WorldWideScience

Sample records for brownian movement

  1. Brownian movement and molecular reality

    CERN Document Server

    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

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

    NARCIS (Netherlands)

    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 fora

  3. Deriving movement properties and the effect of the environment from the Brownian bridge movement model in monkeys and birds

    NARCIS (Netherlands)

    K. Buchin; S. Sijben; E.E. van Loon; N. Sapir; S. Mercier; T.J.M. Arseneau; E.P. Willems

    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 calculat

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

    OpenAIRE

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

    2015-01-01

    Background 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 spat...

  5. Brownian Brownian Motion-1

    OpenAIRE

    Chernov, N.; Dolgopyat, D.

    2008-01-01

    A classical model of Brownian motion consists of a heavy molecule submerged into a gas of light atoms in a closed container. In this work we study a 2D version of this model, where the molecule is a heavy disk of mass M and the gas is represented by just one point particle of mass m = 1, which interacts with the disk and the walls of the container via elastic collisions. Chaotic behavior of the particles is ensured by convex (scattering) walls of the container. We prove that the position and ...

  6. Brownian earthworm

    CERN Document Server

    Burdzy, Krzysztof; Pal, Soumik

    2010-01-01

    We prove that the distance between two reflected Brownian motions outside a sphere in a 3-dimensional flat torus does not converge to 0, a.s., if the radius of the sphere is sufficiently small, relative to the size of the torus.

  7. Canonical active Brownian motion

    OpenAIRE

    Gluck, Alexander; Huffel, Helmuth; Ilijic, Sasa

    2008-01-01

    Active Brownian motion is the complex motion of active Brownian particles. They are active in the sense that they can transform their internal energy into energy of motion and thus create complex motion patterns. Theories of active Brownian motion so far imposed couplings between the internal energy and the kinetic energy of the system. We investigate how this idea can be naturally taken further to include also couplings to the potential energy, which finally leads to a general theory of cano...

  8. Is a Brownian skew?

    CERN Document Server

    Lejay, Antoine; Torres, Soledad

    2011-01-01

    We study the asymptotic behavior of the maximum likelihood estimator corresponding to the observation of a trajectory of a Skew Brownian motion, through a uniform time discretization. We characterize the speed of convergence and the limiting distribution when the step size goes to zero, which in this case are non-classical, under the null hypothesis of the Skew Brownian motion being an usual Brownian motion. This allows to design a test on the skewness parameter. We show that numerical simulations that can be easily performed to estimate the skewness parameter, and provide an application in Biology.

  9. Brownian motion of graphene.

    Science.gov (United States)

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

    2010-12-28

    Brownian motion is a manifestation of the fluctuation-dissipation theorem of statistical mechanics. It regulates systems in physics, biology, chemistry, and finance. We use graphene as prototype material to unravel the consequences of the fluctuation-dissipation theorem in two dimensions, by studying the Brownian motion of optically trapped graphene flakes. These orient orthogonal to the light polarization, due to the optical constants anisotropy. We explain the flake dynamics in the optical trap and measure force and torque constants from the correlation functions of the tracking signals, as well as comparing experiments with a full electromagnetic theory of optical trapping. The understanding of optical trapping of two-dimensional nanostructures gained through our Brownian motion analysis paves the way to light-controlled manipulation and all-optical sorting of biological membranes and anisotropic macromolecules. PMID:21133432

  10. Noncommutative Brownian motion

    CERN Document Server

    Santos, Willien O; Souza, Andre M C

    2016-01-01

    We investigate the Brownian motion of a particle in a two-dimensional noncommutative (NC) space. Using the standard NC algebra embodied by the sympletic Weyl-Moyal formalism we find that noncommutativity induces a non-vanishing correlation between both coordinates at different times. The effect itself stands as a signature of spatial noncommutativity and offers further alternatives to experimentally detect the phenomena.

  11. Thermal Brownian motor

    OpenAIRE

    Meurs, P.; Broeck, C. Van Den

    2005-01-01

    Recently, a thermal Brownian motor was introduced [Van den Broeck, Kawai and Meurs, Phys. Rev. Lett. (2004)], for which an exact microscopic analysis is possible. The purpose of this paper is to review some further properties of this construction, and to discuss in particular specific issues including the relation with macroscopic response and the efficiency at maximum power.

  12. Symmetric Brownian motor

    OpenAIRE

    Gomez-Marin, A.; Sancho, J. M.

    2004-01-01

    In this paper we present a model of a symmetric Brownian motor (SBM) which changes the sign of its velocity when the temperature gradient is inverted. The velocity, external work and efficiency are studied as a function of the temperatures of the baths and other relevant parameters. The motor shows a current reversal when another parameter (a phase shift) is varied. Analytical predictions and results from numerical simulations are performed and agree very well. Generic properties of this type...

  13. Brownian Motion, "Diverse and Undulating"

    CERN Document Server

    Duplantier, Bertrand

    2016-01-01

    We describe in detail the history of Brownian motion, as well as the contributions of Einstein, Sutherland, Smoluchowski, Bachelier, Perrin and Langevin to its theory. The always topical importance in physics of the theory of Brownian motion is illustrated by recent biophysical experiments, where it serves, for instance, for the measurement of the pulling force on a single DNA molecule. In a second part, we stress the mathematical importance of the theory of Brownian motion, illustrated by two chosen examples. The by-now classic representation of the Newtonian potential by Brownian motion is explained in an elementary way. We conclude with the description of recent progress seen in the geometry of the planar Brownian curve. At its heart lie the concepts of conformal invariance and multifractality, associated with the potential theory of the Brownian curve itself.

  14. Deterministic Brownian Motion

    Science.gov (United States)

    Trefan, Gyorgy

    1993-01-01

    The goal of this thesis is to contribute to the ambitious program of the foundation of developing statistical physics using chaos. We build a deterministic model of Brownian motion and provide a microscopic derivation of the Fokker-Planck equation. Since the Brownian motion of a particle is the result of the competing processes of diffusion and dissipation, we create a model where both diffusion and dissipation originate from the same deterministic mechanism--the deterministic interaction of that particle with its environment. We show that standard diffusion which is the basis of the Fokker-Planck equation rests on the Central Limit Theorem, and, consequently, on the possibility of deriving it from a deterministic process with a quickly decaying correlation function. The sensitive dependence on initial conditions, one of the defining properties of chaos insures this rapid decay. We carefully address the problem of deriving dissipation from the interaction of a particle with a fully deterministic nonlinear bath, that we term the booster. We show that the solution of this problem essentially rests on the linear response of a booster to an external perturbation. This raises a long-standing problem concerned with Kubo's Linear Response Theory and the strong criticism against it by van Kampen. Kubo's theory is based on a perturbation treatment of the Liouville equation, which, in turn, is expected to be totally equivalent to a first-order perturbation treatment of single trajectories. Since the boosters are chaotic, and chaos is essential to generate diffusion, the single trajectories are highly unstable and do not respond linearly to weak external perturbation. We adopt chaotic maps as boosters of a Brownian particle, and therefore address the problem of the response of a chaotic booster to an external perturbation. We notice that a fully chaotic map is characterized by an invariant measure which is a continuous function of the control parameters of the map

  15. Continuous optimal partial liquidation of the single stock’s hedging under a-rithmetic Brownian movements%股指期货套期保值不完全变现连续出清策略

    Institute of Scientific and Technical Information of China (English)

    唐衍伟; 陈刚; 刘喜华

    2014-01-01

    The continuous liquidation trajectory of the single hedged stock is derived under the arithmetic Brownian movements,mean-variance utility,and linear market impact. The parameters analysis shows that the investors are like to liquidate quickly if they are more risk averse or the portfolio ’s variance is larger;if the correlation coefficient is negative,they want to execute more quickly and vice versa;the liquidation velocity changes are opposite to that of the correlation coefficient under the given hedging ratio. The partial liquida-tion’s trajectory is more convex than the full liquidation’s. Sometimes,the investors would over liquidate firstly and then recover the position.%假定股票和期货服从算术布朗运动,投资者效用为均值—方差形式,价格冲击为线性,在连续时间框架下,求解单只股票与股指期货套期保值不完全变现的同步出清问题,得到出清轨迹。参数分析表明:当风险厌恶程度较大、组合标准差越大时,投资者倾向于在出清初期出清较大规模的头寸,以降低后期的风险;当ρ<0,随套期保值比的增加,投资者更倾向于快速的出清过程,当ρ>0则相反;在给定套期保值比的情况下,出清速率与相关系数呈反向变化。不完全变现比完全变现的出清轨迹更向下凸,而且可能会出现提前完成出清的情况发生。

  16. Brownian Motion Theory and Experiment

    CERN Document Server

    Basu, K; Basu, Kasturi; Baishya, Kopinjol

    2003-01-01

    Brownian motion is the perpetual irregular motion exhibited by small particles immersed in a fluid. Such random motion of the particles is produced by statistical fluctuations in the collisions they suffer with the molecules of the surrounding fluid. Brownian motion of particles in a fluid (like milk particles in water) can be observed under a microscope. Here we describe a simple experimental set-up to observe Brownian motion and a method of determining the diffusion coefficient of the Brownian particles, based on a theory due to Smoluchowski. While looking through the microscope we focus attention on a fixed small volume, and record the number of particles that are trapped in that volume, at regular intervals of time. This gives us a time-series data, which is enough to determine the diffusion coefficient of the particles to a good degree of accuracy.

  17. Generalization of Brownian Motion with Autoregressive Increments

    CERN Document Server

    Fendick, Kerry

    2011-01-01

    This paper introduces a generalization of Brownian motion with continuous sample paths and stationary, autoregressive increments. This process, which we call a Brownian ray with drift, is characterized by three parameters quantifying distinct effects of drift, volatility, and autoregressiveness. A Brownian ray with drift, conditioned on its state at the beginning of an interval, is another Brownian ray with drift over the interval, and its expected path over the interval is a ray with a slope that depends on the conditioned state. This paper shows how Brownian rays can be applied in finance for the analysis of queues or inventories and the valuation of options. We model a queue's net input process as a superposition of Brownian rays with drift and derive the transient distribution of the queue length conditional on past queue lengths and on past states of the individual Brownian rays comprising the superposition. The transient distributions of Regulated Brownian Motion and of the Regulated Brownian Bridge are...

  18. Anomalous Brownian refrigerator

    Science.gov (United States)

    Rana, Shubhashis; Pal, P. S.; Saha, Arnab; Jayannavar, A. M.

    2016-02-01

    We present a detailed study of a Brownian particle driven by Carnot-type refrigerating protocol operating between two thermal baths. Both the underdamped as well as the overdamped limits are investigated. The particle is in a harmonic potential with time-periodic strength that drives the system cyclically between the baths. Each cycle consists of two isothermal steps at different temperatures and two adiabatic steps connecting them. Besides working as a stochastic refrigerator, it is shown analytically that in the quasistatic regime the system can also act as stochastic heater, depending on the bath temperatures. Interestingly, in non-quasistatic regime, our system can even work as a stochastic heat engine for certain range of cycle time and bath temperatures. We show that the operation of this engine is not reliable. The fluctuations of stochastic efficiency/coefficient of performance (COP) dominate their mean values. Their distributions show power law tails, however the exponents are not universal. Our study reveals that microscopic machines are not the microscopic equivalent of the macroscopic machines that we come across in our daily life. We find that there is no one to one correspondence between the performance of our system under engine protocol and its reverse.

  19. Brownian Carnot engine

    Science.gov (United States)

    Martínez, I. A.; Roldán, É.; Dinis, L.; Petrov, D.; Parrondo, J. M. R.; Rica, R. A.

    2016-01-01

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

  20. Harmonic functions on Walsh's Brownian motion

    OpenAIRE

    Jehring, Kristin Elizabeth

    2009-01-01

    In this dissertation we examine a variation of two- dimensional Brownian motion introduced in 1978 by Walsh. Walsh's Brownian motion can be described as a Brownian motion on the spokes of a (rimless) bicycle wheel. We will construct such a process by randomly assigning an angle to the excursions of a reflecting Brownian motion from 0. With this construction we see that Walsh's Brownian motion in R² behaves like one-dimensional Brownian motion away from the origin, but at the origin behaves di...

  1. Entropic forces in Brownian motion

    CERN Document Server

    Roos, Nico

    2013-01-01

    The interest in the concept of entropic forces has risen considerably since E. Verlinde proposed to interpret the force in Newton s second law and Gravity as entropic forces. Brownian motion, the motion of a small particle (pollen) driven by random impulses from the surrounding molecules, may be the first example of a stochastic process in which such forces are expected to emerge. In this note it is shown that at least two types of entropic motion can be identified in the case of 3D Brownian motion (or random walk). This yields simple derivations of known results of Brownian motion, Hook s law and, applying an external (nonradial) force, Curie s law and the Langevin-Debye equation.

  2. Some Brownian functionals and their laws

    OpenAIRE

    Donati-Martin, C.; Yor, M.

    1997-01-01

    We develop some topics about Brownian motion with a particular emphasis on the study of principal values of Brownian local times. We show some links between principal values and Doob’s $h$-transforms of Brownian motion, for nonpositive harmonic functions $h$. We also give a survey and complement some martingale approaches to Ray–Knight theorems for local times.

  3. STOCHASTIC INTEGRATION FOR TEMPERED FRACTIONAL BROWNIAN MOTION.

    Science.gov (United States)

    Meerschaert, Mark M; Sabzikar, Farzad

    2014-07-01

    Tempered fractional Brownian motion is obtained when the power law kernel in the moving average representation of a fractional Brownian motion is multiplied by an exponential tempering factor. This paper develops the theory of stochastic integrals for tempered fractional Brownian motion. Along the way, we develop some basic results on tempered fractional calculus. PMID:24872598

  4. Perturbative theory for Brownian vortexes.

    Science.gov (United States)

    Moyses, Henrique W; Bauer, Ross O; Grosberg, Alexander Y; Grier, David G

    2015-06-01

    Brownian vortexes are stochastic machines that use static nonconservative force fields to bias random thermal fluctuations into steadily circulating currents. The archetype for this class of systems is a colloidal sphere in an optical tweezer. Trapped near the focus of a strongly converging beam of light, the particle is displaced by random thermal kicks into the nonconservative part of the optical force field arising from radiation pressure, which then biases its diffusion. Assuming the particle remains localized within the trap, its time-averaged trajectory traces out a toroidal vortex. Unlike trivial Brownian vortexes, such as the biased Brownian pendulum, which circulate preferentially in the direction of the bias, the general Brownian vortex can change direction and even topology in response to temperature changes. Here we introduce a theory based on a perturbative expansion of the Fokker-Planck equation for weak nonconservative driving. The first-order solution takes the form of a modified Boltzmann relation and accounts for the rich phenomenology observed in experiments on micrometer-scale colloidal spheres in optical tweezers. PMID:26172698

  5. Radiation Reaction on Brownian Motions

    CERN Document Server

    Seto, Keita

    2016-01-01

    Tracking the real trajectory of a quantum particle is one of the interpretation problem and it is expressed by the Brownian (stochastic) motion suggested by E. Nelson. Especially the dynamics of a radiating electron, namely, radiation reaction which requires us to track its trajectory becomes important in the high-intensity physics by PW-class lasers at present. It has been normally treated by the Furry picture in non-linear QED, but it is difficult to draw the real trajectory of a quantum particle. For the improvement of this, I propose the representation of a stochastic particle interacting with fields and show the way to describe radiation reaction on its Brownian motion.

  6. Efficiency of Brownian heat engines.

    Science.gov (United States)

    Derényi, I; Astumian, R D

    1999-06-01

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

  7. Kingman's coalescent and Brownian motion

    OpenAIRE

    Berestycki, J.; Berestycki, N

    2009-01-01

    We describe a simple construction of Kingman's coalescent in terms of a Brownian excursion. This construction is closely related to, and sheds some new light on, earlier work by Aldous and Warren. Our approach also yields some new results: for instance, we obtain the full multifractal spectrum of Kingman's coalescent. This complements earlier work on Beta-coalescents by the authors and Schweinsberg. Surprisingly, the thick part of the spectrum is not obtained by taking the limit as $\\alpha \\t...

  8. Cooperative Transport of Brownian Particles

    OpenAIRE

    Derenyi, Imre; Vicsek, Tamas

    1998-01-01

    We consider the collective motion of finite-sized, overdamped Brownian particles (e.g., motor proteins) in a periodic potential. Simulations of our model have revealed a number of novel cooperative transport phenomena, including (i) the reversal of direction of the net current as the particle density is increased and (ii) a very strong and complex dependence of the average velocity on both the size and the average distance of the particles.

  9. Operator Fractional Brownian Motion and Martingale Differences

    Directory of Open Access Journals (Sweden)

    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.

  10. G- Brownian motion and Its Applications

    OpenAIRE

    EBRAHIMBEYGI, Atena; DASTRANJ, Elham

    2015-01-01

    Abstract. The concept of G-Brownian motion and G-Ito integral has been introduced by Peng. Also Ito isometry lemma is proved for Ito integral and Brownian motion. In this paper we first investigate the Ito isometry lemma for G-Brownian motion and G-Ito Integral. Then after studying of MG2,0-class functions [4], we introduce Stratonovich integral for G-Brownian motion,say G- Stratonovich integral. Then we present a special construction for G- Stratonovich integral. 

  11. Pricing European option under the time-changed mixed Brownian-fractional Brownian model

    Science.gov (United States)

    Guo, Zhidong; Yuan, Hongjun

    2014-07-01

    This paper deals with the problem of discrete time option pricing by a mixed Brownian-fractional subdiffusive Black-Scholes model. Under the assumption that the price of the underlying stock follows a time-changed mixed Brownian-fractional Brownian motion, we derive a pricing formula for the European call option in a discrete time setting.

  12. Random Brownian scaling identities and splicing of Bessel processes

    OpenAIRE

    Pitman, Jim; Yor, Marc

    1998-01-01

    An identity in distribution due to Knight for Brownian motion is extended in two different ways: first by replacing the supremum of a reflecting Brownian motion by the range of an unreflected Brownian motion and second by replacing the reflecting Brownian motion by a recurrent Bessel process. Both extensions are explained in terms of random Brownian scaling transformations and Brownian excursions. The first extension is related to two different constructions of Itô’s law of ...

  13. Brownian motion of helical flagella.

    Science.gov (United States)

    Hoshikawa, H; Saito, N

    1979-07-01

    We develops a theory of the Brownian motion of a rigid helical object such as bacterial flagella. The statistical properties of the random forces acting on the helical object are discussed and the coefficients of the correlations of the random forces are determined. The averages , and are also calculated where z and theta are the position along and angle around the helix axis respectively. Although the theory is limited to short time interval, direct comparison with experiment is possible by using the recently developed cinematography technique. PMID:16997210

  14. Nonlinear Brownian motion - mean square displacement

    Directory of Open Access Journals (Sweden)

    W.Ebeling

    2004-01-01

    Full Text Available The stochastic dynamics of self-propelled Brownian particles is studied by means of the Langevin and the Fokker-Planck approach. We model the driving by a nonlinear friction function which has a negative part at small velocities, leading to active Brownian motion of the particles. The mean square displacement is estimated analytically and compared with numerical simulations.

  15. Dimensional Properties of Fractional Brownian Motion

    Institute of Scientific and Technical Information of China (English)

    Dong Sheng WU; Yi Min XIAO

    2007-01-01

    Let Bα = {Bα(t),t ∈ RN} be an (N,d)-fractional Brownian motion with Hurst index α∈ (0, 1). By applying the strong local nondeterminism of Bα, we prove certain forms of uniform Hausdorff dimension results for the images of Bα when N > αd. Our results extend those of Kaufman for one-dimensional Brownian motion.

  16. Brownian motion meets Riemann curvature

    International Nuclear Information System (INIS)

    The general covariance of the diffusion equation is exploited in order to explore the curvature effects appearing in Brownian motion over a d-dimensional curved manifold. We use the local frame defined by the so-called Riemann normal coordinates to derive a general formula for the mean-square geodesic distance (MSD) at the short-time regime. This formula is written in terms of O(d) invariants that depend on the Riemann curvature tensor. We study the n-dimensional sphere case to validate these results. We also show that the diffusion for positive constant curvature is slower than the diffusion in a plane space, while the diffusion for negative constant curvature turns out to be faster. Finally the two-dimensional case is emphasized, as it is relevant for single-particle diffusion on biomembranes

  17. Combinatorial fractal Brownian motion model

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    To solve the problem of how to determine the non-scaled interval when processing radar clutter using fractal Brownian motion (FBM) model, a concept of combinatorial FBM model is presented. Since the earth (or sea) surface varies diversely with space, a radar clutter contains several fractal structures, which coexist on all scales. Taking the combination of two FBMs into account, via theoretical derivation we establish a combinatorial FBM model and present a method to estimate its fractal parameters. The correctness of the model and the method is proved by simulation experiments and computation of practial data. Furthermore, we obtain the relationship between fractal parameters when processing combinatorial model with a single FBM model. Meanwhile, by theoretical analysis it is concluded that when combinatorial model is observed on different scales, one of the fractal structures is more obvious.

  18. Blending Brownian motion and heat equation

    CERN Document Server

    Cristiani, Emiliano

    2015-01-01

    In this short communication we present an original way to couple the Brownian motion and the heat equation. More in general, we suggest a way for coupling the Langevin equation for a particle, which describes a single realization of its trajectory, with the associated Fokker-Planck equation, which instead describes the evolution of the particle's probability density function. Numerical results show that it is indeed possible to obtain a regularized Brownian motion and a Brownianized heat equation still preserving the global statistical properties of the solutions. The results also suggest that the more macroscale leads the dynamics the more one can reduce the microscopic degrees of freedom.

  19. Renewal Structure of the Brownian Taut String

    OpenAIRE

    Schertzer, Emmanuel

    2015-01-01

    In a recent paper, M. Lifshits and E. Setterqvist introduced the taut string of a Brownian motion $w$, defined as the function of minimal quadratic energy on $[0,T]$ staying in a tube of fixed width $h>0$ around $w$. The authors showed a Law of Large Number (L.L.N.) for the quadratic energy spent by the string for a large time $T$. In this note, we exhibit a natural renewal structure for the Brownian taut string, which is directly related to the time decomposition of the Brownian motion in te...

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

    Directory of Open Access Journals (Sweden)

    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.

  1. Coulomb Friction Driving Brownian Motors

    International Nuclear Information System (INIS)

    We review a family of models recently introduced to describe Brownian motors under the influence of Coulomb friction, or more general non-linear friction laws. It is known that, if the heat bath is modeled as the usual Langevin equation (linear viscosity plus white noise), additional non-linear friction forces are not sufficient to break detailed balance, i.e. cannot produce a motor effect. We discuss two possibile mechanisms to elude this problem. A first possibility, exploited in several models inspired to recent experiments, is to replace the heat bath's white noise by a “collisional noise”, that is the effect of random collisions with an external equilibrium gas of particles. A second possibility is enlarging the phase space, e.g. by adding an external potential which couples velocity to position, as in a Klein—Kramers equation. In both cases, non-linear friction becomes sufficient to achieve a non-equilibrium steady state and, in the presence of an even small spatial asymmetry, a motor effect is produced. (general)

  2. Active Brownian motion of an asymmetric rigid particle

    CERN Document Server

    Mammadov, Gulmammad

    2012-01-01

    Individual movements of a rod-like self-propelled particle on a flat substrate are quantified. Biological systems that fit into this description may be the Gram-negative delta-proteobacterium Myxococcus xanthus, Gram-negative bacterium Escherichia coli, and Mitochondria. There are also non-living analogues such as vibrated polar granulates and self-driven anisotropic colloidal particles. For that we study the Brownian motion of an asymmetric rod-like rigid particle self-propelled at a fixed speed along its long axis in two dimensions. The motion of such a particle in a uniform external potential field is also considered. The theoretical model presented here is anticipated to better describe individual cell motion as well as intracellular transport in 2D than previous models.

  3. Diffusion of torqued active Brownian particles

    Science.gov (United States)

    Sevilla, Francisco J.

    An analytical approach is used to study the diffusion of active Brownian particles that move at constant speed in three-dimensional space, under the influence of passive (external) and active (internal) torques. The Smoluchowski equation for the position distribution of the particles is obtained from the Kramer-Fokker-Planck equation corresponding to Langevin equations for active Brownian particles subject to torques. In addition of giving explicit formulas for the mean square-displacement, the non-Gaussian behavior is analyzed through the kurtosis of the position distribution that exhibits an oscillatory behavior in the short-time limit. FJS acknowledges support from PAPIIT-UNAM through the grant IN113114

  4. Brownian semistationary processes and volatility/intermittency

    DEFF Research Database (Denmark)

    Barndorff-Nielsen, Ole Eiler; Schmiegel, Jürgen

    A new class of stochastic processes, termed Brownian semistationary processes (BSS), is introduced and discussed. This class has similarities to that of Brownian semimartingales (BSM), but is mainly directed towards the study of stationary processes, and BSS processes are not in general of the...... turbulent velocity fields and is the purely temporal version of the general tempo-spatial framework of ambit processes. The latter, which may have applications also to the finance of energy markets, is briefly considered at the end of the paper, again with reference to the question of inference on the...

  5. Generalized Einstein Relation for Brownian Motion in Tilted Periodic Potential

    OpenAIRE

    Sakaguchi, Hidetsugu

    2006-01-01

    A generalized Einstein relation is studied for Brownian motion in a tilted potential. The exact form of the diffusion constant of the Brownian motion is compared with the generalized Einstein relation. The generalized Einstein relation is a good approximation in a parameter range where the Brownian motion exhibits stepwise motion.

  6. Brownian particles in supramolecular polymer solutions

    NARCIS (Netherlands)

    Gucht, van der J.; Besseling, N.A.M.; Knoben, W.; Bouteiller, L.; Cohen Stuart, M.A.

    2003-01-01

    The Brownian motion of colloidal particles embedded in solutions of hydrogen-bonded supramolecular polymers has been studied using dynamic light scattering. At short times, the motion of the probe particles is diffusive with a diffusion coefficient equal to that in pure solvent. At intermediate time

  7. Brownian shape motion: Fission fragment mass distributions

    Directory of Open Access Journals (Sweden)

    Sierk Arnold J.

    2012-02-01

    Full Text Available It was recently shown that remarkably accurate fission-fragment mass distributions can be obtained by treating the nuclear shape evolution as a Brownian walk on previously calculated five-dimensional potential-energy surfaces; the current status of this novel method is described here.

  8. Brownian coagulation at high particle concentrations

    NARCIS (Netherlands)

    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, emulsi

  9. Brownian Warps for Non-Rigid Registration

    DEFF Research Database (Denmark)

    Nielsen, Mads; Johansen, Peter; Jackson, Andrew D.;

    2008-01-01

    A Brownian motion model in the group of diffeomorphisms has been introduced as inducing a least committed prior on warps. This prior is source-destination symmetric, fulfills a natural semi-group property for warps, and with probability 1 creates invertible warps. Using this as a least committed ...

  10. On Kramers' general theory of Brownian motion

    NARCIS (Netherlands)

    Brinkman, H.C.

    1957-01-01

    Kramer's general theory of Brownian motion 1) based on a diffusion equation in phase space is discussed from the standpoint of statistical thermodynamics. It is concluded that for particles moving in a medium in equilibrium the restrictions imposed by the second law of thermodynamics limit Kramer's

  11. Brownian motion on a smash line

    CERN Document Server

    Ellinas, D; Ellinas, Demosthenes; Tsohantjis, Ioannis

    2000-01-01

    Brownian motion on a smash line algebra (a smash or braided version of the algebra resulting by tensoring the real line and the generalized paragrassmann line algebras), is constructed by means of its Hopf algebraic structure. Further, statistical moments, non stationary generalizations and its diffusion limit are also studied. The ensuing diffusion equation posseses triangular matrix realizations.

  12. Chaos, Dissipation and Quantal Brownian Motion

    OpenAIRE

    Cohen, Doron

    1999-01-01

    Energy absorption by driven chaotic systems, the theory of energy spreading and quantal Brownian motion are considered. In particular we discuss the theory of a classical particle that interacts with quantal chaotic degrees of freedom, and try to relate it to the problem of quantal particle that interacts with an effective harmonic bath.

  13. Exploiting the color of Brownian motion for high-frequency microrheology of Newtonian fluids

    Science.gov (United States)

    Domínguez-García, Pablo; Mor, Flavio M.; Forró, László; Jeney, Sylvia

    2013-09-01

    Einstein's stochastic description of the random movement of small objects in a fluid, i.e. Brownian motion, reveals to be quite different, when observed on short timescales. The limitations of Einstein's theory with respect to particle inertia and hydrodynamic memory yield to the apparition of a colored frequency-dependent component in the spectrum of the thermal forces, which is called "the color of Brownian motion". The knowledge of the characteristic timescales of the motion of a trapped microsphere motion in a Newtonian fluid allowed to develop a high-resolution calibration method for optical interferometry. Well-calibrated correlation quantities, such as the mean square displacement or the velocity autocorrelation function, permit to study the mechanical properties of fluids at high frequencies. These properties are estimated by microrheological calculations based on the theoretical relations between the complex mobility of the beads and the rheological properties of a complex fluid.

  14. Brownian motion, martingales, and stochastic calculus

    CERN Document Server

    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...

  15. Speckle Patterns and 2-Dimensional Brownian Motion

    International Nuclear Information System (INIS)

    We present the results of a Monte Carlo simulation of Brownian Motion on a 2-dimensional lattice with nearest-neighbor interactions described by a linear model. These nearest-neighbor interactions lead to a spatial variance structure on the lattice. The resulting Brownian pattern fluctuates in value from point to point in a manner characteristic of a stationary stochastic process. The value at a lattice point is interpreted as an intensity level. The difference in values in neighboring cells produces a fluctuating intensity pattern on the lattice. Changing the size of the mesh changes the relative size of the speckles. Increasing the mesh size tends to average out the intensity in the direction of the mean of the stationary process. (Author)

  16. Modeling an efficient Brownian heat engine

    Science.gov (United States)

    Asfaw, Mesfin

    2008-09-01

    We discuss the effect of subdividing the ratchet potential on the performance of a tiny Brownian heat engine that is modeled as a Brownian particle hopping in a viscous medium in a sawtooth potential (with or without load) assisted by alternately placed hot and cold heat baths along its path. We show that the velocity, the efficiency and the coefficient of performance of the refrigerator maximize when the sawtooth potential is subdivided into series of smaller connected barrier series. When the engine operates quasistatically, we analytically show that the efficiency of the engine can not approach the Carnot efficiency and, the coefficient of performance of the refrigerator is always less than the Carnot refrigerator due to the irreversible heat flow via the kinetic energy.

  17. Brownian particles in supramolecular polymer solutions

    OpenAIRE

    Gucht, van der, J.; Besseling, N.A.M.; Knoben, W.; Bouteiller, L; Cohen Stuart, M. A.

    2003-01-01

    The Brownian motion of colloidal particles embedded in solutions of hydrogen-bonded supramolecular polymers has been studied using dynamic light scattering. At short times, the motion of the probe particles is diffusive with a diffusion coefficient equal to that in pure solvent. At intermediate time scales the particles are slowed down as a result of trapping in elastic cages formed by the polymer chains, while at longer times the motion is diffusive again, but with a much smaller diffusion c...

  18. Brownian coagulation at high particle concentrations

    OpenAIRE

    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, emulsions, flocculation, air pollution, soot formation, materials manufacture and growth of interstellar dust, to name a few of its applications. With continuous progress in particulate matter processing...

  19. Frustrated Brownian Motion of Nonlocal Solitary Waves

    International Nuclear Information System (INIS)

    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.

  20. Radiation Reaction for a Charged Brownian Particle

    CERN Document Server

    Vlasov, A A

    2002-01-01

    As it is known a model of a charged particle with finite size is a good tool to consider the effects of self- action and backreaction, caused by electromagnetic radiation. In this work the "size" of a charged particle is induced by its stochastic Brownian vibration. Appropriate equation of particle's motion with radiation force is derived. It is shown that the solutions of this equation correctly describe the effects of radiation reaction.

  1. Intrinsic and extrinsic measurement for Brownian motion

    International Nuclear Information System (INIS)

    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 〈δR2〉 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)

  2. Evaluation of Brownian warps for shape alignment

    Science.gov (United States)

    Nielsen, Mads

    2007-03-01

    Many methods are used for warping images to non-rigidly register shapes and objects in between medical images in inter- and intra-patient studies. In landmark-based registration linear methods like thin-plate- or b-splines are often used. These linear methods suffer from a number of theoretical deficiencies: they may break or tear apart the shapes, they are not source-destination symmetric, and may not be invertible. Theoretically more satisfactory models using diffeomorphic approaches like "Large Deformations" and "Brownian warps" have earlier proved (in theory and practice) to remove these deficiencies. In this paper we show that the maximum-likelihood Brownian Warps also generalize better in the case of matching fractured vertebrae to normal vertebrae. X-rays of 10 fractured and 1 normal vertebrae have been annotated by a trained radiologist by 6 so-called height points used for fracture scoring, and by the full boundary. The fractured vertebrae have been registered to the normal vertebra using only the 6 height points as landmarks. After registration the Hausdorff distance between the boundaries is measured. The registrations based on Brownian warps show a significantly lower distance to the original boundary.

  3. Dynamics of Brownian motors in deformable medium

    Science.gov (United States)

    Woulaché, Rosalie Laure; Kepnang Pebeu, Fabrice Maxime; Kofané, Timoléon C.

    2016-10-01

    The directed transport in a one-dimensional overdamped, Brownian motor subjected to a travelling wave potential with variable shape and exposed to an external bias is studied numerically. We focus our attention on the class of Remoissenet-Peyrard parametrized on-site potentials with slight modification, whose shape can be varied as a function of a parameter s, recovering the sine-Gordon shape as the special case. We demonstrate that in the presence of the travelling wave potential the observed dynamical properties of the Brownian motor which crucially depends on the travelling wave speed, the intensity of the noise and the external load is significantly influenced also by the geometry of the system. In particular, we notice that systems with sharp wells and broad barriers favour the transport under the influence of an applied load. The efficiency of transport of Brownian motors in deformable systems remains equal to 1 (in the absence of an applied load) up to a critical value of the travelling wave speed greater than that of the pure sine-Gordon shape.

  4. Continuum limits of random matrices and the Brownian carousel

    OpenAIRE

    Valko, Benedek; Virag, Balint

    2007-01-01

    We show that at any location away from the spectral edge, the eigenvalues of the Gaussian unitary ensemble and its general beta siblings converge to Sine_beta, a translation invariant point process. This process has a geometric description in term of the Brownian carousel, a deterministic function of Brownian motion in the hyperbolic plane. The Brownian carousel, a description of the a continuum limit of random matrices, provides a convenient way to analyze the limiting point processes. We sh...

  5. Collective Transport of Coupled Brownian Motors with Low Randomness

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The transport properties of coupled Brownian motors in rocking ratchet are investigated via solving single particle have been found. In the regime of low-to-moderate D, the average velocity of elastically coupled Brownian with the increase of a single Brownian motor. The results exhibit an interesting cooperative behavior between coupled particles subjected to a rocking force, which can generate directed transport with low randomness or high transport coherence in symmetrical periodic potential.

  6. Application of Brownian model in the northwestern Beijing, China

    Institute of Scientific and Technical Information of China (English)

    冉洪流; 周本刚

    2004-01-01

    The mathematic theory of Brownian passage-time model and its difference from other recurrence models such asPoisson, lognormal, gamma and Weibull, were introduced. We assessed and analyzed the earthquake probabilitiesof the major faults with the elapsed time much greater than the recurrence interval in the northwest region of Beijing (China) in 100-year by using both Brownian passage-time model and Poisson model, and concluded that thecalculated results obtained from Brownian passage-time model is more reasonable.

  7. RESEARCH NOTES On the support of super-Brownian motion with super-Brownian immigration

    Institute of Scientific and Technical Information of China (English)

    洪文明; 钟惠芳

    2001-01-01

    The support properties of the super Brownian motion with random immigration Xρ1 are considered,where the immigration rate is governed by the trajectory of another super-Brownian motion ρ. When both the initial state Xρo of the process and the immigration rate process ρo are of finite measure and with compact supports, the probability of the support of the process Xρi dominated by a ball is given by the solutions of a singular elliptic boundary value problem.

  8. Brownian diode: Molecular motor based on a semi-permeable Brownian particle with internal potential drop

    Energy Technology Data Exchange (ETDEWEB)

    Plyukhin, A.V., E-mail: aplyukhin@anselm.edu [Department of Mathematics, Saint Anselm College, Manchester, NH 03102 (United States)

    2013-06-03

    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.

  9. Lower bounds for distribution of suprema of Brownian increments and Brownian motion normalized by the corresponding modulus functions

    OpenAIRE

    Dobric, Vladimir; Marano, Lisa

    2014-01-01

    The L\\'evy-Ciesielski Construction of Brownian motion is used to determine non-asymptotic estimates for the maximal deviation of increments of a Brownian motion process $(W_{t})_{t\\in \\left[ 0,T\\right] }$ normalized by the global modulus function, for all positive $\\varepsilon $ and $\\delta $. Additionally, uniform results over $\\delta $ are obtained. Using the same method, non-asymptotic estimates for the distribution function for the standard Brownian motion normalized by its local modulus ...

  10. Brownian Motion and its Conditional Descendants

    Science.gov (United States)

    Garbaczewski, Piotr

    It happened before [1] that I have concluded my publication with a special dedication to John R. Klauder. Then, the reason was John's PhD thesis [2] and the questions (perhaps outdated in the eyes of the band-wagon jumpers, albeit still retaining their full vitality [3]): (i) What are the uses of the classical (c-number, non-Grassmann) spinor fields, especially nonlinear ones, what are they for at all ? (ii) What are, if any, the classical partners for Fermi models and fields in particular ? The present dedication, even if not as conspicuously motivated as the previous one by John's research, nevertheless pertains to investigations pursued by John through the years and devoted to the analysis of random noise. Sometimes, re-reading old papers and re-analysing old, frequently forgotten ideas might prove more rewarding than racing the fashions. Following this attitude, let us take as the departure point Schrödinger's original suggestion [4] of the existence of a special class of random processes, which have their origin in the Einstein-Smoluchowski theory of the Brownian motion and its Wiener's codification. The original analysis due to Schrodinger of the probabilistic significance of the heat equation and of its time adjoint in parallel, remained unnoticed by the physics community, and since then forgotten. It reappeared however in the mathematical literature as an inspiration to generalise the concept of Markovian diffusions to the case of Bernstein stochastic processes. But, it stayed without consequences for a deeper understanding of the possible physical phenomena which might underly the corresponding abstract formalism. Schrödinger's objective was to initiate investigations of possible links between quantum theory and the theory of Brownian motion, an attempt which culminated later in the so-called Nelson's stochastic mechanics [8] and its encompassing formalism [7] in which the issue of the Brownian implementation of quantum dynamics is placed in the

  11. Quantum Brownian motion in a Landau level

    Science.gov (United States)

    Cobanera, E.; Kristel, P.; Morais Smith, C.

