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Sample records for fractional brownian motion

  1. STOCHASTIC INTEGRATION FOR TEMPERED FRACTIONAL BROWNIAN MOTION

    PubMed Central

    MEERSCHAERT, MARK M.; SABZIKAR, FARZAD

    2014-01-01

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

  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. Spectral correlations of fractional Brownian motion

    SciTech Connect

    Oigaard, Tor Arne; Hanssen, Alfred; Scharf, Louis L.

    2006-09-15

    Fractional Brownian motion (fBm) is a ubiquitous nonstationary model for many physical processes with power-law time-averaged spectra. In this paper, we exploit the nonstationarity to derive the full spectral correlation structure of fBm. Starting from the time-varying correlation function, we derive two different time-frequency spectral correlation functions (the ambiguity function and the Kirkwood-Rihaczek spectrum), and one dual-frequency spectral correlation function. The dual-frequency spectral correlation has a surprisingly simple structure, with spectral support on three discrete lines. The theoretical predictions are verified by spectrum estimates of Monte Carlo simulations and of a time series of earthquakes with a magnitude of 7 and higher.

  4. 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. PMID:27504243

  5. Perturbative expansion for the maximum of fractional Brownian motion

    NASA Astrophysics Data System (ADS)

    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 tmax 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 .

  6. 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.

  7. A Renormalized Rough Path over Fractional Brownian Motion

    NASA Astrophysics Data System (ADS)

    Unterberger, Jérémie

    2013-06-01

    We construct in this article a rough path over fractional Brownian motion with arbitrary Hurst index by (i) using the Fourier normal ordering algorithm introduced in (Unterberger, Commun Math Phy 298(1):1-36, 2010) to reduce the problem to that of regularizing tree iterated integrals and (ii) applying the Bogolioubov-Parasiuk-Hepp-Zimmermann (BPHZ) renormalization algorithm to Feynman diagrams representing tree iterated integrals.

  8. 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.

  9. Pricing currency options in the mixed fractional Brownian motion

    NASA Astrophysics Data System (ADS)

    Sun, Lin

    2013-08-01

    This paper deals with the problem of pricing European currency options in the mixed fractional Brownian environment. Both the pricing formula and the mixed fractional partial differential equation for European call currency options are obtained. Some Greeks and the estimator of volatility are also provided. Empirical studies and simulation results confirm the theoretical findings and show that the mixed fractional Brownian pricing model is a reasonable one.

  10. 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)

  11. 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.

  12. 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. PMID:26636835

  13. 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.

  14. 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.

  15. Fractional Diffusion Equation, Quantum Subdynamics and EINSTEIN'S Theory of Brownian Motion

    NASA Astrophysics Data System (ADS)

    Abe, Sumiyoshi

    The fractional diffusion equation for describing the anomalous diffusion phenomenon is derived in the spirit of Einstein's 1905 theory of Brownian motion. It is shown how naturally fractional calculus appears in the theory. Then, Einstein's theory is examined in view of quantum theory. An isolated quantum system composed of the objective system and the environment is considered, and then subdynamics of the objective system is formulated. The resulting quantum master equation is found to be of the Lindblad type.

  16. 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.

  17. 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. PMID:25375519

  18. 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

  19. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

  1. 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.

  2. Brownian motion goes ballistic

    NASA Astrophysics Data System (ADS)

    Florin, Ernst-Ludwig

    2012-02-01

    It is the randomness that is considered the hallmark of Brownian motion, but already in Einstein's seminal 1905 paper on Brownian motion it is implied that this randomness must break down at short time scales when the inertia of the particle kicks in. As a result, the particle's trajectories should lose its randomness and become smooth. The characteristic time scale for this transition is given by the ratio of the particle's mass to its viscous drag coefficient. For a 1 μm glass particle in water and at room temperature, this timescale is on the order of 100 ns. Early calculations, however, neglected the inertia of the liquid surrounding the particle which induces a transition from random diffusive to non-diffusive Brownian motion already at much larger timescales. In this first non-diffusive regime, particles of the same size but with different densities still move at almost the same rate as a result of hydrodynamic correlations. To observe Brownian motion that is dominated by the inertia of the particle, i.e. ballistic motion, one has to observe the particle at significantly shorter time scales on the order of nanoseconds. Due to the lack of sufficiently fast and precise detectors, such experiments were so far not possible on individual particles. I will describe how we were able to observe the transition from hydrodynamically dominated Brownian motion to ballistic Brownian motion in a liquid. I will compare our data with current theories for Brownian motion on fast timescales that take into account the inertia of both the liquid and the particle. The newly gained ability to measure the fast Brownian motion of an individual particle paves the way for detailed studies of confined Brownian motion and Brownian motion in heterogeneous media. [4pt] [1] Einstein, A. "Uber die von der molekularkinetischen Theorie der W"arme geforderte Bewegung von in ruhenden Fl"ussigkeiten suspendierten Teilchen. Ann. Phys. 322, 549--560 (1905). [0pt] [2] Lukic, B., S. Jeney, C

  3. 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

    2012-11-01

    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. PMID:23199912

  4. 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.

  5. Perturbation theory for fractional Brownian motion in presence of absorbing boundaries

    NASA Astrophysics Data System (ADS)

    Wiese, Kay Jörg; Majumdar, Satya N.; Rosso, Alberto

    2011-06-01

    Fractional Brownian motion is a Gaussian process x(t) with zero mean and two-time correlations =D(t12H+t22H-|t1-t2|2H), where H, with 0Brownian motion, while for H≠1/2, x(t) is a non-Markovian process. Here we study x(t) in presence of an absorbing boundary at the origin and focus on the probability density P+(x,t) for the process to arrive at x at time t, starting near the origin at time 0, given that it has never crossed the origin. It has a scaling form P+(x,t)~t-HR+(x/tH). Our objective is to compute the scaling function R+(y), which up to now was only known for the Markov case H=1/2. We develop a systematic perturbation theory around this limit, setting H=1/2+ɛ, to calculate the scaling function R+(y) to first order in ɛ. We find that R+(y) behaves as R+(y)~yϕ as y→0 (near the absorbing boundary), while R+(y)~yγexp(-y2/2) as y→∞, with ϕ=1-4ɛ+O(ɛ2) and γ=1-2ɛ+O(ɛ2). Our ɛ-expansion result confirms the scaling relation ϕ=(1-H)/H proposed in Zoia, Rosso, and Majumdar [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.102.120602 102, 120602 (2009)]. We verify our findings via numerical simulations for H=2/3. The tools developed here are versatile, powerful, and adaptable to different situations.

  6. 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. PMID:11114233

  7. Automatic algorithm to decompose discrete paths of fractional Brownian motion into self-similar intrinsic components

    NASA Astrophysics Data System (ADS)

    Vamoş, Călin; Crăciun, Maria; Suciu, Nicolae

    2015-10-01

    Fractional Brownian motion (fBm) is a nonstationary self-similar continuous stochastic process used to model many natural phenomena. A realization of the fBm can be numerically approximated by discrete paths which do not entirely preserve the self-similarity. We investigate the self-similarity at different time scales by decomposing the discrete paths of fBm into intrinsic components. The decomposition is realized by an automatic numerical algorithm based on successive smoothings stopped when the maximum monotonic variation of the averaged time series is reached. The spectral properties of the intrinsic components are analyzed through the monotony spectrum defined as the graph of the amplitudes of the monotonic segments with respect to their lengths (characteristic times). We show that, at intermediate time scales, the mean amplitude of the intrinsic components of discrete fBms scales with the mean characteristic time as a power law identical to that of the corresponding continuous fBm. As an application we consider hydrological time series of the transverse component of the transport process generated as a superposition of diffusive movements on advective transport in random velocity fields. We found that the transverse component has a rich structure of scales, which is not revealed by the analysis of the global variance, and that its intrinsic components may be self-similar only in particular cases.

  8. 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.

  9. The generalized quadratic covariation for fractional Brownian motion with Hurst index less than 1/2

    NASA Astrophysics Data System (ADS)

    Yan, Litan; Liu, Junfeng; Chen, Chao

    2014-11-01

    In this paper, we study the generalized quadratic covariation of f(BH) and BH defined by $ [f(BH),BH](H)t:=\\lim_\\varepsilon\\downarrow 0}(1)/(\\varepsilon2H)\\int 0t{f(BHs+\\varepsilon) -f(BHs)}(BHs+\\varepsilon-BH_s)ds2H in probability, where f is a Borel function and BH is a fractional Brownian motion with Hurst index 0 < H < 1/2. We construct a Banach space {H} of measurable functions such that the generalized quadratic covariation exists in L2(Ω) and the Bouleau-Yor identity takes the form [f(BH),BH]t(H)=-\\int_ {R}}f(x){L}H(dx,t) provided f\\in {H}, where {L}^{H}(x, t) is the weighted local time of BH. These are also extended to the time-dependent case, and as an application we give the identity between the generalized quadratic covariation and the 4-covariation [g(BH), BH, BH, BH] when H = 1/4.

  10. Multifractality and Laplace spectrum of horizontal visibility graphs constructed from fractional Brownian motions

    NASA Astrophysics Data System (ADS)

    Yu, Zu-Guo; Zhang, Huan; Huang, Da-Wen; Lin, Yong; Anh, Vo

    2016-03-01

    Many studies have shown that additional information can be gained on time series by investigating their associated complex networks. In this work, we investigate the multifractal property and Laplace spectrum of the horizontal visibility graphs (HVGs) constructed from fractional Brownian motions. We aim to identify via simulation and curve fitting the form of these properties in terms of the Hurst index H. First, we use the sandbox algorithm to study the multifractality of these HVGs. It is found that multifractality exists in these HVGs. We find that the average fractal dimension < D(0)> of HVGs approximately satisfies the prominent linear formula < D(0)> =2-H ; while the average information dimension < D(1)> and average correlation dimension < D(2)> are all approximately bi-linear functions of H when H≥slant 0.15 . Then, we calculate the spectrum and energy for the general Laplacian operator and normalized Laplacian operator of these HVGs. We find that, for the general Laplacian operator, the average logarithm of second-smallest eigenvalue < \\ln ≤ft({{u}2}\\right)> , the average logarithm of third-smallest eigenvalue < \\ln ≤ft({{u}3}\\right)> , and the average logarithm of maximum eigenvalue < \\ln ≤ft({{u}n}\\right)> of these HVGs are approximately linear functions of H; while the average Laplacian energy < {{E}\\text{nL}}> is approximately a quadratic polynomial function of H. For the normalized Laplacian operator, < \\ln ≤ft({{u}2}\\right)> and < \\ln ≤ft({{u}3}\\right)> of these HVGs approximately satisfy linear functions of H; while < \\ln ≤ft({{u}n}\\right)> and < {{E}\\text{nL}}> are approximately a 4th and cubic polynomial function of H respectively.

  11. 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.

  12. Deterministic Brownian Motion

    NASA Astrophysics Data System (ADS)

    Trefan, Gyorgy

    1993-01-01

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

  13. 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.

  14. Non-Linear Wavelet Regression and Branch & Bound Optimization for the Full Identification of Bivariate Operator Fractional Brownian Motion

    NASA Astrophysics Data System (ADS)

    Frecon, Jordan; Didier, Gustavo; Pustelnik, Nelly; Abry, Patrice

    2016-08-01

    Self-similarity is widely considered the reference framework for modeling the scaling properties of real-world data. However, most theoretical studies and their practical use have remained univariate. Operator Fractional Brownian Motion (OfBm) was recently proposed as a multivariate model for self-similarity. Yet it has remained seldom used in applications because of serious issues that appear in the joint estimation of its numerous parameters. While the univariate fractional Brownian motion requires the estimation of two parameters only, its mere bivariate extension already involves 7 parameters which are very different in nature. The present contribution proposes a method for the full identification of bivariate OfBm (i.e., the joint estimation of all parameters) through an original formulation as a non-linear wavelet regression coupled with a custom-made Branch & Bound numerical scheme. The estimation performance (consistency and asymptotic normality) is mathematically established and numerically assessed by means of Monte Carlo experiments. The impact of the parameters defining OfBm on the estimation performance as well as the associated computational costs are also thoroughly investigated.

  15. 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.

  16. A multiscale guide to Brownian motion

    NASA Astrophysics Data System (ADS)

    Grebenkov, Denis S.; Belyaev, Dmitry; Jones, Peter W.

    2016-01-01

    We revise the Lévy construction of Brownian motion as a simple though rigorous approach to operate with various Gaussian processes. A Brownian path is explicitly constructed as a linear combination of wavelet-based ‘geometrical features’ at multiple length scales with random weights. Such a wavelet representation gives a closed formula mapping of the unit interval onto the functional space of Brownian paths. This formula elucidates many classical results about Brownian motion (e.g., non-differentiability of its path), providing an intuitive feeling for non-mathematicians. The illustrative character of the wavelet representation, along with the simple structure of the underlying probability space, is different from the usual presentation of most classical textbooks. Similar concepts are discussed for the Brownian bridge, fractional Brownian motion, the Ornstein-Uhlenbeck process, Gaussian free fields, and fractional Gaussian fields. Wavelet representations and dyadic decompositions form the basis of many highly efficient numerical methods to simulate Gaussian processes and fields, including Brownian motion and other diffusive processes in confining domains.

  17. 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. PMID:27396746

  18. 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.

  19. 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.

  20. 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.

  1. 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. PMID:10465697

  2. 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.

  3. 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. PMID:16997210

  4. 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.

  5. Brownian motion using video capture

    NASA Astrophysics Data System (ADS)

    Salmon, Reese; Robbins, Candace; Forinash, Kyle

    2002-05-01

    Although other researchers had previously observed the random motion of pollen grains suspended in water through a microscope, Robert Brown's name is associated with this behaviour based on observations he made in 1828. It was not until Einstein's work in the early 1900s however, that the origin of this irregular motion was established to be the result of collisions with molecules which were so small as to be invisible in a light microscope (Einstein A 1965 Investigations on the Theory of the Brownian Movement ed R Furth (New York: Dover) (transl. Cowper A D) (5 papers)). Jean Perrin in 1908 (Perrin J 1923 Atoms (New York: Van Nostrand-Reinhold) (transl. Hammick D)) was able, through a series of painstaking experiments, to establish the validity of Einstein's equation. We describe here the details of a junior level undergraduate physics laboratory experiment where students used a microscope, a video camera and video capture software to verify Einstein's famous calculation of 1905.

  6. The open quantum Brownian motions

    NASA Astrophysics Data System (ADS)

    Bauer, Michel; Bernard, Denis; Tilloy, Antoine

    2014-09-01

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

  7. Nonequilibrium Brownian Motion beyond the Effective Temperature

    PubMed Central

    Gnoli, Andrea; Puglisi, Andrea; Sarracino, Alessandro; Vulpiani, Angelo

    2014-01-01

    The condition of thermal equilibrium simplifies the theoretical treatment of fluctuations as found in the celebrated Einstein’s relation between mobility and diffusivity for Brownian motion. Several recent theories relax the hypothesis of thermal equilibrium resulting in at least two main scenarios. With well separated timescales, as in aging glassy systems, equilibrium Fluctuation-Dissipation Theorem applies at each scale with its own “effective” temperature. With mixed timescales, as for example in active or granular fluids or in turbulence, temperature is no more well-defined, the dynamical nature of fluctuations fully emerges and a Generalized Fluctuation-Dissipation Theorem (GFDT) applies. Here, we study experimentally the mixed timescale regime by studying fluctuations and linear response in the Brownian motion of a rotating intruder immersed in a vibro-fluidized granular medium. Increasing the packing fraction, the system is moved from a dilute single-timescale regime toward a denser multiple-timescale stage. Einstein’s relation holds in the former and is violated in the latter. The violation cannot be explained in terms of effective temperatures, while the GFDT is able to impute it to the emergence of a strong coupling between the intruder and the surrounding fluid. Direct experimental measurements confirm the development of spatial correlations in the system when the density is increased. PMID:24714671

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

    PubMed

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

    2016-04-30

    Longitudinal data are widely analysed using linear mixed models, with 'random slopes' models particularly common. However, when modelling, for example, longitudinal pre-treatment CD4 cell counts in HIV-positive patients, the incorporation of non-stationary stochastic processes such as Brownian motion has been shown to lead to a more biologically plausible model and a substantial improvement in model fit. In this article, we propose two further extensions. Firstly, we propose the addition of a fractional Brownian motion component, and secondly, we generalise the model to follow a multivariate-t distribution. These extensions are biologically plausible, and each demonstrated substantially improved fit on application to example data from the Concerted Action on SeroConversion to AIDS and Death in Europe study. We also propose novel procedures for residual diagnostic plots that allow such models to be assessed. Cohorts of patients were simulated from the previously reported and newly developed models in order to evaluate differences in predictions made for the timing of treatment initiation under different clinical management strategies. A further simulation study was performed to demonstrate the substantial biases in parameter estimates of the mean slope of CD4 decline with time that can occur when random slopes models are applied in the presence of censoring because of treatment initiation, with the degree of bias found to depend strongly on the treatment initiation rule applied. Our findings indicate that researchers should consider more complex and flexible models for the analysis of longitudinal biomarker data, particularly when there are substantial missing data, and that the parameter estimates from random slopes models must be interpreted with caution. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd. PMID:26555755

  9. Elementary simulation of tethered Brownian motion

    NASA Astrophysics Data System (ADS)

    Beausang, John F.; Zurla, Chiara; Finzi, Laura; Sullivan, Luke; Nelson, Philip C.

    2007-06-01

    We describe a simple simulation, suitable for an undergraduate project or graduate problem set, of the Brownian motion of a particle in a Hooke's law potential well. Understanding this physical situation is necessary in many experimental contexts, for instance in single molecule biophysics, and its simulation helps students appreciate the dynamical character of thermal equilibrium. The simulation captures behavior seen in experimental data on tethered particle motion.

  10. Nonisothermal fluctuating hydrodynamics and Brownian motion.

    PubMed

    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. PMID:27078335

  11. 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.

  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. Simulations of magnetic nanoparticle Brownian motion

    PubMed Central

    Reeves, Daniel B.; Weaver, John B.

    2012-01-01

    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. PMID:23319830

  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. Quantum Brownian motion in a Landau level

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  16. 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.

  17. Dynamical objectivity in quantum Brownian motion

    NASA Astrophysics Data System (ADS)

    Tuziemski, J.; Korbicz, J. K.

    2015-11-01

    Classical objectivity as a property of quantum states —a view proposed to explain the observer-independent character of our world from quantum theory, is an important step in bridging the quantum-classical gap. It was recently derived in terms of spectrum broadcast structures for small objects embedded in noisy photon-like environments. However, two fundamental problems have arisen: a description of objective motion and applicability to other types of environments. Here we derive an example of objective states of motion in quantum mechanics by showing the formation of dynamical spectrum broadcast structures in the celebrated, realistic model of decoherence —Quantum Brownian Motion. We do it for realistic, thermal environments and show their noise-robustness. This opens a potentially new method of studying the quantum-to-classical transition.

  18. Brownian motion of particles in nematic fluids

    NASA Astrophysics Data System (ADS)

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

    2011-03-01

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

  19. Inducing Tropical Cyclones to Undergo Brownian Motion

    NASA Astrophysics Data System (ADS)

    Hodyss, D.; McLay, J.; Moskaitis, J.; Serra, E.

    2014-12-01

    Stochastic parameterization has become commonplace in numerical weather prediction (NWP) models used for probabilistic prediction. Here, a specific stochastic parameterization will be related to the theory of stochastic differential equations and shown to be affected strongly by the choice of stochastic calculus. From an NWP perspective our focus will be on ameliorating a common trait of the ensemble distributions of tropical cyclone (TC) tracks (or position), namely that they generally contain a bias and an underestimate of the variance. With this trait in mind we present a stochastic track variance inflation parameterization. This parameterization makes use of a properly constructed stochastic advection term that follows a TC and induces its position to undergo Brownian motion. A central characteristic of Brownian motion is that its variance increases with time, which allows for an effective inflation of an ensemble's TC track variance. Using this stochastic parameterization we present a comparison of the behavior of TCs from the perspective of the stochastic calculi of Itô and Stratonovich within an operational NWP model. The central difference between these two perspectives as pertains to TCs is shown to be properly predicted by the stochastic calculus and the Itô correction. In the cases presented here these differences will manifest as overly intense TCs, which, depending on the strength of the forcing, could lead to problems with numerical stability and physical realism.

  20. Extreme fluctuations of active Brownian motion

    NASA Astrophysics Data System (ADS)

    Pietzonka, Patrick; Kleinbeck, Kevin; Seifert, Udo

    2016-05-01

    In active Brownian motion, an internal propulsion mechanism interacts with translational and rotational thermal noise and other internal fluctuations to produce directed motion. We derive the distribution of its extreme fluctuations and identify its universal properties using large deviation theory. The limits of slow and fast internal dynamics give rise to a kink-like and parabolic behavior of the corresponding rate functions, respectively. For dipolar Janus particles in two- and three-dimensions interacting with a field, we predict a novel symmetry akin to, but different from, the one related to entropy production. Measurements of these extreme fluctuations could thus be used to infer properties of the underlying, often hidden, network of states.

  1. 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…

  2. 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)

  3. 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.

  4. Probability of Brownian motion hitting an obstacle

    SciTech Connect

    Knessl, C.; Keller, J.B.

    2000-02-01

    The probability p(x) that Brownian motion with drift, starting at x, hits an obstacle is analyzed. The obstacle {Omega} is a compact subset of R{sup n}. It is shown that p(x) is expressible in terms of the field U(x) scattered by {Omega} when it is hit by plane wave. Therefore results for U(x), and methods for finding U(x) can be used to determine p(x). The authors illustrate this by obtaining exact and asymptotic results for p(x) when {Omega} is a slit in R{sup 2}, and asymptotic results when {Omega} is a disc in R{sup 3}.

  5. Geometric Brownian Motion with Tempered Stable Waiting Times

    NASA Astrophysics Data System (ADS)

    Gajda, Janusz; Wyłomańska, Agnieszka

    2012-08-01

    One of the earliest system that was used to asset prices description is Black-Scholes model. It is based on geometric Brownian motion and was used as a tool for pricing various financial instruments. However, when it comes to data description, geometric Brownian motion is not capable to capture many properties of present financial markets. One can name here for instance periods of constant values. Therefore we propose an alternative approach based on subordinated tempered stable geometric Brownian motion which is a combination of the popular geometric Brownian motion and inverse tempered stable subordinator. In this paper we introduce the mentioned process and present its main properties. We propose also the estimation procedure and calibrate the analyzed system to real data.

  6. 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.

  7. 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. PMID:25974462

  8. Dynamical and thermodynamical control of open quantum Brownian motion

    NASA Astrophysics Data System (ADS)

    Petruccione, Francesco; Sinayskiy, Ilya

    Open quantum Brownian motion was introduced as a new type of quantum Brownian motion for Brownian particles with internal quantum degrees of freedom. Recently, an example of the microscopic derivation of open quantum Brownian motion has been presented [I. Sinayskiy and F. Petruccione, Phys. Scr. T165, 014017 (2015)]. The microscopic derivation allows to relate the dynamical properties of open Quantum Brownian motion and the thermodynamical properties of the environment. In the present work, we study the possibility of control of the external degrees of freedom of the ''walker'' (position) by manipulating the internal one, e.g. spin, polarization, occupation numbers. In the particular example of the known microscopic derivation the connection between dynamics of the ''walker'' and thermodynamical parameters of the system is established. For the system of open Brownian walkers coupled to the same environment controllable creation of quantum correlations is investigated. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. Non-colliding Brownian Motions and the Extended Tacnode Process

    NASA Astrophysics Data System (ADS)

    Johansson, Kurt

    2013-04-01

    We consider non-colliding Brownian motions with two starting points and two endpoints. The points are chosen so that the two groups of Brownian motions just touch each other, a situation that is referred to as a tacnode. The extended kernel for the determinantal point process at the tacnode point is computed using new methods and given in a different form from that obtained for a single time in previous work by Delvaux, Kuijlaars and Zhang. The form of the extended kernel is also different from that obtained for the extended tacnode kernel in another model by Adler, Ferrari and van Moerbeke. We also obtain the correlation kernel for a finite number of non-colliding Brownian motions starting at two points and ending at arbitrary points.

  14. 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.

  15. 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.

  16. 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

  17. 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.

  18. On modeling animal movements using Brownian motion with measurement error.

    PubMed

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

    2014-02-01

    Modeling animal movements with Brownian motion (or more generally by a Gaussian process) has a long tradition in ecological studies. The recent Brownian bridge movement model (BBMM), which incorporates measurement errors, has been quickly adopted by ecologists because of its simplicity and tractability. We discuss some nontrivial properties of the discrete-time stochastic process that results from observing a Brownian motion with added normal noise at discrete times. In particular, we demonstrate that the observed sequence of random variables is not Markov. Consequently the expected occupation time between two successively observed locations does not depend on just those two observations; the whole path must be taken into account. Nonetheless, the exact likelihood function of the observed time series remains tractable; it requires only sparse matrix computations. The likelihood-based estimation procedure is described in detail and compared to the BBMM estimation. PMID:24669719

  19. 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

  20. Fundamental aspects of quantum Brownian motion

    SciTech Connect

    Haenggi, Peter; Ingold, Gert-Ludwig

    2005-06-01

    With this work we elaborate on the physics of quantum noise in thermal equilibrium and in stationary nonequilibrium. Starting out from the celebrated quantum fluctuation-dissipation theorem we discuss some important consequences that must hold for open, dissipative quantum systems in thermal equilibrium. The issue of quantum dissipation is exemplified with the fundamental problem of a damped harmonic quantum oscillator. The role of quantum fluctuations is discussed in the context of both, the nonlinear generalized quantum Langevin equation and the path integral approach. We discuss the consequences of the time-reversal symmetry for an open dissipative quantum dynamics and, furthermore, point to a series of subtleties and possible pitfalls. The path integral methodology is applied to the decay of metastable states assisted by quantum Brownian noise.

  1. 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.

  2. 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.

  3. Brownian Motion, Concentration Fluctuations and Viscoelasticity in Surfactant Solutions

    NASA Astrophysics Data System (ADS)

    Amin, Samiul; van Zanten, Ryan; Kermis, Thomas; Dees, Stephen; van Zanten, John

    2001-03-01

    There is growing interest in using Brownian or thermal motion of spherical colloidal particles to probe the dynamics of soft materials which exhibit viscoelasticity. In principle, the motion of these colloidal spheres is related to the structure and dynamics of the suspending media. Most current investigations have focused solely on establishing the relationship between the measured Brownian motion and viscoelastic moduli. The approach described here is enhanced in that it utilizes not only measurements of the particle mean squared displacement and suspending medium viscoelastic moduli, but also light scattering characterization of the viscoelastic media whereby the concentration fluctuation relaxation spectrum and the osmotic compressibility are determined. This multiple experimental probe approach allows one to account for both transverse and longitudinal contributions to the suspending medium's response. The approach is illustrated with a whole host of surfactant systems including CTAB/KBr and CTAB/NaSal wormlike micelle solutions as well as aqueous Pluronic solutions.

  4. 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.

  5. Brownian motion model with stochastic parameters for asset prices

    NASA Astrophysics Data System (ADS)

    Ching, Soo Huei; Hin, Pooi Ah

    2013-09-01

    The Brownian motion model may not be a completely realistic model for asset prices because in real asset prices the drift μ and volatility σ may change over time. Presently we consider a model in which the parameter x = (μ,σ) is such that its value x (t + Δt) at a short time Δt ahead of the present time t depends on the value of the asset price at time t + Δt as well as the present parameter value x(t) and m-1 other parameter values before time t via a conditional distribution. The Malaysian stock prices are used to compare the performance of the Brownian motion model with fixed parameter with that of the model with stochastic parameter.

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

    NASA Astrophysics Data System (ADS)

    Huang, Rongxin

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

  7. Anomalous diffusion in quantum Brownian motion with colored noise

    SciTech Connect

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

    2006-03-15

    Anomalous diffusion is discussed in the context of quantum Brownian motion with colored noise. It is shown that earlier results follow simply and directly from the fluctuation-dissipation theorem. The limits on the long-time dependence of anomalous diffusion are shown to be a consequence of the second law of thermodynamics. The special case of an electron interacting with the radiation field is discussed in detail. We apply our results to wave-packet spreading.

  8. Simulating quantum Brownian motion with single trapped ions

    SciTech Connect

    Maniscalco, S.; Piilo, J.; Intravaia, F.; Petruccione, F.; Messina, A.

    2004-05-01

    We study the open system dynamics of a harmonic oscillator coupled with an artificially engineered reservoir. We single out the reservoir and system variables governing the passage between Lindblad-type and non-Lindblad-type dynamics of the reduced system's oscillator. We demonstrate the existence of conditions under which virtual exchanges of energy between system and reservoir take place. We propose to use a single trapped ion coupled to engineered reservoirs in order to simulate quantum Brownian motion.

  9. 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.

