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.

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.

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

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.

Path-length-resolved dynamic light scattering in highly scattering random media: The transition to diffusing wave spectroscopy

NASA Astrophysics Data System (ADS)

Bizheva, Kostadinka K.; Siegel, Andy M.; Boas, David A.

1998-12-01

We used low coherence interferometry to measure Brownian motion within highly scattering random media. A coherence gate was applied to resolve the optical path-length distribution and to separate ballistic from diffusive light. Our experimental analysis provides details on the transition from single scattering to light diffusion and its dependence on the system parameters. We found that the transition to the light diffusion regime occurs at shorter path lengths for media with higher scattering anisotropy or for larger numerical aperture of the focusing optics.

Anomalous diffusion and dynamics of fluorescence recovery after photobleaching in the random-comb model

NASA Astrophysics Data System (ADS)

Yuste, S. B.; Abad, E.; Baumgaertner, A.

2016-07-01

We address the problem of diffusion on a comb whose teeth display varying lengths. Specifically, the length ℓ of each tooth is drawn from a probability distribution displaying power law behavior at large ℓ ,P (ℓ ) ˜ℓ-(1 +α ) (α >0 ). To start with, we focus on the computation of the anomalous diffusion coefficient for the subdiffusive motion along the backbone. This quantity is subsequently used as an input to compute concentration recovery curves mimicking fluorescence recovery after photobleaching experiments in comblike geometries such as spiny dendrites. Our method is based on the mean-field description provided by the well-tested continuous time random-walk approach for the random-comb model, and the obtained analytical result for the diffusion coefficient is confirmed by numerical simulations of a random walk with finite steps in time and space along the backbone and the teeth. We subsequently incorporate retardation effects arising from binding-unbinding kinetics into our model and obtain a scaling law characterizing the corresponding change in the diffusion coefficient. Finally, we show that recovery curves obtained with the help of the analytical expression for the anomalous diffusion coefficient cannot be fitted perfectly by a model based on scaled Brownian motion, i.e., a standard diffusion equation with a time-dependent diffusion coefficient. However, differences between the exact curves and such fits are small, thereby providing justification for the practical use of models relying on scaled Brownian motion as a fitting procedure for recovery curves arising from particle diffusion in comblike systems.

Numerical Simulation of the Perrin-Like Experiments

ERIC Educational Resources Information Center

Mazur, Zygmunt; Grech, Dariusz

2008-01-01

A simple model of the random Brownian walk of a spherical mesoscopic particle in viscous liquids is proposed. The model can be solved analytically and simulated numerically. The analytic solution gives the known Einstein-Smoluchowski diffusion law r[superscript 2] = 2Dt, where the diffusion constant D is expressed by the mass and geometry of a…

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

NASA Astrophysics Data System (ADS)

Najafi, Amin

2014-05-01

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

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.

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.

Conserved linear dynamics of single-molecule Brownian motion.

PubMed

Serag, Maged F; Habuchi, Satoshi

2017-06-06

Macromolecular diffusion in homogeneous fluid at length scales greater than the size of the molecule is regarded as a random process. The mean-squared displacement (MSD) of molecules in this regime increases linearly with time. Here we show that non-random motion of DNA molecules in this regime that is undetectable by the MSD analysis can be quantified by characterizing the molecular motion relative to a latticed frame of reference. Our lattice occupancy analysis reveals unexpected sub-modes of motion of DNA that deviate from expected random motion in the linear, diffusive regime. We demonstrate that a subtle interplay between these sub-modes causes the overall diffusive motion of DNA to appear to conform to the linear regime. Our results show that apparently random motion of macromolecules could be governed by non-random dynamics that are detectable only by their relative motion. Our analytical approach should advance broad understanding of diffusion processes of fundamental relevance.

Conserved linear dynamics of single-molecule Brownian motion

PubMed Central

Serag, Maged F.; Habuchi, Satoshi

2017-01-01

Macromolecular diffusion in homogeneous fluid at length scales greater than the size of the molecule is regarded as a random process. The mean-squared displacement (MSD) of molecules in this regime increases linearly with time. Here we show that non-random motion of DNA molecules in this regime that is undetectable by the MSD analysis can be quantified by characterizing the molecular motion relative to a latticed frame of reference. Our lattice occupancy analysis reveals unexpected sub-modes of motion of DNA that deviate from expected random motion in the linear, diffusive regime. We demonstrate that a subtle interplay between these sub-modes causes the overall diffusive motion of DNA to appear to conform to the linear regime. Our results show that apparently random motion of macromolecules could be governed by non-random dynamics that are detectable only by their relative motion. Our analytical approach should advance broad understanding of diffusion processes of fundamental relevance. PMID:28585925

Conserved linear dynamics of single-molecule Brownian motion

NASA Astrophysics Data System (ADS)

Serag, Maged F.; Habuchi, Satoshi

2017-06-01

Macromolecular diffusion in homogeneous fluid at length scales greater than the size of the molecule is regarded as a random process. The mean-squared displacement (MSD) of molecules in this regime increases linearly with time. Here we show that non-random motion of DNA molecules in this regime that is undetectable by the MSD analysis can be quantified by characterizing the molecular motion relative to a latticed frame of reference. Our lattice occupancy analysis reveals unexpected sub-modes of motion of DNA that deviate from expected random motion in the linear, diffusive regime. We demonstrate that a subtle interplay between these sub-modes causes the overall diffusive motion of DNA to appear to conform to the linear regime. Our results show that apparently random motion of macromolecules could be governed by non-random dynamics that are detectable only by their relative motion. Our analytical approach should advance broad understanding of diffusion processes of fundamental relevance.

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.

Asymmetric skew Bessel processes and their applications to finance

NASA Astrophysics Data System (ADS)

Decamps, Marc; Goovaerts, Marc; Schoutens, Wim

2006-02-01

In this paper, we extend the Harrison and Shepp's construction of the skew Brownian motion (1981) and we obtain a diffusion similar to the two-dimensional Bessel process with speed and scale densities discontinuous at one point. Natural generalizations to multi-dimensional and fractional order Bessel processes are then discussed as well as invariance properties. We call this family of diffusions asymmetric skew Bessel processes in opposition to skew Bessel processes as defined in Barlow et al. [On Walsh's Brownian motions, Seminaire de Probabilities XXIII, Lecture Notes in Mathematics, vol. 1372, Springer, Berlin, New York, 1989, pp. 275-293]. We present factorizations involving (asymmetric skew) Bessel processes with random time. Finally, applications to the valuation of perpetuities and Asian options are proposed.

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

NASA Astrophysics Data System (ADS)

Zhang, Yunxin

2009-07-01

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

Anomalous Diffusion of Single Particles in Cytoplasm

PubMed Central

Regner, Benjamin M.; Vučinić, Dejan; Domnisoru, Cristina; Bartol, Thomas M.; Hetzer, Martin W.; Tartakovsky, Daniel M.; Sejnowski, Terrence J.

2013-01-01

The crowded intracellular environment poses a formidable challenge to experimental and theoretical analyses of intracellular transport mechanisms. Our measurements of single-particle trajectories in cytoplasm and their random-walk interpretations elucidate two of these mechanisms: molecular diffusion in crowded environments and cytoskeletal transport along microtubules. We employed acousto-optic deflector microscopy to map out the three-dimensional trajectories of microspheres migrating in the cytosolic fraction of a cellular extract. Classical Brownian motion (BM), continuous time random walk, and fractional BM were alternatively used to represent these trajectories. The comparison of the experimental and numerical data demonstrates that cytoskeletal transport along microtubules and diffusion in the cytosolic fraction exhibit anomalous (nonFickian) behavior and posses statistically distinct signatures. Among the three random-walk models used, continuous time random walk provides the best representation of diffusion, whereas microtubular transport is accurately modeled with fractional BM. PMID:23601312

The Building Game: From Enumerative Combinatorics to Conformational Diffusion

NASA Astrophysics Data System (ADS)

Johnson-Chyzhykov, Daniel; Menon, Govind

2016-08-01

We study a discrete attachment model for the self-assembly of polyhedra called the building game. We investigate two distinct aspects of the model: (i) enumerative combinatorics of the intermediate states and (ii) a notion of Brownian motion for the polyhedral linkage defined by each intermediate that we term conformational diffusion. The combinatorial configuration space of the model is computed for the Platonic, Archimedean, and Catalan solids of up to 30 faces, and several novel enumerative results are generated. These represent the most exhaustive computations of this nature to date. We further extend the building game to include geometric information. The combinatorial structure of each intermediate yields a systems of constraints specifying a polyhedral linkage and its moduli space. We use a random walk to simulate a reflected Brownian motion in each moduli space. Empirical statistics of the random walk may be used to define the rates of transition for a Markov process modeling the process of self-assembly.

Membrane Diffusion Occurs by Continuous-Time Random Walk Sustained by Vesicular Trafficking.

PubMed

Goiko, Maria; de Bruyn, John R; Heit, Bryan

2018-06-19

Diffusion in cellular membranes is regulated by processes that occur over a range of spatial and temporal scales. These processes include membrane fluidity, interprotein and interlipid interactions, interactions with membrane microdomains, interactions with the underlying cytoskeleton, and cellular processes that result in net membrane movement. The complex, non-Brownian diffusion that results from these processes has been difficult to characterize, and moreover, the impact of factors such as membrane recycling on membrane diffusion remains largely unexplored. We have used a careful statistical analysis of single-particle tracking data of the single-pass plasma membrane protein CD93 to show that the diffusion of this protein is well described by a continuous-time random walk in parallel with an aging process mediated by membrane corrals. The overall result is an evolution in the diffusion of CD93: proteins initially diffuse freely on the cell surface but over time become increasingly trapped within diffusion-limiting membrane corrals. Stable populations of freely diffusing and corralled CD93 are maintained by an endocytic/exocytic process in which corralled CD93 is selectively endocytosed, whereas freely diffusing CD93 is replenished by exocytosis of newly synthesized and recycled CD93. This trafficking not only maintained CD93 diffusivity but also maintained the heterogeneous distribution of CD93 in the plasma membrane. These results provide insight into the nature of the biological and biophysical processes that can lead to significantly non-Brownian diffusion of membrane proteins and demonstrate that ongoing membrane recycling is critical to maintaining steady-state diffusion and distribution of proteins in the plasma membrane. Copyright © 2018 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Lévy walks

NASA Astrophysics Data System (ADS)

Zaburdaev, V.; Denisov, S.; Klafter, J.

2015-04-01

Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in which the dispersal process is faster than dictated by Brownian diffusion. The Lévy-walk model combines two key features, the ability to generate anomalously fast diffusion and a finite velocity of a random walker. Recent results in optics, Hamiltonian chaos, cold atom dynamics, biophysics, and behavioral science demonstrate that this particular type of random walk provides significant insight into complex transport phenomena. This review gives a self-consistent introduction to Lévy walks, surveys their existing applications, including latest advances, and outlines further perspectives.

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.

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

PubMed

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

2012-02-20

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

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

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.

Sustained currents in coupled diffusive systems

NASA Astrophysics Data System (ADS)

Larralde, Hernán; Sanders, David P.

2014-08-01

Coupling two diffusive systems may give rise to a nonequilibrium stationary state (NESS) with a non-trivial persistent, circulating current. We study a simple example that is exactly soluble, consisting of random walkers with different biases towards a reflecting boundary, modelling, for example, Brownian particles with different charge states in an electric field. We obtain analytical expressions for the concentrations and currents in the NESS for this model, and exhibit the main features of the system by numerical simulation.

The one-dimensional asymmetric persistent random walk

NASA Astrophysics Data System (ADS)

Rossetto, Vincent

2018-04-01

Persistent random walks are intermediate transport processes between a uniform rectilinear motion and a Brownian motion. They are formed by successive steps of random finite lengths and directions travelled at a fixed speed. The isotropic and symmetric 1D persistent random walk is governed by the telegrapher’s equation, also called the hyperbolic heat conduction equation. These equations have been designed to resolve the paradox of the infinite speed in the heat and diffusion equations. The finiteness of both the speed and the correlation length leads to several classes of random walks: Persistent random walk in one dimension can display anomalies that cannot arise for Brownian motion such as anisotropy and asymmetries. In this work we focus on the case where the mean free path is anisotropic, the only anomaly leading to a physics that is different from the telegrapher’s case. We derive exact expression of its Green’s function, for its scattering statistics and distribution of first-passage time at the origin. The phenomenology of the latter shows a transition for quantities like the escape probability and the residence time.

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.

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

In Vivo Anomalous Diffusion and Weak Ergodicity Breaking of Lipid Granules

NASA Astrophysics Data System (ADS)

Jeon, Jae-Hyung; Tejedor, Vincent; Burov, Stas; Barkai, Eli; Selhuber-Unkel, Christine; Berg-Sørensen, Kirstine; Oddershede, Lene; Metzler, Ralf

2011-01-01

Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak ergodicity breaking. Namely we demonstrate that at short times the granules perform subdiffusion according to the laws of continuous time random walk theory. The associated violation of ergodicity leads to a characteristic turnover between two scaling regimes of the time averaged mean squared displacement. At longer times the granule motion is consistent with fractional Brownian motion.

Tempered fractional calculus

NASA Astrophysics Data System (ADS)

Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua

2015-07-01

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

TEMPERED FRACTIONAL CALCULUS.

PubMed

Meerschaert, Mark M; Sabzikar, Farzad; Chen, Jinghua

2015-07-15

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

TEMPERED FRACTIONAL CALCULUS

PubMed Central

MEERSCHAERT, MARK M.; SABZIKAR, FARZAD; CHEN, JINGHUA

2014-01-01

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series. PMID:26085690

Tempered fractional calculus

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

Sabzikar, Farzad, E-mail: sabzika2@stt.msu.edu; Meerschaert, Mark M., E-mail: mcubed@stt.msu.edu; Chen, Jinghua, E-mail: cjhdzdz@163.com

2015-07-15

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a temperedmore » fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.« less

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.

Measuring nanoparticle diffusion in an ABELtrap

NASA Astrophysics Data System (ADS)

Dienerowitz, M.; Dienerowitz, F.; Börsch, M.

2018-03-01

Monitoring the Brownian motion of individual nanoscopic objects is key to investigate their transport properties and interactions with their close environment. Most techniques rely on transient diffusion through a detection volume or immobilisation, which restrict observation times or motility. We measure the diffusion coefficient and surface charge of individual nanoparticles and DNA molecules in an anti-Brownian electrokinetic trap (ABELtrap). This instrument is an active feedback trap confining the Brownian motion of a nanoparticle to the detection site by applying an electric field based on the particle’s current position. We simulate the Brownian motion of nanospheres in our sample geometry, including wall effects, due to partial confinement in the third dimension. The theoretically predicted values are in excellent agreement with our diffusion measurements in the ABELtrap. We also demonstrate the ABELtrap’s ability to measure varying sizes of DNA origami structures during denaturation.

Effects of ionic strength and temperature on the aggregation and deposition of multi-walled carbon nanotubes.

PubMed

Wang, Lixin; Yang, Xuezhi; Wang, Qi; Zeng, Yuxuan; Ding, Lei; Jiang, Wei

2017-01-01

The aggregation and deposition of carbon nanotubes (CNTs) determines their transport and fate in natural waters. Therefore, the aggregation kinetics of humic-acid treated multi-walled carbon nanotubes (HA-MWCNTs) was investigated by time-resolved dynamic light scattering in NaCl and CaCl 2 electrolyte solutions. Increased ionic strength induced HA-MWCNT aggregation due to the less negative zeta potential and the reduced electrostatic repulsion. The critical coagulation concentration (CCC) values of HA-MWCNTs were 80mmol/L in NaCl and 1.3mmol/L in CaCl 2 electrolyte, showing that Ca 2+ causes more serious aggregation than Na + . The aggregation behavior of HA-MWCNTs was consistent with Derjaguin-Landau-Verwey-Overbeek theory. The deposition kinetics of HA-MWCNTs was measured by the optical absorbance at 800nm. The critical deposition concentrations for HA-MWCNT in NaCl and CaCl 2 solutions were close to the CCC values, therefore the rate of deposition cannot be increased by changing the ionic strength in the diffusion-limited aggregation regime. The deposition process was correlated to the aggregation since larger aggregates increased gravitational deposition and decreased random Brownian diffusion. HA-MWCNTs hydrodynamic diameters were evaluated at 5, 15 and 25°C. Higher temperature caused faster aggregation due to the reduced electrostatic repulsion and increased random Brownian motion and collision frequency. HA-MWCNTs aggregate faster at higher temperature in either NaCl or CaCl 2 electrolyte due to the decreased electrostatic repulsion and increased random Brownian motion. Our results suggest that CNT aggregation and deposition are two correlated processes governed by the electrolyte, and CNT transport is favored at low ionic strength and low temperature. Copyright © 2016. Published by Elsevier B.V.

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.

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

PubMed

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

2016-04-01

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

A stochastic method for Brownian-like optical transport calculations in anisotropic biosuspensions and blood

NASA Astrophysics Data System (ADS)

Miller, Steven

1998-03-01

A generic stochastic method is presented that rapidly evaluates numerical bulk flux solutions to the one-dimensional integrodifferential radiative transport equation, for coherent irradiance of optically anisotropic suspensions of nonspheroidal bioparticles, such as blood. As Fermat rays or geodesics enter the suspension, they evolve into a bundle of random paths or trajectories due to scattering by the suspended bioparticles. Overall, this can be interpreted as a bundle of Markov trajectories traced out by a "gas" of Brownian-like point photons being scattered and absorbed by the homogeneous distribution of uncorrelated cells in suspension. By considering the cumulative vectorial intersections of a statistical bundle of random trajectories through sets of interior data planes in the space containing the medium, the effective equivalent information content and behavior of the (generally unknown) analytical flux solutions of the radiative transfer equation rapidly emerges. The fluxes match the analytical diffuse flux solutions in the diffusion limit, which verifies the accuracy of the algorithm. The method is not constrained by the diffusion limit and gives correct solutions for conditions where diffuse solutions are not viable. Unlike conventional Monte Carlo and numerical techniques adapted from neutron transport or nuclear reactor problems that compute scalar quantities, this vectorial technique is fast, easily implemented, adaptable, and viable for a wide class of biophotonic scenarios. By comparison, other analytical or numerical techniques generally become unwieldy, lack viability, or are more difficult to utilize and adapt. Illustrative calculations are presented for blood medias at monochromatic wavelengths in the visible spectrum.

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

ERIC Educational Resources Information Center

Krajsek, Simona Strgulc; Vilhar, Barbara

2010-01-01

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

Superimposed Code Theoretic Analysis of Deoxyribonucleic Acid (DNA) Codes and DNA Computing

DTIC Science & Technology

2010-01-01

partitioned by font type) of sequences are allowed to be in each position (e.g., Arial = position 0, Comic = position 1, etc. ) and within each collection...movement was modeled by a Brownian motion 3 dimensional random walk. The one dimensional diffusion coefficient D for the ellipsoid shape with 3...temperature, kB is Boltzmann’s constant, and η is the viscosity of the medium. The random walk motion is modeled by assuming the oligo is on a three

Effective Brownian ratchet separation by a combination of molecular filtering and a self-spreading lipid bilayer system.

PubMed

Motegi, Toshinori; Nabika, Hideki; Fu, Yingqiang; Chen, Lili; Sun, Yinlu; Zhao, Jianwei; Murakoshi, Kei

2014-07-01

A new molecular manipulation method in the self-spreading lipid bilayer membrane by combining Brownian ratchet and molecular filtering effects is reported. The newly designed ratchet obstacle was developed to effectively separate dye-lipid molecules. The self-spreading lipid bilayer acted as both a molecular transport system and a manipulation medium. By controlling the size and shape of ratchet obstacles, we achieved a significant increase in the separation angle for dye-lipid molecules compared to that with the previous ratchet obstacle. A clear difference was observed between the experimental results and the simple random walk simulation that takes into consideration only the geometrical effect of the ratchet obstacles. This difference was explained by considering an obstacle-dependent local decrease in molecular diffusivity near the obstacles, known as the molecular filtering effect at nanospace. Our experimental findings open up a novel controlling factor in the Brownian ratchet manipulation that allow the efficient separation of molecules in the lipid bilayer based on the combination of Brownian ratchet and molecular filtering effects.

Dynamical transition for a particle in a squared Gaussian potential

NASA Astrophysics Data System (ADS)

Touya, C.; Dean, D. S.

2007-02-01

We study the problem of a Brownian particle diffusing in finite dimensions in a potential given by ψ = phi2/2 where phi is Gaussian random field. Exact results for the diffusion constant in the high temperature phase are given in one and two dimensions and it is shown to vanish in a power-law fashion at the dynamical transition temperature. Our results are confronted with numerical simulations where the Gaussian field is constructed, in a standard way, as a sum over random Fourier modes. We show that when the number of Fourier modes is finite the low temperature diffusion constant becomes non-zero and has an Arrhenius form. Thus we have a simple model with a fully understood finite size scaling theory for the dynamical transition. In addition we analyse the nature of the anomalous diffusion in the low temperature regime and show that the anomalous exponent agrees with that predicted by a trap model.

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

NASA Astrophysics Data System (ADS)

Liang, Song

2018-01-01

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

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.

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.

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.

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.

Coiled to diffuse: Brownian motion of a helical bacterium.

PubMed

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

2012-09-11

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

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.

A mathematical model of single target site location by Brownian movement in subcellular compartments.

PubMed

Kuthan, Hartmut

2003-03-07

The location of distinct sites is mandatory for many cellular processes. In the subcompartments of the cell nucleus, only very small numbers of diffusing macromolecules and specific target sites of some types may be present. In this case, we are faced with the Brownian movement of individual macromolecules and their "random search" for single/few specific target sites, rather than bulk-averaged diffusion and multiple sites. In this article, I consider the location of a distant central target site, e.g. a globular protein, by individual macromolecules executing unbiased (i.e. drift-free) random walks in a spherical compartment. For this walk-and-capture model, the closed-form analytic solution of the first passage time probability density function (p.d.f.) has been obtained as well as the first and second moment. In the limit of a large ratio of the radii of the spherical diffusion space and central target, well-known relations for the variance and the first two moments for the exponential p.d.f. were found to hold with high accuracy. These calculations reinforce earlier numerical results and Monte Carlo simulations. A major implication derivable from the model is that non-directed random movement is an effective means for locating single sites in submicron-sized compartments, even when the diffusion coefficients are comparatively small and the diffusing species are present in one copy only. These theoretical conclusions are underscored numerically for effective diffusion constants ranging from 0.5 to 10.0 microm(2) s(-1), which have been reported for a couple of nuclear proteins in their physiological environment. Spherical compartments of submicron size are, for example, the Cajal bodies (size: 0.1-1.0 microm), which are present in 1-5 copies in the cell nucleus. Within a small Cajal body of radius 0.1 microm a single diffusing protein molecule (with D=0.5 microm(2) s(-1)) would encounter a medium-sized protein of radius 2.5 nm within 1 s with a probability near certainty (p=0.98).

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.

The Langevin equation

NASA Astrophysics Data System (ADS)

Pomeau, Yves; Piasecki, Jarosław

2017-11-01

The existence of atoms has been long predicted by philosophers and scientists. The development of thermodynamics and of the statistical interpretation of its concepts at the end of the nineteenth century and in the early years of the twentieth century made it possible to bridge the gap of scales between the macroscopic world and the world of atoms. Einstein and Smoluchowski showed in 1905 and 1906 that the Brownian motion of particles of measurable size is a manifestation of the motion of atoms in fluids. Their derivation was completely different from each other. Langevin showed in 1908 how to put in a coherent framework the subtle effect of the randomness of the atomic world, responsible for the fluctuating force driving the motion of the Brownian particle and the viscosity of the "macroscopic" flow taking place around the same Brownian particle. Whereas viscous forces were already well understood at this time, the "Langevin" force appears there for the first time: it represents the fluctuating part of the interaction between the Brownian particle and the surrounding fluid. We discuss the derivation by Einstein and Smoluchowski as well as a previous paper by Sutherland on the diffusion coefficient of large spheres. Next we present Langevin's short note and explain the fundamental splitting into a random force and a macroscopic viscous force. This brings us to discuss various points, like the kind of constraints on Langevin-like equations. We insist in particular on the one arising from the time-reversal symmetry of the equilibrium fluctuations. Moreover, we discuss another constraint, raised first by Lorentz, which implies that, if the Brownian particle is not very heavy, the viscous force cannot be taken as the standard Stokes drag on an object moving at uniform speed. Lastly, we examine the so-called Langevin-Heisenberg and/or Langevin-Schrödinger equation used in quantum mechanics.

Diffusion in translucent media.

PubMed

Shi, Zhou; Genack, Azriel Z

2018-05-10

Diffusion is the result of repeated random scattering. It governs a wide range of phenomena from Brownian motion, to heat flow through window panes, neutron flux in fuel rods, dispersion of light in human tissue, and electronic conduction. It is universally acknowledged that the diffusion approach to describing wave transport fails in translucent samples thinner than the distance between scattering events such as are encountered in meteorology, astronomy, biomedicine, and communications. Here we show in optical measurements and numerical simulations that the scaling of transmission and the intensity profiles of transmission eigenchannels have the same form in translucent as in opaque media. Paradoxically, the similarities in transport across translucent and opaque samples explain the puzzling observations of suppressed optical and ultrasonic delay times relative to predictions of diffusion theory well into the diffusive regime.

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.

Brownian motion of non-wetting droplets held on a flat solid by gravity

NASA Astrophysics Data System (ADS)

Pomeau, Yves

2013-12-01

At equilibrium a small liquid droplet standing on a solid (dry) horizontal surface it does not wet rests on this surface on a small disc. As predicted and observed if such a droplet is in a low-viscosity vapor the main source of drag for a motion along the surface is the viscous dissipation in the liquid near the disc of contact. This dissipation is minimized by a Huygens-like motion coupling rolling and translation in such a way that the fluid near the disc of contact is almost motionless with respect to the solid. Because of this reduced drag and the associated large mobility the coefficient of Brownian diffusion is much larger than its standard Stokes-Enstein value. This is correct if the weight of the droplet is sufficient to keep it on the solid, instead of being lifted by thermal noise. The coupling between translation along the surface and rotation could be measured by correlated random angular deviations and horizontal displacement in this Brownian motion.

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

PubMed

Fernandes, Miguel X; de la Torre, José García

2002-12-01

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

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.

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.

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

PubMed

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

2014-09-30

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

A molecule-centered method for accelerating the calculation of hydrodynamic interactions in Brownian dynamics simulations containing many flexible biomolecules

PubMed Central

Elcock, Adrian H.

2013-01-01

Inclusion of hydrodynamic interactions (HIs) is essential in simulations of biological macromolecules that treat the solvent implicitly if the macromolecules are to exhibit correct translational and rotational diffusion. The present work describes the development and testing of a simple approach aimed at allowing more rapid computation of HIs in coarse-grained Brownian dynamics simulations of systems that contain large numbers of flexible macromolecules. The method combines a complete treatment of intramolecular HIs with an approximate treatment of the intermolecular HIs which assumes that the molecules are effectively spherical; all of the HIs are calculated at the Rotne-Prager-Yamakawa level of theory. When combined with Fixman’s Chebyshev polynomial method for calculating correlated random displacements, the proposed method provides an approach that is simple to program but sufficiently fast that it makes it computationally viable to include HIs in large-scale simulations. Test calculations performed on very coarse-grained models of the pyruvate dehydrogenase (PDH) E2 complex and on oligomers of ParM (ranging in size from 1 to 20 monomers) indicate that the method reproduces the translational diffusion behavior seen in more complete HI simulations surprisingly well; the method performs less well at capturing rotational diffusion but its discrepancies diminish with increasing size of the simulated assembly. Simulations of residue-level models of two tetrameric protein models demonstrate that the method also works well when more structurally detailed models are used in the simulations. Finally, test simulations of systems containing up to 1024 coarse-grained PDH molecules indicate that the proposed method rapidly becomes more efficient than the conventional BD approach in which correlated random displacements are obtained via a Cholesky decomposition of the complete diffusion tensor. PMID:23914146

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

Transition density of one-dimensional diffusion with discontinuous drift

NASA Technical Reports Server (NTRS)

Zhang, Weijian

1990-01-01

The transition density of a one-dimensional diffusion process with a discontinuous drift coefficient is studied. A probabilistic representation of the transition density is given, illustrating the close connections between discontinuities of the drift and Brownian local times. In addition, some explicit results are obtained based on the trivariate density of Brownian motion, its occupation, and local times.

Generalized Einstein relation for the mutual diffusion coefficient of a binary fluid mixture.

PubMed

Felderhof, B U

2017-08-21

The method employed by Einstein to derive his famous relation between the diffusion coefficient and the friction coefficient of a Brownian particle is used to derive a generalized Einstein relation for the mutual diffusion coefficient of a binary fluid mixture. The expression is compared with the one derived by de Groot and Mazur from irreversible thermodynamics and later by Batchelor for a Brownian suspension. A different result was derived by several other workers in irreversible thermodynamics. For a nearly incompressible solution, the generalized Einstein relation agrees with the expression derived by de Groot and Mazur. The two expressions also agree to first order in solute density. For a Brownian suspension, the result derived from the generalized Smoluchowski equation agrees with both expressions.

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.

Mechanisms underlying anomalous diffusion in the plasma membrane.

PubMed

Krapf, Diego

2015-01-01

The plasma membrane is a complex fluid where lipids and proteins undergo diffusive motion critical to biochemical reactions. Through quantitative imaging analyses such as single-particle tracking, it is observed that diffusion in the cell membrane is usually anomalous in the sense that the mean squared displacement is not linear with time. This chapter describes the different models that are employed to describe anomalous diffusion, paying special attention to the experimental evidence that supports these models in the plasma membrane. We review models based on anticorrelated displacements, such as fractional Brownian motion and obstructed diffusion, and nonstationary models such as continuous time random walks. We also emphasize evidence for the formation of distinct compartments that transiently form on the cell surface. Finally, we overview heterogeneous diffusion processes in the plasma membrane, which have recently attracted considerable interest. Copyright © 2015. Published by Elsevier Inc.

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

NASA Astrophysics Data System (ADS)

Bai, Zhan-Wu; Wang, Ping

2016-03-01

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

Biased Brownian motion in narrow channels with asymmetry and anisotropy

NASA Astrophysics Data System (ADS)

To, Kiwing; Peng, Zheng

2016-11-01

We study Brownian motion of a single millimeter size bead confined in a quasi-two-dimensional horizontal channel with built-in anisotropy and asymmetry. Channel asymmetry is implemented by ratchet walls while anisotropy is introduced using a channel base that is grooved along the channel axis so that a bead can acquire a horizontal impulse perpendicular to the longitudinal direction when it collides with the base. When energy is injected to the channel by vertical vibration, the combination of asymmetric walls and anisotropic base induces an effective force which drives the bead into biased diffusive motion along the channel axis with diffusivity and drift velocity increase with vibration strength. The magnitude of this driving force, which can be measured in experiments of tilted channel, is found to be consistent to those obtained from dynamic mobility and position probability distribution measurements. These results are explained by a simple collision model that suggests the random kinetic energies transfer between different translational degrees of freedom may be turned into useful work in the presence of asymmetry and anisotropy.

Biased Brownian motion in narrow channels with asymmetry and anisotropy

NASA Astrophysics Data System (ADS)

Peng, Zheng; To, Kiwing

2016-08-01

We study Brownian motion of a single millimeter size bead confined in a quasi-two-dimensional horizontal channel with built-in anisotropy and asymmetry. Channel asymmetry is implemented by ratchet walls while anisotropy is introduced using a channel base that is grooved along the channel axis so that a bead can acquire a horizontal impulse perpendicular to the longitudinal direction when it collides with the base. When energy is injected to the channel by vertical vibration, the combination of asymmetric walls and anisotropic base induces an effective force which drives the bead into biased diffusive motion along the channel axis with diffusivity and drift velocity increase with vibration strength. The magnitude of this driving force, which can be measured in experiments on a tilted channel, is found to be consistent with those obtained from dynamic mobility and position probability distribution measurements. These results are explained by a simple collision model that suggests the random kinetic energy transfer between different translational degrees of freedom may be turned into useful work in the presence of asymmetry and anisotropy.

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.

Diffusion of active chiral particles

NASA Astrophysics Data System (ADS)

Sevilla, Francisco J.

2016-12-01

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

Anomalous diffusion due to hindering by mobile obstacles undergoing Brownian motion or Orstein-Ulhenbeck processes.

PubMed

Berry, Hugues; Chaté, Hugues

2014-02-01

In vivo measurements of the passive movements of biomolecules or vesicles in cells consistently report "anomalous diffusion," where mean-squared displacements scale as a power law of time with exponent α<1 (subdiffusion). While the detailed mechanisms causing such behaviors are not always elucidated, movement hindrance by obstacles is often invoked. However, our understanding of how hindered diffusion leads to subdiffusion is based on diffusion amidst randomly located immobile obstacles. Here, we have used Monte Carlo simulations to investigate transient subdiffusion due to mobile obstacles with various modes of mobility. Our simulations confirm that the anomalous regimes rapidly disappear when the obstacles move by Brownian motion. By contrast, mobile obstacles with more confined displacements, e.g., Orstein-Ulhenbeck motion, are shown to preserve subdiffusive regimes. The mean-squared displacement of tracked protein displays convincing power laws with anomalous exponent α that varies with the density of Orstein-Ulhenbeck (OU) obstacles or the relaxation time scale of the OU process. In particular, some of the values we observed are significantly below the universal value predicted for immobile obstacles in two dimensions. Therefore, our results show that subdiffusion due to mobile obstacles with OU type of motion may account for the large variation range exhibited by experimental measurements in living cells and may explain that some experimental estimates are below the universal value predicted for immobile obstacles.

