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Sample records for fractional brownian motion

  1. STOCHASTIC INTEGRATION FOR TEMPERED FRACTIONAL BROWNIAN MOTION.

    PubMed

    Meerschaert, Mark M; Sabzikar, Farzad

    2014-07-01

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

  2. Nonlinear Filtering with Fractional Brownian Motion

    SciTech Connect

    Amirdjanova, A.

    2002-12-19

    Our objective is to study a nonlinear filtering problem for the observation process perturbed by a Fractional Brownian Motion (FBM) with Hurst index 1/2 fractional' Zakai equation for the unnormalized optimal filter is derived.

  3. From fractional Brownian motion to multifractional and multistable motion

    NASA Astrophysics Data System (ADS)

    Falconer, Kenneth

    2015-03-01

    Fractional Brownian motion, introduced by Benoit Mandelbrot and John Van Ness in 1968, has had a major impact on stochastic processes and their applications. We survey a few of the many developments that have stemmed from their ideas. In particular we discuss the local structure of fractional and multifractional Brownian, stable and multistable processes, emphasising the `diagonal' construction of such processes. In all this, the ubiquity and centrality of fractional Brownian motion is striking.

  4. Extreme-value statistics of fractional Brownian motion bridges

    NASA Astrophysics Data System (ADS)

    Delorme, Mathieu; Wiese, Kay Jörg

    2016-11-01

    Fractional Brownian motion is a self-affine, non-Markovian, and translationally invariant generalization of Brownian motion, depending on the Hurst exponent H . Here we investigate fractional Brownian motion where both the starting and the end point are zero, commonly referred to as bridge processes. Observables are the time t+ the process is positive, the maximum m it achieves, and the time tmax when this maximum is taken. Using a perturbative expansion around Brownian motion (H =1/2 ), we give the first-order result for the probability distribution of these three variables and the joint distribution of m and tmax. Our analytical results are tested and found to be in excellent agreement, with extensive numerical simulations for both H >1/2 and H <1/2 . This precision is achieved by sampling processes with a free end point and then converting each realization to a bridge process, in generalization to what is usually done for Brownian motion.

  5. Fractional Brownian motion and long term clinical trial recruitment.

    PubMed

    Zhang, Qiang; Lai, Dejian

    2011-05-01

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

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

    PubMed

    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.

  7. Fractional Brownian motion and motion governed by the fractional Langevin equation in confined geometries

    NASA Astrophysics Data System (ADS)

    Jeon, Jae-Hyung; Metzler, Ralf

    2010-02-01

    Motivated by subdiffusive motion of biomolecules observed in living cells, we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time-averaged mean-squared displacement and displacement correlation) are affected by spatial confinement and dimensionality. In particular, we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain. The general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality. We define the displacement correlation function and find that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single-particle trajectory data.

  8. Fractional Brownian motion and motion governed by the fractional Langevin equation in confined geometries.

    PubMed

    Jeon, Jae-Hyung; Metzler, Ralf

    2010-02-01

    Motivated by subdiffusive motion of biomolecules observed in living cells, we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time-averaged mean-squared displacement and displacement correlation) are affected by spatial confinement and dimensionality. In particular, we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain. The general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality. We define the displacement correlation function and find that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single-particle trajectory data.

  9. Extreme-value statistics of fractional Brownian motion bridges.

    PubMed

    Delorme, Mathieu; Wiese, Kay Jörg

    2016-11-01

    Fractional Brownian motion is a self-affine, non-Markovian, and translationally invariant generalization of Brownian motion, depending on the Hurst exponent H. Here we investigate fractional Brownian motion where both the starting and the end point are zero, commonly referred to as bridge processes. Observables are the time t_{+} the process is positive, the maximum m it achieves, and the time t_{max} when this maximum is taken. Using a perturbative expansion around Brownian motion (H=1/2), we give the first-order result for the probability distribution of these three variables and the joint distribution of m and t_{max}. Our analytical results are tested and found to be in excellent agreement, with extensive numerical simulations for both H>1/2 and H<1/2. This precision is achieved by sampling processes with a free end point and then converting each realization to a bridge process, in generalization to what is usually done for Brownian motion.

  10. Perturbative expansion for the maximum of fractional Brownian motion.

    PubMed

    Delorme, Mathieu; Wiese, Kay Jörg

    2016-07-01

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

  11. Transient aging in fractional Brownian and Langevin-equation motion

    NASA Astrophysics Data System (ADS)

    Kursawe, Jochen; Schulz, Johannes; Metzler, Ralf

    2013-12-01

    Stochastic processes driven by stationary fractional Gaussian noise, that is, fractional Brownian motion and fractional Langevin-equation motion, are usually considered to be ergodic in the sense that, after an algebraic relaxation, time and ensemble averages of physical observables coincide. Recently it was demonstrated that fractional Brownian motion and fractional Langevin-equation motion under external confinement are transiently nonergodic—time and ensemble averages behave differently—from the moment when the particle starts to sense the confinement. Here we show that these processes also exhibit transient aging, that is, physical observables such as the time-averaged mean-squared displacement depend on the time lag between the initiation of the system at time t=0 and the start of the measurement at the aging time ta. In particular, it turns out that for fractional Langevin-equation motion the aging dependence on ta is different between the cases of free and confined motion. We obtain explicit analytical expressions for the aged moments of the particle position as well as the time-averaged mean-squared displacement and present a numerical analysis of this transient aging phenomenon.

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

    NASA Astrophysics Data System (ADS)

    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.

  13. Fractional Brownian motions: memory, diffusion velocity, and correlation functions

    NASA Astrophysics Data System (ADS)

    Fuliński, A.

    2017-02-01

    Fractional Brownian motions (FBMs) have been observed recently in the measured trajectories of individual molecules or small particles in the cytoplasm of living cells and in other dense composite systems, among others. Various types of FBMs differ in a number of ways, including the strength, range and type of damping of the memory encoded in their definitions, but share several basic characteristics: distributions, non-ergodic properties, and scaling of the second moment, which makes it difficult to determine which type of Brownian motion (fractional or normal) the measured trajectory belongs to. Here, we show, by introducing FBMs with regulated range and strength of memory, that it is the structure of memory which determines their physical properties, including mean velocity of diffusion; therefore, the course and kinetics of several processes (including coagulation and some chemical reactions). We also show that autocorrelation functions possess characteristic features which enable identification of an observed FBM, and of the type of memory governing its trajectory. In memoriam Marian Smoluchowski, on the 100th anniversary of the publication of his seminal papers on Brownian motion and diffusion-limited kinetics.

  14. Fractional Brownian Motion:. Theory and Application to DNA Walk

    NASA Astrophysics Data System (ADS)

    Lim, S. C.; Muniandy, S. V.

    2001-09-01

    This paper briefly reviews the theory of fractional Brownian motion (FBM) and its generalization to multifractional Brownian motion (MBM). FBM and MBM are applied to a biological system namely the DNA sequence. By considering a DNA sequence as a fractal random walk, it is possible to model the noncoding sequence of human retinoblastoma DNA as a discrete version of FBM. The average scaling exponent or Hurst exponent of the DNA walk is estimated to be H = 0.60 ± 0.05 using the monofractal R/S analysis. This implies that the mean square fluctuation of DNA walk belongs to anomalous superdiffusion type. We also show that the DNA landscape is not monofractal, instead one has multifractal DNA landscape. The empirical estimates of the Hurst exponent falls approximately within the range H ~ 0.62 - 0.72. We propose two multifractal models, namely the MBM and multiscale FBM to describe the existence of different Hurst exponents in DNA walk.

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

    PubMed

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

    2012-11-07

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

  16. Ergodic properties of fractional Brownian-Langevin motion.

    PubMed

    Deng, Weihua; Barkai, Eli

    2009-01-01

    We investigate the time average mean-square displacement delta;{2}[over ](x(t))=integral_{0};{t-Delta}[x(t;{'}+Delta)-x(t;{'})];{2}dt;{'}(t-Delta) for fractional Brownian-Langevin motion where x(t) is the stochastic trajectory and Delta is the lag time. Unlike the previously investigated continuous-time random-walk model, delta;{2}[over ] converges to the ensemble average x;{2} approximately t;{2H} in the long measurement time limit. The convergence to ergodic behavior is slow, however, and surprisingly the Hurst exponent H=3/4 marks the critical point of the speed of convergence. When H<3/4 , the ergodicity breaking parameter E_{B}=[[delta;{2}[over ](x(t))];{2}-delta;{2}[over ](x(t));{2}]/delta;{2}[over ](x(t));{2} approximately k(H)Deltat;{-1} , when H=3/4 , E_{B} approximately (9/16)(lnt)Deltat;{-1} , and when 3/41 ergodicity is broken and E_{B} approximately 2 . The critical point H=3/4 is marked by the divergence of the coefficient k(H) . Fractional Brownian motion as a model for recent experiments of subdiffusion of mRNA in the cell is briefly discussed, and a comparison with the continuous-time random-walk model is made.

  17. Ergodic properties of fractional Brownian-Langevin motion

    NASA Astrophysics Data System (ADS)

    Deng, Weihua; Barkai, Eli

    2009-01-01

    We investigate the time average mean-square displacement δ2¯(x(t))=∫0t-Δ[x(t'+Δ)-x(t')]2dt'/(t-Δ) for fractional Brownian-Langevin motion where x(t) is the stochastic trajectory and Δ is the lag time. Unlike the previously investigated continuous-time random-walk model, δ2¯ converges to the ensemble average ⟨x2⟩˜t2H in the long measurement time limit. The convergence to ergodic behavior is slow, however, and surprisingly the Hurst exponent H=(3)/(4) marks the critical point of the speed of convergence. When H<(3)/(4) , the ergodicity breaking parameter EB=[⟨[δ2¯(x(t))]2⟩-⟨δ2¯(x(t))⟩2]/⟨δ2¯(x(t))⟩2˜k(H)Δt-1 , when H=(3)/(4) , EB˜((9)/(16))(lnt)Δt-1 , and when (3)/(4)Fractional Brownian motion as a model for recent experiments of subdiffusion of mRNA in the cell is briefly discussed, and a comparison with the continuous-time random-walk model is made.

  18. Mean-squared-displacement statistical test for fractional Brownian motion

    NASA Astrophysics Data System (ADS)

    Sikora, Grzegorz; Burnecki, Krzysztof; Wyłomańska, Agnieszka

    2017-03-01

    Anomalous diffusion in crowded fluids, e.g., in cytoplasm of living cells, is a frequent phenomenon. A common tool by which the anomalous diffusion of a single particle can be classified is the time-averaged mean square displacement (TAMSD). A classical mechanism leading to the anomalous diffusion is the fractional Brownian motion (FBM). A validation of such process for single-particle tracking data is of great interest for experimentalists. In this paper we propose a rigorous statistical test for FBM based on TAMSD. To this end we analyze the distribution of the TAMSD statistic, which is given by the generalized chi-squared distribution. Next, we study the power of the test by means of Monte Carlo simulations. We show that the test is very sensitive for changes of the Hurst parameter. Moreover, it can easily distinguish between two models of subdiffusion: FBM and continuous-time random walk.

  19. Brownian motion

    NASA Astrophysics Data System (ADS)

    Lavenda, B. H.

    1985-02-01

    Brownian motion, the doubly random motion of small particles suspended in a liquid due to molecular collisions, and its implications and applications in the history of modern science are discussed. Topics examined include probabilistic phenomena, the kinetic theory of gases, Einstein's atomic theory of Brownian motion, particle displacement, diffusion measurements, the determination of the mass of the atom and of Avogadro's number, the statistical mechanics of thermodynamics, nonequilibrium systems, Langevin's equation of motion, time-reversed evolution, mathematical analogies, and applications in economics and radio navigation. Diagrams and drawings are provided.

  20. Brownian Motion.

    ERIC Educational Resources Information Center

    Lavenda, Bernard H.

    1985-01-01

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

  1. Brownian Motion.

    ERIC Educational Resources Information Center

    Lavenda, Bernard H.

    1985-01-01

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

  2. Pricing geometric Asian power options under mixed fractional Brownian motion environment

    NASA Astrophysics Data System (ADS)

    Prakasa Rao, B. L. S.

    2016-03-01

    It has been observed that the stock price process can be modeled with driving force as a mixed fractional Brownian motion with Hurst index H > 3/4 whenever long-range dependence is possibly present. We obtain a closed form expression for the price of a geometric Asian option under the mixed fractional Brownian motion environment. We consider also Asian power options when the payoff function is a power function.

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

    PubMed

    Delorme, Mathieu; Wiese, Kay Jörg

    2015-11-20

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

  4. Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions

    SciTech Connect

    Han Yuecai; Hu Yaozhong; Song Jian

    2013-04-15

    We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter H>1/2). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential equation driven by both fractional Brownian motions and the corresponding underlying standard Brownian motions. In addition to this backward equation, the maximum principle also involves the Malliavin derivatives. Our approach is to use conditioning and Malliavin calculus. To arrive at our maximum principle we need to develop some new results of stochastic analysis of the controlled systems driven by fractional Brownian motions via fractional calculus. Our approach of conditioning and Malliavin calculus is also applied to classical system driven by standard Brownian motions while the controller has only partial information. As a straightforward consequence, the classical maximum principle is also deduced in this more natural and simpler way.

  5. Existence and Stability Results for Second-Order Stochastic Equations Driven by Fractional Brownian Motion

    NASA Astrophysics Data System (ADS)

    Revathi, P.; Sakthivel, R.; Song, D.-Y.; Ren, Yong; Zhang, Pei

    2013-09-01

    Fractional Brownian motion has been widely used to model a number of phenomena in diverse fields of science and engineering. In this article, we investigate the existence, uniqueness and stability of mild solutions for a class of second-order nonautonomous neutral stochastic evolution equations with infinite delay driven by fractional Brownian motion (fBm) with Hurst parameter H ∈ (1/2, 1) in Hilbert spaces. More precisely, using semigroup theory and successive approximation approach, we establish a set of sufficient conditions for obtaining the required result under the assumption that coefficients satisfy non-Lipschitz condition with Lipschitz condition being considered as a special case. Further, the result is deduced to study the second-order autonomous neutral stochastic equations with fBm. The results generalize and improve some known results. Finally, as an application, stochastic wave equation with infinite delay driven by fractional Brownian motion is provided to illustrate the obtained theory.

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

    NASA Astrophysics Data System (ADS)

    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.

  7. Fractional non-Brownian motion and trapping-time distributions of grains in rice piles.

    PubMed

    Hopcraft, K I; Tanner, R M; Jakeman, E; Graves, J P

    2001-08-01

    Non-Gaussian height fluctuations occurring on the fueling time scale of a slowly driven rice pile match those observed in some turbulent/critical phenomena, forming an anticorrelated random fractal process with Hurst exponent H=0.2. Inspired by this observation, the concept of fractional Brownian motion (FBM) is extended to treat stochastic processes with skewed increments. Simulations of this process for antipersistent motion have first return time distribution deviating from the t(-2+H) law for FBM. The first return time distribution of this fractional non-Brownian motion describes and quantitatively determines the trapping-time distribution of grains in rice piles upon incorporating a continuous representation of the additional height fluctuations that occur on the time scale between fueling events.

  8. Optimal Control of Stochastic Systems Driven by Fractional Brownian Motions

    DTIC Science & Technology

    2014-10-09

    motion, Warsaw, Poland: Banach Center Publications, (12 2014) TOTAL: 2 PERCENT_SUPPORTEDNAME FTE Equivalent: Total Number: Discipline Cody Clifton 0.25...Discipline Collin Eubanks 0.25 Mathematics 0.25 1 NAME Total Number: Cody Clifton Theodore Lindsey 2 NAME Total Number: PERCENT_SUPPORTEDNAME FTE Equivalent

  9. Implicit Euler approximation of stochastic evolution equations with fractional Brownian motion

    NASA Astrophysics Data System (ADS)

    Kamrani, Minoo; Jamshidi, Nahid

    2017-03-01

    This work was intended as an attempt to motivate the approximation of quasi linear evolution equations driven by infinite-dimensional fractional Brownian motion with Hurst parameter H >1/2 . The spatial approximation method is based on Galerkin and the temporal approximation is based on implicit Euler scheme. An error bound and the convergence of the numerical method are given. The numerical results show usefulness and accuracy of the method.

  10. Mackey-Glass equation driven by fractional Brownian motion

    NASA Astrophysics Data System (ADS)

    Nguyen, Dung Tien

    2012-11-01

    In this paper we introduce a fractional stochastic version of the Mackey-Glass model which is a potential candidate to model objects in biology and finance. By a semi-martingale approximate approach we find an semi-analytical expression for the solution.

  11. Fractional Brownian motion, the Matérn process, and stochastic modeling of turbulent dispersion

    NASA Astrophysics Data System (ADS)

    Lilly, Jonathan M.; Sykulski, Adam M.; Early, Jeffrey J.; Olhede, Sofia C.

    2017-08-01

    Stochastic processes exhibiting power-law slopes in the frequency domain are frequently well modeled by fractional Brownian motion (fBm), with the spectral slope at high frequencies being 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 Matérn 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 Matérn process and its relationship to fBm. An algorithm for the simulation of the Matérn process in O(NlogN) operations is given. Unlike fBm, the Matérn process is found to provide an excellent match to modeling velocities from particle trajectories in an application to two-dimensional fluid turbulence.

  12. Fractional Brownian Motion with Stochastic Variance:. Modeling Absolute Returns in STOCK Markets

    NASA Astrophysics Data System (ADS)

    Roman, H. E.; Porto, M.

    We discuss a model for simulating a long-time memory in time series characterized in addition by a stochastic variance. The model is based on a combination of fractional Brownian motion (FBM) concepts, for dealing with the long-time memory, with an autoregressive scheme with conditional heteroskedasticity (ARCH), responsible for the stochastic variance of the series, and is denoted as FBMARCH. Unlike well-known fractionally integrated autoregressive models, FBMARCH admits finite second moments. The resulting probability distribution functions have power-law tails with exponents similar to ARCH models. This idea is applied to the description of long-time autocorrelations of absolute returns ubiquitously observed in stock markets.

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

    NASA Astrophysics Data System (ADS)

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

    2014-10-01

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

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

    PubMed

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

    2014-10-01

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

  15. Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion

    PubMed Central

    Sun, Jiao-Jiao; Zhou, Shengwu; Zhang, Yan; Han, Miao; Wang, Fei

    2014-01-01

    The pricing problem of lookback option with a fixed proportion of transaction costs is investigated when the underlying asset price follows a fractional Brownian motion process. Firstly, using Leland's hedging method a partial differential equation satisfied by the value of the lookback option is derived. Then we obtain its numerical solution by constructing a Crank-Nicolson format. Finally, the effectiveness of the proposed form is verified through a numerical example. Meanwhile, the impact of transaction cost rate and volatility on lookback option value is discussed. PMID:27433525

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

    NASA Astrophysics Data System (ADS)

    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)), 0<α<1, here dX(τ)=μX(τ)(2H+σX(τ)dBH(τ), as a model of asset prices, which captures the subdiffusive characteristic of financial markets. We find the corresponding subdiffusive Black-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.

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

    NASA Astrophysics Data System (ADS)

    Chen, Yao; Wang, Xudong; Deng, Weihua

    2017-10-01

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

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

    NASA Astrophysics Data System (ADS)

    Chen, Yao; Wang, Xudong; Deng, Weihua

    2017-08-01

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

  19. The pricing of credit default swaps under a generalized mixed fractional Brownian motion

    NASA Astrophysics Data System (ADS)

    He, Xinjiang; Chen, Wenting

    2014-06-01

    In this paper, we consider the pricing of the CDS (credit default swap) under a GMFBM (generalized mixed fractional Brownian motion) model. As the name suggests, the GMFBM model is indeed a generalization of all the FBM (fractional Brownian motion) models used in the literature, and is proved to be able to effectively capture the long-range dependence of the stock returns. To develop the pricing mechanics of the CDS, we firstly derive a sufficient condition for the market modeled under the GMFBM to be arbitrage free. Then under the risk-neutral assumption, the CDS is fairly priced by investigating the two legs of the cash flow involved. The price we obtained involves elementary functions only, and can be easily implemented for practical purpose. Finally, based on numerical experiments, we analyze quantitatively the impacts of different parameters on the prices of the CDS. Interestingly, in comparison with all the other FBM models documented in the literature, the results produced from the GMFBM model are in a better agreement with those calculated from the classical Black-Scholes model.

  20. Simulation of 3D tidal flat topography based on fractional Brownian motion

    NASA Astrophysics Data System (ADS)

    Li, Xing; Wu, Wen; Zhou, Yunxuan; Zhang, Junru

    2010-11-01

    The intertidal zone as is one of the most dynamic areas on the earth and conducting topographic surveys is very difficult. It is particularly hard to obtain elevation information when the tidal flat is a mud flat. In this article, we selected Jiuduansha (Jiuduan Shoal) tidal flat as a test area to demonstrate a fractional Brownian motion model based tidal flat elevation estimation. The Jiuduansha is a large shoal with a large mud flat located in the Changjiang River Estuary. Two Landsat TM images and two CBERS CCD images acquired in different seasons in 2008 were processed and waterlines were extracted from images of different times according to the tidal conditions. By considering the fact that the water surface is actually a curved surface, we dissected the waterlines into waterside points and assigned an elevation value to every point through interpolation of the tidal level data taken from nearby tidal observation stations at the similar time when the satellite images were acquired. With the elevation data of the waterside points and digital sea chart depth data, a digital elevation model (DEM) was constructed using the fractional Brownian motion (fBm) model with a midpoint displacement algorithm through the Matlab toolbox. Finally, a quantitative validation of the model was completed using the 17 ground survey data positions on the tidal flat measured in November 2008. The simulation results show a good visual effect and high precision. The mean square root error is 0.155m respectively for the ground survey.

  1. Simulation of 3D tidal flat topography based on fractional Brownian motion

    NASA Astrophysics Data System (ADS)

    Li, Xing; Wu, Wen; Zhou, Yunxuan; Zhang, Junru

    2009-09-01

    The intertidal zone as is one of the most dynamic areas on the earth and conducting topographic surveys is very difficult. It is particularly hard to obtain elevation information when the tidal flat is a mud flat. In this article, we selected Jiuduansha (Jiuduan Shoal) tidal flat as a test area to demonstrate a fractional Brownian motion model based tidal flat elevation estimation. The Jiuduansha is a large shoal with a large mud flat located in the Changjiang River Estuary. Two Landsat TM images and two CBERS CCD images acquired in different seasons in 2008 were processed and waterlines were extracted from images of different times according to the tidal conditions. By considering the fact that the water surface is actually a curved surface, we dissected the waterlines into waterside points and assigned an elevation value to every point through interpolation of the tidal level data taken from nearby tidal observation stations at the similar time when the satellite images were acquired. With the elevation data of the waterside points and digital sea chart depth data, a digital elevation model (DEM) was constructed using the fractional Brownian motion (fBm) model with a midpoint displacement algorithm through the Matlab toolbox. Finally, a quantitative validation of the model was completed using the 17 ground survey data positions on the tidal flat measured in November 2008. The simulation results show a good visual effect and high precision. The mean square root error is 0.155m respectively for the ground survey.

  2. From Ornstein-Uhlenbeck dynamics to long-memory processes and fractional Brownian motion

    NASA Astrophysics Data System (ADS)

    Eliazar, Iddo; Klafter, Joseph

    2009-02-01

    This article establishes a natural physical path leading from “regular” Ornstein-Uhlenbeck dynamics to “anomalous” long-memory processes and, thereafter, to fractional Brownian motion. Considering a system composed of n different parts—each part conducting its own Ornstein-Uhlenbeck dynamics, and all parts being perturbed by a common external Lévy noise—we show that the collective system-dynamics, in the limit n→∞ , converges to a temporal moving-average of the driving noise. The limiting moving-average process, in turn, can posses a long memory—in which case, when observed over large time scales, further yields fractional Brownian motion. The temporal correlation structure of the limiting moving-average process turns out to be determined by the structural statistical variability of the system’s composing parts. Thus, the emergence of a long memory is a consequence of the intrinsic “quenched disorder” present at the system’s formation epoch rather than the consequence of the external annealed disorder carried in continuously by the driving noise.

  3. Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks

    NASA Astrophysics Data System (ADS)

    Ni, Xiao-Hui; Jiang, Zhi-Qiang; Zhou, Wei-Xing

    2009-10-01

    The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent α is a linear function of the Hurst index H of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from three Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the α∼H linear relationship.

  4. Inverse Gaussian and its inverse process as the subordinators of fractional Brownian motion.

    PubMed

    Wyłomańska, A; Kumar, A; Połoczański, R; Vellaisamy, P

    2016-10-01

    In this paper we study the fractional Brownian motion (FBM) time changed by the inverse Gaussian (IG) process and its inverse, called the inverse to the inverse Gaussian (IIG) process. Some properties of the time-changed processes are similar to those of the classical FBM, such as long-range dependence. However, one can also observe different characteristics that are not satisfied by the FBM. We study the distributional properties of both subordinators, namely, IG and IIG processes, and also that of the FBM time changed by these subordinators. We establish also the connections between the subordinated processes considered and the continuous-time random-walk model. For the application part, we introduce the simulation procedures for both processes and discuss the estimation schemes for their parameters. The effectiveness of these methods is checked for simulated trajectories.

  5. Inverse Gaussian and its inverse process as the subordinators of fractional Brownian motion

    NASA Astrophysics Data System (ADS)

    Wyłomańska, A.; Kumar, A.; Połoczański, R.; Vellaisamy, P.

    2016-10-01

    In this paper we study the fractional Brownian motion (FBM) time changed by the inverse Gaussian (IG) process and its inverse, called the inverse to the inverse Gaussian (IIG) process. Some properties of the time-changed processes are similar to those of the classical FBM, such as long-range dependence. However, one can also observe different characteristics that are not satisfied by the FBM. We study the distributional properties of both subordinators, namely, IG and IIG processes, and also that of the FBM time changed by these subordinators. We establish also the connections between the subordinated processes considered and the continuous-time random-walk model. For the application part, we introduce the simulation procedures for both processes and discuss the estimation schemes for their parameters. The effectiveness of these methods is checked for simulated trajectories.

  6. Sampling fractional Brownian motion in presence of absorption: a Markov chain method.

    PubMed

    Hartmann, Alexander K; Majumdar, Satya N; Rosso, Alberto

    2013-08-01

    We numerically study fractional Brownian motion (fBm) with an absorbing boundary at the origin for selected values of the Hurst exponent Hε[0,1]. Using a Monte Carlo sampling technique, we are able to numerically generate these fBm processes at discrete times for up to 10(7) time steps, even for values as small as H=1/4. The results are compatible with previous analytical results that suggest that the distribution of (rescaled) endpoints y follow a power law P(+)(y)~y(φ) with φ=(1-H)/H, even for small values of H. Furthermore, for H=0.5 we study analytically the finite-length corrections to first order, namely a plateau of P(+)(y) for y→0 which decreases with increasing process length. These corrections are compatible with our numerical results.

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

    PubMed

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

    2012-11-07

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

  8. Center of gravity motions and ankle joint stiffness control in upright undisturbed stance modeled through a fractional Brownian motion framework.

    PubMed

    Rougier, P; Caron, O

    2000-12-01

    The authors modeled the center of gravity vertical projection (CG(v)) and the difference, CP - CG(v), which, combined, constitute the center of pressure (CP) trajectory, as fractional Brownian motion in order to investigate their relative contributions and their spatiotemporal articulation. The results demonstrated that CG(v) and CP - CG(v) motions are both endowed in complementary fashion with strong stochastic and part-deterministic behaviors. In addition, if the temporal coordinates remain similar for all 3 trajectories by definition, the switch between the successive control mechanisms appears for shorter displacements for CP - CG(v) and CG(v) than for CP trajectories. Results deduced from both input (CG(v)) and muscular stiffness (CP - CG(v)) thus provide insight into the way the central nervous system regulates stance control and in particular how CG and CP - CG are controlled.

  9. Brownian motion of graphene.

    PubMed

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

    2010-12-28

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

  10. Existence and exponential stability for neutral stochastic integrodifferential equations with impulses driven by a fractional Brownian motion

    NASA Astrophysics Data System (ADS)

    Arthi, G.; Park, Ju H.; Jung, H. Y.

    2016-03-01

    In this paper, we establish the results on existence and uniqueness of mild solution of impulsive neutral stochastic integrodifferential equations driven by a fractional Brownian motion. Further, by using an impulsive integral inequality, some novel sufficient conditions are derived to ensure the exponential stability of mild solution in the mean square moment. The results are obtained by utilizing the fractional power of operators and the semigroup theory. Finally, an example is presented to demonstrate the effectiveness of the proposed result.

  11. Noncommutative Brownian motion

    NASA Astrophysics Data System (ADS)

    Santos, Willien O.; Almeida, Guilherme M. A.; Souza, Andre M. C.

    2017-08-01

    We investigate the classical Brownian motion of a particle in a two-dimensional noncommutative (NC) space. Using the standard NC algebra embodied by the symplectic Weyl-Moyal formalism we find that noncommutativity induces a nonvanishing correlation between both coordinates at different times. The effect stands out as a signature of spatial noncommutativity and thus could offer a way to experimentally detect the phenomena. We further discuss some limiting scenarios and the trade-off between the scale imposed by the NC structure and the parameters of the Brownian motion itself.

  12. APPARENT/SPURIOUS MULTIFRACTALITY OF DATA SAMPLED FROM FRACTIONAL BROWNIAN/LÉVY MOTIONS (Invited)

    NASA Astrophysics Data System (ADS)

    Neuman, S. P.

    2009-12-01

    Many earth and environmental variables appear to be self-affine (monofractal) or multifractal with spatial (or temporal) increments having exceedance probability tails that decay as powers of -α where 1 < α ≤ 2. The increments can often be characterized by zero-mean symmetric stable distributions with Lévy indices α, suggesting that the variables are samples from corresponding random fields (or processes) constituting fractional Lévy motions (fLm); when α = 2 the distribution is Gaussian and the field constitutes fractional Brownian motion (fBm). The literature considers self-affine and multifractal modes of scaling to be fundamentally different, the first arising from additive and the second from multiplicative random fields or processes. We demonstrate theoretically that data having finite support, sampled across a finite domain from one realization of an additive Gaussian field forming fBm, give rise to positive square (or absolute) increments which behave as if the field was multifractal when in fact it is monofractal. Sampling such data from fLm with 1 < α < 2 causes them to exhibit spurious multifractality. Many data that appear to scale in a qualitatively similar manner (e.g., experimental and simulated turbulent velocities, some simulated porous flow velocities, landscape elevations, rain intensities, river network area and width functions, river flow series, soil water storage and physical properties) have been considered in the literature to be multifractal. It may be worth checking how closely such variables would fit monofractal models of the kind considered in this talk quantitatively.

  13. Fractional Brownian motion time-changed by gamma and inverse gamma process

    NASA Astrophysics Data System (ADS)

    Kumar, A.; Wyłomańska, A.; Połoczański, R.; Sundar, S.

    2017-02-01

    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 kinds 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 rescaled modified cumulative distribution function for estimation of parameters of the second considered process. This method is very useful in description of rounded data, like waiting times of subordinated processes delayed by inverse subordinators. By using the Monte Carlo method we show the effectiveness of proposed estimation procedures. Finally, we present the applications of proposed models to real time series.

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

    NASA Astrophysics Data System (ADS)

    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.

  15. Fractional Brownian Motion and Geodesic Rao Distance for Bone X-ray Image Characterization.

    PubMed

    El Hassouni, Mohammed; Tafraouti, Abdessamad; Toumi, Hechmi; Lespessailles, Eric; Jennane, Rachid

    2016-10-19

    Osteoporosis diagnosis has attracted particular attention in recent decades. Textured images from the microarchitecture of osteoporotic and healthy subjects show a high degree of similarity, increasing the difficulty of classifying such textures. Thus, the evaluation of osteoporosis from bone X-ray images presents a major challenge for pattern recognition and medical applications. The purpose of this paper is to use the fractional Brownian motion (fBm) model and the Probability Density Function (PDF) of its increments to compute a similarity measure with the Rao geodesic distance to classify trabecular bone X-ray images. When evaluated on synthetic fBm images (test vectors) with the well-known Hurst parameter H, the proposed method met our expectations in that a good classification of the synthetic images was achieved. A clinical study was conducted on textured bone X-ray images from two different female populations of osteoporotic patients (fracture cases) and control subjects. Using the proposed method, an Area Under Curve (AUC) rate of 97% was achieved.

  16. On the first crossing distributions in fractional Brownian motion and the mass function of dark matter haloes

    NASA Astrophysics Data System (ADS)

    Hiotelis, Nicos; Del Popolo, Antonino

    2017-03-01

    We construct an integral equation for the first crossing distributions for fractional Brownian motion in the case of a constant barrier and we present an exact analytical solution. Additionally we present first crossing distributions derived by simulating paths from fractional Brownian motion. We compare the results of the analytical solutions with both those of simulations and those of some approximated solutions which have been used in the literature. Finally, we present multiplicity functions for dark matter structures resulting from our analytical approach and we compare with those resulting from N-body simulations. We show that the results of analytical solutions are in good agreement with those of path simulations but differ significantly from those derived from approximated solutions. Additionally, multiplicity functions derived from fractional Brownian motion are poor fits of the those which result from N-body simulations. We also present comparisons with other models which are exist in the literature and we discuss different ways of improving the agreement between analytical results and N-body simulations.

  17. Fractional Brownian motion and fractional Gaussian noise in subsurface hydrology: A review, presentation of fundamental properties, and extensions

    NASA Astrophysics Data System (ADS)

    Molz, F. J.; Liu, H. H.; Szulga, J.

    Recent studies have shown that fractional Brownian motion (fBm) and fractional Gaussian noise (fGn) are useful in characterizing subsurface heterogeneities in addition to geophysical time series. Although these studies have led to a fairly good understanding of some aspects of fBm/fGn, a comprehensive introduction to these stochastic, fractal functions is still lacking in the subsurface hydrology literature. In this paper, efforts have been made to define fBm/fGn and present a development of their mathematical properties in a direct yet rigorous manner. Use of the spectral representation theorem allows one to derive spectral representations for fBm/fGn even though these functions do not have classical Fourier transforms. The discrete and truncated forms of these representations have served as a basis for synthetic generation of fBm/fGn. The discrete spectral representations are developed and various implications discussed. In particular, it is shown that a discrete form of the fBm spectral representation is equivalent to the well known Weierstrass-Mandelbrot random fractal function. Although the full implications are beyond the scope of the present paper, it is observed that discrete spectral representations of fBm constitute stationary processes even though fBm is nonstationary. A new and general spectral density function is introduced for construction of complicated, anisotropic, (3-D) fractals, including those characterized by vertical fGn and horizontal fBm. Such fractals are useful for modeling anisotropic subsurface heterogeneities but cannot be generated with existing schemes. Finally, some basic properties of fractional Lévy motion and concepts of universal multifractals, which can be considered as generalizations of fBm/fGn, are reviewed briefly.

  18. Extremal-point density of scaling processes: From fractional Brownian motion to turbulence in one dimension

    NASA Astrophysics Data System (ADS)

    Huang, Yongxiang; Wang, Lipo; Schmitt, F. G.; Zheng, Xiaobo; Jiang, Nan; Liu, Yulu

    2017-07-01

    In recent years several local extrema-based methodologies have been proposed to investigate either the nonlinear or the nonstationary time series for scaling analysis. In the present work, we study systematically the distribution of the local extrema for both synthesized scaling processes and turbulent velocity data from experiments. The results show that for the fractional Brownian motion (fBm) without intermittency correction the measured extremal-point-density (EPD) agrees well with a theoretical prediction. For a multifractal random walk (MRW) with the lognormal statistics, the measured EPD is independent of the intermittency parameter μ , suggesting that the intermittency correction does not change the distribution of extremal points but changes the amplitude. By introducing a coarse-grained operator, the power-law behavior of these scaling processes is then revealed via the measured EPD for different scales. For fBm the scaling exponent ξ (H ) is found to be ξ (H )=H , where H is Hurst number, while for MRW ξ (μ ) shows a linear relation with the intermittency parameter μ . Such EPD approach is further applied to the turbulent velocity data obtained from a wind tunnel flow experiment with the Taylor scale λ -based Reynolds number Reλ=720 , and a turbulent boundary layer with the momentum thickness θ based Reynolds number Reθ=810 . A scaling exponent ξ ≃0.37 is retrieved for the former case. For the latter one, the measured EPD shows clearly four regimes, which agrees well with the corresponding sublayer structures inside the turbulent boundary layer.

  19. Ultraslow scaled Brownian motion

    NASA Astrophysics Data System (ADS)

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

    2015-06-01

    We define and study in detail utraslow scaled Brownian motion (USBM) characterized by a time dependent diffusion coefficient of the form D(t)≃ 1/t. For unconfined motion the mean squared displacement (MSD) of USBM exhibits an ultraslow, logarithmic growth as function of time, in contrast to the conventional scaled Brownian motion. In a harmonic potential the MSD of USBM does not saturate but asymptotically decays inverse-proportionally to time, reflecting the highly non-stationary character of the process. We show that the process is weakly non-ergodic in the sense that the time averaged MSD does not converge to the regular MSD even at long times, and for unconfined motion combines a linear lag time dependence with a logarithmic term. The weakly non-ergodic behaviour is quantified in terms of the ergodicity breaking parameter. The USBM process is also shown to be ageing: observables of the system depend on the time gap between initiation of the test particle and start of the measurement of its motion. Our analytical results are shown to agree excellently with extensive computer simulations.

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

    PubMed

    Sanders, Lloyd P; Ambjörnsson, Tobias

    2012-05-07

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

  1. Aging scaled Brownian motion

    NASA Astrophysics Data System (ADS)

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

    2015-04-01

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

  2. Aging scaled Brownian motion.

    PubMed

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

    2015-04-01

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

  3. Relativistic Brownian motion

    NASA Astrophysics Data System (ADS)

    Dunkel, Jörn; Hänggi, Peter

    2009-02-01

    Over the past one hundred years, Brownian motion theory has contributed substantially to our understanding of various microscopic phenomena. Originally proposed as a phenomenological paradigm for atomistic matter interactions, the theory has since evolved into a broad and vivid research area, with an ever increasing number of applications in biology, chemistry, finance, and physics. The mathematical description of stochastic processes has led to new approaches in other fields, culminating in the path integral formulation of modern quantum theory. Stimulated by experimental progress in high energy physics and astrophysics, the unification of relativistic and stochastic concepts has re-attracted considerable interest during the past decade. Focusing on the framework of special relativity, we review, here, recent progress in the phenomenological description of relativistic diffusion processes. After a brief historical overview, we will summarize basic concepts from the Langevin theory of nonrelativistic Brownian motions and discuss relevant aspects of relativistic equilibrium thermostatistics. The introductory parts are followed by a detailed discussion of relativistic Langevin equations in phase space. We address the choice of time parameters, discretization rules, relativistic fluctuation-dissipation theorems, and Lorentz transformations of stochastic differential equations. The general theory is illustrated through analytical and numerical results for the diffusion of free relativistic Brownian particles. Subsequently, we discuss how Langevin-type equations can be obtained as approximations to microscopic models. The final part of the article is dedicated to relativistic diffusion processes in Minkowski spacetime. Since the velocities of relativistic particles are bounded by the speed of light, nontrivial relativistic Markov processes in spacetime do not exist; i.e., relativistic generalizations of the nonrelativistic diffusion equation and its Gaussian solutions

  4. Visual information and expert's idea in Hurst index estimation of the fractional Brownian motion using a diffusion type approximation.

    PubMed

    Taheriyoun, Ali R; Moghimbeygi, Meisam

    2017-02-14

    An approximation of the fractional Brownian motion based on the Ornstein-Uhlenbeck process is used to obtain an asymptotic likelihood function. Two estimators of the Hurst index are then presented in the likelihood approach. The first estimator is produced according to the observed values of the sample path; while the second one employs the likelihood function of the incremental process. We also employ visual roughness of realization to restrict the parameter space and to obtain prior information in Bayesian approach. The methods are then compared with three contemporary estimators and an experimental data set is studied.

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

    NASA Astrophysics Data System (ADS)

    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.

  6. Motion of chromosomal loci and the mean-squared displacement of a fractional Brownian motion in the presence of static and dynamic errors

    NASA Astrophysics Data System (ADS)

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

    2015-03-01

    Mean-squared displacement (MSD) analysis is one of the most prevalent tools employed in the application of single-particle tracking to biological systems. In camera-based tracking, the effects of "static error" due to photon fluctuations and "dynamic error" due to motion blur on the MSD have been well-characterized for the case of pure Brownian motion, producing a known constant offset to the straight-line MSD. However, particles tracked in cellular environments often do not undergo pure Brownian motion, but instead can for instance exhibit anomalous diffusion wherein the MSD curve obeys a power law with respect to time, MSD=2D*τα, where D* is an effective diffusion coefficient and 0 < α <= 1. There are a number of models that can explain anomalous diffusive behavior in different subcellular contexts. Of these models, fractional Brownian motion (FBM) has been shown to accurately describe the motion of labeled particles such as mRNA and chromosomal loci as they traverse the cytoplasm or nucleoplasm (i.e. crowded viscoelastic environments). Despite the importance of FBM in biological tracking, there has yet to be a complete treatment of the MSD in the presence of static and dynamic errors analogous to the special case of pure Brownian motion. We here present a closed-form, analytical expression of the FBM MSD in the presence of both types of error. We have previously demonstrated its value in live-cell data by applying it to the study of chromosomal locus motion in budding yeast cells. Here we focus on validations in simulated data.

  7. 111 years of Brownian motion

    PubMed Central

    Kim, Changho

    2017-01-01

    We consider the Brownian motion of a particle and present a tutorial review over the last 111 years since Einstein’s paper in 1905. We describe Einstein’s model, Langevin’s model and the hydrodynamic models, with increasing sophistication on the hydrodynamic interactions between the particle and the fluid. In recent years, the effects of interfaces on the nearby Brownian motion have been the focus of several investigations. We summarize various results and discuss some of the controversies associated with new findings about the changes in Brownian motion induced by the interface. PMID:27396746

  8. 111 years of Brownian motion.

    PubMed

    Bian, Xin; Kim, Changho; Karniadakis, George Em

    2016-08-14

    We consider the Brownian motion of a particle and present a tutorial review over the last 111 years since Einstein's paper in 1905. We describe Einstein's model, Langevin's model and the hydrodynamic models, with increasing sophistication on the hydrodynamic interactions between the particle and the fluid. In recent years, the effects of interfaces on the nearby Brownian motion have been the focus of several investigations. We summarize various results and discuss some of the controversies associated with new findings about the changes in Brownian motion induced by the interface.

  9. Brownian motion from Boltzmann's equation.

    NASA Technical Reports Server (NTRS)

    Montgomery, D.

    1971-01-01

    Two apparently disparate lines of inquiry in kinetic theory are shown to be equivalent: (1) Brownian motion as treated by the (stochastic) Langevin equation and Fokker-Planck equation; and (2) Boltzmann's equation. The method is to derive the kinetic equation for Brownian motion from the Boltzmann equation for a two-component neutral gas by a simultaneous expansion in the density and mass ratios.

  10. Entropic forces in Brownian motion

    NASA Astrophysics Data System (ADS)

    Roos, Nico

    2014-12-01

    Interest in the concept of entropic forces has risen considerably since Verlinde proposed in 2011 to interpret the force in Newton's second law and gravity as entropic forces. Brownian motion—the motion of a small particle (pollen) driven by random impulses from the surrounding molecules—may be the first example of a stochastic process in which such forces are expected to emerge. In this article, it is shown that at least two types of entropic force can be identified in three-dimensional Brownian motion. This analysis yields simple derivations of known results of Brownian motion, Hooke's law, and—applying an external (non-radial) force—Curie's law and the Langevin-Debye equation.

  11. Discretization of Stationary Solutions of Stochastic Systems Driven by Fractional Brownian Motion

    SciTech Connect

    Garrido-Atienza, Maria J. Kloeden, Peter E. Neuenkirch, Andreas

    2009-10-15

    In this article we study the behavior of dissipative systems with additive fractional noise of any Hurst parameter. Under a one-sided dissipative Lipschitz condition on the drift the continuous stochastic system is shown to have a unique stationary solution, which pathwise attracts all other solutions. The same holds for the discretized stochastic system, if the drift-implicit Euler method is used for the discretization. Moreover, the unique stationary solution of the drift-implicit Euler scheme converges to the unique stationary solution of the original system as the stepsize of the discretization decreases.

  12. p-adic Brownian motion

    NASA Astrophysics Data System (ADS)

    Zelenov, E. I.

    2016-12-01

    We define p-adic Brownian motion (Wiener process) and study its properties. We construct a presentation of the trajectories of this process by their series expansions with respect to van der Put's basis and show that they are nowhere differentiable functions satisfying the p-adic Lipschitz condition of order 1. We define the p-adic Wiener measure on the space of continuous functions and study its properties.

  13. Influence of visual feedback on successive control mechanisms in upright quiet stance in humans assessed by fractional Brownian motion modelling.

    PubMed

    Rougier, P

    1999-05-14

    An up-to-date way to model the centre of pressure (CP) trajectories may consist in using fractional Brownian motion (fBm). By doing so, one may note that standing still is in fact controlled by two separate and successive mechanisms. The point raised in this study concerns the nature of these control mechanisms and their level of interaction. Following this idea, visual feedback (VFB), which is known to affect postural control by significantly decreasing sway magnitudes, was used. Twelve healthy adults, instructed to stand as still as possible, were tested under this VFB protocol (via a PC screen). In order to model the CP trajectories as fBm, variograms (mean square distances, MSD, expressed as a function of increasing time intervals deltat) were bi-logarithmically plotted. The main visual effect of VFB on these variograms concerns longest latency scaling regimes which reveal less stochastic and consequently more accurate control (P < 0.05 and P < 0.01 for X and Y components, respectively). An increase in the MSD of the transition point, which corresponds to the switch between the two control mechanisms, is also noted (P < 0.05). Overall, evidence is provided from this data that long latency scaling regimes do operate through a feedback process. Interestingly, this improved determinism in feedback control in turn induces a similar effect on the control operating over the shortest deltat. Thus, by privileging a control strategy based on feedback mechanisms, VFB in turn would make the subjects quicker in their initial displacement in order to reach a position capable of initiating a feedback mechanism.

  14. Fractional Levy motion through path integrals

    SciTech Connect

    Calvo, Ivan; Sanchez, Raul; Carreras, Benjamin A

    2009-01-01

    Fractional Levy motion (fLm) is the natural generalization of fractional Brownian motion in the context of self-similar stochastic processes and stable probability distributions. In this paper we give an explicit derivation of the propagator of fLm by using path integral methods. The propagators of Brownian motion and fractional Brownian motion are recovered as particular cases. The fractional diffusion equation corresponding to fLm is also obtained.

  15. Constructive role of Brownian motion: Brownian motors and Stochastic Resonance

    NASA Astrophysics Data System (ADS)

    Hänggi, Peter

    2005-03-01

    Noise is usually thought of as the enemy of order rather as a constructive influence. For the phenomena of Stochastic Resonance [1] and Brownian motors [2], however, stochastic noise can play a beneficial role in enhancing detection and/or facilitating directed transmission of information in absence of biasing forces. Brownian motion assisted Stochastic Resonance finds useful applications in physical, technological, biological and biomedical contexts [1,3]. The basic principles that underpin Stochastic Resonance are elucidated and novel applications for nonlinear classical and quantum systems will be addressed. The presence of non-equilibrium disturbances enables to rectify Brownian motion so that quantum and classical objects can be directed around on a priori designed routes in biological and physical systems (Brownian motors). In doing so, the energy from the haphazard motion of (quantum) Brownian particles is extracted to perform useful work against an external load. This very concept together with first experimental realizations are discussed [2,4,5]. [1] L. Gammaitoni, P. Hä'nggi, P. Jung and F. Marchesoni, Stochastic Resonance, Rev. Mod. Phys. 70, 223 (1998).[2] R. D. Astumian and P. Hä'nggi, Brownian motors, Physics Today 55 (11), 33 (2002).[3] P. Hä'nggi, Stochastic Resonace in Physics and Biology, ChemPhysChem 3, 285 (2002).[4] H. Linke, editor, Special Issue on Brownian Motors, Applied Physics A 75, No. 2 (2002).[5] P. Hä'nggi, F. Marchesoni, F. Nori, Brownian motors, Ann. Physik (Leipzig) 14, xxx (2004); cond-mat/0410033.

  16. Superdiffusive trajectories in Brownian motion.

    PubMed

    Duplat, Jérôme; Kheifets, Simon; Li, Tongcang; Raizen, Mark G; Villermaux, Emmanuel

    2013-02-01

    The Brownian motion of a microscopic particle in a fluid is one of the cornerstones of statistical physics and the paradigm of a random process. One of the most powerful tools to quantify it was provided by Langevin, who explicitly accounted for a short-time correlated "thermal" force. The Langevin picture predicts ballistic motion, ~t(2) at short-time scales, and diffusive motion ~t at long-time scales, where x is the displacement of the particle during time t, and the average is taken over the thermal distribution of initial conditions. The Langevin equation also predicts a superdiffusive regime, where ~t(3), under the condition that the initial velocity is fixed rather than distributed thermally. We analyze the motion of an optically trapped particle in air and indeed find t(3) dispersion. This observation is a direct proof of the existence of the random, rapidly varying force imagined by Langevin.