  10. Brownian Motion, Fractal Structure and Verification of A. Einstein's Formula

    NASA Astrophysics Data System (ADS)

    Nikolić, Dragiša; Nešić, Ljubiša

    2010-01-01

    The work offers a simple experimental verification of A. Einstein and M. Smoluhovski's formula for Brownian motion. In this experiment we used latex solved in water, glycerin and alcohol while the observations and recording were done with a binocular optical microscope and a digital camera. Video material is recorded in separate files put on the Internet and can be downloaded and used for demonstration in class or further computer processing.

  11. 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.

  12. 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

  13. Teleparallelism, Brownian Motion, Quantum Mechanics and Fluid-Dynamics I

    NASA Astrophysics Data System (ADS)

    Rapoport, Diego

    2002-12-01

    Extending the rules of teleparallelism for the introduction of a metric and a connection with torsion on a smooth manifold, M, we define generalized Brownian motions on M starting with a standard Wiener process. The laplacian operator generating this diffusion is the square of the teleparallelism connection on M, yet it is found to depend on the trace-torsion, and thus we restrict to Riemann-Cartan-Weyl connections. We extend these constructions to the generalized Brownian motions of differential forms. We apply this to give random covariant implicit solutions of the Navier-Stokes equations. We give the constitutive equations for the trace-torsion Q, and obtain a non-linear wave equation with quantum potential term for a scalar ψ appearing in the term d lnψ of Q. We relate the diffusion with drift ∇lnψ, to the heat kernel of quantum gravity for a scalar field. In Q appear two electromagnetic potentials which are proved to produce the time-evolution irreversibility of the Brownian motions. They appear related to the rotational degrees of freedom of a massive non-linear Dirac-Hestenes spinor field which defines a global spinor structure on M and a solution of the Clifford-Maxwell equation.

  14. 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. PMID:26428909

  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. 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.

  18. Dance of Adatom Islands: Brownian Motion, Scaling and Reshaping

    NASA Astrophysics Data System (ADS)

    Metiu, Horia; Weakliem, Paul; Bogicevic, Alex; Liu, Shudun

    1998-03-01

    Dynamics of adatom islands of sizes 17 to 2000 is studied by means of kinetic Monte Carlo simulation. Structures of the islands, especially their relation to the sizes of the islands, are examined in great detail. These information provides us a better understanding of how the diffusion constants of these islands scale with the sizes of the islands. Our earlier prediction that the scaling exponents depend on both the temperature and the systems have recently been confirmed by STM measurements. A simple picture for the Brownian motion of large islands will be presented.

  19. 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.

  20. 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.

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

    NASA Astrophysics Data System (ADS)

    Lisý, Vladimír; Tóthová, Jana

    2016-02-01

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

  2. 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…

  3. Ergodicity convergence test suggests telomere motion obeys fractional dynamics.

    PubMed

    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. PMID:21599212

  4. 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.

  5. 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

  6. A Generalized Brownian Motion Model for Turbulent Relative Particle Dispersion

    NASA Astrophysics Data System (ADS)

    Shivamoggi, Bhimsen

    2015-11-01

    A generalized Brownian motion model has been applied to the turbulent relative particle dispersion problem (Shivamoggi). The fluctuating pressure forces acting on a fluid particle are taken to follow an Uhlenbeck-Ornstein process while it appears plausible to take their correlation time to have a power-law dependence on the flow Reynolds number Re. This ansatz provides an insight into the result that the Richardson-Obukhov scaling holds only in the infinite-Re limit and disappears otherwise. It provides a determination of the Richardson-Obukhov constant g as a function of Re, with an asymptotic constant value in the infinite-Re limit. This ansatz is further shown to be in quantitative agreement, in the small-Re limit, with the Batchelor-Townsend ansatz for the rate of change of the mean square interparticle separation in 3D FDT. My thanks to The Netherlands Organization for Scientific Research for Support.

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

    NASA Astrophysics Data System (ADS)

    Fang, Ying; Wu, Rong

    2009-07-01

    In this paper, we consider a Brownian motion risk model, and in addition, the surplus earns investment income at a constant force of interest. The objective is to find a dividend policy so as to maximize the expected discounted value of dividend payments. It is well known that optimality is achieved by using a barrier strategy for unrestricted dividend rate. However, ultimate ruin of the company is certain if a barrier strategy is applied. In many circumstances this is not desirable. This consideration leads us to impose a restriction on the dividend stream. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. Under this additional constraint, we show that the optimal dividend strategy is formed by a threshold strategy.

  8. 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.

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

    NASA Astrophysics Data System (ADS)

    Germain, David; Leocmach, Mathieu; Gibaud, Thomas

    2016-03-01

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

  10. Study of two-dimensional Debye clusters using Brownian motion

    SciTech Connect

    Sheridan, T.E.; Theisen, W.L.

    2006-06-15

    A two-dimensional Debye cluster is a system of n identical particles confined in a parabolic well and interacting through a screened Coulomb (i.e., a Debye-Hueckel or Yukawa) potential with a Debye length {lambda}. Experiments were performed for 27 clusters with n=3-63 particles (9 {mu}m diam) in a capacitively coupled 9 W rf discharge at a neutral argon pressure of 13.6 mTorr. In the strong-coupling regime each particle exhibits small amplitude Brownian motion about its equilibrium position. These motions were projected onto the center-of-mass and breathing modes and Fourier analyzed to give resonance curves from which the mode frequencies, amplitudes, and damping rates were determined. The ratio of the breathing frequency to the center-of-mass frequency was compared with theory to self-consistently determine the Debye shielding parameter {kappa}, Debye length {lambda}, particle charge q, and mode temperatures. It is found that 1 < or approx. {kappa} < or approx. 2, and {kappa} decreases weakly with n. The particle charge averaged over all measurements is -14 200{+-}200 e, and q decreases slightly with n. The two center-of-mass modes and the breathing mode are found to have the same temperature, indicating that the clusters are in thermal equilibrium with the neutral gas. The average cluster temperature is 399{+-}5 K.

  11. Anisotropic Brownian motion in ordered phases of DNA fragments.

    PubMed

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

    2012-01-01

    Using Fluorescence Recovery After Photobleaching, we investigate the Brownian motion of DNA rod-like fragments in two distinct anisotropic phases with a local nematic symmetry. The height of the measurement volume ensures the averaging of the anisotropy of the in-plane diffusive motion parallel or perpendicular to the local nematic director in aligned domains. Still, as shown in using a model specifically designed to handle such a situation and predicting a non-Gaussian shape for the bleached spot as fluorescence recovery proceeds, the two distinct diffusion coefficients of the DNA particles can be retrieved from data analysis. In the first system investigated (a ternary DNA-lipid lamellar complex), the magnitude and anisotropy of the diffusion coefficient of the DNA fragments confined by the lipid bilayers are obtained for the first time. In the second, binary DNA-solvent system, the magnitude of the diffusion coefficient is found to decrease markedly as DNA concentration is increased from isotropic to cholesteric phase. In addition, the diffusion coefficient anisotropy measured within cholesteric domains in the phase coexistence region increases with concentration, and eventually reaches a high value in the cholesteric phase. PMID:22270455

  12. 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.

  13. Study of two-dimensional Debye clusters using Brownian motion

    NASA Astrophysics Data System (ADS)

    Sheridan, T. E.; Theisen, W. L.

    2006-06-01

    A two-dimensional Debye cluster is a system of n identical particles confined in a parabolic well and interacting through a screened Coulomb (i.e., a Debye-Hückel or Yukawa) potential with a Debye length λ. Experiments were performed for 27 clusters with n =3-63 particles (9μmdiam) in a capacitively coupled 9 W rf discharge at a neutral argon pressure of 13.6mTorr. In the strong-coupling regime each particle exhibits small amplitude Brownian motion about its equilibrium position. These motions were projected onto the center-of-mass and breathing modes and Fourier analyzed to give resonance curves from which the mode frequencies, amplitudes, and damping rates were determined. The ratio of the breathing frequency to the center-of-mass frequency was compared with theory to self-consistently determine the Debye shielding parameter κ, Debye length λ, particle charge q, and mode temperatures. It is found that 1≲κ ≲2, and κ decreases weakly with n. The particle charge averaged over all measurements is -14200±200e, and q decreases slightly with n. The two center-of-mass modes and the breathing mode are found to have the same temperature, indicating that the clusters are in thermal equilibrium with the neutral gas. The average cluster temperature is 399±5K.

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

    NASA Astrophysics Data System (ADS)

    Gupta, Amit; Kumar, Ranganathan

    2007-11-01

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

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

    NASA Astrophysics Data System (ADS)

    Song, Shiyu; Wang, Suxin; Wang, Yongjin

    2016-08-01

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

  16. 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.

  17. Critical frequency control in harmonic quantum Brownian motion

    NASA Astrophysics Data System (ADS)

    Giraldi, Filippo; Petruccione, Francesco

    2013-01-01

    The dissipative effects of a quantum harmonic oscillator, initially set in a coherent state and linearly coupled to a continuous distribution of frequency modes, are analyzed over long time scales in relation to the behavior of the spectral density near an arbitrary band gap, arbitrarily shaped at the higher frequencies. The reservoir is initially set either in the vacuum state or in continuous distributions of coherent states. These distributions are arbitrarily shaped at high frequencies and structured in sub- or super-ohmic configurations near an arbitrary band gap frequency. Similarly to certain decoherence processes of a qubit, critical conditions emerge, such that arbitrarily slow inverse power law relaxations of the expectation values of the observables, are obtained by approaching the boundary between the sub- and the super-ohmic regimes. Also, in such critical conditions, a trapping of the number of excitations appears in the super-ohmic regime. The technique of critical frequency control, emerging in the scenario of the environment-induced decoherence of a qubit via the reservoir engineering approach, is extended to the harmonic quantum Brownian motion.

  18. Impalement dynamics and Brownian motion of solid islands on nanopillars

    NASA Astrophysics Data System (ADS)

    Ignacio, M.; Pierre-Louis, O.

    2012-12-01

    We study the dynamics of solid islands deposited on nanopillars using kinetic Monte Carlo simulations. The islands are initially placed on the top of the pillars, in the so-called Cassie-Baxter state. For high pillars, the dynamics is divided into two phases. The first phase corresponds to the deterministic and irreversible impalement of the island. The dynamics of this phase is governed by surface diffusion. Once the island has collapsed, a second phase is observed where the island exhibits Brownian motion along the pillars, characterized by a diffusion constant Di and a kinetic coefficient Ki accounting for the interaction of the island with the top of the pillars. The random walk stops when the island reaches the bottom of the substrate, where it sticks irreversibly. When the island wettability is small, the island diffusion constant Di is controlled by adatom diffusion, and scales as the inverse of the number of atoms in the island. In contrast, for large wettabilities, we observe that Di oscillates as the island size is increased. The minimum of the oscillations corresponds to nucleation-limited dynamics, where Di is independent of the island size. We also determine the time for partial irreversible collapse on shorter pillars, leading to the so-called Wenzel state. Finally, we discuss the orders of magnitude of the typical duration of these processes.

  19. A simple microviscometric approach based on Brownian motion tracking.

    PubMed

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

    2015-02-01

    Viscosity-an integral property of a liquid-is traditionally determined by mechanical instruments. The most pronounced disadvantage of such an approach is the requirement of a large sample volume, which poses a serious obstacle, particularly in biology and biophysics when working with limited samples. Scaling down the required volume by means of microviscometry based on tracking the Brownian motion of particles can provide a reasonable alternative. In this paper, we report a simple microviscometric approach which can be conducted with common laboratory equipment. The core of this approach consists in a freely available standalone script to process particle trajectory data based on a Newtonian model. In our study, this setup allowed the sample to be scaled down to 10 μl. The utility of the approach was demonstrated using model solutions of glycerine, hyaluronate, and mouse blood plasma. Therefore, this microviscometric approach based on a newly developed freely available script can be suggested for determination of the viscosity of small biological samples (e.g., body fluids). PMID:25725855

  20. 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).

  1. The Ring of Brownian Motion: the good, the bad and the simply silly

    NASA Astrophysics Data System (ADS)

    Hänggi, Peter

    2009-04-01

    In this plenary talk I give an account on the blossoming role that Brownian motion Theory and Experiment played—and still keeps doing so—in germinating and advancing several, partially diverse physical disciplines. Although the use of Brownian motion concepts generally most favorably impacted those scientific areas there are also some abuses where the application of such concepts may not describe satisfactorily physical reality.

  2. Theory of relativistic Brownian motion: the (1+1)-dimensional case.

    PubMed

    Dunkel, Jörn; Hänggi, Peter

    2005-01-01

    We construct a theory for the (1+1)-dimensional Brownian motion in a viscous medium, which is (i) consistent with Einstein's theory of special relativity and (ii) reduces to the standard Brownian motion in the Newtonian limit case. In the first part of this work the classical Langevin equations of motion, governing the nonrelativistic dynamics of a free Brownian particle in the presence of a heat bath (white noise), are generalized in the framework of special relativity. Subsequently, the corresponding relativistic Langevin equations are discussed in the context of the generalized Ito (prepoint discretization rule) versus the Stratonovich (midpoint discretization rule) dilemma: It is found that the relativistic Langevin equation in the Hänggi-Klimontovich interpretation (with the postpoint discretization rule) is the only one that yields agreement with the relativistic Maxwell distribution. Numerical results for the relativistic Langevin equation of a free Brownian particle are presented. PMID:15697675

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

    NASA Astrophysics Data System (ADS)

    Parrondo, J. M. R.; Dinís, Luis

    2004-02-01

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

  4. 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.

  5. 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

  6. The Chaotic Dynamics of Anomalous Dispersion as Modeled by a Nonstationary Extension of Brownian Motion

    NASA Astrophysics Data System (ADS)

    Cushman, J. H.; O'Malley, D.; Park, M.

    2009-04-01

    We construct a family of stochastic processes with independent, nonstationary increments and arbitrary, but apriori specified mean square displacement. The family of processes is shown to be an extension of Brownian motion. 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 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 FSLE of the extended Brownian processes and numerical examples presented. The construction of the extended Brownian processes illustrates that contrary to what has been stated in the literature, a power-law mean-square displacement is not related to a breakdown in the classical CLT.

  7. 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.

  8. 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.

  9. Microscopic theory of Brownian motion revisited: The Rayleigh model

    NASA Astrophysics Data System (ADS)

    Kim, Changho; Karniadakis, George Em

    2013-03-01

    We investigate three force autocorrelation functions , , and and the friction coefficient γ for the Rayleigh model (a massive particle in an ideal gas) by analytic methods and molecular-dynamics (MD) simulations. Here, F and F+ are the total force and the Mori fluctuating force, respectively, whereas F0 is the force on the Brownian particle under the frozen dynamics, where the Brownian particle is held fixed and the solvent particles move under the external potential due to the presence of the Brownian particle. By using ensemble averaging and the ray representation approach, we obtain two expressions for in terms of the one-particle trajectory and corresponding expressions for γ by the time integration of these expressions. Performing MD simulations of the near-Brownian-limit (NBL) regime, we investigate the convergence of and and compare them with . We show that for a purely repulsive potential between the Brownian particle and a solvent particle, both expressions for produce in the NBL regime. On the other hand, for a potential containing an attractive component, the ray representation expression produces only the contribution of the nontrapped solvent particles. However, we show that the net contribution of the trapped particles to γ disappears, and hence we confirm that both the ensemble-averaged expression and the ray representation expression for γ are valid even if the potential contains an attractive component. We also obtain a closed-form expression of γ for the square-well potential. Finally, we discuss theoretical and practical aspects for the evaluation of and γ.

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

    SciTech Connect

    Yu Hongwei; Chen Jun

    2004-12-15

    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.

  11. Observation of Brownian motion in liquids at short times: instantaneous velocity and memory loss.

    PubMed

    Kheifets, Simon; Simha, Akarsh; Melin, Kevin; Li, Tongcang; Raizen, Mark G

    2014-03-28

    Measurement of the instantaneous velocity of Brownian motion of suspended particles in liquid probes the microscopic foundations of statistical mechanics in soft condensed matter. However, instantaneous velocity has eluded experimental observation for more than a century since Einstein's prediction of the small length and time scales involved. We report shot-noise-limited, high-bandwidth measurements of Brownian motion of micrometer-sized beads suspended in water and acetone by an optical tweezer. We observe the hydrodynamic instantaneous velocity of Brownian motion in a liquid, which follows a modified energy equipartition theorem that accounts for the kinetic energy of the fluid displaced by the moving bead. We also observe an anticorrelated thermal force, which is conventionally assumed to be uncorrelated. PMID:24675957

  12. 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. PMID:24762409

  13. 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.

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

    PubMed

    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

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

    NASA Astrophysics Data System (ADS)

    Volpe, Giorgio; Volpe, Giovanni; Gigan, Sylvain

    2014-02-01

    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.

  16. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2013-09-01

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

  18. Quantum Brownian motion for periodic coupling to an Ohmic bath

    SciTech Connect

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

    2007-03-15

    We show theoretically how the periodic coupling between an engineered reservoir and a quantum Brownian particle leads to the formation of a dynamical steady-state which is characterized by an effective temperature above the temperature of the environment. The average steady-state energy of the system has a higher value than expected from the environmental properties. The system experiences repeatedly a non-Markovian behavior--as a consequence the corresponding effective decay for long evolution times is always on average stronger than the Markovian one. We also highlight the consequences of the scheme for the Zeno-anti-Zeno crossover which depends, in addition to the periodicity {tau}, also on the total evolution time of the system.

  19. 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.

  20. 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.

  1. 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.

  2. Theory of relativistic Brownian motion: the (1+3) -dimensional case.

    PubMed

    Dunkel, Jörn; Hänggi, Peter

    2005-09-01

    A theory for (1+3) -dimensional relativistic Brownian motion under the influence of external force fields is put forward. Starting out from a set of relativistically covariant, but multiplicative Langevin equations we describe the relativistic stochastic dynamics of a forced Brownian particle. The corresponding Fokker-Planck equations are studied in the laboratory frame coordinates. In particular, the stochastic integration prescription--i.e., the discretization rule dilemma--is elucidated (prepoint discretization rule versus midpoint discretization rule versus postpoint discretization rule). Remarkably, within our relativistic scheme we find that the postpoint rule (or the transport form) yields the only Fokker-Planck dynamics from which the relativistic Maxwell-Boltzmann statistics is recovered as the stationary solution. The relativistic velocity effects become distinctly more pronounced by going from one to three spatial dimensions. Moreover, we present numerical results for the asymptotic mean-square displacement of a free relativistic Brownian particle moving in 1+3 dimensions. PMID:16241514

  3. 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.

  4. 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. PMID:25196709

  5. 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.…

  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. 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.

  8. 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.

  9. Bragg scattering and Brownian motion dynamics in optically induced crystals of submicron particles.

    PubMed

    Sapiro, R E; Slama, B N; Raithel, G

    2013-05-01

    A set of four confocal laser beams of 1064-nm wavelength is used to prepare optically induced crystals of submicron particles in aqueous solution. Thousands of polystyrene spheres of about 200 nm in diameter are trapped in three dimensions. Bragg scattering patterns obtained with a probe beam of 532-nm wavelength are in agreement with the calculated lattice structure and its polarization dependence. The decay and rise of the Bragg scattering intensity upon switching the lattice off and on reveal the Brownian motion dynamics of the particles in the periodic optical trapping potential. Experimental results agree well with results from trajectory simulations based on the Langevin equation. The results exhibit the interplay between Brownian motion and deterministic forces in an inhomogeneous (near-)periodic optical trapping potential. PMID:23767544

  10. 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.

  11. Equation of motion using fractional calculus

    SciTech Connect

    Kihong, Kwon.

    1991-01-01

    One-dimensional motion of a particle was studied using fractional calculus, which is the differentiation and the integration of arbitrary order. By fractional differentiation, equation of motion could be written in compact form. Fractional parameters were numerically calculated by using the known solutions of general relativistic free fall motion. Also, from the approximate forms for fractional parameters, the physical meanings were found. The fractional parameters depended on the proper time, the mass of gravitating body, and the initial radial coordinate of the particle.

  12. Impulsion of induced magnetic field for Brownian motion of nanoparticles in peristalsis

    NASA Astrophysics Data System (ADS)

    Akbar, Noreen Sher; Raza, M.; Ellahi, R.

    2016-03-01

    In the present study, we examined the effect of induced magnetic field for the peristaltic flow of four different nanoparticles with the base fluid water in the presence of Brownian motion, in a vertical asymmetric channel. The mathematical formulation is presented. Exact solutions have been evaluated for the resulting equations. The obtained expressions for velocity, temperature, pressure gradient and magnetic force function are described through graphs for various pertinent parameters. The streamlines are drawn for some physical quantities to discuss the trapping phenomenon.

  13. Brownian Motion of Stiff Filaments in a Crowded Environment

    NASA Astrophysics Data System (ADS)

    Fakhri, Nikta; MacKintosh, Frederick C.; Lounis, Brahim; Cognet, Laurent; Pasquali, Matteo

    2010-12-01

    The thermal motion of stiff filaments in a crowded environment is highly constrained and anisotropic; it underlies the behavior of such disparate systems as polymer materials, nanocomposites, and the cell cytoskeleton. Despite decades of theoretical study, the fundamental dynamics of such systems remains a mystery. Using near-infrared video microscopy, we studied the thermal diffusion of individual single-walled carbon nanotubes (SWNTs) confined in porous agarose networks. We found that even a small bending flexibility of SWNTs strongly enhances their motion: The rotational diffusion constant is proportional to the filament-bending compliance and is independent of the network pore size. The interplay between crowding and thermal bending implies that the notion of a filament’s stiffness depends on its confinement. Moreover, the mobility of SWNTs and other inclusions can be controlled by tailoring their stiffness.

  14. 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.

  15. Vacuum fluctuations and Brownian motion of a charged test particle near a reflecting boundary

    SciTech Connect

    Yu Hongwei; Ford, L. H.

    2004-09-15

    We study the Brownian motion of a charged test particle coupled to electromagnetic vacuum fluctuations near a perfectly reflecting plane boundary. The presence of the boundary modifies the quantum fluctuations of the electric field, which in turn modifies the motion of the test particle. We calculate the resulting mean squared fluctuations in the velocity and position of the test particle. In the case of directions transverse to the boundary, the results are negative. This can be interpreted as reducing the quantum uncertainty which would otherwise be present.

  16. 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

  17. 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

  18. Quantum Brownian motion on potential surfaces coupled via tunneling in an external electric field[-2mm

    NASA Astrophysics Data System (ADS)

    Thrapsaniotis, E. G.

    2001-07-01

    The present paper deals with the motion of a Brownian particle on two identical but shifted potential surfaces, coupled via a tunneling matrix element in an external electric field. Dissipation is induced by a heat bath represented by an infinite set of harmonic oscillators with a continuum range of frequencies. We derive a perturbative solution for the quantum coherence term of the particle system after performing a small-polaron-like transformation. This is subsequently necessary for the extraction of an equation that describes the reduced dynamics and the minimal action path of the Brownian particle. Finally we extract expressions for the population relaxation rate and the pure quantum-dephasing rate of the two-level system.

  19. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2014-12-01

    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.

  1. 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.

  2. 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.

    2016-06-01

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

  3. 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.

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

    NASA Astrophysics Data System (ADS)

    Pomeau, Yves

    2013-12-01

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

  5. Brownian motion in a rotating fluid: Diffusivity is a function of the rotation rate

    NASA Astrophysics Data System (ADS)

    Ryskin, Gregory

    1988-09-01

    The phenomenological relations between thermodynamic fluxes and forces are normally assumed to be invariant with respect to arbitrary motion of the frame of reference. We describe a breakdown of this invariance strong enough to be observable. It is shown that the diffusivity in a rotating fluid is anisotropic and also smaller in magnitude than in a fluid at rest in an inertial frame, giving rise to a diffusion analog of the Hall effect. For large Brownian particles (e.g., biological macromolecules) the diffusivity may decrease by 50% at the rotation speeds achievable in ultracentrifuges.

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

    NASA Astrophysics Data System (ADS)

    Okabe, Yasunori

    1986-12-01

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

  7. Second-order stochastic leapfrog algorithm for multiplicative noise brownian motion

    PubMed

    Qiang; Habib

    2000-11-01

    A stochastic leapfrog algorithm for the numerical integration of Brownian motion stochastic differential equations with multiplicative noise is proposed and tested. The algorithm has a second-order convergence of moments in a finite time interval and requires the sampling of only one uniformly distributed random variable per time step. The noise may be white or colored. We apply the algorithm to a study of the approach towards equilibrium of an oscillator coupled nonlinearly to a heat bath and investigate the effect of the multiplicative noise (arising from the nonlinear coupling) on the relaxation time. This allows us to test the regime of validity of the energy-envelope approximation method. PMID:11102105

  8. Second-order stochastic leapfrog algorithm for multiplicative noise Brownian motion

    NASA Astrophysics Data System (ADS)

    Qiang, Ji; Habib, Salman

    2000-11-01

    A stochastic leapfrog algorithm for the numerical integration of Brownian motion stochastic differential equations with multiplicative noise is proposed and tested. The algorithm has a second-order convergence of moments in a finite time interval and requires the sampling of only one uniformly distributed random variable per time step. The noise may be white or colored. We apply the algorithm to a study of the approach towards equilibrium of an oscillator coupled nonlinearly to a heat bath and investigate the effect of the multiplicative noise (arising from the nonlinear coupling) on the relaxation time. This allows us to test the regime of validity of the energy-envelope approximation method.

  9. Convolutionless Non-Markovian master equations and quantum trajectories: Brownian motion

    SciTech Connect

    Strunz, Walter T.; Yu Ting

    2004-05-01

    Stochastic Schroedinger equations for quantum trajectories offer an alternative and sometimes superior approach to the study of open quantum system dynamics. Here we show that recently established convolutionless non-Markovian stochastic Schroedinger equations may serve as a powerful tool for the derivation of convolutionless master equations for non-Markovian open quantum systems. The most interesting example is quantum Brownian motion (QBM) of a harmonic oscillator coupled to a heat bath of oscillators, one of the most employed exactly soluble models of open system dynamics. We show explicitly how to establish the direct connection between the exact convolutionless master equation of QBM and the corresponding convolutionless exact stochastic Schroedinger equation.

  10. 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.

  11. New stochastic equation for a harmonic oscillator: Brownian motion with adhesion

    NASA Astrophysics Data System (ADS)

    Gitterman, M.

    2010-11-01

    In addition to the usually considered stochastic harmonic oscillator with an external random force (Brownian motion) or with random frequency and random damping, we consider an oscillator with a random mass for which the particles of the surrounding medium adhere to the oscillator for some (random) time after the collision, thereby changing the oscillator mass. We have calculated the first two moments and the Lyapunov exponent, which describes the stability of the fixed point. This model can be useful for the analysis of chemical and biological solutions as well as for nano-technological devices.

  12. Direct measurements of magnetic interaction-induced cross-correlations of two microparticles in Brownian motion

    PubMed Central

    Romodina, Maria N.; Khokhlova, Maria D.; Lyubin, Evgeny V.; Fedyanin, Andrey A.

    2015-01-01

    The effect of magnetic interactions on the Brownian motion of two magnetic microparticles is investigated. The cross-correlations of the thermal fluctuations of the two magnetic microbeads are directly measured using double-trap optical tweezers. It is experimentally demonstrated that the cross-correlation function is governed by the gradient of the magnetic force between the microparticles. The magnetic forces are measured with femtonewton precision, and the magnetic dipole moments of individual microparticles are determined within an accuracy on the order of fA-m2. PMID:26035153

  13. Emergence of Collective Motion in a Model of Interacting Brownian Particles

    NASA Astrophysics Data System (ADS)

    Dossetti, Victor; Sevilla, Francisco J.

    2015-07-01

    By studying a system of Brownian particles that interact among themselves only through a local velocity-alignment force that does not affect their speed, we show that self-propulsion is not a necessary feature for the flocking transition to take place as long as underdamped particle dynamics can be guaranteed. Moreover, the system transits from stationary phases close to thermal equilibrium, with no net flux of particles, to far-from-equilibrium ones exhibiting collective motion, phase coexistence, long-range order, and giant number fluctuations, features typically associated with ordered phases of models where self-propelled particles with overdamped dynamics are considered.

  14. Emergence of Collective Motion in a Model of Interacting Brownian Particles.

    PubMed

    Dossetti, Victor; Sevilla, Francisco J

    2015-07-31

    By studying a system of Brownian particles that interact among themselves only through a local velocity-alignment force that does not affect their speed, we show that self-propulsion is not a necessary feature for the flocking transition to take place as long as underdamped particle dynamics can be guaranteed. Moreover, the system transits from stationary phases close to thermal equilibrium, with no net flux of particles, to far-from-equilibrium ones exhibiting collective motion, phase coexistence, long-range order, and giant number fluctuations, features typically associated with ordered phases of models where self-propelled particles with overdamped dynamics are considered. PMID:26274444

  15. Existence of Solutions for Stochastic Differential Equations under G-Brownian Motion with Discontinuous Coefficients

    NASA Astrophysics Data System (ADS)

    Faizullah, Faiz

    2012-12-01

    The existence theory for the vector valued stochastic differential equations under G-Brownian motion (G-SDEs) of the type Xt = X0+ ∫to(v;Xv)dv+ ∫t0 g(v;Xv)d(B)v+ ∫t0 h(v;Xv)dBv; t ɛ [0;T]; with first two discontinuous coefficients is established. It is shown that the G-SDEs have more than one solution if the coefficient g or the coefficients f and g simultaneously, are discontinuous functions. The upper and lower solutions method is used and examples are given to explain the theory and its importance.