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.

Active Brownian motion tunable by light.

PubMed

Buttinoni, Ivo; Volpe, Giovanni; Kümmel, Felix; Volpe, Giorgio; Bechinger, Clemens

2012-07-18

Active Brownian particles are capable of taking up energy from their environment and converting it into directed motion; examples range from chemotactic cells and bacteria to artificial micro-swimmers. We have recently demonstrated that Janus particles, i.e. gold-capped colloidal spheres, suspended in a critical binary liquid mixture perform active Brownian motion when illuminated by light. In this paper, we investigate in more detail their swimming mechanism, leading to active Brownian motion. We show that the illumination-borne heating induces a local asymmetric demixing of the binary mixture, generating a spatial chemical concentration gradient which is responsible for the particle's self-diffusiophoretic motion. We study this effect as a function of the functionalization of the gold cap, the particle size and the illumination intensity: the functionalization determines what component of the binary mixture is preferentially adsorbed at the cap and the swimming direction (towards or away from the cap); the particle size determines the rotational diffusion and, therefore, the random reorientation of the particle; and the intensity tunes the strength of the heating and, therefore, of the motion. Finally, we harness this dependence of the swimming strength on the illumination intensity to investigate the behavior of a micro-swimmer in a spatial light gradient, where its swimming properties are space-dependent.

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

Random element method for numerical modeling of diffusional processes

NASA Technical Reports Server (NTRS)

Ghoniem, A. F.; Oppenheim, A. K.

1982-01-01

The random element method is a generalization of the random vortex method that was developed for the numerical modeling of momentum transport processes as expressed in terms of the Navier-Stokes equations. The method is based on the concept that random walk, as exemplified by Brownian motion, is the stochastic manifestation of diffusional processes. The algorithm based on this method is grid-free and does not require the diffusion equation to be discritized over a mesh, it is thus devoid of numerical diffusion associated with finite difference methods. Moreover, the algorithm is self-adaptive in space and explicit in time, resulting in an improved numerical resolution of gradients as well as a simple and efficient computational procedure. The method is applied here to an assortment of problems of diffusion of momentum and energy in one-dimension as well as heat conduction in two-dimensions in order to assess its validity and accuracy. The numerical solutions obtained are found to be in good agreement with exact solution except for a statistical error introduced by using a finite number of elements, the error can be reduced by increasing the number of elements or by using ensemble averaging over a number of solutions.

Brownian motion of solitons in a Bose-Einstein condensate.

PubMed

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

2017-03-07

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

Brownian motion of solitons in a Bose–Einstein condensate

PubMed Central

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

2017-01-01

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

Rad4 recognition-at-a-distance: Physical basis of conformation-specific anomalous diffusion of DNA repair proteins.

PubMed

Kong, Muwen; Van Houten, Bennett

2017-08-01

Since Robert Brown's first observations of random walks by pollen particles suspended in solution, the concept of diffusion has been subject to countless theoretical and experimental studies in diverse fields from finance and social sciences, to physics and biology. Diffusive transport of macromolecules in cells is intimately linked to essential cellular functions including nutrient uptake, signal transduction, gene expression, as well as DNA replication and repair. Advancement in experimental techniques has allowed precise measurements of these diffusion processes. Mathematical and physical descriptions and computer simulations have been applied to model complicated biological systems in which anomalous diffusion, in addition to simple Brownian motion, was observed. The purpose of this review is to provide an overview of the major physical models of anomalous diffusion and corresponding experimental evidence on the target search problem faced by DNA-binding proteins, with an emphasis on DNA repair proteins and the role of anomalous diffusion in DNA target recognition. Copyright © 2016 Elsevier Ltd. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Babel, S.; ten Hagen, B.; Löwen, H.

2014-02-01

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

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.

Diffusion in different models of active Brownian motion

NASA Astrophysics Data System (ADS)

Lindner, B.; Nicola, E. M.

2008-04-01

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

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…

Random-order fractional bistable system and its stochastic resonance

NASA Astrophysics Data System (ADS)

Gao, Shilong; Zhang, Li; Liu, Hui; Kan, Bixia

2017-01-01

In this paper, the diffusion motion of Brownian particles in a viscous liquid suffering from stochastic fluctuations of the external environment is modeled as a random-order fractional bistable equation, and as a typical nonlinear dynamic behavior, the stochastic resonance phenomena in this system are investigated. At first, the derivation process of the random-order fractional bistable system is given. In particular, the random-power-law memory is deeply discussed to obtain the physical interpretation of the random-order fractional derivative. Secondly, the stochastic resonance evoked by random-order and external periodic force is mainly studied by numerical simulation. In particular, the frequency shifting phenomena of the periodical output are observed in SR induced by the excitation of the random order. Finally, the stochastic resonance of the system under the double stochastic excitations of the random order and the internal color noise is also investigated.

Proteins as micro viscosimeters: Brownian motion revisited.

PubMed

Lavalette, Daniel; Hink, Mark A; Tourbez, Martine; Tétreau, Catherine; Visser, Antonie J

2006-08-01

Translational and rotational diffusion coefficients of proteins in solution strongly deviate from the Stokes-Einstein laws when the ambient viscosity is induced by macromolecular co-solutes rather than by a solvent of negligible size as was assumed by A. Einstein one century ago for deriving the laws of Brownian motion and diffusion. Rotational and translational motions experience different micro viscosities and both become a function of the size ratio of protein and macromolecular co-solute. Possible consequences upon fluorescence spectroscopy observations of diffusing proteins within living cells are discussed.

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.

Constrained diffusion or immobile fraction on cell surfaces: a new interpretation.

PubMed Central

Feder, T J; Brust-Mascher, I; Slattery, J P; Baird, B; Webb, W W

1996-01-01

Protein lateral mobility in cell membranes is generally measured using fluorescence photobleaching recovery (FPR). Since the development of this technique, the data have been interpreted by assuming free Brownian diffusion of cell surface receptors in two dimensions, an interpretation that requires that a subset of the diffusing species remains immobile. The origin of this so-called immobile fraction remains a mystery. In FPR, the motions of thousands of particles are inherently averaged, inevitably masking the details of individual motions. Recently, tracking of individual cell surface receptors has identified several distinct types of motion (Gross and Webb, 1988; Ghosh and Webb, 1988, 1990, 1994; Kusumi et al. 1993; Qian et al. 1991; Slattery, 1995), thereby calling into question the classical interpretation of FPR data as free Brownian motion of a limited mobile fraction. We have measured the motion of fluorescently labeled immunoglobulin E complexed to high affinity receptors (Fc epsilon RI) on rat basophilic leukemia cells using both single particle tracking and FPR. As in previous studies, our tracking results show that individual receptors may diffuse freely, or may exhibit restricted, time-dependent (anomalous) diffusion. Accordingly, we have analyzed FPR data by a new model to take this varied motion into account, and we show that the immobile fraction may be due to particles moving with the anomalous subdiffusion associated with restricted lateral mobility. Anomalous subdiffusion denotes random molecular motion in which the mean square displacements grow as a power law in time with a fractional positive exponent less than one. These findings call for a new model of cell membrane structure. PMID:8744314

Diffusion of massive particles around an Abelian-Higgs string

NASA Astrophysics Data System (ADS)

Saha, Abhisek; Sanyal, Soma

2018-03-01

We study the diffusion of massive particles in the space time of an Abelian Higgs string. The particles in the early universe plasma execute Brownian motion. This motion of the particles is modeled as a two dimensional random walk in the plane of the Abelian Higgs string. The particles move randomly in the space time of the string according to their geodesic equations. We observe that for certain values of their energy and angular momentum, an overdensity of particles is observed close to the string. We find that the string parameters determine the distribution of the particles. We make an estimate of the density fluctuation generated around the string as a function of the deficit angle. Though the thickness of the string is small, the length is large and the overdensity close to the string may have cosmological consequences in the early universe.

Diffusion of passive particles in active suspensions

NASA Astrophysics Data System (ADS)

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

2013-11-01

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

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.

A new fundamental model of moving particle for reinterpreting Schroedinger equation

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

Umar, Muhamad Darwis

2012-06-20

The study of Schroedinger equation based on a hypothesis that every particle must move randomly in a quantum-sized volume has been done. In addition to random motion, every particle can do relative motion through the movement of its quantum-sized volume. On the other way these motions can coincide. In this proposed model, the random motion is one kind of intrinsic properties of the particle. The every change of both speed of randomly intrinsic motion and or the velocity of translational motion of a quantum-sized volume will represent a transition between two states, and the change of speed of randomly intrinsicmore » motion will generate diffusion process or Brownian motion perspectives. Diffusion process can take place in backward and forward processes and will represent a dissipative system. To derive Schroedinger equation from our hypothesis we use time operator introduced by Nelson. From a fundamental analysis, we find out that, naturally, we should view the means of Newton's Law F(vector sign) = ma(vector sign) as no an external force, but it is just to describe both the presence of intrinsic random motion and the change of the particle energy.« less

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

NASA Astrophysics Data System (ADS)

Siems, Ullrich; Nielaba, Peter

2018-04-01

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

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.

Brownian motion of boomerang colloidal particles.

PubMed

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

2013-10-18

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

Brownian Motion of Boomerang Colloidal Particles

NASA Astrophysics Data System (ADS)

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

2013-10-01

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

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.

The Diffusion Process in Small Particles and Brownian Motion

NASA Astrophysics Data System (ADS)

Khoshnevisan, M.

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

Aging scaled Brownian motion

NASA Astrophysics Data System (ADS)

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

2015-04-01

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

Aging scaled Brownian motion.

PubMed

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

2015-04-01

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

Brownian motion, old and new, and Irwin's role in my academic life

NASA Astrophysics Data System (ADS)

Lindenberg, Katja

2015-03-01

Irwin Oppenheim's early work on Langevin equations, master equations, and Brownian motion was one of the earliest and strongest reasons for my change of direction from my PhD work in condensed matter theory to my later and lifelong interest in Brownian motion and, more broadly, statistical mechanics. I will talk about some of my most recent work on subdiffusion, a form of anomalous diffusion that describes random motions in crowded or disordered media where motions are hindered by the medium. On a personal note, I knew Irwin for decades, from the time before he had a family (he was a sworn bachelor...until he met his wife) until shortly before his death. For many years, first alone and then with family, Irwin would spend some portion of the cold Boston winter in warm La Jolla, and we would always get together during these visits. For a period of a number of years we decided to take advantage of these visits to write the definitive text in traditional Thermodynamics. We did not make it past about 2/3 of the project, but it was a great learning experience for me while it lasted. Irwin's knowledge and understanding of the subject were breathtaking.

The open quantum Brownian motions

NASA Astrophysics Data System (ADS)

Bauer, Michel; Bernard, Denis; Tilloy, Antoine

2014-09-01

Using quantum parallelism on random walks as the original seed, we introduce new quantum stochastic processes, the open quantum Brownian motions. They describe the behaviors of quantum walkers—with internal degrees of freedom which serve as random gyroscopes—interacting with a series of probes which serve as quantum coins. These processes may also be viewed as the scaling limit of open quantum random walks and we develop this approach along three different lines: the quantum trajectory, the quantum dynamical map and the quantum stochastic differential equation. We also present a study of the simplest case, with a two level system as an internal gyroscope, illustrating the interplay between the ballistic and diffusive behaviors at work in these processes. Notation H_z : orbital (walker) Hilbert space, {C}^{{Z}} in the discrete, L^2({R}) in the continuum H_c : internal spin (or gyroscope) Hilbert space H_sys=H_z\\otimesH_c : system Hilbert space H_p : probe (or quantum coin) Hilbert space, H_p={C}^2 \\rho^tot_t : density matrix for the total system (walker + internal spin + quantum coins) \\bar \\rho_t : reduced density matrix on H_sys : \\bar\\rho_t=\\int dxdy\\, \\bar\\rho_t(x,y)\\otimes | x \\rangle _z\\langle y | \\hat \\rho_t : system density matrix in a quantum trajectory: \\hat\\rho_t=\\int dxdy\\, \\hat\\rho_t(x,y)\\otimes | x \\rangle _z\\langle y | . If diagonal and localized in position: \\hat \\rho_t=\\rho_t\\otimes| X_t \\rangle _z\\langle X_t | ρt: internal density matrix in a simple quantum trajectory Xt: walker position in a simple quantum trajectory Bt: normalized Brownian motion ξt, \\xi_t^\\dagger : quantum noises

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.

Brownian motion of arbitrarily shaped particles in two dimensions.

PubMed

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

2014-11-25

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

Brownian diffusion and thermophoresis mechanisms in Casson fluid over a moving wedge

NASA Astrophysics Data System (ADS)

Ullah, Imran; Shafie, Sharidan; Khan, Ilyas; Hsiao, Kai Long

2018-06-01

The effect of Brownian diffusion and thermophoresis on electrically conducting mixed convection flow of Casson fluid induced by moving wedge is investigated in this paper. It is assumed that the wedge is saturated in a porous medium and experiences the thermal radiation and chemical reaction effects. The transformed nonlinear governing equations are solved numerically by Keller box scheme. Findings reveal that increase in Casson and magnetic parameters reduced the boundary layer thickness. The effect of Brownian motion and thermophoresis parameters are more pronounced on temperature profile as compared to nanoparticles concentration. The presence of thermal radiation assisted the heat transfer rate significantly. The influence of magnetic parameter is observed less significant on temperature and nanoparticles concentration.

Transient anomalous diffusion in periodic systems: ergodicity, symmetry breaking and velocity relaxation

PubMed Central

Spiechowicz, Jakub; Łuczka, Jerzy; Hänggi, Peter

2016-01-01

We study far from equilibrium transport of a periodically driven inertial Brownian particle moving in a periodic potential. As detected for a SQUID ratchet dynamics, the mean square deviation of the particle position from its average may involve three distinct intermediate, although extended diffusive regimes: initially as superdiffusion, followed by subdiffusion and finally, normal diffusion in the asymptotic long time limit. Even though these anomalies are transient effects, their lifetime can be many, many orders of magnitude longer than the characteristic time scale of the setup and turns out to be extraordinarily sensitive to the system parameters like temperature or the potential asymmetry. In the paper we reveal mechanisms of diffusion anomalies related to ergodicity of the system, symmetry breaking of the periodic potential and ultraslow relaxation of the particle velocity towards its steady state. Similar sequences of the diffusive behaviours could be detected in various systems including, among others, colloidal particles in random potentials, glass forming liquids and granular gases. PMID:27492219

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.

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2011-03-01

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

Hybrid colored noise process with space-dependent switching rates

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.; Lawley, Sean D.

2017-07-01

A fundamental issue in the theory of continuous stochastic process is the interpretation of multiplicative white noise, which is often referred to as the Itô-Stratonovich dilemma. From a physical perspective, this reflects the need to introduce additional constraints in order to specify the nature of the noise, whereas from a mathematical perspective it reflects an ambiguity in the formulation of stochastic differential equations (SDEs). Recently, we have identified a mechanism for obtaining an Itô SDE based on a form of temporal disorder. Motivated by switching processes in molecular biology, we considered a Brownian particle that randomly switches between two distinct conformational states with different diffusivities. In each state, the particle undergoes normal diffusion (additive noise) so there is no ambiguity in the interpretation of the noise. However, if the switching rates depend on position, then in the fast switching limit one obtains Brownian motion with a space-dependent diffusivity of the Itô form. In this paper, we extend our theory to include colored additive noise. We show that the nature of the effective multiplicative noise process obtained by taking both the white-noise limit (κ →0 ) and fast switching limit (ɛ →0 ) depends on the order the two limits are taken. If the white-noise limit is taken first, then we obtain Itô, and if the fast switching limit is taken first, then we obtain Stratonovich. Moreover, the form of the effective diffusion coefficient differs in the two cases. The latter result holds even in the case of space-independent transition rates, where one obtains additive noise processes with different diffusion coefficients. Finally, we show that yet another form of multiplicative noise is obtained in the simultaneous limit ɛ ,κ →0 with ɛ /κ2 fixed.

Brownian Motion of Boomerang Colloidal Particles

NASA Astrophysics Data System (ADS)

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

2014-03-01

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

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.

Fractional Brownian motion with a reflecting wall

NASA Astrophysics Data System (ADS)

Wada, Alexander H. O.; Vojta, Thomas

2018-02-01

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

Brownian Motion.

ERIC Educational Resources Information Center

Lavenda, Bernard H.

1985-01-01

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

Localization and Ballistic Diffusion for the Tempered Fractional Brownian-Langevin Motion

NASA Astrophysics Data System (ADS)

Chen, Yao; Wang, Xudong; Deng, Weihua

2017-10-01

This paper discusses the tempered fractional Brownian motion (tfBm), its ergodicity, and the derivation of the corresponding Fokker-Planck equation. Then we introduce the generalized Langevin equation with the tempered fractional Gaussian noise for a free particle, called tempered fractional Langevin equation (tfLe). While the tfBm displays localization diffusion for the long time limit and for the short time its mean squared displacement (MSD) has the asymptotic form t^{2H}, we show that the asymptotic form of the MSD of the tfLe transits from t^2 (ballistic diffusion for short time) to t^{2-2H}, and then to t^2 (again ballistic diffusion for long time). On the other hand, the overdamped tfLe has the transition of the diffusion type from t^{2-2H} to t^2 (ballistic diffusion). The tfLe with harmonic potential is also considered.

The Steady-State Transport of Oxygen through Hemoglobin Solutions

PubMed Central

Keller, K. H.; Friedlander, S. K.

1966-01-01

The steady-state transport of oxygen through hemoglobin solutions was studied to identify the mechanism of the diffusion augmentation observed at low oxygen tensions. A novel technique employing a platinum-silver oxygen electrode was developed to measure the effective diffusion coefficient of oxygen in steady-state transport. The measurements were made over a wider range of hemoglobin and oxygen concentrations than previously reported. Values of the Brownian motion diffusion coefficient of oxygen in hemoglobin solution were obtained as well as measurements of facilitated transport at low oxygen tensions. Transport rates up to ten times greater than ordinary diffusion rates were found. Predictions of oxygen flux were made assuming that the oxyhemoglobin transport coefficient was equal to the Brownian motion diffusivity which was measured in a separate set of experiments. The close correlation between prediction and experiment indicates that the diffusion of oxyhemoglobin is the mechanism by which steady-state oxygen transport is facilitated. PMID:5943608

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.

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…

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.

A random walk description of individual animal movement accounting for periods of rest

NASA Astrophysics Data System (ADS)

Tilles, Paulo F. C.; Petrovskii, Sergei V.; Natti, Paulo L.

2016-11-01

Animals do not move all the time but alternate the period of actual movement (foraging) with periods of rest (e.g. eating or sleeping). Although the existence of rest times is widely acknowledged in the literature and has even become a focus of increased attention recently, the theoretical approaches to describe animal movement by calculating the dispersal kernel and/or the mean squared displacement (MSD) rarely take rests into account. In this study, we aim to bridge this gap. We consider a composite stochastic process where the periods of active dispersal or `bouts' (described by a certain baseline probability density function (pdf) of animal dispersal) alternate with periods of immobility. For this process, we derive a general equation that determines the pdf of this composite movement. The equation is analysed in detail in two special but important cases such as the standard Brownian motion described by a Gaussian kernel and the Levy flight described by a Cauchy distribution. For the Brownian motion, we show that in the large-time asymptotics the effect of rests results in a rescaling of the diffusion coefficient. The movement occurs as a subdiffusive transition between the two diffusive asymptotics. Interestingly, the Levy flight case shows similar properties, which indicates a certain universality of our findings.

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

A random walk description of individual animal movement accounting for periods of rest.

PubMed

Tilles, Paulo F C; Petrovskii, Sergei V; Natti, Paulo L

2016-11-01

Animals do not move all the time but alternate the period of actual movement (foraging) with periods of rest (e.g. eating or sleeping). Although the existence of rest times is widely acknowledged in the literature and has even become a focus of increased attention recently, the theoretical approaches to describe animal movement by calculating the dispersal kernel and/or the mean squared displacement (MSD) rarely take rests into account. In this study, we aim to bridge this gap. We consider a composite stochastic process where the periods of active dispersal or 'bouts' (described by a certain baseline probability density function (pdf) of animal dispersal) alternate with periods of immobility. For this process, we derive a general equation that determines the pdf of this composite movement. The equation is analysed in detail in two special but important cases such as the standard Brownian motion described by a Gaussian kernel and the Levy flight described by a Cauchy distribution. For the Brownian motion, we show that in the large-time asymptotics the effect of rests results in a rescaling of the diffusion coefficient. The movement occurs as a subdiffusive transition between the two diffusive asymptotics. Interestingly, the Levy flight case shows similar properties, which indicates a certain universality of our findings.

A random walk description of individual animal movement accounting for periods of rest

PubMed Central

Tilles, Paulo F. C.

2016-01-01

Animals do not move all the time but alternate the period of actual movement (foraging) with periods of rest (e.g. eating or sleeping). Although the existence of rest times is widely acknowledged in the literature and has even become a focus of increased attention recently, the theoretical approaches to describe animal movement by calculating the dispersal kernel and/or the mean squared displacement (MSD) rarely take rests into account. In this study, we aim to bridge this gap. We consider a composite stochastic process where the periods of active dispersal or ‘bouts’ (described by a certain baseline probability density function (pdf) of animal dispersal) alternate with periods of immobility. For this process, we derive a general equation that determines the pdf of this composite movement. The equation is analysed in detail in two special but important cases such as the standard Brownian motion described by a Gaussian kernel and the Levy flight described by a Cauchy distribution. For the Brownian motion, we show that in the large-time asymptotics the effect of rests results in a rescaling of the diffusion coefficient. The movement occurs as a subdiffusive transition between the two diffusive asymptotics. Interestingly, the Levy flight case shows similar properties, which indicates a certain universality of our findings. PMID:28018645

Swim stress, motion, and deformation of active matter: effect of an external field.

PubMed

Takatori, Sho C; Brady, John F

2014-12-21

We analyze the stress, dispersion, and average swimming speed of self-propelled particles subjected to an external field that affects their orientation and speed. The swimming trajectory is governed by a competition between the orienting influence (i.e., taxis) associated with the external (e.g., magnetic, gravitational, thermal, nutrient concentration) field versus the effects that randomize the particle orientations (e.g., rotary Brownian motion and/or an intrinsic tumbling mechanism like the flagella of bacteria). The swimmers' motion is characterized by a mean drift velocity and an effective translational diffusivity that becomes anisotropic in the presence of the orienting field. Since the diffusivity yields information about the micromechanical stress, the anisotropy generated by the external field creates a normal stress difference in the recently developed "swim stress" tensor [Takatori, Yan, and Brady, Phys. Rev. Lett., 2014]. This property can be exploited in the design of soft, compressible materials in which their size, shape, and motion can be manipulated and tuned by loading the material with active swimmers. Since the swimmers exert different normal stresses in different directions, the material can compress/expand, elongate, and translate depending on the external field strength. Such an active system can be used as nano/micromechanical devices and motors. Analytical solutions are corroborated by Brownian dynamics simulations.

[From Brownian motion to mind imaging: diffusion MRI].

PubMed

Le Bihan, Denis

2006-11-01

The success of diffusion MRI, which was introduced in the mid 1980s is deeply rooted in the powerful concept that during their random, diffusion-driven movements water molecules probe tissue structure at a microscopic scale well beyond the usual image resolution. The observation of these movements thus provides valuable information on the structure and the geometric organization of tissues. The most successful application of diffusion MRI has been in brain ischemia, following the discovery that water diffusion drops at a very early stage of the ischemic event. Diffusion MRI provides some patients with the opportunity to receive suitable treatment at a very acute stage when brain tissue might still be salvageable. On the other hand, diffusion is modulated by the spatial orientation of large bundles of myelinated axons running in parallel through in brain white matter. This feature can be exploited to map out the orientation in space of the white matter tracks and to visualize the connections between different parts of the brain on an individual basis. Furthermore, recent data suggest that diffusion MRI may also be used to visualize rapid dynamic tissue changes, such as neuronal swelling, associated with cortical activation, offering a new and direct approach to brain functional imaging.

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

PubMed

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

2017-10-03

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

Fractional 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.

Fractional Brownian motion with a reflecting wall.

PubMed

Wada, Alexander H O; Vojta, Thomas

2018-02-01

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

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

PubMed

Dobramysl, U; Holcman, D

2018-02-15

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

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.

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.

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)

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

NASA Astrophysics Data System (ADS)

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

2013-02-01

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

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.

Quantitative model of diffuse speckle contrast analysis for flow measurement.

PubMed

Liu, Jialin; Zhang, Hongchao; Lu, Jian; Ni, Xiaowu; Shen, Zhonghua

2017-07-01

Diffuse speckle contrast analysis (DSCA) is a noninvasive optical technique capable of monitoring deep tissue blood flow. However, a detailed study of the speckle contrast model for DSCA has yet to be presented. We deduced the theoretical relationship between speckle contrast and exposure time and further simplified it to a linear approximation model. The feasibility of this linear model was validated by the liquid phantoms which demonstrated that the slope of this linear approximation was able to rapidly determine the Brownian diffusion coefficient of the turbid media at multiple distances using multiexposure speckle imaging. Furthermore, we have theoretically quantified the influence of optical property on the measurements of the Brownian diffusion coefficient which was a consequence of the fact that the slope of this linear approximation was demonstrated to be equal to the inverse of correlation time of the speckle.

Brownian ratchets: How stronger thermal noise can reduce diffusion

NASA Astrophysics Data System (ADS)

Spiechowicz, Jakub; Kostur, Marcin; Łuczka, Jerzy

2017-02-01

We study diffusion properties of an inertial Brownian motor moving on a ratchet substrate, i.e., a periodic structure with broken reflection symmetry. The motor is driven by an unbiased time-periodic symmetric force that takes the system out of thermal equilibrium. For selected parameter sets, the system is in a non-chaotic regime in which we can identify a non-monotonic dependence of the diffusion coefficient on temperature: for low temperature, it initially increases as the temperature grows, passes through its local maximum, next starts to diminish reaching its local minimum, and finally it monotonically increases in accordance with the Einstein linear relation. Particularly interesting is the temperature interval in which diffusion is suppressed by the thermal noise, and we explain this effect in terms of transition rates of a three-state stochastic model.

Brownian ratchets: How stronger thermal noise can reduce diffusion.

PubMed

Spiechowicz, Jakub; Kostur, Marcin; Łuczka, Jerzy

2017-02-01

We study diffusion properties of an inertial Brownian motor moving on a ratchet substrate, i.e., a periodic structure with broken reflection symmetry. The motor is driven by an unbiased time-periodic symmetric force that takes the system out of thermal equilibrium. For selected parameter sets, the system is in a non-chaotic regime in which we can identify a non-monotonic dependence of the diffusion coefficient on temperature: for low temperature, it initially increases as the temperature grows, passes through its local maximum, next starts to diminish reaching its local minimum, and finally it monotonically increases in accordance with the Einstein linear relation. Particularly interesting is the temperature interval in which diffusion is suppressed by the thermal noise, and we explain this effect in terms of transition rates of a three-state stochastic model.

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

NASA Astrophysics Data System (ADS)

Bai, Zhan-Wu; Zhang, Wei

2018-01-01

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

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.

Diffusion with resetting inside a circle

NASA Astrophysics Data System (ADS)

Chatterjee, Abhinava; Christou, Christos; Schadschneider, Andreas

2018-06-01

We study the Brownian motion of a particle in a bounded circular two-dimensional domain in search for a stationary target on the boundary of the domain. The process switches between two modes: one where it performs a two-dimensional diffusion inside the circle and one where it diffuses along the one-dimensional boundary. During the process, the Brownian particle resets to its initial position with a constant rate r . The Fokker-Planck formalism allows us to calculate the mean time to absorption (MTA) as well as the optimal resetting rate for which the MTA is minimized. From the derived analytical results the parameter regions where resetting reduces the search time can be specified. We also provide a numerical method for the verification of our results.

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.

Exponential stability of impulsive stochastic genetic regulatory networks with time-varying delays and reaction-diffusion

DOE PAGES

Cao, Boqiang; Zhang, Qimin; Ye, Ming

2016-11-29

We present a mean-square exponential stability analysis for impulsive stochastic genetic regulatory networks (GRNs) with time-varying delays and reaction-diffusion driven by fractional Brownian motion (fBm). By constructing a Lyapunov functional and using linear matrix inequality for stochastic analysis we derive sufficient conditions to guarantee the exponential stability of the stochastic model of impulsive GRNs in the mean-square sense. Meanwhile, the corresponding results are obtained for the GRNs with constant time delays and standard Brownian motion. Finally, an example is presented to illustrate our results of the mean-square exponential stability analysis.

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

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.

Analysis of Molecular Diffusion by First-Passage Time Variance Identifies the Size of Confinement Zones

PubMed Central

Rajani, Vishaal; Carrero, Gustavo; Golan, David E.; de Vries, Gerda; Cairo, Christopher W.

2011-01-01

The diffusion of receptors within the two-dimensional environment of the plasma membrane is a complex process. Although certain components diffuse according to a random walk model (Brownian diffusion), an overwhelming body of work has found that membrane diffusion is nonideal (anomalous diffusion). One of the most powerful methods for studying membrane diffusion is single particle tracking (SPT), which records the trajectory of a label attached to a membrane component of interest. One of the outstanding problems in SPT is the analysis of data to identify the presence of heterogeneity. We have adapted a first-passage time (FPT) algorithm, originally developed for the interpretation of animal movement, for the analysis of SPT data. We discuss the general application of the FPT analysis to molecular diffusion, and use simulations to test the method against data containing known regions of confinement. We conclude that FPT can be used to identify the presence and size of confinement within trajectories of the receptor LFA-1, and these results are consistent with previous reports on the size of LFA-1 clusters. The analysis of trajectory data for cell surface receptors by FPT provides a robust method to determine the presence and size of confined regions of diffusion. PMID:21402028

Fractional Brownian motion and long term clinical trial recruitment

PubMed Central

Zhang, Qiang; Lai, Dejian

2015-01-01

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

Fractional Brownian motion and long term clinical trial recruitment.

PubMed

Zhang, Qiang; Lai, Dejian

2011-05-01

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

Spatial Mapping of Translational Diffusion Coefficients Using Diffusion Tensor Imaging: A Mathematical Description

PubMed Central

SHETTY, ANIL N.; CHIANG, SHARON; MALETIC-SAVATIC, MIRJANA; KASPRIAN, GREGOR; VANNUCCI, MARINA; LEE, WESLEY

2016-01-01

In this article, we discuss the theoretical background for diffusion weighted imaging and diffusion tensor imaging. Molecular diffusion is a random process involving thermal Brownian motion. In biological tissues, the underlying microstructures restrict the diffusion of water molecules, making diffusion directionally dependent. Water diffusion in tissue is mathematically characterized by the diffusion tensor, the elements of which contain information about the magnitude and direction of diffusion and is a function of the coordinate system. Thus, it is possible to generate contrast in tissue based primarily on diffusion effects. Expressing diffusion in terms of the measured diffusion coefficient (eigenvalue) in any one direction can lead to errors. Nowhere is this more evident than in white matter, due to the preferential orientation of myelin fibers. The directional dependency is removed by diagonalization of the diffusion tensor, which then yields a set of three eigenvalues and eigenvectors, representing the magnitude and direction of the three orthogonal axes of the diffusion ellipsoid, respectively. For example, the eigenvalue corresponding to the eigenvector along the long axis of the fiber corresponds qualitatively to diffusion with least restriction. Determination of the principal values of the diffusion tensor and various anisotropic indices provides structural information. We review the use of diffusion measurements using the modified Stejskal–Tanner diffusion equation. The anisotropy is analyzed by decomposing the diffusion tensor based on symmetrical properties describing the geometry of diffusion tensor. We further describe diffusion tensor properties in visualizing fiber tract organization of the human brain. PMID:27441031

Mean first-passage times of non-Markovian random walkers in confinement.

PubMed

Guérin, T; Levernier, N; Bénichou, O; Voituriez, R

2016-06-16

The first-passage time, defined as the time a random walker takes to reach a target point in a confining domain, is a key quantity in the theory of stochastic processes. Its importance comes from its crucial role in quantifying the efficiency of processes as varied as diffusion-limited reactions, target search processes or the spread of diseases. Most methods of determining the properties of first-passage time in confined domains have been limited to Markovian (memoryless) processes. However, as soon as the random walker interacts with its environment, memory effects cannot be neglected: that is, the future motion of the random walker does not depend only on its current position, but also on its past trajectory. Examples of non-Markovian dynamics include single-file diffusion in narrow channels, or the motion of a tracer particle either attached to a polymeric chain or diffusing in simple or complex fluids such as nematics, dense soft colloids or viscoelastic solutions. Here we introduce an analytical approach to calculate, in the limit of a large confining volume, the mean first-passage time of a Gaussian non-Markovian random walker to a target. The non-Markovian features of the dynamics are encompassed by determining the statistical properties of the fictitious trajectory that the random walker would follow after the first-passage event takes place, which are shown to govern the first-passage time kinetics. This analysis is applicable to a broad range of stochastic processes, which may be correlated at long times. Our theoretical predictions are confirmed by numerical simulations for several examples of non-Markovian processes, including the case of fractional Brownian motion in one and higher dimensions. These results reveal, on the basis of Gaussian processes, the importance of memory effects in first-passage statistics of non-Markovian random walkers in confinement.