  17. Quantum explanation of Brownian motion

    NASA Astrophysics Data System (ADS)

    Gyftopoulos, Elias P.

    2005-04-01

    In ``Investigations of the Brownian movement'', Einstein bases his arguments ``on the molecular-kinetic theory of heat.'' In this article, I provide incontrovertible evidence against the molecular-kinetic conception of heat, and an explanation of Brownian motion that differs from all procedures in the archival literature. The explanation is based on two revolutionary theories, one thermodynamic, and the other quantum mechanical. No heat is involved because heat is a mode of interaction and not a property of any system. In a system that consists of constant amounts and volumes of a solvent and an insoluble solute, the shapes of the two volumes change continuously in time as solvent and solute try to interpenetrate each other as a result of differences in total potentials. The shape changes affect the energy eigenstates that enter the expressions of the stable equilibrium states of solvent and solute. A nonlinear quantum mechanical equation of motion that we conceived redistributes the constituents of the solvent and the solute to the continuously varying density operators without affecting the energy, the amounts of constituents, the volumes, and the entropy of either subsystem. The equation of motion is neither the Schroedinger nor the von Neumann equation because the effects of shape changes are nonunitary. The processes just cited are everlasting because the favorable but ineffective total potential differences are everlasting.

  18. Brownian motion of helical flagella.

    PubMed

    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.

  19. On the excursions of drifted Brownian motion and the successive passage times of Brownian motion

    NASA Astrophysics Data System (ADS)

    Abundo, Mario

    2016-09-01

    By using the law of the excursions of Brownian motion with drift, we find the distribution of the nth passage time of Brownian motion through a straight line S(t) = a + bt. In the special case when b = 0, we extend the result to a space-time transformation of Brownian motion.

  20. Visual information and expert’s idea in Hurst index estimation of the fractional Brownian motion using a diffusion type approximation

    NASA Astrophysics Data System (ADS)

    Taheriyoun, Ali R.; Moghimbeygi, Meisam

    2017-02-01

    An approximation of the fractional Brownian motion based on the Ornstein-Uhlenbeck process is used to obtain an asymptotic likelihood function. Two estimators of the Hurst index are then presented in the likelihood approach. The first estimator is produced according to the observed values of the sample path; while the second one employs the likelihood function of the incremental process. We also employ visual roughness of realization to restrict the parameter space and to obtain prior information in Bayesian approach. The methods are then compared with three contemporary estimators and an experimental data set is studied.

  1. Visual information and expert’s idea in Hurst index estimation of the fractional Brownian motion using a diffusion type approximation

    PubMed Central

    Taheriyoun, Ali R.; Moghimbeygi, Meisam

    2017-01-01

    An approximation of the fractional Brownian motion based on the Ornstein-Uhlenbeck process is used to obtain an asymptotic likelihood function. Two estimators of the Hurst index are then presented in the likelihood approach. The first estimator is produced according to the observed values of the sample path; while the second one employs the likelihood function of the incremental process. We also employ visual roughness of realization to restrict the parameter space and to obtain prior information in Bayesian approach. The methods are then compared with three contemporary estimators and an experimental data set is studied. PMID:28195153

  2. Microscopic derivation of open quantum Brownian motion

    NASA Astrophysics Data System (ADS)

    Petruccione, Francesco; Sinayskiy, Ilya; UKZN Team

    2015-03-01

    Recently a model of open quantum Brownian motion (OQBM) [M. Bauer, D. Bernard, A. Tilloy, Phys. Rev. A 88 (2013) 062340] was introduced as a scaling limit of Open Quantum Walks (OQWs) [S. Attal, F. Petruccione, C. Sabot, I. Sinayskiy, J. Stat. Phys. 147 (20120 832]. OQBM is a new type of quantum Brownian motion where the dynamics of the Brownian particle not only depends on the interactions with a thermal environment, but also depends on the state of the internal degrees of freedom of the Brownian particle. Here, we present the microscopic derivation of the OQBM for a Brownian particle with two internal degrees of freedom. Examples of the dynamics for initial Gaussian and non-Gaussian distributions are presented. This work is based upon research supported by the South African Research Chair Initiative of the Department of Science and Technology and National Research Foundation.

  3. Brownian Motion--a Laboratory Experiment.

    ERIC Educational Resources Information Center

    Kruglak, Haym

    1988-01-01

    Introduces an experiment involving the observation of Brownian motion for college students. Describes the apparatus, experimental procedures, data analysis and results, and error analysis. Lists experimental techniques used in the experiment. Provides a circuit diagram, typical data, and graphs. (YP)

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

    PubMed

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

    2016-04-30

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

  5. Broadband boundary effects on Brownian motion.

    PubMed

    Mo, Jianyong; Simha, Akarsh; Raizen, Mark G

    2015-12-01

    Brownian motion of particles in confined fluids is important for many applications, yet the effects of the boundary over a wide range of time scales are still not well understood. We report high-bandwidth, comprehensive measurements of Brownian motion of an optically trapped micrometer-sized silica sphere in water near an approximately flat wall. At short distances we observe anisotropic Brownian motion with respect to the wall. We find that surface confinement not only occurs in the long time scale diffusive regime but also in the short time scale ballistic regime, and the velocity autocorrelation function of the Brownian particle decays faster than that of a particle in bulk fluid. Furthermore, at low frequencies the thermal force loses its color due to the reflected flow from the no-slip boundary. The power spectrum of the thermal force on the particle near a no-slip boundary becomes flat at low frequencies. This detailed understanding of boundary effects on Brownian motion opens a door to developing a 3D microscope using particles as remote sensors.

  6. Broadband boundary effects on Brownian motion

    NASA Astrophysics Data System (ADS)

    Mo, Jianyong; Simha, Akarsh; Raizen, Mark G.

    2015-12-01

    Brownian motion of particles in confined fluids is important for many applications, yet the effects of the boundary over a wide range of time scales are still not well understood. We report high-bandwidth, comprehensive measurements of Brownian motion of an optically trapped micrometer-sized silica sphere in water near an approximately flat wall. At short distances we observe anisotropic Brownian motion with respect to the wall. We find that surface confinement not only occurs in the long time scale diffusive regime but also in the short time scale ballistic regime, and the velocity autocorrelation function of the Brownian particle decays faster than that of a particle in bulk fluid. Furthermore, at low frequencies the thermal force loses its color due to the reflected flow from the no-slip boundary. The power spectrum of the thermal force on the particle near a no-slip boundary becomes flat at low frequencies. This detailed understanding of boundary effects on Brownian motion opens a door to developing a 3D microscope using particles as remote sensors.

  7. Monotone and boolean unitary Brownian motions

    NASA Astrophysics Data System (ADS)

    Hamdi, Tarek

    2015-06-01

    The additive monotone (respectively boolean) unitary Brownian motion is a non-commutative stochastic process with monotone (respectively boolean) independent and stationary increments which are distributed according to the arcsine law (respectively Bernoulli law). We introduce the monotone and boolean unitary Brownian motions and derive a closed formula for their associated moments. This provides a description of their spectral measures. We prove that, in the monotone case, the multiplicative analog of the arcsine distribution is absolutely continuous with respect to the Haar measure on the unit circle, whereas in the boolean case the multiplicative analog of the Bernoulli distribution is discrete. Finally, we use quantum stochastic calculus to provide a realization of these processes as the stochastic exponential of the correspending additive Brownian motions.

  8. Anomalous Brownian motion and viscoelasticity of the ear's mechanoelectrical transducer

    NASA Astrophysics Data System (ADS)

    Andor-Ardó, Daniel; Kozlov, Andrei; Hudspeth, A. J.

    2009-03-01

    The Brownian motion of a particle in a complex environment is known to display anomalous power-law scaling in which the mean squared displacement is proportional to a fractional power of time. Using laser interferometry and analytical methods of microrheology, we examine nanometer-scale thermal motions of hair bundles in the internal ear and show that these cellular organelles undergo fractional Brownian motion. This anomalous scaling is caused by viscoelasticity of the gating springs, elements that transmit energy in a sound to the mechanosensitive ion channels. These results demonstrate a connection between rheology and auditory physiology, and indicate that statistical properties of the thermal noise in the ear can be determined by dynamics of a small number of key molecules.

  9. Nonisothermal fluctuating hydrodynamics and Brownian motion

    NASA Astrophysics Data System (ADS)

    Falasco, G.; Kroy, K.

    2016-03-01

    The classical theory of Brownian dynamics follows from coarse graining the underlying linearized fluctuating hydrodynamics of the solvent. We extend this procedure to globally nonisothermal conditions, requiring only a local thermal equilibration of the solvent. Starting from the conservation laws, we establish the stochastic equations of motion for the fluid momentum fluctuations in the presence of a suspended Brownian particle. These are then contracted to the nonisothermal generalized Langevin description of the suspended particle alone, for which the coupling to stochastic temperature fluctuations is found to be negligible under typical experimental conditions.

  10. Brownian motion - a laboratory experiment

    NASA Astrophysics Data System (ADS)

    Kruglak, Haym

    1988-09-01

    The availability of latex microspheres, compact television cameras and electronic calculators make it possible to perform an experiment on Brownian movement in one laboratory period. A more accurate value of N can be determined by other methods. However, the experiment described above has several valuable pedagogical outcomes. Undergraduate students get experience with several experimental techniques: (i) recording a `random walk' of a microphere; (ii) plotting a histogram of displacements; (iii) fitting a Gaussian curve to the histogram; (iv) checking the goodness of fit analytically or with probability graph paper; (v) calibrating screen displacements with a diffraction grating; (vi) calculating Avogadro's number from the experimental data; (vii) verifying data validity with the Einstein - Smoluchowski Law. The experiment also provides valuable practice in unit conversion and error analysis. Another instructive feature: the experiment makes the students aware of Einstein's work other than relativity. The students' reactions to the experiment were positive: `interesting', `challenging', `fun'.

  11. Active Brownian motion tunable by light.

    PubMed

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

    2012-07-18

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

  12. Frustrated Brownian Motion of Nonlocal Solitary Waves

    SciTech Connect

    Folli, V.; Conti, C.

    2010-05-14

    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.

  13. Ergodicity breaking in geometric Brownian motion.

    PubMed

    Peters, O; Klein, W

    2013-03-08

    Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by nonergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time average. A common tactic for bringing time averages closer to ensemble averages is diversification. In this Letter, we study the effects of diversification using the concept of ergodicity breaking.

  14. Simulations of magnetic nanoparticle Brownian motion

    NASA Astrophysics Data System (ADS)

    Reeves, Daniel B.; Weaver, John B.

    2012-12-01

    Magnetic nanoparticles are useful in many medical applications because they interact with biology on a cellular level thus allowing microenvironmental investigation. An enhanced understanding of the dynamics of magnetic particles may lead to advances in imaging directly in magnetic particle imaging or through enhanced MRI contrast and is essential for nanoparticle sensing as in magnetic spectroscopy of Brownian motion. Moreover, therapeutic techniques like hyperthermia require information about particle dynamics for effective, safe, and reliable use in the clinic. To that end, we have developed and validated a stochastic dynamical model of rotating Brownian nanoparticles from a Langevin equation approach. With no field, the relaxation time toward equilibrium matches Einstein's model of Brownian motion. In a static field, the equilibrium magnetization agrees with the Langevin function. For high frequency or low amplitude driving fields, behavior characteristic of the linearized Debye approximation is reproduced. In a higher field regime where magnetic saturation occurs, the magnetization and its harmonics compare well with the effective field model. On another level, the model has been benchmarked against experimental results, successfully demonstrating that harmonics of the magnetization carry enough information to infer environmental parameters like viscosity and temperature.

  15. Intrinsic and extrinsic measurement for Brownian motion

    NASA Astrophysics Data System (ADS)

    Castro-Villarreal, Pavel

    2014-05-01

    Based upon the Smoluchowski equation on curved manifolds, three physical observables are considered for Brownian displacement, namely geodesic displacement s, Euclidean displacement δR, and projected displacement δR⊥. The Weingarten-Gauss equations are used to calculate the mean-square Euclidean displacements in the short-time regime. Our findings show that from an extrinsic point of view the geometry of the space affects the Brownian motion in such a way that the particle’s diffusion is decelerated, contrasting with the intrinsic point of view where dynamics is controlled by the sign of the Gaussian curvature (Castro-Villarreal, 2010 J. Stat. Mech. P08006). Furthermore, it is possible to give exact formulas for <δR> and <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.

  16. Performance of Brownian-motion-generated universal portfolios

    NASA Astrophysics Data System (ADS)

    Tan, Choon Peng; Pang, Sook Theng

    2014-06-01

    Investment in a market of m stocks is considered. Generating a universal portfolio using m independent Brownian motions is demonstrated. The asymptotic behaviour of a Brownian-motion-generated universal portfolio is described. The empirical performance of such portfolios on some selected three-stock data sets is analysed. Investment wealth can be increased by varying the drift coefficients or parameters of the Brownian motions.

  17. O'Connell's process as a vicious Brownian motion

    SciTech Connect

    Katori, Makoto

    2011-12-15

    Vicious Brownian motion is a diffusion scaling limit of Fisher's vicious walk model, which is a system of Brownian particles in one dimension such that if two motions meet they kill each other. We consider the vicious Brownian motions conditioned never to collide with each other and call it noncolliding Brownian motion. This conditional diffusion process is equivalent to the eigenvalue process of the Hermitian-matrix-valued Brownian motion studied by Dyson [J. Math. Phys. 3, 1191 (1962)]. Recently, O'Connell [Ann. Probab. (to be published)] introduced a generalization of the noncolliding Brownian motion by using the eigenfunctions (the Whittaker functions) of the quantum Toda lattice in order to analyze a directed polymer model in 1 + 1 dimensions. We consider a system of one-dimensional Brownian motions with a long-ranged killing term as a generalization of the vicious Brownian motion and construct the O'Connell process as a conditional process of the killing Brownian motions to survive forever.

  18. O'Connell's process as a vicious Brownian motion.

    PubMed

    Katori, Makoto

    2011-12-01

    Vicious Brownian motion is a diffusion scaling limit of Fisher's vicious walk model, which is a system of Brownian particles in one dimension such that if two motions meet they kill each other. We consider the vicious Brownian motions conditioned never to collide with each other and call it noncolliding Brownian motion. This conditional diffusion process is equivalent to the eigenvalue process of the Hermitian-matrix-valued Brownian motion studied by Dyson [J. Math. Phys. 3, 1191 (1962)]. Recently, O'Connell [Ann. Probab. (to be published)] introduced a generalization of the noncolliding Brownian motion by using the eigenfunctions (the Whittaker functions) of the quantum Toda lattice in order to analyze a directed polymer model in 1 + 1 dimensions. We consider a system of one-dimensional Brownian motions with a long-ranged killing term as a generalization of the vicious Brownian motion and construct the O'Connell process as a conditional process of the killing Brownian motions to survive forever.

  19. Quantum Darwinism in quantum Brownian motion.

    PubMed

    Blume-Kohout, Robin; Zurek, Wojciech H

    2008-12-12

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

  20. Quantum Darwinism in Quantum Brownian Motion

    NASA Astrophysics Data System (ADS)

    Blume-Kohout, Robin; Zurek, Wojciech H.

    2008-12-01

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

  1. Relativistic Brownian motion on a graphene chip

    NASA Astrophysics Data System (ADS)

    Pototsky, A.; Marchesoni, F.; Kusmartsev, F. V.; Hänggi, P.; Savel'ev, S. E.

    2012-10-01

    Relativistic Brownian motion can be inexpensively demonstrated on a graphene chip. The interplay of stochastic and relativistic dynamics, governing the transport of charge carrier in graphene, induces noise-controlled effects such as (i) a stochastic effective mass, detectable as a suppression of the particle mobility with increasing the temperature; (ii) transverse harmonic mixing, whereby electron transport can be controlled by two orthogonal, commensurate ac drives; (iii) a transverse ratchet effect, measurable as a net current orthogonal to an ac drive on an asymmetric substrate, and (iv) chaotic stochastic resonance. Such properties can be of practical applications in the emerging graphene technology.

  2. Time-averaged MSD of Brownian motion

    NASA Astrophysics Data System (ADS)

    Andreanov, Alexei; Grebenkov, Denis S.

    2012-07-01

    We study the statistical properties of the time-averaged mean-square displacements (TAMSD). This is a standard non-local quadratic functional for inferring the diffusion coefficient from an individual random trajectory of a diffusing tracer in single-particle tracking experiments. For Brownian motion, we derive an exact formula for the Laplace transform of the probability density of the TAMSD by mapping the original problem onto chains of coupled harmonic oscillators. From this formula, we deduce the first four cumulant moments of the TAMSD, the asymptotic behavior of the probability density and its accurate approximation by a generalized Gamma distribution.

  3. Langevin theory of anomalous Brownian motion made simple

    NASA Astrophysics Data System (ADS)

    Tóthová, Jana; Vasziová, Gabriela; Glod, Lukáš; Lisý, Vladimír

    2011-05-01

    During the century from the publication of the work by Einstein (1905 Ann. Phys. 17 549) Brownian motion has become an important paradigm in many fields of modern science. An essential impulse for the development of Brownian motion theory was given by the work of Langevin (1908 C. R. Acad. Sci., Paris 146 530), in which he proposed an 'infinitely more simple' description of Brownian motion than that by Einstein. The original Langevin approach has however strong limitations, which were rigorously stated after the creation of the hydrodynamic theory of Brownian motion (1945). Hydrodynamic Brownian motion is a special case of 'anomalous Brownian motion', now intensively studied both theoretically and in experiments. We show how some general properties of anomalous Brownian motion can be easily derived using an effective method that allows one to convert the stochastic generalized Langevin equation into a deterministic Volterra-type integro-differential equation for the mean square displacement of the particle. Within the Gibbs statistics, the method is applicable to linear equations of motion with any kind of memory during the evolution of the system. We apply it to memoryless Brownian motion in a harmonic potential well and to Brownian motion in fluids, taking into account the effects of hydrodynamic memory. Exploring the mathematical analogy between Brownian motion and electric circuits, which are at nanoscales also described by the generalized Langevin equation, we calculate the fluctuations of charge and current in RLC circuits that are in contact with the thermal bath. Due to the simplicity of our approach it could be incorporated into graduate courses of statistical physics. Once the method is established, it allows bringing to the attention of students and effectively solving a number of attractive problems related to Brownian motion.

  4. Measurement of molecular binding using the Brownian motion of magnetic nanoparticle probes

    NASA Astrophysics Data System (ADS)

    Rauwerdink, Adam M.; Weaver, John B.

    2010-01-01

    Molecular binding is important in many venues including antibody binding for diagnostic and therapeutic agents and pharmaceutical function. We demonstrate that a method of measuring nanoparticle Brownian motion, termed magnetic spectroscopy of nanoparticle Brownian motion (MSB), can be used to monitor molecular binding and the bound fraction. It is plausible that MSB can be used to measure binding in vivo because the same signal has been used to image nanoparticles in nanogram quantities in vivo.

  5. Langevin Theory of Anomalous Brownian Motion Made Simple

    ERIC Educational Resources Information Center

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

    2011-01-01

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

  6. Langevin Theory of Anomalous Brownian Motion Made Simple

    ERIC Educational Resources Information Center

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

    2011-01-01

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

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

    ERIC Educational Resources Information Center

    Kirksey, H. Graden; Jones, Richard F.

    1988-01-01

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

  8. Parallel Molecular Distributed Detection With Brownian Motion.

    PubMed

    Rogers, Uri; Koh, Min-Sung

    2016-12-01

    This paper explores the in vivo distributed detection of an undesired biological agent's (BAs) biomarkers by a group of biological sized nanomachines in an aqueous medium under drift. The term distributed, indicates that the system information relative to the BAs presence is dispersed across the collection of nanomachines, where each nanomachine possesses limited communication, computation, and movement capabilities. Using Brownian motion with drift, a probabilistic detection and optimal data fusion framework, coined molecular distributed detection, will be introduced that combines theory from both molecular communication and distributed detection. Using the optimal data fusion framework as a guide, simulation indicates that a sub-optimal fusion method exists, allowing for a significant reduction in implementation complexity while retaining BA detection accuracy.

  9. Parallel Molecular Distributed Detection with Brownian Motion.

    PubMed

    Rogers, Uri; Koh, Min-Sung

    2016-12-05

    This paper explores the in vivo distributed detection of an undesired biological agent's (BAs) biomarkers by a group of biological sized nanomachines in an aqueous medium under drift. The term distributed, indicates that the system information relative to the BAs presence is dispersed across the collection of nanomachines, where each nanomachine possesses limited communication, computation, and movement capabilities. Using Brownian motion with drift, a probabilistic detection and optimal data fusion framework, coined molecular distributed detection, will be introduced that combines theory from both molecular communication and distributed detection. Using the optimal data fusion framework as a guide, simulation indicates that a suboptimal fusion method exists, allowing for a significant reduction in implementation complexity while retaining BA detection accuracy.

  10. From Constructive Field Theory to Fractional Stochastic Calculus. (II) Constructive Proof of Convergence for the Lévy Area of Fractional Brownian Motion with Hurst Index ${{alpha} {in} ((1)/(8),(1)/(4))}$

    NASA Astrophysics Data System (ADS)

    Magnen, Jacques; Unterberger, Jérémie

    2012-03-01

    {Let $B=(B_1(t),...,B_d(t))$ be a $d$-dimensional fractional Brownian motion with Hurst index $\\alpha<1/4$, or more generally a Gaussian process whose paths have the same local regularity. Defining properly iterated integrals of $B$ is a difficult task because of the low H\\"older regularity index of its paths. Yet rough path theory shows it is the key to the construction of a stochastic calculus with respect to $B$, or to solving differential equations driven by $B$. We intend to show in a series of papers how to desingularize iterated integrals by a weak, singular non-Gaussian perturbation of the Gaussian measure defined by a limit in law procedure. Convergence is proved by using "standard" tools of constructive field theory, in particular cluster expansions and renormalization. These powerful tools allow optimal estimates, and call for an extension of Gaussian tools such as for instance the Malliavin calculus. After a first introductory paper \\cite{MagUnt1}, this one concentrates on the details of the constructive proof of convergence for second-order iterated integrals, also known as L\\'evy area.

  11. Wick type SDEs driven by grey Brownian motion

    NASA Astrophysics Data System (ADS)

    Bock, Wolfgang; da Silva, José Luís

    2017-08-01

    We derive solutions of the Ornstein-Uhlenbeck and of a linear Wick-type stochastic differential equation (SDE) driven by grey Brownian motion. The solutions are characterized to be in a suitable distribution space.

  12. Lagrangian turbulence and the Brownian motion paradox

    NASA Astrophysics Data System (ADS)

    Viecelli, J. A.

    1991-11-01

    The unique properties of three-dimensional hydrodynamic turbulence depend on the nature of the long-range time correlations as well as the spatial correlations. Although Kolmogorov's second similarity hypothesis predicts a power-law spatial scaling exponent for the Eulerian velocity fluctuations in agreement with experiments, it also leads, via the Lagrangian velocity time structure function relationship, to particle dispersion predictions that are inconsistent with enhanced diffusion. Recently, a new computational technique has been developed which can generate random power-law correlated fields in any number of dimensions with unlimited scale range. This new method is used to explore the consequences of a proposed set of assumptions about the nature of the time correlations and their relationship to the spatial correlations. In particular, the Brownian motion paradox is examined and it is shown that it can be resolved if the time domain constraint part of Kolmogorov's second hypothesis is relaxed and replaced with an assumption of space-time isotropy. The proposed modification preserves the observed one-dimensional k-5/3 spatial energy spectrum, allows for enhanced diffusion consistent with Richardson's law, is consistent with Taylor's frozen turbulence assumption under the appropriate conditions, and yields an ω-5/3 frequency spectrum for the velocity fluctuations in a frame at rest with respect to the turbulence.

  13. Noncolliding Brownian Motion and Determinantal Processes

    NASA Astrophysics Data System (ADS)

    Katori, Makoto; Tanemura, Hideki

    2007-12-01

    A system of one-dimensional Brownian motions (BMs) conditioned never to collide with each other is realized as (i) Dyson's BM model, which is a process of eigenvalues of hermitian matrix-valued diffusion process in the Gaussian unitary ensemble (GUE), and as (ii) the h-transform of absorbing BM in a Weyl chamber, where the harmonic function h is the product of differences of variables (the Vandermonde determinant). The Karlin-McGregor formula gives determinantal expression to the transition probability density of absorbing BM. We show from the Karlin-McGregor formula, if the initial state is in the eigenvalue distribution of GUE, the noncolliding BM is a determinantal process, in the sense that any multitime correlation function is given by a determinant specified by a matrix-kernel. By taking appropriate scaling limits, spatially homogeneous and inhomogeneous infinite determinantal processes are derived. We note that the determinantal processes related with noncolliding particle systems have a feature in common such that the matrix-kernels are expressed using spectral projections of appropriate effective Hamiltonians. On the common structure of matrix-kernels, continuity of processes in time is proved and general property of the determinantal processes is discussed.

  14. Biased Brownian motion in extremely corrugated tubes

    NASA Astrophysics Data System (ADS)

    Martens, S.; Schmid, G.; Schimansky-Geier, L.; Hänggi, P.

    2011-12-01

    Biased Brownian motion of point-size particles in a three-dimensional tube with varying cross-section is investigated. In the fashion of our recent work, Martens et al. [Phys. Rev. E 83, 051135 (2011)] we employ an asymptotic analysis to the stationary probability density in a geometric parameter of the tube geometry. We demonstrate that the leading order term is equivalent to the Fick-Jacobs approximation. Expression for the higher order corrections to the probability density is derived. Using this expansion orders, we obtain that in the diffusion dominated regime the average particle current equals the zeroth order Fick-Jacobs result corrected by a factor including the corrugation of the tube geometry. In particular, we demonstrate that this estimate is more accurate for extremely corrugated geometries compared with the common applied method using a spatially-dependent diffusion coefficient D(x, f) which substitutes the constant diffusion coefficient in the common Fick-Jacobs equation. The analytic findings are corroborated with the finite element calculation of a sinusoidal-shaped tube.

  15. Simulation of the active Brownian motion of a microswimmer

    NASA Astrophysics Data System (ADS)

    Volpe, Giorgio; Gigan, Sylvain; Volpe, Giovanni

    2014-07-01

    Unlike passive Brownian particles, active Brownian particles, also known as microswimmers, propel themselves with directed motion and thus drive themselves out of equilibrium. Understanding their motion can provide insight into out-of-equilibrium phenomena associated with biological examples such as bacteria, as well as with artificial microswimmers. We discuss how to mathematically model their motion using a set of stochastic differential equations and how to numerically simulate it using the corresponding set of finite difference equations both in homogenous and complex environments. In particular, we show how active Brownian particles do not follow the Maxwell-Boltzmann distribution—a clear signature of their out-of-equilibrium nature—and how, unlike passive Brownian particles, microswimmers can be funneled, trapped, and sorted.

  16. Spatial extent of branching Brownian motion.

    PubMed

    Ramola, Kabir; Majumdar, Satya N; Schehr, Grégory

    2015-04-01

    We study the one-dimensional branching Brownian motion starting at the origin and investigate the correlation between the rightmost (X(max)≥0) and leftmost (X(min)≤0) visited sites up to time t. At each time step the existing particles in the system either diffuse (with diffusion constant D), die (with rate a), or split into two particles (with rate b). We focus on the regime b≤a where these two extreme values X(max) and X(min) are strongly correlated. We show that at large time t, the joint probability distribution function (PDF) of the two extreme points becomes stationary P(X,Y,t→∞)→p(X,Y). Our exact results for p(X,Y) demonstrate that the correlation between X(max) and X(min) is nonzero, even in the stationary state. From this joint PDF, we compute exactly the stationary PDF p(ζ) of the (dimensionless) span ζ=(X(max)-X(min))/√[D/b], which is the distance between the rightmost and leftmost visited sites. This span distribution is characterized by a linear behavior p(ζ)∼1/2(1+Δ)ζ for small spans, with Δ=(a/b-1). In the critical case (Δ=0) this distribution has a nontrivial power law tail p(ζ)∼8π√[3]/ζ(3) for large spans. On the other hand, in the subcritical case (Δ>0), we show that the span distribution decays exponentially as p(ζ)∼(A(2)/2)ζexp(-√[Δ]ζ) for large spans, where A is a nontrivial function of Δ, which we compute exactly. We show that these asymptotic behaviors carry the signatures of the correlation between X(max) and X(min). Finally we verify our results via direct Monte Carlo simulations.

  17. Directed motion of a Brownian motor in a temperature gradient

    NASA Astrophysics Data System (ADS)

    Liu, Yibing; Nie, Wenjie; Lan, Yueheng

    2017-05-01

    Directed motion of mesoscopic systems in a non-equilibrium environment is of great interest to both scientists and engineers. Here, the translation and rotation of a Brownian motor is investigated under non-equilibrium conditions. An anomalous directed translation is found if the two heads of the Brownian motor are immersed in baths with different particle masses, which is hinted in the analytic computation and confirmed by the numerical simulation. Similar consideration is also used to find the directed movement in the single rotational and translational degree of freedom of the Brownian motor when residing in one thermal bath with a temperature gradient.

  18. Measured quantum probability distribution functions for Brownian motion

    SciTech Connect

    Ford, G. W.; O'Connell, R. F.

    2007-10-15

    The quantum analog of the joint probability distributions describing a classical stochastic process is introduced. A prescription is given for constructing the quantum distribution associated with a sequence of measurements. For the case of quantum Brownian motion this prescription is illustrated with a number of explicit examples. In particular, it is shown how the prescription can be extended in the form of a general formula for the Wigner function of a Brownian particle entangled with a heat bath.

  19. Brownian Motion and the Temperament of Living Cells

    NASA Astrophysics Data System (ADS)

    Tsekov, Roumen; Lensen, Marga C.

    2013-07-01

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

  20. Experimental Study of Short-Time Brownian Motion

    NASA Astrophysics Data System (ADS)

    Mo, Jianyong; Simha, Akarsh; Riegler, David; Raizen, Mark

    2015-03-01

    We report our progress on the study of short-time Brownian motion of optically-trapped microspheres. In earlier work, we observed the instantaneous velocity of microspheres in gas and in liquid, verifying a prediction by Albert Einstein from 1907. We now report a more accurate test of the energy equipartition theorem for a particle in liquid. We also observe boundary effects on Brownian motion in liquid by setting a wall near the trapped particle, which changes the dynamics of the motion. We find that the velocity autocorrelation of the particle decreases faster as the particle gets closer to the wall.

  1. Transport properties of elastically coupled fractional Brownian motors

    NASA Astrophysics Data System (ADS)

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

    2015-11-01

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

  2. Brownian motion on random dynamical landscapes

    NASA Astrophysics Data System (ADS)

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

    2016-03-01

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

  3. Theory of Brownian motion in a Jeffreys fluid

    SciTech Connect

    Raikher, Yu. L.; Rusakov, V. V.

    2010-11-15

    We have constructed a kinetic theory of Brownian motion in a rheologically complex medium-a Jeffreys fluid that is characterized by a combination of two viscosity mechanisms: ordinary and delayed. This model is shown to be much better suited for the interpretation of experiments on the microrheology of viscoelastic media than the standard Maxwell model. In particular, no oscillations of the mean-square particle displacement arise in a Jeffreys fluid, which is a nonremovable artifact of the theory of Brownian motion in a Maxwell fluid. The developed approach can to be used also consider the diffusion of particles in other complex fluids whose rheology is described by phenomenological schemes.

  4. Brownian motion with adhesion: harmonic oscillator with fluctuating mass.

    PubMed

    Gitterman, M; Klyatskin, V I

    2010-05-01

    In contrast to the cases usually studied of a harmonic oscillator subject to a random force (Brownian motion) or having random frequency or random damping, we consider a random mass which corresponds to an oscillator for which the particles of the surrounding medium adhere to it for some (random) time after the collision, thereby changing the oscillator mass. This model, which describes Brownian motion with adhesion, can be useful for the analysis of chemical and biological solutions as well as nanotechnological devices. We consider dichotomous noise and its limiting case, white noise.

  5. Brownian motion of solitons in a Bose-Einstein condensate.

    PubMed

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

    2017-03-07

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

  6. Effect of interfaces on the nearby Brownian motion

    NASA Astrophysics Data System (ADS)

    Huang, Kai; Szlufarska, Izabela

    2015-10-01

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

  7. Effect of interfaces on the nearby Brownian motion.

    PubMed

    Huang, Kai; Szlufarska, Izabela

    2015-10-06

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

  8. Effect of interfaces on the nearby Brownian motion

    PubMed Central

    Huang, Kai; Szlufarska, Izabela

    2015-01-01

    Near-boundary Brownian motion is a classic hydrodynamic problem of great importance in a variety of fields, from biophysics to micro-/nanofluidics. However, owing to challenges in experimental measurements of near-boundary dynamics, the effect of interfaces on Brownian motion has remained elusive. Here we report a computational study of this effect using μs-long large-scale molecular dynamics simulations and our newly developed Green–Kubo relation for friction at the liquid–solid interface. Our computer experiment unambiguously reveals that the t−3/2 long-time decay of the velocity autocorrelation function of a Brownian particle in bulk liquid is replaced by a t−5/2 decay near a boundary. We discover a general breakdown of traditional no-slip boundary condition at short time scales and we show that this breakdown has a profound impact on the near-boundary Brownian motion. Our results demonstrate the potential of Brownian-particle-based micro-/nanosonar to probe the local wettability of liquid–solid interfaces. PMID:26438034

  9. Brownian motion as a new probe of wettability

    NASA Astrophysics Data System (ADS)

    Mo, Jianyong; Simha, Akarsh; Raizen, Mark G.

    2017-04-01

    Understanding wettability is crucial for optimizing oil recovery, semiconductor manufacturing, pharmaceutical industry, and electrowetting. In this letter, we study the effects of wettability on Brownian motion. We consider the cases of a sphere in an unbounded fluid medium, as well as a sphere placed in the vicinity of a plane wall. For the first case, we show the effects of wettability on the statistical properties of the particles' motion, such as velocity autocorrelation, velocity, and thermal force power spectra over a large range of time scales. We also propose a new method to measure wettability based on the particles' Brownian motion. In addition, we compare the boundary effects on Brownian motion imposed by both no-slip and perfect-slip flat walls. We emphasize the surprising boundary effects on Brownian motion imposed by a perfect-slip wall in the parallel direction, such as a higher particle mobility parallel to a perfect flat wall compared to that in the absence of the wall, as well as compared to a particle near a no-slip flat wall.

  10. Brownian motion as a new probe of wettability.

    PubMed

    Mo, Jianyong; Simha, Akarsh; Raizen, Mark G

    2017-04-07

    Understanding wettability is crucial for optimizing oil recovery, semiconductor manufacturing, pharmaceutical industry, and electrowetting. In this letter, we study the effects of wettability on Brownian motion. We consider the cases of a sphere in an unbounded fluid medium, as well as a sphere placed in the vicinity of a plane wall. For the first case, we show the effects of wettability on the statistical properties of the particles' motion, such as velocity autocorrelation, velocity, and thermal force power spectra over a large range of time scales. We also propose a new method to measure wettability based on the particles' Brownian motion. In addition, we compare the boundary effects on Brownian motion imposed by both no-slip and perfect-slip flat walls. We emphasize the surprising boundary effects on Brownian motion imposed by a perfect-slip wall in the parallel direction, such as a higher particle mobility parallel to a perfect flat wall compared to that in the absence of the wall, as well as compared to a particle near a no-slip flat wall.

  11. Quantum Brownian motion model for the stock market

    NASA Astrophysics Data System (ADS)

    Meng, Xiangyi; Zhang, Jian-Wei; Guo, Hong

    2016-06-01

    It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysical framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system-a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenberg's uncertainty relationship of quantum mechanics in an analogous manner. We analyze real stock data of Shanghai Stock Exchange of China and investigate fat-tail phenomena and non-Markovian behaviors of the stock index with the assistance of the quantum Brownian motion model, thereby interpreting and studying the limitations of the classical Brownian motion model for the efficient market hypothesis from a new perspective of quantum open system dynamics.

  12. Brownian dynamics simulation of aerosol coagulation: effect of shear flow of fluid, Brownian motion, and van der Waals interaction

    SciTech Connect

    Gupta, D.

    1986-01-01

    The influence of shear flow, Brownian motion and interparticle forces on the coagulation coefficient are studied; and effects of many-body interactions on the coagulation coefficient for concentrated dispersions are analyzed. This study is conducted in two parts. In the first part, computer experiments are performed using Brownian Dynamics simulation methods. The relative importance of shear flow and Brownian motion, and of shear flow and van der Waals attraction, are characterized by the Peclet number, Pe, and the Flow number, FI, respectively. Results from computer experiments for FL ..-->.. infinity (i.e. no interparticle interactions) show that the principle of superposition underestimates the coagulation rate at low Pe (by as much as 100%) and overestimates the coagulation rate at large Pe (by roughly 30 to 40%). In the second part, the potential of mean force concept from dense gas kinetic theory is used to investigate the effect of particle volume fraction, Phi. It is shown that for large values of Phi, a shielding effect due to surrounding particles results in an attractive force on the particles. This leads to an overall enhancement in the coagulation rate when compared with the results based on the binary interaction potential.

  13. Brownian Motion of a Torsion Pendulum Damped by Internal Friction.

    NASA Astrophysics Data System (ADS)

    Gonzalez, Gabriela Ines

    1995-01-01

    Brownian motion is a well known limit to precision experiments, and it is also going to be a limiting factor in the sensitivity of interferometric gravitational wave detectors. The power spectral density of Brownian motion depends dramatically on the strength and frequency dependence of the energy dissipation in the system of interest. We present here the measurement of Brownian motion of a simple oscillator, a torsion pendulum, where the energy losses are due to internal friction in the suspension fiber. We calculate from these measurements the power spectrum S _theta(f) of the Brownian motion, as well as other statistical functions defined in irreversible thermodynamics, such as the autocorrelation function and conditional probability distributions. We also present a measurement of internal friction as a function of frequency. With this and the physical parameters describing the pendulum, we use the fluctuation -dissipation theorem to calculate S_theta(f). . We then compare the prediction and measurement of S_theta(f), and show excellent agreement over a decade in frequency around the pendulum frequency. The spectrum S_theta(f) is not flat below resonance, and in fact follows a S_theta(f)~1/f law.

  14. Cellular motions and thermal fluctuations: the Brownian ratchet.

    PubMed Central

    Peskin, C S; Odell, G M; Oster, G F

    1993-01-01

    We present here a model for how chemical reactions generate protrusive forces by rectifying Brownian motion. This sort of energy transduction drives a number of intracellular processes, including filopodial protrusion, propulsion of the bacterium Listeria, and protein translocation. Images FIGURE 1 FIGURE 2 FIGURE 3 PMID:8369439

  15. Brownian motion of arbitrarily shaped particles in two dimensions.

    PubMed

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

    2014-11-25

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

  16. Brownian motion in granular gases of viscoelastic particles

    SciTech Connect

    Bodrova, A. S. Brilliantov, N. V.; Loskutov, A. Yu.

    2009-12-15

    A theory is developed of Brownian motion in granular gases (systems of many macroscopic particles undergoing inelastic collisions), where the energy loss in inelastic collisions is determined by a restitution coefficient {epsilon}. Whereas previous studies used a simplified model with {epsilon} = const, the present analysis takes into account the dependence of the restitution coefficient on relative impact velocity. The granular temperature and the Brownian diffusion coefficient are calculated for a granular gas in the homogeneous cooling state and a gas driven by a thermostat force, and their variation with grain mass and size and the restitution coefficient is analyzed. Both equipartition principle and fluctuation-dissipation relations are found to break down. One manifestation of this behavior is a new phenomenon of 'relative heating' of Brownian particles at the expense of cooling of the ambient granular gas.

  17. Quantum Brownian motion with inhomogeneous damping and diffusion

    NASA Astrophysics Data System (ADS)

    Massignan, Pietro; Lampo, Aniello; Wehr, Jan; Lewenstein, Maciej

    2015-03-01

    We analyze the microscopic model of quantum Brownian motion, describing a Brownian particle interacting with a bosonic bath through a coupling which is linear in the creation and annihilation operators of the bath, but may be a nonlinear function of the position of the particle. Physically, this corresponds to a configuration in which damping and diffusion are spatially inhomogeneous. We derive systematically the quantum master equation for the Brownian particle in the Born-Markov approximation and we discuss the appearance of additional terms, for various polynomials forms of the coupling. We discuss the cases of linear and quadratic coupling in great detail and we derive, using Wigner function techniques, the stationary solutions of the master equation for a Brownian particle in a harmonic trapping potential. We predict quite generally Gaussian stationary states, and we compute the aspect ratio and the spread of the distributions. In particular, we find that these solutions may be squeezed (superlocalized) with respect to the position of the Brownian particle. We analyze various restrictions to the validity of our theory posed by non-Markovian effects and by the Heisenberg principle. We further study the dynamical stability of the system, by applying a Gaussian approximation to the time-dependent Wigner function, and we compute the decoherence rates of coherent quantum superpositions in position space. Finally, we propose a possible experimental realization of the physics discussed here, by considering an impurity particle embedded in a degenerate quantum gas.

  18. Experimental Techniques for Detecting Correlated Motion of Brownian Particles

    NASA Astrophysics Data System (ADS)

    Franck, Carl; Durand, Richard V.

    1998-03-01

    We, as well as other workers, have noticed using light microscopy that particles undergoing Brownian motion can appear to linger around each other for long periods of time. The question arises as to whether this lingering is a product of interparticle interactions, or is an artifact due to random thermal motion. By way of answering this question, we developed techniques for dealing with the random nature of the particle motion. We present an algorithm to track individual Brownian particles which can handle the disappearance of a particle due to its temporary movement outside of the field of view. We used the tracking data to create randomized particle trajectories which were subsequently compared with the actual trajectories. This backgrounding technique allowed us to extract information about correlated motion in the midst of Brownian noise. We found(R.V. Durand and C. Franck, Phys. Rev. E 56), 1998 (1997). that the aforementioned apparent correlated motion could have been due to observer misperception. Financial support was provided by the National Science Foundation through grant DMR-9320910 and through MRL Central Facilities at the Materials Science Center at Cornell University (DMR-9121654).

  19. Anomalous diffusion as modeled by a nonstationary extension of Brownian motion.

    PubMed

    Cushman, John H; O'Malley, Daniel; Park, Moongyu

    2009-03-01

    If the mean-square displacement of a stochastic process is proportional to t;{beta} , beta not equal1 , then it is said to be anomalous. We construct a family of Markovian stochastic processes with independent nonstationary increments and arbitrary but a priori specified mean-square displacement. We label the family as an extended Brownian motion and show that they satisfy a Langevin equation with time-dependent diffusion coefficient. If the time derivative of the variance of the process is homogeneous, then by computing the fractal dimension it can be shown that the complexity of the family is the same as that of the Brownian motion. For two particles initially separated by a distance x , the finite-size Lyapunov exponent (FSLE) measures the average rate of exponential separation to a distance ax . An analytical expression is developed for the FSLEs of the extended Brownian processes and numerical examples presented. The explicit construction of these processes illustrates that contrary to what has been stated in the literature, a power-law mean-square displacement is not necessarily related to a breakdown in the classical central limit theorem (CLT) caused by, for example, correlation (fractional Brownian motion or correlated continuous-time random-walk schemes) or infinite variance (Levy motion). The classical CLT, coupled with nonstationary increments, can and often does give rise to power-law moments such as the mean-square displacement.

  20. Anomalous diffusion as modeled by a nonstationary extension of Brownian motion

    NASA Astrophysics Data System (ADS)

    Cushman, John H.; O'Malley, Daniel; Park, Moongyu

    2009-03-01

    If the mean-square displacement of a stochastic process is proportional to tβ , β≠1 , then it is said to be anomalous. We construct a family of Markovian stochastic processes with independent nonstationary increments and arbitrary but a priori specified mean-square displacement. We label the family as an extended Brownian motion and show that they satisfy a Langevin equation with time-dependent diffusion coefficient. If the time derivative of the variance of the process is homogeneous, then by computing the fractal dimension it can be shown that the complexity of the family is the same as that of the Brownian motion. For two particles initially separated by a distance x , the finite-size Lyapunov exponent (FSLE) measures the average rate of exponential separation to a distance ax . An analytical expression is developed for the FSLEs of the extended Brownian processes and numerical examples presented. The explicit construction of these processes illustrates that contrary to what has been stated in the literature, a power-law mean-square displacement is not necessarily related to a breakdown in the classical central limit theorem (CLT) caused by, for example, correlation (fractional Brownian motion or correlated continuous-time random-walk schemes) or infinite variance (Levy motion). The classical CLT, coupled with nonstationary increments, can and often does give rise to power-law moments such as the mean-square displacement.

  1. Relating Brownian motion to diffusion with superparamagnetic colloids

    NASA Astrophysics Data System (ADS)

    Darras, A.; Fiscina, J.; Vandewalle, N.; Lumay, G.

    2017-04-01

    An original experiment is introduced that allows students to relate the Brownian motion of a set of superparamagnetic colloidal particles to their macroscopic diffusion. An external and constant magnetic field is first applied to the colloidal suspension so that the particles self-organize into chains. When the magnetic field is removed, the particles then freely diffuse from their positions in the chain, starting from the same coordinate on the axis perpendicular to the initial chain. This configuration thus enables an observer to study the one dimensional diffusion process, while also observing the underlying Brownian motion of the microscopic particles. Moreover, by studying the evolution of the particle distribution, a measurement of the diffusion coefficient can be obtained. In addition, by repeating this measurement with fluids of various viscosities, the Stokes-Einstein relation may be illustrated.

  2. On a nonstandard Brownian motion and its maximal function

    NASA Astrophysics Data System (ADS)

    Andrade, Bernardo B. de

    2015-07-01

    This article uses Radically Elementary Probability Theory (REPT) to prove results about the Wiener walk (the radically elementary Brownian motion) without the technical apparatus required by stochastic integration. The techniques used replace measure-theoretic tools by discrete probability and the rigorous use of infinitesimals. Specifically, REPT is applied to the results in Palacios (The American Statistician, 2008) to calculate certain expectations related to the Wiener walk and its maximal function. Because Palacios uses mostly combinatorics and no measure theory his results carry over through REPT with minimal changes. The paper also presents a construction of the Wiener walk which is intended to mimic the construction of Brownian motion from "continuous" white noise. A brief review of the nonstandard model on which REPT is based is given in the Appendix in order to minimize the need for previous exposure to the subject.

  3. Convex hull of a Brownian motion in confinement.

    PubMed

    Chupeau, Marie; Bénichou, Olivier; Majumdar, Satya N

    2015-05-01

    We study the effect of confinement on the mean perimeter of the convex hull of a planar Brownian motion, defined as the minimum convex polygon enclosing the trajectory. We use a minimal model where an infinite reflecting wall confines the walk to one side. We show that the mean perimeter displays a surprising minimum with respect to the starting distance to the wall and exhibits a nonanalyticity for small distances. In addition, the mean span of the trajectory in a fixed direction θ∈]0,π/2[, which can be shown to yield the mean perimeter by integration over θ, presents these same two characteristics. This is in striking contrast to the one-dimensional case, where the mean span is an increasing analytical function. The nonmonotonicity in the two-dimensional case originates from the competition between two antagonistic effects due to the presence of the wall: reduction of the space accessible to the Brownian motion and effective repulsion.

  4. Convex hull of a Brownian motion in confinement

    NASA Astrophysics Data System (ADS)

    Chupeau, Marie; Bénichou, Olivier; Majumdar, Satya N.

    2015-05-01

    We study the effect of confinement on the mean perimeter of the convex hull of a planar Brownian motion, defined as the minimum convex polygon enclosing the trajectory. We use a minimal model where an infinite reflecting wall confines the walk to one side. We show that the mean perimeter displays a surprising minimum with respect to the starting distance to the wall and exhibits a nonanalyticity for small distances. In addition, the mean span of the trajectory in a fixed direction θ ∈]0 ,π /2 [ , which can be shown to yield the mean perimeter by integration over θ , presents these same two characteristics. This is in striking contrast to the one-dimensional case, where the mean span is an increasing analytical function. The nonmonotonicity in the two-dimensional case originates from the competition between two antagonistic effects due to the presence of the wall: reduction of the space accessible to the Brownian motion and effective repulsion.

  5. Free Energies and Fluctuations for the Unitary Brownian Motion

    NASA Astrophysics Data System (ADS)

    Dahlqvist, Antoine

    2016-12-01

    We show that the Laplace transforms of traces of words in independent unitary Brownian motions converge towards an analytic function on a non trivial disc. These results allow one to study the asymptotic behavior of Wilson loops under the unitary Yang-Mills measure on the plane with a potential. The limiting objects obtained are shown to be characterized by equations analogue to Schwinger-Dyson's ones, named here after Makeenko and Migdal.