    2016-06-01

    Motivated by questions about the open-system dynamics of topological quantum matter, we investigated the quantum Brownian motion of an electron in a homogeneous magnetic field. When the Fermi length lF=ℏ /(vFmeff) becomes much longer than the magnetic length lB=(ℏc /e B ) 1 /2 , then the spatial coordinates X ,Y of the electron cease to commute, [X ,Y ] =i lB2 . As a consequence, localization of the electron becomes limited by Heisenberg uncertainty, and the linear bath-electron coupling becomes unconventional. Moreover, because the kinetic energy of the electron is quenched by the strong magnetic field, the electron has no energy to give to or take from the bath, and so the usual connection between frictional forces and dissipation no longer holds. These two features make quantum Brownian motion topological, in the regime lF≫lB , which is at the verge of current experimental capabilities. We model topological quantum Brownian motion in terms of an unconventional operator Langevin equation derived from first principles, and solve this equation with the aim of characterizing diffusion. While diffusion in the noncommutative plane turns out to be conventional, with the mean displacement squared being proportional to tα and α =1 , there is an exotic regime for the proportionality constant in which it is directly proportional to the friction coefficient and inversely proportional to the square of the magnetic field: in this regime, friction helps diffusion and the magnetic field suppresses all fluctuations. We also show that quantum tunneling can be completely suppressed in the noncommutative plane for suitably designed metastable potential wells, a feature that might be worth exploiting for storage and protection of quantum information.

  12. Polar Functions of Multiparameter Bifractional Brownian Sheets

    Institute of Scientific and Technical Information of China (English)

    Zhen-long Chen

    2009-01-01

    Let BH,K={BH,K(t), t ∈RN+} be an (N,d)-bifractional Brownian sheet with Hurst indices for BH,Kare investigated. The relationship between the class of continuous functions satisfying the Lipschitz condition and the class of polar-functions of BH,Kis presented. The Hausdorff dimension of the fixed points and an inequality concerning the Kolmogorov's entropy index for BH,Kare obtained. A question proposed by LeGall about the existence of no-polar, continuous functions statisfying the Holder condition is also solved.

  13. Effective diffusion of confined active Brownian swimmers

    Science.gov (United States)

    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.

  14. LINEAR SEARCH FOR A BROWNIAN TARGET MOTION

    Institute of Scientific and Technical Information of China (English)

    A. B. El-Rayes; Abd El-Moneim A. Mohamed; Hamdy M. Abou Gabal

    2003-01-01

    A target is assumed to move according to a Brownian motion on the real line.The searcher starts from the origin and moves in the two directions from the starting point.The object is to detect the target.The purpose of this paper is to find the conditions under which the expected value of the first meeting time of the searcher and the target is finite,and to show the existence of a search plan which made this expected value minimum.

  15. Arithmetic area for m planar Brownian paths

    CERN Document Server

    Desbois, Jean

    2012-01-01

    We pursue the analysis made in [1] on the arithmetic area enclosed by m closed Brownian paths. We pay a particular attention to the random variable S{n1,n2, ...,n} (m) which is the arithmetic area of the set of points, also called winding sectors, enclosed n1 times by path 1, n2 times by path 2, ...,nm times by path m. Various results are obtained in the asymptotic limit m->infinity. A key observation is that, since the paths are independent, one can use in the m paths case the SLE information, valid in the 1-path case, on the 0-winding sectors arithmetic area.

  16. Arithmetic area for m planar Brownian paths

    OpenAIRE

    Desbois, Jean; Ouvry, Stephane

    2012-01-01

    We pursue the analysis made in [1] on the arithmetic area enclosed by m closed Brownian paths. We pay a particular attention to the random variable S{n1,n2, ...,n} (m) which is the arithmetic area of the set of points, also called winding sectors, enclosed n1 times by path 1, n2 times by path 2, ...,nm times by path m. Various results are obtained in the asymptotic limit m->infinity. A key observation is that, since the paths are independent, one can use in the m paths case the SLE informatio...

  17. A Brownian model for recurrent earthquakes

    Science.gov (United States)

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

    2002-01-01

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

  18. Brownian motion of particles in nematic fluids

    Science.gov (United States)

    Yao, Xuxia; Nayani, Karthik; Park, Jung; Srinivasarao, Mohan

    2011-03-01

    We studied the brownian motion of both charged and neutral polystyrene particles in two nematic fluids, a thermotropic liquid crystal, E7, and a lyotropic chromonic liquid crystal, Sunset Yellow FCF (SSY). Homogeneous planar alignment of E7 was easliy achieved by using rubbed polyimide film coated on the glass. For SSY planar mondomain, we used the capillary method recently developed in our lab. By tracking a single particle, the direction dependent diffussion coefficients and Stokes drag were measured in the nematic phase and isotropic phase for both systems.

  19. Quantum Darwinism in Quantum Brownian Motion

    Science.gov (United States)

    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.

  20. Metastable states in Brownian energy landscape

    OpenAIRE

    Cheliotis, Dimitris

    2015-01-01

    Random walks and diffusions in symmetric random environment are known to exhibit metastable behavior: they tend to stay for long times in wells of the environment. For the case that the environment is a one-dimensional two-sided standard Brownian motion, we study the process of depths of the consecutive wells of increasing depth that the motion visits. When these depths are looked in logarithmic scale, they form a stationary renewal cluster process. We give a description of the structure of t...

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

    Science.gov (United States)

    Kirksey, H. Graden; Jones, Richard F.

    1988-01-01

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

  2. Magnetic fields and Brownian motion on the 2-sphere

    International Nuclear Information System (INIS)

    Using constrained path integrals, we study some statistical properties of Brownian paths on the two dimensional sphere. A generalized Levy's law for the probability P(A) that a closed Brownian path encloses an algebraic area A is obtained. Distributions of scaled variables related to the winding of paths around some fixed point are recovered in the asymptotic regime t → ∞

  3. Holographic Brownian motion and time scales in strongly coupled plasmas

    NARCIS (Netherlands)

    A. Nata Atmaja; J. de Boer; M. Shigemori

    2010-01-01

    We study Brownian motion of a heavy quark in field theory plasma in the AdS/CFT setup and discuss the time scales characterizing the interaction between the Brownian particle and plasma constituents. In particular, the mean-free-path time is related to the connected 4-point function of the random fo

  4. The Stepping Motion of Brownian Particle Derived by Nonequilibrium Fluctuation

    Institute of Scientific and Technical Information of China (English)

    ZHAN Yong; ZHAO Tong-Jun; YU Hui; SONG Yan-Li; AN Hai-Long

    2003-01-01

    The direct motion of Brownian particle is considered as a result of system derived by external nonequilibriumfluctuating. The cooperative effects caused by asymmetric ratchet potential, external rocking force and additive colorednoise drive a Brownian particle in the directed stepping motion. This provides this kind of motion of kinesin along amicrotubule observed in experiments with a reasonable explanation.

  5. Properties of Brownian Image Models in Scale-Space

    DEFF Research Database (Denmark)

    Pedersen, Kim Steenstrup

    2003-01-01

    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...... 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...... of natural images in jet space. The consequence of these results is that the Brownian image model can be used as a least committed model of the covariance structure of the distribution of natural images....

  6. Dynamics and Efficiency of Brownian Rotors

    CERN Document Server

    Bauer, Wolfgang R

    2008-01-01

    Brownian rotors play an important role in biological systems and in future nano-technological applications. However the mechanisms determining their dynamics, efficiency and performance remain to be characterized. Here the F0 portion of the F-ATP synthase is considered as a paradigm of a Brownian rotor. In a generic analytical model we analyze the stochastic rotation of F0-like motors as a function of the driving free energy difference and of the free energy profile the rotor is subjected to. The latter is composed of the rotor interaction with its surroundings, of the free energy of chemical transitions, and of the workload. The dynamics and mechanical efficiency of the rotor depends on the magnitude of its stochastic motion driven by the free energy energy difference and its rectification on the reaction-diffusion path. We analyze which free energy profiles provide maximum flow and how their arrangement on the underlying reaction-diffusion path affects rectification and -- by this -- the efficiency.

  7. Objectivisation In Simplified Quantum Brownian Motion Models

    Directory of Open Access Journals (Sweden)

    Jan Tuziemski

    2015-02-01

    Full Text Available The birth of objective properties from the subjective quantum world has been one of the key questions in the quantum-to-classical transition. Based on recent results in the field, we study it in a quantum mechanical model of a boson-boson interaction—quantum Brownian motion. Using various simplifications, we prove a formation for thermal environments of, so called, spectrum broadcast structures, responsible for perceived objectivity. In the quantum measurement limit we prove that this structure is always formed, providing the characteristic timescales. Including self-Hamiltonians of the environment, we show the exponential scaling of the effect with the size of the environment. Finally, in the full model we numerically study the influence of squeezing in the initial state of the environment, showing broader regions of formation than for non-squeezed thermal states.

  8. From Molecular Dynamics to Brownian Dynamics

    CERN Document Server

    Erban, Radek

    2014-01-01

    Three coarse-grained molecular dynamics (MD) models are investigated with the aim of developing and analyzing multiscale methods which use MD simulations in parts of the computational domain and (less detailed) Brownian dynamics (BD) simulations in the remainder of the domain. The first MD model is formulated in one spatial dimension. It is based on elastic collisions of heavy molecules (e.g. proteins) with light point particles (e.g. water molecules). Two three-dimensional MD models are then investigated. The obtained results are applied to a simplified model of protein binding to receptors on the cellular membrane. It is shown that modern BD simulators of intracellular processes can be used in the bulk and accurately coupled with a (more detailed) MD model of protein binding which is used close to the membrane.

  9. Hybrid scheme for Brownian semistationary processes

    DEFF Research Database (Denmark)

    Bennedsen, Mikkel; Lunde, Asger; Pakkanen, Mikko S.

    We introduce a simulation scheme for Brownian semistationary processes, which is based on discretizing the stochastic integral representation of the process in the time domain. We assume that the kernel function of the process is regularly varying at zero. The novel feature of the scheme is to...... approximate the kernel function by a power function near zero and by a step function elsewhere. The resulting approximation of the process is a combination of Wiener integrals of the power function and a Riemann sum, which is why we call this method a hybrid scheme. Our main theoretical result describes the...... asymptotics of the mean square error of the hybrid scheme and we observe that the scheme leads to a substantial improvement of accuracy compared to the ordinary forward Riemann-sum scheme, while having the same computational complexity. We exemplify the use of the hybrid scheme by two numerical experiments...

  10. Cost and Precision of Brownian Clocks

    CERN Document Server

    Barato, Andre C

    2016-01-01

    Brownian clocks are biomolecular networks that can count time. A paradigmatic example are proteins that go through a cycle thus regulating some oscillatory behaviour in a living system. Typically, such a cycle requires free energy often provided by ATP hydrolysis. We investigate the relation between the precision of such a clock and its thermodynamic costs. For clocks driven by a constant thermodynamic force, a given precision requires a minimal cost that diverges as the uncertainty of the clock vanishes. In marked contrast, we show that a clock driven by a periodic variation of an external protocol can achieve arbitrary precision at arbitrarily low cost. This result constitutes a fundamental difference between processes driven by a fixed thermodynamic force and those driven periodically. As a main technical tool, we map a periodically driven system with a deterministic protocol to one subject to an external protocol that changes in stochastic time intervals, which simplifies calculations significantly. In th...

  11. Arithmetic area for m planar Brownian paths

    International Nuclear Information System (INIS)

    We pursue the analysis made in Desbois and Ouvry (2011 J. Stat. Mech. P05024) on the arithmetic area enclosed by m closed Brownian paths. We pay particular attention to the random variable Sn1,n2,...,nm(m), which is the arithmetic area of the set of points, also called winding sectors, enclosed n1 times by path 1, n2 times by path 2,..., and nm times by path m. Various results are obtained in the asymptotic limit m→∞. A key observation is that, since the paths are independent, one can use in the m-path case the SLE information, valid in the one-path case, on the zero-winding sectors arithmetic area

  12. Arithmetic area for m planar Brownian paths

    Science.gov (United States)

    Desbois, Jean; Ouvry, Stéphane

    2012-05-01

    We pursue the analysis made in Desbois and Ouvry (2011 J. Stat. Mech. P05024) on the arithmetic area enclosed by m closed Brownian paths. We pay particular attention to the random variable Sn1, n2,..., nm(m), which is the arithmetic area of the set of points, also called winding sectors, enclosed n1 times by path 1, n2 times by path 2,..., and nm times by path m. Various results are obtained in the asymptotic limit m\\to \\infty . A key observation is that, since the paths are independent, one can use in the m-path case the SLE information, valid in the one-path case, on the zero-winding sectors arithmetic area.

  13. Communication: Memory effects and active Brownian diffusion

    International Nuclear Information System (INIS)

    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

  14. Communication: Memory effects and active Brownian diffusion

    Energy Technology Data Exchange (ETDEWEB)

    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.

  15. On the quantiles of Brownian motion and their hitting times

    OpenAIRE

    Dassios, Angelos

    2005-01-01

    The distribution of the α-quantile of a Brownian motion on an interval [0,t] has been obtained motivated by a problem in financial mathematics. In this paper we generalize these results by calculating an explicit expression for the joint density of the α-quantile of a standard Brownian motion, its first and last hitting times and the value of the process at time t. Our results can easily be generalized to a Brownian motion with drift. It is shown that the first and last hitting times follow a...

  16. Langevin model for a Brownian system with directed motion

    Science.gov (United States)

    Ambía, Francisco; Híjar, Humberto

    2016-08-01

    We propose a model for an active Brownian system that exhibits one-dimensional directed motion. This system consists of two Brownian spherical particles that interact through an elastic potential and have time-dependent radii. We suggest an algorithm by which the sizes of the particles can be varied, such that the center of mass of the system is able to move at an average constant speed in one direction. The dynamics of the system is studied theoretically using a Langevin model, as well as from Brownian Dynamics simulations.

  17. The exit distribution for iterated Brownian motion in cones

    OpenAIRE

    Banuelos, Rodrigo; DeBlassie, Dante

    2004-01-01

    We study the distribution of the exit place of iterated Brownian motion in a cone, obtaining information about the chance of the exit place having large magnitude. Along the way, we determine the joint distribution of the exit time and exit place of Brownian motion in a cone. This yields information on large values of the exit place (harmonic measure) for Brownian motion. The harmonic measure for cones has been studied by many authors for many years. Our results are sharper than any previousl...

  18. Parameter Estimation for Generalized Brownian Motion with Autoregressive Increments

    CERN Document Server

    Fendick, Kerry

    2011-01-01

    This paper develops methods for estimating parameters for a generalization of Brownian motion with autoregressive increments called a Brownian ray with drift. We show that a superposition of Brownian rays with drift depends on three types of parameters - a drift coefficient, autoregressive coefficients, and volatility matrix elements, and we introduce methods for estimating each of these types of parameters using multidimensional times series data. We also cover parameter estimation in the contexts of two applications of Brownian rays in the financial sphere: queuing analysis and option valuation. For queuing analysis, we show how samples of queue lengths can be used to estimate the conditional expectation functions for the length of the queue and for increments in its net input and lost potential output. For option valuation, we show how the Black-Scholes-Merton formula depends on the price of the security on which the option is written through estimates not only of its volatility, but also of a coefficient ...

  19. Reflected Backward Stochastic Differential Equations Driven by Countable Brownian Motions

    Directory of Open Access Journals (Sweden)

    Pengju Duan

    2013-01-01

    Full Text Available This paper deals with a new class of reflected backward stochastic differential equations driven by countable Brownian motions. The existence and uniqueness of the RBSDEs are obtained via Snell envelope and fixed point theorem.

  20. Convergence rates of posterior distributions for Brownian semimartingale models

    NARCIS (Netherlands)

    F.H. van der Meulen; A.W. van der Vaart; J.H. van Zanten

    2006-01-01

    Key words and Phrases: Bayesian estimation, Continuous semimartingale, Dirichlet process, Hellinger distance, Infinite dimensional model, Rate of convergence, Wavelets. We consider the asymptotic behavior of posterior distributions based on continuous observations from a Brownian semimartingale mode

  1. Directed transport of Brownian particles in a changing temperature field

    Energy Technology Data Exchange (ETDEWEB)

    Grillo, A [DMFCI, Facolta di Ingegneria, Universita di Catania. Viale Andrea Doria 6, 95125 Catania (Italy); Jinha, A [HPL-Faculty of Kinesiology, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4 (Canada); Federico, S [HPL-Faculty of Kinesiology, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4 (Canada); Ait-Haddou, R [HPL-Faculty of Kinesiology, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4 (Canada); Herzog, W [HPL-Faculty of Kinesiology, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4 (Canada); Giaquinta, G [DMFCI, Facolta di Ingegneria, Universita di Catania. Viale Andrea Doria 6, 95125 Catania (Italy)

    2008-01-11

    We study the interaction of Brownian particles with a changing temperature field in the presence of a one-dimensional periodic adiabatic potential. We show the existence of directed transport through the determination of the overall current of Brownian particles crossing the boundary of the system. With respect to the case of Brownian particles in a thermal bath, we determine a current which exhibits a contribution explicitly related to the presence of a thermal gradient. Beyond the self-consistent calculation of the temperature and probability density distribution of Brownian particles, we evaluate the energy consumption for directed transport to take place. Our description is based on Streater's model, and solutions are obtained by perturbing the system from its initial thermodynamic equilibrium state.

  2. Rotational Brownian Dynamics simulations of clathrin cage formation

    Energy Technology Data Exchange (ETDEWEB)

    Ilie, Ioana M.; Briels, Wim J. [Computational BioPhysics, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands); MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands); Otter, Wouter K. den, E-mail: w.k.denotter@utwente.nl [Computational BioPhysics, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands); MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands); Multi Scale Mechanics, Faculty of Engineering Technology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands)

    2014-08-14

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

  3. Brownian Motion on a Sphere: Distribution of Solid Angles

    OpenAIRE

    Krishna, M. M. G.; Samuel, Joseph; Sinha, Supurna

    2000-01-01

    We study the diffusion of Brownian particles on the surface of a sphere and compute the distribution of solid angles enclosed by the diffusing particles. This function describes the distribution of geometric phases in two state quantum systems (or polarised light) undergoing random evolution. Our results are also relevant to recent experiments which observe the Brownian motion of molecules on curved surfaces like micelles and biological membranes. Our theoretical analysis agrees well with the...

  4. Brownian motion and gambling: from ratchets to paradoxical games

    CERN Document Server

    Parrondo, J M R

    2014-01-01

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

  5. Symmetry Relations for Trajectories of a Brownian Motor

    OpenAIRE

    Astumian, R. Dean

    2007-01-01

    A Brownian Motor is a nanoscale or molecular device that combines the effects of thermal noise, spatial or temporal asymmetry, and directionless input energy to drive directed motion. Because of the input energy, Brownian motors function away from thermodynamic equilibrium and concepts such as linear response theory, fluctuation dissipation relations, and detailed balance do not apply. The {\\em generalized} fluctuation-dissipation relation, however, states that even under strongly thermodynam...

  6. On two-dimensional fractional Brownian motion and fractional Brownian random field

    OpenAIRE

    Qian, Hong; Raymond, Gary M.; Bassingthwaighte, James B.

    1998-01-01

    As a generalization of one-dimensional fractional Brownian motion (1dfBm), we introduce a class of two-dimensional, self-similar, strongly correlated random walks whose variance scales with power law N2H (0 < H < 1). We report analytical results on the statistical size and shape, and segment distribution of its trajectory in the limit of large N. The relevance of these results to polymer theory is discussed. We also study the basic properties of a second generalization of 1dfBm, the two-dimen...

  7. Brownian dipole rotator in alternating electric field

    Science.gov (United States)

    Rozenbaum, V. M.; Vovchenko, O. Ye.; Korochkova, T. Ye.

    2008-06-01

    The study addresses the azimuthal jumping motion of an adsorbed polar molecule in a periodic n -well potential under the action of an external alternating electric field. Starting from the perturbation theory of the Pauli equation with respect to the weak field intensity, explicit analytical expressions have been derived for the time dependence of the average dipole moment as well as the frequency dependences of polarizability and the average angular velocity, the three quantities exhibiting conspicuous stochastic resonance. As shown, unidirectional rotation can arise only provided simultaneous modulation of the minima and maxima of the potential by an external alternating field. For a symmetric potential of hindered rotation, the average angular velocity, if calculated by the second-order perturbation theory with respect to the field intensity, has a nonzero value only at n=2 , i.e., when two azimuthal wells specify a selected axis in the system. Particular consideration is given to the effect caused by the asymmetry of the two-well potential on the dielectric loss spectrum and other Brownian motion parameters. When the asymmetric potential in a system of dipole rotators arises from the average local fields induced by an orientational phase transition, the characteristics concerned show certain peculiarities which enable detection of the phase transition and determination of its parameters.

  8. Ideal bulk pressure of active Brownian particles

    Science.gov (United States)

    Speck, Thomas; Jack, Robert L.

    2016-06-01

    The extent to which active matter might be described by effective equilibrium concepts like temperature and pressure is currently being discussed intensely. Here, we study the simplest model, an ideal gas of noninteracting active Brownian particles. While the mechanical pressure exerted onto confining walls has been linked to correlations between particles' positions and their orientations, we show that these correlations are entirely controlled by boundary effects. We also consider a definition of local pressure, which describes interparticle forces in terms of momentum exchange between different regions of the system. We present three pieces of analytical evidence which indicate that such a local pressure exists, and we show that its bulk value differs from the mechanical pressure exerted on the walls of the system. We attribute this difference to the fact that the local pressure in the bulk does not depend on boundary effects, contrary to the mechanical pressure. We carefully examine these boundary effects using a channel geometry, and we show a virial formula for the pressure correctly predicts the mechanical pressure even in finite channels. However, this result no longer holds in more complex geometries, as exemplified for a channel that includes circular obstacles.

  9. Engineered swift equilibration of a Brownian particle

    Science.gov (United States)

    Martínez, Ignacio A.; Petrosyan, Artyom; Guéry-Odelin, David; Trizac, Emmanuel; Ciliberto, Sergio

    2016-09-01

    A fundamental and intrinsic property of any device or natural system is its relaxation time τrelax, which is the time it takes to return to equilibrium after the sudden change of a control parameter. Reducing τrelax is frequently necessary, and is often obtained by a complex feedback process. To overcome the limitations of such an approach, alternative methods based on suitable driving protocols have been recently demonstrated, for isolated quantum and classical systems. Their extension to open systems in contact with a thermostat is a stumbling block for applications. Here, we design a protocol, named Engineered Swift Equilibration (ESE), that shortcuts time-consuming relaxations, and we apply it to a Brownian particle trapped in an optical potential whose properties can be controlled in time. We implement the process experimentally, showing that it allows the system to reach equilibrium 100 times faster than the natural equilibration rate. We also estimate the increase of the dissipated energy needed to get such a time reduction. The method paves the way for applications in micro- and nano-devices, where the reduction of operation time represents as substantial a challenge as miniaturization.

  10. Brownian dipole rotator in alternating electric field.

    Science.gov (United States)

    Rozenbaum, V M; Vovchenko, O Ye; Korochkova, T Ye

    2008-06-01

    The study addresses the azimuthal jumping motion of an adsorbed polar molecule in a periodic n -well potential under the action of an external alternating electric field. Starting from the perturbation theory of the Pauli equation with respect to the weak field intensity, explicit analytical expressions have been derived for the time dependence of the average dipole moment as well as the frequency dependences of polarizability and the average angular velocity, the three quantities exhibiting conspicuous stochastic resonance. As shown, unidirectional rotation can arise only provided simultaneous modulation of the minima and maxima of the potential by an external alternating field. For a symmetric potential of hindered rotation, the average angular velocity, if calculated by the second-order perturbation theory with respect to the field intensity, has a nonzero value only at n=2 , i.e., when two azimuthal wells specify a selected axis in the system. Particular consideration is given to the effect caused by the asymmetry of the two-well potential on the dielectric loss spectrum and other Brownian motion parameters. When the asymmetric potential in a system of dipole rotators arises from the average local fields induced by an orientational phase transition, the characteristics concerned show certain peculiarities which enable detection of the phase transition and determination of its parameters. PMID:18643221

  11. Effect of interfaces on the nearby Brownian motion

    CERN Document Server

    Huang, Kai

    2016-01-01

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

  12. Lévy flight and Brownian search patterns of a free-ranging predator reflect different prey field characteristics.

    Science.gov (United States)

    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

  13. Quantum Brownian motion model for the stock market

    Science.gov (United States)

    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.

  14. Brownian dynamics simulations with hard-body interactions: Spherical particles

    CERN Document Server

    Behringer, Hans; 10.1063/1.4761827

    2012-01-01

    A novel approach to account for hard-body interactions in (overdamped) Brownian dynamics simulations is proposed for systems with non-vanishing force fields. The scheme exploits the analytically known transition probability for a Brownian particle on a one-dimensional half-line. The motion of a Brownian particle is decomposed into a component that is affected by hard-body interactions and into components that are unaffected. The hard-body interactions are incorporated by replacing the affected component of motion by the evolution on a half-line. It is discussed under which circumstances this approach is justified. In particular, the algorithm is developed and formulated for systems with space-fixed obstacles and for systems comprising spherical particles. The validity and justification of the algorithm is investigated numerically by looking at exemplary model systems of soft matter, namely at colloids in flow fields and at protein interactions. Furthermore, a thorough discussion of properties of other heurist...

  15. Stochastic calculus for fractional Brownian motion and related processes

    CERN Document Server

    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 0Brownian SDE. The author develops optimal filtering of mixed models including linear case, and studies financial applications and statistical inference with hypotheses testing and parameter estimation. She proves that the market with stock guided by the mixed model is arbitrage-free without any restriction on the dependence of the components and deduces different forms of the Black-Scholes equation for fractional mark...

  16. Brownian Dynamics of charged particles in a constant magnetic field

    CERN Document Server

    Hou, L J; Piel, A; Shukla, P K

    2009-01-01

    Numerical algorithms are proposed for simulating the Brownian dynamics of charged particles in an external magnetic field, taking into account the Brownian motion of charged particles, damping effect and the effect of magnetic field self-consistently. Performance of these algorithms is tested in terms of their accuracy and long-time stability by using a three-dimensional Brownian oscillator model with constant magnetic field. Step-by-step recipes for implementing these algorithms are given in detail. It is expected that these algorithms can be directly used to study particle dynamics in various dispersed systems in the presence of a magnetic field, including polymer solutions, colloidal suspensions and, particularly complex (dusty) plasmas. The proposed algorithms can also be used as thermostat in the usual molecular dynamics simulation in the presence of magnetic field.

  17. Movement and Man at the end of the Random Walks

    CERN Document Server

    Sacripanti, Attilio

    2008-01-01

    In this paper, it is presented the well known aspect of non linearity of internal human body structures. Similarity on the basis of the Fractional Brownian Motion from the static ones, as the geometrical fractals like the Intestine and placenta linings, Airways in lungs, Arterial system in kidneys and so on. To the kinematics ones, as the temporal fractals like Heart beat sequences, Electroencephalograms, Respiratory tidal volumes, DNA sequences mapping and so on. But this internal well known knowledge is astonishing extendible from the internal, through the Brownian basis of the muscular contraction, to the macroscopic external human movements, like the orthostatic equilibrium, gait, running training, judo contest and soccer, basketball, football or water polo games, by means of the ubiquitous continuous presence; the Brownian Dynamics.

  18. Stochastic description of quantum Brownian dynamics

    Science.gov (United States)

    Yan, Yun-An; Shao, Jiushu

    2016-08-01

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

  19. Direct observation of ballistic Brownian motion on a single particle

    OpenAIRE

    Huang, Rongxin; Lukic, Branimir; Jeney, Sylvia; Florin, Ernst-Ludwig

    2010-01-01

    At fast timescales, the self-similarity of random Brownian motion is expected to break down and be replaced by ballistic motion. So far, an experimental verification of this prediction has been out of reach due to a lack of instrumentation fast and precise enough to capture this motion. With a newly developed detector, we have been able to observe the Brownian motion of a single particle in an optical trap with 75 MHz bandwidth and sub-{AA}ngstrom spatial precision. We report the first measur...

  20. DNA transport by a micromachined Brownian ratchet device

    CERN Document Server

    Bader, J S; Henck, S A; Deem, M W; McDermott, G A; Bustillo, J M; Simpson, J W; Mulhern, G T; Rothberg, J M; Bader, Joel S; Hammond, Richard W.; Henck, Steven A.; Deem, Michael W.; Dermott, Gregory A. Mc; Bustillo, James M.; Simpson, John W.; Mulhern, Gregory T.; Rothberg, Jonathan M.

    1999-01-01

    We have micromachined a silicon-chip device that transports DNA with aBrownian ratchet that rectifies the Brownian motion of microscopic particles.Transport properties for a DNA 50mer agree with theoretical predictions, andthe DNA diffusion constant agrees with previous experiments. This type ofmicromachine could provide a generic pump or separation component for DNA orother charged species as part of a microscale lab-on-a-chip. A device withreduced feature size could produce a size-based separation of DNA molecules,with applications including the detection of single nucleotide polymorphisms.

  1. Energy and efficiency optimization of a Brownian heat engine

    Science.gov (United States)

    Bekele, Mulugeta; Yalew, Yeneneh

    2007-03-01

    A simple Brownian heat engine is modeled as a Brownian particle moving in an external sawtooth potential (with or without) load assisted by the thermal kick it gets from alternately placed hot and cold heat reservoirs along its path. We get closed form expression for its current in terms of the parameters characterizing the model. After analyzing the way it consumes energy to do useful work, we also get closed form expressions for its efficiency as well as for its coefficient of performance when the engine performs as a refrigerator. Recently suggested optimization criteria enables us to exhaustively explore and compare the different operating conditions of the engine.

  2. Semicircular canals circumvent Brownian Motion overload of mechanoreceptor hair cells

    DEFF Research Database (Denmark)

    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...... to circumvent Brownian motion overload at the hair bundles. We suggest that the selective advantage of detecting such low frequency stimuli may have favoured the evolution of large guiding structures such as semicircular canals and otoliths to overcome Brownian Motion noise at the level of the mechanoreceptors...

  3. The dimension of the Brownian frontier is greater than 1

    OpenAIRE

    Bishop, Christopher J.; Jones, Peter; Pemantle, Robin; Peres, Yuval

    1995-01-01

    Consider a planar Brownian motion run for finite time. The frontier or ``outer boundary'' of the path is the boundary of the unbounded component of the complement. Burdzy (1989) showed that the frontier has infinite length. We improve this by showing that the Hausdorff dimension of the frontier is strictly greater than 1. (It has been conjectured that the Brownian frontier has dimension $4/3$, but this is still open.) The proof uses Jones's Traveling Salesman Theorem and a self-similar tiling...

  4. Winding statistics of a Brownian particle on a ring

    International Nuclear Information System (INIS)

    We consider a Brownian particle moving on a ring. We study the probability distributions of the total number of turns and the net number of counter-clockwise turns the particle makes until time t. Using a method based on the renewal properties of a Brownian walker, we find exact analytical expressions of these distributions. This method serves as an alternative to the standard path integral techniques which are not always easily adaptable for certain observables. For large t, we show that these distributions have Gaussian scaling forms. We also compute large deviation functions associated to these distributions characterizing atypically large fluctuations. We provide numerical simulations in support of our analytical results. (paper)

  5. Fractional Brownian Motion and Sheet as White Noise Functionals

    Institute of Scientific and Technical Information of China (English)

    Zhi Yuan HUANG; Chu Jin LI; Jian Ping WAN; Ying WU

    2006-01-01

    In this short note, we show that it is more natural to look the fractional Brownian motion as functionals of the standard white noises, and the fractional white noise calculus developed by Hu and (φ)ksendal follows directly from the classical white noise functional calculus. As examples we prove that the fractional Girsanov formula, the Ito type integrals and the fractional Black-Scholes formula are easy consequences of their classical counterparts. An extension to the fractional Brownian sheet is also briefly discussed.

  6. Stability theorems for stochastic differential equations driven by G-Brownian motion

    OpenAIRE

    Zhang, Defei

    2011-01-01

    In this paper, stability theorems for stochastic differential equations and backward stochastic differential equations driven by G-Brownian motion are obtained. We show the existence and uniqueness of solutions to forward-backward stochastic differential equations driven by G-Brownian motion. Stability theorem for forward-backward stochastic differential equations driven by G-Brownian motion is also presented.

  7. Option Pricing in a Fractional Brownian Motion Environment

    OpenAIRE

    Cipian Necula

    2008-01-01

    The purpose of this paper is to obtain a fractional Black-Scholes formula for the price of an option for every t in [0,T], a fractional Black-Scholes equation and a risk-neutral valuation theorem if the underlying is driven by a fractional Brownian motion BH (t), 1/2

  8. The maximum of Brownian motion with parabolic drift

    OpenAIRE

    Janson, Svante; Louchard, Guy; Martin-Löf, Anders

    2010-01-01

    We study the maximum of a Brownian motion with a parabolic drift; this is a random variable that often occurs as a limit of the maximum of discrete processes whose expectations have a maximum at an interior point. We give new series expansions and integral formulas for the distribution and the first two moments, together with numerical values to high precision.

  9. Occupation times distribution for Brownian motion on graphs

    CERN Document Server

    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)

  10. Occupation times distribution for Brownian motion on graphs

    International Nuclear Information System (INIS)

    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)

  11. Occupation times distribution for Brownian motion on graphs

    Energy Technology Data Exchange (ETDEWEB)

    Desbois, Jean [Laboratoire de Physique Theorique et Modeles Statistiques, Universite Paris-Sud, Bat. 100, F-91405 Orsay (France)

    2002-11-22

    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)

  12. Fuzzy Itand#244; Integral Driven by a Fuzzy Brownian Motion

    OpenAIRE

    Didier Kumwimba Seya; Rostin Mabela Makengo; Marcel Rémon; Walo Omana Rebecca

    2015-01-01

    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.

  13. Diffusion of Particle in Hyaluronan Solution, a Brownian Dynamics Simulation

    Science.gov (United States)

    Takasu, Masako; Tomita, Jungo

    2004-04-01

    Diffusion of a particle in hyaluronan solution is investigated using Brownian dynamics simulation. The slowing down of diffusion is observed, in accordance with the experimental results. The temperature dependence of the diffusion is calculated, and a turnover is obtained when the temperature is increased.

  14. Rotational Brownian Motion on Sphere Surface and Rotational Relaxation

    Institute of Scientific and Technical Information of China (English)

    Ekrem Aydner

    2006-01-01

    The spatial components of the autocorrelation function of noninteracting dipoles are analytically obtained in terms of rotational Brownian motion on the surface of a unit sphere using multi-level jumping formalism based on Debye's rotational relaxation model, and the rotational relaxation functions are evaluated.

  15. SOME GEOMETRIC PROPERTIES OF BROWNIAN MOTION ON SIERPINSKI GASKET

    Institute of Scientific and Technical Information of China (English)

    WUJUN; XIAOYIMIN

    1995-01-01

    Let {X(t),t≥0} be Brownian motion on Sierpinski gasket,The Hausdorff and packing dimensions of the image of a ompact set are studied,The uniform Hausdorff and packing dimensions of the inverse image are also discussed.

  16. Brownian motion, geometry, and generalizations of Picard's little theorem

    OpenAIRE

    Goldberg, S. I.; Mueller, C.

    1982-01-01

    Brownian motion is introduced as a tool in Riemannian geometry to show how useful it is in the function theory of manifolds, as well as the study of maps between manifolds. As applications, a generalization of Picard's little theorem, and a version of it for Riemann surfaces of large genus are given.

  17. On the Generalized Brownian Motion and its Applications in Finance

    DEFF Research Database (Denmark)

    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 ...

  18. Brownian molecular rotors: Theoretical design principles and predicted realizations

    OpenAIRE

    Schönborn, Jan Boyke; Herges, Rainer; Hartke, Bernd

    2009-01-01

    We propose simple design concepts for molecular rotors driven by Brownian motion and external photochemical switching. Unidirectionality and efficiency of the motion is measured by explicit simulations. Two different molecular scaffolds are shown to yield viable molecular rotors when decorated with suitable substituents.

  19. ABSOLUTE CONTINUITY FOR INTERACTING MEASURE-VALUED BRANCHING BROWNIAN MOTIONS

    Institute of Scientific and Technical Information of China (English)

    ZHAOXUELEI

    1997-01-01

    The moments and absohite continuity of measure-valued branching Brownian motions with bounded interacting intensity are hivestigated. An estimate of higher order moments is obtained. The ahsolute continuity is verified in the one dimension case. This therehy verifies the conjecture of Méléard and Roelly in [5].

  20. Wrapping Brownian motion and heat kernels II: symmetric spaces

    CERN Document Server

    Maher, David G

    2010-01-01

    In this paper we extend our previous results on wrapping Brownian motion and heat kernels onto compact Lie groups to various symmetric spaces, where a global generalisation of Rouvi\\`ere's formula and the $e$-function are considered. Additionally, we extend some of our results to complex Lie groups, and certain non-compact symmetric spaces.

  1. The valuation of currency options by fractional Brownian motion.

    Science.gov (United States)

    Shokrollahi, Foad; Kılıçman, Adem

    2016-01-01

    This research aims to investigate a model for pricing of currency options in which value governed by the fractional Brownian motion model (FBM). The fractional partial differential equation and some Greeks are also obtained. In addition, some properties of our pricing formula and simulation studies are presented, which demonstrate that the FBM model is easy to use. PMID:27504243

  2. Brownian motion and the parabolicity of minimal graphs

    OpenAIRE

    Neel, Robert W.

    2008-01-01

    We prove that minimal graphs (other than planes) are parabolic in the sense that any bounded harmonic function is determined by its boundary values. The proof relies on using the coupling introduced in the author's earlier paper "A martingale approach to minimal surfaces" to show that Brownian motion on such a minimal graph almost surely strikes the boundary in finite time.

