Brownian movement and molecular reality
Perrin, Jean
2005-01-01
How do we know that molecules really exist? An important clue came from Brownian movement, a concept developed in 1827 by botanist Robert Brown, who noticed that tiny objects like pollen grains shook and moved erratically when viewed under a microscope. Nearly 80 years later, in 1905, Albert Einstein explained this ""Brownian motion"" as the result of bombardment by molecules. Einstein offered a quantitative explanation by mathematically estimating the average distance covered by the particles over time as a result of molecular bombardment. Four years later, Jean Baptiste Perrin wrote Brownia
Thermodynamic and Quantum Thermodynamic Analyses of Brownian Movement
Gyftopoulos, Elias P.
2006-01-01
Thermodynamic and quantum thermodynamic analyses of Brownian movement of a solvent and a colloid passing through neutral thermodynamic equilibrium states only. It is shown that Brownian motors and E. coli do not represent Brownian movement.
Entropic Approach to Brownian Movement.
Neumann, Richard M.
1980-01-01
A diffusional driving force, called the radial force, which is responsible for the increase with time of the scalar separation between a fixed point and a particle undergoing three-dimensional Brownian motion, is derived using Boltzmann's equation. (Author/HM)
Analyzing animal movements using Brownian bridges.
Horne, Jon S; Garton, Edward O; Krone, Stephen M; Lewis, Jesse S
2007-09-01
By studying animal movements, researchers can gain insight into many of the ecological characteristics and processes important for understanding population-level dynamics. We developed a Brownian bridge movement model (BBMM) for estimating the expected movement path of an animal, using discrete location data obtained at relatively short time intervals. The BBMM is based on the properties of a conditional random walk between successive pairs of locations, dependent on the time between locations, the distance between locations, and the Brownian motion variance that is related to the animal's mobility. We describe two critical developments that enable widespread use of the BBMM, including a derivation of the model when location data are measured with error and a maximum likelihood approach for estimating the Brownian motion variance. After the BBMM is fitted to location data, an estimate of the animal's probability of occurrence can be generated for an area during the time of observation. To illustrate potential applications, we provide three examples: estimating animal home ranges, estimating animal migration routes, and evaluating the influence of fine-scale resource selection on animal movement patterns.
On modeling animal movements using Brownian motion with measurement error.
Pozdnyakov, Vladimir; Meyer, Thomas; Wang, Yu-Bo; Yan, Jun
2014-02-01
Modeling animal movements with Brownian motion (or more generally by a Gaussian process) has a long tradition in ecological studies. The recent Brownian bridge movement model (BBMM), which incorporates measurement errors, has been quickly adopted by ecologists because of its simplicity and tractability. We discuss some nontrivial properties of the discrete-time stochastic process that results from observing a Brownian motion with added normal noise at discrete times. In particular, we demonstrate that the observed sequence of random variables is not Markov. Consequently the expected occupation time between two successively observed locations does not depend on just those two observations; the whole path must be taken into account. Nonetheless, the exact likelihood function of the observed time series remains tractable; it requires only sparse matrix computations. The likelihood-based estimation procedure is described in detail and compared to the BBMM estimation.
How superdiffusion gets arrested: Ecological encounters explain shift from Lévy to Brownian movement
De Jager, M.; Bartumeus, F.; Kölzsch, A.; Weissing, F.J.; Hengeveld, G.M.; Nolet, B.A.; Herman, P.M.J.; Van de Koppel, J.
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
How superdiffusion gets arrested: ecological encounters explain shift from Levy to Brownian movement
de Jager, M.; Bartumeus, F.; Kölzsch, A.; Weissing, F.J.; Hengeveld, G.M.; Nolet, B.A.; Herman, P.M.J.; de Koppel, J.
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
How superdiffusion gets arrested: ecological encounters explain shift from Lévy to Brownian movement
Jager, de M.; Bartumeus, F.; Kölzsch, A.; Weissing, F.J.; Hengeveld, G.M.; Nolet, B.A.; Herman, P.M.J.; Koppel, van de J.
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
de Jager, Monique; Bartumeus, Frederic; Kolzsch, Andrea; Weissing, Franz J.; Hengeveld, Geerten M.; Nolet, Bart A.; Herman, Peter M. J.; de Koppel, Johan van
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
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
Brownian Movement and Avogadro's Number: A Laboratory Experiment.
Kruglak, Haym
1988-01-01
Reports an experimental procedure for studying Einstein's theory of Brownian movement using commercially available latex microspheres and a video camera. Describes how students can monitor sphere motions and determine Avogadro's number. Uses a black and white video camera, microscope, and TV. (ML)
Detecting movement patterns using Brownian bridges
Buchin, K.; Sijben, S.; Arseneau, T.J.-M.; Willems, E.P.
2012-01-01
In trajectory data a low sampling rate leads to high uncertainty in between sampling points, which needs to be taken into account in the analysis of such data. However, current algorithms for movement analysis ignore this uncertainty and assume linear movement between sample points. In this paper we
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.
How superdiffusion gets arrested: ecological encounters explain shift from Lévy to Brownian movement
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
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 ...
Quantum description of the Brownian movement in an external field
Svin'in, I.R.
1976-01-01
The Schroedinger equation for brownian motion in an external field is obtained on the basis of the classical Langevin equation. The specific features of the approach proposed are illustrated by the example of the brownian motion of the quantum oscillator. The influence of the fluctuations on the various physical quantities is considered
Presentation of quantum Brownian movement in the collective coordinate method
Oksak, A.I.; Sukhanov, A.D.
2003-01-01
Two explicitly solved models of quantum randomized processes described by the Langevin equation, i. e. a free quantum Brownian particle and a quantum Brownian harmonic oscillator, are considered. The Hamiltonian (string) realization of the models reveals soliton-like structure of classical solutions. Accordingly, the method of zero mode collective coordinate is an adequate means for describing the models quantum dynamics [ru
Fornés, José A
2010-01-15
We use the Brownian dynamics with hydrodynamic interactions simulation in order to describe the movement of a elastically coupled dimer Brownian motor in a ratchet potential. The only external forces considered in our system were the load, the random thermal noise and an unbiased thermal fluctuation. For a given set of parameters we observe direct movement against the load force if hydrodynamic interactions were considered.
Buchin, K.; Sijben, S.; van Loon, E.E.; Sapir, N.; Mercier, S.; Arseneau, T.J.M.; Willems, E.P.
2015-01-01
Background: The Brownian bridge movement model (BBMM) provides a biologically sound approximation of the movement path of an animal based on discrete location data, and is a powerful method to quantify utilization distributions. Computing the utilization distribution based on the BBMM while
Kranstauber, Bart; Kays, Roland; Lapoint, Scott D; Wikelski, Martin; Safi, Kamran
2012-07-01
1. The recently developed Brownian bridge movement model (BBMM) has advantages over traditional methods because it quantifies the utilization distribution of an animal based on its movement path rather than individual points and accounts for temporal autocorrelation and high data volumes. However, the BBMM assumes unrealistic homogeneous movement behaviour across all data. 2. Accurate quantification of the utilization distribution is important for identifying the way animals use the landscape. 3. We improve the BBMM by allowing for changes in behaviour, using likelihood statistics to determine change points along the animal's movement path. 4. This novel extension, outperforms the current BBMM as indicated by simulations and examples of a territorial mammal and a migratory bird. The unique ability of our model to work with tracks that are not sampled regularly is especially important for GPS tags that have frequent failed fixes or dynamic sampling schedules. Moreover, our model extension provides a useful one-dimensional measure of behavioural change along animal tracks. 5. This new method provides a more accurate utilization distribution that better describes the space use of realistic, behaviourally heterogeneous tracks. © 2012 The Authors. Journal of Animal Ecology © 2012 British Ecological Society.
Environmental context explains Lévy and Brownian movement patterns of marine predators.
Humphries, Nicolas E; Queiroz, Nuno; Dyer, Jennifer R M; Pade, Nicolas G; Musyl, Michael K; Schaefer, Kurt M; Fuller, Daniel W; Brunnschweiler, Juerg M; Doyle, Thomas K; Houghton, Jonathan D R; Hays, Graeme C; Jones, Catherine S; Noble, Leslie R; Wearmouth, Victoria J; Southall, Emily J; Sims, David W
2010-06-24
An optimal search theory, the so-called Lévy-flight foraging hypothesis, predicts that predators should adopt search strategies known as Lévy flights where prey is sparse and distributed unpredictably, but that Brownian movement is sufficiently efficient for locating abundant prey. Empirical studies have generated controversy because the accuracy of statistical methods that have been used to identify Lévy behaviour has recently been questioned. Consequently, whether foragers exhibit Lévy flights in the wild remains unclear. Crucially, moreover, it has not been tested whether observed movement patterns across natural landscapes having different expected resource distributions conform to the theory's central predictions. Here we use maximum-likelihood methods to test for Lévy patterns in relation to environmental gradients in the largest animal movement data set assembled for this purpose. Strong support was found for Lévy search patterns across 14 species of open-ocean predatory fish (sharks, tuna, billfish and ocean sunfish), with some individuals switching between Lévy and Brownian movement as they traversed different habitat types. We tested the spatial occurrence of these two principal patterns and found Lévy behaviour to be associated with less productive waters (sparser prey) and Brownian movements to be associated with productive shelf or convergence-front habitats (abundant prey). These results are consistent with the Lévy-flight foraging hypothesis, supporting the contention that organism search strategies naturally evolved in such a way that they exploit optimal Lévy patterns.
Xie, Ping
2009-09-16
A general model is presented for the processive movement of molecular motors such as λ-exonuclease, RecJ and exonuclease I that use digestion of a DNA track to rectify Brownian motion along this track. Using this model, the translocation dynamics of these molecular motors is studied. The sequence-dependent pausing of λ-exonuclease, which results from a site-specific high affinity DNA interaction, is also studied. The theoretical results are consistent with available experimental data. Moreover, the model is used to predict the lifetime distribution and force dependence of these paused states.
Xie Ping
2009-01-01
A general model is presented for the processive movement of molecular motors such as λ-exonuclease, RecJ and exonuclease I that use digestion of a DNA track to rectify Brownian motion along this track. Using this model, the translocation dynamics of these molecular motors is studied. The sequence-dependent pausing of λ-exonuclease, which results from a site-specific high affinity DNA interaction, is also studied. The theoretical results are consistent with available experimental data. Moreover, the model is used to predict the lifetime distribution and force dependence of these paused states.
Mapping migratory flyways in Asia using dynamic Brownian bridge movement models.
Palm, Eric C; Newman, Scott H; Prosser, Diann J; Xiao, Xiangming; Ze, Luo; Batbayar, Nyambayar; Balachandran, Sivananinthaperumal; Takekawa, John Y
2015-01-01
Identifying movement routes and stopover sites is necessary for developing effective management and conservation strategies for migratory animals. In the case of migratory birds, a collection of migration routes, known as a flyway, is often hundreds to thousands of kilometers long and can extend across political boundaries. Flyways encompass the entire geographic range between the breeding and non-breeding areas of a population, species, or a group of species, and they provide spatial frameworks for management and conservation across international borders. Existing flyway maps are largely qualitative accounts based on band returns and survey data rather than observed movement routes. In this study, we use satellite and GPS telemetry data and dynamic Brownian bridge movement models to build upon existing maps and describe waterfowl space use probabilistically in the Central Asian and East Asian-Australasian Flyways. Our approach provided new information on migratory routes that was not easily attainable with existing methods to describe flyways. Utilization distributions from dynamic Brownian bridge movement models identified key staging and stopover sites, migration corridors and general flyway outlines in the Central Asian and East Asian-Australasian Flyways. A map of space use from ruddy shelducks depicted two separate movement corridors within the Central Asian Flyway, likely representing two distinct populations that show relatively strong connectivity between breeding and wintering areas. Bar-headed geese marked at seven locations in the Central Asian Flyway showed heaviest use at several stopover sites in the same general region of high-elevation lakes along the eastern Qinghai-Tibetan Plateau. Our analysis of data from multiple Anatidae species marked at sites throughout Asia highlighted major movement corridors across species and confirmed that the Central Asian and East Asian-Australasian Flyways were spatially distinct. The dynamic Brownian bridge
Buchin, Kevin; Sijben, Stef; van Loon, E Emiel; Sapir, Nir; Mercier, Stéphanie; Marie Arseneau, T Jean; Willems, Erik P
2015-01-01
The Brownian bridge movement model (BBMM) provides a biologically sound approximation of the movement path of an animal based on discrete location data, and is a powerful method to quantify utilization distributions. Computing the utilization distribution based on the BBMM while calculating movement parameters directly from the location data, may result in inconsistent and misleading results. We show how the BBMM can be extended to also calculate derived movement parameters. Furthermore we demonstrate how to integrate environmental context into a BBMM-based analysis. We develop a computational framework to analyze animal movement based on the BBMM. In particular, we demonstrate how a derived movement parameter (relative speed) and its spatial distribution can be calculated in the BBMM. We show how to integrate our framework with the conceptual framework of the movement ecology paradigm in two related but acutely different ways, focusing on the influence that the environment has on animal movement. First, we demonstrate an a posteriori approach, in which the spatial distribution of average relative movement speed as obtained from a "contextually naïve" model is related to the local vegetation structure within the monthly ranging area of a group of wild vervet monkeys. Without a model like the BBMM it would not be possible to estimate such a spatial distribution of a parameter in a sound way. Second, we introduce an a priori approach in which atmospheric information is used to calculate a crucial parameter of the BBMM to investigate flight properties of migrating bee-eaters. This analysis shows significant differences in the characteristics of flight modes, which would have not been detected without using the BBMM. Our algorithm is the first of its kind to allow BBMM-based computation of movement parameters beyond the utilization distribution, and we present two case studies that demonstrate two fundamentally different ways in which our algorithm can be applied to
Sukhanov, A.D.
2004-01-01
Generalized correlations of the Schroedinger indefinitenesses are shown to have the meaning of the fundamental restrictions as to characteristics of space of states in any probability-like theory. Quantum mechanics, as well as, theory of the brownian movement at arbitrary space of time fall in the category of the mentioned theories. One compared correlations of coordinates-pulse indefinitenesses within the mentioned theory with the similar correlation of indefinitenesses for microparticle under the Gaussian wave packet state. One determined that in case of profound distinction in mathematical tools of two theories one observes their conceptual resemblance. It manifests itself under the alternative conditions - short times in one theory correspond to long ones in another theory and vice versa, while in any of the mentioned theories uncontrollable effect of either quantum or thermal type is of crucial importance [ru
Zhang, Jiayuan
2018-01-01
This article proposes a conception of Brownian coil. Brownian coil is a tiny coil with the same size of pollen. Once immersed into designed magnetic field and liquid, the coil will be moved and deformed macroscopically, due to the microscopic thermodynamic molecular collisions. Such deformation and movement will change the magnetic flux through the coil, by which an ElectroMotive Force (EMF) is produced. In this work, Brownian heat exchanger and Brownian generator are further designed to tran...
Using dynamic Brownian bridge movement modelling to measure temporal patterns of habitat selection.
Byrne, Michael E; Clint McCoy, J; Hinton, Joseph W; Chamberlain, Michael J; Collier, Bret A
2014-09-01
Accurately describing animal space use is vital to understanding how wildlife use habitat. Improvements in GPS technology continue to facilitate collection of telemetry data at high spatial and temporal resolutions. Application of the recently introduced dynamic Brownian bridge movement model (dBBMM) to such data is promising as the method explicitly incorporates the behavioural heterogeneity of a movement path into the estimated utilization distribution (UD). Utilization distributions defining space use are normally estimated for time-scales ranging from weeks to months, obscuring much of the fine-scale information available from high-volume GPS data sets. By accounting for movement heterogeneity, the dBBMM provides a rigorous, behaviourally based estimate of space use between each set of relocations. Focusing on UDs generated between individual sets of locations allows us to quantify fine-scale circadian variation in habitat use. We used the dBBMM to estimate UDs bounding individual time steps for three terrestrial species with different life histories to illustrate how the method can be used to identify fine-scale variations in habitat use. We also demonstrate how dBBMMs can be used to characterize circadian patterns of habitat selection and link fine-scale patterns of habitat use to behaviour. We observed circadian patterns of habitat use that varied seasonally for a white-tailed deer (Odocoileus virginianus) and coyote (Canis latrans). We found seasonal patterns in selection by the white-tailed deer and were able to link use of conifer forests and agricultural fields to behavioural state of the coyote. Additionally, we were able to quantify the date in which a Rio Grande wild turkey (Meleagris gallopavo intermedia) initiated laying as well as when during the day, she was most likely to visit the nest site to deposit eggs. The ability to quantify circadian patterns of habitat use may have important implications for research and management of wildlife
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
Svin'in, I.R.
1982-01-01
Description of collective phenomena in heated nuclei within the framework of the Brownian approximation may be conditionally divided into two parts: 1) solution of the problem for some realization of a random force, 2) averaging in a set of all the possible realizations. Results of the present work are setted the first part of the problem in the case of surface quadrupole oscillations of spherical heated nuclei. Quadrupole surface oscillations of heated spherical nuclei are considered in the Brownian motion approximation. The integrals of motion are constructed taking into account the energy and angular momentum conservations for the nucleus in the process of relaxation of the collective excitations. Wave functions are obtained for states having definite values of the integrals of motion in the phonon representation. It is noted that the description scheme developed is easily used with respect to other multipolarity oscillations
Reynolds, A M
2009-01-01
The movement patterns of a diverse range of animals have scale-free characteristics. These characteristics provide necessary but not sufficient conditions for the presence of movement patterns that can be approximated by Levy walks. Nevertheless, it has been widely assumed that the occurrence of scale-free animal movements can indeed be attributed to the presence of Levy walks. This is, in part, because it is known that the super-diffusive properties of Levy walks can be advantageous in random search scenarios when searchers have little or no prior knowledge of target locations. However, fractional Brownian motions (fBms) and fractional Levy motions (fLms) are both scale-free and super-diffusive, and so it is possible that these motions rather than Levy walks underlie some or all occurrences of scale-free animal movement patterns. Here this possibility is examined in numerical simulations through a determination of the searching efficiencies of fBm and fLm searches. It is shown that these searches are less efficient than Levy walk searches. This finding does not rule out the possibility that some animals with scale-free movement patterns are executing fBm and fLm searches, but it does make Levy walk searches the more likely possibility.
Facilitated movement of inertial Brownian motors driven by a load under an asymmetric potential.
Ai, Bao-quan; Liu, Liang-gang
2007-10-01
Based on recent work [L. Machura, M. Kostur, P. Talkner, J. Luczka, and P. Hanggi, Phys. Rev. Lett. 98, 040601 (2007)], we extend the study of inertial Brownian motors to the case of an asymmetric potential. It is found that some transport phenomena appear in the presence of an asymmetric potential. Within tailored parameter regimes, there exists two optimal values of the load at which the mean velocity takes its maximum, which means that a load can facilitate the transport in the two parameter regimes. In addition, the phenomenon of multiple current reversals can be observed when the load is increased.
Allahverdyan, A.E.; Khrennikov, A.; Nieuwenhuizen, Th.M.
2005-01-01
For two classical Brownian particles an analog of continuous-variable quantum entanglement is presented: The common probability distribution of the two coordinates and the corresponding coarse-grained velocities cannot always be prepared via mixing of any factorized distributions referring to the two particles separately. This is possible for particles which have interacted in the past, but do not interact at present. Three factors are crucial for the effect: (1) separation of time scales of coordinate and momentum which motivates the definition of coarse-grained velocities; (2) the resulting uncertainty relations between the coordinate of the Brownian particle and the change of its coarse-grained velocity; (3) the fact that the coarse-grained velocity, though pertaining to a single Brownian particle, is defined on a common context of two particles. The Brownian entanglement is a consequence of a coarse-grained description and disappears for a finer resolution of the Brownian motion. Analogies with the quantum situation are discussed, as well as possibilities of experimental realization of the effect in examples of macroscopic Brownian motion
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.
Coffey, W.T.
1978-01-01
It is shown how three models (based on the theory of the Brownian movement) for the translational motion of an atom in a fluid may be used to calculate explicitly the intermediate scattering functions and differential cross-sections for the incoherent scattering of slow neutrons. In the first model the translational motion of the atom is represented by the motion of a particle in space subjected to no forces other than those arising from the thermal motion of its surroundings. The differential scattering cross-section for this model is then obtained as a continued fraction similar to that given by Sack (Proc. Phys. Soc.; B70:402 and 414 (1957)) for the electric polarisability in his investigation of the role of inertial effects in dielectric relaxation. The second model is a corrected version of the itinerant oscillator model of Sears (Proc. Phys. Soc.; 86:953 (1965)). Here the differential cross-section is obtained in the form of a series and a closed-form expression is found for the intermediate scattering function. The last model to be considered is the harmonically bound particle where again a closed form expression is obtained for the intermediate scattering function. In each case the intermediate scattering function has a mathematical form which is similar to the after-effect function describing the decay of electric polarisation for the rotational versions of the models. (author)
Biased Brownian dynamics for rate constant calculation.
Zou, G; Skeel, R D; Subramaniam, S
2000-01-01
An enhanced sampling method-biased Brownian dynamics-is developed for the calculation of diffusion-limited biomolecular association reaction rates with high energy or entropy barriers. Biased Brownian dynamics introduces a biasing force in addition to the electrostatic force between the reactants, and it associates a probability weight with each trajectory. A simulation loses weight when movement is along the biasing force and gains weight when movement is against the biasing force. The sampl...
Random motion and Brownian rotation
Wyllie, G.
1980-01-01
The course is centred on the Brownian motion - the random movement of molecules arising from thermal fluctuations of the surrounding medium - and starts with the classical theory of A. Einstein, M.v. Smoluchowski and P. Langevin. The first part of this article is quite elementary, and several of the questions raised in it have been instructively treated in a much more sophisticated way in recent reviews by Pomeau and Resibois and by Fox. This simple material may nevertheless be helpful to some readers whose main interest lies in approaching the work on Brownian rotation reviewed in the latter part of the present article. The simplest, and most brutally idealised, problem in our field of interest is that of the random walk in one dimension of space. Its solution leads on, through the diffusivity-mobility relation of Einstein, to Langevin's treatment of the Brownian motion. The application of these ideas to the movement of a molecule in a medium of similar molecules is clearly unrealistic, and much energy has been devoted to finding a suitable generalisation. We shall discuss in particular ideas due to Green, Zwanzig and Mori. (orig./WL)
Brownian modulated optical nanoprobes
Behrend, C.J.; Anker, J.N.; Kopelman, R.
2004-01-01
Brownian modulated optical nanoprobes (Brownian MOONs) are fluorescent micro- and nanoparticles that resemble moons: one hemisphere emits a bright fluorescent signal, while an opaque metal darkens the other hemisphere. Brownian motion causes the particles to tumble and blink erratically as they rotate literally through the phases of the moon. The fluctuating probe signals are separated from optical and electronic backgrounds using principal components analysis or images analysis. Brownian MOONs enable microrheological measurements on size scales and timescales that are difficult to study with other methods. Local chemical concentrations can be measured simultaneously, using spectral characteristics of indicator dyes embedded within the MOONs
Lawler, Gregory F.; Werner, Wendelin
2003-01-01
We define a natural conformally invariant measure on unrooted Brownian loops in the plane and study some of its properties. We relate this measure to a measure on loops rooted at a boundary point of a domain and show how this relation gives a way to ``chronologically add Brownian loops'' to simple curves in the plane.
Rotational and translational Brownian motion
Coffey, W.T.; Salford Univ.
1980-01-01
In this review it is proposed to summarise the work on the theory of the translational and rotational Brownian movement which has been carried on over roughly the past 30 years. The review is intended to take the form of a tutorial paper rather than a list of the results obtained by the various investigators over the period in question. In this vein then it seems appropriate to firstly give a brief account of those parts of the theory of probability which are relevant to the problems under discussion. (orig.)
Directed motion of a Brownian motor in a temperature gradient
Liu, Yibing; Nie, Wenjie; Lan, Yueheng
2017-05-01
Directed motion of mesoscopic systems in a non-equilibrium environment is of great interest to both scientists and engineers. Here, the translation and rotation of a Brownian motor is investigated under non-equilibrium conditions. An anomalous directed translation is found if the two heads of the Brownian motor are immersed in baths with different particle masses, which is hinted in the analytic computation and confirmed by the numerical simulation. Similar consideration is also used to find the directed movement in the single rotational and translational degree of freedom of the Brownian motor when residing in one thermal bath with a temperature gradient.
Brownian motion probe for water-ethanol inhomogeneous mixtures
Furukawa, Kazuki; Judai, Ken
2017-12-01
Brownian motion provides information regarding the microscopic geometry and motion of molecules, insofar as it occurs as a result of molecular collisions with a colloid particle. We found that the mobility of polystyrene beads from the Brownian motion in a water-ethanol mixture is larger than that predicted from the liquid shear viscosity. This indicates that mixing water and ethanol is inhomogeneous in micron-sized probe beads. The discrepancy between the mobility of Brownian motion and liquid mobility can be explained by the way the rotation of the beads in an inhomogeneous viscous solvent converts the translational movement.
Brownian motion using video capture
Salmon, Reese; Robbins, Candace; Forinash, Kyle
2002-01-01
Although other researchers had previously observed the random motion of pollen grains suspended in water through a microscope, Robert Brown's name is associated with this behaviour based on observations he made in 1828. It was not until Einstein's work in the early 1900s however, that the origin of this irregular motion was established to be the result of collisions with molecules which were so small as to be invisible in a light microscope (Einstein A 1965 Investigations on the Theory of the Brownian Movement ed R Furth (New York: Dover) (transl. Cowper A D) (5 papers)). Jean Perrin in 1908 (Perrin J 1923 Atoms (New York: Van Nostrand-Reinhold) (transl. Hammick D)) was able, through a series of painstaking experiments, to establish the validity of Einstein's equation. We describe here the details of a junior level undergraduate physics laboratory experiment where students used a microscope, a video camera and video capture software to verify Einstein's famous calculation of 1905. (author)
Irreversible Brownian Heat Engine
Taye, Mesfin Asfaw
2017-10-01
We model a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a linearly decreasing background temperature. We show that the efficiency of such Brownian heat engine approaches the efficiency of endoreversible engine η =1-√{{Tc/Th}} [23]. On the other hand, the maximum power efficiency of the engine approaches η ^{MAX}=1-({Tc/Th})^{1\\over 4}. It is shown that the optimized efficiency always lies between the efficiency at quasistatic limit and the efficiency at maximum power while the efficiency at maximum power is always less than the optimized efficiency since the fast motion of the particle comes at the expense of the energy cost. If the heat exchange at the boundary of the heat baths is included, we show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature. The role of time on the performance of the motor is also explored via numerical simulations. Our numerical results depict that the time t and the external load dictate the direction of the particle velocity. Moreover, the performance of the heat engine improves with time. At large t (steady state), the velocity, the efficiency and the coefficient of performance of the refrigerator attain their maximum value. Furthermore, we study the effect of temperature by considering a viscous friction that decreases exponentially as the background temperature increases. Our result depicts that the Brownian particle exhibits a fast unidirectional motion when the viscous friction is temperature dependent than that of constant viscous friction. Moreover, the efficiency of this motor is considerably enhanced when the viscous friction is temperature dependent. On the hand, the motor exhibits a higher performance of the refrigerator when the viscous friction is taken to be constant.
Eichhorn, R.; Reimann, P.
2004-04-01
We consider a Brownian particle whose motion is confined to a ``meandering'' pathway and which is driven away from thermal equilibrium by an alternating external force. This system exhibits absolute negative mobility, i.e. when an external static force is applied the particle moves in the direction opposite to that force. We reveal the physical mechanism behind this ``donkey-like'' behavior, and derive analytical approximations that are in excellent agreement with numerical results.
Eichhorn, R.; Reimann, P.
2004-01-01
We consider a Brownian particle whose motion is confined to a ''meandering'' pathway and which is driven away from thermal equilibrium by an alternating external force. This system exhibits absolute negative mobility, i.e. when an external static force is applied the particle moves in the direction opposite to that force. We reveal the physical mechanism behind this ''donkey-like'' behavior, and derive analytical approximations that are in excellent agreement with numerical results. (author)
Constructive role of Brownian motion: Brownian motors and Stochastic Resonance
Hänggi, Peter
2005-03-01
Noise is usually thought of as the enemy of order rather as a constructive influence. For the phenomena of Stochastic Resonance [1] and Brownian motors [2], however, stochastic noise can play a beneficial role in enhancing detection and/or facilitating directed transmission of information in absence of biasing forces. Brownian motion assisted Stochastic Resonance finds useful applications in physical, technological, biological and biomedical contexts [1,3]. The basic principles that underpin Stochastic Resonance are elucidated and novel applications for nonlinear classical and quantum systems will be addressed. The presence of non-equilibrium disturbances enables to rectify Brownian motion so that quantum and classical objects can be directed around on a priori designed routes in biological and physical systems (Brownian motors). In doing so, the energy from the haphazard motion of (quantum) Brownian particles is extracted to perform useful work against an external load. This very concept together with first experimental realizations are discussed [2,4,5]. [1] L. Gammaitoni, P. Hä'nggi, P. Jung and F. Marchesoni, Stochastic Resonance, Rev. Mod. Phys. 70, 223 (1998).[2] R. D. Astumian and P. Hä'nggi, Brownian motors, Physics Today 55 (11), 33 (2002).[3] P. Hä'nggi, Stochastic Resonace in Physics and Biology, ChemPhysChem 3, 285 (2002).[4] H. Linke, editor, Special Issue on Brownian Motors, Applied Physics A 75, No. 2 (2002).[5] P. Hä'nggi, F. Marchesoni, F. Nori, Brownian motors, Ann. Physik (Leipzig) 14, xxx (2004); cond-mat/0410033.
Optimum analysis of a Brownian refrigerator.
Luo, X G; Liu, N; He, J Z
2013-02-01
A Brownian refrigerator with the cold and hot reservoirs alternating along a space coordinate is established. The heat flux couples with the movement of the Brownian particles due to an external force in the spatially asymmetric but periodic potential. After using the Arrhenius factor to describe the behaviors of the forward and backward jumps of the particles, the expressions for coefficient of performance (COP) and cooling rate are derived analytically. Then, through maximizing the product of conversion efficiency and heat flux flowing out, a new upper bound only depending on the temperature ratio of the cold and hot reservoirs is found numerically in the reversible situation, and it is a little larger than the so-called Curzon and Ahlborn COP ε(CA)=(1/√[1-τ])-1. After considering the irreversible factor owing to the kinetic energy change of the moving particles, we find the optimized COP is smaller than ε(CA) and the external force even does negative work on the Brownian particles when they jump from a cold to hot reservoir.
Man'ko, V I
1993-01-01
Brownian motion may be embedded in the Fock space of bosonic free field in one dimension.Extending this correspondence to a family of creation and annihilation operators satisfying a q-deformed algebra, the notion of q-deformation is carried from the algebra to the domain of stochastic processes.The properties of q-deformed Brownian motion, in particular its non-Gaussian nature and cumulant structure,are established.
A hydrodynamic formalism for Brownian systems
Pina, E.; Rosales, M.A.
1981-01-01
A formal hydrodynamic approach to Brownian motion is presented and the corresponding equations are derived. Hydrodynamic quantities are expressed in terms of the physical variables characterizing the Brownian systems. Contact is made with the hydrodynamic model of Quantum Mechanics. (author)
Brownian dynamics with hydrodynamic interactions
Ermak, D.L.; McCammon, J.A.
1978-01-01
A method for simulating the Brownian dynamics of N particles with the inclusion of hydrodynamic interactions is described. The particles may also be subject to the usual interparticle or external forces (e.g., electrostatic) which have been included in previous methods for simulating Brownian dynamics of particles in the absence of hydrodynamic interactions. The present method is derived from the Langevin equations for the N particle assembly, and the results are shown to be consistent with the corresponding Fokker--Planck results. Sample calculations on small systems illustrate the importance of including hydrodynamic interactions in Brownian dynamics simulations. The method should be useful for simulation studies of diffusion limited reactions, polymer dynamics, protein folding, particle coagulation, and other phenomena in solution
Parallel Molecular Distributed Detection With Brownian Motion.
Rogers, Uri; Koh, Min-Sung
2016-12-01
This paper explores the in vivo distributed detection of an undesired biological agent's (BAs) biomarkers by a group of biological sized nanomachines in an aqueous medium under drift. The term distributed, indicates that the system information relative to the BAs presence is dispersed across the collection of nanomachines, where each nanomachine possesses limited communication, computation, and movement capabilities. Using Brownian motion with drift, a probabilistic detection and optimal data fusion framework, coined molecular distributed detection, will be introduced that combines theory from both molecular communication and distributed detection. Using the optimal data fusion framework as a guide, simulation indicates that a sub-optimal fusion method exists, allowing for a significant reduction in implementation complexity while retaining BA detection accuracy.
Quantum equations from Brownian motions
Rajput, B.S.
2011-01-01
Classical Schrodinger and Dirac equations have been derived from Brownian motions of a particle, it has been shown that the classical Schrodinger equation can be transformed to usual Schrodinger Quantum equation on applying Heisenberg uncertainty principle between position and momentum while Dirac Quantum equation follows it's classical counter part on applying Heisenberg uncertainly principle between energy and time without applying any analytical continuation. (author)
The Diffusion Process in Small Particles and Brownian Motion
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.
Slow kinetics of Brownian maxima.
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 motion and stochastic calculus
Karatzas, Ioannis
1998-01-01
This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large num...
Operator Fractional Brownian Motion and Martingale Differences
Hongshuai Dai
2014-01-01
Full Text Available It is well known that martingale difference sequences are very useful in applications and theory. On the other hand, the operator fractional Brownian motion as an extension of the well-known fractional Brownian motion also plays an important role in both applications and theory. In this paper, we study the relation between them. We construct an approximation sequence of operator fractional Brownian motion based on a martingale difference sequence.
Decay ratio for third order Brownian oscillators
Konno, H.; Kanemoto, S.
1998-01-01
We have obtained the analytical expressions of the decay ratios for two types of third order Brownian oscillators which are generalizations of the second order Brownian oscillator driven by the Gaussian-white noise. The resulting expressions will provide us useful baseline information for more complicated practical problems and their applications
Brownian Optimal Stopping and Random Walks
Lamberton, D.
2002-01-01
One way to compute the value function of an optimal stopping problem along Brownian paths consists of approximating Brownian motion by a random walk. We derive error estimates for this type of approximation under various assumptions on the distribution of the approximating random walk
Brownian motion of tethered nanowires.
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.
Feedback control of two-headed Brownian motors in flashing ratchet potential
Zhao A-Ke; Zhang Hong-Wei; Li Yu-Xiao
2010-01-01
We presented a detailed investigation on the movement of two-headed Brownian motors in an asymmetric potential under a feedback control. By numerical simulations the direct current is obtained. The current is periodic in the initial length of spring. There is an optimal value of the spring constant. And the dependence of the current on the opposing force is reversed. Then we found that when the change of the temperature and the opposing force have optimal values, the Brownian motors can also obtain the optimal efficiency
3-d brownian motion simulator for high-sensitivity nanobiotechnological applications.
Toth, Arpád; Banky, Dániel; Grolmusz, Vince
2011-12-01
A wide variety of nanobiotechnologic applications are being developed for nanoparticle based in vitro diagnostic and imaging systems. Some of these systems make possible highly sensitive detection of molecular biomarkers. Frequently, the very low concentration of the biomarkers makes impossible the classical, partial differential equation-based mathematical simulation of the motion of the nanoparticles involved. We present a three-dimensional Brownian motion simulation tool for the prediction of the movement of nanoparticles in various thermal, viscosity, and geometric settings in a rectangular cuvette. For nonprofit users the server is freely available at the site http://brownian.pitgroup.org.
Bivariate Gaussian bridges: directional factorization of diffusion in Brownian bridge models.
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.
A multiscale guide to Brownian motion
Grebenkov, Denis S; Belyaev, Dmitry; Jones, Peter W
2016-01-01
We revise the Lévy construction of Brownian motion as a simple though rigorous approach to operate with various Gaussian processes. A Brownian path is explicitly constructed as a linear combination of wavelet-based ‘geometrical features’ at multiple length scales with random weights. Such a wavelet representation gives a closed formula mapping of the unit interval onto the functional space of Brownian paths. This formula elucidates many classical results about Brownian motion (e.g., non-differentiability of its path), providing an intuitive feeling for non-mathematicians. The illustrative character of the wavelet representation, along with the simple structure of the underlying probability space, is different from the usual presentation of most classical textbooks. Similar concepts are discussed for the Brownian bridge, fractional Brownian motion, the Ornstein-Uhlenbeck process, Gaussian free fields, and fractional Gaussian fields. Wavelet representations and dyadic decompositions form the basis of many highly efficient numerical methods to simulate Gaussian processes and fields, including Brownian motion and other diffusive processes in confining domains. (topical review)
Jeon, Jae-Hyung; Metzler, Ralf
2010-02-01
Motivated by subdiffusive motion of biomolecules observed in living cells, we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time-averaged mean-squared displacement and displacement correlation) are affected by spatial confinement and dimensionality. In particular, we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain. The general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality. We define the displacement correlation function and find that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single-particle trajectory data.
Stock price prediction using geometric Brownian motion
Farida Agustini, W.; Restu Affianti, Ika; Putri, Endah RM
2018-03-01
Geometric Brownian motion is a mathematical model for predicting the future price of stock. The phase that done before stock price prediction is determine stock expected price formulation and determine the confidence level of 95%. On stock price prediction using geometric Brownian Motion model, the algorithm starts from calculating the value of return, followed by estimating value of volatility and drift, obtain the stock price forecast, calculating the forecast MAPE, calculating the stock expected price and calculating the confidence level of 95%. Based on the research, the output analysis shows that geometric Brownian motion model is the prediction technique with high rate of accuracy. It is proven with forecast MAPE value ≤ 20%.
An adjustable Brownian heat engine
Asfaw, Mesfin; Bekele, Mulugeta
2002-09-01
A microscopic heat engine is modeled as a Brownian particle in a sawtooth potential (with load) moving through a highly viscous medium driven by the thermal kick it gets from alternately placed hot and cold heat reservoirs. We found a closed form expression for the current as a function of the parameters characterizing the model. Depending on the values these model parameters take, the engine is also found to function as a refrigerator. Expressions for the efficiency as well as for the refrigerator performance are also reported. Study of how these quantities depend on the model parameters enabled us in identifying the points in the parameter space where the engine performs either with maximum power or with optimized efficiency. The corresponding efficiencies of the engine are then compared with those of the endoreversible and Carnot engines. (author)
The open quantum Brownian motions
Bauer, Michel; Bernard, Denis; Tilloy, Antoine
2014-01-01
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 ⊗H c : system Hilbert space H p : probe (or quantum coin) Hilbert space, H p =C 2 ρ t tot : density matrix for the total system (walker + internal spin + quantum coins) ρ-bar t : reduced density matrix on H sys : ρ-bar t =∫dxdy ρ-bar t (x,y)⊗|x〉 z 〈y| ρ-hat t : system density matrix in a quantum trajectory: ρ-hat t =∫dxdy ρ-hat t (x,y)⊗|x〉 z 〈y|. If diagonal and localized in position: ρ-hat t =ρ t ⊗|X t 〉 z 〈X t | ρ t : internal density matrix in a simple quantum trajectory X t : walker position in a simple quantum trajectory B t : normalized Brownian motion ξ t , ξ t † : quantum noises (paper)
Coupling of lever arm swing and biased Brownian motion in actomyosin.
Qing-Miao Nie
2014-04-01
Full Text Available An important unresolved problem associated with actomyosin motors is the role of Brownian motion in the process of force generation. On the basis of structural observations of myosins and actins, the widely held lever-arm hypothesis has been proposed, in which proteins are assumed to show sequential structural changes among observed and hypothesized structures to exert mechanical force. An alternative hypothesis, the Brownian motion hypothesis, has been supported by single-molecule experiments and emphasizes more on the roles of fluctuating protein movement. In this study, we address the long-standing controversy between the lever-arm hypothesis and the Brownian motion hypothesis through in silico observations of an actomyosin system. We study a system composed of myosin II and actin filament by calculating free-energy landscapes of actin-myosin interactions using the molecular dynamics method and by simulating transitions among dynamically changing free-energy landscapes using the Monte Carlo method. The results obtained by this combined multi-scale calculation show that myosin with inorganic phosphate (Pi and ADP weakly binds to actin and that after releasing Pi and ADP, myosin moves along the actin filament toward the strong-binding site by exhibiting the biased Brownian motion, a behavior consistent with the observed single-molecular behavior of myosin. Conformational flexibility of loops at the actin-interface of myosin and the N-terminus of actin subunit is necessary for the distinct bias in the Brownian motion. Both the 5.5-11 nm displacement due to the biased Brownian motion and the 3-5 nm displacement due to lever-arm swing contribute to the net displacement of myosin. The calculated results further suggest that the recovery stroke of the lever arm plays an important role in enhancing the displacement of myosin through multiple cycles of ATP hydrolysis, suggesting a unified movement mechanism for various members of the myosin family.