Mean first-passage times of non-Markovian random walkers in confinement

NASA Astrophysics Data System (ADS)

Guérin, T.; Levernier, N.; Bénichou, O.; Voituriez, R.

2016-06-01

The first-passage time, defined as the time a random walker takes to reach a target point in a confining domain, is a key quantity in the theory of stochastic processes. Its importance comes from its crucial role in quantifying the efficiency of processes as varied as diffusion-limited reactions, target search processes or the spread of diseases. Most methods of determining the properties of first-passage time in confined domains have been limited to Markovian (memoryless) processes. However, as soon as the random walker interacts with its environment, memory effects cannot be neglected: that is, the future motion of the random walker does not depend only on its current position, but also on its past trajectory. Examples of non-Markovian dynamics include single-file diffusion in narrow channels, or the motion of a tracer particle either attached to a polymeric chain or diffusing in simple or complex fluids such as nematics, dense soft colloids or viscoelastic solutions. Here we introduce an analytical approach to calculate, in the limit of a large confining volume, the mean first-passage time of a Gaussian non-Markovian random walker to a target. The non-Markovian features of the dynamics are encompassed by determining the statistical properties of the fictitious trajectory that the random walker would follow after the first-passage event takes place, which are shown to govern the first-passage time kinetics. This analysis is applicable to a broad range of stochastic processes, which may be correlated at long times. Our theoretical predictions are confirmed by numerical simulations for several examples of non-Markovian processes, including the case of fractional Brownian motion in one and higher dimensions. These results reveal, on the basis of Gaussian processes, the importance of memory effects in first-passage statistics of non-Markovian random walkers in confinement.

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

Brownian Motion and the Temperament of Living Cells

NASA Astrophysics Data System (ADS)

Tsekov, Roumen; Lensen, Marga C.

2013-07-01

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

Modeling meiotic chromosome pairing: nuclear envelope attachment, telomere-led active random motion, and anomalous diffusion

PubMed Central

Marshall, Wallace F.; Fung, Jennifer C.

2016-01-01

The recognition and pairing of homologous chromosomes during meiosis is a complex physical and molecular process involving a combination of polymer dynamics and molecular recognition events. Two highly conserved features of meiotic chromosome behavior are the attachment of telomeres to the nuclear envelope and the active random motion of telomeres driven by their interaction with cytoskeletal motor proteins. Both of these features have been proposed to facilitate the process of homolog pairing, but exactly what role these features play in meiosis remains poorly understood. Here we investigate the roles of active motion and nuclear envelope tethering using a Brownian dynamics simulation in which meiotic chromosomes are represented by a Rouse polymer model subjected to tethering and active forces at the telomeres. We find that tethering telomeres to the nuclear envelope slows down pairing relative to the rates achieved by un-attached chromosomes, but that randomly-directed active forces applied to the telomeres speeds up pairing dramatically in a manner that depends on the statistical properties of the telomere force fluctuations. The increased rate of initial pairing cannot be explained by stretching out of the chromosome conformation but instead seems to correlate with anomalous diffusion of sub-telomeric regions. PMID:27046097

Phylogeography Takes a Relaxed Random Walk in Continuous Space and Time

PubMed Central

Lemey, Philippe; Rambaut, Andrew; Welch, John J.; Suchard, Marc A.

2010-01-01

Research aimed at understanding the geographic context of evolutionary histories is burgeoning across biological disciplines. Recent endeavors attempt to interpret contemporaneous genetic variation in the light of increasingly detailed geographical and environmental observations. Such interest has promoted the development of phylogeographic inference techniques that explicitly aim to integrate such heterogeneous data. One promising development involves reconstructing phylogeographic history on a continuous landscape. Here, we present a Bayesian statistical approach to infer continuous phylogeographic diffusion using random walk models while simultaneously reconstructing the evolutionary history in time from molecular sequence data. Moreover, by accommodating branch-specific variation in dispersal rates, we relax the most restrictive assumption of the standard Brownian diffusion process and demonstrate increased statistical efficiency in spatial reconstructions of overdispersed random walks by analyzing both simulated and real viral genetic data. We further illustrate how drawing inference about summary statistics from a fully specified stochastic process over both sequence evolution and spatial movement reveals important characteristics of a rabies epidemic. Together with recent advances in discrete phylogeographic inference, the continuous model developments furnish a flexible statistical framework for biogeographical reconstructions that is easily expanded upon to accommodate various landscape genetic features. PMID:20203288

Modeling meiotic chromosome pairing: nuclear envelope attachment, telomere-led active random motion, and anomalous diffusion

NASA Astrophysics Data System (ADS)

Marshall, Wallace F.; Fung, Jennifer C.

2016-04-01

The recognition and pairing of homologous chromosomes during meiosis is a complex physical and molecular process involving a combination of polymer dynamics and molecular recognition events. Two highly conserved features of meiotic chromosome behavior are the attachment of telomeres to the nuclear envelope and the active random motion of telomeres driven by their interaction with cytoskeletal motor proteins. Both of these features have been proposed to facilitate the process of homolog pairing, but exactly what role these features play in meiosis remains poorly understood. Here we investigate the roles of active motion and nuclear envelope tethering using a Brownian dynamics simulation in which meiotic chromosomes are represented by a Rouse polymer model subjected to tethering and active forces at the telomeres. We find that tethering telomeres to the nuclear envelope slows down pairing relative to the rates achieved by unattached chromosomes, but that randomly directed active forces applied to the telomeres speed up pairing dramatically in a manner that depends on the statistical properties of the telomere force fluctuations. The increased rate of initial pairing cannot be explained by stretching out of the chromosome conformation but instead seems to correlate with anomalous diffusion of sub-telomeric regions.

Disentangling Random Motion and Flow in a Complex Medium

PubMed Central

Koslover, Elena F.; Chan, Caleb K.; Theriot, Julie A.

2016-01-01

We describe a technique for deconvolving the stochastic motion of particles from large-scale fluid flow in a dynamic environment such as that found in living cells. The method leverages the separation of timescales to subtract out the persistent component of motion from single-particle trajectories. The mean-squared displacement of the resulting trajectories is rescaled so as to enable robust extraction of the diffusion coefficient and subdiffusive scaling exponent of the stochastic motion. We demonstrate the applicability of the method for characterizing both diffusive and fractional Brownian motion overlaid by flow and analytically calculate the accuracy of the method in different parameter regimes. This technique is employed to analyze the motion of lysosomes in motile neutrophil-like cells, showing that the cytoplasm of these cells behaves as a viscous fluid at the timescales examined. PMID:26840734

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.

Two Models of Time Constrained Target Travel between Two Endpoints Constructed by the Application of Brownian Motion and a Random Tour.

DTIC Science & Technology

1983-03-01

the Naval Postgraduate School. As my *advisor, Prof. Gaver suggested and derived the Brownian bridge, as well as nudged me in the right direction when...the * random tour process by deriving the mean square radial distance for a random tour with arbitrary course change distribution to be: EECR I2(V / 2...random tour model, li = Iy = 8, and equation (3)x y results as expected. The notion of an arbitrary course change distribution is important because the

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

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

PubMed

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

2012-03-01

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

Rotational Fourier tracking of diffusing polygons.

PubMed

Mayoral, Kenny; Kennair, Terry P; Zhu, Xiaoming; Milazzo, James; Ngo, Kathy; Fryd, Michael M; Mason, Thomas G

2011-11-01

We use optical microscopy to measure the rotational Brownian motion of polygonal platelets that are dispersed in a liquid and confined by depletion attractions near a wall. The depletion attraction inhibits out-of-plane translational and rotational Brownian fluctuations, thereby facilitating in-plane imaging and video analysis. By taking fast Fourier transforms (FFTs) of the images and analyzing the angular position of rays in the FFTs, we determine an isolated particle's rotational trajectory, independent of its position. The measured in-plane rotational diffusion coefficients are significantly smaller than estimates for the bulk; this difference is likely due to the close proximity of the particles to the wall arising from the depletion attraction.

Noah, Joseph and Convex Hulls

NASA Astrophysics Data System (ADS)

Watkins, N. W.; Chau, Y.; Chapman, S. C.

2010-12-01

The idea of describing animal movement by mathematical models based on diffusion and Brownian motion has a long heritage. It has thus been natural to account for those aspects of motion that depart from the Brownian by the use of models incorporating long memory & subdiffusion (“the Joseph effect”) and/or heavy tails & superdiffusion (“the Noah effect”). My own interest in this problem was originally from a geoscience perspective, and was triggered by the need to model time series in space physics where both effects coincide. Subsequently I have been involved in animal foraging studies [e.g. Edwards et al, Nature, 2007]. I will describe some recent work [Watkins et al, PRE, 2009] which studies how fixed-timestep and variable-timestep formulations of anomalous diffusion are related in the presence of heavy tails and long range memory (stable processes versus the CTRW). Quantities for which different scaling relations are predicted between the two approaches are of particular interest, to aid testability. I will also present some of work in progress on the convex hull of anomalously diffusing walkers, inspired by its possible relevance to the idea of home range in biology, and by Randon-Furling et al’s recent analytical results in the Brownian case [PRL, 2009].

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

PubMed

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

2018-02-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Diffusion, Dispersion, and Uncertainty in Anisotropic Fractal Porous Media

NASA Astrophysics Data System (ADS)

Monnig, N. D.; Benson, D. A.

2007-12-01

Motivated by field measurements of aquifer hydraulic conductivity (K), recent techniques were developed to construct anisotropic fractal random fields, in which the scaling, or self-similarity parameter, varies with direction and is defined by a matrix. Ensemble numerical results are analyzed for solute transport through these 2-D "operator-scaling" fractional Brownian motion (fBm) ln(K) fields. Contrary to some analytic stochastic theories for monofractal K fields, the plume growth rates never exceed Mercado's (1967) purely stratified aquifer growth rate of plume apparent dispersivity proportional to mean distance. Apparent super-stratified growth must be the result of other demonstrable factors, such as initial plume size. The addition of large local dispersion and diffusion does not significantly change the effective longitudinal dispersivity of the plumes. In the presence of significant local dispersion or diffusion, the concentration coefficient of variation CV={σc}/{\\langle c \\rangle} remains large at the leading edge of the plumes. This indicates that even with considerable mixing due to dispersion or diffusion, there is still substantial uncertainty in the leading edge of a plume moving in fractal porous media.

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

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

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

2014-06-07

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

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

NASA Astrophysics Data System (ADS)

Eka Putri, Irana; Gita Redhyka, Grace

2017-07-01

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

Brownian motion of tethered nanowires.

PubMed

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

2014-05-01

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

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.

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.

Brownian motion properties of optoelectronic random bit generators based on laser chaos.

PubMed

Li, Pu; Yi, Xiaogang; Liu, Xianglian; Wang, Yuncai; Wang, Yongge

2016-07-11

The nondeterministic property of the optoelectronic random bit generator (RBG) based on laser chaos are experimentally analyzed from two aspects of the central limit theorem and law of iterated logarithm. The random bits are extracted from an optical feedback chaotic laser diode using a multi-bit extraction technique in the electrical domain. Our experimental results demonstrate that the generated random bits have no statistical distance from the Brownian motion, besides that they can pass the state-of-the-art industry-benchmark statistical test suite (NIST SP800-22). All of them give a mathematically provable evidence that the ultrafast random bit generator based on laser chaos can be used as a nondeterministic random bit source.

Tracer diffusion in active suspensions

NASA Astrophysics Data System (ADS)

Burkholder, Eric W.; Brady, John F.

2017-05-01

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

Slow kinetics of Brownian maxima.

PubMed

Ben-Naim, E; Krapivsky, P L

2014-07-18

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

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.

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.

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

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.

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.

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.

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.

Anisotropic Brownian motion in ordered phases of DNA fragments.

PubMed

Dobrindt, J; Rodrigo Teixeira da Silva, E; Alves, C; Oliveira, C L P; Nallet, F; Andreoli de Oliveira, E; Navailles, L

2012-01-01

Using Fluorescence Recovery After Photobleaching, we investigate the Brownian motion of DNA rod-like fragments in two distinct anisotropic phases with a local nematic symmetry. The height of the measurement volume ensures the averaging of the anisotropy of the in-plane diffusive motion parallel or perpendicular to the local nematic director in aligned domains. Still, as shown in using a model specifically designed to handle such a situation and predicting a non-Gaussian shape for the bleached spot as fluorescence recovery proceeds, the two distinct diffusion coefficients of the DNA particles can be retrieved from data analysis. In the first system investigated (a ternary DNA-lipid lamellar complex), the magnitude and anisotropy of the diffusion coefficient of the DNA fragments confined by the lipid bilayers are obtained for the first time. In the second, binary DNA-solvent system, the magnitude of the diffusion coefficient is found to decrease markedly as DNA concentration is increased from isotropic to cholesteric phase. In addition, the diffusion coefficient anisotropy measured within cholesteric domains in the phase coexistence region increases with concentration, and eventually reaches a high value in the cholesteric phase.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

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

PubMed

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

2018-06-13

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

On time-dependent diffusion coefficients arising from stochastic processes with memory

NASA Astrophysics Data System (ADS)

Carpio-Bernido, M. Victoria; Barredo, Wilson I.; Bernido, Christopher C.

2017-08-01

Time-dependent diffusion coefficients arise from anomalous diffusion encountered in many physical systems such as protein transport in cells. We compare these coefficients with those arising from analysis of stochastic processes with memory that go beyond fractional Brownian motion. Facilitated by the Hida white noise functional integral approach, diffusion propagators or probability density functions (pdf) are obtained and shown to be solutions of modified diffusion equations with time-dependent diffusion coefficients. This should be useful in the study of complex transport processes.

In Silico Neuro-Oncology: Brownian Motion-Based Mathematical Treatment as a Potential Platform for Modeling the Infiltration of Glioma Cells into Normal Brain Tissue.

PubMed

Antonopoulos, Markos; Stamatakos, Georgios

2015-01-01

Intensive glioma tumor infiltration into the surrounding normal brain tissues is one of the most critical causes of glioma treatment failure. To quantitatively understand and mathematically simulate this phenomenon, several diffusion-based mathematical models have appeared in the literature. The majority of them ignore the anisotropic character of diffusion of glioma cells since availability of pertinent truly exploitable tomographic imaging data is limited. Aiming at enriching the anisotropy-enhanced glioma model weaponry so as to increase the potential of exploiting available tomographic imaging data, we propose a Brownian motion-based mathematical analysis that could serve as the basis for a simulation model estimating the infiltration of glioblastoma cells into the surrounding brain tissue. The analysis is based on clinical observations and exploits diffusion tensor imaging (DTI) data. Numerical simulations and suggestions for further elaboration are provided.

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

PubMed

Brenner, Howard

2005-12-01

A quiescent single-component gravity-free gas subject to a small steady uniform temperature gradient T, despite being at rest, is shown to experience a drift velocity UD=-D* gradient ln T, where D* is the gas's nonisothermal self-diffusion coefficient. D* is identified as being the gas's thermometric diffusivity alpha. The latter differs from the gas's isothermal isotopic self-diffusion coefficient D, albeit only slightly. Two independent derivations are given of this drift velocity formula, one kinematical and the other dynamical, both derivations being strictly macroscopic in nature. Within modest experimental and theoretical uncertainties, this virtual drift velocity UD=-alpha gradient ln T is shown to be constitutively and phenomenologically indistinguishable from the well-known experimental and theoretical formulas for the thermophoretic velocity U of a macroscopic (i.e., non-Brownian) non-heat-conducting particle moving under the influence of a uniform temperature gradient through an otherwise quiescent single-component rarefied gas continuum at small Knudsen numbers. Coupled with the size independence of the particle's thermophoretic velocity, the empirically observed equality, U=UD, leads naturally to the hypothesis that these two velocities, the former real and the latter virtual, are, in fact, simply manifestations of the same underlying molecular phenomenon, namely the gas's Brownian movement, albeit biased by the temperature gradient. This purely hydrodynamic continuum-mechanical equality is confirmed by theoretical calculations effected at the kinetic-molecular level on the basis of an existing solution of the Boltzmann equation for a quasi-Lorentzian gas, modulo small uncertainties pertaining to the choice of collision model. Explicitly, this asymptotically valid molecular model allows the virtual drift velocity UD of the light gas and the thermophoretic velocity U of the massive, effectively non-Brownian, particle, now regarded as the tracer particle of the light gas's drift velocity, to each be identified with the Chapman-Enskog "thermal diffusion velocity" of the quasi-Lorentzian gas, here designated by the symbol UM/M, as calculated by de la Mora and Mercer. It is further pointed out that, modulo the collective uncertainties cited above, the common velocities UD,U, and UM/M are identical to the single-component gas's diffuse volume current jv, the latter representing yet another, independent, strictly continuum-mechanical concept. Finally, comments are offered on the extension of the single-component drift velocity notion to liquids, and its application towards rationalizing Soret thermal-diffusion separation phenomena in quasi-Lorentzian liquid-phase binary mixtures composed of disparately sized solute and solvent molecules, with the massive Brownian solute molecules (e.g., colloidal particles) present in disproportionately small amounts relative to that of the solvent.

Overdamping by weakly coupled environments

NASA Astrophysics Data System (ADS)

Esposito, Massimiliano; Haake, Fritz

2005-12-01

A quantum system weakly interacting with a fast environment usually undergoes a relaxation with complex frequencies whose imaginary parts are damping rates quadratic in the coupling to the environment in accord with Fermi’s “golden rule.” We show for various models (spin damped by harmonic-oscillator or random-matrix baths, quantum diffusion, and quantum Brownian motion) that upon increasing the coupling up to a critical value still small enough to allow for weak-coupling Markovian master equations, a different relaxation regime can occur. In that regime, complex frequencies lose their real parts such that the process becomes overdamped. Our results call into question the standard belief that overdamping is exclusively a strong coupling feature.

Introduction to Physical Intelligence

NASA Technical Reports Server (NTRS)

Zak, Michail

2011-01-01

A slight deviation from Newtonian dynamics can lead to new effects associated with the concept of physical intelligence. Non-Newtonian effects such as deviation from classical thermodynamic as well as quantum-like properties have been analyzed. A self-supervised (intelligent) particle that can escape from Brownian motion autonomously is introduced. Such a capability is due to a coupling of the particle governing equation with its own Liouville equation via an appropriate feedback. As a result, the governing equation is self-stabilized, and random oscillations are suppressed, while the Liouville equation takes the form of the Fokker-Planck equation with negative diffusion. Non- Newtonian properties of such a dynamical system as well as thermodynamical implications have been evaluated.

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.

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.

Variance change point detection for fractional Brownian motion based on the likelihood ratio test

NASA Astrophysics Data System (ADS)

Kucharczyk, Daniel; Wyłomańska, Agnieszka; Sikora, Grzegorz

2018-01-01

Fractional Brownian motion is one of the main stochastic processes used for describing the long-range dependence phenomenon for self-similar processes. It appears that for many real time series, characteristics of the data change significantly over time. Such behaviour one can observe in many applications, including physical and biological experiments. In this paper, we present a new technique for the critical change point detection for cases where the data under consideration are driven by fractional Brownian motion with a time-changed diffusion coefficient. The proposed methodology is based on the likelihood ratio approach and represents an extension of a similar methodology used for Brownian motion, the process with independent increments. Here, we also propose a statistical test for testing the significance of the estimated critical point. In addition to that, an extensive simulation study is provided to test the performance of the proposed method.

Fractional phenomenology of cosmic ray anomalous diffusion

NASA Astrophysics Data System (ADS)

Uchaikin, V. V.

2013-11-01

We review the evolution of the cosmic ray diffusion concept from the ordinary (Einstein) model of Brownian motion to the fractional models that appeared in the last decade. The mathematical and physical foundations of these models are discussed, as are their consequences, related problems, and prospects for further development.

Random walk on a leash: a simple single-molecule diffusion model for surface-tethered redox molecules with flexible linkers.

PubMed

Huang, Kuan-Chun; White, Ryan J

2013-08-28

We develop a random walk model to simulate the Brownian motion and the electrochemical response of a single molecule confined to an electrode surface via a flexible molecular tether. We use our simple model, which requires no prior knowledge of the physics of the molecular tether, to predict and better understand the voltammetric response of surface-confined redox molecules when motion of the redox molecule becomes important. The single molecule is confined to a hemispherical volume with a maximum radius determined by the flexible molecular tether (5-20 nm) and is allowed to undergo true three-dimensional diffusion. Distance- and potential-dependent electron transfer probabilities are evaluated throughout the simulations to generate cyclic voltammograms of the model system. We find that at sufficiently slow cyclic voltammetric scan rates the electrochemical reaction behaves like an adsorbed redox molecule with no mass transfer limitation; thus, the peak current is proportional to the scan rate. Conversely, at faster scan rates the diffusional motion of the molecule limits the simulated peak current, which exhibits a linear dependence on the square root of the scan rate. The switch between these two limiting regimes occurs when the diffusion layer thickness, (2Dt)(1/2), is ~10 times the tether length. Finally, we find that our model predicts the voltammetric behavior of a redox-active methylene blue tethered to an electrode surface via short flexible single-stranded, polythymine DNAs, allowing the estimation of diffusion coefficients for the end-tethered molecule.

Anomalous subdiffusion in fluorescence photobleaching recovery: a Monte Carlo study.

PubMed Central

Saxton, M J

2001-01-01

Anomalous subdiffusion is hindered diffusion in which the mean-square displacement of a diffusing particle is proportional to some power of time less than one. Anomalous subdiffusion has been observed for a variety of lipids and proteins in the plasma membranes of a variety of cells. Fluorescence photobleaching recovery experiments with anomalous subdiffusion are simulated to see how to analyze the data. It is useful to fit the recovery curve with both the usual recovery equation and the anomalous one, and to judge the goodness of fit on log-log plots. The simulations show that the simplest approximate treatment of anomalous subdiffusion usually gives good results. Three models of anomalous subdiffusion are considered: obstruction, fractional Brownian motion, and the continuous-time random walk. The models differ significantly in their behavior at short times and in their noise level. For obstructed diffusion the approach to the percolation threshold is marked by a large increase in noise, a broadening of the distribution of diffusion coefficients and anomalous subdiffusion exponents, and the expected abrupt decrease in the mobile fraction. The extreme fluctuations in the recovery curves at and near the percolation threshold result from extreme fluctuations in the geometry of the percolation cluster. PMID:11566793

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

Tracer diffusion in active suspensions.

PubMed

Burkholder, Eric W; Brady, John F

2017-05-01

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

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.

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

PubMed

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

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

A Lévy-flight diffusion model to predict transgenic pollen dispersal.

PubMed

Vallaeys, Valentin; Tyson, Rebecca C; Lane, W David; Deleersnijder, Eric; Hanert, Emmanuel

2017-01-01

The containment of genetically modified (GM) pollen is an issue of significant concern for many countries. For crops that are bee-pollinated, model predictions of outcrossing rates depend on the movement hypothesis used for the pollinators. Previous work studying pollen spread by honeybees, the most important pollinator worldwide, was based on the assumption that honeybee movement can be well approximated by Brownian motion. A number of recent studies, however, suggest that pollinating insects such as bees perform Lévy flights in their search for food. Such flight patterns yield much larger rates of spread, and so the Brownian motion assumption might significantly underestimate the risk associated with GM pollen outcrossing in conventional crops. In this work, we propose a mechanistic model for pollen dispersal in which the bees perform truncated Lévy flights. This assumption leads to a fractional-order diffusion model for pollen that can be tuned to model motion ranging from pure Brownian to pure Lévy. We parametrize our new model by taking the same pollen dispersal dataset used in Brownian motion modelling studies. By numerically solving the model equations, we show that the isolation distances required to keep outcrossing levels below a certain threshold are substantially increased by comparison with the original predictions, suggesting that isolation distances may need to be much larger than originally thought. © 2017 The Author(s).

A Lévy-flight diffusion model to predict transgenic pollen dispersal

PubMed Central

Vallaeys, Valentin; Tyson, Rebecca C.; Lane, W. David; Deleersnijder, Eric

2017-01-01

The containment of genetically modified (GM) pollen is an issue of significant concern for many countries. For crops that are bee-pollinated, model predictions of outcrossing rates depend on the movement hypothesis used for the pollinators. Previous work studying pollen spread by honeybees, the most important pollinator worldwide, was based on the assumption that honeybee movement can be well approximated by Brownian motion. A number of recent studies, however, suggest that pollinating insects such as bees perform Lévy flights in their search for food. Such flight patterns yield much larger rates of spread, and so the Brownian motion assumption might significantly underestimate the risk associated with GM pollen outcrossing in conventional crops. In this work, we propose a mechanistic model for pollen dispersal in which the bees perform truncated Lévy flights. This assumption leads to a fractional-order diffusion model for pollen that can be tuned to model motion ranging from pure Brownian to pure Lévy. We parametrize our new model by taking the same pollen dispersal dataset used in Brownian motion modelling studies. By numerically solving the model equations, we show that the isolation distances required to keep outcrossing levels below a certain threshold are substantially increased by comparison with the original predictions, suggesting that isolation distances may need to be much larger than originally thought. PMID:28123097

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

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

PubMed

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

2012-11-07

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

Does the noise matter? Effects of different kinematogram types on smooth pursuit eye movements and perception

PubMed Central

Schütz, Alexander C.; Braun, Doris I.; Movshon, J. Anthony; Gegenfurtner, Karl R.

2011-01-01

We investigated how the human visual system and the pursuit system react to visual motion noise. We presented three different types of random-dot kinematograms at five different coherence levels. For transparent motion, the signal and noise labels on each dot were preserved throughout each trial, and noise dots moved with the same speed as the signal dots but in fixed random directions. For white noise motion, every 20 ms the signal and noise labels were randomly assigned to each dot and noise dots appeared at random positions. For Brownian motion, signal and noise labels were also randomly assigned, but the noise dots moved at the signal speed in a direction that varied randomly from moment to moment. Neither pursuit latency nor early eye acceleration differed among the different types of kinematograms. Late acceleration, pursuit gain, and perceived speed all depended on kinematogram type, with good agreement between pursuit gain and perceived speed. For transparent motion, pursuit gain and perceived speed were independent of coherence level. For white and Brownian motions, pursuit gain and perceived speed increased with coherence but were higher for white than for Brownian motion. This suggests that under our conditions, the pursuit system integrates across all directions of motion but not across all speeds. PMID:21149307

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.

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 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.

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

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.

Small particle transport across turbulent nonisothermal boundary layers

NASA Technical Reports Server (NTRS)

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

1982-01-01

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

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.

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.

Theory of molecular crowding in Brownian hard-sphere liquids.

PubMed

Zaccone, Alessio; Terentjev, Eugene M

2012-06-01

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

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).

Lévy-like diffusion in eye movements during spoken-language comprehension.

PubMed

Stephen, Damian G; Mirman, Daniel; Magnuson, James S; Dixon, James A

2009-05-01

This study explores the diffusive properties of human eye movements during a language comprehension task. In this task, adults are given auditory instructions to locate named objects on a computer screen. Although it has been convention to model visual search as standard Brownian diffusion, we find evidence that eye movements are hyperdiffusive. Specifically, we use comparisons of maximum-likelihood fit as well as standard deviation analysis and diffusion entropy analysis to show that visual search during language comprehension exhibits Lévy-like rather than Gaussian diffusion.

Lévy-like diffusion in eye movements during spoken-language comprehension

NASA Astrophysics Data System (ADS)

Stephen, Damian G.; Mirman, Daniel; Magnuson, James S.; Dixon, James A.

2009-05-01

This study explores the diffusive properties of human eye movements during a language comprehension task. In this task, adults are given auditory instructions to locate named objects on a computer screen. Although it has been convention to model visual search as standard Brownian diffusion, we find evidence that eye movements are hyperdiffusive. Specifically, we use comparisons of maximum-likelihood fit as well as standard deviation analysis and diffusion entropy analysis to show that visual search during language comprehension exhibits Lévy-like rather than Gaussian diffusion.

Kinetics of diffusion-controlled annihilation with sparse initial conditions

DOE PAGES

Ben-Naim, Eli; Krapivsky, Paul

2016-12-16

Here, we study diffusion-controlled single-species annihilation with sparse initial conditions. In this random process, particles undergo Brownian motion, and when two particles meet, both disappear. We also focus on sparse initial conditions where particles occupy a subspace of dimension δ that is embedded in a larger space of dimension d. Furthermore, we find that the co-dimension Δ = d - δ governs the behavior. All particles disappear when the co-dimension is sufficiently small, Δ ≤ 2; otherwise, a finite fraction of particles indefinitely survive. We establish the asymptotic behavior of the probability S(t) that a test particle survives until time t. When the subspace is a line, δ = 1, we find inverse logarithmic decay,more » $$S\\sim {(\\mathrm{ln}t)}^{-1}$$, in three dimensions, and a modified power-law decay, $$S\\sim (\\mathrm{ln}t){t}^{-1/2}$$, in two dimensions. In general, the survival probability decays algebraically when Δ < 2, and there is an inverse logarithmic decay at the critical co-dimension Δ = 2.« less

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

PubMed Central

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

2011-01-01

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

G-Jitter Induced Magnetohydrodynamics Flow of Nanofluid with Constant Convective Thermal and Solutal Boundary Conditions

PubMed Central

Uddin, Mohammed J.; Khan, Waqar A.; Ismail, Ahmad Izani Md.

2015-01-01

Taking into account the effect of constant convective thermal and mass boundary conditions, we present numerical solution of the 2-D laminar g-jitter mixed convective boundary layer flow of water-based nanofluids. The governing transport equations are converted into non-similar equations using suitable transformations, before being solved numerically by an implicit finite difference method with quasi-linearization technique. The skin friction decreases with time, buoyancy ratio, and thermophoresis parameters while it increases with frequency, mixed convection and Brownian motion parameters. Heat transfer rate decreases with time, Brownian motion, thermophoresis and diffusion-convection parameters while it increases with the Reynolds number, frequency, mixed convection, buoyancy ratio and conduction-convection parameters. Mass transfer rate decreases with time, frequency, thermophoresis, conduction-convection parameters while it increases with mixed convection, buoyancy ratio, diffusion-convection and Brownian motion parameters. To the best of our knowledge, this is the first paper on this topic and hence the results are new. We believe that the results will be useful in designing and operating thermal fluids systems for space materials processing. Special cases of the results have been compared with published results and an excellent agreement is found. PMID:25933066

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

NASA Astrophysics Data System (ADS)

Chen, Chen; Zhao, Bin

2017-12-01

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

Active Brownian particles escaping a channel in single file.

PubMed

Locatelli, Emanuele; Baldovin, Fulvio; Orlandini, Enzo; Pierno, Matteo

2015-02-01

Active particles may happen to be confined in channels so narrow that they cannot overtake each other (single-file conditions). This interesting situation reveals nontrivial physical features as a consequence of the strong interparticle correlations developed in collective rearrangements. We consider a minimal two-dimensional model for active Brownian particles with the aim of studying the modifications introduced by activity with respect to the classical (passive) single-file picture. Depending on whether their motion is dominated by translational or rotational diffusion, we find that active Brownian particles in single file may arrange into clusters that are continuously merging and splitting (active clusters) or merely reproduce passive-motion paradigms, respectively. We show that activity conveys to self-propelled particles a strategic advantage for trespassing narrow channels against external biases (e.g., the gravitational field).

Active Brownian particles escaping a channel in single file

NASA Astrophysics Data System (ADS)

Locatelli, Emanuele; Baldovin, Fulvio; Orlandini, Enzo; Pierno, Matteo

2015-02-01

Active particles may happen to be confined in channels so narrow that they cannot overtake each other (single-file conditions). This interesting situation reveals nontrivial physical features as a consequence of the strong interparticle correlations developed in collective rearrangements. We consider a minimal two-dimensional model for active Brownian particles with the aim of studying the modifications introduced by activity with respect to the classical (passive) single-file picture. Depending on whether their motion is dominated by translational or rotational diffusion, we find that active Brownian particles in single file may arrange into clusters that are continuously merging and splitting (active clusters) or merely reproduce passive-motion paradigms, respectively. We show that activity conveys to self-propelled particles a strategic advantage for trespassing narrow channels against external biases (e.g., the gravitational field).

Memoryless self-reinforcing directionality in endosomal active transport within living cells

NASA Astrophysics Data System (ADS)

Chen, Kejia; Wang, Bo; Granick, Steve

2015-06-01

In contrast to Brownian transport, the active motility of microbes, cells, animals and even humans often follows another random process known as truncated Lévy walk. These stochastic motions are characterized by clustered small steps and intermittent longer jumps that often extend towards the size of the entire system. As there are repeated suggestions, although disagreement, that Lévy walks have functional advantages over Brownian motion in random searching and transport kinetics, their intentional engineering into active materials could be useful. Here, we show experimentally in the classic active matter system of intracellular trafficking that Brownian-like steps self-organize into truncated Lévy walks through an apparent time-independent positive feedback such that directional persistence increases with the distance travelled persistently. A molecular model that allows the maximum output of the active propelling forces to fluctuate slowly fits the experiments quantitatively. Our findings offer design principles for programming efficient transport in active materials.