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

    Directory of Open Access Journals (Sweden)

    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."

  4. Coupling effect of Brownian motion and laminar shear flow on colloid coagulation: a Brownian dynamics simulation study

    Institute of Scientific and Technical Information of China (English)

    Xu Sheng-Hua; Sun Zhi-Wei; Li Xu; Jin Tong Wang

    2012-01-01

    Simultaneous orthokinetic and perikinetic coagulations(SOPCs)are studied for small and large Peclet numbers(Pe)using Brownian dynamics simulation.The results demonstrate that the contributions of the Brownian motion and the shear flow to the overall coagulation rate are basically not additive.At the early stages of coagulation with small Peclet numbers,the ratio of overall coagulation rate to the rate of pure perikinetic coagulation is proportional to Pe1/2,while with high Peclet numbers,the ratio of overall coagulation rate to the rate of pure orthokinetic coagulation is proportional to pe-1/2.Moreover,our results show that the aggregation rate generally changes with time for the SOPC,which is different from that for pure preikinetic and pure orthokinetic coagulations.By comparing the SOPC with pure preikinetic and pure orthokinetic coagulations,we show that the redistribution of particles due to Brownian motion can play a very important role in the SOPC.In addition,the effects of redistribution in the directions perpendicular and parallel to the shear flow direction are different.This perspective explains the behavior of coagulation due to the joint effects of the Brownian motion(perikinetic)and the fluid motion(orthokinetic).

  5. Two-dimensional motion of Brownian swimmers in linear flows.

    Science.gov (United States)

    Sandoval, Mario; Jimenez, Alonso

    2016-03-01

    The motion of viruses and bacteria and even synthetic microswimmers can be affected by thermal fluctuations and by external flows. In this work, we study the effect of linear external flows and thermal fluctuations on the diffusion of those swimmers modeled as spherical active (self-propelled) particles moving in two dimensions. General formulae for their mean-square displacement under a general linear flow are presented. We also provide, at short and long times, explicit expressions for the mean-square displacement of a swimmer immersed in three canonical flows, namely, solid-body rotation, shear and extensional flows. These expressions can now be used to estimate the effect of external flows on the displacement of Brownian microswimmers. Finally, our theoretical results are validated by using Brownian dynamics simulations. PMID:26428909

  6. Multiscale Reaction-Diffusion Algorithms: PDE-Assisted Brownian Dynamics

    KAUST Repository

    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.

  7. Human behavioral regularity, fractional Brownian motion, and exotic phase transition

    Science.gov (United States)

    Li, Xiaohui; Yang, Guang; An, Kenan; Huang, Jiping

    2016-08-01

    The mix of competition and cooperation (C&C) is ubiquitous in human society, which, however, remains poorly explored due to the lack of a fundamental method. Here, by developing a Janus game for treating C&C between two sides (suppliers and consumers), we show, for the first time, experimental and simulation evidences for human behavioral regularity. This property is proved to be characterized by fractional Brownian motion associated with an exotic transition between periodic and nonperiodic phases. Furthermore, the periodic phase echoes with business cycles, which are well-known in reality but still far from being well understood. Our results imply that the Janus game could be a fundamental method for studying C&C among humans in society, and it provides guidance for predicting human behavioral activity from the perspective of fractional Brownian motion.

  8. Fast simulation of Brownian dynamics in a crowded environment

    CERN Document Server

    Smith, Stephen

    2016-01-01

    Brownian dynamics simulations are an increasingly popular tool for understanding spatially-distributed biochemical reaction systems. Recent improvements in our understanding of the cellular environment show that volume exclusion effects are fundamental to reaction networks inside cells. These systems are frequently studied by incorporating inert hard spheres (crowders) into three-dimensional Brownian dynamics simulations, however these methods are extremely slow owing to the sheer number of possible collisions between particles. Here we propose a rigorous "crowder-free" method to dramatically increase simulation speed for crowded biochemical reaction systems by eliminating the need to explicitly simulate the crowders. We consider both the case where the reactive particles are point particles, and where they themselves occupy a volume. We use simulations of simple chemical reaction networks to confirm that our simplification is just as accurate as the original algorithm, and that it corresponds to a large spee...

  9. The maximum of Brownian motion with parabolic drift (Extended abstract)

    OpenAIRE

    Janson, Svante; Louchard, Guy; Martin-Löf, Anders

    2010-01-01

    We study the maximum of a Brownian motion with a parabolic drift; this is a random variable that often occurs as a limit of the maximum of discrete processes whose expectations have a maximum at an interior point. This has some applications in algorithmic and data structures analysis. We give series expansions and integral formulas for the distribution and the first two moments, together with numerical values to high precision.

  10. The frustrated Brownian motion of nonlocal solitary waves

    CERN Document Server

    Folli, Viola

    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 non-paraxial effects. Analytical predictions are compared with numerical simulations based on stochastic partial differential equation

  11. GENERALIZED BROWNIAN SHEET IMAGES AND BESSEL-RIESZ CAPACITY

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    Let (W) be a two-parameter Rd-valued generalized Brownian sheet. The author obtains an explicit Bessel-Riesz capacity estimate for the images of a two-dimensional set under (W). He also presents the connections between the Lebesgue measure of the image of (W) and Bessel-Riesz capacity. His conclusions also solve a problem proposed by J.P.Kahane.

  12. Anyonic partition functions and windings of planar Brownian motion

    International Nuclear Information System (INIS)

    The computation of the N-cycle Brownian paths contribution FN(α) to the N-anyon partition function is addressed. A detailed numerical analysis based on a random walk on a lattice indicates that FN0(α)=product k=1N-1[1-(N/k)α]. In the paramount three-anyon case, one can show that F3(α) is built by linear states belonging to the bosonic, fermionic, and mixed representations of S3

  13. On moments of the integrated exponential Brownian motion

    Science.gov (United States)

    Caravelli, Francesco; Mansour, Toufik; Sindoni, Lorenzo; Severini, Simone

    2016-07-01

    We present new exact expressions for a class of moments of the geometric Brownian motion in terms of determinants, obtained using a recurrence relation and combinatorial arguments for the case of a Itô's Wiener process. We then apply the obtained exact formulas to computing averages of the solution of the logistic stochastic differential equation via a series expansion, and compare the results to the solution obtained via Monte Carlo.

  14. Rapid morphological characterization of isolated mitochondria using Brownian motion†

    OpenAIRE

    Palanisami, Akilan; Fang, Jie; Lowder, Thomas W.; Kunz, Hawley; John H Miller

    2012-01-01

    Mitochondrial morphology has been associated with numerous pathologies including cancer, diabetes, obesity and heart disease. However, the connection is poorly understood—in part due to the difficulty of characterizing the morphology. This impedes the use of morphology as a tool for disease detection/monitoring. Here, we use the Brownian motion of isolated mitochondria to characterize their size and shape in a high throughput fashion. By using treadmill exercise training, mitochondria from he...

  15. Hidden symmetries, instabilities, and current suppression in Brownian ratchets

    OpenAIRE

    Cubero, David; Renzoni, Ferruccio

    2015-01-01

    The operation of Brownian motors is usually described in terms of out-of-equilibrium and symmetrybreaking settings, with the relevant spatiotemporal symmetries identified from the analysis of the equations of motion for the system at hand. When the appropriate conditions are satisfied,symmetry related trajectories with opposite current are thought to balance each other, yielding suppression of transport. The direction of the current can be precisely controlled around these symmetry points by...

  16. Brownian motion vs. pure-jump processes for individual stocks

    OpenAIRE

    Benoît Sévi; César Baena

    2011-01-01

    Using recent activity signature function methodology developed in Todorov and Tauchen (2010), we provide empirical evidence that individual stocks from the New York Stock Exchange are adequately represented by a Brownian motion plus medium to large (rare) jumps thus invalidating the pure-jump process hypothesis proposed in numerous contributions. This result improves our understanding of the fine structure of asset prices and has implications for derivatives pricing.

  17. Non-Markovian weak coupling limit of quantum Brownian motion

    OpenAIRE

    Maniscalco, Sabrina; Piilo, Jyrki; Suominen, Kalle-Antti

    2008-01-01

    We derive and solve analytically the non-Markovian master equation for harmonic quantum Brownian motion proving that, for weak system-reservoir couplings and high temperatures, it can be recast in the form of the master equation for a harmonic oscillator interacting with a squeezed thermal bath. This equivalence guarantees preservation of positivity of the density operator during the time evolution and allows one to establish a connection between the dynamics of Schr\\"odinger cat states in sq...

  18. Amoeba-inspired nanoarchitectonic computing implemented using electrical Brownian ratchets.

    Science.gov (United States)

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

    2015-06-12

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

  19. A discrete impulsive model for random heating and Brownian motion

    Science.gov (United States)

    Ramshaw, John D.

    2010-01-01

    The energy of a mechanical system subjected to a random force with zero mean increases irreversibly and diverges with time in the absence of friction or dissipation. This random heating effect is usually encountered in phenomenological theories formulated in terms of stochastic differential equations, the epitome of which is the Langevin equation of Brownian motion. We discuss a simple discrete impulsive model that captures the essence of random heating and Brownian motion. The model may be regarded as a discrete analog of the Langevin equation, although it is developed ab initio. Its analysis requires only simple algebraic manipulations and elementary averaging concepts, but no stochastic differential equations (or even calculus). The irreversibility in the model is shown to be a consequence of a natural causal stochastic condition that is closely analogous to Boltzmann's molecular chaos hypothesis in the kinetic theory of gases. The model provides a simple introduction to several ostensibly more advanced topics, including random heating, molecular chaos, irreversibility, Brownian motion, the Langevin equation, and fluctuation-dissipation theorems.

  20. Stochastic Calculus with respect to multifractional Brownian motion

    CERN Document Server

    Lebovits, Joachim

    2011-01-01

    Stochastic calculus with respect to fractional Brownian motion (fBm) has attracted a lot of interest in recent years, motivated in particular by applications in finance and Internet traffic modeling. Multifractional Brownian motion (mBm) is a Gaussian extension of fBm that allows to control the pointwise regularity of the paths of the process and to decouple it from its long range dependence properties. This generalization is obtained by replacing the constant Hurst parameter H of fBm by a function h(t). Multifractional Brownian motion has proved useful in many applications, including the ones just mentioned. In this work we extend to mBm the construction of a stochastic integral with respect to fBm. This stochastic integral is based on white noise theory, as originally proposed in [15], [6], [4] and in [5]. In that view, a multifractional white noise is defined, which allows to integrate with respect to mBm a large class of stochastic processes using Wick products. It\\^o formulas (both for tempered distribut...

  1. Semicircular Canals Circumvent Brownian Motion Overload of Mechanoreceptor Hair Cells.

    Directory of Open Access Journals (Sweden)

    Mees Muller

    Full Text Available Vertebrate semicircular canals (SCC first appeared in the vertebrates (i.e. ancestral fish over 600 million years ago. In SCC the principal mechanoreceptors are hair cells, which as compared to cochlear hair cells are distinctly longer (70 vs. 7 μm, 10 times more compliant to bending (44 vs. 500 nN/m, and have a 100-fold higher tip displacement threshold (< 10 μm vs. <400 nm. We have developed biomechanical models of vertebrate hair cells where the bundle is approximated as a stiff, cylindrical elastic rod subject to friction and thermal agitation. Our models suggest that the above differences aid SCC hair cells in circumventing the masking effects of Brownian motion noise of about 70 nm, and thereby permit transduction of very low frequency (<10 Hz signals. We observe that very low frequency mechanoreception requires increased stimulus amplitude, and argue that this is adaptive to circumvent Brownian motion overload at the hair bundles. We suggest that the selective advantage of detecting such low frequency stimuli may have favoured the evolution of large guiding structures such as semicircular canals and otoliths to overcome Brownian Motion noise at the level of the mechanoreceptors of the SCC.

  2. Semicircular Canals Circumvent Brownian Motion Overload of Mechanoreceptor Hair Cells.

    Science.gov (United States)

    Muller, Mees; Heeck, Kier; Elemans, Coen P H

    2016-01-01

    Vertebrate semicircular canals (SCC) first appeared in the vertebrates (i.e. ancestral fish) over 600 million years ago. In SCC the principal mechanoreceptors are hair cells, which as compared to cochlear hair cells are distinctly longer (70 vs. 7 μm), 10 times more compliant to bending (44 vs. 500 nN/m), and have a 100-fold higher tip displacement threshold (< 10 μm vs. <400 nm). We have developed biomechanical models of vertebrate hair cells where the bundle is approximated as a stiff, cylindrical elastic rod subject to friction and thermal agitation. Our models suggest that the above differences aid SCC hair cells in circumventing the masking effects of Brownian motion noise of about 70 nm, and thereby permit transduction of very low frequency (<10 Hz) signals. We observe that very low frequency mechanoreception requires increased stimulus amplitude, and argue that this is adaptive to circumvent Brownian motion overload at the hair bundles. We suggest that the selective advantage of detecting such low frequency stimuli may have favoured the evolution of large guiding structures such as semicircular canals and otoliths to overcome Brownian Motion noise at the level of the mechanoreceptors of the SCC. PMID:27448330

  3. Brownian relaxation of an inelastic sphere in air

    Science.gov (United States)

    Bird, G. A.

    2016-06-01

    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.

  4. Striking movements

    DEFF Research Database (Denmark)

    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 define...... affect the movements. Furthermore, I discuss differences in movement organization, and visual information from striking movements.......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...

  5. Brownian motion at fast time scales and thermal noise imaging

    Science.gov (United States)

    Huang, Rongxin

    This dissertation presents experimental studies on Brownian motion at fast time scales, as well as our recent developments in Thermal Noise Imaging which uses thermal motions of microscopic particles for spatial imaging. As thermal motions become increasingly important in the studies of soft condensed matters, the study of Brownian motion is not only of fundamental scientific interest but also has practical applications. Optical tweezers with a fast position-sensitive detector provide high spatial and temporal resolution to study Brownian motion at fast time scales. A novel high bandwidth detector was developed with a temporal resolution of 30 ns and a spatial resolution of 1 A. With this high bandwidth detector, Brownian motion of a single particle confined in an optical trap was observed at the time scale of the ballistic regime. The hydrodynamic memory effect was fully studied with polystyrene particles of different sizes. We found that the mean square displacements of different sized polystyrene particles collapse into one master curve which is determined by the characteristic time scale of the fluid inertia effect. The particle's inertia effect was shown for particles of the same size but different densities. For the first time the velocity autocorrelation function for a single particle was shown. We found excellent agreement between our experiments and the hydrodynamic theories that take into account the fluid inertia effect. Brownian motion of a colloidal particle can be used to probe three-dimensional nano structures. This so-called thermal noise imaging (TNI) has been very successful in imaging polymer networks with a resolution of 10 nm. However, TNI is not efficient at micrometer scale scanning since a great portion of image acquisition time is wasted on large vacant volume within polymer networks. Therefore, we invented a method to improve the efficiency of large scale scanning by combining traditional point-to-point scanning to explore large vacant

  6. Karhunen-Loève Expansion for the Second Order Detrended Brownian Motion

    Directory of Open Access Journals (Sweden)

    Yongchun Zhou

    2014-01-01

    Full Text Available Based on the norm in the Hilbert Space L2[0,1], the second order detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion into the space spanned by nonlinear function subspace. Karhunen-Loève expansion for this process is obtained together with the relationship of that of a generalized Brownian bridge. As applications, Laplace transform, large deviation, and small deviation are given.

  7. Convergence in Law to Operator Fractional Brownian Motion of Riemann-Liouville Type

    Institute of Scientific and Technical Information of China (English)

    Hong Shuai DAI

    2013-01-01

    In this paper,we extend the well-studied fractional Brownian motion of Riemann-Liouville type to the multivariate case,and the corresponding processes are called operator fractional Brownian motions of Riemann-Liouville type.We also provide two results on approximation to operator fractional Brownian motions of Riemann-Liouville type.The first approximation is based on a Poisson process,and the second one is based on a sequence of I.I.D.random variables.

  8. Self-intersection local times and collision local times of bifractional Brownian motions

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    In this paper, we consider the local time and the self-intersection local time for a bifractional Brownian motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the existence and smoothness of the self-intersection local time and the collision local time, through the strong local nondeterminism of bifractional Brownian motion, L2 convergence and Chaos expansion.

  9. Brownian dynamics in a confined geometry. Experiments and numerical simulations

    OpenAIRE

    Garnier, Nicolas; Ostrowsky, N.

    1991-01-01

    The Brownian dynamics of a colloidal suspension is measured in the immediate vicinity of a rigid surface by the Evanescent Quasielastic Light Scattering Technique. A net decrease of the measured diffusion coefficient is observed, due to the hydrodynamic slowing down of the particles very close to the wall. This effect is all the more important when the particles are allowed to get closer to the wall, i.e. when the range of the static wall/particle repulsive interaction decreases. It thus prov...

  10. A Flashing Model for Transport of Brownian Motors

    Institute of Scientific and Technical Information of China (English)

    赵同军; 展永; 吴建海; 王永宏

    2002-01-01

    A flashing coloured noise model is proposed to describe the motion of a molecular motor. In this model,the overdamped Brownian particle moves in an asymmetric periodic potential with a tashing Ornstein-Ulenbeck coloured noise. The relationship between the current and the parameters-such as the intensity, the correlation time of coloured noise and the flip rate of the noise-is discussed using the Monte Carlo simulation method.Current reversal occurs with the change of the correlation time and the flip rate of coloured noise, which may be related to the directed motion and the current reversal of molecular motors.

  11. Some Results on Fractional Brownian Sheets and Their Local Times

    Institute of Scientific and Technical Information of China (English)

    Zong-mao Cheng; Zheng-yan Lin

    2008-01-01

    Let BHO={BHO(t),E RN+} be a real-valued fractional Brownian sheet. Define the (N,d)-Ganssian random field BH by where BH1,..., BHd are independent copies of BHO. The existence and joint continuity of local times of BH is proven in some given conditions in [22]. We then study further properties of the local times of BH, such as the moments of increments of local times, the large increments and the maximum moduli of continuity of local times and as a result, we answer the questions posed in [22].

  12. Quantum correlations from Brownian diffusion of chaotic level-spacings

    CERN Document Server

    Evangelou, S N

    2004-01-01

    Quantum chaos is linked to Brownian diffusion of the underlying quantum energy level-spacing sequences. The level-spacings viewed as functions of their order execute random walks which imply uncorrelated random increments of the level-spacings while the integrability to chaos transition becomes a change from Poisson to Gauss statistics for the level-spacing increments. This universal nature of quantum chaotic spectral correlations is numerically demonstrated for eigenvalues from random tight binding lattices and for zeros of the Riemann zeta function.

  13. Occupation times for planar and higher dimensional Brownian motion

    International Nuclear Information System (INIS)

    We consider a planar Brownian motion starting from O at time t = 0 and stopped at t. Denoting by T the time spent in a wedge of apex O and angle Θ, we develop a method to compute systematically the moments of T for general Θ values. We apply it to obtain analytically the second and third moments for a general wedge angle and, also, the fourth moment for the quadrant (Θ = π/2). We compare our results with numerical simulations. Finally, with standard perturbation theory, we establish a general formula for the second moment of an orthant occupation time

  14. Moments of inertia and the shapes of Brownian paths

    International Nuclear Information System (INIS)

    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

  15. Algebraic and arithmetic area for $m$ planar Brownian paths

    OpenAIRE

    Desbois, Jean; Ouvry, Stephane

    2011-01-01

    The leading and next to leading terms of the average arithmetic area $$ enclosed by $m\\to\\infty$ independent closed Brownian planar paths, with a given length $t$ and starting from and ending at the same point, is calculated. The leading term is found to be $ \\sim {\\pi t\\over 2}\\ln m$ and the $0$-winding sector arithmetic area inside the $m$ paths is subleading in the asymptotic regime. A closed form expression for the algebraic area distribution is also obtained and discussed.

  16. Occupation times for planar and higher dimensional Brownian motion

    Energy Technology Data Exchange (ETDEWEB)

    Desbois, Jean [CNRS, University Paris Sud, UMR8626, LPTMS, ORSAY CEDEX, F-91405 (France)

    2007-03-09

    We consider a planar Brownian motion starting from O at time t = 0 and stopped at t. Denoting by T the time spent in a wedge of apex O and angle {theta}, we develop a method to compute systematically the moments of T for general {theta} values. We apply it to obtain analytically the second and third moments for a general wedge angle and, also, the fourth moment for the quadrant ({theta} = {pi}/2). We compare our results with numerical simulations. Finally, with standard perturbation theory, we establish a general formula for the second moment of an orthant occupation time.

  17. Anyonic Partition Functions and Windings of Planar Brownian Motion

    OpenAIRE

    Desbois, Jean; Heinemann, Christine; Ouvry, Stéphane

    1994-01-01

    The computation of the $N$-cycle brownian paths contribution $F_N(\\alpha)$ to the $N$-anyon partition function is adressed. A detailed numerical analysis based on random walk on a lattice indicates that $F_N^{(0)}(\\alpha)= \\prod_{k=1}^{N-1}(1-{N\\over k}\\alpha)$. In the paramount $3$-anyon case, one can show that $F_3(\\alpha)$ is built by linear states belonging to the bosonic, fermionic, and mixed representations of $S_3$.

  18. Moments of inertia and the shapes of Brownian paths

    Energy Technology Data Exchange (ETDEWEB)

    Fougere, F.; Desbois, J.

    1993-12-31

    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.

  19. Algebraic and arithmetic area for m planar Brownian paths

    International Nuclear Information System (INIS)

    The leading and next to leading terms of the average arithmetic area (S(m)) enclosed by m→∞ independent closed Brownian planar paths, with a given length t and starting from and ending at the same point, are calculated. The leading term is found to be (S(m)) ∼ (πt/2)lnm and the 0-winding sector arithmetic area inside the m paths is subleading in the asymptotic regime. A closed form expression for the algebraic area distribution is also obtained and discussed

  20. Random functions via Dyson Brownian Motion: progress and problems

    Science.gov (United States)

    Wang, Gaoyuan; Battefeld, Thorsten

    2016-09-01

    We develope a computationally efficient extension of the Dyson Brownian Motion (DBM) algorithm to generate random function in C2 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.

  1. Entropic Ratchet transport of interacting active Brownian particles

    Energy Technology Data Exchange (ETDEWEB)

    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.

  2. Analysis of Brownian Dynamics Simulations of Reversible Bimolecular Reactions

    KAUST Repository

    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.

  3. Phenomenon of Repeated Current Reversals in the Brownian Ratchet

    Institute of Scientific and Technical Information of China (English)

    杨明; 曹力; 吴大进; 李湘莲

    2002-01-01

    We study the probability current of the Brownian particles in a tilted periodic piecewise linear "saw-tooth"potential. It is found that the stationary probability current takes on a maximum value at a given additive noise if the intensity of the multiplicative noise is appropriate and at the same time both noises are correlated;and the direction of the stationary probability current is reversed more than once upon some certain correlation intensities between both noises. It is proven that the occurrence of current reversal is only dependent on the relative intensity of the multiplicative and additive noises, but has nothing to do with the absolute intensities of the two noises.

  4. Cavity-enhanced optical detection of carbon nanotube Brownian motion

    CERN Document Server

    Stapfner, S; Hunger, D; Weig, E M; Reichel, J; Favero, I

    2012-01-01

    Optical cavities with small mode volume are well-suited to detect the vibration of sub-wavelength sized objects. Here we employ a fiber-based, high-finesse optical microcavity to detect the Brownian motion of a freely suspended carbon nanotube at room temperature under vacuum. The optical detection resolves deflections of the oscillating tube down to 50pm/Hz^1/2. A full vibrational spectrum of the carbon nanotube is obtained and confirmed by characterization of the same device in a scanning electron microscope. Our work successfully extends the principles of high-sensitivity optomechanical detection to molecular scale nanomechanical systems.

  5. Role of Brownian Motion Hydrodynamics on Nanofluid Thermal Conductivity

    Energy Technology Data Exchange (ETDEWEB)

    W Evans, J Fish, P Keblinski

    2005-11-14

    We use a simple kinetic theory based analysis of heat flow in fluid suspensions of solid nanoparticles (nanofluids) to demonstrate that the hydrodynamics effects associated with Brownian motion have a minor effect on the thermal conductivity of the nanofluid. Our conjecture is supported by the results of molecular dynamics simulations of heat flow in a model nanofluid with well-dispersed particles. Our findings are consistent with the predictions of the effective medium theory as well as with recent experimental results on well dispersed metal nanoparticle suspensions.

  6. Brownian dynamics simulation for modeling ion permeation across bionanotubes.

    Science.gov (United States)

    Krishnamurthy, Vikram; Chung, Shin-Ho

    2005-03-01

    The principles underlying Brownian dynamics (BD), its statistical consistency, and algorithms for practical implementation are outlined here. The ability to compute current flow across ion channels confers a distinct advantage to BD simulations compared to other simulation techniques. Thus, two obvious applications of BD ion channels are in calculation of the current-voltage and current-concentration curves, which can be directly compared to the physiological measurements to assess the reliability of the model and predictive power of the method. We illustrate how BD simulations are used to unravel the permeation dynamics in two biological ion channels-the KcsA K+ channel and CIC Cl- channel. PMID:15816176

  7. Brownian motion and Harmonic functions on Sol(p,q)

    OpenAIRE

    Brofferio, Sara; Salvatori, Maura; Woess, Wolfgang

    2012-01-01

    The Lie group Sol(p,q) is the semidirect product induced by the action of the real numbers R on the plane R^2 which is given by (x,y) --> (exp{p z} x, exp{-q z} y), where z is in R. Viewing Sol(p,q) as a 3-dimensional manifold, it carries a natural Riemannian metric and Laplace-Beltrami operator. We add a linear drift term in the z-variable to the latter, and study the associated Brownian motion with drift. We derive a central limit theorem and compute the rate of escape. Also, we introduce t...

  8. Brownian Motion and Harmonic Functions on Rotationally Symmetric Manifolds

    OpenAIRE

    March, Peter

    1986-01-01

    We consider Brownian motion $X$ on a rotationally symmetric manifold $M_g = (\\mathbb{R}^n, ds^2), ds^2 = dr^2 + g(r)^2 d\\theta^2$. An integral test is presented which gives a necessary and sufficient condition for the nontriviality of the invariant $\\sigma$-field of $X$, hence for the existence of nonconstant bounded harmonic functions on $M_g$. Conditions on the sectional curvatures are given which imply the convergence or the divergence of the test integral.

  9. Random Functions via Dyson Brownian Motion: Progress and Problems

    CERN Document Server

    Wang, Gaoyuan

    2016-01-01

    We develope a computationally efficient extension of the Dyson Brownian Motion (DBM) algorithm to generate random function in C2 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 used 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.

  10. Minimal Cost of a Brownian Risk without Ruin

    CERN Document Server

    Luo, Shangzhen

    2011-01-01

    In this paper, we study a risk process modeled by a Brownian motion with drift (the diffusion approximation model). The insurance entity can purchase reinsurance to lower its risk and receive cash injections at discrete times to avoid ruin. Proportional reinsurance and excess-of-loss reinsurance are considered. The objective is to find the optimal reinsurance and cash injection strategy that minimizes the total cost to keep the company's surplus process non-negative, i.e. without ruin, where the cost function is defined as the total discounted value of the injections. The optimal solution is found explicitly by solving the according quasi-variational inequalities (QVIs).

  11. Consistent finite-element approach to Brownian polymer dynamics with anisotropic friction.

    Science.gov (United States)

    Cyron, Christian J; Wall, Wolfgang A

    2010-12-01

    In the last decades simulation tools for Brownian dynamics of polymers have attracted more and more interest. Here we present a mathematically consistent finite element approach to the simulation of Brownian polymer dynamics. The viscous damping forces are accounted for by an anisotropic friction model. By comparison with theoretical predictions and experimental data we demonstrate the reliability and efficiency of this method. PMID:21230752

  12. On the expectation of normalized Brownian functionals up to first hitting times

    OpenAIRE

    Elie, Romuald; Rosenbaum, Mathieu; Yor, Marc

    2013-01-01

    Let B be a Brownian motion and T its first hitting time of the level 1. For U a uniform random variable independent of B, we study in depth the distribution of T^{-1/2}B_{UT}, that is the rescaled Brownian motion sampled at uniform time. In particular, we show that this variable is centered.

  13. Thermodynamic characteristics of a Brownian heat pump in a spatially periodic temperature field

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    This paper has studied the thermodynamic performance of a thermal Brownian heat pump,which consists of Brownian particles moving at a periodic sawtooth potential with external forces and contacting with the alternating hot and cold reservoirs along the space coordinate.The heat flows driven by both potential and kinetic energies are taken into account.The analytical expressions for the heating load,coefficient of performance(COP) and power input of the Brownian heat pump are derived and the performance characteristics are obtained by numerical calculations.It is shown that due to the heat flow via the change of kinetic energy of the particles,the Brownian heat pump is always irreversible and the COP can never attain the Carnot COP.The study has also investigated the influences of the operating parameters,i.e.the external force,barrier height of the potential,asymmetry of the sawtooth potential and temperature ratio of the heat reservoirs,on the performance of the Brownian heat pump.The effective regions of external force and barrier height of the potential in which the Brownian motor can operates as a heat pump are determined.The results show that the performance of the Brownian heat pump greatly depends on the parameters;if the parameters are properly chosen,the Brownian heat pump may be controlled to operate in the optimal regimes.

  14. A Simplified Treatment of Brownian Motion and Stochastic Differential Equations Arising in Financial Mathematics

    Science.gov (United States)

    Parlar, Mahmut

    2004-01-01

    Brownian motion is an important stochastic process used in modelling the random evolution of stock prices. In their 1973 seminal paper--which led to the awarding of the 1997 Nobel prize in Economic Sciences--Fischer Black and Myron Scholes assumed that the random stock price process is described (i.e., generated) by Brownian motion. Despite its…

  15. Linear filtering with fractional Brownian motion in the signal and observation processes

    Directory of Open Access Journals (Sweden)

    M. L. Kleptsyna

    1999-01-01

    Full Text Available Integral equations for the mean-square estimate are obtained for the linear filtering problem, in which the noise generating the signal is a fractional Brownian motion with Hurst index h∈(3/4,1 and the noise in the observation process includes a fractional Brownian motion as well as a Wiener process.

  16. Protest movements

    International Nuclear Information System (INIS)

    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.)

  17. Functionals of Brownian motion, localization and metric graphs

    Energy Technology Data Exchange (ETDEWEB)

    Comtet, Alain [Laboratoire de Physique Theorique et Modeles Statistiques, UMR 8626 du CNRS, Universite Paris-Sud, Bat. 100, F-91405 Orsay Cedex (France); Institut Henri Poincare, 11 rue Pierre et Marie Curie, F-75005 Paris (France); Desbois, Jean [Laboratoire de Physique Theorique et Modeles Statistiques, UMR 8626 du CNRS, Universite Paris-Sud, Bat. 100, F-91405 Orsay Cedex (France); Texier, Christophe [Laboratoire de Physique Theorique et Modeles Statistiques, UMR 8626 du CNRS, Universite Paris-Sud, Bat. 100, F-91405 Orsay Cedex (France); Laboratoire de Physique des Solides, UMR 8502 du CNRS, Universite Paris-Sud, Bat. 510, F-91405 Orsay Cedex (France)

    2005-09-16

    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)

  18. Functionals of Brownian motion, localization and metric graphs

    International Nuclear Information System (INIS)

    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)

  19. Intermittency and multifractional Brownian character of geomagnetic time series

    Directory of Open Access Journals (Sweden)

    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.

  20. Time integration for particle Brownian motion determined through fluctuating hydrodynamics

    CERN Document Server

    Delmotte, Blaise

    2015-01-01

    Fluctuating hydrodynamics has been successfully combined with several computational methods to rapidly compute the correlated random velocities of Brownian particles. In the overdamped limit where both particle and fluid inertia are ignored, one must also account for a Brownian drift term in order to successfully update the particle positions. In this paper, we introduce and study a midpoint time integration scheme we refer to as the drifter-corrector (DC) that resolves the drift term for fluctuating hydrodynamics-based methods even when constraints are imposed on the fluid flow to obtain higher-order corrections to the particle hydrodynamic interactions. We explore this scheme in the context of the fluctuating force-coupling method (FCM) where the constraint is imposed on the rate-of-strain averaged over the volume occupied by the particle. For the DC, the constraint need only be imposed once per time step, leading to a significant reduction in computational cost with respect to other schemes. In fact, for f...

  1. Ergodic Properties of Fractional Brownian-Langevin Motion

    CERN Document Server

    Deng, Weihua

    2008-01-01

    We investigate the time average mean square displacement $\\overline{\\delta^2}(x(t))=\\int_0^{t-\\Delta}[x(t^\\prime+\\Delta)-x(t^\\prime)]^2 dt^\\prime/(t-\\Delta)$ for fractional Brownian and Langevin motion. Unlike the previously investigated continuous time random walk model $\\overline{\\delta^2}$ converges to the ensemble average $ \\sim t^{2 H}$ in the long measurement time limit. The convergence to ergodic behavior is however slow, and surprisingly the Hurst exponent $H=3/4$ marks the critical point of the speed of convergence. When $H^2\\sim k(H) \\cdot\\Delta\\cdot t^{-1}$, when $H=3/4$, ${EB} \\sim (9/16)(\\ln t) \\cdot\\Delta \\cdot t^{-1}$, and when $3/4Brownian motion as a model for recent experiments of sub-diffusion of mRNA in the cell is briefly discussed and comparison with the continuous time ran...

  2. Mixed Movements

    DEFF Research Database (Denmark)

    Brabrand, Helle

    2010-01-01

    Mixed Movements is a research project engaged in performance-based architectural drawing. Architectonic implementation questions relations between the human body and a body of architecture by the different ways we handle drawing materials. A drawing may explore architectonic problems at other...... 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....

  3. Movement disorders

    International Nuclear Information System (INIS)

    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

  4. Psychodynamic Movement

    DEFF Research Database (Denmark)

    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...

  5. Differential dynamic microscopy to characterize Brownian motion and bacteria motility

    Science.gov (United States)

    Germain, David; Leocmach, Mathieu; Gibaud, Thomas

    2016-03-01

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

  6. Brownian motion near a liquid-gas interface

    Science.gov (United States)

    Benavides-Parra, Juan Carlos; Jacinto-Méndez, Damián; Brotons, Guillaume; Carbajal-Tinoco, Mauricio D.

    2016-09-01

    By using digital video microscopy, we study the three-dimensional displacement of fluorescent colloidal particles that are located close to a water-air interface. Our technique takes advantage of the diffraction pattern generated by fluorescent spheres that are found below the focal plane of the microscope objective. By means of image analysis software, we are able to determine the spatial location of a few beads in a sequence of digital images, which allows us to reconstruct their trajectories. From their corresponding mean square displacements, we get the diffusion coefficients in the directions parallel and perpendicular to the interface. We find a qualitatively different kind of diffusion between the two directions, in agreement with theoretical predictions that are obtained from established models as well as our own proposals. Quite interesting, we observe the enhanced Brownian motion in the parallel direction.

  7. The genealogy of branching Brownian motion with absorption

    CERN Document Server

    Berestycki, Julien; Schweinsberg, Jason

    2010-01-01

    We consider a system of particles which perform branching Brownian motion with negative drift and are killed upon reaching zero, in the near-critical regime where the total population stays roughly constant with approximately N particles. We show that the characteristic time scale for the evolution of this population is of order (log N)^3, in the sense that when time is measured in these units, the scaled number of particles converges to a variant of Neveu's continuous-state branching process. Furthermore, the genealogy of the particles is then governed by a coalescent process known as the Bolthausen-Sznitman coalescent. This validates the non-rigorous predictions by Brunet, Derrida, Muller, and Munier for a closely related model.

  8. The branching Brownian motion seen from its tip

    CERN Document Server

    Aïdékon, E; Brunet, É; Shi, Z

    2011-01-01

    Very recently, Arguin et al. have proved the conjecture (which can be found in the work of Lalley and Sellke) that the branching Brownian motion seen from its tip (e.g. from its rightmost particle) converges to an invariant point process. The main goal of the present work is to give a complete description of the limit object and an alternative proof of the convergence. As conjectured by Brunet and Derrida and proved by Arguin et al., the structure of this extremal point process turns out to be a certain Poisson point process with exponential intensity in which each atom has been decorated by an independent copy of an auxiliary point process. Here, we give an explicit construction of this decoration point process.

  9. Normal and anomalous diffusion of Brownian particles on disordered potentials

    Science.gov (United States)

    Salgado-García, R.

    2016-07-01

    In this work we study the transition from normal to anomalous diffusion of Brownian particles on disordered potentials. The potential model consists of a series of "potential hills" (defined on a unit cell of constant length) whose heights are chosen randomly from a given distribution. We calculate the exact expression for the diffusion coefficient in the case of uncorrelated potentials for arbitrary distributions. We show that when the potential heights have a Gaussian distribution (with zero mean and a finite variance) the diffusion of the particles is always normal. In contrast, when the distribution of the potential heights is exponentially distributed the diffusion coefficient vanishes when the system is placed below a critical temperature. We calculate analytically the diffusion exponent for the anomalous (subdiffusive) phase by using the so-called "random trap model". Our predictions are tested by means of Langevin simulations obtaining good agreement within the accuracy of our numerical calculations.

  10. Optimal dividends in the Brownian motion risk model with interest

    Science.gov (United States)

    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.

  11. Modeling collective emotions: a stochastic approach based on Brownian agents

    International Nuclear Information System (INIS)

    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)

  12. Semicircular Canals Circumvent Brownian Motion Overload of Mechanoreceptor Hair Cells

    DEFF Research Database (Denmark)

    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 (

  13. Micro rectennas: Brownian ratchets for thermal-energy harvesting

    Energy Technology Data Exchange (ETDEWEB)

    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.

  14. Blowup and Conditionings of $\\psi$-super Brownian Exit Measures

    CERN Document Server

    Athreya, Siva R

    2011-01-01

    We extend earlier results on conditioning of super-Brownian motion to general branching rules. We obtain representations of the conditioned process, both as an $h$-transform, and as an unconditioned superprocess with immigration along a branching tree. Unlike the finite-variance branching setting, these trees are no longer binary, and strictly positive mass can be created at branch points. This construction is singular in the case of stable branching. We analyze this singularity first by approaching the stable branching function via analytic approximations. In this context the singularity of the stable case can be attributed to blow up of the mass created at the first branch of the tree. Other ways of approaching the stable case yield a branching tree that is different in law. To explain this anomaly we construct a family of martingales whose backbones have multiple limit laws.

