ionic tethering in enzyme-ligand binding: insights from simulations.

PubMed

Wade, R C; Gabdoulline, R R; Lüdemann, S K; Lounnas, V

1998-05-26

To bind at an enzyme's active site, a ligand must diffuse or be transported to the enzyme's surface, and, if the binding site is buried, the ligand must diffuse through the protein to reach it. Although the driving force for ligand binding is often ascribed to the hydrophobic effect, electrostatic interactions also influence the binding process of both charged and nonpolar ligands. First, electrostatic steering of charged substrates into enzyme active sites is discussed. This is of particular relevance for diffusion-influenced enzymes. By comparing the results of Brownian dynamics simulations and electrostatic potential similarity analysis for triose-phosphate isomerases, superoxide dismutases, and beta-lactamases from different species, we identify the conserved features responsible for the electrostatic substrate-steering fields. The conserved potentials are localized at the active sites and are the primary determinants of the bimolecular association rates. Then we focus on a more subtle effect, which we will refer to as "ionic tethering." We explore, by means of molecular and Brownian dynamics simulations and electrostatic continuum calculations, how salt links can act as tethers between structural elements of an enzyme that undergo conformational change upon substrate binding, and thereby regulate or modulate substrate binding. This is illustrated for the lipase and cytochrome P450 enzymes. Ionic tethering can provide a control mechanism for substrate binding that is sensitive to the electrostatic properties of the enzyme's surroundings even when the substrate is nonpolar.

[Application of Brownian dynamics to the description of transmembrane ion flow as exemplified by the chloride channel of glycine receptor].

PubMed

Boronovskiĭ, S E; Nartsissov, Ia R

2009-01-01

Using the Brownian dynamics of the movement of hydrated ion in a viscous water solution, a mathematical model has been built, which describes the transport of charged particles through a single protein pore in a lipid membrane. The dependences of transmembrane ion currents on ion concentrations in solution have been obtained. It was shown that, if the geometry of a membrane pore is identical to that of the inner part of the glycine receptor channel and there is no ion selectivity, then the values of both chloride and sodium currents are not greater than 0.5 pA at the physiological concentrations of these ions. If local charge heterogeneity caused by charged amino acid residues of transmembrane protein segments is included into the model calculations, the chloride current increases to about 3.7 pA, which exceeds more than seven times the value for sodium ions under the conditions of the complex channel geometry in the range of physiological concentrations of ions in the solution. The model takes changes in the density of charge distribution both inside the channel and near the protein surface into account. The alteration of pore geometry can be also considered as a parameter at the researcher's option. Thus, the model appears as an effective tool for the description of transmembrane currents for other types of membrane channels.

Conduction properties of KcsA measured using brownian dynamics with flexible carbonyl groups in the selectivity filter.

PubMed

Chung, Shin-Ho; Corry, Ben

2007-07-01

In the narrow segment of an ion conducting pathway, it is likely that a permeating ion influences the positions of the nearby atoms that carry partial or full electronic charges. Here we introduce a method of incorporating the motion of charged atoms lining the pore into Brownian dynamics simulations of ion conduction. The movements of the carbonyl groups in the selectivity filter of the KcsA channel are calculated explicitly, allowing their bond lengths, bond angles, and dihedral angels to change in response to the forces acting upon them. By systematically changing the coefficients of bond stretching and of angle bending, the carbon and oxygen atoms can be made to fluctuate from their fixed positions by varying mean distances. We show that incorporating carbonyl motion in this way does not alter the mechanism of ion conduction and only has a small influence on the computed current. The slope conductance of the channel increases by approximately 25% when the root mean-square fluctuations of the carbonyl groups are increased from 0.01 to 0.61 A. The energy profiles and the number of resident ions in the channel remain unchanged. The method we utilized here can be extended to allow the movement of glutamate or aspartate side chains lining the selectivity filters of other ionic channels.

Auditory hair cell centrioles undergo confined Brownian motion throughout the developmental migration of the kinocilium.

