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

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.

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.

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.

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.

Diffusive mixing and Tsallis entropy

DOE PAGES

O'Malley, Daniel; Vesselinov, Velimir V.; Cushman, John H.

2015-04-29

Brownian motion, the classical diffusive process, maximizes the Boltzmann-Gibbs entropy. The Tsallis q-entropy, which is non-additive, was developed as an alternative to the classical entropy for systems which are non-ergodic. A generalization of Brownian motion is provided that maximizes the Tsallis entropy rather than the Boltzmann-Gibbs entropy. This process is driven by a Brownian measure with a random diffusion coefficient. In addition, the distribution of this coefficient is derived as a function of q for 1 < q < 3. Applications to transport in porous media are considered.

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…

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.

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.

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.

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.

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

PubMed

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

2014-08-14

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

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.

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 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

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

PubMed Central

Volpe, Giorgio; Volpe, Giovanni; Gigan, Sylvain

2014-01-01

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

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.

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

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.

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.

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 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.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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.

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.

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.

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.

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.

Parsing anomalous versus normal diffusive behavior of bedload sediment particles

USGS Publications Warehouse

Fathel, Siobhan; Furbish, David; Schmeeckle, Mark

2016-01-01

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

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.

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

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

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.

Brownian motion and its descendants according to Schrödinger

NASA Astrophysics Data System (ADS)

Garbaczewski, Piotr; Vigier, Jean-Pierre

1992-08-01

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

Brownian motion 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

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.

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.

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.

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

Crossover of two power laws in the anomalous diffusion of a two lipid membrane

NASA Astrophysics Data System (ADS)

Bakalis, Evangelos; Höfinger, Siegfried; Venturini, Alessandro; Zerbetto, Francesco

2015-06-01

Molecular dynamics simulations of a bi-layer membrane made by the same number of 1-palmitoyl-2-oleoyl-glycero-3-phospho-ethanolamine and palmitoyl-oleoyl phosphatidylserine lipids reveal sub-diffusional motion, which presents a crossover between two different power laws. Fractional Brownian motion is the stochastic mechanism that governs the motion in both regimes. The location of the crossover point is justified with simple geometrical arguments and is due to the activation of the mechanism of circumrotation of lipids about each other.

Crossover of two power laws in the anomalous diffusion of a two lipid membrane

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

Bakalis, Evangelos, E-mail: ebakalis@gmail.com, E-mail: francesco.zerbetto@unibo.it; Höfinger, Siegfried; Zerbetto, Francesco, E-mail: ebakalis@gmail.com, E-mail: francesco.zerbetto@unibo.it

2015-06-07

Molecular dynamics simulations of a bi-layer membrane made by the same number of 1-palmitoyl-2-oleoyl-glycero-3-phospho-ethanolamine and palmitoyl-oleoyl phosphatidylserine lipids reveal sub-diffusional motion, which presents a crossover between two different power laws. Fractional Brownian motion is the stochastic mechanism that governs the motion in both regimes. The location of the crossover point is justified with simple geometrical arguments and is due to the activation of the mechanism of circumrotation of lipids about each other.

Crossover of two power laws in the anomalous diffusion of a two lipid membrane.

PubMed

Bakalis, Evangelos; Höfinger, Siegfried; Venturini, Alessandro; Zerbetto, Francesco

2015-06-07

Molecular dynamics simulations of a bi-layer membrane made by the same number of 1-palmitoyl-2-oleoyl-glycero-3-phospho-ethanolamine and palmitoyl-oleoyl phosphatidylserine lipids reveal sub-diffusional motion, which presents a crossover between two different power laws. Fractional Brownian motion is the stochastic mechanism that governs the motion in both regimes. The location of the crossover point is justified with simple geometrical arguments and is due to the activation of the mechanism of circumrotation of lipids about each other.

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.

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.

Nuclear quadrupole resonance lineshape analysis for different motional models: Stochastic Liouville approach

NASA Astrophysics Data System (ADS)

Kruk, D.; Earle, K. A.; Mielczarek, A.; Kubica, A.; Milewska, A.; Moscicki, J.

2011-12-01

A general theory of lineshapes in nuclear quadrupole resonance (NQR), based on the stochastic Liouville equation, is presented. The description is valid for arbitrary motional conditions (particularly beyond the valid range of perturbation approaches) and interaction strengths. It can be applied to the computation of NQR spectra for any spin quantum number and for any applied magnetic field. The treatment presented here is an adaptation of the "Swedish slow motion theory," [T. Nilsson and J. Kowalewski, J. Magn. Reson. 146, 345 (2000), 10.1006/jmre.2000.2125] originally formulated for paramagnetic systems, to NQR spectral analysis. The description is formulated for simple (Brownian) diffusion, free diffusion, and jump diffusion models. The two latter models account for molecular cooperativity effects in dense systems (such as liquids of high viscosity or molecular glasses). The sensitivity of NQR slow motion spectra to the mechanism of the motional processes modulating the nuclear quadrupole interaction is discussed.

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.

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

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.

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.

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

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.

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.

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.

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.

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.

Diffusion limit of Lévy-Lorentz gas is Brownian motion

NASA Astrophysics Data System (ADS)

Magdziarz, Marcin; Szczotka, Wladyslaw

2018-07-01

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

Absorption Kinetics of Phage Lambda on Its Host Under Shear Flow

NASA Astrophysics Data System (ADS)

Yip, C. W.; Wu, X. L.

2000-03-01

Classical blender experiment by Hershey and Chase played a seminal role in illustrating the infectious process of bacteriophage to its host, and showed unequivocally that DNA is responsible for the transmission of heredity. Subsequent works by others have established that interaction between phage particles and bacterial cells is a diffusion-limited process in that, statistically speaking, each collision results in an irreversible infection. However, such a result is hard to reconcile with the fact that the infection appears to be independent of the density of phage receptors on the bacterial cell membrane. Thus, quantitative experiments showing how a phage finds its receptor and how long does it take would be valuable to this paradoxical view. Simple calculations based on Brownian motion of the phage particles show that the interaction time between the receptor and the phage is given by tau=b^2/(5D), where b is the length of the phage and D is its diffusion coefficient. Using a shear flow apparatus we study absorption kinetics of lambda phage on E. Coli (strain YMEL) under different flow conditions, and the results are compared with a simple diffusion model taking into account the hydrodynamic convection and the interaction time tau.

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.

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

Langevin Theory of Anomalous Brownian Motion Made Simple

ERIC Educational Resources Information Center

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

2011-01-01

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

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.

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

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.

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

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.

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.

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.

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.

A surface-bound molecule that undergoes optically biased Brownian rotation.

PubMed

Hutchison, James A; Uji-i, Hiroshi; Deres, Ania; Vosch, Tom; Rocha, Susana; Müller, Sibylle; Bastian, Andreas A; Enderlein, Jörg; Nourouzi, Hassan; Li, Chen; Herrmann, Andreas; Müllen, Klaus; De Schryver, Frans; Hofkens, Johan

2014-02-01

Developing molecular systems with functions analogous to those of macroscopic machine components, such as rotors, gyroscopes and valves, is a long-standing goal of nanotechnology. However, macroscopic analogies go only so far in predicting function in nanoscale environments, where friction dominates over inertia. In some instances, ratchet mechanisms have been used to bias the ever-present random, thermally driven (Brownian) motion and drive molecular diffusion in desired directions. Here, we visualize the motions of surface-bound molecular rotors using defocused fluorescence imaging, and observe the transition from hindered to free Brownian rotation by tuning medium viscosity. We show that the otherwise random rotations can be biased by the polarization of the excitation light field, even though the associated optical torque is insufficient to overcome thermal fluctuations. The biased rotation is attributed instead to a fluctuating-friction mechanism in which photoexcitation of the rotor strongly inhibits its diffusion rate.

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.

On Entropy Production in the Madelung Fluid and the Role of Bohm's Potential in Classical Diffusion

NASA Astrophysics Data System (ADS)

Heifetz, Eyal; Tsekov, Roumen; Cohen, Eliahu; Nussinov, Zohar

2016-07-01

The Madelung equations map the non-relativistic time-dependent Schrödinger equation into hydrodynamic equations of a virtual fluid. While the von Neumann entropy remains constant, we demonstrate that an increase of the Shannon entropy, associated with this Madelung fluid, is proportional to the expectation value of its velocity divergence. Hence, the Shannon entropy may grow (or decrease) due to an expansion (or compression) of the Madelung fluid. These effects result from the interference between solutions of the Schrödinger equation. Growth of the Shannon entropy due to expansion is common in diffusive processes. However, in the latter the process is irreversible while the processes in the Madelung fluid are always reversible. The relations between interference, compressibility and variation of the Shannon entropy are then examined in several simple examples. Furthermore, we demonstrate that for classical diffusive processes, the "force" accelerating diffusion has the form of the positive gradient of the quantum Bohm potential. Expressing then the diffusion coefficient in terms of the Planck constant reveals the lower bound given by the Heisenberg uncertainty principle in terms of the product between the gas mean free path and the Brownian momentum.

Statistical mechanics of an ideal active fluid confined in a channel

NASA Astrophysics Data System (ADS)

Wagner, Caleb; Baskaran, Aparna; Hagan, Michael

The statistical mechanics of ideal active Brownian particles (ABPs) confined in a channel is studied by obtaining the exact solution of the steady-state Smoluchowski equation for the 1-particle distribution function. The solution is derived using results from the theory of two-way diffusion equations, combined with an iterative procedure that is justified by numerical results. Using this solution, we quantify the effects of confinement on the spatial and orientational order of the ensemble. Moreover, we rigorously show that both the bulk density and the fraction of particles on the channel walls obey simple scaling relations as a function of channel width. By considering a constant-flux steady state, an effective diffusivity for ABPs is derived which shows signatures of the persistent motion that characterizes ABP trajectories. Finally, we discuss how our techniques generalize to other active models, including systems whose activity is modeled in terms of an Ornstein-Uhlenbeck process.

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.

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.

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.

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

PubMed

Holtzer, Gretchen L; Velegol, Darrell

2005-10-25

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

Valuation of exotic options in the framework of Levy processes

NASA Astrophysics Data System (ADS)

Milev, Mariyan; Georgieva, Svetla; Markovska, Veneta

2013-12-01

In this paper we explore a straightforward procedure to price derivatives by using the Monte Carlo approach when the underlying process is a jump-diffusion. We have compared the Black-Scholes model with one of its extensions that is the Merton model. The latter model is better in capturing the market's phenomena and is comparative to stochastic volatility models in terms of pricing accuracy. We have presented simulations of asset paths and pricing of barrier options for both Geometric Brownian motion and exponential Levy processes as it is the concrete case of the Merton model. A desired level of accuracy is obtained with simple computer operations in MATLAB for efficient computational time.