  16. Quantum noise in the position measurement of a cavity mirror undergoing Brownian motion

    NASA Astrophysics Data System (ADS)

    Jacobs, K.; Tittonen, I.; Wiseman, H. M.; Schiller, S.

    1999-07-01

    We perform a quantum theoretical calculation of the noise power spectrum for a phase measurement of the light output from a coherently driven optical cavity with a freely moving rear mirror. We examine how the noise resulting from the quantum back action appears among the various contributions from other noise sources. We do not assume an ideal (homodyne) phase measurement, but rather consider phase-modulation detection, which we show has a different shot noise level. We also take into account the effects of thermal damping of the mirror, losses within the cavity, and classical laser noise. We relate our theoretical results to experimental parameters, so as to make direct comparisons with current experiments simple. We also show that in this situation, the standard Brownian motion master equation is inadequate for describing the thermal damping of the mirror, as it produces a spurious term in the steady-state phase-fluctuation spectrum. The corrected Brownian motion master equation [L. Diosi, Europhys. Lett. 22, 1 (1993)] rectifies this inadequacy.

  17. 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

  18. 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. PMID:24593372

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

    NASA Astrophysics Data System (ADS)

    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.

  20. 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. PMID:27176286

  1. 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.

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

    PubMed

    Grimm, Matthias; Franosch, Thomas; Jeney, Sylvia

    2012-08-01

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

  3. 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

    2016-01-01

    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

  4. 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. PMID:27212639

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

    NASA Astrophysics Data System (ADS)

    Daddi-Moussa-Ider, Abdallah; Guckenberger, Achim; Gekle, Stephan

    2016-07-01

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

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

    NASA Astrophysics Data System (ADS)

    Yeh, L.

    1993-06-01

    After extensive investigations over three decades, the linear-coupling model and its equivalents have become the standard microscopic models for quantum harmonic Brownian motion, in which a harmonically bound Brownian particle is coupled to a quantum dissipative heat bath of general type modeled by infinitely many harmonic oscillators. The dynamics of these models have been studied by many authors using the quantum Langevin equation, the path-integral approach, quasi-probability distribution functions (e.g., the Wigner function), etc. However, the quantum Langevin equation is only applicable to some special problems, while other approaches all involve complicated calculations due to the inevitable reduction (i.e., contraction) operation for ignoring/eliminating the degrees of freedom of the heat bath. In this dissertation, the author proposes an improved methodology via a modified phase-space approach which employs the characteristic function (the symplectic Fourier transform of the Wigner function) as the representative of the density operator. This representative is claimed to be the most natural one for performing the reduction, not only because of its simplicity but also because of its manifestation of geometric meaning. Accordingly, it is particularly convenient for studying the time evolution of the Brownian particle with an arbitrary initial state. The power of this characteristic function is illuminated through a detailed study of several physically interesting problems, including the environment-induced damping of quantum interference, the exact quantum Fokker-Planck equations, and the relaxation of non-factorizable initial states. All derivations and calculations are 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.

  7. Quantum Harmonic Brownian Motion in a General Environment: a Modified Phase-Space Approach.

    NASA Astrophysics Data System (ADS)

    Yeh, Leehwa

    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, I propose 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 are 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. With the help of this theorem, the mechanism of this model is examined and the

  8. 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.

  9. Non-intersecting Brownian motions leaving from and going to several points

    NASA Astrophysics Data System (ADS)

    Adler, Mark; van Moerbeke, Pierre; Vanderstichelen, Didier

    2012-03-01

    Consider n non-intersecting Brownian motions on R, depending on time t∈[0,1], with mi particles forced to leave from ai at time t=0, 1≤i≤q, and nj particles forced to end up at bj at time t=1, 1≤j≤p. For arbitrary p and q, it is not known if the distribution of the positions of the non-intersecting Brownian particles at a given time 0

  10. Study of constrained Brownian motion of nanoparticles near an interface using optical tweezers

    NASA Astrophysics Data System (ADS)

    Yang, Hui; Cornaglia, Matteo; Trouillon, Raphaël.; Lehnert, Thomas; Gijs, Martin A. M.

    2015-03-01

    We demonstrate a method to determine the Brownian motion and the diffusion coefficient of a nanoparticle in water in a plane that is parallel to a solid boundary and as function of the distance normal to that boundary by using an optical tweezers instrument. A solution of 190 nm-diameter fluorescent polystyrene nanoparticles in de-ionized (DI) water is introduced in a micro-chamber built from two thin glass substrates. A single particle is trapped by the tweezers and optically moved in the z-direction normal to a substrate. By analyzing a scatter plot of the time-dependent positions of the nanoparticle in the x-y plane in a histogram, the diffusion coefficient parallel to the substrate of the Brownian particle constrained by the substrate is determined as a function of the distance between the substrate and the nanoparticle. The experimental results indicate the increased drag effect on the nanoparticle when it is close to the substrate, as evidenced by an experimental diffusion coefficient nearby the substrate that is about half of that of the particle in the bulk fluid.

  11. 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. PMID:25768490

  12. Quantal Brownian motion from second RPA dynamics at finite temperature: Explicit density operator and related quantities

    NASA Astrophysics Data System (ADS)

    Jang, S.

    1991-07-01

    Within the framework of the quantum dynamical description of Brownian motion, a closed expression for the density operator is extracted from the master equation based on the dynamics of the second random phase approximation (RPA) at finite temperature. The second RPA theory is an extension of the usual RPA theory up to next higher order. The entropy and effective temperature of the system of collective RPA phonons are subsequently calculated by exploiting the analogy with the quantum optics damped oscillator, and their temporal behavior is surveyed by showing how these quantities relax to their equilibrium values. The calculation is carried out without invoking the so-called the resonant approximation, which amounts to ignoring the rapidly oscillating coupling terms. Particular attention is paid to the effect of these coupling terms.

  13. On the Mössbauer studies of harmonically bound quantum oscillators in Brownian motion

    NASA Astrophysics Data System (ADS)

    Razdan, A.

    1999-03-01

    In many biological systems like whole cells, membranes or proteins and some of the polymeric systems, dynamics reveals itself in Mössbauer spectra as a non Lorentzian behaviour above some particular temperature which is characteristic of the system. Moreover mean square displacement and line width show temperature dependence above the characteristic temperature. Brownian motion of harmonically bound oscillator has been able to explain the non-Lorentzian behaviour. In the present paper, a quantum picture of the above model is discussed and lineshape is expressed as the closed form for the extreme overdamping case. In addition to the non-Lorentzian behaviour, the present model also predicts a temperature dependence of mean square displacement and linewidth.

  14. Active and passive Brownian motion of charged particles in two-dimensional plasma models

    SciTech Connect

    Dunkel, Joern; Ebeling, Werner; Trigger, Sergey A.

    2004-10-01

    The dynamics of charged Coulomb grains in a plasma is numerically and analytically investigated. Analogous to recent experiments, it is assumed that the grains are trapped in an external parabolic field. Our simulations are based on a Langevin model, where the grain-plasma interaction is realized by a velocity-dependent friction coefficient and a velocity-independent diffusion coefficient. In addition to the ordinary case of positive (passive) friction between grains and plasma, we also discuss the effects of negative (active) friction. The latter case seems particularly interesting, since recent analytical calculations have shown that friction coefficients with negative parts may appear in some models of ion absorption by grains as well as in models of ion-grain scattering. Such negative friction may cause active Brownian motions of the grains. As our computer simulations show, the influence of negative friction leads to the formation of various stationary modes (rotations, oscillations), which, to some extent, can also be estimated analytically.

  15. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-08-01

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

  17. 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.

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

    PubMed

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

    2016-07-11

    The nondeterministic property of the optoelectronic random bit generator (RBG) based on laser chaos are experimentally analyzed from two aspects of the central limit theorem and law of iterated logarithm. The random bits are extracted from an optical feedback chaotic laser diode using a multi-bit extraction technique in the electrical domain. Our experimental results demonstrate that the generated random bits have no statistical distance from the Brownian motion, besides that they can pass the state-of-the-art industry-benchmark statistical test suite (NIST SP800-22). All of them give a mathematically provable evidence that the ultrafast random bit generator based on laser chaos can be used as a nondeterministic random bit source. PMID:27410852

  19. 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.

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

    PubMed

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

    2016-02-01

    We present a theoretical treatment of overdamped Brownian motion on a time-independent bichromatic periodic potential with spatially fast- and slow-changing components. In our approach, we generalize the Wannier basis commonly used in the analysis of periodic systems to define a basis of S states that are localized at local minima of the potential. We demonstrate that the S states are orthonormal and complete on the length scale of the periodicity of the fast-changing potential, and we use the S-state basis to transform the continuous Smoluchowski equation for the system to a discrete master equation describing hopping between local minima. We identify the parameter regime where the master equation description is valid and show that the interwell hopping rates are well approximated by Kramers' escape rate in the limit of deep potential minima. Finally, we use the master equation to explore the system dynamics and determine the drift and diffusion for the system. PMID:26986305

  1. Using Brownian motion to measure shape asymmetry in mesoscopic matter using optical tweezers.

    PubMed

    Roy, Basudev; Mondal, Argha; Bera, Sudipta K; Banerjee, Ayan

    2016-06-21

    We propose a new method for quantifying shape asymmetry on the mesoscopic scale. The method takes advantage of the intrinsic coupling between rotational and translational Brownian motion (RBM and TBM, respectively) which happens in the case of asymmetric particles. We determine the coupling by measuring different correlation functions of the RBM and TBM for single, morphologically different, weakly trapped red blood cells in optical tweezers. The cells have different degrees of asymmetry that are controllably produced by varying the hypertonicity of their aqueous environment. We demonstrate a clear difference in the nature of the correlation functions both qualitatively and quantitatively for three types of cells having a varying degree of asymmetry. This method can have a variety of applications ranging from early stage disease diagnosis to quality control in microfabrication. PMID:27198612

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

    PubMed

    Berry, Hugues; Chaté, Hugues

    2014-02-01

    In vivo measurements of the passive movements of biomolecules or vesicles in cells consistently report "anomalous diffusion," where mean-squared displacements scale as a power law of time with exponent α<1 (subdiffusion). While the detailed mechanisms causing such behaviors are not always elucidated, movement hindrance by obstacles is often invoked. However, our understanding of how hindered diffusion leads to subdiffusion is based on diffusion amidst randomly located immobile obstacles. Here, we have used Monte Carlo simulations to investigate transient subdiffusion due to mobile obstacles with various modes of mobility. Our simulations confirm that the anomalous regimes rapidly disappear when the obstacles move by Brownian motion. By contrast, mobile obstacles with more confined displacements, e.g., Orstein-Ulhenbeck motion, are shown to preserve subdiffusive regimes. The mean-squared displacement of tracked protein displays convincing power laws with anomalous exponent α that varies with the density of Orstein-Ulhenbeck (OU) obstacles or the relaxation time scale of the OU process. In particular, some of the values we observed are significantly below the universal value predicted for immobile obstacles in two dimensions. Therefore, our results show that subdiffusion due to mobile obstacles with OU type of motion may account for the large variation range exhibited by experimental measurements in living cells and may explain that some experimental estimates are below the universal value predicted for immobile obstacles. PMID:25353510

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

    NASA Astrophysics Data System (ADS)

    Berry, Hugues; Chaté, Hugues

    2014-02-01

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

  4. Microscopic Description of Resonance in the Brownian Motion of Hydrophobic Nanoparticle in Harmonic Potential Trap

    NASA Astrophysics Data System (ADS)

    Park, Jae Hyun

    2014-11-01

    Harmonic potential has been popular for the trapping of micro- and nanoparticles (e.g. optical tweezer). With the rapid development of harmonic potential trapping technology, its application is nowadays being extended to explore the fundamental nature in the random thermal fluctuation of particles in order to confirm the classical theory of Brownian motion. In this study, using extensive molecular dynamics simulations, we investigate the molecule-level features of dynamic response of hydrophobic C60 nanoparticle in harmonic potential trap with water medium. The time-averaged magnitudes of random fluctuation are measured for various trap stiffness and then the virtual mass, the amount of fluid moving together with particle, is extracted from curve fitting. The fluctuation is proportional to the inverse of trap stiffness. The virtual mass is mostly originated from the first hydration shell around the particle and it is not influenced by the stiffness. The resonance in frequency domain is observed as a result of coloured noise in the motion. The effect of stiffness on the resonance is weaker than that on the magnitude of fluctuation because the motion of particle is partially dissipated in the RDF valley between the first and the second hydration shell. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2012R1A1A1042920).

  5. 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. PMID:26103047

  6. 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

  7. 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.

  8. 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

  9. 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…

  10. Noise-enhanced stability and double stochastic resonance of active Brownian motion

    NASA Astrophysics Data System (ADS)

    Zeng, Chunhua; Zhang, Chun; Zeng, Jiakui; Liu, Ruifen; Wang, Hua

    2015-08-01

    In this paper, we study the transient and resonant properties of active Brownian particles (ABPs) in the Rayleigh-Helmholtz (RH) and Schweitzer-Ebeling-Tilch (SET) models, which is driven by the simultaneous action of multiplicative and additive noise and periodic forcing. It is shown that the cross-correlation between two noises (λ) can break the symmetry of the potential to generate motion of the ABPs. In case of no correlation between two noises, the mean first passage time (MFPT) is a monotonic decrease depending on the multiplicative noise, however in case of correlation between two noises, the MFPT exhibits a maximum, depending on the multiplicative noise for both models, this maximum for MFPT identifies the noise-enhanced stability (NES) effect of the ABPs. By comparing with case of no correlation (λ =0.0 ), we find two maxima in the signal-to-noise ratio (SNR) depending on the cross-correlation intensity, i.e. the double stochastic resonance is shown in both models. For the RH model, the SNR exhibits two maxima depending on the multiplicative noise for small cross-correlation intensity, while in the SET model, it exhibits only a maximum depending on the multiplicative noise. Whether λ =0.0 or not, the MFPT is a monotonic decrease, and the SNR exhibits a maximum, depending on the additive noise in both models.

  11. 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.

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

    PubMed

    Elamin, Khalid; Swenson, Jan

    2015-03-01

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

  13. Brownian-motion based simulation of stochastic reaction-diffusion systems for affinity based sensors

    NASA Astrophysics Data System (ADS)

    Tulzer, Gerhard; Heitzinger, Clemens

    2016-04-01

    In this work, we develop a 2D algorithm for stochastic reaction-diffusion systems describing the binding and unbinding of target molecules at the surfaces of affinity-based sensors. In particular, we simulate the detection of DNA oligomers using silicon-nanowire field-effect biosensors. Since these devices are uniform along the nanowire, two dimensions are sufficient to capture the kinetic effects features. The model combines a stochastic ordinary differential equation for the binding and unbinding of target molecules as well as a diffusion equation for their transport in the liquid. A Brownian-motion based algorithm simulates the diffusion process, which is linked to a stochastic-simulation algorithm for association at and dissociation from the surface. The simulation data show that the shape of the cross section of the sensor yields areas with significantly different target-molecule coverage. Different initial conditions are investigated as well in order to aid rational sensor design. A comparison of the association/hybridization behavior for different receptor densities allows optimization of the functionalization setup depending on the target-molecule density.

  14. Brownian-motion based simulation of stochastic reaction-diffusion systems for affinity based sensors.

    PubMed

    Tulzer, Gerhard; Heitzinger, Clemens

    2016-04-22

    In this work, we develop a 2D algorithm for stochastic reaction-diffusion systems describing the binding and unbinding of target molecules at the surfaces of affinity-based sensors. In particular, we simulate the detection of DNA oligomers using silicon-nanowire field-effect biosensors. Since these devices are uniform along the nanowire, two dimensions are sufficient to capture the kinetic effects features. The model combines a stochastic ordinary differential equation for the binding and unbinding of target molecules as well as a diffusion equation for their transport in the liquid. A Brownian-motion based algorithm simulates the diffusion process, which is linked to a stochastic-simulation algorithm for association at and dissociation from the surface. The simulation data show that the shape of the cross section of the sensor yields areas with significantly different target-molecule coverage. Different initial conditions are investigated as well in order to aid rational sensor design. A comparison of the association/hybridization behavior for different receptor densities allows optimization of the functionalization setup depending on the target-molecule density. PMID:26939610

  15. Analysis of functional motions in Brownian molecular machines with an efficient block normal mode approach: myosin-II and Ca2+ -ATPase.

    PubMed

    Li, Guohui; Cui, Qiang

    2004-02-01

    The structural flexibilities of two molecular machines, myosin and Ca(2+)-ATPase, have been analyzed with normal mode analysis and discussed in the context of their energy conversion functions. The normal mode analysis with physical intermolecular interactions was made possible by an improved implementation of the block normal mode (BNM) approach. The BNM results clearly illustrated that the large-scale conformational transitions implicated in the functional cycles of the two motor systems can be largely captured with a small number of low-frequency normal modes. Therefore, the results support the idea that structural flexibility is an essential part of the construction principle of molecular motors through evolution. Such a feature is expected to be more prevalent in motor proteins than in simpler systems (e.g., signal transduction proteins) because in the former, large-scale conformational transitions often have to occur before the chemical events (e.g., ATP hydrolysis in myosin and ATP binding/phosphorylation in Ca(2+)-ATPase). This highlights the importance of Brownian motions associated with the protein domains that are involved in the functional transitions; in this sense, Brownian molecular machines is an appropriate description of molecular motors, although the normal mode results do not address the origin of the ratchet effect. The results also suggest that it might be more appropriate to describe functional transitions in some molecular motors as intrinsic elastic motions modulating local structural changes in the active site, which in turn gets stabilized by the subsequent chemical events, in contrast with the conventional idea of local changes somehow getting amplified into larger-scale motions. In the case of myosin, for example, we favor the idea that Brownian motions associated with the flexible converter propagates to the Switch I/II region, where the salt-bridge formation gets stabilized by ATP hydrolysis, in contrast with the textbook notion that

  16. 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.

  17. 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

  18. 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

  19. Modeling subject-specific phase-dependent effects and variations in longitudinal responses via a geometric Brownian motion process.

    PubMed

    Zhu, Li; Hsieh, Fushing; Li, Juan; Chi, Eric

    2011-08-30

    We address statistical issues regarding modeling a collection of longitudinal response trajectories characterized by the presence of subject-specific phase-dependent effects and variation. To accommodate these two time-varying individual characteristics, we employ a geometric stochastic differential equation for modeling based on a Brownian motion process and develop a two-step paradigm for statistical analysis. This paradigm reverses the order of statistical inference in random effects model. We first extract individual information about phase-dependent treatment effects and volatility parameters for all subjects. Then, we derive the association relationship between the parameters characterizing the individual longitudinal trajectories and the corresponding covariates by means of multiple regression analysis. The stochastic differential equation model and the two-step paradigm together provide significant advantages both in modeling flexibility and in computational efficiency. The modeling flexibility is due to the easy adaptation of temporal change points for subject-specific phase transition in treatment effects, whereas the computational efficiency benefits in part from the independent increment property of Brownian motion that avoids high-dimensional integration. We demonstrate our modeling approach and statistical analysis on a real data set of longitudinal measurements of disease activity scores from a rheumatoid arthritis study. PMID:21751228

  20. 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

    2016-01-01

    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

  1. 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.

  2. 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.

  3. 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. PMID:26395697

  4. 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

    SciTech Connect

    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{sup 2}/2+bx{sup 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.

  5. 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.

  6. Construction of a free Lévy process as high-dimensional limit of a Brownian motion on the unitary group

    NASA Astrophysics Data System (ADS)

    Ulrich, Michaël

    2015-08-01

    It is well known that freeness appears in the high-dimensional limit of independence for matrices. Thus, for instance, the additive free Brownian motion can be seen as the limit of the Brownian motion on hermitian matrices. More generally, it is quite natural to try to build free Lévy processes as high-dimensional limits of classical matricial Lévy processes. We will focus here on one specific such construction, discussing and generalizing the work done previously by Biane in Ref.2, who has shown that the (classical) Brownian motion on the Unitary group U(d) converges to the free multiplicative Brownian motion when d goes to infinity. We shall first recall that result and give an alternative proof for it. We shall then see how this proof can be adapted in a more general context in order to get a free Lévy process on the dual group (in the sense of Voiculescu) U. This result will actually amount to a truly noncommutative limit theorem for classical random variables, of which Biane's result constitutes the case n = 1.

  7. 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.

  8. 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.

  9. 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. PMID:21517377

  10. 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.

  11. Brownian regime of finite-N corrections to particle motion in the XY Hamiltonian mean field model

    NASA Astrophysics Data System (ADS)

    Ribeiro, Bruno V.; Amato, Marco A.; Elskens, Yves

    2016-08-01

    We study the dynamics of the N-particle system evolving in the XY Hamiltonian mean field (HMF) model for a repulsive potential, when no phase transition occurs. Starting from a homogeneous distribution, particles evolve in a mean field created by the interaction with all others. This interaction does not change the homogeneous state of the system, and particle motion is approximately ballistic with small corrections. For initial particle data approaching a waterbag, it is explicitly proved that corrections to the ballistic velocities are in the form of independent Brownian noises over a time scale diverging not slower than {N}2/5 as N\\to ∞ , which proves the propagation of molecular chaos. Molecular dynamics simulations of the XY-HMF model confirm our analytical findings.

  12. Imaging and quantifying Brownian motion of micro- and nanoparticles using phase-resolved Doppler variance optical coherence tomography.

    PubMed

    Kim, Chang Soo; Qi, Wenjuan; Zhang, Jun; Kwon, Young Jik; Chen, Zhongping

    2013-03-01

    Different types and sizes of micro- and nanoparticles have been synthesized and developed for numerous applications. It is crucial to characterize the particle sizes. Traditional dynamic light scattering, a predominant method used to characterize particle size, is unable to provide depth resolved information or imaging functions. Doppler variance optical coherence tomography (OCT) measures the spectral bandwidth of the Doppler frequency shift due to the Brownian motion of the particles utilizing the phase-resolved approach and can provide quantitative information about particle size. Spectral bandwidths of Doppler frequency shifts for various sized particles were quantified and were demonstrated to be inversely proportional to the diameter of the particles. The study demonstrates the phase-resolved Doppler variance spectral domain OCT technique has the potential to be used to investigate the properties of particles in highly scattering media. PMID:23515863

  13. 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

  14. Brownian motion and quantum dynamics of magnetic monopoles in spin ice

    PubMed Central

    Bovo, L.; Bloxsom, J.A.; Prabhakaran, D.; Aeppli, G.; Bramwell, S.T.

    2013-01-01

    Spin ice illustrates many unusual magnetic properties, including zero point entropy, emergent monopoles and a quasi liquid–gas transition. To reveal the quantum spin dynamics that underpin these phenomena is an experimental challenge. Here we show how crucial information is contained in the frequency dependence of the magnetic susceptibility and in its high frequency or adiabatic limit. The typical response of Dy2Ti2O7 spin ice indicates that monopole diffusion is Brownian but is underpinned by spin tunnelling and is influenced by collective monopole interactions. The adiabatic response reveals evidence of driven monopole plasma oscillations in weak applied field, and unconventional critical behaviour in strong applied field. Our results clarify the origin of the relatively high frequency response in spin ice. They disclose unexpected physics and establish adiabatic susceptibility as a revealing characteristic of exotic spin systems. PMID:23443563

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

    PubMed

    Durang, Xavier; Kwon, Chulan; Park, Hyunggyu

    2015-06-01

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

  16. 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. PMID:26066173

  17. 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.

  18. Active Brownian motion of emulsion droplets: Coarsening dynamics at the interface and rotational diffusion.

    PubMed

    Schmitt, M; Stark, H

    2016-08-01

    A micron-sized droplet of bromine water immersed in a surfactant-laden oil phase can swim (S. Thutupalli, R. Seemann, S. Herminghaus, New J. Phys. 13 073021 (2011). The bromine reacts with the surfactant at the droplet interface and generates a surfactant mixture. It can spontaneously phase-separate due to solutocapillary Marangoni flow, which propels the droplet. We model the system by a diffusion-advection-reaction equation for the mixture order parameter at the interface including thermal noise and couple it to fluid flow. Going beyond previous work, we illustrate the coarsening dynamics of the surfactant mixture towards phase separation in the axisymmetric swimming state. Coarsening proceeds in two steps: an initially slow growth of domain size followed by a nearly ballistic regime. On larger time scales thermal fluctuations in the local surfactant composition initiates random changes in the swimming direction and the droplet performs a persistent random walk, as observed in experiments. Numerical solutions show that the rotational correlation time scales with the square of the inverse noise strength. We confirm this scaling by a perturbation theory for the fluctuations in the mixture order parameter and thereby identify the active emulsion droplet as an active Brownian particle. PMID:27562831

  19. 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.

  20. 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.

  1. 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. PMID:23547225

  2. 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.

  3. A proof for insignificant effect of Brownian motion-induced micro-convection on thermal conductivity of nanofluids by utilizing molecular dynamics simulations

    NASA Astrophysics Data System (ADS)

    Babaei, Hasan; Keblinski, Pawel; Khodadadi, J. M.

    2013-02-01

    It has been recently demonstrated through experiments that the observed high enhancements in thermal conductivity of nanofluids are due to aggregation of nanoparticles rather than the previously stated mechanism of the Brownian motion-induced micro-convection. In this paper, we use equilibrium molecular dynamics simulations to investigate the role of micro-convection on the thermal conductivity of well-dispersed nanofluids. We show that while the individual terms in the heat current autocorrelation function associated with nanoparticle diffusion achieve significant values, these terms essentially cancel each other if correctly defined average enthalpy expressions are subtracted. Otherwise, erroneous thermal conductivity enhancements will be predicted, which are attributed to Brownian motion-induced micro-convection. Consequently, micro-convection does not contribute noticeably to the thermal conductivity and the predicted thermal conductivity enhancements are consistent with the effective medium theory.

  4. Computation of the dynamic thermal properties of a three-dimensional unit cell of porous media by Brownian motion simulation

    NASA Astrophysics Data System (ADS)

    Perrot, Camille; Olny, Xavier; Panneton, Raymond; Bouchard, Richard

    2001-05-01

    Acoustic dissipation in porous media is mainly due to viscous and thermal mechanisms that occur in the pores of the microstructure. The purpose of this study is the determination of the macroscopic dynamic acoustic bulk modulus and thermal permeability of real foams from a local scale approach. To achieve this goal, two distinct steps are followed. First, the local geometry of a real foam is obtained using computed microtomography (μCT), then a periodic and regularly paving space tetrakaidecahedron cell is identified from the microstructure. Second, the heat equation is solved for the geometrical model. The paper provides a three-dimensional application of the efficient simulation technique of Brownian motion proposed by Torquato et al. for steady state diffusion-controlled problems [Appl. Phys. Lett. 55, 1847-1849 (1989)] and adapted by Lafarge [Poromechanics II, 708 (2002)] in a bi-dimensional case. The influence of the model's microstructural details (anisotropy, and struts junction and cross-section) on the macroscopic properties are studied. The predictions of the macroscopic properties using this local scale approach are then compared to experimental measurements.

  5. 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. PMID:22320218

  6. 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

  7. Tempered fractional calculus

    NASA Astrophysics Data System (ADS)

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

    2015-07-01

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

  8. 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.

  9. 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.

  10. One-dimensional Brownian motion in hard rods: The adiabatic piston problem

    NASA Astrophysics Data System (ADS)

    Ebrahim Foulaadvand, M.; Shafiee, M. Mehdi

    2013-11-01

    We have investigated the motion characteristics of a movable piston immersed in a one-dimensional gas of hard rods by event-oriented molecular dynamics in the absence of thermal noise. Periodic and reflecting boundary conditions are explored. It is shown that the piston undergoes systematic oscillations with decaying amplitudes in short times before it comes to global thermodynamic equilibrium. Moreover, the diffusion of the piston is explored and analytical expressions for its equilibrium mean-squared displacement (MSD) are obtained. It is shown that the MSD of the piston does not differ much from the normal rods despite its mass and length are significantly larger.

  11. 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.

  12. 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

  13. 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.

  14. 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

  15. 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}> .

  16. 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 Central

    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. PMID:26309390

  17. 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.

  18. 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).

  19. Dynamical universality class of Brownian motion and exact results for a single-impurity s=1/2 XY chain

    NASA Astrophysics Data System (ADS)

    Sen, Surajit

    1996-03-01

    Relaxation phenomena in a class of nondissipative systems with two highly disparate time scales (i.e., Brownian systems) have unique commonalities quantifiable via two scalars. It is shown that the exactly solvable problem of the dynamics of a weakly linked impurity spin in a s=1/2 XY chain belongs to this dynamical universality class and so does that of a heavy mass in an infinite harmonic oscillator chain and a spinless quasi two-dimensional attractive Fermi gas in the long-wavelength limit. The case of the strongly linked impurity in the XY chain is also discussed along with the corresponding limits in the harmonic oscillator chain and the electron-gas problems.