PubMed

Lepelletier, Léa; de Monvel, Jacques Boutet; Buisson, Johanna; Desdouets, Chantal; Petit, Christine

2013-07-02

Planar polarization of the forming hair bundle, the mechanosensory antenna of auditory hair cells, depends on the poorly characterized center-to-edge displacement of a primary cilium, the kinocilium, at their apical surface. Taking advantage of the gradient of hair cell differentiation along the cochlea, we reconstituted a map of the kinocilia displacements in the mouse embryonic cochlea. We then developed a cochlear organotypic culture and video-microscopy approach to monitor the movements of the kinocilium basal body (mother centriole) and its daughter centriole, which we analyzed using particle tracking and modeling. We found that both hair cell centrioles undergo confined Brownian movements around their equilibrium positions, under the apparent constraint of a radial restoring force of ∼0.1 pN. This magnitude depended little on centriole position, suggesting nonlinear interactions with constraining, presumably cytoskeletal elements. The only dynamic change observed during the period of kinocilium migration was a doubling of the centrioles' confinement area taking place early in the process. It emerges from these static and dynamic observations that kinocilia migrate gradually in parallel with the organization of hair cells into rows during cochlear neuroepithelium extension. Analysis of the confined motion of hair cell centrioles under normal and pathological conditions should help determine which structures contribute to the restoring force exerting on them. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Discrete-state representation of ion permeation coupled to fast gating in a model of ClC chloride channels: comparison to multi-ion continuous space Brownian dynamics simulations.

PubMed

Coalson, Rob D; Cheng, Mary Hongying

2010-01-28

A discrete-state model of chloride ion motion in a ClC chloride channel is constructed, following a previously developed multi-ion continuous space model of the same system (Cheng, M. H.; Mamonov, A. B.; Dukes, J. W.; Coalson, R. D. J. Phys. Chem. B 2007, 111, 5956) that included a simplistic representation of the fast gate in this channel. The reducibility of the many-body continuous space to the eight discrete-state model considered in the present work is examined in detail by performing three-dimensional Brownian dynamics simulations of each allowed state-to-state transition in order to extract the appropriate rate constant for this process, and then inserting the pairwise rate constants thereby obtained into an appropriate set of kinetic master equations. Experimental properties of interest, including the rate of Cl(-) ion permeation through the open channel and the average rate of closing of the fast gate as a function of bulk Cl(-) ion concentrations in the intracellular and extracellular electrolyte reservoirs are computed. Good agreement is found between the results obtained via the eight discrete-state model versus the multi-ion continuous space model, thereby encouraging continued development of the discrete-state model to include more complex behaviors observed experimentally in these channels.

Auditory Hair Cell Centrioles Undergo Confined Brownian Motion Throughout the Developmental Migration of the Kinocilium

PubMed Central

Lepelletier, Léa; de Monvel, Jacques Boutet; Buisson, Johanna; Desdouets, Chantal; Petit, Christine

2013-01-01

Planar polarization of the forming hair bundle, the mechanosensory antenna of auditory hair cells, depends on the poorly characterized center-to-edge displacement of a primary cilium, the kinocilium, at their apical surface. Taking advantage of the gradient of hair cell differentiation along the cochlea, we reconstituted a map of the kinocilia displacements in the mouse embryonic cochlea. We then developed a cochlear organotypic culture and video-microscopy approach to monitor the movements of the kinocilium basal body (mother centriole) and its daughter centriole, which we analyzed using particle tracking and modeling. We found that both hair cell centrioles undergo confined Brownian movements around their equilibrium positions, under the apparent constraint of a radial restoring force of ∼0.1 pN. This magnitude depended little on centriole position, suggesting nonlinear interactions with constraining, presumably cytoskeletal elements. The only dynamic change observed during the period of kinocilium migration was a doubling of the centrioles’ confinement area taking place early in the process. It emerges from these static and dynamic observations that kinocilia migrate gradually in parallel with the organization of hair cells into rows during cochlear neuroepithelium extension. Analysis of the confined motion of hair cell centrioles under normal and pathological conditions should help determine which structures contribute to the restoring force exerting on them. PMID:23823223