  6. On moments of the integrated exponential Brownian motion

    NASA Astrophysics Data System (ADS)

    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.

  7. Brownian motion description of heat conduction by phonons.

    PubMed

    Naqvi, K Razi; Waldenstrøm, S

    2005-08-05

    A non-Markovian partial differential equation, rooted in the theory of Brownian motion, is proposed for describing heat conduction by phonons. Although a finite speed of propagation is a built-in feature of the equation, it does not give rise to an inauthentic wave front that results from the application of Cattaneo's equation. Even a simplified, analytically tractable version of the equation yields results close to those found by solving, through more elaborate means, the equation of phonon radiative transfer.

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

    PubMed

    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.

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

    NASA Astrophysics Data System (ADS)

    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.

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

    PubMed Central

    Muller, Mees; Heeck, Kier

    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

  11. Brownian motion of a particle with arbitrary shape

    NASA Astrophysics Data System (ADS)

    Wajnryb, Eligiusz; Cichocki, Bogdan; Ekiel-Jezewska, Maria L.

    2015-11-01

    We consider a single Brownian particle of an arbitrary shape, in general non-axisymmetric. Starting from the Smoluchowski equation we develop a new formalism, which allows to determine the particle rotational and translational motion in a much simpler way as this which is based on the Euler angles and Wigner functions. Our approach makes use of the rotational matrix and irreducible tensors. The essential result of our presentation is that using our new formalism, we derive simple explicit analytical expressions for the cross-correlations of the Brownian translational and rotational displacements. The role of the particle mobility center is determined and discussed. No such formulas have been known yet - instead, numerical Brownian simulations have been extensively used. We compare our analytical results with low Reynolds number experiment and numerical simulations performed at the time scales comparable with the characteristic time of the rotational Brownian diffusion. E.W. and M.L.E.-J. are supported by the Polish National Science Centre under Grant No. 2012/05/B/ST8/ 03010.

  12. Brownian motion: Absolute negative particle mobility

    NASA Astrophysics Data System (ADS)

    Ros, Alexandra; Eichhorn, Ralf; Regtmeier, Jan; Duong, Thanh Tu; Reimann, Peter; Anselmetti, Dario

    2005-08-01

    Noise effects in technological applications, far from being a nuisance, can be exploited with advantage - for example, unavoidable thermal fluctuations have found application in the transport and sorting of colloidal particles and biomolecules. Here we use a microfluidic system to demonstrate a paradoxical migration mechanism in which particles always move in a direction opposite to the net acting force (`absolute negative mobility') as a result of an interplay between thermal noise, a periodic and symmetric microstructure, and a biased alternating-current electric field. This counterintuitive phenomenon could be used for bioanalytical purposes, for example in the separation and fractionation of colloids, biological molecules and cells.

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

    PubMed

    Sandoval, Mario; Jimenez, Alonso

    2016-03-01

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

  14. Semiclassical master equation in Wigners phase space applied to Brownian motion in a periodic potential.

    PubMed

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

    2007-04-01

    The quantum Brownian motion of a particle in a cosine periodic potential V(x)= -V{0}cos(x/x{0}) is treated using the master equation for the time evolution of the Wigner distribution function W(x,p,t) in phase space (x,p) . The dynamic structure factor, escape rate, and jump-length probabilities are evaluated via matrix continued fractions in the manner customarily used for the classical Fokker-Planck equation. The escape rate so yielded is compared with that given analytically by the quantum-mechanical reaction rate solution of the Kramers turnover problem. The matrix continued fraction solution substantially agrees with the analytic solution.

  15. Undergraduate Labs for Biological Physics: Brownian Motion and Optical Trapping

    NASA Astrophysics Data System (ADS)

    Chu, Kelvin; Laughney, A.; Williams, J.

    2006-12-01

    We describe a set of case-study driven labs for an upper-division biological physics course. These labs are motivated by case-studies and consist of inquiry-driven investigations of Brownian motion and optical-trapping experiments. Each lab incorporates two innovative educational techniques to drive the process and application aspects of scientific learning. Case studies are used to encourage students to think independently and apply the scientific method to a novel lab situation. Student input from this case study is then used to decide how to best do the measurement, guide the project and ultimately evaluate the success of the program. Where appropriate, visualization and simulation using VPython is used. Direct visualization of Brownian motion allows students to directly calculate Avogadro's number or the Boltzmann constant. Following case-study driven discussion, students use video microscopy to measure the motion of latex spheres in different viscosity fluids arrive at a good approximation of NA or kB. Optical trapping (laser tweezer) experiments allow students to investigate the consequences of 100-pN forces on small particles. The case study consists of a discussion of the Boltzmann distribution and equipartition theorem followed by a consideration of the shape of the potential. Students can then use video capture to measure the distribution of bead positions to determine the shape and depth of the trap. This work supported by NSF DUE-0536773.

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

    NASA Astrophysics Data System (ADS)

    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.

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

    SciTech Connect

    Wang, Gaoyuan; Battefeld, Thorsten

    2016-09-05

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

  18. Role of Brownian Motion Hydrodynamics on Nanofluid Thermal Conductivity

    SciTech Connect

    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.

  19. Non-Markovian quantum Brownian motion of a harmonic oscillator

    SciTech Connect

    Tang, J.

    1994-02-01

    We apply the density-matrix method to the study of quantum Brownian motion of a harmonic oscillator coupled to a heat bath, a system investigated previously by Caldeira and Leggett using a different method. Unlike the earlier work, in our derivation of the master equation the non-Markovian terms are maintained. Although the same model of interaction is used, discrepancy is found between their results and our equation in the Markovian limit. We also point out that the particular interaction model used by both works cannot lead to the phenomenological generalized Langevin theory of Kubo.

  20. Suspended particle transport through constriction channel with Brownian motion

    NASA Astrophysics Data System (ADS)

    Hanasaki, Itsuo; Walther, Jens H.

    2017-08-01

    It is well known that translocation events of a polymer or rod through pores or narrower parts of micro- and nanochannels have a stochastic nature due to the Brownian motion. However, it is not clear whether the objects of interest need to have a larger size than the entrance to exhibit the deviation from the dynamics of the surrounding fluid. We show by numerical analysis that the particle injection into the narrower part of the channel is affected by thermal fluctuation, where the particles have spherical symmetry and are smaller than the height of the constriction. The Péclet number (Pe) is the order parameter that governs the phenomena, which clarifies the spatio-temporal significance of Brownian motion compared to hydrodynamics. Furthermore, we find that there exists an optimal condition of Pe to attain the highest flow rate of particles relative to the dispersant fluid flow. Our finding is important in science and technology from nanopore DNA sequencers and lab-on-a-chip devices to filtration by porous materials and chromatography.

  1. Momentum coupling in non-Markovian quantum Brownian motion

    NASA Astrophysics Data System (ADS)

    Ferialdi, Luca; Smirne, Andrea

    2017-07-01

    We consider a model of non-Markovian quantum Brownian motion that consists of a harmonic oscillator bilinearly coupled to a thermal bath, both via its position and via its momentum operators. We derive the master equation for such a model, and we solve the equations of motion for a generic Gaussian system state. We then investigate the resulting evolution of the first and second moments for both an Ohmic and a super-Ohmic spectral density. In particular, we show that, irrespective of the specific form of the spectral density, the coupling with the momentum enhances the dissipation experienced by the system, accelerating its relaxation to the equilibrium as well as modifying the asymptotic state of the dynamics. Eventually, we characterize explicitly the non-Markovianity of the evolution using a general criterion which relies on the positivity of the master equation coefficients.

  2. The Statistics of Burgers Turbulence Initialized with Fractional Brownian Noise Data

    NASA Astrophysics Data System (ADS)

    Ryan, Reade

    The statistics of the solution to the inviscid Burgers equation are investigated when the initial velocity potential is fractional Brownian motion. Using the theory of large deviations for Gaussian processes, we characterize the tails of the probability distribution functions (PDFs) of the velocity, the distance between shocks, and the shock strength. These PDFs are shown to decay like ``stretched'' exponentials of the form . Our method of proof can also be used to extend these results to a much larger class of Gaussian potentials. This work generalizes the results of Avellaneda and E [2, 3] on the inviscid Burgers equation with white-noise initial data.

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

    ERIC Educational Resources Information Center

    Parlar, Mahmut

    2004-01-01

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

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

    ERIC Educational Resources Information Center

    Parlar, Mahmut

    2004-01-01

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

  5. On asymptotic behavior of work distributions for driven Brownian motion

    NASA Astrophysics Data System (ADS)

    Holubec, Viktor; Lips, Dominik; Ryabov, Artem; Chvosta, Petr; Maass, Philipp

    2015-12-01

    We propose a simple conjecture for the functional form of the asymptotic behavior of work distributions for driven overdamped Brownian motion of a particle in confining potentials. This conjecture is motivated by the fact that these functional forms are independent of the velocity of the driving for all potentials and protocols, where explicit analytical solutions for the work distributions have been derived in the literature. To test the conjecture, we use Brownian dynamics simulations and a recent theory developed by Engel and Nickelsen (EN theory), which is based on the contraction principle of large deviation theory. Our tests suggest that the conjecture is valid for potentials with a confinement equal to or weaker than the parabolic one, both for equilibrium and for nonequilibrium distributions of the initial particle position. For potentials with stronger confinement, the conjecture fails and gives a good approximate description only for fast driving. In addition we obtain a new analytical solution for the asymptotic behavior of the work distribution for the V-potential by application of the EN theory, and we extend this theory to nonequilibrated initial particle positions.

  6. Monitoring autocorrelated process: A geometric Brownian motion process approach

    NASA Astrophysics Data System (ADS)

    Li, Lee Siaw; Djauhari, Maman A.

    2013-09-01

    Autocorrelated process control is common in today's modern industrial process control practice. The current practice of autocorrelated process control is to eliminate the autocorrelation by using an appropriate model such as Box-Jenkins models or other models and then to conduct process control operation based on the residuals. In this paper we show that many time series are governed by a geometric Brownian motion (GBM) process. Therefore, in this case, by using the properties of a GBM process, we only need an appropriate transformation and model the transformed data to come up with the condition needs in traditional process control. An industrial example of cocoa powder production process in a Malaysian company will be presented and discussed to illustrate the advantages of the GBM approach.

  7. Non-Markovian expansion in quantum Brownian motion

    NASA Astrophysics Data System (ADS)

    Fraga, Eduardo S.; Krein, Gastão; Palhares, Letícia F.

    2014-01-01

    We consider the non-Markovian Langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism. After discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the most common choices, we derive an analytic expansion for the exact non-Markovian dissipation kernel and the corresponding colored noise in the general case that is consistent with the fluctuation-dissipation theorem and incorporates systematically non-local corrections. We illustrate the modifications to results obtained using the traditional (Markovian) Langevin approach in the case of the exponential kernel and analyze the case of the non-Markovian Brownian motion. We present detailed results for the free and the quadratic cases, which can be compared to exact solutions to test the convergence of the method, and discuss potentials of a general nonlinear form.

  8. Diffusion in different models of active Brownian motion

    NASA Astrophysics Data System (ADS)

    Lindner, B.; Nicola, E. M.

    2008-04-01

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

  9. Observation of non-Markovian micromechanical Brownian motion

    PubMed Central

    Gröblacher, S.; Trubarov, A.; Prigge, N.; Cole, G. D.; Aspelmeyer, M.; Eisert, J.

    2015-01-01

    All physical systems are to some extent open and interacting with their environment. This insight, basic as it may seem, gives rise to the necessity of protecting quantum systems from decoherence in quantum technologies and is at the heart of the emergence of classical properties in quantum physics. The precise decoherence mechanisms, however, are often unknown for a given system. In this work, we make use of an opto-mechanical resonator to obtain key information about spectral densities of its condensed-matter heat bath. In sharp contrast to what is commonly assumed in high-temperature quantum Brownian motion describing the dynamics of the mechanical degree of freedom, based on a statistical analysis of the emitted light, it is shown that this spectral density is highly non-Ohmic, reflected by non-Markovian dynamics, which we quantify. We conclude by elaborating on further applications of opto-mechanical systems in open system identification. PMID:26216619

  10. Analytical studies of spectrum broadcast structures in quantum Brownian motion

    NASA Astrophysics Data System (ADS)

    Tuziemski, J.; Korbicz, J. K.

    2016-11-01

    Spectrum broadcast structures are a new and fresh concept in the quantum-to-classical transition, introduced recently in the context of decoherence and the appearance of objective features in quantum mechanics. These are specific quantum state structures, responsible for the objectivization of the decohered state of a system. Recently, they have been demonstrated by means of the well-known quantum Brownian motion model of the recoilless limit (infinitely massive central system), as the principal interest lies in information transfer from the system to the environment. However, a final analysis relied on numerics. Here, after a presentation of the main concepts, we perform analytical studies of the model, showing the timescales and the efficiency of the spectrum broadcast structure formation. We consider a somewhat simplified environment, being random with a uniform distribution of frequencies.

  11. Rotational Brownian Motion: Trajectory, Reversibility and Stochastic Entropy

    NASA Astrophysics Data System (ADS)

    Bandopadhyay, Swarnali; Chaudhuri, Debasish; Jayannavar, A. M.

    2017-08-01

    Stochastic motion of macrospins is similar to driven diffusion of Brownian particles on the surface of a sphere. One crucial difference is in how the micro-states transform under time reversal. This dictates the form of stochastic entropy production (sEP). An excess sEP in the reservoir, in addition to a Clausius term, may appear depending on the interpretation of stochastic trajectory, thereby, precluding such analysis without a detailed knowledge of the governing dynamics. To show this, we derive expressions of sEP using Fokker-Planck equation, and the ratio of probability distributions of time-forward and time-reversed trajectories. We calculate probability distributions of sEP using numerical simulations, and obtain good agreement with the detailed fluctuation theorem. Within adiabatic approximation, analytic form for the distribution function is also derived.

  12. Ergodicity convergence test suggests telomere motion obeys fractional dynamics

    NASA Astrophysics Data System (ADS)

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

    2011-04-01

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

  13. Modeling of locally self-similar processes using multifractional Brownian motion of Riemann-Liouville type.

    PubMed

    Muniandy, S V; Lim, S C

    2001-04-01

    Fractional Brownian motion (FBM) is widely used in the modeling of phenomena with power spectral density of power-law type. However, FBM has its limitation since it can only describe phenomena with monofractal structure or a uniform degree of irregularity characterized by the constant Holder exponent. For more realistic modeling, it is necessary to take into consideration the local variation of irregularity, with the Holder exponent allowed to vary with time (or space). One way to achieve such a generalization is to extend the standard FBM to multifractional Brownian motion (MBM) indexed by a Holder exponent that is a function of time. This paper proposes an alternative generalization to MBM based on the FBM defined by the Riemann-Liouville type of fractional integral. The local properties of the Riemann-Liouville MBM (RLMBM) are studied and they are found to be similar to that of the standard MBM. A numerical scheme to simulate the locally self-similar sample paths of the RLMBM for various types of time-varying Holder exponents is given. The local scaling exponents are estimated based on the local growth of the variance and the wavelet scalogram methods. Finally, an example of the possible applications of RLMBM in the modeling of multifractal time series is illustrated.

  14. Unsteady three-dimensional stagnation-point flow and heat transfer of a nanofluid with thermophoresis and Brownian motion effects

    NASA Astrophysics Data System (ADS)

    Dinarvand, S.; Hosseini, R.; Tamim, H.; Damangir, E.; Pop, I.

    2015-07-01

    An unsteady three-dimensional stagnation-point flow of a nanofluid past a circular cylinder with sinusoidal radius variation is investigated numerically. By introducing new similarity transformations for the velocity, temperature, and nanoparticle volume fraction, the basic equations governing the flow and heat and mass transfer are reduced to highly nonlinear ordinary differential equations. The resulting nonlinear system is solved numerically by the fourth-order Runge-Kutta method with the shooting technique. The thermophoresis and Brownian motion effects occur in the transport equations. The velocity, temperature, and nanoparticle concentration profiles are analyzed with respect to the involved parameters of interest, namely, unsteadiness parameter, Brownian motion parameter, thermophoresis parameter, Prandtl number, and Lewis number. Numerical values of the friction coefficient, diffusion mass flux, and heat flux are computed. It is found that the friction coefficient and heat transfer rate increase with increasing unsteadiness parameter (the highest heat transfer rate at the surface occurs if the thermophoresis and Brownian motion effects are absent) and decrease with increasing both thermophoresis and Brownian motion parameters. The present results are found to be in good agreement with previously published results.

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

    NASA Astrophysics Data System (ADS)

    Peng, Zheng; To, Kiwing

    2016-08-01

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

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

    NASA Astrophysics Data System (ADS)

    To, Kiwing; Peng, Zheng

    2016-11-01

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

  17. A simple microviscometric approach based on Brownian motion tracking

    NASA Astrophysics Data System (ADS)

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

    2015-02-01

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

  18. Characterizing Detrended Fluctuation Analysis of multifractional Brownian motion

    NASA Astrophysics Data System (ADS)

    Setty, V. A.; Sharma, A. S.

    2015-02-01

    The Hurst exponent (H) is widely used to quantify long range dependence in time series data and is estimated using several well known techniques. Recognizing its ability to remove trends the Detrended Fluctuation Analysis (DFA) is used extensively to estimate a Hurst exponent in non-stationary data. Multifractional Brownian motion (mBm) broadly encompasses a set of models of non-stationary data exhibiting time varying Hurst exponents, H(t) as against a constant H. Recently, there has been a growing interest in time dependence of H(t) and sliding window techniques have been used to estimate a local time average of the exponent. This brought to fore the ability of DFA to estimate scaling exponents in systems with time varying H(t) , such as mBm. This paper characterizes the performance of DFA on mBm data with linearly varying H(t) and further test the robustness of estimated time average with respect to data and technique related parameters. Our results serve as a bench-mark for using DFA as a sliding window estimator to obtain H(t) from time series data.

  19. Survival of Near-Critical Branching Brownian Motion

    NASA Astrophysics Data System (ADS)

    Berestycki, Julien; Berestycki, Nathanaël; Schweinsberg, Jason

    2011-06-01

    Consider a system of particles performing branching Brownian motion with negative drift μ= sqrt{2 - \\varepsilon} and killed upon hitting zero. Initially there is one particle at x>0. Kesten (Stoch. Process. Appl. 7:9-47, 1978) showed that the process survives with positive probability if and only if ɛ>0. Here we are interested in the asymptotics as ɛ→0 of the survival probability Q μ ( x). It is proved that if L=π/sqrt{\\varepsilon} then for all x∈ℝ, lim ɛ→0 Q μ ( L+ x)= θ( x)∈(0,1) exists and is a traveling wave solution of the Fisher-KPP equation. Furthermore, we obtain sharp asymptotics of the survival probability when x< L and L- x→∞. The proofs rely on probabilistic methods developed by the authors in (Berestycki et al. in arXiv: 1001.2337, 2010). This completes earlier work by Harris, Harris and Kyprianou (Ann. Inst. Henri Poincaré Probab. Stat. 42:125-145, 2006) and confirms predictions made by Derrida and Simon (Europhys. Lett. 78:60006, 2007), which were obtained using nonrigorous PDE methods.

  20. Inertial and bias effects in the rotational Brownian motion of rodlike molecules in a uniaxial potential

    NASA Astrophysics Data System (ADS)

    Kalmykov, Yuri P.; Titov, Sergey V.; Coffey, William T.

    2011-01-01

    Inertial effects in the rotational Brownian motion in space of a rigid dipolar rotator (needle) in a uniaxial potential biased by an external field giving rise to asymmetry are treated via the infinite hierarchy of differential-recurrence relations for the statistical moments (orientational correlation functions) obtained by averaging the Euler-Langevin equation over its realizations in phase space. The solutions of this infinite hierarchy for the dipole correlation function and its characteristic times are obtained using matrix continued fractions showing that the model simultaneously predicts both slow overbarrier (or interwell) relaxation at low frequencies accompanied by intermediate frequency Debye relaxation due to fast near-degenerate motion in the wells of the potential (intrawell relaxation) as well as the high frequency resonance (Poley) absorption due to librations of the dipole moments. It is further shown that the escape rate of a Brownian particle from a potential well as extended to the Kramers turnover problem via the depopulation factor yields a close approximation to the longest (overbarrier) relaxation time of the system. For zero and small values of the bias field parameter h, both the dipole moment correlation time and the longest relaxation time have Arrhenius behavior (exponential increase with increasing barrier height). While at values of h in excess of a critical value however far less than that required to achieve nucleation, the Arrhenius behavior of the correlation time disappears.

  1. System Plus Reservoir Approach to Quantum Brownian Motion of a Rod-Like Particle

    NASA Astrophysics Data System (ADS)

    Nasr, Z.; Kheirandish, F.

    2017-07-01

    Quantum Brownian motion of a rod-like particle is investigated in the frame work of system plus reservoir model. The quantum mechanical and classical limit for both translational and rotational motions are discussed. Correlation functions, fluctuation-dissipation relations and mean squared values of translational and rotational motions are obtained.

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

    NASA Astrophysics Data System (ADS)

    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.

  3. Parameter inference from hitting times for perturbed Brownian motion.

    PubMed

    Tamborrino, Massimiliano; Ditlevsen, Susanne; Lansky, Peter

    2015-07-01

    A latent internal process describes the state of some system, e.g. the social tension in a political conflict, the strength of an industrial component or the health status of a person. When this process reaches a predefined threshold, the process terminates and an observable event occurs, e.g. the political conflict finishes, the industrial component breaks down or the person dies. Imagine an intervention, e.g., a political decision, maintenance of a component or a medical treatment, is initiated to the process before the event occurs. How can we evaluate whether the intervention had an effect? To answer this question we describe the effect of the intervention through parameter changes of the law governing the internal process. Then, the time interval between the start of the process and the final event is divided into two subintervals: the time from the start to the instant of intervention, denoted by S, and the time between the intervention and the threshold crossing, denoted by R. The first question studied here is: What is the joint distribution of (S,R)? The theoretical expressions are provided and serve as a basis to answer the main question: Can we estimate the parameters of the model from observations of S and R and compare them statistically? Maximum likelihood estimators are calculated and applied on simulated data under the assumption that the process before and after the intervention is described by the same type of model, i.e. a Brownian motion, but with different parameters. Also covariates and handling of censored observations are incorporated into the statistical model, and the method is illustrated on lung cancer data.

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

    PubMed

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

    2014-08-14

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

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

    NASA Astrophysics Data System (ADS)

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

    2003-07-01

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

  6. Anomalous Brownian motion discloses viscoelasticity in the ear’s mechanoelectrical-transduction apparatus

    PubMed Central

    Kozlov, Andrei S.; Andor-Ardó, Daniel; Hudspeth, A. J.

    2012-01-01

    The ear detects sounds so faint that they produce only atomic-scale displacements in the mechanoelectrical transducer, yet thermal noise causes fluctuations larger by an order of magnitude. Explaining how hearing can operate when the magnitude of the noise greatly exceeds that of the signal requires an understanding both of the transducer’s micromechanics and of the associated noise. Using microrheology, we characterize the statistics of this noise; exploiting the fluctuation-dissipation theorem, we determine the associated micromechanics. The statistics reveal unusual Brownian motion in which the mean square displacement increases as a fractional power of time, indicating that the mechanisms governing energy dissipation are related to those of energy storage. This anomalous scaling contradicts the canonical model of mechanoelectrical transduction, but the results can be explained if the micromechanics incorporates viscoelasticity, a salient characteristic of biopolymers. We amend the canonical model and demonstrate several consequences of viscoelasticity for sensory coding. PMID:22328158

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

    NASA Astrophysics Data System (ADS)

    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.

  8. The rate of collisions due to Brownian or gravitational motion of small drops

    NASA Technical Reports Server (NTRS)

    Zhang, Xiaoguang; Davis, Robert H.

    1991-01-01

    Quantitative predictions of the collision rate of two spherical drops undergoing Brownian diffusion or gravitational sedimentation are presented. The diffusion equation for relative Brownian motion of two drops is derived, and the relative motion of pairs of drops in gravitational sedimentation is traced via a trajectory analysis in order to develop theoretical models to determine the collision efficiencies, both with and without interparticle forces applied between the drops. It is concluded that finite collision rates between nondeforming fluid drops are possible for Brownian diffusion or gravitational sedimentation in the absence of attractive forces, in stark contrast to the prediction that lubrication forces prevent rigid spheres from contacting each other unless an attractive force that becomes infinite as the separation approaches zero is applied. Collision rates are shown to increase as the viscosity of the drop-phase decreases. In general, hydrodynamic interactions reduce the collision rates more for gravitational collisions than for Brownian collisions.

  9. Brownian motion in Robertson-Walker spacetimes from electromagnetic vacuum fluctuations

    SciTech Connect

    Bessa, Carlos H. G.; Bezerra, V. B.; Ford, L. H.

    2009-06-15

    We consider the effects of the vacuum fluctuations of a quantized electromagnetic field on particles in an expanding universe. We find that these particles typically undergo Brownian motion and acquire a nonzero mean squared velocity that depends on the scale factor of the universe. This Brownian motion can be interpreted as due to noncancellation of anticorrelated vacuum fluctuations in the time-dependent background spacetime. Alternatively, one can interpret this effect as the particles acquiring energy from the background spacetime geometry, a phenomenon that cannot occur in a static spacetime. We treat several types of coupling between the electromagnetic field and the particles and several model universes. We also consider both free particles, which, on the average, move on geodesics, and particles in bound systems. There are significant differences between these two cases, which illustrates that nongeodesic motion alters the effects of the vacuum fluctuations. We discuss the possible applications of this Brownian motion effect to cosmological scenarios.

  10. Brownian motion of 2D vacancy islands by adatom terrace diffusion.

    PubMed

    Morgenstern, K; Laegsgaard, E; Besenbacher, F

    2001-06-18

    We have studied the Brownian motion of two-dimensional (2D) vacancy islands on Ag(110) at temperatures between 175 and 215 K. While the detachment of adatoms from the island and their diffusion on the terrace are permitted in this temperature range, the periphery diffusion of single adatoms is prohibited. The present scanning tunneling microscopy results provide the first direct experimental proof that the Brownian motion of the islands follows a simple scaling law with terrace diffusion being the rate limiting process. The activation energy of the vacancy island motion is determined to 0.41 eV.

  11. Amplified effect of Brownian motion in bacterial near-surface swimming

    PubMed Central

    Li, Guanglai; Tam, Lick-Kong; Tang, Jay X.

    2008-01-01

    Brownian motion influences bacterial swimming by randomizing displacement and direction. Here, we report that the influence of Brownian motion is amplified when it is coupled to hydrodynamic interaction. We examine swimming trajectories of the singly flagellated bacterium Caulobacter crescentus near a glass surface with total internal reflection fluorescence microscopy and observe large fluctuations over time in the distance of the cell from the solid surface caused by Brownian motion. The observation is compared with computer simulation based on analysis of relevant physical factors, including electrostatics, van der Waals force, hydrodynamics, and Brownian motion. The simulation reproduces the experimental findings and reveals contribution from fluctuations of the cell orientation beyond the resolution of present observation. Coupled with hydrodynamic interaction between the bacterium and the boundary surface, the fluctuations in distance and orientation subsequently lead to variation of the swimming speed and local radius of curvature of swimming trajectory. These results shed light on the fundamental roles of Brownian motion in microbial motility, nutrient uptake, and adhesion. PMID:19015518

  12. Thermodynamic laws and equipartition theorem in relativistic Brownian motion.

    PubMed

    Koide, T; Kodama, T

    2011-06-01

    We extend the stochastic energetics to a relativistic system. The thermodynamic laws and equipartition theorem are discussed for a relativistic Brownian particle and the first and the second law of thermodynamics in this formalism are derived. The relation between the relativistic equipartition relation and the rate of heat transfer is discussed in the relativistic case together with the nature of the noise term.

  13. Model Experiment of Two-Dimentional Brownian Motion by Microcomputer.

    ERIC Educational Resources Information Center

    Mishima, Nobuhiko; And Others

    1980-01-01

    Describes the use of a microcomputer in studying a model experiment (Brownian particles colliding with thermal particles). A flow chart and program for the experiment are provided. Suggests that this experiment may foster a deepened understanding through mutual dialog between the student and computer. (SK)

  14. Hydrodynamics and Brownian motions of a spheroid near a rigid wall.

    PubMed

    De Corato, M; Greco, F; D'Avino, G; Maffettone, P L

    2015-05-21

    In this work, we study in detail the hydrodynamics and the Brownian motions of a spheroidal particle suspended in a Newtonian fluid near a flat rigid wall. We employ 3D Finite Element Method (FEM) simulations to compute how the mobility tensor of the spheroid varies with both the particle-wall separation distance and the particle orientation. We then study the Brownian motion of the spheroid by means of a discretized Langevin equation. We specifically focus on the additional drift terms arising from the position and orientational dependence of the mobility matrix. In this respect, we also propose a numerically convenient approximation of the orientational divergence of the mobility matrix that is required in the solution of the Langevin equation. Our results illustrate that both hydrodynamics and Brownian motions of a spheroidal particle near a confining wall display novel features from those of a sphere in the same type of confinement.

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

    NASA Astrophysics Data System (ADS)

    Yu, Hongwei; Chen, Jun

    2004-12-01

    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.

  16. Coupling of Lever Arm Swing and Biased Brownian Motion in Actomyosin

    PubMed Central

    Nie, Qing-Miao; Togashi, Akio; Sasaki, Takeshi N.; Takano, Mitsunori; Sasai, Masaki; Terada, Tomoki P.

    2014-01-01

    An important unresolved problem associated with actomyosin motors is the role of Brownian motion in the process of force generation. On the basis of structural observations of myosins and actins, the widely held lever-arm hypothesis has been proposed, in which proteins are assumed to show sequential structural changes among observed and hypothesized structures to exert mechanical force. An alternative hypothesis, the Brownian motion hypothesis, has been supported by single-molecule experiments and emphasizes more on the roles of fluctuating protein movement. In this study, we address the long-standing controversy between the lever-arm hypothesis and the Brownian motion hypothesis through in silico observations of an actomyosin system. We study a system composed of myosin II and actin filament by calculating free-energy landscapes of actin-myosin interactions using the molecular dynamics method and by simulating transitions among dynamically changing free-energy landscapes using the Monte Carlo method. The results obtained by this combined multi-scale calculation show that myosin with inorganic phosphate (Pi) and ADP weakly binds to actin and that after releasing Pi and ADP, myosin moves along the actin filament toward the strong-binding site by exhibiting the biased Brownian motion, a behavior consistent with the observed single-molecular behavior of myosin. Conformational flexibility of loops at the actin-interface of myosin and the N-terminus of actin subunit is necessary for the distinct bias in the Brownian motion. Both the 5.5–11 nm displacement due to the biased Brownian motion and the 3–5 nm displacement due to lever-arm swing contribute to the net displacement of myosin. The calculated results further suggest that the recovery stroke of the lever arm plays an important role in enhancing the displacement of myosin through multiple cycles of ATP hydrolysis, suggesting a unified movement mechanism for various members of the myosin family. PMID:24762409

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

    PubMed

    Nie, Qing-Miao; Togashi, Akio; Sasaki, Takeshi N; Takano, Mitsunori; Sasai, Masaki; Terada, Tomoki P

    2014-04-01

    An important unresolved problem associated with actomyosin motors is the role of Brownian motion in the process of force generation. On the basis of structural observations of myosins and actins, the widely held lever-arm hypothesis has been proposed, in which proteins are assumed to show sequential structural changes among observed and hypothesized structures to exert mechanical force. An alternative hypothesis, the Brownian motion hypothesis, has been supported by single-molecule experiments and emphasizes more on the roles of fluctuating protein movement. In this study, we address the long-standing controversy between the lever-arm hypothesis and the Brownian motion hypothesis through in silico observations of an actomyosin system. We study a system composed of myosin II and actin filament by calculating free-energy landscapes of actin-myosin interactions using the molecular dynamics method and by simulating transitions among dynamically changing free-energy landscapes using the Monte Carlo method. The results obtained by this combined multi-scale calculation show that myosin with inorganic phosphate (Pi) and ADP weakly binds to actin and that after releasing Pi and ADP, myosin moves along the actin filament toward the strong-binding site by exhibiting the biased Brownian motion, a behavior consistent with the observed single-molecular behavior of myosin. Conformational flexibility of loops at the actin-interface of myosin and the N-terminus of actin subunit is necessary for the distinct bias in the Brownian motion. Both the 5.5-11 nm displacement due to the biased Brownian motion and the 3-5 nm displacement due to lever-arm swing contribute to the net displacement of myosin. The calculated results further suggest that the recovery stroke of the lever arm plays an important role in enhancing the displacement of myosin through multiple cycles of ATP hydrolysis, suggesting a unified movement mechanism for various members of the myosin family.

  18. Brownian motion of a circle swimmer in a harmonic trap.

    PubMed

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

    2017-02-01

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

  19. Brownian motion of a circle swimmer in a harmonic trap

    NASA Astrophysics Data System (ADS)

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

    2017-02-01

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

  20. Thermal property in Brownian motion of a particle coupled to vacuum fluctuations

    NASA Astrophysics Data System (ADS)

    Oshita, Naritaka; Yamamoto, Kazuhiro; Zhang, Sen

    2014-06-01

    We investigate Brownian motions of a particle coupled to vacuum fluctuations of a quantum field. The Unruh effect predicts that an observer in an accelerated motion sees the Minkowski vacuum as thermally excited. This addresses the problem of whether or not a thermal property appears in a perturbative random motion of a particle in an accelerated motion due to the coupling. We revisit this problem by solving the equation of motion of a particle coupled to vacuum fluctuations including the radiation reaction force. We compute a Fourier integral for the variance of the random velocity in a rigorous manner. Similarly, we consider a particle coupled to vacuum fluctuations in de Sitter spacetime motivated by the argument that an observer in de Sitter spacetime sees the Bunch-Davies vacuum as a thermally excited state with the Gibbons-Hawking temperature. Our investigation clarifies the condition that the energy equipartition relation arises in the Brownian motions of a particle.

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

    NASA Astrophysics Data System (ADS)

    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.

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

    PubMed Central

    Li, Guanglai; Tang, Jay X.

    2009-01-01

    In this letter we propose a kinematic model to explain how collisions with a surface and rotational Brownian motion give rise to accumulation of micro-swimmers 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. PMID:19792689

  3. Accumulation of microswimmers near a surface mediated by collision and rotational Brownian motion.

    PubMed

    Li, Guanglai; Tang, Jay X

    2009-08-14

    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.

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

    PubMed Central

    Volpe, Giorgio; Volpe, Giovanni; Gigan, Sylvain

    2014-01-01

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

  5. Simultaneous sizing and electrophoretic mobility measurement of sub-micron particles using Brownian motion

    PubMed Central

    Palanisami, Akilan; Miller, John H.

    2011-01-01

    The size and surface chemistry of micron scale particles are of fundamental importance in studies of biology and air particulate pollution. However, typical electrophoretic measurements of these and other sub-micron scale particles (300 nm – 1 μm) cannot resolve size information within heterogeneous mixtures unambiguously. Using optical microscopy, we monitor electrophoretic motion together with the Brownian velocity fluctuations—using the latter to measure size by either the Green-Kubo relation or by calibration from known size standards. Particle diameters are resolved to ±12% with 95% confidence. Strikingly, the size resolution improves as particle size decreases due to the increased Brownian motion. The sizing ability of the Brownian assessed electrophoresis method described here complements the electrophoretic mobility resolution of traditional capillary electrophoresis. PMID:20882556

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

    NASA Astrophysics Data System (ADS)

    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.

  7. Quantum Brownian Motion on Non-Commutative Manifolds: Construction, Deformation and Exit Times

    NASA Astrophysics Data System (ADS)

    Das, Biswarup; Goswami, Debashish

    2012-01-01

    We begin with a review and analytical construction of quantum Gaussian process (and quantum Brownian motions) in the sense of Franz (The Theory of Quantum Levy Processes, http://arxiv.org/abs/math/0407488v1 [math.PR], 2009), Schürmann (White noise on bioalgebras. Volume 1544 of Lecture Notes in Mathematics. Berlin: Springer-Verlag, 1993) and others, and then formulate and study in details (with a number of interesting examples) a definition of quantum Brownian motions on those non-commutative manifolds (a la Connes) which are quantum homogeneous spaces of their quantum isometry groups in the sense of Goswami (Commun Math Phys 285(1):141-160, 2009). We prove that bi-invariant quantum Brownian motion can be `deformed' in a suitable sense. Moreover, we propose a non-commutative analogue of the well-known asymptotics of the exit time of classical Brownian motion. We explicitly analyze such asymptotics for a specific example on non-commutative two-torus {mathcal{A}_θ} , which seems to behave like a one-dimensional manifold, perhaps reminiscent of the fact that {mathcal{A}_θ} is a non-commutative model of the (locally one-dimensional) `leaf-space' of the Kronecker foliation.

  8. Conserved linear dynamics of single-molecule Brownian motion

    NASA Astrophysics Data System (ADS)

    Serag, Maged F.; Habuchi, Satoshi

    2017-06-01

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

  9. Brownian motion of a harmonic oscillator in a noninertial reference frame.

    PubMed

    Jiménez-Aquino, J I; Romero-Bastida, M

    2013-08-01

    The Brownian motion of a charged harmonic oscillator in the presence of additional force fields, such as a constant magnetic field and arbitrary time-dependent electric and mechanical forces, is studied in a rotational reference frame under uniform motion. By assuming an isotropic surrounding medium (a scalar friction constant), we solve explicitly the Smoluchowski equation associated with the Langevin equation for the charged harmonic oscillator and calculate the mean square displacements along and orthogonal to the rotation axis.

  10. Power-law behavior in the power spectrum induced by Brownian motion of a domain wall

    NASA Astrophysics Data System (ADS)

    Takesue, Shinji; Mitsudo, Tetsuya; Hayakawa, Hisao

    2003-07-01

    We show that Brownian motion of a one-dimensional domain wall in a large but finite system yields a ω-3/2 power spectrum. This is successfully applied to the totally asymmetric simple exclusion process with open boundaries. An excellent agreement between our theory and numerical results is obtained in a frequency range where the domain wall motion dominates and the discreteness of the system is not effective.

  11. Digital holography for observing aerosol particles undergoing Brownian motion in microgravity conditions

    NASA Astrophysics Data System (ADS)

    Prodi, F.; Santachiara, G.; Travaini, S.; Belosi, F.; Vedernikov, A.; Dubois, F.; Queeckers, P.; Legros, J. C.

    2006-11-01

    Brownian diffusion of aerosol particles was studied in microgravity conditions using a digital holographic velocimeter. Based on digital image processing, the observed volume, recorded on a charge-coupled device (CCD) camera, is reconstructed slice by slice in order to achieve a full focused volume. Three dimensional coordinates of the particles are retrieved by such procedures and particle trajectories are reconstructed by analysing the sequence of the particle position. We deduced that the displacement of particles in microgravity, due to Brownian motion, follows a Gaussian distribution, like at 1 g. Particle sizes obtained from SEM measurements were in good agreement with those calculated from the three dimensional trajectories provided by the holographic microscope.

  12. Clustering of branching Brownian motions in confined geometries

    NASA Astrophysics Data System (ADS)

    Zoia, A.; Dumonteil, E.; Mazzolo, A.; de Mulatier, C.; Rosso, A.

    2014-10-01

    We study the evolution of a collection of individuals subject to Brownian diffusion, reproduction, and disappearance. In particular, we focus on the case where the individuals are initially prepared at equilibrium within a confined geometry. Such systems are widespread in physics and biology and apply for instance to the study of neutron populations in nuclear reactors and the dynamics of bacterial colonies, only to name a few. The fluctuations affecting the number of individuals in space and time may lead to a strong patchiness, with particles clustered together. We show that the analysis of this peculiar behavior can be rather easily carried out by resorting to a backward formalism based on the Green's function, which allows the key physical observables, namely, the particle concentration and the pair correlation function, to be explicitly derived.

  13. Thermal diffusion by Brownian-motion-induced fluid stress.

    PubMed

    Kreft, Jennifer; Chen, Yeng-Long

    2007-08-01

    The Ludwig-Soret effect, the migration of a species due to a temperature gradient, has been extensively studied without a complete picture of its cause emerging. Here we investigate the dynamics of DNA and spherical particles subjected to a thermal gradient using a combination of Brownian dynamics and the lattice Boltzmann method. We observe that the DNA molecules will migrate to colder regions of the channel, an observation also made in experiments. In fact, the thermal diffusion coefficient found agrees quantitatively with the experimentally measured value. We also observe that the thermal diffusion coefficient decreases as the radius of the studied spherical particles increases. Furthermore, we observe that the thermal-fluctuation-fluid-momentum-flux coupling induces a gradient in the stress which leads to thermal migration in both systems.

  14. Thermal diffusion by Brownian-motion-induced fluid stress

    NASA Astrophysics Data System (ADS)

    Kreft, Jennifer; Chen, Yeng-Long

    2007-08-01

    The Ludwig-Soret effect, the migration of a species due to a temperature gradient, has been extensively studied without a complete picture of its cause emerging. Here we investigate the dynamics of DNA and spherical particles subjected to a thermal gradient using a combination of Brownian dynamics and the lattice Boltzmann method. We observe that the DNA molecules will migrate to colder regions of the channel, an observation also made in experiments. In fact, the thermal diffusion coefficient found agrees quantitatively with the experimentally measured value. We also observe that the thermal diffusion coefficient decreases as the radius of the studied spherical particles increases. Furthermore, we observe that the thermal-fluctuation-fluid-momentum-flux coupling induces a gradient in the stress which leads to thermal migration in both systems.

  15. Environment-dependent dissipation in quantum Brownian motion

    SciTech Connect

    Paavola, J.; Piilo, J.; Suominen, K.-A.; Maniscalco, S.

    2009-05-15

    The dissipative dynamics of a quantum Brownian particle is studied for different types of environment. We derive analytic results for the time evolution of the mean energy of the system for Ohmic, sub-Ohmic, and super-Ohmic environments, without performing the Markovian approximation. Our results allow one to establish a direct link between the form of the environmental spectrum and the thermalization dynamics. This in turn leads to a natural explanation of the microscopic physical processes ruling the system time evolution both in the short-time non-Markovian region and in the long-time Markovian one. Our comparative study of thermalization for different environments sheds light on the physical contexts in which non-Markovian dissipation effects are dominant.

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

    NASA Astrophysics Data System (ADS)

    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.

  17. Fractional Feynman-Kac equation for non-brownian functionals.

    PubMed

    Turgeman, Lior; Carmi, Shai; Barkai, Eli

    2009-11-06

    We derive backward and forward fractional Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing anomalous diffusion. Fractional substantial derivatives introduced by Friedrich and co-workers [Phys. Rev. Lett. 96, 230601 (2006)10.1103/PhysRevLett.96.230601] provide the correct fractional framework for the problem. For applications, we calculate the distribution of occupation times in half space and show how the statistics of anomalous functionals is related to weak ergodicity breaking.

  18. Molecular dynamics test of the Brownian description of Na(+) motion in water

    NASA Technical Reports Server (NTRS)

    Wilson, M. A.; Pohorille, A.; Pratt, L. R.

    1985-01-01

    The present paper provides the results of molecular dynamics calculations on a Na(+) ion in aqueous solution. Attention is given to the sodium-oxygen and sodium-hydrogen radial distribution functions, the velocity autocorrelation function for the Na(+) ion, the autocorrelation function of the force on the stationary ion, and the accuracy of Brownian motion assumptions which are basic to hydrodynamic models of ion dyanmics in solution. It is pointed out that the presented calculations provide accurate data for testing theories of ion dynamics in solution. The conducted tests show that it is feasible to calculate Brownian friction constants for ions in aqueous solutions. It is found that for Na(+) under the considered conditions the Brownian mobility is in error by only 60 percent.

  19. Molecular dynamics test of the Brownian description of Na(+) motion in water

    NASA Technical Reports Server (NTRS)

    Wilson, M. A.; Pohorille, A.; Pratt, L. R.

    1985-01-01

    The present paper provides the results of molecular dynamics calculations on a Na(+) ion in aqueous solution. Attention is given to the sodium-oxygen and sodium-hydrogen radial distribution functions, the velocity autocorrelation function for the Na(+) ion, the autocorrelation function of the force on the stationary ion, and the accuracy of Brownian motion assumptions which are basic to hydrodynamic models of ion dyanmics in solution. It is pointed out that the presented calculations provide accurate data for testing theories of ion dynamics in solution. The conducted tests show that it is feasible to calculate Brownian friction constants for ions in aqueous solutions. It is found that for Na(+) under the considered conditions the Brownian mobility is in error by only 60 percent.

  20. Nonlinear-drifted Brownian motion with multiple hidden states for remaining useful life prediction of rechargeable batteries

    NASA Astrophysics Data System (ADS)

    Wang, Dong; Zhao, Yang; Yang, Fangfang; Tsui, Kwok-Leung

    2017-09-01

    Brownian motion with adaptive drift has attracted much attention in prognostics because its first hitting time is highly relevant to remaining useful life prediction and it follows the inverse Gaussian distribution. Besides linear degradation modeling, nonlinear-drifted Brownian motion has been developed to model nonlinear degradation. Moreover, the first hitting time distribution of the nonlinear-drifted Brownian motion has been approximated by time-space transformation. In the previous studies, the drift coefficient is the only hidden state used in state space modeling of the nonlinear-drifted Brownian motion. Besides the drift coefficient, parameters of a nonlinear function used in the nonlinear-drifted Brownian motion should be treated as additional hidden states of state space modeling to make the nonlinear-drifted Brownian motion more flexible. In this paper, a prognostic method based on nonlinear-drifted Brownian motion with multiple hidden states is proposed and then it is applied to predict remaining useful life of rechargeable batteries. 26 sets of rechargeable battery degradation samples are analyzed to validate the effectiveness of the proposed prognostic method. Moreover, some comparisons with a standard particle filter based prognostic method, a spherical cubature particle filter based prognostic method and two classic Bayesian prognostic methods are conducted to highlight the superiority of the proposed prognostic method. Results show that the proposed prognostic method has lower average prediction errors than the particle filter based prognostic methods and the classic Bayesian prognostic methods for battery remaining useful life prediction.

  1. Ratchet motion and current reversal of coupled Brownian motors in pulsating symmetric potentials

    NASA Astrophysics Data System (ADS)

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

    2017-08-01

    In this study, we investigate the collective directed transport of coupled Brownian particles in spatially symmetric periodic potentials under time-periodic pulsating modulations. We find that the coupling between two particles can induce symmetry breaking and consequently collective directed motion. Moreover, the direction of motion can be reversed under certain conditions. The dependence of directed current on various parameters is systematically studied. reverse motion can be achieved by modulating the coupling free length and the phase shift of the pulsating potential. The dynamical mechanism of these transport properties is understood in terms of the effective-potential theory and the space-time transformation invariance. The directed transport of coupled Brownian motors can be manipulated and optimized by adjusting the coupling strength, pulsating frequency, or noise intensity.

  2. Arbitrage with fractional Gaussian processes

    NASA Astrophysics Data System (ADS)

    Zhang, Xili; Xiao, Weilin

    2017-04-01

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

  3. From diffusion to anomalous diffusion: A century after Einstein's Brownian motion

    NASA Astrophysics Data System (ADS)

    Sokolov, I. M.; Klafter, J.

    2005-06-01

    Einstein's explanation of Brownian motion provided one of the cornerstones which underlie the modern approaches to stochastic processes. His approach is based on a random walk picture and is valid for Markovian processes lacking long-term memory. The coarse-grained behavior of such processes is described by the diffusion equation. However, many natural processes do not possess the Markovian property and exhibit anomalous diffusion. We consider here the case of subdiffusive processes, which correspond to continuous-time random walks in which the waiting time for a step is given by a probability distribution with a diverging mean value. Such a process can be considered as a process subordinated to normal diffusion under operational time which depends on this pathological waiting-time distribution. We derive two different but equivalent forms of kinetic equations, which reduce to known fractional diffusion or Fokker-Planck equations for waiting-time distributions following a power law. For waiting time distributions which are not pure power laws one or the other form of the kinetic equation is advantageous, depending on whether the process slows down or accelerates in the course of time.

  4. Pricing model for equity warrants in a mixed fractional Brownian environment and its algorithm

    NASA Astrophysics Data System (ADS)

    Xiao, Wei-Lin; Zhang, Wei-Guo; Zhang, Xili; Zhang, Xiaoli

    2012-12-01

    This paper deals with the problem of pricing equity warrants in a mixed fractional Brownian environment. Based on the quasi-conditional expectation and the Fourier transform, we present the pricing model for equity warrants. Moreover, a hybrid intelligent algorithm, which is based on the Genetic Algorithm, is employed to solve the nonlinear optimization problem. The performance of our model and the proposed algorithm have been illustrated with some numerical examples.