  20. 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

  1. 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. PMID:27439853

  2. Brownian Optimal Stopping and Random Walks

    SciTech Connect

    Lamberton, D.

    2002-06-05

    One way to compute the value function of an optimal stopping problem along Brownian paths consists of approximating Brownian motion by a random walk. We derive error estimates for this type of approximation under various assumptions on the distribution of the approximating random walk.

  3. 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.

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

    DOE PAGESBeta

    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

  5. 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)

  6. 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

  7. Topological classification of Brownian orbits.

    PubMed

    Tanaka, Fumihiko

    2012-09-14

    This paper presents the exact formula for the bivariate probability distribution function of a Brownian particle as a function of its position and velocity, whose orbit makes a specified number of turns around an infinite straight line. In the limit of large friction constant, the solution reduces to the well-known results for random Wiener paths. Topological entanglements of stiff polymers are discussed on the basis of this solution. The method to find the solution is applied to the velocity space of a Brownian motion, and the probability to find a closed path with a specified winding number is obtained. Hence, closed two-dimensional Brownian orbits are classified into regular homotopy classes, whose statistical weight is derived as a function of the total length and the friction constant. PMID:22979890

  8. Fluctuating noise drives Brownian transport

    PubMed Central

    Hasegawa, Yoshihiko; Arita, Masanori

    2012-01-01

    The transport properties of Brownian ratchet were studied in the presence of stochastic intensity noise in both overdamped and underdamped regimes. In the overdamped case, an analytical solution using the matrix-continued fraction method revealed the existence of a maximum current when the noise intensity fluctuates on intermediate timescale regions. Similar effects were observed for the underdamped case by Monte Carlo simulations. The optimal time-correlation for Brownian transport coincided with the experimentally observed time-correlation of the extrinsic noise in Escherichia coli gene expression and implied the importance of environmental noise for molecular mechanisms. PMID:22977101

  9. 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

  10. 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. PMID:23524449

  11. 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.

  12. 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.

  13. 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.

  14. The Riesz-Bessel Fractional Diffusion Equation

    SciTech Connect

    Anh, V.V. McVinish, R.

    2004-05-15

    This paper examines the properties of a fractional diffusion equation defined by the composition of the inverses of the Riesz potential and the Bessel potential. The first part determines the conditions under which the Green function of this equation is the transition probability density function of a Levy motion. This Levy motion is obtained by the subordination of Brownian motion, and the Levy representation of the subordinator is determined. The second part studies the semigroup formed by the Green function of the fractional diffusion equation. Applications of these results to certain evolution equations is considered. Some results on the numerical solution of the fractional diffusion equation are also provided.

  15. An experimental investigation on intra-fractional organ motion effects in lung IMRT treatments

    NASA Astrophysics Data System (ADS)

    Jiang, Steve B.; Pope, Cynthia; Jarrah, Khaled M. Al; Kung, Jong H.; Bortfeld, Thomas; Chen, George T. Y.

    2003-06-01

    Respiration-induced tumour motion can potentially compromise the use of intensity-modulated radiotherapy (IMRT) as a dose escalation tool for lung tumour treatment. We have experimentally investigated the intra-fractional organ motion effects in lung IMRT treatments delivered by multi-leaf collimator (MLC). An in-house made motor-driven platform, which moves sinusoidally with an amplitude of 1 cm and a period of 4 s, was used to mimic tumour motion. Tumour motion was simulated along cranial-caudal direction while MLC leaves moved across the patient from left to right, as in most clinical cases. The dose to a point near the centre of the tumour mass was measured according to geometric and dosimetric parameters from two five-field lung IMRT plans. For each field, measurement was done for two dose rates (300 and 500 MU min-1), three MLC delivery modes (sliding window, step-and-shoot with 10 and 20 intensity levels) and eight equally spaced starting phases of tumour motion. The dose to the measurement point delivered from all five fields was derived for both a single fraction and 30 fractions by randomly sampling from measured dose values of each field at different initial phases. It was found that the mean dose to a moving tumour differs slightly (<2-3%) from that to a static tumour. The variation in breathing phase at the start of dose delivery results in a maximum variation around the mean dose of greater than 30% for one field. The full width at half maximum for the probability distribution of the point dose is up to 8% for all five fields in a single fraction, but less than 1-2% after 30 fractions. In general, lower dose rate can reduce the motion-caused dose variation and therefore might be preferable for lung IMRT when no motion mitigation techniques are used. From the two IMRT cases we studied where tumour motion is perpendicular to MLC leaf motion, the dose variation was found to be insensitive to the MLC delivery mode.

  16. An experimental investigation on intra-fractional organ motion effects in lung IMRT treatments.

    PubMed

    Jiang, Steve B; Pope, Cynthia; Al Jarrah, Khaled M; Kung, Jong H; Bortfeld, Thomas; Chen, George T Y

    2003-06-21

    Respiration-induced tumour motion can potentially compromise the use of intensity-modulated radiotherapy (IMRT) as a dose escalation tool for lung tumour treatment. We have experimentally investigated the intra-fractional organ motion effects in lung IMRT treatments delivered by multi-leaf collimator (MLC). An in-house made motor-driven platform, which moves sinusoidally with an amplitude of 1 cm and a period of 4 s, was used to mimic tumour motion. Tumour motion was simulated along cranial-caudal direction while MLC leaves moved across the patient from left to right, as in most clinical cases. The dose to a point near the centre of the tumour mass was measured according to geometric and dosimetric parameters from two five-field lung IMRT plans. For each field, measurement was done for two dose rates (300 and 500 MU min(-1)), three MLC delivery modes (sliding window, step-and-shoot with 10 and 20 intensity levels) and eight equally spaced starting phases of tumour motion. The dose to the measurement point delivered from all five fields was derived for both a single fraction and 30 fractions by randomly sampling from measured dose values of each field at different initial phases. It was found that the mean dose to a moving tumour differs slightly (<2-3%) from that to a static tumour. The variation in breathing phase at the start of dose delivery results in a maximum variation around the mean dose of greater than 30% for one field. The full width at half maximum for the probability distribution of the point dose is up to 8% for all five fields in a single fraction, but less than 1-2% after 30 fractions. In general, lower dose rate can reduce the motion-caused dose variation and therefore might be preferable for lung IMRT when no motion mitigation techniques are used. From the two IMRT cases we studied where tumour motion is perpendicular to MLC leaf motion, the dose variation was found to be insensitive to the MLC delivery mode. PMID:12870582

  17. 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.

  18. 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.

  19. FRACTIONAL SOLUTE TRANSPORT EQUATION EVALUATED WITH THE MISCIBLE DISPLACEMENT EXPERIMENTAL DATA

    Technology Transfer Automated Retrieval System (TEKTRAN)

    A new solute transport model has been recently developed assuming that the movements of solute particles in hierarchically-structured porous media belongs to the family of Lévy motions rather than to the Brownian motion. The one-dimensional fractional advective-dispersive transport equation, or FADE...

  20. 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

  1. Detecting non-Brownian trait evolution in adaptive radiations.

    PubMed

    Freckleton, Robert P; Harvey, Paul H

    2006-11-01

    Many phylogenetic comparative methods that are currently widely used in the scientific literature assume a Brownian motion model for trait evolution, but the suitability of that model is rarely tested, and a number of important factors might affect whether this model is appropriate or not. For instance, we might expect evolutionary change in adaptive radiations to be driven by the availability of ecological niches. Such evolution has been shown to produce patterns of change that are different from those modelled by the Brownian process. We applied two tests for the assumption of Brownian motion that generally have high power to reject data generated under non-Brownian niche-filling models for the evolution of traits in adaptive radiations. As a case study, we used these tests to explore the evolution of feeding adaptations in two radiations of warblers. In one case, the patterns revealed do not accord with Brownian motion but show characteristics expected under certain niche-filling models. PMID:17090217

  2. 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.

  3. Evaluation of intra- and inter-fraction motion in breast radiotherapy using electronic portal cine imaging.

    PubMed

    Kron, T; Lee, C; Perera, F; Yu, E

    2004-10-01

    Breast irradiation is one of the most challenging problems in radiotherapy due to the complex shape of the target volume, proximity of radiation sensitive normal structures and breathing motion. It was the aim of the present study to use electronic portal imaging (EPI) during treatment to determine intra- and inter-fraction motion in patients undergoing radiotherapy and to correlate the magnitude of motion with patient specific parameters. EPI cine images were acquired from the medial tangential fields of twenty radiotherapy patients on a minimum of 5 days each over the course of their treatment. The treatments were administered using 10 MV X-rays and dynamic wedges on a Varian Clinac 2100CD linear accelerator. Depending on the incident dose and the angle of the wedge, between 4 and 16 images could be acquired in one session using an EPI device based on liquid ionization chambers (Varian). The border between lung and chest-wall could be easily detected in all images and quantitative measurements were taken for the amount of lung in the field and the distance of the breast tissue from the field edges. Inter-fraction variability was found to be about twice as large as intra-fraction variability. The largest variability was detected in cranio/caudal direction (intra-fraction: 1.3 +/- 0.4 mm; inter-fraction: 2.6 +/- 1.3 mm) while the lung involvement varied by 1.1 +/- 0.2 mm and 1.8 +/- 0.6 mm intra- and inter-fraction, respectively. This indicates that the effect of breathing motion on the amount of radiated lung was not of major concern in the patients studied. Of other patient specific parameters such as body weight, breast separation, field size and location of the target, only increasing age was significantly correlated with larger inter-fraction motion. Acquisition of EPI cine loops proved to be a quick and easy technique to establish the amount of patient movement during breast radiotherapy. The relatively small variability found in the present pilot study

  4. The inviscid Burgers equation with initial data of Brownian type

    NASA Astrophysics Data System (ADS)

    She, Zhen-Su; Aurell, Erik; Frisch, Uriel

    1992-09-01

    The solutions to Burgers equation, in the limit of vanishing viscosity, are investigated when the initial velocity is a Brownian motion (or fractional Brownian motion) function, i.e. a Gaussian process with scaling exponent 0< h<1 (type A) or the derivative thereof, with scaling exponent -1< h<0 (type B). Largesize numerical experiments are performed, helped by the fact that the solution is essentially obtained by performing a Legendre transform. The main result is obtained for type A and concerns the Lagrangian function x(a) which gives the location at time t=1 of the fluid particle which started at the location a. It is found to be a complete Devil's staircase. The cumulative probability of Lagrangian shock intervals Δ a (also the distribution of shock amplitudes) follows a ( Δa)- h law for small Δ a. The remaining (regular) Lagrangian locations form a Cantor set of dimension h. In Eulerian coordinates, the shock locations are everywhere dense. The scaling properties of various statistical quantities are also found. Heuristic interpretations are provided for some of these results. Rigorous results for the case of Brownian motion are established in a companion paper by Ya. Sinai. For type B initial velocities (e.g. white noise), there are very few small shocks and shock locations appear to be isolated. Finally, it is shown that there are universality classes of random but smooth (non-scaling) initial velocities such that the long-time large-scale behavior is, after rescaling, the same as for type A or B.

  5. Magnitude and direction of motion with speckle correlation and the optical fractional Fourier transform

    SciTech Connect

    Kelly, Damien P.; Hennelly, Bryan M.; Sheridan, John T

    2005-05-01

    The optical fractional Fourier transform (OFRT) in combination with speckle photography has previously been used to measure the magnitude of surface tilting and translation. Previous OFRT techniques used to determine motion have not been able to discern the direction of the tilt and translation. A simple new approach involving use of correlation is presented to overcome this limitation. Controlled variation of the minimum resolution and dynamical range of measurement is demonstrated. It is then experimentally confirmed that if a rigid body's motion is captured by two OFRT systems of different orders, the direction and magnitude of both the tilting and the in-plane translation motion of the body can be independently determined without a priori knowledge. The experimental results confirm the validity of previous theoretical predictions.

  6. 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.

  7. 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

  8. 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. PMID:23043567

  9. An Introduction to Fractional Diffusion

    NASA Astrophysics Data System (ADS)

    Henry, B. I.; Langlands, T. A. M.; Straka, P.

    The mathematical description of diffusion has a long history with many different formulations including phenomenological models based on conservation of mass and constitutive laws; probabilistic models based on random walks and central limit theorems; microscopic stochastic models based on Brownian motion and Langevin equations; and mesoscopic stochastic models based on master equations and Fokker-Planck equations. A fundamental result common to the different approaches is that the mean square displacement of a diffusing particle scales linearly with time. However there have been numerous experimental measurements in which the mean square displacement of diffusing particles scales as a fractional order power law in time. In recent years a great deal of progress has been made in extending the different models for diffusion to incorporate this fractional diffusion. The tools of fractional calculus have proven very useful in these developments, linking together fractional constitutive laws, continuous time random walks, fractional Langevin equations and fractional Brownian motions. These notes provide a tutorial style overview of standard and fractional diffusion processes.

  10. Fractional diffusion by Levy stochastic motion of charged particles in the presence of a magnetic field

    NASA Astrophysics Data System (ADS)

    Moradi, Sara; Del-Castillo Negrete, Diego

    2015-11-01

    The motion of charged particles in the presence of alpha-stable Levy noise in a constant external magnetic field and linear friction is studied via Monte Carlo numerical simulations. The Levy noise is introduced to model the effect of non-local transport due to fractional diffusion in velocity space. The statistical properties of the velocity moments and energy for various values of the Levy index α are investigated. Of particular interest is the study of the resulting non-Maxwellian particle distribution functions and their dependence on alpha, the magnetic field amplitude, and the friction. We also explore the role of asymmetric Levy noise, the interplay of regular and fractional diffusion, and compute the statistical moments of displacements. Sara Moradi has benefited from a mobility grant funded by the Belgian Federal Science Policy Office and the MSCA of the European Commission (FP7-PEOPLE-COFUND-2008 no. 246540).

  11. 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. PMID:23944411

  12. 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…

  13. 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.

  14. 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.

  15. Tilted brownian ratchet for DNA analysis.

    PubMed

    Huang, Lotien Richard; Cox, Edward C; Austin, Robert H; Sturm, James C

    2003-12-15

    In this paper, we report a factor of 3 improvement in the resolution and a factor of 10 improvement in the speed of fractionation of approximately 100-kb DNA molecules in Brownian ratchet arrays. In our device, the electrophoretic flow is tilted at a small angle relative to the array axis. Tilting accelerates the fractionation speed because a higher fraction of the diffusing molecules is "ratcheted" at each step in the array. Molecules of lengths 48.5 and 164 kb can be separated in approximately 70 min with a resolution of approximately 3.8, using a 12-mm-long array. The Brownian ratchet arrays are not limited to DNA separation, but can, in principle, be used for any particle in this size range. PMID:14670059

  16. 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

  17. Fractional diffusions with time-varying coefficients

    NASA Astrophysics Data System (ADS)

    Garra, Roberto; Orsingher, Enzo; Polito, Federico

    2015-09-01

    This paper is concerned with the fractionalized diffusion equations governing the law of the fractional Brownian motion BH(t). We obtain solutions of these equations which are probability laws extending that of BH(t). Our analysis is based on McBride fractional operators generalizing the hyper-Bessel operators L and converting their fractional power Lα into Erdélyi-Kober fractional integrals. We study also probabilistic properties of the random variables whose distributions satisfy space-time fractional equations involving Caputo and Riesz fractional derivatives. Some results emerging from the analysis of fractional equations with time-varying coefficients have the form of distributions of time-changed random variables.

  18. 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

  19. A method to calculate fission-fragment yields Y(Z,N) versus proton and neutron number in the Brownian shape-motion model. Application to calculations of U and Pu charge yields

    NASA Astrophysics Data System (ADS)

    Möller, Peter; Ichikawa, Takatoshi

    2015-12-01

    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 ɛ_{f1}, right nascent fragment deformation ɛ_{f2} 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.

  20. ECG-gated blood pool tomography in the determination of left ventricular volume, ejection fraction, and wall motion

    SciTech Connect

    Underwood, S.R.; Ell, P.J.; Jarritt, P.H.; Emanuel, R.W.; Swanton, R.H.

    1984-01-01

    ECG-gated blood pool tomography promises to provide a ''gold standard'' for noninvasive measurement of left ventricular volume, ejection fraction, and wall motion. This study compares these measurements with those from planar radionuclide imaging and contrast ventriculography. End diastolic and end systolic blood pool images were acquired tomographically using an IGE400A rotating gamma camera and Star computer, and slices were reconstructed orthogonal to the long axis of the heart. Left ventricular volume was determined by summing the areas of the slices, and wall motion was determined by comparison of end diastolic and end systolic contours. In phantom experiments this provided an accurate measurement of volume (r=0.98). In 32 subjects who were either normal or who had coronary artery disease left ventricular volume (r=0.83) and ejection fraction (r=0.89) correlated well with those using a counts based planar technique. In 16 of 18 subjects who underwent right anterior oblique X-ray contrast ventriculography, tomographic wall motion agreed for anterior, apical, and inferior walls, but abnormal septal motion which was not apparent by contrast ventriculography, was seen in 12 subjects tomographically. All 12 had disease of the left anterior descending coronary artery and might have been expected to have abnormal septal motion. ECG-gated blood pool tomography can thus determine left ventricular volume and ejection fraction accurately, and provides a global description of wall motion in a way that is not possible from any single planar image.

  1. 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

  2. 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.

  3. 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.

  4. 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.

  5. Anomalous rotational relaxation: a fractional Fokker-Planck equation approach.

    PubMed

    Aydiner, Ekrem

    2005-04-01

    In this study we have analytically obtained the relaxation function in terms of rotational correlation functions based on Brownian motion for complex disordered systems in a stochastic framework. We found out that the rotational relaxation function has a fractional form for complex disordered systems, which indicates that relaxation has nonexponential character and obeys the Kohlrausch-William-Watts law, following the Mittag-Leffler decay. PMID:15903722

  6. 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.

  7. Real-time intra-fraction-motion tracking using the treatment couch: a feasibility study

    NASA Astrophysics Data System (ADS)

    D'Souza, Warren D.; Naqvi, Shahid A.; Yu, Cedric X.

    2005-09-01

    Significant differences between planned and delivered treatments may occur due to respiration-induced tumour motion, leading to underdosing of parts of the tumour and overdosing of parts of the surrounding critical structures. Existing methods proposed to counter tumour motion include breath-holds, gating and MLC-based tracking. Breath-holds and gating techniques increase treatment time considerably, whereas MLC-based tracking is limited to two dimensions. We present an alternative solution in which a robotic couch moves in real time in response to organ motion. To demonstrate proof-of-principle, we constructed a miniature adaptive couch model consisting of two movable platforms that simulate tumour motion and couch motion, respectively. These platforms were connected via an electronic feedback loop so that the bottom platform responded to the motion of the top platform. We tested our model with a seven-field step-and-shoot delivery case in which we performed three film-based experiments: (1) static geometry, (2) phantom-only motion and (3) phantom motion with simulated couch motion. Our measurements demonstrate that the miniature couch was able to compensate for phantom motion to the extent that the dose distributions were practically indistinguishable from those in static geometry. Motivated by this initial success, we investigated a real-time couch compensation system consisting of a stereoscopic infra-red camera system interfaced to a robotic couch known as the Hexapod™, which responds in real time to any change in position detected by the cameras. Optical reflectors placed on a solid water phantom were used as surrogates for motion. We tested the effectiveness of couch-based motion compensation for fixed fields and a dynamic arc delivery cases. Due to hardware limitations, we performed film-based experiments (1), (2) and (3), with the robotic couch at a phantom motion period and dose rate of 16 s and 100 MU min-1, respectively. Analysis of film measurements

  8. 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.

  9. Quantum dynamical framework for Brownian heat engines.

    PubMed

    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. PMID:23944437

  10. 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.

  11. Entropy production of a Brownian ellipsoid in the overdamped limit

    NASA Astrophysics Data System (ADS)

    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.

  12. 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)

  13. 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. PMID:26871049

  14. 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.

  15. 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. PMID:24695273

  16. Magnetic field effect on charged Brownian swimmers

    NASA Astrophysics Data System (ADS)

    Sandoval, M.; Velasco, R. M.; Jiménez-Aquino, J. I.

    2016-01-01

    We calculate the effective diffusion of a spherical self-propelled charged particle swimming at low Reynolds number, and subject to a time-dependent magnetic field and thermal agitation. We find that the presence of an external magnetic field may reduce or enhance (depending on the type of swimming and magnetic field applied) the swimmer's effective diffusion, hence we get another possible strategy to control its displacement. For swimmers performing reciprocal motion, and under an oscillating time-dependent magnetic field, mechanical resonance appears when the swimmer and magnetic frequencies coincide, thus enhancing the particle's effective diffusion. Our analytical results are compared with Brownian Dynamics simulations and we obtain excellent agreement.

  17. 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

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. Intensity modulated proton therapy and its sensitivity to treatment uncertainties 2: the potential effects of inter-fraction and inter-field motions

    NASA Astrophysics Data System (ADS)

    Lomax, A. J.

    2008-02-01

    Simple tools for studying the effects of inter-fraction and inter-field motions on intensity modulated proton therapy (IMPT) plans have been developed, and have been applied to both 3D and distal edge tracking (DET) IMPT plans. For the inter-fraction motion, we have investigated the effects of misaligned density heterogeneities, whereas for the inter-field motion analysis, the effects of field misalignment on the plans have been assessed. Inter-fraction motion problems have been analysed using density differentiated error (DDE) distributions, which specifically show the additional problems resulting from misaligned density heterogeneities for proton plans. Likewise, for inter-field motion, we present methods for calculating motion differentiated error (MDE) distributions. DDE and MDE analysis of all plans demonstrate that the 3D approach is generally more robust to both inter-fraction and inter-field motions than the DET approach, but that strong in-field dose gradients can also adversely affect a plan's robustness. An important additional conclusion is that, for certain IMPT plans, even inter-fraction errors cannot necessarily be compensated for by the use of a simple PTV margins, implying that more sophisticated tools need to be developed for uncertainty management and assessment for IMPT treatments at the treatment planning level.

  3. 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

  4. 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

  5. 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.

  6. Review of ultrasound image guidance in external beam radiotherapy: I. Treatment planning and inter-fraction motion management.

    PubMed

    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. PMID:25592664

  7. 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.

  8. Fractional noise destroys or induces a stochastic bifurcation

    NASA Astrophysics Data System (ADS)

    Yang, Qigui; Zeng, Caibin; Wang, Cong

    2013-12-01

    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.

  9. Fractional noise destroys or induces a stochastic bifurcation.

    PubMed

    Yang, Qigui; Zeng, Caibin; Wang, Cong

    2013-12-01

    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. PMID:24387559

  10. 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.

  11. Review of ultrasound image guidance in external beam radiotherapy part II: intra-fraction motion management and novel applications.

    PubMed

    O'Shea, Tuathan; Bamber, Jeffrey; Fontanarosa, Davide; van der Meer, Skadi; Verhaegen, Frank; Harris, Emma

    2016-04-21

    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

  12. 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

  13. A computational method for estimating the dosimetric effect of intra-fraction motion on step-and-shoot IMRT and compensator plans.

    PubMed

    Waghorn, Ben J; Shah, Amish P; Ngwa, Wilfred; Meeks, Sanford L; Moore, Joseph A; Siebers, Jeffrey V; Langen, Katja M

    2010-07-21

    Intra-fraction organ motion during intensity-modulated radiation therapy (IMRT) treatment can cause differences between the planned and the delivered dose distribution. To investigate the extent of these dosimetric changes, a computational model was developed and validated. The computational method allows for calculation of the rigid motion perturbed three-dimensional dose distribution in the CT volume and therefore a dose volume histogram-based assessment of the dosimetric impact of intra-fraction motion on a rigidly moving body. The method was developed and validated for both step-and-shoot IMRT and solid compensator IMRT treatment plans. For each segment (or beam), fluence maps were exported from the treatment planning system. Fluence maps were shifted according to the target position deduced from a motion track. These shifted, motion-encoded fluence maps were then re-imported into the treatment planning system and were used to calculate the motion-encoded dose distribution. To validate the accuracy of the motion-encoded dose distribution the treatment plan was delivered to a moving cylindrical phantom using a programmed four-dimensional motion phantom. Extended dose response (EDR-2) film was used to measure a planar dose distribution for comparison with the calculated motion-encoded distribution using a gamma index analysis (3% dose difference, 3 mm distance-to-agreement). A series of motion tracks incorporating both inter-beam step-function shifts and continuous sinusoidal motion were tested. The method was shown to accurately predict the film's dose distribution for all of the tested motion tracks, both for the step-and-shoot IMRT and compensator plans. The average gamma analysis pass rate for the measured dose distribution with respect to the calculated motion-encoded distribution was 98.3 +/- 0.7%. For static delivery the average film-to-calculation pass rate was 98.7 +/- 0.2%. In summary, a computational technique has been developed to calculate the

  14. 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.

  15. 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

  16. 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.

  17. 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…

  18. 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…

  19. Stochastic Oscillations of General Relativistic Disks Described by a Fractional Langevin Equation with Fractional Gaussian Noise

    NASA Astrophysics Data System (ADS)

    Zhi-Yun, Wang; Pei-Jie, Chen

    2016-06-01

    A generalized Langevin equation driven by fractional Brownian motion is used to describe the vertical oscillations of general relativistic disks. By means of numerical calculation method, the displacements, velocities and luminosities of oscillating disks are explicitly obtained for different Hurst exponent H. The results show that as H increases, the energies and luminosities of oscillating disk are enhanced, and the spectral slope at high frequencies of the power spectrum density of disk luminosity is also increased. This could explain the observational features related to the Intra Day Variability of the BL Lac objects.

  20. 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.

  1. Algorithms for testing of fractional dynamics: a practical guide to ARFIMA modelling

    NASA Astrophysics Data System (ADS)

    Burnecki, Krzysztof; Weron, Aleksander

    2014-10-01

    In this survey paper we present a systematic methodology which demonstrates how to identify the origins of fractional dynamics. We consider three mechanisms which lead to it, namely fractional Brownian motion, fractional Lévy stable motion and an autoregressive fractionally integrated moving average (ARFIMA) process but we concentrate on the ARFIMA modelling. The methodology is based on statistical tools for identification and validation of the fractional dynamics, in particular on an ARFIMA parameter estimator, an ergodicity test, a self-similarity index estimator based on sample p-variation and a memory parameter estimator based on sample mean-squared displacement. A complete list of algorithms needed for this is provided in appendices A-F. Finally, we illustrate the methodology on various empirical data and show that ARFIMA can be considered as a universal model for fractional dynamics. Thus, we provide a practical guide for experimentalists on how to efficiently use ARFIMA modelling for a large class of anomalous diffusion data.

  2. Dynamics and efficiency of Brownian rotors

    NASA Astrophysics Data System (ADS)

    Bauer, Wolfgang R.; Nadler, Walter

    2008-12-01

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

  3. Lagrangian dynamics for classical, Brownian, and quantum mechanical particles

    NASA Astrophysics Data System (ADS)

    Pavon, Michele

    1996-07-01

    In the framework of Nelson's stochastic mechanics [E. Nelson, Dynamical Theories of Brownian Motion (Princeton University, Princeton, 1967); F. Guerra, Phys. Rep. 77, 263 (1981); E. Nelson, Quantum Fluctuations (Princeton University, Princeton, 1985)] we seek to develop the particle counterpart of the hydrodynamic results of M. Pavon [J. Math. Phys. 36, 6774 (1995); Phys. Lett. A 209, 143 (1995)]. In particular, a first form of Hamilton's principle is established. We show that this variational principle leads to the correct equations of motion for the classical particle, the Brownian particle in thermodynamical equilibrium, and the quantum particle. In the latter case, the critical process q satisfies a stochastic Newton law. We then introduce the momentum process p, and show that the pair (q,p) satisfies canonical-like equations.

  4. Dynamics of hierarchical Brownian oscillators

    NASA Astrophysics Data System (ADS)

    Knapp, E. W.

    1988-11-01

    Two hierarchical Brownian oscillator models are introduced by using a discretized Brownian oscillator model. The dynamical behavior of these models is solved exactly. Closed-form expressions for the intermediate scattering function and the energy relaxation function governing the frequency-dependent specific heat are given. A general relationship between the two relaxation functions is established. The case of a rectangular distribution of activation energies for the different hierarchy levels of the oscillator is considered in more detail. There the energy relaxation function decays with a logarithmic slope and the intermediate scattering function exhibits an algebraic long-time decay. The two hierarchical Brownian oscillator models have the same dynamical behavior though they possess a quite different coupling scheme.

  5. Disentangling Random Motion and Flow in a Complex Medium.

    PubMed

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

    2016-02-01

    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

  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. PMID:26788750

  7. Brownian colloids in underdamped and overdamped regimes with nonhomogeneous temperature

    NASA Astrophysics Data System (ADS)

    Sancho, J. M.