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.

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.

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

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.

Generalized moment analysis of magnetic field correlations for accumulations of spherical and cylindrical magnetic pertubers

NASA Astrophysics Data System (ADS)

Kurz, Felix; Kampf, Thomas; Buschle, Lukas; Schlemmer, Heinz-Peter; Bendszus, Martin; Heiland, Sabine; Ziener, Christian

2016-12-01

In biological tissue, an accumulation of similarly shaped objects with a susceptibility difference to the surrounding tissue generates a local distortion of the external magnetic field in magnetic resonance imaging. It induces stochastic field fluctuations that characteristically influence proton spin diffusion in the vicinity of these magnetic perturbers. The magnetic field correlation that is associated with such local magnetic field inhomogeneities can be expressed in the form of a dynamic frequency autocorrelation function that is related to the time evolution of the measured magnetization. Here, an eigenfunction expansion for two simple magnetic perturber shapes, that of spheres and cylinders, is considered for restricted spin diffusion in a simple model geometry. Then, the concept of generalized moment analysis, an approximation technique that is applied in the study of (non-)reactive processes that involve Brownian motion, allows to provide analytical expressions for the correlation function for different exponential decay forms. Results for the biexponential decay for both spherical and cylindrical magnetized objects are derived and compared with the frequently used (less accurate) monoexponential decay forms. They are in asymptotic agreement with the numerically exact value of the correlation function for long and short times.

Brownian dynamics simulations on a hypersphere in 4-space

NASA Astrophysics Data System (ADS)

Nissfolk, Jarl; Ekholm, Tobias; Elvingson, Christer

2003-10-01

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

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.

Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model.

PubMed

Dean, David S; Iorio, Antonio; Marinari, Enzo; Oshanin, Gleb

2016-09-01

The Sinai model of a tracer diffusing in a quenched Brownian potential is a much-studied problem exhibiting a logarithmically slow anomalous diffusion due to the growth of energy barriers with the system size. However, if the potential is random but periodic, the regime of anomalous diffusion crosses over to one of normal diffusion once a tracer has diffused over a few periods of the system. Here we consider a system in which the potential is given by a Brownian bridge on a finite interval (0,L) and then periodically repeated over the whole real line and study the power spectrum S(f) of the diffusive process x(t) in such a potential. We show that for most of realizations of x(t) in a given realization of the potential, the low-frequency behavior is S(f)∼A/f^{2}, i.e., the same as for standard Brownian motion, and the amplitude A is a disorder-dependent random variable with a finite support. Focusing on the statistical properties of this random variable, we determine the moments of A of arbitrary, negative, or positive order k and demonstrate that they exhibit a multifractal dependence on k and a rather unusual dependence on the temperature and on the periodicity L, which are supported by atypical realizations of the periodic disorder. We finally show that the distribution of A has a log-normal left tail and exhibits an essential singularity close to the right edge of the support, which is related to the Lifshitz singularity. Our findings are based both on analytic results and on extensive numerical simulations of the process x(t).

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.

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.

Translocation of a Polymer Chain across a Nanopore: A Brownian Dynamics Simulation Study

NASA Technical Reports Server (NTRS)

Tian, Pu; Smith, Grant D.

2003-01-01

We carried out Brownian dynamics simulation studies of the translocation of single polymer chains across a nanosized pore under the driving of an applied field (chemical potential gradient). The translocation process can be either dominated by the entropic barrier resulted from restricted motion of flexible polymer chains or by applied forces (or chemical gradient across the wall), we focused on the latter case in our studies. Calculation of radius of gyrations at the two opposite sides of the wall shows that the polymer chains are not in equilibrium during the translocation process. Despite this fact, our results show that the one-dimensional diffusion and the nucleation model provide an excellent description of the dependence of average translocation time on the chemical potential gradients, the polymer chain length and the solvent viscosity. In good agreement with experimental results and theoretical predictions, the translocation time distribution of our simple model shows strong non-Gaussian characteristics. It is observed that even for this simple tubelike pore geometry, more than one peak of translocation time distribution can be generated for proper pore diameter and applied field strengths. Both repulsive Weeks-Chandler-Anderson and attractive Lennard-Jones polymer-nanopore interaction were studied, attraction facilitates the translocation process by shortening the total translocation time and dramatically improve the capturing of polymer chain. The width of the translocation time distribution was found to decrease with increasing temperature, increasing field strength, and decreasing pore diameter.

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

Makhnovskii, Yurii A.; Berezhkovskii, Alexander M.; Antipov, Anatoly E.

This paper is devoted to particle transport in a tube formed by alternating wide and narrow sections, in the presence of an external biasing force. The focus is on the effective transport coefficients—mobility and diffusivity, as functions of the biasing force and the geometric parameters of the tube. Dependences of the effective mobility and diffusivity on the tube geometric parameters are known in the limiting cases of no bias and strong bias. The approximations used to obtain these results are inapplicable at intermediate values of the biasing force. To bridge the two limits Brownian dynamics simulations were run to determinemore » the transport coefficients at intermediate values of the force. The simulations were performed for a representative set of tube geometries over a wide range of the biasing force. They revealed that there is a range of the narrow section length, where the force dependence of the mobility has a maximum. In contrast, the diffusivity is a monotonically increasing function of the force. A simple formula is proposed, which reduces to the known dependences of the diffusivity on the tube geometric parameters in both limits of zero and strong bias. At intermediate values of the biasing force, the formula catches the diffusivity dependence on the narrow section length, if the radius of these sections is not too small.« less

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.

Robustness of multidimensional Brownian ratchets as directed transport mechanisms.

PubMed

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

2011-08-07

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

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.

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.

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

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.

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.

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.

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.

Transport behaviors of locally fractional coupled Brownian motors with fluctuating interactions

NASA Astrophysics Data System (ADS)

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

2018-09-01

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

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.

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

NASA Astrophysics Data System (ADS)

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

2012-03-01

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

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.

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.

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

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

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.

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

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

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

2015-03-21

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

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.

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

NASA Astrophysics Data System (ADS)

Bhattacharyay, A.

2018-03-01

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

Particle transport through hydrogels is charge asymmetric.

PubMed

Zhang, Xiaolu; Hansing, Johann; Netz, Roland R; DeRouchey, Jason E

2015-02-03

Transport processes within biological polymer networks, including mucus and the extracellular matrix, play an important role in the human body, where they serve as a filter for the exchange of molecules and nanoparticles. Such polymer networks are complex and heterogeneous hydrogel environments that regulate diffusive processes through finely tuned particle-network interactions. In this work, we present experimental and theoretical studies to examine the role of electrostatics on the basic mechanisms governing the diffusion of charged probe molecules inside model polymer networks. Translational diffusion coefficients are determined by fluorescence correlation spectroscopy measurements for probe molecules in uncharged as well as cationic and anionic polymer solutions. We show that particle transport in the charged hydrogels is highly asymmetric, with diffusion slowed down much more by electrostatic attraction than by repulsion, and that the filtering capability of the gel is sensitive to the solution ionic strength. Brownian dynamics simulations of a simple model are used to examine key parameters, including interaction strength and interaction range within the model networks. Simulations, which are in quantitative agreement with our experiments, reveal the charge asymmetry to be due to the sticking of particles at the vertices of the oppositely charged polymer networks. Copyright © 2015 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Two-dimensional transport in structured optical force landscapes

NASA Astrophysics Data System (ADS)

Xiao, Ke

The overdamped transport of a Brownian particle in a structured force landscape has been studied extensively for a century. Even such well-studied examples as Brownian transport in a one-dimensional tilted washboard potential continue to yield surprising results, with recent discoveries including the giant enhancement of diffusion at the depinning transition, and the so-called "thermal ratchet effect". The transport phenomena in higher-dimensional systems should be substantially richer, but remain largely unexplored. In this Thesis we study the biased diffusion of colloidal spheres through two-dimensional force landscapes created with holographic optical tweezers (HOT). These studies take advantage of holographic video microscopy (HVM), which enables us to follow spheres' three-dimensional motions with nanometer resolution while simultaneously measuring their radii and refractive indexes with part-per-thousand resolution. Using these techniques we investigated the kinetically and statistically locked-in transport of colloidal spheres through arrays of optical traps, and confirmed previously untested predictions for kinetically locked-in transport that can be used for sorting applications with previously unheard finesse. Extending this result to highly structured two-dimensional landscapes, we developed prismatic optical fractionation, in which objects with different physical properties are deflected into different directions, a phenomenon analogous to a prism dispersing different wavelengths of light into different directions. Our simulational and experimental studies revealed the important role that thermal fluctuations play in establishing the hierarchy of kinetically locked-in states. We also investigated Brownian motion in a two-dimensional optical force landscape that varies in time. The traps for these studies were arranged in particular pattern called a "Fibonacci spiral" that is both the densest arrangement of circular objects with a circular domain and also particularly endowed with useful and interesting symmetries. Periodically rotating this pattern gives rise to transport in the both radial and azimuthal dimensions, whose direction depends on the angle and speed of rotation as well as the inter-trap separation. This deceptively simple system displays an extremely rich pattern of flux reversals in both dimensions and creates new avenues for studying the departure from equilibrium in noise-driven machines.

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.

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.

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.

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.

Nucleation of rotating crystals by Thiovulum majus bacteria

NASA Astrophysics Data System (ADS)

Petroff, A. P.; Libchaber, A.

2018-01-01

Thiovulum majus self-organize on glass surfaces into active two-dimensional crystals of rotating cells. Unlike classical crystals, these bacterial crystallites continuously rotate and reorganize as the power of rotating cells is dissipated by the surrounding flow. In this article, we describe the earliest stage of crystallization, the attraction of two bacteria into a hydrodynamically-bound dimer. This process occurs in three steps. First a free-swimming cell collides with the wall and becomes hydrodynamically bound to the two-dimensional surface. We present a simple model to understand how viscous forces localize cells near the chamber walls. Next, the cell diffuses over the surface for an average of 63+/- 6 s before escaping to the bulk fluid. The diffusion coefficient {D}{{eff}}=7.98 +/- 0.1 μ {{{m}}}2 {{{s}}}-1 of these 8.5 μ {{m}} diameter cells corresponds to a temperature of (4.16+/- 0.05)× {10}4 K, and thus cannot be explained by equilibrium fluctuations. Finally, two cells coalesce into a rotating dimer when the convergent flow created by each cell overwhelms their active Brownian motion. This occurs when cells diffuse to within a distance of 13.3 ± 0.2 μm of each other.