  5. A Study of Brownian Motion Using Light Scattering

    ERIC Educational Resources Information Center

    Clark, Noel A.; Lunacek, Joseph H.

    1969-01-01

    Describes an apparatus designed to investigate molecular motion by means of light scattering. Light from a He-Ne laser is focused into a cell containing a suspension of polystyrene spheres. The scattered light, collected on the photosurface of a photomultiplier tube, is analyzed. The apparatus won first prize in Demonstration Lecture Apparatus in…

  6. A Study of Brownian Motion Using Light Scattering

    ERIC Educational Resources Information Center

    Clark, Noel A.; Lunacek, Joseph H.

    1969-01-01

    Describes an apparatus designed to investigate molecular motion by means of light scattering. Light from a He-Ne laser is focused into a cell containing a suspension of polystyrene spheres. The scattered light, collected on the photosurface of a photomultiplier tube, is analyzed. The apparatus won first prize in Demonstration Lecture Apparatus in…

  7. A Study of Brownian Motion Using Light Scattering

    ERIC Educational Resources Information Center

    Clark, Noel A.; And Others

    1970-01-01

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

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

    NASA Astrophysics Data System (ADS)

    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 X1(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 =X1(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[-(c2/4 -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.

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

    PubMed

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

    2016-04-01

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

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

    NASA Astrophysics Data System (ADS)

    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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-11-01

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

  12. Nonlinear Transport and Anomalous Brownian Motion in Soft-Mode Turbulence

    NASA Astrophysics Data System (ADS)

    Tamura, Koyo; Yusuf, Yusril; Hidaka, Yoshiki; Kai, Shoichi

    2001-10-01

    Soft-mode turbulence (SMT) is a recently discovered type of spatiotemporal chaos observed in the electrohydrodynamic instability (EHD) of a nematic liquid crystal with homeotropic alignment. Its novelty is that it occurs as the first supercritical bifurcation from a stable stationary state in the weakly nonlinear regime of EHD. A particle, small compared to the characteristic length of the macroscopic flow, injected in SMT travels with random velocity similar to a particle in Brownian motion. We find that the particle trajectory exhibits anomalous Brownian motion such as pumped flight and that the macroscopic diffusion constant due to weak turbulence is about 103 times larger than the diffusion constant associated with the rest state. The stochastic properties of SMT are discussed.

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

    PubMed

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

    2016-11-01

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

  14. Switching effect on the quantum Brownian motion near a reflecting boundary

    SciTech Connect

    Seriu, Masafumi; Wu, C.-H.

    2008-02-15

    The quantum Brownian motion of a charged particle in the electromagnetic vacuum fluctuations is investigated near a perfectly reflecting flat boundary, taking into account the smooth switching process in the measurement. Constructing a smooth switching function by gluing together a plateau and the Lorentzian switching tails, it is shown that the switching tails have a great influence on the measurement of the Brownian motion in the quantum vacuum. Indeed, it turns out that the result with a smooth switching function and the one with a sudden switching function are qualitatively quite different. It is also shown that anticorrelations between the switching tails and the main measuring part plays an essential role in this switching effect. The switching function can also be interpreted as a prototype of a nonequilibrium process in a realistic measurement, so that the switching effect found here is expected to be significant in actual applications in vacuum physics.

  15. Fractional brownian functions as mathematical models of natural rhythm in architecture.

    PubMed

    Cirovic, Ivana M

    2014-10-01

    Carl Bovill suggested and described a method of generating rhythm in architecture with the help of fractional Brownian functions, as they are mathematical models of natural rhythm. A relationship established in the stated procedure between fractional Brownian functions as models of rhythm, and the observed group of architectural elements, is recognized as an analogical relationship, and the procedure of generating rhythm as a process of analogical transfer from the natural domain to the architectural domain. Since analogical transfer implies relational similarity of two domains, and the establishment of one-to-one correspondence, this paper is trying to determine under which conditions such correspondence could be established. For example, if the values of the observed visual feature of architectural elements are not similar to each other in a way in which they can form a monotonically increasing, or a monotonically decreasing bounded sequence, then the structural alignment and the one-to-one correspondence with a single fractional Brownian function cannot be established, hence, this function is deemed inappropriate as a model for the architectural rhythm. In this case we propose overlapping of two or more functions, so that each of them is an analog for one subset of mutually similar values of the visual feature of architectural elements.

  16. Study of Submicron Particle Size Distribution by Laser Doppler Measurement of Brownian Motion.

    DTIC Science & Technology

    1987-01-30

    BROWNIAN MOTION .............. -- e-ee..... 6-1 6.1 Thermal Characteristics of the Particles ........ 6-2 6.2 Thermophoresis of the Particles oo-ee...for particles such as soot particles which have a high absorptivity. 6.2 Thermophoresis of the Particles When a particle with non-zero absorptivity is...illuminated by a laser beam, thermophoresis occurs because a temperature gradient is set up so that the illuminated side of the particle has a higher

  17. Brownian motion of massive skyrmions in magnetic thin films

    SciTech Connect

    Troncoso, Roberto E.; Núñez, Álvaro S.

    2014-12-15

    We report on the thermal effects on the motion of current-driven massive magnetic skyrmions. The reduced equation for the motion of skyrmion has the form of a stochastic generalized Thiele’s equation. We propose an ansatz for the magnetization texture of a non-rigid single skyrmion that depends linearly with the velocity. By using this ansatz it is found that the skyrmion mass tensor is closely related to intrinsic skyrmion parameters, such as Gilbert damping, skyrmion-charge and dissipative force. We have found an exact expression for the average drift velocity as well as the mean-square velocity of the skyrmion. The longitudinal and transverse mobility of skyrmions for small spin-velocity of electrons is also determined and found to be independent of the skyrmion mass.

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

    PubMed Central

    Böttcher, Björn

    2010-01-01

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

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

    PubMed

    Böttcher, Björn

    2010-12-03

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

  20. Brownian motion of a drop with hysteresis dissipation.

    PubMed

    Chaudhury, Manoj K; Mettu, Srinivas

    2008-06-17

    Small water drops placed on a low-energy substrate with a slight tilt were vibrated parallel to the support with bands of Gaussian white noise of different powers. The drops drifted downward on the inclined support accompanied with random forward and backward movements. For a hysteresis free surface, the drift velocity should only be the product of the component of the gravitational acceleration and the Langevin relaxation time, being independent of the power of noise. On the other hand, in the presence of hysteresis, as is the case here, the drift velocity depends strongly on the power of the noise. This result illustrates the role of hysteresis in the drifted motion of drops on a surface subjected to vibration, which has important bearings on various forms of work fluctuation relations.

  1. Population variability in the Active Brownian Particle model of Daphnia motions

    NASA Astrophysics Data System (ADS)

    Moss, Frank; Erdmann, Udo; Schimansky-Geier, Lutz; Ordmann, Anke

    2004-03-01

    Three characteristic motions of foraging biological agents are predicted by the Active Brownian Particle model [1]. These are random motions about the minimum of a central attracting potential, a bifurcation to bidirectional circular motions about the axis of symmetry of the potential, and a transition to vortex motion. All three can be observed in swarms of the zooplankton Daphnia swimming in light fields. Here we focus on the bidirectional circular motions in 2-D space [1]. The mean radii, as well as other characteristics of the paths, are determined by three strength parameters appropriate to individual Daphnia: energy uptake from the medium, metabolistic drain, and dissipation due to movement. It is shown that individual variability can be represented by distributions of these strength parameters. Conditions for which the experimental data are best described by the model are discussed. [1] U. Erdmann, W. Ebeling and V. S. Anishchenko, Excitation of rotational modes in two-dimensional systems of driven Brownian particles. Phys. Rev. E 65, 061106 (2002)

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

    PubMed Central

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

    2011-01-01

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

  3. Brownian motion of a nano-colloidal particle: the role of the solvent.

    PubMed

    Torres-Carbajal, Alexis; Herrera-Velarde, Salvador; Castañeda-Priego, Ramón

    2015-07-15

    Brownian motion is a feature of colloidal particles immersed in a liquid-like environment. Usually, it can be described by means of the generalised Langevin equation (GLE) within the framework of the Mori theory. In principle, all quantities that appear in the GLE can be calculated from the molecular information of the whole system, i.e., colloids and solvent molecules. In this work, by means of extensive Molecular Dynamics simulations, we study the effects of the microscopic details and the thermodynamic state of the solvent on the movement of a single nano-colloid. In particular, we consider a two-dimensional model system in which the mass and size of the colloid are two and one orders of magnitude, respectively, larger than the ones associated with the solvent molecules. The latter ones interact via a Lennard-Jones-type potential to tune the nature of the solvent, i.e., it can be either repulsive or attractive. We choose the linear momentum of the Brownian particle as the observable of interest in order to fully describe the Brownian motion within the Mori framework. We particularly focus on the colloid diffusion at different solvent densities and two temperature regimes: high and low (near the critical point) temperatures. To reach our goal, we have rewritten the GLE as a second kind Volterra integral in order to compute the memory kernel in real space. With this kernel, we evaluate the momentum-fluctuating force correlation function, which is of particular relevance since it allows us to establish when the stationarity condition has been reached. Our findings show that even at high temperatures, the details of the attractive interaction potential among solvent molecules induce important changes in the colloid dynamics. Additionally, near the critical point, the dynamical scenario becomes more complex; all the correlation functions decay slowly in an extended time window, however, the memory kernel seems to be only a function of the solvent density. Thus, the

  4. Direct observation of brownian motion of lipids in a membrane.

    PubMed Central

    Lee, G M; Ishihara, A; Jacobson, K A

    1991-01-01

    Nanovid microscopy, which uses 30- to 40-nm colloidal gold probes combined with video-enhanced contrast, can be used to examine random and directed movements of individual molecules in the plasma membrane of living cells. To validate the technique in a model system, the movements of lipid molecules were followed in a supported, planar bilayer containing fluorescein-conjugated phosphatidylethanolamine (Fl-PtdEtn) labeled with 30-nm gold anti-fluorescein (anti-Fl). Multivalent gold probes were prepared by conjugating only anti-Fl to the gold. Paucivalent probes were prepared by mixing an irrelevant antibody with the anti-Fl prior to conjugation. The membrane-bound gold particles moved in random patterns that were indistinguishable from those produced by computer simulations of two-dimensional random motion. The multivalent gold probes had an average lateral diffusion coefficient (D) of 0.26 x 10(-8) cm2/sec, and paucivalent probes had an average D of 0.73 x 10(-8) cm2/sec. Sixteen percent of the multivalent and 50% of the paucivalent probes had values for D in excess of 0.6 x 10(-8) cm2/sec, which, after allowance for stochastic variation, are consistent with the D of 1.3 x 10(-8) cm2/sec measured by fluorescence recovery after photobleaching of Fl-PtdEtn in the planar bilayer. The effect of valency on diffusion suggests that the multivalent gold binds several lipids forming a disk up to 30-40 nm in diameter, resulting in reduced diffusion with respect to the paucivalent gold, which binds one or a very few lipids. Provided the valency of the gold probe is considered in the interpretation of the results. Nanovid microscopy is a valid method for analyzing the movements of single or small groups of molecules within membranes. Images PMID:1712486

  5. Magneto hall effect on unsteady elastico-viscous nanofluid slip flow in a channel in presence of thermal radiation and heat generation with Brownian motion

    NASA Astrophysics Data System (ADS)

    Karim, M. Enamul; Samad, M. Abdus; Ferdows, M.

    2017-06-01

    The present note investigates the magneto hall effect on unsteady flow of elastico-viscous nanofluid in a channel with slip boundary considering the presence of thermal radiation and heat generation with Brownian motion. Numerical results are achieved by solving the governing equations by the implicit Finite Difference Method (FDM) obtaining primary and secondary velocities, temperature, nanoparticles volume fraction and concentration distributions within the boundary layer entering into the problem. The influences of several interesting parameters such as elastico-viscous parameter, magnetic field, hall parameter, heat generation, thermal radiation and Brownian motion parameters on velocity, heat and mass transfer characteristics of the fluid flow are discussed with the help of graphs. Also the effects of the pertinent parameters, which are of physical and engineering interest, such as Skin friction parameter, Nusselt number and Sherwood number are sorted out. It is found that the flow field and other quantities of physical concern are significantly influenced by these parameters.

  6. On Certain Functionals of the Maximum of Brownian Motion and Their Applications

    NASA Astrophysics Data System (ADS)

    Perret, Anthony; Comtet, Alain; Majumdar, Satya N.; Schehr, Grégory

    2015-12-01

    We consider a Brownian motion (BM) x(τ ) and its maximal value x_{max } = max _{0 ≤ τ ≤ t} x(τ ) on a fixed time interval [0, t]. We study functionals of the maximum of the BM, of the form {O}_{max }(t)=int _0^t V(x_{max } - x(τ )) {d}τ where V( x) can be any arbitrary function and develop various analytical tools to compute their statistical properties. These tools rely in particular on (i) a "counting paths" method and (ii) a path-integral approach. In particular, we focus on the case where V(x) = δ (x-r), with r a real parameter, which is relevant to study the density of near-extreme values of the BM (the so called density of states), ρ (r,t), which is the local time of the BM spent at given distance r from the maximum. We also provide a thorough analysis of the family of functionals {T}_{α }(t)=int _0^t (x_{max } - x(τ ))^α {{d}}τ corresponding to V(x) = x^α with α real. As α is varied, T_α (t) interpolates between different interesting observables. For instance, for α =1, T_{α = 1}(t) is a random variable of the "area", or "Airy", type while for α =-1/2 it corresponds to the maximum time spent by a ballistic particle through a Brownian random potential. On the other hand, for α = -1, it corresponds to the cost of the optimal algorithm to find the maximum of a discrete random walk, proposed by Odlyzko. We revisit here, using tools of theoretical physics, the statistical properties of this algorithm which had been studied before using probabilistic methods. Finally, we extend our methods to constrained BM, including in particular the Brownian bridge, i.e., the Brownian motion starting and ending at the origin.

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

    PubMed Central

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

    2014-01-01

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

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

    PubMed

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

    2014-12-23

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-09-01

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

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

    NASA Astrophysics Data System (ADS)

    Lindenberg, Katja

    2015-03-01

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

  11. Fractional Brownian Motion, Wavelets, and Infrared Detector Noise

    DTIC Science & Technology

    1993-03-01

    swale 3 of (a) FIGURE 31.54-Hertz Amber Camera Data and Daubechies 10 WaveleL 64 NAWCWPNS TP 8103 REFERENCES I. D. A. Scribner, K. A. Sarkady , M. R. Kruer...Arrays," SPIE Focal Plane Arrays: Technology and Applications, Vol. 865 (1987), pp. 185-202. 3. D. A. Scribner, K. A. Sarkady , M. R. Kruer, and J. C...Infrared Detectors and Arrays (1989), pp. 255-64. 4. D. A. Scribner, K. A. Sarkady , J. T. Caulfield, M. R. Kruer, G. Katz, J. C. Gridley, and Charles

  12. A quantitative immunosensing technique based on the measurement of nanobeads' Brownian motion.

    PubMed

    Fan, Yu-Jui; Sheen, Horn-Jiunn; Hsu, Chia-Jui; Liu, Cheng-Pang; Lin, Shiming; Wu, Kuang-Chong

    2009-12-15

    A novel bio-sensing technique based on the measurement of nanobeads' Brownian motion using a micro-particle tracking velocimetry (micro-PTV) has been successfully developed to detect antigen-antibody interactions. The rapid interaction between antigens (C-reactive proteins, CRPs) and nanobeads with conjugated antibodies (anti-CRPs) has enabled real-time detection of CRPs to be easily carried out. During the binding process of CRPs to nanobeads, the mean value of the beads' diameters increases so that the Brownian velocity decreases with the increase of time. Moreover, higher CRP concentration leads to a lower Brownian velocity of the nanobeads in the equilibrium state. From the results, the limit of detection 0.1microg/ml was observed and could be further improved by using smaller nanobeads. Moreover, based on kinetic analysis, the average dissociation constant K(D)=(6.48+/-1.43)x10(-7) found by this technique for anti-CRP was shown to be in close agreement with the literature values obtained by dual-polarization interferometry (DPI) and indirect competition enzyme-linked immunosorbent assay (ELISA). This simple sensing method can further be used to detect other bio-molecules and viruses.

  13. Unidirectional Brownian motion observed in an in silico single molecule experiment of an actomyosin motor

    PubMed Central

    Takano, Mitsunori; Terada, Tomoki P.; Sasai, Masaki

    2010-01-01

    The actomyosin molecular motor, the motor composed of myosin II and actin filament, is responsible for muscle contraction, converting chemical energy into mechanical work. Although recent single molecule and structural studies have shed new light on the energy-converting mechanism, the physical basis of the molecular-level mechanism remains unclear because of the experimental limitations. To provide a clue to resolve the controversy between the lever-arm mechanism and the Brownian ratchet-like mechanism, we here report an in silico single molecule experiment of an actomyosin motor. When we placed myosin on an actin filament and allowed myosin to move along the filament, we found that myosin exhibits a unidirectional Brownian motion along the filament. This unidirectionality was found to arise from the combination of a nonequilibrium condition realized by coupling to the ATP hydrolysis and a ratchet-like energy landscape inherent in the actin-myosin interaction along the filament, indicating that a Brownian ratchet-like mechanism contributes substantially to the energy conversion of this molecular motor. PMID:20385833

  14. Separation of superparamagnetic particles through ratcheted Brownian motion and periodically switching magnetic fields.

    PubMed

    Liu, Fan; Jiang, Li; Tan, Huei Ming; Yadav, Ashutosh; Biswas, Preetika; van der Maarel, Johan R C; Nijhuis, Christian A; van Kan, Jeroen A

    2016-11-01

    Brownian ratchet based particle separation systems for application in lab on chip devices have drawn interest and are subject to ongoing theoretical and experimental investigations. We demonstrate a compact microfluidic particle separation chip, which implements an extended on-off Brownian ratchet scheme that actively separates and sorts particles using periodically switching magnetic fields, asymmetric sawtooth channel sidewalls, and Brownian motion. The microfluidic chip was made with Polydimethylsiloxane (PDMS) soft lithography of SU-8 molds, which in turn was fabricated using Proton Beam Writing. After bonding of the PDMS chip to a glass substrate through surface activation by oxygen plasma treatment, embedded electromagnets were cofabricated by the injection of InSn metal into electrode channels. This fabrication process enables rapid production of high resolution and high aspect ratio features, which results in parallel electrodes accurately aligned with respect to the separation channel. The PDMS devices were tested with mixtures of 1.51 μm, 2.47 μm, and 2.60 μm superparamagnetic particles suspended in water. Experimental results show that the current device design has potential for separating particles with a size difference around 130 nm. Based on the promising results, we will be working towards extending this design for the separation of cells or biomolecules.

  15. Brownian motors

    NASA Astrophysics Data System (ADS)

    Hänggi, P.; Marchesoni, F.; Nori, F.

    2005-02-01

    In systems possessing a spatial or dynamical symmetry breaking, thermal Brownian motion combined with unbiased, non-equilibrium noise gives rise to a channelling of chance that can be used to exercise control over systems at the micro- and even on the nano-scale. This theme is known as the Brownian motor concept. The constructive role of (the generally overdamped) Brownian motion is exemplified for a noise-induced transport of particles within various set-ups. We first present the working principles and characteristics with a proof-of-principle device, a diffusive temperature Brownian motor. Next, we consider very recent applications based on the phenomenon of signal mixing. The latter is particularly simple to implement experimentally in order to optimize and selectively control a rich variety of directed transport behaviors. The subtleties and also the potential for Brownian motors operating in the quantum regime are outlined and some state-of-the-art applications, together with future roadways, are presented.

  16. Wigner function approach to the quantum Brownian motion of a particle in a potential.

    PubMed

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

    2007-07-14

    Recent progress in our understanding of quantum effects on the Brownian motion in an external potential is reviewed. This problem is ubiquitous in physics and chemistry, particularly in the context of decay of metastable states, for example, the reversal of the magnetization of a single domain ferromagnetic particle, kinetics of a superconducting tunnelling junction, etc. Emphasis is laid on the establishment of master equations describing the diffusion process in phase space analogous to the classical Fokker-Planck equation. In particular, it is shown how Wigner's [E. P. Wigner, Phys. Rev., 1932, 40, 749] method of obtaining quantum corrections to the classical equilibrium Maxwell-Boltzmann distribution may be extended to the dissipative non-equilibrium dynamics governing the quantum Brownian motion in an external potential V(x), yielding a master equation for the Wigner distribution function W(x,p,t) in phase space (x,p). The explicit form of the master equation so obtained contains quantum correction terms up to o(h(4)) and in the classical limit, h --> 0, reduces to the classical Klein-Kramers equation. For a quantum oscillator, the method yields an evolution equation coinciding in all respects with that of Agarwal [G. S. Agarwal, Phys. Rev. A, 1971, 4, 739]. In the high dissipation limit, the master equation reduces to a semi-classical Smoluchowski equation describing non-inertial quantum diffusion in configuration space. The Wigner function formulation of quantum Brownian motion is further illustrated by finding quantum corrections to the Kramers escape rate, which, in appropriate limits, reduce to those yielded via quantum generalizations of reaction rate theory.

  17. Fluctuating Hydrodynamics Approach for the Simulation of Nanoparticle Brownian Motion in a Newtonian Fluid.

    PubMed

    Uma, B; Ayyaswamy, P S; Radhakrishnan, R; Eckmann, D M

    2012-06-01

    The Brownian motion of a nanoparticle in an incompressible Newtonian fluid (quiescent or fully developed Poiseuille flow) has been investigated with an arbitrary Lagrangian-Eulerian based finite element method. Results for the motion in a compressible fluid medium are estimated. Thermal fluctuations from the fluid are implemented using a fluctuating hydrodynamics approach. The instantaneous flow around the particle and the particle motion are fully resolved. Carriers of two different sizes with three different densities have been investigated (nearly neutrally buoyant). The numerical results show that (a) the calculated temperature of the nearly neutrally buoyant Brownian particle in a quiescent fluid satisfies the equipartition theorem; (b) the translational and rotational decay of the velocity autocorrelation functions result in algebraic tails, over long time; (c) the translational and rotational mean square displacements of the particle obeys Stokes-Einstein and Stokes-Einstein-Debye relations, respectively. Larger the particle, longer the time taken to attain this limit; and (d) the parallel and perpendicular diffusivities of the particle closer to the wall are consistent with the analytical results, where available.

  18. Weak electrolytes, Brownian motion, vortices in superfluid films, and Odins Aker

    NASA Astrophysics Data System (ADS)

    McCauley, Joseph L.

    1995-01-01

    A brief sketch of the author's days at Yale as Lars Onsager's last physics student is followed by the contributions of the Onsager school to our current understanding of persistent current decays and vortex pinning in very thin superfluid films. The resulting theory is an interplay of three subjects that were dear to Onsager's heart: electrolytes, vortices in superfluids, and Brownian motion. The discussion also surveys a topic of current interest, the role played by defects and boundaries in producing the "stiffness" that characterizes superfluids. The article ends with a few words about the author's connection to Norway.

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

    PubMed

    Xie, Ping

    2009-09-16

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

  20. The Kardar-Parisi-Zhang Equation as Scaling Limit of Weakly Asymmetric Interacting Brownian Motions

    NASA Astrophysics Data System (ADS)

    Diehl, Joscha; Gubinelli, Massimiliano; Perkowski, Nicolas

    2017-09-01

    We consider a system of infinitely many interacting Brownian motions that models the height of a one-dimensional interface between two bulk phases. We prove that the large scale fluctuations of the system are well approximated by the solution to the KPZ equation provided the microscopic interaction is weakly asymmetric. The proof is based on the martingale solutions of Gonçalves and Jara (Arch Ration Mech Anal 212(2):597-644, 2014) and the corresponding uniqueness result of Gubinelli and Perkowski (Energy solutions of KPZ are unique, 2015).

  1. Slower deviations of the branching Brownian motion and of branching random walks

    NASA Astrophysics Data System (ADS)

    Derrida, Bernard; Shi, Zhan

    2017-08-01

    We have shown recently how to calculate the large deviation function of the position X\\max(t) of the rightmost particle of a branching Brownian motion at time t. This large deviation function exhibits a phase transition at a certain negative velocity. Here we extend this result to more general branching random walks and show that the probability distribution of X\\max(t) has, asymptotically in time, a prefactor characterized by a non trivial power law. Dedicated to John Cardy on the occasion of his 70th birthday.

  2. Spatiotemporal spin fluctuations caused by spin-orbit-coupled Brownian motion

    NASA Astrophysics Data System (ADS)

    Poshakinskiy, A. V.; Tarasenko, S. A.

    2015-07-01

    We develop a theory of thermal fluctuations of spin density emerging in a two-dimensional electron gas. The spin fluctuations probed at spatially separated spots of the sample are correlated due to Brownian motion of electrons and spin-orbit coupling. We calculate the spatiotemporal correlation functions of the spin density for both ballistic and diffusive transport of electrons and analyze them for different types of spin-orbit interaction, including the isotropic Rashba model and the persistent spin helix regime. The measurement of spatial spin fluctuations provides direct access to the parameters of spin-orbit coupling and spin transport in conditions close to thermal equilibrium.

  3. Brownian motion and finite approximations of quantum systems over local fields

    NASA Astrophysics Data System (ADS)

    Bakken, Erik Makino; Digernes, Trond; Weisbart, David

    We give a stochastic proof of the finite approximability of a class of Schrödinger operators over a local field, thereby completing a program of establishing in a non-Archimedean setting corresponding results and methods from the Archimedean (real) setting. A key ingredient of our proof is to show that Brownian motion over a local field can be obtained as a limit of random walks over finite grids. Also, we prove a Feynman-Kac formula for the finite systems, and show that the propagator at the finite level converges to the propagator at the infinite level.

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

    NASA Astrophysics Data System (ADS)

    Silva, Antonio

    2005-03-01

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

  5. Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion

    PubMed Central

    Bodrova, Anna S.; Chechkin, Aleksei V.; Cherstvy, Andrey G.; Safdari, Hadiseh; Sokolov, Igor M.; Metzler, Ralf

    2016-01-01

    It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases. PMID:27462008

  6. Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion.

    PubMed

    Bodrova, Anna S; Chechkin, Aleksei V; Cherstvy, Andrey G; Safdari, Hadiseh; Sokolov, Igor M; Metzler, Ralf

    2016-07-27

    It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.

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

    PubMed

    Dettmer, Simon L; Keyser, Ulrich F; Pagliara, Stefano

    2014-02-01

    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.

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

    SciTech Connect

    Dettmer, Simon L.; Keyser, Ulrich F.; Pagliara, Stefano

    2014-02-15

    In this article we present methods for measuring hindered Brownian motion in the confinement of complex 3D geometries using digital video microscopy. Here we discuss essential features of automated 3D particle tracking as well as diffusion data analysis. By introducing local mean squared displacement-vs-time curves, we are able to simultaneously measure the spatial dependence of diffusion coefficients, tracking accuracies and drift velocities. Such local measurements allow a more detailed and appropriate description of strongly heterogeneous systems as opposed to global measurements. Finite size effects of the tracking region on measuring mean squared displacements are also discussed. The use of these methods was crucial for the measurement of the diffusive behavior of spherical polystyrene particles (505 nm diameter) in a microfluidic chip. The particles explored an array of parallel channels with different cross sections as well as the bulk reservoirs. For this experiment we present the measurement of local tracking accuracies in all three axial directions as well as the diffusivity parallel to the channel axis while we observed no significant flow but purely Brownian motion. Finally, the presented algorithm is suitable also for tracking of fluorescently labeled particles and particles driven by an external force, e.g., electrokinetic or dielectrophoretic forces.

  9. Facets on the convex hull of d -dimensional Brownian and Lévy motion

    NASA Astrophysics Data System (ADS)

    Randon-Furling, Julien; Wespi, Florian

    2017-03-01

    For stationary, homogeneous Markov processes (viz., Lévy processes, including Brownian motion) in dimension d ≥3 , we establish an exact formula for the average number of (d -1 ) -dimensional facets that can be defined by d points on the process's path. This formula defines a universality class in that it is independent of the increments' distribution, and it admits a closed form when d =3 , a case which is of particular interest for applications in biophysics, chemistry, and polymer science. We also show that the asymptotical average number of facets behaves as ˜2 (T /Δ t)lnd -1, where T is the total duration of the motion and Δ t is the minimum time lapse separating points that define a facet.

  10. Temperature-dependent effect of percolation and Brownian motion on the thermal conductivity of TiO2-ethanol nanofluids.

    PubMed

    Li, Chien-Cheng; Hau, Nga Yu; Wang, Yuechen; Soh, Ai Kah; Feng, Shien-Ping

    2016-06-01

    Ethanol-based nanofluids have attracted much attention due to the enhancement in heat transfer and their potential applications in nanofluid-type fuels and thermal storage. Most research has been conducted on ethanol-based nanofluids containing various nanoparticles in low mass fraction; however, to-date such studies based on high weight fraction of nanoparticles are limited due to the poor stability problem. In addition, very little existing work has considered the inevitable water content in ethanol for the change of thermal conductivity. In this paper, the highly stable and well-dispersed TiO2-ethanol nanofluids of high weight fraction of up to 3 wt% can be fabricated by stirred bead milling, which enables the studies of thermal conductivity of TiO2-ethanol nanofluids over a wide range of operating temperatures. Our results provide evidence that the enhanced thermal conductivity is mainly contributed by the percolation network of nanoparticles at low temperatures, while it is in combination with both Brownian motion and local percolation of nanoparticle clustering at high temperatures.

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

    SciTech Connect

    Yeh, L. |

    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.

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

    PubMed

    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.

  13. Physical insight into the thermodynamic uncertainty relation using Brownian motion in tilted periodic potentials

    NASA Astrophysics Data System (ADS)

    Hyeon, Changbong; Hwang, Wonseok

    2017-07-01

    Using Brownian motion in periodic potentials V (x ) tilted by a force f , we provide physical insight into the thermodynamic uncertainty relation, a recently conjectured principle for statistical errors and irreversible heat dissipation in nonequilibrium steady states. According to the relation, nonequilibrium output generated from dissipative processes necessarily incurs an energetic cost or heat dissipation q , and in order to limit the output fluctuation within a relative uncertainty ɛ , at least 2 kBT /ɛ2 of heat must be dissipated. Our model shows that this bound is attained not only at near-equilibrium [f ≪V'(x ) ] but also at far-from-equilibrium [f ≫V'(x ) ] , more generally when the dissipated heat is normally distributed. Furthermore, the energetic cost is maximized near the critical force when the barrier separating the potential wells is about to vanish and the fluctuation of Brownian particles is maximized. These findings indicate that the deviation of heat distribution from Gaussianity gives rise to the inequality of the uncertainty relation, further clarifying the meaning of the uncertainty relation. Our derivation of the uncertainty relation also recognizes a bound of nonequilibrium fluctuations that the variance of dissipated heat (σq2) increases with its mean (μq), and it cannot be smaller than 2 kBT μq .

  14. Combination of fractional Brownian random field and lacunarity for iris recognition

    NASA Astrophysics Data System (ADS)

    Liu, Kai; Zhou, Weidong; Wang, Yu

    2011-10-01

    Feature extraction plays a vital role in iris recognition, affecting the performance of iris recognition algorithm strongly. In this paper, we present an individual recognition algorithm using fractal dimension based on fractional Brownian random field and lacunarity in feature extraction. Making use of the fractal feature of iris, such as self-similarity and random patterns, fractal dimension can extract texture information effectively. Lacunarity overcomes the limitation of fractal dimension that fractal sets with different textures may share the same fractal dimension value. The combination of fractal dimension and lacunarity makes the feature extraction more comprehensive and distinguishable. The experimental results show that this recognition algorithm can obtain great performance on CASIA 1.0 iris database

  15. Volume fraction instability in an oscillating non-Brownian iso-dense suspension.

    NASA Astrophysics Data System (ADS)

    Roht, Y. L.; Gauthier, G.; Hulin, J. P.; Salin, D.; Chertcoff, R.; Auradou, H.; Ippolito, I.

    2017-06-01

    The instability of an iso-dense non-Brownian suspension of polystyrene beads of diameter 40 μm dispersed in a water-glycerol mixture submitted to a periodic square wave oscillating flow in a Hele-Shaw cell is studied experimentally. The instability gives rise to stationary bead concentration waves transverse to the flow. It has been observed for average particle volume fractions between 0.25 and 0.4, for periods of the square wave flow variation between 0.4 and 10 s and in finite intervals of the amplitude of the fluid displacement. The study shows that the wavelength λ increases roughly linearly with the amplitude of the oscillatory flow; on the other hand, λ is independent of the particle concentration and of the period of oscillation of the flow although the minimum threshold amplitude for observing the instability increases with the period.

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

    PubMed

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

    2017-10-03

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

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

    PubMed

    Brenner, Howard

    2005-12-01

    A quiescent single-component gravity-free gas subject to a small steady uniform temperature gradient T, despite being at rest, is shown to experience a drift velocity UD=-D* gradient ln T, where D* is the gas's nonisothermal self-diffusion coefficient. D* is identified as being the gas's thermometric diffusivity alpha. The latter differs from the gas's isothermal isotopic self-diffusion coefficient D, albeit only slightly. Two independent derivations are given of this drift velocity formula, one kinematical and the other dynamical, both derivations being strictly macroscopic in nature. Within modest experimental and theoretical uncertainties, this virtual drift velocity UD=-alpha gradient ln T is shown to be constitutively and phenomenologically indistinguishable from the well-known experimental and theoretical formulas for the thermophoretic velocity U of a macroscopic (i.e., non-Brownian) non-heat-conducting particle moving under the influence of a uniform temperature gradient through an otherwise quiescent single-component rarefied gas continuum at small Knudsen numbers. Coupled with the size independence of the particle's thermophoretic velocity, the empirically observed equality, U=UD, leads naturally to the hypothesis that these two velocities, the former real and the latter virtual, are, in fact, simply manifestations of the same underlying molecular phenomenon, namely the gas's Brownian movement, albeit biased by the temperature gradient. This purely hydrodynamic continuum-mechanical equality is confirmed by theoretical calculations effected at the kinetic-molecular level on the basis of an existing solution of the Boltzmann equation for a quasi-Lorentzian gas, modulo small uncertainties pertaining to the choice of collision model. Explicitly, this asymptotically valid molecular model allows the virtual drift velocity UD of the light gas and the thermophoretic velocity U of the massive, effectively non-Brownian, particle, now regarded as the tracer particle

  18. Large Deviations for the Branching Brownian Motion in Presence of Selection or Coalescence

    NASA Astrophysics Data System (ADS)

    Derrida, Bernard; Shi, Zhan

    2016-06-01

    The large deviation function has been known for a long time in the literature for the displacement of the rightmost particle in a branching random walk (BRW), or in a branching Brownian motion (BBM). More recently a number of generalizations of the BBM and of the BRW have been considered where selection or coalescence mechanisms tend to limit the exponential growth of the number of particles. Here we try to estimate the large deviation function of the position of the rightmost particle for several such generalizations: the L-BBM, the N-BBM, and the coalescing branching random walk (CBRW) which is closely related to the noisy FKPP equation. Our approach allows us to obtain only upper bounds on these large deviation functions. One noticeable feature of our results is their non analytic dependence on the parameters (such as the coalescence rate in the CBRW).

  19. Time multiplexing super-resolution nanoscopy based on the Brownian motion of gold nanoparticles

    NASA Astrophysics Data System (ADS)

    Ilovitsh, Tali; Ilovitsh, Asaf; Wagner, Omer; Zalevsky, Zeev

    2017-02-01

    Super-resolution localization microscopy can overcome the diffraction limit and achieve a tens of order improvement in resolution. It requires labeling the sample with fluorescent probes followed with their repeated cycles of activation and photobleaching. This work presents an alternative approach that is free from direct labeling and does not require the activation and photobleaching cycles. Fluorescently labeled gold nanoparticles in a solution are distributed on top of the sample. The nanoparticles move in a random Brownian motion, and interact with the sample. By obscuring different areas in the sample, the nanoparticles encode the sub-wavelength features. A sequence of images of the sample is captured and decoded by digital post processing to create the super-resolution image. The achievable resolution is limited by the additive noise and the size of the nanoparticles. Regular nanoparticles with diameter smaller than 100nm are barely seen in a conventional bright field microscope, thus fluorescently labeled gold nanoparticles were used, with proper

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

    NASA Astrophysics Data System (ADS)

    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.

  1. Magnetic spectroscopy of nanoparticle Brownian motion measurement of microenvironment matrix rigidity.

    PubMed

    Weaver, John B; Rauwerdink, Kristen M; Rauwerdink, Adam M; Perreard, Irina M

    2013-12-01

    The rigidity of the extracellular matrix and of the integrin links to the cytoskeleton regulates signaling cascades, controlling critical aspects of cancer progression including metastasis and angiogenesis. We demonstrate that the matrix stiffness can be monitored using magnetic spectroscopy of nanoparticle Brownian motion (MSB). We measured the MSB signal from nanoparticles bound to large dextran polymers. The number of glutaraldehyde induced cross-links was used as a surrogate for material stiffness. There was a highly statistically significant change in the MSB signal with the number of cross-links especially prominent at higher frequencies. The p-values were all highly significant. We conclude that the MSB signal can be used to identify and monitor changes in the stiffness of the local matrix to which the nanoparticles are bound.

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

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

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

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

    SciTech Connect

    Anastopoulos, C.; Kechribaris, S.; Mylonas, D.

    2010-10-15

    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 time scales.

  4. On the use of reverse Brownian motion to accelerate hybrid simulations

    NASA Astrophysics Data System (ADS)

    Bakarji, Joseph; Tartakovsky, Daniel M.

    2017-04-01

    Multiscale and multiphysics simulations are two rapidly developing fields of scientific computing. Efficient coupling of continuum (deterministic or stochastic) constitutive solvers with their discrete (stochastic, particle-based) counterparts is a common challenge in both kinds of simulations. We focus on interfacial, tightly coupled simulations of diffusion that combine continuum and particle-based solvers. The latter employs the reverse Brownian motion (rBm), a Monte Carlo approach that allows one to enforce inhomogeneous Dirichlet, Neumann, or Robin boundary conditions and is trivially parallelizable. We discuss numerical approaches for improving the accuracy of rBm in the presence of inhomogeneous Neumann boundary conditions and alternative strategies for coupling the rBm solver with its continuum counterpart. Numerical experiments are used to investigate the convergence, stability, and computational efficiency of the proposed hybrid algorithm.

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

    NASA Astrophysics Data System (ADS)

    Avan, Jean; Grosjean, Nicolas; Huillet, Thierry

    2015-04-01

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

  6. Brownian entanglement

    SciTech Connect

    Allahverdyan, A.E.; Khrennikov, A.; Nieuwenhuizen, Th.M.

    2005-09-15

    For two classical Brownian particles an analog of continuous-variable quantum entanglement is presented: The common probability distribution of the two coordinates and the corresponding coarse-grained velocities cannot always be prepared via mixing of any factorized distributions referring to the two particles separately. This is possible for particles which have interacted in the past, but do not interact at present. Three factors are crucial for the effect: (1) separation of time scales of coordinate and momentum which motivates the definition of coarse-grained velocities; (2) the resulting uncertainty relations between the coordinate of the Brownian particle and the change of its coarse-grained velocity; (3) the fact that the coarse-grained velocity, though pertaining to a single Brownian particle, is defined on a common context of two particles. The Brownian entanglement is a consequence of a coarse-grained description and disappears for a finer resolution of the Brownian motion. Analogies with the quantum situation are discussed, as well as possibilities of experimental realization of the effect in examples of macroscopic Brownian motion.

  7. Thon rings from amorphous ice and implications of beam-induced Brownian motion in single particle electron cryo-microscopy.

    PubMed

    McMullan, G; Vinothkumar, K R; Henderson, R

    2015-11-01

    We have recorded dose-fractionated electron cryo-microscope images of thin films of pure flash-frozen amorphous ice and pre-irradiated amorphous carbon on a Falcon II direct electron detector using 300 keV electrons. We observe Thon rings [1] in both the power spectrum of the summed frames and the sum of power spectra from the individual frames. The Thon rings from amorphous carbon images are always more visible in the power spectrum of the summed frames whereas those of amorphous ice are more visible in the sum of power spectra from the individual frames. This difference indicates that while pre-irradiated carbon behaves like a solid during the exposure, amorphous ice behaves like a fluid with the individual water molecules undergoing beam-induced motion. Using the measured variation in the power spectra amplitude with number of electrons per image we deduce that water molecules are randomly displaced by a mean squared distance of ∼1.1 Å(2) for every incident 300 keV e(-)/Å(2). The induced motion leads to an optimal exposure with 300 keV electrons of 4.0 e(-)/Å(2) per image with which to observe Thon rings centred around the strong 3.7 Å scattering peak from amorphous ice. The beam-induced movement of the water molecules generates pseudo-Brownian motion of embedded macromolecules. The resulting blurring of single particle images contributes an additional term, on top of that from radiation damage, to the minimum achievable B-factor for macromolecular structure determination.

  8. Thon rings from amorphous ice and implications of beam-induced Brownian motion in single particle electron cryo-microscopy

    PubMed Central

    G. McMullan; Vinothkumar, K.R.; Henderson, R.

    2015-01-01

    We have recorded dose-fractionated electron cryo-microscope images of thin films of pure flash-frozen amorphous ice and pre-irradiated amorphous carbon on a Falcon II direct electron detector using 300 keV electrons. We observe Thon rings [1] in both the power spectrum of the summed frames and the sum of power spectra from the individual frames. The Thon rings from amorphous carbon images are always more visible in the power spectrum of the summed frames whereas those of amorphous ice are more visible in the sum of power spectra from the individual frames. This difference indicates that while pre-irradiated carbon behaves like a solid during the exposure, amorphous ice behaves like a fluid with the individual water molecules undergoing beam-induced motion. Using the measured variation in the power spectra amplitude with number of electrons per image we deduce that water molecules are randomly displaced by a mean squared distance of ∼1.1 Å2 for every incident 300 keV e−/Å2. The induced motion leads to an optimal exposure with 300 keV electrons of 4.0 e−/Å2 per image with which to observe Thon rings centred around the strong 3.7 Å scattering peak from amorphous ice. The beam-induced movement of the water molecules generates pseudo-Brownian motion of embedded macromolecules. The resulting blurring of single particle images contributes an additional term, on top of that from radiation damage, to the minimum achievable B-factor for macromolecular structure determination. PMID:26103047

  9. Nanoblinker: Brownian Motion Powered Bio-Nanomachine for FRET Detection of Phagocytic Phase of Apoptosis

    PubMed Central

    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

  10. Brownian dynamics studies on DNA gel electrophoresis. II. ``Defect'' dynamics in the elongation-contraction motion

    NASA Astrophysics Data System (ADS)

    Azuma, Ryuzo

    2002-10-01

    By means of the Brownian dynamics (BD) method of simulations we have developed, we study the dynamics of individual DNA molecules which are undergoing constant field gel electrophoresis (CFGE), focusing on the relevance of the "defect" concept due to de Gennes in CFGE. The corresponding objects, which we call slack beads (s-beads), are explicitly introduced in our BD model. In equilibrium under a vanishing field, the distance between s-beads and their hopping range is found to be randomly distributed following a Poisson distribution. In strong fields, where a chain undergoes elongation-contraction motion, s-beads are observed to be alternately annihilated in elongation and created in the contraction of the chain. On the other hand, the distribution of hopping ranges of s-beads does not differ much from that in equilibrium. The results indicate that in the elongation-contraction motion of the chain, a large number of random movements of s-beads are involved. We have also confirmed that these features of s-beads agree qualitatively with those of s-monomers in the extended bond fluctuation model (EBFM) which we recently proposed. This agreement strongly supports the stochastic semilocal movement of s-monomers which we a priori introduced into the EBFM.

  11. Nanoblinker: Brownian motion powered bio-nanomachine for FRET detection of phagocytic phase of apoptosis.

    PubMed

    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.

  12. From Mechanical Motion to Brownian Motion, Thermodynamics and Particle Transport Theory

    ERIC Educational Resources Information Center

    Bringuier, E.

    2008-01-01

    The motion of a particle in a medium is dealt with either as a problem of mechanics or as a transport process in non-equilibrium statistical physics. The two kinds of approach are often unrelated as they are taught in different textbooks. The aim of this paper is to highlight the link between the mechanical and statistical treatments of particle…

  13. From Mechanical Motion to Brownian Motion, Thermodynamics and Particle Transport Theory

    ERIC Educational Resources Information Center

    Bringuier, E.

    2008-01-01

    The motion of a particle in a medium is dealt with either as a problem of mechanics or as a transport process in non-equilibrium statistical physics. The two kinds of approach are often unrelated as they are taught in different textbooks. The aim of this paper is to highlight the link between the mechanical and statistical treatments of particle…

  14. A kinetic equation for linear stable fractional motion with applications to space plasma physics

    SciTech Connect

    Watkins, Nicholas W; Credgington, Daniel; Sanchez, Raul; Rosenberg, SJ; Chapman, Sandra C

    2009-01-01

    Levy flights and fractional Brownian motion have become exemplars of the heavy-tailed jumps and long-ranged memory widely seen in physics. Natural time series frequently combine both effects, and linear fractional stable motion (lfsm) is a model process of this type, combining {alpha}-stable jumps with a memory kernel. In contrast complex physical spatiotemporal diffusion processes where both the above effects compete have for many years been modeled using the fully fractional kinetic equation for the continuous-time random walk (CTRW), with power laws in the probability density functions of both jump size and waiting time. We derive the analogous kinetic equation for lfsm and show that it has a diffusion coefficient with a power law in time rather than having a fractional time derivative like the CTRW. We discuss some preliminary results on the scaling of burst 'sizes' and 'durations' in lfsm time series, with applications to modeling existing observations in space physics and elsewhere.

  15. Solution of the master equation for Wigner's quasiprobability distribution in phase space for the Brownian motion of a particle in a double well potential.

    PubMed

    Coffey, William T; Kalmykov, Yuri P; Titov, Serguey V

    2007-08-21

    Quantum effects in the Brownian motion of a particle in the symmetric double well potential V(x)=ax(2)2+bx(4)4 are treated using the semiclassical master equation for the time evolution of the Wigner distribution function W(x,p,t) in phase space (x,p). The equilibrium position autocorrelation function, dynamic susceptibility, and escape rate are evaluated via matrix continued fractions in the manner customarily used for the classical Fokker-Planck equation. The escape rate so yielded has a quantum correction depending strongly on the barrier height and is compared with that given analytically by the quantum mechanical reaction rate solution of the Kramers turnover problem. The matrix continued fraction solution substantially agrees with the analytic solution. Moreover, the low-frequency part of the spectrum associated with noise assisted Kramers transitions across the potential barrier may be accurately described by a single Lorentzian with characteristic frequency given by the quantum mechanical reaction rate.

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

    PubMed Central

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

    2010-01-01

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

  17. KiloHertz Bandwidth, Dual-Stage Haptic Device Lets You Touch Brownian Motion.

    PubMed

    Lu, Tianming; Pacoret, Cecile; Heriban, David; Mohand-Ousaid, Abdenbi; Regnier, Stephane; Hayward, Vincent

    2016-12-23

    This paper describes a haptic interface that has a uniform response over the entire human tactile frequency range. Structural mechanics makes it very difficult to implement articulated mechanical systems that can transmit high frequency signals. Here, we separated the frequency range into two frequency bands. The lower band is within the first structural mode of the corresponding haptic device while the higher one can be transmitted accurately by a fast actuator operating from conservation of momentum, that is, without reaction forces to the ground. To couple the two systems, we adopted a channel separation approach akin to that employed in the design of acoustic reproduction systems. The two channels are recombined at the tip of the device to give a uniform frequency response from DC to one kHz. In terms of mechanical design, the high-frequency transducer was embedded inside the tip of the main stage so that during operation, the human operator has only to interact with a single finger interface. In order to exemplify the type of application that would benefit from this kind of interface, we applied it to the haptic exploration with microscopic scales objects which are known to behave with very fast dynamics. The novel haptic interface was bilaterally coupled with a micromanipulation platform to demonstrate its capabilities. Operators could feel interaction forces arising from contact as well as those resulting from Brownian motion and could manoeuvre a micro bead in the absence of vision.

  18. 3D tracking the Brownian motion of colloidal particles using digital holographic microscopy and joint reconstruction.

    PubMed

    Verrier, Nicolas; Fournier, Corinne; Fournel, Thierry

    2015-06-01

    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 problem 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 problem 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 setup based on a low-end microscope objective (×20, 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 2×2×5  nm3 for position under additive white Gaussian noise assumption.