    2015-12-01

    The motion of Brownian particles when temperature is spatially dependent is studied by stochastic simulations and theoretical analysis. Nonequilibrium steady probability distributions Ps t(z ,v ) for both underdamped and overdamped regimes are analyzed. The existence of local kinetic energy equipartition theorem is also discussed. The transition between both regimes is characterized by a dimensionless friction parameter. This study is applied to three physical systems of colloidal particles.

  8. Brownian colloids in underdamped and overdamped regimes with nonhomogeneous temperature.

    PubMed

    Sancho, J M

    2015-12-01

    The motion of Brownian particles when temperature is spatially dependent is studied by stochastic simulations and theoretical analysis. Nonequilibrium steady probability distributions P(st)(z,v) for both underdamped and overdamped regimes are analyzed. The existence of local kinetic energy equipartition theorem is also discussed. The transition between both regimes is characterized by a dimensionless friction parameter. This study is applied to three physical systems of colloidal particles. PMID:26764635

  9. Molecular Motors: Power Strokes Outperform Brownian Ratchets.

    PubMed

    Wagoner, Jason A; Dill, Ken A

    2016-07-01

    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. PMID:27136319

  10. 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.

  11. 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.

  12. Fractional-calculus diffusion equation

    PubMed Central

    2010-01-01

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

  13. 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.

  14. Perturbative theory for Brownian vortexes.

    PubMed

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

    2015-06-01

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

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

    NASA Astrophysics Data System (ADS)

    Najafi, Amin

    2014-05-01

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

  16. Development of a real-time monitoring system for intra-fractional motion in intracranial treatment using pressure sensors.

    PubMed

    Inata, Hiroki; Araki, Fujio; Kuribayashi, Yuta; Hamamoto, Yasushi; Nakayama, Shigeki; Sodeoka, Noritaka; Kiriyama, Tetsukazu; Nishizaki, Osamu

    2015-09-21

    This study developed a dedicated real-time monitoring system to detect intra-fractional head motion in intracranial radiotherapy using pressure sensors. The dedicated real-time monitoring system consists of pressure sensors with a thickness of 0.6 mm and a radius of 9.1 mm, a thermoplastic mask, a vacuum pillow, and a baseplate. The four sensors were positioned at superior-inferior and right-left sides under the occipital area. The sampling rate of pressure sensors was set to 5 Hz. First, we confirmed that the relationship between the force and the displacement of the vacuum pillow follows Hook's law. Next, the spring constant for the vacuum pillow was determined from the relationship between the force given to the vacuum pillow and the displacement of the head, detected by Cyberknife target locating system (TLS) acquisitions in clinical application. Finally, the accuracy of our system was evaluated by using the 2  ×  2 confusion matrix. The regression lines between the force, y, and the displacement, x, of the vacuum pillow were given by y = 3.8x, y = 4.4x, and y = 5.0x when the degree of inner pressure was  -12 kPa,-20 kPa, and  -27 kPa, respectively. The spring constant of the vacuum pillow was 1.6 N mm(-1) from the 6D positioning data of a total of 2999 TLS acquisitions in 19 patients. Head motions of 1 mm, 1.5 mm, and 2 mm were detected in real-time with the accuracies of 67%, 84%, and 89%, respectively. Our system can detect displacement of the head continuously during every interval of TLS with a resolution of 1-2 mm without any radiation exposure. PMID:26348273

  17. A prospective comparison of echocardiographic wall motion score index and radionuclide ejection fraction in predicting outcome following acute myocardial infarction

    PubMed Central

    Galasko, G; Basu, S; Lahiri, A; Senior, R

    2001-01-01

    OBJECTIVE—To characterise echocardiographic wall motion score index (WMSI) as a surrogate measure of left ventricular ejection fraction (EF) following acute myocardial infarction (AMI) and to compare its prognostic value with that of EF measured by radionuclide ventriculography (RNV).
DESIGN—A prospective study to compare baseline echocardiographic WMSI with RNV EF in consecutive patients thrombolysed for AMI, both performed on the same day before discharge, and their relative prognostic values in predicting cardiac events.
SETTING—District general hospital coronary care unit and cardiology department.
PATIENTS—120 consecutive patients free of exclusion criteria thrombolysed for AMI and followed up for a mean (SD) of 13 (10) months.
INTERVENTIONS—None.
MAIN OUTCOME MEASURES—Correlation coefficients and receiver operating characteristic curve analyses plus cardiac event rates at follow up between RNV EF and echocardiographic WMSI.
RESULTS—WMSI correlated well with RNV EF. The best corresponding WMSIs for EFs 45%, 40%, and 35% were 0.6, 0.8, and 1.1, respectively. There were 42 cardiac events during follow up. Although both RNV EF and WMSI were strong univariate predictors of cardiac events, only WMSI independently predicted outcome in a multivariate model. All three WMSI cut offs significantly predicted events, while an RNV EF cut off of ⩽ 45% v > 45% failed to reach significance.
CONCLUSIONS—Although both RNV and echocardiographic WMSI strongly predicted cardiac outcome, WMSI, a cheaper and more readily available technique, is more discriminatory, especially in cases of mild left ventricular dysfunction following AMI.


Keywords: echocardiographic wall motion score index; radionuclide ventriculography; prognosis; acute myocardial infarction PMID:11514477

  18. Tissue feature-based intra-fractional motion tracking for stereoscopic x-ray image guided radiotherapy

    NASA Astrophysics Data System (ADS)

    Xie, Yaoqin; Xing, Lei; Gu, Jia; Liu, Wu

    2013-06-01

    Real-time knowledge of tumor position during radiation therapy is essential to overcome the adverse effect of intra-fractional organ motion. The goal of this work is to develop a tumor tracking strategy by effectively utilizing the inherent image features of stereoscopic x-ray images acquired during dose delivery. In stereoscopic x-ray image guided radiation delivery, two orthogonal x-ray images are acquired either simultaneously or sequentially. The essence of markerless tumor tracking is the reliable identification of inherent points with distinct tissue features on each projection image and their association between two images. The identification of the feature points on a planar x-ray image is realized by searching for points with high intensity gradient. The feature points are associated by using the scale invariance features transform descriptor. The performance of the proposed technique is evaluated by using images of a motion phantom and four archived clinical cases acquired using either a CyberKnife equipped with a stereoscopic x-ray imaging system, or a LINAC equipped with an onboard kV imager and an electronic portal imaging device. In the phantom study, the results obtained using the proposed method agree with the measurements to within 2 mm in all three directions. In the clinical study, the mean error is 0.48 ± 0.46 mm for four patient data with 144 sequential images. In this work, a tissue feature-based tracking method for stereoscopic x-ray image guided radiation therapy is developed. The technique avoids the invasive procedure of fiducial implantation and may greatly facilitate the clinical workflow.

  19. Discontinuous shear thickening in Brownian suspensions by dynamic simulation

    PubMed Central

    Mari, Romain; Seto, Ryohei; Morris, Jeffrey F.; Denn, Morton M.

    2015-01-01

    Dynamic particle-scale numerical simulations are used to show that the shear thickening observed in dense colloidal, or Brownian, suspensions is of a similar nature to that observed in noncolloidal suspensions, i.e., a stress-induced transition from a flow of lubricated near-contacting particles to a flow of a frictionally contacting network of particles. Abrupt (or discontinuous) shear thickening is found to be a geometric rather than hydrodynamic phenomenon; it stems from the strong sensitivity of the jamming volume fraction to the nature of contact forces between suspended particles. The thickening obtained in a colloidal suspension of purely hard frictional spheres is qualitatively similar to experimental observations. However, the agreement cannot be made quantitative with only hydrodynamics, frictional contacts, and Brownian forces. Therefore, the role of a short-range repulsive potential mimicking the stabilization of actual suspensions on the thickening is studied. The effects of Brownian and repulsive forces on the onset stress can be combined in an additive manner. The simulations including Brownian and stabilizing forces show excellent agreement with experimental data for the viscosity η and the second normal stress difference N2. PMID:26621744

  20. Introduction on background medium theory about celestial body motion orbit and foundation of fractional-dimension calculus about self-similar fractal measure calculation

    NASA Astrophysics Data System (ADS)

    Yan, Kun

    2007-04-01

    In this paper, by discussing the basic hypotheses about the continuous orbit and discrete orbit in two research directions of the background medium theory for celestial body motion, the concrete equation forms and their summary of the theoretic frame of celestial body motion are introduced. Future more, by discussing the general form of Binet's equation of celestial body motion orbit and it's solution of the advance of the perihelion of planets, the relations and differences between the continuous orbit theory and Newton's gravitation theory and Einstein's general relativity are given. And by discussing the fractional-dimension expanded equation for the celestial body motion orbits, the concrete equations and the prophesy data of discrete orbit or stable orbits of celestial bodies which included the planets in the Solar system, satellites in the Uranian system, satellites in the Earth system and satellites obtaining the Moon obtaining from discrete orbit theory are given too. Especially, as the preliminary exploration and inference to the gravitation curve of celestial bodies in broadly range, the concept for the ideal black hole with trend to infinite in mass density difficult to be formed by gravitation only is explored. By discussing the position hypothesis of fractional-dimension derivative about general function and the formula form the hypothesis of fractional-dimension derivative about power function, the concrete equation formulas of fractional-dimension derivative, differential and integral are described distinctly further, and the difference between the fractional-dimension derivative and the fractional-order derivative are given too. Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension calculus about general fractal measure are discussed again, and the differences with Hausdorff measure method or the covering method at present are given. By applying

  1. Financial Brownian Particle in the Layered Order-Book Fluid and Fluctuation-Dissipation Relations

    NASA Astrophysics Data System (ADS)

    Yura, Yoshihiro; Takayasu, Hideki; Sornette, Didier; Takayasu, Misako

    2014-03-01

    We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of comprehensive market data enables us to identify all motions of the fluid particles. Correlations between the motions of the Brownian particle and its surrounding fluid particles reflect specific layering interactions; in the inner layer the correlation is strong and with short memory, while in the outer layer it is weaker and with long memory. By interpreting and estimating the contribution from the outer layer as a drag resistance, we demonstrate the validity of the fluctuation-dissipation relation in this nonmaterial Brownian motion process.

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

    NASA Astrophysics Data System (ADS)

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

    2014-06-01

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

  3. Brownian relaxation of an inelastic sphere in air

    NASA Astrophysics Data System (ADS)

    Bird, G. A.

    2016-06-01

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

  4. Efficiency of Brownian heat engines.

    PubMed

    Derényi, I; Astumian, R D

    1999-06-01

    We study the efficiency of one-dimensional thermally driven Brownian ratchets or heat engines. We identify and compare the three basic setups characterized by the type of the connection between the Brownian particle and the two heat reservoirs: (i) simultaneous, (ii) alternating in time, and (iii) position dependent. We make a clear distinction between the heat flow via the kinetic and the potential energy of the particle, and show that the former is always irreversible and it is only the third setup where the latter is reversible when the engine works quasistatically. We also show that in the third setup the heat flow via the kinetic energy can be reduced arbitrarily, proving that even for microscopic heat engines there is no fundamental limit of the efficiency lower than that of a Carnot cycle. PMID:11969723

  5. Hidden Symmetries, Instabilities, and Current Suppression in Brownian Ratchets

    NASA Astrophysics Data System (ADS)

    Cubero, David; Renzoni, Ferruccio

    2016-01-01

    The operation of Brownian motors is usually described in terms of out-of-equilibrium and symmetry-breaking settings, with the relevant spatiotemporal symmetries identified from the analysis of the equations of motion for the system at hand. When the appropriate conditions are satisfied, symmetry-related trajectories with opposite current are thought to balance each other, yielding suppression of transport. The direction of the current can be precisely controlled around these symmetry points by finely tuning the driving parameters. Here we demonstrate, by studying a prototypical Brownian ratchet system, the existence of hidden symmetries, which escape identification by the standard symmetry analysis, and which require different theoretical tools for their revelation. Furthermore, we show that system instabilities may lead to spontaneous symmetry breaking with unexpected generation of directed transport.

  6. Brownian dipole rotator in alternating electric field.

    PubMed

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

    2008-06-01

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

  7. Brownian dipole rotator in alternating electric field

    NASA Astrophysics Data System (ADS)

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

    2008-06-01

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

  8. Brownian ratchets and Parrondo's games

    NASA Astrophysics Data System (ADS)

    Harmer, Gregory P.; Abbott, Derek; Taylor, Peter G.; Parrondo, Juan M. R.

    2001-09-01

    Parrondo's games present an apparently paradoxical situation where individually losing games can be combined to win. In this article we analyze the case of two coin tossing games. Game B is played with two biased coins and has state-dependent rules based on the player's current capital. Game B can exhibit detailed balance or even negative drift (i.e., loss), depending on the chosen parameters. Game A is played with a single biased coin that produces a loss or negative drift in capital. However, a winning expectation is achieved by randomly mixing A and B. One possible interpretation pictures game A as a source of "noise" that is rectified by game B to produce overall positive drift—as in a Brownian ratchet. Game B has a state-dependent rule that favors a losing coin, but when this state dependence is broken up by the noise introduced by game A, a winning coin is favored. In this article we find the parameter space in which the paradoxical effect occurs and carry out a winning rate analysis. The significance of Parrondo's games is that they are physically motivated and were originally derived by considering a Brownian ratchet—the combination of the games can be therefore considered as a discrete-time Brownian ratchet. We postulate the use of games of this type as a toy model for a number of physical and biological processes and raise a number of open questions for future research.

  9. Elastic coefficient of a single polymer chain by using Brownian dynamics analysis

    NASA Astrophysics Data System (ADS)

    Horinaka, J.; Maniwa, T.; Oharada, K.; Takigawa, T.

    2007-08-01

    The elastic coefficient of a single polystyrene chain has been experimentally evaluated by using Brownian dynamics analysis. The Brownian motion of the chain is probed using a particle trapped by optical tweezers with a negligibly small spring constant. The displacement of the particle due to Brownian motion is measured by an interferometer assembled using the same laser beam as the optical tweezers. Two methods are employed for Brownian dynamics analysis: (1) the analysis of the time course of the displacement of the particle and (2) the fitting of the power spectrum of Brownian motion with a Lorentzian. The elastic constant of a polystyrene chain in dichloromethane at 21 °C is estimated to be 6.4×10-6 and 1.1×10-5 N/m when methods (1) and (2) are employed, respectively. The elastic constant obtained by approximating the polystyrene chain to a freely jointed chain is in agreement with the experimentally evaluated elastic constant.

  10. Statistical Properties of Thermal Noise Driving the Brownian Particles in Fluids

    NASA Astrophysics Data System (ADS)

    Tóthová, Jana; Lisý, Vladimír

    2016-02-01

    In several recent works high-resolution interferometric detection allowed to study the Brownian motion of optically trapped microparticles in air and fluids. The observed positional fluctuations of the particles are well described by the generalized Langevin equation with the Boussinesq-Basset "history force" instead of the Stokes friction, which is valid only for the steady motion. Recently, also the time correlation function of the thermal random force Fth driving the Brownian particles through collisions with the surrounding molecules has been measured. In the present contribution we propose a method to describe the statistical properties of Fth in incompressible fluids. Our calculations show that the time decay of the correlator is significantly slower than that found in the literature. It is also shown how the "color" of the thermal noise can be determined from the measured positions of the Brownian particles.

  11. Subdiffusive motion of a polymer composed of subdiffusive monomers

    PubMed Central

    Weber, Stephanie C.; Theriot, Julie A.; Spakowitz, Andrew J.

    2016-01-01

    We use Brownian dynamics simulations and analytical theory to investigate the physical principles underlying subdiffusive motion of a polymer. Simulations of a single circular polymer reveal that relaxation of the elastic Rouse modes dominates monomer motion, even under strong confinement. Thus, we incorporate two anomalous diffusion models into the theoretical framework of the Rouse model for polymer dynamics. First, a polymer is considered moving within a viscoelastic fluid, in which monomers experience frictional memory described by fractional Brownian motion. Second, we examine a polymer whose monomers are subjected to random pausing events according to the continuous time random walk model. We derive scaling laws for the mean square displacement of a monomer within a polymer, as well as the velocity autocorrelation function. Unlike particles, which exhibit the same ensemble-averaged behavior regardless of subdiffusive mechanism, subdiffusive monomer motion leads to widely varying behavior for a polymer depending on the root cause of the monomer subdiffusion. Our results can be applied directly to experiments as diagnostic tools for determining the dominant physical mechanism underlying anomalous subdiffusive polymer dynamics. PMID:20866654

  12. Light scattering and dynamics of interacting Brownian particles

    NASA Technical Reports Server (NTRS)

    Tsang, T.; Tang, H. T.

    1982-01-01

    The relative motions of interacting Brownian particles in liquids may be described as radial diffusion in an effective potential of the mean force. By using a harmonic approximation for the effective potential, the intermediate scattering function may also be evaluated. For polystyrene spheres of 250 A mean radius in aqueous environment at 0.00125 g/cu cm concentration, the results for the calculated mean square displacement are in qualitative agreement with experimental data from photon correlation spectroscopy. Because of the interactions, the functions deviate considerably from the exponential forms for the free particles.

  13. 4D ultrasound speckle tracking of intra-fraction prostate motion: a phantom-based comparison with x-ray fiducial tracking using CyberKnife

    NASA Astrophysics Data System (ADS)

    O'Shea, Tuathan P.; Garcia, Leo J.; Rosser, Karen E.; Harris, Emma J.; Evans, Philip M.; Bamber, Jeffrey C.

    2014-04-01

    This study investigates the use of a mechanically-swept 3D ultrasound (3D-US) probe for soft-tissue displacement monitoring during prostate irradiation, with emphasis on quantifying the accuracy relative to CyberKnife® x-ray fiducial tracking. An US phantom, implanted with x-ray fiducial markers was placed on a motion platform and translated in 3D using five real prostate motion traces acquired using the Calypso system. Motion traces were representative of all types of motion as classified by studying Calypso data for 22 patients. The phantom was imaged using a 3D swept linear-array probe (to mimic trans-perineal imaging) and, subsequently, the kV x-ray imaging system on CyberKnife. A 3D cross-correlation block-matching algorithm was used to track speckle in the ultrasound data. Fiducial and US data were each compared with known phantom displacement. Trans-perineal 3D-US imaging could track superior-inferior (SI) and anterior-posterior (AP) motion to ≤0.81 mm root-mean-square error (RMSE) at a 1.7 Hz volume rate. The maximum kV x-ray tracking RMSE was 0.74 mm, however the prostate motion was sampled at a significantly lower imaging rate (mean: 0.04 Hz). Initial elevational (right-left RL) US displacement estimates showed reduced accuracy but could be improved (RMSE <2.0 mm) using a correlation threshold in the ultrasound tracking code to remove erroneous inter-volume displacement estimates. Mechanically-swept 3D-US can track the major components of intra-fraction prostate motion accurately but exhibits some limitations. The largest US RMSE was for elevational (RL) motion. For the AP and SI axes, accuracy was sub-millimetre. It may be feasible to track prostate motion in 2D only. 3D-US also has the potential to improve high tracking accuracy for all motion types. It would be advisable to use US in conjunction with a small (˜2.0 mm) centre-of-mass displacement threshold in which case it would be possible to take full advantage of the accuracy and high imaging

  14. Space-fractional Fokker-Planck equation and optimization of random search processes in the presence of an external bias

    NASA Astrophysics Data System (ADS)

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

    2014-11-01

    Based on the space-fractional Fokker-Planck equation with a δ-sink term, we study the efficiency of random search processes based on Lévy flights with power-law distributed jump lengths in the presence of an external drift, for instance, an underwater current, an airflow, or simply the preference of the searcher based on prior experience. While Lévy flights turn out to be efficient search processes when the target is upstream relative to the starting point, in the downstream scenario, regular Brownian motion turns out to be advantageous. This is caused by the occurrence of leapovers of Lévy flights, due to which Lévy flights typically overshoot a point or small interval. Studying the solution of the fractional Fokker-Planck equation, we establish criteria when the combination of the external stream and the initial distance between the starting point and the target favours Lévy flights over the regular Brownian search. Contrary to the common belief that Lévy flights with a Lévy index α = 1 (i.e. Cauchy flights) are optimal for sparse targets, we find that the optimal value for α may range in the entire interval (1, 2) and explicitly include Brownian motion as the most efficient search strategy overall.

  15. Non-intersecting Brownian walkers and Yang-Mills theory on the sphere

    NASA Astrophysics Data System (ADS)

    Forrester, Peter J.; Majumdar, Satya N.; Schehr, Grégory

    2011-03-01

    We study a system of N non-intersecting Brownian motions on a line segment [0,L] with periodic, absorbing and reflecting boundary conditions. We show that the normalized reunion probabilities of these Brownian motions in the three models can be mapped to the partition function of two-dimensional continuum Yang-Mills theory on a sphere respectively with gauge groups U(N), Sp(2N) and SO(2N). Consequently, we show that in each of these Brownian motion models, as one varies the system size L, a third order phase transition occurs at a critical value L=L(N)˜√{N} in the large N limit. Close to the critical point, the reunion probability, properly centered and scaled, is identical to the Tracy-Widom distribution describing the probability distribution of the largest eigenvalue of a random matrix. For the periodic case we obtain the Tracy-Widom distribution corresponding to the GUE random matrices, while for the absorbing and reflecting cases we get the Tracy-Widom distribution corresponding to GOE random matrices. In the absorbing case, the reunion probability is also identified as the maximal height of N non-intersecting Brownian excursions ("watermelons" with a wall) whose distribution in the asymptotic scaling limit is then described by GOE Tracy-Widom law. In addition, large deviation formulas for the maximum height are also computed.

  16. Phase transitions driven by Lévy stable noise: Exact solutions and stability analysis of nonlinear fractional Fokker-Planck equations

    NASA Astrophysics Data System (ADS)

    Ichiki, A.; Shiino, M.

    2009-08-01

    Phase transitions and effects of external noise on many-body systems are one of the main topics in physics. In mean-field coupled nonlinear dynamical stochastic systems driven by Brownian noise, various types of phase transitions including nonequilibrium ones may appear. A Brownian motion is a special case of Lévy motion and the stochastic process based on the latter is an alternative choice for studying cooperative phenomena in various fields. Recently, fractional Fokker-Planck equations associated with Lévy noise have attracted much attention and behaviors of systems with double-well potential subjected to Lévy noise have been studied intensively. However, most of such studies have resorted to numerical computation. We construct an analytically solvable model to study the occurrence of phase transitions driven by Lévy stable noise.

  17. Transient cluster formation in sheared non-Brownian suspensions

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

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

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

    PubMed

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

    2016-02-01

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

  19. Brownian Ratchets in Biophysics: from Diffusing Phospholipids to Polymerizing Actin Filaments

    NASA Astrophysics Data System (ADS)

    van Oudenaarden, Alexander

    2000-03-01

    In the 'Feynman Lectures on Physics' Feynman introduces a mechanical ratchet and pawl subjected to thermal fluctuations to demonstrate the impossibility to violate the second law of thermodynamics. Since this introduction the Brownian ratchet has evolved from Gedanken experiments to real experiments in the interdisciplinary sciences such as biophysics and biochemistry. In this symposium I will present two experiments in which the concept Brownian ratchet is of key importance. The first experiment addresses a so-called geometrical Brownian ratchet [1]. This ratchet consists of a two-dimensional microfabricated periodic array of asymmetric diffusion barriers. As an experimental realization of a two-dimensional fluid of Brownian particles, a bilayer of phospholipid molecules is used. I will demonstrate that the geometrical Brownian ratchet can be used as a molecular sieve to separate mixtures of membrane molecules without the need to extract them from the membrane. In the second experiment I explore the spontaneous symmetry breaking of polymerizing actin networks [2]. Small submicron size beads coated uniformly with a protein that catalyzes actin polymerization, are initially surrounded by a symmetrical cloud of actin filaments. This symmetry can be broken spontaneously after which the beads undergo directional motion with constant velocity. I will present a simple stochastic theory, in which each filament is modeled as an elastic Brownian ratchet that qualitatively reproduces the experimental results. The presence of the bead couples the dynamics of different filaments which results in a complex collective system of interacting Brownian ratchets that exhibits an emergent symmetry breaking behavior. [1] A. van Oudenaarden and S. G. Boxer, Science 285, 1046 (1999). [2] A. van Oudenaarden and J. A. Theriot, Nature Cell Biology 1, 493 (1999).

  20. Swarming behavior of gradient-responsive Brownian particles in a porous medium.

    PubMed

    Grančič, Peter; Štěpánek, František

    2012-07-01

    Active targeting by Brownian particles in a fluid-filled porous environment is investigated by computer simulation. The random motion of the particles is enhanced by diffusiophoresis with respect to concentration gradients of chemical signals released by the particles in the proximity of a target. The mathematical model, based on a combination of the Brownian dynamics method and a diffusion problem is formulated in terms of key parameters that include the particle diffusiophoretic mobility and the signaling threshold (the distance from the target at which the particles release their chemical signals). The results demonstrate that even a relatively simple chemical signaling scheme can lead to a complex collective behavior of the particles and can be a very efficient way of guiding a swarm of Brownian particles towards a target, similarly to the way colonies of living cells communicate via secondary messengers. PMID:23005461

  1. Swarming behavior of gradient-responsive Brownian particles in a porous medium

    NASA Astrophysics Data System (ADS)

    Grančič, Peter; Štěpánek, František

    2012-07-01

    Active targeting by Brownian particles in a fluid-filled porous environment is investigated by computer simulation. The random motion of the particles is enhanced by diffusiophoresis with respect to concentration gradients of chemical signals released by the particles in the proximity of a target. The mathematical model, based on a combination of the Brownian dynamics method and a diffusion problem is formulated in terms of key parameters that include the particle diffusiophoretic mobility and the signaling threshold (the distance from the target at which the particles release their chemical signals). The results demonstrate that even a relatively simple chemical signaling scheme can lead to a complex collective behavior of the particles and can be a very efficient way of guiding a swarm of Brownian particles towards a target, similarly to the way colonies of living cells communicate via secondary messengers.

  2. Counter-effect of Brownian and elastic forces on the liquid-to-solid transition of microgel suspensions.

    PubMed

    Di Lorenzo, Fany; Seiffert, Sebastian

    2015-07-14

    Suspensions of microgel particles undergo a transition from liquid-like to solid-like mechanics upon increase of the microgel packing fraction. We study the opposed effects of the microgel softness and size on this transition. We tune the softness of the microgels by varying their polymer crosslinking density, while we simultaneously and independently vary their size and the contribution of Brownian particle motion by investigating two sets of colloidal-scale microgels synthesized by precipitation polymerization, along with one set of granular-scale microgels prepared by droplet-templated polymerization in microfluidic devices. We find that the microgel packing fraction at which the liquid-to-solid transition occurs depends on both the size and the softness of the microgel particles: small and soft microgels undergo this transition at much larger packing fractions than stiff microgels of the same size and than larger microgels with the same softness. This work suggests a systematic strategy to quantitatively predict this transition. PMID:26053542

  3. Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise

    PubMed Central

    Zeng, Caibin; Yang, Qigui; Cao, Junfei

    2014-01-01

    This paper deals with the following type of stochastic partial differential equations (SPDEs) perturbed by an infinite dimensional fractional Brownian motion with a suitable volatility coefficient Φ: dX(t) = A(X(t))dt+Φ(t)dBH(t), where A is a nonlinear operator satisfying some monotonicity conditions. Using the variational approach, we prove the existence and uniqueness of variational solutions to such system. Moreover, we prove that this variational solution generates a random dynamical system. The main results are applied to a general type of nonlinear SPDEs and the stochastic generalized p-Laplacian equation. PMID:24574903

  4. Bifurcation dynamics of the tempered fractional Langevin equation.

    PubMed

    Zeng, Caibin; Yang, Qigui; Chen, YangQuan

    2016-08-01

    Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings. PMID:27586627

  5. Bifurcation dynamics of the tempered fractional Langevin equation

    NASA Astrophysics Data System (ADS)

    Zeng, Caibin; Yang, Qigui; Chen, YangQuan

    2016-08-01

    Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.