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

Fractional Brownian motors and stochastic resonance

NASA Astrophysics Data System (ADS)

Goychuk, Igor; Kharchenko, Vasyl

2012-05-01

We study fluctuating tilt Brownian ratchets based on fractional subdiffusion in sticky viscoelastic media characterized by a power law memory kernel. Unlike the normal diffusion case, the rectification effect vanishes in the adiabatically slow modulation limit and optimizes in a driving frequency range. It is shown also that the anomalous rectification effect is maximal (stochastic resonance effect) at optimal temperature and can be of surprisingly good quality. Moreover, subdiffusive current can flow in the counterintuitive direction upon a change of temperature or driving frequency. The dependence of anomalous transport on load exhibits a remarkably simple universality.

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.

Photoinduced nanobubble-driven superfast diffusion of nanoparticles imaged by 4D electron microscopy

PubMed Central

Fu, Xuewen; Chen, Bin; Tang, Jau; Zewail, Ahmed H.

2017-01-01

Dynamics of active or propulsive Brownian particles in nonequilibrium status have recently attracted great interest in many fields including artificial micro/nanoscopic motors and biological entities. Understanding of their dynamics can provide insight into the statistical properties of physical and biological systems far from equilibrium. We report the translational dynamics of photon-activated gold nanoparticles (NPs) in water imaged by liquid-cell four-dimensional electron microscopy (4D-EM) with high spatiotemporal resolution. Under excitation of femtosecond laser pulses, we observed that those NPs exhibit superfast diffusive translation with a diffusion constant four to five orders of magnitude greater than that in the absence of laser excitation. The measured diffusion constant follows a power-law dependence on the laser fluence and a linear increase with the laser repetition rate, respectively. This superfast diffusion of the NPs is induced by a strong random driving force arising from the photoinduced steam nanobubbles (NBs) near the NP surface. In contrast, the NPs exhibit a superfast ballistic translation at a short time scale down to nanoseconds. Combining with a physical model simulation, this study reveals a photoinduced NB propulsion mechanism for propulsive motion, providing physical insights into better design of light-activated artificial micro/nanomotors. The liquid-cell 4D-EM also provides the potential of studying other numerical dynamical behaviors in their native environments. PMID:28875170

Perturbative expansion for the maximum of fractional Brownian motion.

PubMed

Delorme, Mathieu; Wiese, Kay Jörg

2016-07-01

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

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

Self-diffusion in dense granular shear flows.

PubMed

Utter, Brian; Behringer, R P

2004-03-01

Diffusivity is a key quantity in describing velocity fluctuations in granular materials. These fluctuations are the basis of many thermodynamic and hydrodynamic models which aim to provide a statistical description of granular systems. We present experimental results on diffusivity in dense, granular shear flows in a two-dimensional Couette geometry. We find that self-diffusivities D are proportional to the local shear rate gamma; with diffusivities along the direction of the mean flow approximately twice as large as those in the perpendicular direction. The magnitude of the diffusivity is D approximately gamma;a(2), where a is the particle radius. However, the gradient in shear rate, coupling to the mean flow, and strong drag at the moving boundary lead to particle displacements that can appear subdiffusive or superdiffusive. In particular, diffusion appears to be superdiffusive along the mean flow direction due to Taylor dispersion effects and subdiffusive along the perpendicular direction due to the gradient in shear rate. The anisotropic force network leads to an additional anisotropy in the diffusivity that is a property of dense systems and has no obvious analog in rapid flows. Specifically, the diffusivity is suppressed along the direction of the strong force network. A simple random walk simulation reproduces the key features of the data, such as the apparent superdiffusive and subdiffusive behavior arising from the mean velocity field, confirming the underlying diffusive motion. The additional anisotropy is not observed in the simulation since the strong force network is not included. Examples of correlated motion, such as transient vortices, and Lévy flights are also observed. Although correlated motion creates velocity fields which are qualitatively different from collisional Brownian motion and can introduce nondiffusive effects, on average the system appears simply diffusive.

Fitting a function to time-dependent ensemble averaged data.

PubMed

Fogelmark, Karl; Lomholt, Michael A; Irbäck, Anders; Ambjörnsson, Tobias

2018-05-03

Time-dependent ensemble averages, i.e., trajectory-based averages of some observable, are of importance in many fields of science. A crucial objective when interpreting such data is to fit these averages (for instance, squared displacements) with a function and extract parameters (such as diffusion constants). A commonly overlooked challenge in such function fitting procedures is that fluctuations around mean values, by construction, exhibit temporal correlations. We show that the only available general purpose function fitting methods, correlated chi-square method and the weighted least squares method (which neglects correlation), fail at either robust parameter estimation or accurate error estimation. We remedy this by deriving a new closed-form error estimation formula for weighted least square fitting. The new formula uses the full covariance matrix, i.e., rigorously includes temporal correlations, but is free of the robustness issues, inherent to the correlated chi-square method. We demonstrate its accuracy in four examples of importance in many fields: Brownian motion, damped harmonic oscillation, fractional Brownian motion and continuous time random walks. We also successfully apply our method, weighted least squares including correlation in error estimation (WLS-ICE), to particle tracking data. The WLS-ICE method is applicable to arbitrary fit functions, and we provide a publically available WLS-ICE software.

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.

The effective temperature for the thermal fluctuations in hot Brownian motion

NASA Astrophysics Data System (ADS)

Srivastava, Mayank; Chakraborty, Dipanjan

2018-05-01

We revisit the effective parameter description of hot Brownian motion—a scenario where a colloidal particle is kept at an elevated temperature than the ambient fluid. Due to the time scale separation between heat diffusion and particle motion, a stationary halo of hot fluid is carried along with the particle resulting in a spatially varying comoving temperature and viscosity profile. The resultant Brownian motion in the overdamped limit can be well described by a Langevin equation with effective parameters such as effective temperature THBM and friction coefficient ζHBM that quantifies the thermal fluctuations and the diffusivity of the particle. These parameters can exactly be calculated using the framework of fluctuating hydrodynamics and require the knowledge of the complete flow field and the temperature field around the particle. Additionally, it was also observed that configurational and kinetic degrees of freedom admit to different effective temperatures, THB M x and THB M v, respectively, with the former predicted accurately from fluctuating hydrodynamics. A more rigorous calculation by Falasco et al. [Phys. Rev. E 90, 032131-10 (2014)] extends the overdamped description to a generalized Langevin equation where the effective temperature becomes frequency dependent and consequently, for any temperature measurement from a Brownian trajectory requires the knowledge of this frequency dependence. We use this framework to expand on the earlier work and look at the first order correction to the limiting values in the hydrodynamic limit and the kinetic limit. We use the linearized Stokes equation and a constant viscosity approximation to calculate the dissipation function in the fluid. The effective temperature is calculated from the weighted average of the temperature field with the dissipation function. Further, we provide a closed form analytical result for effective temperature in the small as well as high frequency limit. Since hot Brownian motion can be used to probe the local environment in complex systems, we have also calculated the effective diffusivity of the particle in the small frequency limit. To look into the kinetic temperature, the velocity autocorrelation function is computed from the generalized Langevin equation and the Wiener-Khinchine theorem and numerically integrated to evaluate THB M v as a function of the ratio of particle density and fluid density ρP/ρ0. The two limiting cases of ρP/ρ0 → 0 and ρP/ρ0 → ∞ is also discussed.

Killing (absorption) versus survival in random motion

NASA Astrophysics Data System (ADS)

Garbaczewski, Piotr

2017-09-01

We address diffusion processes in a bounded domain, while focusing on somewhat unexplored affinities between the presence of absorbing and/or inaccessible boundaries. For the Brownian motion (Lévy-stable cases are briefly mentioned) model-independent features are established of the dynamical law that underlies the short-time behavior of these random paths, whose overall lifetime is predefined to be long. As a by-product, the limiting regime of a permanent trapping in a domain is obtained. We demonstrate that the adopted conditioning method, involving the so-called Bernstein transition function, works properly also in an unbounded domain, for stochastic processes with killing (Feynman-Kac kernels play the role of transition densities), provided the spectrum of the related semigroup operator is discrete. The method is shown to be useful in the case, when the spectrum of the generator goes down to zero and no isolated minimal (ground state) eigenvalue is in existence, like in the problem of the long-term survival on a half-line with a sink at origin.

Local discretization method for overdamped Brownian motion on a potential with multiple deep wells.

PubMed

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

2016-11-01

We present a general method for transforming the continuous diffusion equation describing overdamped Brownian motion on a time-independent potential with multiple deep wells to a discrete master equation. The method is based on an expansion in localized basis states of local metastable potentials that match the full potential in the region of each potential well. Unlike previous basis methods for discretizing Brownian motion on a potential, this approach is valid for periodic potentials with varying multiple deep wells per period and can also be applied to nonperiodic systems. We apply the method to a range of potentials and find that potential wells that are deep compared to five times the thermal energy can be associated with a discrete localized state while shallower wells are better incorporated into the local metastable potentials of neighboring deep potential wells.

Local discretization method for overdamped Brownian motion on a potential with multiple deep wells

NASA Astrophysics Data System (ADS)

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

2016-11-01

We present a general method for transforming the continuous diffusion equation describing overdamped Brownian motion on a time-independent potential with multiple deep wells to a discrete master equation. The method is based on an expansion in localized basis states of local metastable potentials that match the full potential in the region of each potential well. Unlike previous basis methods for discretizing Brownian motion on a potential, this approach is valid for periodic potentials with varying multiple deep wells per period and can also be applied to nonperiodic systems. We apply the method to a range of potentials and find that potential wells that are deep compared to five times the thermal energy can be associated with a discrete localized state while shallower wells are better incorporated into the local metastable potentials of neighboring deep potential wells.

The power of a single trajectory

NASA Astrophysics Data System (ADS)

Schnellbächer, Nikolas D.; Schwarz, Ulrich S.

2018-03-01

Random walks are often evaluated in terms of their mean squared displacements, either for a large number of trajectories or for one very long trajectory. An alternative evaluation is based on the power spectral density, but here it is less clear which information can be extracted from a single trajectory. For continuous-time Brownian motion, Krapf et al now have mathematically proven that the one property that can be reliably extracted from a single trajectory is the frequency dependence of the ensemble-averaged power spectral density (Krapf et al 2018 New J. Phys. 20 023029). Their mathematical analysis also identifies the appropriate frequency window for this procedure and shows that the diffusion coefficient can be extracted by averaging over a small number of trajectories. The authors have verified their analytical results both by computer simulations and experiments.

Self-Diffusion of Drops in a Dilute Sheared Emulsion

NASA Technical Reports Server (NTRS)

Loewenberg, Michael; Hinch, E. J.

1996-01-01

Self-diffusion coefficients that describe cross-flow migration of non-Brownian drops in a dilute sheared emulsion were obtained by trajectory calculations. A boundary integral formulation was used to describe pairwise interactions between deformable drops; interactions between undeformed drops were described with mobility functions for spherical drops. The results indicate that drops have large anisotropic self-diffusivities which depend strongly on the drop viscosity and modestly on the shear-rate. Pairwise interactions between drops in shear-flow do not appreciably promote drop breakup.

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.

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

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.

Mixed convection of magnetohydrodynamic nanofluids inside microtubes at constant wall temperature

NASA Astrophysics Data System (ADS)

Moshizi, S. A.; Zamani, M.; Hosseini, S. J.; Malvandi, A.

2017-05-01

Laminar fully developed mixed convection of magnetohydrodynamic nanofluids inside microtubes at a constant wall temperature (CWT) under the effects of a variable directional magnetic field is investigated numerically. Nanoparticles are assumed to have slip velocities relative to the base fluid owing to thermophoretic diffusion (temperature gradient driven force) and Brownian diffusion (concentration gradient driven force). The no-slip boundary condition is avoided at the fluid-solid mixture to assess the non-equilibrium region at the fluid-solid interface. A scale analysis is performed to estimate the relative significance of the pertaining parameters that should be included in the governing equations. After the effects of pertinent parameters on the pressure loss and heat transfer enhancement were considered, the figure of merit (FoM) is employed to evaluate and optimize the thermal performance of heat exchange equipment. The results indicate the optimum thermal performance is obtained when the thermophoresis overwhelms the Brownian diffusion, which is for larger nanoparticles. This enhancement boosts when the buoyancy force increases. In addition, increasing the magnetic field strength and slippage at the fluid-solid interface enhances the thermal performance.

Probing short-range protein Brownian motion in the cytoplasm of living cells.

PubMed

Di Rienzo, Carmine; Piazza, Vincenzo; Gratton, Enrico; Beltram, Fabio; Cardarelli, Francesco

2014-12-23

The translational motion of molecules in cells deviates from what is observed in dilute solutions. Theoretical models provide explanations for this effect but with predictions that drastically depend on the nanoscale organization assumed for macromolecular crowding agents. A conclusive test of the nature of the translational motion in cells is missing owing to the lack of techniques capable of probing crowding with the required temporal and spatial resolution. Here we show that fluorescence-fluctuation analysis of raster scans at variable timescales can provide this information. By using green fluorescent proteins in cells, we measure protein motion at the unprecedented timescale of 1 μs, unveiling unobstructed Brownian motion from 25 to 100 nm, and partially suppressed diffusion above 100 nm. Furthermore, experiments on model systems attribute this effect to the presence of relatively immobile structures rather than to diffusing crowding agents. We discuss the implications of these results for intracellular processes.

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.

On modeling animal movements using Brownian motion with measurement error.

PubMed

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

2014-02-01

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

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.

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.

Optimization and universality of Brownian search in a basic model of quenched heterogeneous media

NASA Astrophysics Data System (ADS)

Godec, Aljaž; Metzler, Ralf

2015-05-01

The kinetics of a variety of transport-controlled processes can be reduced to the problem of determining the mean time needed to arrive at a given location for the first time, the so-called mean first-passage time (MFPT) problem. The occurrence of occasional large jumps or intermittent patterns combining various types of motion are known to outperform the standard random walk with respect to the MFPT, by reducing oversampling of space. Here we show that a regular but spatially heterogeneous random walk can significantly and universally enhance the search in any spatial dimension. In a generic minimal model we consider a spherically symmetric system comprising two concentric regions with piecewise constant diffusivity. The MFPT is analyzed under the constraint of conserved average dynamics, that is, the spatially averaged diffusivity is kept constant. Our analytical calculations and extensive numerical simulations demonstrate the existence of an optimal heterogeneity minimizing the MFPT to the target. We prove that the MFPT for a random walk is completely dominated by what we term direct trajectories towards the target and reveal a remarkable universality of the spatially heterogeneous search with respect to target size and system dimensionality. In contrast to intermittent strategies, which are most profitable in low spatial dimensions, the spatially inhomogeneous search performs best in higher dimensions. Discussing our results alongside recent experiments on single-particle tracking in living cells, we argue that the observed spatial heterogeneity may be beneficial for cellular signaling processes.

A Diffusion Approximation Based on Renewal Processes with Applications to Strongly Biased Run-Tumble Motion.

PubMed

Thygesen, Uffe Høgsbro

2016-03-01

We consider organisms which use a renewal strategy such as run-tumble when moving in space, for example to perform chemotaxis in chemical gradients. We derive a diffusion approximation for the motion, applying a central limit theorem due to Anscombe for renewal-reward processes; this theorem has not previously been applied in this context. Our results extend previous work, which has established the mean drift but not the diffusivity. For a classical model of tumble rates applied to chemotaxis, we find that the resulting chemotactic drift saturates to the swimming velocity of the organism when the chemical gradients grow increasingly steep. The dispersal becomes anisotropic in steep gradients, with larger dispersal across the gradient than along the gradient. In contrast to one-dimensional settings, strong bias increases dispersal. We next include Brownian rotation in the model and find that, in limit of high chemotactic sensitivity, the chemotactic drift is 64% of the swimming velocity, independent of the magnitude of the Brownian rotation. We finally derive characteristic timescales of the motion that can be used to assess whether the diffusion limit is justified in a given situation. The proposed technique for obtaining diffusion approximations is conceptually and computationally simple, and applicable also when statistics of the motion is obtained empirically or through Monte Carlo simulation of the motion.

Theory and Applications of Random Fields.

DTIC Science & Technology

1986-11-01

sheet, the natural generalisation to Rk, k>l, of the Brownian motion on the line. Good, general, asymptotic bounds are, however, now known. For...research described, as well as a list of conferences attended and visits made to American universities under the auspices and financing of the grant...some even more complex space. There, very little is known, even if one restricts attention to supposedly simple fields, such as the so called Brownian

Quantifying the degree of persistence in random amoeboid motion based on the Hurst exponent of fractional Brownian motion.

PubMed

Makarava, Natallia; Menz, Stephan; Theves, Matthias; Huisinga, Wilhelm; Beta, Carsten; Holschneider, Matthias

2014-10-01

Amoebae explore their environment in a random way, unless external cues like, e.g., nutrients, bias their motion. Even in the absence of cues, however, experimental cell tracks show some degree of persistence. In this paper, we analyzed individual cell tracks in the framework of a linear mixed effects model, where each track is modeled by a fractional Brownian motion, i.e., a Gaussian process exhibiting a long-term correlation structure superposed on a linear trend. The degree of persistence was quantified by the Hurst exponent of fractional Brownian motion. Our analysis of experimental cell tracks of the amoeba Dictyostelium discoideum showed a persistent movement for the majority of tracks. Employing a sliding window approach, we estimated the variations of the Hurst exponent over time, which allowed us to identify points in time, where the correlation structure was distorted ("outliers"). Coarse graining of track data via down-sampling allowed us to identify the dependence of persistence on the spatial scale. While one would expect the (mode of the) Hurst exponent to be constant on different temporal scales due to the self-similarity property of fractional Brownian motion, we observed a trend towards stronger persistence for the down-sampled cell tracks indicating stronger persistence on larger time scales.

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.

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

Multiscale simulations of anisotropic particles combining molecular dynamics and Green's function reaction dynamics

NASA Astrophysics Data System (ADS)

Vijaykumar, Adithya; Ouldridge, Thomas E.; ten Wolde, Pieter Rein; Bolhuis, Peter G.

2017-03-01

The modeling of complex reaction-diffusion processes in, for instance, cellular biochemical networks or self-assembling soft matter can be tremendously sped up by employing a multiscale algorithm which combines the mesoscopic Green's Function Reaction Dynamics (GFRD) method with explicit stochastic Brownian, Langevin, or deterministic molecular dynamics to treat reactants at the microscopic scale [A. Vijaykumar, P. G. Bolhuis, and P. R. ten Wolde, J. Chem. Phys. 143, 214102 (2015)]. Here we extend this multiscale MD-GFRD approach to include the orientational dynamics that is crucial to describe the anisotropic interactions often prevalent in biomolecular systems. We present the novel algorithm focusing on Brownian dynamics only, although the methodology is generic. We illustrate the novel algorithm using a simple patchy particle model. After validation of the algorithm, we discuss its performance. The rotational Brownian dynamics MD-GFRD multiscale method will open up the possibility for large scale simulations of protein signalling networks.

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

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

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

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.

Brownian Motion at Lipid Membranes: A Comparison of Hydrodynamic Models Describing and Experiments Quantifying Diffusion within Lipid Bilayers.

PubMed

Block, Stephan

2018-05-22

The capability of lipid bilayers to exhibit fluid-phase behavior is a fascinating property, which enables, for example, membrane-associated components, such as lipids (domains) and transmembrane proteins, to diffuse within the membrane. These diffusion processes are of paramount importance for cells, as they are for example involved in cell signaling processes or the recycling of membrane components, but also for recently developed analytical approaches, which use differences in the mobility for certain analytical purposes, such as in-membrane purification of membrane proteins or the analysis of multivalent interactions. Here, models describing the Brownian motion of membrane inclusions (lipids, peptides, proteins, and complexes thereof) in model bilayers (giant unilamellar vesicles, black lipid membranes, supported lipid bilayers) are summarized and model predictions are compared with the available experimental data, thereby allowing for evaluating the validity of the introduced models. It will be shown that models describing the diffusion in freestanding (Saffman-Delbrück and Hughes-Pailthorpe-White model) and supported bilayers (the Evans-Sackmann model) are well supported by experiments, though only few experimental studies have been published so far for the latter case, calling for additional tests to reach the same level of experimental confirmation that is currently available for the case of freestanding bilayers.

Spontaneous Mechanical Buckling in Two-Dimensional Materials: A Power Source for Ambient Vibration Energy Harvesters

NASA Astrophysics Data System (ADS)

Thibado, Paul; Kumar, Pradeep; Singh, Surendra

Internet-of-Things (IoT) is projected to become a multi-trillion-dollar market, but most applications cannot afford replacing batteries on such a large scale, driving the need for battery alternatives. We recently discovered that freestanding graphene membranes are in perpetual motion when held at room temperature. Surprisingly, the random up-down motion of the membrane does not follow classical Brownian motion, but instead is super-diffusive at short times and sub-diffusive at long times. Furthermore, the velocity probability distribution function is non-Gaussian and follows the heavy-tailed Cauchy-Lorentz distribution, consistent with Lévy flights. Molecular dynamics simulations reveal that mechanical buckling is spontaneously occurring, and that this is the mechanism responsible for the anomalous movement. Bucking in this system occurs when the local material suddenly flips from concave to convex. The higher kinetic energy associated with this motion is derived from the surrounding thermal waste heat, and it may be converted into an electrical current and used as the active component of small power generators known as ambient vibration energy harvesters. thibado@uark.edu.

Quantum power source: putting in order of a Brownian motion without Maxwell's demon

NASA Astrophysics Data System (ADS)

Aristov, Vitaly V.; Nikulov, A. V.

2003-07-01

The problem of possible violation of the second law of thermodynamics is discussed. It is noted that the task of the well known challenge to the second law called Maxwell's demon is put in order a chaotic perpetual motion and if any ordered Brownian motion exists then the second law can be broken without this hypothetical intelligent entity. The postulate of absolute randomness of any Brownian motion saved the second law in the beginning of the 20th century when it was realized as perpetual motion. This postulate can be proven in the limits of classical mechanics but is not correct according to quantum mechanics. Moreover some enough known quantum phenomena, such as the persistent current at non-zero resistance, are an experimental evidence of the non-chaotic Brownian motion with non-zero average velocity. An experimental observation of a dc quantum power soruce is interperted as evidence of violation of the second law.

Mode-selective control of thermal Brownian vibration of micro-resonator (Generation of a thermal no-equilibrium state by mechanical feedback control)

NASA Astrophysics Data System (ADS)

Kawamura, Y.; Kanegae, R.

2017-09-01

Recently, there have been various attempts to dampen the vibration amplitude of the Brownian motion of a microresonator below the thermal vibration amplitude, with the goal of reaching the quantum ground vibration level. To further develop the approach of reaching the quantum ground state, it is essential to clarify whether or not coupling exists between the different vibration modes of the resonator. In this paper, the mode-selective control of thermal Brownian vibration is shown. The first and the second vibration modes of a micro-cantilever moved by a random Brownian motion are cooled selectively and independently below the thermal vibration amplitude, as determined by the statistical thermodynamic theory, using a mechanical feedback control method. This experimental result shows that the thermal no-equilibrium condition was generated by mechanical feedback control.

Anomalous yet Brownian.

PubMed

Wang, Bo; Anthony, Stephen M; Bae, Sung Chul; Granick, Steve

2009-09-08

We describe experiments using single-particle tracking in which mean-square displacement is simply proportional to time (Fickian), yet the distribution of displacement probability is not Gaussian as should be expected of a classical random walk but, instead, is decidedly exponential for large displacements, the decay length of the exponential being proportional to the square root of time. The first example is when colloidal beads diffuse along linear phospholipid bilayer tubes whose radius is the same as that of the beads. The second is when beads diffuse through entangled F-actin networks, bead radius being less than one-fifth of the actin network mesh size. We explore the relevance to dynamic heterogeneity in trajectory space, which has been extensively discussed regarding glassy systems. Data for the second system might suggest activated diffusion between pores in the entangled F-actin networks, in the same spirit as activated diffusion and exponential tails observed in glassy systems. But the first system shows exceptionally rapid diffusion, nearly as rapid as for identical colloids in free suspension, yet still displaying an exponential probability distribution as in the second system. Thus, although the exponential tail is reminiscent of glassy systems, in fact, these dynamics are exceptionally rapid. We also compare with particle trajectories that are at first subdiffusive but Fickian at the longest measurement times, finding that displacement probability distributions fall onto the same master curve in both regimes. The need is emphasized for experiments, theory, and computer simulation to allow definitive interpretation of this simple and clean exponential probability distribution.

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.

Fundamental energy limits of SET-based Brownian NAND and half-adder circuits. Preliminary findings from a physical-information-theoretic methodology

NASA Astrophysics Data System (ADS)

Ercan, İlke; Suyabatmaz, Enes

2018-06-01

The saturation in the efficiency and performance scaling of conventional electronic technologies brings about the development of novel computational paradigms. Brownian circuits are among the promising alternatives that can exploit fluctuations to increase the efficiency of information processing in nanocomputing. A Brownian cellular automaton, where signals propagate randomly and are driven by local transition rules, can be made computationally universal by embedding arbitrary asynchronous circuits on it. One of the potential realizations of such circuits is via single electron tunneling (SET) devices since SET technology enable simulation of noise and fluctuations in a fashion similar to Brownian search. In this paper, we perform a physical-information-theoretic analysis on the efficiency limitations in a Brownian NAND and half-adder circuits implemented using SET technology. The method we employed here establishes a solid ground that enables studying computational and physical features of this emerging technology on an equal footing, and yield fundamental lower bounds that provide valuable insights into how far its efficiency can be improved in principle. In order to provide a basis for comparison, we also analyze a NAND gate and half-adder circuit implemented in complementary metal oxide semiconductor technology to show how the fundamental bound of the Brownian circuit compares against a conventional paradigm.

Asymptotics of the evolution semigroup associated with a scalar field in the presence of a non-linear electromagnetic field

NASA Astrophysics Data System (ADS)

Albeverio, Sergio; Tamura, Hiroshi

2018-04-01

We consider a model describing the coupling of a vector-valued and a scalar homogeneous Markovian random field over R4, interpreted as expressing the interaction between a charged scalar quantum field coupled with a nonlinear quantized electromagnetic field. Expectations of functionals of the random fields are expressed by Brownian bridges. Using this, together with Feynman-Kac-Itô type formulae and estimates on the small time and large time behaviour of Brownian functionals, we prove asymptotic upper and lower bounds on the kernel of the transition semigroup for our model. The upper bound gives faster than exponential decay for large distances of the corresponding resolvent (propagator).

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.

Theory of slightly fluctuating ratchets

NASA Astrophysics Data System (ADS)

Rozenbaum, V. M.; Shapochkina, I. V.; Lin, S. H.; Trakhtenberg, L. I.

2017-04-01

We consider a Brownian particle moving in a slightly fluctuating potential. Using the perturbation theory on small potential fluctuations, we derive a general analytical expression for the average particle velocity valid for both flashing and rocking ratchets with arbitrary, stochastic or deterministic, time dependence of potential energy fluctuations. The result is determined by the Green's function for diffusion in the time-independent part of the potential and by the features of correlations in the fluctuating part of the potential. The generality of the result allows describing complex ratchet systems with competing characteristic times; these systems are exemplified by the model of a Brownian photomotor with relaxation processes of finite duration.

Powering a burnt bridges Brownian ratchet: a model for an extracellular motor driven by proteolysis of collagen.

PubMed

Saffarian, Saveez; Qian, Hong; Collier, Ivan; Elson, Elliot; Goldberg, Gregory

2006-04-01

Biased diffusion of collagenase on collagen fibrils may represent the first observed adenosine triphosphate-independent extracellular molecular motor. The magnitude of force generated by the enzyme remains unclear. We propose a propulsion mechanism based on a burnt bridges Brownian ratchet model with a varying degree of coupling of the free energy from collagen proteolysis to the enzyme motion. When constrained by experimental observations, our model predicts 0.1 pN stall force for individual collagenase molecules. A dimer, surprisingly, can generate a force in the range of 5 pN, suggesting that the motor can be of biological significance.

Self-assembly of robotic micro- and nanoswimmers using magnetic nanoparticles

NASA Astrophysics Data System (ADS)

Cheang, U. Kei; Kim, Min Jun

2015-03-01

Micro- and nanoscale robotic swimmers are very promising to significantly enhance the performance of particulate drug delivery by providing high accuracy at extremely small scales. Here, we introduce micro- and nanoswimmers fabricated using self-assembly of nanoparticles and control via magnetic fields. Nanoparticles self-align into parallel chains under magnetization. The swimmers exhibit flexibility under a rotating magnetic field resulting in chiral structures upon deformation, thereby having the prerequisite for non-reciprocal motion to move about at low Reynolds number. The swimmers are actuated wirelessly using an external rotating magnetic field supplied by approximate Helmholtz coils. By controlling the concentration of the suspended magnetic nanoparticles, the swimmers can be modulated into different sizes. Nanoscale swimmers are largely influenced by Brownian motion, as observed from their jerky trajectories. The microswimmers, which are roughly three times larger, are less vulnerable to the effects from Brownian motion. In this paper, we demonstrate responsive directional control of micro- and nanoswimmers and compare their respective diffusivities and trajectories to characterize the implications of Brownian disturbance on the motions of small and large swimmers. We then performed a simulation using a kinematic model for the magnetic swimmers including the stochastic nature of Brownian motion.

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.

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).

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

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.

Intermediate scattering function of an anisotropic active Brownian particle

PubMed Central

Kurzthaler, Christina; Leitmann, Sebastian; Franosch, Thomas

2016-01-01

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

Intermediate scattering function of an anisotropic active Brownian particle.

PubMed

Kurzthaler, Christina; Leitmann, Sebastian; Franosch, Thomas

2016-10-10

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

Intermediate scattering function of an anisotropic active Brownian particle

NASA Astrophysics Data System (ADS)

Kurzthaler, Christina; Leitmann, Sebastian; Franosch, Thomas

2016-10-01

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

Communication: Coordinate-dependent diffusivity from single molecule trajectories

NASA Astrophysics Data System (ADS)

Berezhkovskii, Alexander M.; Makarov, Dmitrii E.

2017-11-01

Single-molecule observations of biomolecular folding are commonly interpreted using the model of one-dimensional diffusion along a reaction coordinate, with a coordinate-independent diffusion coefficient. Recent analysis, however, suggests that more general models are required to account for single-molecule measurements performed with high temporal resolution. Here, we consider one such generalization: a model where the diffusion coefficient can be an arbitrary function of the reaction coordinate. Assuming Brownian dynamics along this coordinate, we derive an exact expression for the coordinate-dependent diffusivity in terms of the splitting probability within an arbitrarily chosen interval and the mean transition path time between the interval boundaries. This formula can be used to estimate the effective diffusion coefficient along a reaction coordinate directly from single-molecule trajectories.

Ratchet effect for nanoparticle transport in hair follicles.

PubMed

Radtke, Matthias; Patzelt, Alexa; Knorr, Fanny; Lademann, Jürgen; Netz, Roland R

2017-07-01

The motion of a single rigid nanoparticle inside a hair follicle is investigated by means of Brownian dynamics simulations. The cuticular hair structure is modeled as a periodic asymmetric ratchet-shaped surface. Induced by oscillating radial hair motion we find directed nanoparticle transport into the hair follicle with maximal velocity at a specific optimal frequency and an optimal particle size. We observe flow reversal when switching from radial to axial oscillatory hair motion. We also study the diffusion behavior and find strongly enhanced diffusion for axial motion with a diffusivity significantly larger than for free diffusion. Copyright © 2016 Elsevier B.V. All rights reserved.

Black-Scholes model under subordination

NASA Astrophysics Data System (ADS)

Stanislavsky, A. A.

2003-02-01

In this paper, we consider a new mathematical extension of the Black-Scholes (BS) model in which the stochastic time and stock share price evolution is described by two independent random processes. The parent process is Brownian, and the directing process is inverse to the totally skewed, strictly α-stable process. The subordinated process represents the Brownian motion indexed by an independent, continuous and increasing process. This allows us to introduce the long-term memory effects in the classical BS model.

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.

Probing short-range protein Brownian motion in the cytoplasm of living cells

PubMed Central

Di Rienzo, Carmine; Piazza, Vincenzo; Gratton, Enrico; Beltram, Fabio; Cardarelli, Francesco

2014-01-01

The translational motion of molecules in cells deviates from what is observed in dilute solutions. Theoretical models provide explanations for this effect but with predictions that drastically depend on the nanoscale organization assumed for macromolecular crowding agents. A conclusive test of the nature of the translational motion in cells is missing owing to the lack of techniques capable of probing crowding with the required temporal and spatial resolution. Here we show that fluorescence-fluctuation analysis of raster scans at variable timescales can provide this information. By using green fluorescent proteins in cells, we measure protein motion at the unprecedented timescale of 1 μs, unveiling unobstructed Brownian motion from 25 to 100 nm, and partially suppressed diffusion above 100 nm. Furthermore, experiments on model systems attribute this effect to the presence of relatively immobile structures rather than to diffusing crowding agents. We discuss the implications of these results for intracellular processes. PMID:25532887

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.