  19. Brownian motion of a classical harmonic oscillator in a magnetic field.

    PubMed

    Jiménez-Aquino, J I; Velasco, R M; Uribe, F J

    2008-05-01

    In this paper, the stochastic diffusion process of a charged classical harmonic oscillator in a constant magnetic field is exactly described through the analytical solution of the associated Langevin equation. Due to the presence of the magnetic field, stochastic diffusion takes place across and along the magnetic field. Along the magnetic field, the Brownian motion is exactly the same as that of the ordinary one-dimensional classical harmonic oscillator, which was very well described in Chandrasekhar's celebrated paper [Rev. Mod. Phys. 15, 1 (1943)]. Across the magnetic field, the stochastic process takes place on a plane, perpendicular to the magnetic field. For internally Gaussian white noise, this planar-diffusion process is exactly described through the first two moments of the positions and velocities and their corresponding cross correlations. In the absence of the magnetic field, our analytical results are the same as those calculated by Chandrasekhar for the ordinary harmonic oscillator. The stochastic planar diffusion is also well characterized in the overdamped approximation, through the solutions of the Langevin equation.

  20. From Brownian motion to operational risk: Statistical physics and financial markets

    NASA Astrophysics Data System (ADS)

    Voit, Johannes

    2003-04-01

    High-frequency returns of the DAX German blue chip stock index are used to test geometric Brownian motion, the standard model for financial time series. Even on a 15-s time scale, the linear correlations of DAX returns have a zero-time delta function which carries 90% of the weight, while the remaining 10% are positively correlated with a decay time of 53 s and negatively correlated on a 9.4-min scale. The probability density of the returns possesses fat tails with power laws whose exponents continuously increase with time scales. It is suggested that hydrodynamic turbulence may provide a phenomenological framework for the description of these data, and at the same time, open a way to use them for risk-management purposes, e.g. option pricing and hedging. Option pricing also is the cornerstone of credit valuation, an area of much practical importance not considered explicitly in most other physics-inspired papers on finance. Finally, operational risk is introduced as a new risk category currently emphasized by regulators, which will become important in many banks in the near future.

  1. Scale Relativistic signature in the Brownian motion of micro-spheres in optical traps

    NASA Astrophysics Data System (ADS)

    Lebohec, Stephan

    2017-09-01

    The development of mechanics of nondifferentiable paths36 suggested by Scale Relativity31,32 results in a foundation of Quantum Mechanics30,37 including Schrödinger’s equation and all the other axioms under the assumption the path nondifferentiability can be described as a Wiener process at the resolution-scale of observation. This naturally brings under question the possibility that the statistics of the dynamics of macroscopic systems fulfilling this hypothesis could fall under a quantum-like description with the Planck constant replaced with some other constant, possibly system specific, and corresponding to a diffusion coefficient. The observation of such a quantum-like dynamics would establish if the Scale Relativistic principle is implemented in macroscopic complex or chaotic systems. This would have major implications for the study of structure formation dynamics in various research fields. In this paper, I investigate the possibility for the detection of such an effect in the Brownian motion of a micro-sphere in an optical trap. I find that, if it exists, the observation of the transition to a quantum-like regime is within reach of modern experiments.

  2. Molecular sensing with magnetic nanoparticles using magnetic spectroscopy of nanoparticle Brownian motion.

    PubMed

    Zhang, Xiaojuan; Reeves, Daniel B; Perreard, Irina M; Kett, Warren C; Griswold, Karl E; Gimi, Barjor; Weaver, John B

    2013-12-15

    Functionalized magnetic nanoparticles (mNPs) have shown promise in biosensing and other biomedical applications. Here we use functionalized mNPs to develop a highly sensitive, versatile sensing strategy required in practical biological assays and potentially in vivo analysis. We demonstrate a new sensing scheme based on magnetic spectroscopy of nanoparticle Brownian motion (MSB) to quantitatively detect molecular targets. MSB uses the harmonics of oscillating mNPs as a metric for the freedom of rotational motion, thus reflecting the bound state of the mNP. The harmonics can be detected in vivo from nanogram quantities of iron within 5s. Using a streptavidin-biotin binding system, we show that the detection limit of the current MSB technique is lower than 150 pM (0.075 pmole), which is much more sensitive than previously reported techniques based on mNP detection. Using mNPs conjugated with two anti-thrombin DNA aptamers, we show that thrombin can be detected with high sensitivity (4 nM or 2 pmole). A DNA-DNA interaction was also investigated. The results demonstrated that sequence selective DNA detection can be achieved with 100 pM (0.05 pmole) sensitivity. The results of using MSB to sense these interactions, show that the MSB based sensing technique can achieve rapid measurement (within 10s), and is suitable for detecting and quantifying a wide range of biomarkers or analytes. It has the potential to be applied in variety of biomedical applications or diagnostic analyses.

  3. Brownian motion of a matter-wave bright soliton moving through a thermal cloud of distinct atoms

    NASA Astrophysics Data System (ADS)

    McDonald, R. G.; Bradley, A. S.

    2016-06-01

    Taking an open quantum system approach, we derive a collective equation of motion for the dynamics of a matter-wave bright soliton moving through a thermal cloud of a distinct atomic species. The reservoir interaction involves energy transfer without particle transfer between the soliton and thermal cloud, thus damping the soliton motion without altering its stability against collapse. We derive a Langevin equation for the soliton center-of-mass velocity in the form of an Ornstein-Uhlenbeck process with analytical drift and diffusion coefficients. This collective motion is confirmed by simulations of the full stochastic projected Gross-Pitaevskii equation for the matter-wave field. The system offers a pathway for experimentally observing the elusive energy-damping reservoir interaction and a clear realization of collective Brownian motion for a mesoscopic superfluid droplet.

  4. Brownian motion on \\lbrack 0,\\infty) with linear drift, reflected at zero: exact asymptotics for ergodic means

    NASA Astrophysics Data System (ADS)

    Fatalov, V. R.

    2017-07-01

    For the Brownian motion X_μ(t) on the half-axis \\lbrack 0,∞) with linear drift μ, reflected at zero and for fixed numbers p>0, δ>0, d>0, a ≥ 0, we calculate the exact asymptotics as T\\to∞ of the mathematical expectations and probabilities \\displaystyle \\mathsf E\\biggl \\lbrack \\exp\\biggl\\{-δ\\int_0T X_μ......l\\{\\frac1 T\\int_0T X_μ^p(t) dt as well as of their conditional versions. For p=1 we give explicit formulae for the emerging constants via the Airy function. We consider an application of the results obtained to the problem of studying the behaviour of a Brownian particle in a gravitational field in a container bounded below by an impenetrable wall when μ=-mg/(2kT K), where m is the mass of the Brownian particle, g is the gravitational acceleration, k is the Boltzmann constant, T K is the temperature in the Kelvin scale. The analysis is conducted by the Laplace method for the sojourn time of homogeneous Markov processes. Bibliography: 31 titles.

  5. Application of Brownian motion theory to the analysis of membrane channel ionic trajectories calculated by molecular dynamics.

    PubMed Central

    Jakobsson, E; Chiu, S W

    1988-01-01

    This paper shows how Brownian motion theory can be used to analyze features of individual ion trajectories in channels as calculated by molecular dynamics, and that its use permits more precise determinations of diffusion coefficients than would otherwise be possible. We also show how a consideration of trajectories of single particles can distinguish between effects due to the magnitude of the diffusion coefficient and effects due to barriers and wells in the potential profile, effects which can not be distinguished by consideration of average fluxes. PMID:2465032

  6. Statistical thermodynamics of quantum Brownian motion: construction of perpetuum mobile of the second kind.

    PubMed

    Nieuwenhuizen, Th M; Allahverdyan, A E

    2002-09-01

    The Brownian motion of a quantum particle in a harmonic confining potential and coupled to harmonic quantum thermal bath is exactly solvable. Though this system presents at high temperatures a pedagogic example to explain the laws of thermodynamics, it is shown that at low enough temperatures the stationary state is non-Gibbsian due to an entanglement with the bath. In physical terms, this happens when the cloud of bath modes around the particle starts to play a nontrivial role, namely, when the bath temperature T is smaller than the coupling energy. Indeed, equilibrium thermodynamics of the total system, particle plus bath, does not imply standard equilibrium thermodynamics for the particle itself at low T. Various formulations of the second law are found to be invalid at low T. First, the Clausius inequality can be violated, because heat can be extracted from the zero point energy of the cloud of bath modes. Second, when the width of the confining potential is suddenly changed, there occurs a relaxation to equilibrium during which the entropy production is partly negative. In this process the energy put on the particle does not relax monotonically, but oscillates between particle and bath, even in the limit of strong damping. Third, for nonadiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Conditions are put forward under which perpetuum mobility of the second kind, having one or several work extraction cycles, enter the realm of condensed matter physics. Fourth, it follows that the equivalence between different formulations of the second law (e.g., those by Clausius and Thomson) can be violated at low temperatures. These effects are the consequence of quantum entanglement in the presence of the slightly off-equilibrium nature of the thermal bath, and become important when the characteristic quantum time scale variant Planck's over 2pi /k

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

    PubMed Central

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

    2016-01-01

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

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

    PubMed

    Moussavi-Baygi, R; Mofrad, M R K

    2016-07-29

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

  9. Joule heating monitoring in a microfluidic channel by observing the Brownian motion of an optically trapped microsphere.

    PubMed

    Brans, Toon; Strubbe, Filip; Schreuer, Caspar; Vandewiele, Stijn; Neyts, Kristiaan; Beunis, Filip

    2015-09-01

    Electric fields offer a variety of functionalities to Lab-on-a-Chip devices. The use of these fields often results in significant Joule heating, affecting the overall performance of the system. Precise knowledge of the temperature profile inside a microfluidic device is necessary to evaluate the implications of heat dissipation. This article demonstrates how an optically trapped microsphere can be used as a temperature probe to monitor Joule heating in these devices. The Brownian motion of the bead at room temperature is compared with the motion when power is dissipated in the system. This gives an estimate of the temperature increase at a specific location in a microfluidic channel. We demonstrate this method with solutions of different ionic strengths, and establish a precision of 0.9 K and an accuracy of 15%. Furthermore, it is demonstrated that transient heating processes can be monitored with this technique, albeit with a limited time resolution.

  10. Coarse-graining Brownian motion: from particles to a discrete diffusion equation.

    PubMed

    de la Torre, J A; Español, Pep

    2011-09-21

    We study the process of coarse-graining in a simple model of diffusion of Brownian particles. At a detailed level of description, the system is governed by a Brownian dynamics of non-interacting particles. The coarse-level is described by discrete concentration variables defined in terms of Delaunay cells. These coarse variables obey a stochastic differential equation that can be understood as a discrete version of a diffusion equation. We study different models for the two basic building blocks of this equation which are the free energy function and the diffusion matrix. The free energy function is shown to be non-additive due to the overlapping of cells in the Delaunay construction. The diffusion matrix is state dependent in principle, but for near-equilibrium situations it is shown that it may be safely evaluated at the equilibrium value of the concentration field.

  11. Normalized functionals of first passage Brownian motion and a curious connection with the maximal relative height of fluctuating interfaces

    NASA Astrophysics Data System (ADS)

    Kearney, Michael J.; Martin, Richard J.

    2016-05-01

    A study is made of the normalized functionals { M }\\equiv M/{T}{1/2} and { A }\\equiv A/{T}{3/2} associated with one-dimensional first passage Brownian motion with positive initial condition, where M is the maximum value attained and A is the area swept out up to the random time T at which the process first reaches zero. Both { M } and { A } involve two strongly correlated random variables associated with a given Brownian path. Through their study, fresh insights are provided into the fundamental nature of such first passage processes and the underlying correlations. The probability density and the moments of { M } and { A } are calculated exactly and the theoretical results are shown to be in good agreement with those derived from simulations. Intriguingly, there is a precise equivalence in law between the variable { A } and the maximal relative height of the fluctuating interface in the one-dimensional Edwards-Wilkinson model with free boundary conditions. This observation leads to some interesting and still partially unresolved questions.

  12. Brownian motion in time-dependent logarithmic potential: Exact results for dynamics and first-passage properties.

    PubMed

    Ryabov, Artem; Berestneva, Ekaterina; Holubec, Viktor

    2015-09-21

    The paper addresses Brownian motion in the logarithmic potential with time-dependent strength, U(x, t) = g(t)log(x), subject to the absorbing boundary at the origin of coordinates. Such model can represent kinetics of diffusion-controlled reactions of charged molecules or escape of Brownian particles over a time-dependent entropic barrier at the end of a biological pore. We present a simple asymptotic theory which yields the long-time behavior of both the survival probability (first-passage properties) and the moments of the particle position (dynamics). The asymptotic survival probability, i.e., the probability that the particle will not hit the origin before a given time, is a functional of the potential strength. As such, it exhibits a rather varied behavior for different functions g(t). The latter can be grouped into three classes according to the regime of the asymptotic decay of the survival probability. We distinguish 1. the regular (power-law decay), 2. the marginal (power law times a slow function of time), and 3. the regime of enhanced absorption (decay faster than the power law, e.g., exponential). Results of the asymptotic theory show good agreement with numerical simulations.

  13. Convex hull of N planar Brownian motions: exact results and an application to ecology.

    PubMed

    Randon-Furling, Julien; Majumdar, Satya N; Comtet, Alain

    2009-10-02

    We compute exactly the mean perimeter and area of the convex hull of N independent planar Brownian paths each of duration T, both for open and closed paths. We show that the mean perimeter =alpha N sqrt[T] and the mean area =beta(N)T for all T. The prefactors alpha N and beta N, computed exactly for all N, increase very slowly (logarithmically) with increasing N. This slow growth is a consequence of extreme value statistics and has interesting implications in an ecological context in estimating the home range of a herd of animals with a population size N.

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

    NASA Astrophysics Data System (ADS)

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

    2017-06-01

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

  15. The moment method for boundary layer problems in Brownian motion theory

    SciTech Connect

    Widder, M.E.; Titulaer, U.M. )

    1989-08-01

    The authors apply Grad's moment method, with Hermite moments and Marshak-type boundary conditions, to several boundary layer problems for the Klein-Kramers equation, the kinetic equation for noninteracting Brownian particles, and study its convergence properties as the number of moments is increased. The errors in various quantities of physical interest decrease asymptotically as inverse powers of this number; the exponent is roughly three times as large as in an earlier variational method, based on an expansion in the exact boundary layer eigenfunctions. For the case of a fully absorbing wall (the Milne problem) they obtain full agreement with the recent exact solution of Marshall and Watson; the relevant slip coefficient, the Milne length, is reproduced with an accuracy better than 10{sup {minus}6}. They also consider partially absorbing walls, with specular or diffuse reflection of nonabsorbed particles. In the latter case they allow for a temperature difference between the wall and the medium in which the particles move. There is no a priori reason why their method should work only for Brownian dynamics; one may hope to extend it to a broad class of linear transport equations. As a first test, they looked at the Milne problem for the BGK equation. In spite of the completely different analytic structure of the boundary layer eigenfunctions, the agreement with the exact solution is almost as good as for the Klein-Kramers equation.

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

    SciTech Connect

    Fleming, C.H.; Roura, Albert; Hu, B.L.

    2011-05-15

    Research Highlights: > We study the model of a quantum oscillator linearly coupled to a bath of oscillators. > We derive the master equation and solutions for general spectra and temperatures. > We generalize to cases with an external force and arbitrary number of oscillators. > Other derivations have incorrect diffusion and force response for nonlocal damping. > We give exact results for ohmic, sub-ohmic and supra-ohmic environments. - Abstract: 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.

  17. Brownian shape motion on five-dimensional potential-energy surfaces:nuclear fission-fragment mass distributions.

    PubMed

    Randrup, Jørgen; Möller, Peter

    2011-04-01

    Although nuclear fission can be understood qualitatively as an evolution of the nuclear shape, a quantitative description has proven to be very elusive. In particular, until now, there existed no model with demonstrated predictive power for the fission-fragment mass yields. Exploiting the expected strongly damped character of nuclear dynamics, we treat the nuclear shape evolution in analogy with Brownian motion and perform random walks on five-dimensional fission potential-energy surfaces which were calculated previously and are the most comprehensive available. Test applications give good reproduction of highly variable experimental mass yields. This novel general approach requires only a single new global parameter, namely, the critical neck size at which the mass split is frozen in, and the results are remarkably insensitive to its specific value.

  18. Numerical study of the tight-binding approach to overdamped Brownian motion on a tilted periodic potential

    NASA Astrophysics Data System (ADS)

    Challis, K. J.

    2016-12-01

    We present a numerical study of the tight-binding approach to overdamped Brownian motion on a tilted periodic potential. In the tight-binding method the probability density is expanded on a basis of Wannier states to transform the Smoluchowski equation to a discrete master equation that can be interpreted in terms of thermal hopping between potential minima. We calculate the Wannier states and hopping rates for a variety of potentials, including tilted cosine and ratchet potentials. For deep potential minima the Wannier states are well localized and the hopping rates between nearest-neighbor states are qualitatively well described by Kramers' escape rate. The next-nearest-neighbor hopping rates are negative and must be negligible compared to the nearest-neighbor rates for the discrete master equation treatment to be valid. We find that the validity of the master equation extends beyond the quantitative applicability of Kramers' escape rate.

  19. Experimental verification of near-wall hindered diffusion for the Brownian motion of nanoparticles using evanescent wave microscopy

    NASA Astrophysics Data System (ADS)

    Banerjee, Arindam; Kihm, Kenneth D.

    2005-10-01

    A total internal reflection fluorescence microscopy technique coupled with three-dimensional tracking of nanoparticles is used to experimentally verify the theory on near-wall hindered Brownian motion [Goldman , Chem. Eng. Sci. 22, 637 (1967); Brenner, Chem. Eng. Sci. 16, 242 (1967)] very close to the solid surface (within ˜1μm ). The measured mean square displacements (MSDs) in the lateral x-y directions show good agreement with the theory for all tested nanoparticles of radii 50, 100, 250, and 500 nm. However, the measured MSDs in the z direction deviate substantially from the theory particularly for the case of smaller particles of 50 and 100 nm radius. Since the theory considers only the hydrodynamic interaction of moving particles with a stationary solid wall, additionally possible interaction forces like gravitational forces, van der Waals forces, and electro-osmotic forces have been examined to delineate the physical reasons for the discrepancy.

  20. Brownian Shape Motion on Five-Dimensional Potential-Energy Surfaces:Nuclear Fission-Fragment Mass Distributions

    SciTech Connect

    Randrup, Joergen; Moeller, Peter

    2011-04-01

    Although nuclear fission can be understood qualitatively as an evolution of the nuclear shape, a quantitative description has proven to be very elusive. In particular, until now, there existed no model with demonstrated predictive power for the fission-fragment mass yields. Exploiting the expected strongly damped character of nuclear dynamics, we treat the nuclear shape evolution in analogy with Brownian motion and perform random walks on five-dimensional fission potential-energy surfaces which were calculated previously and are the most comprehensive available. Test applications give good reproduction of highly variable experimental mass yields. This novel general approach requires only a single new global parameter, namely, the critical neck size at which the mass split is frozen in, and the results are remarkably insensitive to its specific value.

  1. Observation of Brownian motion of a micrometer-size bead in water by off-axis digital holographic microscopy

    NASA Astrophysics Data System (ADS)

    Bae, Yoon-Sung; Jeon, Phil-Jun; Lee, Hee-Jung

    2015-07-01

    An effective volumetric measurement method for determination of the 3D position of a single particle based on off-axis digital holographic microscopy is presented in this paper. 3 μm polystyrene bead suspended water is used as a particle to be traced in our experiment. We have demonstrated the feasibility of our method by observing the bead undergoing Brownian motion in water by implemented setup. For fast determination, a series of transverse intensity images are numerically reconstructed from a single hologram of the bead, then centroid technique is applied to the reconstructed images for enhancing the position resolution. Nano-meter scale resolution with a frame rate of 30 is achieved in this experiment in both lateral and transverse direction.

  2. Structure-based Molecular Simulations Reveal the Enhancement of Biased Brownian Motions in Single-headed Kinesin

    PubMed Central

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

    2013-01-01

    Kinesin is a family of molecular motors that move unidirectionally along microtubules (MT) using ATP hydrolysis free energy. In the family, the conventional two-headed kinesin was experimentally characterized to move unidirectionally through “walking” in a hand-over-hand fashion by coordinated motions of the two heads. Interestingly a single-headed kinesin, a truncated KIF1A, still can generate a biased Brownian movement along MT, as observed by in vitro single molecule experiments. Thus, KIF1A must use a different mechanism from the conventional kinesin to achieve the unidirectional motions. Based on the energy landscape view of proteins, for the first time, we conducted a set of molecular simulations of the truncated KIF1A movements over an ATP hydrolysis cycle and found a mechanism exhibiting and enhancing stochastic forward-biased movements in a similar way to those in experiments. First, simulating stand-alone KIF1A, we did not find any biased movements, while we found that KIF1A with a large friction cargo-analog attached to the C-terminus can generate clearly biased Brownian movements upon an ATP hydrolysis cycle. The linked cargo-analog enhanced the detachment of the KIF1A from MT. Once detached, diffusion of the KIF1A head was restricted around the large cargo which was located in front of the head at the time of detachment, thus generating a forward bias of the diffusion. The cargo plays the role of a diffusional anchor, or cane, in KIF1A “walking.” PMID:23459019

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

    NASA Astrophysics Data System (ADS)

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

    2017-01-01

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

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

    PubMed

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

    2017-01-01

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

  5. Non-Markovian Brownian motion in a magnetic field and time-dependent force fields

    NASA Astrophysics Data System (ADS)

    Hidalgo-Gonzalez, J. C.; Jiménez-Aquino, J. I.; Romero-Bastida, M.

    2016-11-01

    This work focuses on the derivation of the velocity and phase-space generalized Fokker-Planck equations for a Brownian charged particle embedded in a memory thermal bath and under the action of force fields: a constant magnetic field and arbitrary time-dependent force fields. To achieve the aforementioned goal we use a Gaussian but non-Markovian generalized Langevin equation with an arbitrary friction memory kernel. In a similar way, the generalized diffusion equation in the zero inertia limit is also derived. Additionally we show, in the absence of the time-dependent external forces, that, if the fluctuation-dissipation relation of the second kind is valid, then the generalized Langevin dynamics associated with the charged particle reaches a stationary state in the large-time limit. The consistency of our theoretical results is also verified when they are compared with those derived in the absence of the force fields and in the Markovian case.

  6. Brownian dynamics simulation of substrate motion near active site of enzyme entrapped inside reverse micelle.

    PubMed

    Ermakova, Elena A; Zakhartchenko, Nataliya L; Zuev, Yuri F

    2010-08-01

    Brownian dynamics simulation has been applied to analyze the influence of the electrostatic field of a reverse micelle on the enzyme-substrate complex formation inside a micelle. The probability that the enzyme-substrate complex will form from serine protease (trypsin) and the specific hydrophilic cationic substrate Nalpha-benzoyl-L: -arginine ethyl ester has been studied within the framework of the encounter complex formation theory. It has been shown that surfactant charge, dipole moments created by charged surfactant molecules and counterions, and permittivity of the inner core of reverse micelles can all be used as regulatory parameters to alter the substrate orientation near the active site of the enzyme and to change the probability that the enzyme-substrate complex will form.

  7. Composite generalized Langevin equation for Brownian motion in different hydrodynamic and adhesion regimes.

    PubMed

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

    2015-05-01

    We present a composite generalized Langevin equation as a unified framework for bridging the hydrodynamic, Brownian, and adhesive spring forces associated with a nanoparticle at different positions from a wall, namely, a bulklike regime, a near-wall regime, and a lubrication regime. The particle velocity autocorrelation function dictates the dynamical interplay between the aforementioned forces, and our proposed methodology successfully captures the well-known hydrodynamic long-time tail with context-dependent scaling exponents and oscillatory behavior due to the binding interaction. Employing the reactive flux formalism, we analyze the effect of hydrodynamic variables on the particle trajectory and characterize the transient kinetics of a particle crossing a predefined milestone. The results suggest that both wall-hydrodynamic interactions and adhesion strength impact the particle kinetics.

  8. Fractional Whirl Motion in Wave Journal Bearings

    NASA Technical Reports Server (NTRS)

    Dimofte, Florin; Hendricks, Robert C.

    1996-01-01

    Unloaded gas, plain journal bearings experience sub-synchronous whirl motion due to fluid film instabilities and wall contact usually occurs immediately after the onset of the whirl motion. An alternative is the wave journal bearing which significantly improves bearing stability. The predicted threshold where the sub-synchronous whirl motion starts was well confirmed by the experimental observation. In addition, both a two-wave and a three-wave journal bearing can operate free of sub-synchronous whirl motion over a large range in speeds. When the sub-synchronous whirl motion occurs, both the two-wave and three-wave bearing can run in a whirl orbit well within the bearing clearance. At large clearances and wave amplitudes a two-wave bearing, unliKe other bearings, can exhibit a sub-synchronous whirl movement at both low and high speeds, but can run extremely stable and without whirl at intermediate speeds. Moreover, in these cases, the whirl frequencies are close to a quarter of the synchronous speed. The three-wave bearing can exhibit sub-synchronous whirl motion only after a specific threshold when the speed increases and the whirl frequencies are close to half of the synchronous speed.

  9. Fractional Whirl Motion in Wave Journal Bearings

    NASA Technical Reports Server (NTRS)

    Dimofte, Florin; Hendricks, Robert C.

    1996-01-01

    Unloaded gas, plain journal bearings experience sub-synchronous whirl motion due to fluid film instabilities and wall contact usually occurs immediately after the onset of the whirl motion. An alternative is the wave journal bearing which significantly improves bearing stability. The predicted threshold where the sub-synchronous whirl motion starts was well confirmed by the experimental observation. In addition, both a two-wave and a three-wave journal bearing can operate free of sub-synchronous whirl motion over a large range in speeds. When the sub-synchronous whirl motion occurs, both the two-wave and three-wave bearing can run in a whirl orbit well within the bearing clearance. At large clearances and wave amplitudes a two-wave bearing, unliKe other bearings, can exhibit a sub-synchronous whirl movement at both low and high speeds, but can run extremely stable and without whirl at intermediate speeds. Moreover, in these cases, the whirl frequencies are close to a quarter of the synchronous speed. The three-wave bearing can exhibit sub-synchronous whirl motion only after a specific threshold when the speed increases and the whirl frequencies are close to half of the synchronous speed.

  10. Inter-fraction variations in respiratory motion models

    NASA Astrophysics Data System (ADS)

    McClelland, J. R.; Hughes, S.; Modat, M.; Qureshi, A.; Ahmad, S.; Landau, D. B.; Ourselin, S.; Hawkes, D. J.

    2011-01-01

    Respiratory motion can vary dramatically between the planning stage and the different fractions of radiotherapy treatment. Motion predictions used when constructing the radiotherapy plan may be unsuitable for later fractions of treatment. This paper presents a methodology for constructing patient-specific respiratory motion models and uses these models to evaluate and analyse the inter-fraction variations in the respiratory motion. The internal respiratory motion is determined from the deformable registration of Cine CT data and related to a respiratory surrogate signal derived from 3D skin surface data. Three different models for relating the internal motion to the surrogate signal have been investigated in this work. Data were acquired from six lung cancer patients. Two full datasets were acquired for each patient, one before the course of radiotherapy treatment and one at the end (approximately 6 weeks later). Separate models were built for each dataset. All models could accurately predict the respiratory motion in the same dataset, but had large errors when predicting the motion in the other dataset. Analysis of the inter-fraction variations revealed that most variations were spatially varying base-line shifts, but changes to the anatomy and the motion trajectories were also observed.

  11. Inter-fraction variations in respiratory motion models.

    PubMed

    McClelland, J R; Hughes, S; Modat, M; Qureshi, A; Ahmad, S; Landau, D B; Ourselin, S; Hawkes, D J

    2011-01-07

    Respiratory motion can vary dramatically between the planning stage and the different fractions of radiotherapy treatment. Motion predictions used when constructing the radiotherapy plan may be unsuitable for later fractions of treatment. This paper presents a methodology for constructing patient-specific respiratory motion models and uses these models to evaluate and analyse the inter-fraction variations in the respiratory motion. The internal respiratory motion is determined from the deformable registration of Cine CT data and related to a respiratory surrogate signal derived from 3D skin surface data. Three different models for relating the internal motion to the surrogate signal have been investigated in this work. Data were acquired from six lung cancer patients. Two full datasets were acquired for each patient, one before the course of radiotherapy treatment and one at the end (approximately 6 weeks later). Separate models were built for each dataset. All models could accurately predict the respiratory motion in the same dataset, but had large errors when predicting the motion in the other dataset. Analysis of the inter-fraction variations revealed that most variations were spatially varying base-line shifts, but changes to the anatomy and the motion trajectories were also observed.

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

    NASA Astrophysics Data System (ADS)

    Eka Putri, Irana; Gita Redhyka, Grace

    2017-07-01

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

  13. The Effect of Brownian Motion on the Trajectory of Diffusiophoretic Locomotors near a Solid Boundary

    NASA Astrophysics Data System (ADS)

    Mozaffari, Ali; Sharifi-Mood, Nima; Koplik, Joel; Maldarelli, Charles

    2015-11-01

    Diffusiophoretically self-propelled locomotors are a class of active colloids in which a particle autonomously swims through the liquid as a result of an unbalanced interaction with solute molecules asymmetrically distributed around the colloid. This solute distribution is maintained by a reaction which produces the solute on one catalytically active side of the Janus motor colloid. For the simplest case of diffusiophoretic self-propulsion near a planar infinite wall with zero solute flux, and repulsive solute-colloid interactions, hydrodynamic solutions for deterministic Stokes flow have shown that that for large catalytically active areas pointed away from the wall, and for distances less than the particle radius, the particles can skim at a constant distance along the surface without rotation, or can become stationary. To examine the effect of thermal fluctuations on the stability of these regimes for small motor sizes, Brownian dynamics simulations including the hydrodynamic interaction with the wall are undertaken, and we identify critical Peclet numbers above which the skimming and stationary regimes are stable. Below these values, less predictable behavior is found in which the colloid can be repelled from or intersect with the wall.

  14. A hydrodynamic/Brownian motion model of thermal diffusion in liquids

    NASA Astrophysics Data System (ADS)

    Bielenberg, James R.; Brenner, Howard

    2005-10-01

    A recently modified formulation of fluid-mechanical transport processes, which has been shown to correctly predict the thermophoretic force on a rigid isolated particle in a single-component fluid continuum (gas or liquid), is combined with steady-state Stokes-Einstein-type sedimentation-equilibrium/Boltzmann distribution-like arguments appropriate to a dilute suspension of such particles, each regarded as Brownian, so as to furnish an elementary hydrodynamic theory for thermal diffusion separation phenomena in dilute binary liquid-phase mixtures (the Ludwig/Soret effect) for the case of a disparate solute/solvent molecular size ratio. The results of the theory are shown to accord well with experiments on polymer solutions in regard to both the magnitude and algebraic sign of the Soret coefficient, as well as with respect to the effects of temperature and mixture composition on this coefficient. An extension (albeit less rigorous) of the preceding theory to the case of nondilute, thermodynamically ideal, binary solutions of miscible liquids of comparable molecular size also yields results in reasonable accord with experiments.

  15. Solutions to Master equations of quantum Brownian motion in a general environment with external force

    SciTech Connect

    Roura, Albert; Fleming, C H; Hu, B L

    2008-01-01

    We revisit the model of a system made up of a Brownian quantum oscillator linearly coupled to an environment made up of many quantum oscillators at finite temperature. We show that the HPZ master equation for the reduced density matrix derived earlier [B.L. Hu, J.P. Paz, Y. Zhang, Phys. Rev. D 45, 2843 (1992)] has incorrectly specified coefficients for the case of nonlocal dissipation. We rederive the QBM master equation, correctly specifying all coefficients, and determine the position uncertainty to be free of excessive cutoff sensitivity. Our coefficients and solutions are reduced entirely to contour integration for analytic spectra at arbitrary temperature, coupling strength, and cut-off. As an illustration we calculate the master equation coefficients and solve the master equation for ohmic coupling (with finite cutoff) and example supra-ohmic and sub-ohmic spectral densities. We determine the effect of an external force on the quantum oscillator and also show that our representation of the master equation and solutions naturally extends to a system of multiple oscillators bilinearly coupled to themselves and the bath in arbitrary fashion. This produces a formula for investigating the standard quantum limit which is central to addressing many theoretical issues in macroscopic quantum phenomena and experimental concerns related to low temperature precision measurements. We find that in a dissipative environment, all initial states settle down to a Gaussian density matrix whose covariance is determined by the thermal reservoir and whose mean is determined by the external force. We specify the thermal covariance for the spectral densities we explore.

  16. A Monte Carlo Simulation of Brownian Motion in the Freshman Laboratory

    ERIC Educational Resources Information Center

    Anger, C. D.; Prescott, J. R.

    1970-01-01

    Describes a dry- lab" experiment for the college freshman laboratory, in which the essential features of Browian motion are given principles, using the Monte Carlo technique. Calculations principles, using the Monte Carlo technique. Calculations are carried out by a computation sheme based on computer language. Bibliography. (LC)

  17. Framing the features of Brownian motion and thermophoresis on radiative nanofluid flow past a rotating stretching sheet with magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Mabood, F.; Ibrahim, S. M.; Khan, W. A.

    This article addresses the combined effects of chemical reaction and viscous dissipation on MHD radiative heat and mass transfer of nanofluid flow over a rotating stretching surface. The model used for the nanofluid incorporates the effects of the Brownian motion and thermophoresis in the presence of heat source. Similarity transformation variables have been used to model the governing equations of momentum, energy, and nanoparticles concentration. Runge-Kutta-Fehlberg method with shooting technique is applied to solve the resulting coupled ordinary differential equations. Physical features for all pertinent parameters on the dimensionless velocity, temperature, skin friction coefficient, and heat and mass transfer rates are analyzed graphically. The numerical comparison has also presented for skin friction coefficient and local Nusselt number as a special case for our study. It is noted that fluid velocity enhances when rotational parameter is increased. Surface heat transfer rate enhances for larger values of Prandtl number and heat source parameter while mass transfer rate increases for larger values of chemical reaction parameter.

  18. Estimating Brownian motion dispersal rate, longevity and population density from spatially explicit mark-recapture data on tropical butterflies.

    PubMed

    Tufto, Jarle; Lande, Russell; Ringsby, Thor-Harald; Engen, Steinar; Saether, Bernt-Erik; Walla, Thomas R; DeVries, Philip J

    2012-07-01

    1. We develop a Bayesian method for analysing mark-recapture data in continuous habitat using a model in which individuals movement paths are Brownian motions, life spans are exponentially distributed and capture events occur at given instants in time if individuals are within a certain attractive distance of the traps. 2. The joint posterior distribution of the dispersal rate, longevity, trap attraction distances and a number of latent variables representing the unobserved movement paths and time of death of all individuals is computed using Gibbs sampling. 3. An estimate of absolute local population density is obtained simply by dividing the Poisson counts of individuals captured at given points in time by the estimated total attraction area of all traps. Our approach for estimating population density in continuous habitat avoids the need to define an arbitrary effective trapping area that characterized previous mark-recapture methods in continuous habitat. 4. We applied our method to estimate spatial demography parameters in nine species of neotropical butterflies. Path analysis of interspecific variation in demographic parameters and mean wing length revealed a simple network of strong causation. Larger wing length increases dispersal rate, which in turn increases trap attraction distance. However, higher dispersal rate also decreases longevity, thus explaining the surprising observation of a negative correlation between wing length and longevity. © 2012 The Authors. Journal of Animal Ecology © 2012 British Ecological Society.

  19. Brownian motion studies of viscoelastic colloidal gels by rotational single particle tracking

    DOE PAGES

    Liang, Mengning; Harder, Ross; Robinson, Ian K.

    2014-04-14

    Colloidal gels have unique properties due to a complex microstructure which forms into an extended network. Although the bulk properties of colloidal gels have been studied, there has been difficulty correlating those properties with individual colloidal dynamics on the microscale due to the very high viscosity and elasticity of the material. We utilize rotational X-ray tracking (RXT) to investigate the rotational motion of component crystalline colloidal particles in a colloidal gel of alumina and decanoic acid. Our investigation has determined that the high elasticity of the bulk is echoed by a high elasticity experienced by individual colloidal particles themselves butmore » also finds an unexpected high degree of rotational diffusion, indicating a large degree of freedom in the rotational motion of individual colloids even within a tightly bound system.« less

  20. Brownian motion studies of viscoelastic colloidal gels by rotational single particle tracking

    PubMed Central

    Liang, Mengning; Harder, Ross; Robinson, Ian K.

    2014-01-01

    Colloidal gels have unique properties due to a complex microstructure which forms into an extended network. Although the bulk properties of colloidal gels have been studied, there has been difficulty correlating those properties with individual colloidal dynamics on the microscale due to the very high viscosity and elasticity of the material. We utilize rotational X-ray tracking (RXT) to investigate the rotational motion of component crystalline colloidal particles in a colloidal gel of alumina and decanoic acid. Our investigation has determined that the high elasticity of the bulk is echoed by a high elasticity experienced by individual colloidal particles themselves but also finds an unexpected high degree of rotational diffusion, indicating a large degree of freedom in the rotational motion of individual colloids even within a tightly bound system. PMID:25075336

  1. Brownian dynamics studies on DNA gel electrophoresis. I. Numerical method and ``periodic'' behavior of elongation-contraction motions

    NASA Astrophysics Data System (ADS)

    Azuma, Ryuzo; Takayama, Hajime

    2002-10-01

    The dynamics of a DNA molecule which is undergoing constant field gel electrophoresis (CFGE) is studied by a Brownian dynamics simulation method we have developed. In the method a DNA molecule is modeled as a chain of spherical electrolyte beads and the gel as a three-dimensional array of immobile beads. With the constraint for the separation of each pair of bonded beads to be less than a certain fixed value, as well as with the excluded volume effect, the simultaneous Langevin equations of motion for the beads are solved by means of the Lagrangian multiplier method. The resultant mobilities μ as a function of electric field coincide satisfactorily with the corresponding experimental results, once the time, the length, and the field of the simulation are properly scaled. In relatively strong fields "periodic" behavior is found in the chain dynamics and is examined through the time evolution of the radius of the longer principal axis, Rl(t). It is found that the mean width of a peak in Rl(t), or a period of one elongation-contraction process of the chain, is proportional to the number of beads in the chain, M, while the mean period between two such adjacent peaks is independent of M for large M. These results, combined with the observation that the chain moves to the field direction by the distance proportional to M in each elongation-contraction motion, yield the saturation of mobility for large M. This explains the reason that CFGE cannot separate DNA according to their size L(∝M) for large L.

  2. Tempered fractional calculus

    SciTech Connect

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

    2015-07-15

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

  3. Fractional-order variational optical flow model for motion estimation.

    PubMed

    Chen, Dali; Sheng, Hu; Chen, YangQuan; Xue, Dingyü

    2013-05-13

    A new class of fractional-order variational optical flow models, which generalizes the differential of optical flow from integer order to fractional order, is proposed for motion estimation in this paper. The corresponding Euler-Lagrange equations are derived by solving a typical fractional variational problem, and the numerical implementation based on the Grünwald-Letnikov fractional derivative definition is proposed to solve these complicated fractional partial differential equations. Theoretical analysis reveals that the proposed fractional-order variational optical flow model is the generalization of the typical Horn and Schunck (first-order) variational optical flow model and the second-order variational optical flow model, which provides a new idea for us to study the optical flow model and has an important theoretical implication in optical flow model research. The experiments demonstrate the validity of the generalization of differential order.

  4. Quantifying intra- and inter-fractional motion in breast radiotherapy

    SciTech Connect

    Jones, Scott; Fitzgerald, Rhys; Owen, Rebecca; Ramsay, Jonathan

    2015-03-15

    The magnitude of intra- and inter-fractional variation in the set up of breast cancer patients treated with tangential megavoltage photon beams was investigated using an electronic portal imaging device (EPID). Daily cine-EPID images were captured during delivery of the tangential fields for ten breast cancer patients treated in the supine position. Measurements collected from each image included the central lung distance (CLD), central flash distance (CFD), superior axial measurement (SAM) and the inferior axial measurement (IAM). The variation of motion within a fraction (intra-fraction) and the variation between fractions (inter-fraction) was analysed to quantify set up variation and motion due to respiration. Altogether 3775 EPID images were collected from 10 patients. The effect of respiratory motion during treatment was <0.1 cm standard deviation (SD) in the anterior–posterior (AP) direction. The inter-fraction movement caused by variations in daily set up was larger at 0.28 cm SD in the AP direction. Superior–inferior (SI) variation was more difficult to summarise and proved unreliable as the measurements were taken to an ambiguous point on the images. It was difficult to discern true SI movement from that implicated by AP movement. There is minimal intra-fractional chest wall motion due to respiration during treatment. Inter-fractional variation was larger, however, on average it remained within departmental tolerance (0.5 cm) for set up variations. This review of our current breast technique provides confidence in the feasibility of utilising advanced treatment techniques (field-in-field, intensity modulated radiotherapy or volumetric modulated arc therapy) following a review of the current imaging protocol.

  5. Biorthonormal eigenbasis of a Markovian master equation for the quantum Brownian motion

    SciTech Connect

    Tay, B. A.; Petrosky, T.

    2008-11-15

    The solution to a quantum Markovian master equation of a harmonic oscillator weakly coupled to a thermal reservoir is investigated as a non-Hermitian eigenvalue problem in space coordinates. In terms of a pair of quantum action-angle variables, the equation becomes separable and a complete set of biorthogonal eigenfunctions can be constructed. Properties of quantum states, such as the change in the quantum coherence length, damping in the motion, and disappearance of the spatial interference pattern, can then be described as the decay of the nonequilibrium modes in the eigenbasis expansion. It is found that the process of gaining quantum coherence from the environment takes a longer time than the opposite process of losing quantum coherence to the environment. An estimate of the time scales of these processes is obtained.

  6. Anomalous versus Slowed-Down Brownian Diffusion in the Ligand-Binding Equilibrium

    PubMed Central

    Soula, Hédi; Caré, Bertrand; Beslon, Guillaume; Berry, Hugues

    2013-01-01

    Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes. PMID:24209851

  7. Anomalous versus slowed-down Brownian diffusion in the ligand-binding equilibrium.

    PubMed

    Soula, Hédi; Caré, Bertrand; Beslon, Guillaume; Berry, Hugues

    2013-11-05

    Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.

  8. Fractional Levy stable motion for modeling speckle image

    NASA Astrophysics Data System (ADS)

    Li, Xutao; Jin, Lianwen; Peng, Fuyuan; Zhu, Aiping

    2008-03-01

    Recently, stable processes have turned out to be good models for many impulsive signals and noises. The speckle noise in underwater, SAR and the cosmic background images has been proved to have heavy tails distributions and Long Rang Dependent (LRD) structures. In this paper, the Fractional Levy Stable Motion (FLSM) is introduced to model such speckle phenomenon. The synthesis approaches employing Random Midpoint Displacement (RMD) and FFT technology are presented to generate such speckle image respectively. Then, we introduce Wavelet Analysis (WA) method to estimate the LRD exponent H and propose two new technologies in estimation H parameter by Fractional Low Order Moment (FLOM) and Fractional Spectrum (FS) respectively.

  9. Langevin analysis for time-nonlocal Brownian motion with algebraic memories and delay interactions

    NASA Astrophysics Data System (ADS)

    Chase, Matthew; McKetterick, Tom J.; Giuggioli, Luca; Kenkre, V. M.

    2016-04-01

    Starting from a Langevin equation with memory describing the attraction of a particle to a center, we investigate its transport and response properties corresponding to two special forms of the memory: one is algebraic, i.e., power-law, and the other involves a delay. We examine the properties of the Green function of the Langevin equation and encounter Mittag-Leffler and Lambert W-functions well-known in the literature. In the presence of white noise, we study two experimental situations, one involving the motional narrowing of spectral lines and the other the steady-state size of the particle under consideration. By comparing the results to counterparts for a simple exponential memory, we uncover instructive similarities and differences. Perhaps surprisingly, we find that the Balescu-Swenson theorem that states that non-Markoffian equations do not add anything new to the description of steady-state or equilibrium observables is violated for our system in that the saturation size of the particle in the steady-state depends on the memory function utilized. A natural generalization of the Smoluchowski equation for the time-local case is examined and found to satisfy the Balescu-Swenson theorem and describe accurately the first moment but not the second and higher moments. We also calculate two-time correlation functions for all three cases of the memory, and show how they differ from (tend to) their Markoffian counterparts at small (large) values of the difference between the two times.

  10. TEMPERED FRACTIONAL CALCULUS

    PubMed Central

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

    2014-01-01

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

  11. Estimating the viscoelastic moduli of complex fluids from observation of Brownian motion of a particle confined to a harmonic trap.

    PubMed

    Felderhof, B U

    2011-05-28

    A procedure is proposed to estimate the viscoelastic properties of a complex fluid from the behavior of the velocity autocorrelation function of a suspended Brownian particle, trapped in a harmonic potential. The procedure is tested for a model complex fluid with a given frequency-dependent shear viscosity. The analysis shows that the procedure can provide a rather accurate prediction of the viscoelastic properties of the fluid on the basis of experimental data on the velocity autocorrelation function of the trapped Brownian particle in a limited range of time.

  12. Level repulsion exponent β for many-body localization transitions and for Anderson localization transitions via Dyson Brownian motion

    NASA Astrophysics Data System (ADS)

    Monthus, Cécile

    2016-03-01

    The generalization of the Dyson Brownian motion approach of random matrices to Anderson localization (AL) models (Chalker et al 1996 Phys. Rev. Lett. 77 554) and to many-body localization (MBL) Hamiltonians (Serbyn and Moore 2015 arXiv:1508.07293) is revisited to extract the level repulsion exponent β, where β =1 in the delocalized phase governed by the Wigner-Dyson statistics, β =0 , in the localized phase governed by the Poisson statistics, and 0<{βc}<1 at the critical point. The idea is that the Gaussian disorder variables h i are promoted to Gaussian stationary processes h i (t) in order to sample the disorder stationary distribution with some time correlation τ. The statistics of energy levels can then be studied via Langevin and Fokker-Planck equations. For the MBL quantum spin Hamiltonian with random fields h i , we obtain β =2qn,n+1\\text{EA}(N)/qn,n\\text{EA}(N) in terms of the Edwards-Anderson matrix qnm\\text{EA}(N)\\equiv \\frac{1}{N}{\\sum}i=1N|< {φn}|σ iz|{φm}> {{|}2} for the same eigenstate m  =  n and for consecutive eigenstates m  =  n  +  1. For the Anderson localization tight-binding Hamiltonian with random on-site energies h i , we find β =2{{Y}n,n+1}(N)/≤ft({{Y}n,n}(N)-{{Y}n,n+1}(N)\\right) in terms of the density correlation matrix {{Y}nm}(N)\\equiv {\\sum}i=1N|< {φn}|i> {{|}2}|< i|{φm}> {{|}2} for consecutive eigenstates m  =  n  +  1, while the diagonal element m  =  n corresponds to the inverse participation ratio {{Y}nn}(N)\\equiv {\\sum}i=1N|< {φn}|i> {{|}4} of the eigenstate |{φn}> .

  13. All that Brownian motion

    NASA Astrophysics Data System (ADS)

    Dürr, D.

    I shall present here some recent results in the mathematical rigorous study of nonequilibrium statistical mechanics. These results have been obtained in collaboration with S.Goldstein and J.L.Lebowitz.

  14. Electrical autonomous Brownian gyrator

    NASA Astrophysics Data System (ADS)

    Chiang, K.-H.; Lee, C.-L.; Lai, P.-Y.; Chen, Y.-F.

    2017-09-01

    We study experimentally and theoretically the steady-state dynamics of a simple stochastic electronic system featuring two resistor-capacitor circuits coupled by a third capacitor. The resistors are subject to thermal noises at real temperatures. The voltage fluctuation across each resistor can be compared to a one-dimensional Brownian motion. However, the collective dynamical behavior, when the resistors are subject to distinct thermal baths, is identical to that of a Brownian gyrator, as first proposed by Filliger and Reimann [Phys. Rev. Lett. 99, 230602 (2007), 10.1103/PhysRevLett.99.230602]. The average gyrating dynamics is originated from the absence of detailed balance due to unequal thermal baths. We look into the details of this stochastic gyrating dynamics, its dependences on the temperature difference and coupling strength, and the mechanism of heat transfer through this simple electronic circuit. Our work affirms the general principle and the possibility of a Brownian ratchet working near room temperature scale.

  15. Coarse-grained picture of Brownian motion in water: Role of size and interaction distance range on the nature of randomness.

    PubMed

    Hanasaki, Itsuo; Nagura, Ryo; Kawano, Satoyuki

    2015-03-14

    The Brownian motion of a particle in a fluid is often described by the linear Langevin equation, in which it is assumed that the mass of the particle is sufficiently large compared to the surrounding fluid molecules. This assumption leads to a diffusion coefficient that is independent of the particle mass. The Stokes-Einstein equation indicates that the diffusion coefficient depends solely on the particle size, but the concept of size can be ambiguous when close to the molecular scale. We first examine the Brownian motion of simple model particles based on short-range interactions in water by the molecular dynamics method and show that the diffusion coefficient can vary with mass when this mass is comparable to that of the solvent molecules, and that this effect is evident when the solute particle size is sufficiently small. We then examine the properties of a water molecule considered as a solute in the bulk solvent consisting of the remainder of the water. A comparison with simple solute models is used to clarify the role of force fields. The long-range Coulomb interaction between water molecules is found to lead to a Gaussian force distribution in spite of a mass ratio and nominal size ratio of unity, such that solutes with short-range interactions exhibit non-Gaussian force distribution. Thus, the range of the interaction distance determines the effective size even if it does not represent the volume excluded by the repulsive force field.