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…

Benoit Mandelbrot in finance

NASA Astrophysics Data System (ADS)

Walter, Christian

2015-03-01

The following sections are included: * Introduction * The Noah and Joseph effects and the non-Gaussian and non-Brownian issues of the financial theory * The first model of Mandelbrot (1962): α-stable motion with paretian tails * The second model of Mandelbrot (1965): fractional brownian motion with aperiodic cycles * The third model of Mandelbrot (1967): time changed Brownian motion with stochastic clock * Appendix: a tale of fat tails * Bibliography

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.

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.

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.

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.

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.

Modelling and analysis of bacterial tracks suggest an active reorientation mechanism in Rhodobacter sphaeroides

PubMed Central

Rosser, Gabriel; Baker, Ruth E.; Armitage, Judith P.; Fletcher, Alexander G.

2014-01-01

Most free-swimming bacteria move in approximately straight lines, interspersed with random reorientation phases. A key open question concerns varying mechanisms by which reorientation occurs. We combine mathematical modelling with analysis of a large tracking dataset to study the poorly understood reorientation mechanism in the monoflagellate species Rhodobacter sphaeroides. The flagellum on this species rotates counterclockwise to propel the bacterium, periodically ceasing rotation to enable reorientation. When rotation restarts the cell body usually points in a new direction. It has been assumed that the new direction is simply the result of Brownian rotation. We consider three variants of a self-propelled particle model of bacterial motility. The first considers rotational diffusion only, corresponding to a non-chemotactic mutant strain. Two further models incorporate stochastic reorientations, describing ‘run-and-tumble’ motility. We derive expressions for key summary statistics and simulate each model using a stochastic computational algorithm. We also discuss the effect of cell geometry on rotational diffusion. Working with a previously published tracking dataset, we compare predictions of the models with data on individual stopping events in R. sphaeroides. This provides strong evidence that this species undergoes some form of active reorientation rather than simple reorientation by Brownian rotation. PMID:24872500

Dynamic simulations of the inhomogeneous sedimentation of rigid fibres

NASA Astrophysics Data System (ADS)

Butler, Jason E.; Shaqfeh, Eric S. G.

2002-10-01

We have simulated the dynamics of suspensions of fibres sedimenting in the limit of zero Reynolds number. In these simulations, the dominant inter-particle force arises from hydrodynamic interactions between the rigid, non-Brownian fibres. The simulation algorithm uses slender-body theory to model the linear and rotational velocities of each fibre. To include far-field interactions between the fibres, the line distribution of force on each fibre is approximated by making a Legendre polynomial expansion of the disturbance velocity on the fibre, where only the first two terms of the expansion are retained in the calculation. Thus, the resulting linear force distribution can be specified completely by a centre-of-mass force, a couple, and a stresslet. Short-range interactions between particles are included using a lubrication approximation, and an infinite suspension is simulated by using periodic boundary conditions. Our numerical results confirm that the sedimentation of these non-spherical, orientable particles differs qualitatively from the sedimentation of spherical particles. The simulations demonstrate that an initially homogeneous, settling suspension develops clusters, or streamers, which are particle rich surrounded by clarified fluid. The instability which causes the heterogeneous structure arises solely from hydrodynamic interactions which couple the particle orientation and the sedimentation rate in particle clusters. Depending upon the concentration and aspect ratio, the formation of clusters of particles can enhance the sedimentation rate of the suspension to a value in excess of the maximum settling speed of an isolated particle. The suspension of fibres tends to orient with gravity during the sedimentation process. The average velocities and orientations, as well as their distributions, compare favourably with previous experimental measurements.

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.

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.