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.

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.

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.

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.

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.

Random diffusion and leverage effect in financial markets.

PubMed

Perelló, Josep; Masoliver, Jaume

2003-03-01

We prove that Brownian market models with random diffusion coefficients provide an exact measure of the leverage effect [J-P. Bouchaud et al., Phys. Rev. Lett. 87, 228701 (2001)]. This empirical fact asserts that past returns are anticorrelated with future diffusion coefficient. Several models with random diffusion have been suggested but without a quantitative study of the leverage effect. Our analysis lets us to fully estimate all parameters involved and allows a deeper study of correlated random diffusion models that may have practical implications for many aspects of financial markets.

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.

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.

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

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).

Brownian motion on random dynamical landscapes

NASA Astrophysics Data System (ADS)

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

2016-03-01

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

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

PubMed

Mody, Nipa A; King, Michael R

2007-05-22

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

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.

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

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.

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

Electrodeposition in microgravity: Ground-based experiments

NASA Technical Reports Server (NTRS)

Riley, C.; Coble, H. D.

1982-01-01

Electrodeposition was studied at one-hundreth g and compared with bench studies at 1 g. The low gravity was achieved during KC-135 aircraft parobolic flights. Flow in a simple cobalt cell (1 M CoSO4) operating under typical commercial conditions (10 to 20 mA/sq cm and 1 V) was monitored with a Schlieren optical system. Natural convection was absent at one-hundreth g. Quantitative comparisons on a cobalt cell with shielded electrodes using interferometry were carried out. Fringe shift differences indicate greater semi-infinite linear diffusion at 1 g than at one-hundreth g for cobalt. Since a shielded electrode operates under diffusion controlled conditions, no differences between 1 g and one-hundreth g would be expected. Similar comparisons on a shielded electrode copper cell were inconclusive. Bench codeposition experiments using polystyrene neutral buoyancy particles coupled with a shielded electrode cobalt cell were begun. Tracking of 12 micron particles showed no measurable difference between thermal/Brownian motion when the cell was operational or nonoperational. Initial experiments on codeposition quality showed a strong dependence upon cathode surface preparation in a shielded electrode configuration.

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.

Algorithms for Brownian first-passage-time estimation

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2009-09-01

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

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.

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.

Optimization of nanoparticle focusing by coupling thermophoresis and engineered vortex in a microfluidic channel

NASA Astrophysics Data System (ADS)

Zhao, Chao; Cao, Zhibo; Fraser, John; Oztekin, Alparslan; Cheng, Xuanhong

2017-01-01

Enriching nanoparticles in an aqueous solution is commonly practiced for various applications. Despite recent advances in microfluidic technologies, a general method to concentrate nanoparticles in a microfluidic channel in a label free and continuous flow fashion is not yet available, due to strong Brownian motion on the nanoscale. Recent research of thermophoresis indicates that thermophoretic force can overcome the Brownian force to direct nanoparticle movement. Coupling thermophoresis with natural convection on the microscale has been shown to induce significant enrichment of biomolecules in a thermal diffusion column. However, the column operates in a batch process, and the concentrated samples are inconvenient to retrieve. We have recently designed a microfluidic device that combines a helical fluid motion and simple one-dimensional temperature gradient to achieve effective nanoparticle focusing in a continuous flow. The helical convection is introduced by microgrooves patterned on the channel floor, which directly controls the focusing speed and power. Here, COMSOL simulations are conducted to study how the device geometry and flow rate influence transport and subsequent nanoparticle focusing, with a constant temperature gradient. The results demonstrate a complex dependence of nanoparticle accumulation on the microgroove tilting angle, depth, and spacing, as well as channel width and flow rate. Further dimensional analyses reveal that the ratio between particle velocities induced by thermophoretic and fluid inertial forces governs the particle concentration factor, with a maximum concentration at a ratio of approximately one. This simple relationship provides fundamental insights about nanoparticle transport in coupled flow and thermal fields. The study also offers a useful guideline to the design and operation of nanoparticle concentrators based on combining engineered helical fluid motion subject to phoretic fields.

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.

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.

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.

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.

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

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.

Velocity Gradient Power Functional for Brownian Dynamics.

PubMed

de Las Heras, Daniel; Schmidt, Matthias

2018-01-12

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

Velocity Gradient Power Functional for Brownian Dynamics

NASA Astrophysics Data System (ADS)

de las Heras, Daniel; Schmidt, Matthias

2018-01-01

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

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.

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.

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

PubMed Central

Mody, Nipa A.; King, Michael R.

2008-01-01

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

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.

Ratcheted electrophoresis of Brownian particles

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

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

2016-05-16

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

Brownian 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

Unlikely Fluctuations and Non-Equilibrium Work Theorems-A Simple Example.

PubMed

Muzikar, Paul

2016-06-30

An exciting development in statistical mechanics has been the elucidation of a series of surprising equalities involving the work done during a nonequilibrium process. Astumian has presented an elegant example of such an equality, involving a colloidal particle undergoing Brownian motion in the presence of gravity. We analyze this example; its simplicity, and its link to geometric Brownian motion, allows us to clarify the inner workings of the equality. Our analysis explicitly shows the important role played by large, unlikely fluctuations.

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.

Intrachain exciton dynamics in conjugated polymer chains in solution.

PubMed

Tozer, Oliver Robert; Barford, William

2015-08-28

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

Analogies Between Colloidal Sedimentation and Turbulent Convection at High Prandtl Numbers

NASA Technical Reports Server (NTRS)

Tong, P.; Ackerson, B. J.

1999-01-01

A new set of coarse-grained equations of motion is proposed to describe concentration and velocity fluctuations in a dilute sedimenting suspension of non-Brownian particles. With these equations, colloidal sedimentation is found to be analogous to turbulent convection at high Prandtl numbers. Using Kraichnan's mixing-length theory, we obtain scaling relations for the diffusive dissipation length delta(sub theta), the velocity variance delta u, and the concentration variance delta phi. The obtained scaling laws over varying particle radius alpha and volume fraction phi(sub ) are in excellent agreement with the recent experiment by Segre, Herbolzheimer, and Chaikin. The analogy between colloidal sedimentation and turbulent convection gives a simple interpretation for the existence of a velocity cut-off length, which prevents hydrodynamic dispersion coefficients from being divergent. It also provides a coherent framework for the study of sedimentation dynamics in different colloidal systems.

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.

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.

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.

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

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.

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.

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

PubMed

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

2018-05-09

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

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.

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.

Monte Carlo algorithms for Brownian phylogenetic models.

PubMed

Horvilleur, Benjamin; Lartillot, Nicolas

2014-11-01

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

Feller processes: the next generation in modeling. Brownian motion, Lévy processes and beyond.

PubMed

Böttcher, Björn

2010-12-03

We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space dependent mixing of Lévy processes. Brownian Motion is one of the most frequently used continuous time Markov processes in applications. In recent years also Lévy processes, of which Brownian Motion is a special case, have become increasingly popular. Lévy processes are spatially homogeneous, but empirical data often suggest the use of spatially inhomogeneous processes. Thus it seems necessary to go to the next level of generalization: Feller processes. These include Lévy processes and in particular brownian motion as special cases but allow spatial inhomogeneities. Many properties of Feller processes are known, but proving the very existence is, in general, very technical. Moreover, an applicable framework for the generation of sample paths of a Feller process was missing. We explain, with practitioners in mind, how to overcome both of these obstacles. In particular our simulation technique allows to apply Monte Carlo methods to Feller processes.

Feller Processes: The Next Generation in Modeling. Brownian Motion, Lévy Processes and Beyond

PubMed Central

Böttcher, Björn

2010-01-01

We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space dependent mixing of Lévy processes. Brownian Motion is one of the most frequently used continuous time Markov processes in applications. In recent years also Lévy processes, of which Brownian Motion is a special case, have become increasingly popular. Lévy processes are spatially homogeneous, but empirical data often suggest the use of spatially inhomogeneous processes. Thus it seems necessary to go to the next level of generalization: Feller processes. These include Lévy processes and in particular Brownian motion as special cases but allow spatial inhomogeneities. Many properties of Feller processes are known, but proving the very existence is, in general, very technical. Moreover, an applicable framework for the generation of sample paths of a Feller process was missing. We explain, with practitioners in mind, how to overcome both of these obstacles. In particular our simulation technique allows to apply Monte Carlo methods to Feller processes. PMID:21151931

Quantum dynamical framework for Brownian heat engines

NASA Astrophysics Data System (ADS)

Agarwal, G. S.; Chaturvedi, S.

2013-07-01

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

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

[Using Molecular Simulations to Understand Complex Nanoscale Dynamic Phenomena in Polymer Solutions

NASA Technical Reports Server (NTRS)

Smith, Grant

2004-01-01

The first half of the project concentrated on molecular simulation studies of the translocation of model molecules for single-stranded DNA through a nanosized pore. This has resulted in the publication, Translocation of a polymer chain across a nanopore: A Brownian dynamics simulation study, by Pu Tian and Grant D. Smith, JOURNAL OF CHEMICAL PHYSICS VOLUME 119, NUMBER 21 1 DECEMBER 2003, which is attached to this report. In this work we carried out Brownian dynamics simulation studies of the translocation of single polymer chains across a nanosized pore under the driving of an applied field (chemical potential gradient) designed to mimic an electrostatic field. The translocation process can be either dominated by the entropic barrier resulted from restricted motion of flexible polymer chains or by applied forces (or chemical gradient). We focused on the latter case in our studies. Calculation of radius of gyration of the translocating chain at the two opposite sides of the wall shows that the polymer chains are not in equilibrium during the translocation process. Despite this fact, our results show that the one-dimensional diffusion and the nucleation model provide an excellent description of the dependence of average translocation time on the chemical potential gradients, the polymer chain length and the solvent viscosity. In good agreement with experimental results and theoretical predictions, the translocation time distribution of our simple model shows strong non-Gaussian characteristics. It is observed that even for this simple tube-like pore geometry, more than one peak of translocation time distribution can be generated for proper pore diameter and applied field strengths. Both repulsive Weeks-Chandler-Anderson and attractive Lennard-Jones polymer-nanopore interaction were studied. Attraction facilitates the translocation process by shortening the total translocation time and dramatically improve the capturing of polymer chain. The width of the translocation time distribution was found to decrease with increasing temperature, increasing field strength, and decreasing pore diameter.

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.

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

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.

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

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

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

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.