Transport properties of elastically coupled fractional Brownian motors

NASA Astrophysics Data System (ADS)

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

2015-11-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

FRAP to Characterize Molecular Diffusion and Interaction in Various Membrane Environments.

PubMed

Pincet, Frédéric; Adrien, Vladimir; Yang, Rong; Delacotte, Jérôme; Rothman, James E; Urbach, Wladimir; Tareste, David

2016-01-01

Fluorescence recovery after photobleaching (FRAP) is a standard method used to study the dynamics of lipids and proteins in artificial and cellular membrane systems. The advent of confocal microscopy two decades ago has made quantitative FRAP easily available to most laboratories. Usually, a single bleaching pattern/area is used and the corresponding recovery time is assumed to directly provide a diffusion coefficient, although this is only true in the case of unrestricted Brownian motion. Here, we propose some general guidelines to perform FRAP experiments under a confocal microscope with different bleaching patterns and area, allowing the experimentalist to establish whether the molecules undergo Brownian motion (free diffusion) or whether they have restricted or directed movements. Using in silico simulations of FRAP measurements, we further indicate the data acquisition criteria that have to be verified in order to obtain accurate values for the diffusion coefficient and to be able to distinguish between different diffusive species. Using this approach, we compare the behavior of lipids in three different membrane platforms (supported lipid bilayers, giant liposomes and sponge phases), and we demonstrate that FRAP measurements are consistent with results obtained using other techniques such as Fluorescence Correlation Spectroscopy (FCS) or Single Particle Tracking (SPT). Finally, we apply this method to show that the presence of the synaptic protein Munc18-1 inhibits the interaction between the synaptic vesicle SNARE protein, VAMP2, and its partner from the plasma membrane, Syn1A.

Self-thermophoresis and thermal self-diffusion in liquids and gases.

PubMed

Brenner, Howard

2010-09-01

This paper demonstrates the existence of self-thermophoresis, a phenomenon whereby a virtual thermophoretic force arising from a temperature gradient in a quiescent single-component liquid or gas acts upon an individual molecule of that fluid in much the same manner as a "real" thermophoretic force acts upon a macroscopic, non-Brownian body immersed in that same fluid. In turn, self-thermophoresis acting in concert with Brownian self-diffusion gives rise to the phenomenon of thermal self-diffusion in single-component fluids. The latter furnishes quantitative explanations of both thermophoresis in pure fluids and thermal diffusion in binary mixtures (the latter composed of a dilute solution of a physicochemically inert solute whose molecules are large compared with those of the solvent continuum). Explicitly, the self-thermophoretic theory furnishes a simple expression for both the thermophoretic velocity U of a macroscopic body in a single-component fluid subjected to a temperature gradient ∇T , and the intimately related binary thermal diffusion coefficient D{T} for a two-component colloidal or macromolecular mixture. The predicted expressions U=-D{T}∇T≡-βD{S}∇T and D{T}=βD{S} (with β and D{S} the pure solvent's respective thermal expansion and isothermal self-diffusion coefficients) are each noted to accord reasonably well with experimental data for both liquids and gases. The likely source of systematic deviations of the predicted values of D{T} from these data is discussed. This appears to be the first successful thermodiffusion theory applicable to both liquids and gases, a not insignificant achievement considering that the respective thermal diffusivities and thermophoretic velocities of these two classes of fluids differ by as much as six orders of magnitude.

Time scale of diffusion in molecular and cellular biology

NASA Astrophysics Data System (ADS)

Holcman, D.; Schuss, Z.

2014-05-01

Diffusion is the driver of critical biological processes in cellular and molecular biology. The diverse temporal scales of cellular function are determined by vastly diverse spatial scales in most biophysical processes. The latter are due, among others, to small binding sites inside or on the cell membrane or to narrow passages between large cellular compartments. The great disparity in scales is at the root of the difficulty in quantifying cell function from molecular dynamics and from simulations. The coarse-grained time scale of cellular function is determined from molecular diffusion by the mean first passage time of molecular Brownian motion to a small targets or through narrow passages. The narrow escape theory (NET) concerns this issue. The NET is ubiquitous in molecular and cellular biology and is manifested, among others, in chemical reactions, in the calculation of the effective diffusion coefficient of receptors diffusing on a neuronal cell membrane strewn with obstacles, in the quantification of the early steps of viral trafficking, in the regulation of diffusion between the mother and daughter cells during cell division, and many other cases. Brownian trajectories can represent the motion of a molecule, a protein, an ion in solution, a receptor in a cell or on its membrane, and many other biochemical processes. The small target can represent a binding site or an ionic channel, a hidden active site embedded in a complex protein structure, a receptor for a neurotransmitter on the membrane of a neuron, and so on. The mean time to attach to a receptor or activator determines diffusion fluxes that are key regulators of cell function. This review describes physical models of various subcellular microdomains, in which the NET coarse-grains the molecular scale to a higher cellular-level, thus clarifying the role of cell geometry in determining subcellular function.

Covering Ground: Movement Patterns and Random Walk Behavior in Aquilonastra anomala Sea Stars.

PubMed

Lohmann, Amanda C; Evangelista, Dennis; Waldrop, Lindsay D; Mah, Christopher L; Hedrick, Tyson L

2016-10-01

The paths animals take while moving through their environments affect their likelihood of encountering food and other resources; thus, models of foraging behavior abound. To collect movement data appropriate for comparison with these models, we used time-lapse photography to track movements of a small, hardy, and easy-to-obtain organism, Aquilonastra anomala sea stars. We recorded the sea stars in a tank over many hours, with and without a food cue. With food present, they covered less distance, as predicted by theory; this strategy would allow them to remain near food. We then compared the paths of the sea stars to three common models of animal movement: Brownian motion, Lévy walks, and correlated random walks; we found that the sea stars' movements most closely resembled a correlated random walk. Additionally, we compared the search performance of models of Brownian motion, a Lévy walk, and a correlated random walk to that of a model based on the sea stars' movements. We found that the behavior of the modeled sea star walk was similar to that of the modeled correlated random walk and the Brownian motion model, but that the sea star walk was slightly more likely than the other walks to find targets at intermediate distances. While organisms are unlikely to follow an idealized random walk in all details, our data suggest that comparing the effectiveness of an organism's paths to those from theory can give insight into the organism's actual movement strategy. Finally, automated optical tracking of invertebrates proved feasible, and A. anomala was revealed to be a tractable, 2D-movement study system.

Aging in mortal superdiffusive Lévy walkers.

PubMed

Stage, Helena

2017-12-01

A growing body of literature examines the effects of superdiffusive subballistic movement premeasurement (aging or time lag) on observations arising from single-particle tracking. A neglected aspect is the finite lifetime of these Lévy walkers, be they proteins, cells, or larger structures. We examine the effects of aging on the motility of mortal walkers, and discuss the means by which permanent stopping of walkers may be categorized as arising from "natural" death or experimental artifacts such as low photostability or radiation damage. This is done by comparison of the walkers' mean squared displacement (MSD) with the front velocity of propagation of a group of walkers, which is found to be invariant under time lags. For any running time distribution of a mortal random walker, the MSD is tempered by the stopping rate θ. This provides a physical interpretation for truncated heavy-tailed diffusion processes and serves as a tool by which to better classify the underlying running time distributions of random walkers. Tempering of aged MSDs raises the issue of misinterpreting superdiffusive motion which appears Brownian or subdiffusive over certain time scales.

Aging in mortal superdiffusive Lévy walkers

NASA Astrophysics Data System (ADS)

Stage, Helena

2017-12-01

A growing body of literature examines the effects of superdiffusive subballistic movement premeasurement (aging or time lag) on observations arising from single-particle tracking. A neglected aspect is the finite lifetime of these Lévy walkers, be they proteins, cells, or larger structures. We examine the effects of aging on the motility of mortal walkers, and discuss the means by which permanent stopping of walkers may be categorized as arising from "natural" death or experimental artifacts such as low photostability or radiation damage. This is done by comparison of the walkers' mean squared displacement (MSD) with the front velocity of propagation of a group of walkers, which is found to be invariant under time lags. For any running time distribution of a mortal random walker, the MSD is tempered by the stopping rate θ . This provides a physical interpretation for truncated heavy-tailed diffusion processes and serves as a tool by which to better classify the underlying running time distributions of random walkers. Tempering of aged MSDs raises the issue of misinterpreting superdiffusive motion which appears Brownian or subdiffusive over certain time scales.

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

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.

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.

Existence, uniqueness and regularity of a time-periodic probability density distribution arising in a sedimentation-diffusion problem

NASA Technical Reports Server (NTRS)

Nitsche, Ludwig C.; Nitsche, Johannes M.; Brenner, Howard

1988-01-01

The sedimentation and diffusion of a nonneutrally buoyant Brownian particle in vertical fluid-filled cylinder of finite length which is instantaneously inverted at regular intervals are investigated analytically. A one-dimensional convective-diffusive equation is derived to describe the temporal and spatial evolution of the probability density; a periodicity condition is formulated; the applicability of Fredholm theory is established; and the parameter-space regions are determined within which the existence and uniqueness of solutions are guaranteed. Numerical results for sample problems are presented graphically and briefly characterized.

Electronic Noise and Fluctuations in Solids

NASA Astrophysics Data System (ADS)

Kogan, Sh.

2008-07-01

Preface; Part I. Introduction. Some Basic Concepts of the Theory of Random Processes: 1. Probability density functions. Moments. Stationary processes; 2. Correlation function; 3. Spectral density of noise; 4. Ergodicity and nonergodicity of random processes; 5. Random pulses and shot noise; 6. Markov processes. General theory; 7. Discrete Markov processes. Random telegraph noise; 8. Quasicontinuous (Diffusion-like) Markov processes; 9. Brownian motion; 10. Langevin approach to the kinetics of fluctuations; Part II. Fluctuation-Dissipation Relations in Equilibrium Systems: 11. Derivation of fluctuation-dissipation relations; 12. Equilibrium noise in quasistationary circuits. Nyquist theorem; 13. Fluctuations of electromagnetic fields in continuous media; Part III. Fluctuations in Nonequilibrium Gases: 14. Some basic concepts of hot-electrons' physics; 15. Simple model of current fluctuations in a semiconductor with hot electrons; 16. General kinetic theory of quasiclassical fluctuations in a gas of particles. The Boltzmann-Langevin equation; 17. Current fluctuations and noise temperature; 18. Current fluctuations and diffusion in a gas of hot electrons; 19. One-time correlation in nonequilibrium gases; 20. Intervalley noise in multivalley semiconductors; 21. Noise of hot electrons emitting optical phonons in the streaming regime; 22. Noise in a semiconductor with a postbreakdown stable current filament; Part IV. Generation-recombination noise: 23. G-R noise in uniform unipolar semiconductors; 24. Noise produced by recombination and diffusion; Part V. Noise in quantum ballistic systems: 25. Introduction; 26. Equilibrium noise and shot noise in quantum conductors; 27. Modulation noise in quantum point contacts; 28. Transition from a ballistic conductor to a macroscopic one; 29. Noise in tunnel junctions; Part VI. Resistance noise in metals: 30. Incoherent scattering of electrons by mobile defects; 31. Effect of mobile scattering centers on the electron interference pattern; 32. Fluctuations of the number of diffusing scattering centers; 33. Temperature fluctuations and the corresponding noise; Part VII. Noise in strongly disordered conductors: 34. Basic ideas of the percolation theory; 35. Resistance fluctuations in percolation systems. 36. Experiments; Part VIII. Low-frequency noise with an 1/f-type spectrum and random telegraph noise: 37. Introduction; 38. Some general properties of 1/f noise; 39. Basic models of 1/f noise; 40./f noise in metals; 41. Low-frequency noise in semiconductors; 42. Magnetic noise in spin glasses and some other magnetic systems; 43. Temperature fluctuations as a possible source of 1/f noise; 44. Random telegraph noise; 45. Fluctuations with 1/f spectrum in other systems; 46. General conclusions on 1/f noise; Part IX. Noise in Superconductors and Superconducting Structures: 47. Noise in Josephson junctions; 48. Noise in type II superconductors; References; Subject index.

An algorithm for emulsion stability simulations: account of flocculation, coalescence, surfactant adsorption and the process of Ostwald ripening.

PubMed

Urbina-Villalba, German

2009-03-01

The first algorithm for Emulsion Stability Simulations (ESS) was presented at the V Conferencia Iberoamericana sobre Equilibrio de Fases y Diseño de Procesos [Luis, J.; García-Sucre, M.; Urbina-Villalba, G. Brownian Dynamics Simulation of Emulsion Stability In: Equifase 99. Libro de Actas, 1(st) Ed., Tojo J., Arce, A., Eds.; Solucion's: Vigo, Spain, 1999; Volume 2, pp. 364-369]. The former version of the program consisted on a minor modification of the Brownian Dynamics algorithm to account for the coalescence of drops. The present version of the program contains elaborate routines for time-dependent surfactant adsorption, average diffusion constants, and Ostwald ripening.

Brownian dynamics of confined rigid bodies

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

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

2015-10-14

We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust, space efficient, and easy to accumulate. We construct a system of overdamped Langevin equations in the quaternion representation that accounts for hydrodynamic effects, preserves the unit-norm constraint on the quaternion, and is time reversible with respect to the Gibbs-Boltzmann distribution at equilibrium. We introduce two schemes for temporal integration of the overdamped Langevin equations of motion, one based on the Fixman midpoint method and the othermore » based on a random finite difference approach, both of which ensure that the correct stochastic drift term is captured in a computationally efficient way. We study several examples of rigid colloidal particles diffusing near a no-slip boundary and demonstrate the importance of the choice of tracking point on the measured translational mean square displacement (MSD). We examine the average short-time as well as the long-time quasi-two-dimensional diffusion coefficient of a rigid particle sedimented near a bottom wall due to gravity. For several particle shapes, we find a choice of tracking point that makes the MSD essentially linear with time, allowing us to estimate the long-time diffusion coefficient efficiently using a Monte Carlo method. However, in general, such a special choice of tracking point does not exist, and numerical techniques for simulating long trajectories, such as the ones we introduce here, are necessary to study diffusion on long time scales.« less

Reproductive pair correlations and the clustering of organisms.

PubMed

Young, W R; Roberts, A J; Stuhne, G

2001-07-19

Clustering of organisms can be a consequence of social behaviour, or of the response of individuals to chemical and physical cues. Environmental variability can also cause clustering: for example, marine turbulence transports plankton and produces chlorophyll concentration patterns in the upper ocean. Even in a homogeneous environment, nonlinear interactions between species can result in spontaneous pattern formation. Here we show that a population of independent, random-walking organisms ('brownian bugs'), reproducing by binary division and dying at constant rates, spontaneously aggregates. Using an individual-based model, we show that clusters form out of spatially homogeneous initial conditions without environmental variability, predator-prey interactions, kinesis or taxis. The clustering mechanism is reproductively driven-birth must always be adjacent to a living organism. This clustering can overwhelm diffusion and create non-poissonian correlations between pairs (parent and offspring) or organisms, leading to the emergence of patterns.

Diffuse charge dynamics in ionic thermoelectrochemical systems.

PubMed

Stout, Robert F; Khair, Aditya S

2017-08-01

Thermoelectrics are increasingly being studied as promising electrical generators in the ongoing search for alternative energy sources. In particular, recent experimental work has examined thermoelectric materials containing ionic charge carriers; however, the majority of mathematical modeling has been focused on their steady-state behavior. Here, we determine the time scales over which the diffuse charge dynamics in ionic thermoelectrochemical systems occur by analyzing the simplest model thermoelectric cell: a binary electrolyte between two parallel, blocking electrodes. We consider the application of a temperature gradient across the device while the electrodes remain electrically isolated from each other. This results in a net voltage, called the thermovoltage, via the Seebeck effect. At the same time, the Soret effect results in migration of the ions toward the cold electrode. The charge dynamics are described mathematically by the Poisson-Nernst-Planck equations for dilute solutions, in which the ion flux is driven by electromigration, Brownian diffusion, and thermal diffusion under a temperature gradient. The temperature evolves according to the heat equation. This nonlinear set of equations is linearized in the (experimentally relevant) limit of a "weak" temperature gradient. From this, we show that the time scale on which the thermovoltage develops is the Debye time, 1/Dκ^{2}, where D is the Brownian diffusion coefficient of both ion species, and κ^{-1} is the Debye length. However, the concentration gradient due to the Soret effect develops on the bulk diffusion time, L^{2}/D, where L is the distance between the electrodes. For thin diffuse layers, which is the condition under which most real devices operate, the Debye time is orders of magnitude less than the diffusion time. Therefore, rather surprisingly, the majority of ion motion occurs after the steady thermovoltage has developed. Moreover, the dynamics are independent of the thermal diffusion coefficients, which simply set the magnitude of the steady-state thermovoltage.

Diffuse charge dynamics in ionic thermoelectrochemical systems

NASA Astrophysics Data System (ADS)

Stout, Robert F.; Khair, Aditya S.

2017-08-01

Thermoelectrics are increasingly being studied as promising electrical generators in the ongoing search for alternative energy sources. In particular, recent experimental work has examined thermoelectric materials containing ionic charge carriers; however, the majority of mathematical modeling has been focused on their steady-state behavior. Here, we determine the time scales over which the diffuse charge dynamics in ionic thermoelectrochemical systems occur by analyzing the simplest model thermoelectric cell: a binary electrolyte between two parallel, blocking electrodes. We consider the application of a temperature gradient across the device while the electrodes remain electrically isolated from each other. This results in a net voltage, called the thermovoltage, via the Seebeck effect. At the same time, the Soret effect results in migration of the ions toward the cold electrode. The charge dynamics are described mathematically by the Poisson-Nernst-Planck equations for dilute solutions, in which the ion flux is driven by electromigration, Brownian diffusion, and thermal diffusion under a temperature gradient. The temperature evolves according to the heat equation. This nonlinear set of equations is linearized in the (experimentally relevant) limit of a "weak" temperature gradient. From this, we show that the time scale on which the thermovoltage develops is the Debye time, 1 /D κ2 , where D is the Brownian diffusion coefficient of both ion species, and κ-1 is the Debye length. However, the concentration gradient due to the Soret effect develops on the bulk diffusion time, L2/D , where L is the distance between the electrodes. For thin diffuse layers, which is the condition under which most real devices operate, the Debye time is orders of magnitude less than the diffusion time. Therefore, rather surprisingly, the majority of ion motion occurs after the steady thermovoltage has developed. Moreover, the dynamics are independent of the thermal diffusion coefficients, which simply set the magnitude of the steady-state thermovoltage.

Effects of curved midline and varying width on the description of the effective diffusivity of Brownian particles

NASA Astrophysics Data System (ADS)

Chávez, Yoshua; Chacón-Acosta, Guillermo; Dagdug, Leonardo

2018-05-01

Axial diffusion in channels and tubes of smoothly-varying geometry can be approximately described as one-dimensional diffusion in the entropy potential with a position-dependent effective diffusion coefficient, by means of the modified Fick–Jacobs equation. In this work, we derive analytical expressions for the position-dependent effective diffusivity for two-dimensional asymmetric varying-width channels, and for three-dimensional curved midline tubes, formed by straight walls. To this end, we use a recently developed theoretical framework using the Frenet–Serret moving frame as the coordinate system (2016 J. Chem. Phys. 145 074105). For narrow tubes and channels, an effective one-dimensional description reducing the diffusion equation to a Fick–Jacobs-like equation in general coordinates is used. From this last equation, one can calculate the effective diffusion coefficient applying Neumann boundary conditions.

Solution of a modified fractional diffusion equation

NASA Astrophysics Data System (ADS)

Langlands, T. A. M.

2006-07-01

Recently, a modified fractional diffusion equation has been proposed [I. Sokolov, J. Klafter, From diffusion to anomalous diffusion: a century after Einstein's brownian motion, Chaos 15 (2005) 026103; A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V.Yu. Gonchar, Distributed order time fractional diffusion equation, Frac. Calc. Appl. Anal. 6 (3) (2003) 259279; I.M. Sokolov, A.V. Checkin, J. Klafter, Distributed-order fractional kinetics, Acta. Phys. Pol. B 35 (2004) 1323.] for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. In this letter we give the solution of the modified equation on an infinite domain. In contrast to the solution of the traditional fractional diffusion equation, the solution of the modified equation requires an infinite series of Fox functions instead of a single Fox function.

Facilitated Diffusion of Transcription Factor Proteins with Anomalous Bulk Diffusion.

PubMed

Liu, Lin; Cherstvy, Andrey G; Metzler, Ralf

2017-02-16

What are the physical laws of the diffusive search of proteins for their specific binding sites on DNA in the presence of the macromolecular crowding in cells? We performed extensive computer simulations to elucidate the protein target search on DNA. The novel feature is the viscoelastic non-Brownian protein bulk diffusion recently observed experimentally. We examine the influence of the protein-DNA binding affinity and the anomalous diffusion exponent on the target search time. In all cases an optimal search time is found. The relative contribution of intermittent three-dimensional bulk diffusion and one-dimensional sliding of proteins along the DNA is quantified. Our results are discussed in the light of recent single molecule tracking experiments, aiming at a better understanding of the influence of anomalous kinetics of proteins on the facilitated diffusion mechanism.

Influence of mass diffusion on the stability of thermophoretic growth of a solid from the vapor phase

NASA Technical Reports Server (NTRS)

Castillo, J. L.; Garcia-Ybarra, P. L.; Rosner, D. E.

1991-01-01

The stability of solid planar growth from a binary vapor phase with a condensing species dilute in a carrier gas is examined when the ratio of depositing to carrier species molecular mass is large and the main diffusive transport mechanism is thermal diffusion. It is shown that a deformation of the solid-gas interface induces a deformation of the gas phase isotherms that increases the thermal gradients and thereby the local mass deposition rate at the crests and reduces them at the valleys. The initial surface deformation is enhanced by the modified deposition rates in the absence of appreciable Fick/Brownian diffusion and interfacial energy effects.

Diffusion of torqued active particles

NASA Astrophysics Data System (ADS)

Sandoval, Mario; Lauga, Eric

2012-11-01

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

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

Feynman-Kac equation for anomalous processes with space- and time-dependent forces

NASA Astrophysics Data System (ADS)

Cairoli, Andrea; Baule, Adrian

2017-04-01

Functionals of a stochastic process Y(t) model many physical time-extensive observables, for instance particle positions, local and occupation times or accumulated mechanical work. When Y(t) is a normal diffusive process, their statistics are obtained as the solution of the celebrated Feynman-Kac equation. This equation provides the crucial link between the expected values of diffusion processes and the solutions of deterministic second-order partial differential equations. When Y(t) is non-Brownian, e.g. an anomalous diffusive process, generalizations of the Feynman-Kac equation that incorporate power-law or more general waiting time distributions of the underlying random walk have recently been derived. A general representation of such waiting times is provided in terms of a Lévy process whose Laplace exponent is directly related to the memory kernel appearing in the generalized Feynman-Kac equation. The corresponding anomalous processes have been shown to capture nonlinear mean square displacements exhibiting crossovers between different scaling regimes, which have been observed in numerous experiments on biological systems like migrating cells or diffusing macromolecules in intracellular environments. However, the case where both space- and time-dependent forces drive the dynamics of the generalized anomalous process has not been solved yet. Here, we present the missing derivation of the Feynman-Kac equation in such general case by using the subordination technique. Furthermore, we discuss its extension to functionals explicitly depending on time, which are of particular relevance for the stochastic thermodynamics of anomalous diffusive systems. Exact results on the work fluctuations of a simple non-equilibrium model are obtained. An additional aim of this paper is to provide a pedagogical introduction to Lévy processes, semimartingales and their associated stochastic calculus, which underlie the mathematical formulation of anomalous diffusion as a subordinated process.

Random Matrix Approach to Quantum Adiabatic Evolution Algorithms

NASA Technical Reports Server (NTRS)

Boulatov, Alexei; Smelyanskiy, Vadier N.

2004-01-01

We analyze the power of quantum adiabatic evolution algorithms (Q-QA) for solving random NP-hard optimization problems within a theoretical framework based on the random matrix theory (RMT). We present two types of the driven RMT models. In the first model, the driving Hamiltonian is represented by Brownian motion in the matrix space. We use the Brownian motion model to obtain a description of multiple avoided crossing phenomena. We show that the failure mechanism of the QAA is due to the interaction of the ground state with the "cloud" formed by all the excited states, confirming that in the driven RMT models. the Landau-Zener mechanism of dissipation is not important. We show that the QAEA has a finite probability of success in a certain range of parameters. implying the polynomial complexity of the algorithm. The second model corresponds to the standard QAEA with the problem Hamiltonian taken from the Gaussian Unitary RMT ensemble (GUE). We show that the level dynamics in this model can be mapped onto the dynamics in the Brownian motion model. However, the driven RMT model always leads to the exponential complexity of the algorithm due to the presence of the long-range intertemporal correlations of the eigenvalues. Our results indicate that the weakness of effective transitions is the leading effect that can make the Markovian type QAEA successful.

Diffusing diffusivity: Rotational diffusion in two and three dimensions

NASA Astrophysics Data System (ADS)

Jain, Rohit; Sebastian, K. L.

2017-06-01

We consider the problem of calculating the probability distribution function (pdf) of angular displacement for rotational diffusion in a crowded, rearranging medium. We use the diffusing diffusivity model and following our previous work on translational diffusion [R. Jain and K. L. Sebastian, J. Phys. Chem. B 120, 3988 (2016)], we show that the problem can be reduced to that of calculating the survival probability of a particle undergoing Brownian motion, in the presence of a sink. We use the approach to calculate the pdf for the rotational motion in two and three dimensions. We also propose new dimensionless, time dependent parameters, αr o t ,2 D and αr o t ,3 D, which can be used to analyze the experimental/simulation data to find the extent of deviation from the normal behavior, i.e., constant diffusivity, and obtain explicit analytical expressions for them, within our model.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Self-assembly of actin monomers into long filaments: Brownian dynamics simulations

NASA Astrophysics Data System (ADS)

Guo, Kunkun; Shillcock, Julian; Lipowsky, Reinhard

2009-07-01

Brownian dynamics simulations are used to study the dynamical process of self-assembly of actin monomers into long filaments containing up to 1000 actin protomers. In order to overcome the large separation of time scales between the diffusive motion of the free monomers and the relatively slow attachment and detachment processes at the two ends of the filaments, we introduce a novel rescaling procedure by which we speed all dynamical processes related to actin polymerization and depolymerization up by the same factor. In general, the actin protomers within a filament can attain three different states corresponding to a bound adenosine triphosphate (ATP), adenosine diphosphate with inorganic phosphate (ADP/P), and ADP molecule. The simplest situation that has been studied experimentally is provided by the polymerization of ADP-actin, for which all protomers are identical. This case is used to unravel certain relations between the filament's physical properties and the model parameters such as the attachment rate constant and the size of the capture zone, the detachment rate and the probability of the detached event, as well as the growth rate and waiting times between two successive attachment/detachment events. When a single filament is allowed to grow in a bath of constant concentration of free ADP-actin monomers, its growth rate increases linearly with the free monomer concentration in quantitative agreement with in vitro experiments. The results also show that the waiting time is governed by exponential distributions and that the two ends of a filament undergo biased random walks. The filament length fluctuations are described by a length diffusion constant that is found to attain a constant value at low ADP-actin concentration and to increase linearly with this concentration. It is straightforward to apply our simulation code to more complex processes such as polymerization of ATP-actin coupled to ATP hydrolysis, force generation by filaments, formation of filament bundles, and filament-membrane interactions.

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

From Lévy to Brownian: a computational model based on biological fluctuation.

PubMed

Nurzaman, Surya G; Matsumoto, Yoshio; Nakamura, Yutaka; Shirai, Kazumichi; Koizumi, Satoshi; Ishiguro, Hiroshi

2011-02-03

Theoretical studies predict that Lévy walks maximizes the chance of encountering randomly distributed targets with a low density, but Brownian walks is favorable inside a patch of targets with high density. Recently, experimental data reports that some animals indeed show a Lévy and Brownian walk movement patterns when forage for foods in areas with low and high density. This paper presents a simple, Gaussian-noise utilizing computational model that can realize such behavior. We extend Lévy walks model of one of the simplest creature, Escherichia coli, based on biological fluctuation framework. We build a simulation of a simple, generic animal to observe whether Lévy or Brownian walks will be performed properly depends on the target density, and investigate the emergent behavior in a commonly faced patchy environment where the density alternates. Based on the model, animal behavior of choosing Lévy or Brownian walk movement patterns based on the target density is able to be generated, without changing the essence of the stochastic property in Escherichia coli physiological mechanism as explained by related researches. The emergent behavior and its benefits in a patchy environment are also discussed. The model provides a framework for further investigation on the role of internal noise in realizing adaptive and efficient foraging behavior.

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.

On the contributions of diffusion and thermal activation to electron transfer between Phormidium laminosum plastocyanin and cytochrome f: Brownian dynamics simulations with explicit modeling of nonpolar desolvation interactions and electron transfer events.

PubMed

Gabdoulline, Razif R; Wade, Rebecca C

2009-07-08

The factors that determine the extent to which diffusion and thermal activation processes govern electron transfer (ET) between proteins are debated. The process of ET between plastocyanin (PC) and cytochrome f (CytF) from the cyanobacterium Phormidium laminosum was initially thought to be diffusion-controlled but later was found to be under activation control (Schlarb-Ridley, B. G.; et al. Biochemistry 2005, 44, 6232). Here we describe Brownian dynamics simulations of the diffusional association of PC and CytF, from which ET rates were computed using a detailed model of ET events that was applied to all of the generated protein configurations. The proteins were modeled as rigid bodies represented in atomic detail. In addition to electrostatic forces, which were modeled as in our previous simulations of protein-protein association, the proteins interacted by a nonpolar desolvation (hydrophobic) force whose derivation is described here. The simulations yielded close to realistic residence times of transient protein-protein encounter complexes of up to tens of microseconds. The activation barrier for individual ET events derived from the simulations was positive. Whereas the electrostatic interactions between P. laminosum PC and CytF are weak, simulations for a second cyanobacterial PC-CytF pair, that from Nostoc sp. PCC 7119, revealed ET rates influenced by stronger electrostatic interactions. In both cases, the simulations imply significant contributions to ET from both diffusion and thermal activation processes.

Thermophoresis of a Brownian particle driven by inhomogeneous thermal fluctuation

NASA Astrophysics Data System (ADS)

Tsuji, Tetsuro; Saita, Sho; Kawano, Satoyuki

2018-03-01

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

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

Binary data corruption due to a Brownian agent

NASA Astrophysics Data System (ADS)

Newman, T. J.; Triampo, Wannapong

1999-05-01

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

A Study of Brownian Motion Using Light Scattering

ERIC Educational Resources Information Center

Clark, Noel A.; And Others

1970-01-01

Presents an advanced laboratory experiment and lecture demonstration by which the intensity spectrum of light scattered by a suspension of particles in a fluid can be studied. From this spectrum, it is possible to obtain quantitative information about the motion of the particles, including an accurate determination of their diffusion constant.…

Convective-diffusion-based fluorescence correlation spectroscopy for detection of a trace amount of E. coli in water.

PubMed

Qing, De-Kui; Mengüç, M Pinar; Payne, Fred A; Danao, Mary-Grace C

2003-06-01

Fluorescence correlation spectroscopy (FCS) is adapted for a new procedure to detect trace amounts of Escherichia coli in water. The present concept is based on convective diffusion rather than Brownian diffusion and employs confocal microscopy as in traditional FCS. With this system it is possible to detect concentrations as small as 1.5 x 10(5) E. coli per milliliter (2.5 x 10(-16) M). This concentration corresponds to an approximately 1.0-nM level of Rhodamine 6G dyes. A detailed analysis of the optical system is presented, and further improvements for the procedure are discussed.

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

NASA Astrophysics Data System (ADS)

Hanasaki, Itsuo; Ooi, Yuto

2018-06-01

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

A novel Kinetic Monte Carlo algorithm for Non-Equilibrium Simulations

NASA Astrophysics Data System (ADS)

Jha, Prateek; Kuzovkov, Vladimir; Grzybowski, Bartosz; Olvera de La Cruz, Monica

2012-02-01

We have developed an off-lattice kinetic Monte Carlo simulation scheme for reaction-diffusion problems in soft matter systems. The definition of transition probabilities in the Monte Carlo scheme are taken identical to the transition rates in a renormalized master equation of the diffusion process and match that of the Glauber dynamics of Ising model. Our scheme provides several advantages over the Brownian dynamics technique for non-equilibrium simulations. Since particle displacements are accepted/rejected in a Monte Carlo fashion as opposed to moving particles following a stochastic equation of motion, nonphysical movements (e.g., violation of a hard core assumption) are not possible (these moves have zero acceptance). Further, the absence of a stochastic ``noise'' term resolves the computational difficulties associated with generating statistically independent trajectories with definitive mean properties. Finally, since the timestep is independent of the magnitude of the interaction forces, much longer time-steps can be employed than Brownian dynamics. We discuss the applications of this scheme for dynamic self-assembly of photo-switchable nanoparticles and dynamical problems in polymeric systems.