Stochastic Physicochemical Dynamics

NASA Astrophysics Data System (ADS)

Tsekov, R.

2001-02-01

Thermodynamic Relaxation in Quantum Systems: A new approach to quantum Markov processes is developed and the corresponding Fokker-Planck equation is derived. The latter is examined to reproduce known results from classical and quantum physics. It was also applied to the phase-space description of a mechanical system thus leading to a new treatment of this problem different from the Wigner presentation. The equilibrium probability density obtained in the mixed coordinate-momentum space is a reasonable extension of the Gibbs canonical distribution. The validity of the Einstein fluctuation-dissipation relation is discussed in respect to the type of relaxation in an isothermal system. The first model, presuming isothermic fluctuations, leads to the Einstein formula. The second model supposes adiabatic fluctuations and yields another relation between the diffusion coefficient and mobility of a Brownian particle. A new approach to relaxations in quantum systems is also proposed that demonstrates applicability only of the adiabatic model for description of the quantum Brownian dynamics. Stochastic Dynamics of Gas Molecules: A stochastic Langevin equation is derived, describing the thermal motion of a molecule immersed in a rested fluid of identical molecules. The fluctuation-dissipation theorem is proved and a number of correlation characteristics of the molecular Brownian motion are obtained. A short review of the classical theory of Brownian motion is presented. A new method is proposed for derivation of the Fokker-Planck equations, describing the probability density evolution, from stochastic differential equations. It is also proven via the central limit theorem that the white noise is only Gaussian. The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Ito and Stratonovich forms, is introduced. It is shown that the new presentation is more appropriate for the description of thermodynamic fluctuations. The range of validity of the Boltzmann-Einstein principle is also discussed and a generalized alternative is proposed. Both expressions coincide in the small fluctuation limit, providing a normal distribution density. Fluctuation Stability of Thin Liquid Films: Memory effect of Brownian motion in an incompressible fluid is studied. The reasoning is based on the Mori-Zwanzig formalism and a new formulation of the Langevin force as a result of collisions between an effective and the Brownian particles. Thus, the stochastic force autocorrelation function with finite dispersion and the corresponding Brownian particle velocity autocorrelation function are obtained. It is demonstrated that the dynamic structure is very important for the rate of drainage of a thin liquid film and it can be effectively taken into account by a dynamic fractal dimension. It is shown that the latter is a powerful tool for description of the film drainage and classifies all the known results from the literature. The obtained general expression for the thinning rate is a heuristic one and predicts variety of drainage models, which are even difficult to simulate in practice. It is a typical example of a scaling law, which explains the origin of the complicate dependence of the thinning rate on the film radius. On the basis of the theory of stochastic processes the evolution of the spatial correlation function of the surface waves on a thin liquid film as well as the corresponding root mean square amplitude A(t) and number of uncorrelated subdomains N(t) are obtained. A formulation of the life time of unstable nonthinning films is proposed, based on the evolution of A and N. It is shown that the presence of uncorrelated subdomains shortens the life time of the film. Some numerical results for A(t) and N(t) at different film thicknesses h and areas S, are demonstrated, taking into account only van der Waals and capillary forces. Resonant Diffusion in Molecular Solid Structures: A new approach to Brownian motion of atomic clusters on solid surfaces is developed. The main topic discussed is the dependence of the diffusion coefficient on the fit between the surface static potential and the internal cluster configuration. It is shown this dependence is non-monotonous, which is the essence of the so-called resonant diffusion. Assuming quicker inner motion of the cluster than its translation, adiabatic separation of these variables is possible and a relatively simple expression for the diffusion coefficient is obtained. In this way, the role of cluster vibrations is accounted for, thus leading to a more complex resonance in the cluster surface mobility. Diffusion of normal alkanes in one-dimensional zeolites is theoretically studied on the basis of the stochastic equation formalism. The calculated diffusion coefficient accounts for the vibrations of the diffusing molecule and zeolite framework, molecule-zeolite interaction, and specific structure of the zeolite. It is shown that when the interaction potential is predominantly determined by the zeolite pore structure, the diffusion coefficient varies periodically with the number of carbon atoms of the alkane molecule, a phenomenon called resonant diffusion. A criterion for observable resonance is obtained from the balance between the interaction potentials of the molecule due to the atomic and pore structures of the zeolite. It shows that the diffusion is not resonant in zeolites without pore structure, such as ZSM-12. Moreover, even in zeolites with developed pore structure no resonant dependence of the diffusion constant can be detected if the pore structure energy barriers are not at least three times higher than the atomic structure energy barriers. The role of the alkane molecule vibrations is examined as well and a surprising effect of suppression of the diffusion in comparison with the case of a rigid molecule is observed. This effect is explained with the balance between the static and dynamic interaction of the molecule and zeolite. Catalytic Kinetics of Chemical Dissociation: A unified description of the catalytic effect of Cu-exchanged zeolites is proposed for the decomposition of NO. A general expression for the rate constant of NO decomposition is obtained by assuming that the rate-determining step consists of the transferring of a single atom associated with breaking of the N-O bond. The analysis is performed on the base of the generalized Langevin equation and takes into account both the potential interactions in the system and the memory effects due to the zeolite vibrations. Two different mechanisms corresponding to monomolecular and bimolecular NO decomposition are discussed. The catalytic effect in the monomolecular mechanism is related to both the Cu+ ions and zeolite O-vacancies, while in the case of the bimolecular mechanism the zeolite contributes through dissipation only. The comparison of the theoretically calculated rate constants with experimental results reveals additional information about the geometric and energetic characteristics of the active centers and confirms the logic of the proposed models.