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

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.

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.

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.

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.

Quantitative Characterization of the Microstructure and Transport Properties of Biopolymer Networks

PubMed Central

Jiao, Yang; Torquato, Salvatore

2012-01-01

Biopolymer networks are of fundamental importance to many biological processes in normal and tumorous tissues. In this paper, we employ the panoply of theoretical and simulation techniques developed for characterizing heterogeneous materials to quantify the microstructure and effective diffusive transport properties (diffusion coefficient De and mean survival time τ) of collagen type I networks at various collagen concentrations. In particular, we compute the pore-size probability density function P(δ) for the networks and present a variety of analytical estimates of the effective diffusion coefficient De for finite-sized diffusing particles, including the low-density approximation, the Ogston approximation, and the Torquato approximation. The Hashin-Strikman upper bound on the effective diffusion coefficient De and the pore-size lower bound on the mean survival time τ are used as benchmarks to test our analytical approximations and numerical results. Moreover, we generalize the efficient first-passage-time techniques for Brownian-motion simulations in suspensions of spheres to the case of fiber networks and compute the associated effective diffusion coefficient De as well as the mean survival time τ, which is related to nuclear magnetic resonance (NMR) relaxation times. Our numerical results for De are in excellent agreement with analytical results for simple network microstructures, such as periodic arrays of parallel cylinders. Specifically, the Torquato approximation provides the most accurate estimates of De for all collagen concentrations among all of the analytical approximations we consider. We formulate a universal curve for τ for the networks at different collagen concentrations, extending the work of Yeong and Torquato [J. Chem. Phys. 106, 8814 (1997)]. We apply rigorous cross-property relations to estimate the effective bulk modulus of collagen networks from a knowledge of the effective diffusion coefficient computed here. The use of cross-property relations to link other physical properties to the transport properties of collagen networks is also discussed. PMID:22683739

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

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.

Calculation of the Maxwell stress tensor and the Poisson-Boltzmann force on a solvated molecular surface using hypersingular boundary integrals

NASA Astrophysics Data System (ADS)

Lu, Benzhuo; Cheng, Xiaolin; Hou, Tingjun; McCammon, J. Andrew

2005-08-01

The electrostatic interaction among molecules solvated in ionic solution is governed by the Poisson-Boltzmann equation (PBE). Here the hypersingular integral technique is used in a boundary element method (BEM) for the three-dimensional (3D) linear PBE to calculate the Maxwell stress tensor on the solvated molecular surface, and then the PB forces and torques can be obtained from the stress tensor. Compared with the variational method (also in a BEM frame) that we proposed recently, this method provides an even more efficient way to calculate the full intermolecular electrostatic interaction force, especially for macromolecular systems. Thus, it may be more suitable for the application of Brownian dynamics methods to study the dynamics of protein/protein docking as well as the assembly of large 3D architectures involving many diffusing subunits. The method has been tested on two simple cases to demonstrate its reliability and efficiency, and also compared with our previous variational method used in BEM.

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.

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

PubMed Central

Volpe, Giovanni

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

Volpe, Giorgio; Volpe, Giovanni

2017-10-01

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

Brownian systems with spatially inhomogeneous activity

NASA Astrophysics Data System (ADS)

Sharma, A.; Brader, J. M.

2017-09-01

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

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.

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.

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.

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.

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.

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.

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.

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

A simple microviscometric approach based on Brownian motion tracking.

PubMed

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

2015-02-01

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

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

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

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

2016-07-15

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

A Fractional Differential Kinetic Equation and Applications to Modelling Bursts in Turbulent Nonlinear Space Plasmas

NASA Astrophysics Data System (ADS)

Watkins, N. W.; Rosenberg, S.; Sanchez, R.; Chapman, S. C.; Credgington, D.

2008-12-01

Since the 1960s Mandelbrot has advocated the use of fractals for the description of the non-Euclidean geometry of many aspects of nature. In particular he proposed two kinds of model to capture persistence in time (his Joseph effect, common in hydrology and with fractional Brownian motion as the prototype) and/or prone to heavy tailed jumps (the Noah effect, typical of economic indices, for which he proposed Lévy flights as an exemplar). Both effects are now well demonstrated in space plasmas, notably in the turbulent solar wind. Models have, however, typically emphasised one of the Noah and Joseph parameters (the Lévy exponent μ and the temporal exponent β) at the other's expense. I will describe recent work in which we studied a simple self-affine stable model-linear fractional stable motion, LFSM, which unifies both effects and present a recently-derived diffusion equation for LFSM. This replaces the second order spatial derivative in the equation of fBm with a fractional derivative of order μ, but retains a diffusion coefficient with a power law time dependence rather than a fractional derivative in time. I will also show work in progress using an LFSM model and simple analytic scaling arguments to study the problem of the area between an LFSM curve and a threshold. This problem relates to the burst size measure introduced by Takalo and Consolini into solar-terrestrial physics and further studied by Freeman et al [PRE, 2000] on solar wind Poynting flux near L1. We test how expressions derived by other authors generalise to the non-Gaussian, constant threshold problem. Ongoing work on extension of these LFSM results to multifractals will also be discussed.

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

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.

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.

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.

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

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.

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.

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.

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.

Polymer deformation in Brownian ratchets: theory and molecular dynamics simulations.

PubMed

Kenward, Martin; Slater, Gary W

2008-11-01

We examine polymers in the presence of an applied asymmetric sawtooth (ratchet) potential which is periodically switched on and off, using molecular dynamics (MD) simulations with an explicit Lennard-Jones solvent. We show that the distribution of the center of mass for a polymer in a ratchet is relatively wide for potential well depths U0 on the order of several kBT. The application of the ratchet potential also deforms the polymer chains. With increasing U0 the Flory exponent varies from that for a free three-dimensional (3D) chain, nu=35 (U0=0), to that corresponding to a 2D compressed (pancake-shaped) polymer with a value of nu=34 for moderate U0. This has the added effect of decreasing a polymer's diffusion coefficient from its 3D value D3D to that of a pancaked-shaped polymer moving parallel to its minor axis D2D. The result is that a polymer then has a time-dependent diffusion coefficient D(t) during the ratchet off time. We further show that this suggests a different method to operate a ratchet, where the off time of the ratchet, toff, is defined in terms of the relaxation time of the polymer, tauR. We also derive a modified version of the Bader ratchet model [Bader, Proc. Natl. Acad. Sci. U.S.A. 96, 13165 (1999)] which accounts for this deformation and we present a simple expression to describe the time dependent diffusion coefficient D(t). Using this model we then illustrate that polymer deformation can be used to modulate polymer migration in a ratchet potential.

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.

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

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.

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).

Modeling the electrophoretic separation of short biological molecules in nanofluidic devices

NASA Astrophysics Data System (ADS)

Fayad, Ghassan; Hadjiconstantinou, Nicolas

2010-11-01

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

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

REVIEW ARTICLE: How do biomolecular systems speed up and regulate rates?

NASA Astrophysics Data System (ADS)

Zhou, Huan-Xiang

2005-09-01

The viability of a biological system depends upon careful regulation of the rates of various processes. These rates have limits imposed by intrinsic chemical or physical steps (e.g., diffusion). These limits can be expanded by interactions and dynamics of the biomolecules. For example, (a) a chemical reaction is catalyzed when its transition state is preferentially bound to an enzyme; (b) the folding of a protein molecule is speeded up by specific interactions within the transition-state ensemble and may be assisted by molecular chaperones; (c) the rate of specific binding of a protein molecule to a cellular target can be enhanced by mechanisms such as long-range electrostatic interactions, nonspecific binding and folding upon binding; (d) directional movement of motor proteins is generated by capturing favorable Brownian motion through intermolecular binding energy; and (e) conduction and selectivity of ions through membrane channels are controlled by interactions and the dynamics of channel proteins. Simple physical models are presented here to illustrate these processes and provide a unifying framework for understanding speed attainment and regulation in biomolecular systems.

Non-constant link tension coefficient in the tumbling-snake model subjected to simple shear

NASA Astrophysics Data System (ADS)

Stephanou, Pavlos S.; Kröger, Martin

2017-11-01

The authors of the present study have recently presented evidence that the tumbling-snake model for polymeric systems has the necessary capacity to predict the appearance of pronounced undershoots in the time-dependent shear viscosity as well as an absence of equally pronounced undershoots in the transient two normal stress coefficients. The undershoots were found to appear due to the tumbling behavior of the director u when a rotational Brownian diffusion term is considered within the equation of motion of polymer segments, and a theoretical basis concerning the use of a link tension coefficient given through the nematic order parameter had been provided. The current work elaborates on the quantitative predictions of the tumbling-snake model to demonstrate its capacity to predict undershoots in the time-dependent shear viscosity. These predictions are shown to compare favorably with experimental rheological data for both polymer melts and solutions, help us to clarify the microscopic origin of the observed phenomena, and demonstrate in detail why a constant link tension coefficient has to be abandoned.

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.

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

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.

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.

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.

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.

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.

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.

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

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.

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.

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

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.

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.

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.

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

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

Inertial effects in suspension dynamics

NASA Astrophysics Data System (ADS)

Subramanian, Ganesh

2002-04-01

This work analyses the role of small but finite particle inertia on the microstructure of suspensions of heavy particles subjected to an external flow. The magnitude of particle inertia is characterized by the Stokes number (St), defined as the ratio of the inertial relaxation time of a particle to the flow time scale. Fluid inertia is neglected so that the fluid motion satisfies the quasi-steady Stokes equations. The statistics of the particles is governed by a Fokker-Planck equation in position and velocity space. For small St, a multiple scales formalism is developed to solve for the phase-space probability density of a single spherical Brownian particle in a linear flow. Though valid for an arbitrary flow field, the method fails for a spatially varying mass and drag coefficient. In all cases, however, a Chapman-Enskog-like formulation provides a valid multi-scale description of the dynamics both for a single Brownian particle and a suspension of interacting particles. For long times, the leading order solution simplifies to the product of a local Maxwellian in velocity space and a spatial density satisfying the Smoluchowski equation. The higher order corrections capture both short-time momentum relaxations and long-time deviations from the Maxwellian. The inertially corrected Smoluchowski equation includes a non-Fickian term at O( St). The pair problem is solved to O(St) for non-Brownian spherical particles in simple shear flow. In contrast to the zero inertia case, the relative trajectories of two particles are asymmetric. Open trajectories in the plane of shear suffer a downward displacement in the velocity gradient direction. The surface of the reference sphere 'repels' nearby trajectories that spiral out onto a new stable limit cycle in the shearing plane. This limit cycle acts as a local attractor and all in-plane trajectories from an initial offset of O(St½ ) or less approach the limit cycle. The topology of the off-plane trajectories is more complicated because the gradient displacement changes sign away from the plane of shear. The 'neutral' off-plane trajectory with zero net gradient displacement acts to separate trajectories spiralling onto contact from those that go off to infinity. The aforementioned asymmetry leads to a non-Newtonian rheology and self-diffusivities in the gradient and vorticity directions that scale as St2ln St and St2, respectively.