  16. Multibuilding Block Janus Synthesized by Seed-Mediated Self-Assembly for Enhanced Photothermal Effects and Colored Brownian Motion in an Optical Trap.

    PubMed

    Sansanaphongpricha, Kanokwan; DeSantis, Michael C; Chen, Hongwei; Cheng, Wei; Sun, Kai; Wen, Bo; Sun, Duxin

    2017-02-01

    The asymmetrical features and unique properties of multibuilding block Janus nanostructures (JNSs) provide superior functions for biomedical applications. However, their production process is very challenging. This problem has hampered the progress of JNS research and the exploration of their applications. In this study, an asymmetrical multibuilding block gold/iron oxide JNS has been generated to enhance photothermal effects and display colored Brownian motion in an optical trap. JNS is formed by seed-mediated self-assembly of nanoparticle-loaded thermocleavable micelles, where the hydrophobic backbones of the polymer are disrupted at high temperatures, resulting in secondary self-assembly and structural rearrangement. The JNS significantly enhances photothermal effects compared to their homogeneous counterpart after near-infrared (NIR) light irradiation. The asymmetrical distribution of gold and iron oxide within JNS also generates uneven thermophoretic force to display active colored Brownian rotational motion in a single-beam gradient optical trap. These properties indicate that the asymmetrical JNS could be employed as a strong photothermal therapy mediator and a fuel-free nanoscale Janus motor under NIR light.

  17. Fractional Lévy stable motion can model subdiffusive dynamics

    NASA Astrophysics Data System (ADS)

    Burnecki, Krzysztof; Weron, Aleksander

    2010-08-01

    We show in this paper that the sample (time average) mean-squared displacement (MSD) of the fractional Lévy α -stable motion behaves very differently from the corresponding ensemble average (second moment). While the ensemble average MSD diverges for α<2 , the sample MSD may exhibit either subdiffusion, normal diffusion, or superdiffusion. Thus, H -self-similar Lévy stable processes can model either a subdiffusive, diffusive or superdiffusive dynamics in the sense of sample MSD. We show that the character of the process is controlled by a sign of the memory parameter d=H-1/α . We also introduce a sample p -variation dynamics test which allows to distinguish between two models of subdiffusive dynamics. Finally, we illustrate a subdiffusive behavior of the fractional Lévy stable motion on biological data describing the motion of individual fluorescently labeled mRNA molecules inside live E. coli cells, but it may concern many other fields of contemporary experimental physics.

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

    PubMed

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

    2016-07-01

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

  19. Irreversible Brownian Heat Engine

    NASA Astrophysics Data System (ADS)

    Taye, Mesfin Asfaw

    2017-09-01

    We model a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a linearly decreasing background temperature. We show that the efficiency of such Brownian heat engine approaches the efficiency of endoreversible engine η =1-√{{Tc/Th}} [23]. On the other hand, the maximum power efficiency of the engine approaches η ^{MAX}=1-({Tc/Th})^{1\\over 4} . It is shown that the optimized efficiency always lies between the efficiency at quasistatic limit and the efficiency at maximum power while the efficiency at maximum power is always less than the optimized efficiency since the fast motion of the particle comes at the expense of the energy cost. If the heat exchange at the boundary of the heat baths is included, we show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature. The role of time on the performance of the motor is also explored via numerical simulations. Our numerical results depict that the time t and the external load dictate the direction of the particle velocity. Moreover, the performance of the heat engine improves with time. At large t (steady state), the velocity, the efficiency and the coefficient of performance of the refrigerator attain their maximum value. Furthermore, we study the effect of temperature by considering a viscous friction that decreases exponentially as the background temperature increases. Our result depicts that the Brownian particle exhibits a fast unidirectional motion when the viscous friction is temperature dependent than that of constant viscous friction. Moreover, the efficiency of this motor is considerably enhanced when the viscous friction is temperature dependent. On the hand, the motor exhibits a higher performance of the refrigerator when the viscous friction is taken to be constant.

  20. Meandering Brownian Donkeys

    NASA Astrophysics Data System (ADS)

    Eichhorn, R.; Reimann, P.

    2004-04-01

    We consider a Brownian particle whose motion is confined to a ``meandering'' pathway and which is driven away from thermal equilibrium by an alternating external force. This system exhibits absolute negative mobility, i.e. when an external static force is applied the particle moves in the direction opposite to that force. We reveal the physical mechanism behind this ``donkey-like'' behavior, and derive analytical approximations that are in excellent agreement with numerical results.

  1. Switching of myosin-V motion between the lever-arm swing and brownian search-and-catch.

    PubMed

    Fujita, Keisuke; Iwaki, Mitsuhiro; Iwane, Atsuko H; Marcucci, Lorenzo; Yanagida, Toshio

    2012-07-17

    Motor proteins are force-generating nanomachines that are highly adaptable to their ever-changing biological environments and have a high energy conversion efficiency. Here we constructed an imaging system that uses optical tweezers and a DNA handle to visualize elementary mechanical processes of a nanomachine under load. We apply our system to myosin-V, a well-known motor protein that takes 72 nm 'hand-over-hand' steps composed of a 'lever-arm swing' and a 'brownian search-and-catch'. We find that the lever-arm swing generates a large proportion of the force at low load (<0.5 pN), resulting in 3 k(B)T of work. At high load (1.9 pN), however, the contribution of the brownian search-and-catch increases to dominate, reaching 13 k(B)T of work. We believe the ability to switch between these two force-generation modes facilitates myosin-V function at high efficiency while operating in a dynamic intracellular environment.

  2. Bacterial Translocation Ratchets: Shared Physical Principles with Different Molecular Implementations: How bacterial secretion systems bias Brownian motion for efficient translocation of macromolecules.

    PubMed

    Hepp, Christof; Maier, Berenike

    2017-10-01

    Secretion systems enable bacteria to import and secrete large macromolecules including DNA and proteins. While most components of these systems have been identified, the molecular mechanisms of macromolecular transport remain poorly understood. Recent findings suggest that various bacterial secretion systems make use of the translocation ratchet mechanism for transporting polymers across the cell envelope. Translocation ratchets are powered by chemical potential differences generated by concentration gradients of ions or molecules that are specific to the respective secretion systems. Bacteria employ these potential differences for biasing Brownian motion of the macromolecules within the conduits of the secretion systems. Candidates for this mechanism include DNA import by the type II secretion/type IV pilus system, DNA export by the type IV secretion system, and protein export by the type I secretion system. Here, we propose that these three secretion systems employ different molecular implementations of the translocation ratchet mechanism. © 2017 The Authors. BioEssays Published by WILEY Periodicals, Inc.

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

    PubMed

    Antonopoulos, Markos; Stamatakos, Georgios

    2015-01-01

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

  4. Brownian ratchets in physics and biology

    NASA Astrophysics Data System (ADS)

    Bier, Martin

    1997-06-01

    Thirty years ago Feynman et al. presented a paradox in the Lectures on Physics: an imagined device could let Brownian motion do work by allowing it in one direction and blocking it in the opposite direction. In the chapter Feynman et al. eventually show that such ratcheting can only be achieved if there is, in compliance with the basic conservation laws, some energy input from an external source. Now that technology is going into ever smaller dimensions, ratcheting Brownian motion seems to be a real possibility in nanotechnological applications. Furthermore, Brownian motion plays an essential role in the action of motor proteins (individual molecules that convert chemical energy into motion).

  5. Brownian Emitters

    NASA Astrophysics Data System (ADS)

    Tsekov, Roumen

    2016-06-01

    A Brownian harmonic oscillator, which dissipates energy either by friction or via emission of electromagnetic radiation, is considered. This Brownian emitter is driven by the surrounding thermo-quantum fluctuations, which are theoretically described by the fluctuation-dissipation theorem. It is shown how the Abraham-Lorentz force leads to dependence of the half-width on the peak frequency of the oscillator amplitude spectral density. It is found that for the case of a charged particle moving in vacuum at zero temperature, its root-mean-square velocity fluctuation is a universal constant, equal to roughly 1/18 of the speed of light. The relevant Fokker-Planck and Smoluchowski equations are also derived.

  6. Confined Brownian ratchets.

    PubMed

    Malgaretti, Paolo; Pagonabarraga, Ignacio; Rubi, J Miguel

    2013-05-21

    We analyze the dynamics of Brownian ratchets in a confined environment. The motion of the particles is described by a Fick-Jakobs kinetic equation in which the presence of boundaries is modeled by means of an entropic potential. The cases of a flashing ratchet, a two-state model, and a ratchet under the influence of a temperature gradient are analyzed in detail. We show the emergence of a strong cooperativity between the inherent rectification of the ratchet mechanism and the entropic bias of the fluctuations caused by spatial confinement. Net particle transport may take place in situations where none of those mechanisms leads to rectification when acting individually. The combined rectification mechanisms may lead to bidirectional transport and to new routes to segregation phenomena. Confined Brownian ratchets could be used to control transport in mesostructures and to engineer new and more efficient devices for transport at the nanoscale.

  7. Confined Brownian ratchets

    NASA Astrophysics Data System (ADS)

    Malgaretti, Paolo; Pagonabarraga, Ignacio; Rubi, J. Miguel

    2013-05-01

    We analyze the dynamics of Brownian ratchets in a confined environment. The motion of the particles is described by a Fick-Jakobs kinetic equation in which the presence of boundaries is modeled by means of an entropic potential. The cases of a flashing ratchet, a two-state model, and a ratchet under the influence of a temperature gradient are analyzed in detail. We show the emergence of a strong cooperativity between the inherent rectification of the ratchet mechanism and the entropic bias of the fluctuations caused by spatial confinement. Net particle transport may take place in situations where none of those mechanisms leads to rectification when acting individually. The combined rectification mechanisms may lead to bidirectional transport and to new routes to segregation phenomena. Confined Brownian ratchets could be used to control transport in mesostructures and to engineer new and more efficient devices for transport at the nanoscale.

  8. Application of the fractional Levy motion to precipitation data

    NASA Astrophysics Data System (ADS)

    Kuzuha, Y.; Tachinami, S.; Gomi, C.

    2012-12-01

    We applied the fractional Lévy motion model to precipitation data, referring to Lavallée (2004) and Lavallée (2008). The data we used were from the Global Preciptiation Climatology Centre (GPCC) monthly precipitation dataset. These data consist of 360 (longitude) × 180 (latitude) × 1336 (monthly, 1901-2012). First, we constructed four datasets: time series of average monthly precipitation of the top (maximum) 1000 precipitation observation stations, top 10, top 100, and top 500. Next, according to Lavallée (2004) and Lavallée (2008), using Fourier transformation, convolution (filtering) and inverse Fourier transformation, we obtained random variables Xt (Lavallée, 2004) from Yt (precipitation). We transformed from Yt to Xt. Finally, we fitted the Lévy law to Xt. As a preliminary result, we present examples of the values of the Lévy law parameters: alpha, beta, gamma, and delta for the "top 100" dataset. Parameters obtained were (1.17, 0.0, 257.6, 0.28; maximum likelihood), (1.10, 0.0, 250.0, -0.99; quantile algorithm), and (1.20, 0.0, 265.1, 0.57; empirical characteristic function algorithm). We used J. P. Nolan's algorithm. The values are quite sensitive to the algorithm that is used. At the Fall meeting, we will present considerations and results obtained using precipitation data other than those of the GPCC. J. P. Nolan, http://academic2.american.edu/~jpnolan/stable/stable.html Lavallée (2004), Stochastic modeling of climatic variability in dendrochronology, GRL, 31, L15202. Lavallée (2008), On the random nature of earthquake sources and ground motions; a unified theory, Advances in Geophysics, 50, chapter 16. Acknowledgement: We thank Dr. D. Lavallee for his comments and suggestions.; An example of results which we obtained. On a log-log plot, PDF of the Lévy law (red line) is more appropriate than the Gaussian law (blue line) in terms of heavy tail or extreme values. This is consistent with Lavallée (2004) and Lavallée (2008) who used slip

  9. Entropic Approach to Brownian Movement.

    ERIC Educational Resources Information Center

    Neumann, Richard M.

    1980-01-01

    A diffusional driving force, called the radial force, which is responsible for the increase with time of the scalar separation between a fixed point and a particle undergoing three-dimensional Brownian motion, is derived using Boltzmann's equation. (Author/HM)

  10. A new numerical method for investigation of thermophoresis and Brownian motion effects on MHD nanofluid flow and heat transfer between parallel plates partially filled with a porous medium

    NASA Astrophysics Data System (ADS)

    Sayehvand, Habib-Olah; Basiri Parsa, Amir

    Numerical investigation the problem of nanofluid heat and mass transfer in a channel partially filled with a porous medium in the presence of uniform magnetic field is carried out by a new computational iterative approach known as the spectral local linearization method (SLLM). The similarity solution is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations which are then solved by SLLM and validity of our solutions is verified by the numerical results (fourth-order Runge-Kutta scheme with the shooting method). In modeling the flow in the channel, the effects of flow inertia, Brinkman friction, nanoparticles concentration and thickness of the porous region are taken into account. The results are obtained for velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number. Also, effects of active parameters such as viscosity parameter, Hartmann number, Darcy number, Prandtl number, Schmidt number, Eckert number, Brownian motion parameter, thermophoresis parameter and the thickness of porous region on the hydrodynamics, heat and mass transfer behaviors are investigated.

  11. A method to calculate fission-fragment yields Y(Z,N) versus proton and neutron number in the Brownian shape-motion model

    DOE PAGES

    Moller, Peter; Ichikawa, Takatoshi

    2015-12-23

    In this study, we propose a method to calculate the two-dimensional (2D) fission-fragment yield Y(Z,N) versus both proton and neutron number, with inclusion of odd-even staggering effects in both variables. The approach is to use the Brownian shape-motion on a macroscopic-microscopic potential-energy surface which, for a particular compound system is calculated versus four shape variables: elongation (quadrupole moment Q2), neck d, left nascent fragment spheroidal deformation ϵf1, right nascent fragment deformation ϵf2 and two asymmetry variables, namely proton and neutron numbers in each of the two fragments. The extension of previous models 1) introduces a method to calculate this generalizedmore » potential-energy function and 2) allows the correlated transfer of nucleon pairs in one step, in addition to sequential transfer. In the previous version the potential energy was calculated as a function of Z and N of the compound system and its shape, including the asymmetry of the shape. We outline here how to generalize the model from the “compound-system” model to a model where the emerging fragment proton and neutron numbers also enter, over and above the compound system composition.« less

  12. A method to calculate fission-fragment yields Y(Z,N) versus proton and neutron number in the Brownian shape-motion model

    SciTech Connect

    Moller, Peter; Ichikawa, Takatoshi

    2015-12-23

    In this study, we propose a method to calculate the two-dimensional (2D) fission-fragment yield Y(Z,N) versus both proton and neutron number, with inclusion of odd-even staggering effects in both variables. The approach is to use the Brownian shape-motion on a macroscopic-microscopic potential-energy surface which, for a particular compound system is calculated versus four shape variables: elongation (quadrupole moment Q2), neck d, left nascent fragment spheroidal deformation ϵf1, right nascent fragment deformation ϵf2 and two asymmetry variables, namely proton and neutron numbers in each of the two fragments. The extension of previous models 1) introduces a method to calculate this generalized potential-energy function and 2) allows the correlated transfer of nucleon pairs in one step, in addition to sequential transfer. In the previous version the potential energy was calculated as a function of Z and N of the compound system and its shape, including the asymmetry of the shape. We outline here how to generalize the model from the “compound-system” model to a model where the emerging fragment proton and neutron numbers also enter, over and above the compound system composition.

  13. Subpopulation-based correspondence modelling for improved respiratory motion estimation in the presence of inter-fraction motion variations.

    PubMed

    Wilms, Matthias; Werner, René; Yamamoto, Tokihiro; Handels, Heinz; Ehrhardt, Jan

    2017-06-26

    Correspondence modelling between low-dimensional breathing signals and internal organ motion is a prerequisite for application of advanced techniques in radiotherapy of moving targets. Patient-specific correspondence models can, for example, be built prior to treatment based on a planning 4D CT and simultaneously acquired breathing signals. Reliability of pre-treatment-built models depends, however, on the degree of patient-specific inter-fraction motion variations. This study investigates whether motion estimation accuracy in the presence of inter-fraction motion variations can be improved using correspondence models that incorporate motion information from different patients. The underlying assumption is that inter-patient motion variations resemble patient-specific inter-fraction motion variations for subpopulations of patients with similar breathing characteristics. The hypothesis is tested by integrating a sparse manifold clustering approach into a regression-based correspondence modelling framework that allows for automated identification of patient subpopulations. The evaluation is based on a total of 73 lung 4D CT data sets, including two cohorts of patients with repeat 4D CT scans (cohort 1: 14 patients; cohort 2: ten patients). The results are consistent for both cohorts: The subpopulation-based modelling approach outperforms general population modelling (models built on all data sets available) as well as pre-treatment-built models trained on only the patient-specific motion information. The results thereby support the hypothesis and illustrate the potential of subpopulation-based correspondence modelling.

  14. Subpopulation-based correspondence modelling for improved respiratory motion estimation in the presence of inter-fraction motion variations

    NASA Astrophysics Data System (ADS)

    Wilms, Matthias; Werner, René; Yamamoto, Tokihiro; Handels, Heinz; Ehrhardt, Jan

    2017-07-01

    Correspondence modelling between low-dimensional breathing signals and internal organ motion is a prerequisite for application of advanced techniques in radiotherapy of moving targets. Patient-specific correspondence models can, for example, be built prior to treatment based on a planning 4D CT and simultaneously acquired breathing signals. Reliability of pre-treatment-built models depends, however, on the degree of patient-specific inter-fraction motion variations. This study investigates whether motion estimation accuracy in the presence of inter-fraction motion variations can be improved using correspondence models that incorporate motion information from different patients. The underlying assumption is that inter-patient motion variations resemble patient-specific inter-fraction motion variations for subpopulations of patients with similar breathing characteristics. The hypothesis is tested by integrating a sparse manifold clustering approach into a regression-based correspondence modelling framework that allows for automated identification of patient subpopulations. The evaluation is based on a total of 73 lung 4D CT data sets, including two cohorts of patients with repeat 4D CT scans (cohort 1: 14 patients; cohort 2: ten patients). The results are consistent for both cohorts: The subpopulation-based modelling approach outperforms general population modelling (models built on all data sets available) as well as pre-treatment-built models trained on only the patient-specific motion information. The results thereby support the hypothesis and illustrate the potential of subpopulation-based correspondence modelling.

  15. Mechanical energy and equivalent differential equations of motion for single-degree-of-freedom fractional oscillators

    NASA Astrophysics Data System (ADS)

    Yuan, Jian; Zhang, Youan; Liu, Jingmao; Shi, Bao; Gai, Mingjiu; Yang, Shujie

    2017-06-01

    This paper addresses the total mechanical energy and equivalent differential equation of motion for single degree of freedom fractional oscillators. Based on the energy storage and dissipation properties of the Caputo fractional derivatives, the expression for total mechanical energy in the single degree of freedom fractional oscillators is firstly presented. The energy regeneration due to the external exciting force and the energy loss due to the fractional damping force during the vibratory motion are analyzed. Furthermore, based on the mean energy dissipation and storage in the fractional damping element in steady-state vibration, two new concepts, namely mean equivalent viscous damping and mean equivalent stiffness are suggested and the above coefficient values are evaluated. By this way, the fractional differential equations of motion for single-degree-of-freedom fractional oscillators are equivalently transformed into integer-order ordinary differential equations.

  16. Brownian vortexes

    NASA Astrophysics Data System (ADS)

    Sun, Bo; Lin, Jiayi; Darby, Ellis; Grosberg, Alexander Y.; Grier, David G.

    2009-07-01

    Mechanical equilibrium at zero temperature does not necessarily imply thermodynamic equilibrium at finite temperature for a particle confined by a static but nonconservative force field. Instead, the diffusing particle can enter into a steady state characterized by toroidal circulation in the probability flux, which we call a Brownian vortex. The circulatory bias in the particle’s thermally driven trajectory is not simply a deterministic response to the solenoidal component of the force but rather reflects interplay between advection and diffusion in which thermal fluctuations extract work from the nonconservative force field. As an example of this previously unrecognized class of stochastic heat engines, we consider a colloidal sphere diffusing in a conventional optical tweezer. We demonstrate both theoretically and experimentally that nonconservative optical forces bias the particle’s fluctuations into toroidal vortexes whose circulation can reverse direction with temperature or laser power.

  17. Two dimensional fractional projectile motion in a resisting medium

    NASA Astrophysics Data System (ADS)

    Rosales, Juan; Guía, Manuel; Gómez, Francisco; Aguilar, Flor; Martínez, Juan

    2014-07-01

    In this paper we propose a fractional differential equation describing the behavior of a two dimensional projectile in a resisting medium. In order to maintain the dimensionality of the physical quantities in the system, an auxiliary parameter k was introduced in the derivative operator. This parameter has a dimension of inverse of seconds (sec)-1 and characterizes the existence of fractional time components in the given system. It will be shown that the trajectories of the projectile at different values of γ and different fixed values of velocity v 0 and angle θ, in the fractional approach, are always less than the classical one, unlike the results obtained in other studies. All the results obtained in the ordinary case may be obtained from the fractional case when γ = 1.

  18. Two dimensional fractional projectile motion in a resisting medium

    NASA Astrophysics Data System (ADS)

    Rosales, Juan J.; Guía, Manuel; Gómez, Francisco; Aguilar, Flor; Martínez, Juan

    2014-07-01

    In this paper we propose a fractional differential equation describing the behavior of a two dimensional projectile in a resisting medium. In order to maintain the dimensionality of the physical quantities in the system, an auxiliary parameter k was introduced in the derivative operator. This parameter has a dimension of inverse of seconds ( sec)-1 and characterizes the existence of fractional time components in the given system. It will be shown that the trajectories of the projectile at different values of γ and different fixed values of velocity v 0 and angle θ, in the fractional approach, are always less than the classical one, unlike the results obtained in other studies. All the results obtained in the ordinary case may be obtained from the fractional case when γ = 1.

  19. Mechanical properties of sensory hair bundles are reflected in their Brownian motion measured with a laser differential interferometer.

    PubMed Central

    Denk, W; Webb, W W; Hudspeth, A J

    1989-01-01

    By optically probing with a focused, low-power laser beam, we measured the spontaneous deflection fluctuations of the sensory hair bundles on frog saccular hair cells with a sensitivity of about 1 pm/square root of Hz. The preparation was illuminated by two orthogonally polarized laser beams separated by only about 0.2 microns at their foci in the structure under investigation. Slight movement of the object from one beam toward the other caused a change of the phase difference between the transmitted beams and an intensity modulation at the detector where the beams interfered. Maintenance of the health of the cells and function of the transduction mechanism were occasionally confirmed by measuring the intracellular resting potential and the sensitivity of transduction. The root-mean-square (rms) displacement of approximately 3.5 nm at a hair bundle's tip suggests a stiffness of about 350 microN/m, in agreement with measurements made with a probe attached to a bundle's tip. The spectra resemble those of overdamped harmonic oscillators with roll-off frequencies between 200 and 800 Hz. Because the roll-off frequencies depended strongly on the viscosity of the bathing medium, we conclude that hair-bundle motion is mainly damped by the surrounding fluid. PMID:2787510

  20. Intra-fraction motion of the prostate is a random walk

    NASA Astrophysics Data System (ADS)

    Ballhausen, H.; Li, M.; Hegemann, N.-S.; Ganswindt, U.; Belka, C.

    2015-01-01

    A random walk model for intra-fraction motion has been proposed, where at each step the prostate moves a small amount from its current position in a random direction. Online tracking data from perineal ultrasound is used to validate or reject this model against alternatives. Intra-fraction motion of a prostate was recorded by 4D ultrasound (Elekta Clarity system) during 84 fractions of external beam radiotherapy of six patients. In total, the center of the prostate was tracked for 8 h in intervals of 4 s. Maximum likelihood model parameters were fitted to the data. The null hypothesis of a random walk was tested with the Dickey-Fuller test. The null hypothesis of stationarity was tested by the Kwiatkowski-Phillips-Schmidt-Shin test. The increase of variance in prostate position over time and the variability in motility between fractions were analyzed. Intra-fraction motion of the prostate was best described as a stochastic process with an auto-correlation coefficient of ρ = 0.92  ±  0.13. The random walk hypothesis (ρ = 1) could not be rejected (p = 0.27). The static noise hypothesis (ρ = 0) was rejected (p < 0.001). The Dickey-Fuller test rejected the null hypothesis ρ = 1 in 25% to 32% of cases. On average, the Kwiatkowski-Phillips-Schmidt-Shin test rejected the null hypothesis ρ = 0 with a probability of 93% to 96%. The variance in prostate position increased linearly over time (r2 = 0.9  ±  0.1). Variance kept increasing and did not settle at a maximum as would be expected from a stationary process. There was substantial variability in motility between fractions and patients with maximum aberrations from isocenter ranging from 0.5 mm to over 10 mm in one patient alone. In conclusion, evidence strongly suggests that intra-fraction motion of the prostate is a random walk and neither static (like inter-fraction setup errors) nor stationary (like a cyclic motion such as breathing, for example). The prostate tends to drift away from the

  1. Fractional calculus in hydrologic modeling: A numerical perspective

    PubMed Central

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

    2013-01-01

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

  2. Fractional Calculus in Hydrologic Modeling: A Numerical Perspective

    SciTech Connect

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

    2012-01-01

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

  3. Fractional calculus in hydrologic modeling: A numerical perspective.

    PubMed

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

    2013-01-01

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

  4. Ergodic properties of fractional Langevin motion with spatial correlated noise

    NASA Astrophysics Data System (ADS)

    Duan, H.-G.; Liang, X.-T.

    2012-06-01

    In this paper, using fractional Langevin equation, we investigate the diffusion behavior of particles in the potential with spatial correlated noise (random disorder). Weak ergodicity breaking is revealed by plotting time averaged mean square displacement and ergodicity breaking parameter. The results are consistent with continuous time random walk (CTRW) and also in agreement with the properties of ones obtained with experiments.

  5. Analysis of football player's motion in view of fractional calculus

    NASA Astrophysics Data System (ADS)

    Couceiro, Micael S.; Clemente, Filipe M.; Martins, Fernando M. L.

    2013-06-01

    Accurately retrieving the position of football players over time may lay the foundations for a whole series of possible new performance metrics for coaches and assistants. Despite the recent developments of automatic tracking systems, the misclassification problem ( i.e., misleading a given player by another) still exists and requires human operators as final evaluators. This paper proposes an adaptive fractional calculus (FC) approach to improve the accuracy of tracking methods by estimating the position of players based on their trajectory so far. One half-time of an official football match was used to evaluate the accuracy of the proposed approach under different sampling periods of 250, 500 and 1000 ms. Moreover, the performance of the FC approach was compared with position-based and velocity-based methods. The experimental evaluation shows that the FC method presents a high classification accuracy for small sampling periods. Such results suggest that fractional dynamics may fit the trajectory of football players, thus being useful to increase the autonomy of tracking systems.

  6. Analysis of football player's motion in view of fractional calculus

    NASA Astrophysics Data System (ADS)

    Couceiro, Micael; Clemente, Filipe; Martins, Fernando

    2013-06-01

    Accurately retrieving the position of football players over time may lay the foundations for a whole series of possible new performance metrics for coaches and assistants. Despite the recent developments of automatic tracking systems, the misclassification problem (i.e., misleading a given player by another) still exists and requires human operators as final evaluators. This paper proposes an adaptive fractional calculus (FC) approach to improve the accuracy of tracking methods by estimating the position of players based on their trajectory so far. One half-time of an official football match was used to evaluate the accuracy of the proposed approach under different sampling periods of 250, 500 and 1000 ms. Moreover, the performance of the FC approach was compared with position-based and velocity-based methods. The experimental evaluation shows that the FC method presents a high classification accuracy for small sampling periods. Such results suggest that fractional dynamics may fit the trajectory of football players, thus being useful to increase the autonomy of tracking systems.

  7. Brownian Motion, "Diverse and Undulating"

    NASA Astrophysics Data System (ADS)

    Duplantier, Bertrand

    Truly man is a marvelously vain, diverse, and undulating object. It is hard to found any constant and uniform judgment on him. Michel de Montaigne, Les Essais, Book I, Chapter 1: "By diverse means we arrive at the same end"; in The Complete Essays of Montaigne, Donald M. Frame transl., Stanford University Press (1958).

  8. Instantaneous Control of Brownian Motion.

    DTIC Science & Technology

    1981-10-01

    0561 (NR-047-200) WITH THE OFFICE OF NAVAL RESEARCH Gerald J. Lieberman, Project Director Reproduction in Whole or in Part is Permitted for any Purpose...definition of ALt to t = 0. It will be convenient to denote by P and X the continuous parts of R and L respectively, meaning that (4.1) Pt Rt " AR and Xt L...O,T], and we have simplified the general form of 12 (T) by using the fact that oW is the so-called continuous martinqale part of Z and <aW, W>t = a2t

  9. Intra-fraction respiratory motion and baseline drift during breast Helical Tomotherapy.

    PubMed

    Ricotti, Rosalinda; Ciardo, Delia; Fattori, Giovanni; Leonardi, Maria Cristina; Morra, Anna; Dicuonzo, Samantha; Rojas, Damaris Patricia; Pansini, Floriana; Cambria, Raffaella; Cattani, Federica; Gianoli, Chiara; Spinelli, Chiara; Riboldi, Marco; Baroni, Guido; Orecchia, Roberto; Jereczek-Fossa, Barbara Alicja

    2017-01-01

    To investigate the intra-fraction breast motion during long-lasting treatments of breast cancer with Helical Tomotherapy by means of an optical tracking system. A set of seven radio-transparent passive markers was placed on the thoraco-abdominal surface of twenty breast cancer patients and tracked by an infrared tracking system. A continuous non-invasive monitoring of intra-fraction motion from patient setup verification and correction to the end of radiation delivery was thus obtained. The measured displacements were analysed in terms of cyclic respiratory motion and slow baseline drift. The average monitoring time per patient was 15.57min. The breathing amplitude of the chest was less than 2mm, on average, along all anatomical directions. The baseline drift of the body led to more significant setup uncertainties than the respiratory motion. The main intra-fraction baseline drifts were in posterior and inferior directions and occurred within the first eight minutes of monitoring. Considering the intra-fraction motion only, the resultant clinical-to-planning target volume safety margins are highly patient-specific and largely anisotropic. The non-respiratory motion occurring during prolonged treatments induces notable uncertainties. Non-invasive continuous monitoring of patient setup variations including baseline drifts is recommended in order to minimize dosimetric deviations, which might jeopardize the therapeutic ratio between target coverage and the sparing of organs at risk. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

  10. Intra-fraction motion of the prostate is not increased by patient couch shifts.

    PubMed

    Ballhausen, Hendrik; Ganswindt, Ute; Belka, Claus; Li, Minglun

    2016-03-22

    During a fraction of external beam radiotherapy for prostate cancer, a mismatch between target volume and dose coverage may accumulate over time due to intra-fraction motion. One way to remove the residual error is to perform a couch shift in opposite direction. In principle, such couch shifts could cause secondary displacements of the patient and prostate. Hence it is interesting to investigate if couch shifts might amplify intra-fraction motion. Intra-fraction motion of the prostate and patient couch position were simultaneously recorded during 359 fractions in 15 patients. During this time, a total of 22 couch shifts of up to 31.5 mm along different axes were recorded. Prostate position and couch position were plotted before, during and after each couch shift. There was no visible impact of couch shifts on prostate motion. The standard deviation of prostate position was calculated before, during and after each couch shift. The standard deviation did not significantly increase during couch shifts (by 3 % on average, p = 0.88) and even slightly decreased after a couch shift (by 37 % on average; p = 0.02). Shifts of the patient couch did not adversely affect the motion of the prostate relative to the patient couch. Hence, shifts of the patient couch may be a viable way to correct the position of the prostate relative to the dose distribution.

  11. Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell model

    NASA Astrophysics Data System (ADS)

    Wenchang, Tan; Mingyu, Xu

    2002-08-01

    The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. The flow near a wall suddenly set in motion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model. Exact solutions of velocity and stress are obtained by using the discrete inverse Laplace transform of the sequential fractional derivatives. It is found that the effect of the fractional orders in the constitutive relationship on the flow field is significant. The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate, for large times the viscoelastic effects become weak.

  12. Temporally Anticorrelated Motion of Nanoparticles at a Liquid Interface.

    PubMed

    Wang, Dapeng; Hu, Renfeng; Skaug, Michael J; Schwartz, Daniel K

    2015-01-02

    Quantum dots at the hexane-glycerol interface exhibited unexpected behavior including highly dynamic adsorption/desorption, where the lateral nanoparticle motion was anomalously fast immediately after adsorption and prior to desorption. At the interface, particles exhibited pseudo-Brownian lateral motion, in which the instantaneous diffusion coefficient was temporally anticorrelated, in agreement with our simulations involving fractional Brownian motion in the surface-normal direction. These phenomena suggest that, in contrast to the conventional picture for colloidal particles, nanoparticles explore a landscape of metastable interfacial positions, with different exposures to the two adjacent phases.

  13. A new method to reconstruct intra-fractional prostate motion in volumetric modulated arc therapy

    NASA Astrophysics Data System (ADS)

    Chi, Y.; Rezaeian, N. H.; Shen, C.; Zhou, Y.; Lu, W.; Yang, M.; Hannan, R.; Jia, X.

    2017-07-01

    Intra-fractional motion is a concern during prostate radiation therapy, as it may cause deviations between planned and delivered radiation doses. Because accurate motion information during treatment delivery is critical to address dose deviation, we developed the projection marker matching method (PM3), a novel method for prostate motion reconstruction in volumetric modulated arc therapy. The purpose of this method is to reconstruct in-treatment prostate motion trajectory using projected positions of implanted fiducial markers measured in kV x-ray projection images acquired during treatment delivery. We formulated this task as a quadratic optimization problem. The objective function penalized the distance from the reconstructed 3D position of each fiducial marker to the corresponding straight line, defined by the x-ray projection of the marker. Rigid translational motion of the prostate and motion smoothness along the temporal dimension were assumed and incorporated into the optimization model. We tested the motion reconstruction method in both simulation and phantom experimental studies. We quantified the accuracy using 3D normalized root-mean-square (RMS) error defined as the norm of a vector containing ratios between the absolute RMS errors and corresponding motion ranges in three dimensions. In the simulation study with realistic prostate motion trajectories, the 3D normalized RMS error was on average ~0.164 (range from 0.097 to 0.333 ). In an experimental study, a prostate phantom was driven to move along a realistic prostate motion trajectory. The 3D normalized RMS error was ~0.172 . We also examined the impact of the model parameters on reconstruction accuracy, and found that a single set of parameters can be used for all the tested cases to accurately reconstruct the motion trajectories. The motion trajectory derived by PM3 may be incorporated into novel strategies, including 4D dose reconstruction and adaptive treatment replanning to address motion

  14. Ratcheted electrophoresis of Brownian particles

    SciTech Connect

    Kowalik, Mikołaj; Bishop, Kyle J. M.

    2016-05-16

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

  15. Ratcheted electrophoresis of Brownian particles

    NASA Astrophysics Data System (ADS)

    Kowalik, Mikołaj; Bishop, Kyle J. M.

    2016-05-01

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

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

    PubMed

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

    2014-01-07

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

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

    PubMed Central

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

    2014-01-01

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

  18. Enhancing ejection fraction measurement through 4D respiratory motion compensation in cardiac PET imaging.

    PubMed

    Tang, Jing; Wang, Xinhui; Gao, Xiangzhen; Segars, Paul; Lodge, Martin; Rahmim, Arman

    2017-03-02

    ECG gated cardiac PET imaging measures functional parameters such as left ventricle (LV) ejection fraction (EF), providing diagnostic and prognostic information for management of patients with coronary artery disease (CAD). Respiratory motion degrades spatial resolution and affects the accuracy in measuring the LV volumes for EF calculation. The goal of this study is to systematically investigate the effect of respiratory motion correction on the estimation of end-diastolic volume (EDV), end-systolic volume (ESV), and EF, especially on the separation of normal and abnormal EFs. We developed a respiratory motion incorporated 4D PET image reconstruction technique which uses all gated-frame data to acquire a motion-suppressed image. Using the standard XCAT phantom and two individual-specific volunteer XCAT phantoms, we simulated dual-gated myocardial perfusion imaging data for normally and abnormally beating hearts. With and without respiratory motion correction, we measured the EDV, ESV, and EF from the cardiac gated reconstructed images. For all the phantoms, the estimated volumes increased and the biases significantly reduced with motion correction compared with those without. Furthermore, the improvement of ESV measurement in the abnormally beating heart led to better separation of normal and abnormal EFs. The simulation study demonstrated the significant effect of respiratory motion correction on cardiac imaging data with motion amplitude as small as 0.7 cm. The larger the motion amplitude the more improvement respiratory motion correction brought about on the measurement of EF. Using data-driven respiratory gating, we also demonstrated the effect of respiratory motion correction on estimation of the above functional parameters from list mode patient data. Respiratory motion correction is shown to improve the accuracy of EF measurement in clinical cardiac PET imaging.

  19. Enhancing ejection fraction measurement through 4D respiratory motion compensation in cardiac PET imaging

    NASA Astrophysics Data System (ADS)

    Tang, Jing; Wang, Xinhui; Gao, Xiangzhen; Segars, W. Paul; Lodge, Martin A.; Rahmim, Arman

    2017-06-01

    ECG gated cardiac PET imaging measures functional parameters such as left ventricle (LV) ejection fraction (EF), providing diagnostic and prognostic information for management of patients with coronary artery disease (CAD). Respiratory motion degrades spatial resolution and affects the accuracy in measuring the LV volumes for EF calculation. The goal of this study is to systematically investigate the effect of respiratory motion correction on the estimation of end-diastolic volume (EDV), end-systolic volume (ESV), and EF, especially on the separation of normal and abnormal EFs. We developed a respiratory motion incorporated 4D PET image reconstruction technique which uses all gated-frame data to acquire a motion-suppressed image. Using the standard XCAT phantom and two individual-specific volunteer XCAT phantoms, we simulated dual-gated myocardial perfusion imaging data for normally and abnormally beating hearts. With and without respiratory motion correction, we measured the EDV, ESV, and EF from the cardiac-gated reconstructed images. For all the phantoms, the estimated volumes increased and the biases significantly reduced with motion correction compared with those without. Furthermore, the improvement of ESV measurement in the abnormally beating heart led to better separation of normal and abnormal EFs. The simulation study demonstrated the significant effect of respiratory motion correction on cardiac imaging data with motion amplitude as small as 0.7 cm. The larger the motion amplitude the more improvement respiratory motion correction brought about on the EF measurement. Using data-driven respiratory gating, we also demonstrated the effect of respiratory motion correction on estimating the above functional parameters from list mode patient data. Respiratory motion correction has been shown to improve the accuracy of EF measurement in clinical cardiac PET imaging.

  20. Measurement of inter and intra fraction organ motion in radiotherapy using cone beam CT projection images

    NASA Astrophysics Data System (ADS)

    Marchant, T. E.; Amer, A. M.; Moore, C. J.

    2008-02-01

    A method is presented for extraction of intra and inter fraction motion of seeds/markers within the patient from cone beam CT (CBCT) projection images. The position of the marker is determined on each projection image and fitted to a function describing the projection of a fixed point onto the imaging panel at different gantry angles. The fitted parameters provide the mean marker position with respect to the isocentre. Differences between the theoretical function and the actual projected marker positions are used to estimate the range of intra fraction motion and the principal motion axis in the transverse plane. The method was validated using CBCT projection images of a static marker at known locations and of a marker moving with known amplitude. The mean difference between actual and measured motion range was less than 1 mm in all directions, although errors of up to 5 mm were observed when large amplitude motion was present in an orthogonal direction. In these cases it was possible to calculate the range of motion magnitudes consistent with the observed marker trajectory. The method was shown to be feasible using clinical CBCT projections of a pancreas cancer patient.

  1. SU-E-J-183: Quantification of Motion During Hypo-Fractionated Prostate Cancer Radiation Therapy

    SciTech Connect

    Ravindranath, B; Zhang, P; Xiong, J; Mageras, G; Hunt, M

    2015-06-15

    Purpose: To quantify patient motion during hypo-fractionated prostate cancer treatment as tracked by Calypso™ 4D localization system. Methods: 50 prostate cancer patients with implanted Calypso beacons underwent hypofractionated IMRT treatment. Typical fraction size was 5 with doses of 5–8 Gy/fraction. 213 traces from the 50 patients were analyzed to quantify the probability of motion vs time starting from beam-on. Couch corrections applied by therapists were undone to obtain the natural course of patient motion. The Calypso data was used to identify vector displacements greater than 2 mm from the starting position. The direction of this vector was classified into one of the 26 directions (combinations of L/R, A/P, S/I). The probability of motion >2mm was estimated by computing the fraction of traces that exceed the 2mm threshold at each time point. The violating motion points were also binned by direction in order to identify specific directions that were more prone to movement. Results: The overall probability of motion greater than 2 mm at 5 and 10 minutes from beam-on were 27 % and 50% respectively. The primary directions in which motion occurred were Posterior-Inferior (PI) and Inferior (I) with a probability of 8.5% and 4% at 5 minutes and 10% for both at 10 minutes. Motion was classified into the following bins: 0–2, 2–3, 3–4, 4–5, 5–6, 6–7, 7–8 and greater than 8 mm. It is observed that motion < 2mm decreases from the first 5 minutes to the next while the higher magnitude components increase with time. Conclusion: The probability of prostate motion increases with time. The trend seen in the PI and I directions can be attributed to physiological factors like bladder filling. This probability can be factored in for scheduling intrafraction imaging and used to compare dosimetric impact of VMAT vs. IMRT plans. This work is supported in part by Varian Medical Systems.

  2. Intra- and Inter-Fraction Mediastinal Nodal Region Motion: Implications for Internal Target Volume Expansions

    PubMed Central

    Thomas, Jonathan G.; Kashani, Rojano; Balter, James M.; Tatro, Daniel; Kong, Feng-Ming; Pan, Charlie C.

    2009-01-01

    Purpose/Objective The purpose of this study is to determine the intra- and inter-fraction motion of mediastinal lymph node regions. Materials/Methods Ten patients with non-small cell lung cancer underwent controlled inhale and exhale CT scans during two sessions (40 total data sets) and mediastinal nodal stations 1–8 [Chapet, et al, IJROBP 2005;63:170–8] were outlined. Corresponding CT scans from different sessions were registered to remove setup error and in this reference frame, the center-of-mass (COM) of each nodal station was compared for right-left (RL), anterior-posterior (AP), and superior-inferior (SI) displacement. In addition, an anisotropic volume expansion encompassing the change of the nodal region margins in all directions was used. Intra-fraction displacement was determined by comparing same session inhale-exhale scans. Inter-fraction reproducibility of nodal regions was determined by comparing the same respiratory phase scans between two sessions. Results Intra-fraction displacement of COM varied between nodal stations. All nodal regions moved posteriorly and superiorly with exhalation, and inferior nodal stations showed the most motion. Based on anisotropic expansion, nodal regions expanded mostly in the RL direction from inhale to exhale. The inter-patient variations in intra-fraction displacement were large compared to the displacements themselves. Moreover, there was substantial inter-fractional displacement (∼5 mm). Conclusions Mediastinal lymph node regions clearly move during breathing. Additionally, deformation of nodal regions between inhale and exhale occurs. The degree of motion and deformation varies by station and by individual. This study indicates the potential advantage of characterizing individualized nodal region motion to safely maximize conformality of mediastinal nodal targets. PMID:19410142

  3. SU-E-J-133: Evaluation of Inter- and Intra-Fractional Pancreas Tumor Residual Motions with Abdominal Compression

    SciTech Connect

    Li, Y; Shi, F; Tian, Z; Jia, X; Meyer, J; Jiang, S; Mao, W

    2014-06-01

    Purpose: Abdominal compression (AC) has been widely used to reduce pancreas motion due to respiration for pancreatic cancer patients undergoing stereotactic body radiotherapy (SBRT). However, the inter-fractional and intra-fractional patient motions may degrade the treatment. The purpose of this work is to study daily CBCT projections and 4DCT to evaluate the inter-fractional and intra-fractional pancreatic motions. Methods: As a standard of care at our institution, 4D CT scan was performed for treatment planning. At least two CBCT scans were performed for daily treatment. Retrospective studies were performed on patients with implanted internal fiducial markers or surgical clips. The initial motion pattern was obtained by extracting marker positions on every phase of 4D CT images. Daily motions were presented by marker positions on CBCT scan projection images. An adaptive threshold segmentation algorithm was used to extract maker positions. Both marker average positions and motion ranges were compared among three sets of scans, 4D CT, positioning CBCT, and conformal CBCT, for inter-fractional and intra-fractional motion variations. Results: Data from four pancreatic cancer patients were analyzed. These patients had three fiducial markers implanted. All patients were treated by an Elekta Synergy with single fraction SBRT. CBCT projections were acquired by XVI. Markers were successfully detected on most of the projection images. The inter-fractional changes were determined by 4D CT and the first CBCT while the intra-fractional changes were determined by multiple CBCT scans. It is found that the average motion range variations are within 2 mm, however, the average marker positions may drift by 6.5 mm. Conclusion: The patients respiratory motion variation for pancreas SBRT with AC was evaluated by detecting markers from CBCT projections and 4DCT, both the inter-fraction and intra-fraction motion range change is small but the drift of marker positions may be comparable

  4. Strategies for reducing intra-fraction motion induced dosimetric effects in proton therapy

    NASA Astrophysics Data System (ADS)

    Zhao, Li

    Intra-fraction respiration motion during radiation delivery presents a major challenge to radiation therapy. There has been a growing effort to characterize and manage internal organ motion in radiation therapy, however very few studies focus on tackling this issue in proton therapy. Current practice for treating lung tumors in proton therapy is still to apply population-based margins to account for internal tumor motion, which can lead to target underdosage and normal tissue overdosage. This thesis explores the intra-fraction motion induced dosimetric effects from both computational treatment planning and experimental studies. Four-dimensional CT scans are used to analyze the patient-specific tumor motion characteristics. A feasible method to design the range compensator by using the maximum intensity projection (MIP) images is proposed. Results demonstrate that this MIP approach ensures adequate tumor coverage throughout the entire respiratory cycle whilst maintaining normal tissue dose under clinical constraints. Based on 4D-CT scans, dose convolution is used for assessing the accuracy of Gaussian probability density function for modeling the patient-specific respiratory motion on dose distribution. Non-negligible dose discrepancy is observed in comparisons of convolved dose distributions, and patient-specific respiration PDF is advocated. In addition, an experimental phantom study primarily focusing on the interplay effect between target motion and the scanning beam motion is implemented in two proton beam delivery systems: double scattering and uniform scanning. Measurement results suggest that dose blurring effect is dominant, and interplay effect is trivial in the uniform scanning system due to dose repainting.

  5. Brownian dynamics without Green's functions

    SciTech Connect

    Delong, Steven; Donev, Aleksandar; Usabiaga, Florencio Balboa; Delgado-Buscalioni, Rafael; Griffith, Boyce E.

    2014-04-07

    We develop a Fluctuating Immersed Boundary (FIB) method for performing Brownian dynamics simulations of confined particle suspensions. Unlike traditional methods which employ analytical Green's functions for Stokes flow in the confined geometry, the FIB method uses a fluctuating finite-volume Stokes solver to generate the action of the response functions “on the fly.” Importantly, we demonstrate that both the deterministic terms necessary to capture the hydrodynamic interactions among the suspended particles, as well as the stochastic terms necessary to generate the hydrodynamically correlated Brownian motion, can be generated by solving the steady Stokes equations numerically only once per time step. This is accomplished by including a stochastic contribution to the stress tensor in the fluid equations consistent with fluctuating hydrodynamics. We develop novel temporal integrators that account for the multiplicative nature of the noise in the equations of Brownian dynamics and the strong dependence of the mobility on the configuration for confined systems. Notably, we propose a random finite difference approach to approximating the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. Through comparisons with analytical and existing computational results, we numerically demonstrate the ability of the FIB method to accurately capture both the static (equilibrium) and dynamic properties of interacting particles in flow.