  6. Engineering Autonomous Chemomechanical Nanomachines Using Brownian Ratchets

    NASA Astrophysics Data System (ADS)

    Lavella, Gabriel

    Nanoscale machines which directly convert chemical energy into mechanical work are ubiquitous in nature and are employed to perform a diverse set of tasks such as transporting molecules, maintaining molecular gradients, and providing motion to organisms. Their widespread use in nature suggests that large technological rewards can be obtained by designing synthetic machines that use similar mechanisms. This thesis addresses the technological adaptation of a specific mechanism known as the Brownian ratchet for the design of synthetic autonomous nanomachines. My efforts were focused more specifically on synthetic chemomechanical ratchets which I deem will be broadly applicable in the life sciences. In my work I have theoretically explored the biophysical mechanisms and energy landscapes that give rise to the ratcheting phenomena and devised devices that operate off these principles. I demonstrate two generations of devices that produce mechanical force/deformation in response to a user specified ligand. The first generation devices, fabricatied using a combination nanoscale lithographic processes and bioconjugation techniques, were used to provide evidence that the proposed ratcheting phenomena can be exploited in synthetic architectures. Second generation devices fabricated using self-assembled DNA/hapten motifs were constructed to gain a precise understanding of ratcheting dynamics and design constraints. In addition, the self-assembled devices enabled fabrication en masse, which I feel will alleviate future experimental hurdles in analysis and facilitate its adaptation to technologies. The product of these efforts is an architecture that has the potential to enable numerous technologies in biosensing and drug delivery. For example, the coupling of molecule-specific actuation to the release of drugs or signaling molecules from nanocapsules or porous materials could be transformative. Such architectures could provide possible avenues to pressing issues in biology and

  7. Charge mobility induced by Brownian fluctuations in π-conjugated polymers in solution.

    PubMed

    Poole, Jessica Ellen; Damry, Djamshid Ahmud; Tozer, Oliver Robert; Barford, William

    2016-01-28

    We study the motion of a doped charge in a π-conjugated polymer chain in solution subject to Brownian fluctuations. Specifically, we take poly(para-phenylene) to be our model system where the Brownian fluctuations cause rotational motion of the phenylene rings. The instantaneous torsional fluctuations cause Anderson localization of the charge wavefunction, with the lower-energy spectrum being composed of local ground states and the higher-energy spectrum being composed of quasi-extended states. At low temperatures, additional charge localization occurs via torsional relaxation. The dynamical torsional fluctuations lead to two distinct modes of motion of the charge: adiabatic and non-adiabatic. Adiabatic motion is a 'crawling' motion of the charge along the polymer chain while the charge remains in its local ground state. Non-adiabatic motion is a rapid 'hopping' motion as the charge is excited into higher energy quasi-extended states and travels ballistically along the chain before relaxing into a local ground state. The adiabatic motion dominates at low temperatures, and exhibits a linear temperature dependence and thus a constant zero-field charge mobility. Non-adiabatic motion begins to dominate as the temperature is increased, as the charge is thermally excited into higher energy states. At high temperatures the diffusion constant becomes almost temperature independent, indicating a decrease in the charge mobility with increasing temperature, which we attribute to the charge localization length being a decreasing function of temperature at high temperatures. PMID:26699806

  8. Dosimetric consequences of inter-fraction breathing-pattern variation on radiotherapy with personalized motion-assessed margins

    NASA Astrophysics Data System (ADS)

    Kavanagh, A.; McQuaid, D.; Evans, P.; Webb, S.; Guckenberger, M.

    2011-11-01

    The data from eight patients who had undergone stereotactic body radiotherapy were selected due to their 4D-CT planning scans showing that their tumours had respiratory induced motion trajectories of large amplitude (greater than 9 mm in cranio-caudal direction). Radiotherapy plans with personalized motion-assessed margins were generated for these eight patients. The margins were generated by inverse 4D planning on an eight-bin phase-sorted 4D-CT scan. The planning was done on an in-house software system with a non-rigid registration stage being completed using freely available software. The resultant plans were then recalculated on a 4D-CT scan taken later during the course of treatment. Simulated image-guided patient set-up was used to align the geometric centres of the tumour region and minimize any misalignment between the two reconstructions. In general, the variation in the patient breathing patterns was found to be very small. Consequently, the degradation of the mean dose to the tumour region was found to be around a few percent (<3%) and hence was not a large effect.

  9. Stochastic description of quantum Brownian dynamics

    NASA Astrophysics Data System (ADS)

    Yan, Yun-An; Shao, Jiushu

    2016-08-01

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

  10. SU-C-BRF-02: Surface Imaging Based Analysis of Intra-Fraction Motion for Breast Radiotherapy Patients

    SciTech Connect

    Wiant, D; Wentworth, S; Maurer, J; Vanderstraeten, C; Terrell, J; Sintay, B

    2014-06-15

    Purpose: To quantify and characterize intrafraction motion for breast radiotherapy treatments using 3D surface imaging. Methods: Thirty free breathing breast patients were monitored with 3D surface imaging over a total of 831 monitoring sessions. Mean translations and rotations were calculated over each minute, each session, and over all sessions combined. The percentage of each session that the root mean square (RMS) of the linear translations were outside of 2 mm, 3 mm, 4 mm, and 5 mm were determined for each patient. Correlations between mean translations per minute and time and between standard deviation per minute and time were evaluated using Pearson's r value. Results: The mean RMS translation averaged over all patients was 2.63 mm +/- 1.63 mm. The patients spent an average of 52%, 24%, 11%, and 5% of the monitoring time outside of 2 mm, 3 mm, 4 mm, and 5 mm RMS tolerances, respectively. The RMS values averaged over all patients were 2.95 mm +/- 1.67 mm, 3.21 +/- 2.11, and 3.57 mm +/- 2.23 mm over the 5th, 10th, and 15th minutes of monitoring, respectively. The RMS values (r = 0.95, p = 0) and the standard deviations of the RMS values (r = 0.97, p = 0) both showed strong significant correlations with time. Conclusion: The majority of patients treatment time is spent within 5 mm of the isocenter. Patient position tends to drift with increasing time in the session. Treatment length should be considered when determining planning margins. An 8 mm margin on a target volume would account for two standard deviations of motion for a treatment up to 15 minutes in length.

  11. Extension of the NCAT phantom for the investigation of intra-fraction respiratory motion in IMRT using 4D Monte Carlo

    NASA Astrophysics Data System (ADS)

    McGurk, Ross; Seco, Joao; Riboldi, Marco; Wolfgang, John; Segars, Paul; Paganetti, Harald

    2010-03-01

    The purpose of this work was to create a computational platform for studying motion in intensity modulated radiotherapy (IMRT). Specifically, the non-uniform rational B-spline (NURB) cardiac and torso (NCAT) phantom was modified for use in a four-dimensional Monte Carlo (4D-MC) simulation system to investigate the effect of respiratory-induced intra-fraction organ motion on IMRT dose distributions as a function of diaphragm motion, lesion size and lung density. Treatment plans for four clinical scenarios were designed: diaphragm peak-to-peak amplitude of 1 cm and 3 cm, and two lesion sizes—2 cm and 4 cm diameter placed in the lower lobe of the right lung. Lung density was changed for each phase using a conservation of mass calculation. Further, a new heterogeneous lung model was implemented and tested. Each lesion had an internal target volume (ITV) subsequently expanded by 15 mm isotropically to give the planning target volume (PTV). The PTV was prescribed to receive 72 Gy in 40 fractions. The MLC leaf sequence defined by the planning system for each patient was exported and used as input into the MC system. MC simulations using the dose planning method (DPM) code together with deformable image registration based on the NCAT deformation field were used to find a composite dose distribution for each phantom. These composite distributions were subsequently analyzed using information from the dose volume histograms (DVH). Lesion motion amplitude has the largest effect on the dose distribution. Tumor size was found to have a smaller effect and can be mitigated by ensuring the planning constraints are optimized for the tumor size. The use of a dynamic or heterogeneous lung density model over a respiratory cycle does not appear to be an important factor with a <= 0.6% change in the mean dose received by the ITV, PTV and right lung. The heterogeneous model increases the realism of the NCAT phantom and may provide more accurate simulations in radiation therapy

  12. Brownian dynamics of a microswimmer

    NASA Astrophysics Data System (ADS)

    Lobaskin, V.; Lobaskin, D.; Kulić, I. M.

    2008-04-01

    We report on dynamic properties of a simple model microswimmer composed of three spheres and propelling itself in a viscous fluid by spinning motion of the spheres under zero net torque constraint. At a fixed temperature and increasing the spinning frequency, the swimmer demonstrates a transition from dissipation-dominated to a pumping-dominated motion regime characterized by negative effective friction coefficient. In the limit of high frequencies, the diffusion of the swimmer can be described by a model of an active particle with constant velocity.

  13. Determining inter-fractional motion of the uterus using 3D ultrasound imaging during radiotherapy for cervical cancer

    NASA Astrophysics Data System (ADS)

    Baker, Mariwan; Jensen, Jørgen Arendt; Behrens, Claus F.

    2014-03-01

    Uterine positional changes can reduce the accuracy of radiotherapy for cervical cancer patients. The purpose of this study was to; 1) Quantify the inter-fractional uterine displacement using a novel 3D ultrasound (US) imaging system, and 2) Compare the result with the bone match shift determined by Cone- Beam CT (CBCT) imaging.Five cervical cancer patients were enrolled in the study. Three of them underwent weekly CBCT imaging prior to treatment and bone match shift was applied. After treatment delivery they underwent a weekly US scan. The transabdominal scans were conducted using a Clarity US system (Clarity® Model 310C00). Uterine positional shifts based on soft-tissue match using US was performed and compared to bone match shifts for the three directions. Mean value (+/-1 SD) of the US shifts were (mm); anterior-posterior (A/P): (3.8+/-5.5), superior-inferior (S/I) (-3.5+/-5.2), and left-right (L/R): (0.4+/-4.9). The variations were larger than the CBCT shifts. The largest inter-fractional displacement was from -2 mm to +14 mm in the AP-direction for patient 3. Thus, CBCT bone matching underestimates the uterine positional displacement due to neglecting internal uterine positional change to the bone structures. Since the US images were significantly better than the CBCT images in terms of soft-tissue visualization, the US system can provide an optional image-guided radiation therapy (IGRT) system. US imaging might be a better IGRT system than CBCT, despite difficulty in capturing the entire uterus. Uterine shifts based on US imaging contains relative uterus-bone displacement, which is not taken into consideration using CBCT bone match.

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

    PubMed

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

    2014-02-01

    Developing molecular systems with functions analogous to those of macroscopic machine components, such as rotors, gyroscopes and valves, is a long-standing goal of nanotechnology. However, macroscopic analogies go only so far in predicting function in nanoscale environments, where friction dominates over inertia. In some instances, ratchet mechanisms have been used to bias the ever-present random, thermally driven (Brownian) motion and drive molecular diffusion in desired directions. Here, we visualize the motions of surface-bound molecular rotors using defocused fluorescence imaging, and observe the transition from hindered to free Brownian rotation by tuning medium viscosity. We show that the otherwise random rotations can be biased by the polarization of the excitation light field, even though the associated optical torque is insufficient to overcome thermal fluctuations. The biased rotation is attributed instead to a fluctuating-friction mechanism in which photoexcitation of the rotor strongly inhibits its diffusion rate. PMID:24441983

  15. Biased Brownian dynamics for rate constant calculation.

    PubMed

    Zou, G; Skeel, R D; Subramaniam, S

    2000-08-01

    An enhanced sampling method-biased Brownian dynamics-is developed for the calculation of diffusion-limited biomolecular association reaction rates with high energy or entropy barriers. Biased Brownian dynamics introduces a biasing force in addition to the electrostatic force between the reactants, and it associates a probability weight with each trajectory. A simulation loses weight when movement is along the biasing force and gains weight when movement is against the biasing force. The sampling of trajectories is then biased, but the sampling is unbiased when the trajectory outcomes are multiplied by their weights. With a suitable choice of the biasing force, more reacted trajectories are sampled. As a consequence, the variance of the estimate is reduced. In our test case, biased Brownian dynamics gives a sevenfold improvement in central processing unit (CPU) time with the choice of a simple centripetal biasing force. PMID:10919998

  16. Diffusion of torqued active Brownian particles

    NASA Astrophysics Data System (ADS)

    Sevilla, Francisco J.

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

  17. Absolute negative mobility of interacting Brownian particles

    NASA Astrophysics Data System (ADS)

    Ou, Ya-li; Hu, Cai-tian; Wu, Jian-chun; Ai, Bao-quan

    2015-12-01

    Transport of interacting Brownian particles in a periodic potential is investigated in the presence of an ac force and a dc force. From Brownian dynamic simulations, we find that both the interaction between particles and the thermal fluctuations play key roles in the absolute negative mobility (the particle noisily moves backwards against a small constant bias). When no the interaction acts, there is only one region where the absolute negative mobility occurs. In the presence of the interaction, the absolute negative mobility may appear in multiple regions. The weak interaction can be helpful for the absolute negative mobility, while the strong interaction has a destructive impact on it.

  18. Modeling an efficient Brownian heat engine

    NASA Astrophysics Data System (ADS)

    Asfaw Taye, Mesfin

    2008-03-01

    We investigate the effect of subdividing the ratchet potential on the performance of a tiny Brownian heat engine that modeled as a Brownian particle hopping in a viscous medium in a sawtooth potential (with or without load) assisted by alternately placed hot and cold heat baths along its path. We obtain analytic expression for the steady state current. The expressions for velocity, efficiency and coefficient of performance of refrigerator are reported for different number of barrier subdivisions. We find that the velocity, the efficiency and the coefficient of performance of the refrigerator maximize as the number of barrier subdivisions increase.

  19. Reduction of a wave packet in quantum Brownian motion

    SciTech Connect

    Unruh, W.G. ); Zurek, W.H.

    1989-08-15

    The effect of the environment on a quantum system is studied on an exactly solvable model: a harmonic oscillator interacting with a one-dimensional massless scalar field. We show that in an open quantum system, dissipation can cause decorrelation on a time scale significantly shorter than the relaxation time which characterizes the approach of the system to thermodynamic equilibrium. In particular, we demonstrate that the density matrix decays rapidly toward a mixture of approximate eigenstates'' of the pointer observable,'' which commutes with the system-environment interaction Hamiltonian. This observable can be regarded as continuously, if inaccurately, monitored by the scalar field environment. Both because in a harmonic oscillator the state of the system rotates in the phase space and because the effective environment measurement'' is weak, the system, on the short collision'' time scale (1/{Gamma}), maintains a coherence in this pointer observable on time scales of order ({gamma}/{Omega}ln({Gamma}/{Omega})){sup 1/2} and on longer time scales settles into a mixture of coherent states with a dispersion approximately consistent with the vacuum state. The master equation satisfied by the exact solution differs from the other master equations derived both for the high-temperature limit and for {ital T}=0. We discuss these differences and study the transition region between the high- and low-temperature regimes. We also consider the behavior of the system in the short-time transient'' regime. For {ital T}=0, we find that, in the long-time limit, the system behaves as if it were subject to 1/{ital f} noise.'' The generality of our model is considered and its predictions are compared with previous treatments of related problems. Some of the possible applications of the results to experimentally realizable situations are outlined.

  20. Reduction of a wave packet in quantum Brownian motion

    NASA Astrophysics Data System (ADS)

    Unruh, W. G.; Zurek, W. H.

    1989-08-01

    The effect of the environment on a quantum system is studied on an exactly solvable model: a harmonic oscillator interacting with a one-dimensional massless scalar field. We show that in an open quantum system, dissipation can cause decorrelation on a time scale significantly shorter than the relaxation time which characterizes the approach of the system to thermodynamic equilibrium. In particular, we demonstrate that the density matrix decays rapidly toward a mixture of ``approximate eigenstates'' of the ``pointer observable,'' which commutes with the system-environment interaction Hamiltonian. This observable can be regarded as continuously, if inaccurately, monitored by the scalar field environment. Both because in a harmonic oscillator the state of the system rotates in the phase space and because the effective environment ``measurement'' is weak, the system, on the short ``collision'' time scale (1/Γ), maintains a coherence in this pointer observable on time scales of order [γ/Ωln(Γ/Ω)]1/2 and on longer time scales settles into a mixture of coherent states with a dispersion approximately consistent with the vacuum state. The master equation satisfied by the exact solution differs from the other master equations derived both for the high-temperature limit and for T=0. We discuss these differences and study the transition region between the high- and low-temperature regimes. We also consider the behavior of the system in the short-time ``transient'' regime. For T=0, we find that, in the long-time limit, the system behaves as if it were subject to ``1/f noise.'' The generality of our model is considered and its predictions are compared with previous treatments of related problems. Some of the possible applications of the results to experimentally realizable situations are outlined. The significance of the environment-induced reduction of the wave packet for cosmological models is also briefly considered.

  1. Brownian motion of electrons in time-dependent magnetic fields.

    NASA Technical Reports Server (NTRS)

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

    1973-01-01

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

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

    PubMed

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

    2016-08-19

    We study the correlations between the maxima m and M of a Brownian motion (BM) on the time intervals [0,t_{1}] and [0,t_{2}], with t_{2}>t_{1}. We determine the exact forms of the distribution functions P(m,M) and P(G=M-m), and calculate the moments E{(M-m)^{k}} and the cross-moments E{m^{l}M^{k}} with arbitrary integers l and k. We show that correlations between m and M decay as sqrt[t_{1}/t_{2}] when t_{2}/t_{1}→∞, revealing strong memory effects in the statistics of the BM maxima. We also compute the Pearson correlation coefficient ρ(m,M) and the power spectrum of M_{t}, and we discuss a possibility of extracting the ensemble-averaged diffusion coefficient in single-trajectory experiments using a single realization of the maximum process. PMID:27588841

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

    SciTech Connect

    Padding, J. T.; Briels, W. J.

    2014-12-28

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

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

    NASA Astrophysics Data System (ADS)

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

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

  5. Brownian scattering of a spinon in a Luttinger liquid

    NASA Astrophysics Data System (ADS)

    Rieder, M.-T.; Levchenko, A.; Micklitz, T.

    2014-12-01

    We consider strongly interacting one-dimensional electron liquids where elementary excitations carry either spin or charge. At small temperatures a spinon created at the bottom of its band scatters off low-energy spin and charge excitations and follows the diffusive motion of a Brownian particle in momentum space. We calculate the mobility characterizing these processes and show that the resulting diffusion coefficient of the spinon is parametrically enhanced at low temperatures compared to that of a mobile impurity in a spinless Luttinger liquid. We briefly discuss that this hints at the relevance of spin in the process of equilibration of strongly interacting one-dimensional electrons, and comment on implications for transport in clean single-channel quantum wires.

  6. Skewed Brownian Fluctuations in Single-Molecule Magnetic Tweezers

    PubMed Central

    Burnham, Daniel R.; De Vlaminck, Iwijn; Henighan, Thomas; Dekker, Cees

    2014-01-01

    Measurements in magnetic tweezers rely upon precise determination of the position of a magnetic microsphere. Fluctuations in the position due to Brownian motion allows calculation of the applied force, enabling deduction of the force-extension response function for a single DNA molecule that is attached to the microsphere. The standard approach relies upon using the mean of position fluctuations, which is valid when the microsphere axial position fluctuations obey a normal distribution. However, here we demonstrate that nearby surfaces and the non-linear elasticity of DNA can skew the distribution. Through experiment and simulations, we show that such a skewing leads to inaccurate position measurements which significantly affect the extracted DNA extension and mechanical properties, leading to up to two-fold errors in measured DNA persistence length. We develop a simple, robust and easily implemented method to correct for such mismeasurements. PMID:25265383

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

    PubMed

    Padding, J T; Briels, W J

    2014-12-28

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

  8. Dynamic correlations in Brownian many-body systems.

    PubMed

    Brader, Joseph M; Schmidt, Matthias

    2014-01-21

    For classical Brownian systems driven out of equilibrium, we derive inhomogeneous two-time correlation functions from functional differentiation of the one-body density and current with respect to external fields. In order to allow for appropriate freedom upon building the derivatives, we formally supplement the Smoluchowski dynamics by a source term, which vanishes at the physical solution. These techniques are applied to obtain a complete set of dynamic Ornstein-Zernike equations, which serve for the development of approximation schemes. The rules of functional calculus lead naturally to non-Markovian equations of motion for the two-time correlators. Memory functions are identified as functional derivatives of a unique space- and time-nonlocal dissipation power functional. PMID:25669360

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

    NASA Astrophysics Data System (ADS)

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

    2016-08-01

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

  10. Solutions that enable ablative radiotherapy for large liver tumors: Fractionated dose painting, simultaneous integrated protection, motion management, and computed tomography image guidance.

    PubMed

    Crane, Christopher H; Koay, Eugene J

    2016-07-01

    The emergence and success of stereotactic body radiation therapy (SBRT) for the treatment of lung cancer have led to its rapid adoption for liver cancers. SBRT can achieve excellent results for small liver tumors. However, the vast majority of physicians interpret SBRT as meaning doses of radiation (range, 4-20 Gray [Gy]) that may not be ablative but are delivered within about 1 week (ie, in 3-6 fractions). Adherence to this approach has limited the effectiveness of SBRT for large liver tumors (>7 cm) because of the need to reduce doses to meet organ constraints. The prognosis for patients who present with large liver tumors is poor, with a median survival ≤12 months, and most of these patients die from tumor-related liver failure. Herein, the authors present a comprehensive solution to achieve ablative SBRT doses for patients with large liver tumors by using a combination of classic, modern, and novel concepts of radiotherapy: fractionation, dose painting, motion management, image guidance, and simultaneous integrated protection. The authors discuss these concepts in the context of large, inoperable liver tumors and review how this approach can substantially prolong survival for patients, most of whom otherwise have a very poor prognosis and few effective treatment options. Cancer 2016;122:1974-86. © 2016 American Cancer Society. PMID:26950735

  11. A Comparative Study of the Determination of Ferrofluid Particle Size by Means of Rotational Brownian Motion and Translational Brownian Motion

    NASA Astrophysics Data System (ADS)

    Fannin, P. C.; Charles, S. W.; Kopčanský, P.; Timko, M.; Ocelík, V.; Koneracká, M.; Tomčo, L.; Turek, I.; Štelina, J.; Musil, C.

    2001-06-01

    Two methods, the Toroidal Technique and the Forced Rayleigh Scattering (FRS) method, were used in the determination of the size of magnetic particles and their aggregates in magnetic fluids. The toroidal technique was used in the determination of the complex, frequency dependent magnetic susceptibility, x(w)=x'(w) - ix"(w) of magnetic fluids consisting of two colloidal suspensions of cobalt ferrite in hexadecene and a colloidal suspension of magnetite in isopar m with corresponding saturation magnetisation of 45.5 mT, 20 mT and 90 mT, respectively. Plots of the susceptibility components against frequency f over the range 10 Hz to 1 MHz, are shown to have approximate Debye-type profiles with the presence of relaxation components being indicated by the frequency, f max, of the maximum of the loss-peak in the x"(w) profiles. The FRS method (the interference of two intense laser beams in the thin film of magnetic fluid) was used to create the periodical structure of needle like clusters of magnetic particles. This creation is caused by a thermodiffusion effect known as the Soret effect. The obtained structures are indicative of as a self diffraction effect of the used primary laser beams. The relaxation phenomena arising from the switching off of the laser interference field is discussed in terms of a spectrum of relaxation times. This spectrum is proportional to the hydrodynamic particle size distribution. Corresponding calculations of particle hydrodynamic radius obtained by both mentioned methods indicate the presence of aggregates of magnetic particles.

  12. Effective diffusion of confined active Brownian swimmers.

    PubMed

    Sandoval, Mario; Dagdug, Leornardo

    2014-12-01

    We theoretically find the effect of confinement and thermal fluctuations on the diffusivity of a spherical active swimmer moving inside a two-dimensional narrow cavity of general shape. The explicit formulas for the effective diffusion coefficient of a swimmer moving inside two particular cavities are presented. We also compare our analytical results with Brownian dynamics simulations and we obtain excellent agreement. PMID:25615133

  13. Scaling the fractional advective-dispersive equation for numerical evaluation of microbial dynamics in confined geometries with sticky boundaries

    SciTech Connect

    Parashar, R.; Cushman, J.H.

    2008-06-20

    Microbial motility is often characterized by 'run and tumble' behavior which consists of bacteria making sequences of runs followed by tumbles (random changes in direction). As a superset of Brownian motion, Levy motion seems to describe such a motility pattern. The Eulerian (Fokker-Planck) equation describing these motions is similar to the classical advection-diffusion equation except that the order of highest derivative is fractional, {alpha} element of (0, 2]. The Lagrangian equation, driven by a Levy measure with drift, is stochastic and employed to numerically explore the dynamics of microbes in a flow cell with sticky boundaries. The Eulerian equation is used to non-dimensionalize parameters. The amount of sorbed time on the boundaries is modeled as a random variable that can vary over a wide range of values. Salient features of first passage time are studied with respect to scaled parameters.

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

    NASA Astrophysics Data System (ADS)

    Sugioka, Hideyuki

    2016-03-01

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

  15. Numerical Study of Fractional Ensemble Average Transport Equations

    NASA Astrophysics Data System (ADS)

    Kim, S.; Park, Y.; Gyeong, C. B.; Lee, O.

    2014-12-01

    In this presentation, a newly developed theory is applied to the case of stationary and non-stationary stochastic advective flow field, and a numerical solution method is presented for the resulting fractional Fokker-Planck equation (fFPE), which describes the evolution of the probability density function (PDF) of contaminant concentration. The derived fFPE is evaluated for three different form: 1) purely advective form, 2) second-order moment form and 3) second-order cumulant form. The Monte Carlo analysis of the fractional governing equation is then performed in a stochastic flow field, generated by a fractional Brownian motion for the stationary and non-stationary stochastic advection, in order to provide a benchmark for the results obtained from the fFPEs. When compared to the Monte Carlo simulation based PDFs and their ensemble average, the second-order cumulant form gives a good fit in terms of the shape and mode of the PDF of the contaminant concentration. Therefore, it is quite promising that the non-Fickian transport behavior can be modeled by the derived fractional ensemble average transport equations either by means of the long memory in the underlying stochastic flow, or by means of the time-space non-stationarity of the underlying stochastic flow, or by means of the time and space fractional derivatives of the transport equations. This subject is supported by Korea Ministry of Environment as "The Eco Innovation Project : Non-point source pollution control research group"

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

    NASA Astrophysics Data System (ADS)

    Yariv, Ehud; Schnitzer, Ory

    2014-09-01

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

  17. Ratcheting of Brownian swimmers in periodically corrugated channels: a reduced Fokker-Planck approach.

    PubMed

    Yariv, Ehud; Schnitzer, Ory

    2014-09-01

    We consider the motion of self-propelling Brownian particles in two-dimensional periodically corrugated channels. The point-size swimmers propel themselves in a direction which fluctuates by Brownian rotation; in addition, they undergo Brownian motion. The impermeability of the channel boundaries in conjunction with an asymmetry of the unit-cell geometry enables ratcheting, where a nonzero particle current is animated along the channel. This effect is studied here in the continuum limit using a diffusion-advection description of the probability density in a four-dimensional position-orientation space. Specifically, the mean particle velocity is calculated using macrotransport (generalized Taylor-dispersion) theory. This description reveals that the ratcheting mechanism is indirect: swimming gives rise to a biased spatial particle distribution which in turn results in a purely diffusive net current. For a slowly varying channel geometry, the dependence of this current upon the channel geometry and fluid-particle parameters is studied via a long-wave approximation over a reduced two-dimensional space. This allows for a straightforward seminumerical solution. In the limit where both rotational diffusion and swimming are strong, we find an asymptotic approximation to the particle current, scaling inversely with the square of the swimming Péclet number. For a given swimmer-fluid system, this limit is physically realized with increasing unit-cell size. PMID:25314403

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

    SciTech Connect

    Karzar-Jeddi, Mehdi; Fan, Tai-Hsi; Tuinier, Remco; Taniguchi, Takashi

    2014-06-07

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

  19. Modeling an efficient Brownian heat engine

    NASA Astrophysics Data System (ADS)

    Asfaw, Mesfin

    2008-09-01

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

  20. Brownian thermal noise in multilayer coated mirrors

    NASA Astrophysics Data System (ADS)

    Hong, Ting; Yang, Huan; Gustafson, Eric K.; Adhikari, Rana X.; Chen, Yanbei

    2013-04-01

    We analyze the Brownian thermal noise of a multilayer dielectric coating used in high-precision optical measurements, including interferometric gravitational-wave detectors. We assume the coating material to be isotropic, and therefore study thermal noises arising from shear and bulk losses of the coating materials. We show that coating noise arises not only from layer thickness fluctuations, but also from fluctuations of the interface between the coating and substrate, driven by fluctuating shear stresses of the coating. Although thickness fluctuations of different layers are statistically independent, there exists a finite coherence between the layers and the substrate-coating interface. In addition, photoelastic coefficients of the thin layers (so far not accurately measured) further influence the thermal noise, although at a relatively low level. Taking into account uncertainties in material parameters, we show that significant uncertainties still exist in estimating coating Brownian noise.

  1. Trajectories of the ribosome as a Brownian nanomachine

    PubMed Central

    Dashti, Ali; Schwander, Peter; Langlois, Robert; Fung, Russell; Li, Wen; Hosseinizadeh, Ahmad; Liao, Hstau Y.; Pallesen, Jesper; Sharma, Gyanesh; Stupina, Vera A.; Simon, Anne E.; Dinman, Jonathan D.; Frank, Joachim; Ourmazd, Abbas

    2014-01-01

    A Brownian machine, a tiny device buffeted by the random motions of molecules in the environment, is capable of exploiting these thermal motions for many of the conformational changes in its work cycle. Such machines are now thought to be ubiquitous, with the ribosome, a molecular machine responsible for protein synthesis, increasingly regarded as prototypical. Here we present a new analytical approach capable of determining the free-energy landscape and the continuous trajectories of molecular machines from a large number of snapshots obtained by cryogenic electron microscopy. We demonstrate this approach in the context of experimental cryogenic electron microscope images of a large ensemble of nontranslating ribosomes purified from yeast cells. The free-energy landscape is seen to contain a closed path of low energy, along which the ribosome exhibits conformational changes known to be associated with the elongation cycle. Our approach allows model-free quantitative analysis of the degrees of freedom and the energy landscape underlying continuous conformational changes in nanomachines, including those important for biological function. PMID:25422471

  2. Simulating Brownian suspensions with fluctuating hydrodynamics

    NASA Astrophysics Data System (ADS)

    Delmotte, Blaise; Keaveny, Eric E.