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.

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.

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

Transport driven by biharmonic forces: impact of correlated thermal noise.

PubMed

Machura, L; Łuczka, J

2010-09-01

We study an inertial brownian particle moving in a symmetric periodic substrate, driven by a zero-mean biharmonic force and correlated thermal noise. The brownian motion is described in terms of a generalized Langevin equation with an exponentially correlated gaussian noise term, obeying the fluctuation-dissipation theorem. We analyze impact of nonzero correlation time of thermal noise on transport properties of the brownian particle. We identify regimes where the increase of the correlation time intensifies long-time transport of the brownian particle. The opposite effect is also found: longer correlation time reduces the stationary velocity of the particle. The correlation time induced multiple current reversal is detected. We reveal that thermal noise of nonzero correlation time can radically enhance long-time velocity of the brownian particle in regimes where in the white noise limit the velocity is extremely small. All transport properties can be tested in the setup consisting of a resistively and capacitively shunted Josephson junction device.

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 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.

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

Fractional noise destroys or induces a stochastic bifurcation

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

Yang, Qigui, E-mail: qgyang@scut.edu.cn; Zeng, Caibin, E-mail: zeng.cb@mail.scut.edu.cn; School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640

2013-12-15

Little seems to be known about the stochastic bifurcation phenomena of non-Markovian systems. Our intention in this paper is to understand such complex dynamics by a simple system, namely, the Black-Scholes model driven by a mixed fractional Brownian motion. The most interesting finding is that the multiplicative fractional noise not only destroys but also induces a stochastic bifurcation under some suitable conditions. So it opens a possible way to explore the theory of stochastic bifurcation in the non-Markovian framework.

Elasticity and critical bending moment of model colloidal aggregates.

PubMed

Pantina, John P; Furst, Eric M

2005-04-08

The bending mechanics of singly bonded colloidal aggregates are measured using laser tweezers. We find that the colloidal bonds are capable of supporting significant torques, providing a direct measurement of the tangential interactions between particles. A critical bending moment marks the limit of linear bending elasticity, past which small-scale rearrangements occur. These mechanical properties underlie the rheology and dynamics of colloidal gels formed by diffusion-limited cluster aggregation, and give critical insight into the contact interactions between Brownian particles.

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.