  15. Temporal Correlations of the Running Maximum of a Brownian Trajectory

    Science.gov (United States)

    Bénichou, Olivier; Krapivsky, P. L.; Mejía-Monasterio, Carlos; Oshanin, Gleb

    2016-08-01

    We study the correlations between the maxima m and M of a Brownian motion (BM) on the time intervals [0 ,t1] and [0 ,t2], with t2>t1. We determine the exact forms of the distribution functions P (m ,M ) and P (G =M -m ), and calculate the moments E {(M-m ) k} and the cross-moments E {mlMk} with arbitrary integers l and k . We show that correlations between m and M decay as √{t1/t2 } when t2/t1→∞ , revealing strong memory effects in the statistics of the BM maxima. We also compute the Pearson correlation coefficient ρ (m ,M ) and the power spectrum of Mt, and we discuss a possibility of extracting the ensemble-averaged diffusion coefficient in single-trajectory experiments using a single realization of the maximum process.

  16. On a non-linear transformation between Brownian martingales

    CERN Document Server

    Shkolnikov, Mykhaylo

    2012-01-01

    The paper studies a non-linear transformation between Brownian martingales, which is given by the inverse of the pricing operator in the mathematical finance terminology. Subsequently, the solvability of systems of equations corresponding to such transformations is investigated. The latter give rise to novel monotone pathwise couplings of an arbitrary number of certain diffusion processes with varying diffusion coefficients. In the case that there is an uncountable number of these diffusion processes and that the index set is an interval such couplings can be viewed as models for the growth of one-dimensional random surfaces. With this motivation in mind, we derive the appropriate stochastic partial differential equations for the growth of such surfaces.

  17. An Efficient Method to Study Nondiffusive Motion of Brownian Particles

    Directory of Open Access Journals (Sweden)

    Lisý Vladimír

    2016-01-01

    Full Text Available The experimental access to short timescales has pointed to the inadequacy of the standard Langevin theory of the Brownian motion (BM in fluids. The hydrodynamic theory of the BM describes well the observed motion of the particles; however, the published approach should be improved in several points. In particular, it leads to incorrect correlation properties of the thermal noise driving the particles. In our contribution we present an efficient method, which is applicable to linear generalized Langevin equations describing the BM of particles with any kind of memory and apply it to interpret the experiments where nondiffusive BM of particles was observed. It is shown that the applicability of the method is much broader, allowing, among all, to obtain efficient solutions of various problems of anomalous BM.

  18. BROWNIAN HEAT TRANSFER ENHANCEMENT IN THE TURBULENT REGIME

    Directory of Open Access Journals (Sweden)

    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.

  19. Brownian Dynamics of Colloidal Particles in Lyotropic Chromonic Liquid Crystals

    Science.gov (United States)

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

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

  20. Momentum conserving Brownian dynamics propagator for complex soft matter fluids.

    Science.gov (United States)

    Padding, J T; Briels, W J

    2014-12-28

    We present a Galilean invariant, momentum conserving first order Brownian dynamics scheme for coarse-grained simulations of highly frictional soft matter systems. Friction forces are taken to be with respect to moving background material. The motion of the background material is described by locally averaged velocities in the neighborhood of the dissolved coarse coordinates. The velocity variables are updated by a momentum conserving scheme. The properties of the stochastic updates are derived through the Chapman-Kolmogorov and Fokker-Planck equations for the evolution of the probability distribution of coarse-grained position and velocity variables, by requiring the equilibrium distribution to be a stationary solution. We test our new scheme on concentrated star polymer solutions and find that the transverse current and velocity time auto-correlation functions behave as expected from hydrodynamics. In particular, the velocity auto-correlation functions display a long time tail in complete agreement with hydrodynamics. PMID:25554134

  1. On the first-passage time of integrated Brownian motion

    Directory of Open Access Journals (Sweden)

    Christian H. Hesse

    2005-01-01

    Full Text Available Let (Bt;t≥0 be a Brownian motion process starting from B0=ν and define Xν(t=∫0tBsds. For a≥0, set τa,ν:=inf{t:Xν(t=a} (with inf φ=∞. We study the conditional moments of τa,ν given τa,ν<∞. Using martingale methods, stopping-time arguments, as well as the method of dominant balance, we obtain, in particular, an asymptotic expansion for the conditional mean E(τa,ν|τa,ν<∞ as ν→∞. Through a series of simulations, it is shown that a truncation of this expansion after the first few terms provides an accurate approximation to the unknown true conditional mean even for small ν.

  2. Transient cluster formation in sheared non-Brownian suspensions.

    Science.gov (United States)

    Thøgersen, Kjetil; Dabrowski, Marcin; Malthe-Sørenssen, Anders

    2016-02-01

    We perform numerical simulations of non-Brownian suspensions in the laminar flow regime to study the scaling behavior of particle clusters and collisions under shear. As the particle fraction approaches the maximum packing fraction, large transient clusters appear in the system. We use methods from percolation theory to discuss the cluster size distribution. We also give a scaling relation for the percolation threshold as well as system size effects through time-dependent fluctuations of this threshold and relate them to system size. System size effects are important close to the maximum packing fraction due to the divergence of the cluster length scale. We then investigate the transient nature of the clusters through characterization of particle collisions and show that collision times exhibit scale-invariant properties. Finally, we show that particle collision times can be modeled as first-passage processes. PMID:26986381

  3. Effect of Brownian Coagulation on the Liquid-liquid Decomposition in Gas-atomized Alloy Drops

    Institute of Scientific and Technical Information of China (English)

    Jiuzhou ZHAO; Lingling GAO; Jie HE; L.Ratke

    2006-01-01

    Modeling and simulation have been carried out for Al-Pb alloys to investigate the Brownian coagulation effect on the microstructure development in a gas-atomized drop during the liquid-liquid decomposition.The results indicate that Brownian coagulation has a weak effect on the nucleation and a relatively strong effect on coarsening the minority phase droplets. The influence of Brownian coagulation on the liquid-liquid decomposition decreases with the increase in the diameter (or the decrease in the cooling rate) of the atomized drop.

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

    Science.gov (United States)

    Delorme, Mathieu; Wiese, Kay Jörg

    2015-11-20

    Fractional Brownian motion is a non-Markovian Gaussian process X_{t}, indexed by the Hurst exponent H. It generalizes standard Brownian motion (corresponding to H=1/2). We study the probability distribution of the maximum m of the process and the time t_{max} at which the maximum is reached. They are encoded in a path integral, which we evaluate perturbatively around a Brownian, setting H=1/2+ϵ. This allows us to derive analytic results beyond the scaling exponents. Extensive numerical simulations for different values of H test these analytical predictions and show excellent agreement, even for large ϵ. PMID:26636835

  5. Role of Brownian motion on the thermal conductivity enhancement of nanofluids

    Science.gov (United States)

    Gupta, Amit; Kumar, Ranganathan

    2007-11-01

    This study involves Brownian dynamics simulations of a real nanofluid system in which the interparticle potential is determined based on Debye length and surface interaction of the fluid and the solid. This paper shows that Brownian motion can increase the thermal conductivity of the nanofluid by 6% primarily due to "random walk" motion and not only through diffusion. This increase is limited by the maximum concentration for each particle size and is below that predicted by the effective medium theory. Beyond the maximum limit, particle aggregates begin to form. Brownian motion contribution stays as a constant beyond a certain particle diameter.

  6. Oscillation of harmonic functions for subordinate Brownian motion and its applications

    OpenAIRE

    Kim, Panki; Lee, Yunju

    2012-01-01

    In this paper, we establish an oscillation estimate of nonnegative harmonic functions for a pure-jump subordinate Brownian motion. The infinitesimal generator of such subordinate Brownian motion is an integro-differential operator. As an application, we give a probabilistic proof of the following form of relative Fatou theorem for such subordinate Brownian motion X in bounded kappa-fat open set; if u is a positive harmonic function with respect to X in a bounded kappa-fat open set D and h is ...

  7. Gracious Movement

    Directory of Open Access Journals (Sweden)

    Lev Kreft

    2012-07-01

    Full Text Available In 1984 Christopher Cordner offered a critical view on theories of graceful movement in sport developed by Ng. G. Wulk, David Best and Joseph Kupfer. In 2001 Paul Davis criticized his view. Cordner responded, rejecting all the criticism. More than a century before, Herbert Spencer and Jean-Marie Guyau had a similar controversy over grace. Both exchanges of opinion involve three positions: that grace is the most efficient movement and therefore something quantitative and measurable; that grace is expression of the wholeness of person and the world; and that grace is something which neither science nor philosophy can explain. To clarify these conflicting issues, this article proposes to examine the history of the notion which goes back to the Latin gratia and has root in the Ancient Greek charis, and to apply the concepts of cultural anchor and thin coherence, following John R. Searle’s explanation that we produce epistemically objective accounts of ontologically subjective reality.

  8. Mean Mobility and Rotation Number in Time-inhomogenous Brownian Ratchets

    Institute of Scientific and Technical Information of China (English)

    张雪娟

    2004-01-01

    @@ Recently, Brownian ratchets have attracted considerable attention due to their abitlity to realize a unidirectional transport only throught the use of a proper asymmetry and thermal noise fluctuation, for recent review, see[1,2].

  9. On the weak convergence of super-Brownian motion with immigration

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    We prove fluctuation limit theorems for the occupation times of super-Brownian motion with immigration. The weak convergence of the processes is established, which improves the results in references. The limiting processes are Gaussian processes.

  10. On the time of the maximum of Brownian motion with drift

    Directory of Open Access Journals (Sweden)

    Emannuel Buffet

    2003-01-01

    Full Text Available The distribution of the time at which Brownian motion with drift attains its maximum on a given interval is obtained by elementary methods. The proof depends on a remarkable integral identity involving Gaussian distribution functions.

  11. Moderate deviations for the quenched mean of the super-Brownian motion with random immigration

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Moderate deviations for the quenched mean of the super-Brownian motion with random immigration are proved for 3≤d≤6, which fills in the gap between central limit theorem(CLT)and large deviation principle(LDP).

  12. On some properties of reflected skew Brownian motions and applications to dispersion in heterogeneous media

    Science.gov (United States)

    Song, Shiyu; Wang, Suxin; Wang, Yongjin

    2016-08-01

    Motivated by the close connection between the skew Brownian motion and the random particle motion in heterogeneous media, we investigate the reflected skew Brownian motion and try to find out its relationship with the corresponding dispersion problem when there exists a reflecting boundary. Through the use of the knowledge of stochastic analysis, we provide some basic properties of reflected skew Brownian motions, including the transition density, the Laplace transform of the first passage time, and some related results. A simple method to generate the sample path is also proposed. At the end of this paper, we reveal the strong relationship between the reflected skew Brownian motion and the solute dispersion in the presence of a sharp interface and a reflecting boundary.

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

    OpenAIRE

    Volpe, Giorgio; Volpe, Giovanni; Gigan, Sylvain

    2014-01-01

    The motion of particles in random potentials occurs in several natural phenomena ranging from the mobility of organelles within a biological cell to the diffusion of stars within a galaxy. A Brownian particle moving in the random optical potential associated to a speckle, i.e., a complex interference pattern generated by the scattering of coherent light by a random medium, provides an ideal mesoscopic model system to study such phenomena. Here, we derive a theory for the motion of a Brownian ...

  14. The probability of an encounter of two Brownian particles before escape

    CERN Document Server

    holcman, D

    2009-01-01

    We study the probability of two Brownian particles to meet before one of them exits a finite interval. We obtain an explicit expression for the probability as a function of the initial distance of 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.

  15. Applying Brownian motion to the study of birth-death chains

    CERN Document Server

    Markowsky, Greg

    2011-01-01

    Basic properties of Brownian motion are used to derive two results concerning birth-death chains. First, the probability of extinction is calculated. Second, sufficient conditions on the transition probabilities of a birth-death chain are given to ensure that the expected value of the chain converges to a limit. The theory of Brownian motion local time figures prominently in the proof of the second result.

  16. Characteristic function and Spitzer's law for the winding angle distribution of planar brownian curves

    International Nuclear Information System (INIS)

    Using the analogy between brownian motion and Quantum Mechanics, we study the winding angle θ of planar brownian curves around a given point, say the origin O. In particular, we compute the characteristic function for the probability distribution of θ and recover Spitzer's law in the limit of infinitely large times. Finally, we study the (large) change in the winding angle distribution when we add a repulsive potential at the origin

  17. On exponential stability for stochastic differential equations disturbed by G-Brownian motion

    OpenAIRE

    Fei, Weiyin; Fei, Chen

    2013-01-01

    We first introduce the calculus of Peng's G-Brownian motion on a sublinear expectation space $(\\Omega, {\\cal H}, \\hat{\\mathbb{E}})$. Then we investigate the exponential stability of paths for a class of stochastic differential equations disturbed by a G-Brownian motion in the sense of quasi surely (q.s.). The analyses consist in G-Lyapunov function and some special inequalities. Various sufficient conditions are obtained to ensure the stability of strong solutions. In particular, by means of ...

  18. Recurrence and transience for normally reflected Brownian motion in warped product manifolds

    OpenAIRE

    de Lima, Levi Lopes

    2016-01-01

    We establish an integral test describing the exact cut-off between recurrence and transience for normally reflected Brownian motion in certain unbounded domains in a class of warped product manifolds. Besides extending a previous result by Pinsky \\cite{P1}, who treated the case in which the ambient space is flat, our result recovers the classical test for the standard Brownian motion in model spaces. Moreover, it allows us to discuss the recurrence/transience dichotomy for certain generalized...

  19. Self-intersection local times and collision local times of bifractional Brownian motions

    Institute of Scientific and Technical Information of China (English)

    JIANG YiMing; WANG YongJin

    2009-01-01

    In this paper, we consider the local time and the self-intersection local time for a bifrac-tional Brownish motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the existence and smoothness of the self-intersection local time and the collision local time, through the strong local nondeterminism of bifractional Brownian motion, L2 convergence and Chaos expansion.

  20. Computational movement analysis

    CERN Document Server

    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

  1. Estimating the contribution of Brownian and Néel relaxation in a magnetic fluid through dynamic magnetic susceptibility measurements

    Science.gov (United States)

    Maldonado-Camargo, L.; Torres-Díaz, I.; Chiu-Lam, A.; Hernández, M.; Rinaldi, C.

    2016-08-01

    We demonstrate how dynamic magnetic susceptibility measurements (DMS) can be used to estimate the relative contributions of Brownian and Néel relaxation to the dynamic magnetic response of a magnetic fluid, a suspension of magnetic nanoparticles. The method applies to suspensions with particles that respond through Brownian or Néel relaxation and for which the characteristic Brownian and Néel relaxation times are widely separated. First, we illustrate this using magnetic fluids consisting of mixtures of particles that relax solely by the Brownian or Néel mechanisms. Then, it is shown how the same approach can be applied to estimate the relative contributions of Brownian and Néel relaxation in a suspension consisting of particles obtained from a single synthesis and whose size distribution straddles the transition from Néel to Brownian relaxation.

  2. Glassy dynamics of Brownian particles with velocity-dependent friction

    Science.gov (United States)

    Yazdi, Anoosheh; Sperl, Matthias

    2016-09-01

    We consider a two-dimensional model system of Brownian particles in which slow particles are accelerated while fast particles are damped. The motion of the individual particles is described by a Langevin equation with Rayleigh-Helmholtz velocity-dependent friction. In the case of noninteracting particles, the time evolution equations lead to a non-Gaussian velocity distribution. The velocity-dependent friction allows negative values of the friction or energy intakes by slow particles, which we consider active motion, and also causes breaking of the fluctuation dissipation relation. Defining the effective temperature proportional to the second moment of velocity, it is shown that for a constant effective temperature the higher the noise strength, the lower the number of active particles in the system. Using the Mori-Zwanzig formalism and the mode-coupling approximation, the equations of motion for the density autocorrelation function are derived. The equations are solved using the equilibrium structure factors. The integration-through-transients approach is used to derive a relation between the structure factor in the stationary state considering the interacting forces, and the conventional equilibrium static structure factor.

  3. Survival of near-critical branching Brownian motion

    CERN Document Server

    Berestycki, Julien; Schweinsberg, Jason

    2010-01-01

    Consider a system of particles performing branching Brownian motion with negative drift $\\mu = \\sqrt{2 - \\epsilon}$ and killed upon hitting zero. Initially there is one particle at $x>0$. Kesten showed that the process survives with positive probability if and only if $\\epsilon>0$. Here we are interested in the asymptotics as $\\eps\\to 0$ of the survival probability $Q_\\mu(x)$. It is proved that if $L= \\pi/\\sqrt{\\epsilon}$ then for all $x \\in \\R$, $\\lim_{\\epsilon \\to 0} Q_\\mu(L+x) = \\theta(x) \\in (0,1)$ exists and is a travelling wave solution of the Fisher-KPP equation. Furthermore, we obtain sharp asymptotics of the survival probability when $x

  4. Brownian dynamics simulations of ellipsoidal magnetizable particle suspensions

    Science.gov (United States)

    Torres-Díaz, I.; Rinaldi, C.

    2014-06-01

    The rotational motion of soft magnetic tri-axial ellipsoidal particles suspended in a Newtonian fluid has been studied using rotational Brownian dynamics simulations by solving numerically the stochastic angular momentum equation in an orientational space described by the quaternion parameters. The model is applicable to particles where the effect of shape anisotropy is dominant. The algorithm quantifies the magnetization of a monodisperse suspension of tri-axial ellipsoids in dilute limit conditions under applied constant and time-varying magnetic fields. The variation of the relative permeability with the applied magnetic field of the particle's bulk material was included in the simulations. The results show that the equilibrium magnetization of a suspension of magnetizable tri-axial ellipsoids saturates at high magnetic field amplitudes. Additionally, the dynamic susceptibility at low magnetic field intensity presents a peak in the out-of-phase component, which is significantly smaller than the in-phase component and depends on the Langevin parameter. The dynamic magnetization of the particle suspension is in phase with the magnetic field at low and high frequencies far from the peak of the out-of-phase component.

  5. Magnetoviscosity in dilute ferrofluids from rotational brownian dynamics simulations.

    Science.gov (United States)

    Soto-Aquino, D; Rinaldi, C

    2010-10-01

    Ferrofluids are suspensions of magnetic nanoparticles which respond to imposed magnetic fields by changing their viscosity without losing their fluidity. Prior work on modeling the behavior of ferrofluids has focused on using phenomenological suspension-scale continuum equations. A disadvantage of this approach is the controversy surrounding the equation describing the rate of change of the ferrofluid magnetization, the so-called magnetization relaxation equation. In this contribution the viscosity of dilute suspensions of spherical magnetic nanoparticles suspended in a Newtonian fluid and under applied shear and constant magnetic fields is studied through rotational brownian dynamics simulations. Simulation results are compared with the predictions of suspension-scale models based on three magnetization relaxation equations. Excellent agreement is observed between simulation results and the predictions of an equation due to Martsenyuk, Raikher, and Shliomis. Good qualitative agreement is observed with predictions of other equations, although these models fail to accurately predict the magnitude and shear rate dependence of the magnetic-field-dependent effective viscosity. Finally, simulation results over a wide range of conditions are collapsed into master curves using a Mason number defined based on the balance of hydrodynamic and magnetic torques. PMID:21230393

  6. Nanofluidic Brownian Ratchet via atomically-stepped surfaces

    Science.gov (United States)

    Rahmani, Amir; Colosqui, Carlos

    2015-11-01

    Theoretical analysis and fully atomistic molecular dynamics simulations reveal a Brownian ratchet mechanism by which thermal motion can drive the directional displacement of liquids confined in micro- or nanoscale channels and pores. The particular systems discussed in this talk consist of two immiscible liquids confined in a slit-like nanochannel with atomically-stepped surfaces. Mean displacement rates reported in molecular dynamics simulations are in close agreement with theoretical predictions via analytical solution of a Smoluchowski equation for the probability density of the position of the liquid-liquid interface. The direction of the thermally-driven displacement of liquid is determined by the nanostructure surface geometry and thus imbibition or drainage can occur against the direction of action of capillary forces. The studied surface nanostructure with directional asymmetry can control the dynamics of wetting processes such as capillary filling, wicking, and imbibition in porous materials. The proposed physical mechanisms and derived analytical expressions can be applied to design nanofluidic and microfluidic devices for passive handling and separation.

  7. Phase transition in non-brownian fiber suspensions

    Science.gov (United States)

    Franceschini, Alexandre; Filippidi, Emmanouella; Guazzelli, Elizabeth; Pine, David

    2012-11-01

    The simple shear of a suspension of fibers tends to align them with the flow direction. We previously reported that the oscillatory shear of neutrally buoyant non-Brownian fibers align them with the vorticity (Franceschini A. et al. PRL, 2011). We interpreted this phenomenon as the minimization of a ``corrected volume fraction'' defined as a function of the strain amplitude, the average orientation and the volume fraction. Below a critical value of this parameter, the system becomes fully reversible after a few periods. Above it, fluctuations remain and the fibers align with the vorticity, subsequently reducing the value of this corrected volume fraction. We present here the collective behavior of fibers constrained at the liquid-air interface. By pinning the liquid on the wall of a Couette cell, we can have a flat interface. By modifying the surface of the fibers, we get rid of most of surface tension mediated fiber-fiber interactions. In this 2D configuration we can measure spatial correlations, as well as the position and orientation of every fiber at each shear cycle. We similarly define a ``corrected surface fraction'' and see how this parameter help us understand the difference between the surface behavior and the suspension behavior. This work was supported by the NSF through the NYU MRSEC, Award DMR:0820341. Additional support was provided by a Lavoisier Fellowship (AF) and from the Onassis Foundation (EF).

  8. Virial pressure in systems of spherical active Brownian particles.

    Science.gov (United States)

    Winkler, Roland G; Wysocki, Adam; Gompper, Gerhard

    2015-09-01

    The pressure of suspensions of self-propelled objects is studied theoretically and by simulation of spherical active Brownian particles (ABPs). We show that for certain geometries, the mechanical pressure as force/area of confined systems can be equally expressed by bulk properties, which implies the existence of a nonequilibrium equation of state. Exploiting the virial theorem, we derive expressions for the pressure of ABPs confined by solid walls or exposed to periodic boundary conditions. In both cases, the pressure comprises three contributions: the ideal-gas pressure due to white-noise random forces, an activity-induced pressure ("swim pressure"), which can be expressed in terms of a product of the bare and a mean effective particle velocity, and the contribution by interparticle forces. We find that the pressure of spherical ABPs in confined systems explicitly depends on the presence of the confining walls and the particle-wall interactions, which has no correspondence in systems with periodic boundary conditions. Our simulations of three-dimensional ABPs in systems with periodic boundary conditions reveal a pressure-concentration dependence that becomes increasingly nonmonotonic with increasing activity. Above a critical activity and ABP concentration, a phase transition occurs, which is reflected in a rapid and steep change of the pressure. We present and discuss the pressure for various activities and analyse the contributions of the individual pressure components. PMID:26221908

  9. Virial pressure in systems of spherical active Brownian particles.

    Science.gov (United States)

    Winkler, Roland G; Wysocki, Adam; Gompper, Gerhard

    2015-09-01

    The pressure of suspensions of self-propelled objects is studied theoretically and by simulation of spherical active Brownian particles (ABPs). We show that for certain geometries, the mechanical pressure as force/area of confined systems can be equally expressed by bulk properties, which implies the existence of a nonequilibrium equation of state. Exploiting the virial theorem, we derive expressions for the pressure of ABPs confined by solid walls or exposed to periodic boundary conditions. In both cases, the pressure comprises three contributions: the ideal-gas pressure due to white-noise random forces, an activity-induced pressure ("swim pressure"), which can be expressed in terms of a product of the bare and a mean effective particle velocity, and the contribution by interparticle forces. We find that the pressure of spherical ABPs in confined systems explicitly depends on the presence of the confining walls and the particle-wall interactions, which has no correspondence in systems with periodic boundary conditions. Our simulations of three-dimensional ABPs in systems with periodic boundary conditions reveal a pressure-concentration dependence that becomes increasingly nonmonotonic with increasing activity. Above a critical activity and ABP concentration, a phase transition occurs, which is reflected in a rapid and steep change of the pressure. We present and discuss the pressure for various activities and analyse the contributions of the individual pressure components.

  10. Brownian dynamics simulations of nanosheet solutions under shear.

    Science.gov (United States)

    Xu, Yueyi; Green, Micah J

    2014-07-14

    The flow-induced conformation dynamics of nanosheets are simulated using a Brownian Dynamics (BD) formulation applied to a bead-rod sheetlike molecular model. This is the first-ever use of BD to simulate flow-induced dynamics of two-dimensional structures. Using this framework, we simulate dilute suspensions of coarse-grained nanosheets and compute conformation dynamics for simple shear flow. The data show power law scaling relationships between nanosheet parameters (such as bending moduli and molecular weight) and the resulting intrinsic viscosity and conformation. For nonzero bending moduli, an effective dimension of 2.77 at equilibrium is calculated from the scaling relationship between radius of gyration and molecular weight. We also find that intrinsic viscosity varies with molecular weight with an exponent of 2.12 ± 0.23; this dependence is significantly larger than those found for linear polymers. Weak shear thinning is observed at high Weissenberg number (Wi). This simulation method provides a computational basis for developing manufacturing processes for nanosheet-derived materials by relating flow forces and nanosheet parameters to the resulting material morphology.

  11. From Brownian Dynamics to Markov Chain: An Ion Channel Example

    KAUST Repository

    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.

  12. Modelling Collective Opinion Formation by Means of Active Brownian Particles

    CERN Document Server

    Schweitzer, F; Schweitzer, Frank; Holyst, Janusz

    1999-01-01

    The concept of active Brownian particles is used to model a collective opinion formation process. It is assumed that individuals in community create a two-component communication field that influences the change of opinions of other persons and/or can induce their migration. The communication field is described by a reaction-diffusion equation, meaning that it has a certain lifetime, which models memory effects, further it can spread out in the community. Within our stochastic approach, the opinion change of the individuals is described by a master equation, while the migration is described by a set of Langevin equations, coupled by the communication field. In the mean-field limit which holds for fast communication, we derive a critical population size, above which the community separates into a majority and a minority with opposite opinions. The existence of external support (e.g. from mass media) can change the ratio between minority and majority, until above a critical external support the supported subpop...

  13. Biased Brownian motion in narrow channels with asymmetry and anisotropy

    Science.gov (United States)

    Peng, Zheng; To, Kiwing

    2016-08-01

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

  14. Movement in Architecture: A Spacial Movement Theory

    OpenAIRE

    Mitchell, Lauren Coleen

    2010-01-01

    As the body moves through space ephemeral lines of movement are created. These lines of movement are influenced by body tendencies. We learn from the body by watching the path and patterning of movement. From the study of the movement of the body, theories of spacial movement were developed. The goal of my project is to draw from spacial movement theory to create an architectural expression that motivates movement of the body on my site and through my building. The focus of my thesis is ...

  15. A generalized Brownian motion model for turbulent relative particle dispersion

    Science.gov (United States)

    Shivamoggi, B. K.

    2016-08-01

    There is speculation that the difficulty in obtaining an extended range with Richardson-Obukhov scaling in both laboratory experiments and numerical simulations is due to the finiteness of the flow Reynolds number Re in these situations. In this paper, a generalized Brownian motion model has been applied to describe the relative particle dispersion problem in more realistic turbulent flows and to shed some light on this issue. The fluctuating pressure forces acting on a fluid particle are taken to be a colored noise and follow a stationary process and are described by the Uhlenbeck-Ornstein model while it appears plausible to take their correlation time to have a power-law dependence on Re, thus introducing a bridge between the Lagrangian quantities and the Eulerian parameters for this problem. This ansatz is in qualitative agreement with the possibility of a connection speculated earlier by Corrsin [26] between the white-noise representation for the fluctuating pressure forces and the large-Re assumption in the Kolmogorov [4] theory for the 3D fully developed turbulence (FDT) as well as a similar argument of Monin and Yaglom [23] and a similar result of Sawford [13] and Borgas and Sawford [24]. It also provides an insight into the result that the Richardson-Obukhov scaling holds only in the infinite-Re limit and disappears otherwise. This ansatz further provides a determination of the Richardson-Obukhov constant g as a function of Re, with an asymptotic constant value in the infinite-Re limit. It is shown to lead to full agreement, in the small-Re limit as well, with the Batchelor-Townsend [27] scaling for the rate of change of the mean square interparticle separation in 3D FDT, hence validating its soundness further.

  16. Movement disorders.

    Science.gov (United States)

    Stoessl, A Jon; Mckeown, Martin J

    2016-01-01

    Movement disorders can be hypokinetic (e.g., parkinsonism), hyperkinetic, or dystonic in nature and commonly arise from altered function in nuclei of the basal ganglia or their connections. As obvious structural changes are often limited, standard imaging plays less of a role than in other neurologic disorders. However, structural imaging is indicated where clinical presentation is atypical, particularly if the disorder is abrupt in onset or remains strictly unilateral. More recent advances in magnetic resonance imaging (MRI) may allow for differentiation between Parkinson's disease and atypical forms of parkinsonism. Functional imaging can assess regional cerebral blood flow (functional MRI (fMRI), positron emission tomography (PET), or single-photon emission computed tomography (SPECT)), cerebral glucose metabolism (PET), neurochemical and neuroreceptor status (PET and SPECT), and pathologic processes such as inflammation or abnormal protein deposition (PET) (Table 49.1). Cerebral blood flow can be assessed at rest, during the performance of motor or cognitive tasks, or in response to a variety of stimuli. In appropriate situations, the correct imaging modality and/or combination of modalities can be used to detect early disease or even preclinical disease, and to monitor disease progression and the effects of disease-modifying interventions. Various approaches are reviewed here. PMID:27430452

  17. Two-component Brownian coagulation: Monte Carlo simulation and process characterization

    Institute of Scientific and Technical Information of China (English)

    Haibo Zhao; Chu guang Zheng

    2011-01-01

    The compositional distribution within aggregates of a given size is essential to the functionality of composite aggregates that are usually enlarged by rapid Brownian coagulation.There is no analytical solution for the process of such two-component systems.Monte Carlo method is an effective numerical approach for two-component coagulation.In this paper,the differentially weighted Monte Carlo method is used to investigate two-component Brownian coagulation,respectively,in the continuum regime,the freemolecular regime and the transition regime.It is found that ( 1 ) for Brownian coagulation in the continuum regime and in the free-molecular regime,the mono-variate compositional distribution,i.e.,the number density distribution function of one component amount (in the form of volume of the component in aggregates) satisfies self-preserving form the same as particle size distribution in mono-component Brownian coagulation; (2) however,for Brownian coagulation in the transition regime the mono-variate compositional distribution cannot reach self-similarity; and (3) the bivariate compositional distribution,i.e.,the combined number density distribution function of two component amounts in the three regimes satisfies a semi self-preserving form.Moreover,other new features inherent to aggregative mixing are also demonstrated; e.g.,the degree of mixing between components,which is largely controlled by the initial compositional mass fraction,improves as aggregate size increases.

  18. Brownian motion in a speckle light field: tunable anomalous diffusion and selective optical manipulation.

    Science.gov (United States)

    Volpe, Giorgio; Volpe, Giovanni; Gigan, Sylvain

    2014-01-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

    Zhang Yunxin, E-mail: xyz@fudan.edu.c [School of Mathematical Sciences, Fudan University, Shanghai 200433 (China); Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai (China); Centre for Computational Systems Biology, Fudan University (China)

    2009-07-20

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

  20. Quantum Brownian motion in a bath of parametric oscillators a model for system-field interactions

    CERN Document Server

    Hu, B L; Andrew Matacz

    1993-01-01

    The quantum Brownian motion paradigm provides a unified framework where one can see the interconnection of some basic quantum statistical processes like decoherence, dissipation, particle creation, noise and fluctuation. We treat the case where the Brownian particle is coupled linearly to a bath of time dependent quadratic oscillators. While the bath mimics a scalar field, 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. This method enables one to trace the source of statistical processes like 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 origi...

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

    Science.gov (United States)

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

    2003-07-01

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

  2. Holographic Brownian Motion in Three-Dimensional Gödel Black Hole

    International Nuclear Information System (INIS)

    By using the AdS/CFT correspondence and Gödel black hole background, we study the dynamics of heavy quark under a rotating plasma. In that case we follow Atmaja (2013) about Brownian motion in BTZ black hole. In this paper we receive some new results for the case of α2l2≠1. In this case, we must redefine the angular velocity of string fluctuation. We obtain the time evolution of displacement square and angular velocity and show that it behaves as a Brownian particle in non relativistic limit. In this plasma, it seems that relating the Brownian motion to physical observables is rather a difficult work. But our results match with Atmaja work in the limit α2l2→1

  3. Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere

    Science.gov (United States)

    Millen, J.; Deesuwan, T.; Barker, P.; Anders, J.

    2014-06-01

    Einstein realized that the fluctuations of a Brownian particle can be used to ascertain the properties of its environment. A large number of experiments have since exploited the Brownian motion of colloidal particles for studies of dissipative processes, providing insight into soft matter physics and leading to applications from energy harvesting to medical imaging. Here, we use heated optically levitated nanospheres to investigate the non-equilibrium properties of the gas surrounding them. Analysing the sphere's Brownian motion allows us to determine the temperature of the centre-of-mass motion of the sphere, its surface temperature and the heated gas temperature in two spatial dimensions. We observe asymmetric heating of the sphere and gas, with temperatures reaching the melting point of the material. This method offers opportunities for accurate temperature measurements with spatial resolution on the nanoscale, and provides a means for testing non-equilibrium thermodynamics.

  4. Brownian ratchets from statistical physics to bio and nano-motors

    CERN Document Server

    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.

  5. Brownian motion of a charged test particle in vacuum between two conducting plates

    CERN Document Server

    Yu, H; Yu, Hongwei; Chen, Jun

    2004-01-01

    The Brownian motion of a charged test particle caused by quantum electromagnetic vacuum fluctuations between two perfectly conducting plates is examined and the mean squared fluctuations in the velocity and position of the test particle are calculated. Our results show that the Brownian motion in the direction normal to the plates is reinforced in comparison to that in the single-plate case. The effective temperature associated with this normal Brownian motion could be three times as large as that in the single-plate case. However, the negative dispersions for the velocity and position in the longitudinal directions, which could be interpreted as reducing the quantum uncertainties of the particle, acquire positive corrections due to the presence of the second plate, and are thus weakened.

  6. Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere.

    Science.gov (United States)

    Millen, J; Deesuwan, T; Barker, P; Anders, J

    2014-06-01

    Einstein realized that the fluctuations of a Brownian particle can be used to ascertain the properties of its environment. A large number of experiments have since exploited the Brownian motion of colloidal particles for studies of dissipative processes, providing insight into soft matter physics and leading to applications from energy harvesting to medical imaging. Here, we use heated optically levitated nanospheres to investigate the non-equilibrium properties of the gas surrounding them. Analysing the sphere's Brownian motion allows us to determine the temperature of the centre-of-mass motion of the sphere, its surface temperature and the heated gas temperature in two spatial dimensions. We observe asymmetric heating of the sphere and gas, with temperatures reaching the melting point of the material. This method offers opportunities for accurate temperature measurements with spatial resolution on the nanoscale, and provides a means for testing non-equilibrium thermodynamics. PMID:24793558

  7. (Quantum) Fractional Brownian Motion and Multifractal Processes under the Loop of a Tensor Networks

    CERN Document Server

    Descamps, Benoît

    2016-01-01

    We derive fractional Brownian motion and stochastic processes with multifractal properties using a framework of network of Gaussian conditional probabilities. This leads to the derivation of new representations of fractional Brownian motion. These constructions are inspired from renormalization. The main result of this paper consists of constructing each increment of the process from two-dimensional gaussian noise inside the light-cone of each seperate increment. Not only does this allows us to derive fractional Brownian motion, we can introduce extensions with multifractal flavour. In another part of this paper, we discuss the use of the multi-scale entanglement renormalization ansatz (MERA), introduced in the study critical systems in quantum spin lattices, as a method for sampling integrals with respect to such multifractal processes. After proper calibration, a MERA promises the generation of a sample of size $N$ of a multifractal process in the order of $O(N\\log(N))$, an improvement over the known method...

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

    DEFF Research Database (Denmark)

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

    2013-01-01

    We present and demonstrate a new method for on-chip Brownian relaxation measurements on magnetic nanobeads in the time domain using magnetoresistive sensors. The beads are being magnetized by the sensor self-field arising from the bias current passed through the sensors and thus no external...... 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...... magnetic fields are needed. First, the method is demonstrated on Brownian relaxation measurements of beads with nominal sizes of 40, 80, 130, and 250 nm. The results are found to compare well to those obtained by an already established measurement technique in the frequency domain. Next, we demonstrate...

  9. A Brownian model for recurrent volcanic eruptions: an application to Miyakejima volcano (Japan)

    Science.gov (United States)

    Garcia-Aristizabal, Alexander; Marzocchi, Warner; Fujita, Eisuke

    2012-03-01

    The definition of probabilistic models as mathematical structures to describe the response of a volcanic system is a plausible approach to characterize the temporal behavior of volcanic eruptions and constitutes a tool for long-term eruption forecasting. This kind of approach is motivated by the fact that volcanoes are complex systems in which a completely deterministic description of the processes preceding eruptions is practically impossible. To describe recurrent eruptive activity, we apply a physically motivated probabilistic model based on the characteristics of the Brownian passage-time (BPT) distribution; the physical process defining this model can be described by the steady rise of a state variable from a ground state to a failure threshold; adding Brownian perturbations to the steady loading produces a stochastic load-state process (a Brownian relaxation oscillator) in which an eruption relaxes the load state to begin a new eruptive cycle. The Brownian relaxation oscillator and Brownian passage-time distribution connect together physical notions of unobservable loading and failure processes of a point process with observable response statistics. The Brownian passage-time model is parameterized by the mean rate of event occurrence, μ, and the aperiodicity about the mean, α. We apply this model to analyze the eruptive history of Miyakejima volcano, Japan, finding a value of 44.2 (±6.5 years) for the μ parameter and 0.51 (±0.01) for the (dimensionless) α parameter. The comparison with other models often used in volcanological literature shows that this physically motivated model may be a good descriptor of volcanic systems that produce eruptions with a characteristic size. BPT is clearly superior to the Exponential distribution, and the fit to the data is comparable to other two-parameters models. Nonetheless, being a physically motivated model, it provides an insight into the macro-mechanical processes driving the system.