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

NASA Astrophysics Data System (ADS)

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

2010-04-01

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

First-passage time of Brownian motion with dry friction.

PubMed

Chen, Yaming; Just, Wolfram

2014-02-01

We provide an analytic solution to the first-passage time (FPT) problem of a piecewise-smooth stochastic model, namely Brownian motion with dry friction, using two different but closely related approaches which are based on eigenfunction decompositions on the one hand and on the backward Kolmogorov equation on the other. For the simple case containing only dry friction, a phase-transition phenomenon in the spectrum is found which relates to the position of the exit point, and which affects the tail of the FPT distribution. For the model containing as well a driving force and viscous friction the impact of the corresponding stick-slip transition and of the transition to ballistic exit is evaluated quantitatively. The proposed model is one of the very few cases where FPT properties are accessible by analytical means.

From Random Walks to Brownian Motion, from Diffusion to Entropy: Statistical Principles in Introductory Physics

NASA Astrophysics Data System (ADS)

Reeves, Mark

2014-03-01

Entropy changes underlie the physics that dominates biological interactions. Indeed, introductory biology courses often begin with an exploration of the qualities of water that are important to living systems. However, one idea that is not explicitly addressed in most introductory physics or biology textbooks is dominant contribution of the entropy in driving important biological processes towards equilibrium. From diffusion to cell-membrane formation, to electrostatic binding in protein folding, to the functioning of nerve cells, entropic effects often act to counterbalance deterministic forces such as electrostatic attraction and in so doing, allow for effective molecular signaling. A small group of biology, biophysics and computer science faculty have worked together for the past five years to develop curricular modules (based on SCALEUP pedagogy) that enable students to create models of stochastic and deterministic processes. Our students are first-year engineering and science students in the calculus-based physics course and they are not expected to know biology beyond the high-school level. In our class, they learn to reduce seemingly complex biological processes and structures to be described by tractable models that include deterministic processes and simple probabilistic inference. The students test these models in simulations and in laboratory experiments that are biologically relevant. The students are challenged to bridge the gap between statistical parameterization of their data (mean and standard deviation) and simple model-building by inference. This allows the students to quantitatively describe realistic cellular processes such as diffusion, ionic transport, and ligand-receptor binding. Moreover, the students confront ``random'' forces and traditional forces in problems, simulations, and in laboratory exploration throughout the year-long course as they move from traditional kinematics through thermodynamics to electrostatic interactions. This talk will present a number of these exercises, with particular focus on the hands-on experiments done by the students, and will give examples of the tangible material that our students work with throughout the two-semester sequence of their course on introductory physics with a bio focus. Supported by NSF DUE.

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.

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.

[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.

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.

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

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.

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.

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.

Power spectrum analysis with least-squares fitting: amplitude bias and its elimination, with application to optical tweezers and atomic force microscope cantilevers.

PubMed

Nørrelykke, Simon F; Flyvbjerg, Henrik

2010-07-01

Optical tweezers and atomic force microscope (AFM) cantilevers are often calibrated by fitting their experimental power spectra of Brownian motion. We demonstrate here that if this is done with typical weighted least-squares methods, the result is a bias of relative size between -2/n and +1/n on the value of the fitted diffusion coefficient. Here, n is the number of power spectra averaged over, so typical calibrations contain 10%-20% bias. Both the sign and the size of the bias depend on the weighting scheme applied. Hence, so do length-scale calibrations based on the diffusion coefficient. The fitted value for the characteristic frequency is not affected by this bias. For the AFM then, force measurements are not affected provided an independent length-scale calibration is available. For optical tweezers there is no such luck, since the spring constant is found as the ratio of the characteristic frequency and the diffusion coefficient. We give analytical results for the weight-dependent bias for the wide class of systems whose dynamics is described by a linear (integro)differential equation with additive noise, white or colored. Examples are optical tweezers with hydrodynamic self-interaction and aliasing, calibration of Ornstein-Uhlenbeck models in finance, models for cell migration in biology, etc. Because the bias takes the form of a simple multiplicative factor on the fitted amplitude (e.g. the diffusion coefficient), it is straightforward to remove and the user will need minimal modifications to his or her favorite least-squares fitting programs. Results are demonstrated and illustrated using synthetic data, so we can compare fits with known true values. We also fit some commonly occurring power spectra once-and-for-all in the sense that we give their parameter values and associated error bars as explicit functions of experimental power-spectral values.

Quasi-steady-state analysis of coupled flashing ratchets.

PubMed

Levien, Ethan; Bressloff, Paul C

2015-10-01

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

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.

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

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.

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.

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

Entropy-based separation of yeast cells using a microfluidic system of conjoined spheres

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

Huang, Kai-Jian; Qin, S.-J., E-mail: shuijie.qin@gmail.com; Bai, Zhong-Chen

2013-11-21

A physical model is derived to create a biological cell separator that is based on controlling the entropy in a microfluidic system having conjoined spherical structures. A one-dimensional simplified model of this three-dimensional problem in terms of the corresponding effects of entropy on the Brownian motion of particles is presented. This dynamic mechanism is based on the Langevin equation from statistical thermodynamics and takes advantage of the characteristics of the Fokker-Planck equation. This mechanism can be applied to manipulate biological particles inside a microfluidic system with identical, conjoined, spherical compartments. This theoretical analysis is verified by performing a rapid andmore » a simple technique for separating yeast cells in these conjoined, spherical microfluidic structures. The experimental results basically match with our theoretical model and we further analyze the parameters which can be used to control this separation mechanism. Both numerical simulations and experimental results show that the motion of the particles depends on the geometrical boundary conditions of the microfluidic system and the initial concentration of the diffusing material. This theoretical model can be implemented in future biophysics devices for the optimized design of passive cell sorters.« less

Fluctuation, dissipation, and a non-equilibrium ``equation of state'' via nonlinear microrheology of hydrodynamically interacting colloids

NASA Astrophysics Data System (ADS)

Chu, Henry; Zia, Roseanna

2014-11-01

In our recently developed non-equilibrium Stokes-Einstein relation for microrheology, we showed that, in the absence of hydrodynamic interactions, the stress in a suspension is given by a balance between fluctuation and dissipation. Here we generalize our theory to develop a simple analytical relation connecting diffusive fluctuation, viscous dissipation and suspension stress in systems of hydrodynamically interacting colloids. In active microrheology, a Brownian probe is driven through a complex medium. The strength of probe forcing compared to the entropic restoring force defines a Peclet number, Pe. In the absence of hydrodynamics, normal stress differences scale as Pe4 and Pe for weak and strong probe forcing, respectively. But as hydrodynamics become important, interparticle forces give way to lubrication interactions and the normal stresses scale as Pe2 and Peδln(Pe), where 0.773 <= δ <= 1 as hydrodynamics vary from strong to weak. The new phenomenological theory is shown to agree with standard micromechanical definitions of the stress. A connection is made between the stress and an effective temperature of the medium, prompting the interpretation of the particle stress as the energy density, and the expression for osmotic pressure as a ``non-equilibrium equation of state.''

Modeling of submicrometer aerosol penetration through sintered granular membrane filters.

PubMed

Marre, Sonia; Palmeri, John; Larbot, André; Bertrand, Marielle

2004-06-01

We present a deep-bed aerosol filtration model that can be used to estimate the efficiency of sintered granular membrane filters in the region of the most penetrating particle size. In this region the capture of submicrometer aerosols, much smaller than the filter pore size, takes place mainly via Brownian diffusion and direct interception acting in synergy. By modeling the disordered sintered grain packing of such filters as a simple cubic lattice, and mapping the corresponding 3D connected pore volume onto a discrete cylindrical pore network, the efficiency of a granular filter can be estimated, using new analytical results for the efficiency of cylindrical pores. This model for aerosol penetration in sintered granular filters includes flow slip and the kinetics of particle capture by the pore surface. With a unique choice for two parameters, namely the structural tortuosity and effective kinetic coefficient of particle adsorption, this semiempirical model can account for the experimental efficiency of a new class of "high-efficiency particulate air" ceramic membrane filters as a function of particle size over a wide range of filter thickness and texture (pore size and porosity) and operating conditions (face velocity).

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.

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.

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.

Steady states of OQBM: Central Limit Theorem, Gaussian and non-Gaussian behavior

NASA Astrophysics Data System (ADS)

Petruccione, Francesco; Sinayskiy, Ilya

Open Quantum Brownian Motion (OQBM) describes a Brownian particle with an additional internal quantum degree of freedom. Originally, it was introduced as a scaling limit of Open Quantum Walks (OQWs). Recently, it was noted, that for the model of free OQBM with a two-level system as an internal degree of freedom and decoherent coupling to a dissipative environment, one could use weak external driving of the internal degree of freedom to manipulate the steady-state position of the walker. This observation establishes a useful connection between controllable parameters of the OQBM, e.g. driving strengths and magnitude of detuning, and its steady state properties. Although OQWs satisfy a central limit theorem (CLT), it is known, that OQBM, in general, does not. The aim of this work is to derive steady states for some particular OQBMs and observe possible transitions from Gaussian to non-Gaussian behavior depending on the choice of quantum coin and as a function of diffusion coefficient and dissipation strength.

Best dispersal strategies in spatially heterogeneous environments: optimization of the principal eigenvalue for indefinite fractional Neumann problems.

PubMed

Pellacci, Benedetta; Verzini, Gianmaria

2018-05-01

We study the positive principal eigenvalue of a weighted problem associated with the Neumann spectral fractional Laplacian. This analysis is related to the investigation of the survival threshold in population dynamics. Our main result concerns the optimization of such threshold with respect to the fractional order [Formula: see text], the case [Formula: see text] corresponding to the standard Neumann Laplacian: when the habitat is not too fragmented, the principal positive eigenvalue can not have local minima for [Formula: see text]. As a consequence, the best strategy for survival is either following the diffusion with [Formula: see text] (i.e. Brownian diffusion), or with the lowest possible s (i.e. diffusion allowing long jumps), depending on the size of the domain. In addition, we show that analogous results hold for the standard fractional Laplacian in [Formula: see text], in periodic environments.