Coupling of lever arm swing and biased Brownian motion in actomyosin.
Nie, Qing-Miao; Togashi, Akio; Sasaki, Takeshi N; Takano, Mitsunori; Sasai, Masaki; Terada, Tomoki P
2014-04-01
An important unresolved problem associated with actomyosin motors is the role of Brownian motion in the process of force generation. On the basis of structural observations of myosins and actins, the widely held lever-arm hypothesis has been proposed, in which proteins are assumed to show sequential structural changes among observed and hypothesized structures to exert mechanical force. An alternative hypothesis, the Brownian motion hypothesis, has been supported by single-molecule experiments and emphasizes more on the roles of fluctuating protein movement. In this study, we address the long-standing controversy between the lever-arm hypothesis and the Brownian motion hypothesis through in silico observations of an actomyosin system. We study a system composed of myosin II and actin filament by calculating free-energy landscapes of actin-myosin interactions using the molecular dynamics method and by simulating transitions among dynamically changing free-energy landscapes using the Monte Carlo method. The results obtained by this combined multi-scale calculation show that myosin with inorganic phosphate (Pi) and ADP weakly binds to actin and that after releasing Pi and ADP, myosin moves along the actin filament toward the strong-binding site by exhibiting the biased Brownian motion, a behavior consistent with the observed single-molecular behavior of myosin. Conformational flexibility of loops at the actin-interface of myosin and the N-terminus of actin subunit is necessary for the distinct bias in the Brownian motion. Both the 5.5-11 nm displacement due to the biased Brownian motion and the 3-5 nm displacement due to lever-arm swing contribute to the net displacement of myosin. The calculated results further suggest that the recovery stroke of the lever arm plays an important role in enhancing the displacement of myosin through multiple cycles of ATP hydrolysis, suggesting a unified movement mechanism for various members of the myosin family.
Brownian motion in a flowing fluid revisited
Ramshaw, J.D.
1981-01-01
It is shown how the phenomenon of osmosis may be treated using the phenomenological theory of Brownian motion in a flowing fluid. The theory is also generalized to include viscous stresses in the particle and mixture momentum equations
A multiscale approach to Brownian motors
Pavliotis, G.A.
2005-01-01
The problem of Brownian motion in a periodic potential, under the influence of external forcing, which is either random or periodic in time, is studied in this Letter. Multiscale techniques are used to derive general formulae for the steady state particle current and the effective diffusion tensor. These formulae are then applied to calculate the effective diffusion coefficient for a Brownian particle in a periodic potential driven simultaneously by additive Gaussian white and colored noise. Our theoretical findings are supported by numerical simulations
On some generalization of fractional Brownian motions
Wang Xiaotian; Liang Xiangqian; Ren Fuyao; Zhang Shiying
2006-01-01
The multifractional Brownian motion (mBm) is a continuous Gaussian process that extends the classical fractional Brownian motion (fBm) defined by Barton and Vincent Poor [Barton RJ, Vincent Poor H. IEEE Trans Inform 1988;34(5):943] and Decreusefond and Ustuenel [Decreusefond L, Ustuenel AS. Potential Anal 1999;10:177]. In addition, an innovational representation of fBm is given
Deep inelastic collisions viewed as Brownian motion
Gross, D.H.E.; Freie Univ. Berlin
1980-01-01
Non-equilibrium transport processes like Brownian motion, are studied since perhaps 100 years and one should ask why does one not use these theories to explain deep inelastic collision data. These theories have reached a high standard of sophistication, experience, and precision that I believe them to be very usefull for our problem. I will try to sketch a possible form of an advanced theory of Brownian motion that seems to be suitable for low energy heavy ion collisions. (orig./FKS)
Dissipation and decoherence in Brownian motion
Bellomo, Bruno [Dipartimento di Scienze Fisiche ed Astronomiche dell' Universita di Palermo, Via Archirafi, 36, 90123 Palermo (Italy); Barnett, Stephen M [Department of Physics, University of Strathclyde, Glasgow G4 0NG (United Kingdom); Jeffers, John [Department of Physics, University of Strathclyde, Glasgow G4 0NG (United Kingdom)
2007-05-15
We consider the evolution of a Brownian particle described by a measurement-based master equation. We derive the solution to this equation for general initial conditions and apply it to a Gaussian initial state. We analyse the effects of the diffusive terms, present in the master equation, and describe how these modify uncertainties and coherence length. This allows us to model dissipation and decoherence in quantum Brownian motion.
Brownian quasi-particles in statistical physics
Tellez-Arenas, A.; Fronteau, J.; Combis, P.
1979-01-01
The idea of a Brownian quasi-particle and the associated differentiable flow (with nonselfadjoint forces) are used here in the context of a stochastic description of the approach towards statistical equilibrium. We show that this quasi-particle flow acquires, at equilibrium, the principal properties of a conservative Hamiltonian flow. Thus the model of Brownian quasi-particles permits us to establish a link between the stochastic description and the Gibbs description of statistical equilibrium
Area distribution of an elastic Brownian motion
Rajabpour, M A
2009-01-01
We calculate the excursion and meander area distributions of the elastic Brownian motion by using the self-adjoint extension of the Hamiltonian of the free quantum particle on the half line. We also give some comments on the area of the Brownian motion bridge on the real line with the origin removed. We will focus on the power of self-adjoint extension to investigate different possible boundary conditions for the stochastic processes. We also discuss some possible physical applications.
From Levy to Brownian: a computational model based on biological fluctuation.
Surya G Nurzaman
Full Text Available 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.
From Lévy to Brownian: a computational model based on biological fluctuation.
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.
A Brownian Bridge Movement Model to Track Mobile Targets
2016-09-01
Defense or the U.S. Government . IRB Protocol number ____N/A____. 12a. DISTRIBUTION / AVAILABILITY STATEMENT Approved for public release. Distribution...attributes and the probability of detection is explored through a meta -experiment. The experiment utilizes a three-stage algorithm that generates heat maps...explored through a meta -experiment. The experiment utilizes a three-stage algorithm that generates heat maps, deploys sensors and randomizes intelligence
Static structure of active Brownian hard disks
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.
Reflection Negative Kernels and Fractional Brownian Motion
Palle E. T. Jorgensen
2018-06-01
Full Text Available In this article we study the connection of fractional Brownian motion, representation theory and reflection positivity in quantum physics. We introduce and study reflection positivity for affine isometric actions of a Lie group on a Hilbert space E and show in particular that fractional Brownian motion for Hurst index 0 < H ≤ 1 / 2 is reflection positive and leads via reflection positivity to an infinite dimensional Hilbert space if 0 < H < 1 / 2 . We also study projective invariance of fractional Brownian motion and relate this to the complementary series representations of GL 2 ( R . We relate this to a measure preserving action on a Gaussian L 2 -Hilbert space L 2 ( E .
Non-Markovian Effects on the Brownian Motion of a Free Particle
Bolivar, A. O.
2010-01-01
Non-Markovian effects upon the Brownian movement of a free particle in the presence as well as in the absence of inertial force are investigated within the framework of Fokker-Planck equations (Rayleigh and Smoluchowski equations). More specifically, it is predicted that non-Markovian features can enhance the values of the mean square displacement and momentum, thereby assuring the mathematical property of differentiability of the these physically observable quantities.
Eigenfunction expansion for fractional Brownian motions
Maccone, C.
1981-01-01
The fractional Brownian motions, a class of nonstationary stochastic processes defined as the Riemann-Liouville fractional integral/derivative of the Brownian motion, are studied. It is shown that these processes can be regarded as the output of a suitable linear system of which the input is the white noise. Their autocorrelation is then derived with a study of their standard-deviation curves. Their power spectra are found by resorting to the nonstationary spectral theory. And finally their eigenfunction expansion (Karhunen-Loeve expansion) is obtained: the eigenfunctions are proved to be suitable Bessel functions and the eigenvalues zeros of the Bessel functions. (author)
Zelan, M; Hagman, H; Labaigt, G; Jonsell, S; Dion, C M
2011-02-01
The rectification of noise into directed movement or useful energy is utilized by many different systems. The peculiar nature of the energy source and conceptual differences between such Brownian motor systems makes a characterization of the performance far from straightforward. In this work, where the Brownian motor consists of atoms interacting with dissipative optical lattices, we adopt existing theory and present experimental measurements for both the efficiency and the transport coherence. We achieve up to 0.3% for the efficiency and 0.01 for the Péclet number.
Relaxation property of the fractional Brownian particle
Wang Litan; Lung, C.W.
1988-08-01
Dynamic susceptibility of a diffusion system associated with the fractional Brownian motion (fBm) was examined for the fractal property of the Non-Debye relaxation process. The comparisons between fBm and other approaches were made. Anomalous diffusion and the Non-Debye relaxation processes were discussed with this approach. (author). 8 refs, 1 fig
Generalized Arcsine Laws for Fractional Brownian Motion.
Sadhu, Tridib; Delorme, Mathieu; Wiese, Kay Jörg
2018-01-26
The three arcsine laws for Brownian motion are a cornerstone of extreme-value statistics. For a Brownian B_{t} starting from the origin, and evolving during time T, one considers the following three observables: (i) the duration t_{+} the process is positive, (ii) the time t_{last} the process last visits the origin, and (iii) the time t_{max} when it achieves its maximum (or minimum). All three observables have the same cumulative probability distribution expressed as an arcsine function, thus the name arcsine laws. We show how these laws change for fractional Brownian motion X_{t}, a non-Markovian Gaussian process indexed by the Hurst exponent H. It generalizes standard Brownian motion (i.e., H=1/2). We obtain the three probabilities using a perturbative expansion in ϵ=H-1/2. While all three probabilities are different, this distinction can only be made at second order in ϵ. Our results are confirmed to high precision by extensive numerical simulations.
Brownian coagulation at high particle concentrations
Trzeciak, T.M.
2012-01-01
The process of Brownian coagulation, whereby particles are brought together by thermal motion and grow by collisions, is one of the most fundamental processes influencing the final properties of particulate matter in a variety of technically important systems. It is of importance in colloids,
Brownian motion, martingales, and stochastic calculus
Le Gall, Jean-François
2016-01-01
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested i...
Fractional Brownian motion with a reflecting wall
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 implications of these findings, in particular, for applications that are dominated by rare events.
Current fluctuations of interacting active Brownian particles
Pre, Trevor Grand; Limmer, David T.
2018-01-01
We derive the distribution function for particle currents for a system of interacting active Brownian particles in the long time limit using large deviation theory and a weighted many body expansion. We find the distribution is non-Gaussian, except in the limit of passive particles. The non-Gaussian fluctuations can be understood from the effective potential the particles experience when conditioned on a given current. This potential suppresses fluctuations of the particle's orientation, and ...
Time-averaged MSD of Brownian motion
Andreanov, Alexei; Grebenkov, Denis
2012-01-01
We study the statistical properties of the time-averaged mean-square displacements (TAMSD). This is a standard non-local quadratic functional for inferring the diffusion coefficient from an individual random trajectory of a diffusing tracer in single-particle tracking experiments. For Brownian motion, we derive an exact formula for the Laplace transform of the probability density of the TAMSD by mapping the original problem onto chains of coupled harmonic oscillators. From this formula, we de...
Brownian motion, dynamical randomness and irreversibility
Gaspard, Pierre
2005-01-01
A relationship giving the entropy production as the difference between a time-reversed entropy per unit time and the standard one is applied to stochastic processes of diffusion of Brownian particles between two reservoirs at different concentrations. The entropy production in the nonequilibrium steady state is interpreted in terms of a time asymmetry in the dynamical randomness between the forward and backward paths of the diffusion process
Brownian motion in short range random potentials
Romero, A.H.; Romero, A.H.; Sancho, J.M.
1998-01-01
A numerical study of Brownian motion of noninteracting particles in random potentials is presented. The dynamics are modeled by Langevin equations in the high friction limit. The random potentials are Gaussian distributed and short ranged. The simulations are performed in one and two dimensions. Different dynamical regimes are found and explained. Effective subdiffusive exponents are obtained and commented on. copyright 1998 The American Physical Society
Frustrated Brownian Motion of Nonlocal Solitary Waves
Folli, V.; Conti, C.
2010-01-01
We investigate the evolution of solitary waves in a nonlocal medium in the presence of disorder. By using a perturbational approach, we show that an increasing degree of nonlocality may largely hamper the Brownian motion of self-trapped wave packets. The result is valid for any kind of nonlocality and in the presence of nonparaxial effects. Analytical predictions are compared with numerical simulations based on stochastic partial differential equations.
The quantum brownian particle and memory effects
Britani, J.R.; Mizrahi, S.S.; Pimentel, B.M.
1991-01-01
The Quantum Brownian particle, immersed in a heat bath, is described by a statistical operator whose evolution is ruled by a Generalized Master Equation (GME). The heat bath degrees of freedom are considered to be either white noise or coloured noise correlated,while the GME is considered under either the Markov or Non-Markov approaches. The comparison between these considerations are fully developed and their physical meaning is discussed. (author)
Intrinsic and extrinsic measurement for Brownian motion
Castro-Villarreal, Pavel
2014-01-01
Based upon the Smoluchowski equation on curved manifolds, three physical observables are considered for Brownian displacement, namely geodesic displacement s, Euclidean displacement δR, and projected displacement δR ⊥ . The Weingarten–Gauss equations are used to calculate the mean-square Euclidean displacements in the short-time regime. Our findings show that from an extrinsic point of view the geometry of the space affects the Brownian motion in such a way that the particle’s diffusion is decelerated, contrasting with the intrinsic point of view where dynamics is controlled by the sign of the Gaussian curvature (Castro-Villarreal, 2010 J. Stat. Mech. P08006). Furthermore, it is possible to give exact formulas for 〈δR〉 and 〈δR 2 〉 on spheres and minimal surfaces, which are valid for all values of time. In the latter case, surprisingly, Brownian motion corresponds to the usual diffusion in flat geometries, albeit minimal surfaces have non-zero Gaussian curvature. Finally, the two-dimensional case is emphasized due to its close relation to surface self-diffusion in fluid membranes. (paper)
Interacting Brownian Swarms: Some Analytical Results
Guillaume Sartoretti
2016-01-01
Full Text Available We consider the dynamics of swarms of scalar Brownian agents subject to local imitation mechanisms implemented using mutual rank-based interactions. For appropriate values of the underlying control parameters, the swarm propagates tightly and the distances separating successive agents are iid exponential random variables. Implicitly, the implementation of rank-based mutual interactions, requires that agents have infinite interaction ranges. Using the probabilistic size of the swarm’s support, we analytically estimate the critical interaction range below that flocked swarms cannot survive. In the second part of the paper, we consider the interactions between two flocked swarms of Brownian agents with finite interaction ranges. Both swarms travel with different barycentric velocities, and agents from both swarms indifferently interact with each other. For appropriate initial configurations, both swarms eventually collide (i.e., all agents interact. Depending on the values of the control parameters, one of the following patterns emerges after collision: (i Both swarms remain essentially flocked, or (ii the swarms become ultimately quasi-free and recover their nominal barycentric speeds. We derive a set of analytical flocking conditions based on the generalized rank-based Brownian motion. An extensive set of numerical simulations corroborates our analytical findings.
Quantum dynamical framework for Brownian heat engines
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.
Properties of Brownian Image Models in Scale-Space
Pedersen, Kim Steenstrup
2003-01-01
Brownian images) will be discussed in relation to linear scale-space theory, and it will be shown empirically that the second order statistics of natural images mapped into jet space may, within some scale interval, be modeled by the Brownian image model. This is consistent with the 1/f 2 power spectrum...... law that apparently governs natural images. Furthermore, the distribution of Brownian images mapped into jet space is Gaussian and an analytical expression can be derived for the covariance matrix of Brownian images in jet space. This matrix is also a good approximation of the covariance matrix......In this paper it is argued that the Brownian image model is the least committed, scale invariant, statistical image model which describes the second order statistics of natural images. Various properties of three different types of Gaussian image models (white noise, Brownian and fractional...
Time rescaling and Gaussian properties of the fractional Brownian motions
Maccone, C.
1981-01-01
The fractional Brownian motions are proved to be a class of Gaussian (normal) stochastic processes suitably rescaled in time. Some consequences affecting their eigenfunction expansion (Karhunen-Loeve expansion) are inferred. A known formula of Cameron and Martin is generalized. The first-passage time probability density is found. The partial differential equation of the fractional Brownian diffusion is obtained. And finally the increments of the fractional Brownian motions are proved to be independent for nonoverlapping time intervals. (author)
Plyukhin, A.V.
2013-01-01
A model of an autonomous isothermal Brownian motor with an internal propulsion mechanism is considered. The motor is a Brownian particle which is semi-transparent for molecules of surrounding ideal gas. Molecular passage through the particle is controlled by a potential similar to that in the transition rate theory, i.e. characterized by two stationary states with a finite energy difference separated by a potential barrier. The internal potential drop maintains the diode-like asymmetry of molecular fluxes through the particle, which results in the particle's stationary drift.
O'Connell's process as a vicious Brownian motion
Katori, Makoto
2011-01-01
Vicious Brownian motion is a diffusion scaling limit of Fisher's vicious walk model, which is a system of Brownian particles in one dimension such that if two motions meet they kill each other. We consider the vicious Brownian motions conditioned never to collide with each other and call it noncolliding Brownian motion. This conditional diffusion process is equivalent to the eigenvalue process of the Hermitian-matrix-valued Brownian motion studied by Dyson [J. Math. Phys. 3, 1191 (1962)]. Recently, O'Connell [Ann. Probab. (to be published)] introduced a generalization of the noncolliding Brownian motion by using the eigenfunctions (the Whittaker functions) of the quantum Toda lattice in order to analyze a directed polymer model in 1 + 1 dimensions. We consider a system of one-dimensional Brownian motions with a long-ranged killing term as a generalization of the vicious Brownian motion and construct the O'Connell process as a conditional process of the killing Brownian motions to survive forever.
Langevin theory of anomalous Brownian motion made simple
Tothova, Jana; Vasziova, Gabriela; Lisy, VladimIr; Glod, Lukas
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 'infinitely more simple' description of Brownian motion than that by Einstein. The original Langevin approach has however strong limitations, which were rigorously stated after the creation of the hydrodynamic theory of Brownian motion (1945). Hydrodynamic Brownian motion is a special case of 'anomalous Brownian motion', now intensively studied both theoretically and in experiments. We show how some general properties of anomalous Brownian motion can be easily derived using an effective method that allows one to convert the stochastic generalized Langevin equation into a deterministic Volterra-type integro-differential equation for the mean square displacement of the particle. Within the Gibbs statistics, the method is applicable to linear equations of motion with any kind of memory during the evolution of the system. We apply it to memoryless Brownian motion in a harmonic potential well and to Brownian motion in fluids, taking into account the effects of hydrodynamic memory. Exploring the mathematical analogy between Brownian motion and electric circuits, which are at nanoscales also described by the generalized Langevin equation, we calculate the fluctuations of charge and current in RLC circuits that are in contact with the thermal bath. Due to the simplicity of our approach it could be incorporated into graduate courses of statistical physics. Once the method is established, it allows bringing to the attention of students and effectively solving a number of attractive problems related to Brownian motion.
Okuyama, Kikuo; Kousaka, Yasuo; Yoshida, Tetsuo
1976-01-01
The behavior of aerosols undergoing Brownian coagulation. Brownian diffusion and gravitational settling in a closed chamber was studied by solving the basic equation, the so-called population balance equation, numerically for a polydisperse aerosol system and analytically for a monodisperse system, and then the results were examined by experiment. In solving the basic equation, two dimensionless parameters, which are determined by the initial properties of an aerosol and the chamber dimension and also characterize the relative effects of Brownian coagulation and Brownian diffusion to gravitational settling, were introduced in order to generalize the behavior under arbitrary conditions. The calculated results, the time-dependent changes in particle number concentration and particle size distribution for a polydisperse system, were presented graphically by using the above two parameters. And further using these parameters, the domains of the three controlling factors were mapped to show the extent of each effect of these factors under various conditions for a monodisperse system. Some of the calculated results were compared with the experimental results obtained by the ultramicroscopic size analysis previously developed by the authors. (auth.)
The relativistic Brownian motion: Interdisciplinary applications
Aragones-Munoz, A; Sandoval-Villalbazo, A
2010-01-01
Relativistic Brownian motion theory will be applied to the study of analogies between physical and economic systems, emphasizing limiting cases in which Gaussian distributions are no longer valid. The characteristic temperatures of the particles will be associated with the concept of variance, and this will allow us to choose whether the pertinent distribution is classical or relativistic, while working specific situations. The properties of particles can be interpreted as economic variables, in order to study the behavior of markets in terms of Levy financial processes, since markets behave as stochastic systems. As far as we know, the application of the Juettner distribution to the study of economic systems is a new idea.
Effective diffusion of confined active Brownian swimmers
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.
Time-averaged MSD of Brownian motion
Andreanov, Alexei; Grebenkov, Denis S
2012-01-01
We study the statistical properties of the time-averaged mean-square displacements (TAMSD). This is a standard non-local quadratic functional for inferring the diffusion coefficient from an individual random trajectory of a diffusing tracer in single-particle tracking experiments. For Brownian motion, we derive an exact formula for the Laplace transform of the probability density of the TAMSD by mapping the original problem onto chains of coupled harmonic oscillators. From this formula, we deduce the first four cumulant moments of the TAMSD, the asymptotic behavior of the probability density and its accurate approximation by a generalized Gamma distribution
Eigenfunction statistics of Wishart Brownian ensembles
Shukla, Pragya
2017-01-01
We theoretically analyze the eigenfunction fluctuation measures for a Hermitian ensemble which appears as an intermediate state of the perturbation of a stationary ensemble by another stationary ensemble of Wishart (Laguerre) type. Similar to the perturbation by a Gaussian stationary ensemble, the measures undergo a diffusive dynamics in terms of the perturbation parameter but the energy-dependence of the fluctuations is different in the two cases. This may have important consequences for the eigenfunction dynamics as well as phase transition studies in many areas of complexity where Brownian ensembles appear. (paper)
Quantum Darwinism in Quantum Brownian Motion
Blume-Kohout, Robin; Zurek, Wojciech H.
2008-12-01
Quantum Darwinism—the redundant encoding of information about a decohering system in its environment—was proposed to reconcile the quantum nature of our Universe with apparent classicality. We report the first study of the dynamics of quantum Darwinism in a realistic model of decoherence, quantum Brownian motion. Prepared in a highly squeezed state—a macroscopic superposition—the system leaves records whose redundancy increases rapidly with initial delocalization. Redundancy appears rapidly (on the decoherence time scale) and persists for a long time.
Time-averaged MSD of Brownian motion
Andreanov, Alexei; Grebenkov, Denis S.
2012-07-01
We study the statistical properties of the time-averaged mean-square displacements (TAMSD). This is a standard non-local quadratic functional for inferring the diffusion coefficient from an individual random trajectory of a diffusing tracer in single-particle tracking experiments. For Brownian motion, we derive an exact formula for the Laplace transform of the probability density of the TAMSD by mapping the original problem onto chains of coupled harmonic oscillators. From this formula, we deduce the first four cumulant moments of the TAMSD, the asymptotic behavior of the probability density and its accurate approximation by a generalized Gamma distribution.
Laser light scattering in Brownian medium
Suwono; Santoso, Budi; Baiquni, A.
1983-01-01
The principle of laser light scattering in Brownian medium and photon correlation spectroscopy are described in detail. Their application to the study of the behaviour of a polystyrene latex solution are discussed. The auto-correlation function of light scattered by the polystyrene latex solution in various angle, various temperature and in various sample times, have been measured. Information on the translation diffusion coefficient and size on the particle can be obtained from the auto-correlation function. Good agreement between the available data and experiment is shown. (author)
Microscopic derivation of open quantum Brownian motion: a particular example
Sinayskiy, Ilya; Petruccione, Francesco
2015-01-01
The microscopic derivation of a new type of Brownian motion, namely open quantum Brownian motion (OQBM) is presented. The quantum master equation for OQBM is derived for a weakly driven system interacting with a decoherent environment. Examples of the dynamics for initial Gaussian and non-Gaussian distributions are presented. Both examples demonstrate convergence of the OQBM dynamics to Gaussian distributions. (topical article)
Diffusion in one dimensional random medium and hyperbolic Brownian motion
Comtet, A.; Monthus, C.; Paris-6 Univ., 75
1995-03-01
Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. This relationship is analyzed in detail and various distributions are studied using stochastic calculus and functional integration. (author) 17 refs
Simple Brownian diffusion an introduction to the standard theoretical models
Gillespie, Daniel T
2013-01-01
Brownian diffusion, the motion of large molecules in a sea of very many much smaller molecules, is topical because it is one of the ways in which biologically important molecules move about inside living cells. This book presents the mathematical physics that underlies the four simplest models of Brownian diffusion.
A Brownian motor mechanism of translocation and strand separation by hepatitis C virus helicase.
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.
Self-induced temperature gradients in Brownian dynamics
Devine, Jack; Jack, M. W.
2017-12-01
Brownian systems often surmount energy barriers by absorbing and emitting heat to and from their local environment. Usually, the temperature gradients created by this heat exchange are assumed to dissipate instantaneously. Here we relax this assumption to consider the case where Brownian dynamics on a time-independent potential can lead to self-induced temperature gradients. In the same way that externally imposed temperature gradients can cause directed motion, these self-induced gradients affect the dynamics of the Brownian system. The result is a coupling between the local environment and the Brownian subsystem. We explore the resulting dynamics and thermodynamics of these coupled systems and develop a robust method for numerical simulation. In particular, by focusing on one-dimensional situations, we show that self-induced temperature gradients reduce barrier-crossing rates. We also consider a heat engine and a heat pump based on temperature gradients induced by a Brownian system in a nonequilibrium potential.
A bipedal DNA Brownian motor with coordinated legs.
Omabegho, Tosan; Sha, Ruojie; Seeman, Nadrian C
2009-04-03
A substantial challenge in engineering molecular motors is designing mechanisms to coordinate the motion between multiple domains of the motor so as to bias random thermal motion. For bipedal motors, this challenge takes the form of coordinating the movement of the biped's legs so that they can move in a synchronized fashion. To address this problem, we have constructed an autonomous DNA bipedal walker that coordinates the action of its two legs by cyclically catalyzing the hybridization of metastable DNA fuel strands. This process leads to a chemically ratcheted walk along a directionally polar DNA track. By covalently cross-linking aliquots of the walker to its track in successive walking states, we demonstrate that this Brownian motor can complete a full walking cycle on a track whose length could be extended for longer walks. We believe that this study helps to uncover principles behind the design of unidirectional devices that can function without intervention. This device should be able to fulfill roles that entail the performance of useful mechanical work on the nanometer scale.
Greczylo, Tomasz; Debowska, Ewa
2007-01-01
The authors make comments and remarks on the papers by Salmon et al (2002 Eur. J. Phys. 23 249-53) and their own (2005 Eur. J. Phys. 26 827-33) concerning Brownian motion in two-dimensional space. New, corrected results of calculations and measurements for students' experiments on finding the viscosity of liquids from Brownian motion are presented. (letters and comments)
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.
Danish A. Ahmed; Sergei V. Petrovskii; Paulo F. C. Tilles
2018-01-01
Many empirical and theoretical studies indicate that Brownian motion and diffusion models as its mean field counterpart provide appropriate modeling techniques for individual insect movement. However, this traditional approach has been challenged, and conflicting evidence suggests that an alternative movement pattern such as Lévy walks can provide a better description. Lévy walks differ from Brownian motion since they allow for a higher frequency of large steps, resulting in a f...
Fractional Brownian motion and long term clinical trial recruitment.
Zhang, Qiang; Lai, Dejian
2011-05-01
Prediction of recruitment in clinical trials has been a challenging task. Many methods have been studied, including models based on Poisson process and its large sample approximation by Brownian motion (BM), however, when the independent incremental structure is violated for BM model, we could use fractional Brownian motion to model and approximate the underlying Poisson processes with random rates. In this paper, fractional Brownian motion (FBM) is considered for such conditions and compared to BM model with illustrated examples from different trials and simulations.
Conformal geometry and invariants of 3-strand Brownian braids
Nechaev, Sergei; Voituriez, Raphael
2005-01-01
We propose a simple geometrical construction of topological invariants of 3-strand Brownian braids viewed as world lines of 3 particles performing independent Brownian motions in the complex plane z. Our construction is based on the properties of conformal maps of doubly-punctured plane z to the universal covering surface. The special attention is paid to the case of indistinguishable particles. Our method of conformal maps allows us to investigate the statistical properties of the topological complexity of a bunch of 3-strand Brownian braids and to compute the expectation value of the irreducible braid length in the non-Abelian case
Breaking the symmetry of a Brownian motor with symmetric potentials
Hagman, H; Zelan, M; Dion, C M
2011-01-01
The directed transport of Brownian particles requires a system with an asymmetry and with non-equilibrium noise. Here we investigate numerically alternative ways of fulfilling these requirements for a two-state Brownian motor, realized with Brownian particles alternating between two phase-shifted, symmetric potentials. We show that, besides the previously known spatio-temporal asymmetry based on unequal transfer rates between the potentials, inequalities in the potential depths, the frictions, or the equilibrium temperatures of the two potentials also generate the required asymmetry. We also show that the effects of the thermal noise and the noise of the transfer's randomness depend on the way the asymmetry is induced.
Communication: Memory effects and active Brownian diffusion
Ghosh, Pulak K. [Department of Chemistry, Presidency University, Kolkata 700073 (India); Li, Yunyun, E-mail: yunyunli@tongji.edu.cn [Center for Phononics and Thermal Energy Science, Tongji University, Shanghai 200092 (China); Marchegiani, Giampiero [Dipartimento di Fisica, Università di Camerino, I-62032 Camerino (Italy); Marchesoni, Fabio [Center for Phononics and Thermal Energy Science, Tongji University, Shanghai 200092 (China); Dipartimento di Fisica, Università di Camerino, I-62032 Camerino (Italy)
2015-12-07
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.
Brownian Motion of Boomerang Colloidal Particles
Wei, Qi-Huo; Konya, Andrew; Wang, Feng; Selinger, Jonathan V.; Sun, Kai; Chakrabarty, Ayan
2014-03-01
We present experimental and theoretical studies on the Brownian motion of boomerang colloidal particles confined between two glass plates. Our experimental observations show that the mean displacements are biased towards the center of hydrodynamic stress (CoH), and that the mean-square displacements exhibit a crossover from short-time faster to long-time slower diffusion with the short-time diffusion coefficients dependent on the points used for tracking. A model based on Langevin theory elucidates that these behaviors are ascribed to the superposition of two diffusive modes: the ellipsoidal motion of the CoH and the rotational motion of the tracking point with respect to the CoH.
Brownian motion with multiplicative noises revisited
Kuroiwa, T; Miyazaki, K
2014-01-01
The Langevin equation with multiplicative noise and a state-dependent transport coefficient should always complemented with the proper interpretation rule of the noise, such as the Itô and Stratonovich conventions. Although the mathematical relationship between the different rules and how to translate from one rule to another are well established, the subject of which is a more physically natural rule still remains controversial. In this communication, we derive the overdamped Langevin equation with multiplicative noise for Brownian particles, by systematically eliminating the fast degrees of freedom of the underdamped Langevin equation. The Langevin equations obtained here vary depending on the choice of the noise conventions but they are different representations for an identical phenomenon. The results apply to multi-variable, nonequilibrium, non-stationary systems, and other general settings. (fast track communication)
Factorization Procedure for Harmonically Bound Brownian Particle
Omolo, JK.
2006-01-01
The method of factorization to solve the problem of the one-dimensional harmonically bound Brownian particle was applied. Assuming the the rapidily fluctuating random force is Gaussian and has an infinitely short correlation time, explicit expressions for the position-position,velocity-velocity, and the position-velocity correlation functions, which are also use to write down appropriate distribution functions were used. The correlation and distribution functions for the complex quantity (amplititude) which provides the expressions for the position and velocity of the particle are calculated. Finally, Fokker-Planck equations for the joint probability distribution functions for the amplititude and it's complex conjugate as well as for the position and velocity of the particle are obtained. (author)
Yukawa Potential, Panharmonic Measure and Brownian Motion
Antti Rasila
2018-05-01
Full Text Available This paper continues our earlier investigation, where a walk-on-spheres (WOS algorithm for Monte Carlo simulation of the solutions of the Yukawa and the Helmholtz partial differential equations (PDEs was developed by using the Duffin correspondence. In this paper, we investigate the foundations behind the algorithm for the case of the Yukawa PDE. We study the panharmonic measure, which is a generalization of the harmonic measure for the Yukawa PDE. We show that there are natural stochastic definitions for the panharmonic measure in terms of the Brownian motion and that the harmonic and the panharmonic measures are all mutually equivalent. Furthermore, we calculate their Radon–Nikodym derivatives explicitly for some balls, which is a key result behind the WOS algorithm.
Brownian motion of a nano-colloidal particle: the role of the solvent.
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
Puchkov, Evgeny O
2010-06-01
In the vacuoles of Saccharomyces cerevisiae yeast cells, vividly moving insoluble polyphosphate complexes (IPCs) movement of the IPCs and to evaluate the viscosity in the vacuoles using the obtained data. Studies were conducted on S. cerevisiae cells stained by DAPI and fluorescein isothyocyanate-labelled latex microspheres, using fluorescence microscopy combined with computer image analysis (ImageJ software, NIH, USA). IPC movement was photorecorded and shown to be Brownian motion. On latex microspheres, a methodology was developed for measuring a fluorescing particle's two-dimensional (2D) displacements and its size. In four yeast cells, the 2D displacements and sizes of the IPCs were evaluated. Apparent viscosity values in the vacuoles of the cells, computed by the Einstein-Smoluchowski equation using the obtained data, were found to be 2.16 +/- 0.60, 2.52 +/- 0.63, 3.32 +/- 0.9 and 11.3 +/- 1.7 cP. The first three viscosity values correspond to 30-40% glycerol solutions. The viscosity value of 11.3 +/- 1.7 cP was supposed to be an overestimation, caused by the peculiarities of the vacuole structure and/or volume in this particular cell. This conclusion was supported by the particular quality of the Brownian motion trajectories set in this cell as compared to the other three cells.
An image encryption scheme based on three-dimensional Brownian motion and chaotic system
Chai Xiu-Li; Yuan Ke; Gan Zhi-Hua; Lu Yang; Chen Yi-Ran
2017-01-01
At present, many chaos-based image encryption algorithms have proved to be unsafe, few encryption schemes permute the plain images as three-dimensional (3D) bit matrices, and thus bits cannot move to any position, the movement range of bits are limited, and based on them, in this paper we present a novel image encryption algorithm based on 3D Brownian motion and chaotic systems. The architecture of confusion and diffusion is adopted. Firstly, the plain image is converted into a 3D bit matrix and split into sub blocks. Secondly, block confusion based on 3D Brownian motion (BCB3DBM) is proposed to permute the position of the bits within the sub blocks, and the direction of particle movement is generated by logistic-tent system (LTS). Furthermore, block confusion based on position sequence group (BCBPSG) is introduced, a four-order memristive chaotic system is utilized to give random chaotic sequences, and the chaotic sequences are sorted and a position sequence group is chosen based on the plain image, then the sub blocks are confused. The proposed confusion strategy can change the positions of the bits and modify their weights, and effectively improve the statistical performance of the algorithm. Finally, a pixel level confusion is employed to enhance the encryption effect. The initial values and parameters of chaotic systems are produced by the SHA 256 hash function of the plain image. Simulation results and security analyses illustrate that our algorithm has excellent encryption performance in terms of security and speed. (paper)
Conformal correlation functions in the Brownian loop soup
Camia, Federico; Gandolfi, Alberto; Kleban, Matthew
2016-01-01
We define and study a set of operators that compute statistical properties of the Brownian loop soup, a conformally invariant gas of random Brownian loops (Brownian paths constrained to begin and end at the same point) in two dimensions. We prove that the correlation functions of these operators have many of the properties of conformal primaries in a conformal field theory, and compute their conformal dimension. The dimensions are real and positive, but have the novel feature that they vary continuously as a periodic function of a real parameter. We comment on the relation of the Brownian loop soup to the free field, and use this relation to establish that the central charge of the loop soup is twice its intensity.
Conformal correlation functions in the Brownian loop soup
Camia, Federico, E-mail: federico.camia@nyu.edu [New York University Abu Dhabi (United Arab Emirates); VU University, Amsterdam (Netherlands); Gandolfi, Alberto, E-mail: albertogandolfi@nyu.edu [New York University Abu Dhabi (United Arab Emirates); Università di Firenze (Italy); Kleban, Matthew, E-mail: kleban@nyu.edu [New York University Abu Dhabi (United Arab Emirates); Center for Cosmology and Particle Physics, Department of Physics, New York University (United States)
2016-01-15
We define and study a set of operators that compute statistical properties of the Brownian loop soup, a conformally invariant gas of random Brownian loops (Brownian paths constrained to begin and end at the same point) in two dimensions. We prove that the correlation functions of these operators have many of the properties of conformal primaries in a conformal field theory, and compute their conformal dimension. The dimensions are real and positive, but have the novel feature that they vary continuously as a periodic function of a real parameter. We comment on the relation of the Brownian loop soup to the free field, and use this relation to establish that the central charge of the loop soup is twice its intensity.
Conformal correlation functions in the Brownian loop soup
Federico Camia
2016-01-01
Full Text Available We define and study a set of operators that compute statistical properties of the Brownian loop soup, a conformally invariant gas of random Brownian loops (Brownian paths constrained to begin and end at the same point in two dimensions. We prove that the correlation functions of these operators have many of the properties of conformal primaries in a conformal field theory, and compute their conformal dimension. The dimensions are real and positive, but have the novel feature that they vary continuously as a periodic function of a real parameter. We comment on the relation of the Brownian loop soup to the free field, and use this relation to establish that the central charge of the loop soup is twice its intensity.
An explicit local uniform large deviation bound for Brownian bridges
Wittich, O.
2005-01-01
By comparing curve length in a manifold and a standard sphere, we prove a local uniform bound for the exponent in the Large Deviation formula that describes the concentration of Brownian bridges to geodesics.
Near-Field, On-Chip Optical Brownian Ratchets.
Wu, Shao-Hua; Huang, Ningfeng; Jaquay, Eric; Povinelli, Michelle L
2016-08-10
Nanoparticles in aqueous solution are subject to collisions with solvent molecules, resulting in random, Brownian motion. By breaking the spatiotemporal symmetry of the system, the motion can be rectified. In nature, Brownian ratchets leverage thermal fluctuations to provide directional motion of proteins and enzymes. In man-made systems, Brownian ratchets have been used for nanoparticle sorting and manipulation. Implementations based on optical traps provide a high degree of tunability along with precise spatiotemporal control. Here, we demonstrate an optical Brownian ratchet based on the near-field traps of an asymmetrically patterned photonic crystal. The system yields over 25 times greater trap stiffness than conventional optical tweezers. Our technique opens up new possibilities for particle manipulation in a microfluidic, lab-on-chip environment.
Manipulation and controlled amplification of Brownian motion of microcantilever sensors
Mehta, Adosh; Cherian, Suman; Hedden, David; Thundat, Thomas
2001-01-01
Microcantilevers, such as those used in atomic force microscopy, undergo Brownian motion due to mechanical thermal noise. The root mean square amplitude of the Brownian motion of a cantilever typically ranges from 0.01--0.1 nm, which limits its use in practical applications. Here we describe a technique by which the Brownian amplitude and the Q factor in air and water can be amplified by three and two orders of magnitude, respectively. This technique is similar to a positive feedback oscillator, wherein the Brownian motion of the vibrating cantilever controls the frequency output of the oscillator. This technique can be exploited to improve sensitivity of microcantilever-based chemical and biological sensors, especially for sensors in liquid environments
From a stochastic to a macroscopic approach to brownian motion
Bocquet, L.
1998-01-01
In this lecture, we examine the dynamics of suspensions of mesoscopic (Brownian) particles in a molecular fluid, starting from first principles. We introduce the technique of multiple time-scales to derive the Fokker-Planck equation for a single, or for a set of interacting Brownian particles, starting from the Liouville equation for the full system (Brownian particles and discrete bath). The limitations of the Fokker-Planck equation will then be emphasized. In particular, we shall point out that under ''standard'' experimental conditions, the Fokker-Planck description cannot be correct and that non-Markovian effects are expected. A microscopic description in the true experimental limit confirms this breakdown and leads to a ''generalized'' (non-Markovian and non-local in velocity space) Fokker-Planck equation, which describes the thermalization of the Brownian particle. (author)
Directed Transport of Brownian Particles in a Periodic Channel
Jiang Jie; Ai Bao-Quan; Wu Jian-Chun
2015-01-01
The transport of Brownian particles in the infinite channel within an external force along the axis of the channel has been studied. In this paper, we study the transport of Brownian particle in the infinite channel within an external force along the axis of the channel and an external force in the transversal direction. In this more sophisticated situation, some property is similar to the simple situation, but some interesting property also appears. (paper)
Volume of the domain visited by N spherical Brownian particles
Berezhkovskii, A.M.