  6. Brownian dynamics without Green's functions.

    PubMed

    Delong, Steven; Usabiaga, Florencio Balboa; Delgado-Buscalioni, Rafael; Griffith, Boyce E; Donev, Aleksandar

    2014-04-07

    We develop a Fluctuating Immersed Boundary (FIB) method for performing Brownian dynamics simulations of confined particle suspensions. Unlike traditional methods which employ analytical Green's functions for Stokes flow in the confined geometry, the FIB method uses a fluctuating finite-volume Stokes solver to generate the action of the response functions "on the fly." Importantly, we demonstrate that both the deterministic terms necessary to capture the hydrodynamic interactions among the suspended particles, as well as the stochastic terms necessary to generate the hydrodynamically correlated Brownian motion, can be generated by solving the steady Stokes equations numerically only once per time step. This is accomplished by including a stochastic contribution to the stress tensor in the fluid equations consistent with fluctuating hydrodynamics. We develop novel temporal integrators that account for the multiplicative nature of the noise in the equations of Brownian dynamics and the strong dependence of the mobility on the configuration for confined systems. Notably, we propose a random finite difference approach to approximating the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. Through comparisons with analytical and existing computational results, we numerically demonstrate the ability of the FIB method to accurately capture both the static (equilibrium) and dynamic properties of interacting particles in flow.

  7. Generalized formulation of Brownian Vortexes

    NASA Astrophysics Data System (ADS)

    Moyses, Henrique; Bauer, Ross; Grier, David

    2013-03-01

    Brownian vortexes are stochastic noise driven machines that arise from the motion of particles subjected to static non conservative force fields. This motion is characterized by a toroidal circulation in the probability flux whose direction can be tuned by changing the temperature of the system. A discrete minimal model for Brownian Vortexes were described by previous work done by B.Sun, D.G.Grier and A.Y.Grosberg. Here we theoretically look for a continuous model in the form of a generalization of the equilibrium Boltzmann relation for the probability density in the case where the driven forces have a non conservative solenoidal component. This generalized relation features the temperature induced probability flux reversal. We further extend our theory to time dependent force fields and study the possibility of stochastic resonance in the characteristic frequency of circulation of the driven particle. This model is experimentally applied to investigate the motion of colloidal spheres in an optical trap whose intensity is oscillatory in time.

  8. Tempered fractional Feynman-Kac equation: Theory and examples.

    PubMed

    Wu, Xiaochao; Deng, Weihua; Barkai, Eli

    2016-03-01

    Functionals of Brownian and non-Brownian motions have diverse applications and attracted a lot of interest among scientists. This paper focuses on deriving the forward and backward fractional Feynman-Kac equations describing the distribution of the functionals of the space and time-tempered anomalous diffusion, belonging to the continuous time random walk class. Several examples of the functionals are explicitly treated, including the occupation time in half-space, the first passage time, the maximal displacement, the fluctuations of the occupation fraction, and the fluctuations of the time-averaged position.

  9. Fractional-wrapped branes with rotation, linear motion and background fields

    NASA Astrophysics Data System (ADS)

    Maghsoodi, Elham; Kamani, Davoud

    2017-09-01

    We obtain two boundary states corresponding to the two folds of a fractional-wrapped Dp-brane, i.e. the twisted version under the orbifold C2 /Z2 and the untwisted version. The brane has rotation and linear motion, in the presence of the following background fields: the Kalb-Ramond tensor, a U (1) internal gauge potential and a tachyon field. The rotation and linear motion are inside the volume of the brane. The brane lives in the d-dimensional spacetime, with the orbifold-toroidal structure Tn ×R 1 , d - n - 5 ×C2 /Z2 in the twisted sector. Using these boundary states we calculate the interaction amplitude of two parallel fractional Dp-branes with the foregoing setup. Various properties of this amplitude such as the long-range behavior will be analyzed.

  10. Anti-Brownian traps for studies on single molecules.

    PubMed

    Fields, Alexander P; Cohen, Adam E

    2010-01-01

    Until recently, Brownian motion was seen as an immutable feature of small particles in room-temperature liquids. Molecules, viruses, organelles, and small cells jiggle incessantly due to countless collisions with thermally agitated molecules of solvent. Einstein showed in 1905 that this motion is intimately linked to the tendency of every system to relax toward thermal equilibrium. In recent years, we and others have realized that Brownian motion is not as inescapable as one might think. By tracking the motion of a small particle and applying correction forces to the particle or to the measurement apparatus, one can largely suppress the Brownian motion of particles as small as a few nanometers in diameter, in aqueous solution at room temperature. This new ability to stabilize single molecules has led to a host of studies on topics ranging from the conformational dynamics of DNA to the optical properties of metal nanoparticles. In this review, we outline the physical principles behind suppression of Brownian motion. We discuss the relative merits of several systems that have been implemented. We give examples of studies performed with our anti-Brownian Electrokinetic trap (ABEL trap) as well as other anti-Brownian traps, and we discuss prospects for future research. Copyright (c) 2010 Elsevier Inc. All rights reserved.

  11. On the effect of intrafraction motion in a single fraction step-shoot IMRT.

    PubMed

    Zhuang, Tingliang

    2015-07-01

    The authors studied the respiratory motion effect in a single step-shoot intensity modulated radiotherapy (IMRT) to assess the basic properties of the uncertainty in the delivered dose due to the unknown starting phase of the motion. Using computer simulations, the motion-averaged dose for open beams with various field sizes was calculated for two one-dimensional trajectories with different motion amplitudes at 20 equally spaced starting phases. The properties of the standard deviation (SD) of delivered dose were analyzed. The dependence of SD on the field size, motion amplitude, and delivery time was investigated and experimentally validated. To study effect of number of small monitor unit (MU) segments on the dose uncertainty, the authors generated 1000 pairs of multisegment beams such that each pair consists of two beams with the same total MU and different segment MU. The SD at the central axis point was compared for each pair. The authors proved that the direct time-dependent dose accumulation can be calculated using a convolution formula for a single fraction step-shoot IMRT treatment. Single segment simulation showed that the maximum dose uncertainty occurred symmetrically at the beam penumbra for a sinusoidal motion. For other sinusoidal motions (sin(2n) n > 1), the maximum dose uncertainty occurred at asymmetrical locations and may be beyond the penumbra region. The SD of relative dose periodically varied with delivery time with decreasing envelope for both motion trajectories. The SD of absolute dose was a periodic function of the delivery time for a given field size and motion amplitude and was proved to be true for any periodic motion. The SD reduced to zero when the delivery time was an integer multiple of the motion period. Analytical function σA=3βsin(2)π/Tδt-4/3sin(4)π/Tδt+2/3sin(6)π/Tδt was found to fit the delivery time dependence of the SD for motions studied in this paper and was verified with experimental data and an irregular motion

  12. Near-Field, On-Chip Optical Brownian Ratchets.

    PubMed

    Wu, Shao-Hua; Huang, Ningfeng; Jaquay, Eric; Povinelli, Michelle L

    2016-08-10

    Nanoparticles in aqueous solution are subject to collisions with solvent molecules, resulting in random, Brownian motion. By breaking the spatiotemporal symmetry of the system, the motion can be rectified. In nature, Brownian ratchets leverage thermal fluctuations to provide directional motion of proteins and enzymes. In man-made systems, Brownian ratchets have been used for nanoparticle sorting and manipulation. Implementations based on optical traps provide a high degree of tunability along with precise spatiotemporal control. Here, we demonstrate an optical Brownian ratchet based on the near-field traps of an asymmetrically patterned photonic crystal. The system yields over 25 times greater trap stiffness than conventional optical tweezers. Our technique opens up new possibilities for particle manipulation in a microfluidic, lab-on-chip environment.

  13. Adiabatically driven Brownian pumps.

    PubMed

    Rozenbaum, Viktor M; Makhnovskii, Yurii A; Shapochkina, Irina V; Sheu, Sheh-Yi; Yang, Dah-Yen; Lin, Sheng Hsien

    2013-07-01

    We investigate a Brownian pump which, being powered by a flashing ratchet mechanism, produces net particle transport through a membrane. The extension of the Parrondo's approach developed for reversible Brownian motors [Parrondo, Phys. Rev. E 57, 7297 (1998)] to adiabatically driven pumps is given. We demonstrate that the pumping mechanism becomes especially efficient when the time variation of the potential occurs adiabatically fast or adiabatically slow, in perfect analogy with adiabatically driven Brownian motors which exhibit high efficiency [Rozenbaum et al., Phys. Rev. E 85, 041116 (2012)]. At the same time, the efficiency of the pumping mechanism is shown to be less than that of Brownian motors due to fluctuations of the number of particles in the membrane.

  14. Quantification of intra-fraction motion in breast radiotherapy using supine magnetic resonance imaging.

    PubMed

    van Heijst, Tristan C F; Philippens, Mariëlle E P; Charaghvandi, Ramona K; den Hartogh, Mariska D; Lagendijk, Jan J W; van den Bongard, H J G Desirée; van Asselen, Bram

    2016-02-07

    In early-stage breast-cancer patients, accelerated partial-breast irradiation techniques (APBI) and hypofractionation are increasingly implemented after breast-conserving surgery (BCS). For a safe and effective radiation therapy (RT), the influence of intra-fraction motion during dose delivery becomes more important as associated fraction durations increase and targets become smaller. Current image-guidance techniques are insufficient to characterize local target movement in high temporal and spatial resolution for extended durations. Magnetic resonance imaging (MRI) can provide high soft-tissue contrast, allow fast imaging, and acquire images during longer periods. The goal of this study was to quantify intra-fraction motion using MRI scans from 21 breast-cancer patients, before and after BCS, in supine RT position, on two time scales. High-temporal 2-dimensional (2D) MRI scans (cine-MRI), acquired every 0.3 s during 2 min, and three 3D MRI scans, acquired over 20 min, were performed. The tumor (bed) and whole breast were delineated on 3D scans and delineations were transferred to the cine-MRI series. Consecutive scans were rigidly registered and delineations were transformed accordingly. Motion in sub-second time-scale (derived from cine-MRI) was generally regular and limited to a median of 2 mm. Infrequently, large deviations were observed, induced by deep inspiration, but these were temporary. Movement on multi-minute scale (derived from 3D MRI) varied more, although medians were restricted to 2.2 mm or lower. Large whole-body displacements (up to 14 mm over 19 min) were sparsely observed. The impact of motion on standard RT techniques is likely small. However, in novel hypofractionated APBI techniques, whole-body shifts may affect adequate RT delivery, given the increasing fraction durations and smaller targets. Motion management may thus be required. For this, on-line MRI guidance could be provided by a hybrid MRI/RT modality, such as the

  15. Quantification of intra-fraction motion in breast radiotherapy using supine magnetic resonance imaging

    NASA Astrophysics Data System (ADS)

    van Heijst, Tristan C. F.; Philippens, Mariëlle E. P.; Charaghvandi, Ramona K.; den Hartogh, Mariska D.; Lagendijk, Jan J. W.; Desirée van den Bongard, H. J. G.; van Asselen, Bram

    2016-02-01

    In early-stage breast-cancer patients, accelerated partial-breast irradiation techniques (APBI) and hypofractionation are increasingly implemented after breast-conserving surgery (BCS). For a safe and effective radiation therapy (RT), the influence of intra-fraction motion during dose delivery becomes more important as associated fraction durations increase and targets become smaller. Current image-guidance techniques are insufficient to characterize local target movement in high temporal and spatial resolution for extended durations. Magnetic resonance imaging (MRI) can provide high soft-tissue contrast, allow fast imaging, and acquire images during longer periods. The goal of this study was to quantify intra-fraction motion using MRI scans from 21 breast-cancer patients, before and after BCS, in supine RT position, on two time scales. High-temporal 2-dimensional (2D) MRI scans (cine-MRI), acquired every 0.3 s during 2 min, and three 3D MRI scans, acquired over 20 min, were performed. The tumor (bed) and whole breast were delineated on 3D scans and delineations were transferred to the cine-MRI series. Consecutive scans were rigidly registered and delineations were transformed accordingly. Motion in sub-second time-scale (derived from cine-MRI) was generally regular and limited to a median of 2 mm. Infrequently, large deviations were observed, induced by deep inspiration, but these were temporary. Movement on multi-minute scale (derived from 3D MRI) varied more, although medians were restricted to 2.2 mm or lower. Large whole-body displacements (up to 14 mm over 19 min) were sparsely observed. The impact of motion on standard RT techniques is likely small. However, in novel hypofractionated APBI techniques, whole-body shifts may affect adequate RT delivery, given the increasing fraction durations and smaller targets. Motion management may thus be required. For this, on-line MRI guidance could be provided by a hybrid MRI/RT modality, such as the

  16. Motion detection using extended fractional Fourier transform and digital speckle photography.

    PubMed

    Bhaduri, Basanta; Tay, C J; Quan, C; Sheppard, Colin J R

    2010-05-24

    Digital speckle photography is a useful tool for measuring the motion of optically rough surfaces from the speckle shift that takes place at the recording plane. A simple correlation based digital speckle photographic system has been proposed that implements two simultaneous optical extended fractional Fourier transforms (EFRTs) of different orders using only a single lens and detector to simultaneously detect both the magnitude and direction of translation and tilt by capturing only two frames: one before and another after the object motion. The dynamic range and sensitivity of the measurement can be varied readily by altering the position of the mirror/s used in the optical setup. Theoretical analysis and experiment results are presented.

  17. Displacements Of Brownian Particles In Terms Of Marian Von Smoluchowski's Heuristic Model

    ERIC Educational Resources Information Center

    Klein, Hermann; Woermann, Dietrich

    2005-01-01

    Albert Einstein's theory of the Brownian motion, Marian von Smoluchowski's heuristic model, and Perrin's experimental results helped to bring the concept of molecules from a state of being a useful hypothesis in chemistry to objects existing in reality. Central to the theory of Brownian motion is the relation between mean particle displacement and…

  18. Displacements Of Brownian Particles In Terms Of Marian Von Smoluchowski's Heuristic Model

    ERIC Educational Resources Information Center

    Klein, Hermann; Woermann, Dietrich

    2005-01-01

    Albert Einstein's theory of the Brownian motion, Marian von Smoluchowski's heuristic model, and Perrin's experimental results helped to bring the concept of molecules from a state of being a useful hypothesis in chemistry to objects existing in reality. Central to the theory of Brownian motion is the relation between mean particle displacement and…

  19. An excursion approach to maxima of the Brownian bridge.

    PubMed

    Perman, Mihael; Wellner, Jon A

    2014-09-01

    Distributions of functionals of Brownian bridge arise as limiting distributions in non-parametric statistics. In this paper we will give a derivation of distributions of extrema of the Brownian bridge based on excursion theory for Brownian motion. The idea of rescaling and conditioning on the local time has been used widely in the literature. In this paper it is used to give a unified derivation of a number of known distributions, and a few new ones. Particular cases of calculations include the distribution of the Kolmogorov-Smirnov statistic and the Kuiper statistic.

  20. An excursion approach to maxima of the Brownian bridge

    PubMed Central

    Perman, Mihael; Wellner, Jon A.

    2016-01-01

    Distributions of functionals of Brownian bridge arise as limiting distributions in non-parametric statistics. In this paper we will give a derivation of distributions of extrema of the Brownian bridge based on excursion theory for Brownian motion. The idea of rescaling and conditioning on the local time has been used widely in the literature. In this paper it is used to give a unified derivation of a number of known distributions, and a few new ones. Particular cases of calculations include the distribution of the Kolmogorov-Smirnov statistic and the Kuiper statistic. PMID:27134338

  1. The Brownian mean field model

    NASA Astrophysics Data System (ADS)

    Chavanis, Pierre-Henri

    2014-05-01

    We discuss the dynamics and thermodynamics of the Brownian mean field (BMF) model which is a system of N Brownian particles moving on a circle and interacting via a cosine potential. It can be viewed as the canonical version of the Hamiltonian mean field (HMF) model. The BMF model displays a second order phase transition from a homogeneous phase to an inhomogeneous phase below a critical temperature T c = 1 / 2. We first complete the description of this model in the mean field approximation valid for N → +∞. In the strong friction limit, the evolution of the density towards the mean field Boltzmann distribution is governed by the mean field Smoluchowski equation. For T < T c , this equation describes a process of self-organization from a non-magnetized (homogeneous) phase to a magnetized (inhomogeneous) phase. We obtain an analytical expression for the temporal evolution of the magnetization close to T c . Then, we take fluctuations (finite N effects) into account. The evolution of the density is governed by the stochastic Smoluchowski equation. From this equation, we derive a stochastic equation for the magnetization and study its properties both in the homogenous and inhomogeneous phase. We show that the fluctuations diverge at the critical point so that the mean field approximation ceases to be valid. Actually, the limits N → +∞ and T → T c do not commute. The validity of the mean field approximation requires N( T - T c ) → +∞ so that N must be larger and larger as T approaches T c . We show that the direction of the magnetization changes rapidly close to T c while its amplitude takes a long time to relax. We also indicate that, for systems with long-range interactions, the lifetime of metastable states scales as e N except close to a critical point. The BMF model shares many analogies with other systems of Brownian particles with long-range interactions such as self-gravitating Brownian particles, the Keller-Segel model describing the chemotaxis

  2. Ergodicity and Parameter Estimates for Infinite-Dimensional Fractional Ornstein-Uhlenbeck Process

    SciTech Connect

    Maslowski, Bohdan Pospisil, Jan

    2008-06-15

    Existence and ergodicity of a strictly stationary solution for linear stochastic evolution equations driven by cylindrical fractional Brownian motion are proved. Ergodic behavior of non-stationary infinite-dimensional fractional Ornstein-Uhlenbeck processes is also studied. Based on these results, strong consistency of suitably defined families of parameter estimators is shown. The general results are applied to linear parabolic and hyperbolic equations perturbed by a fractional noise.

  3. Detection of Brownian Torque in a Magnetically-Driven Rotating Microsystem

    NASA Astrophysics Data System (ADS)

    Romodina, Maria N.; Lyubin, Evgeny V.; Fedyanin, Andrey A.

    2016-02-01

    Thermal fluctuations significantly affect the behavior of microscale systems rotating in shear flow, such as microvortexes, microbubbles, rotating micromotors, microactuators and other elements of lab-on-a-chip devices. The influence of Brownian torque on the motion of individual magnetic microparticles in a rotating magnetic field is experimentally determined using optical tweezers. Rotational Brownian motion induces the flattening of the breakdown transition between the synchronous and asynchronous modes of microparticle rotation. The experimental findings regarding microparticle rotation in the presence of Brownian torque are compared with the results of numerical Brownian dynamics simulations.

  4. Detection of Brownian Torque in a Magnetically-Driven Rotating Microsystem

    PubMed Central

    Romodina, Maria N.; Lyubin, Evgeny V.; Fedyanin, Andrey A.

    2016-01-01

    Thermal fluctuations significantly affect the behavior of microscale systems rotating in shear flow, such as microvortexes, microbubbles, rotating micromotors, microactuators and other elements of lab-on-a-chip devices. The influence of Brownian torque on the motion of individual magnetic microparticles in a rotating magnetic field is experimentally determined using optical tweezers. Rotational Brownian motion induces the flattening of the breakdown transition between the synchronous and asynchronous modes of microparticle rotation. The experimental findings regarding microparticle rotation in the presence of Brownian torque are compared with the results of numerical Brownian dynamics simulations. PMID:26876334

  5. Detection of Brownian Torque in a Magnetically-Driven Rotating Microsystem.

    PubMed

    Romodina, Maria N; Lyubin, Evgeny V; Fedyanin, Andrey A

    2016-02-15

    Thermal fluctuations significantly affect the behavior of microscale systems rotating in shear flow, such as microvortexes, microbubbles, rotating micromotors, microactuators and other elements of lab-on-a-chip devices. The influence of Brownian torque on the motion of individual magnetic microparticles in a rotating magnetic field is experimentally determined using optical tweezers. Rotational Brownian motion induces the flattening of the breakdown transition between the synchronous and asynchronous modes of microparticle rotation. The experimental findings regarding microparticle rotation in the presence of Brownian torque are compared with the results of numerical Brownian dynamics simulations.

  6. A Comparison between heat transfer performance of rectangular and semicircular tubes considering boundary effects on Brownian motions in the presence of Ag / water nanofluids: Applicable in the design of cooling system of photovoltaic cells.

    PubMed

    Jafarimoghaddam, Amin; Aberoumand, Sadegh

    2017-01-01

    The present study aims to experimentally investigate heat transfer performance of rectangular and semicircular tubes in the presence of Ag / water nanofluids. The nanoparticles of Ag (silver) were used in seven different volume concentrations of 0.03%, 0.07%, 0.1%, 0.2%, 0.4%, 1% and 2%. The experiment was conducted in relatively low Reynolds numbers of 301 to 740. A heater with the power of 200 W was used to keep the outer surface of the tubes under a constant heat flux condition. In addition, the rectangular tube has been designed within the same length as the semicircular one and also within the same hydraulic diameter. Moreover, the average nanoparticles size was 20 nm. The outcome results of the present empirical work indicate that, for all the examined Reynolds numbers, the semicircular tube has higher convective heat transfer coefficient for all the utilized volume concentrations of Ag nanoparticles. The possible reasons behind this advantage are discussed through the present work mainly by taking the boundary effect on Brownian motions into account. Coming to this point that the conventional design for cooling system of photovoltaic cells is a heat sink with the rectangular graves, it is discussed that using a semicircular design may have the advantage over the rectangular one in convective heat transfer coefficient enhancement and hence a better cooling performance for these solar cells.

  7. A Comparison between heat transfer performance of rectangular and semicircular tubes considering boundary effects on Brownian motions in the presence of Ag / water nanofluids: Applicable in the design of cooling system of photovoltaic cells

    PubMed Central

    Aberoumand, Sadegh

    2017-01-01

    The present study aims to experimentally investigate heat transfer performance of rectangular and semicircular tubes in the presence of Ag / water nanofluids. The nanoparticles of Ag (silver) were used in seven different volume concentrations of 0.03%, 0.07%, 0.1%, 0.2%, 0.4%, 1% and 2%. The experiment was conducted in relatively low Reynolds numbers of 301 to 740. A heater with the power of 200 W was used to keep the outer surface of the tubes under a constant heat flux condition. In addition, the rectangular tube has been designed within the same length as the semicircular one and also within the same hydraulic diameter. Moreover, the average nanoparticles size was 20 nm. The outcome results of the present empirical work indicate that, for all the examined Reynolds numbers, the semicircular tube has higher convective heat transfer coefficient for all the utilized volume concentrations of Ag nanoparticles. The possible reasons behind this advantage are discussed through the present work mainly by taking the boundary effect on Brownian motions into account. Coming to this point that the conventional design for cooling system of photovoltaic cells is a heat sink with the rectangular graves, it is discussed that using a semicircular design may have the advantage over the rectangular one in convective heat transfer coefficient enhancement and hence a better cooling performance for these solar cells. PMID:28753603

  8. Three-dimensional tracking of Brownian motion of a particle trapped in optical tweezers with a pair of orthogonal tracking beams and the determination of the associated optical force constants.

    PubMed

    Wei, Ming-Tzo; Chiou, Arthur

    2005-07-25

    We report the first experimental results on quantitative mapping of three-dimensional optical force field on a silica micro-particle and on a Chinese hamster ovary cell trapped in optical tweezers by using a pair of orthogonal laser beams in conjunction with two quadrant photo-diodes to track the particle's (or the cell's) trajectory, analyze its Brownian motion, and calculate the optical force constants in a three-dimensional parabolic potential model. For optical tweezers with a 60x objective lens (NA = 0.85), a trapping beam wavelength lambda = 532nm, and a trapping optical power of 75mW, the optical force constants along the axial and the transverse directions (of the trapping beam) were measured to be approximately 1.1x10-8N/m and 1.3x10-7N/m, respectively, for a silica particle (diameter = 2.58microm), and 3.1x10-8 N/m and 2.3x10-7 N/m, respectively, for a Chinese hamster ovary cell (diameter ~ 10 microm to 15microm). The set of force constants (Kx, Ky, and Kz ) completely defines the optical force field E(x, y, z) = [Kx x2 + Ky y2 + Kz z2]/2 (in the parabolic potential approximation) on the trapped particle. Practical advantages and limitations of using a pair of orthogonal tracking beams are discussed.

  9. Myosin V is a biological Brownian machine

    PubMed Central

    Fujita, Keisuke; Iwaki, Mitsuhiro

    2014-01-01

    Myosin V is a vesicle transporter that unidirectionally walks along cytoskeletal actin filaments by converting the chemical energy of ATP into mechanical work. Recently, it was found that myosin V force generation is a composition of two processes: a lever-arm swing, which involves a conformational change in the myosin molecule, and a Brownian search-and-catch, which involves a diffusive “search” by the motor domain that is followed by an asymmetric “catch” in the forward actin target such that Brownian motion is rectified. Here we developed a system that combines optical tweezers with DNA nano-material to show that the Brownian search-and-catch mechanism is the energetically dominant process at near stall force, providing 13 kBT of work compared to just 3 kBT by the lever-arm swing. Our result significantly reconsiders the lever-arm swinging model, which assumes the swing dominantly produces work (>10 kBT), and sheds light on the Brownian search-and-catch as a driving process. PMID:27493501

  10. Brownian dynamics simulation of electrostatically interacting proteins

    NASA Astrophysics Data System (ADS)

    Ermakova, E.; Krushelnitsky, A. G.; Fedotov, V. D.

    Brownian dynamics simulation software has been developed to study the dynamics of proteins as a whole in solution. The proteins were modelled as spheres with point dipoles embedded in the centre of sphere. A set of Brownian dynamics simulations at different values of the dipole moments, protein concentration and translational diffusion coefficient was performed to investigate the influence of interprotein electrostatic interactions on dynamic protein behaviour in solution. It was shown that these interactions led to the slowing down of protein rotation and a complex non-exponential shape of the rotational correlation function. Analysis of the correlation functions was performed within the frame of the model of electrostatic interprotein interactions advanced earlier on the basis of NMR and dielectric spectroscopy data. This model assumes that, due to electrostatic interactions, protein Brownian rotation becomes anisotropic. The lifetime of this anisotropy is controlled mainly by translational diffusion of proteins. Thus, the correlation function can be decomposed into two components corresponding to anisotropic Brownian rotation and an isotropic motion of an external electric field vector produced by the surrounding proteins.

  11. Myosin V is a biological Brownian machine.

    PubMed

    Fujita, Keisuke; Iwaki, Mitsuhiro

    2014-01-01

    Myosin V is a vesicle transporter that unidirectionally walks along cytoskeletal actin filaments by converting the chemical energy of ATP into mechanical work. Recently, it was found that myosin V force generation is a composition of two processes: a lever-arm swing, which involves a conformational change in the myosin molecule, and a Brownian search-and-catch, which involves a diffusive "search" by the motor domain that is followed by an asymmetric "catch" in the forward actin target such that Brownian motion is rectified. Here we developed a system that combines optical tweezers with DNA nano-material to show that the Brownian search-and-catch mechanism is the energetically dominant process at near stall force, providing 13 kBT of work compared to just 3 kBT by the lever-arm swing. Our result significantly reconsiders the lever-arm swinging model, which assumes the swing dominantly produces work (>10 kBT), and sheds light on the Brownian search-and-catch as a driving process.

  12. Inter- and intra-fraction motion during radiation therapy to the whole breast in the supine position: a systematic review.

    PubMed

    Michalski, Andrea; Atyeo, John; Cox, Jennifer; Rinks, Marianne

    2012-10-01

    Inter- and intra-fraction motion during radiation therapy for breast cancer has been a widely researched topic. Recently, however, with the emergence of new technologies and techniques such as intensity modulated radiation therapy (IMRT), field in field, volumetric modulated arc therapy (VMAT), tomotherapy and partial breast irradiation (PBI), the magnitude of this movement has become more important. The aim of this study is to provide a comprehensive summary of the literature relating to the magnitude of motion during radiation therapy for a breast cancer patient. A systematic review of the literature was conducted using Medline, Cinhal, Embase, Scopus and Web of Science. Studies included were limited to women having radical radiation therapy to the whole breast in the supine position. Studies needed to report quantitatively on the magnitude of inter- and intra-fraction motion using electronic portal imaging, port films or kilovoltage imaging techniques. Eighteen articles fitted the selection criteria. The averages of random and systematic error for inter- and intra-fraction movement were reported using central lung distance, central irradiated width, central beam edge to skin distance and cranio-caudal distance measurements, or isocentric matching techniques. Inter-fraction motion was consistently larger than intra-fraction motion but, on average, within a 5 mm tolerance. There were, though, large maximum inter- and intra-fraction variations observed in the measurements of individual patients, which indicate the need for daily inter- and intra- fraction motion management before implementing IMRT, VMAT, tomotherapy or PBI techniques. © 2012 The Authors. Journal of Medical Imaging and Radiation Oncology © 2012 The Royal Australian and New Zealand College of Radiologists.

  13. Fractional motion model for characterization of anomalous diffusion from NMR signals.

    PubMed

    Fan, Yang; Gao, Jia-Hong

    2015-07-01

    Measuring molecular diffusion has been used to characterize the properties of living organisms and porous materials. NMR is able to detect the diffusion process in vivo and noninvasively. The fractional motion (FM) model is appropriate to describe anomalous diffusion phenomenon in crowded environments, such as living cells. However, no FM-based NMR theory has yet been established. Here, we present a general formulation of the FM-based NMR signal under the influence of arbitrary magnetic field gradient waveforms. An explicit analytic solution of the stretched exponential decay format for NMR signals with finite-width Stejskal-Tanner bipolar pulse magnetic field gradients is presented. Signals from a numerical simulation matched well with the theoretical prediction. In vivo diffusion-weighted brain images were acquired and analyzed using the proposed theory, and the resulting parametric maps exhibit remarkable contrasts between different brain tissues.

  14. Fractional motion model for characterization of anomalous diffusion from NMR signals

    NASA Astrophysics Data System (ADS)

    Fan, Yang; Gao, Jia-Hong

    2015-07-01

    Measuring molecular diffusion has been used to characterize the properties of living organisms and porous materials. NMR is able to detect the diffusion process in vivo and noninvasively. The fractional motion (FM) model is appropriate to describe anomalous diffusion phenomenon in crowded environments, such as living cells. However, no FM-based NMR theory has yet been established. Here, we present a general formulation of the FM-based NMR signal under the influence of arbitrary magnetic field gradient waveforms. An explicit analytic solution of the stretched exponential decay format for NMR signals with finite-width Stejskal-Tanner bipolar pulse magnetic field gradients is presented. Signals from a numerical simulation matched well with the theoretical prediction. In vivo diffusion-weighted brain images were acquired and analyzed using the proposed theory, and the resulting parametric maps exhibit remarkable contrasts between different brain tissues.

  15. A novel crowd flow model based on linear fractional stable motion

    NASA Astrophysics Data System (ADS)

    Wei, Juan; Zhang, Hong; Wu, Zhenya; He, Junlin; Guo, Yangyong

    2016-03-01

    For the evacuation dynamics in indoor space, a novel crowd flow model is put forward based on Linear Fractional Stable Motion. Based on position attraction and queuing time, the calculation formula of movement probability is defined and the queuing time is depicted according to linear fractal stable movement. At last, an experiment and simulation platform can be used for performance analysis, studying deeply the relation among system evacuation time, crowd density and exit flow rate. It is concluded that the evacuation time and the exit flow rate have positive correlations with the crowd density, and when the exit width reaches to the threshold value, it will not effectively decrease the evacuation time by further increasing the exit width.

  16. Cooperative rectification in confined Brownian ratchets.

    PubMed

    Malgaretti, Paolo; Pagonabarraga, Ignacio; Rubí, J Miguel

    2012-01-01

    We analyze the rectified motion of a Brownian particle in a confined environment. We show the emergence of strong cooperativity between the inherent rectification of the ratchet mechanism and the entropic bias of the fluctuations caused by spatial confinement. Net particle transport may develop even in situations where separately the ratchet and the geometric restrictions do not give rise to particle motion. The combined rectification effects can lead to bidirectional transport depending on particle size, resulting in a different route for segregation. The reported mechanism can be used to control transport in mesostructures and nanodevices in which particles move in a reduced space. © 2012 American Physical Society

  17. Six-Dimensional Correction of Intra-Fractional Prostate Motion with CyberKnife Stereotactic Body Radiation Therapy

    PubMed Central

    Lei, Siyuan; Piel, Nathaniel; Oermann, Eric K.; Chen, Viola; Ju, Andrew W.; Dahal, Kedar N.; Hanscom, Heather N.; Kim, Joy S.; Yu, Xia; Zhang, Guowei; Collins, Brian T.; Jha, Reena; Dritschilo, Anatoly; Suy, Simeng; Collins, Sean P.

    2011-01-01

    Large fraction radiation therapy offers a shorter course of treatment and radiobiological advantages for prostate cancer treatment. The CyberKnife is an attractive technology for delivering large fraction doses based on the ability to deliver highly conformal radiation therapy to moving targets. In addition to intra-fractional translational motion (left–right, superior–inferior, and anterior–posterior), prostate rotation (pitch, roll, and yaw) can increase geographical miss risk. We describe our experience with six-dimensional (6D) intra-fraction prostate motion correction using CyberKnife stereotactic body radiation therapy (SBRT). Eighty-eight patients were treated by SBRT alone or with supplemental external radiation therapy. Trans-perineal placement of four gold fiducials within the prostate accommodated X-ray guided prostate localization and beam adjustment. Fiducial separation and non-overlapping positioning permitted the orthogonal imaging required for 6D tracking. Fiducial placement accuracy was assessed using the CyberKnife fiducial extraction algorithm. Acute toxicities were assessed using Common Toxicity Criteria v3. There were no Grade 3, or higher, complications and acute morbidity was minimal. Ninety-eight percent of patients completed treatment employing 6D prostate motion tracking with intra-fractional beam correction. Suboptimal fiducial placement limited treatment to 3D tracking in two patients. Our experience may guide others in performing 6D correction of prostate motion with CyberKnife SBRT. PMID:22655248

  18. Six-Dimensional Correction of Intra-Fractional Prostate Motion with CyberKnife Stereotactic Body Radiation Therapy.

    PubMed

    Lei, Siyuan; Piel, Nathaniel; Oermann, Eric K; Chen, Viola; Ju, Andrew W; Dahal, Kedar N; Hanscom, Heather N; Kim, Joy S; Yu, Xia; Zhang, Guowei; Collins, Brian T; Jha, Reena; Dritschilo, Anatoly; Suy, Simeng; Collins, Sean P

    2011-01-01

    Large fraction radiation therapy offers a shorter course of treatment and radiobiological advantages for prostate cancer treatment. The CyberKnife is an attractive technology for delivering large fraction doses based on the ability to deliver highly conformal radiation therapy to moving targets. In addition to intra-fractional translational motion (left-right, superior-inferior, and anterior-posterior), prostate rotation (pitch, roll, and yaw) can increase geographical miss risk. We describe our experience with six-dimensional (6D) intra-fraction prostate motion correction using CyberKnife stereotactic body radiation therapy (SBRT). Eighty-eight patients were treated by SBRT alone or with supplemental external radiation therapy. Trans-perineal placement of four gold fiducials within the prostate accommodated X-ray guided prostate localization and beam adjustment. Fiducial separation and non-overlapping positioning permitted the orthogonal imaging required for 6D tracking. Fiducial placement accuracy was assessed using the CyberKnife fiducial extraction algorithm. Acute toxicities were assessed using Common Toxicity Criteria v3. There were no Grade 3, or higher, complications and acute morbidity was minimal. Ninety-eight percent of patients completed treatment employing 6D prostate motion tracking with intra-fractional beam correction. Suboptimal fiducial placement limited treatment to 3D tracking in two patients. Our experience may guide others in performing 6D correction of prostate motion with CyberKnife SBRT.

  19. Paul Langevin's 1908 paper ``On the Theory of Brownian Motion'' [``Sur la théorie du mouvement brownien,'' C. R. Acad. Sci. (Paris) 146, 530-533 (1908)

    NASA Astrophysics Data System (ADS)

    Lemons, Don S.; Gythiel, Anthony

    1997-11-01

    We present a translation of Paul Langevin's landmark paper. In it Langevin successfully applied Newtonian dynamics to a Brownian particle and so invented an analytical approach to random processes which has remained useful to this day.

  20. SU-E-J-187: Management of Optic Organ Motion in Fractionated Stereotactic Radiotherapy

    SciTech Connect

    Manning, M; Maurer, J

    2015-06-15

    Purpose: Fractionated stereotactic radiotherapy (FSRT) for optic nerve tumors can potentially use planning target volume (PTV) expansions as small as 1–5 mm. However, the motion of the intraorbital segment of the optic nerve has not been studied. Methods: A subject with a right optic nerve sheath meningioma underwent CT simulation in three fixed gaze positions: right, left, and fixed forward at a marker. The gross tumor volume (GTV) and the organs-at-risk (OAR) were contoured on all three scans. An IMRT plan using 10 static non-coplanar fields to 50.4 Gy in 28 fractions was designed to treat the fixed-forward gazing GTV with a 1 mm PTV, then resulting coverage was evaluated for the GTV in the three positions. As an alternative, the composite structures were computed to generate the internal target volume (ITV), 1 mm expansion free-gazing PTV, and planning organat-risk volumes (PRVs) for free-gazing treatment. A comparable IMRT plan was created for the free-gazing PTV. Results: If the patient were treated using the fixed forward gaze plan looking straight, right, and left, the V100% for the GTV was 100.0%, 33.1%, and 0.1%, respectively. The volumes of the PTVs for fixed gaze and free-gazing plans were 0.79 and 2.21 cc, respectively, increasing the PTV by a factor of 2.6. The V100% for the fixed gaze and free-gazing plans were 0.85 cc and 2.8 cc, respectively increasing the treated volume by a factor of 3.3. Conclusion: Fixed gaze treatment appears to provide greater organ sparing than free-gazing. However unanticipated intrafraction right or left gaze can produce a geometric miss. Further study of optic nerve motion appears to be warranted in areas such as intrafraction optical confirmation of fixed gaze and optimized gaze directions to minimize lens and other normal organ dose in cranial radiotherapy.

  1. Fractional Fokker-Planck Equation and Black-Scholes Formula in Composite-Diffusive Regime

    NASA Astrophysics Data System (ADS)

    Liang, Jin-Rong; Wang, Jun; Lǔ, Long-Jin; Gu, Hui; Qiu, Wei-Yuan; Ren, Fu-Yao

    2012-01-01

    In statistical physics, anomalous diffusion plays an important role, whose applications have been found in many areas. In this paper, we introduce a composite-diffusive fractional Brownian motion X α, H ( t)= X H ( S α ( t)), 0< α, H<1, driven by anomalous diffusions as a model of asset prices and discuss the corresponding fractional Fokker-Planck equation and Black-Scholes formula. We obtain the fractional Fokker-Planck equation governing the dynamics of the probability density function of the composite-diffusive fractional Brownian motion and find the Black-Scholes differential equation driven by the stock asset X α, H ( t) and the corresponding Black-Scholes formula for the fair prices of European option.

  2. Directional sensitivity of anomalous diffusion in human brain assessed by tensorial fractional motion model.

    PubMed

    Xu, Boyan; Gong, Gaolang; Fan, Yang; Wu, Bing; Gao, Jia-Hong

    2017-10-01

    Anisotropic diffusion in the nervous system is most commonly modeled by apparent diffusion tensor, which is based on regular diffusion theory. However, the departure of diffusion-induced signal attenuation from a mono-exponential form implies that there is anomalous diffusion. Recently, a novel diffusion NMR theory based on the fractional motion (FM) model, which is an anomalous diffusion model, has been proposed. While the FM model has been applied to both healthy subjects and tumor patients, its anisotropy in the nervous system remains elusive. In this study, this issue was addressed by measuring the FM-related parameters in 12 non-collinear directions. A metric to quantify the directional deviation was derived. Furthermore, the FM-related parameters were modeled as tensors and analyzed in analogy with the conventional diffusion tensor imaging (DTI). Experimental results, which were obtained for 15 healthy subjects at 3T, exhibited pronounced anisotropy of the FM-related parameters, although the effects were smaller than the apparent diffusion coefficient (ADC). The tensorial nature for α, which is the Noah exponent in the FM model, showed behavior similar to the ADC, especially the principal eigenvector for α aligned with the dominant white matter fiber directions. The Hurst exponent H in the FM model, however, showed no correlation with the major fiber directions. The anisotropy of the FM model may provide complementary information to DTI and may have potential for tractography and detecting brain abnormalities. Copyright © 2017 Elsevier Inc. All rights reserved.

  3. Real-time prostate motion assessment: image-guidance and the temporal dependence of intra-fraction motion

    PubMed Central

    2013-01-01

    Background The rapid adoption of image-guidance in prostate intensity-modulated radiotherapy (IMRT) results in longer treatment times, which may result in larger intrafraction motion, thereby negating the advantage of image-guidance. This study aims to qualify and quantify the contribution of image-guidance to the temporal dependence of intrafraction motion during prostate IMRT. Methods One-hundred and forty-three patients who underwent conventional IMRT (n=67) or intensity-modulated arc therapy (IMAT/RapidArc, n=76) for localized prostate cancer were evaluated. Intrafraction motion assessment was based on continuous RL (lateral), SI (longitudinal), and AP (vertical) positional detection of electromagnetic transponders at 10 Hz. Daily motion amplitudes were reported as session mean, median, and root-mean-square (RMS) displacements. Temporal effect was evaluated by categorizing treatment sessions into 4 different classes: IMRTc (transponder only localization), IMRTcc (transponder + CBCT localization), IMATc (transponder only localization), or IMATcc (transponder + CBCT localization). Results Mean/median session times were 4.15/3.99 min (IMATc), 12.74/12.19 min (IMATcc), 5.99/5.77 min (IMRTc), and 12.98/12.39 min (IMRTcc), with significant pair-wise difference (p<0.0001) between all category combinations except for IMRTcc vs. IMATcc (p>0.05). Median intrafraction motion difference between CBCT and non-CBCT categories strongly correlated with time for RMS (t-value=17.29; p<0.0001), SI (t-value=−4.25; p<0.0001), and AP (t-value=2.76; p<0.0066), with a weak correlation for RL (t-value=1.67; p=0.0971). Treatment time reduction with non-CBCT treatment categories showed reductions in the observed intrafraction motion: systematic error (Σ)<0.6 mm and random error (σ)<1.2 mm compared with ≤0.8 mm and <1.6 mm, respectively, for CBCT-involved treatment categories. Conclusions For treatment durations >4-6 minutes, and without any intrafraction motion mitigation protocol

  4. Brownian Heat Engines -- from Leidenfrost Droplets to Nanowire Thermoelectrics

    NASA Astrophysics Data System (ADS)

    Linke, Heiner

    2007-03-01

    A Brownian heat engine is a system that rectifies the flow of Brownian particles to transform local temperature variations into directed motion (work). In the context of electronics, this is the principle of thermoelectric energy conversion. For a long time it was thought that Brownian heat engines (and thermoelectric devices) are inherently irreversible and would therefore necessarily fall short of the Carnot limit for the energy conversion efficiency. I will introduce the concept of a Brownian heat engine, and will discuss how quantum energy-filtering can in fact be used to design a Carnot efficient, Brownian heat engine [1]. I will then present two experimental systems. The first, heat-propelled Leidenfrost droplets [2], is not really `Brownian' but nevertheless a very entertaining and illustrative ratchet heat engine. The second is our experimental effort to demonstrate a near-Carnot efficient thermal-to-electric energy converter [3] based on a quantum dot embedded into a heterostructure nanowire [4]. The physics behind this novel thermoelectric system, and the status of experiments will be discussed. [1] T. E. Humphrey, R. Newbury, R. P. Taylor, H. Linke, Phys. Rev. Lett. 89, 116801 (2002). [2] H. Linke et al., Phys. Rev. Lett. 96, 154502 (2006). [3] M. O'Dwyer, T. E. Humphrey, H. Linke, Nanotechnology 17, S338 (2006). [4] M. T. Bj"ork et al., Nano Letters 2, 87 (2002).

  5. Incidence of Changes in Respiration-Induced Tumor Motion and Its Relationship With Respiratory Surrogates During Individual Treatment Fractions

    SciTech Connect

    Malinowski, Kathleen; McAvoy, Thomas J.; George, Rohini; Dietrich, Sonja; D'Souza, Warren D.

    2012-04-01

    Purpose: To determine how frequently (1) tumor motion and (2) the spatial relationship between tumor and respiratory surrogate markers change during a treatment fraction in lung and pancreas cancer patients. Methods and Materials: A Cyberknife Synchrony system radiographically localized the tumor and simultaneously tracked three respiratory surrogate markers fixed to a form-fitting vest. Data in 55 lung and 29 pancreas fractions were divided into successive 10-min blocks. Mean tumor positions and tumor position distributions were compared across 10-min blocks of data. Treatment margins were calculated from both 10 and 30 min of data. Partial least squares (PLS) regression models of tumor positions as a function of external surrogate marker positions were created from the first 10 min of data in each fraction; the incidence of significant PLS model degradation was used to assess changes in the spatial relationship between tumors and surrogate markers. Results: The absolute change in mean tumor position from first to third 10-min blocks was >5 mm in 13% and 7% of lung and pancreas cases, respectively. Superior-inferior and medial-lateral differences in mean tumor position were significantly associated with the lobe of lung. In 61% and 54% of lung and pancreas fractions, respectively, margins calculated from 30 min of data were larger than margins calculated from 10 min of data. The change in treatment margin magnitude for superior-inferior motion was >1 mm in 42% of lung and 45% of pancreas fractions. Significantly increasing tumor position prediction model error (mean {+-} standard deviation rates of change of 1.6 {+-} 2.5 mm per 10 min) over 30 min indicated tumor-surrogate relationship changes in 63% of fractions. Conclusions: Both tumor motion and the relationship between tumor and respiratory surrogate displacements change in most treatment fractions for patient in-room time of 30 min.

  6. Quantum dynamical framework for Brownian heat engines

    NASA Astrophysics Data System (ADS)

    Agarwal, G. S.; Chaturvedi, S.

    2013-07-01

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

  7. The Brownian dynamics of a lipid vesicle

    NASA Astrophysics Data System (ADS)

    Zhao, Hong; Shaqfeh, Eric

    2011-11-01

    We propose a Brownian dynamics simulation method to study the motion of a lipid vesicle in a suspending fluid. The lipid bilayer of the vesicle is modeled as a two-dimensional fluidic membrane with bending resistance and a high local area dilatational modulus. Using a Stokes flow boundary integral equation method, we calculate the grand mobility tensor of the deformable membrane at arbitrary viscosity ratio between the fluid inside and outside the vesicle. The fluctuation-dissipation theorem, as well as the drifting due to the configuration dependence of the diffusivity tensor, are rigorously accounted for. The flow transitions (tank-treading, tumbling and trembling) and the particle stresslet for an athermal vesicle in a simple shear flow calculated by the present method are in good agreement with existing results by a spectral boundary integral equation method. We demonstrate that the effect of Brownian motion is most significant for a tumbling vesicle. The thermal fluctuation tilts the vesicle off the shear plane, and the disruption of the originally two-dimensional tumbling orbit results in a qualitatively different three-dimensional ``wobbling'' motion. The change to the suspension rheology due to the altered dynamics is discussed.

  8. Non-cooperative Brownian donkeys: A solvable 1D model

    NASA Astrophysics Data System (ADS)

    Jiménez de Cisneros, B.; Reimann, P.; Parrondo, J. M. R.

    2003-12-01

    A paradigmatic 1D model for Brownian motion in a spatially symmetric, periodic system is tackled analytically. Upon application of an external static force F the system's response is an average current which is positive for F < 0 and negative for F > 0 (absolute negative mobility). Under suitable conditions, the system approaches 100% efficiency when working against the external force F.

  9. Entropy production of a Brownian ellipsoid in the overdamped limit.

    PubMed

    Marino, Raffaele; Eichhorn, Ralf; Aurell, Erik

    2016-01-01

    We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called "anomalous" contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the "anomalous" entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the "anomalous entropy" for prolate and oblate spheroids and for near-spherical Brownian particles.

  10. Brownian Movement and Avogadro's Number: A Laboratory Experiment.

    ERIC Educational Resources Information Center

    Kruglak, Haym

    1988-01-01

    Reports an experimental procedure for studying Einstein's theory of Brownian movement using commercially available latex microspheres and a video camera. Describes how students can monitor sphere motions and determine Avogadro's number. Uses a black and white video camera, microscope, and TV. (ML)

  11. Brownian Movement and Avogadro's Number: A Laboratory Experiment.

    ERIC Educational Resources Information Center

    Kruglak, Haym

    1988-01-01

    Reports an experimental procedure for studying Einstein's theory of Brownian movement using commercially available latex microspheres and a video camera. Describes how students can monitor sphere motions and determine Avogadro's number. Uses a black and white video camera, microscope, and TV. (ML)

  12. Brownian forces in sheared granular matter.

    PubMed

    Baldassarri, A; Dalton, F; Petri, A; Zapperi, S; Pontuale, G; Pietronero, L

    2006-03-24

    We present results from a series of experiments on a granular medium sheared in a Couette geometry and show that their statistical properties can be computed in a quantitative way from the assumption that the resultant from the set of forces acting in the system performs a Brownian motion. The same assumption has been utilized, with success, to describe other phenomena, such as the Barkhausen effect in ferromagnets, and so the scheme suggests itself as a more general description of a wider class of driven instabilities.