  10. An exactly solvable model for Brownian motion : III. Motion of a heavy mass in a linear chain

    NARCIS (Netherlands)

    Ullersma, P.

    1966-01-01

    The theory on Brownian motion, developed in previous papers1) 2) is applied to a linear chain with harmonic coupling between nearest neighbours. All masses are equal except for one which is heavy compared to the others. This heavy particle behaves as a Brownian particle, which is not subject to an e

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

    Science.gov (United States)

    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

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

    Science.gov (United States)

    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

  13. Accumulation of Microswimmers near a Surface Mediated by Collision and Rotational Brownian Motion

    Science.gov (United States)

    Li, Guanglai; Tang, Jay X.

    2009-08-01

    In this Letter we propose a kinematic model to explain how collisions with a surface and rotational Brownian motion give rise to accumulation of microswimmers near a surface. In this model, an elongated microswimmer invariably travels parallel to the surface after hitting it from an oblique angle. It then swims away from the surface, facilitated by rotational Brownian motion. Simulations based on this model reproduce the density distributions measured for the small bacteria E. coli and Caulobacter crescentus, as well as for the much larger bull spermatozoa swimming between two walls.

  14. An Approach to Enhance the Efficiency of a Brownian Heat Engine

    Institute of Scientific and Technical Information of China (English)

    ZHANG Yan-Ping; HE Ji-Zhou; XIAO Yu-Ling

    2011-01-01

    A Brownian microscopic heat engine, driven by temperature difference and consisting of a Brownian particle moving in a sawtooth potential with an external load, is investigated. The heat Hows, driven by both potential and kinetic energies, are taken into account. Based on the master equation, the expressions for efficiency and power output are derived analytically, and performance characteristic curves are plotted. It is shown that the heat How via the kinetic energy of the particle decreases. The efficiency of the engine is enhanced, but the power output reduces as the a shape parameter of the sawtooth potential increases. The influence of the a shape parameter on efficiency and power output is then analyzed in detail.%A Brownian microscopic heat engine,driven by temperature difference and consisting of a Brownian particle moving in a sawtooth potential with an external load,is investigated.The heat flows,driven by both potential and kinetic energies,are taken into account.Based on the master equation,the expressions for efficiency and power output are derived analytically,and performance characteristic curves are plotted.It is shown that the heat flow via the kinetic energy of the particle decreases.The efficiency of the engine is enhanced,but the power output reduces as the α shape parameter of the sawtooth potential increases.The influence of the α shape parameter on efficiency and power output is then analyzed in detail.Like the Carnot cycle,the Brownian heat engine can extract work from the temperature difference between heat reservoirs,where the Brownian working material operates as a transducer of thermal energy into mechanical work.In the last few decades,the study of Brownian heat engines has received considerable attention,not only for the construction of the miniaturized engine that helps us utilize energy resources at microscopic scales,but also for a better understanding of nonequilibrium statistical physics.[1-3] The thermodynamic properties of the

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

    Energy Technology Data Exchange (ETDEWEB)

    Ilie, Ioana M.; Briels, Wim J. [Computational Biophysics, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands); MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands); Otter, Wouter K. den, E-mail: w.k.denotter@utwente.nl [Computational Biophysics, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands); MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands); Multi Scale Mechanics, Faculty of Engineering Technology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands)

    2015-03-21

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

  16. Brownian Motion in wedges, last passage time and the second arc-sine law

    OpenAIRE

    Comtet, Alain; Desbois, Jean

    2003-01-01

    We consider a planar Brownian motion starting from $O$ at time $t=0$ and stopped at $t=1$ and a set $F= \\{OI_i ; i=1,2,..., n\\}$ of $n$ semi-infinite straight lines emanating from $O$. Denoting by $g$ the last time when $F$ is reached by the Brownian motion, we compute the probability law of $g$. In particular, we show that, for a symmetric $F$ and even $n$ values, this law can be expressed as a sum of $\\arcsin $ or $(\\arcsin)^2 $ functions. The original result of Levy is recovered as the spe...

  17. Brownian motion after Einstein and Smoluchowski: Some new applications and new experiments

    DEFF Research Database (Denmark)

    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...... that it requires an understanding of Brownian motion beyond Einstein's and Smoluchowski's for its calibration, and can measure effects not present in their theories. This is illustrated with some applications, current and potential. It is also shown how addition of a controlled forced motion on the nano...

  18. Brownian motion in a singular potential and a fractal renewal process

    Science.gov (United States)

    Ouyang, H. F.; Huang, Z. Q.; Ding, E. J.

    1995-10-01

    We have proposed a model for the one-dimensional Brownian motion of a single particle in a singular potential field in our previous paper [Phys. Rev. E 50, 2491 (1994)]. In this Brief Report, we further discuss this model and show that, in some special cases, the Brownian motion can be considered as a finite-valued alternating renewal process, which has been investigated by Lowen and Teich [Phys. Rev. E 47, 992 (1993)]. The numerical results here are in agreement with those drawn by Lowen and Teich.

  19. Lorentz Invariance and Brownian Motion of Test Particles with Constant Classical Velocity in Electromagnetic Vacuum

    Institute of Scientific and Technical Information of China (English)

    ZHANG Jia-Lin; YU Hong-Wei

    2005-01-01

    @@ We show that the velocity and position dispersions of a test particle with a nonzero constant classical velocity undergoing Brownian motion caused by electromagnetic vacuum fluctuations in a space with plane boundaries can be obtained from those of the static case by Lorentz transformation. We explicitly derive the Lorentz transformations relating the dispersions of the two cases and then apply them to the case of the Brownian motion of a test particle with a constant classical velocity parallel to the boundary between two conducting planes. Our results show that the influence of a nonzero initial velocity is negligible for nonrelativistic test particles.

  20. Brownian agents and active particles collective dynamics in the natural and social sciences

    CERN Document Server

    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

  1. Brownian Motion, Bridge, Excursion, and Meander Characterized by Sampling at Independent Uniform Times

    OpenAIRE

    Pitman, Jim

    1999-01-01

    For a random process $X$ consider the random vector defined by the values of $X$ at times $0 \\lt U_{n,1} \\lt ... \\lt U_{n,n} \\lt 1$ and the minimal values of $X$ on each of the intervals between consecutive pairs of these times, where the $U_{n,i}$ are the order statistics of $n$ independent uniform $(0,1)$ variables, independent of $X$. The joint law of this random vector is explicitly described when $X$ is a Brownian motion. Corresponding results for Brownian bridge, excursion, and meander ...

  2. On-chip measurements of Brownian relaxation vs. concentration of 40nm magnetic beads

    DEFF Research Database (Denmark)

    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...

  3. Brownian Agents and Active Particles: Collective Dynamics in the Natural and Social Sciences

    International Nuclear Information System (INIS)

    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

  4. Continuous time Black-Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime

    Science.gov (United States)

    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)), 0Black-Scholes equation and the Black-Scholes formula for the fair prices of European option, the turnover and transaction costs of replicating strategies. We also give the total transaction costs.

  5. Time-changed geometric fractional Brownian motion and option pricing with transaction costs

    Science.gov (United States)

    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.

  6. Accumulation of microswimmers near surface due to steric confinement and rotational Brownian motion

    Science.gov (United States)

    Li, Guanglai; Tang, Jay

    2009-03-01

    Microscopic swimmers display some intriguing features dictated by Brownian motion, low Reynolds number fluid mechanics, and boundary confinement. We re-examine the reported accumulation of swimming bacteria or bull spermatozoa near the boundaries of a fluid chamber, and propose a kinematic model to explain how collision with surface, confinement and rotational Brownian motion give rise to the accumulation of micro-swimmers near a surface. In this model, an elongated microswimmer invariably travels parallel to the surface after hitting it from any incident angle. It then takes off and swims away from the surface after some time due to rotational Brownian motion. Based on this analysis, we obtain through computer simulation steady state density distributions that reproduce the ones measured for the small bacteria E coli and Caulobacter crescentus, as well as for the much larger bull spermatozoa swimming near surfaces. These results suggest strongly that Brownian dynamics and surface confinement are the dominant factors for the accumulation of microswimmers near a surface.

  7. Influence of Brownian Diffusion on Levitation of Bodies in Magnetic Fluid

    Directory of Open Access Journals (Sweden)

    V. Bashtovoi

    2013-12-01

    Full Text Available The present work deals with experimental investigation of the levitation of magnetic and non-magnetic bodies in a magnetic fluid when essentially influenced by Brownian diffusion of magnetic particles in it. It is established that the point of levitation of bodies in a magnetic fluid varies with time.

  8. EFFECTIVE DIFFUSION AND EFFECTIVE DRAG COEFFICIENT OF A BROWNIAN PARTICLE IN A PERIODIC POTENTIAL

    Institute of Scientific and Technical Information of China (English)

    Hongyun Wang

    2011-01-01

    We study the stochastic motion of a Brownian particle driven by a constant force over a static periodic potential.We show that both the effective diffusion and the effective drag coefficient are mathematically well-defined and we derive analytic expressions for these two quantities.We then investigate the asymptotic behaviors of the effective diffusion and the effective drag coefficient,respectively,for small driving force and for large driving force.In the case of small driving force,the effective diffusion is reduced from its Brownian value by a factor that increases exponentially with the amplitude of the potential.The effective drag coefficient is increased by approximately the same factor.As a result,the Einstein relation between the diffusion coefficient and the drag coefficient is approximately valid when the driving force is small.For moderately large driving force,both the effective diffusion and the effective drag coefficient are increased from their Brownian values,and the Einstein relation breaks down. In the limit of very large driving force,both the effective diffusion and the effective drag coefficient converge to their Brownian values and the Einstein relation is once again valid.

  9. Brownian Motion on a Pseudo Sphere in Minkowski Space R^l_v

    Science.gov (United States)

    Jiang, Xiaomeng; Li, Yong

    2016-10-01

    For a Brownian motion moving on a pseudo sphere in Minkowski space R^l_v of radius r starting from point X, we obtain the distribution of hitting a fixed point on this pseudo sphere with l≥ 3 by solving Dirichlet problems. The proof is based on the method of separation of variables and the orthogonality of trigonometric functions and Gegenbauer polynomials.

  10. Influence of Brownian Diffusion on Levitation of Bodies in Magnetic Fluid

    OpenAIRE

    V. Bashtovoi; A. Reks; S. Klimovich; А. Motsar; P. Ryapolov; A. Storozhenko; I. Shabanova

    2013-01-01

    The present work deals with experimental investigation of the levitation of magnetic and non-magnetic bodies in a magnetic fluid when essentially influenced by Brownian diffusion of magnetic particles in it. It is established that the point of levitation of bodies in a magnetic fluid varies with time.

  11. Pricing Perpetual American Put Option in theMixed Fractional Brownian Motion

    Institute of Scientific and Technical Information of China (English)

    2015-01-01

    Under the assumption of the underlying asset is driven by the mixed fractional Brownian motion, we obtain the mixed fractionalBlack-Scholes partial differential equation by fractional Ito formula, and the pricing formula of perpetual American put option bythis partial differential equation theory.

  12. Enhancement of transport properties of a Brownian particle due to quantum effects: Smoluchowski limit

    International Nuclear Information System (INIS)

    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.

  13. Enhancement of transport properties of a Brownian particle due to quantum effects: Smoluchowski limit

    Energy Technology Data Exchange (ETDEWEB)

    Shit, Anindita [Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103 (India); Chattopadhyay, Sudip, E-mail: sudip_chattopadhyay@rediffmail.com [Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103 (India); Chaudhuri, Jyotipratim Ray, E-mail: jprc_8@yahoo.com [Department of Physics, Katwa College, Katwa, Burdwan 713130 (India)

    2012-03-13

    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:: Black-Right-Pointing-Pointer Transport of a quantum Brownian particle in a periodic potential has been addressed. Black-Right-Pointing-Pointer Governing quantum Smoluchowski equation (QSE) includes state dependent diffusion. Black-Right-Pointing-Pointer A coordinate transformation is used to recast QSE with constant diffusion. Black-Right-Pointing-Pointer Transport properties increases in comparison to the corresponding classical result. Black-Right-Pointing-Pointer 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.

  14. Some scaled limit theorems for an immigration super-Brownian motion

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper,the small time limit behaviors for an immigration super-Brownian motion are studied,where the immigration is determined by Lebesgue measure.We first prove a functional central limit theorem,and then study the large and moderate deviations associated with this central tendency.

  15. Existence and stability results for neutral stochastic delay differential equations driven by a fractional Brownian motion

    Directory of Open Access Journals (Sweden)

    R. Maheswari

    2015-03-01

    Full Text Available In this paper we investigate the existence, uniqueness, asymptotic behavior of mild solutions to neutral stochastic differential equations with delays driven by a fractional Brownian motion in a Hilbert space. The cases of finite and infinite delays are analyzed.

  16. On stochastic integration for volatility modulated Brownian-driven Volterra processes via white noise analysis

    DEFF Research Database (Denmark)

    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...

  17. On stochastic integration for volatility modulated Brownian-driven Volterra processes via white noise analysis

    DEFF Research Database (Denmark)

    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 discussed...

  18. On-chip measurement of the Brownian relaxation frequency of magnetic beads using magnetic tunneling junctions

    DEFF Research Database (Denmark)

    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...

  19. Brownian motion with variable drift: 0-1 laws, hitting probabilities and Hausdorff dimension

    CERN Document Server

    Peres, Yuval

    2010-01-01

    By the Cameron--Martin theorem, if a function $f$ is in the Dirichlet space $D$, then $B+f$ has the same a.s. properties as standard Brownian motion, $B$. In this paper we examine properties of $B+f$ when $f \

  20. SOME RESULTS ON LAG INCREMENTS OF PRINCIPAL VALUE OF BROWNIAN LOCAL TIME

    Institute of Scientific and Technical Information of China (English)

    WenJiwei

    2002-01-01

    Let W be a standard Brownian motion,and define Y(t) =∫ods/W(s) as Cauchy's principal value related to the local time of W. We study some limit results on lag increments of Y(t) and obtain various results all of which are related to earlier work by Hanson and Russo in 1983.

  1. Stochastic optimal control problem with infinite horizon driven by G-Brownian motion

    OpenAIRE

    Hu, Mingshang; Wang, Falei

    2016-01-01

    The present paper considers a stochastic optimal control problem, in which the cost function is defined through a backward stochastic differential equation with infinite horizon driven by G-Brownian motion. Then we study the regularities of the value function and establish the dynamic programming principle. Moreover, we prove that the value function is the uniqueness viscosity solution of the related HJBI equation.

  2. The oscillation of the occupation time process of super- Brownian motion on Sierpinski gasket

    Institute of Scientific and Technical Information of China (English)

    郭军义

    2000-01-01

    The occupation time process of super-Brownian motion on the Sierpinski gasket is studied. It is shown that this process does not possess stable property in the long run, but oscillates periodically in some sense. Other convergence properties are also studied.

  3. The oscillation of the occupation time process of super-Brownian motion on Sierpinski gasket

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    The occupation time process of super-Brownian motion on the Sierpinski gasket is studied. It is shown that this process does not possess stable property in the long run, but oscillates periodically in some sense. Other convergence properties are also studied.

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

    Science.gov (United States)

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

    2011-03-01

    We explore the issue of a quantum-noise-induced directed transport of an overdamped Brownian particle that is allowed to move in a spatially periodic potential. The established system-reservoir model has been employed here to study the quantum-noise-induced transport of a Brownian particle in a periodic potential, where the reservoir is being modulated externally by a Gaussian-colored noise. The mobility of the Brownian particle in the linear response regime has been calculated. Then, using Einstein's relation, the analytical expression for the diffusion rate is evaluated for any arbitrary periodic potential for the high-temperature quantum regime. PMID:21517472

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

    Directory of Open Access Journals (Sweden)

    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.

  6. An alternative expression for the Black-Scholes formula in terms of Brownian first and last passage times

    OpenAIRE

    Madan, D.; Roynette, Bernard; Yor, Marc

    2008-01-01

    The celebrated Black-Scholes formula which gives the price of a European option, may be expressed as the cumulative function of a last passage time of Brownian motion. A related result involving first passage times is also obtained.

  7. Eye Movement Disorders

    Science.gov (United States)

    ... t work properly. There are many kinds of eye movement disorders. Two common ones are Strabismus - a disorder ... of the eyes, sometimes called "dancing eyes" Some eye movement disorders are present at birth. Others develop over ...

  8. Tectonic Plate Movement.

    Science.gov (United States)

    Landalf, Helen

    1998-01-01

    Presents an activity that employs movement to enable students to understand concepts related to plate tectonics. Argues that movement brings topics to life in a concrete way and helps children retain knowledge. (DDR)

  9. Virial theorem and dynamical evolution of self-gravitating Brownian particles and bacterial populations in an unbounded domain

    OpenAIRE

    Chavanis, Pierre-Henri; Sire, Clement

    2005-01-01

    We derive the Virial theorem appropriate to the generalized Smoluchowski-Poisson system describing self-gravitating Brownian particles and bacterial populations (chemotaxis). We extend previous works by considering the case of an unbounded domain and an arbitrary equation of state. We use the Virial theorem to study the diffusion (evaporation) of an isothermal Brownian gas above the critical temperature T_c in dimension d=2 and show how the effective diffusion coefficient and the Einstein rel...

  10. Characterisation of a three-dimensional Brownian motor in optical lattices

    CERN Document Server

    Sjolund, P; Dion, C M; Hagman, H; Jonsell, S; Kastberg, A

    2007-01-01

    We present here a detailed study of the behaviour of a three dimensional Brownian motor based on cold atoms in a double optical lattice [P. Sjolund et al., Phys. Rev. Lett. 96, 190602 (2006)]. This includes both experiments and numerical simulations of a Brownian particle. The potentials used are spatially and temporally symmetric, but combined spatiotemporal symmetry is broken by phase shifts and asymmetric transfer rates between potentials. The diffusion of atoms in the optical lattices is rectified and controlled both in direction and speed along three dimensions. We explore a large range of experimental parameters, where irradiances and detunings of the optical lattice lights are varied within the dissipative regime. Induced drift velocities in the order of one atomic recoil velocity have been achieved.

  11. Impurity driven Brownian motion of solitons in elongated Bose-Einstein Condensates

    CERN Document Server

    Aycock, L M; Genkina, D; Lu, H -I; Galitski, V; Spielman, I B

    2016-01-01

    Solitons, spatially-localized, mobile excitations resulting from an interplay between nonlinearity and dispersion, are ubiquitous in physical systems from water channels and oceans to optical fibers and Bose-Einstein condensates (BECs). For the first time, we observed and controlled the Brownian motion of solitons. We launched long-lived dark solitons in highly elongated $^{87}\\rm{Rb}$ 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 (1-D), 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-1-D scattering theory of impurity atoms interacting with a soliton, giving diffusion coefficients consistent with experiment.

  12. Exact analytical solutions to the master equation of quantum Brownian motion for a general environment

    CERN Document Server

    Fleming, C H; Hu, B L

    2010-01-01

    We revisit the model of a quantum Brownian oscillator linearly coupled to an environment of quantum oscillators at finite temperature. By introducing a compact and particularly well-suited formulation, we give a rather quick and direct derivation of the master equation and its solutions for general spectral functions and arbitrary temperatures. The flexibility of our approach allows for an immediate generalization to cases with an external force and with an arbitrary number of Brownian oscillators. More importantly, we point out an important mathematical subtlety concerning boundary-value problems for integro-differential equations which led to incorrect master equation coefficients and impacts on the description of nonlocal dissipation effects in all earlier derivations. Furthermore, we provide explicit, exact analytical results for the master equation coefficients and its solutions in a wide variety of cases, including ohmic, sub-ohmic and supra-ohmic environments with a finite cut-off.

  13. Characterization of turbulence stability through the identification of multifractional Brownian motions

    Science.gov (United States)

    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.

  14. Quantal Brownian Motion from RPA dynamics: The master and Fokker-Planck equations

    International Nuclear Information System (INIS)

    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.)

  15. Brownian motion in wedges, last passage time and the second arc-sine law

    Energy Technology Data Exchange (ETDEWEB)

    Comtet, Alain [Laboratoire de Physique Theorique et Modeles Statistiques. Universite Paris-Sud, Bat. 100, F-91405 Orsay Cedex (France); Desbois, Jean [Laboratoire de Physique Theorique et Modeles Statistiques. Universite Paris-Sud, Bat. 100, F-91405 Orsay Cedex (France)

    2003-05-02

    We consider a planar Brownian motion starting from O at time t = 0 and stopped at t = 1 and a set F = OI{sub i}; i = 1, 2, ..., n of n semi-infinite straight lines emanating from O. Denoting by g the last time when F is reached by the Brownian motion, we compute the probability law of g. In particular, we show that, for a symmetric F and even n values, this law can be expressed as a sum of arcsin or (arcsin){sup 2} functions. The original result of Levy is recovered as the special case n = 2. A relation with the problem of reaction-diffusion of a set of three particles in one dimension is discussed. (letter to the editor)

  16. Brownian motion in wedges, last passage time and the second arc-sine law

    International Nuclear Information System (INIS)

    We consider a planar Brownian motion starting from O at time t = 0 and stopped at t = 1 and a set F = OIi; i = 1, 2, ..., n of n semi-infinite straight lines emanating from O. Denoting by g the last time when F is reached by the Brownian motion, we compute the probability law of g. In particular, we show that, for a symmetric F and even n values, this law can be expressed as a sum of arcsin or (arcsin)2 functions. The original result of Levy is recovered as the special case n = 2. A relation with the problem of reaction-diffusion of a set of three particles in one dimension is discussed. (letter to the editor)

  17. On Nonlinear Quantum Mechanics, Brownian Motion, Weyl Geometry and Fisher Information

    Directory of Open Access Journals (Sweden)

    Castro C.

    2006-01-01

    Full Text Available A new nonlinear Schrödinger equation is obtained explicitly from the (fractal Brownian motion of a massive particle with a complex-valued diffusion constant. Real-valued energy plane-wave solutions and solitons exist in the free particle case. One remarkable feature of this nonlinear Schrödinger equation based on a (fractal Brownian motion model, over all the other nonlinear QM models, is that the quantummechanical energy functional coincides precisely with the field theory one. We finalize by showing why a complex momentum is essential to fully understand the physical implications of Weyl’s geometry in QM, along with the interplay between Bohm’s Quantum potential and Fisher Information which has been overlooked by several authors in the past.

  18. Characterization of turbulence stability through the identification of multifractional Brownian motions

    Directory of Open Access Journals (Sweden)

    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.

  19. A weak limit theorem for numerical approximation of Brownian semi-stationary processes

    DEFF Research Database (Denmark)

    Podolskij, Mark; Thamrongrat, Nopporn

    In this paper we present a weak limit theorem for a numerical approximation of Brownian semi-stationary processes studied in [14]. In the original work of [14] the authors propose to use Fourier transformation to embed a given one dimensional (Levy) Brownian semi-stationary process into a two......-parameter stochastic field. For the latter they use a simple iteration procedure and study the strong approximation error of the resulting numerical scheme given that the volatility process is fully observed. In this work we present the corresponding weak limit theorem for the setting, where the volatility....../drift process needs to be numerically simulated. In particular, weak approximation errors for smooth test functions can be obtained from our asymptotic theory....

  20. Social movements and science

    DEFF Research Database (Denmark)

    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...

  1. Movement and Space

    DEFF Research Database (Denmark)

    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...

  2. Brownian inventory models with convex holding cost, Part 2: Discount-optimal controls

    OpenAIRE

    Jim Dai; Dacheng Yao

    2013-01-01

    We consider an inventory system in which inventory level fluctuates as a Brownian motion in the absence of control. The inventory continuously accumulates cost at a rate that is a general convex function of the inventory level, which can be negative when there is a backlog. At any time, the inventory level can be adjusted by a positive or negative amount, which incurs a fixed positive cost and a proportional cost. The challenge is to find an adjustment policy ...

  3. Maximum likelihood drift estimation for the mixing of two fractional Brownian motions

    OpenAIRE

    Mishura, Yuliya

    2015-01-01

    We construct the maximum likelihood estimator (MLE) of the unknown drift parameter $\\theta\\in \\mathbb{R}$ in the linear model $X_t=\\theta t+\\sigma B^{H_1}(t)+B^{H_2}(t),\\;t\\in[0,T],$ where $B^{H_1}$ and $B^{H_2}$ are two independent fractional Brownian motions with Hurst indices $\\frac12

  4. Stability of Linear Stochastic Differential Equations with Respect to Fractional Brownian Motion

    Institute of Scientific and Technical Information of China (English)

    SHU Hui-sheng; CHEN Chun-li; WEI Guo-liang

    2009-01-01

    This paper is concerned with the stochastically stability for the m -dimensional linear stochastic differential equations with respect to fractional Brownian motion (FBM) with Hurst parameter H∈ (1/2, 1). On the basis of the pioneering work of Duncan and Hu, a Ito's formula is given.An improved derivative operator to Lyapunov functions is constructed, and the sufficient conditions for the stochastically stability of linear stochastic differential equations driven by FBM are established. These extend the stochastic Lyapunov stability theories.

  5. Random variables as pathwise integrals with respect to fractional Brownian motion

    CERN Document Server

    Mishura, Yuliya; Valkeila, Esko

    2011-01-01

    We show that a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand $g$ can have any prescribed distribution, moreover, we give both necessary and sufficient conditions when random variables can be represented in this form. We also prove that any random variable is a value of such integral in some improper sense. We discuss some applications of these results, in particular, to fractional Black--Scholes model of financial market.

  6. Level-statistics in Disordered Systems: A single parametric scaling and Connection to Brownian Ensembles

    OpenAIRE

    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...

  7. Fractional Brownian Motion Approximation Based on Fractional Integration of a White Noise

    OpenAIRE

    Chechkin, A. V.; Gonchar, V. Yu.

    1999-01-01

    We study simple approximations to fractional Gaussian noise and fractional Brownian motion. The approximations are based on spectral properties of the noise. They allow one to consider the noise as the result of fractional integration/differentiation of a white Gaussian noise. We study correlation properties of the approximation to fractional Gaussian noise and point to the peculiarities of persistent and anti-persistent behaviors. We also investigate self-similar properties of the approximat...

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

    OpenAIRE

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

    2012-01-01

    Diffusion is often the rate determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. This paper proposes a new hybrid diffusion method that couples the strengths of each of these two methods. The method is derived for a general multidimensional system, and is presented using a basic test case for 1D linear and radially symmetri...

  9. Optimal stochastic control and optimal consumption and portfolio with G-Brownian motion

    OpenAIRE

    Fei, Weiyin; Fei, Chen

    2013-01-01

    By the calculus of Peng's G-sublinear expectation and G-Brownian motion on a sublinear expectation space $(\\Omega, {\\cal H}, \\hat{\\mathbb{E}})$, we first set up an optimality principle of stochastic control problem. Then we investigate an optimal consumption and portfolio decision with a volatility ambiguity by the derived verification theorem. Next the two-fund separation theorem is explicitly obtained. And an illustrative example is provided.

  10. MULTI-DIMENSIONAL GEOMETRIC BROWNIAN MOTIONS, ONSAGER-MACHLUP FUNCTIONS, AND APPLICATIONS TO MATHEMATICAL FINANCE

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    The solutions of the following bilinearstochastic differential equation are stud-ied (X) where Atk, Bt are (deterministic)continuous matrix-valued functions of t and w1(t),..., wm(t) are m independent standard Brownian motions. Conditions are given such thatthe solution is positive if the initial condition is positive.The equation the most probable path must satisfy is also derived and applied to a mathematicalfinance problem.

  11. Boundary behavior of a constrained Brownian motion between reflecting-repellent walls

    OpenAIRE

    Lépingle, Dominique

    2009-01-01

    International audience Stochastic variational inequalities provide a unified treatment for stochastic differential equations living in a closed domain with normal reflection and (or) singular repellent drift. When the domain is a polyhedron, we prove that the reflected-repelled Brownian motion does not hit the non-smooth part of the boundary. A sufficient condition for non-hitting a face of the polyhedron is derived from the one-dimensional case. A complete answer to the question of attain...

  12. Generalized Scaling and the Master Variable for Brownian Magnetic Nanoparticle Dynamics

    OpenAIRE

    Reeves, Daniel B.; Yipeng Shi; Weaver, John B.

    2016-01-01

    Understanding the dynamics of magnetic particles can help to advance several biomedical nanotechnologies. Previously, scaling relationships have been used in magnetic spectroscopy of nanoparticle Brownian motion (MSB) to measure biologically relevant properties (e.g., temperature, viscosity, bound state) surrounding nanoparticles in vivo. Those scaling relationships can be generalized with the introduction of a master variable found from non-dimensionalizing the dynamical Langevin equation. T...

  13. Fractional Brownian motion, the Matern process, and stochastic modeling of turbulent dispersion

    CERN Document Server

    Lilly, J M; Early, J J; Olhede, S C

    2016-01-01

    Stochastic process exhibiting power-law slopes in the frequency domain are frequently well modeled by fractional Brownian motion (fBm). In particular, the spectral slope at high frequencies is associated with the degree of small-scale roughness or fractal dimension. However, a broad class of real-world signals have a high-frequency slope, like fBm, but a plateau in the vicinity of zero frequency. This low-frequency plateau, it is shown, implies that the temporal integral of the process exhibits diffusive behavior, dispersing from its initial location at a constant rate. Such processes are not well modeled by fBm, which has a singularity at zero frequency corresponding to an unbounded rate of dispersion. A more appropriate stochastic model is a much lesser-known random process called the Matern process, which is shown herein to be a damped version of fractional Brownian motion. This article first provides a thorough introduction to fractional Brownian motion, then examines the details of the Matern process and...

  14. Bessel processes and hyperbolic Brownian motions stopped at different random times

    CERN Document Server

    D'Ovidio, Mirko

    2010-01-01

    Iterated Bessel processes R^\\gamma(t), t>0, \\gamma>0 and their counterparts on hyperbolic spaces, i.e. hyperbolic Brownian motions B^{hp}(t), t>0 are examined and their probability laws derived. The higher-order partial differential equations governing the distributions of I_R(t)=_1R^\\gamma(_2R^\\gamma(t)), t>0 and J_R(t) =_1R^\\gamma(|_2R^\\gamma(t)|^2), t>0 are obtained and discussed. Processes of the form R^\\gamma(T_t), t>0, B^{hp}(T_t), t>0 where T_t=\\inf{s: B(s)=t} are examined and numerous probability laws derived, including the Student law, the arcsin laws (also their asymmetric versions), the Lamperti distribution of the ratio of independent positively skewed stable random variables and others. For the process R^{\\gamma}(T^\\mu_t), t>0 (where T^\\mu_t = \\inf{s: B^\\mu(s)=t} and B^\\mu is a Brownian motion with drift \\mu) the explicit probability law and the governing equation are obtained. For the hyperbolic Brownian motions on the Poincar\\'e half-spaces H^+_2, H^+_3 we study B^{hp}(T_t), t>0 and the corresp...

  15. Ratcheting of Brownian swimmers in periodically corrugated channels: A reduced Fokker-Planck approach

    Science.gov (United States)

    Yariv, Ehud; Schnitzer, Ory

    2014-09-01

    We consider the motion of self-propelling Brownian particles in two-dimensional periodically corrugated channels. The point-size swimmers propel themselves in a direction which fluctuates by Brownian rotation; in addition, they undergo Brownian motion. The impermeability of the channel boundaries in conjunction with an asymmetry of the unit-cell geometry enables ratcheting, where a nonzero particle current is animated along the channel. This effect is studied here in the continuum limit using a diffusion-advection description of the probability density in a four-dimensional position-orientation space. Specifically, the mean particle velocity is calculated using macrotransport (generalized Taylor-dispersion) theory. This description reveals that the ratcheting mechanism is indirect: swimming gives rise to a biased spatial particle distribution which in turn results in a purely diffusive net current. For a slowly varying channel geometry, the dependence of this current upon the channel geometry and fluid-particle parameters is studied via a long-wave approximation over a reduced two-dimensional space. This allows for a straightforward seminumerical solution. In the limit where both rotational diffusion and swimming are strong, we find an asymptotic approximation to the particle current, scaling inversely with the square of the swimming Péclet number. For a given swimmer-fluid system, this limit is physically realized with increasing unit-cell size.

  16. Vertices of the least concave majorant of Brownian motion with parabolic drift

    CERN Document Server

    Groeneboom, Piet

    2010-01-01

    It was shown in Groeneboom (1983) that the least concave majorant of one-sided Brownian motion without drift can be characterized by a jump process with independent increments, which is the inverse of the process of slopes of the least concave majorant. This result can be used to prove the result of Sparre Andersen (1954) that the number of vertices of the smallest concave majorant of the empirical distribution function of a sample of size n from the uniform distribution on [0,1] is asymptotically normal, with an asymptotic expectation and variance which are both of order log n. A similar (Markovian) inverse jump process was introduced in Groeneboom (1989), in an analysis of the least concave majorant of two-sided Brownian motion with a parabolic drift. This process is quite different from the process for one-sided Brownian motion without drift: the number of vertices in a (corresponding slopes) interval has an expectation proportional to the length of the interval and the variance of the number of vertices i...

  17. [Sleep related movement disorders].

    Science.gov (United States)

    Suzuki, Keisuke; Miyamoto, Masayuki; Miyamoto, Tomoyuki; Hirata, Koichi

    2015-06-01

    Sleep related movement disorders (SRMD) are characterized by simple, stereotyped movements occur during sleep, with the exception of restless legs syndrome (RLS). RLS has the following essential features; an urge to move the legs usually accompanied by uncomfortable sensation in the legs, improvement of symptoms after movement (non-stereotypical movements, such as walking and stretching, to reduce symptoms), and symptoms occur or worsen during periods of rest and in the evening and night. However, RLS is closely associated with periodic limb movement, which shows typical stererotyped limb movements. In the International Classification of Sleep Disorders, 3rd edition, sleep disturbances or daytime symptoms are prerequiste for a diagnosis of SRMD. We here review diagnosis and treatment of SRMD. PMID:26065126

  18. MOVEMENT DISORDERS IN CHILDREN

    Directory of Open Access Journals (Sweden)

    Sujitnath

    2016-01-01

    Full Text Available Involuntary movements of different types are associated with many diseases in children. Movement disorders in adult have been published in different journals, but in children these disorders have been ignored, even in most of the paediatric neurology books. Here is a brief attempt to describe different types of movement disorders and their various names in different diseases. Possible investigations and treatment of the disorders have been described in short.

  19. The mathematics of movement

    Science.gov (United States)

    Johnson, D.H.

    1999-01-01

    Review of: Quantitative Analysis of Movement: Measuring and Modeling Population Redistribution in Animals and Plants. Peter Turchin. 1998. Sinauer Associates, Sunderland, MA. 306 pages. $38.95 (paper).

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

    Science.gov (United States)

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

    2016-09-01

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

  1. Quantum harmonic Brownian motion in a general environment: A modified phase-space approach

    Energy Technology Data Exchange (ETDEWEB)

    Yeh, L. [Univ. of California, Berkeley, CA (United States). Dept. of Physics]|[Lawrence Berkeley Lab., CA (United States)

    1993-06-23

    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.

  2. [Dance/Movement Therapy.

    Science.gov (United States)

    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…

  3. Studying Social Movements

    DEFF Research Database (Denmark)

    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 ...

  4. Randomness Of Amoeba Movements

    Science.gov (United States)

    Hashiguchi, S.; Khadijah, Siti; Kuwajima, T.; Ohki, M.; Tacano, M.; Sikula, J.

    2005-11-01

    Movements of amoebas were automatically traced using the difference between two successive frames of the microscopic movie. It was observed that the movements were almost random in that the directions and the magnitudes of the successive two steps are not correlated, and that the distance from the origin was proportional to the square root of the step number.

  5. Exploring pedestrian movement patterns

    NARCIS (Netherlands)

    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 n

  6. Dynamics of human movement

    NARCIS (Netherlands)

    Koopman, Bart H.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

  7. 85 Engaging Movement Activities.

    Science.gov (United States)

    Weikart, Phyllis S.; Carlton, Elizabeth B.

    This book presents activities to keep K-6 students moving in a variety of ways as they learn. The movement experiences are planned around key curriculum concepts in movement and music as well as in academic curriculum areas. The experiences develop students' basic timing, language abilities, vocabulary, concentration, planning skills, and…

  8. Relationships involving spatial transitions for Brownian particles within a potential-well.

    Science.gov (United States)

    Brody, Ross

    2007-03-01

    Using an optical tweezer apparatus we have trapped single latex spheres and analyzed their Brownian motion within a potential well. By considering transitions from various initial and final positions within the well, we experimentally show that the ratio of conditional probabilities, P(xf,t+δt|xi,t)/P(xi,t+δt|xf,t), is independent of δt. We also show the instanton times corresponding to last-touch-first-touch (LTFT) trajectories obey the equality, LTFT(xi->xf)=LTFT(xf->xi), shown by Bier et al. [Phys. Rev. E 59,422 (1999)].

  9. Self-assembly of actin monomers into long filaments: Brownian Dynamics simulations

    DEFF Research Database (Denmark)

    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...... to unravel certain relations between thefilament's physical properties and the model parameters such as the attachment rate constant and the size of the capture zone, the detachment rate and the probability of the detached event, as well as the growth rate and waiting times between two successive attachment...

  10. Optimal Control of Brownian Inventory Models with Convex Holding Cost: Average Cost Case

    OpenAIRE

    Dai, Jim; Yao, Dacheng

    2011-01-01

    We consider an inventory system in which inventory level fluctuates as a Brownian motion in the absence of control. The inventory continuously accumulates cost at a rate that is a general convex function of the inventory level, which can be negative when there is a backlog. At any time, the inventory level can be adjusted by a positive or negative amount, which incurs a fixed cost and a proportional cost. The challenge is to find an adjustment policy that balances the holding cost and adjustm...

  11. Optimal Control of Brownian Inventory Models with Convex Inventory Cost: Discounted Cost Case

    OpenAIRE

    Dai, Jim; Yao, Dacheng

    2011-01-01

    We consider an inventory system in which inventory level fluctuates as a Brownian motion in the absence of control. The inventory continuously accumulates cost at a rate that is a general convex function of the inventory level, which can be negative when there is a backlog. At any time, the inventory level can be adjusted by a positive or negative amount, which incurs a fixed positive cost and a proportional cost. The challenge is to find an adjustment policy that balances the inventory cost ...