1994-01-01
The average value and variance of the volume of the domain visited in time t by N spherical Brownian particles starting initially at the same point are presented as quadratures of the solutions of simple diffusion problems of the survival of a point Brownian particle in the presence of one and two spherical traps. As an illustration, explicit time dependences are obtained for the average volume in one and three dimensions
Fast orthogonal transforms and generation of Brownian paths.
Leobacher, Gunther
2012-04-01
We present a number of fast constructions of discrete Brownian paths that can be used as alternatives to principal component analysis and Brownian bridge for stratified Monte Carlo and quasi-Monte Carlo. By fast we mean that a path of length [Formula: see text] can be generated in [Formula: see text] floating point operations. We highlight some of the connections between the different constructions and we provide some numerical examples.
Estimation of the global regularity of a multifractional Brownian motion
Lebovits, Joachim; Podolskij, Mark
This paper presents a new estimator of the global regularity index of a multifractional Brownian motion. Our estimation method is based upon a ratio statistic, which compares the realized global quadratic variation of a multifractional Brownian motion at two different frequencies. We show that a ...... that a logarithmic transformation of this statistic converges in probability to the minimum of the Hurst functional parameter, which is, under weak assumptions, identical to the global regularity index of the path....
QUANTUM STOCHASTIC PROCESSES: BOSON AND FERMION BROWNIAN MOTION
A.E.Kobryn
2003-01-01
Full Text Available Dynamics of quantum systems which are stochastically perturbed by linear coupling to the reservoir can be studied in terms of quantum stochastic differential equations (for example, quantum stochastic Liouville equation and quantum Langevin equation. In order to work it out one needs to define the quantum Brownian motion. As far as only its boson version has been known until recently, in the present paper we present the definition which makes it possible to consider the fermion Brownian motion as well.
Brownian dynamics simulations of insulin microspheres formation
Li, Wei; Chakrabarti, Amit; Gunton, James
2010-03-01
Recent experiments have indicated a novel, aqueous process of microsphere insulin fabrication based on controlled phase separation of protein from water-soluble polymers. We investigate the insulin microsphere crystal formation from insulin-PEG-water systems via 3D Brownian Dynamics simulations. We use the two component Asakura-Oosawa model to simulate the kinetics of this colloid polymer mixture. We first perform a deep quench below the liquid-crystal boundary that leads to fractal formation. We next heat the system to obtain a break-up of the fractal clusters and subsequently cool the system to obtain a spherical aggregation of droplets with a relatively narrow size distribution. We analyze the structure factor S(q) to identify the cluster dimension. S(q) crosses over from a power law q dependence of 1.8 (in agreement with DLCA) to 4 as q increases, which shows the evolution from fractal to spherical clusters. By studying the bond-order parameters, we find the phase transition from liquid-like droplets to crystals which exhibit local HCP and FCC order. This work is supported by grants from the NSF and Mathers Foundation.
From Brownian motion to power of fluctuations
B. Berche
2012-12-01
Full Text Available The year 2012 marks the 140th birth anniversary of Marian Smoluchowski (28.05.1872-5.09.1917, a man who "made ground-breaking contribution to the theory of Brownian motion, the theory of sedimentation, the statistical nature of the Second Law, the theory and practice of density fluctuations (critical opalescence. During his final years of scientific creativity his pioneering theory of coagulation and diffusion-limited reaction rate appeared. These outstanding achievements present true gems which dominate the description of soft matter physics and chemical physics as well as the related areas up till now!" This quotation was taken from the lecture by Peter Hanggi given at international conference Statistical Physics: Modern Trends and Applications that took place in Lviv, Ukraine on July 3-6, 2012 (see conference web-page for more details and was dedicated to the commemoration of Smoluchowski's work. This and forthcoming issues of the Condensed Matter Physics contain papers presented at this conference.
Spherical particle Brownian motion in viscous medium as non-Markovian random process
Morozov, Andrey N.; Skripkin, Alexey V.
2011-01-01
The Brownian motion of a spherical particle in an infinite medium is described by the conventional methods and integral transforms considering the entrainment of surrounding particles of the medium by the Brownian particle. It is demonstrated that fluctuations of the Brownian particle velocity represent a non-Markovian random process. The features of Brownian motion in short time intervals and in small displacements are considered. -- Highlights: → Description of Brownian motion considering the entrainment of medium is developed. → We find the equations for statistical characteristics of impulse fluctuations. → Brownian motion at small time intervals is considered. → Theoretical results and experimental data are compared.
M. Jayachandra Babu
2017-12-01
Full Text Available The knowledge of heat and mass transfer of MHD flows over different geometries is very important for heat exchangers design, transpiration, fiber coating, etc. With this initiation, a mathematical model is proposed to investigate the two-dimensional flow, heat and mass transfer of magnetohydrodynamic flow over three different geometries (vertical cone, vertical wedge, and a vertical plate. Cattaneo-Christov heat flux with external magnetic field, thermophoresis and Brownian movement effect are introduced in the model. Runge-Kutta and Newtonâs methods are employed to solve the altered governing nonlinear equations. The influences of the parameters of concern on the common profiles (velocity, temperature, and concentration are conversed (in three cases. By viewing the same parameters, skin friction coefficient, heat and mass transfer rates are discussed with the assistance of tables. It is discovered that the momentum and thermal boundary layers are non-uniform for the MHD flow over three geometries (vertical cone, wedge, and a plate. Thermal and solutal Grashof numbers regulate the temperature and concentration fields. The heat and mass transfer rates of the flow over a cone are highly influenced by the thermal relaxation parameter. Keywords: MHD, Cattaneo-Christov heat flux, Thermal relaxation, Thermophoresis, Brownian motion
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.
Brites, Carlos D. S.; Xie, Xiaoji; Debasu, Mengistie L.; Qin, Xian; Chen, Runfeng; Huang, Wei; Rocha, João; Liu, Xiaogang; Carlos, Luís D.
2016-10-01
Brownian motion is one of the most fascinating phenomena in nature. Its conceptual implications have a profound impact in almost every field of science and even economics, from dissipative processes in thermodynamic systems, gene therapy in biomedical research, artificial motors and galaxy formation to the behaviour of stock prices. However, despite extensive experimental investigations, the basic microscopic knowledge of prototypical systems such as colloidal particles in a fluid is still far from being complete. This is particularly the case for the measurement of the particles' instantaneous velocities, elusive due to the rapid random movements on extremely short timescales. Here, we report the measurement of the instantaneous ballistic velocity of Brownian nanocrystals suspended in both aqueous and organic solvents. To achieve this, we develop a technique based on upconversion nanothermometry. We find that the population of excited electronic states in NaYF4:Yb/Er nanocrystals at thermal equilibrium can be used for temperature mapping of the nanofluid with great thermal sensitivity (1.15% K-1 at 296 K) and a high spatial resolution (<1 μm). A distinct correlation between the heat flux in the nanofluid and the temporal evolution of Er3+ emission allows us to measure the instantaneous velocity of nanocrystals with different sizes and shapes.
Browndye: A software package for Brownian dynamics
Huber, Gary A.; McCammon, J. Andrew
2010-11-01
A new software package, Browndye, is presented for simulating the diffusional encounter of two large biological molecules. It can be used to estimate second-order rate constants and encounter probabilities, and to explore reaction trajectories. Browndye builds upon previous knowledge and algorithms from software packages such as UHBD, SDA, and Macrodox, while implementing algorithms that scale to larger systems. Program summaryProgram title: Browndye Catalogue identifier: AEGT_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGT_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: MIT license, included in distribution No. of lines in distributed program, including test data, etc.: 143 618 No. of bytes in distributed program, including test data, etc.: 1 067 861 Distribution format: tar.gz Programming language: C++, OCaml ( http://caml.inria.fr/) Computer: PC, Workstation, Cluster Operating system: Linux Has the code been vectorised or parallelized?: Yes. Runs on multiple processors with shared memory using pthreads RAM: Depends linearly on size of physical system Classification: 3 External routines: uses the output of APBS [1] ( http://www.poissonboltzmann.org/apbs/) as input. APBS must be obtained and installed separately. Expat 2.0.1, CLAPACK, ocaml-expat, Mersenne Twister. These are included in the Browndye distribution. Nature of problem: Exploration and determination of rate constants of bimolecular interactions involving large biological molecules. Solution method: Brownian dynamics with electrostatic, excluded volume, van der Waals, and desolvation forces. Running time: Depends linearly on size of physical system and quadratically on precision of results. The included example executes in a few minutes.
Engineering Autonomous Chemomechanical Nanomachines Using Brownian Ratchets
Lavella, Gabriel
Nanoscale machines which directly convert chemical energy into mechanical work are ubiquitous in nature and are employed to perform a diverse set of tasks such as transporting molecules, maintaining molecular gradients, and providing motion to organisms. Their widespread use in nature suggests that large technological rewards can be obtained by designing synthetic machines that use similar mechanisms. This thesis addresses the technological adaptation of a specific mechanism known as the Brownian ratchet for the design of synthetic autonomous nanomachines. My efforts were focused more specifically on synthetic chemomechanical ratchets which I deem will be broadly applicable in the life sciences. In my work I have theoretically explored the biophysical mechanisms and energy landscapes that give rise to the ratcheting phenomena and devised devices that operate off these principles. I demonstrate two generations of devices that produce mechanical force/deformation in response to a user specified ligand. The first generation devices, fabricatied using a combination nanoscale lithographic processes and bioconjugation techniques, were used to provide evidence that the proposed ratcheting phenomena can be exploited in synthetic architectures. Second generation devices fabricated using self-assembled DNA/hapten motifs were constructed to gain a precise understanding of ratcheting dynamics and design constraints. In addition, the self-assembled devices enabled fabrication en masse, which I feel will alleviate future experimental hurdles in analysis and facilitate its adaptation to technologies. The product of these efforts is an architecture that has the potential to enable numerous technologies in biosensing and drug delivery. For example, the coupling of molecule-specific actuation to the release of drugs or signaling molecules from nanocapsules or porous materials could be transformative. Such architectures could provide possible avenues to pressing issues in biology and
Makarava, Natallia; Menz, Stephan; Theves, Matthias; Huisinga, Wilhelm; Beta, Carsten; Holschneider, Matthias
2014-10-01
Amoebae explore their environment in a random way, unless external cues like, e.g., nutrients, bias their motion. Even in the absence of cues, however, experimental cell tracks show some degree of persistence. In this paper, we analyzed individual cell tracks in the framework of a linear mixed effects model, where each track is modeled by a fractional Brownian motion, i.e., a Gaussian process exhibiting a long-term correlation structure superposed on a linear trend. The degree of persistence was quantified by the Hurst exponent of fractional Brownian motion. Our analysis of experimental cell tracks of the amoeba Dictyostelium discoideum showed a persistent movement for the majority of tracks. Employing a sliding window approach, we estimated the variations of the Hurst exponent over time, which allowed us to identify points in time, where the correlation structure was distorted ("outliers"). Coarse graining of track data via down-sampling allowed us to identify the dependence of persistence on the spatial scale. While one would expect the (mode of the) Hurst exponent to be constant on different temporal scales due to the self-similarity property of fractional Brownian motion, we observed a trend towards stronger persistence for the down-sampled cell tracks indicating stronger persistence on larger time scales.
Sims, David W; Humphries, Nicolas E; Bradford, Russell W; Bruce, Barry D
2012-03-01
1. Search processes play an important role in physical, chemical and biological systems. In animal foraging, the search strategy predators should use to search optimally for prey is an enduring question. Some models demonstrate that when prey is sparsely distributed, an optimal search pattern is a specialised random walk known as a Lévy flight, whereas when prey is abundant, simple Brownian motion is sufficiently efficient. These predictions form part of what has been termed the Lévy flight foraging hypothesis (LFF) which states that as Lévy flights optimise random searches, movements approximated by optimal Lévy flights may have naturally evolved in organisms to enhance encounters with targets (e.g. prey) when knowledge of their locations is incomplete. 2. Whether free-ranging predators exhibit the movement patterns predicted in the LFF hypothesis in response to known prey types and distributions, however, has not been determined. We tested this using vertical and horizontal movement data from electronic tagging of an apex predator, the great white shark Carcharodon carcharias, across widely differing habitats reflecting different prey types. 3. Individual white sharks exhibited movement patterns that predicted well the prey types expected under the LFF hypothesis. Shark movements were best approximated by Brownian motion when hunting near abundant, predictable sources of prey (e.g. seal colonies, fish aggregations), whereas movements approximating truncated Lévy flights were present when searching for sparsely distributed or potentially difficult-to-detect prey in oceanic or shelf environments, respectively. 4. That movement patterns approximated by truncated Lévy flights and Brownian behaviour were present in the predicted prey fields indicates search strategies adopted by white sharks appear to be the most efficient ones for encountering prey in the habitats where such patterns are observed. This suggests that C. carcharias appears capable of exhibiting
Exponential functionals of Brownian motion, I: Probability laws at fixed time
Matsumoto, Hiroyuki; Yor, Marc
2005-01-01
This paper is the first part of our survey on various results about the distribution of exponential type Brownian functionals defined as an integral over time of geometric Brownian motion. Several related topics are also mentioned.
Brownian dynamic simulations and experiments of MR fluids
Segovia-Gutiérrez, J P; Vicente, J de; Hidalgo, R; Puertas, A M
2013-01-01
The use of computational techniques in magnetorheology is not new. I general, these approaches assume dipolar magnetic interactions, hard sphere repulsions, and no-slip conditions. In this contribution we focus on the dynamics of the equilibrium state in the presence of uniaxial DC fields. To achieve this goal we make use of Brownian Dynamic Simulations. We highlight the importance of the Brownian forces versus magnetic dipolar interaction in the range of low magnetic field strengths. We monitor the formation of columnar structures and their dynamics, in competition with the Brownian motion, until a hexatic crystal phase appears at high field strengths for monodisperse systems. The shear viscosity is computed from the Einstein relation and eventually compared with experimental data at very low-shear rates. A reasonably good agreement between both data sets is observed.
Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus
Yuquan Cang
2014-01-01
Full Text Available We study the asymptotic behavior of the sequence Sn=∑i=0n-1K(nαSiH1(Si+1H2-SiH2, as n tends to infinity, where SH1 and SH2 are two independent subfractional Brownian motions with indices H1 and H2, respectively. K is a kernel function and the bandwidth parameter α satisfies some hypotheses in terms of H1 and H2. Its limiting distribution is a mixed normal law involving the local time of the sub-fractional Brownian motion SH1. We mainly use the techniques of Malliavin calculus with respect to sub-fractional Brownian motion.
Cosmophysical Factors in the Fluctuation Amplitude Spectrum of Brownian Motion
Kaminsky A. V.
2010-04-01
Full Text Available Phenomenon of the regular variability of the fine structure of the fluctuation in the amplitude distributions (shapes of related histograms for the case of Brownian motion was investigated. We took an advantage of the dynamic light scattering method (DLS to get a stochastically fluctuated signal determined by Brownian motion. Shape of the histograms is most likely to vary, synchronous, in two proximally located independent cells containing Brownian particles. The synchronism persists in the cells distant at 2m from each other, and positioned meridionally. With a parallel-wise positioning of the cells, high probability of the synchronous variation in the shape of the histograms by local time has been observed. This result meets the previous conclusion about the dependency of histogram shapes ("fluctuation amplitudes" of the spectra of stochastic processes upon rotation of the Earth.
Cosmophysical Factors in the Fluctuation Amplitude Spectrum of Brownian Motion
Kaminsky A. V.
2010-07-01
Full Text Available Phenomenon of the regular variability of the fine structure of the fluctuation in the am- plitude distributions (shapes of related histograms for the case of Brownian motion was investigated. We took an advantage of the dynamic light scattering method (DLS to get a stochastically fluctuated signal determined by Brownian motion. Shape of the histograms is most likely to vary, synchronous, in two proximally located independent cells containing Brownian particles. The synchronism persists in the cells distant at 2 m from each other, and positioned meridionally. With a parallel-wise positioning of the cells, high probability of the synchronous variation in the shape of the histograms by local time has been observed. This result meets the previous conclusion about the dependency of histogram shapes (“fluctuation amplitudes” of the spectra of stochastic processes upon rotation of the Earth.
Non-colliding Brownian Motions and the Extended Tacnode Process
Johansson, Kurt
2013-04-01
We consider non-colliding Brownian motions with two starting points and two endpoints. The points are chosen so that the two groups of Brownian motions just touch each other, a situation that is referred to as a tacnode. The extended kernel for the determinantal point process at the tacnode point is computed using new methods and given in a different form from that obtained for a single time in previous work by Delvaux, Kuijlaars and Zhang. The form of the extended kernel is also different from that obtained for the extended tacnode kernel in another model by Adler, Ferrari and van Moerbeke. We also obtain the correlation kernel for a finite number of non-colliding Brownian motions starting at two points and ending at arbitrary points.
Stochastic calculus for fractional Brownian motion and related processes
Mishura, Yuliya S
2008-01-01
The theory of fractional Brownian motion and other long-memory processes are addressed in this volume. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. Among these are results about Levy characterization of fractional Brownian motion, maximal moment inequalities for Wiener integrals including the values 0
Brownian gas models for extreme-value laws
Eliazar, Iddo
2013-01-01
In this paper we establish one-dimensional Brownian gas models for the extreme-value laws of Gumbel, Weibull, and Fréchet. A gas model is a countable collection of independent particles governed by common diffusion dynamics. The extreme-value laws are the universal probability distributions governing the affine scaling limits of the maxima and minima of ensembles of independent and identically distributed one-dimensional random variables. Using the recently introduced concept of stationary Poissonian intensities, we construct two gas models whose global statistical structures are stationary, and yield the extreme-value laws: a linear Brownian motion gas model for the Gumbel law, and a geometric Brownian motion gas model for the Weibull and Fréchet laws. The stochastic dynamics of these gas models are studied in detail, and closed-form analytical descriptions of their temporal correlation structures, their topological phase transitions, and their intrinsic first-passage-time fluxes are presented. (paper)
Quantum Brownian motion model for the stock market
Meng, Xiangyi; Zhang, Jian-Wei; Guo, Hong
2016-06-01
It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysical framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system-a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenberg's uncertainty relationship of quantum mechanics in an analogous manner. We analyze real stock data of Shanghai Stock Exchange of China and investigate fat-tail phenomena and non-Markovian behaviors of the stock index with the assistance of the quantum Brownian motion model, thereby interpreting and studying the limitations of the classical Brownian motion model for the efficient market hypothesis from a new perspective of quantum open system dynamics.
Deterministic Brownian motion generated from differential delay equations.
Lei, Jinzhi; Mackey, Michael C
2011-10-01
This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential delay equation and then numerically investigate the probabilistic properties of chaotic solutions of the same equation. Our results show that solutions of the deterministic equation with randomly selected initial conditions display a Gaussian-like density for long time, but the densities are supported on an interval of finite measure. Using these chaotic solutions as velocities, we are able to produce Brownian-like motions, which show statistical properties akin to those of a classical Brownian motion over both short and long time scales. Several conjectures are formulated for the probabilistic properties of the solution of the differential delay equation. Numerical studies suggest that these conjectures could be "universal" for similar types of "chaotic" dynamics, but we have been unable to prove this.
Algorithm for generating a Brownian motion on a sphere
Carlsson, Tobias; Elvingson, Christer; Ekholm, Tobias
2010-01-01
We present a new algorithm for generation of a random walk on a two-dimensional sphere. The algorithm is obtained by viewing the 2-sphere as the equator in the 3-sphere surrounded by an infinitesimally thin band with boundary which reflects Brownian particles and then applying known effective methods for generating Brownian motion on the 3-sphere. To test the method, the diffusion coefficient was calculated in computer simulations using the new algorithm and, for comparison, also using a commonly used method in which the particle takes a Brownian step in the tangent plane to the 2-sphere and is then projected back to the spherical surface. The two methods are in good agreement for short time steps, while the method presented in this paper continues to give good results also for larger time steps, when the alternative method becomes unstable.
van Megen, W; Martinez, V A; Bryant, G
2009-12-18
The current correlation function is determined from dynamic light scattering measurements of a suspension of particles with hard spherelike interactions. For suspensions in thermodynamic equilibrium we find scaling of the space and time variables of the current correlation function. This finding supports the notion that the movement of suspended particles can be described in terms of uncorrelated Brownian encounters. However, in the metastable fluid, at volume fractions above freezing, this scaling fails.
The Intersection Probability of Brownian Motion and SLEκ
Shizhong Zhou
2015-01-01
Full Text Available By using excursion measure Poisson kernel method, we obtain a second-order differential equation of the intersection probability of Brownian motion and SLEκ. Moreover, we find a transformation such that the second-order differential equation transforms into a hypergeometric differential equation. Then, by solving the hypergeometric differential equation, we obtain the explicit formula of the intersection probability for the trace of the chordal SLEκ and planar Brownian motion started from distinct points in an upper half-plane H-.
Stochastic flows in the Brownian web and net
Schertzer, E.; Sun, R.; Swart, Jan M.
2014-01-01
Roč. 227, č. 1065 (2014), s. 1-160 ISSN 0065-9266 R&D Projects: GA ČR GA201/07/0237; GA ČR GA201/09/1931 Institutional support: RVO:67985556 Keywords : Brownian web * Brownian net * stochastic flow of kernels * measure-valued process * Howitt-Warren flow * linear system * random walk in random environment * finite graph representation Subject RIV: BA - General Mathematics Impact factor: 1.727, year: 2014 http://library.utia.cas.cz/separaty/2013/SI/swart-0396636.pdf
On the Generalized Brownian Motion and its Applications in Finance
Høg, Esben; Frederiksen, Per; Schiemert, Daniel
This paper deals with dynamic term structure models (DTSMs) and proposes a new way to handle the limitation of the classical affine models. In particular, the paper expands the exibility of the DTSMs by applying generalized Brownian motions with dependent increments as the governing force...... of the state variables instead of standard Brownian motions. This is a new direction in pricing non defaultable bonds. By extending the theory developed by Dippon & Schiemert (2006a), the paper developes a bond market with memory, and proves the absence of arbitrage. The framework is readily extendable...
Survival probabilities for branching Brownian motion with absorption
Harris, John; Harris, Simon
2007-01-01
We study a branching Brownian motion (BBM) with absorption, in which particles move as Brownian motions with drift $-\\rho$, undergo dyadic branching at rate $\\beta>0$, and are killed on hitting the origin. In the case $\\rho>\\sqrt{2\\beta}$ the extinction time for this process, $\\zeta$, is known to be finite almost surely. The main result of this article is a large-time asymptotic formula for the survival probability $P^x(\\zeta>t)$ in the case $\\rho>\\sqrt{2\\beta}$, where $P^x$ is...
Finding viscosity of liquids from Brownian motion at students' laboratory
Greczylo, Tomasz; Debowska, Ewa
2005-01-01
Brownian motion appears to be a good subject for investigation at advanced students' laboratory [1]. The paper presents such an investigation carried out in Physics Laboratory II at the Institute of Experimental Physics of Wroclaw University. The experiment has been designed to find viscosity of liquids from Brownian motion phenomenon. Authors use modern technology that helps to proceed with measurements and makes the procedure less time and effort consuming. Discussion of the process of setting up the experiment and the results obtained for three different solutions of glycerin in water are presented. Advantages and disadvantages of the apparatus are pointed out along with descriptions of possible future uses
Brownian motion of solitons in a Bose-Einstein condensate.
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.
A bowel movement is the last stop in the movement of food through your digestive tract. Your stool passes out of ... what you eat and drink. Sometimes a bowel movement isn't normal. Diarrhea happens when stool passes ...
Statistical properties of laser light scattering in Brownian medium
Suwono; Santoso, Budi; Baiquni, A.
1983-01-01
Relationship between statistical properties of laser light scattering in Brownian medium and photon-counting distributions are described in detail. A coherence optical detection has been constructed and by using photon-counting technique the ensemble distribution of the scattered field within space and time coherence has been measured. Good agreement between theory and experiment is shown. (author)
Occupation times distribution for Brownian motion on graphs
Desbois, J
2002-01-01
Considering a Brownian motion on a general graph, we study the joint law for the occupation times on all the bonds. In particular, we show that the Laplace transform of this distribution can be expressed as the ratio of two determinants. We give two formulations, with arc or vertex matrices, for this result and discuss a simple example. (letter to the editor)
Velocity persistence of Brownian particles generated in a glow discharge
Hurd, A.J.; Ho, P.
1989-01-01
Quasielastic light scattering from Brownian particles in the rarefied environment of a glow discharge exhibits Gaussianlike intensity correlation functions owing to the long mean free paths of the particles. The shape of the correlation function depends on the particles' average thermal velocity and friction coefficient, which can be related to aggregate mass and structure, and indicates a crossover from kinetic to hydrodynamic behavior
Phase transition for absorbed Brownian motion with drift
Ferrari, P.A.; Martinez, S.; San Martin, J.
1997-01-01
We study one-dimensional Brownian motion with constant drift toward the origin and initial distribution concentrated in the strictly positive real line. We say that at the first time the process hits the origin, it is absorbed. We study the asymptotic behavior, as t → ∞, of m t , the conditional distribution at time zero of the process conditioned on survival up to time t and on the process having a fixed value at time t. We find that there is a phase transition in the decay rate of the initial condition. For fast decay rate (subcritical case) m t is localized, in the critical case m t is located around √t, and for slow rates (supercritical case) m, is located around t. The critical rate is given by the decay of the minimal quasistationary distribution of this process. We also study in each case the asymptotic distribution of the process, scaled by √t, conditioned as before. We prove that in the subcritical case this distribution is a Brownian excursion. In the critical case it is a Brownian bridge attaining 0 for the first time at time 1, with some initial distribution. In the supercritical case, after centering around the expected value-which is of the order of t we show that this process converges to a Brownian bridge arriving at 0 at time 1 and with a Gaussian initial distribution
Brownian motion, Minkowski space and principle of special relativity
Caubet, J.-P.
1977-01-01
From the assumption that the brownian diffusion locally behaves like an ideal gas (pressure being inversely proportional to volume according to Boyle's law) one can deduce the signature +++- of the Minkowski space, the Lorentz addition of velocities, and the principle of special relativity [fr
Entropy production of a Brownian ellipsoid in the overdamped limit.
Marino, Raffaele; Eichhorn, Ralf; Aurell, Erik
2016-01-01
We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called "anomalous" contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the "anomalous" entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the "anomalous entropy" for prolate and oblate spheroids and for near-spherical Brownian particles.
Asset pricing puzzles explained by incomplete Brownian equilibria
Christensen, Peter Ove; Larsen, Kasper
We examine a class of Brownian based models which produce tractable incomplete equilibria. The models are based on finitely many investors with heterogeneous exponential utilities over intermediate consumption who receive partially unspanned income. The investors can trade continuously on a finit...... markets. Consequently, our model can simultaneously help explaining the risk-free rate and equity premium puzzles....
Non-cooperative Brownian donkeys: A solvable 1D model
Jiménez de Cisneros, B.; Reimann, P.; Parrondo, J. M. R.
2003-12-01
A paradigmatic 1D model for Brownian motion in a spatially symmetric, periodic system is tackled analytically. Upon application of an external static force F the system's response is an average current which is positive for F 0 (absolute negative mobility). Under suitable conditions, the system approaches 100% efficiency when working against the external force F.
From Brownian Dynamics to Markov Chain: An Ion Channel Example
Chen, Wan; Erban, Radek; Chapman, S. Jonathan
2014-01-01
is illustrated with a two-ion one-well channel. The stationary probability of states is compared with that from both Brownian dynamics simulation and the hierarchical Fokker-Planck equations. The conductivity of the channel is also studied, and the optimal
The escape of brownian particle over potential barriers
Zhong Yunxiao
1985-01-01
A convenient method is introduced to calculate the rate of escape of Brownian particle over potential barriers by exact solution of Smoluchowskian equation. This method is applied to calculate the nuclear fission probabilities. The results for four different cases are compared with the results of other theories
Thermodynamic laws and equipartition theorem in relativistic Brownian motion.
Koide, T; Kodama, T
2011-06-01
We extend the stochastic energetics to a relativistic system. The thermodynamic laws and equipartition theorem are discussed for a relativistic Brownian particle and the first and the second law of thermodynamics in this formalism are derived. The relation between the relativistic equipartition relation and the rate of heat transfer is discussed in the relativistic case together with the nature of the noise term.
Effects of 4-aminopyridine on organelle movement in cultured mouse dorsal root ganglion neurites.
Hiruma, Hiromi; Kawakami, Tadashi
2010-03-01
Aminopyridines, widely used as a K(+) channel blocker, are membrane-permeable weak bases and have the ability to form vacuoles in the cytoplasm. The vacuoles originate from acidic organelles such as lysosomes. Here, we investigated the effects of 4-aminopyridine (4-AP) on organelle movement in neurites of cultured mouse dorsal root ganglion (DRG) neurons by using video-enhanced microscopy. Some experiments were carried out using fluorescent dyes for lysosomes and mitochondria and confocal microscopy. Treatment of DRG neurons with 4 mM 4-AP caused Brownian movement of some lysosomes within 5 min. The Brownian movement gradually became rapid and vacuoles were formed around individual lysosomes 10-20 min after the start of treatment. Axonal transport of organelles was inhibited by 4-AP. Lysosomes showing Brownian movement were not transported in longitudinal direction of the neurite and the transport of mitochondria was interrupted by vacuoles. The 4-AP-induced Brownian movement of lysosomes with vacuole formation and inhibition of axonal transport were prevented by the simultaneous treatment with vacuolar H(+) ATPase inhibitor bafilomycin A1 or in Cl(-)-free SO(4)(2-) medium. These results indicate that changes in organelle movement by 4-AP are related to vacuole formation and the vacuolar H(+) ATPase and Cl(-) are required for the effects of 4-AP.
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."
Ryo Kanada
Full Text Available 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 Reaction-Diffusion Algorithms: PDE-Assisted Brownian Dynamics
Franz, Benjamin
2013-06-19
Two algorithms that combine Brownian dynami cs (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use of a mean-field reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD simulations with PDEs by randomly creating new particles close to the interface, which partitions the domain, and by reincorporating particles into the continuum PDE-description when they cross the interface. The second PBD algorithm introduces an overlap region, where both descriptions exist in parallel. It is shown that the overlap region is required to accurately compute variances using PBD simulations. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented. © 2013 Society for Industrial and Applied Mathematics.
Exact master equation for a noncommutative Brownian particle
Costa Dias, Nuno; Nuno Prata, Joao
2009-01-01
We derive the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators on the plane with spatial noncommutativity. The results obtained are exact to all orders in the noncommutative parameter. As a by-product we derive some miscellaneous results such as the equilibrium Wigner distribution for the reservoir of noncommutative oscillators, the weak coupling limit of the master equation and a set of sufficient conditions for strict purity decrease of the Brownian particle. Finally, we consider a high-temperature Ohmic model and obtain an estimate for the time scale of the transition from noncommutative to ordinary quantum mechanics. This scale is considerably smaller than the decoherence scale
CNT based thermal Brownian motor to pump water in nanodevices
Oyarzua, Elton; Zambrano, Harvey; Walther, Jens Honore
2016-01-01
asymmetry drive the water ow in a preferential direction. We systematically modified the magnitude of the applied thermal gradient and the axial position of the fixed points. The analysis involves measurement of the vibrational modes in the CNTs using a Fast Fourier Transform (FFT) algorithm. We observed......Brownian molecular motors are nanoscale machines that exploit thermal fluctuations for directional motion by employing mechanisms such as the Feynman-Smoluchowski ratchet. In this study, using Non Equilibrium Molecular Dynamics, we propose a novel thermal Brownian motor for pumping water through...... Carbon Nanotubes (CNTs). To achieve this we impose a thermal gradient along the axis of a CNT filled with water and impose, in addition, a spatial asymmetry by flxing specific zones on the CNT in order to modify the vibrational modes of the CNT. We find that the temperature gradient and imposed spatial...
Synchronization and collective motion of globally coupled Brownian particles
Sevilla, Francisco J; Heiblum-Robles, Alexandro; Dossetti, Victor
2014-01-01
In this work, we study a system of passive Brownian (non-self-propelled) particles in two dimensions, interacting only through a social-like force (velocity alignment in this case) that resembles Kuramoto's coupling among phase oscillators. We show that the kinematical stationary states of the system go from a phase in thermal equilibrium with no net flux of particles, to far-from-equilibrium phases exhibiting collective motion by increasing the coupling among particles. The mechanism that leads to the instability of the equilibrium phase relies on the competition between two time scales, namely, the mean collision time of the Brownian particles in a thermal bath and the time it takes for a particle to orient its direction of motion along the direction of motion of the group. Our results show a clear connection between collective motion and the Kuramoto model for synchronization, in our case, for the direction of motion of the particles. (paper)
Brownian motion model with stochastic parameters for asset prices
Ching, Soo Huei; Hin, Pooi Ah
2013-09-01
The Brownian motion model may not be a completely realistic model for asset prices because in real asset prices the drift μ and volatility σ may change over time. Presently we consider a model in which the parameter x = (μ,σ) is such that its value x (t + Δt) at a short time Δt ahead of the present time t depends on the value of the asset price at time t + Δt as well as the present parameter value x(t) and m-1 other parameter values before time t via a conditional distribution. The Malaysian stock prices are used to compare the performance of the Brownian motion model with fixed parameter with that of the model with stochastic parameter.
Fuzzy Itand#244; Integral Driven by a Fuzzy Brownian Motion
Didier Kumwimba Seya
2015-11-01
Full Text Available In this paper we take into account the fuzzy stochastic integral driven by fuzzy Brownian motion. To define the metric between two fuzzy numbers and to take into account the limit of a sequence of fuzzy numbers, we invoke the Hausdorff metric. First this fuzzy stochastic integral is constructed for fuzzy simple stochastic functions, then the construction is done for fuzzy stochastic integrable functions.
Continuous state branching processes in random environment: The Brownian case
Palau, Sandra; Pardo, Juan Carlos
2015-01-01
We consider continuous state branching processes that are perturbed by a Brownian motion. These processes are constructed as the unique strong solution of a stochastic differential equation. The long-term extinction and explosion behaviours are studied. In the stable case, the extinction and explosion probabilities are given explicitly. We find three regimes for the asymptotic behaviour of the explosion probability and, as in the case of branching processes in random environment, we find five...
New methods for simulation of fractional Brownian motion
Yin, Z.M.
1996-01-01
We present new algorithms for simulation of fractional Brownian motion (fBm) which comprises a set of important random functions widely used in geophysical and physical modeling, fractal image (landscape) simulating, and signal processing. The new algorithms, which are both accurate and efficient, allow us to generate not only a one-dimensional fBm process, but also two- and three-dimensional fBm fields. 23 refs., 3 figs
Quantum work fluctuation theorem: Nonergodic Brownian motion case
Bai, Zhan-Wu
2014-01-01
The work fluctuations of a quantum Brownian particle driven by an external force in a general nonergodic heat bath are studied under a general initial state. The exact analytical expression of the work probability distribution function is derived. Results show the existence of a quantum asymptotic fluctuation theorem, which is in general not a direct generalization of its classical counterpart. The form of this theorem is dependent on the structure of the heat bath and the specified initial condition.
Anyonic partition functions and windings of planar Brownian motion
Desbois, J.; Heinemann, C.; Ouvry, S.
1995-01-01
The computation of the N-cycle Brownian paths contribution F N (α) to the N-anyon partition function is addressed. A detailed numerical analysis based on a random walk on a lattice indicates that F N 0 (α)=product k=1 N-1 [1-(N/k)α]. In the paramount three-anyon case, one can show that F 3 (α) is built by linear states belonging to the bosonic, fermionic, and mixed representations of S 3
Algorithms for Brownian first-passage-time estimation
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.
On the Humble Origins of the Brownian Entropic Force
Neumann, Richard M.
2015-01-01
Recognition that certain forces arising from the averaging of the multiple impacts of a solute particle by the surrounding solvent particles undergoing random thermal motion can be of an entropic nature has led to the incorporation of these forces and their related entropies into theoretical protocols ranging from molecular-dynamics simulations to the modeling of quarkonium suppression in particle physics. Here we present a rigorous derivation of this Brownian entropic force by means of the c...
Lepelletier, Léa; de Monvel, Jacques Boutet; Buisson, Johanna; Desdouets, Chantal; Petit, Christine
2013-07-02
Planar polarization of the forming hair bundle, the mechanosensory antenna of auditory hair cells, depends on the poorly characterized center-to-edge displacement of a primary cilium, the kinocilium, at their apical surface. Taking advantage of the gradient of hair cell differentiation along the cochlea, we reconstituted a map of the kinocilia displacements in the mouse embryonic cochlea. We then developed a cochlear organotypic culture and video-microscopy approach to monitor the movements of the kinocilium basal body (mother centriole) and its daughter centriole, which we analyzed using particle tracking and modeling. We found that both hair cell centrioles undergo confined Brownian movements around their equilibrium positions, under the apparent constraint of a radial restoring force of ∼0.1 pN. This magnitude depended little on centriole position, suggesting nonlinear interactions with constraining, presumably cytoskeletal elements. The only dynamic change observed during the period of kinocilium migration was a doubling of the centrioles' confinement area taking place early in the process. It emerges from these static and dynamic observations that kinocilia migrate gradually in parallel with the organization of hair cells into rows during cochlear neuroepithelium extension. Analysis of the confined motion of hair cell centrioles under normal and pathological conditions should help determine which structures contribute to the restoring force exerting on them. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.
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 αmovement 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.
Gautestad, Arild O
2012-09-07
Animals moving under the influence of spatio-temporal scaling and long-term memory generate a kind of space-use pattern that has proved difficult to model within a coherent theoretical framework. An extended kind of statistical mechanics is needed, accounting for both the effects of spatial memory and scale-free space use, and put into a context of ecological conditions. Simulations illustrating the distinction between scale-specific and scale-free locomotion are presented. The results show how observational scale (time lag between relocations of an individual) may critically influence the interpretation of the underlying process. In this respect, a novel protocol is proposed as a method to distinguish between some main movement classes. For example, the 'power law in disguise' paradox-from a composite Brownian motion consisting of a superposition of independent movement processes at different scales-may be resolved by shifting the focus from pattern analysis at one particular temporal resolution towards a more process-oriented approach involving several scales of observation. A more explicit consideration of system complexity within a statistical mechanical framework, supplementing the more traditional mechanistic modelling approach, is advocated.
Brownian relaxation of an inelastic sphere in air
Bird, G. A., E-mail: gab@gab.com.au [University of Sydney, Sydney, NSW 2006 (Australia)
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. 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.
Reflected Brownian motions in the KPZ universality class
Weiss, Thomas; Spohn, Herbert
2017-01-01
This book presents a detailed study of a system of interacting Brownian motions in one dimension. The interaction is point-like such that the n-th Brownian motion is reflected from the Brownian motion with label n-1. This model belongs to the Kardar-Parisi-Zhang (KPZ) universality class. In fact, because of the singular interaction, many universal properties can be established with rigor. They depend on the choice of initial conditions. Discussion addresses packed and periodic initial conditions (Chapter 5), stationary initial conditions (Chapter 6), and mixtures thereof (Chapter 7). The suitably scaled spatial process will be proven to converge to an Airy process in the long time limit. A chapter on determinantal random fields and another one on Airy processes are added to have the notes self-contained. These notes serve as an introduction to the KPZ universality class, illustrating the main concepts by means of a single model only. The notes will be of interest to readers from interacting diffusion processe...
Adiabatic Processes Realized with a Trapped Brownian Particle
Martínez, Ignacio A.; Roldán, Édgar; Dinis, Luis; Petrov, Dmitri; Rica, Raúl A.
2015-03-01
The ability to implement adiabatic processes in the mesoscale is of key importance in the study of artificial or biological micro- and nanoengines. Microadiabatic processes have been elusive to experimental implementation due to the difficulty in isolating Brownian particles from their fluctuating environment. Here we report on the experimental realization of a microscopic quasistatic adiabatic process employing a trapped Brownian particle. We circumvent the complete isolation of the Brownian particle by designing a protocol where both characteristic volume and temperature of the system are changed in such a way that the entropy of the system is conserved along the process. We compare the protocols that follow from either the overdamped or underdamped descriptions, demonstrating that the latter is mandatory in order to obtain a vanishing average heat flux to the particle. We provide analytical expressions for the distributions of the fluctuating heat and entropy and verify them experimentally. Our protocols could serve to implement the first microscopic engine that is able to attain the fundamental limit for the efficiency set by Carnot.
Collective motion of active Brownian particles with polar alignment.