Dispersion in Rectangular Networks: Effective Diffusivity and Large-Deviation Rate Function

NASA Astrophysics Data System (ADS)

Tzella, Alexandra; Vanneste, Jacques

2016-09-01

The dispersion of a diffusive scalar in a fluid flowing through a network has many applications including to biological flows, porous media, water supply, and urban pollution. Motivated by this, we develop a large-deviation theory that predicts the evolution of the concentration of a scalar released in a rectangular network in the limit of large time t ≫1 . This theory provides an approximation for the concentration that remains valid for large distances from the center of mass, specifically for distances up to O (t ) and thus much beyond the O (t1 /2) range where a standard Gaussian approximation holds. A byproduct of the approach is a closed-form expression for the effective diffusivity tensor that governs this Gaussian approximation. Monte Carlo simulations of Brownian particles confirm the large-deviation results and demonstrate their effectiveness in describing the scalar distribution when t is only moderately large.

The influence of ionic strength on DNA diffusion in gel networks

NASA Astrophysics Data System (ADS)

Fu, Yuanxi; Jee, Ah-Young; Kim, Hyeong-Ju; Granick, Steve

Cations are known to reduce the rigidity of the DNA molecules by screening the negative charge along the sugar phosphate backbone. This was established by optical tweezer pulling experiment of immobilized DNA strands. However, little is known regarding the influence of ions on the motion of DNA molecules as they thread through network meshes. We imaged in real time the Brownian diffusion of fluorescent labeled lambda-DNA in an agarose gel network in the presence of salt with monovalent or multivalent cations. Each movie was analyzed using home-written program to yield a trajectory of center of the mass and the accompanying history of the shape fluctuations. One preliminary finding is that ionic strength has a profound influence on the slope of the trace of mean square displacement (MSD) versus time. The influence of ionic strength on DNA diffusion in gel networks.

Model and Comparative Study for Flow of Viscoelastic Nanofluids with Cattaneo-Christov Double Diffusion

PubMed Central

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

2017-01-01

Here two classes of viscoelastic fluids have been analyzed in the presence of Cattaneo-Christov double diffusion expressions of heat and mass transfer. A linearly stretched sheet has been used to create the flow. Thermal and concentration diffusions are characterized firstly by introducing Cattaneo-Christov fluxes. Novel features regarding Brownian motion and thermophoresis are retained. The conversion of nonlinear partial differential system to nonlinear ordinary differential system has been taken into place by using suitable transformations. The resulting nonlinear systems have been solved via convergent approach. Graphs have been sketched in order to investigate how the velocity, temperature and concentration profiles are affected by distinct physical flow parameters. Numerical values of skin friction coefficient and heat and mass transfer rates at the wall are also computed and discussed. Our observations demonstrate that the temperature and concentration fields are decreasing functions of thermal and concentration relaxation parameters. PMID:28046011

Contributions of microtubule rotation and dynamic instability to kinetochore capture

NASA Astrophysics Data System (ADS)

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

2014-03-01

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

Sedimentation and gravitational instability of Escherichia coli Suspension

NASA Astrophysics Data System (ADS)

Salin, Dominique; Douarche, Carine

2017-11-01

The successive runs and tumbles of Escherichia coli bacteria provide an active matter suspension of rod-like particles with a large swimming, Brownian like, diffusion. As opposed to inactive elongated particles, this diffusion prevents clustering of the particles and hence instability in the gravity field. We measure the time dependent E . coli concentration profile during their sedimentation. After some hours, due to the dioxygen consumption, a motile / non-motile front forms leading to a Rayleigh-Taylor type gravitational instability. Analysing both sedimentation and instability in the framework of active particle suspensions, we can measure the relevant bacteria hydrodynamic characteristics such as its single particle sedimentation velocity and its hindrance volume. Comparing these quantities to the ones of equivalent passive particles (ellipsoid, rod) we tentatively infer the effective shape and size of the bacteria involved in its buoyancy induced advection and diffusion. Laboratoire FAST University Paris Saclay France.

Catalytic micromotor generating self-propelled regular motion through random fluctuation.

PubMed

Yamamoto, Daigo; Mukai, Atsushi; Okita, Naoaki; Yoshikawa, Kenichi; Shioi, Akihisa

2013-07-21

Most of the current studies on nano∕microscale motors to generate regular motion have adapted the strategy to fabricate a composite with different materials. In this paper, we report that a simple object solely made of platinum generates regular motion driven by a catalytic chemical reaction with hydrogen peroxide. Depending on the morphological symmetry of the catalytic particles, a rich variety of random and regular motions are observed. The experimental trend is well reproduced by a simple theoretical model by taking into account of the anisotropic viscous effect on the self-propelled active Brownian fluctuation.

Catalytic micromotor generating self-propelled regular motion through random fluctuation

NASA Astrophysics Data System (ADS)

Yamamoto, Daigo; Mukai, Atsushi; Okita, Naoaki; Yoshikawa, Kenichi; Shioi, Akihisa

2013-07-01

Most of the current studies on nano/microscale motors to generate regular motion have adapted the strategy to fabricate a composite with different materials. In this paper, we report that a simple object solely made of platinum generates regular motion driven by a catalytic chemical reaction with hydrogen peroxide. Depending on the morphological symmetry of the catalytic particles, a rich variety of random and regular motions are observed. The experimental trend is well reproduced by a simple theoretical model by taking into account of the anisotropic viscous effect on the self-propelled active Brownian fluctuation.

Short- and long-time diffusion and dynamic scaling in suspensions of charged colloidal particles

NASA Astrophysics Data System (ADS)

Banchio, Adolfo J.; Heinen, Marco; Holmqvist, Peter; Nägele, Gerhard

2018-04-01

We report on a comprehensive theory-simulation-experimental study of collective and self-diffusion in concentrated suspensions of charge-stabilized colloidal spheres. In theory and simulation, the spheres are assumed to interact directly by a hard-core plus screened Coulomb effective pair potential. The intermediate scattering function, fc(q, t), is calculated by elaborate accelerated Stokesian dynamics (ASD) simulations for Brownian systems where many-particle hydrodynamic interactions (HIs) are fully accounted for, using a novel extrapolation scheme to a macroscopically large system size valid for all correlation times. The study spans the correlation time range from the colloidal short-time to the long-time regime. Additionally, Brownian Dynamics (BD) simulation and mode-coupling theory (MCT) results of fc(q, t) are generated where HIs are neglected. Using these results, the influence of HIs on collective and self-diffusion and the accuracy of the MCT method are quantified. It is shown that HIs enhance collective and self-diffusion at intermediate and long times. At short times self-diffusion, and for wavenumbers outside the structure factor peak region also collective diffusion, are slowed down by HIs. MCT significantly overestimates the slowing influence of dynamic particle caging. The dynamic scattering functions obtained in the ASD simulations are in overall good agreement with our dynamic light scattering (DLS) results for a concentration series of charged silica spheres in an organic solvent mixture, in the experimental time window and wavenumber range. From the simulation data for the time derivative of the width function associated with fc(q, t), there is indication of long-time exponential decay of fc(q, t), for wavenumbers around the location of the static structure factor principal peak. The experimental scattering functions in the probed time range are consistent with a time-wavenumber factorization scaling behavior of fc(q, t) that was first reported by Segrè and Pusey [Phys. Rev. Lett. 77, 771 (1996)] for suspensions of hard spheres. Our BD simulation and MCT results predict a significant violation of exact factorization scaling which, however, is approximately restored according to the ASD results when HIs are accounted for, consistent with the experimental findings for fc(q, t). Our study of collective diffusion is amended by simulation and theoretical results for the self-intermediate scattering function, fs(q, t), and its non-Gaussian parameter α2(t) and for the particle mean squared displacement W(t) and its time derivative. Since self-diffusion properties are not assessed in standard DLS measurements, a method to deduce W(t) approximately from fc(q, t) is theoretically validated.

Comment on “On the Crooks fluctuation theorem and the Jarzynski equality” [J. Chem. Phys. 129, 091101 (2008)

PubMed Central

Adib, Artur B.

2009-01-01

It has recently been argued that a self-consistency condition involving the Jarzynski equality (JE) and the Crooks fluctuation theorem (CFT) is violated for a simple Brownian process [L. Y. Chen, J. Chem. Phys.129, 091101 (2008)]. This note adopts the definitions in the original formulation of the JE and CFT and demonstrates the contrary. PMID:19566186

Comment on ``On the Crooks fluctuation theorem and the Jarzynski equality'' [J. Chem. Phys. 129, 091101 (2008)

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2009-06-01

It has recently been argued that a self-consistency condition involving the Jarzynski equality (JE) and the Crooks fluctuation theorem (CFT) is violated for a simple Brownian process [L. Y. Chen, J. Chem. Phys.129, 091101 (2008)]. This note adopts the definitions in the original formulation of the JE and CFT and demonstrates the contrary.

Hydrodynamics of soap films probed by two-particle microrheology

NASA Astrophysics Data System (ADS)

Prasad, Vikram; Weeks, Eric R.

2007-11-01

A soap film consists of a thin water layer that is separated from two bulk air phases above and below it by surfactant monolayers. The flow fields in the soap film created in response to a perturbation depend on coupling between these different phases, the exact nature of which is unknown. In order to determine this coupling, we use polystyrene spheres as tracer particles and track their diffusive motions in the soap film. The correlated Brownian motion of pairs of particles (two-particle microrheology) maps out the flow field, and provides a measure of the surface viscosity of the soap film as well. This measured surface viscosity agrees well with the value obtained from self diffusion of single particles (one-particle microrheology) in the film.

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

Elasticity and critical bending moment of model colloidal aggregates.

PubMed

Pantina, John P; Furst, Eric M

2005-04-08

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

Conduction at the onset of chaos

NASA Astrophysics Data System (ADS)

Baldovin, Fulvio

2017-02-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

Dyer, Oliver T.; Ball, Robin C.

2017-03-01

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

Fractional Brownian motion and the critical dynamics of zipping polymers.

PubMed

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

2012-03-01

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

A Brownian motor mechanism of translocation and strand separation by hepatitis C virus helicase.