    2015-12-01

    Fluctuating hydrodynamics has been successfully combined with several computational methods to rapidly compute the correlated random velocities of Brownian particles. In the overdamped limit where both particle and fluid inertia are ignored, one must also account for a Brownian drift term in order to successfully update the particle positions. In this paper, we present an efficient computational method for the dynamic simulation of Brownian suspensions with fluctuating hydrodynamics that handles both computations and provides a similar approximation as Stokesian Dynamics for dilute and semidilute suspensions. This advancement relies on combining the fluctuating force-coupling method (FCM) with a new midpoint time-integration scheme we refer to as the drifter-corrector (DC). The DC resolves the drift term for fluctuating hydrodynamics-based methods at a minimal computational cost when constraints are imposed on the fluid flow to obtain the stresslet corrections to the particle hydrodynamic interactions. With the DC, this constraint needs only to be imposed once per time step, reducing the simulation cost to nearly that of a completely deterministic simulation. By performing a series of simulations, we show that the DC with fluctuating FCM is an effective and versatile approach as it reproduces both the equilibrium distribution and the evolution of particulate suspensions in periodic as well as bounded domains. In addition, we demonstrate that fluctuating FCM coupled with the DC provides an efficient and accurate method for large-scale dynamic simulation of colloidal dispersions and the study of processes such as colloidal gelation.

  3. Fractional diffusion equation for an n -dimensional correlated Lévy walk

    NASA Astrophysics Data System (ADS)

    Taylor-King, Jake P.; Klages, Rainer; Fedotov, Sergei; Van Gorder, Robert A.

    2016-07-01

    Lévy walks define a fundamental concept in random walk theory that allows one to model diffusive spreading faster than Brownian motion. They have many applications across different disciplines. However, so far the derivation of a diffusion equation for an n -dimensional correlated Lévy walk remained elusive. Starting from a fractional Klein-Kramers equation here we use a moment method combined with a Cattaneo approximation to derive a fractional diffusion equation for superdiffusive short-range auto-correlated Lévy walks in the large time limit, and we solve it. Our derivation discloses different dynamical mechanisms leading to correlated Lévy walk diffusion in terms of quantities that can be measured experimentally.

  4. Fractional diffusion equation for an n-dimensional correlated Lévy walk.

    PubMed

    Taylor-King, Jake P; Klages, Rainer; Fedotov, Sergei; Van Gorder, Robert A

    2016-07-01

    Lévy walks define a fundamental concept in random walk theory that allows one to model diffusive spreading faster than Brownian motion. They have many applications across different disciplines. However, so far the derivation of a diffusion equation for an n-dimensional correlated Lévy walk remained elusive. Starting from a fractional Klein-Kramers equation here we use a moment method combined with a Cattaneo approximation to derive a fractional diffusion equation for superdiffusive short-range auto-correlated Lévy walks in the large time limit, and we solve it. Our derivation discloses different dynamical mechanisms leading to correlated Lévy walk diffusion in terms of quantities that can be measured experimentally. PMID:27575074

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

    PubMed Central

    2014-01-01

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

  6. Fokker-Planck equation with arbitrary dc and ac fields: continued fraction method.

    PubMed

    Lee, Chee Kong; Gong, Jiangbin

    2011-07-01

    The continued fraction method (CFM) is used to solve the Fokker-Planck equation with arbitrary dc and ac fields. With an appropriate choice of basis functions, the Fokker-Planck equation is converted into a set of linear algebraic equations with short-ranged coupling and then CFM is implemented to obtain numerical solutions with high efficiency. Both a proposed perturbative CFM and the numerically exact matrix CFM are used to study the nonlinear response of driven systems, with their results compared to assess the validity regime of the perturbative approach. The proposed perturbative CFM approach needs scalar quantities only and hence is more efficient within its validity regime. Two nonlinear systems of different nature are used as examples: molecular dipole (rotational Brownian motion) and particle in a periodic potential (translational Brownian motion). The associated full dynamics is presented in the compact form of hysteresis loops. It is observed that as the strength of an AC driving field increases, pronounced nonlinear effects are manifested in the deformation of the hysteresis loops. PMID:21867110

  7. Brownian transport in corrugated channels with inertia

    NASA Astrophysics Data System (ADS)

    Ghosh, P. K.; Hänggi, P.; Marchesoni, F.; Nori, F.; Schmid, G.

    2012-08-01

    Transport of suspended Brownian particles dc driven along corrugated narrow channels is numerically investigated in the regime of finite damping. We show that inertial corrections cannot be neglected as long as the width of the channel bottlenecks is smaller than an appropriate particle diffusion length, which depends on the the channel corrugation and the drive intensity. With such a diffusion length being inversely proportional to the damping constant, transport through sufficiently narrow obstructions turns out to be always sensitive to the viscosity of the suspension fluid. The inertia corrections to the transport quantifiers, mobility, and diffusivity markedly differ for smoothly and sharply corrugated channels.

  8. A Brownian model for recurrent earthquakes

    USGS Publications Warehouse

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

    2002-01-01

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

  9. Momentum relaxation of a relativistic Brownian particle.

    PubMed

    Felderhof, B U

    2012-12-01

    The momentum relaxation of a relativistic Brownian particle immersed in a fluid is studied on the basis of the Fokker-Planck equation for the relativistic Ornstein-Uhlenbeck process. An analytical expression is derived for the short-time relaxation rate. The relaxation spectrum has both discrete and continuum components. It is shown that the Fokker-Planck equation under consideration is closely related to the Schrödinger equation for the hydrogen atom. Hence it follows that there is an infinite number of discrete states. The momentum autocorrelation function is calculated numerically for a strongly relativistic particle. PMID:23367889

  10. Effective diffusion of confined active Brownian swimmers

    NASA Astrophysics Data System (ADS)

    Sandoval, Mario; Dagdug, Leonardo

    2014-11-01

    We find theoretically the effect of confinement and thermal fluctuations, on the diffusivity of a spherical active swimmer moving inside a two-dimensional narrow cavity of general shape. The explicit formulas for the effective diffusion coefficient of a swimmer moving inside two particular cavities are presented. We also compare our analytical results with Brownian Dynamics simulations and we obtain excellent agreement. L.D. thanks Consejo Nacional de Ciencia y Tecnologia (CONACyT) Mexico, for partial support by Grant No. 176452. M. S. thanks CONACyT and Programa de Mejoramiento de Profesorado (PROMEP) for partially funding this work under Grant No. 103.5/13/6732.

  11. The molecular motion of bovine serum albumin under physiological conditions is ion specific.

    PubMed

    Medda, Luca; Monduzzi, Maura; Salis, Andrea

    2015-04-18

    Specific ion effects on the Brownian molecular motion of BSA protein under physiological conditions are investigated. New useful insights into Hofmeister phenomena related to electrolyte-protein interactions are presented. PMID:25782536

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

    NASA Astrophysics Data System (ADS)

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

    2015-03-01

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

  13. A Nanoscale, Liquid-Phase DNA Separation Device Based on Brownian Ratchets

    NASA Astrophysics Data System (ADS)

    Bader, Joel S.

    1998-03-01

    Realizing the goals of the Human Genome Project depends on the ability to perform size-based separations of DNA molecules. DNA analysis has traditionally required inconvenient gel-based electrophoretic separations. We describe a novel, micromachined, non-electrophoretic device suitable for lab-on-a-chip applications. The device is designed to transport DNA using an asymmetric, periodic potential to rectify Brownian motion. The separation occurs in a homogeneous liquid, avoiding the use of gels or other special media. Experimental results from a working prototype NanoNiagara device validate theoretical predictions of its ability to transport DNA molecules based on size.

  14. Noise-to-signal transition of a Brownian particle in the cubic potential: I. general theory

    NASA Astrophysics Data System (ADS)

    Filip, Radim; Zemánek, Pavel

    2016-06-01

    The noise-to-signal transitions are very interesting processes in physics, as they might transform environmental noise to useful mechanical effects. We theoretically analyze stochastic noise-to-signal transition of overdamped Brownian motion of a particle in the cubic potential. The particle reaches thermal equilibrium with its environment in the quadratic potential which is suddenly swapped to the cubic potential. We predict a simultaneous increase of both the displacement and signal-to-noise ratio in the cubic potential for the position linearly powered by the temperature of the particle environment. The short-time analysis and numerical simulations fully confirm different dynamical regimes of this noise-to-signal transition.

  15. Statistics of a Flux in Burgers Turbulencewith One-Sided Brownian Initial Data

    NASA Astrophysics Data System (ADS)

    Bertoin, J.; Giraud, C.; Isozaki, Y.

    We study the statistics of the flux of particles crossing the origin, which is induced by the dynamics of ballistic aggregation in dimension 1, under certain random initial conditions for the system. More precisely, we consider the cases when particles are uniformly distributed on at the initial time, and if u(x,t) denotes the velocity of the particle located at x at time t, then u(x,0)= 0 for x<0 and (u(x,0), x>= 0) is either a white noise or a Brownian motion.

  16. Brownian dynamics simulations of ellipsoidal magnetizable particle suspensions

    NASA Astrophysics Data System (ADS)

    Torres-Díaz, I.; Rinaldi, C.

    2014-06-01

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

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

    PubMed Central

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

    2015-01-01

    Mitochondrial morphology has been associated with numerous pathologies including cancer, diabetes, obesity and heart disease. However, the connection is poorly understood—in part due to the difficulty of characterizing the morphology. This impedes the use of morphology as a tool for disease detection/monitoring. Here, we use the Brownian motion of isolated mitochondria to characterize their size and shape in a high throughput fashion. By using treadmill exercise training, mitochondria from heart and gastrocnemius of Balb/c mice were modulated in size and used to investigate the protocol. Consistent with previous reports, the heart mitochondria of untrained mice increased 5% in diameter immediately after a single bout of moderate exercise (1.091 ± 0.004 μm) as compared to completely sedentary controls (1.040 ± 0.022 μm). In addition, no change was observed in the size of gastrocnemius mitochondria (1.025 ± 0.018 μm), which was also in agreement with previous studies. The method was also successfully applied to smaller Saccharomyces cerevisiae mitochondria. PMID:26435755

  18. Performance Estimation for Two-Dimensional Brownian Rotary Ratchet Systems

    NASA Astrophysics Data System (ADS)

    Tutu, Hiroki; Horita, Takehiko; Ouchi, Katsuya

    2015-04-01

    Within the context of the Brownian ratchet model, a molecular rotary system that can perform unidirectional rotations induced by linearly polarized ac fields and produce positive work under loads was studied. The model is based on the Langevin equation for a particle in a two-dimensional (2D) three-tooth ratchet potential of threefold symmetry. The performance of the system is characterized by the coercive torque, i.e., the strength of the load competing with the torque induced by the ac driving field, and the energy efficiency in force conversion from the driving field to the torque. We propose a master equation for coarse-grained states, which takes into account the boundary motion between states, and develop a kinetic description to estimate the mean angular momentum (MAM) and powers relevant to the energy balance equation. The framework of analysis incorporates several 2D characteristics and is applicable to a wide class of models of smooth 2D ratchet potential. We confirm that the obtained expressions for MAM, power, and efficiency of the model can enable us to predict qualitative behaviors. We also discuss the usefulness of the torque/power relationship for experimental analyses, and propose a characteristic for 2D ratchet systems.

  19. Brownian aggregation rate of colloid particles with several active sites

    SciTech Connect

    Nekrasov, Vyacheslav M.; Yurkin, Maxim A.; Chernyshev, Andrei V.; Polshchitsin, Alexey A.; Yakovleva, Galina E.; Maltsev, Valeri P.

    2014-08-14

    We theoretically analyze the aggregation kinetics of colloid particles with several active sites. Such particles (so-called “patchy particles”) are well known as chemically anisotropic reactants, but the corresponding rate constant of their aggregation has not yet been established in a convenient analytical form. Using kinematic approximation for the diffusion problem, we derived an analytical formula for the diffusion-controlled reaction rate constant between two colloid particles (or clusters) with several small active sites under the following assumptions: the relative translational motion is Brownian diffusion, and the isotropic stochastic reorientation of each particle is Markovian and arbitrarily correlated. This formula was shown to produce accurate results in comparison with more sophisticated approaches. Also, to account for the case of a low number of active sites per particle we used Monte Carlo stochastic algorithm based on Gillespie method. Simulations showed that such discrete model is required when this number is less than 10. Finally, we applied the developed approach to the simulation of immunoagglutination, assuming that the formed clusters have fractal structure.

  20. Nanofluidic Brownian Ratchet via atomically-stepped surfaces

    NASA Astrophysics Data System (ADS)

    Rahmani, Amir; Colosqui, Carlos

    2015-11-01

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

  1. Dynamics of non-Brownian fiber suspensions under periodic shear.

    PubMed

    Franceschini, Alexandre; Filippidi, Emmanouela; Guazzelli, Elisabeth; Pine, David J

    2014-09-21

    We report experiments studying the dynamics of dense non-Brownian fiber suspensions subjected to periodic oscillatory shear. We find that periodic shear initially causes fibers to collide and to undergo irreversible diffusion. As time progresses, the fibers tend to orient in the vorticity direction while the number of collisions decreases. Ultimately, the system goes to one of two steady states: an absorbing steady state, where collisions cease and the fibers undergo reversible trajectories; an active state, where fibers continue to collide causing them to diffuse and undergo irreversible trajectories. Collisions between fibers can be characterized by an effective volume fraction Φ with a critical volume fraction Φc that separates absorbing from active (diffusing) steady states. The effective volume fraction Φ depends on the mean fiber orientation and thus decreases in time as fibers progressively orient under periodic shear. In the limit that the temporal evolution of Φ is slow compared to the activity relaxation time τ, all the data for all strain amplitudes and all concentrations can be scaled onto a single master curve with a functional dependence well-described by t(-β/ν)R(e(-t)R), where tR is the rescaled time. As Φ → Φc, τ diverges. Therefore, for experiments in which Φ(t) starts above Φc but goes to a steady state below Φc, departures from scaling are observed for Φ very near Φc. The critical exponents are measured to be β = 0.84 ± 0.04 and ν = 1.1 ± 0.1, which is consistent with the Manna universality class for directed percolation. PMID:25068577

  2. Brownian simulations and unidirectional flux in diffusion.

    PubMed

    Singer, A; Schuss, Z

    2005-02-01

    The prediction of ionic currents in protein channels of biological membranes is one of the central problems of computational molecular biophysics. Existing continuum descriptions of ionic permeation fail to capture the rich phenomenology of the permeation process, so it is therefore necessary to resort to particle simulations. Brownian dynamics (BD) simulations require the connection of a small discrete simulation volume to large baths that are maintained at fixed concentrations and voltages. The continuum baths are connected to the simulation through interfaces, located in the baths sufficiently far from the channel. Average boundary concentrations have to be maintained at their values in the baths by injecting and removing particles at the interfaces. The particles injected into the simulation volume represent a unidirectional diffusion flux, while the outgoing particles represent the unidirectional flux in the opposite direction. The classical diffusion equation defines net diffusion flux, but not unidirectional fluxes. The stochastic formulation of classical diffusion in terms of the Wiener process leads to a Wiener path integral, which can split the net flux into unidirectional fluxes. These unidirectional fluxes are infinite, though the net flux is finite and agrees with classical theory. We find that the infinite unidirectional flux is an artifact caused by replacing the Langevin dynamics with its Smoluchowski approximation, which is classical diffusion. The Smoluchowski approximation fails on time scales shorter than the relaxation time 1/gamma of the Langevin equation. We find that the probability of Brownian trajectories that cross an interface in one direction in unit time Deltat equals that of the probability of the corresponding Langevin trajectories if gammaDeltat=2 . That is, we find the unidirectional flux (source strength) needed to maintain average boundary concentrations in a manner consistent with the physics of Brownian particles. This

  3. Self-Consistent Simulation of the Brownian Stage of Dust Growth

    NASA Technical Reports Server (NTRS)

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

    1996-01-01

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

  4. Brownian Dynamics Simulations of Dispersed Graphene Sheets

    NASA Astrophysics Data System (ADS)

    Xu, Yueyi; Green, Micah

    2013-03-01

    Past simulations of the dynamics of dispersed graphene sheets are limited to static fluids on small timescales, with little attention devoted to flow dynamics. To address this need, we investigated how flow fields affect graphene morphology dynamics using a coarse-grained model; this relatively untouched area is critical given the importance of graphene solution-processing of multifunctional devices and materials. In particular, we developed a Brownian Dynamics (BD) algorithm to study the morphology of sheetlike macromolecules in dilute, flowing solutions. We used a bead-rod lattice to represent the mesoscopic conformation of individual two dimensional sheets. We then analyzed the morphology dynamic modes (stretching, tumbling, crumpling) of these molecules as a function of sheet size, Weissenberg number, and bending stiffness. Our results indicate the model can successfully simulate a range of dynamic modes in a given flow field and yield fundamental insight into the flow processing of graphene sheets.

  5. Communication: Memory effects and active Brownian diffusion.

    PubMed

    Ghosh, Pulak K; Li, Yunyun; Marchegiani, Giampiero; Marchesoni, Fabio

    2015-12-01

    A self-propelled artificial microswimmer is often modeled as a ballistic Brownian particle moving with constant speed aligned along one of its axis, but changing direction due to random collisions with the environment. Similarly to thermal noise, its angular randomization is described as a memoryless stochastic process. Here, we speculate that finite-time correlations in the orientational dynamics can affect the swimmer's diffusivity. To this purpose, we propose and solve two alternative models. In the first one, we simply assume that the environmental fluctuations governing the swimmer's propulsion are exponentially correlated in time, whereas in the second one, we account for possible damped fluctuations of the propulsion velocity around the swimmer's axis. The corresponding swimmer's diffusion constants are predicted to get, respectively, enhanced or suppressed upon increasing the model memory time. Possible consequences of this effect on the interpretation of the experimental data are discussed. PMID:26646861

  6. Communication: Memory effects and active Brownian diffusion

    NASA Astrophysics Data System (ADS)

    Ghosh, Pulak K.; Li, Yunyun; Marchegiani, Giampiero; Marchesoni, Fabio

    2015-12-01

    A self-propelled artificial microswimmer is often modeled as a ballistic Brownian particle moving with constant speed aligned along one of its axis, but changing direction due to random collisions with the environment. Similarly to thermal noise, its angular randomization is described as a memoryless stochastic process. Here, we speculate that finite-time correlations in the orientational dynamics can affect the swimmer's diffusivity. To this purpose, we propose and solve two alternative models. In the first one, we simply assume that the environmental fluctuations governing the swimmer's propulsion are exponentially correlated in time, whereas in the second one, we account for possible damped fluctuations of the propulsion velocity around the swimmer's axis. The corresponding swimmer's diffusion constants are predicted to get, respectively, enhanced or suppressed upon increasing the model memory time. Possible consequences of this effect on the interpretation of the experimental data are discussed.

  7. Arithmetic area for m planar Brownian paths

    NASA Astrophysics Data System (ADS)

    Desbois, Jean; Ouvry, Stéphane

    2012-05-01

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

  8. Communication: Memory effects and active Brownian diffusion

    SciTech Connect

    Ghosh, Pulak K.; Li, Yunyun; Marchegiani, Giampiero; Marchesoni, Fabio

    2015-12-07

    A self-propelled artificial microswimmer is often modeled as a ballistic Brownian particle moving with constant speed aligned along one of its axis, but changing direction due to random collisions with the environment. Similarly to thermal noise, its angular randomization is described as a memoryless stochastic process. Here, we speculate that finite-time correlations in the orientational dynamics can affect the swimmer’s diffusivity. To this purpose, we propose and solve two alternative models. In the first one, we simply assume that the environmental fluctuations governing the swimmer’s propulsion are exponentially correlated in time, whereas in the second one, we account for possible damped fluctuations of the propulsion velocity around the swimmer’s axis. The corresponding swimmer’s diffusion constants are predicted to get, respectively, enhanced or suppressed upon increasing the model memory time. Possible consequences of this effect on the interpretation of the experimental data are discussed.

  9. Local collective motion analysis for multi-probe dynamic imaging and microrheology.

    PubMed

    Khan, Manas; Mason, Thomas G

    2016-08-01

    Dynamical artifacts, such as mechanical drift, advection, and hydrodynamic flow, can adversely affect multi-probe dynamic imaging and passive particle-tracking microrheology experiments. Alternatively, active driving by molecular motors can cause interesting non-Brownian motion of probes in local regions. Existing drift-correction techniques, which require large ensembles of probes or fast temporal sampling, are inadequate for handling complex spatio-temporal drifts and non-Brownian motion of localized domains containing relatively few probes. Here, we report an analytical method based on local collective motion (LCM) analysis of as few as two probes for detecting the presence of non-Brownian motion and for accurately eliminating it to reveal the underlying Brownian motion. By calculating an ensemble-average, time-dependent, LCM mean square displacement (MSD) of two or more localized probes and comparing this MSD to constituent single-probe MSDs, we can identify temporal regimes during which either thermal or athermal motion dominates. Single-probe motion, when referenced relative to the moving frame attached to the multi-probe LCM trajectory, provides a true Brownian MSD after scaling by an appropriate correction factor that depends on the number of probes used in LCM analysis. We show that LCM analysis can be used to correct many different dynamical artifacts, including spatially varying drifts, gradient flows, cell motion, time-dependent drift, and temporally varying oscillatory advection, thereby offering a significant improvement over existing approaches. PMID:27269299

  10. Local collective motion analysis for multi-probe dynamic imaging and microrheology

    NASA Astrophysics Data System (ADS)

    Khan, Manas; Mason, Thomas G.

    2016-08-01

    Dynamical artifacts, such as mechanical drift, advection, and hydrodynamic flow, can adversely affect multi-probe dynamic imaging and passive particle-tracking microrheology experiments. Alternatively, active driving by molecular motors can cause interesting non-Brownian motion of probes in local regions. Existing drift-correction techniques, which require large ensembles of probes or fast temporal sampling, are inadequate for handling complex spatio-temporal drifts and non-Brownian motion of localized domains containing relatively few probes. Here, we report an analytical method based on local collective motion (LCM) analysis of as few as two probes for detecting the presence of non-Brownian motion and for accurately eliminating it to reveal the underlying Brownian motion. By calculating an ensemble-average, time-dependent, LCM mean square displacement (MSD) of two or more localized probes and comparing this MSD to constituent single-probe MSDs, we can identify temporal regimes during which either thermal or athermal motion dominates. Single-probe motion, when referenced relative to the moving frame attached to the multi-probe LCM trajectory, provides a true Brownian MSD after scaling by an appropriate correction factor that depends on the number of probes used in LCM analysis. We show that LCM analysis can be used to correct many different dynamical artifacts, including spatially varying drifts, gradient flows, cell motion, time-dependent drift, and temporally varying oscillatory advection, thereby offering a significant improvement over existing approaches.

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

    PubMed

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

    2016-03-28

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

  12. Fast antibody fragment motion: flexible linkers act as entropic spring

    DOE PAGESBeta

    Stingaciu, Laura R.; Ivanova, Oxana; Ohl, Michael; Biehl, Ralf; Richter, Dieter

    2016-03-29

    A flexible linker region between three fragments allows antibodies to adjust their binding sites to an antigen or receptor. Using Neutron Spin Echo Spectroscopy we observed fragment motion on a timescale of 7 ns with motional amplitudes of about 1 nm relative to each other. The mechanistic complexity of the linker region can be described by a spring model with Brownian motion of the fragments in a harmonic potential. Displacements, timescale, friction and force constant of the underlying dynamics are accessed. The force constant exhibits a similar strength to an entropic spring, with friction of the fragment matching the unboundmore » state. The observed fast motions are fluctuations in pre-existing equilibrium configurations. In conclusion, the Brownian motion of domains in a harmonic potential is the appropriate model to examine functional hinge motions dependent on the structural topology and highlights the role of internal forces and friction to function.« less

  13. Fast antibody fragment motion: flexible linkers act as entropic spring

    PubMed Central

    Stingaciu, Laura R.; Ivanova, Oxana; Ohl, Michael; Biehl, Ralf; Richter, Dieter

    2016-01-01

    A flexible linker region between three fragments allows antibodies to adjust their binding sites to an antigen or receptor. Using Neutron Spin Echo Spectroscopy we observed fragment motion on a timescale of 7 ns with motional amplitudes of about 1 nm relative to each other. The mechanistic complexity of the linker region can be described by a spring model with Brownian motion of the fragments in a harmonic potential. Displacements, timescale, friction and force constant of the underlying dynamics are accessed. The force constant exhibits a similar strength to an entropic spring, with friction of the fragment matching the unbound state. The observed fast motions are fluctuations in pre-existing equilibrium configurations. The Brownian motion of domains in a harmonic potential is the appropriate model to examine functional hinge motions dependent on the structural topology and highlights the role of internal forces and friction to function. PMID:27020739

  14. Fast antibody fragment motion: flexible linkers act as entropic spring.

    PubMed

    Stingaciu, Laura R; Ivanova, Oxana; Ohl, Michael; Biehl, Ralf; Richter, Dieter

    2016-01-01

    A flexible linker region between three fragments allows antibodies to adjust their binding sites to an antigen or receptor. Using Neutron Spin Echo Spectroscopy we observed fragment motion on a timescale of 7 ns with motional amplitudes of about 1 nm relative to each other. The mechanistic complexity of the linker region can be described by a spring model with Brownian motion of the fragments in a harmonic potential. Displacements, timescale, friction and force constant of the underlying dynamics are accessed. The force constant exhibits a similar strength to an entropic spring, with friction of the fragment matching the unbound state. The observed fast motions are fluctuations in pre-existing equilibrium configurations. The Brownian motion of domains in a harmonic potential is the appropriate model to examine functional hinge motions dependent on the structural topology and highlights the role of internal forces and friction to function. PMID:27020739

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

    NASA Astrophysics Data System (ADS)

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

    2016-03-01

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

  16. Rotational Brownian Dynamics simulations of clathrin cage formation

    SciTech Connect

    Ilie, Ioana M.; Briels, Wim J.; Otter, Wouter K. den

    2014-08-14

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

  17. Fast orthogonal transforms and generation of Brownian paths

    PubMed Central

    Leobacher, Gunther

    2012-01-01

    We present a number of fast constructions of discrete Brownian paths that can be used as alternatives to principal component analysis and Brownian bridge for stratified Monte Carlo and quasi-Monte Carlo. By fast we mean that a path of length n can be generated in O(nlog(n)) floating point operations. We highlight some of the connections between the different constructions and we provide some numerical examples. PMID:23471545

  18. Transient Response of Seismicity and Earthquake Probabilities to Stress Transfer in a Brownian Earthquake Model

    NASA Astrophysics Data System (ADS)

    Ellsworth, W. L.; Matthews, M. V.; Simpson, R. W.

    2001-12-01

    A statistical mechanical description of elastic rebound is used to study earthquake interaction and stress transfer effects in a point process model of earthquakes. The model is a Brownian Relaxation Oscillator (BRO) in which a random walk (standard Brownian motion) is added to a steady tectonic loading to produce a stochastic load state process. Rupture occurs in this model when the load state reaches a critical value. The load state is a random variable and may be described at any point in time by its probability density. Load state evolves toward the failure threshold due to tectonic loading (drift), and diffuses due to Brownian motion (noise) according to a diffusion equation. The Brownian perturbation process formally represents the sum total of all factors, aside from tectonic loading, that govern rupture. Physically, these factors may include effects of earthquakes external to the source, aseismic loading, interaction effects within the source itself, healing, pore pressure evolution, etc. After a sufficiently long time, load state always evolves to a steady state probability density that is independent of the initial condition and completely described by the drift rate and noise scale. Earthquake interaction and stress transfer effects are modeled by an instantaneous change in the load state. A negative step reduces the probability of failure, while a positive step may either immediately trigger rupture or increase the failure probability (hazard). When the load state is far from failure, the effects are well-approximated by ``clock advances'' that shift the unperturbed hazard down or up, as appropriate for the sign of the step. However, when the load state is advanced in the earthquake cycle, the response is a sharp, temporally localized decrease or increase in hazard. Recovery of the hazard is characteristically ``Omori like'' ( ~ 1/t), which can be understood in terms of equilibrium thermodynamical considerations since state evolution is diffusion with

  19. Brownian Dynamics Simulation of Macromolecule Diffusion in a Protocell

    NASA Astrophysics Data System (ADS)

    Ando, Tadashi; Skolnick, Jeffrey

    2011-01-01

    The interiors of all living cells are highly crowded with macro molecules, which differs considerably the thermodynamics and kinetics of biological reactions between in vivo and in vitro. For example, the diffusion of green fluorescent protein (GFP) in E. coli is ~10-fold slower than in dilute conditions. In this study, we performed Brownian dynamics (BD) simulations of rigid macromolecules in a crowded environment mimicking the cytosol of E. coli to study the motions of macromolecules. The simulation systems contained 35 70S ribosomes, 750 glycolytic enzymes, 75 GFPs, and 392 tRNAs in a 100 nm × 100 nm × 100 nm simulation box, where the macromolecules were represented by rigid-objects of one bead per amino acid or four beads per nucleotide models. Diffusion tensors of these molecules in dilute solutions were estimated by using a hydrodynamic theory to take into account the diffusion anisotropy of arbitrary shaped objects in the BD simulations. BD simulations of the system where each macromolecule is represented by its Stokes radius were also performed for comparison. Excluded volume effects greatly reduce the mobility of molecules in crowded environments for both molecular-shaped and equivalent sphere systems. Additionally, there were no significant differences in the reduction of diffusivity over the entire range of molecular size between two systems. However, the reduction in diffusion of GFP in these systems was still 4-5 times larger than for the in vivo experiment. We will discuss other plausible factors that might cause the large reduction in diffusion in vivo.