Martín-Gómez, Aitor; Levis, Demian; Díaz-Guilera, Albert; Pagonabarraga, Ignacio
2018-04-04
We present a comprehensive computational study of the collective behavior emerging from the competition between self-propulsion, excluded volume interactions and velocity-alignment in a two-dimensional model of active particles. We consider an extension of the active brownian particles model where the self-propulsion direction of the particles aligns with the one of their neighbors. We analyze the onset of collective motion (flocking) in a low-density regime (10% surface area) and show that it is mainly controlled by the strength of velocity-alignment interactions: the competition between self-propulsion and crowding effects plays a minor role in the emergence of flocking. However, above the flocking threshold, the system presents a richer pattern formation scenario than analogous models without alignment interactions (active brownian particles) or excluded volume effects (Vicsek-like models). Depending on the parameter regime, the structure of the system is characterized by either a broad distribution of finite-sized polar clusters or the presence of an amorphous, highly fluctuating, large-scale traveling structure which can take a lane-like or band-like form (and usually a hybrid structure which is halfway in between both). We establish a phase diagram that summarizes collective behavior of polar active brownian particles and propose a generic mechanism to describe the complexity of the large-scale structures observed in systems of repulsive self-propelled particles.
Biased and flow driven Brownian motion in periodic channels
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.
... Loss of coordination; Coordination impairment; Ataxia; Clumsiness; Uncoordinated movement ... Smooth graceful movement requires a balance between different muscle groups. A part of the brain called the cerebellum manages this balance.
On the validity of Brownian assumptions in the spin van der Waals model
Oh, Suhk Kun
1985-01-01
A simple Brownian motion theory of the spin van der Waals model, which can be stationary, Markoffian or Gaussian, is studied. By comparing the Brownian motion theory with an exact theory called the generalized Langevin equation theory, the validity of the Brownian assumptions is tested. Thereby, it is shown explicitly how the Markoffian and Gaussian properties are modified in the spin van der Waals model under the influence of quantum fluctuations and long range ordering. (Author)
Wagner, P.
2009-01-01
On this poster some reasons of slope movements on the territory of the Slovak Republic are presented. Slope movements induced deterioration of land and forests, endangering of towns villages, and communications as well as hydro-engineering structures. Methods of preventing and stabilisation of slope movements are presented.
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
Movement - uncontrolled or slow
Dystonia; Involuntary slow and twisting movements; Choreoathetosis; Leg and arm movements - uncontrollable; Arm and leg movements - uncontrollable; Slow involuntary movements of large muscle groups; Athetoid movements
Random functions via Dyson Brownian Motion: progress and problems
Wang, Gaoyuan; Battefeld, Thorsten
2016-01-01
We develope a computationally efficient extension of the Dyson Brownian Motion (DBM) algorithm to generate random function in C"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 hoc modification of DBM that suppresses this growth to some degree.
Random functions via Dyson Brownian Motion: progress and problems
Wang, Gaoyuan; Battefeld, Thorsten [Institute for Astrophysics, University of Goettingen,Friedrich Hund Platz 1, D-37077 Goettingen (Germany)
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 hoc modification of DBM that suppresses this growth to some degree.
Entropic Ratchet transport of interacting active Brownian particles
Ai, Bao-Quan; He, Ya-Feng; Zhong, Wei-Rong
2014-01-01
Directed transport of interacting active (self-propelled) Brownian particles is numerically investigated in confined geometries (entropic barriers). The self-propelled velocity can break thermodynamical equilibrium and induce the directed transport. It is found that the interaction between active particles can greatly affect the ratchet transport. For attractive particles, on increasing the interaction strength, the average velocity first decreases to its minima, then increases, and finally decreases to zero. For repulsive particles, when the interaction is very weak, there exists a critical interaction at which the average velocity is minimal, nearly tends to zero, however, for the strong interaction, the average velocity is independent of the interaction
Entropic Ratchet transport of interacting active Brownian particles
Ai, Bao-Quan, E-mail: aibq@hotmail.com [Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, 510006 Guangzhou (China); He, Ya-Feng [College of Physics Science and Technology, Hebei University, 071002 Baoding (China); Zhong, Wei-Rong, E-mail: wrzhong@jnu.edu.cn [Department of Physics and Siyuan Laboratory, College of Science and Engineering, Jinan University, 510632 Guangzhou (China)
2014-11-21
Directed transport of interacting active (self-propelled) Brownian particles is numerically investigated in confined geometries (entropic barriers). The self-propelled velocity can break thermodynamical equilibrium and induce the directed transport. It is found that the interaction between active particles can greatly affect the ratchet transport. For attractive particles, on increasing the interaction strength, the average velocity first decreases to its minima, then increases, and finally decreases to zero. For repulsive particles, when the interaction is very weak, there exists a critical interaction at which the average velocity is minimal, nearly tends to zero, however, for the strong interaction, the average velocity is independent of the interaction.
Analysis of Brownian Dynamics Simulations of Reversible Bimolecular Reactions
Lipková, Jana
2011-01-01
A class of Brownian dynamics algorithms for stochastic reaction-diffusion models which include reversible bimolecular reactions is presented and analyzed. The method is a generalization of the λ-bcȳ model for irreversible bimolecular reactions which was introduced in [R. Erban and S. J. Chapman, Phys. Biol., 6(2009), 046001]. The formulae relating the experimentally measurable quantities (reaction rate constants and diffusion constants) with the algorithm parameters are derived. The probability of geminate recombination is also investigated. © 2011 Society for Industrial and Applied Mathematics.
Whitening filter and innovational representation of fractional Brownian motion
Wang Xiaotian; Wu Min
2009-01-01
In this paper, by means of fractional differential-integral technique we give a new whitening filter formula for fractional Brownian motion defined by Mandelbrot and van Ness [Mandelbrot BB, van Ness JW. SIAM Rev 1968;10(4):422]. This new formula has potential use in time series analysis and in detecting signals as Barton and Vincent Poor [Barton RJ, Vincent Poor H. IEEE Trans Inform Theory 1988;34(5):943] have shown. Another potential application of it is behavioral finance, where the arbitrage opportunities that come from the reversal effect of stock returns, can be eliminated by such a formula.
Moments of inertia and the shapes of Brownian paths
Fougere, F.; Desbois, J.
1993-01-01
The joint probability law of the principal moments of inertia of Brownian paths (open or closed) is computed, using constrained path integrals and Random Matrix Theory. The case of two-dimensional paths is discussed in detail. In particular, it is shown that the ratio of the average values of the largest and smallest moments is equal to 4.99 (open paths) and 3.07 (closed paths). Results of numerical simulations are also presented, which include investigation of the relationships between the moments of inertia and the arithmetic area enclosed by a path. (authors) 28 refs., 2 figs
Theory of Brownian motion with the Alder-Wainwright effect
Okabe, Y.
1986-01-01
The Stokes-Boussinesq-Langevin equation, which describes the time evolution of Brownian motion with the Alder-Wainwright effect, can be treated in the framework of the theory of KMO-Langevin equations which describe the time evolution of a real, stationary Gaussian process with T-positivity (reflection positivity) originating in axiomatic quantum field theory. After proving the fluctuation-dissipation theorems for KMO-Langevin equations, the authors obtain an explicit formula for the deviation from the classical Einstein relation that occurs in the Stokes-Boussinesq-Langevin equation with a white noise as its random force. The authors interested in whether or not it can be measured experimentally
Permutation entropy of fractional Brownian motion and fractional Gaussian noise
Zunino, L.; Perez, D.G.; Martin, M.T.; Garavaglia, M.; Plastino, A.; Rosso, O.A.
2008-01-01
We have worked out theoretical curves for the permutation entropy of the fractional Brownian motion and fractional Gaussian noise by using the Bandt and Shiha [C. Bandt, F. Shiha, J. Time Ser. Anal. 28 (2007) 646] theoretical predictions for their corresponding relative frequencies. Comparisons with numerical simulations show an excellent agreement. Furthermore, the entropy-gap in the transition between these processes, observed previously via numerical results, has been here theoretically validated. Also, we have analyzed the behaviour of the permutation entropy of the fractional Gaussian noise for different time delays
Nuclear resonant scattering of synchrotron radiation from nuclei in the Brownian motion
Razdan, Ashok
2003-01-01
The time evolution of the coherent forward scattering of the synchrotron radiation for resonant nuclei in Brownian motion is studied. Apart from target thickness, the appearance of the dynamical beats also depends on 'α' which is the ratio of the harmonic force constant to the damping force constant of harmonic oscillator undergoing Brownian motion
On the biased motion of a brownian particle for the pausing time behavior of the CTRW
Kim, K.S.
1982-01-01
The purpose of this paper is to discuss the biased Brownian motion with the absorbing barrier for the pausing time behavior of the CTRW (continuous-time random walk method), regarding a Brownian particle as a walker. For two pausing time density functions, the respective values for the transport averaged velocity and the dispersion are calculated as the time t becomes large. (KAERI)
Dynamics of a Brownian particle in a plasma in the long-time limit
Dickman, R.; Varley, R.L.
1981-01-01
The velocity autocorrelation function (VAF) of a Brownian particle in a plasma is calculated in the long-time limit. The Brownian particle VAF exhibits the same qualitative behavior as the electron VAF in a one-component plasma: oscillations at the plasma frequency and decay approx. t -3 sup(/) 2 . (orig.)
Under which conditions is quantum Brownian motion observable in a microscope?
Helseth, L.E.
2010-01-01
We investigate under which conditions we can expect to observe quantum Brownian motion in a microscope. Using the fluctuation-dissipation theorem, we investigate quantum Brownian motion in an ohmic bath, and estimate temporal and spatial accuracy required to observe a crossover from classical to quantum behavior.
Statistics of the first passage time of Brownian motion conditioned by maximum value or area
Kearney, Michael J; Majumdar, Satya N
2014-01-01
We derive the moments of the first passage time for Brownian motion conditioned by either the maximum value or the area swept out by the motion. These quantities are the natural counterparts to the moments of the maximum value and area of Brownian excursions of fixed duration, which we also derive for completeness within the same mathematical framework. Various applications are indicated. (paper)
Hydrodynamically Coupled Brownian Dynamics simulations for flow on non-Newtonian fluids
Ahuja, Vishal Raju
2018-01-01
This thesis deals with model development for particle-based flow simulations of non-Newtonian fluids such as polymer solutions. A novel computational technique called Hydrodynamically Coupled Brownian Dynamics (HCBD) is presented in this thesis. This technique essentially couples the Brownian motion
Srihirun, B; Meleshko, S V; Schulz, E
2006-01-01
The definition of an admitted Lie group of transformations for stochastic differential equations has been already presented for equations with one-dimensional Brownian motion. The transformation of the dependent variables involves time as well, and it has been proven that Brownian motion is transformed to Brownian motion. In this paper, we will discuss this concept for stochastic differential equations involving multi-dimensional Brownian motion and present applications to a variety of stochastic differential equations
Gautestad, Arild O
2013-03-01
The flow of GPS data on animal space is challenging old paradigms, such as the issue of the scale-free Lévy walk versus scale-specific Brownian motion. Since these movement classes often require different protocols with respect to ecological analyses, further theoretical development in this field is important. I describe central concepts such as scale-specific versus scale-free movement and the difference between mechanistic and statistical-mechanical levels of analysis. Next, I report how a specific sampling scheme may have produced much confusion: a Lévy walk may be wrongly categorized as Brownian motion if the duration of a move, or bout, is used as a proxy for step length and a move is subjectively defined. Hence, the categorization and recategorization of movement class compliance surrounding the Lévy walk controversy may have been based on a statistical artifact. This issue may be avoided by collecting relocations at a fixed rate at a temporal scale that minimizes over- and undersampling.
The single- and double-particle properties and the current reversal of coupled Brownian motors
Li, Chen-Pu; Chen, Hong-Bin; Zheng, Zhi-Gang; Fan, Hong; Shen, Wen-Mei
2017-01-01
In this paper, we investigate the directed transport of coupled Brownian motors composed of two identical particles which is individually subject to a time-symmetric rocking force in spatially-symmetric periodic potentials. We find that both the coupling free length and the coupling strength can induce the reversed motion of the coupled Brownian motors, the essence of which is the coupled Brownian motors can exhibit completely different single- or double-particle properties under certain conditions. Namely, the current reversal is the result of the mutual conversion between the single- and double-particle properties of the coupled Brownian motors. Moreover, the directed current of coupled Brownian motors can be optimized and manipulated by adjusting the strength, the period, the phase difference of the rocking forces, and the noise intensity. (paper)
Mathematical interpretation of Brownian motor model: Limit cycles and directed transport phenomena
Yang, Jianqiang; Ma, Hong; Zhong, Suchuang
2018-03-01
In this article, we first suggest that the attractor of Brownian motor model is one of the reasons for the directed transport phenomenon of Brownian particle. We take the classical Smoluchowski-Feynman (SF) ratchet model as an example to investigate the relationship between limit cycles and directed transport phenomenon of the Brownian particle. We study the existence and variation rule of limit cycles of SF ratchet model at changing parameters through mathematical methods. The influences of these parameters on the directed transport phenomenon of a Brownian particle are then analyzed through numerical simulations. Reasonable mathematical explanations for the directed transport phenomenon of Brownian particle in SF ratchet model are also formulated on the basis of the existence and variation rule of the limit cycles and numerical simulations. These mathematical explanations provide a theoretical basis for applying these theories in physics, biology, chemistry, and engineering.
Brownian dynamics of a protein-polymer chain complex in a solid-state nanopore
Wells, Craig C.; Melnikov, Dmitriy V.; Gracheva, Maria E.
2017-08-01
We study the movement of a polymer attached to a large protein inside a nanopore in a thin silicon dioxide membrane submerged in an electrolyte solution. We use Brownian dynamics to describe the motion of a negatively charged polymer chain of varying lengths attached to a neutral protein modeled as a spherical bead with a radius larger than that of the nanopore, allowing the chain to thread the nanopore but preventing it from translocating. The motion of the protein-polymer complex within the pore is also compared to that of a freely translocating polymer. Our results show that the free polymer's standard deviations in the direction normal to the pore axis is greater than that of the protein-polymer complex. We find that restrictions imposed by the protein, bias, and neighboring chain segments aid in controlling the position of the chain in the pore. Understanding the behavior of the protein-polymer chain complex may lead to methods that improve molecule identification by increasing the resolution of ionic current measurements.
Dynamic tracking of a nano-particle in fluids under Brownian motions
Wu, X C; Zhang, W J; Sammynaiken, R
2008-01-01
Most previous studies on H 2 S were devoted to its toxic effects. However, recently there have been increasing evidences which show that endogenously generated H 2 S in specific mammalian tissues has certain significant positive physiological effects such as a neuromodulator and vasorelaxant in a membrane receptor-independent manner. In order to know the functions of endogenous H 2 S, low concentration and high accuracy measurement of H 2 S is a must. Furthermore, this measurement is desired to be real-time and non-invasive. It is reported that low concentration and nano quantity of H 2 S can be detected in water solutions and sera using carbon nanotubes with the fluorescence by confocal laser scanning microscopy. However, because of the Brownian motion of the small particle (carbon nanotube), a control system must be developed to track the movement of the particle in fluids. In this paper, we present a study to track a carbon nanotube which absorbs H 2 S in water or serum using a Raman microscope or confocal laser scanning microscope. In particular, we developed a novel control system for this task. Simulation has shown that our system works very well.
Translational and Brownian motion in laser-Doppler flowmetry of large tissue volumes
Binzoni, T; Leung, T S; Seghier, M L; Delpy, D T
2004-01-01
This study reports the derivation of a precise mathematical relationship existing between the different p-moments of the power spectrum of the photoelectric current, obtained from a laser-Doppler flowmeter (LDF), and the red blood cell speed. The main purpose is that both the Brownian (defining the 'biological zero') and the translational movements are taken into account, clarifying in this way what the exact contribution of each parameter is to the LDF derived signals. The derivation of the equations is based on the quasi-elastic scattering theory and holds for multiple scattering (i.e. measurements in large tissue volumes and/or very high red blood cell concentration). The paper also discusses why experimentally there exists a range in which the relationship between the first moment of the power spectrum and the average red blood cells speed may be considered as 'linear' and what are the physiological determinants that can result in nonlinearity. A correct way to subtract the biological zero from the LDF data is also proposed. The findings should help in the design of improved LDF instruments and in the interpretation of experimental data
Undergraduate Labs for Biological Physics: Brownian Motion and Optical Trapping
Chu, Kelvin; Laughney, A.; Williams, J.
2006-12-01
We describe a set of case-study driven labs for an upper-division biological physics course. These labs are motivated by case-studies and consist of inquiry-driven investigations of Brownian motion and optical-trapping experiments. Each lab incorporates two innovative educational techniques to drive the process and application aspects of scientific learning. Case studies are used to encourage students to think independently and apply the scientific method to a novel lab situation. Student input from this case study is then used to decide how to best do the measurement, guide the project and ultimately evaluate the success of the program. Where appropriate, visualization and simulation using VPython is used. Direct visualization of Brownian motion allows students to directly calculate Avogadro's number or the Boltzmann constant. Following case-study driven discussion, students use video microscopy to measure the motion of latex spheres in different viscosity fluids arrive at a good approximation of NA or kB. Optical trapping (laser tweezer) experiments allow students to investigate the consequences of 100-pN forces on small particles. The case study consists of a discussion of the Boltzmann distribution and equipartition theorem followed by a consideration of the shape of the potential. Students can then use video capture to measure the distribution of bead positions to determine the shape and depth of the trap. This work supported by NSF DUE-0536773.
Intermittency and multifractional Brownian character of geomagnetic time series
G. Consolini
2013-07-01
Full Text Available The Earth's magnetosphere exhibits a complex behavior in response to the solar wind conditions. This behavior, which is described in terms of mutifractional Brownian motions, could be the consequence of the occurrence of dynamical phase transitions. On the other hand, it has been shown that the dynamics of the geomagnetic signals is also characterized by intermittency at the smallest temporal scales. Here, we focus on the existence of a possible relationship in the geomagnetic time series between the multifractional Brownian motion character and the occurrence of intermittency. In detail, we investigate the multifractional nature of two long time series of the horizontal intensity of the Earth's magnetic field as measured at L'Aquila Geomagnetic Observatory during two years (2001 and 2008, which correspond to different conditions of solar activity. We propose a possible double origin of the intermittent character of the small-scale magnetic field fluctuations, which is related to both the multifractional nature of the geomagnetic field and the intermittent character of the disturbance level. Our results suggest a more complex nature of the geomagnetic response to solar wind changes than previously thought.
First passage Brownian functional properties of snowmelt dynamics
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.
Functionals of Brownian motion, localization and metric graphs
Comtet, Alain; Desbois, Jean; Texier, Christophe
2005-01-01
We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of Brownian motion arise in the study of electronic transport in weakly disordered metals (weak localization). Two aspects of the physics of the one-dimensional strong localization are reviewed: some properties of the scattering by a random potential (time delay distribution) and a study of the spectrum of a random potential on a bounded domain (the extreme value statistics of the eigenvalues). Then we mention several results concerning the diffusion on graphs, and more generally the spectral properties of the Schroedinger operator on graphs. The interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated. Finally, we consider a two-dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices. We recall the connection between spectral properties of this model and winding functionals of planar Brownian motion. (topical review)
Active Brownian particles with velocity-alignment and active fluctuations
Großmann, R; Schimansky-Geier, L; Romanczuk, P
2012-01-01
We consider a model of active Brownian particles (ABPs) with velocity alignment in two spatial dimensions with passive and active fluctuations. Here, active fluctuations refers to purely non-equilibrium stochastic forces correlated with the heading of an individual active particle. In the simplest case studied here, they are assumed to be independent stochastic forces parallel (speed noise) and perpendicular (angular noise) to the velocity of the particle. On the other hand, passive fluctuations are defined by a noise vector independent of the direction of motion of a particle, and may account, for example, for thermal fluctuations. We derive a macroscopic description of the ABP gas with velocity-alignment interaction. Here, we start from the individual-based description in terms of stochastic differential equations (Langevin equations) and derive equations of motion for the coarse-grained kinetic variables (density, velocity and temperature) via a moment expansion of the corresponding probability density function. We focus here on the different impact of active and passive fluctuations on onset of collective motion and show how active fluctuations in the active Brownian dynamics can change the phase-transition behaviour of the system. In particular, we show that active angular fluctuations lead to an earlier breakdown of collective motion and to the emergence of a new bistable regime in the mean-field case. (paper)
Active Brownian motion models and applications to ratchets
Fiasconaro, A.; Ebeling, W.; Gudowska-Nowak, E.
2008-10-01
We give an overview over recent studies on the model of Active Brownian Motion (ABM) coupled to reservoirs providing free energy which may be converted into kinetic energy of motion. First, we present an introduction to a general concept of active Brownian particles which are capable to take up energy from the source and transform part of it in order to perform various activities. In the second part of our presentation we consider applications of ABM to ratchet systems with different forms of differentiable potentials. Both analytical and numerical evaluations are discussed for three cases of sinusoidal, staircaselike and Mateos ratchet potentials, also with the additional loads modelled by tilted potential structure. In addition, stochastic character of the kinetics is investigated by considering perturbation by Gaussian white noise which is shown to be responsible for driving the directionality of the asymptotic flux in the ratchet. This stochastically driven directionality effect is visualized as a strong nonmonotonic dependence of the statistics of the right versus left trajectories of motion leading to a net current of particles. Possible applications of the ratchet systems to molecular motors are also briefly discussed.
Maximum-entropy description of animal movement.
Fleming, Chris H; Subaşı, Yiğit; Calabrese, Justin M
2015-03-01
We introduce a class of maximum-entropy states that naturally includes within it all of the major continuous-time stochastic processes that have been applied to animal movement, including Brownian motion, Ornstein-Uhlenbeck motion, integrated Ornstein-Uhlenbeck motion, a recently discovered hybrid of the previous models, and a new model that describes central-place foraging. We are also able to predict a further hierarchy of new models that will emerge as data quality improves to better resolve the underlying continuity of animal movement. Finally, we also show that Langevin equations must obey a fluctuation-dissipation theorem to generate processes that fall from this class of maximum-entropy distributions when the constraints are purely kinematic.
Brownian Ratchet Mechanism for Faithful Segregation of Low-Copy-Number Plasmids.
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
Wells, Craig; Hulings, Zachery; Melnikov, Dmitriy; Gracheva, Maria
We study a nanopore inside a silicon dioxide membrane submerged in a KCl solution with a negatively charged polymer chain of varying lengths whose movement is described using Brownian dynamics. The polymer is attached to a molecule with a radius larger than that of the nanopore's which acts as a molecular stop, allowing the chain to thread the nanopore but preventing it from translocating. We found that the polymer chain's variation of movement along the nanopore decreased when increasing applied biases and chain lengths for portions of the chain closest to the molecular stop. The chain displacement within the pore is also compared to a freely translocating polymer where preliminary results show the free polymer having a greater variation in the radial direction. Overall, our preliminary results indicate that the radial direction of the polymer chain is dominated by the confinement in the narrow nanopore with restrictions imposed by the molecular stop and bias playing a lesser role. Understanding the interaction behavior of the polymer chain-stop molecule may lead to methods that decrease movement variation, facilitating an improvement on characterizing and identification of molecules. NSF DMR and CBET Grant No. 1352218.
Gautestad, Arild O; Mysterud, Atle
2013-01-01
The Lévy flight foraging hypothesis predicts a transition from scale-free Lévy walk (LW) to scale-specific Brownian motion (BM) as an animal moves from resource-poor towards resource-rich environment. However, the LW-BM continuum implies a premise of memory-less search, which contradicts the cognitive capacity of vertebrates. We describe methods to test if apparent support for LW-BM transitions may rather be a statistical artifact from movement under varying intensity of site fidelity. A higher frequency of returns to previously visited patches (stronger site fidelity) may erroneously be interpreted as a switch from LW towards BM. Simulations of scale-free, memory-enhanced space use illustrate how the ratio between return events and scale-free exploratory movement translates to varying strength of site fidelity. An expanded analysis of GPS data of 18 female red deer, Cervus elaphus, strengthens previous empirical support of memory-enhanced and scale-free space use in a northern forest ecosystem. A statistical mechanical model architecture that describes foraging under environment-dependent variation of site fidelity may allow for higher realism of optimal search models and movement ecology in general, in particular for vertebrates with high cognitive capacity.
Spirin, Alexander S
2009-11-17
A model of the ATP-dependent unidirectional movement of the 43S ribosomal initiation complex (=40S ribosomal subunit + eIF1 + eIF1A + eIF2.GTP.Met-tRNA(i) + eIF3) during scanning of the 5'-untranslated region of eukaryotic mRNA is proposed. The model is based on the principles of molecular Brownian ratchet machines and explains several enigmatic data concerning the scanning complex. In this model, the one-dimensional diffusion of the ribosomal initiation complex along the mRNA chain is rectified into the net-unidirectional 5'-to-3' movement by the Feynman ratchet-and-pawl mechanism. The proposed mechanism is organized by the heterotrimeric protein eIF4F (=eIF4A + eIF4E + eIF4G), attached to the scanning ribosomal particle via eIF3, and the RNA-binding protein eIF4B that is postulated to play the role of the pawl. The energy for the useful work of the ratchet-and-pawl mechanism is supplied from ATP hydrolysis induced by the eIF4A subunit: ATP binding and its hydrolysis alternately change the affinities of eIF4A for eIF4B and for mRNA, resulting in the restriction of backward diffusional sliding of the 43S ribosomal complex along the mRNA chain, while stochastic movements ahead are allowed.
Large scale Brownian dynamics of confined suspensions of rigid particles
Sprinkle, Brennan; Balboa Usabiaga, Florencio; Patankar, Neelesh A.; Donev, Aleksandar
2017-12-01
We introduce methods for large-scale Brownian Dynamics (BD) simulation of many rigid particles of arbitrary shape suspended in a fluctuating fluid. Our method adds Brownian motion to the rigid multiblob method [F. Balboa Usabiaga et al., Commun. Appl. Math. Comput. Sci. 11(2), 217-296 (2016)] at a cost comparable to the cost of deterministic simulations. We demonstrate that we can efficiently generate deterministic and random displacements for many particles using preconditioned Krylov iterative methods, if kernel methods to efficiently compute the action of the Rotne-Prager-Yamakawa (RPY) mobility matrix and its "square" root are available for the given boundary conditions. These kernel operations can be computed with near linear scaling for periodic domains using the positively split Ewald method. Here we study particles partially confined by gravity above a no-slip bottom wall using a graphical processing unit implementation of the mobility matrix-vector product, combined with a preconditioned Lanczos iteration for generating Brownian displacements. We address a major challenge in large-scale BD simulations, capturing the stochastic drift term that arises because of the configuration-dependent mobility. Unlike the widely used Fixman midpoint scheme, our methods utilize random finite differences and do not require the solution of resistance problems or the computation of the action of the inverse square root of the RPY mobility matrix. We construct two temporal schemes which are viable for large-scale simulations, an Euler-Maruyama traction scheme and a trapezoidal slip scheme, which minimize the number of mobility problems to be solved per time step while capturing the required stochastic drift terms. We validate and compare these schemes numerically by modeling suspensions of boomerang-shaped particles sedimented near a bottom wall. Using the trapezoidal scheme, we investigate the steady-state active motion in dense suspensions of confined microrollers, whose
Rucht, D.
1989-01-01
The author describes the development of protest movements in postwar Germay and outlines two essential overlapping 'flow cycles'. The first of these was characterised by the restaurative postwar years. It culminated and ended in the students' revolt. This revolt is at the same time the start of a second cycle of protest which encompasses all subsequent individual movement and is initated by an economic, political and sociocultural procrastination of modernisation. This cycle culminates in the late 70s and early 80s and clearly lost momentum over the last few years. The follwoing phases and themes are described profoundly: against restauration and armament in the 1950; the revolutionary impatience of the students' movement, politisation of everyday life by the womens' movement and citizens' action groups, antinuclear- and ecological movement, differentiation and stabilisation of the movement in the 70s and 80s; break-up and continuity in the German protest behaviour. The paper contains a detailed chronicle of protest activities since 1945. (orig.) [de
BROWNIAN HEAT TRANSFER ENHANCEMENT IN THE TURBULENT REGIME
Suresh Chandrasekhar
2016-08-01
Full Text Available The paper presents convection heat transfer of a turbulent flow Al2O3/water nanofluid in a circular duct. The duct is a under constant and uniform heat flux. The paper computationally investigates the system’s thermal behavior in a wide range of Reynolds number and also volume concentration up to 6%. To obtain the nanofluid thermophysical properties, the Hamilton-Crosser model along with the Brownian motion effect are utilized. Then the thermal performance of the system with the nanofluid is compared to the conventional systems which use water as the working fluid. The results indicate that the use of nanofluid of 6% improves the heat transfer rate up to 36.8% with respect to pure water. Therefore, using the Al2O3/water nanofluid instead of water can be a great choice when better heat transfer is needed.
Change of particle size distribution during Brownian coagulation
Lee, K.W.
1984-01-01
Change in particle size distribution due to Brownian coagulation in the continuum regime has been stuied analytically. A simple analytic solution for the size distribution of an initially lognormal distribution is obtained based on the assumption that the size distribution during the coagulation process attains or can, at least, be represented by a time dependent lognormal function. The results are found to be in a form that corrects Smoluchowski's solution for both polydispersity and size-dependent kernel. It is further shown that regardless of whether the initial distribution is narrow or broad, the spread of the distribution is characterized by approaching a fixed value of the geometric standard deviation. This result has been compared with the self-preserving distribution obtained by similarity theory. (Author)
Brownian rotational relaxation and power absorption in magnetite nanoparticles
Goya, G.F.; Fernandez-Pacheco, R.; Arruebo, M.; Cassinelli, N.; Ibarra, M.R.
2007-01-01
We present a study of the power absorption efficiency in several magnetite-based colloids, to asses their potential as magnetic inductive hyperthermia (MIH) agents. Relaxation times τ were measured through the imaginary susceptibility component χ ' '(T), and analyzed within Debye's theory of dipolar fluid. The results indicated Brownian rotational relaxation and allowed to calculate the hydrodynamic radius close to the values obtained from photon correlation. The study of the colloid performances as power absorbers showed no detectable increase of temperature for dextran-coated Fe 3 O 4 nanoparticles, whereas a second Fe 3 O 4 -based dispersion of similar concentration could be heated up to 12K after 30min under similar experimental conditions. The different power absorption efficiencies are discussed in terms of the magnetic structure of the nanoparticles
Brownian rotational relaxation and power absorption in magnetite nanoparticles
Goya, G.F. [Institute of Nanoscience of Aragon (INA), University of Zaragoza, 50009 Zaragoza (Spain)]. E-mail: goya@unizar.es; Fernandez-Pacheco, R. [Institute of Nanoscience of Aragon (INA), University of Zaragoza, 50009 Zaragoza (Spain); Arruebo, M. [Institute of Nanoscience of Aragon (INA), University of Zaragoza, 50009 Zaragoza (Spain); Cassinelli, N. [Electronics Division, Bauer and Associates, Buenos Aires (Argentina); Facultad de Ingenieria, UNLP (Argentina); Ibarra, M.R. [Institute of Nanoscience of Aragon (INA), University of Zaragoza, 50009 Zaragoza (Spain)
2007-09-15
We present a study of the power absorption efficiency in several magnetite-based colloids, to asses their potential as magnetic inductive hyperthermia (MIH) agents. Relaxation times {tau} were measured through the imaginary susceptibility component {chi}{sup '}'(T), and analyzed within Debye's theory of dipolar fluid. The results indicated Brownian rotational relaxation and allowed to calculate the hydrodynamic radius close to the values obtained from photon correlation. The study of the colloid performances as power absorbers showed no detectable increase of temperature for dextran-coated Fe{sub 3}O{sub 4} nanoparticles, whereas a second Fe{sub 3}O{sub 4}-based dispersion of similar concentration could be heated up to 12K after 30min under similar experimental conditions. The different power absorption efficiencies are discussed in terms of the magnetic structure of the nanoparticles.
Modeling collective emotions: a stochastic approach based on Brownian agents
Schweitzer, F.
2010-01-01
We develop a agent-based framework to model the emergence of collective emotions, which is applied to online communities. Agents individual emotions are described by their valence and arousal. Using the concept of Brownian agents, these variables change according to a stochastic dynamics, which also considers the feedback from online communication. Agents generate emotional information, which is stored and distributed in a field modeling the online medium. This field affects the emotional states of agents in a non-linear manner. We derive conditions for the emergence of collective emotions, observable in a bimodal valence distribution. Dependent on a saturated or a super linear feedback between the information field and the agent's arousal, we further identify scenarios where collective emotions only appear once or in a repeated manner. The analytical results are illustrated by agent-based computer simulations. Our framework provides testable hypotheses about the emergence of collective emotions, which can be verified by data from online communities. (author)
Optimal dividends in the Brownian motion risk model with interest
Fang, Ying; Wu, Rong
2009-07-01
In this paper, we consider a Brownian motion risk model, and in addition, the surplus earns investment income at a constant force of interest. The objective is to find a dividend policy so as to maximize the expected discounted value of dividend payments. It is well known that optimality is achieved by using a barrier strategy for unrestricted dividend rate. However, ultimate ruin of the company is certain if a barrier strategy is applied. In many circumstances this is not desirable. This consideration leads us to impose a restriction on the dividend stream. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. Under this additional constraint, we show that the optimal dividend strategy is formed by a threshold strategy.
Micro rectennas: Brownian ratchets for thermal-energy harvesting
Pan, Y.; Powell, C. V.; Balocco, C.; Song, A. M.
2014-01-01
We experimentally demonstrated the operation of a rectenna for harvesting thermal (blackbody) radiation and converting it into dc electric power. The device integrates an ultrafast rectifier, the self-switching nanodiode, with a wideband log-periodic spiral microantenna. The radiation from the thermal source drives the rectenna out of thermal equilibrium, permitting the rectification of the excess thermal fluctuations from the antenna. The power conversion efficiency increases with the source temperatures up to 0.02% at 973 K. The low efficiency is attributed mainly to the impedance mismatch between antenna and rectifier, and partially to the large field of view of the antenna. Our device not only opens a potential solution for harvesting thermal energy but also provides a platform for experimenting with Brownian ratchets
Micro rectennas: Brownian ratchets for thermal-energy harvesting
Pan, Y.; Powell, C. V.; Song, A. M.; Balocco, C.
2014-12-01
We experimentally demonstrated the operation of a rectenna for harvesting thermal (blackbody) radiation and converting it into dc electric power. The device integrates an ultrafast rectifier, the self-switching nanodiode, with a wideband log-periodic spiral microantenna. The radiation from the thermal source drives the rectenna out of thermal equilibrium, permitting the rectification of the excess thermal fluctuations from the antenna. The power conversion efficiency increases with the source temperatures up to 0.02% at 973 K. The low efficiency is attributed mainly to the impedance mismatch between antenna and rectifier, and partially to the large field of view of the antenna. Our device not only opens a potential solution for harvesting thermal energy but also provides a platform for experimenting with Brownian ratchets.
Exact analytical thermodynamic expressions for a Brownian heat engine
Taye, Mesfin Asfaw
2015-09-01
The nonequilibrium thermodynamics feature of a Brownian motor operating between two different heat baths is explored as a function of time t . Using the Gibbs entropy and Schnakenberg microscopic stochastic approach, we find exact closed form expressions for the free energy, the rate of entropy production, and the rate of entropy flow from the system to the outside. We show that when the system is out of equilibrium, it constantly produces entropy and at the same time extracts entropy out of the system. Its entropy production and extraction rates decrease in time and saturate to a constant value. In the long time limit, the rate of entropy production balances the rate of entropy extraction, and at equilibrium both entropy production and extraction rates become zero. Furthermore, via the present model, many thermodynamic theories can be checked.
Directed transport of confined Brownian particles with torque
Radtke, Paul K.; Schimansky-Geier, Lutz
2012-05-01
We investigate the influence of an additional torque on the motion of Brownian particles confined in a channel geometry with varying width. The particles are driven by random fluctuations modeled by an Ornstein-Uhlenbeck process with given correlation time τc. The latter causes persistent motion and is implemented as (i) thermal noise in equilibrium and (ii) noisy propulsion in nonequilibrium. In the nonthermal process a directed transport emerges; its properties are studied in detail with respect to the correlation time, the torque, and the channel geometry. Eventually, the transport mechanism is traced back to a persistent sliding of particles along the even boundaries in contrast to scattered motion at uneven or rough ones.
Large Scale Brownian Dynamics of Confined Suspensions of Rigid Particles
Donev, Aleksandar; Sprinkle, Brennan; Balboa, Florencio; Patankar, Neelesh
2017-11-01
We introduce new numerical methods for simulating the dynamics of passive and active Brownian colloidal suspensions of particles of arbitrary shape sedimented near a bottom wall. The methods also apply for periodic (bulk) suspensions. Our methods scale linearly in the number of particles, and enable previously unprecedented simulations of tens to hundreds of thousands of particles. We demonstrate the accuracy and efficiency of our methods on a suspension of boomerang-shaped colloids. We also model recent experiments on active dynamics of uniform suspensions of spherical microrollers. This work was supported in part by the National Science Foundation under award DMS-1418706, and by the U.S. Department of Energy under award DE-SC0008271.
Micro rectennas: Brownian ratchets for thermal-energy harvesting
Pan, Y.; Powell, C. V.; Balocco, C., E-mail: claudio.balocco@durham.ac.uk [School of Engineering and Computing Sciences, Durham University, Durham DH1 3LE (United Kingdom); Song, A. M. [School of Electrical and Electronic Engineering, University of Manchester, Manchester M13 9PL (United Kingdom)
2014-12-22
We experimentally demonstrated the operation of a rectenna for harvesting thermal (blackbody) radiation and converting it into dc electric power. The device integrates an ultrafast rectifier, the self-switching nanodiode, with a wideband log-periodic spiral microantenna. The radiation from the thermal source drives the rectenna out of thermal equilibrium, permitting the rectification of the excess thermal fluctuations from the antenna. The power conversion efficiency increases with the source temperatures up to 0.02% at 973 K. The low efficiency is attributed mainly to the impedance mismatch between antenna and rectifier, and partially to the large field of view of the antenna. Our device not only opens a potential solution for harvesting thermal energy but also provides a platform for experimenting with Brownian ratchets.
Elastic moduli of a Brownian colloidal glass former
Fritschi, S.; Fuchs, M.
2018-01-01
The static, dynamic and flow-dependent shear moduli of a binary mixture of Brownian hard disks are studied by an event-driven molecular dynamics simulation. Thereby, the emergence of rigidity close to the glass transition encoded in the static shear modulus G_∞ is accessed by three methods. Results from shear stress auto-correlation functions, elastic dispersion relations, and the elastic response to strain deformations upon the start-up of shear flow are compared. This enables one to sample the time-dependent shear modulus G(t) consistently over several decades in time. By that a very precise specification of the glass transition point and of G_∞ is feasible. Predictions by mode coupling theory of a finite shear modulus at the glass transition, of α-scaling in fluid states close to the transition, and of shear induced decay in yielding glass states are tested and broadly verified.
Hybrid finite element and Brownian dynamics method for charged particles
Huber, Gary A., E-mail: ghuber@ucsd.edu; Miao, Yinglong [Howard Hughes Medical Institute, University of California San Diego, La Jolla, California 92093-0365 (United States); Zhou, Shenggao [Department of Mathematics and Mathematical Center for Interdiscipline Research, Soochow University, 1 Shizi Street, Suzhou, 215006 Jiangsu (China); Li, Bo [Department of Mathematics and Quantitative Biology Graduate Program, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112 (United States); McCammon, J. Andrew [Howard Hughes Medical Institute, University of California San Diego, La Jolla, California 92093 (United States); Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093-0365 (United States); Department of Pharmacology, University of California San Diego, La Jolla, California 92093-0636 (United States)
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 using a basic test case for a one-dimensional linear system with one charged species and a radially symmetric system with three charged species.
Semicircular canals circumvent Brownian Motion overload of mechanoreceptor hair cells
Muller, Mees; Heeck, Kier; Elemans, Coen P H
2016-01-01
Vertebrate semicircular canals (SCC) first appeared in the vertebrates (i.e. ancestral fish) over 600 million years ago. In SCC the principal mechanoreceptors are hair cells, which as compared to cochlear hair cells are distinctly longer (70 vs. 7 μm), 10 times more compliant to bending (44 vs. 500...... nN/m), and have a 100-fold higher tip displacement threshold (hair cells where the bundle is approximated as a stiff, cylindrical elastic rod subject to friction and thermal agitation. Our models suggest that the above...... differences aid SCC hair cells in circumventing the masking effects of Brownian motion noise of about 70 nm, and thereby permit transduction of very low frequency (
Dahl, Sofia
2011-01-01
Like all music performance, percussion playing requires high control over timing and sound properties. Specific to percussionists, however, is the need to adjust the movement to different instruments with varying physical properties and tactile feedback to the player. Furthermore, the well defined...... note onsets and short interaction times between player and instrument do not allow for much adjustment once a stroke is initiated. The paper surveys research that shows a close relationship between movement and sound production, and how playing conditions such as tempo and the rebound after impact...
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
On the motion of a Brownian particle with an asymmetric bias
Kim, K.S.