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

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.

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

PubMed Central

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

2010-01-01

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

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

PubMed

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

2010-04-21

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

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.

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

PubMed

Jannasch, Anita; Mahamdeh, Mohammed; Schäffer, Erik

2011-11-25

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

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.

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.

Fractional calculus in hydrologic modeling: A numerical perspective

PubMed Central

Benson, David A.; Meerschaert, Mark M.; Revielle, Jordan

2013-01-01

Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus. PMID:23524449

Book Review:

NASA Astrophysics Data System (ADS)

McKane, Alan

2003-12-01

This is a book about the modelling of complex systems and, unlike many books on this subject, concentrates on the discussion of specific systems and gives practical methods for modelling and simulating them. This is not to say that the author does not devote space to the general philosophy and definition of complex systems and agent-based modelling, but the emphasis is definitely on the development of concrete methods for analysing them. This is, in my view, to be welcomed and I thoroughly recommend the book, especially to those with a theoretical physics background who will be very much at home with the language and techniques which are used. The author has developed a formalism for understanding complex systems which is based on the Langevin approach to the study of Brownian motion. This is a mesoscopic description; details of the interactions between the Brownian particle and the molecules of the surrounding fluid are replaced by a randomly fluctuating force. Thus all microscopic detail is replaced by a coarse-grained description which encapsulates the essence of the interactions at the finer level of description. In a similar way, the influences on Brownian agents in a multi-agent system are replaced by stochastic influences which sum up the effects of these interactions on a finer scale. Unlike Brownian particles, Brownian agents are not structureless particles, but instead have some internal states so that, for instance, they may react to changes in the environment or to the presence of other agents. Most of the book is concerned with developing the idea of Brownian agents using the techniques of statistical physics. This development parallels that for Brownian particles in physics, but the author then goes on to apply the technique to problems in biology, economics and the social sciences. This is a clear and well-written book which is a useful addition to the literature on complex systems. It will be interesting to see if the use of Brownian agents becomes a standard tool in the study of complex systems in the future.

Mechanics of single cells: rheology, time dependence, and fluctuations.

PubMed

Massiera, Gladys; Van Citters, Kathleen M; Biancaniello, Paul L; Crocker, John C

2007-11-15

The results of mechanical measurements on single cultured epithelial cells using both magnetic twisting cytometry (MTC) and laser tracking microrheology (LTM) are described. Our unique approach uses laser deflection for high-performance tracking of cell-adhered magnetic beads either in response to an oscillatory magnetic torque (MTC) or due to random Brownian or ATP-dependent forces (LTM). This approach is well suited for accurately determining the rheology of single cells, the study of temporal and cell-to-cell variations in the MTC signal amplitude, and assessing the statistical character of the tracers' random motion in detail. The temporal variation of the MTC rocking amplitude is surprisingly large and manifests as a frequency-independent multiplicative factor having a 1/f spectrum in living cells, which disappears upon ATP depletion. In the epithelial cells we study, random bead position fluctuations are Gaussian to the limits of detection both in the Brownian and ATP-dependent cases, unlike earlier studies on other cell types.

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

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.

Structure-based molecular simulations reveal the enhancement of biased Brownian motions in single-headed kinesin.

PubMed

Kanada, Ryo; Kuwata, Takeshi; Kenzaki, Hiroo; Takada, Shoji

2013-01-01

Kinesin is a family of molecular motors that move unidirectionally along microtubules (MT) using ATP hydrolysis free energy. In the family, the conventional two-headed kinesin was experimentally characterized to move unidirectionally through "walking" in a hand-over-hand fashion by coordinated motions of the two heads. Interestingly a single-headed kinesin, a truncated KIF1A, still can generate a biased Brownian movement along MT, as observed by in vitro single molecule experiments. Thus, KIF1A must use a different mechanism from the conventional kinesin to achieve the unidirectional motions. Based on the energy landscape view of proteins, for the first time, we conducted a set of molecular simulations of the truncated KIF1A movements over an ATP hydrolysis cycle and found a mechanism exhibiting and enhancing stochastic forward-biased movements in a similar way to those in experiments. First, simulating stand-alone KIF1A, we did not find any biased movements, while we found that KIF1A with a large friction cargo-analog attached to the C-terminus can generate clearly biased Brownian movements upon an ATP hydrolysis cycle. The linked cargo-analog enhanced the detachment of the KIF1A from MT. Once detached, diffusion of the KIF1A head was restricted around the large cargo which was located in front of the head at the time of detachment, thus generating a forward bias of the diffusion. The cargo plays the role of a diffusional anchor, or cane, in KIF1A "walking."

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.

A spin echo sequence with a single-sided bipolar diffusion gradient pulse to obtain snapshot diffusion weighted images in moving media

NASA Astrophysics Data System (ADS)

Freidlin, R. Z.; Kakareka, J. W.; Pohida, T. J.; Komlosh, M. E.; Basser, P. J.

2012-08-01

In vivo MRI data can be corrupted by motion. Motion artifacts are particularly troublesome in Diffusion Weighted MRI (DWI), since the MR signal attenuation due to Brownian motion can be much less than the signal loss due to dephasing from other types of complex tissue motion, which can significantly degrade the estimation of self-diffusion coefficients, diffusion tensors, etc. This paper describes a snapshot DWI sequence, which utilizes a novel single-sided bipolar diffusion sensitizing gradient pulse within a spin echo sequence. The proposed method shortens the diffusion time by applying a single refocused bipolar diffusion gradient on one side of a refocusing RF pulse, instead of a set of diffusion sensitizing gradients, separated by a refocusing RF pulse, while reducing the impact of magnetic field inhomogeneity by using a spin echo sequence. A novel MRI phantom that can exhibit a range of complex motions was designed to demonstrate the robustness of the proposed DWI sequence.

Brownian relaxation of an inelastic sphere in air

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

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

2016-06-15

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

Single-Molecule Resolution of Antimicrobial Peptide Interactions with Supported Lipid A Bilayers.

PubMed

Nelson, Nathaniel; Schwartz, Daniel K

2018-06-05

The molecular interactions between antimicrobial peptides (AMPs) and lipid A-containing supported lipid bilayers were probed using single-molecule total internal reflection fluorescence microscopy. Hybrid supported lipid bilayers with lipid A outer leaflets and phospholipid (1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE)) inner leaflets were prepared and characterized, and the spatiotemporal trajectories of individual fluorescently labeled LL37 and Melittin AMPs were determined as they interacted with the bilayer surfaces comprising either monophosphoryl or diphosphoryl lipid A (from Escherichia coli) to determine the impact of electrostatic interactions. Large numbers of trajectories were obtained and analyzed to obtain the distributions of surface residence times and the statistics of the spatial trajectories. Interestingly, the AMP species were sensitive to subtle differences in the charge of the lipid, with both peptides diffusing more slowly and residing longer on the diphosphoryl lipid A. Furthermore, the single-molecule dynamics indicated a qualitative difference between the behavior of AMPs on hybrid Lipid A bilayers and on those composed entirely of DOPE. Whereas AMPs interacting with a DOPE bilayer exhibited two-dimensional Brownian diffusion with a diffusion coefficient of ∼1.7 μm 2 /s, AMPs adsorbed to the lipid A surface exhibited much slower apparent diffusion (on the order of ∼0.1 μm 2 /s) and executed intermittent trajectories that alternated between two-dimensional Brownian diffusion and desorption-mediated three-dimensional flights. Overall, these findings suggested that bilayers with lipid A in the outer leaflet, as it is in bacterial outer membranes, are valuable model systems for the study of the initial stage of AMP-bacterium interactions. Furthermore, single-molecule dynamics was sensitive to subtle differences in electrostatic interactions between cationic AMPs and monovalent or divalent anionic lipid A moieties. Copyright © 2018 Biophysical Society. All rights reserved.

On propagators of nonlocal relativistic diffusion of galactic cosmic rays

NASA Astrophysics Data System (ADS)

Uchaikin, V. V.; Sibatov, R. T.

2018-01-01

This report discusses a new model of cosmic ray propagation in the Galaxy. In contrast to the known models based on the principles of Brownian motion, the proposed model agrees with the relativistic principle of speed limitation and takes into account the large-scale turbulence of the interstellar medium, justifying introduction of fractional differential operators.

A Production Network Model and Its Diffusion Approximation.

DTIC Science & Technology

1982-09-01

ordinary Riemann-Stieltjes integrals. Proof. By making minor changes in the proof of the Kunita-Watanabe [91 change of variable formula it can be shown...n.) converges meakly to I, where X Is a Brownian motion wlth drift p and covarlance mtrx A - (ajj) djj b I! (41) aij 2 f Puj(a) do The proof of Lemna

Microcapsules ejecting nanosized species into the environment.

PubMed

De Geest, Bruno G; McShane, Michael J; Demeester, Jo; De Smedt, Stefaan C; Hennink, Wim E

2008-11-05

In this communication we report on microcapsules which eject nanoparticles into the environment. The speed of the nanoparticles ejected in water is approximately 800-fold faster than their Brownian diffusion. Such microcarriers may allow nanosized species to travel long distances, in short times, through highly viscous environments and may find applications in e.g. drug delivery and tissue engineering.

From Lévy to Brownian: A Computational Model Based on Biological Fluctuation

PubMed Central

Nurzaman, Surya G.; Matsumoto, Yoshio; Nakamura, Yutaka; Shirai, Kazumichi; Koizumi, Satoshi; Ishiguro, Hiroshi

2011-01-01

Background Theoretical studies predict that Lévy walks maximizes the chance of encountering randomly distributed targets with a low density, but Brownian walks is favorable inside a patch of targets with high density. Recently, experimental data reports that some animals indeed show a Lévy and Brownian walk movement patterns when forage for foods in areas with low and high density. This paper presents a simple, Gaussian-noise utilizing computational model that can realize such behavior. Methodology/Principal Findings We extend Lévy walks model of one of the simplest creature, Escherichia coli, based on biological fluctuation framework. We build a simulation of a simple, generic animal to observe whether Lévy or Brownian walks will be performed properly depends on the target density, and investigate the emergent behavior in a commonly faced patchy environment where the density alternates. Conclusions/Significance Based on the model, animal behavior of choosing Lévy or Brownian walk movement patterns based on the target density is able to be generated, without changing the essence of the stochastic property in Escherichia coli physiological mechanism as explained by related researches. The emergent behavior and its benefits in a patchy environment are also discussed. The model provides a framework for further investigation on the role of internal noise in realizing adaptive and efficient foraging behavior. PMID:21304911

Multiscale models and stochastic simulation methods for computing rare but key binding events in cell biology

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

Guerrier, C.; Holcman, D., E-mail: david.holcman@ens.fr; Mathematical Institute, Oxford OX2 6GG, Newton Institute

The main difficulty in simulating diffusion processes at a molecular level in cell microdomains is due to the multiple scales involving nano- to micrometers. Few to many particles have to be simulated and simultaneously tracked while there are exploring a large portion of the space for binding small targets, such as buffers or active sites. Bridging the small and large spatial scales is achieved by rare events representing Brownian particles finding small targets and characterized by long-time distribution. These rare events are the bottleneck of numerical simulations. A naive stochastic simulation requires running many Brownian particles together, which is computationallymore » greedy and inefficient. Solving the associated partial differential equations is also difficult due to the time dependent boundary conditions, narrow passages and mixed boundary conditions at small windows. We present here two reduced modeling approaches for a fast computation of diffusing fluxes in microdomains. The first approach is based on a Markov mass-action law equations coupled to a Markov chain. The second is a Gillespie's method based on the narrow escape theory for coarse-graining the geometry of the domain into Poissonian rates. The main application concerns diffusion in cellular biology, where we compute as an example the distribution of arrival times of calcium ions to small hidden targets to trigger vesicular release.« less

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.

Non-Brownian diffusion in lipid membranes: Experiments and simulations.

PubMed

Metzler, R; Jeon, J-H; Cherstvy, A G

2016-10-01

The dynamics of constituents and the surface response of cellular membranes-also in connection to the binding of various particles and macromolecules to the membrane-are still a matter of controversy in the membrane biophysics community, particularly with respect to crowded membranes of living biological cells. We here put into perspective recent single particle tracking experiments in the plasma membranes of living cells and supercomputing studies of lipid bilayer model membranes with and without protein crowding. Special emphasis is put on the observation of anomalous, non-Brownian diffusion of both lipid molecules and proteins embedded in the lipid bilayer. While single component, pure lipid bilayers in simulations exhibit only transient anomalous diffusion of lipid molecules on nanosecond time scales, the persistence of anomalous diffusion becomes significantly longer ranged on the addition of disorder-through the addition of cholesterol or proteins-and on passing of the membrane lipids to the gel phase. Concurrently, experiments demonstrate the anomalous diffusion of membrane embedded proteins up to macroscopic time scales in the minute time range. Particular emphasis will be put on the physical character of the anomalous diffusion, in particular, the occurrence of ageing observed in the experiments-the effective diffusivity of the measured particles is a decreasing function of time. Moreover, we present results for the time dependent local scaling exponent of the mean squared displacement of the monitored particles. Recent results finding deviations from the commonly assumed Gaussian diffusion patterns in protein crowded membranes are reported. The properties of the displacement autocorrelation function of the lipid molecules are discussed in the light of their appropriate physical anomalous diffusion models, both for non-crowded and crowded membranes. In the last part of this review we address the upcoming field of membrane distortion by elongated membrane-binding particles. We discuss how membrane compartmentalisation and the particle-membrane binding energy may impact the dynamics and response of lipid membranes. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.

Analysis of single quantum-dot mobility inside 1D nanochannel devices

NASA Astrophysics Data System (ADS)

Hoang, H. T.; Segers-Nolten, I. M.; Tas, N. R.; van Honschoten, J. W.; Subramaniam, V.; Elwenspoek, M. C.

2011-07-01

We visualized individual quantum dots using a combination of a confining nanochannel and an ultra-sensitive microscope system, equipped with a high numerical aperture lens and a highly sensitive camera. The diffusion coefficients of the confined quantum dots were determined from the experimentally recorded trajectories according to the classical diffusion theory for Brownian motion in two dimensions. The calculated diffusion coefficients were three times smaller than those in bulk solution. These observations confirm and extend the results of Eichmann et al (2008 Langmuir 24 714-21) to smaller particle diameters and more narrow confinement. A detailed analysis shows that the observed reduction in mobility cannot be explained by conventional hydrodynamic theory.

Anomalous Diffusion of Particles Dispersed in Xanthan Solutions Subjected to Shear Flow

NASA Astrophysics Data System (ADS)

Takikawa, Yoshinori; Yasuta, Muneharu; Fujii, Shuji; Orihara, Hiroshi; Tanaka, Yoshimi; Nishinari, Katsuyoshi

2018-05-01

Xanthan gum exhibits viscoelastic and shear-thinning properties. We investigate the Brownian motion of particles dispersed in xanthan gum solutions that are subjected to simple shear flow. The mean square displacements (MSDs) are obtained in both the flow and vorticity directions. In the absence of shear flow, subdiffusion is observed, MSD ∝ tα with α < 1, where t is time. In the presence of shear flow, however, the exponent α becomes larger together with the MSD itself in both the flow and vorticity directions. We show that the diffusion is enhanced by Taylor dispersion in the flow direction, whereas in the vorticity direction it is enhanced by nonthermal self-diffusion.

Active Brownian motion in a narrow channel

NASA Astrophysics Data System (ADS)

Ao, X.; Ghosh, P. K.; Li, Y.; Schmid, G.; Hänggi, P.; Marchesoni, F.

2014-12-01

We review recent advances in rectification control of artificial microswimmers, also known as Janus particles, diffusing along narrow, periodically corrugated channels. The swimmer self-propulsion mechanism is modeled so as to incorporate a nonzero torque (propulsion chirality). We first summarize the effects of chirality on the autonomous current of microswimmers freely diffusing in channels of different geometries. In particular, left-right and upside-down asymmetric channels are shown to exhibit different transport properties. We then report new results on the dependence of the diffusivity of chiral microswimmers on the channel geometry and their own self-propulsion mechanism. The self-propulsion torque turns out to play a key role as a transport control parameter.

Flow of nanofluid past a Riga plate

NASA Astrophysics Data System (ADS)

Ahmad, Adeel; Asghar, Saleem; Afzal, Sumaira

2016-03-01

This paper studies the mixed convection boundary layer flow of a nanofluid past a vertical Riga plate in the presence of strong suction. The mathematical model incorporates the Brownian motion and thermophoresis effects due to nanofluid and the Grinberg-term for the wall parallel Lorentz force due to Riga plate. The analytical solution of the problem is presented using the perturbation method for small Brownian and thermophoresis diffusion parameters. The numerical solution is also presented to ensure the reliability of the asymptotic method. The comparison of the two solutions shows an excellent agreement. The correlation expressions for skin friction, Nusselt number and Sherwood number are developed by performing linear regression on the obtained numerical data. The effects of nanofluid and the Lorentz force due to Riga plate, on the skin friction are discussed.

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.

Conditions for extreme sensitivity of protein diffusion in membranes to cell environments

PubMed Central

Tserkovnyak, Yaroslav; Nelson, David R.

2006-01-01

We study protein diffusion in multicomponent lipid membranes close to a rigid substrate separated by a layer of viscous fluid. The large-distance, long-time asymptotics for Brownian motion are calculated by using a nonlinear stochastic Navier–Stokes equation including the effect of friction with the substrate. The advective nonlinearity, neglected in previous treatments, gives only a small correction to the renormalized viscosity and diffusion coefficient at room temperature. We find, however, that in realistic multicomponent lipid mixtures, close to a critical point for phase separation, protein diffusion acquires a strong power-law dependence on temperature and the distance to the substrate H, making it much more sensitive to cell environment, unlike the logarithmic dependence on H and very small thermal correction away from the critical point. PMID:17008402

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.

On the genealogy of branching random walks and of directed polymers

NASA Astrophysics Data System (ADS)

Derrida, Bernard; Mottishaw, Peter

2016-08-01

It is well known that the mean-field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta functions. Here we show that the leading finite-size correction to this distribution of overlaps has a universal character which can be computed explicitly. Our results can also be interpreted as genealogical properties of branching Brownian motion or of branching random walks.

Stock market context of the Lévy walks with varying velocity

NASA Astrophysics Data System (ADS)

Kutner, Ryszard

2002-11-01

We developed the most general Lévy walks with varying velocity, shorter called the Weierstrass walks (WW) model, by which one can describe both stationary and non-stationary stochastic time series. We considered a non-Brownian random walk where the walker moves, in general, with a velocity that assumes a different constant value between the successive turning points, i.e., the velocity is a piecewise constant function. This model is a kind of Lévy walks where we assume a hierarchical, self-similar in a stochastic sense, spatio-temporal representation of the main quantities such as waiting-time distribution and sojourn probability density (which are principal quantities in the continuous-time random walk formalism). The WW model makes possible to analyze both the structure of the Hurst exponent and the power-law behavior of kurtosis. This structure results from the hierarchical, spatio-temporal coupling between the walker displacement and the corresponding time of the walks. The analysis uses both the fractional diffusion and the super Burnett coefficients. We constructed the diffusion phase diagram which distinguishes regions occupied by classes of different universality. We study only such classes which are characteristic for stationary situations. We thus have a model ready for describing the data presented, e.g., in the form of moving averages; the operation is often used for stochastic time series, especially financial ones. The model was inspired by properties of financial time series and tested for empirical data extracted from the Warsaw stock exchange since it offers an opportunity to study in an unbiased way several features of stock exchange in its early stage.

Maxima of two random walks: Universal statistics of lead changes

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

Ben-Naim, E.; Krapivsky, P. L.; Randon-Furling, J.

2016-04-18

In this study, we investigate statistics of lead changes of the maxima of two discrete-time random walks in one dimension. We show that the average number of lead changes grows asmore » $${\\pi }^{-1}\\mathrm{ln}t$$ in the long-time limit. We present theoretical and numerical evidence that this asymptotic behavior is universal. Specifically, this behavior is independent of the jump distribution: the same asymptotic underlies standard Brownian motion and symmetric Lévy flights. We also show that the probability to have at most n lead changes behaves as $${t}^{-1/4}{(\\mathrm{ln}t)}^{n}$$ for Brownian motion and as $${t}^{-\\beta (\\mu )}{(\\mathrm{ln}t)}^{n}$$ for symmetric Lévy flights with index μ. The decay exponent $$\\beta \\equiv \\beta (\\mu )$$ varies continuously with the Lévy index when $$0\\lt \\mu \\lt 2$$, and remains constant $$\\beta =1/4$$ for $$\\mu \\gt 2$$.« less

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

Shear-induced reversibility of 2D colloidal suspensions in the presence of minimal thermal noise.

PubMed

Farhadi, Somayeh; Arratia, Paulo E

2017-06-14

The effects of minimal thermal noise on particle rearrangements in cyclically sheared colloidal suspensions are experimentally investigated using particle tracking methods. Our experimental model system consists of polystyrene microspheres adsorbed at an oil-water interface, in which the particles exhibit small but non-negligible Brownian motion. Experiments are performed on bidisperse (1.0 and 1.2 μm in diameter) systems, which form area fractions of 0.20 and 0.32 at the interface. We first characterize the thermal (Brownian) noise using particle diffusivities at quiescent states, and show that under our experimental flow conditions both systems (0.20 and 0.32 area fraction) behave as athermal, in the sense that the particle diffusion time scale is larger than the flow time scale. We then characterize particle rearrangements as a function of strain amplitude, and show that small but finite levels of thermal noise affect the reversibility dynamics, even in effectively athermal systems. Our data indicate that as thermal noise is slightly increased in a cyclically sheared athermal system, the fraction of reversible rearrangements is reduced, the reversible cycles become unstable, and the rearrangement hysteresis is significantly hindered.

Prediction of the filtrate particle size distribution from the pore size distribution in membrane filtration: Numerical correlations from computer simulations

NASA Astrophysics Data System (ADS)

Marrufo-Hernández, Norma Alejandra; Hernández-Guerrero, Maribel; Nápoles-Duarte, José Manuel; Palomares-Báez, Juan Pedro; Chávez-Rojo, Marco Antonio

2018-03-01

We present a computational model that describes the diffusion of a hard spheres colloidal fluid through a membrane. The membrane matrix is modeled as a series of flat parallel planes with circular pores of different sizes and random spatial distribution. This model was employed to determine how the size distribution of the colloidal filtrate depends on the size distributions of both, the particles in the feed and the pores of the membrane, as well as to describe the filtration kinetics. A Brownian dynamics simulation study considering normal distributions was developed in order to determine empirical correlations between the parameters that characterize these distributions. The model can also be extended to other distributions such as log-normal. This study could, therefore, facilitate the selection of membranes for industrial or scientific filtration processes once the size distribution of the feed is known and the expected characteristics in the filtrate have been defined.

Stable Lévy motion with inverse Gaussian subordinator

NASA Astrophysics Data System (ADS)

Kumar, A.; Wyłomańska, A.; Gajda, J.

2017-09-01

In this paper we study the stable Lévy motion subordinated by the so-called inverse Gaussian process. This process extends the well known normal inverse Gaussian (NIG) process introduced by Barndorff-Nielsen, which arises by subordinating ordinary Brownian motion (with drift) with inverse Gaussian process. The NIG process found many interesting applications, especially in financial data description. We discuss here the main features of the introduced subordinated process, such as distributional properties, existence of fractional order moments and asymptotic tail behavior. We show the connection of the process with continuous time random walk. Further, the governing fractional partial differential equations for the probability density function is also obtained. Moreover, we discuss the asymptotic distribution of sample mean square displacement, the main tool in detection of anomalous diffusion phenomena (Metzler et al., 2014). In order to apply the stable Lévy motion time-changed by inverse Gaussian subordinator we propose a step-by-step procedure of parameters estimation. At the end, we show how the examined process can be useful to model financial time series.

Quantifying Multistate Cytoplasmic Molecular Diffusion in Bacterial Cells via Inverse Transform of Confined Displacement Distribution.

PubMed

Chen, Tai-Yen; Jung, Won; Santiago, Ace George; Yang, Feng; Krzemiński, Łukasz; Chen, Peng

2015-11-12

Single-molecule tracking (SMT) of fluorescently tagged cytoplasmic proteins can provide valuable information on the underlying biological processes in living cells via subsequent analysis of the displacement distributions; however, the confinement effect originated from the small size of a bacterial cell skews the protein's displacement distribution and complicates the quantification of the intrinsic diffusive behaviors. Using the inverse transformation method, we convert the skewed displacement distribution (for both 2D and 3D imaging conditions) back to that in free space for systems containing one or multiple (non)interconverting Brownian diffusion states, from which we can reliably extract the number of diffusion states as well as their intrinsic diffusion coefficients and respective fractional populations. We further demonstrate a successful application to experimental SMT data of a transcription factor in living E. coli cells. This work allows a direct quantitative connection between cytoplasmic SMT data with diffusion theory for analyzing molecular diffusive behavior in live bacteria.

Quantifying Multistate Cytoplasmic Molecular Diffusion in Bacterial Cells via Inverse Transform of Confined Displacement Distribution

PubMed Central

2016-01-01

Single-molecule tracking (SMT) of fluorescently tagged cytoplasmic proteins can provide valuable information on the underlying biological processes in living cells via subsequent analysis of the displacement distributions; however, the confinement effect originated from the small size of a bacterial cell skews the protein’s displacement distribution and complicates the quantification of the intrinsic diffusive behaviors. Using the inverse transformation method, we convert the skewed displacement distribution (for both 2D and 3D imaging conditions) back to that in free space for systems containing one or multiple (non)interconverting Brownian diffusion states, from which we can reliably extract the number of diffusion states as well as their intrinsic diffusion coefficients and respective fractional populations. We further demonstrate a successful application to experimental SMT data of a transcription factor in living E. coli cells. This work allows a direct quantitative connection between cytoplasmic SMT data with diffusion theory for analyzing molecular diffusive behavior in live bacteria. PMID:26491971

Fractional-calculus diffusion equation

PubMed Central

2010-01-01

Background Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. Conclusions The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis. PMID:20492677

Narrow Escape of Interacting Diffusing Particles

NASA Astrophysics Data System (ADS)

Agranov, Tal; Meerson, Baruch

2018-03-01

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

Brownian motion of electrons in time-dependent magnetic fields.

NASA Technical Reports Server (NTRS)

Iverson, G. J.; Williams, R. M.

1973-01-01

The behavior of a weakly ionized plasma in slowly varying time-dependent magnetic fields is studied through an extension of Williamson's stochastic theory. In particular, attention is focused on the properties of electron diffusion in the plane perpendicular to the direction of the magnetic field, when the field strength is large. It is shown that, in the strong field limit, the classical 1/B-squared dependence of the perpendicular diffusion coefficient is obtained for two models in which the field B(t) is monotonic in t and for two models in which B(t) possesses at least one turning point.

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.

Photoinduced diffusion molecular transport

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

Rozenbaum, Viktor M., E-mail: vik-roz@mail.ru, E-mail: litrakh@gmail.com; Dekhtyar, Marina L.; Lin, Sheng Hsien

2016-08-14

We consider a Brownian photomotor, namely, the directed motion of a nanoparticle in an asymmetric periodic potential under the action of periodic rectangular resonant laser pulses which cause charge redistribution in the particle. Based on the kinetics for the photoinduced electron redistribution between two or three energy levels of the particle, the time dependence of its potential energy is derived and the average directed velocity is calculated in the high-temperature approximation (when the spatial amplitude of potential energy fluctuations is small relative to the thermal energy). The thus developed theory of photoinduced molecular transport appears applicable not only to conventionalmore » dichotomous Brownian motors (with only two possible potential profiles) but also to a much wider variety of molecular nanomachines. The distinction between the realistic time dependence of the potential energy and that for a dichotomous process (a step function) is represented in terms of relaxation times (they can differ on the time intervals of the dichotomous process). As shown, a Brownian photomotor has the maximum average directed velocity at (i) large laser pulse intensities (resulting in short relaxation times on laser-on intervals) and (ii) excited state lifetimes long enough to permit efficient photoexcitation but still much shorter than laser-off intervals. A Brownian photomotor with optimized parameters is exemplified by a cylindrically shaped semiconductor nanocluster which moves directly along a polar substrate due to periodically photoinduced dipole moment (caused by the repetitive excited electron transitions to a non-resonant level of the nanocylinder surface impurity).« less

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.

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.

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.

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.

Three-dimensional nanoscale imaging by plasmonic Brownian microscopy

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Probing transcription factor diffusion dynamics in the living mammalian embryo with photoactivatable fluorescence correlation spectroscopy.

PubMed

Kaur, Gurpreet; Costa, Mauro W; Nefzger, Christian M; Silva, Juan; Fierro-González, Juan Carlos; Polo, Jose M; Bell, Toby D M; Plachta, Nicolas

2013-01-01

Transcription factors use diffusion to search the DNA, yet the mechanisms controlling transcription factor diffusion during mammalian development remain poorly understood. Here we combine photoactivation and fluorescence correlation spectroscopy to study transcription factor diffusion in developing mouse embryos. We show that the pluripotency-associated transcription factor Oct4 displays both fast and Brownian and slower subdiffusive behaviours that are controlled by DNA interactions. Following cell lineage specification, the slower DNA-interacting diffusion fraction distinguishes pluripotent from extraembryonic cell nuclei. Similar to Oct4, Sox2 shows slower diffusion in pluripotent cells while Cdx2 displays opposite dynamics, suggesting that slow diffusion may represent a general feature of transcription factors in lineages where they are essential. Slow Oct4 subdiffusive behaviours are conserved in embryonic stem cells and induced pluripotent stem cells (iPS cells), and lost during differentiation. We also show that Oct4 diffusion depends on its interaction with ERG-associated protein with SET domain. Photoactivation and fluorescence correlation spectroscopy provides a new intravital approach to study transcription factor diffusion in complex in vivo systems.

Fractional Progress Toward Understanding the Fractional Diffusion Limit: The Electromagnetic Response of Spatially Correlated Geomaterials

NASA Astrophysics Data System (ADS)

Weiss, C. J.; Beskardes, G. D.; Everett, M. E.

2016-12-01

In this presentation we review the observational evidence for anomalous electromagnetic diffusion in near-surface geophysical exploration and how such evidence is consistent with a detailed, spatially-correlated geologic medium. To date, the inference of multi-scale geologic correlation is drawn from two independent methods of data analysis. The first of which is analogous to seismic move-out, where the arrival time of an electromagnetic pulse is plotted as a function of transmitter/receiver separation. The "anomalous" diffusion is evident by the fractional-order power law behavior of these arrival times, with an exponent value between unity (pure diffusion) and 2 (lossless wave propagation). The second line of evidence comes from spectral analysis of small-scale fluctuations in electromagnetic profile data which cannot be explained in terms of instrument, user or random error. Rather, the power-law behavior of the spectral content of these signals (i.e., power versus wavenumber) and their increments reveals them to lie in a class of signals with correlations over multiple length scales, a class of signals known formally as fractional Brownian motion. Numerical results over simulated geology with correlated electrical texture - representative of, for example, fractures, sedimentary bedding or metamorphic lineation - are consistent with the (albeit limited, but growing) observational data, suggesting a possible mechanism and modeling approach for a more realistic geology. Furthermore, we show how similar simulated results can arise from a modeling approach where geologic texture is economically captured by a modified diffusion equation containing exotic, but manageable, fractional derivatives. These derivatives arise physically from the generalized convolutional form for the electromagnetic constitutive laws and thus have merit beyond mere mathematical convenience. In short, we are zeroing in on the anomalous, fractional diffusion limit from two converging directions: a zooming down of the macroscopic (fractional derivative) view; and, a heuristic homogenization of the atomistic (brute force discretization) view.

On the theory of Brownian motion with the Alder-Wainwright effect

NASA Astrophysics Data System (ADS)

Okabe, Yasunori

1986-12-01

The Stokes-Boussinesq-Langevin equation, which describes the time evolution of Brownian motion with the Alder-Wainwright effect, can be treated in the framework of the theory of KMO-Langevin equations which describe the time evolution of a real, stationary Gaussian process with T-positivity (reflection positivity) originating in axiomatic quantum field theory. After proving the fluctuation-dissipation theorems for KMO-Langevin equations, we obtain an explicit formula for the deviation from the classical Einstein relation that occurs in the Stokes-Boussinesq-Langevin equation with a white noise as its random force. We are interested in whether or not it can be measured experimentally.

Brownian Motion of Asymmetric Boomerang Colloidal Particles

NASA Astrophysics Data System (ADS)

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

2014-03-01

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

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

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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.