  20. Ideal bulk pressure of active Brownian particles

    NASA Astrophysics Data System (ADS)

    Speck, Thomas; Jack, Robert L.

    2016-06-01

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

  1. Ideal bulk pressure of active Brownian particles.

    PubMed

    Speck, Thomas; Jack, Robert L

    2016-06-01

    The extent to which active matter might be described by effective equilibrium concepts like temperature and pressure is currently being discussed intensely. Here, we study the simplest model, an ideal gas of noninteracting active Brownian particles. While the mechanical pressure exerted onto confining walls has been linked to correlations between particles' positions and their orientations, we show that these correlations are entirely controlled by boundary effects. We also consider a definition of local pressure, which describes interparticle forces in terms of momentum exchange between different regions of the system. We present three pieces of analytical evidence which indicate that such a local pressure exists, and we show that its bulk value differs from the mechanical pressure exerted on the walls of the system. We attribute this difference to the fact that the local pressure in the bulk does not depend on boundary effects, contrary to the mechanical pressure. We carefully examine these boundary effects using a channel geometry, and we show a virial formula for the pressure correctly predicts the mechanical pressure even in finite channels. However, this result no longer holds in more complex geometries, as exemplified for a channel that includes circular obstacles. PMID:27415318

  2. Hydrodynamically enforced entropic trapping of Brownian particles

    NASA Astrophysics Data System (ADS)

    Martens, Steffen; Schmid, Gerhard; Straube, Arthur; Schimansky-Geier, Lutz; Hänggi, Peter

    2014-03-01

    In small systems on length scales spatial confinement causes entropic forces that in turn implies spectacular consequences for the control for mass and charge transport. In view of its importance, recent efforts in theory triggered activities which allow for an approximate description that involves a reduction of dimensionality; thus making detailed predictions tractable. Up to present days, the focus was on the role of conservative forces and its interplay with confinement. Within the presented work, we overcome this limitation and succeeded in considering also non-conservative forces that derive from a vector potential [S. Martens et al., PRL 110, 010601 (2013)]. A relevant application is the fluid flow across microfluidic structures where a solute of Brownian particles is subject to both, an external bias and a pressure-driven flow. Then a new phenomenon emerges; namely, the intriguing finding of identically vanishing average particle flow which is accompanied by a colossal suppression of diffusion. This entropy-induced phenomenon, which we termed hydrodynamically enforced entropic trapping, offers the unique opportunity to separate particles of the same size in a tunable manner [S. Martens et al., Eur. Phys. ST 222, 2453-2463 (2013)].

  3. Branch migration enzyme as a Brownian ratchet

    PubMed Central

    Rasnik, Ivan; Jeong, Yong-Joo; McKinney, Sean A; Rajagopal, Vaishnavi; Patel, Smita S; Ha, Taekjip

    2008-01-01

    In recent years, it has been shown that helicases are able to perform functions beyond their traditional role in unwinding of double-stranded nucleic acids; yet the mechanistic aspects of these different activities are not clear. Our kinetic studies of Holliday junction branch migration catalysed by a ring-shaped helicase, T7 gp4, show that heterology of as little as a single base stalls catalysed branch migration. Using single-molecule analysis, one can locate the stall position to within a few base pairs of the heterology. Our data indicate that the presence of helicase alone promotes junction unfolding, which accelerates spontaneous branch migration, and individual time traces reveal complex trajectories consistent with random excursions of the branch point. Our results suggest that instead of actively unwinding base pairs as previously thought, the helicase exploits the spontaneous random walk of the junction and acts as a Brownian ratchet, which walks along duplex DNA while facilitating and biasing branch migration in a specific direction. PMID:18511910

  4. Nanoparticle volume fraction with heat and mass transfer on MHD mixed convection flow in a nanofluid in the presence of thermo-diffusion under convective boundary condition

    NASA Astrophysics Data System (ADS)

    Kandasamy, R.; Jeyabalan, C.; Sivagnana Prabhu, K. K.

    2016-02-01

    This article examines the influence of thermophoresis, Brownian motion of the nanoparticles with variable stream conditions in the presence of magnetic field on mixed convection heat and mass transfer in the boundary layer region of a semi-infinite porous vertical plate in a nanofluid under the convective boundary conditions. The transformed boundary layer ordinary differential equations are solved numerically using Maple 18 software with fourth-fifth order Runge-Kutta-Fehlberg method. Numerical results are presented both in tabular and graphical forms illustrating the effects of these parameters with magnetic field on momentum, thermal, nanoparticle volume fraction and solutal concentration boundary layers. The numerical results obtained for the velocity, temperature, volume fraction, and concentration profiles reveal interesting phenomenon, some of these qualitative results are presented through plots. It is interesting to note that the magnetic field plays a dominant role on nanofluid flow under the convective boundary conditions.

  5. Dynamic self-assembly of non-Brownian spheres studied by molecular dynamics simulations

    NASA Astrophysics Data System (ADS)

    Carvente, O.; Salazar-Cruz, M.; Peñuñuri, F.; Ruiz-Suárez, J. C.

    2016-02-01

    Granular self-assembly of confined non-Brownian spheres under gravity is studied by molecular dynamics simulations. Starting from a disordered phase, dry or cohesive spheres organize, by vibrational annealing, into body-centered-tetragonal or face-centered-cubic structures, respectively. During the self-assembling process, isothermal and isodense points are observed. The existence of such points indicates that both granular temperature and packing fraction undergo an inversion process that may be in the core of crystal nucleation. Around the isothermal point, a sudden growth of granular clusters having the maximum coordination number takes place, indicating the outcome of a first-order phase transition. We propose a heuristic equation that successfully describes the dynamic evolution of the local packing fraction in terms of the local granular temperature, along the entire crystallization process.

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

    NASA Astrophysics Data System (ADS)

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

    2013-02-01

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

  7. BROMOCEA Code: An Improved Grand Canonical Monte Carlo/Brownian Dynamics Algorithm Including Explicit Atoms.

    PubMed

    Solano, Carlos J F; Pothula, Karunakar R; Prajapati, Jigneshkumar D; De Biase, Pablo M; Noskov, Sergei Yu; Kleinekathöfer, Ulrich

    2016-05-10

    All-atom molecular dynamics simulations have a long history of applications studying ion and substrate permeation across biological and artificial pores. While offering unprecedented insights into the underpinning transport processes, MD simulations are limited in time-scales and ability to simulate physiological membrane potentials or asymmetric salt solutions and require substantial computational power. While several approaches to circumvent all of these limitations were developed, Brownian dynamics simulations remain an attractive option to the field. The main limitation, however, is an apparent lack of protein flexibility important for the accurate description of permeation events. In the present contribution, we report an extension of the Brownian dynamics scheme which includes conformational dynamics. To achieve this goal, the dynamics of amino-acid residues was incorporated into the many-body potential of mean force and into the Langevin equations of motion. The developed software solution, called BROMOCEA, was applied to ion transport through OmpC as a test case. Compared to fully atomistic simulations, the results show a clear improvement in the ratio of permeating anions and cations. The present tests strongly indicate that pore flexibility can enhance permeation properties which will become even more important in future applications to substrate translocation. PMID:27088446

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

    PubMed

    Mériguet, G; Jardat, M; Turq, P

    2004-09-22

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

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

    PubMed

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

    2010-06-01

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

  10. The use of modern electronic flat panel devices for image guided radiation therapy:. Image quality comparison, intra fraction motion monitoring and quality assurance applications

    NASA Astrophysics Data System (ADS)

    Nill, S.; Stützel, J.; Häring, P.; Oelfke, U.

    2008-06-01

    With modern radiotherapy delivery techniques like intensity modulated radiotherapy (IMRT) it is possible to delivery a more conformal dose distribution to the tumor while better sparing the organs at risk (OAR) compared to 3D conventional radiation therapy. Due to the theoretically high dose conformity achievable it is very important to know the exact position of the target volume during the treatment. With more and more modern linear accelerators equipped with imaging devices this is now almost possible. These imaging devices are using energies between 120kV and 6MV and therefore different detector systems are used but the vast majority is using amorphous silicon flat panel devices with different scintilator screens and build up materials. The technical details and the image quality of these systems are discussed and first results of the comparison are presented. In addition new methods to deal with motion management and quality assurance procedures are shortly discussed.

  11. Long-time dynamics of Met-enkephalin: comparison of theory with Brownian dynamics simulations.

    PubMed Central

    Kostov, K S; Freed, K F

    1999-01-01

    A recent theory for the long time dynamics of flexible chain molecules is applied for the first time to a peptide of biological importance, the neurotransmitter met-enkephalin. The dynamics of met-enkephalin is considerably more complicated than that of the previously studied glycine oligomers; met-enkephalin contains the interesting motions of phenyl groups and of side chains relative to the backbone, motions that are present in general flexible peptides. The theory extends the generalized Rouse (GR) model used to study the dynamics of polymers by providing a systematic procedure for including the contributions from the memory function matrices neglected in the GR theory. The new method describes the dynamics by time correlation functions instead of individual trajectories. These correlation functions are analytically expressed in terms of a set of equilibrium averages and the eigenvalues and eigenfunctions of the diffusion operator. The predictions of the theory are compared with Brownian dynamics (BD) simulations, so that both theory and simulation use identical potential functions and solvent models. The theory thus contains no adjustable parameters. Inclusion of the memory function contributions profoundly affects the dynamics. The theory produces very good agreement with the BD simulations for the global motions of met-enkephalin. It also correctly predicts the long-time relaxation rate for local motions. PMID:9876130

  12. Brownian dynamic simulations of electrophoresis and electro-stretching of DNA molecules in polymer gels.

    NASA Astrophysics Data System (ADS)

    Larson, Ronald; Graham, Richard

    2006-03-01

    We derive a model for the motion of long DNA chains entangled in a concentrated gel matrix in the presence of a strong electric field. The model is adapted from a tube-based slip-link approach, which was originally intended to model the rheology of entangled polymer fluids, and is suitable for solution by Brownian dynamic simulation. We account for the constraining effect of the surrounding matrix, motion due to the electric field and finite extensibility of the DNA chain. We are able investigate the effect of molecular weight and field strength on the DNA drift velocity in a constant electric field, along with molecular stretching in an oscillating field. Both examples have applications in DNA separation and sequencing. Our approach includes a detailed treatment of the chain end motion through the matrix, which our simulations demonstrate has a significant role in the DNA dynamics, particularly in oscillating fields. The model provides a convenient formalism for further refinements. For example, large fields may tend to cause hernia-like chain loops to protrude from the main tube. Furthermore, to model matrices comprised of linear polymers we can include the effect of constraint release, in which the confinement experienced by the DNA is diminished by the motion of the matrix chains.

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

    NASA Astrophysics Data System (ADS)

    Dubina, Sean Hyun; Wedgewood, Lewis Edward

    2016-07-01

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

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

    PubMed

    Mezzasalma, Stefano A

    2007-03-15

    The theoretical basis of a recent theory of Brownian relativity for polymer solutions is deepened and reexamined. After the problem of relative diffusion in polymer solutions is addressed, its two postulates are formulated in all generality. The former builds a statistical equivalence between (uncorrelated) timelike and shapelike reference frames, that is, among dynamical trajectories of liquid molecules and static configurations of polymer chains. The latter defines the "diffusive horizon" as the invariant quantity to work with in the special version of the theory. Particularly, the concept of universality in polymer physics corresponds in Brownian relativity to that of covariance in the Einstein formulation. Here, a "universal" law consists of a privileged observation, performed from the laboratory rest frame and agreeing with any diffusive reference system. From the joint lack of covariance and simultaneity implied by the Brownian Lorentz-Poincaré transforms, a relative uncertainty arises, in a certain analogy with quantum mechanics. It is driven by the difference between local diffusion coefficients in the liquid solution. The same transformation class can be used to infer Fick's second law of diffusion, playing here the role of a gauge invariance preserving covariance of the spacetime increments. An overall, noteworthy conclusion emerging from this view concerns the statistics of (i) static macromolecular configurations and (ii) the motion of liquid molecules, which would be much more related than expected. PMID:17223124

  15. Lock-and-key dimerization in dense Brownian systems of hard annular sector particles.

    PubMed

    Hodson, Wade D; Mason, Thomas G

    2016-08-01

    We develop a translational-rotational cage model that describes the behavior of dense two-dimensional (2D) Brownian systems of hard annular sector particles (ASPs), resembling C shapes. At high particle densities, pairs of ASPs can form mutually interdigitating lock-and-key dimers. This cage model considers either one or two mobile central ASPs which can translate and rotate within a static cage of surrounding ASPs that mimics the system's average local structure and density. By comparing with recent measurements made on dispersions of microscale lithographic ASPs [P. Y. Wang and T. G. Mason, J. Am. Chem. Soc. 137, 15308 (2015)JACSAT0002-786310.1021/jacs.5b10549], we show that mobile two-particle predictions of the probability of dimerization P_{dimer}, equilibrium constant K, and 2D osmotic pressure Π_{2D} as a function of the particle area fraction ϕ_{A} correspond closely to these experiments. By contrast, predictions based on only a single mobile particle do not agree well with either the two-particle predictions or the experimental data. Thus, we show that collective entropy can play an essential role in the behavior of dense Brownian systems composed of nontrivial hard shapes, such as ASPs. PMID:27627263

  16. Energy and efficiency optimization of a Brownian heat engine

    NASA Astrophysics Data System (ADS)

    Bekele, Mulugeta; Yalew, Yeneneh

    2007-03-01

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

  17. Noise-to-signal transition of a Brownian particle in the cubic potential: II. optical trapping geometry

    NASA Astrophysics Data System (ADS)

    Zemánek, Pavel; Šiler, Martin; Brzobohatý, Oto; Jákl, Petr; Filip, Radim

    2016-06-01

    The noise-to-signal transitions belong to an exciting group of processes in physics. In Filip and Zemánek (2016, J. Opt. 18 065401) we theoretically analyse the stochastic noise-to-signal transition of overdamped Brownian motion of a particle in the cubic potential. In this part, we propose a feasible experimental setup for a proof-of-principle experiment that uses methods of optical trapping in shaped laser beams which provide cubic and quadratic potentials. Theoretical estimates and results from the numerical simulations indicate that the noise-to-signal transition can be observed under realistic experimental conditions.

  18. Thermophoresis and Brownian effects on the Blasius flow of a nanofluid due to a curved surface with thermal radiation

    NASA Astrophysics Data System (ADS)

    Naveed, M.; Abbas, Z.; Sajid, M.

    2016-06-01

    In this analysis, we have discussed the Blasius flow of a nanofluid over a curved surface coiled in a circle of radius R . The physical situation is formulated in a mathematical model using a curvilinear coordinates system. The model is considered for the nanofluid including the effects of Brownian motion and thermophoresis in the presence of thermal radiation. A similarity solution of the developed ordinary differential equations is obtained numerically using the shooting method. The influence of the various involved parameters on the flow phenomena are analyzed through graphs and tables.

  19. Pushing single molecule techniques to microsecond resolution proves that T4 Lysozyme is a Brownian ratchet

    NASA Astrophysics Data System (ADS)

    Akhterov, Maxim V.; Choi, Yongki; Olsen, Tivoli J.; Sims, Patrick C.; Iftikhar, Mariam; Gul, O. Tolga; Corso, Brad L.; Weiss, Gregory A.; Collins, Philip G.

    2015-03-01

    Single-molecule techniques can monitor conformational dynamics of proteins, but such methods usually lack the resolution to directly observe conformational pathways or intermediate conformational states. We have recently described a single-molecule electronic technique that breaks this barrier. Using a 1 MHz-bandwidth carbon nanotube transistor, the transition pathways between open and closed conformations of T4 lysozyme have been recorded with a microsecond resolution. We directly resolve a smooth, continuous transition with an average duration of 37 microseconds. Unexpectedly, the mechanical closing and re-opening of the enzyme have identical distributions of transition durations, and the motion is independent of the enzyme catalyzing the substrate. These results illustrate the principle of microscopic reversibility applied to a Brownian ratchet, with lysozyme tracing a single pathway for closing and the reverse pathway for enzyme opening, regardless of its instantaneous catalytic productivity.

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

    PubMed Central

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

    2016-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Sevilla, Francisco J.

    2015-03-01

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

  2. Optimal Consumption in a Brownian Model with Absorption and Finite Time Horizon

    SciTech Connect

    Grandits, Peter

    2013-04-15

    We construct {epsilon}-optimal strategies for the following control problem: Maximize E[{integral}{sub [0,{tau})}e{sup -{beta}s} dC{sub s}+e{sup -{beta}{tau}}X{sub {tau}}] , where X{sub t}=x+{mu}t+{sigma}W{sub t}-C{sub t}, {tau}{identical_to}inf{l_brace}t>0|X{sub t}=0{r_brace} Logical-And T, T>0 is a fixed finite time horizon, W{sub t} is standard Brownian motion, {mu}, {sigma} are constants, and C{sub t} describes accumulated consumption until time t. It is shown that {epsilon}-optimal strategies are given by barrier strategies with time-dependent barriers.

  3. Microfluidic Lagrangian Trap for Brownian Particles: Three-Dimensional Focusing down to the Nanoscale

    NASA Astrophysics Data System (ADS)

    De Santo, Ilaria; D'Avino, Gaetano; Romeo, Giovanni; Greco, Francesco; Netti, Paolo A.; Maffettone, Pier Luca

    2014-12-01

    Several technologies and biotechnologies employing small-sized particles in microfluidics and nanofluidics rely on the ability of hampering thermal motion for progress. We experimentally demonstrate that nanoparticles suspended in a dilute polymer solution in Poiseuille flow can be trapped in the central region of a microtube, with a trapping efficiency that depends on the squared flow rate. The trap force is caused by the viscoelasticity of the suspending fluid, and can be modulated by selecting liquids with specific rheology. We also propose a simple theoretical argument that supports the experimental evidence, and links the trapping force to a dimensionless parameter comparing viscoelastic normal forces and Brownian forces. The theoretical argument distills into a simple equation, which could be used to downscale flow cytometers, or to design microfluidic devices for counting, coding, or separating nanoparticles.

  4. Brownian motors in the low-energy approximation: Classification and properties

    SciTech Connect

    Rozenbaum, V. M.

    2010-04-15

    We classify Brownian motors based on the expansion of their velocity in terms of the reciprocal friction coefficient. The two main classes of motors (with dichotomic fluctuations in homogeneous force and periodic potential energy) are characterized by different analytical dependences of their mean velocity on the spatial and temporal asymmetry coefficients and by different adiabatic limits. The competition between the spatial and temporal asymmetries gives rise to stopping points. The transition through these points can be achieved by varying the asymmetry coefficients, temperature, and other motor parameters, which can be used, for example, for nanoparticle segregation. The proposed classification separates out a new type of motors based on synchronous fluctuations in symmetric potential and applied homogeneous force. As an example of this type of motors, we consider a near-surface motor whose two-dimensional motion (parallel and perpendicular to the substrate plane) results from fluctuations in external force inclined to the surface.

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

    NASA Astrophysics Data System (ADS)

    Sevilla, Francisco J.; Gómez Nava, Luis Alberto

    2014-03-01

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

  6. Optimization of Brownian ratchets for the manipulation of charged components within supported lipid bilayers

    NASA Astrophysics Data System (ADS)

    Roth, J. S.; Zhang, Y.; Bao, P.; Cheetham, M. R.; Han, X.; Evans, S. D.

    2015-05-01

    In probability theory, there is a counter-intuitive result that it is possible to construct a winning strategy from two individually losing (or at most breaking-even) "games" by alternating between them. The work presented here demonstrates the application of this principle to supported lipid bilayers (SLBs) in order to create directed motion of charged lipid components in the membrane, which was achieved through the use of "Brownian ratchets" in patterned SLBs. Both a finite element analysis model and an experimental setup have been used to investigate the role of key parameters for the operation of these ratchets: (1) the asymmetry of the ratchet teeth and (2) the relation of the ratchet height to the period of the applied electric field. Importantly, we find that the efficiency of the ratchet for a given charged species is dependent on the diffusion coefficient. This opens the possibility for separation of membrane species according to their size or viscous drag coefficient within the membrane.

  7. Parallel Brownian dynamics simulations with the message-passing and PGAS programming models

    NASA Astrophysics Data System (ADS)

    Teijeiro, C.; Sutmann, G.; Taboada, G. L.; Touriño, J.

    2013-04-01

    The simulation of particle dynamics is among the most important mechanisms to study the behavior of molecules in a medium under specific conditions of temperature and density. Several models can be used to compute efficiently the forces that act on each particle, and also the interactions between them. This work presents the design and implementation of a parallel simulation code for the Brownian motion of particles in a fluid. Two different parallelization approaches have been followed: (1) using traditional distributed memory message-passing programming with MPI, and (2) using the Partitioned Global Address Space (PGAS) programming model, oriented towards hybrid shared/distributed memory systems, with the Unified Parallel C (UPC) language. Different techniques for domain decomposition and work distribution are analyzed in terms of efficiency and programmability, in order to select the most suitable strategy. Performance results on a supercomputer using up to 2048 cores are also presented for both MPI and UPC codes.

  8. Circular motion of asymmetric self-propelling particles.

    PubMed

    Kümmel, Felix; ten Hagen, Borge; Wittkowski, Raphael; Buttinoni, Ivo; Eichhorn, Ralf; Volpe, Giovanni; Löwen, Hartmut; Bechinger, Clemens

    2013-05-10

    Micron-sized self-propelled (active) particles can be considered as model systems for characterizing more complex biological organisms like swimming bacteria or motile cells. We produce asymmetric microswimmers by soft lithography and study their circular motion on a substrate and near channel boundaries. Our experimental observations are in full agreement with a theory of Brownian dynamics for asymmetric self-propelled particles, which couples their translational and orientational motion. PMID:23705745

  9. Circular Motion of Asymmetric Self-Propelling Particles

    NASA Astrophysics Data System (ADS)

    Kümmel, Felix; ten Hagen, Borge; Wittkowski, Raphael; Buttinoni, Ivo; Eichhorn, Ralf; Volpe, Giovanni; Löwen, Hartmut; Bechinger, Clemens

    2013-05-01

    Micron-sized self-propelled (active) particles can be considered as model systems for characterizing more complex biological organisms like swimming bacteria or motile cells. We produce asymmetric microswimmers by soft lithography and study their circular motion on a substrate and near channel boundaries. Our experimental observations are in full agreement with a theory of Brownian dynamics for asymmetric self-propelled particles, which couples their translational and orientational motion.

  10. Brownian dynamics determine universality of charge transport in ionic liquids

    SciTech Connect

    Sangoro, Joshua R; Iacob, Ciprian; Mierzwa, Michal; Paluch, Marian; Kremer, Friedrich

    2012-01-01

    Broadband dielectric spectroscopy is employed to investigate charge transport in a variety of glass-forming ionic liquids over wide frequency, temperature and pressure ranges. Using a combination of Einstein, Einstein-Smoluchowski, and Langevin relations, the observed universal scaling of charge transport in ionic liquids is traced back to the dominant role of Brownian dynamics.

  11. Brownian colloidal particles: Ito, Stratonovich, or a different stochastic interpretation

    NASA Astrophysics Data System (ADS)

    Sancho, J. M.

    2011-12-01

    Recent experiments on Brownian colloidal particles have been studied theoretically in terms of overdamped Langevin equations with multiplicative white noise using an unconventional stochastic interpretation. Complementary numerical simulations of the same system are well described using the conventional Stratonovich interpretation. Here we address this dichotomy from a more generic starting point: the underdamped Langevin equation and its corresponding Fokker-Planck equation.

  12. Brownian Gyrator: A Minimal Heat Engine on the Nanoscale

    NASA Astrophysics Data System (ADS)

    Filliger, Roger; Reimann, Peter

    2007-12-01

    A Brownian particle moving in the vicinity of a generic potential minimum under the influence of dissipation and thermal noise from two different heat baths is shown to act as a minimal heat engine, generating a systematic torque onto the physical object at the origin of the potential and an opposite torque onto the medium generating the dissipation.

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

    NASA Astrophysics Data System (ADS)

    Takasu, Masako; Tomita, Jungo

    2004-04-01

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

  14. The Inviscid Burgers Equation with Brownian Initial Velocity

    NASA Astrophysics Data System (ADS)

    Bertoin, Jean

    The law of the (Hopf-Cole) solution of the inviscid Burgers equation with Brownian initial velocity is made explicit. As examples of applications, we investigate the smoothness of the solution, the statistical distribution of the shocks, we determine the exact Hausdorff function of the Lagrangian regular points and investigate the existence of Lagrangian regular points in a fixed Borel set.

  15. Bacterial Motion in Quasi Two Dimensions

    NASA Astrophysics Data System (ADS)

    Wu, X. L.; Libchaber, Albert

    2000-03-01

    We study the effect of bacterial motion on micron-scale beads in a freely suspended soap film. Given the size of bacteria and beads, the geometry of the experiment is quasi-two-dimensional. Large positional fluctuations are observed for beads as large as 10 um in diameter, and the mean-square displacements, measured using video imaging, indicate superdiffusion on short times and normal diffusion on long times. Though the phenomenon is similar to Brownian motion of small particles, its physical origin is different and can be attributed to collective dynamics of bacteria.

  16. Stochastic thermodynamics of active Brownian particles

    NASA Astrophysics Data System (ADS)

    Ganguly, Chandrima; Chaudhuri, Debasish

    2013-09-01

    Examples of self-propulsion in strongly fluctuating environments are abundant in nature, e.g., molecular motors and pumps operating in living cells. Starting from the Langevin equation of motion, we develop a stochastic thermodynamic description of noninteracting self-propelled particles using simple models of velocity-dependent forces. We derive fluctuation theorems for entropy production and a modified fluctuation-dissipation relation, characterizing the linear response in nonequilibrium steady states. We study these notions in a simple model of molecular motors, and in the Rayleigh-Helmholtz and energy-depot models of self-propelled particles.

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

    PubMed

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

    2013-01-01

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

  18. The advective-dispersive equation with spatial fractional derivatives as a model for tracer transport in structured soil

    Technology Transfer Automated Retrieval System (TEKTRAN)

    The classical model to describe solute transport in soil is based on the advective-dispersive equation where Fick’s law is used to explain dispersion. From the microscopic point of view this is equivalent to consider that the motion of the particles of solute may be simulated by the Brownian motion....

  19. Brownian dynamics of confined rigid bodies.

    PubMed

    Delong, Steven; Balboa Usabiaga, Florencio; Donev, Aleksandar

    2015-10-14

    We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust, space efficient, and easy to accumulate. We construct a system of overdamped Langevin equations in the quaternion representation that accounts for hydrodynamic effects, preserves the unit-norm constraint on the quaternion, and is time reversible with respect to the Gibbs-Boltzmann distribution at equilibrium. We introduce two schemes for temporal integration of the overdamped Langevin equations of motion, one based on the Fixman midpoint method and the other based on a random finite difference approach, both of which ensure that the correct stochastic drift term is captured in a computationally efficient way. We study several examples of rigid colloidal particles diffusing near a no-slip boundary and demonstrate the importance of the choice of tracking point on the measured translational mean square displacement (MSD). We examine the average short-time as well as the long-time quasi-two-dimensional diffusion coefficient of a rigid particle sedimented near a bottom wall due to gravity. For several particle shapes, we find a choice of tracking point that makes the MSD essentially linear with time, allowing us to estimate the long-time diffusion coefficient efficiently using a Monte Carlo method. However, in general, such a special choice of tracking point does not exist, and numerical techniques for simulating long trajectories, such as the ones we introduce here, are necessary to study diffusion on long time scales. PMID:26472363

  20. Brownian dynamics of confined rigid bodies

    NASA Astrophysics Data System (ADS)

    Delong, Steven; Balboa Usabiaga, Florencio; Donev, Aleksandar

    2015-10-01

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