1981-01-01
On the infinite three dimensional cubic lattice, the transport process of a Brownian particle biased on the direction (in the case of nearest-neighbor jumping) is discussed. The Brownian particle is considered as a walker of the random process. By introducing the theorem that the probability density P(l,t) becomes Gaussian for large t, P(l,t) is completely specified when the first and second moments of P(l,t) become known. The respective values for the transprot averaged velocity and dispersion of a biased Brownian particle are obtained. Finally as t becomes large we find Gaussian packets of a biased Brownian particle which propagate with a constant velocity and have a dispersion proportional to time t. (KAERI)
Second order limit laws for occupation times of the fractional Brownian motion
Xu, Fangjun
2013-01-01
We prove second order limit laws for (additive) functionals of the $d$-dimensional fractional Brownian motion with Hurst index $H=\\frac{1}{d}$, using the method of moments, extending the Kallianpur-Robbins law.
Suryawan, Herry P.; Gunarso, Boby
2017-01-01
The generalized mixed fractional Brownian motion is defined by taking linear combinations of a finite number of independent fractional Brownian motions with different Hurst parameters. It is a Gaussian process with stationary increments, posseses self-similarity property, and, in general, is neither a Markov process nor a martingale. In this paper we study the generalized mixed fractional Brownian motion within white noise analysis framework. As a main result, we prove that for any spatial dimension and for arbitrary Hurst parameter the self-intersection local times of the generalized mixed fractional Brownian motions, after a suitable renormalization, are well-defined as Hida white noise distributions. The chaos expansions of the self-intersection local times in the terms of Wick powers of white noises are also presented. (paper)
Asian Option Pricing with Monotonous Transaction Costs under Fractional Brownian Motion
Di Pan
2013-01-01
Full Text Available Geometric-average Asian option pricing model with monotonous transaction cost rate under fractional Brownian motion was established. The method of partial differential equations was used to solve this model and the analytical expressions of the Asian option value were obtained. The numerical experiments show that Hurst exponent of the fractional Brownian motion and transaction cost rate have a significant impact on the option value.
On the distribution of estimators of diffusion constants for Brownian motion
Boyer, Denis; Dean, David S
2011-01-01
We discuss the distribution of various estimators for extracting the diffusion constant of single Brownian trajectories obtained by fitting the squared displacement of the trajectory. The analysis of the problem can be framed in terms of quadratic functionals of Brownian motion that correspond to the Euclidean path integral for simple Harmonic oscillators with time dependent frequencies. Explicit analytical results are given for the distribution of the diffusion constant estimator in a number of cases and our results are confirmed by numerical simulations.
The probability of an encounter of two Brownian particles before escape
Holcman, D; Kupka, I
2009-01-01
We study the probability of meeting of two Brownian particles before one of them exits a finite interval. We obtain an explicit expression for the probability as a function of the initial distance between the two particles using the Weierstrass elliptic function. We also find the law of the meeting location. Brownian simulations show the accuracy of our analysis. Finally, we discuss some applications to the probability that a double-strand DNA break repairs in confined environments.
On correlations between certain random variables associated with first passage Brownian motion
Kearney, Michael J; Pye, Andrew J; Martin, Richard J
2014-01-01
We analyse how the area swept out by a Brownian motion up to its first passage time correlates with the first passage time itself, obtaining several exact results in the process. Additionally, we analyse the relationship between the time average of a Brownian motion during a first passage and the maximum value attained. The results, which find various applications, are in excellent agreement with simulations. (paper)
The Pricing of Vulnerable Options in a Fractional Brownian Motion Environment
Chao Wang
2015-01-01
Full Text Available Under the assumption of the stock price, interest rate, and default intensity obeying the stochastic differential equation driven by fractional Brownian motion, the jump-diffusion model is established for the financial market in fractional Brownian motion setting. With the changes of measures, the traditional pricing method is simplified and the general pricing formula is obtained for the European vulnerable option with stochastic interest rate. At the same time, the explicit expression for it comes into being.
McMullan, G., E-mail: gm2@mrc-lmb.cam.ac.uk; Vinothkumar, K.R.; Henderson, R.
2015-11-15
We have recorded dose-fractionated electron cryo-microscope images of thin films of pure flash-frozen amorphous ice and pre-irradiated amorphous carbon on a Falcon II direct electron detector using 300 keV electrons. We observe Thon rings [1] in both the power spectrum of the summed frames and the sum of power spectra from the individual frames. The Thon rings from amorphous carbon images are always more visible in the power spectrum of the summed frames whereas those of amorphous ice are more visible in the sum of power spectra from the individual frames. This difference indicates that while pre-irradiated carbon behaves like a solid during the exposure, amorphous ice behaves like a fluid with the individual water molecules undergoing beam-induced motion. Using the measured variation in the power spectra amplitude with number of electrons per image we deduce that water molecules are randomly displaced by a mean squared distance of ∼1.1 Å{sup 2} for every incident 300 keV e{sup −}/Å{sup 2}. The induced motion leads to an optimal exposure with 300 keV electrons of 4.0 e{sup −}/Å{sup 2} per image with which to observe Thon rings centred around the strong 3.7 Å scattering peak from amorphous ice. The beam-induced movement of the water molecules generates pseudo-Brownian motion of embedded macromolecules. The resulting blurring of single particle images contributes an additional term, on top of that from radiation damage, to the minimum achievable B-factor for macromolecular structure determination. - Highlights: • Thon rings can be seen from amorphous ice. • Radiation damage to amorphous ice randomly displaces water molecules. • Each incident 300 keV e{sup −}/Å{sup 2} displaces water molecules on average by ∼1 Å. • Macromolecules embedded in amorphous ice undergo beam induced Brownian motion.
Leenders, K.L.
1986-01-01
This thesis describes the measurement of brain-tissue functions in patients with movement disorders using positron emission tomography (PET). This scanning technique is a method for direct in vivo quantitation of the regional tissue content of positron emitting radionuclides in brain (or other organs) in an essentially non-invasive way. Ch. 2 outlines some general features of PET and describes the scanner which has been used for the studies in this thesis. Also the tracer methodology, as applied to data investigations of movement disorders, are discussed. Ch. 3 contains the results of the PET investigations which were performed in the study of movement disorders. The results are presented in the form of 12 papers. The main goals of these studies were the understanding of the pathophysiology of Parkinson's disease, Huntington's chorea, Steele-Richardson-Olzewski syndrome and special case reports. Ch. 4 summarizes the results of these publications and Ch. 5 concludes the main part of this thesis with a general discussion of movement disorders in relation to PET investigations. 697 refs.; 60 figs.; 31 tabs
Pedersen, Inge Nygaard
2002-01-01
This chapter/article describes the historical development of the disciplin Psychodynamic Movement. The importance of this disciplin for self-experience and for training in developing a therapist identy for the music therapy students are emphasized. Prototypeexercises developed and simplified...
Brabrand, Helle
2010-01-01
levels than those related to building, and this exploration is a special challenge and competence implicit artistic development work. The project Mixed Movements generates drawing-material, not primary as representation, but as a performance-based media, making the body being-in-the-media felt and appear...... as possible operational moves....
Danish A. Ahmed
2018-05-01
Full Text Available Many empirical and theoretical studies indicate that Brownian motion and diffusion models as its mean field counterpart provide appropriate modeling techniques for individual insect movement. However, this traditional approach has been challenged, and conflicting evidence suggests that an alternative movement pattern such as Lévy walks can provide a better description. Lévy walks differ from Brownian motion since they allow for a higher frequency of large steps, resulting in a faster movement. Identification of the ‘correct’ movement model that would consistently provide the best fit for movement data is challenging and has become a highly controversial issue. In this paper, we show that this controversy may be superficial rather than real if the issue is considered in the context of trapping or, more generally, survival probabilities. In particular, we show that almost identical trap counts are reproduced for inherently different movement models (such as the Brownian motion and the Lévy walk under certain conditions of equivalence. This apparently suggests that the whole ‘Levy or diffusion’ debate is rather senseless unless it is placed into a specific ecological context, e.g., pest monitoring programs.
Biased Brownian motion mechanism for processivity and directionality of single-headed myosin-VI.
Iwaki, Mitsuhiro; Iwane, Atsuko Hikikoshi; Ikebe, Mitsuo; Yanagida, Toshio
2008-01-01
Conventional form to function as a vesicle transporter is not a 'single molecule' but a coordinated 'two molecules'. The coordinated two molecules make it complicated to reveal its mechanism. To overcome the difficulty, we adopted a single-headed myosin-VI as a model protein. Myosin-VI is an intracellular vesicle and organelle transporter that moves along actin filaments in a direction opposite to most other known myosin classes. The myosin-VI was expected to form a dimer to move processively along actin filaments with a hand-over-hand mechanism like other myosin organelle transporters. However, wild-type myosin-VI was demonstrated to be monomer and single-headed, casting doubt on its processivity. Using single molecule techniques, we show that green fluorescent protein (GFP)-fused single-headed myosin-VI does not move processively. However, when coupled to a 200 nm polystyrene bead (comparable to an intracellular vesicle in size) at a ratio of one head per bead, single-headed myosin-VI moves processively with large (40 nm) steps. Furthermore, we found that a single-headed myosin-VI-bead complex moved more processively in a high-viscous solution (40-fold higher than water) similar to cellular environment. Because diffusion of the bead is 60-fold slower than myosin-VI heads alone in water, we propose a model in which the bead acts as a diffusional anchor for the myosin-VI, enhancing the head's rebinding following detachment and supporting processive movement of the bead-monomer complex. This investigation will help us understand how molecular motors utilize Brownian motion in cells.
Chung, Shin-Ho; Corry, Ben
2007-07-01
In the narrow segment of an ion conducting pathway, it is likely that a permeating ion influences the positions of the nearby atoms that carry partial or full electronic charges. Here we introduce a method of incorporating the motion of charged atoms lining the pore into Brownian dynamics simulations of ion conduction. The movements of the carbonyl groups in the selectivity filter of the KcsA channel are calculated explicitly, allowing their bond lengths, bond angles, and dihedral angels to change in response to the forces acting upon them. By systematically changing the coefficients of bond stretching and of angle bending, the carbon and oxygen atoms can be made to fluctuate from their fixed positions by varying mean distances. We show that incorporating carbonyl motion in this way does not alter the mechanism of ion conduction and only has a small influence on the computed current. The slope conductance of the channel increases by approximately 25% when the root mean-square fluctuations of the carbonyl groups are increased from 0.01 to 0.61 A. The energy profiles and the number of resident ions in the channel remain unchanged. The method we utilized here can be extended to allow the movement of glutamate or aspartate side chains lining the selectivity filters of other ionic channels.
Tufto, Jarle; Lande, Russell; Ringsby, Thor-Harald; Engen, Steinar; Saether, Bernt-Erik; Walla, Thomas R; DeVries, Philip J
2012-07-01
1. We develop a Bayesian method for analysing mark-recapture data in continuous habitat using a model in which individuals movement paths are Brownian motions, life spans are exponentially distributed and capture events occur at given instants in time if individuals are within a certain attractive distance of the traps. 2. The joint posterior distribution of the dispersal rate, longevity, trap attraction distances and a number of latent variables representing the unobserved movement paths and time of death of all individuals is computed using Gibbs sampling. 3. An estimate of absolute local population density is obtained simply by dividing the Poisson counts of individuals captured at given points in time by the estimated total attraction area of all traps. Our approach for estimating population density in continuous habitat avoids the need to define an arbitrary effective trapping area that characterized previous mark-recapture methods in continuous habitat. 4. We applied our method to estimate spatial demography parameters in nine species of neotropical butterflies. Path analysis of interspecific variation in demographic parameters and mean wing length revealed a simple network of strong causation. Larger wing length increases dispersal rate, which in turn increases trap attraction distance. However, higher dispersal rate also decreases longevity, thus explaining the surprising observation of a negative correlation between wing length and longevity. © 2012 The Authors. Journal of Animal Ecology © 2012 British Ecological Society.
Studying protein assembly with reversible Brownian dynamics of patchy particles
Klein, Heinrich C. R.; Schwarz, Ulrich S.
2014-01-01
Assembly of protein complexes like virus shells, the centriole, the nuclear pore complex, or the actin cytoskeleton is strongly determined by their spatial structure. Moreover, it is becoming increasingly clear that the reversible nature of protein assembly is also an essential element for their biological function. Here we introduce a computational approach for the Brownian dynamics of patchy particles with anisotropic assemblies and fully reversible reactions. Different particles stochastically associate and dissociate with microscopic reaction rates depending on their relative spatial positions. The translational and rotational diffusive properties of all protein complexes are evaluated on-the-fly. Because we focus on reversible assembly, we introduce a scheme which ensures detailed balance for patchy particles. We then show how the macroscopic rates follow from the microscopic ones. As an instructive example, we study the assembly of a pentameric ring structure, for which we find excellent agreement between simulation results and a macroscopic kinetic description without any adjustable parameters. This demonstrates that our approach correctly accounts for both the diffusive and reactive processes involved in protein assembly
Negative mobility of a Brownian particle: Strong damping regime
Słapik, A.; Łuczka, J.; Spiechowicz, J.
2018-02-01
We study impact of inertia on directed transport of a Brownian particle under non-equilibrium conditions: the particle moves in a one-dimensional periodic and symmetric potential, is driven by both an unbiased time-periodic force and a constant force, and is coupled to a thermostat of temperature T. Within selected parameter regimes this system exhibits negative mobility, which means that the particle moves in the direction opposite to the direction of the constant force. It is known that in such a setup the inertial term is essential for the emergence of negative mobility and it cannot be detected in the limiting case of overdamped dynamics. We analyse inertial effects and show that negative mobility can be observed even in the strong damping regime. We determine the optimal dimensionless mass for the presence of negative mobility and reveal three mechanisms standing behind this anomaly: deterministic chaotic, thermal noise induced and deterministic non-chaotic. The last origin has never been reported. It may provide guidance to the possibility of observation of negative mobility for strongly damped dynamics which is of fundamental importance from the point of view of biological systems, all of which in situ operate in fluctuating environments.
From Brownian Dynamics to Markov Chain: An Ion Channel Example
Chen, Wan
2014-02-27
A discrete rate theory for multi-ion channels is presented, in which the continuous dynamics of ion diffusion is reduced to transitions between Markovian discrete states. In an open channel, the ion permeation process involves three types of events: an ion entering the channel, an ion escaping from the channel, or an ion hopping between different energy minima in the channel. The continuous dynamics leads to a hierarchy of Fokker-Planck equations, indexed by channel occupancy. From these the mean escape times and splitting probabilities (denoting from which side an ion has escaped) can be calculated. By equating these with the corresponding expressions from the Markov model, one can determine the Markovian transition rates. The theory is illustrated with a two-ion one-well channel. The stationary probability of states is compared with that from both Brownian dynamics simulation and the hierarchical Fokker-Planck equations. The conductivity of the channel is also studied, and the optimal geometry maximizing ion flux is computed. © 2014 Society for Industrial and Applied Mathematics.
Characterizing Detrended Fluctuation Analysis of multifractional Brownian motion
Setty, V. A.; Sharma, A. S.
2015-02-01
The Hurst exponent (H) is widely used to quantify long range dependence in time series data and is estimated using several well known techniques. Recognizing its ability to remove trends the Detrended Fluctuation Analysis (DFA) is used extensively to estimate a Hurst exponent in non-stationary data. Multifractional Brownian motion (mBm) broadly encompasses a set of models of non-stationary data exhibiting time varying Hurst exponents, H(t) as against a constant H. Recently, there has been a growing interest in time dependence of H(t) and sliding window techniques have been used to estimate a local time average of the exponent. This brought to fore the ability of DFA to estimate scaling exponents in systems with time varying H(t) , such as mBm. This paper characterizes the performance of DFA on mBm data with linearly varying H(t) and further test the robustness of estimated time average with respect to data and technique related parameters. Our results serve as a bench-mark for using DFA as a sliding window estimator to obtain H(t) from time series data.
Study of two-dimensional Debye clusters using Brownian motion
Sheridan, T.E.; Theisen, W.L.
2006-01-01
A two-dimensional Debye cluster is a system of n identical particles confined in a parabolic well and interacting through a screened Coulomb (i.e., a Debye-Hueckel or Yukawa) potential with a Debye length λ. Experiments were performed for 27 clusters with n=3-63 particles (9 μm diam) in a capacitively coupled 9 W rf discharge at a neutral argon pressure of 13.6 mTorr. In the strong-coupling regime each particle exhibits small amplitude Brownian motion about its equilibrium position. These motions were projected onto the center-of-mass and breathing modes and Fourier analyzed to give resonance curves from which the mode frequencies, amplitudes, and damping rates were determined. The ratio of the breathing frequency to the center-of-mass frequency was compared with theory to self-consistently determine the Debye shielding parameter κ, Debye length λ, particle charge q, and mode temperatures. It is found that 1 < or approx. κ < or approx. 2, and κ decreases weakly with n. The particle charge averaged over all measurements is -14 200±200 e, and q decreases slightly with n. The two center-of-mass modes and the breathing mode are found to have the same temperature, indicating that the clusters are in thermal equilibrium with the neutral gas. The average cluster temperature is 399±5 K
Bose polaron as an instance of quantum Brownian motion
Aniello Lampo
2017-09-01
Full Text Available We study the dynamics of a quantum impurity immersed in a Bose-Einstein condensate as an open quantum system in the framework of the quantum Brownian motion model. We derive a generalized Langevin equation for the position of the impurity. The Langevin equation is an integrodifferential equation that contains a memory kernel and is driven by a colored noise. These result from considering the environment as given by the degrees of freedom of the quantum gas, and thus depend on its parameters, e.g. interaction strength between the bosons, temperature, etc. We study the role of the memory on the dynamics of the impurity. When the impurity is untrapped, we find that it exhibits a super-diffusive behavior at long times. We find that back-flow in energy between the environment and the impurity occurs during evolution. When the particle is trapped, we calculate the variance of the position and momentum to determine how they compare with the Heisenberg limit. One important result of this paper is that we find position squeezing for the trapped impurity at long times. We determine the regime of validity of our model and the parameters in which these effects can be observed in realistic experiments.
Theory of molecular crowding in Brownian hard-sphere liquids.
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.
Performance Estimation for Two-Dimensional Brownian Rotary Ratchet Systems
Tutu, Hiroki; Horita, Takehiko; Ouchi, Katsuya
2015-04-01
Within the context of the Brownian ratchet model, a molecular rotary system that can perform unidirectional rotations induced by linearly polarized ac fields and produce positive work under loads was studied. The model is based on the Langevin equation for a particle in a two-dimensional (2D) three-tooth ratchet potential of threefold symmetry. The performance of the system is characterized by the coercive torque, i.e., the strength of the load competing with the torque induced by the ac driving field, and the energy efficiency in force conversion from the driving field to the torque. We propose a master equation for coarse-grained states, which takes into account the boundary motion between states, and develop a kinetic description to estimate the mean angular momentum (MAM) and powers relevant to the energy balance equation. The framework of analysis incorporates several 2D characteristics and is applicable to a wide class of models of smooth 2D ratchet potential. We confirm that the obtained expressions for MAM, power, and efficiency of the model can enable us to predict qualitative behaviors. We also discuss the usefulness of the torque/power relationship for experimental analyses, and propose a characteristic for 2D ratchet systems.
Studying protein assembly with reversible Brownian dynamics of patchy particles
Klein, Heinrich C. R. [Institute for Theoretical Physics, Heidelberg University, 69120 Heidelberg (Germany); Schwarz, Ulrich S., E-mail: ulrich.schwarz@bioquant.uni-heidelberg.de [Institute for Theoretical Physics, Heidelberg University, 69120 Heidelberg (Germany); BioQuant, Heidelberg University, 69120 Heidelberg (Germany)
2014-05-14
Assembly of protein complexes like virus shells, the centriole, the nuclear pore complex, or the actin cytoskeleton is strongly determined by their spatial structure. Moreover, it is becoming increasingly clear that the reversible nature of protein assembly is also an essential element for their biological function. Here we introduce a computational approach for the Brownian dynamics of patchy particles with anisotropic assemblies and fully reversible reactions. Different particles stochastically associate and dissociate with microscopic reaction rates depending on their relative spatial positions. The translational and rotational diffusive properties of all protein complexes are evaluated on-the-fly. Because we focus on reversible assembly, we introduce a scheme which ensures detailed balance for patchy particles. We then show how the macroscopic rates follow from the microscopic ones. As an instructive example, we study the assembly of a pentameric ring structure, for which we find excellent agreement between simulation results and a macroscopic kinetic description without any adjustable parameters. This demonstrates that our approach correctly accounts for both the diffusive and reactive processes involved in protein assembly.
T-cell movement on the reticular network.
Donovan, Graham M; Lythe, Grant
2012-02-21
The idea that the apparently random motion of T cells in lymph nodes is a result of movement on a reticular network (RN) has received support from dynamic imaging experiments and theoretical studies. We present a mathematical representation of the RN consisting of edges connecting vertices that are randomly distributed in three-dimensional space, and models of lymphocyte movement on such networks including constant speed motion along edges and Brownian motion, not in three-dimensions, but only along edges. The simplest model, in which a cell moves with a constant speed along edges, is consistent with mean-squared displacement proportional to time over intervals long enough to include several changes of direction. A non-random distribution of turning angles is one consequence of motion on a preformed network. Confining cell movement to a network does not, in itself, increase the frequency of cell-cell encounters. Copyright © 2011 Elsevier Ltd. All rights reserved.
Predicting oscillatory dynamics in the movement of territorial animals.
Giuggioli, L; Potts, J R; Harris, S
2012-07-07
Understanding ecological processes relies upon the knowledge of the dynamics of each individual component. In the context of animal population ecology, the way animals move and interact is of fundamental importance in explaining a variety of observed patterns. Here, we present a theoretical investigation on the movement dynamics of interacting scent-marking animals. We study how the movement statistics of territorial animals is responsible for the appearance of damped oscillations in the mean square displacement (MSD) of the animals. This non-monotonicity is shown to depend on one dimensionless parameter, given by the ratio of the correlation distance between successive steps to the size of the territory. As that parameter increases, the time dependence of the animal's MSD displays a transition from monotonic, characteristic of Brownian walks, to non-monotonic, characteristic of highly correlated walks. The results presented here represent a novel way of determining the degree of persistence in animal movement processes within confined regions.
Computational movement analysis
Laube, Patrick
2014-01-01
This SpringerBrief discusses the characteristics of spatiotemporal movement data, including uncertainty and scale. It investigates three core aspects of Computational Movement Analysis: Conceptual modeling of movement and movement spaces, spatiotemporal analysis methods aiming at a better understanding of movement processes (with a focus on data mining for movement patterns), and using decentralized spatial computing methods in movement analysis. The author presents Computational Movement Analysis as an interdisciplinary umbrella for analyzing movement processes with methods from a range of fi
Covering Ground: Movement Patterns and Random Walk Behavior in Aquilonastra anomala Sea Stars.
Lohmann, Amanda C; Evangelista, Dennis; Waldrop, Lindsay D; Mah, Christopher L; Hedrick, Tyson L
2016-10-01
The paths animals take while moving through their environments affect their likelihood of encountering food and other resources; thus, models of foraging behavior abound. To collect movement data appropriate for comparison with these models, we used time-lapse photography to track movements of a small, hardy, and easy-to-obtain organism, Aquilonastra anomala sea stars. We recorded the sea stars in a tank over many hours, with and without a food cue. With food present, they covered less distance, as predicted by theory; this strategy would allow them to remain near food. We then compared the paths of the sea stars to three common models of animal movement: Brownian motion, Lévy walks, and correlated random walks; we found that the sea stars' movements most closely resembled a correlated random walk. Additionally, we compared the search performance of models of Brownian motion, a Lévy walk, and a correlated random walk to that of a model based on the sea stars' movements. We found that the behavior of the modeled sea star walk was similar to that of the modeled correlated random walk and the Brownian motion model, but that the sea star walk was slightly more likely than the other walks to find targets at intermediate distances. While organisms are unlikely to follow an idealized random walk in all details, our data suggest that comparing the effectiveness of an organism's paths to those from theory can give insight into the organism's actual movement strategy. Finally, automated optical tracking of invertebrates proved feasible, and A. anomala was revealed to be a tractable, 2D-movement study system.
Lim, S C; Teo, L P
2009-01-01
Single-file diffusion behaves as normal diffusion at small time and as subdiffusion at large time. These properties can be described in terms of fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann–Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with a step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as a solution of the fractional Langevin equation with zero damping. Various kinds of fractional Langevin equations and their generalizations are then considered in order to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where the dissipative memory kernel is a Dirac delta function, a power-law function and a combination of these functions are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of a process that begins as ballistic motion
Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions
Han Yuecai; Hu Yaozhong; Song Jian
2013-01-01
We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter H>1/2). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential equation driven by both fractional Brownian motions and the corresponding underlying standard Brownian motions. In addition to this backward equation, the maximum principle also involves the Malliavin derivatives. Our approach is to use conditioning and Malliavin calculus. To arrive at our maximum principle we need to develop some new results of stochastic analysis of the controlled systems driven by fractional Brownian motions via fractional calculus. Our approach of conditioning and Malliavin calculus is also applied to classical system driven by standard Brownian motions while the controller has only partial information. As a straightforward consequence, the classical maximum principle is also deduced in this more natural and simpler way.
Brownian ratchets from statistical physics to bio and nano-motors
Cubero, David
2016-01-01
Illustrating the development of Brownian ratchets, from their foundations, to their role in the description of life at the molecular scale and in the design of artificial nano-machinery, this text will appeal to both advanced graduates and researchers entering the field. Providing a self-contained introduction to Brownian ratchets, devices which rectify microscopic fluctuations, Part I avoids technicalities and sets out the broad range of physical systems where the concept of ratchets is relevant. Part II supplies a single source for a complete and modern theoretical analysis of ratchets in regimes such as classical vs quantum and stochastic vs deterministic, and in Part III readers are guided through experimental developments in different physical systems, each highlighting a specific unique feature of ratchets. The thorough and systematic approach to the topic ensures that this book provides a complete guide to Brownian ratchets for newcomers and established researchers in physics, biology and biochemistry.
Critique of the Brownian approximation to the generalized Langevin equation in lattice dynamics
Diestler, D.J.; Riley, M.E.
1985-01-01
We consider the classical motion of a harmonic lattice in which only those atoms in a certain subset of the lattice (primary zone) may interact with an external force. The formally exact generalized Langevin equation (GLE) for the primary zone is an appropriate description of the dynamics. We examine a previously proposed Brownian, or frictional damping, approximation that reduces the GLE to a set of coupled ordinary Langevin equations for the primary atoms. It is shown that the solution of these equations can contain undamped motion if there is more than one atom in the primary zone. Such motion is explicitly demonstrated for a model that has been used to describe energy transfer in atom--surface collisions. The inability of the standard Brownian approximation to yield an acceptable, physically meaningful result for primary zones comprising more than one atom suggests that the Brownian approximation may introduce other spurious dynamical effects. Further work on damping of correlated motion in lattices is needed
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.
Analytical Solutions of a Model for Brownian Motion in the Double Well Potential
Liu Ai-Jie; Zheng Lian-Cun; Zhang Xin-Xin; Ma Lian-Xi
2015-01-01
In this paper, the analytical solutions of Schrödinger equation for Brownian motion in a double well potential are acquired by the homotopy analysis method and the Adomian decomposition method. Double well potential for Brownian motion is always used to obtain the solutions of Fokker—Planck equation known as the Klein—Kramers equation, which is suitable for separation and additive Hamiltonians. In essence, we could study the random motion of Brownian particles by solving Schrödinger equation. The analytical results obtained from the two different methods agree with each other well. The double well potential is affected by two parameters, which are analyzed and discussed in details with the aid of graphical illustrations. According to the final results, the shapes of the double well potential have significant influence on the probability density function. (general)
Achieving swift equilibration of a Brownian particle using flow-fields
Patra, Ayoti; Jarzynski, Christopher
Can a system be driven to a targeted equilibrium state on a timescale that is much shorter than its natural equilibration time? In a recent experiment, the swift equilibration of an overdamped Brownian particle was achieved by use of an appropriately designed, time-dependent optical trap potential. Motivated by these results, we develop a general theoretical approach for guiding an ensemble of Brownian particles to track the instantaneous equilibrium distribution of a desired potential U (q , t) . In our approach, we use flow-fields associated with the parametric evolution of the targeted equilibrium state to construct an auxiliary potential U (q , t) , such that dynamics under the composite potential U (t) + U (t) achieves the desired evolution. Our results establish a close connection between the swift equilibration of Brownian particles, quantum shortcuts to adiabaticity, and the dissipationless driving of a classical, Hamiltonian system.
Financial Brownian Particle in the Layered Order-Book Fluid and Fluctuation-Dissipation Relations
Yura, Yoshihiro; Takayasu, Hideki; Sornette, Didier; Takayasu, Misako
2014-03-01
We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of comprehensive market data enables us to identify all motions of the fluid particles. Correlations between the motions of the Brownian particle and its surrounding fluid particles reflect specific layering interactions; in the inner layer the correlation is strong and with short memory, while in the outer layer it is weaker and with long memory. By interpreting and estimating the contribution from the outer layer as a drag resistance, we demonstrate the validity of the fluctuation-dissipation relation in this nonmaterial Brownian motion process.
Brownian motion in Robertson-Walker spacetimes from electromagnetic vacuum fluctuations
Bessa, Carlos H. G.; Bezerra, V. B.; Ford, L. H.
2009-01-01
We consider the effects of the vacuum fluctuations of a quantized electromagnetic field on particles in an expanding universe. We find that these particles typically undergo Brownian motion and acquire a nonzero mean squared velocity that depends on the scale factor of the universe. This Brownian motion can be interpreted as due to noncancellation of anticorrelated vacuum fluctuations in the time-dependent background spacetime. Alternatively, one can interpret this effect as the particles acquiring energy from the background spacetime geometry, a phenomenon that cannot occur in a static spacetime. We treat several types of coupling between the electromagnetic field and the particles and several model universes. We also consider both free particles, which, on the average, move on geodesics, and particles in bound systems. There are significant differences between these two cases, which illustrates that nongeodesic motion alters the effects of the vacuum fluctuations. We discuss the possible applications of this Brownian motion effect to cosmological scenarios.
Swarming behavior of gradient-responsive Brownian particles in a porous medium
Grančič, Peter; Štěpánek, František
2012-07-01
Active targeting by Brownian particles in a fluid-filled porous environment is investigated by computer simulation. The random motion of the particles is enhanced by diffusiophoresis with respect to concentration gradients of chemical signals released by the particles in the proximity of a target. The mathematical model, based on a combination of the Brownian dynamics method and a diffusion problem is formulated in terms of key parameters that include the particle diffusiophoretic mobility and the signaling threshold (the distance from the target at which the particles release their chemical signals). The results demonstrate that even a relatively simple chemical signaling scheme can lead to a complex collective behavior of the particles and can be a very efficient way of guiding a swarm of Brownian particles towards a target, similarly to the way colonies of living cells communicate via secondary messengers.
Non-intersecting Brownian motions leaving from and going to several points
Adler, Mark; van Moerbeke, Pierre; Vanderstichelen, Didier
2012-03-01
Consider n non-intersecting Brownian motions on R, depending on time t∈[0,1], with mi particles forced to leave from ai at time t=0, 1≤i≤q, and nj particles forced to end up at bj at time t=1, 1≤j≤p. For arbitrary p and q, it is not known if the distribution of the positions of the non-intersecting Brownian particles at a given time 0miracle! Unfortunately we were unable to find its explicit expression. The case p=q=2 will be discussed in the last section.
Brownian agents and active particles collective dynamics in the natural and social sciences
Schweitzer, Frank
2007-01-01
""This book lays out a vision for a coherent framework for understanding complex systems"" (from the foreword by J. Doyne Farmer). By developing the genuine idea of Brownian agents, the author combines concepts from informatics, such as multiagent systems, with approaches of statistical many-particle physics. This way, an efficient method for computer simulations of complex systems is developed which is also accessible to analytical investigations and quantitative predictions. The book demonstrates that Brownian agent models can be successfully applied in many different contexts, ranging from
Brownian Agents and Active Particles: Collective Dynamics in the Natural and Social Sciences
McKane, Alan
2003-01-01
This is a book about the modelling of complex systems and, unlike many books on this subject, concentrates on the discussion of specific systems and gives practical methods for modelling and simulating them. This is not to say that the author does not devote space to the general philosophy and definition of complex systems and agent-based modelling, but the emphasis is definitely on the development of concrete methods for analysing them. This is, in my view, to be welcomed and I thoroughly recommend the book, especially to those with a theoretical physics background who will be very much at home with the language and techniques which are used. The author has developed a formalism for understanding complex systems which is based on the Langevin approach to the study of Brownian motion. This is a mesoscopic description; details of the interactions between the Brownian particle and the molecules of the surrounding fluid are replaced by a randomly fluctuating force. Thus all microscopic detail is replaced by a coarse-grained description which encapsulates the essence of the interactions at the finer level of description. In a similar way, the influences on Brownian agents in a multi-agent system are replaced by stochastic influences which sum up the effects of these interactions on a finer scale. Unlike Brownian particles, Brownian agents are not structureless particles, but instead have some internal states so that, for instance, they may react to changes in the environment or to the presence of other agents. Most of the book is concerned with developing the idea of Brownian agents using the techniques of statistical physics. This development parallels that for Brownian particles in physics, but the author then goes on to apply the technique to problems in biology, economics and the social sciences. This is a clear and well-written book which is a useful addition to the literature on complex systems. It will be interesting to see if the use of Brownian agents becomes
Brownian Motion of 2D Vacancy Islands by Adatom Terrace Diffusion
Morgenstern, Karina; Laegsgaard, Erik; Besenbacher, Flemming
2001-01-01
We have studied the Brownian motion of two-dimensional (2D) vacancy islands on Ag(110) at temperatures between 175 and 215K. While the detachment of adatoms from the island and their diffusion on the terrace are permitted in this temperature range, the periphery diffusion of single adatoms is prohibited. The present scanning tunneling microscopy results provide the first direct experimental proof that the Brownian motion of the islands follows a simple scaling law with terrace diffusion being the rate limiting process. The activation energy of the vacancy island motion is determined to 0.41eV
Evidence for intermittency and a truncated power law from highly resolved aphid movement data.
Mashanova, Alla; Oliver, Tom H; Jansen, Vincent A A
2010-01-06
Power laws are increasingly used to describe animal movement. Despite this, the use of power laws has been criticized on both empirical and theoretical grounds, and alternative models based on extensions of conventional random walk theory (Brownian motion) have been suggested. In this paper, we analyse a large volume of data of aphid walking behaviour (65,068 data points), which provides a highly resolved dataset to investigate the pattern of movement. We show that aphid movement is intermittent--with alternations of a slow movement with frequent change of direction and a fast, relatively directed movement--and that the fast movement consists of two phases--a strongly directed phase that gradually changes into an uncorrelated random walk. By measuring the mean-squared displacement and the duration of non-stop movement episodes we found that both spatial and temporal aspects of aphid movement are best described using a truncated power law approach. We suggest that the observed spatial pattern arises from the duration of non-stop movement phases rather than from correlations in turning angles. We discuss the implications of these findings for interpreting movement data, such as distinguishing between movement and non-movement, and the effect of the range of data used in the analysis on the conclusions.
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.
Boronovskiĭ, S E; Nartsissov, Ia R
2009-01-01
Using the Brownian dynamics of the movement of hydrated ion in a viscous water solution, a mathematical model has been built, which describes the transport of charged particles through a single protein pore in a lipid membrane. The dependences of transmembrane ion currents on ion concentrations in solution have been obtained. It was shown that, if the geometry of a membrane pore is identical to that of the inner part of the glycine receptor channel and there is no ion selectivity, then the values of both chloride and sodium currents are not greater than 0.5 pA at the physiological concentrations of these ions. If local charge heterogeneity caused by charged amino acid residues of transmembrane protein segments is included into the model calculations, the chloride current increases to about 3.7 pA, which exceeds more than seven times the value for sodium ions under the conditions of the complex channel geometry in the range of physiological concentrations of ions in the solution. The model takes changes in the density of charge distribution both inside the channel and near the protein surface into account. The alteration of pore geometry can be also considered as a parameter at the researcher's option. Thus, the model appears as an effective tool for the description of transmembrane currents for other types of membrane channels.
Characteristics of broadband slow earthquakes explained by a Brownian model
Ide, S.; Takeo, A.
2017-12-01
Brownian slow earthquake (BSE) model (Ide, 2008; 2010) is a stochastic model for the temporal change of seismic moment release by slow earthquakes, which can be considered as a broadband phenomena including tectonic tremors, low frequency earthquakes, and very low frequency (VLF) earthquakes in the seismological frequency range, and slow slip events in geodetic range. Although the concept of broadband slow earthquake may not have been widely accepted, most of recent observations are consistent with this concept. Then, we review the characteristics of slow earthquakes and how they are explained by BSE model. In BSE model, the characteristic size of slow earthquake source is represented by a random variable, changed by a Gaussian fluctuation added at every time step. The model also includes a time constant, which divides the model behavior into short- and long-time regimes. In nature, the time constant corresponds to the spatial limit of tremor/SSE zone. In the long-time regime, the seismic moment rate is constant, which explains the moment-duration scaling law (Ide et al., 2007). For a shorter duration, the moment rate increases with size, as often observed for VLF earthquakes (Ide et al., 2008). The ratio between seismic energy and seismic moment is constant, as shown in Japan, Cascadia, and Mexico (Maury et al., 2017). The moment rate spectrum has a section of -1 slope, limited by two frequencies corresponding to the above time constant and the time increment of the stochastic process. Such broadband spectra have been observed for slow earthquakes near the trench axis (Kaneko et al., 2017). This spectrum also explains why we can obtain VLF signals by stacking broadband seismograms relative to tremor occurrence (e.g., Takeo et al., 2010; Ide and Yabe, 2014). The fluctuation in BSE model can be non-Gaussian, as far as the variance is finite, as supported by the central limit theorem. Recent observations suggest that tremors and LFEs are spatially characteristic
Non-Brownian diffusion in lipid membranes: Experiments and simulations.
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
Noise-to-signal transition of a Brownian particle in the cubic potential: I. general theory
Filip, R.; Zemánek, Pavel
2016-01-01
Roč. 18, č. 6 (2016), 065401:1-8 ISSN 2040-8978 R&D Projects: GA ČR GB14-36681G Institutional support: RVO:68081731 Keywords : optically trapped particles * Brownian motion * optomechanics Subject RIV: BH - Optics, Masers, Lasers Impact factor: 1.741, year: 2016
Brownian dynamics of aggregation kinetics of hard spheres with flexibele bounds
Rzepiela, A.A.; Opheusden, van J.; Vliet, van T.
2001-01-01
Brownian dynamics (BD) simulations have been performed on the aggregation dynamics of colloidal particles within the context of a ball-and-string model. Particles are treated as hard spheres that can bind irreversibly through a string attached to their surface. The model is set up to mimic some
The first-passage area for drifted Brownian motion and the moments of the Airy distribution
Kearney, Michael J; Majumdar, Satya N; Martin, Richard J
2007-01-01
An exact expression for the distribution of the area swept out by a drifted Brownian motion till its first-passage time is derived. A study of the asymptotic behaviour confirms earlier conjectures and clarifies their range of validity. The analysis leads to a simple closed-form solution for the moments of the Airy distribution. (fast track communication)
Svin'in, I.R.
1982-01-01
The Brownian motion of a quadrupole quantum oscillator is considered as a model of surface quadrupole oscillations of heated spherical nuclei. The integrals of the motion related to energy and angular momentum conservation are constructed and the wave functions are obtained for states with definite values of these integrals of the motion in the phonon representation
Time-changed geometric fractional Brownian motion and option pricing with transaction costs
Gu, Hui; Liang, Jin-Rong; Zhang, Yun-Xiu
2012-08-01
This paper deals with the problem of discrete time option pricing by a fractional subdiffusive Black-Scholes model. The price of the underlying stock follows a time-changed geometric fractional Brownian motion. By a mean self-financing delta-hedging argument, the pricing formula for the European call option in discrete time setting is obtained.
Wang, Jun; Liang, Jin-Rong; Lv, Long-Jin; Qiu, Wei-Yuan; Ren, Fu-Yao
2012-02-01
In this paper, we study the problem of continuous time option pricing with transaction costs by using the homogeneous subdiffusive fractional Brownian motion (HFBM) Z(t)=X(Sα(t)), 0transaction costs of replicating strategies. We also give the total transaction costs.