Mass Transfer and Rheology of Fiber Suspensions

NASA Astrophysics Data System (ADS)

Wang, Jianghui

Rheological and mass transfer properties of non-Brownian fiber suspensions are affected by fiber characteristics, fiber interactions, and processing conditions. In this thesis we develop several simulation methods to study the dynamics of single fibers in simple shear flow, as well as the rheology and mass transfer of fiber suspensions. Isolated, rigid, neutrally-buoyant, non-Brownian, slightly curved, nonchiral fibers in simple shear flow of an incompressible Newtonian fluid at low Reynolds number can drift steadily in the gradient direction without external forces or torques. The average drift velocity and direction depend on the fiber aspect ratio, curvature and initial orientation. The drift results from the coupling of rotational and translational dynamics, and the combined effects of flipping, scooping, and spinning motions of the fiber. Irreversible fiber collisions in the suspensions cause shear-induced diffusion. The shear-induced self-diffusivity of dilute suspensions of fibers increases with increasing concentration and increasing static friction between contacts. The diffusivities in both the gradient and vorticity directions are larger for suspensions of curved fibers than for suspensions of straight fibers. For suspensions of curved fibers, significant enhancements in the diffusivity in the gradient direction are attributed to fiber drift in the gradient direction. The shear-induced self-diffusivity of concentrated suspensions of fibers increases with increasing concentration before fiber networks or flocs are formed, after which the diffusivity decreases with increasing concentration. The diffusivity increases with increasing fiber equilibrium bending angle, effective stiffness, coefficient of static friction, and rate of collisions. The specific viscosity of fiber suspensions increases with increasing fiber curvature, friction coefficient between mechanical contacts, and solids concentration. The specific viscosity increases linearly with concentration in the dilute regime, and increases with the cube of the concentration in the semi-dilute regime. Concentrated fiber suspensions are highly viscous, shear thinning, and exhibit significant yield stresses and normal stress differences. Yield stresses scale with volume concentration and fiber aspect ratio in the same way as that observed in experiments. The first normal stress difference increases linearly with shear rate. The shear-induced diffusivity increases linearly with the derivative of the particle contribution to stress for dilute suspensions with respective to concentration. This correlation between rheology and shear-induced diffusion makes it possible to predict diffusivity from easily measured rheological properties.

Optimized green fluorescent protein fused to FoF1-ATP synthase for single-molecule FRET using a fast anti-Brownian electrokinetic trap

NASA Astrophysics Data System (ADS)

Dienerowitz, Maria; Ilchenko, Mykhailo; Su, Bertram; Deckers-Hebestreit, Gabriele; Mayer, Günter; Henkel, Thomas; Heitkamp, Thomas; Börsch, Michael

2016-02-01

Observation times of freely diffusing single molecules in solution are limited by the photophysics of the attached fluorescence markers and by a small observation volume in the femtolitre range that is required for a sufficient signal-to-background ratio. To extend diffusion-limited observation times through a confocal detection volume, A. E. Cohen and W. E. Moerner have invented and built the ABELtrap -- a microfluidic device to actively counteract Brownian motion of single nanoparticles with an electrokinetic trap. Here we present a version of an ABELtrap with a laser focus pattern generated by electro-optical beam deflectors and controlled by a programmable FPGA chip. This ABELtrap holds single fluorescent nanoparticles for more than 100 seconds, increasing the observation time of fluorescent nanoparticles compared to free diffusion by a factor of 10000. To monitor conformational changes of individual membrane proteins in real time, we record sequential distance changes between two specifically attached dyes using Förster resonance energy transfer (smFRET). Fusing the a-subunit of the FoF1-ATP synthase with mNeonGreen results in an improved signal-to-background ratio at lower laser excitation powers. This increases our measured trap duration of proteoliposomes beyond 2 s. Additionally, we observe different smFRET levels attributed to varying distances between the FRET donor (mNeonGreen) and acceptor (Alexa568) fluorophore attached at the a- and c-subunit of the FoF1-ATP synthase respectively.

Electrostatic steering and ionic tethering in enzyme–ligand binding: Insights from simulations

PubMed Central

Wade, Rebecca C.; Gabdoulline, Razif R.; Lüdemann, Susanna K.; Lounnas, Valère

1998-01-01

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 β-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. PMID:9600896

Crowding Induces Complex Ergodic Diffusion and Dynamic Elongation of Large DNA Molecules

PubMed Central

Chapman, Cole D.; Gorczyca, Stephanie; Robertson-Anderson, Rae M.

2015-01-01

Despite the ubiquity of molecular crowding in living cells, the effects of crowding on the dynamics of genome-sized DNA are poorly understood. Here, we track single, fluorescent-labeled large DNA molecules (11, 115 kbp) diffusing in dextran solutions that mimic intracellular crowding conditions (0–40%), and determine the effects of crowding on both DNA mobility and conformation. Both DNAs exhibit ergodic Brownian motion and comparable mobility reduction in all conditions; however, crowder size (10 vs. 500 kDa) plays a critical role in the underlying diffusive mechanisms and dependence on crowder concentration. Surprisingly, in 10-kDa dextran, crowder influence saturates at ∼20% with an ∼5× drop in DNA diffusion, in stark contrast to exponentially retarded mobility, coupled to weak anomalous subdiffusion, with increasing concentration of 500-kDa dextran. Both DNAs elongate into lower-entropy states (compared to random coil conformations) when crowded, with elongation states that are gamma distributed and fluctuate in time. However, the broadness of the distribution of states and the time-dependence and length scale of elongation length fluctuations depend on both DNA and crowder size with concentration having surprisingly little impact. Results collectively show that mobility reduction and coil elongation of large crowded DNAs are due to a complex interplay between entropic effects and crowder mobility. Although elongation and initial mobility retardation are driven by depletion interactions, subdiffusive dynamics, and the drastic exponential slowing of DNA, up to ∼300×, arise from the reduced mobility of larger crowders. Our results elucidate the highly important and widely debated effects of cellular crowding on genome-sized DNA. PMID:25762333

Analytical approximations for spatial stochastic gene expression in single cells and tissues

PubMed Central

Smith, Stephen; Cianci, Claudia; Grima, Ramon

2016-01-01

Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared with their deterministic counterparts, and hence little is currently known of the significance of intrinsic noise in a spatial setting. Starting from the reaction–diffusion master equation (RDME) describing stochastic reaction–diffusion processes, we here derive expressions for the approximate steady-state mean concentrations which are explicit functions of the dimensionality of space, rate constants and diffusion coefficients. The expressions have a simple closed form when the system consists of one effective species. These formulae show that, even for spatially homogeneous systems, mean concentrations can depend on diffusion coefficients: this contradicts the predictions of deterministic reaction–diffusion processes, thus highlighting the importance of intrinsic noise. We confirm our theory by comparison with stochastic simulations, using the RDME and Brownian dynamics, of two models of stochastic and spatial gene expression in single cells and tissues. PMID:27146686

Anomalous Diffusion of Water in Lamellar Membranes Formed by Pluronic Polymers

NASA Astrophysics Data System (ADS)

Zhang, Zhe; Ohl, Michael; Han, Youngkyu; Smith, Gregory; Do, Changwoo; Biology; Soft-Matter Division, Oak Ridge National Laboratory Team; Julich CenterNeutron Science Team

Water diffusion is playing an important role in polymer systems. We calculated the water diffusion coefficient at different layers along z-direction which is perpendicular to the lamellar membrane formed by Pluronic block copolymers (L62: (EO6-PO34-EO6)) with the molecular dynamics simulation trajectories. Water molecules at bulk layers are following the normal diffusion, while that at hydration layers formed by polyethylene oxide (PEO) and hydrophobic layers formed by polypropylene oxide (PPO) are following anomalous diffusion. We find that although the subdiffusive regimes at PEO layers and PPO layers are the same, which is the fractional Brownian motion, however, the dynamics are different, i.e. diffusion at the PEO layers is much faster than that at the PPO layers, and meanwhile it exhibits a normal diffusive approximation within a short time period which is governed by the localized free self-diffusion, but becomes subdiffusive after t >8 ps, which is governed by the viscoelastic medium. The Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy; and Zhe Zhang gratefully acknowledges financial support from Julich Center for Neutron Science.

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

Dynamic interactions between a membrane binding protein and lipids induce fluctuating diffusivity

PubMed Central

Yamamoto, Eiji; Akimoto, Takuma; Kalli, Antreas C.; Yasuoka, Kenji; Sansom, Mark S. P.

2017-01-01

Pleckstrin homology (PH) domains are membrane-binding lipid recognition proteins that interact with phosphatidylinositol phosphate (PIP) molecules in eukaryotic cell membranes. Diffusion of PH domains plays a critical role in biological reactions on membrane surfaces. Although diffusivity can be estimated by long-time measurements, it lacks information on the short-time diffusive nature. We reveal two diffusive properties of a PH domain bound to the surface of a PIP-containing membrane using molecular dynamics simulations. One is fractional Brownian motion, attributed to the motion of the lipids with which the PH domain interacts. The other is temporally fluctuating diffusivity; that is, the short-time diffusivity of the bound protein changes substantially with time. Moreover, the diffusivity for short-time measurements is intrinsically different from that for long-time measurements. This fluctuating diffusivity results from dynamic changes in interactions between the PH domain and PIP molecules. Our results provide evidence that the complexity of protein-lipid interactions plays a crucial role in the diffusion of proteins on biological membrane surfaces. Changes in the diffusivity of PH domains and related membrane-bound proteins may in turn contribute to the formation/dissolution of protein complexes in membranes. PMID:28116358

Generalized Riemann hypothesis and stochastic time series

NASA Astrophysics Data System (ADS)

Mussardo, Giuseppe; LeClair, André

2018-06-01

Using the Dirichlet theorem on the equidistribution of residue classes modulo q and the Lemke Oliver–Soundararajan conjecture on the distribution of pairs of residues on consecutive primes, we show that the domain of convergence of the infinite product of Dirichlet L-functions of non-principal characters can be extended from down to , without encountering any zeros before reaching this critical line. The possibility of doing so can be traced back to a universal diffusive random walk behavior of a series C N over the primes which underlies the convergence of the infinite product of the Dirichlet functions. The series C N presents several aspects in common with stochastic time series and its control requires to address a problem similar to the single Brownian trajectory problem in statistical mechanics. In the case of the Dirichlet functions of non principal characters, we show that this problem can be solved in terms of a self-averaging procedure based on an ensemble of block variables computed on extended intervals of primes. Those intervals, called inertial intervals, ensure the ergodicity and stationarity of the time series underlying the quantity C N . The infinity of primes also ensures the absence of rare events which would have been responsible for a different scaling behavior than the universal law of the random walks.

Fractional Brownian motion and multivariate-t models for longitudinal biomedical data, with application to CD4 counts in HIV-positive patients.

PubMed

Stirrup, Oliver T; Babiker, Abdel G; Carpenter, James R; Copas, Andrew J

2016-04-30

Longitudinal data are widely analysed using linear mixed models, with 'random slopes' models particularly common. However, when modelling, for example, longitudinal pre-treatment CD4 cell counts in HIV-positive patients, the incorporation of non-stationary stochastic processes such as Brownian motion has been shown to lead to a more biologically plausible model and a substantial improvement in model fit. In this article, we propose two further extensions. Firstly, we propose the addition of a fractional Brownian motion component, and secondly, we generalise the model to follow a multivariate-t distribution. These extensions are biologically plausible, and each demonstrated substantially improved fit on application to example data from the Concerted Action on SeroConversion to AIDS and Death in Europe study. We also propose novel procedures for residual diagnostic plots that allow such models to be assessed. Cohorts of patients were simulated from the previously reported and newly developed models in order to evaluate differences in predictions made for the timing of treatment initiation under different clinical management strategies. A further simulation study was performed to demonstrate the substantial biases in parameter estimates of the mean slope of CD4 decline with time that can occur when random slopes models are applied in the presence of censoring because of treatment initiation, with the degree of bias found to depend strongly on the treatment initiation rule applied. Our findings indicate that researchers should consider more complex and flexible models for the analysis of longitudinal biomarker data, particularly when there are substantial missing data, and that the parameter estimates from random slopes models must be interpreted with caution. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Memoryless control of boundary concentrations of diffusing particles.

PubMed

Singer, A; Schuss, Z; Nadler, B; Eisenberg, R S

2004-12-01

Flux between regions of different concentration occurs in nearly every device involving diffusion, whether an electrochemical cell, a bipolar transistor, or a protein channel in a biological membrane. Diffusion theory has calculated that flux since the time of Fick (1855), and the flux has been known to arise from the stochastic behavior of Brownian trajectories since the time of Einstein (1905), yet the mathematical description of the behavior of trajectories corresponding to different types of boundaries is not complete. We consider the trajectories of noninteracting particles diffusing in a finite region connecting two baths of fixed concentrations. Inside the region, the trajectories of diffusing particles are governed by the Langevin equation. To maintain average concentrations at the boundaries of the region at their values in the baths, a control mechanism is needed to set the boundary dynamics of the trajectories. Different control mechanisms are used in Langevin and Brownian simulations of such systems. We analyze models of controllers and derive equations for the time evolution and spatial distribution of particles inside the domain. Our analysis shows a distinct difference between the time evolution and the steady state concentrations. While the time evolution of the density is governed by an integral operator, the spatial distribution is governed by the familiar Fokker-Planck operator. The boundary conditions for the time dependent density depend on the model of the controller; however, this dependence disappears in the steady state, if the controller is of a renewal type. Renewal-type controllers, however, produce spurious boundary layers that can be catastrophic in simulations of charged particles, because even a tiny net charge can have global effects. The design of a nonrenewal controller that maintains concentrations of noninteracting particles without creating spurious boundary layers at the interface requires the solution of the time-dependent Fokker-Planck equation with absorption of outgoing trajectories and a source of ingoing trajectories on the boundary (the so called albedo problem).

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

PubMed

Sanders, Lloyd P; Ambjörnsson, Tobias

2012-05-07

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

Determination of the hydrodynamic friction matrix for various anisotropic particles

NASA Astrophysics Data System (ADS)

Kraft, Daniela; Wittkowksi, Raphael; Löwen, Hartmut; Pine, David

2013-03-01

The relationship between the shape of a colloidal particle and its Brownian motion can be captured by the hydrodynamic friction matrix. It fully describes the translational and rotational diffusion along the particle's main axes as well as the coupling between rotational and translational diffusion. We observed a wide variety of anisotropic colloidal particles with confocal microscopy and calculated the hydrodynamic friction matrix from the particle trajectories. We find that symmetries in the particle shape are reflected in the entries of the friction matrix. We compare our experimentally obtained results with numerical simulations and theoretical predictions. Financial support through a Rubicon grant by the Netherlands Organisation for Scientific Research.

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.

A renewal jump-diffusion process with threshold dividend strategy

NASA Astrophysics Data System (ADS)

Li, Bo; Wu, Rong; Song, Min

2009-06-01

In this paper, we consider a jump-diffusion risk process with the threshold dividend strategy. Both the distributions of the inter-arrival times and the claims are assumed to be in the class of phase-type distributions. The expected discounted dividend function and the Laplace transform of the ruin time are discussed. Motivated by Asmussen [S. Asmussen, Stationary distributions for fluid flow models with or without Brownian noise, Stochastic Models 11 (1) (1995) 21-49], instead of studying the original process, we study the constructed fluid flow process and their closed-form formulas are obtained in terms of matrix expression. Finally, numerical results are provided to illustrate the computation.

Cattaneo-Christov double-diffusion theory for three-dimensional flow of viscoelastic nanofluid with the effect of heat generation/absorption

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Qayyum, Sajid; Shehzad, Sabir Ali; Alsaedi, Ahmed

2018-03-01

The present research article focuses on three-dimensional flow of viscoelastic(second grade) nanofluid in the presence of Cattaneo-Christov double-diffusion theory. Flow caused is due to stretching sheet. Characteristics of heat transfer are interpreted by considering the heat generation/absorption. Nanofluid theory comprises of Brownian motion and thermophoresis. Cattaneo-Christov double-diffusion theory is introduced in the energy and concentration expressions. Such diffusions are developed as a part of formulating the thermal and solutal relaxation times framework. Suitable variables are implemented for the conversion of partial differential systems into a sets of ordinary differential equations. The transformed expressions have been explored through homotopic algorithm. Behavior of sundry variables on the velocities, temperature and concentration are scrutinized graphically. Numerical values of skin friction coefficients are also calculated and examined. Here thermal field enhances for heat generation parameter while reverse situation is noticed for heat absorption parameter.

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

NASA Astrophysics Data System (ADS)

Long, Fei; Zhu, Jia-Pei

2018-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2007-01-01

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

Noisy swimming at low Reynolds numbers.

PubMed

Dunkel, Jörn; Zaid, Irwin M

2009-08-01

Small organisms (e.g., bacteria) and artificial microswimmers move due to a combination of active swimming and passive Brownian motion. Considering a simplified linear three-sphere swimmer, we study how the swimmer size regulates the interplay between self-driven and diffusive behavior at low Reynolds number. Starting from the Kirkwood-Smoluchowski equation and its corresponding Langevin equation, we derive formulas for the orientation correlation time, the mean velocity and the mean-square displacement in three space dimensions. The validity of the analytical results is illustrated through numerical simulations. Tuning the swimmer parameters to values that are typical of bacteria, we find three characteristic regimes: (i) Brownian motion at small times, (ii) quasiballistic behavior at intermediate time scales, and (iii) quasidiffusive behavior at large times due to noise-induced rotation. Our analytical results can be useful for a better quantitative understanding of optimal foraging strategies in bacterial systems, and they can help to construct more efficient artificial microswimmers in fluctuating fluids.

Numerical modeling of time-dependent bio-convective stagnation flow of a nanofluid in slip regime

NASA Astrophysics Data System (ADS)

Kumar, Rakesh; Sood, Shilpa; Shehzad, Sabir Ali; Sheikholeslami, Mohsen

A numerical investigation of unsteady stagnation point flow of bioconvective nanofluid due to an exponential deforming surface is made in this research. The effects of Brownian diffusion, thermophoresis, slip velocity and thermal jump are incorporated in the nanofluid model. By utilizing similarity transformations, the highly nonlinear partial differential equations governing present nano-bioconvective boundary layer phenomenon are reduced into ordinary differential system. The resultant expressions are solved for numerical solution by employing a well-known implicit finite difference approach termed as Keller-box method (KBM). The influence of involved parameters (unsteadiness, bioconvection Schmidt number, velocity slip, thermal jump, thermophoresis, Schmidt number, Brownian motion, bioconvection Peclet number) on the distributions of velocity, temperature, nanoparticle and motile microorganisms concentrations, the coefficient of local skin-friction, rate of heat transport, Sherwood number and local density motile microorganisms are exhibited through graphs and tables.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-11-01

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

A fractal process of hydrogen diffusion in a-Si:H with exponential energy distribution

NASA Astrophysics Data System (ADS)

Hikita, Harumi; Ishikawa, Hirohisa; Morigaki, Kazuo

2017-04-01

Hydrogen diffusion in a-Si:H with exponential distribution of the states in energy exhibits the fractal structure. It is shown that a probability P(t) of the pausing time t has a form of tα (α: fractal dimension). It is shown that the fractal dimension α = Tr/T0 (Tr: hydrogen temperature, T0: a temperature corresponding to the width of exponential distribution of the states in energy) is in agreement with the Hausdorff dimension. A fractal graph for the case of α ≤ 1 is like the Cantor set. A fractal graph for the case of α > 1 is like the Koch curves. At α = ∞, hydrogen migration exhibits Brownian motion. Hydrogen diffusion in a-Si:H should be the fractal process.

Osmotic propulsion: the osmotic motor.

PubMed

Córdova-Figueroa, Ubaldo M; Brady, John F

2008-04-18

A model for self-propulsion of a colloidal particle--the osmotic motor--immersed in a dispersion of "bath" particles is presented. The nonequilibrium concentration of bath particles induced by a surface chemical reaction creates an osmotic pressure imbalance on the motor causing it to move. The ratio of the speed of reaction to that of diffusion governs the bath particle distribution which is employed to calculate the driving force on the motor, and from which the self-induced osmotic velocity is determined. For slow reactions, the self-propulsion is proportional to the reaction velocity. When surface reaction dominates over diffusion the osmotic velocity cannot exceed the diffusive speed of the bath particles. Implications of these features for different bath particle volume fractions and motor sizes are discussed. Theoretical predictions are compared with Brownian dynamics simulations.

Fluorescence Correlation Spectroscopy to Study Diffusion of Polymer Chains within Layered Hydrogen-Bonded Polymer Films

NASA Astrophysics Data System (ADS)

Pristinski, Denis; Kharlampieva, Evguenia; Sukhishvili, Svetlana

2002-03-01

Fluorescence Correlation Spectroscopy (FCS) has been used to probe molecular motions within polymer multilayers formed by hydrogen-bonding sequential self-assembly. Polyethylene glycol (PEG) molecules were end-labeled with the fluorescent tags, and self-assembled with polymethacrylic acid (PMAA) using layer-by-layer deposition. We have found that molecules included in the top adsorbed layer have significant mobility at the millisecond time scale, probably due to translational diffusion. However, their dynamics deviate from classical Brownian motion with a single diffusion time. Possible reasons for the deviation are discussed. We found that motions were significantly slowed with increasing depth within the PEG/PMAA multilayer. This phenomena occured in a narrow pH range around 4.0 in which intermolecular interactions were relatively weak.

Osmotic Propulsion: The Osmotic Motor

NASA Astrophysics Data System (ADS)

Córdova-Figueroa, Ubaldo M.; Brady, John F.

2008-04-01

A model for self-propulsion of a colloidal particle—the osmotic motor—immersed in a dispersion of “bath” particles is presented. The nonequilibrium concentration of bath particles induced by a surface chemical reaction creates an osmotic pressure imbalance on the motor causing it to move. The ratio of the speed of reaction to that of diffusion governs the bath particle distribution which is employed to calculate the driving force on the motor, and from which the self-induced osmotic velocity is determined. For slow reactions, the self-propulsion is proportional to the reaction velocity. When surface reaction dominates over diffusion the osmotic velocity cannot exceed the diffusive speed of the bath particles. Implications of these features for different bath particle volume fractions and motor sizes are discussed. Theoretical predictions are compared with Brownian dynamics simulations.

Nonequilibrium Chromosome Looping via Molecular Slip Links

NASA Astrophysics Data System (ADS)

Brackley, C. A.; Johnson, J.; Michieletto, D.; Morozov, A. N.; Nicodemi, M.; Cook, P. R.; Marenduzzo, D.

2017-09-01

We propose a model for the formation of chromatin loops based on the diffusive sliding of molecular slip links. These mimic the behavior of molecules like cohesin, which, along with the CTCF protein, stabilize loops which contribute to organizing the genome. By combining 3D Brownian dynamics simulations and 1D exactly solvable nonequilibrium models, we show that diffusive sliding is sufficient to account for the strong bias in favor of convergent CTCF-mediated chromosome loops observed experimentally. We also find that the diffusive motion of multiple slip links along chromatin is rectified by an intriguing ratchet effect that arises if slip links bind to the chromatin at a preferred "loading site." This emergent collective behavior favors the extrusion of loops which are much larger than the ones formed by single slip links.

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

Characterization of Stationary Distributions of Reflected Diffusions

DTIC Science & Technology

2014-01-01

Reiman , M. I. (2003). Fluid and heavy traffic limits for a generalized processor sharing model. Ann. Appl. Probab., 13, 100-139. [37] Ramanan, K. and... Reiman , M. I. (2008). The heavy traffic limit of an unbalanced generalized processor sharing model. Ann. Appl. Probab., 18, 22-58. [38] Reed, J. and...Control and Computing. [39] Reiman , M. I. and Williams, R. J. (1988). A boundary property of semimartingale reflecting Brownian motions. Probab. Theor

The effect of shear flow on the rotational diffusivity of a single axisymmetric particle

NASA Astrophysics Data System (ADS)

Leahy, Brian; Koch, Donald; Cohen, Itai

2014-11-01

Colloidal suspensions of nonspherical particles abound in the world around us, from red blood cells in arteries to kaolinite discs in clay. Understanding the orientation dynamics of these particles is important for suspension rheology and particle self-assembly. However, even for the simplest case of dilute suspensions in simple shear flow, the orientation dynamics of Brownian nonspherical particles are poorly understood at large shear rates. Here, we analytically calculate the time-dependent orientation distributions of particles confined to the flow-gradient plane when the rotary diffusion is small but nonzero. For both startup and oscillatory shear flows, we find a coordinate change that maps the convection-diffusion equation to a simple diffusion equation with an enhanced diffusion constant, simplifying the orientation dynamics. For oscillatory shear, this enhanced diffusion drastically alters the quasi-steady orientation distributions. Our theory of the unsteady orientation dynamics provides an understanding of a nonspherical particle suspension's rheology for a large class of unsteady flows. For particles with aspect ratio 10 under oscillatory shear, the rotary diffusion and intrinsic viscosity vary with amplitude by a factor of ~ 40 and ~ 2 , respectively.

Diffusion of multiple species with excluded-volume effects.

PubMed

Bruna, Maria; Chapman, S Jonathan

2012-11-28

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial differential equations. In this paper we consider multiple interacting subpopulations/species and study how the inter-species competition emerges at the population level. Each individual is described as a finite-size hard core interacting particle undergoing brownian motion. The link between the discrete stochastic equations of motion and the continuum model is considered systematically using the method of matched asymptotic expansions. The system for two species leads to a nonlinear cross-diffusion system for each subpopulation, which captures the enhancement of the effective diffusion rate due to excluded-volume interactions between particles of the same species, and the diminishment due to particles of the other species. This model can explain two alternative notions of the diffusion coefficient that are often confounded, namely collective diffusion and self-diffusion. Simulations of the discrete system show good agreement with the analytic results.

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

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

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.

Rolling and aging in temperature-ramp soft adhesion

NASA Astrophysics Data System (ADS)

Boniello, Giuseppe; Tribet, Christophe; Marie, Emmanuelle; Croquette, Vincent; Zanchi, Dražen

2018-01-01

Immediately before adsorption to a horizontal substrate, sinking polymer-coated colloids can undergo a complex sequence of landing, jumping, crawling, and rolling events. Using video tracking, we studied the soft adhesion to a horizontal flat plate of micron-size colloids coated by a controlled molar fraction f of the poly(lysine)-grafted-poly(N-isopropylacrylamide) (PLL-g-PNIPAM) which is a temperature-sensitive polymer. We ramp the temperature from below to above Tc=32 ±1∘C , at which the PNIPAM polymer undergoes a transition, triggering attractive interaction between microparticles and surface. The adsorption rate, the effective in-plane (x -y ) diffusion constant, and the average residence time distribution over z were extracted from the Brownian motion records during last seconds before immobilization. Experimental data are understood within a rate-equations-based model that includes aging effects and includes three populations: the untethered, the rolling, and the arrested colloids. We show that preadsorption dynamics casts a characteristic scaling function α (f ) proportional to the number of available PNIPAM patches met by soft contact during Brownian rolling. In particular, the increase of in-plane diffusivity with increasing f is understood: The stickiest particles have the shortest rolling regime prior to arrest, so that their motion is dominated by the untethered phase.

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.

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

A General Model for Estimating Macroevolutionary Landscapes.

PubMed

Boucher, Florian C; Démery, Vincent; Conti, Elena; Harmon, Luke J; Uyeda, Josef

2018-03-01

The evolution of quantitative characters over long timescales is often studied using stochastic diffusion models. The current toolbox available to students of macroevolution is however limited to two main models: Brownian motion and the Ornstein-Uhlenbeck process, plus some of their extensions. Here, we present a very general model for inferring the dynamics of quantitative characters evolving under both random diffusion and deterministic forces of any possible shape and strength, which can accommodate interesting evolutionary scenarios like directional trends, disruptive selection, or macroevolutionary landscapes with multiple peaks. This model is based on a general partial differential equation widely used in statistical mechanics: the Fokker-Planck equation, also known in population genetics as the Kolmogorov forward equation. We thus call the model FPK, for Fokker-Planck-Kolmogorov. We first explain how this model can be used to describe macroevolutionary landscapes over which quantitative traits evolve and, more importantly, we detail how it can be fitted to empirical data. Using simulations, we show that the model has good behavior both in terms of discrimination from alternative models and in terms of parameter inference. We provide R code to fit the model to empirical data using either maximum-likelihood or Bayesian estimation, and illustrate the use of this code with two empirical examples of body mass evolution in mammals. FPK should greatly expand the set of macroevolutionary scenarios that can be studied since it opens the way to estimating macroevolutionary landscapes of any conceivable shape. [Adaptation; bounds; diffusion; FPK model; macroevolution; maximum-likelihood estimation; MCMC methods; phylogenetic comparative data; selection.].

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

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.

Anomalous transport in the crowded world of biological cells

NASA Astrophysics Data System (ADS)

Höfling, Felix; Franosch, Thomas

2013-04-01

A ubiquitous observation in cell biology is that the diffusive motion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarizing their densely packed and heterogeneous structures. The most familiar phenomenon is a sublinear, power-law increase of the mean-square displacement (MSD) as a function of the lag time, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations in time, non-Gaussian distributions of spatial displacements, heterogeneous diffusion and a fraction of immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarize some widely used theoretical models: Gaussian models like fractional Brownian motion and Langevin equations for visco-elastic media, the continuous-time random walk model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Particular emphasis is put on the spatio-temporal properties of the transport in terms of two-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even if the MSDs are identical. Then, we review the theory underlying commonly applied experimental techniques in the presence of anomalous transport like single-particle tracking, fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP). We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where a variety of model systems mimic physiological crowding conditions. Finally, computer simulations are discussed which play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.

Jump-Diffusion models and structural changes for asset forecasting in hydrology

NASA Astrophysics Data System (ADS)

Tranquille Temgoua, André Guy; Martel, Richard; Chang, Philippe J. J.; Rivera, Alfonso

2017-04-01

Impacts of climate change on surface water and groundwater are of concern in many regions of the world since water is an essential natural resource. Jump-Diffusion models are generally used in economics and other related fields but not in hydrology. The potential application could be made for hydrologic data series analysis and forecast. The present study uses Jump-Diffusion models by adding structural changes to detect fluctuations in hydrologic processes in relationship with climate change. The model implicitly assumes that modifications in rivers' flowrates can be divided into three categories: (a) normal changes due to irregular precipitation events especially in tropical regions causing major disturbance in hydrologic processes (this component is modelled by a discrete Brownian motion); (b) abnormal, sudden and non-persistent modifications in hydrologic proceedings are handled by Poisson processes; (c) the persistence of hydrologic fluctuations characterized by structural changes in hydrological data related to climate variability. The objective of this paper is to add structural changes in diffusion models with jumps, in order to capture the persistence of hydrologic fluctuations. Indirectly, the idea is to observe if there are structural changes of discharge/recharge over the study area, and to find an efficient and flexible model able of capturing a wide variety of hydrologic processes. Structural changes in hydrological data are estimated using the method of nonlinear discrete filters via Method of Simulated Moments (MSM). An application is given using sensitive parameters such as baseflow index and recession coefficient to capture discharge/recharge. Historical dataset are examined by the Volume Spread Analysis (VSA) to detect real time and random perturbations in hydrologic processes. The application of the method allows establishing more accurate hydrologic parameters. The impact of this study is perceptible in forecasting floods and groundwater recession. Keywords: hydrologic processes, Jump-Diffusion models, structural changes, forecast, climate change

Hemoglobin diffusion and the dynamics of oxygen capture by red blood cells.

PubMed

Longeville, Stéphane; Stingaciu, Laura-Roxana

2017-09-05

Translational diffusion of macromolecules in cell is generally assumed to be anomalous due high macromolecular crowding of the milieu. Red blood cells are a special case of cells filled quasi exclusively (95% of the dry weight of the cell) with an almost spherical protein: hemoglobin. Hemoglobin diffusion has since a long time been recognized as facilitating the rate of oxygen diffusion through a solution. We address in this paper the question on how hemoglobin diffusion in the red blood cells can help the oxygen capture at the cell level and hence to improve oxygen transport. We report a measurement by neutron spin echo spectroscopy of the diffusion of hemoglobin in solutions with increasing protein concentration. We show that hemoglobin diffusion in solution can be described as Brownian motion up to physiological concentration and that hemoglobin diffusion in the red blood cells and in solutions at similar concentration are the same. Finally, using a simple model and the concentration dependence of the diffusion of the protein reported here, we show that hemoglobin concentration observed in human red blood cells ([Formula: see text]330 g.L -1 ) corresponds to an optimum for oxygen transport for individuals under strong activity.

Hemoglobin diffusion and the dynamics of oxygen capture by red blood cells

DOE PAGES

Longeville, Stéphane; Stingaciu, Laura-Roxana

2017-09-05

Translational diffusion of macromolecules in cell is generally assumed to be anomalous due high macromolecular crowding of the milieu. Red blood cells are a special case of cells filled quasi exclusively (95% of the dry weight of the cell) with an almost spherical protein: hemoglobin. Hemoglobin diffusion has since a long time been recognized as facilitating the rate of oxygen diffusion through a solution. We address in this paper the question on how hemoglobin diffusion in the red blood cells can help the oxygen capture at the cell level and hence to improve oxygen transport. We report a measurement bymore » neutron spin echo spectroscopy of the diffusion of hemoglobin in solutions with increasing protein concentration. We show that hemoglobin diffusion in solution can be described as Brownian motion up to physiological concentration and that hemoglobin diffusion in the red blood cells and in solutions at similar concentration are the same. Finally, using a simple model and the concentration dependence of the diffusion of the protein reported here, we show that hemoglobin concentration observed in human red blood cells (≃330 g.L -1) corresponds to an optimum for oxygen transport for individuals under strong activity.« less

Hemoglobin diffusion and the dynamics of oxygen capture by red blood cells

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

Longeville, Stéphane; Stingaciu, Laura-Roxana

Translational diffusion of macromolecules in cell is generally assumed to be anomalous due high macromolecular crowding of the milieu. Red blood cells are a special case of cells filled quasi exclusively (95% of the dry weight of the cell) with an almost spherical protein: hemoglobin. Hemoglobin diffusion has since a long time been recognized as facilitating the rate of oxygen diffusion through a solution. We address in this paper the question on how hemoglobin diffusion in the red blood cells can help the oxygen capture at the cell level and hence to improve oxygen transport. We report a measurement bymore » neutron spin echo spectroscopy of the diffusion of hemoglobin in solutions with increasing protein concentration. We show that hemoglobin diffusion in solution can be described as Brownian motion up to physiological concentration and that hemoglobin diffusion in the red blood cells and in solutions at similar concentration are the same. Finally, using a simple model and the concentration dependence of the diffusion of the protein reported here, we show that hemoglobin concentration observed in human red blood cells (≃330 g.L -1) corresponds to an optimum for oxygen transport for individuals under strong activity.« less

Experimental detection of long-distance interactions between biomolecules through their diffusion behavior: numerical study.