PubMed

Levin, Mikhail K; Gurjar, Madhura; Patel, Smita S

2005-05-01

Helicases translocate along their nucleic acid substrates using the energy of ATP hydrolysis and by changing conformations of their nucleic acid-binding sites. Our goal is to characterize the conformational changes of hepatitis C virus (HCV) helicase at different stages of ATPase cycle and to determine how they lead to translocation. We have reported that ATP binding reduces HCV helicase affinity for nucleic acid. Now we identify the stage of the ATPase cycle responsible for translocation and unwinding. We show that a rapid directional movement occurs upon helicase binding to DNA in the absence of ATP, resulting in opening of several base pairs. We propose that HCV helicase translocates as a Brownian motor with a simple two-stroke cycle. The directional movement step is fueled by single-stranded DNA binding energy while ATP binding allows for a brief period of random movement that prepares the helicase for the next cycle.

Dependence of Brownian and Néel relaxation times on magnetic field strength

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

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

2014-01-15

Purpose: In magnetic particle imaging (MPI) and magnetic particle spectroscopy (MPS) the relaxation time of the magnetization in response to externally applied magnetic fields is determined by the Brownian and Néel relaxation mechanisms. Here the authors investigate the dependence of the relaxation times on the magnetic field strength and the implications for MPI and MPS. Methods: The Fokker–Planck equation with Brownian relaxation and the Fokker–Planck equation with Néel relaxation are solved numerically for a time-varying externally applied magnetic field, including a step-function, a sinusoidally varying, and a linearly ramped magnetic field. For magnetic fields that are applied as a stepmore » function, an eigenvalue approach is used to directly calculate both the Brownian and Néel relaxation times for a range of magnetic field strengths. For Néel relaxation, the eigenvalue calculations are compared to Brown's high-barrier approximation formula. Results: The relaxation times due to the Brownian or Néel mechanisms depend on the magnitude of the applied magnetic field. In particular, the Néel relaxation time is sensitive to the magnetic field strength, and varies by many orders of magnitude for nanoparticle properties and magnetic field strengths relevant for MPI and MPS. Therefore, the well-known zero-field relaxation times underestimate the actual relaxation times and, in particular, can underestimate the Néel relaxation time by many orders of magnitude. When only Néel relaxation is present—if the particles are embedded in a solid for instance—the authors found that there can be a strong magnetization response to a sinusoidal driving field, even if the period is much less than the zero-field relaxation time. For a ferrofluid in which both Brownian and Néel relaxation are present, only one relaxation mechanism may dominate depending on the magnetic field strength, the driving frequency (or ramp time), and the phase of the magnetization relative to the applied magnetic field. Conclusions: A simple treatment of Néel relaxation using the common zero-field relaxation time overestimates the relaxation time of the magnetization in situations relevant for MPI and MPS. For sinusoidally driven (or ramped) systems, whether or not a particular relaxation mechanism dominates or is even relevant depends on the magnetic field strength, the frequency (or ramp time), and the phase of the magnetization relative to the applied magnetic field.« less

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

PubMed

Hahn, Melinda W; O'Meliae, Charles R

2004-01-01

The deposition and reentrainment of particles in porous media have been examined theoretically and experimentally. A Brownian Dynamics/Monte Carlo (MC/BD) model has been developed that simulates the movement of Brownian particles near a collector under "unfavorable" chemical conditions and allows deposition in primary and secondary minima. A simple Maxwell approach has been used to estimate particle attachment efficiency by assuming deposition in the secondary minimum and calculating the probability of reentrainment. The MC/BD simulations and the Maxwell calculations support an alternative view of the deposition and reentrainment of Brownian particles under unfavorable chemical conditions. These calculations indicate that deposition into and subsequent release from secondary minima can explain reported discrepancies between classic model predictions that assume irreversible deposition in a primary well and experimentally determined deposition efficiencies that are orders of magnitude larger than Interaction Force Boundary Layer (IFBL) predictions. The commonly used IFBL model, for example, is based on the notion of transport over an energy barrier into the primary well and does not address contributions of secondary minimum deposition. A simple Maxwell model based on deposition into and reentrainment from secondary minima is much more accurate in predicting deposition rates for column experiments at low ionic strengths. It also greatly reduces the substantial particle size effects inherent in IFBL models, wherein particle attachment rates are predicted to decrease significantly with increasing particle size. This view is consistent with recent work by others addressing the composition and structure of the first few nanometers at solid-water interfaces including research on modeling water at solid-liquid interfaces, surface speciation, interfacial force measurements, and the rheological properties of concentrated suspensions. It follows that deposition under these conditions will depend on the depth of the secondary minimum and that some transition between secondary and primary depositions should occur when the height of the energy barrier is on the order of several kT. When deposition in secondary minima predominates, observed deposition should increase with increasing ionic strength, particle size, and Hamaker constant. Since an equilibrium can develop between bound and bulk particles, the collision efficiency [alpha] can no longer be considered a constant for a given physical and chemical system. Rather, in many cases it can decrease over time until it eventually reaches zero as equilibrium is established.

Active Brownian agents with concentration-dependent chemotactic sensitivity.

PubMed

Meyer, Marcel; Schimansky-Geier, Lutz; Romanczuk, Pawel

2014-02-01

We study a biologically motivated model of overdamped, autochemotactic Brownian agents with concentration-dependent chemotactic sensitivity. The agents in our model move stochastically and produce a chemical ligand at their current position. The ligand concentration obeys a reaction-diffusion equation and acts as a chemoattractant for the agents, which bias their motion towards higher concentrations of the dynamically altered chemical field. We explore the impact of concentration-dependent response to chemoattractant gradients on large-scale pattern formation, by deriving a coarse-grained macroscopic description of the individual-based model, and compare the conditions for emergence of inhomogeneous solutions for different variants of the chemotactic sensitivity. We focus primarily on the so-called receptor-law sensitivity, which models a nonlinear decrease of chemotactic sensitivity with increasing ligand concentration. Our results reveal qualitative differences between the receptor law, the constant chemotactic response, and the so-called log law, with respect to stability of the homogeneous solution, as well as the emergence of different patterns (labyrinthine structures, clusters, and bubbles) via spinodal decomposition or nucleation. We discuss two limiting cases, where the model can be reduced to the dynamics of single species: (I) the agent density governed by a density-dependent effective diffusion coefficient and (II) the ligand field with an effective bistable, time-dependent reaction rate. In the end, we turn to single clusters of agents, studying domain growth and determining mean characteristics of the stationary inhomogeneous state. Analytical results are confirmed and extended by large-scale GPU simulations of the individual based model.

Hanle effect in nonmonochromatic laser light

NASA Astrophysics Data System (ADS)

Ryan, R. E.; Bergeman, T. H.

1991-06-01

We report results of calculations on the Hanle effect in a J=0⇆J=1 atomic transition with three types of model fluctuating light fields: (a) the Brownian-motion phase-diffusion field, as produced in recent experiments by Arnett et al. [Phys. Rev. A 41, 2580 (1990)]; (b) Gaussian amplitude fluctuations; and (c) the chaotic field model, in which real and imaginary parts of the electric-field amplitude fluctuate. For the stochastic density-matrix equations, we use methods developed by Zoller and co-workers [e.g., Dixit, Zoller, and Lambropoulos, Phys. Rev. A 21, 1289 (1980)] employing the Fokker-Planck operator and leading to matrix continued-fraction expansions. The Hanle effect is of interest as a prototype for multisublevel atomic transitions. The width of the Hanle dip at zero magnetic field reflects the tendency of the light field to preserve the coherence between excited-state sublevels. For monochromatic light, the Hanle dip width increases as the square root of light intensity. When the laser bandwidth increases, power broadening of the coherence dip normally decreases. However, with the Brownian-motion phase-diffusion model, if the laser spectral profile is nearly Gaussian, broadening the laser up to several times the natural width of the atomic line does not diminish the Hanle dip width. With amplitude fluctuations, even in the limit of monochromatic light, power broadening of the Hanle dip with intensity is reduced by one-third to one-half depending on the particular model.

Elucidating the role of select cytoplasmic proteins in altering diffusion of integrin receptors.

PubMed

Sander, Suzanne; Arora, Neha; Smith, Emily A

2012-06-01

Cytoplasmic proteins that affect integrin diffusion in the cell membrane are identified using a combination of fluorescence recovery after photobleaching (FRAP) and RNA interference. Integrin receptors are essential for many cellular events, and alterations in lateral diffusion are one mechanism for modulating their function. In cells expressing native cytoplasmic protein concentrations and spread on a slide containing integrin extracellular ligand, 45 ± 2% of the integrin is mobile with a time-dependent 5.2 ± 0.9 × 10(-9) cm(2)/s diffusion coefficient at 1 s. The time exponent is 0.90 ± 0.07, indicating integrin diffusion moderately slows at longer times. The role of a specific cytoplasmic protein in altering integrin diffusion is revealed through changes in the FRAP curve after reducing the cytoplasmic protein's expression. Decreased expression of cytoplasmic proteins rhea, focal adhesion kinase (FAK), or steamer duck decreases the integrin mobile fraction. For rhea and FAK, there is a concomitant shift to Brownian (i.e., time-independent) diffusion at reduced concentrations of these proteins. In contrast, when the expression of actin 42A, dreadlocks, paxillin, integrin-linked kinase (ILK), or vinculin is reduced, integrin diffusion generally becomes more constrained with an increase in the integrin mobile fraction. This same change in integrin diffusion is measured in the absence of integrin extracellular ligand. The results indicate breaking the extracellular ligand-integrin-cytoskeletal linkage alters integrin diffusion properties, and, in most cases, there is no correlation between integrin and lipid diffusion properties.

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…

The importance of Soret transport in the production of high purity silicon for solar cells

NASA Technical Reports Server (NTRS)

Srivastava, R.

1985-01-01

Temperature-gradient-driven diffusion, or Soret transport, of silicon vapor and liquid droplets is analyzed under conditions typical of current production reactors for obtaining high purity silicon for solar cells. Contrary to the common belief that Soret transport is negligible, it is concluded that some 15-20 percent of the silicon vapor mass flux to the reactor walls is caused by the high temperature gradients that prevail inside such reactors. Moreover, since collection of silicon is also achieved via deposition of silicon droplets onto the walls, the Soret transport mechanism becomes even more crucial due to size differences between diffusing species. It is shown that for droplets in the 0.01 to 1 micron diameter range, collection by Soret transport dominates both Brownian and turbulent mechanisms.

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

PubMed Central

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

2014-01-01

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

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

PubMed

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

2014-01-07

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

Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning.

PubMed

Hellander, Stefan; Hellander, Andreas; Petzold, Linda

2017-12-21

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

Steric exclusion and protein conformation determine the localization of plasma membrane transporters.