The mode coupling theory in the FDR-preserving field theory of interacting Brownian particles
Kim, Bongsoo; Kawasaki, Kyozi
2007-01-01
We develop a renormalized perturbation theory for the dynamics of interacting Brownian particles, which preserves the fluctuation-dissipation relation order by order. We then show that the resulting one-loop theory gives a closed equation for the density correlation function, which is identical with that in the standard mode coupling theory. (fast track communication)
Durrett, Richard; Kesten, Harry; Spitzer, Frank
1991-01-01
..., made the transparency used in the printing process. STUDENTS OF FRANK SPITZERSTUDENTS OF FRANK SPITZER 1957 J. W. Lamperti, On the asymptotic behavior of recurrent and almostrecurrent events. 1964 W. W. Whitman, Some strong laws for random walks and Brownian motion. 1965 J. C. Mineka, The existence and uniqueness of positive solutions to the Wien...
Orbital diamagnetism of a charged Brownian particle undergoing birth-death process
Jayannawar, A.M.; Kumar, N.
1980-06-01
We consider the magnetic response of a charged Brownian particle undergoing a stochastic birth-death process. The latter simulates the electron-hole pair production and recombination in semiconductors. We obtain non-zero, orbital diamagnetism which can be large without violating the Van Leeuwen theorem. (author)
Shit, Anindita; Chattopadhyay, Sudip; Chaudhuri, Jyotipratim Ray
2012-01-01
Graphical abstract: By invoking physically motivated coordinate transformation into quantum Smoluchowski equation, we have presented a transparent treatment for the determination of the effective diffusion coefficient and current of a quantum Brownian particle. Substantial enhancement in the efficiency of the diffusive transport is envisaged due to the quantum correction effects. Highlights:: ► Transport of a quantum Brownian particle in a periodic potential has been addressed. ► Governing quantum Smoluchowski equation (QSE) includes state dependent diffusion. ► A coordinate transformation is used to recast QSE with constant diffusion. ► Transport properties increases in comparison to the corresponding classical result. ► This enhancement is purely a quantum effect. - Abstract: The transport property of a quantum Brownian particle that interacts strongly with a bath (in which a typical damping constant by far exceeds a characteristic frequency of the isolated system) under the influence of a tilted periodic potential has been studied by solving quantum Smoluchowski equation (QSE). By invoking physically motivated coordinate transformation into QSE, we have presented a transparent treatment for the determination of the effective diffusion coefficient of a quantum Brownian particle and the current (the average stationary velocity). Substantial enhancement in the efficiency of the diffusive transport is envisaged due to the quantum correction effects only if the bath temperature hovers around an appropriate range of intermediate values. Our findings also confirm the results obtained in the classical cases.
An Extreme-Value Analysis of the LIL for Brownian Motion
Khoshnevisan, Davar; Levin, David; Shi, Zhan
2005-01-01
We use excursion theory and the ergodic theorem to present an extreme-value analysis of the classical law of the iterated logarithm (LIL) for Brownian motion. A simplified version of our method also proves, in a paragraph, the classical theorem of Darling and Erdős (1956).
Non-Markovian quantum Brownian motion in one dimension in electric fields
Shen, H. Z.; Su, S. L.; Zhou, Y. H.; Yi, X. X.
2018-04-01
Quantum Brownian motion is the random motion of quantum particles suspended in a field (or an effective field) resulting from their collision with fast-moving modes in the field. It provides us with a fundamental model to understand various physical features concerning open systems in chemistry, condensed-matter physics, biophysics, and optomechanics. In this paper, without either the Born-Markovian or rotating-wave approximation, we derive a master equation for a charged-Brownian particle in one dimension coupled with a thermal reservoir in electric fields. The effect of the reservoir and the electric fields is manifested as time-dependent coefficients and coherent terms, respectively, in the master equation. The two-photon correlation between the Brownian particle and the reservoir can induce nontrivial squeezing dynamics to the particle. We derive a current equation including the source from the driving fields, transient current from the system flowing into the environment, and the two-photon current caused by the non-rotating-wave term. The presented results then are compared with that given by the rotating-wave approximation in the weak-coupling limit, and these results are extended to a more general quantum network involving an arbitrary number of coupled-Brownian particles. The presented formalism might open a way to better understand exactly the non-Markovian quantum network.
Groeneboom, P.; Jongbloed, G.; Wellner, J.A.
2001-01-01
A process associated with integrated Brownian motion is introduced that characterizes the limit behavior of nonparametric least squares and maximum likelihood estimators of convex functions and convex densities, respectively. We call this process “the invelope” and show that it is an almost surely
On-chip Brownian relaxation measurements of magnetic nanobeads in the time domain
Østerberg, Frederik Westergaard; Rizzi, Giovanni; Hansen, Mikkel Fougt
2013-01-01
the time and frequency domain methods on Brownian relaxation detection of clustering of streptavidin coated magnetic beads in the presence of different concentrations of biotin-conjugated bovine serum albumin and obtain comparable results. In the time domain, a measurement is carried out in less than 30 s...
Brownian motion in a field of force and the diffusion theory of chemical reactions. II
Brinkman, H.C.
1956-01-01
H. A. Kramers has studied the rate of chemical reactions in view of the Brownian forces caused by a surrounding medium in temperature equilibrium. In a previous paper 3) the author gave a solution of Kramers' diffusion equation in phase space by systematic development. In this paper the general
Configurational entropy and effective temperature in systems of active Brownian particles
Preisler, Zdeněk; Dijkstra, Marjolein
2016-01-01
We propose a method to determine the effective density of states and configurational entropy in systems of active Brownian particles by measuring the probability distribution function of potential energy at varying temperatures. Assuming that the entropy is a continuous and monotonically increasing
Donolato, M.; Sogne, E.; Dalslet, Bjarke Thomas
2011-01-01
We demonstrate the detection of the Brownian relaxation frequency of 250 nm diameter magnetic beads using a lab-on-chip platform based on current lines for exciting the beads with alternating magnetic fields and highly sensitive magnetic tunnel junction (MTJ) sensors with a superparamagnetic free...
Non-intersecting Brownian walkers and Yang-Mills theory on the sphere
Forrester, Peter J.; Majumdar, Satya N.; Schehr, Gregory
2011-01-01
We study a system of N non-intersecting Brownian motions on a line segment [0,L] with periodic, absorbing and reflecting boundary conditions. We show that the normalized reunion probabilities of these Brownian motions in the three models can be mapped to the partition function of two-dimensional continuum Yang-Mills theory on a sphere respectively with gauge groups U(N), Sp(2N) and SO(2N). Consequently, we show that in each of these Brownian motion models, as one varies the system size L, a third order phase transition occurs at a critical value L=L c (N)∼√(N) in the large N limit. Close to the critical point, the reunion probability, properly centered and scaled, is identical to the Tracy-Widom distribution describing the probability distribution of the largest eigenvalue of a random matrix. For the periodic case we obtain the Tracy-Widom distribution corresponding to the GUE random matrices, while for the absorbing and reflecting cases we get the Tracy-Widom distribution corresponding to GOE random matrices. In the absorbing case, the reunion probability is also identified as the maximal height of N non-intersecting Brownian excursions ('watermelons' with a wall) whose distribution in the asymptotic scaling limit is then described by GOE Tracy-Widom law. In addition, large deviation formulas for the maximum height are also computed.
The Onsager reciprocity relation and generalized efficiency of a thermal Brownian motor
Tian-Fu, Gao; Jin-Can, Chen; Yue, Zhang
2009-01-01
Based on a general model of Brownian motors, the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically. It is found that the Onsager reciprocity relation holds and the Onsager coefficients are not affected by the kinetic energy change due to the particle's motion. Only when the heat leak in the system is negligible can the determinant of the Onsager matrix vanish. Moreover, the influence of the main parameters characterizing the model on the generalized efficiency of the Brownian motor is discussed in detail. The characteristic curves of the generalized efficiency varying with these parameters are presented, and the maximum generalized efficiency and the corresponding optimum parameters are determined. The results obtained here are of general significance. They are used to analyze the performance characteristics of the Brownian motors operating in the three interesting cases with zero heat leak, zero average drift velocity or a linear response relation, so that some important conclusions in current references are directly included in some limit cases of the present paper. (general)
Brownian motion after Einstein and Smoluchowski: Some new applications and new experiments
Dávid, Selmeczi; Tolic-Nørrelykke, S.F.; Schäffer, E.
2007-01-01
The first half of this review describes the development in mathematical models of Brownian motion after Einstein's and Smoluchowski's seminal papers and current applications to optical tweezers. This instrument of choice among single-molecule biophysicists is also an instrument of such precision ...
E. Barndorff-Nielsen, Ole; Benth, Fred Espen; Szozda, Benedykt
This paper generalizes the integration theory for volatility modulated Brownian-driven Volterra processes onto the space G* of Potthoff-Timpel distributions. Sufficient conditions for integrability of generalized processes are given, regularity results and properties of the integral are discussed...
Barndorff-Nielsen, Ole E.; Benth, Fred Espen; Szozda, Benedykt
This paper generalizes the integration theory for volatility modulated Brownian-driven Volterra processes onto the space G∗ of Potthoff--Timpel distributions. Sufficient conditions for integrability of generalized processes are given, regularity results and properties of the integral are discusse...
Large shear deformation of particle gels studied by Brownian Dynamics simulations
Rzepiela, A.A.; Opheusden, van J.H.J.; Vliet, van T.
2004-01-01
Brownian Dynamics (BD) simulations have been performed to study structure and rheology of particle gels under large shear deformation. The model incorporates soft spherical particles, and reversible flexible bond formation. Two different methods of shear deformation are discussed, namely affine and
Wang, Dong; Zhao, Yang; Yang, Fangfang; Tsui, Kwok-Leung
2017-09-01
Brownian motion with adaptive drift has attracted much attention in prognostics because its first hitting time is highly relevant to remaining useful life prediction and it follows the inverse Gaussian distribution. Besides linear degradation modeling, nonlinear-drifted Brownian motion has been developed to model nonlinear degradation. Moreover, the first hitting time distribution of the nonlinear-drifted Brownian motion has been approximated by time-space transformation. In the previous studies, the drift coefficient is the only hidden state used in state space modeling of the nonlinear-drifted Brownian motion. Besides the drift coefficient, parameters of a nonlinear function used in the nonlinear-drifted Brownian motion should be treated as additional hidden states of state space modeling to make the nonlinear-drifted Brownian motion more flexible. In this paper, a prognostic method based on nonlinear-drifted Brownian motion with multiple hidden states is proposed and then it is applied to predict remaining useful life of rechargeable batteries. 26 sets of rechargeable battery degradation samples are analyzed to validate the effectiveness of the proposed prognostic method. Moreover, some comparisons with a standard particle filter based prognostic method, a spherical cubature particle filter based prognostic method and two classic Bayesian prognostic methods are conducted to highlight the superiority of the proposed prognostic method. Results show that the proposed prognostic method has lower average prediction errors than the particle filter based prognostic methods and the classic Bayesian prognostic methods for battery remaining useful life prediction.
... Publications Patient Organizations International Parkinson and Movement Disorder Society National Institute of Mental Health (NIMH) See all related organizations Publications Order NINDS Publications Definition Psychogenic movement is an unwanted muscle movement such ...
Xiao-Li Ding
2018-01-01
Full Text Available In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. Finally, we give three examples to demonstrate the applicability of our obtained results.
A random walk description of individual animal movement accounting for periods of rest
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.
APM_GUI: analyzing particle movement on the cell membrane and determining confinement.
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.
APM_GUI: analyzing particle movement on the cell membrane and determining confinement
Menchón Silvia A
2012-02-01
Full Text Available Abstract Background 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,. Results 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. Conclusions 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.
Minoura, Itsushi; Katayama, Eisaku; Sekimoto, Ken; Muto, Etsuko
2010-01-01
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 ...
Xiao-Li Ding; Juan J. Nieto
2018-01-01
In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochast...
Berg-Soerensen, Kirstine; Flyvbjerg, Henrik
2005-01-01
One hundred years after Einstein modelled Brownian motion, a central aspect of this motion in incompressible fluids has not been verified experimentally: the thermal noise that drives the Brownian particle, is not white, as in Einstein's simple theory. It is slightly coloured, due to hydrodynamics and the fluctuation-dissipation theorem. This theoretical result from the 1970s was prompted by computer simulation results in apparent violation of Einstein's theory. We discuss how a direct experimental observation of this colour might be carried out by using optical tweezers to separate the thermal noise from the particle's dynamic response to it. Since the thermal noise is almost white, very good statistics is necessary to resolve its colour. That requires stable equipment and long recording times, possibly making this experiment one for the future only. We give results for experimental requirements and for stochastic errors as functions of experimental window and measurement time, and discuss some potential sources of systematic errors
Lee, K. C.
2013-02-01
Multifractional Brownian motions have become popular as flexible models in describing real-life signals of high-frequency features in geoscience, microeconomics, and turbulence, to name a few. The time-changing Hurst exponent, which describes regularity levels depending on time measurements, and variance, which relates to an energy level, are two parameters that characterize multifractional Brownian motions. This research suggests a combined method of estimating the time-changing Hurst exponent and variance using the local variation of sampled paths of signals. The method consists of two phases: initially estimating global variance and then accurately estimating the time-changing Hurst exponent. A simulation study shows its performance in estimation of the parameters. The proposed method is applied to characterization of atmospheric stability in which descriptive statistics from the estimated time-changing Hurst exponent and variance classify stable atmosphere flows from unstable ones.
K. C. Lee
2013-02-01
Full Text Available Multifractional Brownian motions have become popular as flexible models in describing real-life signals of high-frequency features in geoscience, microeconomics, and turbulence, to name a few. The time-changing Hurst exponent, which describes regularity levels depending on time measurements, and variance, which relates to an energy level, are two parameters that characterize multifractional Brownian motions. This research suggests a combined method of estimating the time-changing Hurst exponent and variance using the local variation of sampled paths of signals. The method consists of two phases: initially estimating global variance and then accurately estimating the time-changing Hurst exponent. A simulation study shows its performance in estimation of the parameters. The proposed method is applied to characterization of atmospheric stability in which descriptive statistics from the estimated time-changing Hurst exponent and variance classify stable atmosphere flows from unstable ones.
Quantal Brownian Motion from RPA dynamics: The master and Fokker-Planck equations
Yannouleas, C.
1984-05-01
From the purely quantal RPA description of the damped harmonic oscillator and of the corresponding Brownian Motion within the full space (phonon subspace plus reservoir), a master equation (as well as a Fokker-Planck equation) for the reduced density matrix (for the reduced Wigner function, respectively) within the phonon subspace is extracted. The RPA master equation agrees with the master equation derived by the time-dependent perturbative approaches which utilize Tamm-Dancoff Hilbert spaces and invoke the rotating wave approximation. Since the RPA yields a full, as well as a contracted description, it can account for both the kinetic and the unperturbed oscillator momenta. The RPA description of the quantal Brownian Motion contrasts with the descriptions provided by the time perturbative approaches whether they invoke or not the rotating wave approximation. The RPA description also contrasts with the phenomenological phase space quantization. (orig.)
Linear response approach to active Brownian particles in time-varying activity fields
Merlitz, Holger; Vuijk, Hidde D.; Brader, Joseph; Sharma, Abhinav; Sommer, Jens-Uwe
2018-05-01
In a theoretical and simulation study, active Brownian particles (ABPs) in three-dimensional bulk systems are exposed to time-varying sinusoidal activity waves that are running through the system. A linear response (Green-Kubo) formalism is applied to derive fully analytical expressions for the torque-free polarization profiles of non-interacting particles. The activity waves induce fluxes that strongly depend on the particle size and may be employed to de-mix mixtures of ABPs or to drive the particles into selected areas of the system. Three-dimensional Langevin dynamics simulations are carried out to verify the accuracy of the linear response formalism, which is shown to work best when the particles are small (i.e., highly Brownian) or operating at low activity levels.
A short note on the mean exit time of the Brownian motion
Cadeddu, Lucio; Farina, Maria Antonietta
We investigate the functional Ω↦ℰ(Ω) where Ω runs through the set of compact domains of fixed volume v in any Riemannian manifold (M,g) and where ℰ(Ω) is the mean exit time from Ω of the Brownian motion. We give an alternative analytical proof of a well-known fact on its critical points proved by McDonald: the critical points of ℰ(Ω) are harmonic domains.
A one-dimensional gravitationally interacting gas and the convex minorant of Brownian motion
Suidan, T M
2001-01-01
The surprising connection between a one-dimensional gravitationally interacting gas of sticky particles and the convex minorant process generated by Brownian motion on [0,1] is studied. A study is made of the dynamics of this 1-D gas system by identifying three distinct clustering regimes and the time scales at which they occur. At the critical moment of time the mass distribution of the gas can be computed in terms of functionals of the convex minorant process
Quantum Brownian motion in a bath of parametric oscillators: A model for system-field interactions
Hu, B.L.; Matacz, A.
1994-01-01
The quantum Brownian motion paradigm provides a unified framework where one can see the interconnection of some basic quantum statistical processes such as decoherence, dissipation, particle creation, noise, and fluctuation. The present paper continues the investigation begun in earlier papers on the quantum Brownian motion in a general environment via the influence functional formalism. Here, the Brownian particle is coupled linearly to a bath of the most general time-dependent quadratic oscillators. This bath of parametric oscillators minics a scalar field, while the motion of the Brownian particle modeled by a single oscillator could be used to depict the behavior of a particle detector, a quantum field mode, or the scale factor of the Universe. An important result of this paper is the derivation of the influence functional encompassing the noise and dissipation kernels in terms of the Bogolubov coefficients, thus setting the stage for the influence functional formalism treatment of problems in quantum field theory in curved spacetime. This method enables one to trace the source of statistical processes such as decoherence and dissipation to vacuum fluctuations and particle creation, and in turn impart a statistical mechanical interpretation of quantum field processes. With this result we discuss the statistical mechanical origin of quantum noise and thermal radiance from black holes and from uniformly accelerated observers in Minkowski space as well as from the de Sitter universe discovered by Hawking, Unruh, and Gibbons and Hawking. We also derive the exact evolution operator and master equation for the reduced density matrix of the system interacting with a parametric oscillator bath in an initial squeezed thermal state. These results are useful for decoherence and back reaction studies for systems and processes of interest in semiclassical cosmology and gravity. Our model and results are also expected to be useful for related problems in quantum optics
Maximizing the Mean Exit Time of a Brownian Motion from an Interval
Mario Lefebvre
2011-01-01
Full Text Available Let X(t be a controlled one-dimensional standard Brownian motion starting from x∈(−d,d. The problem of optimally controlling X(t until |X(t|=d for the first time is solved explicitly in a particular case. The maximal value that the instantaneous reward given for survival in (−d,d can take is determined.
Probability laws related to the Jacobi theta and Riemann zeta function and Brownian excursions
Biane, P.; Pitman, J.; Yor, M.
1999-01-01
This paper reviews known results which connect Riemann's integral representations of his zeta function, involving Jacobi's theta function and its derivatives, to some particular probability laws governing sums of independent exponential variables. These laws are related to one-dimensional Brownian motion and to higher dimensional Bessel processes. We present some characterizations of these probability laws, and some approximations of Riemann's zeta function which are related to these laws.
Asymptotic theory for Brownian semi-stationary processes with application to turbulence
Corcuera, José Manuel; Hedevang, Emil; Pakkanen, Mikko S.
2013-01-01
This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of the BSS model. We review the limit theory discussed......, which allow to obtain a valid central limit theorem for the critical region. Finally, we apply our statistical theory to turbulence data....
Shukla, Pragya
2004-01-01
We find that the statistics of levels undergoing metal-insulator transition in systems with multi-parametric Gaussian disorders and non-interacting electrons behaves in a way similar to that of the single parametric Brownian ensembles \\cite{dy}. The latter appear during a Poisson $\\to$ Wigner-Dyson transition, driven by a random perturbation. The analogy provides the analytical evidence for the single parameter scaling of the level-correlations in disordered systems as well as a tool to obtai...
Cheng, Mary Hongying; Coalson, Rob D; Tang, Pei
2010-11-24
Bacterial Gloeobacter violaceus pentameric ligand-gated ion channel (GLIC) is activated to cation permeation upon lowering the solution pH. Its function can be modulated by anesthetic halothane. In the present work, we integrate molecular dynamics (MD) and Brownian dynamics (BD) simulations to elucidate the ion conduction, charge selectivity, and halothane modulation mechanisms in GLIC, based on recently resolved X-ray crystal structures of the open-channel GLIC. MD calculations of the potential of mean force (PMF) for a Na(+) revealed two energy barriers in the extracellular domain (R109 and K38) and at the hydrophobic gate of transmembrane domain (I233), respectively. An energy well for Na(+) was near the intracellular entrance: the depth of this energy well was modulated strongly by the protonation state of E222. The energy barrier for Cl(-) was found to be 3-4 times higher than that for Na(+). Ion permeation characteristics were determined through BD simulations using a hybrid MD/continuum electrostatics approach to evaluate the energy profiles governing the ion movement. The resultant channel conductance and a near-zero permeability ratio (P(Cl)/P(Na)) were comparable to experimental data. On the basis of these calculations, we suggest that a ring of five E222 residues may act as an electrostatic gate. In addition, the hydrophobic gate region may play a role in charge selectivity due to a higher dehydration energy barrier for Cl(-) ions. The effect of halothane on the Na(+) PMF was also evaluated. Halothane was found to perturb salt bridges in GLIC that may be crucial for channel gating and open-channel stability, but had no significant impact on the single ion PMF profiles.
McMullan, G; Vinothkumar, K R; Henderson, R
2015-11-01
We have recorded dose-fractionated electron cryo-microscope images of thin films of pure flash-frozen amorphous ice and pre-irradiated amorphous carbon on a Falcon II direct electron detector using 300 keV electrons. We observe Thon rings [1] in both the power spectrum of the summed frames and the sum of power spectra from the individual frames. The Thon rings from amorphous carbon images are always more visible in the power spectrum of the summed frames whereas those of amorphous ice are more visible in the sum of power spectra from the individual frames. This difference indicates that while pre-irradiated carbon behaves like a solid during the exposure, amorphous ice behaves like a fluid with the individual water molecules undergoing beam-induced motion. Using the measured variation in the power spectra amplitude with number of electrons per image we deduce that water molecules are randomly displaced by a mean squared distance of ∼1.1 Å(2) for every incident 300 keV e(-)/Å(2). The induced motion leads to an optimal exposure with 300 keV electrons of 4.0 e(-)/Å(2) per image with which to observe Thon rings centred around the strong 3.7 Å scattering peak from amorphous ice. The beam-induced movement of the water molecules generates pseudo-Brownian motion of embedded macromolecules. The resulting blurring of single particle images contributes an additional term, on top of that from radiation damage, to the minimum achievable B-factor for macromolecular structure determination. Copyright © 2015 The Authors. Published by Elsevier B.V. All rights reserved.
Stochastic interactions of two Brownian hard spheres in the presence of depletants
Karzar-Jeddi, Mehdi; Fan, Tai-Hsi; Tuinier, Remco; Taniguchi, Takashi
2014-01-01
A quantitative analysis is presented for the stochastic interactions of a pair of Brownian hard spheres in non-adsorbing polymer solutions. The hard spheres are hypothetically trapped by optical tweezers and allowed for random motion near the trapped positions. The investigation focuses on the long-time correlated Brownian motion. The mobility tensor altered by the polymer depletion effect is computed by the boundary integral method, and the corresponding random displacement is determined by the fluctuation-dissipation theorem. From our computations it follows that the presence of depletion layers around the hard spheres has a significant effect on the hydrodynamic interactions and particle dynamics as compared to pure solvent and uniform polymer solution cases. The probability distribution functions of random walks of the two interacting hard spheres that are trapped clearly shift due to the polymer depletion effect. The results show that the reduction of the viscosity in the depletion layers around the spheres and the entropic force due to the overlapping of depletion zones have a significant influence on the correlated Brownian interactions
Dual-frequency magnetic particle imaging of the Brownian particle contribution
Viereck, Thilo, E-mail: t.viereck@tu-bs.de; Kuhlmann, Christian; Draack, Sebastian; Schilling, Meinhard; Ludwig, Frank
2017-04-01
Magnetic particle imaging (MPI) is an emerging medical imaging modality based on the non-linear response of magnetic nanoparticles to an exciting magnetic field. MPI has been recognized as a fast imaging technique with high spatial resolution in the mm range. For some applications of MPI, especially in the field of functional imaging, the determination of the particle mobility (Brownian rotation) is of great interest, as it enables binding detection in MPI. It also enables quantitative imaging in the presence of Brownian-dominated particles, which is otherwise implausible. Discrimination of different particle responses in MPI is possible via the joint reconstruction approach. In this contribution, we propose a dual-frequency acquisition scheme to enhance sensitivity and contrast in the detection of different particle mobilities compared to a standard single-frequency MPI protocol. The method takes advantage of the fact, that the magnetization response of the tracer is strongly frequency-dependent, i.e. for low excitation frequencies a stronger Brownian contribution is observed.
Brownian motion in complex fluids: venerable field and frontier of modern physics
Vizcarra-Rendon, A.; Medina-Noyola, M.; Ruiz-Estrada, H.; Arauz-Lara, J.L.
1989-01-01
This paper reviews the current status of our understanding of tracer-diffusion phenomena in colloidal suspensions. This is the most direct observation of the Brownian motion executed by labelled Brownian particles interacting with the rest of colloidal particles in a suspension. The fundamental description of this phenomenon constitutes today one of the most relevant problems in the process of understanding the dynamic properties of this important class of complex fluids, from the experimental and theoretical perspective of physical research. This paper describes the recent developments in the extension of the classical theory of Brownian motion and its application to the description of the effects of direct and hydrodynamic interactions among colloidal particles. As a result, a coherent pictured has emerged in which the agreement between theory and experiment from nature fields of physics. The moral of the paper is that the use of well established concepts as statistical physics, assisted by modern experimental techniques, are contributing to transform complex fluids into a more amialbe class of materials from the point of view of the physicist. (Author)
On-chip measurements of Brownian relaxation vs. concentration of 40nm magnetic beads
Østerberg, Frederik Westergaard; Rizzi, Giovanni; Hansen, Mikkel Fougt
2012-01-01
We present on-chip Brownian relaxation measurements on a logarithmic dilution series of 40 nm beads dispersed in water with bead concentrations between 16 mu g/ml and 4000 mu g/ml. The measurements are performed using a planar Hall effect bridge sensor at frequencies up to 1 MHz. No external fields...... are needed as the beads are magnetized by the field generated by the applied sensor bias current. We show that the Brownian relaxation frequency can be extracted from fitting the Cole-Cole model to measurements for bead concentrations of 64 mu g/ml or higher and that the measured dynamic magnetic response...... is proportional to the bead concentration. For bead concentrations higher than or equal to 500 mu g/ml, we extract a hydrodynamic diameter of 47(1) nm for the beads, which is close to the nominal bead size of 40 nm. Furthermore, we study the signal vs. bead concentration at a fixed frequency close to the Brownian...
Feller processes: the next generation in modeling. Brownian motion, Lévy processes and beyond.
Björn Böttcher
Full Text Available 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.
Theory of relativistic Brownian motion in the presence of electromagnetic field in (1+1) dimension
Mukhopadhyay, Annesh; Bandyopadhyay, M.; Bhamidipati, C.
2018-04-01
In this work, we consider the relativistic generalization of the theory of Brownian motion for the (1+1) dimensional case, which is again consistent with Einstein's special theory of relativity and reduces to standard Brownian motion in the Newtonian limit. All the generalizations are made considering Special theory of relativity into account. The particle under consideration has a velocity close to the speed of light and is a free Brownian particle suspended in a heat bath. With this generalization the velocity probability density functions are also obtained using Ito, Stratonovich and Hanggi-Klimontovich approach of pre-point, mid-point and post-point discretization rule. Subsequently, in our work, we have obtained the relativistic Langevin equations in the presence of an electromagnetic field. Finally, taking a special case of a constant vector potential and a constant electric field into account the Langevin equations are solved for the momentum and subsequently the velocity of the particle. Using a similar approach to the Fokker-planck equations of motion, the velocity distributions are also obtained in the presence of a constant vector potential and are plotted, which shows essential deviations from the one obtained without a potential. Our constant potential model can be realized in an optical potential.
Smoldyn on graphics processing units: massively parallel Brownian dynamics simulations.
Dematté, Lorenzo
2012-01-01
Space is a very important aspect in the simulation of biochemical systems; recently, the need for simulation algorithms able to cope with space is becoming more and more compelling. Complex and detailed models of biochemical systems need to deal with the movement of single molecules and particles, taking into consideration localized fluctuations, transportation phenomena, and diffusion. A common drawback of spatial models lies in their complexity: models can become very large, and their simulation could be time consuming, especially if we want to capture the systems behavior in a reliable way using stochastic methods in conjunction with a high spatial resolution. In order to deliver the promise done by systems biology to be able to understand a system as whole, we need to scale up the size of models we are able to simulate, moving from sequential to parallel simulation algorithms. In this paper, we analyze Smoldyn, a widely diffused algorithm for stochastic simulation of chemical reactions with spatial resolution and single molecule detail, and we propose an alternative, innovative implementation that exploits the parallelism of Graphics Processing Units (GPUs). The implementation executes the most computational demanding steps (computation of diffusion, unimolecular, and bimolecular reaction, as well as the most common cases of molecule-surface interaction) on the GPU, computing them in parallel on each molecule of the system. The implementation offers good speed-ups and real time, high quality graphics output
Fiore, Andrew M.; Swan, James W.
2018-01-01
Brownian Dynamics simulations are an important tool for modeling the dynamics of soft matter. However, accurate and rapid computations of the hydrodynamic interactions between suspended, microscopic components in a soft material are a significant computational challenge. Here, we present a new method for Brownian dynamics simulations of suspended colloidal scale particles such as colloids, polymers, surfactants, and proteins subject to a particular and important class of hydrodynamic constraints. The total computational cost of the algorithm is practically linear with the number of particles modeled and can be further optimized when the characteristic mass fractal dimension of the suspended particles is known. Specifically, we consider the so-called "stresslet" constraint for which suspended particles resist local deformation. This acts to produce a symmetric force dipole in the fluid and imparts rigidity to the particles. The presented method is an extension of the recently reported positively split formulation for Ewald summation of the Rotne-Prager-Yamakawa mobility tensor to higher order terms in the hydrodynamic scattering series accounting for force dipoles [A. M. Fiore et al., J. Chem. Phys. 146(12), 124116 (2017)]. The hydrodynamic mobility tensor, which is proportional to the covariance of particle Brownian displacements, is constructed as an Ewald sum in a novel way which guarantees that the real-space and wave-space contributions to the sum are independently symmetric and positive-definite for all possible particle configurations. This property of the Ewald sum is leveraged to rapidly sample the Brownian displacements from a superposition of statistically independent processes with the wave-space and real-space contributions as respective covariances. The cost of computing the Brownian displacements in this way is comparable to the cost of computing the deterministic displacements. The addition of a stresslet constraint to the over-damped particle
Dependence of Brownian and Néel relaxation times on magnetic field strength
Deissler, Robert J.; Wu, Yong; Martens, Michael A.
2014-01-01
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 step 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
... this page: //medlineplus.gov/ency/article/001548.htm Stereotypic movement disorder To use the sharing features on this page, please enable JavaScript. Stereotypic movement disorder is a condition in which a person makes ...
... work properly. There are many kinds of eye movement disorders. Two common ones are Strabismus - a disorder ... in "crossed eyes" or "walleye." Nystagmus - fast, uncontrollable movements of the eyes, sometimes called "dancing eyes" Some ...
Overview of Movement Disorders
... of Delirium Additional Content Medical News Overview of Movement Disorders By Hector A. Gonzalez-Usigli, MD, Professor ... Neurology, HE UMAE Centro Médico Nacional de Occidente; Movement Disorders Clinic, Neurology at IMSS Alberto Espay, MD, ...
Independence of Movement Preparation and Movement Initiation.
Haith, Adrian M; Pakpoor, Jina; Krakauer, John W
2016-03-09
Initiating a movement in response to a visual stimulus takes significantly longer than might be expected on the basis of neural transmission delays, but it is unclear why. In a visually guided reaching task, we forced human participants to move at lower-than-normal reaction times to test whether normal reaction times are strictly necessary for accurate movement. We found that participants were, in fact, capable of moving accurately ∼80 ms earlier than their reaction times would suggest. Reaction times thus include a seemingly unnecessary delay that accounts for approximately one-third of their duration. Close examination of participants' behavior in conventional reaction-time conditions revealed that they generated occasional, spontaneous errors in trials in which their reaction time was unusually short. The pattern of these errors could be well accounted for by a simple model in which the timing of movement initiation is independent of the timing of movement preparation. This independence provides an explanation for why reaction times are usually so sluggish: delaying the mean time of movement initiation relative to preparation reduces the risk that a movement will be initiated before it has been appropriately prepared. Our results suggest that preparation and initiation of movement are mechanistically independent and may have a distinct neural basis. The results also demonstrate that, even in strongly stimulus-driven tasks, presentation of a stimulus does not directly trigger a movement. Rather, the stimulus appears to trigger an internal decision whether to make a movement, reflecting a volitional rather than reactive mode of control. Copyright © 2016 the authors 0270-6474/16/363007-10$15.00/0.
Riisgaard Hansen, Thomas; Eriksson, Eva; Lykke-Olesen, Andreas
2005-01-01
In this paper we explore the space in which movement based interaction takes place. We have in several projects explored how fixed and mobile cameras can be used in movement based interaction and will shortly describe these projects. Based on our experience with working with movement......-based interaction we will briefly introduce and discuss how learning, mapping and multi-user interaction are important when designing movement based interaction....
Maelzer, H.
Calculation of temporal height changes for the determination of recent vertical crustal movements in northern, western, and southern Germany is described. Precise geodetic measurements and their analysis for the determination of recent crustal movements in north-eastern Iceland, western Venezuela, and central Peru are described. Determination of recent vertical crustal movements by leveling and gravity data; geodetic modeling of deformations and recent crustal movements; geodetic modeling of plate motions; and instrumental developments in geodetic measuring are discussed.
Jamison, Andrew
2006-01-01
The article examines the role of social movements in the development of scientific knowledge. Interactions between social movements and science in broad, historical terms are discussed. The relations between the new social movements of the 1960s and 1970s and changes in the contemporary scientific...
Bocquet, L.; Hansen, J.P.; Piasecki, J.
1997-01-01
In this work, we show that in any finite system, the binary friction tenser for two Brownian particles cannot be directly estimated from an evaluation of the microscopic Green Kubo formula, involving the time integral of force-force autocorrelation functions. This pitfall is associated with a subtle inversion of the thermodynamic and long-time limits and leads to spurious results for the estimates of the friction matrix based on molecular dynamics simulations. Starting from a careful analysis of the coupled Langevin equations for two interacting Brownian particles, we derive a method to circumvent these effects and extract the binary friction tenser from the correlation function matrix of the instantaneous forces exerted by the bath particles on the fixed Brownian particles, and from the relaxation of the total momentum of the bath in a finite system. The general methodology is applied to the case of two hard or soft Brownian spheres in a bath of light particles. Numerical estimates of the relevant correlation functions and of the resulting self and mutual components of the matrix of friction tensors are obtained by molecular dynamics simulations for various spacings between the Brownian particles
Quantum harmonic Brownian motion in a general environment: A modified phase-space approach
Yeh, L.
1993-01-01
After extensive investigations over three decades, the linear-coupling model and its equivalents have become the standard microscopic models for quantum harmonic Brownian motion, in which a harmonically bound Brownian particle is coupled to a quantum dissipative heat bath of general type modeled by infinitely many harmonic oscillators. The dynamics of these models have been studied by many authors using the quantum Langevin equation, the path-integral approach, quasi-probability distribution functions (e.g., the Wigner function), etc. However, the quantum Langevin equation is only applicable to some special problems, while other approaches all involve complicated calculations due to the inevitable reduction (i.e., contraction) operation for ignoring/eliminating the degrees of freedom of the heat bath. In this dissertation, the author proposes an improved methodology via a modified phase-space approach which employs the characteristic function (the symplectic Fourier transform of the Wigner function) as the representative of the density operator. This representative is claimed to be the most natural one for performing the reduction, not only because of its simplicity but also because of its manifestation of geometric meaning. Accordingly, it is particularly convenient for studying the time evolution of the Brownian particle with an arbitrary initial state. The power of this characteristic function is illuminated through a detailed study of several physically interesting problems, including the environment-induced damping of quantum interference, the exact quantum Fokker-Planck equations, and the relaxation of non-factorizable initial states. All derivations and calculations axe shown to be much simplified in comparison with other approaches. In addition to dynamical problems, a novel derivation of the fluctuation-dissipation theorem which is valid for all quantum linear systems is presented
Lee, Song Hi
2010-01-01
We presented a molecular dynamics (MD) simulation study of friction behavior between two very massive Brownian particles (BPs) oriented along the z axis with BP centers at -R 12 /2 and R 12 /2 in a Lennard-Jones solvent as a function of the inter-particle separation, R 12 . In order to fix the BPs in space an MD simulation method with the mass of the BP as 10 90 g/mol was employed in which the total momentum of the system was conserved. The cross friction coefficients of x- and y-components are nearly insensitive to R 12 but that of z-component varies with R 12 in good accord with the simple hydrodynamic approximation. On the other hand, the self-friction coefficients are estimated as a very small difference from the single particle friction coefficients, ξ 0 , at all inter-particle separations which agrees with the simple hydrodynamic approximation. Consequently ξ (-) xx is nearly independent of R 12 and equal to its asymptotic value of twice the single particle friction coefficient, and the other relative friction, ξ (-) zz , is in good agreement with the simple hydrodynamic approximation. Molecular theory of Brownian motion of a single heavy particle in a fluid had received a considerable attention in earlier years. After molecular dynamics (MD) simulation technique was utilized, this subject has been widely studied by a variety of MD simulation methods. The common issues here were about the long time behavior of the force and velocity autocorrelation functions, the system size dependent friction coefficient of a massive Brownian particle, and test of the Stokes-Einstein law
Diffusion limit of Lévy-Lorentz gas is Brownian motion
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.
Rigos, A.A.; Wilemski, G.
1992-01-01
The shear thinning behavior of a sterically stabilized nonaqueous colloidal suspension was investigated using nonequilibrium Brownian dynamics simulations of systems with 108 and 256 particles. At a volume fraction of 0.4, the suspension is thixotropic: it has a reversible shear thinning transition from a disordered state to an ordered, lamellar state with triangularly packed strings of particles. The time scale for the transition is set by the free particle diffusion constant. For the smaller system, the transition occurs gradually with increasing shear rate. For the larger system, the transition is sharp and discontinuous shear thinning is found. 34 refs., 9 figs., 1 tab
Stability Analysis and Application for Delayed Neural Networks Driven by Fractional Brownian Noise.
Zhou, Wuneng; Zhou, Xianghui; Yang, Jun; Zhou, Jun; Tong, Dongbing
2018-05-01
This paper deals with two types of the stability problem for the delayed neural networks driven by fractional Brownian noise (FBN). The existence and the uniqueness of the solution to the main system with respect to FBN are proved via fixed point theory. Based on Hilbert-Schmidt operator theory and analytic semigroup principle, the mild solution of the stochastic neural networks is obtained. By applying the stochastic analytic technique and some well-known inequalities, the asymptotic stability criteria and the exponential stability condition are established. Both numerical example and practical application for synchronization control of multiagent system are provided to illustrate the effectiveness and potential of the proposed techniques.
Ai Baoquan; Wang Liqiu; Liu Lianggang
2006-01-01
We study the thermodynamic features of a thermal motor driven by temperature differences, which consists of a Brownian particle moving in a sawtooth potential with an external load. The motor can work as a heat engine or a refrigerator under different conditions. The heat flow driven by both potential and kinetic energy is considered. The former is reversible when the engine works quasistatically and the latter is always irreversible. The efficiency of the heat engine (Coefficient Of Performance (COP) of a refrigerator) can never approach Carnot efficiency (COP)
Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion.
Sun, Jiao-Jiao; Zhou, Shengwu; Zhang, Yan; Han, Miao; Wang, Fei
2014-01-01
The pricing problem of lookback option with a fixed proportion of transaction costs is investigated when the underlying asset price follows a fractional Brownian motion process. Firstly, using Leland's hedging method a partial differential equation satisfied by the value of the lookback option is derived. Then we obtain its numerical solution by constructing a Crank-Nicolson format. Finally, the effectiveness of the proposed form is verified through a numerical example. Meanwhile, the impact of transaction cost rate and volatility on lookback option value is discussed.
A bimodal temom model for particle Brownian coagulation in the continuum-slip regime
He Qing
2016-01-01
Full Text Available In this paper, a bimodal Taylor-series expansion moment of method is proposed to deal with Brownian coagulation in the continuum-slip regime, where the non-linear terms in the Cunningham correction factor is approximated by Taylor-series expansion technology. The results show that both the number concentration and volume fraction decrease with time in the smaller mode due to the intra and inter coagulation, and the asymptotic behavior of the larger mode is as same as that in the continuum regime.