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

    Science.gov (United States)

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

    2008-02-01

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

  13. Escape rate of an active Brownian particle over a potential barrier.

    Science.gov (United States)

    Burada, P S; Lindner, B

    2012-03-01

    We study the dynamics of an active Brownian particle with a nonlinear friction function located in a spatial cubic potential. For strong but finite damping, the escape rate of the particle over the spatial potential barrier shows a nonmonotonic dependence on the noise intensity. We relate this behavior to the fact that the active particle escapes from a limit cycle rather than from a fixed point and that a certain amount of noise can stabilize the sojourn of the particle on this limit cycle. PMID:22587135

  14. Branching Brownian motion with selection of the N right-most particles: An approximate model

    CERN Document Server

    Maillard, Pascal

    2011-01-01

    We present an approximation to the Brunet--Derrida model of supercritical branching Brownian motion on the real line with selection of the $N$ right-most particles, valid when the population size $N$ is large. It consists of introducing a random space-time barrier at which particles are instantaneously killed in such a way that the population size stays almost constant over time. We prove that the suitably recentered position of this barrier converges at the $\\log^3 N$ timescale to a L\\'evy process, which we identify. This validates the physicists' predictions about the fluctuations in the Brunet--Derrida model.

  15. Second order asymptotics for Brownian motion among a heavy tailed Poissonian potential

    CERN Document Server

    Fukushima, Ryoki

    2010-01-01

    We consider the Feynman-Kac functional associated with a Brownian motion among a random potential. The potential is defined by attaching a heavy tailed positive potential around the Poisson point process. This model was first considered by Pastur~(1977) and the first order term of the moment asymptotics was determined. In this paper, both moment and almost sure asymptotics are determined up to the second order. As an application, we also derive the second order asymptotics of the integrated density of states of the corresponding random Schr\\"{o}dinger operator.

  16. Optimal Policy for Brownian Inventory Models with General Convex Inventory Cost

    Institute of Scientific and Technical Information of China (English)

    Da-cheng YAO

    2013-01-01

    We study an inventory system in which products are ordered from outside to meet demands,and the cumulative demand is governed by a Brownian motion.Excessive demand is backlogged.We suppose that the shortage and holding costs associated with the inventory are given by a general convex function.The product ordering from outside incurs a linear ordering cost and a setup fee.There is a constant leadtime when placing an order.The optimal policy is established so as to minimize the discounted cost including the inventory cost and ordering cost.

  17. Brownian Ratchet Driven by a Rocking Forcing with Broken Temporal Symmetry

    Institute of Scientific and Technical Information of China (English)

    LIU Feng-Zhi; LI Xiao-Wen; ZHENG Zhi-Gang

    2003-01-01

    The ratchet motion of a Brownian particle in a symmetric periodic potential under a rocking force thatbreaks the temporal symmetry is studied. As long as the relaxation time in the thermal background is much shorter thanthe forcing period, the unidirectional transport can be analytically treated. By solving the Fokker-Planck equations, weget an analytical expression of the current. This result indicates that with an appropriate match between the potentialfield, the asymmetric ac force and the thermal noise, a net current can be achieved. The current versus thermal noiseexhibits a stochastic-resonance-like behavior.

  18. Liouville quantum gravity and the Brownian map II: geodesics and continuity of the embedding

    OpenAIRE

    Miller, Jason; Sheffield, Scott

    2016-01-01

    We endow the $\\sqrt{8/3}$-Liouville quantum gravity sphere with a metric space structure and show that the resulting metric measure space agrees in law with the Brownian map. Recall that a Liouville quantum gravity sphere is a priori naturally parameterized by the Euclidean sphere ${\\mathbf S}^2$. Previous work in this series used quantum Loewner evolution (QLE) to construct a metric $d_{\\mathcal Q}$ on a countable dense subset of ${\\mathbf S}^2$. Here we show that $d_{\\mathcal Q}$ a.s. exten...

  19. A limit theorem for moments in space of the increments of Brownian local time

    OpenAIRE

    Campese, Simon

    2015-01-01

    We proof a limit theorem for moments in space of the increments of Brownian local time. As special cases for the second and third moments, previous results by Chen et al. (Ann. Prob. 38, 2010, no. 1) and Rosen (Stoch. Dyn. 11, 2011, no. 1), which were later reproven by Hu and Nualart (Electron. Commun. Probab. 14, 2009; Electron. Commun. Probab. 15, 2010) and Rosen (S\\'eminaire de Probabilit\\'es XLIII, Springer, 2011) are included. Furthermore, a conjecture of Rosen for the fourth moment is s...

  20. Joint distributions of partial and global maxima of a Brownian bridge

    Science.gov (United States)

    Bénichou, Olivier; Krapivsky, P. L.; Mejía-Monasterio, Carlos; Oshanin, Gleb

    2016-08-01

    We analyze the joint distributions and temporal correlations between the partial maximum m and the global maximum M achieved by a Brownian bridge on the subinterval [0,{t}1] and on the entire interval [0,t], respectively. We determine three probability distribution functions: the joint distribution P(m,M) of both maxima; the distribution P(m) of the partial maximum; and the distribution {{\\Pi }}(G) of the gap between the maxima, G=M-m. We present exact results for the moments of these distributions and quantify the temporal correlations between m and M by calculating the Pearson correlation coefficient.

  1. Binary data corruption due to a Brownian agent. II. Two dimensions, competing agents, and generalized couplings.

    Science.gov (United States)

    Triampo, W; Newman, T J

    1999-08-01

    This work is a continuation of our previous investigation of binary data corruption due to a Brownian agent [Phys. Rev. E 59, 5172 (1999)]. We extend our study in three main directions which allow us to make closer contact with real bistable systems. These are (i) a detailed analysis of two dimensions, (ii) the case of competing agents, and (iii) the cases of asymmetric and quenched random couplings. Most of our results are obtained by extending our original phenomenological model, and are supported by extensive numerical simulations.

  2. Asymptotic theory for Brownian semi-stationary processes with application to turbulence

    DEFF Research Database (Denmark)

    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......-stationary processes. In "Prokhorov and Contemporary Probability Theory", Springer.] and present some new connections to fractional diffusion models. We apply our probabilistic results to construct a family of estimators for the smoothness parameter of the BSS process. In this context we develop estimates with gaps......, which allow to obtain a valid central limit theorem for the critical region. Finally, we apply our statistical theory to turbulence data....

  3. EPR statistical mixture of correlated states with fractional brownian process induced by third party interaction

    CERN Document Server

    Tamburini, F; Bianchini, A

    1999-01-01

    A time-correlated EPR pairs protocol is analized, based on detection of fractal correlated signals into a statistical mixture of EPR correlated pairs: an approximated alpha-Fractional Brownian Motion (FBM) is induced on the group of EPR pairs (e.g. by sender-third party eavesdropper-like interactions as in Ekert quantum cryptography), to be detected by the receiver using a non - orthogonal wavelet filter, able to characterize the FBM from a noisy enviroment by formalizing a nonlinear optimization problem for the FBM alpha-characteristic parameter extimation.

  4. Effect of internal viscosity on Brownian dynamics of DNA molecules in shear flow.

    Science.gov (United States)

    Yang, Xiao-Dong; Melnik, Roderick V N

    2007-04-01

    The results of Brownian dynamics simulations of a single DNA molecule in shear flow are presented taking into account the effect of internal viscosity. The dissipative mechanism of internal viscosity is proved necessary in the research of DNA dynamics. A stochastic model is derived on the basis of the balance equation for forces acting on the chain. The Euler method is applied to the solution of the model. The extensions of DNA molecules for different Weissenberg numbers are analyzed. Comparison with the experimental results available in the literature is carried out to estimate the contribution of the effect of internal viscosity.

  5. Virial theorem for rotating self-gravitating Brownian particles and two-dimensional point vortices

    OpenAIRE

    Chavanis, Pierre-Henri

    2009-01-01

    We derive the proper form of Virial theorem for a system of rotating self-gravitating Brownian particles. We show that, in the two-dimensional case, it takes a very simple form that can be used to obtain general results about the dynamics of the system without being required to solve the Smoluchowski-Poisson system explicitly. We also develop the analogy between self-gravitating systems and two-dimensional point vortices and derive a Virial-like relation for the vortex system.

  6. Brownian Dynamics Simulation of Microstructures and Elongational Viscosities of Micellar Surfactant Solution

    Institute of Scientific and Technical Information of China (English)

    WEI Jin-Jia; KAWAGUCHI Yasuo; YU Bo; LI Feng-Chen

    2008-01-01

    @@ Brownian dynamics simulation is conducted for a dilute surfactant solution under a steady uniaxial elongational flow.A new inter-cluster potential is used for the interaction among surfactant micelles to determine the micellar network structures in the surfactant solution.The micellar network is successfully simulated.It is formed at low elongation rates and destroyed by high elongation rates.The computed elongational viscosities show elongation-thinning characteristics.The relationship between the elongational viscosities and the microstructure of the surfactant solution is revealed.

  7. Brownian motion, random walks on trees, and harmonic measure on polynomial Julia sets

    OpenAIRE

    Emerson, Nathaniel D.

    2006-01-01

    We consider the harmonic measure on a disconnected polynomial Julia set in terms of Brownian motion. We show that the harmonic measure of any connected component of such a Julia set is zero. Associated to the polynomial is a combinatorial model, the tree with dynamics. We define a measure on the tree, which is a combinatorial version on harmonic measure. We show that this measure is isomorphic to the harmonic measure on the Julia set. The measure induces a random walk on the tree, which is is...

  8. Harnack Inequality and Regularity for a Product of Symmetric Stable Process and Brownian Motion

    OpenAIRE

    Karli, Deniz

    2010-01-01

    In this paper, we consider a product of a symmetric stable process in $\\mathbb{R}^d$ and a one-dimensional Brownian motion in $\\mathbb{R}^+$. Then we define a class of harmonic functions with respect to this product process. We show that bounded non-negative harmonic functions in the upper-half space satisfy Harnack inequality and prove that they are locally H\\"older continuous. We also argue a result on Littlewood-Paley functions which are obtained by the $\\alpha$-harmonic extension of an $L...

  9. Suppression of a Brownian noise in a hole-type sensor due to induced-charge electro-osmosis

    Science.gov (United States)

    Sugioka, Hideyuki

    2016-03-01

    Noise reduction is essential for a single molecular sensor. Thus, we propose a novel noise reduction mechanism using a hydrodynamic force due to induced-charge electro-osmosis (ICEO) in a hole-type sensor and numerically examine the performance. By the boundary element method that considers both a Brownian motion and an ICEO flow of a polarizable particle, we find that the Brownian noise in a current signal is suppressed significantly in a converging channel because of the ICEO flow around the particle in the presence of an electric field. Further, we propose a simple model that explains a numerically obtained threshold voltage of the suppression of the Brownian noise due to ICEO. We believe that our findings contribute greatly to developments of a single molecular sensor.

  10. The Development of Coordinated Movement.

    Science.gov (United States)

    Montanaro, Silvana Quattrocchi

    2002-01-01

    Discusses stages of movement in the first 3 years of life with a philosophical dimension regarding evolutionary aspects of movement as first manifestation of "will." Describes how the early childhood environment is prepared to allow for movement and the connection between movement and brain development. Discusses the contribution of movement to…

  11. Limitation of the Least Square Method in the Evaluation of Dimension of Fractal Brownian Motions

    CERN Document Server

    Qiao, Bingqiang; Zeng, Houdun; Li, Xiang; Dai, Benzhong

    2015-01-01

    With the standard deviation for the logarithm of the re-scaled range $\\langle |F(t+\\tau)-F(t)|\\rangle$ of simulated fractal Brownian motions $F(t)$ given in a previous paper \\cite{q14}, the method of least squares is adopted to determine the slope, $S$, and intercept, $I$, of the log$(\\langle |F(t+\\tau)-F(t)|\\rangle)$ vs $\\rm{log}(\\tau)$ plot to investigate the limitation of this procedure. It is found that the reduced $\\chi^2$ of the fitting decreases with the increase of the Hurst index, $H$ (the expectation value of $S$), which may be attributed to the correlation among the re-scaled ranges. Similarly, it is found that the errors of the fitting parameters $S$ and $I$ are usually smaller than their corresponding standard deviations. These results show the limitation of using the simple least square method to determine the dimension of a fractal time series. Nevertheless, they may be used to reinterpret the fitting results of the least square method to determine the dimension of fractal Brownian motions more...

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

    Science.gov (United States)

    Grimm, Matthias; Franosch, Thomas; Jeney, Sylvia

    2012-08-01

    We have developed an in situ method to calibrate optical tweezers experiments and simultaneously measure the size of the trapped particle or the viscosity of the surrounding fluid. The positional fluctuations of the trapped particle are recorded with a high-bandwidth photodetector. We compute the mean-square displacement, as well as the velocity autocorrelation function of the sphere, and compare it to the theory of Brownian motion including hydrodynamic memory effects. A careful measurement and analysis of the time scales characterizing the dynamics of the harmonically bound sphere fluctuating in a viscous medium directly yields all relevant parameters. Finally, we test the method for different optical trap strengths, with different bead sizes and in different fluids, and we find excellent agreement with the values provided by the manufacturers. The proposed approach overcomes the most commonly encountered limitations in precision when analyzing the power spectrum of position fluctuations in the region around the corner frequency. These low frequencies are usually prone to errors due to drift, limitations in the detection, and trap linearity as well as short acquisition times resulting in poor statistics. Furthermore, the strategy can be generalized to Brownian motion in more complex environments, provided the adequate theories are available. PMID:23005790

  13. Supercritical super-Brownian motion with a general branching mechanism and travelling waves

    CERN Document Server

    Kyprianou, A E; Murillo-Salas, A; Ren, Y -X

    2010-01-01

    We consider the classical problem of existence, uniqueness and asymptotics of monotone solutions to the travelling wave equation associated to the parabolic semi-group equation of a super-Brownian motion with a general branching mechanism. Whilst we are strongly guided by the probabilistic reasoning of Kyprianou (2004) for branching Brownian motion, the current paper offers a number of new insights. Our analysis incorporates the role of Seneta-Heyde norming which, in the current setting, draws on classical work of Grey (1974). We give a pathwise explanation of Evans' immortal particle picture (the spine decomposition) which uses the Dynkin-Kuznetsov N-measure as a key ingredient. Moreover, in the spirit of Neveu's stopping lines we make repeated use of Dynkin's exit measures. Additional complications arise from the general nature of the branching mechanism. As a consequence of the analysis we also offer an exact X(log X)^2 moment dichotomy for the almost sure convergence of the so-called derivative martingale...

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

    Science.gov (United States)

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

    2016-04-01

    Consider a one-dimensional branching Brownian motion and rescale the coordinate and time so that the rates of branching and diffusion are both equal to 1. If X_{1}(t) is the position of the rightmost particle of the branching Brownian motion at time t, the empirical velocity c of this rightmost particle is defined as c=X_{1}(t)/t. Using the Fisher-Kolmogorov-Petrovsky-Piscounov equation, we evaluate the probability distribution P(c,t) of this empirical velocity c in the long-time t limit for c>2. It is already known that, for a single seed particle, P(c,t)∼exp[-(c^{2}/4-1)t] up to a prefactor that can depend on c and t. Here we show how to determine this prefactor. The result can be easily generalized to the case of multiple seed particles and to branching random walks associated with other traveling-wave equations. PMID:27176286

  15. Realization of a Brownian engine to study transport phenomena: a semiclassical approach.

    Science.gov (United States)

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

    2010-06-01

    Brownian particles moving in a periodic potential with or without external load are often used as good theoretical models for the phenomenological studies of microscopic heat engines. The model that we propose here, assumes the particle to be moving in a nonequilibrium medium and we have obtained the exact expression for the stationary current density. We have restricted our consideration to the overdamped motion of the Brownian particle. We present here a self-consistent theory based on the system-reservoir coupling model, within a microscopic approach, of fluctuation induced transport in the semiclassical limit for a general system coupled with two heat baths kept at different temperatures. This essentially puts forth an approach to semiclassical state-dependent diffusion. We also explore the possibility of observing a current when the temperature of the two baths are different, and also envisage that our system may act as a Carnot engine even when the bath temperatures are the same. The condition for such a construction has been elucidated. PMID:20866383

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

    Science.gov (United States)

    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.

  17. Observing Brownian motion and measuring temperatures in vibration-fluidized granular matter

    International Nuclear Information System (INIS)

    Understanding the behaviour of granular media, either at rest or moving under external driving, is a difficult task, although it is important and of very practical interest. Describing the motion of each individual grain is complicated, not only because of the large number of grains, but also because the mechanisms of interaction at the grain level involve complex contact forces. One would like to have, in fact, a description in terms of a few macroscopic quantities. Since a granular medium resembles a liquid or a gas when strongly vibrated or when flowing out of a container, a natural approach is to adopt usual equilibrium statistical mechanics tools in order to test if such a macroscopic description is possible. In other words, an interesting question is to investigate whether one can model granular media, when close to a liquid-like state for example, using viscosity, temperature, and so on, as one does for normal liquids. With this aim in view, we have developed a non-equilibrium version of the classical Brownian motion experiment. In particular, we have observed the motion of a torsion oscillator immersed in an externally vibrated granular medium of glass spheres, and have collected evidence that the motion is Brownian-like. An approximate fluctuation-dissipation relation holds, and we can define temperature-like and viscosity-like parameters

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

    International Nuclear Information System (INIS)

    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

  19. Self-Propelling Nanomotors in the Presence of Strong Brownian Forces

    Science.gov (United States)

    2014-01-01

    Motility in living systems is due to an array of complex molecular nanomotors that are essential for the function and survival of cells. These protein nanomotors operate not only despite of but also because of stochastic forces. Artificial means of realizing motility rely on local concentration or temperature gradients that are established across a particle, resulting in slip velocities at the particle surface and thus motion of the particle relative to the fluid. However, it remains unclear if these artificial motors can function at the smallest of scales, where Brownian motion dominates and no actively propelled living organisms can be found. Recently, the first reports have appeared suggesting that the swimming mechanisms of artificial structures may also apply to enzymes that are catalytically active. Here we report a scheme to realize artificial Janus nanoparticles (JNPs) with an overall size that is comparable to that of some enzymes ∼30 nm. Our JNPs can catalyze the decomposition of hydrogen peroxide to water and oxygen and thus actively move by self-electrophoresis. Geometric anisotropy of the Pt–Au Janus nanoparticles permits the simultaneous observation of their translational and rotational motion by dynamic light scattering. While their dynamics is strongly influenced by Brownian rotation, the artificial Janus nanomotors show bursts of linear ballistic motion resulting in enhanced diffusion. PMID:24707952

  20. Brownian nanoimaging of interface dynamics and ligand-receptor binding at cell surfaces in 3-D.

    Science.gov (United States)

    Kuznetsov, Igor R; Evans, Evan A

    2013-04-01

    We describe a method for nanoimaging interfacial dynamics and ligand-receptor binding at surfaces of live cells in 3-D. The imaging probe is a 1-μm diameter glass bead confined by a soft laser trap to create a "cloud" of fluctuating states. Using a facile on-line method of video image analysis, the probe displacements are reported at ~10 ms intervals with bare precisions (±SD) of 4-6 nm along the optical axis (elevation) and 2 nm in the transverse directions. We demonstrate how the Brownian distributions are analyzed to characterize the free energy potential of each small probe in 3-D taking into account the blur effect of its motions during CCD image capture. Then, using the approach to image interactions of a labeled probe with lamellae of leukocytic cells spreading on cover-glass substrates, we show that deformations of the soft distribution in probe elevations provide both a sensitive long-range sensor for defining the steric topography of a cell lamella and a fast telemetry for reporting rare events of probe binding with its surface receptors. Invoking established principles of Brownian physics and statistical thermodynamics, we describe an off-line method of super resolution that improves precision of probe separations from a non-reactive steric boundary to ~1 nm.

  1. Harmonically bound Brownian motion in fluids under shear: Fokker-Planck and generalized Langevin descriptions.

    Science.gov (United States)

    Híjar, Humberto

    2015-02-01

    We study the Brownian motion of a particle bound by a harmonic potential and immersed in a fluid with a uniform shear flow. We describe this problem first in terms of a linear Fokker-Planck equation which is solved to obtain the probability distribution function for finding the particle in a volume element of its associated phase space. We find the explicit form of this distribution in the stationary limit and use this result to show that both the equipartition law and the equation of state of the trapped particle are modified from their equilibrium form by terms increasing as the square of the imposed shear rate. Subsequently, we propose an alternative description of this problem in terms of a generalized Langevin equation that takes into account the effects of hydrodynamic correlations and sound propagation on the dynamics of the trapped particle. We show that these effects produce significant changes, manifested as long-time tails and resonant peaks, in the equilibrium and nonequilibrium correlation functions for the velocity of the Brownian particle. We implement numerical simulations based on molecular dynamics and multiparticle collision dynamics, and observe a very good quantitative agreement between the predictions of the model and the numerical results, thus suggesting that this kind of numerical simulations could be used as complement of current experimental techniques. PMID:25768490

  2. Structural properties of charge-stabilized ferrofluids under a magnetic field: a Brownian dynamics study.

    Science.gov (United States)

    Mériguet, G; Jardat, M; Turq, P

    2004-09-22

    We present Brownian dynamics simulations of real charge-stabilized ferrofluids, which are stable colloidal dispersions of magnetic nanoparticles, with and without the presence of an external magnetic field. The colloidal suspensions are treated as collections of monodisperse spherical particles, bearing point dipoles at their centers and undergoing translational and rotational Brownian motions. The overall repulsive isotropic interactions between particles, governed by electrostatic repulsions, are taken into account by a one-component effective pair interaction potential. The potential parameters are fitted in order that computed structure factors are close to the experimental ones. Two samples of ferrofluid differing by the particle diameter and consequently by the intensity of the magnetic interaction are considered here. The magnetization and birefringence curves are computed: a deviation from the ideal Langevin behaviors is observed if the dipolar moment of particles is sufficiently large. Structure factors are also computed from simulations with and without an applied magnetic field H: the microstructure of the repulsive ferrofluid becomes anisotropic under H. Even our simple modeling of the suspension allows us to account for the main experimental features: an increase of the peak intensity is observed in the direction perpendicular to the field whereas the peak intensity decreases in the direction parallel to the field. PMID:15367036

  3. Single potassium niobate nano/microsized particles as local mechano-optical Brownian probes.

    Science.gov (United States)

    Mor, Flavio M; Sienkiewicz, Andrzej; Magrez, Arnaud; Forró, László; Jeney, Sylvia

    2016-03-28

    Perovskite alkaline niobates, due to their strong nonlinear optical properties, including birefringence and the capability to produce second-harmonic generation (SHG) signals, attract a lot of attention as potential candidates for applications as local nano/microsized mechano-optical probes. Here, we report on an implementation of photonic force microscopy (PFM) to explore the Brownian motion and optical trappability of monocrystalline potassium niobate (KNbO3) nano/microsized particles having sizes within the range of 50 to 750 nm. In particular, we exploit the anisotropic translational diffusive regime of the Brownian motion to quantify thermal fluctuations and optical forces of singly-trapped KNbO3 particles within the optical trapping volume of a PFM microscope. We also show that, under near-infrared (NIR) excitation of the highly focused laser beam of the PFM microscope, a single optically-trapped KNbO3 particle reveals a strong SHG signal manifested by a narrow peak (λ(em) = 532 nm) at half the excitation wavelength (λ(ex) = 1064 nm). Moreover, we demonstrate that the thus induced SHG emission can be used as a local light source that is capable of optically exciting molecules of an organic dye, Rose Bengal (RB), which adhere to the particle surface, through the mechanism of luminescence energy transfer (LET). PMID:26956197

  4. Music and movement

    OpenAIRE

    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...

  5. Generalized Pareto for Pattern-Oriented Random Walk Modelling of Organisms' Movements.

    Science.gov (United States)

    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.

  6. Single potassium niobate nano/microsized particles as local mechano-optical Brownian probes

    Science.gov (United States)

    Mor, Flavio M.; Sienkiewicz, Andrzej; Magrez, Arnaud; Forró, László; Jeney, Sylvia

    2016-03-01

    Perovskite alkaline niobates, due to their strong nonlinear optical properties, including birefringence and the capability to produce second-harmonic generation (SHG) signals, attract a lot of attention as potential candidates for applications as local nano/microsized mechano-optical probes. Here, we report on an implementation of photonic force microscopy (PFM) to explore the Brownian motion and optical trappability of monocrystalline potassium niobate (KNbO3) nano/microsized particles having sizes within the range of 50 to 750 nm. In particular, we exploit the anisotropic translational diffusive regime of the Brownian motion to quantify thermal fluctuations and optical forces of singly-trapped KNbO3 particles within the optical trapping volume of a PFM microscope. We also show that, under near-infrared (NIR) excitation of the highly focused laser beam of the PFM microscope, a single optically-trapped KNbO3 particle reveals a strong SHG signal manifested by a narrow peak (λem = 532 nm) at half the excitation wavelength (λex = 1064 nm). Moreover, we demonstrate that the thus induced SHG emission can be used as a local light source that is capable of optically exciting molecules of an organic dye, Rose Bengal (RB), which adhere to the particle surface, through the mechanism of luminescence energy transfer (LET).Perovskite alkaline niobates, due to their strong nonlinear optical properties, including birefringence and the capability to produce second-harmonic generation (SHG) signals, attract a lot of attention as potential candidates for applications as local nano/microsized mechano-optical probes. Here, we report on an implementation of photonic force microscopy (PFM) to explore the Brownian motion and optical trappability of monocrystalline potassium niobate (KNbO3) nano/microsized particles having sizes within the range of 50 to 750 nm. In particular, we exploit the anisotropic translational diffusive regime of the Brownian motion to quantify thermal

  7. Movement coordination during conversation.

    Science.gov (United States)

    Latif, Nida; Barbosa, Adriano V; Vatikiotis-Bateson, Eric; Vatiokiotis-Bateson, Eric; Castelhano, Monica S; Munhall, K G

    2014-01-01

    Behavioral coordination and synchrony contribute to a common biological mechanism that maintains communication, cooperation and bonding within many social species, such as primates and birds. Similarly, human language and social systems may also be attuned to coordination to facilitate communication and the formation of relationships. Gross similarities in movement patterns and convergence in the acoustic properties of speech have already been demonstrated between interacting individuals. In the present studies, we investigated how coordinated movements contribute to observers' perception of affiliation (friends vs. strangers) between two conversing individuals. We used novel computational methods to quantify motor coordination and demonstrated that individuals familiar with each other coordinated their movements more frequently. Observers used coordination to judge affiliation between conversing pairs but only when the perceptual stimuli were restricted to head and face regions. These results suggest that observed movement coordination in humans might contribute to perceptual decisions based on availability of information to perceivers. PMID:25119189

  8. Movement coordination during conversation.

    Directory of Open Access Journals (Sweden)

    Nida Latif

    Full Text Available Behavioral coordination and synchrony contribute to a common biological mechanism that maintains communication, cooperation and bonding within many social species, such as primates and birds. Similarly, human language and social systems may also be attuned to coordination to facilitate communication and the formation of relationships. Gross similarities in movement patterns and convergence in the acoustic properties of speech have already been demonstrated between interacting individuals. In the present studies, we investigated how coordinated movements contribute to observers' perception of affiliation (friends vs. strangers between two conversing individuals. We used novel computational methods to quantify motor coordination and demonstrated that individuals familiar with each other coordinated their movements more frequently. Observers used coordination to judge affiliation between conversing pairs but only when the perceptual stimuli were restricted to head and face regions. These results suggest that observed movement coordination in humans might contribute to perceptual decisions based on availability of information to perceivers.

  9. Organizations, coalitions, and movements

    OpenAIRE

    Diani, Mario; Bison, Ivano

    2004-01-01

    This article uses empirical evidence on networks of voluntary organizations mobilizing on ethnic minority, environmental, and social exclusion issues in two British cities, to differentiate between social movement processes and other, cognate collective action dynamics. Social movement processes are identified as the building and reproducing of dense informal networks between a multiplicity of actors, sharing a collective identity, and engaged in social and/or political conflict. They are con...

  10. Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations

    Institute of Scientific and Technical Information of China (English)

    PENG ShiGe

    2009-01-01

    This is a survey on normal distributions and the related central limit theorem under sublinear expectation. We also present Brownian motion under sublinear expectations and the related stochastic calculus of Ito's type. The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk, statistics and other industrial problems.

  11. Harmonic measures of the half-plane and balls for the hyperbolic Brownian motion and Ornstein-Uhlenbeck diffusions

    OpenAIRE

    Byczkowski, Tomasz; Chorowski, Jakub; Graczyk, Piotr; Malecki, Jacek

    2011-01-01

    The purpose of the paper is to provide integral representations of the Poisson kernel for a half-space and balls for hyperbolic Brownian motion and for the classical Ornstein-Uhlenbeck process. The method of proof is based on Girsanov's theorem and yields more complete results as those based on Feynmann-Kac technique.

  12. Survey on normal distributions,central limit theorem,Brownian motion and the related stochastic calculus under sublinear expectations

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    This is a survey on normal distributions and the related central limit theorem under sublinear expectation.We also present Brownian motion under sublinear expectations and the related stochastic calculus of It?’s type.The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk,statistics and other industrial problems.

  13. Psychostimulants and movement disorders.

    Directory of Open Access Journals (Sweden)

    Andres eAsser

    2015-04-01

    Full Text Available Psychostimulants are a diverse group of substances with their main psychomotor effects resembling those of amphetamine, methamphetamine, cocaine or cathinone. Due to their potential as drugs of abuse, recreational use of most of these substances is illegal since the 1971 Convention on Psychotropic Substances. In recent years, new psychoactive substances have emerged mainly as synthetic cathinones with new molecules frequently complementing the list.Psychostimulant related movement disorders are a known entity often seen in emergency rooms around the world. These admissions are becoming more frequent as are fatalities associated with drug abuse. Still the legal constraints of the novel synthetic molecules are bypassed. At the same time chronic and permanent movement disorders are much less frequently encountered. These disorders frequently manifest as a combination of movement disorders. The more common symptoms include agitation, tremor, hyperkinetic and stereotypical movements, cognitive impairment, and also hyperthermia and cardiovascular dysfunction.The pathophysiological mechanisms behind the clinical manifestations have been researched for decades. The common denominator is the monoaminergic signaling. Dopamine has received the most attention but further research has demonstrated involvement of other pathways. Common mechanisms linking psychostimulant use and several movement disorders exist.

  14. Effect of solvent on directional drift in Brownian motion of particle/molecule with broken symmetry

    Science.gov (United States)

    Kong, FanDong; Sheng, Nan; Wan, RongZheng; Hu, GuoHui; Fang, HaiPing

    2016-08-01

    The directional drifting of particles/molecules with broken symmetry has received increasing attention. Through molecular dynamics simulations, we investigate the effects of various solvents on the time-dependent directional drifting of a particle with broken symmetry. Our simulations show that the distance of directional drift of the asymmetrical particle is reduced while the ratio of the drift to the mean displacement of the particle is enhanced with increasing mass, size, and interaction strength of the solvent atoms in a short time range. Among the parameters considered, solvent atom size is a particularly influential factor for enhancing the directional drift of asymmetrical particles, while the effects of the interaction strength and the mass of the solvent atoms are relatively weaker. These findings are of great importance to the understanding and control of the Brownian motion of particles in various physical, chemical, and biological processes within finite time spans.

  15. Inference on the hurst parameter and the variance of diffusions driven by fractional Brownian motion

    CERN Document Server

    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...

  16. Clustering determines the survivor for competing Brownian and L\\'evy walkers

    CERN Document Server

    Heinsalu, Els; López, Cristóbal

    2013-01-01

    The competition between two ecologically similar species that use the same resources and differ from each other only in the type of spatial motion they undergo is studied. The latter is assumed to be described either by Brownian motion or L\\'evy flights. Competition is taken into account by assuming that individuals reproduce in a density-dependent fashion. It is observed that no influence of the type of motion occurs when the two species are in a well-mixed unstructured state. However, as soon as the species develop spatial clustering, the one forming more concentrated clusters gets a competitive advantage and eliminates the other. Similar competitive advantage would occur between walkers of the same type but with different diffusivities if this leads also to different clustering. Coexistence of both species is also possible under certain conditions.

  17. 3D tracking the Brownian motion of colloidal particles using digital holographic microscopy and joint reconstruction

    CERN Document Server

    Verrier, Nicolas; Fournel, Thierry

    2015-01-01

    In-line digital holography is a valuable tool for sizing, locating and tracking micro- or nano-objects in a volume. When a parametric imaging model is available, Inverse Problems approaches provide a straightforward estimate of the object parameters by fitting data with the model, thereby allowing accurate reconstruction. As recently proposed and demonstrated, combining pixel super-resolution techniques with Inverse Problems approaches improves the estimation of particle size and 3D-position. Here we demonstrate the accurate tracking of colloidal particles in Brownian motion. Particle size and 3D-position are jointly optimized from video holograms acquired with a digital holographic microscopy set up based on a "low-end" microscope objective ($\\times 20$, $\\rm NA\\ 0.5$). Exploiting information redundancy makes it possible to characterize particles with a standard deviation of 15 nm in size and a theoretical resolution of 2 x 2 x 5 nm$^3$ for position under additive white Gaussian noise assumption.

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

    Science.gov (United States)

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

    2010-03-01

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

  19. Modeling Philippine Stock Exchange Composite Index Using Weighted Geometric Brownian Motion Forecasts

    Directory of Open Access Journals (Sweden)

    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.

  20. Generalized uncertainty relations and entanglement dynamics in quantum Brownian motion models

    CERN Document Server

    Anastopoulos, C; Mylonas, D

    2010-01-01

    We study entanglement dynamics in quantum Brownian motion (QBM) models. Our main tool is the Wigner function propagator. Time evolution in the Wigner picture is physically intuitive and it leads to a simple derivation of a master equation for any number of system harmonic oscillators and spectral density of the environment. It also provides generalized uncertainty relations, valid for any initial state that allow a characterization of the environment in terms of the modifications it causes to the system's dynamics. In particular, the uncertainty relations are very informative about the entanglement dynamics of Gaussian states, and to a lesser extent for other families of states. For concreteness, we apply these techniques to a bipartite QBM model, describing the processes of entanglement creation, disentanglement and decoherence at all temperatures and timescales.

  1. On the Brownian gas: a field theory with a Poissonian ground state

    Energy Technology Data Exchange (ETDEWEB)

    Velenich, Andrea; Chamon, Claudio [Physics Department, Boston University, 590 Commonwealth Avenue, Boston, MA 02215 (United States); Cugliandolo, Leticia F [Universite Pierre et Marie Curie-Paris VI, LPTHE UMR 7589, Place Jussieu, 75252 Paris Cedex 05 (France); Kreimer, Dirk [Department of Mathematics and Statistics, Boston University, 111 Cummington Street, Boston, MA 02215 (United States)], E-mail: velenich@bu.edu

    2008-06-13

    As a first step toward a successful field theory of Brownian particles in interaction, we study exactly the non-interacting case, its combinatorics and nonlinear time-reversal symmetry. Even though the particles do not interact, the field theory contains an interaction term: the vertex is the hallmark of the original particle nature of the gas and it enforces the constraint of a strictly positive density field, as opposed to a Gaussian free field. We compute exactly all the n-point density correlation functions, determine non-perturbatively the Poissonian nature of the ground state and emphasize the futility of any coarse-graining assumption for the derivation of the field theory. We finally verify explicitly, on the n-point functions, the fluctuation-dissipation theorem implied by the time-reversal symmetry of the action.

  2. A wavelet based uniform approximation of fractional Brownian motion with parallel implementation

    CERN Document Server

    Hong, Dawei; Birget, Jean-Camille; Lun, Desmond

    2011-01-01

    We construct a wavelet based approximation of fractional Brownian motion of Hurst index H in (0, 1). For practical applications, the constructed approximation is uniform in discrete time, and can be implemented by a fast parallel algorithm. The convergence rate of the approximation is derived, which is expressed by a large deviation bound. The convergence rate reaches the optimal rate O(N^{-H} \\sqrt{log N}). Here the optimality in theory was proved by K\\"uhn and Linde. We also demonstrate that there is a factor (H(1 -H))^{-1/2} behind the above big O which causes or accelerates the degradation of the convergence rate as $H$ tends to 1_- or 0_+, respectively.

  3. Particle mobility between two planar elastic membranes: Brownian motion and membrane deformation

    CERN Document Server

    Daddi-Moussa-Ider, Abdallah; Gekle, Stephan

    2016-01-01

    We study the motion of a solid particle immersed in a Newtonian fluid and confined between two parallel elastic membranes possessing shear and bending rigidity. The hydrodynamic mobility depends on the frequency of the particle motion due to the elastic energy stored in the membrane. Unlike the single-membrane case, a coupling between shearing and bending exists. The commonly used approximation of superposing two single-membrane contributions is found to give reasonable results only for motions in the parallel, but not in the perpendicular direction. We also compute analytically the membrane deformation resulting from the motion of the particle, showing that the presence of the second membrane reduces deformation. Using the fluctuation-dissipation theorem we compute the Brownian motion of the particle, finding a long-lasting subdiffusive regime at intermediate time scales. We finally assess the accuracy of the employed point-particle approximation via boundary-integral simulations for a truly extended particl...

  4. A semiclassical approach to explore the bistable kinetics of a Brownian particle in a nonequilibrium environment

    International Nuclear Information System (INIS)

    We explore the noise-induced barrier crossing dynamics of a Brownian particle in the high temperature quantum regime under large damping. We assume the associated heat bath not to be in thermal equilibrium; it is rather driven by an externally applied random force which exposes the system particles to a nonequilibrium environment. We propose a system + reservoir model to study the stochastic Langevin dynamics. We also construct the corresponding Fokker–Planck equation in the said regime and solve it to explore the bistable kinetics. We investigate the role of different parameters in shaping the nature of such a bistable kinetics in detail and hence allowing one to get some insight into the very complicated dynamics of quantum dissipative system(s). Finally, we analyze the semiclassical rate vis-à-vis the classical analog

  5. Brownian dynamics and molecular dynamics study of the association between hydrogenase and ferredoxin from Chlamydomonas reinhardtii.