PubMed

Bianchi, Frans; Syga, Łukasz; Moiset, Gemma; Spakman, Dian; Schavemaker, Paul E; Punter, Christiaan M; Seinen, Anne-Bart; van Oijen, Antoine M; Robinson, Andrew; Poolman, Bert

2018-02-05

The plasma membrane (PM) of Saccharomyces cerevisiae contains membrane compartments, MCC/eisosomes and MCPs, named after the protein residents Can1 and Pma1, respectively. Using high-resolution fluorescence microscopy techniques we show that Can1 and the homologous transporter Lyp1 are able to diffuse into the MCC/eisosomes, where a limited number of proteins are conditionally trapped at the (outer) edge of the compartment. Upon addition of substrate, the immobilized proteins diffuse away from the MCC/eisosomes, presumably after taking a different conformation in the substrate-bound state. Our data indicate that the mobile fraction of all integral plasma membrane proteins tested shows extremely slow Brownian diffusion through most of the PM. We also show that proteins with large cytoplasmic domains, such as Pma1 and synthetic chimera of Can1 and Lyp1, are excluded from the MCC/eisosomes. We hypothesize that the distinct localization patterns found for these integral membrane proteins in S. cerevisiae arises from a combination of slow lateral diffusion, steric exclusion, and conditional trapping in membrane compartments.

Single-Molecule Imaging of Wnt3A Protein Diffusion on Living Cell Membranes.

PubMed

Lippert, Anna; Janeczek, Agnieszka A; Fürstenberg, Alexandre; Ponjavic, Aleks; Moerner, W E; Nusse, Roel; Helms, Jill A; Evans, Nicholas D; Lee, Steven F

2017-12-19

Wnt proteins are secreted, hydrophobic, lipidated proteins found in all animals that play essential roles in development and disease. Lipid modification is thought to facilitate the interaction of the protein with its receptor, Frizzled, but may also regulate the transport of Wnt protein and its localization at the cell membrane. Here, by employing single-molecule fluorescence techniques, we show that Wnt proteins associate with and diffuse on the plasma membranes of living cells in the absence of any receptor binding. We find that labeled Wnt3A transiently and dynamically associates with the membranes of Drosophila Schneider 2 cells, diffuses with Brownian kinetics on flattened membranes and on cellular protrusions, and does not transfer between cells in close contact. In S2 receptor-plus (S2R+) cells, which express Frizzled receptors, membrane diffusion rate is reduced and membrane residency time is increased. These results provide direct evidence of Wnt3A interaction with living cell membranes, and represent, to our knowledge, a new system for investigating the dynamics of Wnt transport. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

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.

Molecular model for the diffusion of associating telechelic polymer networks

NASA Astrophysics Data System (ADS)

Ramirez, Jorge; Dursch, Thomas; Olsen, Bradley

Understanding the mechanisms of motion and stress relaxation of associating polymers at the molecular level is critical for advanced technological applications such as enhanced oil-recovery, self-healing materials or drug delivery. In associating polymers, the strength and rates of association/dissociation of the reversible physical crosslinks govern the dynamics of the network and therefore all the macroscopic properties, like self-diffusion and rheology. Recently, by means of forced Rayleigh scattering experiments, we have proved that associating polymers of different architectures show super-diffusive behavior when the free motion of single molecular species is slowed down by association/dissociation kinetics. Here we discuss a new molecular picture for unentangled associating telechelic polymers that considers concentration, molecular weight, number of arms of the molecules and equilibrium and rate constants of association/dissociation. The model predicts super-diffusive behavior under the right combination of values of the parameters. We discuss some of the predictions of the model using scaling arguments, show detailed results from Brownian dynamics simulations of the FRS experiments, and attempt to compare the predictions of the model to experimental data.

Computational methods for diffusion-influenced biochemical reactions.

PubMed

Dobrzynski, Maciej; Rodríguez, Jordi Vidal; Kaandorp, Jaap A; Blom, Joke G

2007-08-01

We compare stochastic computational methods accounting for space and discrete nature of reactants in biochemical systems. Implementations based on Brownian dynamics (BD) and the reaction-diffusion master equation are applied to a simplified gene expression model and to a signal transduction pathway in Escherichia coli. In the regime where the number of molecules is small and reactions are diffusion-limited predicted fluctuations in the product number vary between the methods, while the average is the same. Computational approaches at the level of the reaction-diffusion master equation compute the same fluctuations as the reference result obtained from the particle-based method if the size of the sub-volumes is comparable to the diameter of reactants. Using numerical simulations of reversible binding of a pair of molecules we argue that the disagreement in predicted fluctuations is due to different modeling of inter-arrival times between reaction events. Simulations for a more complex biological study show that the different approaches lead to different results due to modeling issues. Finally, we present the physical assumptions behind the mesoscopic models for the reaction-diffusion systems. Input files for the simulations and the source code of GMP can be found under the following address: http://www.cwi.nl/projects/sic/bioinformatics2007/

Complimentary aspects of diffusion imaging and fMRI: II. Elucidating contributions to the fMRI signal with diffusion sensitization.

PubMed

Mulkern, Robert V; Haker, Steven J; Maier, Stephan E

2007-07-01

Tissue water molecules reside in different biophysical compartments. For example, water molecules in the vasculature reside for variable periods of time within arteries, arterioles, capillaries, venuoles and veins, and may be within blood cells or blood plasma. Water molecules outside of the vasculature, in the extravascular space, reside, for a time, either within cells or within the interstitial space between cells. Within these different compartments, different types of microscopic motion that water molecules may experience have been identified and discussed. These range from Brownian diffusion to more coherent flow over the time scales relevant to functional magnetic resonance imaging (fMRI) experiments, on the order of several 10s of milliseconds. How these different types of motion are reflected in magnetic resonance imaging (MRI) methods developed for "diffusion" imaging studies has been an ongoing and active area of research. Here we briefly review the ideas that have developed regarding these motions within the context of modern "diffusion" imaging techniques and, in particular, how they have been accessed in attempts to further our understanding of the various contributions to the fMRI signal changes sought in studies of human brain activation.

Application of ToFSIMS to Studying Surface Diffusion: Do cocaine and heroin form a two-dimensional gas on surfaces?

NASA Astrophysics Data System (ADS)

Avci, Recep; Maccagnano, Sara; Bohannan, Gary; Gresham, Gary; Groenewold, Gary

2001-03-01

Imaging time-of-flight secondary ion mass spectroscopy ( ToFSIMS) is a practical tool for studying the movement of molecules on material surfaces as a function of time. The high detection sensitivity, rapid data acquisition and reasonable spatial resolution present ideal conditions for such studies. An application of ToFSIMS is presented characterizing the diffusion of large molecules on gold-coated Si wafers. Polydimethylsiloxane (PDMS) was selected for study because it contaminates material surfaces and can be detected easily. Also, the temperature dependent diffusion properties of hydrochlorinated heroin and cocaine are presented as part of a forensic application. While the PDMS diffusion could be explained by a two-dimensional ( 2-D) Brownian motion with a Gaussian probability distribution function (pdf) with a diffusion coefficient of 1.6 μ m^2/sec, the cocaine and to a lesser extent heroin were observed to move nearly freely on the surfaces as though they were part of a 2-D gas evaporating in 2-D from a condensed phase. The results could be described reasonably well using an extreme Lévi pdf with an index of stability α<= 0.01.

Role of insulin receptor and insulin signaling on αPS2CβPS integrins' lateral diffusion.

PubMed

Mainali, Dipak; Syed, Aleem; Arora, Neha; Smith, Emily A

2014-12-01

Integrins are ubiquitous transmembrane receptors with adhesion and signaling properties. The influence of insulin receptor and insulin signaling on αPS2CβPS integrins' lateral diffusion was studied using single particle tracking in S2 cells before and after reducing the insulin receptor expression or insulin stimulation. Insulin signaling was monitored by Western blotting for phospho-Akt expression. The expression of the insulin receptor was reduced using RNA interference (RNAi). After insulin receptor RNAi, four significant changes were measured in integrin diffusion properties: (1) there was a 24% increase in the mobile integrin population, (2) 14% of the increase was represented by integrins with Brownian diffusion, (3) for integrins that reside in confined zones of diffusion, there was a 45% increase in the diameter of the confined zone, and (4) there was a 29% increase in the duration integrins spend in confined zones of diffusion. In contrast to reduced expression of the insulin receptor, which alters integrin diffusion properties, insulin stimulation alone or insulin stimulation under conditions of reduced insulin receptor expression have minimal effects on altering the measured integrin diffusion properties. The differences in integrin diffusion measured after insulin receptor RNAi in the presence or absence of insulin stimulation may be the result of other insulin signaling pathways that are activated at reduced insulin receptor conditions. No change in the average integrin diffusion coefficient was measured for any conditions included in this study.

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

PubMed

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

2006-01-28

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

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

NASA Astrophysics Data System (ADS)

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

2006-01-01

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

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.

Analysis of activation energy in Couette-Poiseuille flow of nanofluid in the presence of chemical reaction and convective boundary conditions

NASA Astrophysics Data System (ADS)

Zeeshan, A.; Shehzad, N.; Ellahi, R.

2018-03-01

The motivation of the current article is to explore the energy activation in MHD radiative Couette-Poiseuille flow nanofluid in horizontal channel with convective boundary conditions. The mathematical model of Buongiorno [1] effectively describes the current flow analysis. Additionally, the impact of chemical reaction is also taken in account. The governing flow equations are simplified with the help of boundary layer approximations. Non-linear coupled equations for momentum, energy and mass transfer are tackled with analytical (HAM) technique. The influence of dimensionless convergence parameter like Brownian motion parameter, radiation parameter, buoyancy ratio parameter, dimensionless activation energy, thermophoresis parameter, temperature difference parameter, dimensionless reaction rate, Schmidt number, Brinkman number, Biot number and convection diffusion parameter on velocity, temperature and concentration profiles are discussed graphically and in tabular form. From the results, it is elaborate that the nanoparticle concentration is directly proportional to the chemical reaction with activation energy and the performance of Brownian motion on nanoparticle concentration gives reverse pattern to that of thermophoresis parameter.

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.

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.

Mixed convection peristaltic flow of third order nanofluid with an induced magnetic field.

PubMed

Noreen, Saima

2013-01-01

This research is concerned with the peristaltic flow of third order nanofluid in an asymmetric channel. The governing equations of third order nanofluid are modelled in wave frame of reference. Effect of induced magnetic field is considered. Long wavelength and low Reynolds number situation is tackled. Numerical solutions of the governing problem are computed and analyzed. The effects of Brownian motion and thermophoretic diffusion of nano particles are particularly emphasized. Physical quantities such as velocity, pressure rise, temperature, induced magnetic field and concentration distributions are discussed.