PubMed

Nardecchia, Ilaria; Spinelli, Lionel; Preto, Jordane; Gori, Matteo; Floriani, Elena; Jaeger, Sebastien; Ferrier, Pierre; Pettini, Marco

2014-08-01

The dynamical properties and diffusive behavior of a collection of mutually interacting particles are numerically investigated for two types of long-range interparticle interactions: Coulomb-electrostatic and dipole-electrodynamic. It is shown that when the particles are uniformly distributed throughout the accessible space, the self-diffusion coefficient is always lowered by the considered interparticle interactions, irrespective of their attractive or repulsive character. This fact is also confirmed by a simple model to compute the correction to the Brownian diffusion coefficient due to the interactions among the particles. These interactions are also responsible for the onset of dynamical chaos and an associated chaotic diffusion which still follows an Einstein-Fick-like law for the mean-square displacement as a function of time. Transitional phenomena are observed for Coulomb-electrostatic (repulsive) and dipole-electrodynamic (attractive) interactions considered both separately and in competition. The outcomes reported in this paper clearly indicate a feasible experimental method to probe the activation of resonant electrodynamic interactions among biomolecules.

Simple rules for passive diffusion through the nuclear pore complex

PubMed Central

Mironska, Roxana; Kim, Seung Joong

2016-01-01

Passive macromolecular diffusion through nuclear pore complexes (NPCs) is thought to decrease dramatically beyond a 30–60-kD size threshold. Using thousands of independent time-resolved fluorescence microscopy measurements in vivo, we show that the NPC lacks such a firm size threshold; instead, it forms a soft barrier to passive diffusion that intensifies gradually with increasing molecular mass in both the wild-type and mutant strains with various subsets of phenylalanine-glycine (FG) domains and different levels of baseline passive permeability. Brownian dynamics simulations replicate these findings and indicate that the soft barrier results from the highly dynamic FG repeat domains and the diffusing macromolecules mutually constraining and competing for available volume in the interior of the NPC, setting up entropic repulsion forces. We found that FG domains with exceptionally high net charge and low hydropathy near the cytoplasmic end of the central channel contribute more strongly to obstruction of passive diffusion than to facilitated transport, revealing a compartmentalized functional arrangement within the NPC. PMID:27697925

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

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

Guo, Ran; Du, Jiulin, E-mail: jiulindu@aliyun.com

2015-08-15

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalousmore » diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution.« less

Effective conductivity, dielectric constant, and diffusion coefficient of digitized composite media via first-passage-time equations

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

Torquato, S.; Kim, I.C.; Cule, D.

1999-02-01

We generalize the Brownian motion simulation method of Kim and Torquato [J. Appl. Phys. {bold 68}, 3892 (1990)] to compute the effective conductivity, dielectric constant and diffusion coefficient of digitized composite media. This is accomplished by first generalizing the {ital first-passage-time equations} to treat first-passage regions of arbitrary shape. We then develop the appropriate first-passage-time equations for digitized media: first-passage squares in two dimensions and first-passage cubes in three dimensions. A severe test case to prove the accuracy of the method is the two-phase periodic checkerboard in which conduction, for sufficiently large phase contrasts, is dominated by corners that joinmore » two conducting-phase pixels. Conventional numerical techniques (such as finite differences or elements) do not accurately capture the local fields here for reasonable grid resolution and hence lead to inaccurate estimates of the effective conductivity. By contrast, we show that our algorithm yields accurate estimates of the effective conductivity of the periodic checkerboard for widely different phase conductivities. Finally, we illustrate our method by computing the effective conductivity of the random checkerboard for a wide range of volume fractions and several phase contrast ratios. These results always lie within rigorous four-point bounds on the effective conductivity. {copyright} {ital 1999 American Institute of Physics.}« less

Anisotropic rotational diffusion studied by passage saturation transfer electron paramagnetic resonance

NASA Astrophysics Data System (ADS)

Robinson, Bruce H.; Dalton, Larry R.

1980-01-01

The stochastic Liouville equation for the spin density matrix is modified to consider the effects of Brownian anisotropic rotational diffusion upon electron paramagnetic resonance (EPR) and saturation transfer electron paramagnetic resonance (ST-EPR) spectra. Spectral shapes and the ST-EPR parameters L″/L, C'/C, and H″/H defined by Thomas, Dalton, and Hyde at X-band microwave frequencies [J. Chem. Phys. 65, 3006 (1976)] are examined and discussed in terms of the rotational times τ∥ and τ⊥ and in terms of other defined correlation times for systems characterized by magnetic tensors of axial symmetry and for systems characterized by nonaxially symmetric magnetic tensors. For nearly axially symmetric magnetic tensors, such as nitroxide spin labels studied employing 1-3 GHz microwaves, ST-EPR spectra for systems undergoing anisotropic rotational diffusion are virtually indistinguishable from spectra for systems characterized by isotropic diffusion. For nonaxially symmetric magnetic tensors, such as nitroxide spin labels studied employing 8-35 GHz microwaves, the high field region of the ST-EPR spectra, and hence the H″/H parameter, will be virtually indistinguishable from spectra, and parameter values, obtained for isotropic diffusion. On the other hand, the central spectral region at x-band microwave frequencies, and hence the C'/C parameter, is sensitive to the anisotropic diffusion model provided that a unique and static relationship exists between the magnetic and diffusion tensors. Random labeling or motion of the spin label relative to the biomolecule whose hydrodynamic properties are to be investigated will destroy spectral sensitivity to anisotropic motion. The sensitivity to anisotropic motion is enhanced in proceeding to 35 GHz with the increased sensitivity evident in the low field half of the EPR and ST-EPR spectra. The L″/L parameter is thus a meaningful indicator of anisotropic motion when compared with H″/H parameter analysis. However, consideration of spectral shapes suggests that the C'/C parameter definition is not meaningfully extended from 9.5 to 35 GHz. Alternative definitions of the L″/L and C'/C parameters are proposed for those microwave frequencies for which the electron Zeeman anisotropy is comparable to or greater than the electron-nitrogen nuclear hyperfine anisotropy.

Dynamical Signatures of Living Systems

NASA Technical Reports Server (NTRS)

Zak, M.

1999-01-01

One of the main challenges in modeling living systems is to distinguish a random walk of physical origin (for instance, Brownian motions) from those of biological origin and that will constitute the starting point of the proposed approach. As conjectured, the biological random walk must be nonlinear. Indeed, any stochastic Markov process can be described by linear Fokker-Planck equation (or its discretized version), only that type of process has been observed in the inanimate world. However, all such processes always converge to a stable (ergodic or periodic) state, i.e., to the states of a lower complexity and high entropy. At the same time, the evolution of living systems directed toward a higher level of complexity if complexity is associated with a number of structural variations. The simplest way to mimic such a tendency is to incorporate a nonlinearity into the random walk; then the probability evolution will attain the features of diffusion equation: the formation and dissipation of shock waves initiated by small shallow wave disturbances. As a result, the evolution never "dies:" it produces new different configurations which are accompanied by an increase or decrease of entropy (the decrease takes place during formation of shock waves, the increase-during their dissipation). In other words, the evolution can be directed "against the second law of thermodynamics" by forming patterns outside of equilibrium in the probability space. Due to that, a specie is not locked up in a certain pattern of behavior: it still can perform a variety of motions, and only the statistics of these motions is constrained by this pattern. It should be emphasized that such a "twist" is based upon the concept of reflection, i.e., the existence of the self-image (adopted from psychology). The model consists of a generator of stochastic processes which represents the motor dynamics in the form of nonlinear random walks, and a simulator of the nonlinear version of the diffusion equation which represents the mental dynamics. It has been demonstrated that coupled mental-motor dynamics can simulate emerging self-organization, prey-predator games, collaboration and competition, "collective brain," etc.

Stochastic mechanics of reciprocal diffusions

NASA Astrophysics Data System (ADS)

Levy, Bernard C.; Krener, Arthur J.

1996-02-01

The dynamics and kinematics of reciprocal diffusions were examined in a previous paper [J. Math. Phys. 34, 1846 (1993)], where it was shown that reciprocal diffusions admit a chain of conservation laws, which close after the first two laws for two disjoint subclasses of reciprocal diffusions, the Markov and quantum diffusions. For the case of quantum diffusions, the conservation laws are equivalent to Schrödinger's equation. The Markov diffusions were employed by Schrödinger [Sitzungsber. Preuss. Akad. Wiss. Phys. Math Kl. 144 (1931); Ann. Inst. H. Poincaré 2, 269 (1932)], Nelson [Dynamical Theories of Brownian Motion (Princeton University, Princeton, NJ, 1967); Quantum Fluctuations (Princeton University, Princeton, NJ, 1985)], and other researchers to develop stochastic formulations of quantum mechanics, called stochastic mechanics. We propose here an alternative version of stochastic mechanics based on quantum diffusions. A procedure is presented for constructing the quantum diffusion associated to a given wave function. It is shown that quantum diffusions satisfy the uncertainty principle, and have a locality property, whereby given two dynamically uncoupled but statistically correlated particles, the marginal statistics of each particle depend only on the local fields to which the particle is subjected. However, like Wigner's joint probability distribution for the position and momentum of a particle, the finite joint probability densities of quantum diffusions may take negative values.

Development of Mouse Lung Deposition Models

DTIC Science & Technology

2015-07-01

information on deposition of ultrafine particles in the URT of mice either by measurements or theoretical modeling. Comparison of the nasal structure of... ultrafine particles in rats to be extended to mice. Based on measurements in the nasal casts of rats, Cheng et al. [12] obtained the following...expression for losses of ultrafine particles in the nasal passages of rats by Brownian diffusion during inhalation and exhalation. γβα− − −=η QD

Diffusion tensor optical coherence tomography

NASA Astrophysics Data System (ADS)

Marks, Daniel L.; Blackmon, Richard L.; Oldenburg, Amy L.

2018-01-01

In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.

Rumor spreading model with noise interference in complex social networks

NASA Astrophysics Data System (ADS)

Zhu, Liang; Wang, Youguo

2017-03-01

In this paper, a modified susceptible-infected-removed (SIR) model has been proposed to explore rumor diffusion on complex social networks. We take variation of connectivity into consideration and assume the variation as noise. On the basis of related literature on virus networks, the noise is described as standard Brownian motion while stochastic differential equations (SDE) have been derived to characterize dynamics of rumor diffusion both on homogeneous networks and heterogeneous networks. Then, theoretical analysis on homogeneous networks has been demonstrated to investigate the solution of SDE model and the steady state of rumor diffusion. Simulations both on Barabási-Albert (BA) network and Watts-Strogatz (WS) network display that the addition of noise accelerates rumor diffusion and expands diffusion size, meanwhile, the spreading speed on BA network is much faster than on WS network under the same noise intensity. In addition, there exists a rumor diffusion threshold in statistical average meaning on homogeneous network which is absent on heterogeneous network. Finally, we find a positive correlation between peak value of infected individuals and noise intensity while a negative correlation between rumor lifecycle and noise intensity overall.

Transport and fluctuation-dissipation relations in asymptotic and preasymptotic diffusion across channels with variable section.

PubMed

Forte, Giuseppe; Cecconi, Fabio; Vulpiani, Angelo

2014-12-01

We study the asymptotic and preasymptotic diffusive properties of Brownian particles in channels whose section varies periodically in space. The effective diffusion coefficient D(eff) is numerically determined by the asymptotic behavior of the root mean square displacement in different geometries, considering even cases of steep variations of the channel boundaries. Moreover, we compared the numerical results to the predictions from the various corrections proposed in the literature to the well known Fick-Jacobs approximation. Building an effective one-dimensional equation for the longitudinal diffusion, we obtain an approximation for the effective diffusion coefficient. Such a result goes beyond a perturbation approach, and it is in good agreement with the actual values obtained by the numerical simulations. We discuss also the preasymptotic diffusion which is observed up to a crossover time whose value, in the presence of strong spatial variation of the channel cross section, can be very large. In addition, we show how the Einstein's relation between the mean drift induced by a small external field and the mean square displacement of the unperturbed system is valid in both asymptotic and preasymptotic regimes.

Fully Anisotropic Rotational Diffusion Tensor from Molecular Dynamics Simulations.

PubMed

Linke, Max; Köfinger, Jürgen; Hummer, Gerhard

2018-05-31

We present a method to calculate the fully anisotropic rotational diffusion tensor from molecular dynamics simulations. Our approach is based on fitting the time-dependent covariance matrix of the quaternions that describe the rigid-body rotational dynamics. Explicit analytical expressions have been derived for the covariances by Favro, which are valid irrespective of the degree of anisotropy. We use these expressions to determine an optimal rotational diffusion tensor from trajectory data. The molecular structures are aligned against a reference by optimal rigid-body superposition. The quaternion covariances can then be obtained directly from the rotation matrices used in the alignment. The rotational diffusion tensor is determined by a fit to the time-dependent quaternion covariances, or directly by Laplace transformation and matrix diagonalization. To quantify uncertainties in the fit, we derive analytical expressions and compare them with the results of Brownian dynamics simulations of anisotropic rotational diffusion. We apply the method to microsecond long trajectories of the Dickerson-Drew B-DNA dodecamer and of horse heart myoglobin. The anisotropic rotational diffusion tensors calculated from simulations agree well with predictions from hydrodynamics.

Resonances arising from hydrodynamic memory in Brownian motion.

PubMed

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

2011-10-05

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

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

Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field

NASA Astrophysics Data System (ADS)

Das, Joydip; Mondal, Shrabani; Bag, Bidhan Chandra

2017-10-01

In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.

Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field.

PubMed

Das, Joydip; Mondal, Shrabani; Bag, Bidhan Chandra

2017-10-28

In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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.

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.

Brownian Ratchet Mechanism for Faithful Segregation of Low-Copy-Number Plasmids.

PubMed

Hu, Longhua; Vecchiarelli, Anthony G; Mizuuchi, Kiyoshi; Neuman, Keir C; Liu, Jian

2017-04-11

Bacterial plasmids are extrachromosomal DNA that provides selective advantages for bacterial survival. Plasmid partitioning can be remarkably robust. For high-copy-number plasmids, diffusion ensures that both daughter cells inherit plasmids after cell division. In contrast, most low-copy-number plasmids need to be actively partitioned by a conserved tripartite ParA-type system. ParA is an ATPase that binds to chromosomal DNA; ParB is the stimulator of the ParA ATPase and specifically binds to the plasmid at a centromere-like site, parS. ParB stimulation of the ParA ATPase releases ParA from the bacterial chromosome, after which it takes a long time to reset its DNA-binding affinity. We previously demonstrated in vitro that the ParA system can exploit this biochemical asymmetry for directed cargo transport. Multiple ParA-ParB bonds can bridge a parS-coated cargo to a DNA carpet, and they can work collectively as a Brownian ratchet that directs persistent cargo movement with a ParA-depletion zone trailing behind. By extending this model, we suggest that a similar Brownian ratchet mechanism recapitulates the full range of actively segregated plasmid motilities observed in vivo. We demonstrate that plasmid motility is tuned as the replenishment rate of the ParA-depletion zone progressively increases relative to the cargo speed, evolving from diffusion to pole-to-pole oscillation, local excursions, and, finally, immobility. When the plasmid replicates, the daughters largely display motilities similar to that of their mother, except that when the single-focus progenitor is locally excursive, the daughter foci undergo directed segregation. We show that directed segregation maximizes the fidelity of plasmid partition. Given that local excursion and directed segregation are the most commonly observed modes of plasmid motility in vivo, we suggest that the operation of the ParA-type partition system has been shaped by evolution for high fidelity of plasmid segregation. Published by Elsevier Inc.

Superimposed Code Theorectic Analysis of DNA Codes and DNA Computing

DTIC Science & Technology

2010-03-01

because only certain collections (partitioned by font type) of sequences are allowed to be in each position (e.g., Arial = position 0, Comic ...rigidity of short oligos and the shape of the polar charge. Oligo movement was modeled by a Brownian motion 3 dimensional random walk. The one...temperature, kB is Boltz he viscosity of the medium. The random walk motion is modeled by assuming the oligo is on a three dimensional lattice and may

Enhanced diffusion with abnormal temperature dependence in underdamped space-periodic systems subject to time-periodic driving

NASA Astrophysics Data System (ADS)

Marchenko, I. G.; Marchenko, I. I.; Zhiglo, A. V.

2018-01-01

We present a study of the diffusion enhancement of underdamped Brownian particles in a one-dimensional symmetric space-periodic potential due to external symmetric time-periodic driving with zero mean. We show that the diffusivity can be enhanced by many orders of magnitude at an appropriate choice of the driving amplitude and frequency. The diffusivity demonstrates abnormal (decreasing) temperature dependence at the driving amplitudes exceeding a certain value. At any fixed driving frequency Ω normal temperature dependence of the diffusivity is restored at low enough temperatures, T

Anisotropic swim stress in active matter with nematic order

NASA Astrophysics Data System (ADS)

Yan, Wen; Brady, John F.

2018-05-01

Active Brownian particles (ABPs) transmit a swim pressure {{{\\Pi }}}{{swim}}=n\\zeta {D}{{swim}} to the container boundaries, where ζ is the drag coefficient, D swim is the swim diffusivity and n is the uniform bulk number density far from the container walls. In this work we extend the notion of the isotropic swim pressure to the anisotropic tensorial swim stress {{\\boldsymbol{σ }}}{{swim}}=-n\\zeta {{\\boldsymbol{D}}}{{swim}}, which is related to the anisotropic swim diffusivity {{\\boldsymbol{D}}}{{swim}}. We demonstrate this relationship with ABPs that achieve nematic orientational order via a bulk external field. The anisotropic swim stress is obtained analytically for dilute ABPs in both 2D and 3D systems. The anisotropy, defined as the ratio of the maximum to the minimum of the three principal stresses, is shown to grow exponentially with the strength of the external field. We verify that the normal component of the anisotropic swim stress applies a pressure {{{\\Pi }}}{{swim}}=-({{\\boldsymbol{σ }}}{{swim}}\\cdot {\\boldsymbol{n}})\\cdot {\\boldsymbol{n}} on a wall with normal vector {\\boldsymbol{n}}, and, through Brownian dynamics simulations, this pressure is shown to be the force per unit area transmitted by the active particles. Since ABPs have no friction with a wall, the difference between the normal and tangential stress components—the normal stress difference—generates a net flow of ABPs along the wall, which is a generic property of active matter systems.

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

NASA Astrophysics Data System (ADS)

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

2018-09-01

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

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

Contributions of Microtubule Dynamic Instability and Rotational Diffusion to Kinetochore Capture.

PubMed

Blackwell, Robert; Sweezy-Schindler, Oliver; Edelmaier, Christopher; Gergely, Zachary R; Flynn, Patrick J; Montes, Salvador; Crapo, Ammon; Doostan, Alireza; McIntosh, J Richard; Glaser, Matthew A; Betterton, Meredith D

2017-02-07

Microtubule dynamic instability allows search and capture of kinetochores during spindle formation, an important process for accurate chromosome segregation during cell division. Recent work has found that microtubule rotational diffusion about minus-end attachment points contributes to kinetochore capture in fission yeast, but the relative contributions of dynamic instability and rotational diffusion are not well understood. We have developed a biophysical model of kinetochore capture in small fission-yeast nuclei using hybrid Brownian dynamics/kinetic Monte Carlo simulation techniques. With this model, we have studied the importance of dynamic instability and microtubule rotational diffusion for kinetochore capture, both to the lateral surface of a microtubule and at or near its end. Over a range of biologically relevant parameters, microtubule rotational diffusion decreased capture time, but made a relatively small contribution compared to dynamic instability. At most, rotational diffusion reduced capture time by 25%. Our results suggest that while microtubule rotational diffusion can speed up kinetochore capture, it is unlikely to be the dominant physical mechanism for typical conditions in fission yeast. In addition, we found that when microtubules undergo dynamic instability, lateral captures predominate even in the absence of rotational diffusion. Counterintuitively, adding rotational diffusion to a dynamic microtubule increases the probability of end-on capture. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Statistical signatures of a targeted search by bacteria

NASA Astrophysics Data System (ADS)

Jashnsaz, Hossein; Anderson, Gregory G.; Pressé, Steve

2017-12-01

Chemoattractant gradients are rarely well-controlled in nature and recent attention has turned to bacterial chemotaxis toward typical bacterial food sources such as food patches or even bacterial prey. In environments with localized food sources reminiscent of a bacterium’s natural habitat, striking phenomena—such as the volcano effect or banding—have been predicted or expected to emerge from chemotactic models. However, in practice, from limited bacterial trajectory data it is difficult to distinguish targeted searches from an untargeted search strategy for food sources. Here we use a theoretical model to identify statistical signatures of a targeted search toward point food sources, such as prey. Our model is constructed on the basis that bacteria use temporal comparisons to bias their random walk, exhibit finite memory and are subject to random (Brownian) motion as well as signaling noise. The advantage with using a stochastic model-based approach is that a stochastic model may be parametrized from individual stochastic bacterial trajectories but may then be used to generate a very large number of simulated trajectories to explore average behaviors obtained from stochastic search strategies. For example, our model predicts that a bacterium’s diffusion coefficient increases as it approaches the point source and that, in the presence of multiple sources, bacteria may take substantially longer to locate their first source giving the impression of an untargeted search strategy.

Review of Recent Developments on Using an Off-Lattice Monte Carlo Approach to Predict the Effective Thermal Conductivity of Composite Systems with Complex Structures

PubMed Central

Gong, Feng; Duong, Hai M.; Papavassiliou, Dimitrios V.

2016-01-01

Here, we present a review of recent developments for an off-lattice Monte Carlo approach used to investigate the thermal transport properties of multiphase composites with complex structure. The thermal energy was quantified by a large number of randomly moving thermal walkers. Different modes of heat conduction were modeled in appropriate ways. The diffusive heat conduction in the polymer matrix was modeled with random Brownian motion of thermal walkers within the polymer, and the ballistic heat transfer within the carbon nanotubes (CNTs) was modeled by assigning infinite speed of thermal walkers in the CNTs. Three case studies were conducted to validate the developed approach, including three-phase single-walled CNTs/tungsten disulfide (WS2)/(poly(ether ether ketone) (PEEK) composites, single-walled CNT/WS2/PEEK composites with the CNTs clustered in bundles, and complex graphene/poly(methyl methacrylate) (PMMA) composites. In all cases, resistance to heat transfer due to nanoscale phenomena was also modeled. By quantitatively studying the influencing factors on the thermal transport properties of the multiphase composites, it was found that the orientation, aggregation and morphology of fillers, as well as the interfacial thermal resistance at filler-matrix interfaces would limit the transfer of heat in the composites. These quantitative findings may be applied in the design and synthesis of multiphase composites with specific thermal transport properties. PMID:28335270

Wave-particle interaction in the Faraday waves.

PubMed

Francois, N; Xia, H; Punzmann, H; Shats, M

2015-10-01

Wave motion in disordered Faraday waves is analysed in terms of oscillons or quasi-particles. The motion of these oscillons is measured using particle tracking tools and it is compared with the motion of fluid particles on the water surface. Both the real floating particles and the oscillons, representing the collective fluid motion, show Brownian-type dispersion exhibiting ballistic and diffusive mean squared displacement at short and long times, respectively. While the floating particles motion has been previously explained in the context of two-dimensional turbulence driven by Faraday waves, no theoretical description exists for the random walk type motion of oscillons. It is found that the r.m.s velocity ⟨μ̃(osc)⟩(rms) of oscillons is directly related to the turbulent r.m.s. velocity ⟨μ̃⟩(rms) of the fluid particles in a broad range of vertical accelerations. The measured ⟨μ̃(osc)⟩(rms) accurately explains the broadening of the frequency spectra of the surface elevation observed in disordered Faraday waves. These results suggest that 2D turbulence is the driving force behind both the randomization of the oscillons motion and the resulting broadening of the wave frequency spectra. The coupling between wave motion and hydrodynamic turbulence demonstrated here offers new perspectives for predicting complex fluid transport from the knowledge of wave field spectra and vice versa.

Effective conductivity of suspensions of hard spheres by Brownian motion simulation

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

Chan Kim, I.; Torquato, S.

1991-02-15

A generalized Brownian motion simulation technique developed by Kim and Torquato (J. Appl. Phys. {bold 68}, 3892 (1990)) is applied to compute exactly'' the effective conductivity {sigma}{sub {ital e}} of heterogeneous media composed of regular and random distributions of hard spheres of conductivity {sigma}{sub 2} in a matrix of conductivity {sigma}{sub 1} for virtually the entire volume fraction range and for several values of the conductivity ratio {alpha}={sigma}{sub 2}/{sigma}{sub 1}, including superconducting spheres ({alpha}={infinity}) and perfectly insulating spheres ({alpha}=0). A key feature of the procedure is the use of {ital first}-{ital passage}-{ital time} equations in the two homogeneous phases andmore » at the two-phase interface. The method is shown to yield {sigma}{sub {ital e}} accurately with a comparatively fast execution time. The microstructure-sensitive analytical approximation of {sigma}{sub {ital e}} for dispersions derived by Torquato (J. Appl. Phys. {bold 58}, 3790 (1985)) is shown to be in excellent agreement with our data for random suspensions for the wide range of conditions reported here.« less

Ensemble solute transport in two-dimensional operator-scaling random fields

NASA Astrophysics Data System (ADS)

Monnig, Nathan D.; Benson, David A.; Meerschaert, Mark M.

2008-02-01

Motivated by field measurements of aquifer hydraulic conductivity (K), recent techniques were developed to construct anisotropic fractal random fields in which the scaling, or self-similarity parameter, varies with direction and is defined by a matrix. Ensemble numerical results are analyzed for solute transport through these two-dimensional "operator-scaling" fractional Brownian motion ln(K) fields. Both the longitudinal and transverse Hurst coefficients, as well as the "radius of isotropy" are important to both plume growth rates and the timing and duration of breakthrough. It is possible to create operator-scaling fractional Brownian motion fields that have more "continuity" or stratification in the direction of transport. The effects on a conservative solute plume are continually faster-than-Fickian growth rates, highly non-Gaussian shapes, and a heavier tail early in the breakthrough curve. Contrary to some analytic stochastic theories for monofractal K fields, the plume growth rates never exceed A. Mercado's (1967) purely stratified aquifer growth rate of plume apparent dispersivity proportional to mean distance. Apparent superstratified growth must be the result of other demonstrable factors, such as initial plume size.

Reactive multi-particle collision dynamics with reactive boundary conditions

NASA Astrophysics Data System (ADS)

Sayyidmousavi, Alireza; Rohlf, Katrin

2018-07-01

In the present study, an off-lattice particle-based method called the reactive multi-particle collision (RMPC) dynamics is extended to model reaction-diffusion systems with reactive boundary conditions in which the a priori diffusion coefficient of the particles needs to be maintained throughout the simulation. To this end, the authors have made use of the so-called bath particles whose purpose is only to ensure proper diffusion of the main particles in the system. In order to model partial adsorption by a reactive boundary in the RMPC, the probability of a particle being adsorbed, once it hits the boundary, is calculated by drawing an analogy between the RMPC and Brownian Dynamics. The main advantages of the RMPC compared to other molecular based methods are less computational cost as well as conservation of mass, energy and momentum in the collision and free streaming steps. The proposed approach is tested on three reaction-diffusion systems and very good agreement with the solutions to their corresponding partial differential equations is observed.

Persistence and Adaptation in Immunity: T Cells Balance the Extent and Thoroughness of Search

PubMed Central

Fricke, G. Matthew; Letendre, Kenneth A.; Moses, Melanie E.; Cannon, Judy L.

2016-01-01

Effective search strategies have evolved in many biological systems, including the immune system. T cells are key effectors of the immune response, required for clearance of pathogenic infection. T cell activation requires that T cells encounter antigen-bearing dendritic cells within lymph nodes, thus, T cell search patterns within lymph nodes may be a crucial determinant of how quickly a T cell immune response can be initiated. Previous work suggests that T cell motion in the lymph node is similar to a Brownian random walk, however, no detailed analysis has definitively shown whether T cell movement is consistent with Brownian motion. Here, we provide a precise description of T cell motility in lymph nodes and a computational model that demonstrates how motility impacts T cell search efficiency. We find that both Brownian and Lévy walks fail to capture the complexity of T cell motion. Instead, T cell movement is better described as a correlated random walk with a heavy-tailed distribution of step lengths. Using computer simulations, we identify three distinct factors that contribute to increasing T cell search efficiency: 1) a lognormal distribution of step lengths, 2) motion that is directionally persistent over short time scales, and 3) heterogeneity in movement patterns. Furthermore, we show that T cells move differently in specific frequently visited locations that we call “hotspots” within lymph nodes, suggesting that T cells change their movement in response to the lymph node environment. Our results show that like foraging animals, T cells adapt to environmental cues, suggesting that adaption is a fundamental feature of biological search. PMID:26990103

Dynamic least-squares kernel density modeling of Fokker-Planck equations with application to neural population.

PubMed

Shotorban, Babak

2010-04-01

The dynamic least-squares kernel density (LSQKD) model [C. Pantano and B. Shotorban, Phys. Rev. E 76, 066705 (2007)] is used to solve the Fokker-Planck equations. In this model the probability density function (PDF) is approximated by a linear combination of basis functions with unknown parameters whose governing equations are determined by a global least-squares approximation of the PDF in the phase space. In this work basis functions are set to be Gaussian for which the mean, variance, and covariances are governed by a set of partial differential equations (PDEs) or ordinary differential equations (ODEs) depending on what phase-space variables are approximated by Gaussian functions. Three sample problems of univariate double-well potential, bivariate bistable neurodynamical system [G. Deco and D. Martí, Phys. Rev. E 75, 031913 (2007)], and bivariate Brownian particles in a nonuniform gas are studied. The LSQKD is verified for these problems as its results are compared against the results of the method of characteristics in nondiffusive cases and the stochastic particle method in diffusive cases. For the double-well potential problem it is observed that for low to moderate diffusivity the dynamic LSQKD well predicts the stationary PDF for which there is an exact solution. A similar observation is made for the bistable neurodynamical system. In both these problems least-squares approximation is made on all phase-space variables resulting in a set of ODEs with time as the independent variable for the Gaussian function parameters. In the problem of Brownian particles in a nonuniform gas, this approximation is made only for the particle velocity variable leading to a set of PDEs with time and particle position as independent variables. Solving these PDEs, a very good performance by LSQKD is observed for a wide range of diffusivities.

Theory and simulation of the time-dependent rate coefficients of diffusion-influenced reactions.

PubMed Central

Zhou, H X; Szabo, A

1996-01-01

A general formalism is developed for calculating the time-dependent rate coefficient k(t) of an irreversible diffusion-influenced reaction. This formalism allows one to treat most factors that affect k(t), including rotational Brownian motion and conformational gating of reactant molecules and orientation constraint for product formation. At long times k(t) is shown to have the asymptotic expansion k(infinity)[1 + k(infinity) (pie Dt)-1/2 /4 pie D + ...], where D is the relative translational diffusion constant. An approximate analytical method for calculating k(t) is presented. This is based on the approximation that the probability density of the reactant pair in the reactive region keeps the equilibrium distribution but with a decreasing amplitude. The rate coefficient then is determined by the Green function in the absence of chemical reaction. Within the framework of this approximation, two general relations are obtained. The first relation allows the rate coefficient for an arbitrary amplitude of the reactivity to be found if the rate coefficient for one amplitude of the reactivity is known. The second relation allows the rate coefficient in the presence of conformational gating to be found from that in the absence of conformational gating. The ratio k(t)/k(0) is shown to be the survival probability of the reactant pair at time t starting from an initial distribution that is localized in the reactive region. This relation forms the basis of the calculation of k(t) through Brownian dynamics simulations. Two simulation procedures involving the propagation of nonreactive trajectories initiated only from the reactive region are described and illustrated on a model system. Both analytical and simulation results demonstrate the accuracy of the equilibrium-distribution approximation method. PMID:8913584

Self-Consistent Simulation of the Brownian Stage of Dust Growth

NASA Technical Reports Server (NTRS)

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

1996-01-01

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

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.

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

PubMed

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

2016-07-01

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

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.

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.