    Science.gov (United States)

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

    2008-10-01

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

  6. Territory Covered by N Self-Propelled Brownian Agents in 2 dimensions

    Science.gov (United States)

    Sevilla, Francisco J.; Gómez Nava, Luis Alberto

    2014-03-01

    We consider the problem of the territory covered by N non-interacting self-propelled Brownian agents where self-propulsion is modeled by a non-linear friction term in the Langevin-like equations of motion for each agent. Our study generalizes, to a continuous time and space description, the well known problem of the territory explored by N Random Walkers. Numerical and analytical approaches are presented to exhibit the effects of self-propulsion on the many independent agents exploring two dimensional homogenous regions. Our results may have a wide range of applications in a variaty of non-equilibrium systems. FJSP and LAGN aknowledge PAPIIT-IN113114 and PAEP-PCF-UNAM.

  7. Diffusion theory of Brownian particles moving at constant speed in D dimensions

    Science.gov (United States)

    Sevilla, Francisco J.

    2015-03-01

    The propagation of Brownian-active particles that move at constant speed in the limit of short times, differs from wave-like propagation in that active particles propagate without leaving a wake trailing characteristic of wave propagation in even dimensions. In the long time regime, normal diffusion is expected due to random fluctuations that disperse the particle direction of motion. A phenomenological equation that describe the transition from the behavior free of effects of wake, to the normal diffusion of the particles is proposed. A comparison of the results predicted by such equation with those obtained from models using Langevin equations is presented in the spherically symmetric case. FJS acknowledges support from PAPIIT-UNAM through the Grant IN113114.

  8. Anomalous Brownian motion of colloidal particle in a nematic environment: effect of the director fluctuations

    Directory of Open Access Journals (Sweden)

    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.

  9. Super-Brownian motion: Lp-convergence of martingales through the pathwise spine decomposition

    CERN Document Server

    Murillo-Salas, A E Kyprianou A

    2011-01-01

    Evans (1992) described the semi-group of a superprocess with quadratic branching mechanism under a martingale change of measure in terms of the semi-group of an immortal particle and the semigroup of the superprocess prior to the change of measure. This result, commonly referred to as the spine decomposition, alludes to a pathwise decomposition in which independent copies of the original process `immigrate' along the path of the immortal particle. For branching particle diffusions the analogue of this decomposition has already been demonstrated in the pathwise sense, see for example Hardy and Harris (2009). The purpose of this short note is to exemplify a new {\\it pathwise} spine decomposition for supercritical super-Brownian motion with general branching mechanism (cf. Kyprianou et al. (2010)) by studying $L^p$ convergence of naturally underlying additive martingales in the spirit of analogous arguments for branching particle diffusions due to Hardys and Harris (2009). Amongst other ingredients, the Dynkin-K...

  10. Conditioning super-Brownian motion on its boundary statistics and fragmentation

    CERN Document Server

    Salisbury, Thomas S

    2012-01-01

    We condition super-Brownian motion on "boundary statistics" of the exit measure $X_D$ from a bounded domain $D$. These are random variables defined on an auxiliary probability space generated by sampling from the exit measure $X_D$. Two particular examples are: conditioning on a Poisson random measure with intensity $\\beta X_D$; and conditioning on $X_D$ itself. We find the conditional laws as $h$-transforms of the original SBM law using Dynkin's formulation of $X$-harmonic functions. We give explicit expression for the (extended) $X$-harmonic functions considered. We also obtain explicit constructions of these conditional laws in terms of branching particle systems. For example, we give a fragmentation system description of the law of SBM conditioned on $X_D=\

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

    CERN Document Server

    Bortolas, E; Dotti, M; Spera, M; Mapelli, M

    2016-01-01

    Massive black hole binaries (BHBs) are expected to be one of the most powerful sources of gravitational waves (GWs) in the frequency range of the pulsar timing array and of forthcoming space-borne detectors. They are believed to form in the final stages of galaxy mergers, and then harden by slingshot ejections of passing stars. However, evolution via the slingshot mechanism may be ineffective if the reservoir of interacting stars is not readily replenished, and the binary shrinking may come to a halt at roughly a parsec separation. Recent simulations suggest that the departure from spherical symmetry, naturally produced in merger remnants, leads to efficient loss cone refilling, preventing the binary from stalling. However, current N-body simulations able to accurately follow the evolution of BHBs are limited to very modest particle numbers. Brownian motion may artificially enhance the loss cone refilling rate in low-N simulations, where the binary encounters a larger population of stars due its random motion...

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

    CERN Document Server

    Erban, Radek

    2015-01-01

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

  13. A Langevin Approach to a Classical Brownian Oscillator in an Electromagnetic Field

    Science.gov (United States)

    Espinoza Ortiz, J. S.; Bauke, F. C.; Lagos, R. E.

    2016-08-01

    We consider a charged Brownian particle bounded by an harmonic potential, embedded in a Markovian heat bath and driven from equilibrium by external electric and magnetic fields. We develop a quaternionic-like (or Pauli spinor-like) representation, hitherto exploited in classical Lorentz related dynamics. Within this formalism, in a very straight forward and elegant fashion, we compute the exact solution for the resulting generalized Langevin equation, for the case of a constant magnetic field. For the case the source electromagnetic fields satisfy Maxwell's equations, yielding spinor-like Mathieu equations, we compute the solutions within the JWKB approximation. With the solutions at hand we further compute spatial, velocities and crossed time correlations. In particular we study the (kinetically defined) nonequilbrium temperature. Therefore, we can display the system's time evolution towards equilibrium or towards non equilibrium (steady or not) states.

  14. Near field magnetostatics and Neel Brownian interactions mediated magnetorheological characteristics of highly stable nano ferrocolloids

    CERN Document Server

    Katiyar, Ajay; Das, Sarit K; Nandi, Tandra

    2015-01-01

    Magnetic nanocolloids with synthesized super paramagnetic Fe3O4 nanoparticles (SPION) (5 to 15 nm) dispersed in insitu developed Polyethylene Glycol (PEG 400) and nano silica complex have been synthesized. The PEG nano Silica complex physically encapsulates the SPIONs, ensuring no phase separation under high magnetic fields (1.2 T). Exhaustive magnetorheological investigations have been performed to comprehend the structural behavior and response of the ferrocolloids. Remarkable stability and reversibility have been observed under magnetic field for concentrated systems. The results exhibit the impact of particle concentration, size and encapsulation efficiency on parameters such as shear viscosity, yield stress, viscoelastic moduli, magnetoviscous hysteresis etc. Analytical models to reveal the system mechanism and mathematically predict the magnetoviscosity and magneto yield stress has been theorized. The mechanistic approach based on near field magnetostatics and Neel Brownian interactivities can predict t...

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

    Science.gov (United States)

    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. PMID:27410852

  16. Measurements of Brownian relaxation of magnetic nanobeads using planar Hall effect bridge sensors

    DEFF Research Database (Denmark)

    Østerberg, Frederik Westergaard; Rizzi, Giovanni; Zardán Gómez de la Torre, T.;

    2013-01-01

    We compare measurements of the Brownian relaxation response of magnetic nanobeads in suspension using planar Hall effect sensors of cross geometry and a newly proposed bridge geometry. We find that the bridge sensor yields six times as large signals as the cross sensor, which results in a more...... accurate determination of the hydrodynamic size of the magnetic nanobeads. Finally, the bridge sensor has successfully been used to measure the change in dynamic magnetic response when rolling circle amplified DNA molecules are bound to the magnetic nanobeads. The change is validated by measurements...... performed in a commercial AC susceptometer. The presented bridge sensor is, thus, a promising component in future lab-on-a-chip biosensors for detection of clinically relevant analytes, including bacterial genomic DNA and proteins....

  17. Correlation functions for restricted Brownian motion from the ballistic through to the diffusive regimes

    International Nuclear Information System (INIS)

    We calculate the spectra of the correlation functions for fields with arbitrary spatial dependence as seen by Brownian particles in bounded geometries from knowledge of the spectra of the conditional probability density functions in the infinite domain. Our results show a significant difference for the spectra for 1D, 2D and 3D motions. To our knowledge this is the first demonstration of the influence of dimensionality on the form of the correlation functions. Our results also show the different power dependence on frequency for the ballistic and diffusive cases and the treatment of the crossover is unique. -- Highlights: ► Spectrum of the correlation function for fields with arbitrary spatial dependence. ► Valid for the diffusive and ballistic motions and the problematic crossover region. ► Calculation of the spectra in 1, 2 and 3 dimensions. ► Application to gradient induced relaxation in nmr, and to the search for new forces.

  18. Overdamped limit and inverse-friction expansion for Brownian motion in an inhomogeneous medium.

    Science.gov (United States)

    Durang, Xavier; Kwon, Chulan; Park, Hyunggyu

    2015-06-01

    We revisit the problem of the overdamped (large-friction) limit of the Brownian dynamics in an inhomogeneous medium characterized by a position-dependent friction coefficient and a multiplicative noise (local temperature) in one-dimensional space. Starting from the Kramers equation and analyzing it through the expansion in terms of eigenfunctions of a quantum harmonic oscillator, we derive analytically the corresponding Fokker-Planck equation in the overdamped limit. The result is fully consistent with the previous finding by Sancho, San Miguel, and Dürr [J. Stat. Phys. 28, 291 (1982)]. Our method allows us to generalize the Brinkman's hierarchy, and thus it would be straightforward to obtain higher-order corrections in a systematic inverse-friction expansion without any assumption. Our results are confirmed by numerical simulations for simple examples. PMID:26172672

  19. GPU accelerated Monte Carlo simulation of Brownian motors dynamics with CUDA

    CERN Document Server

    Spiechowicz, J; Machura, L

    2014-01-01

    This work presents an updated and extended guide on methods of a proper acceleration of the Monte Carlo integration of stochastic differential equations with the commonly available NVIDIA Graphics Processing Units using the CUDA programming environment. We outline the general aspects of the scientific computing on graphics cards and demonstrate them with two models of a well known phenomenon of the noise induced transport of Brownian motors in periodic structures. As a source of fluctuations in the considered systems we selected the three most commonly occurring noises: the Gaussian white noise, the white Poissonian noise and the dichotomous process also known as a random telegraph signal. The detailed discussion on various aspects of the applied numerical schemes is also presented. The measured speedup can be of the astonishing order of 2000 when compared to a typical CPU. This number significantly expands the range of problems solvable by use of stochastic simulations, allowing even an interactive research ...

  20. Numerical Methods for Computing Effective Transport Properties of Flashing Brownian Motors

    CERN Document Server

    Latorre, Juan C; Pavliotis, Grigorios A

    2013-01-01

    We develop a numerical algorithm for computing the effective drift and diffusivity of the steady-state behavior of an overdamped particle driven by a periodic potential whose amplitude is modulated in time by multiplicative noise and forced by additive Gaussian noise (the mathematical structure of a flashing Brownian motor). The numerical algorithm is based on a spectral decomposition of the solution to the Fokker-Planck equation with periodic boundary conditions and the cell problem which result from homogenization theory. We also show that the numerical method of Wang, Peskin, Elston (WPE, 2003) for computing said quantities is equivalent to that resulting from homogenization theory. We show how to adapt the WPE numerical method to this problem by means of discretizing the multiplicative noise via a finite-volume method into a discrete-state Markov jump process which preserves many important properties of the original continuous-state process, such as its invariant distribution and detailed balance. Our num...

  1. The double-temperature ratchet model and current reversal of coupled Brownian motors

    CERN Document Server

    Li, Chen-pu; Zheng, Zhi-gang

    2016-01-01

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

  2. Generalized Scaling and the Master Variable for Brownian Magnetic Nanoparticle Dynamics

    Science.gov (United States)

    Reeves, Daniel B.; Shi, Yipeng; Weaver, John B.

    2016-01-01

    Understanding the dynamics of magnetic particles can help to advance several biomedical nanotechnologies. Previously, scaling relationships have been used in magnetic spectroscopy of nanoparticle Brownian motion (MSB) to measure biologically relevant properties (e.g., temperature, viscosity, bound state) surrounding nanoparticles in vivo. Those scaling relationships can be generalized with the introduction of a master variable found from non-dimensionalizing the dynamical Langevin equation. The variable encapsulates the dynamical variables of the surroundings and additionally includes the particles’ size distribution and moment and the applied field’s amplitude and frequency. From an applied perspective, the master variable allows tuning to an optimal MSB biosensing sensitivity range by manipulating both frequency and field amplitude. Calculation of magnetization harmonics in an oscillating applied field is also possible with an approximate closed-form solution in terms of the master variable and a single free parameter. PMID:26959493

  3. Stochastic shell models driven by a multiplicative fractional Brownian-motion

    Science.gov (United States)

    Bessaih, Hakima; Garrido-Atienza, María J.; Schmalfuss, Björn

    2016-04-01

    We prove existence and uniqueness of the solution of a stochastic shell-model. The equation is driven by an infinite dimensional fractional Brownian-motion with Hurst-parameter H ∈(1 / 2 , 1) , and contains a non-trivial coefficient in front of the noise which satisfies special regularity conditions. The appearing stochastic integrals are defined in a fractional sense. First, we prove the existence and uniqueness of variational solutions to approximating equations driven by piecewise linear continuous noise, for which we are able to derive important uniform estimates in some functional spaces. Then, thanks to a compactness argument and these estimates, we prove that these variational solutions converge to a limit solution, which turns out to be the unique pathwise mild solution associated to the shell-model with fractional noise as driving process.

  4. Transport coefficients for a confined Brownian ratchet operating between two heat reservoirs

    Science.gov (United States)

    Ryabov, A.; Holubec, V.; Yaghoubi, M. H.; Varga, M.; Foulaadvand, M. E.; Chvosta, P.

    2016-09-01

    We discuss two-dimensional diffusion of a Brownian particle confined to a periodic asymmetric channel with soft walls modeled by a parabolic potential. In the channel, the particle experiences different thermal noise intensities, or temperatures, in the transversal and longitudinal directions. The model is inspired by the famous Feynman’s ratchet and pawl. Although the standard Fick-Jacobs approximation predicts correctly the effective diffusion coefficient, it fails to capture the ratchet effect. Deriving a correction, which breaks the local detailed balance with the transversal noise source, we obtain a correct mean velocity of the particle and a stationary probability density in the potential unit cell. The derived results are exact for small channel width. Yet, we check by exact numerical calculation that they qualitatively describe the ratchet effect observed for an arbitrary width of the channel.

  5. A MAP estimator based on geometric Brownian motion for sample distances of laser triangulation data

    Science.gov (United States)

    Herrmann, Markus; Otesteanu, Marius

    2016-11-01

    The proposed algorithm is designed to enhance the line-detection stability in laser-stripe sensors. Despite their many features and capabilities, these sensors become unstable when measuring in dark or strongly-reflective environments. Ambiguous points within a camera image can appear on dark surfaces and be confused with noise when the laser-reflection intensity approaches noise level. Similar problems arise when strong reflections within the sensor image have intensities comparable to that of the laser. In these circumstances, it is difficult to determine the most probable point for the laser line. Hence, the proposed algorithm introduces a maximum a posteriori estimator, based on geometric Brownian motion, to provide a range estimate for the expected location of the reflected laser line.

  6. Movement as utopia.

    Science.gov (United States)

    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. PMID:20027697

  7. Hydrodynamic interactions of two nearly touching Brownian spheres in a stiff potential: Effect of fluid inertia

    International Nuclear Information System (INIS)

    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

  8. The effect of temperature dependence of viscosity on a Brownian heat engine

    Science.gov (United States)

    Taye, Mesfin Asfaw; Duki, Solomon Fekade

    2015-12-01

    We modeled a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a spatially varying temperature. The strength for the viscous friction γ( x) is considered to decrease exponentially when the temperature T( x) of the medium increases ( γ( x) = B e - AT( x)) as proposed originally by Reynolds [O. Reynolds, Phil. Trans. R. Soc. London 177, 157 (1886)]. Our result depicts that the velocity of the motor is considerably higher when the viscous friction is temperature dependent than that of the case where the viscous friction is temperature independent. The dependence of the efficiency η as well as the coefficient of performance of the refrigerator P ref on model parameters is also explored. If the motor designed to achieve a high velocity against a frictional drag, in the absence of external load f, we show that Carnot efficiency or Carnot refrigerator is unattainable even at quasistatic limit as long as the viscous friction is temperature dependent A ≠ 0. On the contrary, in the limit A → 0 or in general in the presence of an external load (for any A) f ≠ 0, at quasistatic limit, Carnot efficiency or Carnot refrigerator is attainable as long as the heat exchange via kinetic energy is omitted. For all cases, far from quasistatic limit, the efficiency and the coefficient of performance of the refrigerator are higher for constant γ case than the case where γ is temperature dependent. On the other hand, if one includes the heat exchange at the boundary of the heat baths, Carnot efficiency or Carnot refrigerator is unattainable even at quasistatic limit. Moreover, the dependence for the optimized and maximum power efficiencies on the determinant model parameters is explored.

  9. Hydrodynamic interactions of two nearly touching Brownian spheres in a stiff potential: Effect of fluid inertia

    Energy Technology Data Exchange (ETDEWEB)

    Radiom, Milad, E-mail: milad.radiom@unige.ch; Ducker, William, E-mail: wducker@vt.edu [Department of Chemical Engineering, Virginia Tech, Blacksburg, Virginia 24060 (United States); Robbins, Brian; Paul, Mark [Department of Mechanical Engineering, Virginia Tech, Blacksburg, Virginia 24060 (United States)

    2015-02-15

    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{sup −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.

  10. New models and predictions for Brownian coagulation of non-interacting spheres.

    Science.gov (United States)

    Kelkar, Aniruddha V; Dong, Jiannan; Franses, Elias I; Corti, David S

    2013-01-01

    The classical steady-state Smoluchowski model for Brownian coagulation is evaluated using Brownian Dynamics Simulations (BDS) as a benchmark. The predictions of this approach compare favorably with the results of BDS only in the dilute limit, that is, for volume fractions of φ≤5×10(-4). From the solution of the more general unsteady-state diffusion equation, a new model for coagulation is developed. The resulting coagulation rate constant is time-dependent and approaches the steady-state limit only at large times. Moreover, in contrast to the Smoluchowski model, this rate constant depends on the particle size, with the transient effects becoming more significant at larger sizes. The predictions of the unsteady-state model agree well with the BDS results up to volume fractions of about φ=0.1, at which the aggregation half-time predicted by the Smoluchowski model is five times that of the BDS. A new procedure to extract the aggregation rate constant from simulation results based on this model is presented. The choice of the rate constant kernel used in the population balance equations for complete aggregation is also evaluated. Extension of the new model to a variable rate constant kernel leads to increased accuracy of the predictions, especially for φ≤5×10(-3). This size-dependence of the rate constant kernel affects particularly the predictions for initially polydisperse sphere systems. In addition, the model is extended to account in a novel way for both short-range viscous two-particle interactions and long-range many-particle Hydrodynamic Interactions (HI). Predictions including HI agree best with the BDS results. The new models presented here offer accurate and computationally less-intensive predictions of the coagulation dynamics while also accounting for hydrodynamic coupling. PMID:23036339

  11. The Consequences of Social Movements

    OpenAIRE

    Bosi, Lorenzo; Giugni, Marco Gabriele; Uba, Katrin

    2016-01-01

    Social movements have attracted much attention in recent years, both from scholars and among the wider public. This book examines the consequences of social movements, covering such issues as the impact of social movements on the life course of participants and the population in general, on political elites and markets, and on political parties and processes of social movement institutionalization. The volume makes a significant contribution to research on social movement outcomes in three wa...

  12. [Architecture and movement].

    Science.gov (United States)

    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.

  13. Measuring Facial Movement

    Science.gov (United States)

    Ekman, Paul; Friesen, Wallace V.

    1976-01-01

    The Facial Action Code (FAC) was derived from an analysis of the anatomical basis of facial movement. The development of the method is explained, contrasting it to other methods of measuring facial behavior. An example of how facial behavior is measured is provided, and ideas about research applications are discussed. (Author)

  14. The Matter of Movement

    DEFF Research Database (Denmark)

    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...

  15. Fluid Movement and Creativity

    Science.gov (United States)

    Slepian, Michael L.; Ambady, Nalini

    2012-01-01

    Cognitive scientists describe creativity as fluid thought. Drawing from findings on gesture and embodied cognition, we hypothesized that the physical experience of fluidity, relative to nonfluidity, would lead to more fluid, creative thought. Across 3 experiments, fluid arm movement led to enhanced creativity in 3 domains: creative generation,…

  16. Material and Affective Movements

    DEFF Research Database (Denmark)

    Rasmussen, Lisa Rosén

    2014-01-01

    . The chapter traces the former pupil’s memories of physical and affective movements within the larger context of school and discovers surprisingly diverse modes of knowing, relating, and attending to things, teachers and classmates among and between the three generations. It thus taps into the rich realms...

  17. Psychogenic Movement Disorders

    Directory of Open Access Journals (Sweden)

    Chakravarty Ambar

    2004-01-01

    Full Text Available Psychogenic movement Disorders (PMD may result from somatoform disorders, factitious disorders, malingering, depression anxiety disorders and less frequently, histrionic personality disorders. First recognized by Henry Head in early twentieth century, PMD s commonly encountered and clues to their differentiation from organic disease. A generally accepted management protocol has been outlined.

  18. Movement: A Clinical Investigation

    Directory of Open Access Journals (Sweden)

    Kazem Dalaie

    2015-10-01

    Full Text Available Objectives: One major drawback of orthodontic treatment is its long duration due to slow tooth movement and the pain at the onset of treatment following application of forces. There is controversy regarding the efficacy of laser for decreasing the treatment time and pain of orthodontic treatment. The purpose of this study was to investigate the effect of low level diode laser on the rate of orthodontic tooth movement and the associated pain.Materials and Methods: In this double blind randomized controlled clinical trial, 12 or- thodontic patients referring to Shahid Beheshti School of Dentistry for first premolar ex- traction were randomly selected and allocated to gallium aluminum-arsenide laser (Ga,Al,As diode laser, 880 nm, 100 mW, 5 j/cm2, 8 points, 80 seconds, continuous mode or control group. The patients initially underwent leveling and alignment using the sectional system. Force (150 gr was applied to each canine tooth via sectional closing loops. The loops were activated every month. The rate of tooth movement and pain were monitored over the treatment period and recorded on days 1, 3, 7, 30, 33, 37, 60, 63 and 67. Two-way ANOVA was used for comparison of groups.Results: There was no significant difference in terms of tooth movement and pain scores between the irradiated and non-irradiated sides at any time point (P>0.05.Conclusion: Although laser enhanced orthodontic tooth movement in the upper jaw, we failed to provide solid evidence to support the efficacy of laser for expediting tooth move- ment or reducing the associated pain.

  19. The Study of Biomolecule-Substrate Interactions by Single Molecule Force Spectroscopy and Brownian Dynamics Simulations

    Science.gov (United States)

    Cook, Sara Iliafar

    T, respectively). In addition to the binding strength of ssDNA nucleotide to surfaces, it is equally as important to understand the dynamics of these interactions. The force response of a simple chain-like polymeric molecule (representative of single stranded DNA) was studied using Brownian dynamics to shed light on these dynamics and the features that may be masked in SMFS experiments. Through simulations at slow peeling rates, our Brownian dynamics model confirmed the predictions of an equilibrium statistical thermodynamic model. Faster removal rates resulted in deviations from equilibrium which were dominated by a combination of Stokes (viscous) drag and a finite desorption rate of the monomeric units. Furthermore, the force probe's thermal fluctuations were shown to be affected by the spring constant of the contact mode AFM cantilever Consequently, this effect provided evidence on the source of disappearance for certain key features such as force spikes, associated with the desorption of individual links and predicted by the statistical thermodynamic model under displacement control, from SMFS experiments. In studying the elastic response of a freely jointed chain stretched in 2D and 3D, we obtained analytical expressions for two modes of stretching: i) when force is applied only to one end of the chain, and ii) when the applied force is distributed uniformly throughout the chain. By comparing, we confirmed that these expressions correctly predict the results obtained from our Brownian dynamics simulations as well as experimental results from the literature.

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

    Science.gov (United States)

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

    2015-03-01

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

  1. Interplay between optical, viscous and elastic forces on an optically trapped Brownian particle immersed in a viscoelastic fluid

    CERN Document Server

    Domínguez-García, P; Jeney, Sylvia

    2016-01-01

    We provide a detailed study of the interplay between the different interactions which appear in the Brownian motion of a micronsized sphere immersed in a viscoelastic fluid measured with optical trapping interferometry. To explore a wide range of viscous, elastic and optical forces, we analyze two different viscoelastic solutions at various concentrations, which provide a dynamic polymeric structure surrounding the Brownian sphere. Our experiments show that, depending of the fluid, optical forces, even if small, slightly modify the complex modulus at low frequencies. Based on our findings, we propose an alternative methodology to calibrate this kind of experimental set-up when non-Newtonian fluids are used. Understanding the influence of the optical potential is essential for a correct interpretation of the mechanical properties obtained by optically-trapped probe-based studies of biomaterials and living matter.

  2. Two-sided reflected Markov-modulated Brownian motion with applications to fluid queues and dividend payouts

    CERN Document Server

    D'Auria, Bernardo

    2011-01-01

    In this paper we study a reflected Markov-modulated Brownian motion with a two sided reflection in which the drift, diffusion coefficient and the two boundaries are (jointly) modulated by a finite state space irreducible continuous time Markov chain. The goal is to compute the stationary distribution of this Markov process, which in addition to the complication of having a stochastic boundary can also include jumps at state change epochs of the underlying Markov chain because of the boundary changes. We give the general theory and then specialize to the case where the underlying Markov chain has two states. Moreover, motivated by an application of optimal dividend strategies, we consider the case where the lower barrier is zero and the upper barrier is subject to control. In this case we generalized earlier results from the case of a reflected Brownian motion to the Markov modulated case.

  3. Chip-Based Measurements of Brownian Relaxation of Magnetic Beads Using a Planar Hall Effect Magnetic Field Sensor

    Science.gov (United States)

    Østerberg, Frederik W.; Dalslet, Bjarke T.; Snakenborg, Detlef; Johansson, Christer; Hansen, Mikkel F.

    2010-12-01

    We present a simple `click-on' fluidic system with integrated electrical contacts, which is suited for electrical measurements on chips in microfluidic systems. We show that microscopic magnetic field sensors based on the planar Hall effect can be used for detecting the complex magnetic response 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.

  4. Confronting Islamic Jihadist Movements

    Directory of Open Access Journals (Sweden)

    M. Afzal Upal

    2015-05-01

    Full Text Available This paper argues that in order to win the long-term fight against Islamic Jihadist movements, we must confront their ideological foundations and provide the majority of Muslims with an alternative narrative that satisfies their social identity needs for a positive esteem.  By analysing social identity dynamics of Western-Muslim interactions, this paper presents some novel ideas that can lead to the creation of such a narrative.

  5. COMBINING MODULES FOR MOVEMENT

    OpenAIRE

    Bizzi, E; Cheung, V.C.K.; d’Avella, A.; Saltiel, P.; Tresch, M.

    2007-01-01

    We review experiments supporting the hypothesis that the vertebrate motor system produces movements by combining a small number of units of motor output. Using a variety of approaches such as microstimulation of the spinal cord, NMDA iontophoresis, and an examination of natural behaviors in intact and deafferented animals we have provided evidence for a modular organization of the spinal cord. A module is a functional unit in the spinal cord that generates a specific motor output by imposing ...

  6. Monitoring underground movements

    CERN Multimedia

    Antonella Del Rosso

    2015-01-01

    On 16 September 2015 at 22:54:33 (UTC), an 8.3-magnitude earthquake struck off the coast of Chile. 11,650 km away, at CERN, a new-generation instrument – the Precision Laser Inclinometer (PLI) – recorded the extreme event. The PLI is being tested by a JINR/CERN/ATLAS team to measure the movements of underground structures and detectors.   The Precision Laser Inclinometer during assembly. The instrument has proven very accurate when taking measurements of the movements of underground structures at CERN.    The Precision Laser Inclinometer is an extremely sensitive device capable of monitoring ground angular oscillations in a frequency range of 0.001-1 Hz with a precision of 10-10 rad/Hz1/2. The instrument is currently installed in one of the old ISR transfer tunnels (TT1) built in 1970. However, its final destination could be the ATLAS cavern, where it would measure and monitor the fine movements of the underground structures, which can affect the precise posi...

  7. Kinetics of Hexagonal Cylinders to Face-centered Cubic Spheres Transition of Triblock Copolymer in Selective Solvent: Brownian Dynamics Simulation

    OpenAIRE

    LI Minghai; Liu, Yongsheng; Bansil, Rama

    2010-01-01

    The kinetics of the transformation from the hexagonal packed cylinder (HEX) phase to the face-centered-cubic (FCC) phase was simulated using Brownian Dynamics for an ABA triblock copolymer in a selective solvent for the A block. The kinetics was obtained by instantaneously changing either the temperature of the system or the well-depth of the Lennard-Jones potential. Detailed analysis showed that the transformation occurred via a rippling mechanism. The simulation results indicated that the o...

  8. Effective quantum Brownian dynamics in presence of a rapidly oscillating space-dependent time-periodic field.

    Science.gov (United States)

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

    2011-06-01

    We explore the Brownian dynamics in the quantum regime (by investigating the quantum Langevin and Smoluchowski equations) in terms of an effective time-independent Hamiltonian in the presence of a rapidly oscillating field. We achieve this by systematically expanding the time-dependent system-reservoir Hamiltonian in the inverse of driving frequency with a systematic time-scale separation and invoking a quantum gauge transformation within the framework of Floquet theorem. PMID:21797289

  9. Mean Square Displacement Analysis of Single-Particle Trajectories with Localization Error: Brownian Motion in Isotropic Medium

    OpenAIRE

    Michalet, Xavier

    2010-01-01

    We examine the capability of mean square displacement analysis to extract reliable values of the diffusion coefficient D of single particle undergoing Brownian motion in an isotropic medium in the presence of localization uncertainty. The theoretical results, supported by simulations, show that a simple unweighted least square fit of the MSD curve can provide the best estimate of D provided an optimal number of MSD points is used for the fit. We discuss the practical implications of these res...

  10. Search reliability and search efficiency of combined Lévy–Brownian motion: long relocations mingled with thorough local exploration

    Science.gov (United States)

    Palyulin, Vladimir V.; Chechkin, Aleksei V.; Klages, Rainer; Metzler, Ralf

    2016-09-01

    A combined dynamics consisting of Brownian motion and Lévy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of doing so economically of such dynamics thus poses an important problem. Here we model this dynamics by a one-dimensional fractional Fokker–Planck equation combining unbiased Brownian motion and Lévy flights. By solving this equation both analytically and numerically we show that the superposition of recurrent Brownian motion and Lévy flights with stable exponent α \\lt 1, by itself implying zero probability of hitting a point on a line, leads to transient motion with finite probability of hitting any point on the line. We present results for the exact dependence of the values of both the search reliability and the search efficiency on the distance between the starting and target positions as well as the choice of the scaling exponent α of the Lévy flight component.

  11. Dependence of the Apex Angle of an Inverted Pyramidal-Shaped Container on Crystallization of Brownian Particles

    Science.gov (United States)

    Kanatsu, Youhei; Sato, Masahide

    2015-11-01

    Large grains of a close-packed colloidal crystal have been experimentally shown to form in an inverted pyramidal pit by sedimentation [S. Matsuo et al., ext-link ext-link-type="uri" xlink:href="http://dx.doi.org/10.1063/1.1583138" xlink:type="simple">Appl. Phys. Lett. 82, 4285 (2003)ext-link>]. Keeping this experiment in mind, we study the crystallization of Brownian particles. We carry out Brownian dynamics simulations in an inverted pyramidal-shaped container. The Brownian particles settle out toward the apex of the container by a uniform external force. If the apex angle is suitable, large grains with the face-centered cubic (fcc) structure are formed [Y. Kanatsu and M. Sato, ext-link ext-link-type="uri" xlink:href="http://dx.doi.org/10.7566/JPSJ.84.044601" xlink:type="simple">J. Phys. Soc. Jpn. 84, 044601 (2015)ext-link>]. When the apex angle deviates from a suitable value, the number of hexagonal close-packed (hcp) structured particles, Nhcp, increases with increasing angle deviation. The formation of the hcp structure is induced by disordered particles remaining in the center region of the container.

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

    Science.gov (United States)

    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. PMID:17223124

  13. Search reliability and search efficiency of combined Lévy-Brownian motion: long relocations mingled with thorough local exploration

    Science.gov (United States)

    Palyulin, Vladimir V.; Chechkin, Aleksei V.; Klages, Rainer; Metzler, Ralf

    2016-09-01

    A combined dynamics consisting of Brownian motion and Lévy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of doing so economically of such dynamics thus poses an important problem. Here we model this dynamics by a one-dimensional fractional Fokker-Planck equation combining unbiased Brownian motion and Lévy flights. By solving this equation both analytically and numerically we show that the superposition of recurrent Brownian motion and Lévy flights with stable exponent α \\lt 1, by itself implying zero probability of hitting a point on a line, leads to transient motion with finite probability of hitting any point on the line. We present results for the exact dependence of the values of both the search reliability and the search efficiency on the distance between the starting and target positions as well as the choice of the scaling exponent α of the Lévy flight component.

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

    Science.gov (United States)

    Dubina, Sean Hyun; Wedgewood, Lewis Edward

    2016-07-01

    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.

  15. Virial theorem and dynamical evolution of self-gravitating Brownian particles in an unbounded domain. II. Inertial models.

    Science.gov (United States)

    Chavanis, Pierre-Henri; Sire, Clément

    2006-06-01

    We propose a general kinetic and hydrodynamic description of self-gravitating Brownian particles in d dimensions. We go beyond the usual approximations by considering inertial effects and finite-N effects while previous works use a mean-field approximation valid in a proper thermodynamic limit (N --> +infinity) and consider an overdamped regime (xi --> +infinity). We recover known models in some particular cases of our general description. We derive the expression of the virial theorem for self-gravitating Brownian particles and study the linear dynamical stability of isolated clusters of particles and uniform systems by using techniques introduced in astrophysics. We investigate the influence of the equation of state, of the dimension of space, and of the friction coefficient on the dynamical stability of the system. We obtain the exact expression of the critical temperature Tc for a multicomponents self-gravitating Brownian gas in d = 2. We also consider the limit of weak frictions, xi --> 0, and derive the orbit-averaged Kramers equation. PMID:16906911

  16. Virial theorem and dynamical evolution of self-gravitating Brownian particles in an unbounded domain. II. Inertial models.

    Science.gov (United States)

    Chavanis, Pierre-Henri; Sire, Clément

    2006-06-01

    We propose a general kinetic and hydrodynamic description of self-gravitating Brownian particles in d dimensions. We go beyond the usual approximations by considering inertial effects and finite-N effects while previous works use a mean-field approximation valid in a proper thermodynamic limit (N --> +infinity) and consider an overdamped regime (xi --> +infinity). We recover known models in some particular cases of our general description. We derive the expression of the virial theorem for self-gravitating Brownian particles and study the linear dynamical stability of isolated clusters of particles and uniform systems by using techniques introduced in astrophysics. We investigate the influence of the equation of state, of the dimension of space, and of the friction coefficient on the dynamical stability of the system. We obtain the exact expression of the critical temperature Tc for a multicomponents self-gravitating Brownian gas in d = 2. We also consider the limit of weak frictions, xi --> 0, and derive the orbit-averaged Kramers equation.

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

    Science.gov (United States)

    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.

  18. Human preference for air movement

    DEFF Research Database (Denmark)

    Toftum, Jørn; Melikov, Arsen Krikor; Tynel, A.;

    2002-01-01

    Human preference for air movement was studied at slightly cool, neutral, and slightly warm overall thermal sensations and at temperatures ranging from 18 deg.C to 28 deg.C. Air movement preference depended on both thermal sensation and temperature, but large inter-individual differences existed...... between subjects. Preference for less air movement was linearly correlated with draught discomfort, but the percentage of subjects who felt draught was lower than the percentage who preferred less air movement....

  19. Eye movements when viewing advertisements

    OpenAIRE

    Emily eHiggins; Mallorie eLeinenger; Keith eRayner

    2014-01-01

    In this selective review, we examine key findings on eye movements when viewing advertisements. We begin with a brief, general introduction to the properties and neural underpinnings of saccadic eye movements. Next, we provide an overview of eye movement behavior during reading, scene perception, and visual search, since each of these activities is, at various times, involved in viewing ads. We then review the literature on eye movements when viewing print ads and warning labels (of the kind ...

  20. Brownian motion of single glycerol molecules in an aqueous solution as studied by dynamic light scattering.

    Science.gov (United States)

    Elamin, Khalid; Swenson, Jan

    2015-03-01

    Aqueous solutions of glycerol are investigated by dynamic light scattering (DLS) over the whole concentration range (10-98 wt.% water) and in the temperature range 283-303 K. The measurements reveal one slow relaxation process in the geometry of polarized light scattering. This process is present in the whole concentration range, although it is very weak at the highest and lowest water concentrations and is considerably slower than the structural α relaxation, which is too fast to be observed on the experimental time scale in the measured temperature range. The relaxation time of the observed process exhibits a 1/q2 dependence, proving that it is due to long-range translational diffusion. The Stokes-Einstein relation is used to estimate the hydrodynamic radius of the diffusing particles and from these calculations it is evident that the observed relaxation process is due to the Brownian motion of single or a few glycerol molecules. The fact that it is possible to study the self-diffusion of such small molecules may stimulate a broadening of the research field used to be covered by the DLS technique. PMID:25871109

  1. EVOLUTION OF NUMBER CONCENTRATION OF NANO-PARTICLES UNDERGOING BROWNIAN COAGULATION IN THE TRANSITION REGIME

    Institute of Scientific and Technical Information of China (English)

    WANG Yu-ming; LIN Jian-zhong

    2011-01-01

    Evolution of number concentration of nanoparticles undergoing Brownian coagulation in the transition regime is studied theoretically and numerically.The results show that the curves of particle size distribution move toward the area with large particle diameters,the curve peak becomes lower and the range that particle diameters cover becomes wider as time elapses.In the process of coagulation the particles with small diameter disappear gradually and the particle size distribution remains a log-normal distribution.The change rate of the particle size distribution is more appreciable at the initial stage than that at the final stage.The initial Knudsen number has a significant effect on the coagulation rate which increases with decreasing the initial Knudsen number.The larger the initial geometric standard deviation is,the smaller the curve peak is,and the wider the area that curves cover is.The initial geometric standard deviation has a significant effect on the particle size distribution which can remain a self-preserving state when the initial geometric standard deviation is smaller than 2.With the increase of the diversity of initial particle size,the particle size distribution does not obey the log-normal distribution any more as time elapses.