Revealing virtual processes of a quantum Brownian particle in phase space
Maniscalco, S
2005-01-01
The short-time dynamics of a quantum Brownian particle in a harmonic potential is studied in phase space. An exact non-Markovian analytic approach to calculate the time evolution of the Wigner function is presented. The dynamics of the Wigner function of an initially squeezed state is analysed. It is shown that virtual exchanges of energy between the particle and the reservoir, characterizing the non-Lindblad short-time dynamics where system-reservoir correlations are not negligible, show up in phase space
Dechant, A; Lutz, E; Kessler, D A; Barkai, E
2012-05-01
We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and the fluctuations of the time-averaged position of the particle for large but finite times. We characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential, and we support our predictions with extensive Langevin simulations. While the Boltzmann measure is used to obtain stationary correlation functions, we show how the non-normalizable infinite covariant density is related to the superaging behavior.
On Drift Parameter Estimation in Models with Fractional Brownian Motion by Discrete Observations
Yuliya Mishura
2014-06-01
Full Text Available We study a problem of an unknown drift parameter estimation in a stochastic differen- tial equation driven by fractional Brownian motion. We represent the likelihood ratio as a function of the observable process. The form of this representation is in general rather complicated. However, in the simplest case it can be simplified and we can discretize it to establish the a. s. convergence of the discretized version of maximum likelihood estimator to the true value of parameter. We also investigate a non-standard estimator of the drift parameter showing further its strong consistency.
Self-assembly of actin monomers into long filaments: Brownian Dynamics simulations
Shillcock, Julian C.
2009-01-01
Brownian dynamics simulations are used to study the dynamical process of self-assembly of actin monomers into long filaments containing up to 1000 actin protomers. In order to overcome the large separation of time scales between the diffusive motion of the freemonomers and the relatively slow....../detachment events. When a single filament is allowed to grow in a bath of constant concentration of free ADP-actin monomers, its growth rate increases linearly with the free monomer concentration in quantitative agreement with in vitro experiments. Theresults also show that the waiting time is governed by...
Singularity spectra of fractional Brownian motions as a multi-fractal
Kim, T.S.; Kim, S.
2004-01-01
Fractional Brownian motion acts as a random process with statistical self-similarity in time and self-affinity in shape. From these properties, the complicated patterns can be suitably represented by it with a minimal parameter and less memory. By considering its statistical property through the power spectrum density we can see that this process is not stationary, even though its differential motion is stationary. So in this paper, by taking the wavelet transform instead of Fourier transformation we investigate its multi-fractal spectrum as a multi-fractal model
Chain propagator, mass, and universality in polymer solutions from Brownian relativity
Mezzasalma, Stefano A.
2005-01-01
A Lagrangian theory for single chains in polymer solutions is addressed via a recent Brownian relativity. By employing generalized diffusive coordinates, statements of covariance and diffusivity invariance result into free particle Lagrangians, where mass turns out to rise as a universal spacetime property. It descends from lowering diffusivity (or curving spacetime), so identifying a mechanism which conceptually resemble those ruling macromolecular scaling laws. An extended chain propagator recovers the Gaussian end-to-end distribution and, in the limits of time-like and space-like orbits, the dualism for diffusive paths and polymer random-walks
Soskin, S.M.
1987-01-01
The authors examine Brownian motion in a square well with reflecting walls. An exact solution is obtained for the corresponding Einstein-Fokker-Planck equation, which is used to find the coordinate correlation function in explicit form. The correlation function, normalized to the square of the distance between the walls, typically exhibits a similarity property: its behavior as a function of time, friction, temperature, and wall separation reduces to a function of one simple combination of those four quantities. The limiting cases of low and high friction are investigated in detail, with explicit expressions being derived for the spectrum
Schmidt, Christian; Piel, Alexander
2015-10-01
The Brownian motion of a single particle in the plasma sheath is studied to separate the effect of stochastic heating by charge fluctuations from heating by collective effects. By measuring the particle velocities in the ballistic regime and by carefully determining the particle mass from the Epstein drag it is shown that for a pressure of 10 Pa, which is typical of many experiments, the proper kinetic temperature of the Brownian particle remains close to the gas temperature and rises only slightly with particle size. This weak effect is confirmed by a detailed model for charging and charge fluctuations in the sheath. A substantial temperature rise is found for decreasing pressure, which approximately shows the expected scaling with p-2. The system under study is an example for non-equilibrium Brownian motion under the influence of white noise without corresponding dissipation.
Craven, Galen T.; Nitzan, Abraham
2018-01-01
Statistical properties of Brownian motion that arise by analyzing, separately, trajectories over which the system energy increases (upside) or decreases (downside) with respect to a threshold energy level are derived. This selective analysis is applied to examine transport properties of a nonequilibrium Brownian process that is coupled to multiple thermal sources characterized by different temperatures. Distributions, moments, and correlation functions of a free particle that occur during upside and downside events are investigated for energy activation and energy relaxation processes and also for positive and negative energy fluctuations from the average energy. The presented results are sufficiently general and can be applied without modification to the standard Brownian motion. This article focuses on the mathematical basis of this selective analysis. In subsequent articles in this series, we apply this general formalism to processes in which heat transfer between thermal reservoirs is mediated by activated rate processes that take place in a system bridging them.
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.
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.
Østerberg, Frederik Westergaard; Dalslet, Bjarke Thomas; Snakenborg, Detlef
2010-01-01
using only the self-field arising from the bias current applied to the sensors as excitation field. We present measurements on a suspension of magnetic beads with a nominal diameter of 250 nm vs. temperature and find that the observations are consistent with the Cole-Cole model for Brownian relaxation...... with a constant hydrodynamic bead diameter when the temperature dependence of the viscosity of water is taken into account. These measurements demonstrate the feasibility of performing measurements of the Brownian relaxation response in a lab-on-a-chip system and constitute the first step towards an integrated...... biosensor based on the detection of the dynamic response of magnetic beads....
Ichikawa, Takashi; Yoneda, Yasuaki; Hanatsumi, Masaharu.
1997-01-01
The present invention provides a device suitable to accurate recognition for the moving state of reactor core fuels as an object to be monitored in a nuclear power plant. Namely, the device of the present invention prepares each of scheduled paths for the movement of the object to be monitored and executed moving paths along with the movement based on the information of the movement obtained from scheduled information for the movement of the reactor core fuels as a object to be monitored and the actual movement of the object to be monitored. The results of the preparation are outputted. As an output mode, (1) the results of preparation for each of the paths for movement and the results of the monitoring obtained by monitoring the state of the object to be monitored are jointed and outputted, (2) images showing each of the paths for the movement are formed, and the formed images are displayed on a screen, and (3) each of the moving paths is prepared as an image, and the image is displayed together with the image of the regions before and after the movement of the object to be monitored. In addition, obtained images of each of the paths for the movement and the monitored images obtained by monitoring the state of the object to be monitored are joined and displayed. (I.S.)
Classification of movement disorders.
Fahn, Stanley
2011-05-01
The classification of movement disorders has evolved. Even the terminology has shifted, from an anatomical one of extrapyramidal disorders to a phenomenological one of movement disorders. The history of how this shift came about is described. The history of both the definitions and the classifications of the various neurologic conditions is then reviewed. First is a review of movement disorders as a group; then, the evolving classifications for 3 of them--parkinsonism, dystonia, and tremor--are covered in detail. Copyright © 2011 Movement Disorder Society.
Sensation of Movement will discuss the role of sensation in the control of action, bodily self-recognition, and sense of agency. Sensing movement is dependent on a range of information received by the brain, from signalling in the peripheral sensory organs to the establishment of higher order goals....... This volume will question whether one type of information is more relevant for the ability to sense and control movements, and demonstrate the importance of integrating neuroscientific knowledge with philosophical perspectives, in order to arrive at new insights into how sensation of movement can be studied...
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.
Hyeon, Changbong; Hwang, Wonseok
2017-07-01
Using Brownian motion in periodic potentials V (x ) tilted by a force f , we provide physical insight into the thermodynamic uncertainty relation, a recently conjectured principle for statistical errors and irreversible heat dissipation in nonequilibrium steady states. According to the relation, nonequilibrium output generated from dissipative processes necessarily incurs an energetic cost or heat dissipation q , and in order to limit the output fluctuation within a relative uncertainty ɛ , at least 2 kBT /ɛ2 of heat must be dissipated. Our model shows that this bound is attained not only at near-equilibrium [f ≪V'(x ) ] but also at far-from-equilibrium [f ≫V'(x ) ] , more generally when the dissipated heat is normally distributed. Furthermore, the energetic cost is maximized near the critical force when the barrier separating the potential wells is about to vanish and the fluctuation of Brownian particles is maximized. These findings indicate that the deviation of heat distribution from Gaussianity gives rise to the inequality of the uncertainty relation, further clarifying the meaning of the uncertainty relation. Our derivation of the uncertainty relation also recognizes a bound of nonequilibrium fluctuations that the variance of dissipated heat (σq2) increases with its mean (μq), and it cannot be smaller than 2 kBT μq .
Molecular dynamics test of the Brownian description of Na+ motion in water
Wilson, M.A.; Pohorille, A.; Pratt, L.R.
1985-01-01
The autocorrelation function of the velocity of an infinitely dilute Na + ion in aqueous solution, and the autocorrelation function of the force exerted on a stationary Na + under the same conditions are evaluated by molecular dynamics calculations. The results are used to test the accuracy of Brownian motion assumptions which are basic to hydrodynamic models of ion dynamics in solution. The self-diffusion coefficient of the Na + ion predicted by Brownian motion theory is (0.65 +- 0.1) x 10 -5 cm 2 /s. This value is about 60% greater than the one obtained for the proper dynamics of the finite mass ion, (0.4 +- 0.1) x 10 -5 cm 2 /s. The numerically correct velocity autocorrelation function is nonexponential, and the autocorrelation of the force on the stationary ion does not decay faster than the ion velocity autocorrelation function. Motivated by previous hydrodynamic modeling of friction kernels, we examine the approximation in which the memory function for the velocity autocorrelation function is identified with the autocorrelation function of the force on the stationary ion. The overall agreement between this approximation for the velocity autocorrelation function and the numerically correct answer is quite good
Arai, Noriyoshi; Yasuoka, Kenji; Koishi, Takahiro; Ebisuzaki, Toshikazu; Zeng, Xiao Cheng
2013-06-12
The "asymmetric Brownian ratchet model", a variation of Feynman's ratchet and pawl system, is invoked to understand the kinesin walking behavior along a microtubule. The model system, consisting of a motor and a rail, can exhibit two distinct binding states, namely, the random Brownian state and the asymmetric potential state. When the system is transformed back and forth between the two states, the motor can be driven to "walk" in one direction. Previously, we suggested a fundamental mechanism, that is, bubble formation in a nanosized channel surrounded by hydrophobic atoms, to explain the transition between the two states. In this study, we propose a more realistic and viable switching method in our computer simulation of molecular motor walking. Specifically, we propose a thermosensitive polymer model with which the transition between the two states can be controlled by temperature pulses. Based on this new motor system, the stepping size and stepping time of the motor can be recorded. Remarkably, the "walking" behavior observed in the newly proposed model resembles that of the realistic motor protein. The bubble formation based motor not only can be highly efficient but also offers new insights into the physical mechanism of realistic biomolecule motors.
Palanisamy, Duraivelan; den Otter, Wouter K.
2018-05-01
We present an efficient general method to simulate in the Stokesian limit the coupled translational and rotational dynamics of arbitrarily shaped colloids subject to external potential forces and torques, linear flow fields, and Brownian motion. The colloid's surface is represented by a collection of spherical primary particles. The hydrodynamic interactions between these particles, here approximated at the Rotne-Prager-Yamakawa level, are evaluated only once to generate the body's (11 × 11) grand mobility matrix. The constancy of this matrix in the body frame, combined with the convenient properties of quaternions in rotational Brownian Dynamics, enables an efficient simulation of the body's motion. Simulations in quiescent fluids yield correct translational and rotational diffusion behaviour and sample Boltzmann's equilibrium distribution. Simulations of ellipsoids and spherical caps under shear, in the absence of thermal fluctuations, yield periodic orbits in excellent agreement with the theories by Jeffery and Dorrepaal. The time-varying stress tensors provide the Einstein coefficient and viscosity of dilute suspensions of these bodies.
The pricing of credit default swaps under a generalized mixed fractional Brownian motion
He, Xinjiang; Chen, Wenting
2014-06-01
In this paper, we consider the pricing of the CDS (credit default swap) under a GMFBM (generalized mixed fractional Brownian motion) model. As the name suggests, the GMFBM model is indeed a generalization of all the FBM (fractional Brownian motion) models used in the literature, and is proved to be able to effectively capture the long-range dependence of the stock returns. To develop the pricing mechanics of the CDS, we firstly derive a sufficient condition for the market modeled under the GMFBM to be arbitrage free. Then under the risk-neutral assumption, the CDS is fairly priced by investigating the two legs of the cash flow involved. The price we obtained involves elementary functions only, and can be easily implemented for practical purpose. Finally, based on numerical experiments, we analyze quantitatively the impacts of different parameters on the prices of the CDS. Interestingly, in comparison with all the other FBM models documented in the literature, the results produced from the GMFBM model are in a better agreement with those calculated from the classical Black-Scholes model.
Generalized Langevin Theory Of The Brownian Motion And The Dynamics Of Polymers In Solution
Tothova, J.; Lisy, V.
2015-01-01
The review deals with a generalization of the Rouse and Zimm bead-spring models of the dynamics of flexible polymers in dilute solutions. As distinct from these popular theories, the memory in the polymer motion is taken into account. The memory naturally arises as a consequence of the fluid and bead inertia within the linearized Navier-Stokes hydrodynamics. We begin with a generalization of the classical theory of the Brownian motion, which forms the basis of any theory of the polymer dynamics. The random force driving the Brownian particles is not the white one as in the Langevin theory, but “colored”, i.e., statistically correlated in time, and the friction force on the particles depends on the history of their motion. An efficient method of solving the resulting generalized Langevin equations is presented and applied to the solution of the equations of motion of polymer beads. The memory effects lead to several peculiarities in the time correlation functions used to describe the dynamics of polymer chains. So, the mean square displacement of the polymer coils contains algebraic long-time tails and at short times it is ballistic. It is shown how these features reveal in the experimentally observable quantities, such as the dynamic structure factors of the scattering or the viscosity of polymer solutions. A phenomenological theory is also presented that describes the dependence of these quantities on the polymer concentration in solution. (author)
Dettmer, Simon L.; Keyser, Ulrich F.; Pagliara, Stefano [Cavendish Laboratory, University of Cambridge, 19 J J Thomson Avenue, Cambridge CB3 0HE (United Kingdom)
2014-02-15
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 these 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.
Correlational approach to study interactions between dust Brownian particles in a plasma
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.
Brownian motion, old and new, and Irwin's role in my academic life
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.
Solano, Carlos J F; Pothula, Karunakar R; Prajapati, Jigneshkumar D; De Biase, Pablo M; Noskov, Sergei Yu; Kleinekathöfer, Ulrich
2016-05-10
All-atom molecular dynamics simulations have a long history of applications studying ion and substrate permeation across biological and artificial pores. While offering unprecedented insights into the underpinning transport processes, MD simulations are limited in time-scales and ability to simulate physiological membrane potentials or asymmetric salt solutions and require substantial computational power. While several approaches to circumvent all of these limitations were developed, Brownian dynamics simulations remain an attractive option to the field. The main limitation, however, is an apparent lack of protein flexibility important for the accurate description of permeation events. In the present contribution, we report an extension of the Brownian dynamics scheme which includes conformational dynamics. To achieve this goal, the dynamics of amino-acid residues was incorporated into the many-body potential of mean force and into the Langevin equations of motion. The developed software solution, called BROMOCEA, was applied to ion transport through OmpC as a test case. Compared to fully atomistic simulations, the results show a clear improvement in the ratio of permeating anions and cations. The present tests strongly indicate that pore flexibility can enhance permeation properties which will become even more important in future applications to substrate translocation.
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.
Exploring pedestrian movement patterns
Orellana, D.A.
2012-01-01
The main objective of this thesis is to develop an approach for exploring, analysing and interpreting movement patterns of pedestrians interacting with the environment. This objective is broken down in sub-objectives related to four research questions. A case study of the movement of visitors in a
Fenichel, Emily, Ed.
1994-01-01
This newsletter theme issue focuses on dance, play, and movement therapy for infants and toddlers with disabilities. Individual articles are: "Join My Dance: The Unique Movement Style of Each Infant and Toddler Can Invite Communication, Expression and Intervention" (Suzi Tortora); "Dynamic Play Therapy: An Integrated Expressive Arts Approach to…
Koopman, Hubertus F.J.M.
2010-01-01
The part of (bio)mechanics that studies the interaction of forces on the human skeletal system and its effect on the resulting movement is called rigid body dynamics. Some basic concepts are presented: A mathematical formulation to describe human movement and how this relates on the mechanical loads
Generalized Pareto for Pattern-Oriented Random Walk Modelling of Organisms' Movements.
Sophie Bertrand
Full Text Available How organisms move and disperse is crucial to understand how population dynamics relates to the spatial heterogeneity of the environment. Random walk (RW models are typical tools to describe movement patterns. Whether Lévy or alternative RW better describes forager movements is keenly debated. We get around this issue using the Generalized Pareto Distribution (GPD. GPD includes as specific cases Normal, exponential and power law distributions, which underlie Brownian, Poisson-like and Lévy walks respectively. Whereas previous studies typically confronted a limited set of candidate models, GPD lets the most likely RW model emerge from the data. We illustrate the wide applicability of the method using GPS-tracked seabird foraging movements and fishing vessel movements tracked by Vessel Monitoring System (VMS, both collected in the Peruvian pelagic ecosystem. The two parameters from the fitted GPD, a scale and a shape parameter, provide a synoptic characterization of the observed movement in terms of characteristic scale and diffusive property. They reveal and quantify the variability, among species and individuals, of the spatial strategies selected by predators foraging on a common prey field. The GPD parameters constitute relevant metrics for (1 providing a synthetic and pattern-oriented description of movement, (2 using top predators as ecosystem indicators and (3 studying the variability of spatial behaviour among species or among individuals with different personalities.
Spontaneous reverse movement of mRNA-bound tRNA through the ribosome.
Konevega, Andrey L; Fischer, Niels; Semenkov, Yuri P; Stark, Holger; Wintermeyer, Wolfgang; Rodnina, Marina V
2007-04-01
During the translocation step of protein synthesis, a complex of two transfer RNAs bound to messenger RNA (tRNA-mRNA) moves through the ribosome. The reaction is promoted by an elongation factor, called EF-G in bacteria, which, powered by GTP hydrolysis, induces an open, unlocked conformation of the ribosome that allows for spontaneous tRNA-mRNA movement. Here we show that, in the absence of EF-G, there is spontaneous backward movement, or retrotranslocation, of two tRNAs bound to mRNA. Retrotranslocation is driven by the gain in affinity when a cognate E-site tRNA moves into the P site, which compensates the affinity loss accompanying the movement of peptidyl-tRNA from the P to the A site. These results lend support to the diffusion model of tRNA movement during translocation. In the cell, tRNA movement is biased in the forward direction by EF-G, which acts as a Brownian ratchet and prevents backward movement.
Generalized Pareto for Pattern-Oriented Random Walk Modelling of Organisms' Movements.
Bertrand, Sophie; Joo, Rocío; Fablet, Ronan
2015-01-01
How organisms move and disperse is crucial to understand how population dynamics relates to the spatial heterogeneity of the environment. Random walk (RW) models are typical tools to describe movement patterns. Whether Lévy or alternative RW better describes forager movements is keenly debated. We get around this issue using the Generalized Pareto Distribution (GPD). GPD includes as specific cases Normal, exponential and power law distributions, which underlie Brownian, Poisson-like and Lévy walks respectively. Whereas previous studies typically confronted a limited set of candidate models, GPD lets the most likely RW model emerge from the data. We illustrate the wide applicability of the method using GPS-tracked seabird foraging movements and fishing vessel movements tracked by Vessel Monitoring System (VMS), both collected in the Peruvian pelagic ecosystem. The two parameters from the fitted GPD, a scale and a shape parameter, provide a synoptic characterization of the observed movement in terms of characteristic scale and diffusive property. They reveal and quantify the variability, among species and individuals, of the spatial strategies selected by predators foraging on a common prey field. The GPD parameters constitute relevant metrics for (1) providing a synthetic and pattern-oriented description of movement, (2) using top predators as ecosystem indicators and (3) studying the variability of spatial behaviour among species or among individuals with different personalities.
Fractal analysis of lateral movement in biomembranes.
Gmachowski, Lech
2018-04-01
Lateral movement of a molecule in a biomembrane containing small compartments (0.23-μm diameter) and large ones (0.75 μm) is analyzed using a fractal description of its walk. The early time dependence of the mean square displacement varies from linear due to the contribution of ballistic motion. In small compartments, walking molecules do not have sufficient time or space to develop an asymptotic relation and the diffusion coefficient deduced from the experimental records is lower than that measured without restrictions. The model makes it possible to deduce the molecule step parameters, namely the step length and time, from data concerning confined and unrestricted diffusion coefficients. This is also possible using experimental results for sub-diffusive transport. The transition from normal to anomalous diffusion does not affect the molecule step parameters. The experimental literature data on molecular trajectories recorded at a high time resolution appear to confirm the modeled value of the mean free path length of DOPE for Brownian and anomalous diffusion. Although the step length and time give the proper values of diffusion coefficient, the DOPE speed calculated as their quotient is several orders of magnitude lower than the thermal speed. This is interpreted as a result of intermolecular interactions, as confirmed by lateral diffusion of other molecules in different membranes. The molecule step parameters are then utilized to analyze the problem of multiple visits in small compartments. The modeling of the diffusion exponent results in a smooth transition to normal diffusion on entering a large compartment, as observed in experiments.
Islamic Puritanism Movements in Indonesia as Transnational Movements
Benny Baskara
2017-04-01
Full Text Available Islamic puritanism movements are the movements compelling to return to the teachings of Quran and Sunnah, as the pure teachings of Islam and abandon even abolish other teachings outside the teachings of Quran and Sunnah. The movements of Islamic puritanism can be considered as transnational movements because they spread their teachings and ideologies, create organizations, networks, and provide financial supports across nations. This paper describes Islamic puritanism movements in Indonesia and their transnational connections. Some Islamic puritanism movements in Indonesia can be considered as part of Islamic transnational movements, in which most of the movements are centered in the Middle East. In Indonesia, Islamic puritanism movements firstly appeared in the beginning of the nineteenth century, called Padri movement in West Sumatra. It was then continued to the emergence of Islamic organizations in the twentieth century. Recently, Islamic puritanism movements in Indonesia mostly take form as Salafism-Wahabism movements.
Cullen, Pauline
2015-01-01
Ireland’s long history of patriarchy is matched by the ongoing evolution of its women’s movements. Today’s complex, transnational feminism finds its precursor in the colonial era. The first wave of the Irish women’s movement dates from the mid-19th century, with the franchise secured for women in 1918 while still under British colonial rule. First-wave feminists played a role in the nationalist movement, but their demands were sidelined later, during the construction of a conserva...
Nasev, Lence
2012-01-01
Rhythm is one of the fundamental elements without which music would not exist. In plays with singing, a child learns to synchronize its movements with the rhythm of music from a very early age. The skill of movement plays a major role in the learning of music and thus deserves an important place in the school curriculum. In this paper, an overview is made of the most important music pedagogues who introduced movement, and at the same time perceived its importance in learning musical conte...
Double-temperature ratchet model and current reversal of coupled Brownian motors
Li, Chen-Pu; Chen, Hong-Bin; Zheng, Zhi-Gang
2017-12-01
On the basis of the transport features and experimental phenomena observed in studies of molecular motors, we propose a double-temperature ratchet model of coupled motors to reveal the dynamical mechanism of cooperative transport of motors with two heads, where the interactions and asynchrony between two motor heads are taken into account. We investigate the collective unidirectional transport of coupled system and find that the direction of motion can be reversed under certain conditions. Reverse motion can be achieved by modulating the coupling strength, coupling free length, and asymmetric coefficient of the periodic potential, which is understood in terms of the effective potential theory. The dependence of the directed current on various parameters is studied systematically. Directed transport of coupled Brownian motors can be manipulated and optimized by adjusting the pulsation period or the phase shift of the pulsation temperature.
On the joint residence time of N independent two-dimensional Brownian motions
Benichou, O; Coppey, M; Klafter, J; Moreau, M; Oshanin, G
2003-01-01
We study the behaviour of several joint residence times of N independent Brownian particles in a disc of radius R in two dimensions. We consider: (i) the time T N (t) spent by all N particles simultaneously in the disc within the time interval [0, t], (ii) the time T (m) N (t) which at least m out of N particles spend together in the disc within the time interval [0, t], and (iii) the time T-tilde (m) N (t) which exactly m out of N particles spend together in the disc within the time interval [0, t]. We obtain very simple exact expressions for the expectations of these three residence times in the limit t → ∞
Ni Xiaohui; Jiang Zhiqiang; Zhou Weixing
2009-01-01
The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent α is a linear function of the Hurst index H of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from three Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the α∼H linear relationship.
Inference on the hurst parameter and the variance of diffusions driven by fractional Brownian motion
Berzin, Corinne; León, José R
2014-01-01
This book is devoted to a number of stochastic models that display scale invariance. It primarily focuses on three issues: probabilistic properties, statistical estimation and simulation of the processes considered. It will be of interest to probability specialists, who will find here an uncomplicated presentation of statistics tools, and to those statisticians who wants to tackle the most recent theories in probability in order to develop Central Limit Theorems in this context; both groups will also benefit from the section on simulation. Algorithms are described in great detail, with a focus on procedures that is not usually found in mathematical treatises. The models studied are fractional Brownian motions and processes that derive from them through stochastic differential equations. Concerning the proofs of the limit theorems, the “Fourth Moment Theorem” is systematically used, as it produces rapid and helpful proofs that can serve as models for the future. Readers will also find elegant and new proof...
Li, Feng-guo; Ai, Bao-quan
2014-04-01
Transport of overdamped Brownian particles in a periodic hydrodynamical channel is investigated in the presence of an asymmetric unbiased force, a transverse gravitational force, and a pressure-driven flow. With the help of the generalized Fick-Jacobs approach, we obtain an analytical expression for the directed current and the generalized potential of mean force. It is found that, when the transverse gravitational force is larger than a certain value, the current is suppressed. Moreover, when the temporal asymmetry parameter of the unbiased force is negative, the current is always negative. However, when the temporal asymmetry parameter is positive, the transverse gravitational force and the pressure drop not only determine the direction of the current but also affect its amplitude. In particular, the competition between the asymmetric unbiased force and the pressure drop can result in multiple current reversals.
Gayo Willy
2016-01-01
Full Text Available Philippine Stock Exchange Composite Index (PSEi is the main stock index of the Philippine Stock Exchange (PSE. PSEi is computed using a weighted mean of the top 30 publicly traded companies in the Philippines, called component stocks. It provides a single value by which the performance of the Philippine stock market is measured. Unfortunately, these weights, which may vary for every trading day, are not disclosed by the PSE. In this paper, we propose a model of forecasting the PSEi by estimating the weights based on historical data and forecasting each component stock using Monte Carlo simulation based on a Geometric Brownian Motion (GBM assumption. The model performance is evaluated and its forecast compared is with the results using a direct GBM forecast of PSEi over different forecast periods. Results showed that the forecasts using WGBM will yield smaller error compared to direct GBM forecast of PSEi.
Brownian motion properties of optoelectronic random bit generators based on laser chaos.
Li, Pu; Yi, Xiaogang; Liu, Xianglian; Wang, Yuncai; Wang, Yongge
2016-07-11
The nondeterministic property of the optoelectronic random bit generator (RBG) based on laser chaos are experimentally analyzed from two aspects of the central limit theorem and law of iterated logarithm. The random bits are extracted from an optical feedback chaotic laser diode using a multi-bit extraction technique in the electrical domain. Our experimental results demonstrate that the generated random bits have no statistical distance from the Brownian motion, besides that they can pass the state-of-the-art industry-benchmark statistical test suite (NIST SP800-22). All of them give a mathematically provable evidence that the ultrafast random bit generator based on laser chaos can be used as a nondeterministic random bit source.
Estimating the Counterparty Risk Exposure by Using the Brownian Motion Local Time
Bonollo Michele
2017-06-01
Full Text Available In recent years, the counterparty credit risk measure, namely the default risk in over-the-counter (OTC derivatives contracts, has received great attention by banking regulators, specifically within the frameworks of Basel II and Basel III. More explicitly, to obtain the related risk figures, one is first obliged to compute intermediate output functionals related to the mark-to-market position at a given time no exceeding a positive and finite time horizon. The latter implies an enormous amount of computational effort is needed, with related highly time consuming procedures to be carried out, turning out into significant costs. To overcome the latter issue, we propose a smart exploitation of the properties of the (local time spent by the Brownian motion close to a given value.
Simulating Stock Prices Using Geometric Brownian Motion: Evidence from Australian Companies
Krishna Reddy
2016-09-01
Full Text Available This study uses the geometric Brownian motion (GBM method to simulate stock price paths, and tests whether the simulated stock prices align with actual stock returns. The sample for this study was based on the large listed Australian companies listed on the S&P/ASX 50 Index. Daily stock price data was obtained from the Thomson One database over the period 1 January 2013 to 31 December 2014. The findings are slightly encouraging as results show that over all time horizons the chances of a stock price simulated using GBM moving in the same direction as real stock prices was a little greater than 50 percent. However, the results improved slightly when portfolios were formed.
Maximum distance between the Leader and the Laggard for three Brownian walkers
Majumdar, Satya N; Bray, Alan J
2010-01-01
We consider three independent Brownian walkers moving on a line. The process terminates when the leftmost walker (the 'Leader') meets either of the other two walkers. For arbitrary values of the diffusion constants D 1 (the Leader), D 2 and D 3 of the three walkers, we compute the probability distribution P(m|y 2 , y 3 ) of the maximum distance m between the Leader and the current rightmost particle (the 'Laggard') during the process, where y 2 and y 3 are the initial distances between the Leader and the other two walkers. The result has, for large m, the form P(m|y 2 , y 3 ) ∼ A(y 2 , y 3 )m −δ , where δ = (2π − θ)/(π − θ) and θ= cos -1 (D 1 /√((D 1 +D 2 )(D 1 +D 3 ))). The amplitude A(y 2 , y 3 ) is also determined exactly
Scaling laws for fractional Brownian motion with power-law clock
O'Malley, Daniel; Cushman, John H; Johnson, Graham
2011-01-01
We study the mean first passage time (MFPT) for fractional Brownian motion (fBm) in a finite interval with absorbing boundaries at each end. Analytical arguments are used to suggest a simple scaling law for the MFPT and numerical experiments are performed to verify its accuracy. The same approach is used to derive a scaling law for fBm with a power-law clock (fBm-plc). The MFPT scaling laws are employed to develop scaling laws for the finite-size Lyapunov exponent (FSLE) of fBm and fBm-plc. We apply these results to diffusion of a large polymer in a region with absorbing boundaries. (letter)
Autocorrelated process control: Geometric Brownian Motion approach versus Box-Jenkins approach
Salleh, R. M.; Zawawi, N. I.; Gan, Z. F.; Nor, M. E.
2018-04-01
Existing of autocorrelation will bring a significant effect on the performance and accuracy of process control if the problem does not handle carefully. When dealing with autocorrelated process, Box-Jenkins method will be preferred because of the popularity. However, the computation of Box-Jenkins method is too complicated and challenging which cause of time-consuming. Therefore, an alternative method which known as Geometric Brownian Motion (GBM) is introduced to monitor the autocorrelated process. One real case of furnace temperature data is conducted to compare the performance of Box-Jenkins and GBM methods in monitoring autocorrelation process. Both methods give the same results in terms of model accuracy and monitoring process control. Yet, GBM is superior compared to Box-Jenkins method due to its simplicity and practically with shorter computational time.
Nucleation theory in Langevin's approach and lifetime of a Brownian particle in potential wells.
Alekseechkin, N V
2008-07-14
The multivariable theory of nucleation suggested by Alekseechkin [J. Chem. Phys. 124, 124512 (2006)] is further developed in the context of Langevin's approach. The use of this approach essentially enhances the capability of the nucleation theory, because it makes possible to consider the cases of small friction which are not taken into account by the classical Zel'dovich-Frenkel theory and its multivariable extensions. The procedure for the phenomenological determination of the nucleation parameters is described. Using the similarity of the Kramers model with that of nucleation, the lifetime of a Brownian particle in potential wells in various dimensionalities is calculated with the help of the expression for the steady state nucleation rate.
Density profiles of granular gases studied by molecular dynamics and Brownian bridges
Peñuñuri, F.; Montoya, J. A.; Carvente, O.
2018-02-01
Despite the inherent frictional forces and dissipative collisions, confined granular matter can be regarded as a system in a stationary state if we inject energy continuously. Under these conditions, both the density and the granular temperature are, in general, non-monotonic variables along the height of the container. In consequence, an analytical description of a granular system is hard to conceive. Here, by using molecular dynamics simulations, we measure the packing fraction profiles for a vertically vibrating three-dimensional granular system in several gaseous-like stationary states. We show that by using the Brownian bridge concept, the determined packing fraction profiles can be reproduced accurately and give a complete description of the distribution of the particles inside the simulation box.
Duan, Zhao-Wen; Li, Wei; Xie, Ping; Dou, Shuo-Xing; Wang, Peng-Ye
2010-04-01
Using Brownian dynamics simulation, we studied the effect of histone modifications on conformations of an array of nucleosomes in a segment of chromatin. The simulation demonstrated that the segment of chromatin shows the dynamic behaviour that its conformation can switch between a state with nearly all of the histones being wrapped by DNA and a state with nearly all of the histones being unwrapped by DNA, thus involving the “cross-talking" interactions among the histones. Each state can stay for a sufficiently long time. These conformational states are essential for gene expression or gene silence. The simulation also shows that these conformational states can be inherited by the daughter DNAs during DNA replication, giving a theoretical explanation of the epigenetic phenomenon.
Zhao-Wen, Duan; Wei, Li; Ping, Xie; Shuo-Xing, Dou; Peng-Ye, Wang
2010-01-01
Using Brownian dynamics simulation, we studied the effect of histone modifications on conformations of an array of nucleosomes in a segment of chromatin. The simulation demonstrated that the segment of chromatin shows the dynamic behaviour that its conformation can switch between a state with nearly all of the histones being wrapped by DNA and a state with nearly all of the histones being unwrapped by DNA, thus involving the “cross-talking” interactions among the histones. Each state can stay for a sufficiently long time. These conformational states are essential for gene expression or gene silence. The simulation also shows that these conformational states can be inherited by the daughter DNAs during DNA replication, giving a theoretical explanation of the epigenetic phenomenon. (cross-disciplinary physics and related areas of science and technology)
Localization and Ballistic Diffusion for the Tempered Fractional Brownian-Langevin Motion
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.
T. Turiv
2015-06-01
Full Text Available As recently reported [Turiv T. et al., Science, 2013, Vol. 342, 1351], fluctuations in the orientation of the liquid crystal (LC director can transfer momentum from the LC to a colloid, such that the diffusion of the colloid becomes anomalous on a short time scale. Using video microscopy and single particle tracking, we investigate random thermal motion of colloidal particles in a nematic liquid crystal for the time scales shorter than the expected time of director fluctuations. At long times, compared to the characteristic time of the nematic director relaxation we observe typical anisotropic Brownian motion with the mean square displacement (MSD linear in time τ and inversly proportional to the effective viscosity of the nematic medium. At shorter times, however, the dynamics is markedly nonlinear with MSD growing more slowly (subdiffusion or faster (superdiffusion than τ. These results are discussed in the context of coupling of colloidal particle's dynamics to the director fluctuation dynamics.
Special relativity and the Karhunen-Loeve expansion of Brownian motion
Maccone, C.
1987-01-01
The connection between special relativity and the theory of the time-rescaled Gaussian stochastic processes is brought to light. It is given the general expression of the Karhunen-Loewe expansion for the Brownian motion whose variable is the proper time. The relevant eigenfunctions are proved to be Bessel functions, and their stability is discussed. The eigenvalues are shown to be the zeros of certain linear combinations of the Bessel functions and their partials. The energy distribution of such a class of processes is investigated, and it is given explicit formulae for both its mean value and variance. Finally it is studied in detail the Karhumen-Loeve expansion for a case of relativistic decelerated motion whose analysis is feasible in closed form
Li, Feng-guo; Ai, Bao-quan
2014-01-01
Transport of overdamped Brownian particles in a periodic hydrodynamical channel is investigated in the presence of an asymmetric unbiased force, a transverse gravitational force, and a pressure-driven flow. With the help of the generalized Fick–Jacobs approach, we obtain an analytical expression for the directed current and the generalized potential of mean force. It is found that, when the transverse gravitational force is larger than a certain value, the current is suppressed. Moreover, when the temporal asymmetry parameter of the unbiased force is negative, the current is always negative. However, when the temporal asymmetry parameter is positive, the transverse gravitational force and the pressure drop not only determine the direction of the current but also affect its amplitude. In particular, the competition between the asymmetric unbiased force and the pressure drop can result in multiple current reversals. (paper)
Lorenzo Marcucci
Full Text Available Muscular force generation in response to external stimuli is the result of thermally fluctuating, cyclical interactions between myosin and actin, which together form the actomyosin complex. Normally, these fluctuations are modelled using transition rate functions that are based on muscle fiber behaviour, in a phenomenological fashion. However, such a basis reduces the predictive power of these models. As an alternative, we propose a model which uses direct single molecule observations of actomyosin fluctuations reported in the literature. We precisely estimate the actomyosin potential bias and use diffusion theory to obtain a brownian ratchet model that reproduces the complete cross-bridge cycle. The model is validated by simulating several macroscopic experimental conditions, while its interpretation is compatible with two different force-generating scenarios.
Bhattacharyya, Debankur; Paul, Shibashis; Ghosh, Shyamolina; Ray, Deb Shankar
2018-04-01
We consider the Brownian motion of a collection of particles each with an additional degree of freedom. The degree of freedom of a particle (or, in general, a molecule) can assume distinct values corresponding to certain states or conformations. The time evolution of the additional degree of freedom of a particle is guided by those of its neighbors as well as the temperature of the system. We show that the local averaging over these degrees of freedom results in emergence of a collective order in the dynamics in the form of selection or dominance of one of the isomers leading to a symmetry-broken state. Our statistical model captures the basic features of homochirality, e.g., autocatalysis and chiral inhibition.
Ergodicity breaking and ageing of underdamped Brownian dynamics with quenched disorder
Guo, Wei; Li, Yong; Song, Wen-Hua; Du, Lu-Chun
2018-03-01
The dynamics of an underdamped Brownian particle moving in one-dimensional quenched disorder under the action of an external force is investigated. Within the tailored parameter regime, the transiently anomalous diffusion and ergodicity breaking, spanning several orders of magnitude in time, have been obtained. The ageing nature of the system weakens as the dissipation of the system increases for other given parameters. Its origin is ascribed to the highly local heterogeneity of the disorder. Two kinds of approximations (in the stationary state), respectively, for large bias and large damping are derived. These results may be helpful in further understanding the nontrivial response of nonlinear dynamics, and also have potential applications to experiments and activities of biological processes.
The path integral formulation of fractional Brownian motion for the general Hurst exponent
Calvo, I; Sanchez, R
2008-01-01
In 1995, Sebastian (1995 J. Phys. A: Math. Gen. 28 4305) gave a path integral computation of the propagator of subdiffusive fractional Brownian motion (fBm), i.e. fBm with a Hurst or self-similarity exponent H element of (0, 1/2). The extension of Sebastian's calculation to superdiffusion, H element of (1/2, 1], becomes however quite involved due to the appearance of additional boundary conditions on fractional derivatives of the path. In this communication, we address the construction of the path integral representation in a different fashion, which allows us to treat both subdiffusion and superdiffusion on an equal footing. The derivation of the propagator of fBm for the general Hurst exponent is then performed in a neat and unified way. (fast track communication)
On the use of reverse Brownian motion to accelerate hybrid simulations
Bakarji, Joseph; Tartakovsky, Daniel M., E-mail: tartakovsky@stanford.edu
2017-04-01
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 strategies 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.
The French ecological movement
Sansen, Bernard
1977-01-01
The analysis of the ecological Movement in France is presented: its organisation, its topics, its position with respect to the main political trends. The accent is put in particular on the antinuclear contestation [fr
Miao, Linling; Young, Charles D.; Sing, Charles E.