  13. SU-E-J-135: An Investigation of Ultrasound Imaging for 3D Intra-Fraction Prostate Motion Estimation

    SciTech Connect

    O'Shea, T; Harris, E; Bamber, J; Evans, P

    2014-06-01

    Purpose: This study investigates the use of a mechanically swept 3D ultrasound (US) probe to estimate intra-fraction motion of the prostate during radiation therapy using an US phantom and simulated transperineal imaging. Methods: A 3D motion platform was used to translate an US speckle phantom while simulating transperineal US imaging. Motion patterns for five representative types of prostate motion, generated from patient data previously acquired with a Calypso system, were using to move the phantom in 3D. The phantom was also implanted with fiducial markers and subsequently tracked using the CyberKnife kV x-ray system for comparison. A normalised cross correlation block matching algorithm was used to track speckle patterns in 3D and 2D US data. Motion estimation results were compared with known phantom translations. Results: Transperineal 3D US could track superior-inferior (axial) and anterior-posterior (lateral) motion to better than 0.8 mm root-mean-square error (RMSE) at a volume rate of 1.7 Hz (comparable with kV x-ray tracking RMSE). Motion estimation accuracy was poorest along the US probe's swept axis (right-left; RL; RMSE < 4.2 mm) but simple regularisation methods could be used to improve RMSE (< 2 mm). 2D US was found to be feasible for slowly varying motion (RMSE < 0.5 mm). 3D US could also allow accurate radiation beam gating with displacement thresholds of 2 mm and 5 mm exhibiting a RMSE of less than 0.5 mm. Conclusion: 2D and 3D US speckle tracking is feasible for prostate motion estimation during radiation delivery. Since RL prostate motion is small in magnitude and frequency, 2D or a hybrid (2D/3D) US imaging approach which also accounts for potential prostate rotations could be used. Regularisation methods could be used to ensure the accuracy of tracking data, making US a feasible approach for gating or tracking in standard or hypo-fractionated prostate treatments.

  14. Criticality in Brownian ensembles

    NASA Astrophysics Data System (ADS)

    Sadhukhan, Suchetana; Shukla, Pragya

    2017-07-01

    A Brownian ensemble appears as a nonequilibrium state of transition from one universality class of random matrix ensembles to another one. The parameter governing the transition is, in general, size-dependent, resulting in a rapid approach of the statistics, in infinite size limit, to one of the two universality classes. Our detailed analysis, however, reveals the appearance of a new scale-invariant spectral statistics, nonstationary along the spectrum, associated with multifractal eigenstates, and different from the two end-points if the transition parameter becomes size-independent. The number of such critical points during transition is governed by a competition between the average perturbation strength and the local spectral density. The results obtained here have applications to wide-ranging complex systems, e.g., those modeled by multiparametric Gaussian ensembles or column constrained ensembles.

  15. TH-A-BRF-04: Intra-Fraction Motion Characterization for Early Stage Rectal Cancer Using Cine-MRI

    SciTech Connect

    Kleijnen, J; Asselen, B; Burbach, M; Intven, M; Reerink, O; Philippens, M; Lagendijk, J; Raaymakers, B

    2014-06-15

    Purpose: To investigate the intra-fraction motion in patients with early stage rectal cancer using cine-MRI. Methods: Sixteen patient diagnosed with early stage rectal cancer underwent 1.5 T MR imaging prior to each treatment fraction of their short course radiotherapy (n=76). During each scan session, three 2D sagittal cine-MRIs were performed: at the beginning (Start), after 9:30 minutes (Mid), and after 18 minutes (End). Each cine-MRI has a duration of one minute at 2Hz temporal resolution, resulting in a total of 3:48 hours of cine-MRI. Additionally, standard T2-weighted (T2w) imaging was performed. Clinical target volume (CTV) an tumor (GTV) were delineated on the T2w scan and transferred to the first time-point of each cine-MRI scan. Within each cine-MRI, the first frame was registered to the remaining frames of the scan, using a non-rigid B-spline registration. To investigate potential drifts, a similar registration was performed between the first frame of the Start and End scans.To evaluate the motion, the distances by which the edge pixels of the delineations move in anterior-posterior (AP) and cranial-caudal (CC) direction, were determined using the deformation field of the registrations. The distance which incorporated 95% of these edge pixels (dist95%) was determined within each cine-MRI, and between Start- End scans, respectively. Results: Within a cine-MRI, we observed an average dist95% for the CTV of 1.3mm/1.5mm (SD=0.7mm/0.6mm) and for the GTV of 1.2mm/1.5mm (SD=0.8mm/0.9mm), in respectively AP/CC. For the CTV motion between the Start and End scan, an average dist95% of 5.5mm/5.3mm (SD=3.1mm/2.5mm) was found, in respectively AP/CC. For the GTV motion, an average dist95% of 3.6mm/3.9mm (SD=2.2mm/2.5mm) was found in AP/CC, respectively. Conclusion: Although intra-fraction motion within a one minute cine-MRI is limited, substantial intra-fraction motion was observed within the 18 minute time period between the Start and End cine-MRI.

  16. Brownian versus Newtonian devitrification of hard-sphere glasses

    NASA Astrophysics Data System (ADS)

    Montero de Hijes, Pablo; Rosales-Pelaez, Pablo; Valeriani, Chantal; Pusey, Peter N.; Sanz, Eduardo

    2017-08-01

    In a recent molecular dynamics simulation work it has been shown that glasses composed of hard spheres crystallize via cooperative, stochastic particle displacements called avalanches [E. Sanz et al., Proc. Natl. Acad. Sci. USA 111, 75 (2014), 10.1073/pnas.1308338110]. In this Rapid Communication we investigate if such a devitrification mechanism is also present when the dynamics is Brownian rather than Newtonian. The research is motivated in part by the fact that colloidal suspensions, an experimental realization of hard-sphere systems, undergo Brownian motion. We find that Brownian hard-sphere glasses do crystallize via avalanches with very similar characteristics to those found in the Newtonian case. We briefly discuss the implications of these findings for experiments on colloids.

  17. Near-field optically driven Brownian motors (Conference Presentation)

    NASA Astrophysics Data System (ADS)

    Wu, Shao-Hua; Huang, Ningfeng; Jaquay, Eric; Povinelli, Michelle L.

    2016-09-01

    Brownian ratchets are of fundamental interest in fields from statistical physics to molecular motors. The realization of Brownian ratchets in engineered systems opens up the potential to harness thermal energy for directed motion, with applications in transport and sorting of nanoparticles. Implementations based on optical traps provide a high degree of tunability along with precise spatiotemporal control. Near-field optical methods provide particular flexibility and ease of on-chip integration with other microfluidic components. Here, we demonstrate the first all-optical, near-field Brownian ratchet. Our approach uses an asymmetrically patterned photonic crystal and yields an ultra-stable trap stiffness of 253.6 pN/nm-W, 100x greater than conventional optical tweezers. By modulating the laser power, optical ratcheting with transport speed of 1 micron/s can be achieved, allowing a variety of dynamical lab-on-a-chip applications. The resulting transport speed matches well with the theoretical prediction.

  18. Brownian dynamics of charged particles in a constant magnetic field

    SciTech Connect

    Hou, L. J.; Piel, A.; Miskovic, Z. L.; Shukla, P. K.

    2009-05-15

    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.

  19. Ultrasound tracking for intra-fractional motion compensation in radiation therapy.

    PubMed

    Schwaab, J; Prall, M; Sarti, C; Kaderka, R; Bert, C; Kurz, C; Parodi, K; Günther, M; Jenne, J

    2014-07-01

    Modern techniques as ion beam therapy or 4D imaging require precise target position information. However, target motion particularly in the abdomen due to respiration or patient movement is still a challenge and demands methods that detect and compensate this motion. Ultrasound represents a non-invasive, dose-free and model-independent alternative to fluoroscopy, respiration belt or optical tracking of the patient surface. Thus, ultrasound based motion tracking was integrated into irradiation with actively scanned heavy ions. In a first in vitro experiment, the ultrasound tracking system was used to compensate diverse sinusoidal target motions in two dimensions. A time delay of ∼200 ms between target motion and reported position data was compensated by a prediction algorithm (artificial neural network). The irradiated films proved feasibility of the proposed method. Furthermore, a practicable and reliable calibration workflow was developed to enable the transformation of ultrasound tracking data to the coordinates of the treatment delivery or imaging system - even if the ultrasound probe moves due to respiration. A first proof of principle experiment was performed during time-resolved positron emission tomography (4DPET) to test the calibration workflow and to show the accuracy of an ultrasound based motion tracking in vitro. The results showed that optical ultrasound tracking can reach acceptable accuracies and encourage further research.

  20. Power functional theory for Brownian dynamics.

    PubMed

    Schmidt, Matthias; Brader, Joseph M

    2013-06-07

    Classical density functional theory (DFT) provides an exact variational framework for determining the equilibrium properties of inhomogeneous fluids. We report a generalization of DFT to treat the non-equilibrium dynamics of classical many-body systems subject to Brownian dynamics. Our approach is based upon a dynamical functional consisting of reversible free energy changes and irreversible power dissipation. Minimization of this "free power" functional with respect to the microscopic one-body current yields a closed equation of motion. In the equilibrium limit the theory recovers the standard variational principle of DFT. The adiabatic dynamical density functional theory is obtained when approximating the power dissipation functional by that of an ideal gas. Approximations to the excess (over ideal) power dissipation yield numerically tractable equations of motion beyond the adiabatic approximation, opening the door to the systematic study of systems far from equilibrium.

  1. SU-C-17A-05: Quantification of Intra-Fraction Motion of Breast Tumors Using Cine-MRI

    SciTech Connect

    Heijst, T van; Philippens, M; Bongard, D van den; Asselen, B van; Lagendijk, J; Kleijnen, J; Hartogh, M den

    2014-06-01

    Purpose: Magnetic resonance imaging (MRI) enables direct characterization of intra-fraction motion ofbreast tumors, due to high softtissue contrast and geometric accuracy. The purpose is to analyzethis motion in early-stage breast-cancer patients using pre-operative supine cine-MRI. Methods: MRI was performed in 12 female early-stage breast-cancer patients on a 1.5-T Ingenia (Philips)wide-bore scanner in supine radiotherapy (RT) position, prior to breast-conserving surgery. Twotwodimensional (2D) T2-weighted balanced fast-field echo (cine-MRI) sequences were added tothe RT protocol, oriented through the tumor. They were alternately acquired in the transverse andsagittal planes, every 0.3 s during 1 min. A radiation oncologist delineated gross target volumes(GTVs) on 3D contrast-enhanced MRI. Clinical target volumes (CTV = GTV + 15 mm isotropic)were generated and transferred onto the fifth time-slice of the time-series, to which subsequents lices were registered using a non-rigid Bspline algorithm; delineations were transformed accordingly. To evaluate intra-fraction CTV motion, deformation fields between the transformed delineations were derived to acquire the distance ensuring 95% surface coverage during scanning(P95%), for all in-plane directions: anteriorposterior (AP), left-right (LR), and caudal-cranial(CC). Information on LR was derived from transverse scans, CC from sagittal scans, AP fromboth sets. Results: Time-series with registration errors - induced by motion artifacts - were excluded by visual inspection. For our analysis, 11 transverse, and 8 sagittal time-series were taken into account. Themedian P95% calculated in AP (19 series), CC (8), and LR (11) was 1.8 mm (range: 0.9–4.8), 1.7mm (0.8–3.6), and 1.0 mm (0.6–3.5), respectively. Conclusion: Intra-fraction motion analysis of breast tumors was achieved using cine-MRI. These first results show that in supine RT position, motion amplitudes are limited. This information can be used for adaptive RT

  2. Brownian transport controlled by dichotomic and thermal fluctuations

    NASA Astrophysics Data System (ADS)

    Kula, J.; Kostur, M.; Łuczka, J.

    1998-09-01

    We study transport of Brownian particles in spatially periodic structures, driven by both thermal equilibrium fluctuations and dichotomic noise of zero mean values. Introducing specific scaling, we show that the dimensionless Newton-Langevin type equation governing the motion of Brownian particles is very well approximated by the overdamped dynamics; inertial effects can be neglected because for generic systems dimensionless mass is many orders less than a dimensionless friction coefficient. An exact probability current, proportional to the mean drift velocity of particles, is obtained for a piecewise linear spatially periodic potential. We analyze in detail properties of the macroscopic averaged motion of particles. In dependence on statistics of both sources of fluctuations, the directed transport of particles exhibits such distinctive non-monotonic behavior as: bell-shaped dependence (there exists optimal statistics of fluctuations maximizing velocity) and reversal in the direction of macroscopic motion (there exists critical statistics at which the drift velocity is zero).

  3. Simulation of a Brownian particle in an optical trap

    NASA Astrophysics Data System (ADS)

    Volpe, Giorgio; Volpe, Giovanni

    2013-03-01

    An optically trapped Brownian particle is a sensitive probe of molecular and nanoscopic forces. An understanding of its motion, which is caused by the interplay of random and deterministic contributions, can lead to greater physical insight into the behavior of stochastic phenomena. The modeling of realistic stochastic processes typically requires advanced mathematical tools. We discuss a finite difference algorithm to compute the motion of an optically trapped particle and the numerical treatment of the white noise term. We then treat the transition from the ballistic to the diffusive regime due to the presence of inertial effects on short time scales and examine the effect of an optical trap on the motion of the particle. We also outline how to use simulations of optically trapped Brownian particles to gain understanding of nanoscale force and torque measurements, and of more complex phenomena, such as Kramers transitions, stochastic resonant damping, and stochastic resonance.

  4. SU-E-J-151: Day-To-Day Variations in Fraction-Specific Motion Modeling Using Patient 4DCBCT Images

    SciTech Connect

    Dhou, S; Cai, W; Hurwitz, M; Williams, C; Cifter, F; Myronakis, M; Lewis, J; Ionascu, D

    2015-06-15

    Purpose: The goal of this study is to quantify the interfraction reproducibility of patient-specific motion models derived from 4DCBCT acquired on the day of treatment of lung cancer stereotactic body radiotherapy (SBRT) patients. Methods: Motion models are derived from patient 4DCBCT images acquired daily over 3–5 fractions of treatment by 1) applying deformable image registration between each 4DCBCT image and a reference phase from that day, resulting in a set of displacement vector fields (DVFs), and 2) performing principal component analysis (PCA) on the DVFs to derive a motion model. The motion model from the first day of treatment is compared to motion models from each successive day of treatment to quantify variability in motion models generated from different days. Four SBRT patient datasets have been acquired thus far in this IRB approved study. Results: Fraction-specific motion models for each fraction and patient were derived and PCA eigenvectors and their associated eigenvalues are compared for each fraction. For the first patient dataset, the average root mean square error between the first two eigenvectors associated with the highest two eigenvalues, in four fractions was 0.1, while it was 0.25 between the last three PCA eigenvectors associated with the lowest three eigenvalues. It was found that the eigenvectors and eigenvalues of PCA motion models for each treatment fraction have variations and the first few eigenvectors are shown to be more stable across treatment fractions than others. Conclusion: Analysis of this dataset showed that the first two eigenvectors of the PCA patient-specific motion models derived from 4DCBCT were stable over the course of several treatment fractions. The third, fourth, and fifth eigenvectors had larger variations.

  5. Brownian relaxation of interacting magnetic nanoparticles in a colloid subjected to a pulsatile magnetic field.

    PubMed

    Sarangi, S; Tan, I C; Brazdeikis, A

    2011-05-01

    We have investigated and modeled the effect of interaction among magnetic particles and the magnitude and duration of external applied magnetic field on Brownian relaxation in a colloidal suspension. In the case of interacting magnetic particles, Brownian relaxation depends on the interparticle dipole-dipole interaction, which slows down the overall Brownian relaxation process of magnetic particles in the colloidal suspension. The individual magnetic particle experiences torque when a pulsatile magnetic field is applied. The torque due to the external field randomizes the particle rotation similar to that of the thermal energy. A faster Brownian relaxation is observed when individual magnetic particles are magnetized for a short duration. Magnetizing the magnetic particle for a longer duration suppress the rotational motion hence the effect of torque on Brownian relaxation.

  6. Persistence of a Brownian particle in a time-dependent potential.

    PubMed

    Chakraborty, D

    2012-05-01

    We investigate the persistence probability of a Brownian particle in a harmonic potential, which decays to zero at long times, leading to an unbounded motion of the Brownian particle. We consider two functional forms for the decay of the confinement, an exponential decay and an algebraic decay. Analytical calculations and numerical simulations show that for the case of the exponential relaxation, the dynamics of Brownian particle at short and long times are independent of the parameters of the relaxation. On the contrary, for the algebraic decay of the confinement, the dynamics at long times is determined by the exponent of the decay. Finally, using the two-time correlation function for the position of the Brownian particle, we construct the persistence probability for the Brownian walker in such a scenario.

  7. Patient Motion and Targeting Accuracy in Robotic Spinal Radiosurgery: 260 Single-Fraction Fiducial-Free Cases

    SciTech Connect

    Fuerweger, Christoph; Drexler, Christian; Kufeld, Markus; Muacevic, Alexander; Wowra, Berndt; Schlaefer, Alexander

    2010-11-01

    Purpose: To evaluate clinical targeting precision and assess patient movement data during fiducial-free, single-fraction spinal radiosurgery with the Cyberknife (CK). Methods and Materials: Image-guided spine tracking accuracy was tested using two phantoms. Movement patterns (three translations, roll, pitch and yaw) were obtained from log files of 260 patient treatments (47 cervical, 89 thoracic, 90 lumbar, and 34 pelvic/sacral). For two treatments (average and maximum motion scenario), we added offsets to all beams according to recorded patient movements and recalculated the delivered dose distribution to simulate the dosimetric impact of intrafraction motion. Results: Phantom spine position was registered with an accuracy of <0.2 mm for translational and <0.3{sup o} for rotational directions. Residual patient motion yielded mean targeting errors per beam of 0.28 {+-} 0.13 mm (X), 0.25 {+-} 0.15 mm (Y), 0.19 {+-} 0.11 mm (Z) and 0.40 {+-} 0.20{sup o} (roll), 0.20 {+-} 0.08{sup o} (pitch), and 0.19 {+-} 0.08{sup o} (yaw). Spine region had little influence on overall targeting error, which was <1 mm for more than 95% of treatments (median, 0.48 mm). In the maximum motion case, target coverage decreased by 1.7% (from 92.1% to 90.4%) for the 20-Gy prescription isodose. Spinal cord volume receiving more than 8 Gy increased slightly, from 2.41 to 2.46 cm{sup 3}. Conclusions: Submillimeter targeting precision was obtained for fiducial-free spinal radiosurgery despite patient motion. Patient motion has little effect on the delivered dose distribution when image-guided correction of beam aiming is employed.

  8. Brownian Carnot engine.

    PubMed

    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 baths1. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors2 and some artificial micro-engines3-5 operate. As described by stochastic thermodynamics6,7, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit8. 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 temperatures9-11. 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.

  9. Brownian Carnot engine

    NASA Astrophysics Data System (ADS)

    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.

  10. Anomalous Brownian refrigerator

    NASA Astrophysics Data System (ADS)

    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.

  11. Active Brownian rods

    NASA Astrophysics Data System (ADS)

    Peruani, Fernando

    2016-11-01

    Bacteria, chemically-driven rods, and motility assays are examples of active (i.e. self-propelled) Brownian rods (ABR). The physics of ABR, despite their ubiquity in experimental systems, remains still poorly understood. Here, we review the large-scale properties of collections of ABR moving in a dissipative medium. We address the problem by presenting three different models, of decreasing complexity, which we refer to as model I, II, and III, respectively. Comparing model I, II, and III, we disentangle the role of activity and interactions. In particular, we learn that in two dimensions by ignoring steric or volume exclusion effects, large-scale nematic order seems to be possible, while steric interactions prevent the formation of orientational order at large scales. The macroscopic behavior of ABR results from the interplay between active stresses and local alignment. ABR exhibit, depending on where we locate ourselves in parameter space, a zoology of macroscopic patterns that ranges from polar and nematic bands to dynamic aggregates.

  12. Brownian Carnot engine

    PubMed Central

    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 baths1. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors2 and some artificial micro-engines3–5 operate. As described by stochastic thermodynamics6,7, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit8. 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 temperatures9–11. 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. PMID:27330541

  13. Climate Data Records (CDRs) for Ice Motion, Ice Age, and Melt Pond Fraction

    NASA Astrophysics Data System (ADS)

    Tschudi, M. A.; Maslanik, J. A.; Fowler, C.; Stroeve, J. C.; Rigor, I. G.

    2010-12-01

    Remotely-sensed Arctic sea ice motion, sea ice age, and melt pond coverage have been proposed for development into full CDRs. The first has a considerable history of use, while the latter two are relatively new products. Our technique to estimate sea ice motion utilizes images from SSM/I, as well as the Scanning Multichannel Microwave Radiometer (SMMR) and the series of Advanced Very High Resolution Radiometer (AVHRR) sensors to estimate the daily motion of ice parcels. This method is augmented by incorporating ice motion observations from the network of drifting buoys deployed as part of the International Arctic Buoy Program. Our technique to calculate ice age relies on following the actual age of the ice for each ice parcel, categorizing the parcel as first-year ice, second-year ice, etc. based on how many summer melt seasons the ice parcel survives. Our method to estimate melt pond coverage on sea ice involves solving a set of linear equations that relate each surface feature’s individual reflectance within the sensor’s (currently using the MODIS surface reflectance product, MOD09) pixel to the overall reflectance in that pixel. These three research-grade products have been interpolated onto 25x25 km grid points spanning the entire Arctic Ocean using the Equal-Area Scalable Earth (EASE) grid.

  14. Fractional noise destroys or induces a stochastic bifurcation

    SciTech Connect

    Yang, Qigui; Zeng, Caibin; Wang, Cong

    2013-12-15

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

  15. Fractional noise destroys or induces a stochastic bifurcation

    SciTech Connect

    Yang, Qigui; Zeng, Caibin; Wang, Cong

    2013-12-15

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

  16. Preliminary Evaluation of a Novel Thermoplastic Mask System with Intra-fraction Motion Monitoring for Future Use with Image-Guided Gamma Knife.

    PubMed

    Li, Winnie; Bootsma, Gregory; Von Schultz, Oscar; Carlsson, Per; Laperriere, Normand; Millar, Barbara-Ann; Jaffray, David; Chung, Caroline

    2016-03-13

    OBJECTIVES : A non-invasive immobilization system consisting of a thermoplastic mask with image-guidance using cone-beam CT (CBCT) and infrared (IR) tracking has been developed to ensure minimal inter- and intra-fractional movement during Gamma Knife radiosurgery. Prior to clinical use for patients on a Gamma Knife, this study clinically evaluates the accuracy and stability of this novel immobilization system with image-guidance in patients treated with standard fractionated radiation therapy on a linear accelerator. This prospective cohort study evaluated adult patients planned for fractionated brain radiotherapy. Patients were immobilized with a thermoplastic mask (with the nose cut out) and customized head cushion. A reflective marker was placed on the patient's nose tip and tracked with a stereoscopic IR camera throughout treatment. For each fraction, a pre-treatment, verification (after any translational correction for inter-fraction set-up variation), and post-treatment CBCT was acquired to evaluate inter- and intra-fraction movement of the target and nose. Intra-fraction motion of the nose tip measured on CBCT and IR tracking were compared. RESULTS : Corresponding data from 123 CBCT and IR datasets from six patients are summarized. The mean ± standard deviation (SD) intra-fraction motion of the nose tip was 0.41±0.36 mm based on pre- and post-treatment CBCT data compared with 0.56±0.51 mm using IR tracking. The maximum intra-fraction motion of the nose tip was 1.7 mm using CBCT and 3.2 mm using IR tracking. The mean ± SD intra-fraction motion of the target was 0.34±0.25 mm, and the maximum intra-fraction motion was 1.5 mm. This initial clinical evaluation of the thermoplastic mask immobilization system using both IR tracking and CBCT demonstrate that mean intra-fraction motion of the nose and target is small. The presence of isolated measures of larger intra-fraction motion supports the need for image-guidance and intra-fraction motion management when

  17. Preliminary Evaluation of a Novel Thermoplastic Mask System with Intra-fraction Motion Monitoring for Future Use with Image-Guided Gamma Knife

    PubMed Central

    Bootsma, Gregory; Von Schultz, Oscar; Carlsson, Per; Laperriere, Normand; Millar, Barbara-Ann; Jaffray, David; Chung, Caroline

    2016-01-01

    Objectives  A non-invasive immobilization system consisting of a thermoplastic mask with image-guidance using cone-beam CT (CBCT) and infrared (IR) tracking has been developed to ensure minimal inter- and intra-fractional movement during Gamma Knife radiosurgery. Prior to clinical use for patients on a Gamma Knife, this study clinically evaluates the accuracy and stability of this novel immobilization system with image-guidance in patients treated with standard fractionated radiation therapy on a linear accelerator. Materials & methods This prospective cohort study evaluated adult patients planned for fractionated brain radiotherapy. Patients were immobilized with a thermoplastic mask (with the nose cut out) and customized head cushion. A reflective marker was placed on the patient’s nose tip and tracked with a stereoscopic IR camera throughout treatment. For each fraction, a pre-treatment, verification (after any translational correction for inter-fraction set-up variation), and post-treatment CBCT was acquired to evaluate inter- and intra-fraction movement of the target and nose. Intra-fraction motion of the nose tip measured on CBCT and IR tracking were compared. Results  Corresponding data from 123 CBCT and IR datasets from six patients are summarized. The mean ± standard deviation (SD) intra-fraction motion of the nose tip was 0.41±0.36 mm based on pre- and post-treatment CBCT data compared with 0.56±0.51 mm using IR tracking. The maximum intra-fraction motion of the nose tip was 1.7 mm using CBCT and 3.2 mm using IR tracking. The mean ± SD intra-fraction motion of the target was 0.34±0.25 mm, and the maximum intra-fraction motion was 1.5 mm. Conclusions: This initial clinical evaluation of the thermoplastic mask immobilization system using both IR tracking and CBCT demonstrate that mean intra-fraction motion of the nose and target is small. The presence of isolated measures of larger intra-fraction motion supports the need for image-guidance and

  18. Halo common proper motion stars - Subdwarf distance scale, halo binary fraction, and UBVRI colors

    NASA Technical Reports Server (NTRS)

    Ryan, Sean G.

    1992-01-01

    Common proper motion stars identified by Luyten (1979, 1980) were selected according to reduced proper motion and photometric criteria to produce a list of candidate halo objects. UBVRI photometry was obtained to identify genuine halo parts. About 20 percent of the stars with (Fe/H) less than -1.0 were found to have random errors not less than several x 0.1 mag in distance modulus, in addition to the photometric errors, thought to be due to the existence of close binary companions to some of the common proper motion stars. The implications of these errors for kinematic studies of field Population II stars are considered. Systematic errors of order 16 percent were also detected in distances derived from the U-B,B-V deblanketing technique. It is suggested that Population II field stars did not originate in globular clusters which subsequently disintegrated but formed in less dense environments. Several K subdwarfs were found with very high UV excesses, comparable with those predicted by some synthetic colors.

  19. Smoluchowski diffusion equation for active Brownian swimmers

    NASA Astrophysics Data System (ADS)

    Sevilla, Francisco J.; Sandoval, Mario

    2015-05-01

    We study the free diffusion in two dimensions of active Brownian swimmers subject to passive fluctuations on the translational motion and to active fluctuations on the rotational one. The Smoluchowski equation is derived from a Langevin-like model of active swimmers and analytically solved in the long-time regime for arbitrary values of the Péclet number; this allows us to analyze the out-of-equilibrium evolution of the positions distribution of active particles at all time regimes. Explicit expressions for the mean-square displacement and for the kurtosis of the probability distribution function are presented and the effects of persistence discussed. We show through Brownian dynamics simulations that our prescription for the mean-square displacement gives the exact time dependence at all times. The departure of the probability distribution from a Gaussian, measured by the kurtosis, is also analyzed both analytically and computationally. We find that for the inverse of Péclet numbers ≲0.1 , the distance from Gaussian increases as ˜t-2 at short times, while it diminishes as ˜t-1 in the asymptotic limit.

  20. Effective diffusivity in active Brownian suspensions

    NASA Astrophysics Data System (ADS)

    Burkholder, Eric; Brady, John

    2016-11-01

    We study the single-particle diffusion of a Brownian probe of size R in a suspension comprised of a Newtonian solvent and a dilute dispersion of active Brownian particles (ABPs) with size a, characteristic swim velocity U0, and a reorientation time τR. These ABPs, or "swimmers," have a run length l =U0τR , and a mechanical activity ksTs =ζaU02τR / 6 , where ζa is the Stokes drag coefficient of a swimmer. When the swimmers are inactive, collisions between the probe and the swimmers sterically hinder the probe's diffusive motion. When the activity of the swimmers is greater than the Boltzmann energy, ksTs >kB T , rather than being sterically hindered, the probe diffusivity is actually greater than its Stokes-Einstein-Sutherland diffusivity due to the mechanical energy imparted to the probe upon collisions with the swimmers. The active contribution to the effective diffusivity is a non-monotonic function of the swimmers' run length compared to the contact length between the probe and a swimmer: l / (R + a) . Comparisons are made to previous theoretical and experimental investigations of the hydrodynamic diffusion of a colloidal particle in a dilute suspension of swimming bacteria. NSF Grant No. CBET 1437570.

  1. SU-E-T-292: Sensitivity of Fractionated Lung IMPT Treatments to Setup Uncertainties and Motion Effects

    SciTech Connect

    Dowdell, S; Grassberger, C; Paganetti, H

    2014-06-01

    Purpose: Evaluate the sensitivity of intensity-modulated proton therapy (IMPT) lung treatments to systematic and random setup uncertainties combined with motion effects. Methods: Treatment plans with single-field homogeneity restricted to ±20% (IMPT-20%) were compared to plans with no restriction (IMPT-full). 4D Monte Carlo simulations were performed for 10 lung patients using the patient CT geometry with either ±5mm systematic or random setup uncertainties applied over a 35 × 2.5Gy(RBE) fractionated treatment course. Intra-fraction, inter-field and inter-fraction motions were investigated. 50 fractionated treatments with systematic or random setup uncertainties applied to each fraction were generated for both IMPT delivery methods and three energy-dependent spot sizes (big spots - BS σ=18-9mm, intermediate spots - IS σ=11-5mm, small spots - SS σ=4-2mm). These results were compared to a Monte Carlo recalculation of the original treatment plan, with results presented as the difference in EUD (ΔEUD), V{sub 95} (ΔV{sub 95}) and target homogeneity (ΔD{sub 1}–D{sub 99}) between the 4D simulations and the Monte Carlo calculation on the planning CT. Results: The standard deviations in the ΔEUD were 1.95±0.47(BS), 1.85±0.66(IS) and 1.31±0.35(SS) times higher in IMPT-full compared to IMPT-20% when ±5mm systematic setup uncertainties were applied. The ΔV{sub 95} variations were also 1.53±0.26(BS), 1.60±0.50(IS) and 1.38±0.38(SS) times higher for IMPT-full. For random setup uncertainties, the standard deviations of the ΔEUD from 50 simulated fractionated treatments were 1.94±0.90(BS), 2.13±1.08(IS) and 1.45±0.57(SS) times higher in IMPTfull compared to IMPT-20%. For all spot sizes considered, the ΔD{sub 1}-D{sub 99} coincided within the uncertainty limits for the two IMPT delivery methods, with the mean value always higher for IMPT-full. Statistical analysis showed significant differences between the IMPT-full and IMPT-20% dose distributions for the

  2. Demonstration of a Controllable Three-Dimensional Brownian Motor in Symmetric Potentials

    SciTech Connect

    Sjoelund, P.; Petra, S.J.H.; Dion, C.M.; Jonsell, S.; Nylen, M.; Kastberg, A.; Sanchez-Palencia, L.

    2006-05-19

    We demonstrate a Brownian motor, based on cold atoms in optical lattices, where isotropic random fluctuations are rectified in order to induce controlled atomic motion in arbitrary directions. In contrast to earlier demonstrations of ratchet effects, our Brownian motor operates in potentials that are spatially and temporally symmetric, but where spatiotemporal symmetry is broken by a phase shift between the potentials and asymmetric transfer rates between them. The Brownian motor is demonstrated in three dimensions and the noise-induced drift is controllable in our system.

  3. Review of ultrasound image guidance in external beam radiotherapy: I. Treatment planning and inter-fraction motion management

    NASA Astrophysics Data System (ADS)

    Fontanarosa, Davide; van der Meer, Skadi; Bamber, Jeffrey; Harris, Emma; O'Shea, Tuathan; Verhaegen, Frank

    2015-02-01

    In modern radiotherapy, verification of the treatment to ensure the target receives the prescribed dose and normal tissues are optimally spared has become essential. Several forms of image guidance are available for this purpose. The most commonly used forms of image guidance are based on kilovolt or megavolt x-ray imaging. Image guidance can also be performed with non-harmful ultrasound (US) waves. This increasingly used technique has the potential to offer both anatomical and functional information. This review presents an overview of the historical and current use of two-dimensional and three-dimensional US imaging for treatment verification in radiotherapy. The US technology and the implementation in the radiotherapy workflow are described. The use of US guidance in the treatment planning process is discussed. The role of US technology in inter-fraction motion monitoring and management is explained, and clinical studies of applications in areas such as the pelvis, abdomen and breast are reviewed. A companion review paper (O’Shea et al 2015 Phys. Med. Biol. submitted) will extensively discuss the use of US imaging for intra-fraction motion quantification and novel applications of US technology to RT.

  4. Review of ultrasound image guidance in external beam radiotherapy part II: intra-fraction motion management and novel applications

    NASA Astrophysics Data System (ADS)

    O'Shea, Tuathan; Bamber, Jeffrey; Fontanarosa, Davide; van der Meer, Skadi; Verhaegen, Frank; Harris, Emma

    2016-04-01

    Imaging has become an essential tool in modern radiotherapy (RT), being used to plan dose delivery prior to treatment and verify target position before and during treatment. Ultrasound (US) imaging is cost-effective in providing excellent contrast at high resolution for depicting soft tissue targets apart from those shielded by the lungs or cranium. As a result, it is increasingly used in RT setup verification for the measurement of inter-fraction motion, the subject of Part I of this review (Fontanarosa et al 2015 Phys. Med. Biol. 60 R77-114). The combination of rapid imaging and zero ionising radiation dose makes US highly suitable for estimating intra-fraction motion. The current paper (Part II of the review) covers this topic. The basic technology for US motion estimation, and its current clinical application to the prostate, is described here, along with recent developments in robust motion-estimation algorithms, and three dimensional (3D) imaging. Together, these are likely to drive an increase in the number of future clinical studies and the range of cancer sites in which US motion management is applied. Also reviewed are selections of existing and proposed novel applications of US imaging to RT. These are driven by exciting developments in structural, functional and molecular US imaging and analytical techniques such as backscatter tissue analysis, elastography, photoacoustography, contrast-specific imaging, dynamic contrast analysis, microvascular and super-resolution imaging, and targeted microbubbles. Such techniques show promise for predicting and measuring the outcome of RT, quantifying normal tissue toxicity, improving tumour definition and defining a biological target volume that describes radiation sensitive regions of the tumour. US offers easy, low cost and efficient integration of these techniques into the RT workflow. US contrast technology also has potential to be used actively to assist RT by manipulating the tumour cell environment and by

  5. Active Brownian particles escaping a channel in single file.

    PubMed

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

    2015-02-01

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

  6. Simultaneous Study of Brownian and Néel Relaxation Phenomena in Ferrofluids by Mössbauer Spectroscopy.

    PubMed

    Landers, J; Salamon, S; Remmer, H; Ludwig, F; Wende, H

    2016-02-10

    We demonstrate the ability of Mössbauer spectroscopy to simultaneously investigate Brownian motion and Néel relaxation in ferrofluidic samples. For this purpose, Mössbauer spectra of coated iron oxide nanoparticles with core diameters of 6.0-26.4 nm dissolved in 70 vol % glycerol solution were recorded in the temperature range of 234-287 K and compared to low-temperature spectra without Brownian motion. By comparison to theory, we were able to determine the particle coating thickness and the dynamic viscosity of the fluid from the broadening of the absorption lines (Brownian motion), as well as the state of Néel relaxation. Results from Mössbauer spectroscopy were crosschecked by AC-susceptometry at several temperatures for Brownian motion and in the high-frequency regime (100 Hz-1 MHz) for Néel relaxation.

  7. Motion.

    ERIC Educational Resources Information Center

    Brand, Judith, Ed.

    2002-01-01

    This issue of Exploratorium Magazine focuses on the topic of motion. Contents include: (1) "First Word" (Zach Tobias); (2) "Cosmic Collisions" (Robert Irion); (3) "The Mobile Cell" (Karen E. Kalumuck); (4) "The Paths of Paths" (Steven Vogel); (5) "Fragments" (Pearl Tesler); (6) "Moving Pictures" (Amy Snyder); (7) "Plants on the Go" (Katharine…

  8. Motion.

    ERIC Educational Resources Information Center

    Gerhart, James B.; Nussbaum, Rudi H.

    This monograph was written for the Conference on the New Instructional Materials in Physics held at the University of Washington in summer, 1965. It is intended for use in an introductory course in college physics. It consists of an extensive qualitative discussion of motion followed by a detailed development of the quantitative methods needed to…

  9. Motion.

    ERIC Educational Resources Information Center

    Brand, Judith, Ed.

    2002-01-01

    This issue of Exploratorium Magazine focuses on the topic of motion. Contents include: (1) "First Word" (Zach Tobias); (2) "Cosmic Collisions" (Robert Irion); (3) "The Mobile Cell" (Karen E. Kalumuck); (4) "The Paths of Paths" (Steven Vogel); (5) "Fragments" (Pearl Tesler); (6) "Moving Pictures" (Amy Snyder); (7) "Plants on the Go" (Katharine…

  10. Molecular Motors: Power Strokes Outperform Brownian Ratchets.

    PubMed

    Wagoner, Jason A; Dill, Ken A

    2016-07-07

    Molecular motors convert chemical energy (typically from ATP hydrolysis) to directed motion and mechanical work. Their actions are often described in terms of "Power Stroke" (PS) and "Brownian Ratchet" (BR) mechanisms. Here, we use a transition-state model and stochastic thermodynamics to describe a range of mechanisms ranging from PS to BR. We incorporate this model into Hill's diagrammatic method to develop a comprehensive model of motor processivity that is simple but sufficiently general to capture the full range of behavior observed for molecular motors. We demonstrate that, under all conditions, PS motors are faster, more powerful, and more efficient at constant velocity than BR motors. We show that these differences are very large for simple motors but become inconsequential for complex motors with additional kinetic barrier steps.

  11. Brownian Ratchets: Transport Controlled by Thermal Noise

    NASA Astrophysics Data System (ADS)

    Kula, J.; Czernik, T.; Łuczka, J.

    1998-02-01

    We analyze directed transport of overdamped Brownian particles in a 1D spatially periodic potential that are subjected to both zero-mean thermal equilibrium Nyquist noise and zero-mean exponentially correlated dichotomous fluctuations. We show that particles can reverse the direction of average motion upon a variation of noise parameters if two fundamental symmetries, namely, the reflection symmetry of the spatial periodic structure, and the statistical symmetry of dichotomous fluctuations, are broken. There is a critical thermal noise intensity Dc, or equivalently a critical temperature Tc, at which the mean velocity of particles is zero. Below Tc and above Tc particles move in opposite directions. At fixed temperature, there is a region of noise parameters in which particles of different linear size are transported in opposite directions.

  12. Thermal equilibrium of two quantum Brownian particles

    SciTech Connect

    Valente, D. M.; Caldeira, A. O.

    2010-01-15

    The influence of the environment in the thermal equilibrium properties of a bipartite continuous variable quantum system is studied. The problem is treated within a system-plus-reservoir approach. The considered model reproduces the Brownian motion when the two particles are isolated and induces an effective interaction between them, depending on the choice of the spectral function of the bath. The coupling between the system and the environment guarantees the translational invariance of the system in the absence of an external potential. The entanglement between the particles is measured by the logarithmic negativity, which is shown to monotonically decrease with the increase of the temperature. A range of finite temperatures is found in which entanglement is still induced by the reservoir.

  13. Non-Brownian dynamics and strategy of amoeboid cell locomotion

    NASA Astrophysics Data System (ADS)

    Nishimura, Shin I.; Ueda, Masahiro; Sasai, Masaki

    2012-04-01

    Amoeboid cells such as Dictyostelium discoideum and Madin-Darby canine kidney cells show the non-Brownian dynamics of migration characterized by the superdiffusive increase of mean-squared displacement. In order to elucidate the physical mechanism of this non-Brownian dynamics, a computational model is developed which highlights a group of inhibitory molecules for actin polymerization. Based on this model, we propose a hypothesis that inhibitory molecules are sent backward in the moving cell to accumulate at the rear of cell. The accumulated inhibitory molecules at the rear further promote cell locomotion to form a slow positive feedback loop of the whole-cell scale. The persistent straightforward migration is stabilized with this feedback mechanism, but the fluctuation in the distribution of inhibitory molecules and the cell shape deformation concurrently interrupt the persistent motion to turn the cell into a new direction. A sequence of switching behaviors between persistent motions and random turns gives rise to the superdiffusive migration in the absence of the external guidance signal. In the complex environment with obstacles, this combined process of persistent motions and random turns drives the simulated amoebae to solve the maze problem in a highly efficient way, which suggests the biological advantage for cells to bear the non-Brownian dynamics.

  14. Large scale simulations of Brownian suspensions

    NASA Astrophysics Data System (ADS)

    Viera, Marc Nathaniel

    Particle suspensions occur in a wide variety of natural and engineering materials. Some examples are colloids, polymers, paints, and slurries. These materials exhibit complex behavior owing to the forces which act among the particles and are transmitted through the fluid medium. Depending on the application, particle sizes range from large macroscopic molecules of 100mum to smaller colloidal particles in the range of 10nm to 1mum. Particles of this size interact though interparticle forces such as electrostatic and van der Waals, as well as hydrodynamic forces transmitted through the fluid medium. Additionally, the particles are subjected to random thermal fluctuations in the fluid giving rise to Brownian motion. The central objective of our research is to develop efficient numerical algorithms for the large scale dynamic simulation of particle suspensions. While previous methods have incurred a computational cost of O(N3), where N is the number of particles, we have developed a novel algorithm capable of solving this problem in O(N ln N) operations. This has allowed us to perform dynamic simulations with up to 64,000 particles and Monte Carlo realizations of up to 1 million particles. Our algorithm follows a Stokesian dynamics formulation by evaluating many-body hydrodynamic interactions using a far-field multipole expansion combined with a near-field lubrication correction. The breakthrough O(N ln N) scaling is obtained by employing a Particle-Mesh-Ewald (PME) approach whereby near-field interactions are evaluated directly and far-field interactions are evaluated using a grid based velocity computed with FFT's. This approach is readily extended to include the effects of Brownian motion. For interacting particles, the fluctuation-dissipation theorem requires that the individual Brownian forces satisfy a correlation based on the N body resistance tensor R. The accurate modeling of these forces requires the computation of a matrix square root R 1/2 for matrices up

  15. Microstructure from simulated Brownian suspension flows at large shear rate

    NASA Astrophysics Data System (ADS)

    Morris, Jeffrey F.; Katyal, Bhavana

    2002-06-01

    Pair microstructure of concentrated Brownian suspensions in simple-shear flow is studied by sampling of configurations from dynamic simulations by the Stokesian Dynamics technique. Simulated motions are three dimensional with periodic boundary conditions to mimic an infinitely extended suspension. Hydrodynamic interactions through Newtonian fluid and Brownian motion are the only physical influences upon the motion of the monodisperse hard-sphere particles. The dimensionless parameters characterizing the suspension are the particle volume fraction and Péclet number, defined, respectively, as φ=(4π/3)na3 with n the number density and a the sphere radius, and Pe=6πηγ˙a3/kT with η the fluid viscosity, γ˙ the shear rate, and kT the thermal energy. The majority of the results reported are from simulations at Pe=1000; results of simulations at Pe=1, 25, and 100 are also reported for φ=0.3 and φ=0.45. The pair structure is characterized by the pair distribution function, g(r)=P1|1(r)/n, where P1|1(r) is the conditional probability of finding a pair at a separation vector r. The structure under strong shearing exhibits an accumulation of pair probability at contact, and angular distortion (from spherical symmetry at Pe=0), with both effects increasing with Pe. Flow simulations were performed at Pe=1000 for eight volume fractions in the range 0.2⩽φ⩽0.585. For φ=0.2-0.3, the pair structure at contact, g(|r|=2)≡g(2), is found to exhibit a single region of strong correlation, g(2)≫1, at points around the axis of compression, with a particle-deficient wake in the extensional zones. A qualitative change in microstructure is observed between φ=0.3 and φ=0.37. For φ⩾0.37, the maximum g(2) lies at points in the shear plane nearly on the x axis of the bulk simple shear flow Ux=γ˙y, while at smaller φ, the maximum g(2) lies near the compressional axis; long-range string ordering is not observed. For φ=0.3 and φ=0.45, g(2)˜Pe0.7 for 1⩽Pe⩽1000, a

  16. Disentangling Random Motion and Flow in a Complex Medium.

    PubMed

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

    2016-02-02

    We describe a technique for deconvolving the stochastic motion of particles from large-scale fluid flow in a dynamic environment such as that found in living cells. The method leverages the separation of timescales to subtract out the persistent component of motion from single-particle trajectories. The mean-squared displacement of the resulting trajectories is rescaled so as to enable robust extraction of the diffusion coefficient and subdiffusive scaling exponent of the stochastic motion. We demonstrate the applicability of the method for characterizing both diffusive and fractional Brownian motion overlaid by flow and analytically calculate the accuracy of the method in different parameter regimes. This technique is employed to analyze the motion of lysosomes in motile neutrophil-like cells, showing that the cytoplasm of these cells behaves as a viscous fluid at the timescales examined. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

  17. Disentangling Random Motion and Flow in a Complex Medium

    PubMed Central

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

    2016-01-01

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

  18. Perturbative theory for Brownian vortexes

    NASA Astrophysics Data System (ADS)

    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.

  19. Thermophoretically modified aerosol Brownian coagulation

    NASA Astrophysics Data System (ADS)

    Arias-Zugasti, Manuel; Rosner, Daniel E.

    2011-08-01

    A theory of aerosol coagulation rates resulting from continuum-regime Brownian coagulation in the presence of size-dependent particle thermophoresis is developed and explored here. We are motivated by a wide variety of applications in which particle Brownian coagulation occurs in a nonisothermal gas where differential thermophoretic drift contributes to, but does not dominate, the encounter frequency between suspended spherical particles (e.g., mist droplets) of different sizes. We employ a Smoluchowski-like population-balance to demonstrate the relative roles of Brownian diffusion and thermophoresis in shaping the short and long time (asymptotic or “coagulation-aged”) mist-droplet size distribution (DSD) function. To carry out these combined-mechanism DSD-evolution calculations we developed a rational “coupled” coagulation rate constant (allowing for simultaneous Brownian diffusion and relative thermophoretic drift) rather than simply adding the relevant individual coagulation “kernels.” Dimensionless criteria are provided to facilitate precluding other coagulation mechanisms not considered here (such as simultaneous sedimentation or Marangoni-flow-induced mist-droplet phoresis) and potential complications not included in the present model [as finite-rate coalescence, initial departures from the continuum (Stokes drag-) limit, and even dense (nonideal) vapor effects].

  20. Thermophoretically modified aerosol brownian coagulation.

    PubMed

    Arias-Zugasti, Manuel; Rosner, Daniel E

    2011-08-01

    A theory of aerosol coagulation rates resulting from continuum-regime brownian coagulation in the presence of size-dependent particle thermophoresis is developed and explored here. We are motivated by a wide variety of applications in which particle brownian coagulation occurs in a nonisothermal gas where differential thermophoretic drift contributes to, but does not dominate, the encounter frequency between suspended spherical particles (e.g., mist droplets) of different sizes. We employ a Smoluchowski-like population-balance to demonstrate the relative roles of brownian diffusion and thermophoresis in shaping the short and long time (asymptotic or "coagulation-aged") mist-droplet size distribution (DSD) function. To carry out these combined-mechanism DSD-evolution calculations we developed a rational "coupled" coagulation rate constant (allowing for simultaneous brownian diffusion and relative thermophoretic drift) rather than simply adding the relevant individual coagulation "kernels." Dimensionless criteria are provided to facilitate precluding other coagulation mechanisms not considered here (such as simultaneous sedimentation or Marangoni-flow-induced mist-droplet phoresis) and potential complications not included in the present model [as finite-rate coalescence, initial departures from the continuum (Stokes drag-) limit, and even dense (nonideal) vapor effects].