  2. Numerically pricing American options under the generalized mixed fractional Brownian motion model

    Science.gov (United States)

    Chen, Wenting; Yan, Bowen; Lian, Guanghua; Zhang, Ying

    2016-06-01

    In this paper, we introduce a robust numerical method, based on the upwind scheme, for the pricing of American puts under the generalized mixed fractional Brownian motion (GMFBM) model. By using portfolio analysis and applying the Wick-Itô formula, a partial differential equation (PDE) governing the prices of vanilla options under the GMFBM is successfully derived for the first time. Based on this, we formulate the pricing of American puts under the current model as a linear complementarity problem (LCP). Unlike the classical Black-Scholes (B-S) model or the generalized B-S model discussed in Cen and Le (2011), the newly obtained LCP under the GMFBM model is difficult to be solved accurately because of the numerical instability which results from the degeneration of the governing PDE as time approaches zero. To overcome this difficulty, a numerical approach based on the upwind scheme is adopted. It is shown that the coefficient matrix of the current method is an M-matrix, which ensures its stability in the maximum-norm sense. Remarkably, we have managed to provide a sharp theoretic error estimate for the current method, which is further verified numerically. The results of various numerical experiments also suggest that this new approach is quite accurate, and can be easily extended to price other types of financial derivatives with an American-style exercise feature under the GMFBM model.

  3. Magnetoviscosity of dilute suspensions of magnetic ellipsoids obtained through rotational Brownian dynamics simulations.

    Science.gov (United States)

    Sánchez, J H; Rinaldi, C

    2009-03-15

    The magnetic field dependent viscosity (magnetoviscosity) of dilute suspensions of magnetic tri-axial ellipsoidal particles suspended in a Newtonian fluid and under applied shear and magnetic fields was studied numerically. Brownian dynamics simulations were performed to compute the intrinsic magnetoviscosity of the suspension. Results are presented for the response of dilute suspensions of ellipsoidal particles to constant magnetic and shear flow fields. Suspensions of ellipsoidal particles show a significant effect of aspect ratio on the intrinsic magnetoviscosity of the suspension, and this effect is more pronounced as the aspect ratio becomes more extreme. The use of an effective rotational diffusion coefficient D(r,eff) collapses the normalized intrinsic magnetoviscosity of all suspensions to a master curve as a function of Péclet number with the Langevin parameter alpha=(mu(0)muH)/(k(B)T) as parameter, up to a critical value of alpha for which the results for suspensions of spherical particles deviate from those of suspensions of ellipsoids. This discrepancy is attributed to the action of the shear-torque on the ellipsoidal particles, which tends to orient these particles in the direction of maximum deformation of the simple shear flow, and which does not act on spherical particles. PMID:19100560

  4. Time- and ensemble-averages in evolving systems: the case of Brownian particles in random potentials.

    Science.gov (United States)

    Bewerunge, Jörg; Ladadwa, Imad; Platten, Florian; Zunke, Christoph; Heuer, Andreas; Egelhaaf, Stefan U

    2016-07-28

    Anomalous diffusion is a ubiquitous phenomenon in complex systems. It is often quantified using time- and ensemble-averages to improve statistics, although time averages represent a non-local measure in time and hence can be difficult to interpret. We present a detailed analysis of the influence of time- and ensemble-averages on dynamical quantities by investigating Brownian particles in a rough potential energy landscape (PEL). Initially, the particle ensemble is randomly distributed, but the occupancy of energy values evolves towards the equilibrium distribution. This relaxation manifests itself in the time evolution of time- and ensemble-averaged dynamical measures. We use Monte Carlo simulations to study particle dynamics in a potential with a Gaussian distribution of energy values, where the long-time limit of the diffusion coefficient is known from theory. In our experiments, individual colloidal particles are exposed to a laser speckle pattern inducing a non-Gaussian roughness and are followed by optical microscopy. The relaxation depends on the kind and degree of roughness of the PEL. It can be followed and quantified by the time- and ensemble-averaged mean squared displacement. Moreover, the heterogeneity of the dynamics is characterized using single-trajectory analysis. The results of this work are relevant for the correct interpretation of single-particle tracking experiments in general. PMID:27353405

  5. Finite time extinction of super-Brownian motions with deterministic catalyst

    Institute of Scientific and Technical Information of China (English)

    REN; Yanxia(任艳霞); WANG; Yongjin(王永进)

    2003-01-01

    In this paper we consider a super-Brownian motion X with branching mechanism k(x)za, where k(x) > 0 is a bounded Holder continuous function on Rd and infx∈Rd k(x) = 0. We prove that if k(x) ≥‖x‖-1(0 ≤ l <∞) for sufficiently large x, then X has compact support property, and for dimension d = 1, if k(x) ≥ exp(-l‖x‖)(0 ≤ l <∞) for sufficiently large x, then X also has compact support property. The maximal order of k(x) for finite time extinction is different between d = 1, d = 2 and d ≥3: it is O(‖x‖-(a+1))in one dimension, O(‖x‖-2(log ‖x‖)-(a+1)) in two dimensions, and O(‖x‖2) in higher dimensions. These growth orders also turn out to be the maximum order for the nonexistence of a positive solution for 1/2△u =k(x)uα.

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

    International Nuclear Information System (INIS)

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

  7. Filamentous Biopolymers on Surfaces: Atomic Force Microscopy Images Compared with Brownian Dynamics Simulation of Filament Deposition

    Science.gov (United States)

    Mücke, Norbert; Klenin, Konstantin; Kirmse, Robert; Bussiek, Malte; Herrmann, Harald; Hafner, Mathias; Langowski, Jörg

    2009-01-01

    Nanomechanical properties of filamentous biopolymers, such as the persistence length, may be determined from two-dimensional images of molecules immobilized on surfaces. For a single filament in solution, two principal adsorption scenarios are possible. Both scenarios depend primarly on the interaction strength between the filament and the support: i) For interactions in the range of the thermal energy, the filament can freely equilibrate on the surface during adsorption; ii) For interactions much stronger than the thermal energy, the filament will be captured by the surface without having equilibrated. Such a ‘trapping’ mechanism leads to more condensed filament images and hence to a smaller value for the apparent persistence length. To understand the capture mechanism in more detail we have performed Brownian dynamics simulations of relatively short filaments by taking the two extreme scenarios into account. We then compared these ‘ideal’ adsorption scenarios with observed images of immobilized vimentin intermediate filaments on different surfaces. We found a good agreement between the contours of the deposited vimentin filaments on mica (‘ideal’ trapping) and on glass (‘ideal’ equilibrated) with our simulations. Based on these data, we have developed a strategy to reliably extract the persistence length of short worm-like chain fragments or network forming filaments with unknown polymer-surface interactions. PMID:19888472

  8. Filamentous biopolymers on surfaces: atomic force microscopy images compared with Brownian dynamics simulation of filament deposition.

    Directory of Open Access Journals (Sweden)

    Norbert Mücke

    Full Text Available Nanomechanical properties of filamentous biopolymers, such as the persistence length, may be determined from two-dimensional images of molecules immobilized on surfaces. For a single filament in solution, two principal adsorption scenarios are possible. Both scenarios depend primarily on the interaction strength between the filament and the support: i For interactions in the range of the thermal energy, the filament can freely equilibrate on the surface during adsorption; ii For interactions much stronger than the thermal energy, the filament will be captured by the surface without having equilibrated. Such a 'trapping' mechanism leads to more condensed filament images and hence to a smaller value for the apparent persistence length. To understand the capture mechanism in more detail we have performed Brownian dynamics simulations of relatively short filaments by taking the two extreme scenarios into account. We then compared these 'ideal' adsorption scenarios with observed images of immobilized vimentin intermediate filaments on different surfaces. We found a good agreement between the contours of the deposited vimentin filaments on mica ('ideal' trapping and on glass ('ideal' equilibrated with our simulations. Based on these data, we have developed a strategy to reliably extract the persistence length of short worm-like chain fragments or network forming filaments with unknown polymer-surface interactions.

  9. Depletion forces induce visco-elasto-capillary thinning of non-Brownian suspensions

    Science.gov (United States)

    Harich, R.; Deblais, A.; Colin, A.; Kellay, H.

    2016-06-01

    Droplet pinch-off, which occurs when a drop of liquid detaches from a capillary, can be strongly modified in the presence of complex fluids such as polymer solutions and suspensions giving rise to long and slender filaments that thin slowly in time. While for polymers, the molecular conformations of the molecules in the filament are responsible for such a behavior, in suspensions the mechanisms at play remain to be deciphered. Here we show, experimentally, that while liquid bridges of non-Brownian suspensions of moderate concentrations have a thinning behavior very close to that of the solvent, the addition of short-chain polymers inducing depletion attractions between the particles in the suspension changes the thinning dynamics and gives rise to exponential thinning in time. The characteristic time of this dynamics increases with polymer concentration and therefore the intensity of the depletion forces at play. The tunability of this dynamics may be important for injket and 3D printing applications where short rupture times are sought for or in other situations where drop formation has to be minimized or inhibited.

  10. DNA electrophoresis in tri-block copolymer gels--experiments and Brownian dynamics simulation

    Science.gov (United States)

    Wei, Ling; van Winkle, David H.

    2015-03-01

    The mobility of double-stranded DNA ladders in Pluronics®P105, P123 and F127, was measured by two-dimensional gel electrophoresis. Pluronics®are triblock copolymers which form gel-like phases of micelles arranged with cubic order at room temperature. A 10 base pair and a 25 base pair DNA ladder were used as samples in gel electrophoresis. The monotonically decreasing mobility with increasing length observed in the agarose separations is not observed in separations in Pluronics®. Rather, a complicated dependence of mobility on DNA length is observed, where mobility vs. length increases for short DNA molecules then decreases for longer molecules. There is also a variation of mobility with length correlated to the micelle diameter. Brownian dynamics simulations of a discrete wormlike chain model were performed to simulate short DNA molecules migrating in free solution and in a face-centered cubic matrix. By incorporating hydrodynamic interactions, the trend of simulated length-dependent mobility qualitatively agrees with experimental measurements.

  11. Brownian inventory models with convex holding cost, Part 2: Discount-optimal controls

    Directory of Open Access Journals (Sweden)

    Jim Dai

    2014-01-01

    Full Text Available We consider an inventory system in which inventory level fluctuates as a Brownian motion in the absence of control. The inventory continuously accumulates cost at a rate that is a general convex function of the inventory level, which can be negative when there is a backlog. At any time, the inventory level can be adjusted by a positive or negative amount, which incurs a fixed positive cost and a proportional cost. The challenge is to find an adjustment policy that balances the inventory cost and adjustment cost to minimize the expected total discounted cost. We provide a tutorial on using a three-step lower-bound approach to solving the optimal control problem under a discounted cost criterion. In addition, we prove that a four-parameter control band policy is optimal among all feasible policies. A key step is the constructive proof of the existence of a unique solution to the free boundary problem. The proof leads naturally to an algorithm to compute the four parameters of the optimal control band policy.

  12. The generalization of a class of impulse stochastic control models of a geometric Brownian motion

    Institute of Scientific and Technical Information of China (English)

    LIU XiaoPeng; LIU KunHui

    2009-01-01

    Recently, international academic circles advanced a class of new stochastic control models of a geometric Brownian motion which is an important kind of impulse control models whose cost structure is different from the others before, and it has a broad applying background and important theoretical significance in financial control and management of investment. This paper generalizes substantially the above stochastic control models under quite extensive conditions and describes the models more exactly under more normal theoretical system of stochastic process. By establishing a set of proper variational equations and proving the existence of its solution, and applying the means of stochastic analysis, this paper proves that the generalized stochastic control models have optimal controls.Meanwhile, we also analyze the structure of optimal controls carefully. Besides, we study the solution function of variational equations in a relatively deep-going way, which constitutes the value function of control models to some extent. Because the analysis methods of this paper are greatly different from those of original reference, this paper possesses considerable originality to some extent. In addition,this paper gives the strict proof to the part of original reference which is not fairly well-knit in analyses,and makes analyses and discussions of the model have the exactitude of mathematical sense.

  13. Isotropic Brownian motions over complex fields as a solvable model for May-Wigner stability analysis

    Science.gov (United States)

    Ipsen, J. R.; Schomerus, H.

    2016-09-01

    We consider matrix-valued stochastic processes known as isotropic Brownian motions, and show that these can be solved exactly over complex fields. While these processes appear in a variety of questions in mathematical physics, our main motivation is their relation to a May-Wigner-like stability analysis, for which we obtain a stability phase diagram. The exact results establish the full joint probability distribution of the finite-time Lyapunov exponents, and may be used as a starting point for a more detailed analysis of the stability-instability phase transition. Our derivations rest on an explicit formulation of a Fokker-Planck equation for the Lyapunov exponents. This formulation happens to coincide with an exactly solvable class of models of the Calgero-Sutherland type, originally encountered for a model of phase-coherent transport. The exact solution over complex fields describes a determinantal point process of biorthogonal type similar to recent results for products of random matrices, and is also closely related to Hermitian matrix models with an external source.

  14. Analysis of Brownian Particles for finding the shortest path in networks

    Directory of Open Access Journals (Sweden)

    huan yan qian

    2013-07-01

    Full Text Available In this paper, we propose a method to analyze the shortest path finding between two nodes in complex networks. In this method, we first find that single Brownian particle follows the shortest path between source node and destination node in the probability of where denotes the shortest path steps between two nodes. To be compared with single particle utilization, then we specially analyze the multiple particles. We compute the probability of particles’ taking the shortest path between and when particles starts simultaneously from the source and head to the destination as . It’s very clear that there must be particles taking the shortest path to arrive at the destination in the multiple particles environment. And with the number of increasing, the arriving probability first arise and then drop down rapidly until to zero. In the end, we make the experiments and confirm our theoretical analysis. Our results would provide valuable usage for some applications such as finding the optimal routing in wireless sensor networks.

  15. Brownian limits, local limits, extreme value and variance asymptotics for convex hulls in the ball

    CERN Document Server

    Calka, Pierre; Yukich, J E

    2009-01-01

    The paper of Schreiber and Yukich [40] establishes an asymptotic representation for random convex polytope geometry in the unit ball $\\B_d, d \\geq 2,$ in terms of the general theory of stabilizing functionals of Poisson point processes as well as in terms of the so-called generalized paraboloid growth process. This paper further exploits this connection, introducing also a dual object termed the paraboloid hull process. Via these growth processes we establish local functional and measure-level limit theorems for the properly scaled radius-vector and support functions as well as for curvature measures and $k$-face empirical measures of convex polytopes generated by high density Poisson samples. We use general techniques of stabilization theory to establish Brownian sheet limits for the defect volume and mean width functionals, and we provide explicit variance asymptotics and central limit theorems for the $k$-face and intrinsic volume functionals. We establish extreme value theorems for radius-vector and suppo...

  16. Fractional Brownian motion time-changed by gamma and inverse gamma process

    CERN Document Server

    Kumar, A; Połoczański, R; Sundar, S

    2016-01-01

    Many real time-series exhibit behavior adequate to long range dependent data. Additionally very often these time-series have constant time periods and also have characteristics similar to Gaussian processes although they are not Gaussian. Therefore there is need to consider new classes of systems to model these kind of empirical behavior. Motivated by this fact in this paper we analyze two processes which exhibit long range dependence property and have additional interesting characteristics which may be observed in real phenomena. Both of them are constructed as the superposition of fractional Brownian motion (FBM) and other process. In the first case the internal process, which plays role of the time, is the gamma process while in the second case the internal process is its inverse. We present in detail their main properties paying main attention to the long range dependence property. Moreover, we show how to simulate these processes and estimate their parameters. We propose to use a novel method based on re...

  17. Brownian localization: A generalized coupling model yielding a nonergodic Langevin equation description

    Institute of Scientific and Technical Information of China (English)

    Liu Jian; Wang Hai-Yan; Bao Jing-Dong

    2013-01-01

    A minimal system-plus-reservoir model yielding a nonergodic Langevin equation is proposed,which originates from the cubic-spectral density of environmental oscillators and momentum-dependent coupling.This model allows ballistic diffusion and classical localization simultaneously,in which the fluctuation-dissipation relation is still satisfied but the Khinchin theorem is broken.The asymptotical equilibrium for a nonergodic system requires the initial thermal equilibrium,however,when the system starts from nonthermal conditions,it does not approach the equilibration even though a nonlinear potential is used to bound the particle,this can be confirmed by the zeroth law of thermodynamics.In the dynamics of Brownian localization,due to the memory damping function inducing a constant term,our results show that the stationary distribution of the system depends on its initial preparation of coordinate rather than momentum.The coupled oscillator chain with a fixed end boundary acts as a heat bath,which has long been used in studies of collinear atom/solid-surface scattering and lattice vibration,we investigate this problem from the viewpoint of nonergodicity.

  18. Experimental study of the stochastic heating of a single Brownian particle by charge fluctuations

    Science.gov (United States)

    Schmidt, Christian; Piel, Alexander

    2016-08-01

    The Brownian motion of a micro-particle, which is suspended in the sheath of a radio-frequency discharge, is studied by high-speed video microscopy. In this environment, stochastic heating by charge fluctuations is expected, which should lead to an anisotropic kinetic temperature of the particle with a preferential heating in the direction of the mean electric field in the sheath. The stochastic heating should become more effective at low gas pressures where cooling by the neutral gas becomes ineffective. Our refined experiments confirm the anisotropic heating and the temperature rise for diminishing pressure. Particle-in-cell simulations have guided us in modifying the gap width of the discharge and to specify the dependence of the plasma density on gas pressure as n i ∝ p 1 / 2 . Since the stochastic heating rate also depends on the life-time of charge fluctuations, a temperature scaling T kin ∝ p 3 / 2 results, which is in agreement with the experimental data. The experimental procedure to eliminate other spurious heating mechanisms is described in detail.

  19. Horizontal visibility graphs transformed from fractional Brownian motions: Topological properties versus Hurst index

    CERN Document Server

    Xie, Wen-Jie

    2010-01-01

    Nonlinear time series analysis aims at understanding the dynamics of stochastic or chaotic processes. In recent years, quite a few methods have been proposed to transform a single time series to a complex network so that the dynamics of the process can be understood by investigating the topological properties of the network. We study the topological properties of horizontal visibility graphs constructed from fractional Brownian motions with different Hurst index $H\\in(0,1)$. Special attention has been paid to the impact of Hurst index on the topological properties. It is found that the clustering coefficient $C$ decreases when $H$ increases. We also found that the mean length $L$ of the shortest paths increases exponentially with $H$ for fixed length $N$ of the original time series. In addition, $L$ increases linearly with respect to $N$ when $H$ is close to 1 and in a logarithmic form when $H$ is close to 0. Although the occurrence of different motifs changes with $H$, the motif rank pattern remains unchange...

  20. Detection of two-sided alternatives in a Brownian motion model

    CERN Document Server

    Hadjiliadis, Olympia

    2007-01-01

    This work examines the problem of sequential detection of a change in the drift of a Brownian motion in the case of two-sided alternatives. Applications to real life situations in which two-sided changes can occur are discussed. Traditionally, 2-CUSUM stopping rules have been used for this problem due to their asymptotically optimal character as the mean time between false alarms tends to $\\infty$. In particular, attention has focused on 2-CUSUM harmonic mean rules due to the simplicity in calculating their first moments. In this paper, we derive closed-form expressions for the first moment of a general 2-CUSUM stopping rule. We use these expressions to obtain explicit upper and lower bounds for it. Moreover, we derive an expression for the rate of change of this first moment as one of the threshold parameters changes. Based on these expressions we obtain explicit upper and lower bounds to this rate of change. Using these expressions we are able to find the best 2-CUSUM stopping rule with respect to the exten...

  1. Nanoblinker: Brownian Motion Powered Bio-Nanomachine for FRET Detection of Phagocytic Phase of Apoptosis

    Science.gov (United States)

    Minchew, Candace L.; Didenko, Vladimir V.

    2014-01-01

    We describe a new type of bio-nanomachine which runs on thermal noise. The machine is solely powered by the random motion of water molecules in its environment and does not ever require re-fuelling. The construct, which is made of DNA and vaccinia virus topoisomerase protein, can detect DNA damage by employing fluorescence. It uses Brownian motion as a cyclic motor to continually separate and bring together two types of fluorescent hairpins participating in FRET. This bio-molecular oscillator is a fast and specific sensor of 5′OH double-strand DNA breaks present in phagocytic phase of apoptosis. The detection takes 30 s in solution and 3 min in cell suspensions. The phagocytic phase is critical for the effective execution of apoptosis as it ensures complete degradation of the dying cells’ DNA, preventing release of pathological, viral and tumor DNA and self-immunization. The construct can be used as a smart FRET probe in studies of cell death and phagocytosis. PMID:25268504

  2. Multifractality and Laplace spectrum of horizontal visibility graphs constructed from fractional Brownian motions

    Science.gov (United States)

    Yu, Zu-Guo; Zhang, Huan; Huang, Da-Wen; Lin, Yong; Anh, Vo

    2016-03-01

    Many studies have shown that additional information can be gained on time series by investigating their associated complex networks. In this work, we investigate the multifractal property and Laplace spectrum of the horizontal visibility graphs (HVGs) constructed from fractional Brownian motions. We aim to identify via simulation and curve fitting the form of these properties in terms of the Hurst index H. First, we use the sandbox algorithm to study the multifractality of these HVGs. It is found that multifractality exists in these HVGs. We find that the average fractal dimension of HVGs approximately satisfies the prominent linear formula =2-H ; while the average information dimension and average correlation dimension are all approximately bi-linear functions of H when H≥slant 0.15 . Then, we calculate the spectrum and energy for the general Laplacian operator and normalized Laplacian operator of these HVGs. We find that, for the general Laplacian operator, the average logarithm of second-smallest eigenvalue , the average logarithm of third-smallest eigenvalue , and the average logarithm of maximum eigenvalue of these HVGs are approximately linear functions of H; while the average Laplacian energy is approximately a quadratic polynomial function of H. For the normalized Laplacian operator, and of these HVGs approximately satisfy linear functions of H; while and are approximately a 4th and cubic polynomial function of H respectively.

  3. Stochastic Stokes' Drift, Homogenized Functional Inequalities, and Large Time Behavior of Brownian Ratchets

    KAUST Repository

    Blanchet, Adrien

    2009-01-01

    A periodic perturbation of a Gaussian measure modifies the sharp constants in Poincarae and logarithmic Sobolev inequalities in the homogeniz ation limit, that is, when the period of a periodic perturbation converges to zero. We use variational techniques to determine the homogenized constants and get optimal convergence rates toward s equilibrium of the solutions of the perturbed diffusion equations. The study of these sharp constants is motivated by the study of the stochastic Stokes\\' drift. It also applies to Brownian ratchets and molecular motors in biology. We first establish a transport phenomenon. Asymptotically, the center of mass of the solution moves with a constant velocity, which is determined by a doubly periodic problem. In the reference frame attached to the center of mass, the behavior of the solution is governed at large scale by a diffusion with a modified diffusion coefficient. Using the homogenized logarithmic Sobolev inequality, we prove that the solution converges in self-similar variables attached to t he center of mass to a stationary solution of a Fokker-Planck equation modulated by a periodic perturbation with fast oscillations, with an explicit rate. We also give an asymptotic expansion of the traveling diffusion front corresponding to the stochastic Stokes\\' drift with given potential flow. © 2009 Society for Industrial and Applied Mathematics.

  4. Brownian dynamics simulation of peeling a strongly-adsorbed polymer molecule from a frictionless substrate.

    Science.gov (United States)

    Iliafar, Sara; Vezenov, Dmitri; Jagota, Anand

    2013-02-01

    We used brownian dynamics to study the peeling of a polymer molecule, represented by a freely jointed chain, from a frictionless surface in an implicit solvent with parameters representative of single-stranded DNA adsorbed on graphite. For slow peeling rates, simulations match the predictions of an equilibrium statistical thermodynamic model. We show that deviations from equilibrium peeling forces are dominated by a combination of Stokes (viscous) drag forces acting on the desorbed section of the chain and a finite rate of hopping over a desorption barrier. Characteristic velocities separating equilibrium and nonequilibrium regimes are many orders of magnitude higher than values accessible in force spectroscopy experiments. Finite probe stiffness resulted in disappearance of force spikes due to desorption of individual links predicted by the statistical thermodynamic model under displacement control. Probe fluctuations also masked sharp transitions in peeling force between blocks of distinct sequences, indicating limitation in the ability of single-molecule force spectroscopy to distinguish small differences in homologous molecular structures.

  5. COMPUTER SIMULATION OF LOCAL MOBILITY IN DENDRIMERS WITH ASYMMETRIC BRANCHING BY BROWNIAN DYNAMICS METHOD

    Directory of Open Access Journals (Sweden)

    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.

  6. Conformation and translational diffusion of a xanthan polyelectrolyte chain: Brownian dynamics simulation and single molecule tracking

    Science.gov (United States)

    Chun, Myung-Suk; Kim, Chongyoup; Lee, Duck E.

    2009-05-01

    In our recent Brownian dynamics (BD) simulation study, the structure and dynamics of anionic polyelectrolyte xanthan in bulk solution as well as confined spaces of slitlike channel were examined by applying a coarse-grained model with nonlinear bead-spring discretization of a whole chain [J. Jeon and M.-S. Chun, J. Chem. Phys. 126, 154904 (2007)]. This model goes beyond other simulations as they did not consider both long-range electrostatic and hydrodynamic interactions between pairs of beads. Simulation parameters are obtained from the viscometric method of rheology data on the native and sonicated xanthan polysaccharides, which have a contour length less than 1μm . The size of the semiflexible polyelectrolyte can be well described by the wormlike chain model once the electrostatic effects are taken into account by the persistence length measured at a long length scale. For experimental verifications, single molecule visualization was performed on fluorescein-labeled xanthan using an inverted fluorescence microscope, and the motion of an individual molecule was quantified. Experimental results on the conformational changes in xanthan chain in the electrolyte solution have a reasonable trend to agree with the prediction by BD simulations. In the translational diffusion induced by the Debye screening effect, the simulation prediction reveals slightly higher values compared to those of our measurements, although it agrees with the literature data. Considering the experimental restrictions, our BD simulations are verified to model the single polyelectrolyte well.

  7. Energy and Movement

    CERN Document Server

    90, Sol

    2011-01-01

    Updated for 2011, Energy and Movement, is one book in the Britannica Illustrated Science Library Series that covers today's most popular science topics, from digital TV to microchips to touchscreens and beyond. Perennial subjects in earth science, life science, and physical science are all explored in detail. Amazing graphics-more than 1,000 per title-combined with concise summaries help students understand complex subjects. Correlated to the science curriculum in grades 5-9, each title also contains a glossary with full definitions for vocabulary.

  8. The Evidence Movement

    DEFF Research Database (Denmark)

    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....... This article analyses how the idea is practised in the areas of health, social welfare and education and shows that evidence-producing organizations work differently. Some subscribe to the hierarchy of evidence, others to a typology of evidence. The consequences of these variations are discussed....

  9. Mungiki as Youth Movement

    DEFF Research Database (Denmark)

    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...... of snuff tobacco, revolutionary talk and generational exclusion, it is argued that one way of understanding the connection between the various elements is to look at specific youth practices that cut across apparently separate activities. This reveals that youth in the Mungiki discourse is a highly...

  10. Tracking the Poster Movement

    DEFF Research Database (Denmark)

    Christensen, Line Hjorth

    2015-01-01

    commercial and graphic design of various kinds of which British and Foreign Posters offers a particularly rich example. The exhibition attracted commercial, artistic and curatorial forces substantiating the idea of a movement, and approached commercial art from a perspective that raised new awareness towards...... graphic material in urban and museum space alike. To clarify the curatorial approach the analysis draws on a theoretical scheme of ecological semiotics, the concept of counterability and contextualising displays, which I name poster milieux: the 1931 case demonstrates how contemporary commercial art...

  11. Knowledge through movement

    DEFF Research Database (Denmark)

    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 reintroduc....... The current focus on the head and lack of attention to the body unifies society to focus on cognitive learning. This has implications for the values created by this system. Learning Lab Denmark aims to examine new ways of reintroducing the body into learning....

  12. [Movement disorders is psychiatric diseases].

    Science.gov (United States)

    Hidasi, Zoltan; Salacz, Pal; Csibri, Eva

    2014-12-01

    Movement disorders are common in psychiatry. The movement disorder can either be the symptom of a psychiatric disorder, can share a common aetiological factor with it, or can be the consequence of psychopharmacological therapy. Most common features include tic, stereotypy, compulsion, akathisia, dyskinesias, tremor, hypokinesia and disturbances of posture and gait. We discuss characteristics and clinical importance of these features. Movement disorders are frequently present in mood disorders, anxiety disorders, schizophrenia, catatonia, Tourette-disorder and psychogenic movement disorder, leading to differential-diagnostic and therapeutical difficulties in everyday practice. Movement disorders due to psychopharmacotherapy can be classified as early-onset, late-onset and tardive. Frequent psychiatric comorbidity is found in primary movement disorders, such as Parkinson's disease, Wilson's disease, Huntington's disease, diffuse Lewy-body disorder. Complex neuropsychiatric approach is effective concerning overlapping clinical features and spectrums of disorders in terms of movement disorders and psychiatric diseases. PMID:25577484

  13. Simulation of the Brownian coagulation of nanoparticles with initial bimodal size distribution via moment method

    Institute of Scientific and Technical Information of China (English)

    Jian-Zhong Lin; Fu-Jun Gan

    2012-01-01

    The Brownian coagulation of nanoparticles with initial bimodal size distribution,i.e.,mode i and j,is numerically studied using the moment method.Evolutions of particle number concentration,geometric average diameter and geometric standard deviation are given in the free molecular regime,the continuum regime,the free molecular regimand transition regime,the free molecular regime and contin-uum regime,respectively.The results show that,both in the free molecular regime and the continuum regime,the number concentration of mode i and j decreases with increasing time.The evolutions of particle geometric average diameter with different initial size distribution are quite different.Both intra-modal and inter-modal coagulation finally make the polydispersed size distribution become monodispersed.As time goes by,the size distribution with initial bimodal turns to be unimodal and shifts to a larger particle size range.In the free molecular regime and transition regime,the intermodal coagulation becomes dominant when the number concentrations of mode i and j are of the same order.The effects of the number concentration of mode i and mode j on the evolution of geometric average diameter of mode j are negligible,while the effects of the number concentration of mode j on the evolution of geometric average diameter of mode j is distinct.In the free molecular regime and continuum regime,the higher the initial number concentration of mode j,the more obvious the variation of the number concentration of mode i.

  14. Brownian Dynamics of a Suspension of Particles with Constrained Voronoi Cell Volumes

    KAUST Repository

    Singh, John P.

    2015-06-23

    © 2015 American Chemical Society. Solvent-free polymer-grafted nanoparticle fluids consist of inorganic core particles fluidized by polymers tethered to their surfaces. The attachment of the suspending fluid to the particle surface creates a strong penalty for local variations in the fluid volume surrounding the particles. As a model of such a suspension we perform Brownian dynamics of an equilibrium system consisting of hard spheres which experience a many-particle potential proportional to the variance of the Voronoi volumes surrounding each particle (E = α(Vi-V0)2). The coefficient of proportionality α can be varied such that pure hard sphere dynamics is recovered as α → 0, while an incompressible array of hairy particles is obtained as α →. As α is increased the distribution of Voronoi volumes becomes narrower, the mean coordination number of the particle increases and the variance in the number of nearest neighbors decreases. The nearest neighbor peaks in the pair distribution function are suppressed and shifted to larger radial separations as the constraint acts to maintain relatively uniform interstitial regions. The structure factor of the model suspension satisfies S(k=0) → 0 as α → in accordance with expectation for a single component (particle plus tethered fluid) incompressible system. The tracer diffusivity of the particles is reduced by the volume constraint and goes to zero at φ 0.52, indicating an earlier glass transition than has been observed in hard sphere suspensions. The total pressure of the suspension grows in proportion to (αkBT)1/2 as the strength of the volume-constraint potential grows. This stress arises primarily from the interparticle potential forces, while the hard-sphere collisional contribution to the stress is suppressed by the volume constraint.

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

    Science.gov (United States)

    Sanders, Lloyd P; Ambjörnsson, Tobias

    2012-05-01

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

  16. Brownian dynamics simulations of polyelectrolyte adsorption in shear flow with hydrodynamic interaction.

    Science.gov (United States)

    Hoda, Nazish; Kumar, Satish

    2007-12-21

    The adsorption of single polyelectrolyte molecules in shear flow is studied using Brownian dynamics simulations with hydrodynamic interaction (HI). Simulations are performed with bead-rod and bead-spring chains, and electrostatic interactions are incorporated through a screened Coulombic potential with excluded volume accounted for by the repulsive part of a Lennard-Jones potential. A correction to the Rotne-Prager-Yamakawa tensor is derived that accounts for the presence of a planar wall. The simulations show that migration away from an uncharged wall, which is due to bead-wall HI, is enhanced by increases in the strength of flow and intrachain electrostatic repulsion, consistent with kinetic theory predictions. When the wall and polyelectrolyte are oppositely charged, chain behavior depends on the strength of electrostatic screening. For strong screening, chains get depleted from a region close to the wall and the thickness of this depletion layer scales as N(1/3)Wi(2/3) at high Wi, where N is the chain length and Wi is the Weissenberg number. At intermediate screening, bead-wall electrostatic attraction competes with bead-wall HI, and it is found that there is a critical Weissenberg number for desorption which scales as N(-1/2)kappa(-3)(l(B)|sigmaq|)(3/2), where kappa is the inverse screening length, l(B) is the Bjerrum length, sigma is the surface charge density, and q is the bead charge. When the screening is weak, adsorbed chains are observed to align in the vorticity direction at low shear rates due to the effects of repulsive intramolecular interactions. At higher shear rates, the chains align in the flow direction. The simulation method and results of this work are expected to be useful for a number of applications in biophysics and materials science in which polyelectrolyte adsorption plays a key role.

  17. Oscillatory shear response of dilute ferrofluids: predictions from rotational Brownian dynamics simulations and ferrohydrodynamics modeling.

    Science.gov (United States)

    Soto-Aquino, D; Rosso, D; Rinaldi, C

    2011-11-01

    Ferrofluids are colloidal suspensions of magnetic nanoparticles that exhibit normal liquid behavior in the absence of magnetic fields but respond to imposed magnetic fields by changing their viscosity without loss of fluidity. The response of ferrofluids to constant shear and magnetic fields has received a lot of attention, but the response of ferrofluids to oscillatory shear remains largely unexplored. In the present work we used rotational Brownian dynamics to study the dynamic properties of ferrofluids with thermally blocked nanoparticles under oscillatory shear and constant magnetic fields. Comparisons between simulations and modeling using the ferrohydrodynamics equations were also made. Simulation results show that, for small rotational Péclet number, the in-phase and out-of-phase components of the complex viscosity depend on the magnitude of the magnetic field and frequency of the shear, following a Maxwell-like model with field-dependent viscosity and characteristic time equal to the field-dependent transverse magnetic relaxation time of the nanoparticles. Comparison between simulations and the numerical solution of the ferrohydrodynamic equations shows that the oscillatory rotational magnetoviscosity for an oscillating shear field obtained using the kinetic magnetization relaxation equation quantitatively agrees with simulations for a wide range of Péclet number and Langevin parameter but has quantitative deviations from the simulations at high values of the Langevin parameter. These predictions indicate an apparent elastic character to the rheology of these suspensions, even though we are considering the infinitely dilute limit in which there are negligible particle-particle interactions and, as such, chains do not form. Additionally, an asymptotic analytical solution of the ferrohydrodynamics equations, valid for Peferrofluids under conditions of small shear rates. At higher shear rates the Cox-Merz rule ceases to apply. PMID:22181497

  18. Parametric Human Movements

    DEFF Research Database (Denmark)

    Herzog, Dennis

    The thesis aims at the learning of action primitives and their application on the perceptive side (tracking/recognition) and the generative side (synthesizing for robot control). A motivation is to use a unified primitive representation applicable on both sides. The thesis considers arm actions...... to imitation and intertwined tracking/recognition. Both approaches utilize PHMMs. In the imitation application, a humanoid robot is enabled to relocate objects. It is important to synthesize movements such that the robot can reach for arbitrarily located objects, which requires the adaption of the PHMM...... parameters. Since actions and parameters are learned from demonstration of another (human) embodiment, it is necessary to map both (actions and parameters) consistently on the robot. A rule-learning experiment shows the robot successfully handling several objects. In the tracking and recognition application...

  19. West African Antislavery Movements

    DEFF Research Database (Denmark)

    Hahonou, Eric Komlavi; Pelckmans, Lotte

    2011-01-01

    to unite, mobilize and struggle. Members of anti-slavery movements with slave origins accessed power positions through peaceful electoral processes in Benin, mali, Niger and Mauritania. People of slave origins gained ground in local politics of a number of municipalities. In localities where anti-slavery......In the context of liberalization of West African political regimes, the upsurge of audacious political entrepreneurs who want to end chattel slavery in their nation-state, resulted in the legal criminalisation of slavery in both Mauritania (2007) and Niger (2003) and in a proposal to revise...... the penal code of Mali. Anti-slavery activists not only address their claims to their national governments but also intend to initiate change at local level. In that respect the democratic decentralization reforms were significant because they allowed educated anti-slavery activists to appeal their brethren...

  20. The Circular Camera Movement

    DEFF Research Database (Denmark)

    Hansen, Lennard Højbjerg

    2014-01-01

    It has been an accepted precept in film theory that specific stylistic features do not express specific content. Nevertheless, it is possible to find many examples in the history of film in which stylistic features do express specific content: for instance, the circular camera movement is used...... repeatedly to convey the feeling of a man and a woman falling in love. This raises the question of why producers and directors choose certain stylistic features to narrate certain categories of content. Through the analysis of several short film and TV clips, this article explores whether...... or not there are perceptual aspects related to specific stylistic features that enable them to be used for delimited narrational purposes. The article further attempts to reopen this particular stylistic debate by exploring the embodied aspects of visual perception in relation to specific stylistic features...