2017-07-01
Brownian Dynamics (BD) simulations are a standard tool for understanding the dynamics of polymers in and out of equilibrium. Quantitative comparison can be made to rheological measurements of dilute polymer solutions, as well as direct visual observations of fluorescently labeled DNA. The primary computational challenge with BD is the expensive calculation of hydrodynamic interactions (HI), which are necessary to capture physically realistic dynamics. The full HI calculation, performed via a Cholesky decomposition every time step, scales with the length of the polymer as O(N3). This limits the calculation to a few hundred simulated particles. A number of approximations in the literature can lower this scaling to O(N2 - N2.25), and explicit solvent methods scale as O(N); however both incur a significant constant per-time step computational cost. Despite this progress, there remains a need for new or alternative methods of calculating hydrodynamic interactions; large polymer chains or semidilute polymer solutions remain computationally expensive. In this paper, we introduce an alternative method for calculating approximate hydrodynamic interactions. Our method relies on an iterative scheme to establish self-consistency between a hydrodynamic matrix that is averaged over simulation and the hydrodynamic matrix used to run the simulation. Comparison to standard BD simulation and polymer theory results demonstrates that this method quantitatively captures both equilibrium and steady-state dynamics after only a few iterations. The use of an averaged hydrodynamic matrix allows the computationally expensive Brownian noise calculation to be performed infrequently, so that it is no longer the bottleneck of the simulation calculations. We also investigate limitations of this conformational averaging approach in ring polymers.
Phillips, Carolyn L.; Anderson, Joshua A.; Glotzer, Sharon C.
2011-01-01
Highlights: → Molecular Dynamics codes implemented on GPUs have achieved two-order of magnitude computational accelerations. → Brownian Dynamics and Dissipative Particle Dynamics simulations require a large number of random numbers per time step. → We introduce a method for generating small batches of pseudorandom numbers distributed over many threads of calculations. → With this method, Dissipative Particle Dynamics is implemented on a GPU device without requiring thread-to-thread communication. - Abstract: Brownian Dynamics (BD), also known as Langevin Dynamics, and Dissipative Particle Dynamics (DPD) are implicit solvent methods commonly used in models of soft matter and biomolecular systems. The interaction of the numerous solvent particles with larger particles is coarse-grained as a Langevin thermostat is applied to individual particles or to particle pairs. The Langevin thermostat requires a pseudo-random number generator (PRNG) to generate the stochastic force applied to each particle or pair of neighboring particles during each time step in the integration of Newton's equations of motion. In a Single-Instruction-Multiple-Thread (SIMT) GPU parallel computing environment, small batches of random numbers must be generated over thousands of threads and millions of kernel calls. In this communication we introduce a one-PRNG-per-kernel-call-per-thread scheme, in which a micro-stream of pseudorandom numbers is generated in each thread and kernel call. These high quality, statistically robust micro-streams require no global memory for state storage, are more computationally efficient than other PRNG schemes in memory-bound kernels, and uniquely enable the DPD simulation method without requiring communication between threads.
Tang Hong; Lin Jianzhong
2013-01-01
The moment method can be used to determine the time evolution of particle size distribution due to Brownian coagulation based on the general dynamic equation (GDE). But the function form of the initial particle size distribution must be determined beforehand for the moment method. If the assumed function type of the initial particle size distribution has an obvious deviation from the true particle population, the evolution of particle size distribution may be different from the real evolution tendency. Thus, a simple and general method is proposed based on the moment method. In this method, the Johnson's S B function is chosen as a general distribution function to fit the initial distributions including the log normal (L-N), Rosin–Rammler (R-R), normal (N-N) and gamma distribution functions, respectively. Meanwhile, using the modified beta function to fit the L-N, R-R, N-N and gamma functions is also conducted as a comparison in order to present the advantage of the Johnson's S B function as the general distribution function. And then, the time evolution of particle size distributions using the Johnson's S B function as the initial distribution can be obtained by several lower order moment equations of the Johnson's S B function in conjunction with the GDE during the Brownian coagulation process. Simulation experiments indicate that fairly reasonable results of the time evolution of particle size distribution can be obtained with this proposed method in the free molecule regime, transition regime and continuum plus near continuum regime, respectively, at the early time stage of evolution. The Johnson's S B function has the ability of describing the early time evolution of different initial particle size distributions. (paper)
Radiom, Milad; Ducker, William; Robbins, Brian; Paul, Mark
2015-01-01
The hydrodynamic interaction of two closely spaced micron-scale spheres undergoing Brownian motion was measured as a function of their separation. Each sphere was attached to the distal end of a different atomic force microscopy cantilever, placing each sphere in a stiff one-dimensional potential (0.08 Nm −1 ) with a high frequency of thermal oscillations (resonance at 4 kHz). As a result, the sphere’s inertial and restoring forces were significant when compared to the force due to viscous drag. We explored interparticle gap regions where there was overlap between the two Stokes layers surrounding each sphere. Our experimental measurements are the first of their kind in this parameter regime. The high frequency of oscillation of the spheres means that an analysis of the fluid dynamics would include the effects of fluid inertia, as described by the unsteady Stokes equation. However, we find that, for interparticle separations less than twice the thickness of the wake of the unsteady viscous boundary layer (the Stokes layer), the hydrodynamic interaction between the Brownian particles is well-approximated by analytical expressions that neglect the inertia of the fluid. This is because elevated frictional forces at narrow gaps dominate fluid inertial effects. The significance is that interparticle collisions and concentrated suspensions at this condition can be modeled without the need to incorporate fluid inertia. We suggest a way to predict when fluid inertial effects can be ignored by including the gap-width dependence into the frequency number. We also show that low frequency number analysis can be used to determine the microrheology of mixtures at interfaces
Movement and personality development
Aida M. Aylamazyan
2017-06-01
Full Text Available The paper discusses the role of the movement in the process of shaping the personality, its importance as a mechanism for personality development is considered. The issue of the movement has always occupied a central place in Russian psychology. However, subsequently the movement began to be considered primarily as an executive action in human life. The role of movement in personality development can vary depending on the level it occupies in the hierarchical structure of activity, and also on the type of movement, its character, and the way it is constructed. Under certain conditions, the movement can express the attitude of the subject to the surrounding world and people. Many foreign and Russian psychologists point to a special place of the postural tonic component of the motor movement, the posture in personal regulation. The posture reflects his/her personal attitudes, the system of relationships, and, above all, the emotional attitude or emotional assessment of the current situation, the interest in the actions performed. Mastering the tonic level of motor management is based on the emotional regulation, so the ability to regulate one’s own pose is an important stage in the personality development. Posture tonic regulation of motor movements in humans reveals a qualitatively different character than in animals, this being due to the person’s facing the task of mastering his’her posture, arbitrary retention of the body in one or another position. Maintaining a vertical posture requires constant activity at an arbitrary and involuntary level of mental regulation. Mastering the posture of an unstable equilibrium presupposes the emergence of the «I» and is the last stage of the development. The way a person solves the motor task of maintaining the vertical position of the body reflects his/her specific personal strategy or attitude.
The result of the synergy between four doctoral projects and an advanced MA-level course on Bronze Age Europe, this integrated assemblage of articles represents a variety of different subjects united by a single theme: movement. Ranging from theoretical discussion of the various responses to and ...... period of European prehistory. In so doing, the text not only addresses transmission and reception, but also the conceptualization of mobility within a world which was literally Rooted in Movement....
Paraneoplastic autoimmune movement disorders.
Lim, Thien Thien
2017-11-01
To provide an overview of paraneoplastic autoimmune disorders presenting with various movement disorders. The spectrum of paraneoplastic autoimmune disorders has been expanding with the discovery of new antibodies against cell surface and intracellular antigens. Many of these paraneoplastic autoimmune disorders manifest as a form of movement disorder. With the discovery of new neuronal antibodies, an increasing number of idiopathic or neurodegenerative movement disorders are now being reclassified as immune-mediated movement disorders. These include anti-N-methyl-d-aspartate receptor (NMDAR) encephalitis which may present with orolingual facial dyskinesia and stereotyped movements, CRMP-5 IgG presenting with chorea, anti-Yo paraneoplastic cerebellar degeneration presenting with ataxia, anti-VGKC complex (Caspr2 antibodies) neuromyotonia, opsoclonus-myoclonus-ataxia syndrome, and muscle rigidity and episodic spasms (amphiphysin, glutamic acid decarboxylase, glycine receptor, GABA(A)-receptor associated protein antibodies) in stiff-person syndrome. Movement disorders may be a presentation for paraneoplastic autoimmune disorders. Recognition of these disorders and their common phenomenology is important because it may lead to the discovery of an occult malignancy. Copyright © 2017 Elsevier Ltd. All rights reserved.
Xiang, Xin
2017-12-11
Nuclear movement within a cell occurs in a variety of eukaryotic organisms including yeasts and filamentous fungi. Fungal molecular genetic studies identified the minus-end-directed microtubule motor cytoplasmic dynein as a critical protein for nuclear movement or orientation of the mitotic spindle contained in the nucleus. Studies in the budding yeast first indicated that dynein anchored at the cortex via its anchoring protein Num1 exerts pulling force on an astral microtubule to orient the anaphase spindle across the mother-daughter axis before nuclear division. Prior to anaphase, myosin V interacts with the plus end of an astral microtubule via Kar9-Bim1/EB1 and pulls the plus end along the actin cables to move the nucleus/spindle close to the bud neck. In addition, pushing or pulling forces generated from cortex-linked polymerization or depolymerization of microtubules drive nuclear movements in yeasts and possibly also in filamentous fungi. In filamentous fungi, multiple nuclei within a hyphal segment undergo dynein-dependent back-and-forth movements and their positioning is also influenced by cytoplasmic streaming toward the hyphal tip. In addition, nuclear movement occurs at various stages of fungal development and fungal infection of plant tissues. This review discusses our current understanding on the mechanisms of nuclear movement in fungal organisms, the importance of nuclear positioning and the regulatory strategies that ensure the proper positioning of nucleus/spindle. Published by Elsevier Ltd.
Antiglobalization movements and their critics
Corry, Olaf
2012-01-01
inequity, organize transnationally, and maintain a critical stance toward significant aspects of the state system. For this reason, many supporters favor other terms such as alterglobalization movement, global justice movement , or simply the movement of movements . Critics accuse the movements...... of ideological incoherence, self-interested protectionism, and illiberal and undemocratic political methods, and point to Western liberal elite dominance within the movements. The debate has ...
[Scenes in movement. Movement disorders on film].
Olivares Romero, J
2010-03-01
There are publications in which various neurological diseases are analysed on film. However, no references have been found on movement disorders in this medium. A total of 104 documents were collected and reviewed using the internet movie data base (IMDb). The majority were associated with dystonia, Parkinson's and tics, were American commercial productions, and the most common genre was drama. The cinema usually depicts old men with developed Parkinson's disease. However, motor complications only appear in 19% and non-motor symptoms in 14%. The image of dystonia is generally that of a young man, with disabling dystonia secondary to childhood cerebral palsy. Tics appear associated with Tourette's syndrome, with the excessive use of obscene expressions and with very few references to other important aspects of this syndrome, such as mood and behavioural changes. The majority of tremors portrayed on film are associated with Parkinsonism and are not pathological. Myoclonus appears anecdotically and is normally symptomatic. Parkinson's disease is the type of movement disorder that the cinema portrays with greater neurological honesty and in a more dignified manner.
Uldam, Julie; McCurdy, Patrick
2013-01-01
The research method of participant observation has long been used by scholars interested in the motivations, dynamics, tactics and strategies of social movements from a movement perspective. Despite participant observation being a common research method, there have been very few efforts to bring...... together this literature, which has often been spread across disciplines. This makes it difficult to identify the various challenges (and their interrelation) facing participant observers. Consequently, this article first reviews how participant observation roles have been conceptualised in general...... and then draws specific links to how the method has been used in the study of activism and social movements. In doing so, this article brings together key academic debates on participant observation, which have been considered separately, such as insider/outsider and overt/covert, but not previously been brought...
Couton, Philippe; López, José Julián
2009-10-01
Opposition to utopianism on ontological and political grounds has seemingly relegated it to a potentially dangerous form of antiquated idealism. This conclusion is based on a restrictive view of utopia as excessively ordered panoptic discursive constructions. This overlooks the fact that, from its inception, movement has been central to the utopian tradition. The power of utopianism indeed resides in its ability to instantiate the tension between movement and place that has marked social transformations in the modern era. This tension continues in contemporary discussions of movement-based social processes, particularly international migration and related identity formations, such as open borders transnationalism and cosmopolitanism. Understood as such, utopia remains an ongoing and powerful, albeit problematic instrument of social and political imagination.
Haddad, Zoubida; Abu-Nada, Eiyad; Oztop, Hakan F.; Mataoui, Amina
2012-01-01
Natural convection heat transfer and fluid flow of CuO-Water nano-fluids is studied using the Rayleigh-Benard problem. A two component non-homogenous equilibrium model is used for the nano-fluid that incorporates the effects of Brownian motion and thermophoresis. Variable thermal conductivity and variable viscosity are taken into account in this work. Finite volume method is used to solve governing equations. Results are presented by streamlines, isotherms, nano-particle distribution, local and mean Nusselt numbers and nano-particle profiles at top and bottom side. Comparison of two cases as absence of Brownian and thermophoresis effects and presence of Brownian and thermophoresis effects showed that higher heat transfer is formed with the presence of Brownian and thermophoresis effect. In general, by considering the role of thermophoresis and Brownian motion, an enhancement in heat transfer is observed at any volume fraction of nano-particles. However, the enhancement is more pronounced at low volume fraction of nano-particles and the heat transfer decreases by increasing nano-particle volume fraction. On the other hand, by neglecting the role of thermophoresis and Brownian motion, deterioration in heat transfer is observed and this deterioration elevates by increasing the volume fraction of nano-particles. (authors)
Jennifer Fortuna
2017-10-01
Full Text Available Johnson Simon, an artist based in West Palm Beach, FL, provided the cover art for the Fall 2017 edition of The Open Journal of Occupational Therapy (OJOT. “Dancing in Motion” is a 36” x 60” painting made from acrylic on canvas. Johnson always wanted to become a dancer. He was born with cerebral palsy, and therefore physical limitations make it difficult for Johnson to coordinate his body movements. Through use of vibrant colors and bold strokes, Johnson’s expressionist paintings evoke movement and motion. Occupational therapy helped Johnson discover his artistic abilities. Painting empowered him to move without limitations
On-chip measurements of Brownian relaxation of magnetic beads with diameters from 10 nm to 250 nm
Østerberg, Frederik Westergaard; Rizzi, Giovanni; Hansen, Mikkel Fougt
2013-01-01
We demonstrate the use of planar Hall effect magnetoresistive sensors for AC susceptibility measurements of magnetic beads with frequencies ranging from DC to 1 MHz. This wide frequency range allows for measuring Brownian relaxation of magnetic beads with diameters ranging from 10 nm to 250 nm....... Brownian relaxation is measured for six different magnetic bead types and their hydrodynamic diameters are determined. The hydrodynamic diameters are found to be within 40% of the nominal bead diameters. We discuss the applicability of the different bead types for volume-based biosensing with respect...... to sedimentation, magnetic trapping, and signal per bead. Among the investigated beads, we conclude that the beads with a nominal diameter of 80 nm are best suited for future on-chip volume-based biosensing experiments using planar Hall effect sensors....
Shilong Li
2018-03-01
Full Text Available In this paper, we introduce a class of stochastic interest model driven by a compoundPoisson process and a Brownian motion, in which the jumping times of force of interest obeyscompound Poisson process and the continuous tiny fluctuations are described by Brownian motion, andthe adjustment in each jump of interest force is assumed to be random. Based on the proposed interestmodel, we discuss the expected discounted function, the validity of the model and actuarial presentvalues of life annuities and life insurances under different parameters and distribution settings. Ournumerical results show actuarial values could be sensitive to the parameters and distribution settings,which shows the importance of introducing this kind interest model.
Ilalan, Deniz
2016-01-01
Highlights: • Hausdorff dimension of the Elliott Wave trajectories is computed. • Linkage between Elliott Wave principle and fractional Brownian motion is proposed. • Log-normality of stock returns is discussed from a fractal point of view. - Abstract: This paper examines one of the vital technical analysis indicators known as the Elliott wave principle. Since these waves have a fractal nature with patterns that are not exact, we first determine the dimension of them. Our second aim is to find a linkage between Elliott wave principle and fractional Brownian motion via comparing their Hausdorff dimensions. Thirdly, we consider the Nikkei 225 index during Japan asset price bubble, which is a perfect example of an Elliott wave.
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.
Godrèche, Claude
2017-05-01
The probability distribution of the longest interval between two zeros of a simple random walk starting and ending at the origin, and of its continuum limit, the Brownian bridge, was analysed in the past by Rosén and Wendel, then extended by the latter to stable processes. We recover and extend these results using simple concepts of renewal theory, which allows to revisit past and recent works of the physics literature.
Godrèche, Claude
2017-01-01
The probability distribution of the longest interval between two zeros of a simple random walk starting and ending at the origin, and of its continuum limit, the Brownian bridge, was analysed in the past by Rosén and Wendel, then extended by the latter to stable processes. We recover and extend these results using simple concepts of renewal theory, which allows to revisit past and recent works of the physics literature. (paper)
Dubina, Sean Hyun, E-mail: sdubin2@uic.edu; Wedgewood, Lewis Edward, E-mail: wedge@uic.edu [Department of Chemical Engineering, University of Illinois at Chicago, 810 S. Clinton St. (MC 110), Chicago, Illinois 60607-4408 (United States)
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 by 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.
Hiotelis, Nicos [1st Lyceum of Athens, Ipitou 15, Plaka, 10557, Athens (Greece); Popolo, Antonino Del, E-mail: adelpopolo@oact.inaf.it, E-mail: hiotelis@ipta.demokritos.gr [Dipartimento di Fisica e Astronomia, University Of Catania, Viale Andrea Doria 6, 95125, Catania (Italy)
2017-03-01
We construct an integral equation for the first crossing distributions for fractional Brownian motion in the case of a constant barrier and we present an exact analytical solution. Additionally we present first crossing distributions derived by simulating paths from fractional Brownian motion. We compare the results of the analytical solutions with both those of simulations and those of some approximated solutions which have been used in the literature. Finally, we present multiplicity functions for dark matter structures resulting from our analytical approach and we compare with those resulting from N-body simulations. We show that the results of analytical solutions are in good agreement with those of path simulations but differ significantly from those derived from approximated solutions. Additionally, multiplicity functions derived from fractional Brownian motion are poor fits of the those which result from N-body simulations. We also present comparisons with other models which are exist in the literature and we discuss different ways of improving the agreement between analytical results and N-body simulations.
Tang Hong; Lin Jianzhong
2011-01-01
The extinction coefficient of atmospheric aerosol particles influences the earth’s radiation balance directly or indirectly, and it can be determined by the scattering and absorption characteristics of aerosol particles. The problem of estimating the change of extinction coefficient due to time evolution of bimodal particle size distribution is studied, and two improved methods for calculating the Brownian coagulation coefficient and the condensation growth rate are proposed, respectively. Through the improved method based on Otto kernel, the Brownian coagulation coefficient can be expressed simply in powers of particle volume for the entire particle size regime based on the fitted polynomials of the mean enhancement function. Meanwhile, the improved method based on Fuchs–Sutugin kernel is developed to obtain the condensation growth rate for the entire particle size regime. And then, the change of the overall extinction coefficient of bimodal distributions undergoing Brownian coagulation and condensation can be estimated comprehensively for the entire particle size regime. Simulation experiments indicate that the extinction coefficients obtained with the improved methods coincide fairly well with the true values, which provide a simple, reliable, and general method to estimate the change of extinction coefficient for the entire particle size regime during the bimodal particle dynamic processes.
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.
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.
Lin Bihong; Chen Jincan
2009-01-01
It is shown that a microscopic system consisting of Brownian particles moving in a spatially asymmetric but periodic potential (ratchet) and contacting with the alternating hot and cold reservoirs along space coordinate and an external force applying on the particles may work as a refrigerator. In order to clarify the underlying physical pictures of the system, the heat flows via both the potential energy and the kinetic energy of the particles are considered simultaneously. Based on an Arrhenius' factor describing the forward and backward particle currents, expressions for some important performance parameters of the refrigerator, such as the coefficient of performance, cooling rate and power input, are derived analytically. The maximum coefficient of performance and cooling rate are numerically calculated for some given parameters. The influence of the main parameters such as the external force, barrier height of the potential, asymmetry of the potential and temperature ratio of the heat reservoirs on the performance of the Brownian refrigerator is discussed. The optimum criteria of some characteristic parameters are given. It is found that the Brownian refrigerator may be controlled to operate in different regions through the choice of several parameters
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.
H. R. Ehteram
2016-01-01
Full Text Available In this paper the effect of using various models for conductivity and viscosity considering Brownian motion of nanoparticles is investigated. This study is numerically conducted inside a cavity full of Water-Al2O3 nanofluid at the case of mixed convection heat transfer. The effect of some parameters such as the nanoparticle volume fraction, Rayleigh, Richardson and Reynolds numbers has been examined. The governing equations with specified boundary conditions has been solved using finite volume method. A computer code has been prepared for this purpose. The results are presented in form of stream functions, isotherms, Nusselt number and the flow power with and without the Brownian motion taken into consideration. The results show that for all the applied models the stream functions and isotherm have approximately same patterns and no considerable difference has been observed. In all the studied models when considering the Brownian motion, the average Nusselt number is higher than not taking this effect into account. The models of Koo-Kleinstreuer and Li-Kleinstreuer give almost same values for the maximum stream function and average Nusselt number. It is also true about the models of Vajjha-Das and Xiao et al.
Dubina, Sean Hyun; Wedgewood, Lewis Edward
2016-01-01
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 by 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.
A movement ecology paradigm for unifying organismal movement research.
Nathan, Ran; Getz, Wayne M; Revilla, Eloy; Holyoak, Marcel; Kadmon, Ronen; Saltz, David; Smouse, Peter E
2008-12-09
Movement of individual organisms is fundamental to life, quilting our planet in a rich tapestry of phenomena with diverse implications for ecosystems and humans. Movement research is both plentiful and insightful, and recent methodological advances facilitate obtaining a detailed view of individual movement. Yet, we lack a general unifying paradigm, derived from first principles, which can place movement studies within a common context and advance the development of a mature scientific discipline. This introductory article to the Movement Ecology Special Feature proposes a paradigm that integrates conceptual, theoretical, methodological, and empirical frameworks for studying movement of all organisms, from microbes to trees to elephants. We introduce a conceptual framework depicting the interplay among four basic mechanistic components of organismal movement: the internal state (why move?), motion (how to move?), and navigation (when and where to move?) capacities of the individual and the external factors affecting movement. We demonstrate how the proposed framework aids the study of various taxa and movement types; promotes the formulation of hypotheses about movement; and complements existing biomechanical, cognitive, random, and optimality paradigms of movement. The proposed framework integrates eclectic research on movement into a structured paradigm and aims at providing a basis for hypothesis generation and a vehicle facilitating the understanding of the causes, mechanisms, and spatiotemporal patterns of movement and their role in various ecological and evolutionary processes. "Now we must consider in general the common reason for moving with any movement whatever." (Aristotle, De Motu Animalium, 4th century B.C.).
Rationality in Human Movement.
O'Brien, Megan K; Ahmed, Alaa A
2016-01-01
It long has been appreciated that humans behave irrationally in economic decisions under risk: they fail to objectively consider uncertainty, costs, and rewards and instead exhibit risk-seeking or risk-averse behavior. We hypothesize that poor estimates of motor variability (influenced by motor task) and distorted probability weighting (influenced by relevant emotional processes) contribute to characteristic irrationality in human movement decisions.
Ayres, Phil
2015-01-01
This contribution concerns itself with the design and realisation of architectures that operate with material dynamics. It presents this concern as a counter to the consideration of movement in architecture as something conceptualised from the position of the observer. The contribution draws upon...
Jensen, Søren Kjær; Moser, T.
2003-01-01
In: Children and adolescents in movement - perspectives and ideas. The Danish Ministry of Culture, pages 150 - 162. 2003 Short description: the article debunks a lot of the myths surrounding body and learning, and replace them with a vision about another kind of learning. The aim is to reintroduce...
Rasmussen, Jacob
2010-01-01
Like many other African countries, Kenya has a large and growing youth population. Some of the youths are mobilized into militant and political networks; one of these is the Mungiki movement. The article explores Mungiki’s combination of politics, religion and Kikuyu traditions. Using the examples...
Hansen, Hanne Foss; Rieper, Olaf
2009-01-01
The evidence movement and the idea of systematic reviews, defined as summaries of the results of already existing evaluation and research projects, have gained considerable support in recent years as many international as well as national evidence-producing organizations have been established...
Managing Movement as Partnership
Kimbrell, Sinead
2011-01-01
The associate director of education at Hubbard Street Dance Chicago recounts her learning and teaching through managing the Movement as Partnership program. Included are detailed descriptions of encounters with teachers and students as they create choreography reflective of their inquiry into integrating dance and literacy arts curriculum in the…
Carmichael, Karla D.
This paper's premise is that music, movement, and poetry are unique and creative methods to be used by the counselor in working with both children and adults. Through these media, the counselor generates material for the counseling session that may not be available through more traditional "talk therapies." The choice of music as a counseling…
Carina Assuncao
2018-01-01
Full Text Available Today, the juxtaposition between physical bodies and the gameworld is ever more fluid. Virtual Reality headsets are available at game stores with more AAA games being created for the format. The release of the Nintendo Switch and its dynamic JoyCon controllers reintroduce haptic movement based controls. Pokémon GO’s augmented reality took gamers outdoors and has encouraged the Harry Potter franchise to follow in its mobile footsteps. Each development encourages a step further into the digital world. At the same time, the movement of bodies always has political dimensions. We live in a world where walls seem like solutions to the movement of bodies, while the mere meeting of bodies elsewhere – for sex, marriage and other reasons – is still forbidden by many states’ rules. Games and game-like interfaces have shown the ability to bend those rules, and to sometimes project other worlds and rule systems over our world in order to make bodies move and meet. For this special issue on ‘Body Movements’, Press Start invited authors to focus on embodiment, body movements, political bodies, community bodies, virtual bodies, physical bodies, feminine, masculine, trans- bodies, agency or its lack, and anything else in between. The response to this invitation was variegated, and provocative, as outlined here.
Morocco's February 20 Movement
2018-02-20
Feb 20, 2018 ... Council for the Development of Social Science Research in Africa, 2017 ... revolted several times, namely in big cities like Casablanca, Marrakech or .... region in order to take advantage of their experience and acquire a regional ..... Undoubtedly, with social networking, the dynamics of protest movements.
Rivallan, Armel
2012-01-01
Leading an architectural project means accompanying the movement which it induces within the teams. Between questioning, uncertainty and fear, the organisational changes inherent to the new facility must be subject to constructive and ongoing exchanges. Ethics, safety and training are revised and the unit projects are sometimes modified.
Kravchenko-Balasha, Nataly; Shin, Young Shik; Sutherland, Alex; Levine, R D; Heath, James R
2016-05-17
Controlling cell migration is important in tissue engineering and medicine. Cell motility depends on factors such as nutrient concentration gradients and soluble factor signaling. In particular, cell-cell signaling can depend on cell-cell separation distance and can influence cellular arrangements in bulk cultures. Here, we seek a physical-based approach, which identifies a potential governed by cell-cell signaling that induces a directed cell-cell motion. A single-cell barcode chip (SCBC) was used to experimentally interrogate secreted proteins in hundreds of isolated glioblastoma brain cancer cell pairs and to monitor their relative motions over time. We used these trajectories to identify a range of cell-cell separation distances where the signaling was most stable. We then used a thermodynamics-motivated analysis of secreted protein levels to characterize free-energy changes for different cell-cell distances. We show that glioblastoma cell-cell movement can be described as Brownian motion biased by cell-cell potential. To demonstrate that the free-energy potential as determined by the signaling is the driver of motion, we inhibited two proteins most involved in maintaining the free-energy gradient. Following inhibition, cell pairs showed an essentially random Brownian motion, similar to the case for untreated, isolated single cells.
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.
Chen Song
Full Text Available The macroscopic Nernst-Planck (NP theory has often been used for predicting ion channel currents in recent years, but the validity of this theory at the microscopic scale has not been tested. In this study we systematically tested the ability of the NP theory to accurately predict channel currents by combining and comparing the results with those of Brownian dynamics (BD simulations. To thoroughly test the theory in a range of situations, calculations were made in a series of simplified cylindrical channels with radii ranging from 3 to 15 Å, in a more complex 'catenary' channel, and in a realistic model of the mechanosensitive channel MscS. The extensive tests indicate that the NP equation is applicable in narrow ion channels provided that accurate concentrations and potentials can be input as the currents obtained from the combination of BD and NP match well with those obtained directly from BD simulations, although some discrepancies are seen when the ion concentrations are not radially uniform. This finding opens a door to utilising the results of microscopic simulations in continuum theory, something that is likely to be useful in the investigation of a range of biophysical and nano-scale applications and should stimulate further studies in this direction.
Song, Chen; Corry, Ben
2011-01-01
The macroscopic Nernst-Planck (NP) theory has often been used for predicting ion channel currents in recent years, but the validity of this theory at the microscopic scale has not been tested. In this study we systematically tested the ability of the NP theory to accurately predict channel currents by combining and comparing the results with those of Brownian dynamics (BD) simulations. To thoroughly test the theory in a range of situations, calculations were made in a series of simplified cylindrical channels with radii ranging from 3 to 15 Å, in a more complex 'catenary' channel, and in a realistic model of the mechanosensitive channel MscS. The extensive tests indicate that the NP equation is applicable in narrow ion channels provided that accurate concentrations and potentials can be input as the currents obtained from the combination of BD and NP match well with those obtained directly from BD simulations, although some discrepancies are seen when the ion concentrations are not radially uniform. This finding opens a door to utilising the results of microscopic simulations in continuum theory, something that is likely to be useful in the investigation of a range of biophysical and nano-scale applications and should stimulate further studies in this direction.
Correlation Properties of (Discrete Fractional Gaussian Noise and Fractional Brownian Motion
Didier Delignières
2015-01-01
Full Text Available The fractional Gaussian noise/fractional Brownian motion framework (fGn/fBm has been widely used for modeling and interpreting physiological and behavioral data. The concept of 1/f noise, reflecting a kind of optimal complexity in the underlying systems, is of central interest in this approach. It is generally considered that fGn and fBm represent a continuum, punctuated by the boundary of “ideal” 1/f noise. In the present paper, we focus on the correlation properties of discrete-time versions of these processes (dfGn and dfBm. We especially derive a new analytical expression of the autocorrelation function (ACF of dfBm. We analyze the limit behavior of dfGn and dfBm when they approach their upper and lower limits, respectively. We show that, as H approaches 1, the ACF of dfGn tends towards 1 at all lags, suggesting that dfGn series tend towards straight line. Conversely, as H approaches 0, the ACF of dfBm tends towards 0 at all lags, suggesting that dfBm series tend towards white noise. These results reveal a severe breakdown of correlation properties around the 1/f boundary and challenge the idea of a smooth transition between dfGn and dfBm processes. We discuss the implications of these findings for the application of the dfGn/dfBm model to experimental series, in terms of theoretical interpretation and modeling.
Phase synchronization for two Brownian motors with bistable coupling on a ratchet
Mateos, Jose L.; Alatriste, F.R.
2010-01-01
Graphical abstract: We study phase synchronization for a walker with two Brownian motors with bistable coupling on a ratchet and show a connection between synchronization and optimal transport. - Abstract: We study phase synchronization for a walker on a ratchet potential. The walker consist of two particles coupled by a bistable potential that allow the interchange of the order of the particles while moving through a one-dimensional asymmetric periodic ratchet potential. We consider the deterministic and the stochastic dynamics of the center of mass of the walker in a tilted ratchet potential with an external periodic forcing, in the overdamped case. The ratchet potential has to be tilted in order to obtain a rotator or self-sustained nonlinear oscillator in the absence of external periodic forcing. This oscillator has an intrinsic frequency that can be entrained with the frequency of the external driving. We introduced a linear phase through a set of discrete time events and the associated average frequency, and show that this frequency can be synchronized with the frequency of the external driving. In this way, we can properly characterize the phenomenon of synchronization through Arnold tongues and show that the local maxima in the average velocity of the center of mass of the walker, both in the deterministic case and in the presence of noise, correspond to the borders of these Arnold tongues. In this way, we established a connection between optimal transport in ratchets and the phenomenon of phase synchronization.
Rate laws of the self-induced aggregation kinetics of Brownian particles
Mondal, Shrabani; Sen, Monoj Kumar; Baura, Alendu; Bag, Bidhan Chandra
2016-03-01
In this paper we have studied the self induced aggregation kinetics of Brownian particles in the presence of both multiplicative and additive noises. In addition to the drift due to the self aggregation process, the environment may induce a drift term in the presence of a multiplicative noise. Then there would be an interplay between the two drift terms. It may account qualitatively the appearance of the different laws of aggregation process. At low strength of white multiplicative noise, the cluster number decreases as a Gaussian function of time. If the noise strength becomes appreciably large then the variation of cluster number with time is fitted well by the mono exponentially decaying function of time. For additive noise driven case, the decrease of cluster number can be described by the power law. But in case of multiplicative colored driven process, cluster number decays multi exponentially. However, we have explored how the rate constant (in the mono exponentially cluster number decaying case) depends on strength of interference of the noises and their intensity. We have also explored how the structure factor at long time depends on the strength of the cross correlation (CC) between the additive and the multiplicative noises.
Brenner, H.
1991-01-01
Macrotransport processes (generalized Taylor dispersion phenomena) constitute coarse-grained descriptions of comparable convective diffusive-reactive microtransport processes, the latter supposed governed by microscale linear constitutive equations and boundary conditions, but characterized by spatially nonuniform phenomenological coefficients. Following a brief review of existing applications of the theory, the author focuses - by way of background information-upon the original (and now classical) Taylor - Aris dispersion problem, involving the combined convective and molecular diffusive transport of a point-size Brownian solute molecule (tracer) suspended in a Poiseuille solvent flow within a circular tube. A series of elementary generalizations of this prototype problem to chromatographic-like solute transport processes in tubes is used to illustrate some novel statistical-physical features. These examples emphasize the fact that a solute molecule may, on average, move axially down the tube at a different mean velocity (either larger or smaller) than that of a solvent molecule. Moreover, this solute molecule may suffer axial dispersion about its mean velocity at a rate greatly exceeding that attributable to its axial molecular diffusion alone. Such chromatographic anomalies represent novel macroscale non-linearities originating from physicochemical interactions between spatially inhomogeneous convective-diffusive-reactive microtransport processes
High-precision tracking of brownian boomerang colloidal particles confined in quasi two dimensions.
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.
Phillips, Carolyn L.; Anderson, Joshua A.; Glotzer, Sharon C.
2011-08-01
Brownian Dynamics (BD), also known as Langevin Dynamics, and Dissipative Particle Dynamics (DPD) are implicit solvent methods commonly used in models of soft matter and biomolecular systems. The interaction of the numerous solvent particles with larger particles is coarse-grained as a Langevin thermostat is applied to individual particles or to particle pairs. The Langevin thermostat requires a pseudo-random number generator (PRNG) to generate the stochastic force applied to each particle or pair of neighboring particles during each time step in the integration of Newton's equations of motion. In a Single-Instruction-Multiple-Thread (SIMT) GPU parallel computing environment, small batches of random numbers must be generated over thousands of threads and millions of kernel calls. In this communication we introduce a one-PRNG-per-kernel-call-per-thread scheme, in which a micro-stream of pseudorandom numbers is generated in each thread and kernel call. These high quality, statistically robust micro-streams require no global memory for state storage, are more computationally efficient than other PRNG schemes in memory-bound kernels, and uniquely enable the DPD simulation method without requiring communication between threads.
DePuit, Ryan J; Squires, Todd M
2012-01-01
Active and nonlinear microrheology experiments involve a colloidal probe that is forced to move within a material, with the goal of recovering the nonlinear rheological response properties of the material. Various mechanisms cause discrepancies between the nonlinear rheology measured microrheologically and macroscopically, including direct probe-bath collisions, the Lagrangian unsteadiness experienced by the material elements, and the spatially inhomogeneous and rheologically mixed strain field set up around the probe. Here, we perform computational nonlinear microrheology experiments, in which a colloidal probe translates through a dilute suspension of Brownian ellipsoids, whose results we compare against analogous computational experiments on the macroscopic shear rheology of the same model material. The quantitative impact of each of the mechanisms for micro-macro-discrepancy can thus be computed directly, with additional computational experiments performed where the processes in question are ‘turned off’. We show that all three discrepancy mechanisms impact the microrheological measurement quantitatively, and that none can be neglected. This motivates a search for microrheological probes whose geometry or forcing is optimized to minimize these impacts, which we present in a companion article.
Brownian dynamic study of an enzyme metabolon in the TCA cycle: Substrate kinetics and channeling.
Huang, Yu-Ming M; Huber, Gary A; Wang, Nuo; Minteer, Shelley D; McCammon, J Andrew
2018-02-01
Malate dehydrogenase (MDH) and citrate synthase (CS) are two pacemaking enzymes involved in the tricarboxylic acid (TCA) cycle. Oxaloacetate (OAA) molecules are the intermediate substrates that are transferred from the MDH to CS to carry out sequential catalysis. It is known that, to achieve a high flux of intermediate transport and reduce the probability of substrate leaking, a MDH-CS metabolon forms to enhance the OAA substrate channeling. In this study, we aim to understand the OAA channeling within possible MDH-CS metabolons that have different structural orientations in their complexes. Three MDH-CS metabolons from native bovine, wild-type porcine, and recombinant sources, published in recent work, were selected to calculate OAA transfer efficiency by Brownian dynamics (BD) simulations and to study, through electrostatic potential calculations, a possible role of charges that drive the substrate channeling. Our results show that an electrostatic channel is formed in the metabolons of native bovine and recombinant porcine enzymes, which guides the oppositely charged OAA molecules passing through the channel and enhances the transfer efficiency. However, the channeling probability in a suggested wild-type porcine metabolon conformation is reduced due to an extended diffusion length between the MDH and CS active sites, implying that the corresponding arrangements of MDH and CS result in the decrease of electrostatic steering between substrates and protein surface and then reduce the substrate transfer efficiency from one active site to another. © 2017 The Protein Society.
Bandyopadhyay, Malay; Gupta, Shamik; Segal, Dvira
2011-03-01
We investigate DNA breathing dynamics by suggesting and examining several Brownian functionals associated with bubble lifetime and reactivity. Bubble dynamics is described as an overdamped random walk in the number of broken base pairs. The walk takes place on the Poland-Scheraga free-energy landscape. We suggest several probability distribution functions that characterize the breathing process, and adopt the recently studied backward Fokker-Planck method and the path decomposition method as elegant and flexible tools for deriving these distributions. In particular, for a bubble of an initial size x₀, we derive analytical expressions for (i) the distribution P(t{f}|x₀) of the first-passage time t{f}, characterizing the bubble lifetime, (ii) the distribution P(A|x₀) of the area A until the first-passage time, providing information about the effective reactivity of the bubble to processes within the DNA, (iii) the distribution P(M) of the maximum bubble size M attained before the first-passage time, and (iv) the joint probability distribution P(M,t{m}) of the maximum bubble size M and the time t{m} of its occurrence before the first-passage time. These distributions are analyzed in the limit of small and large bubble sizes. We supplement our analytical predictions with direct numericalsimulations of the related Langevin equation, and obtain a very good agreement in the appropriate limits. The nontrivial scaling behavior of the various quantities analyzed here can, in principle, be explored experimentally.
Siksik, May; Krishnamurthy, Vikram
2017-09-01
This paper proposes a multi-dielectric Brownian dynamics simulation framework for design-space-exploration (DSE) studies of ion-channel permeation. The goal of such DSE studies is to estimate the channel modeling-parameters that minimize the mean-squared error between the simulated and expected "permeation characteristics." To address this computational challenge, we use a methodology based on statistical inference that utilizes the knowledge of channel structure to prune the design space. We demonstrate the proposed framework and DSE methodology using a case study based on the KcsA ion channel, in which the design space is successfully reduced from a 6-D space to a 2-D space. Our results show that the channel dielectric map computed using the framework matches with that computed directly using molecular dynamics with an error of 7%. Finally, the scalability and resolution of the model used are explored, and it is shown that the memory requirements needed for DSE remain constant as the number of parameters (degree of heterogeneity) increases.
O. V. Shavykin
2016-09-01
Full Text Available The Brownian dynamics method has been used to study the effect of the branching asymmetry on the local orientational mobility of segments and bonds in dendrimers in good solvent. “Coarse-grained” models of flexible dendrimers with different branching symmetry but with the same average segment length were considered. The frequency dependences of the rate of the spin-lattice relaxation nuclear magnetic resonance (NMR [1/T1H(H] for segments or bonds located at different distances from terminal monomers were calculated. After the exclusion of the contribution of the overall dendrimer rotation the position of the maxima of the frequency dependences [1/T1H(ωH] for different segments with the same length doesn’t depend on their location inside a dendrimer both for phantom models and for models with excluded volume interactions. This effect doesn’t depend also on the branching symmetry, but the position of the maximum [1/T1H(ωH] is determined by the segment length. For bonds inside segments the positions of the maximum [1/T1H(ωH] coincide for all models considered. Therefore, the obtained earlier conclusion about the weak influence of the excluded volume interactions on the local dynamics in the flexible symmetric dendrimers can be generalized for dendrimers with an asymmetric branching.