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Sample records for fractional brownian motion

  1. STOCHASTIC INTEGRATION FOR TEMPERED FRACTIONAL BROWNIAN MOTION.

    PubMed

    Meerschaert, Mark M; Sabzikar, Farzad

    2014-07-01

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

  2. STOCHASTIC INTEGRATION FOR TEMPERED FRACTIONAL BROWNIAN MOTION.

    PubMed

    Meerschaert, Mark M; Sabzikar, Farzad

    2014-07-01

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

  3. 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.

  4. 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.

  5. Fractional Brownian motion, fractional Gaussian noise, and Tsallis permutation entropy

    NASA Astrophysics Data System (ADS)

    Zunino, L.; Pérez, D. G.; Kowalski, A.; Martín, M. T.; Garavaglia, M.; Plastino, A.; Rosso, O. A.

    2008-10-01

    In this work, we analyze two important stochastic processes, the fractional Brownian motion and fractional Gaussian noise, within the framework of the Tsallis permutation entropy. This entropic measure, evaluated after using the Bandt & Pompe method to extract the associated probability distribution, is shown to be a powerful tool to characterize fractal stochastic processes. It allows for a better discrimination of the processes than the Shannon counterpart for appropriate ranges of values of the entropic index. Moreover, we find the optimum value of this entropic index for the stochastic processes under study.

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

    PubMed

    Shokrollahi, Foad; Kılıçman, Adem

    2016-01-01

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

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

    PubMed

    Jeon, Jae-Hyung; Metzler, Ralf

    2010-02-01

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

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

    PubMed

    Delorme, Mathieu; Wiese, Kay Jörg

    2016-07-01

    Brownian motion is the only random process which is Gaussian, scale invariant, and Markovian. Dropping the Markovian property, i.e., allowing for memory, one obtains a class of processes called fractional Brownian motion, indexed by the Hurst exponent H. For H=1/2, Brownian motion is recovered. We develop a perturbative approach to treat the nonlocality in time in an expansion in ɛ=H-1/2. This allows us to derive analytic results beyond scaling exponents for various observables related to extreme value statistics: the maximum m of the process and the time t_{max} at which this maximum is reached, as well as their joint distribution. We test our analytical predictions with extensive numerical simulations for different values of H. They show excellent agreement, even for H far from 1/2. PMID:27575103

  9. 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 .

  10. Long Memory in Finance and Fractional Brownian Motion

    NASA Astrophysics Data System (ADS)

    Kuroda, K.; Murai, J.

    We present a mathematical model of the trade signs and trade volumes, andderive a fractional Brownian motion as a scaling limit of the signed volume process which describes a super-diffusive nature. In our model, we assume that traders place a market order at a single time or divide their order into two chunks and place orders at different times. When they divide their order into two chunks, the probability distribution of the time lag t of divided orders is assumed to decay as an inverse power law of t with exponent α. We obtain three types of scaling limit of the signed volume process according to the three cases of the value of α, (i) α < 1, (ii) α = 1, and (iii) α > 1. (See Theorem 4.1.) We prove that a fractional Brownian motion having a super diffusive nature is obtained in a scaling limit of a signed volume process if and only if α < 1.

  11. 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.

  12. 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.

  13. Ergodic properties of fractional Brownian-Langevin motion.

    PubMed

    Deng, Weihua; Barkai, Eli

    2009-01-01

    We investigate the time average mean-square displacement delta;{2}[over ](x(t))=integral_{0};{t-Delta}[x(t;{'}+Delta)-x(t;{'})];{2}dt;{'}(t-Delta) for fractional Brownian-Langevin motion where x(t) is the stochastic trajectory and Delta is the lag time. Unlike the previously investigated continuous-time random-walk model, delta;{2}[over ] converges to the ensemble average x;{2} approximately t;{2H} in the long measurement time limit. The convergence to ergodic behavior is slow, however, and surprisingly the Hurst exponent H=3/4 marks the critical point of the speed of convergence. When H<3/4 , the ergodicity breaking parameter E_{B}=[[delta;{2}[over ](x(t))];{2}-delta;{2}[over ](x(t));{2}]/delta;{2}[over ](x(t));{2} approximately k(H)Deltat;{-1} , when H=3/4 , E_{B} approximately (9/16)(lnt)Deltat;{-1} , and when 3/41 ergodicity is broken and E_{B} approximately 2 . The critical point H=3/4 is marked by the divergence of the coefficient k(H) . Fractional Brownian motion as a model for recent experiments of subdiffusion of mRNA in the cell is briefly discussed, and a comparison with the continuous-time random-walk model is made. PMID:19257006

  14. Brownian motion

    NASA Astrophysics Data System (ADS)

    Lavenda, B. H.

    1985-02-01

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

  15. 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)

  16. 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.

  17. 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.

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

    NASA Astrophysics Data System (ADS)

    Roman, H. E.; Porto, M.

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

  19. 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.

  20. 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.

  1. 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

  2. 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.

  3. 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

  4. 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.

  5. Volatility of unevenly sampled fractional Brownian motion: an application to ice core records

    NASA Astrophysics Data System (ADS)

    Davidsen, J.; Griffin, J.

    2008-12-01

    The analysis of many natural time series and especially those related to ice core records often suffers from uneven sampling intervals. Here, we introduce a method that allows one to reliably estimate the volatility properties of fractional Brownian motion despite uneven sampling. It is based on the linear correlations of the process which are used to rescale the volatility series. For high-resolution temperature proxy records from Antarctica, we confirm that its volatility properties reveal a strong nonlinear component in the time series for time scales of 1 - 100 kyr. The results suggest that temperature increments appear in clusters of big and small increments --- a big (positive or negative) climate change is most likely followed by a big (positive or negative) climate change and a small climate change is most likely followed by a small climate change.

  6. Volatility of unevenly sampled fractional Brownian motion: an application to ice core records

    NASA Astrophysics Data System (ADS)

    Davidsen, J.; Griffin, J.

    2009-05-01

    The analysis of many natural time series and especially those related to ice core records often suffers from uneven sampling intervals. Here, we introduce a method that allows one to reliably estimate the volatility properties of fractional Brownian motion despite uneven sampling. It is based on the linear correlations of the process which are used to rescale the volatility series. For high-resolution temperature proxy records from Antarctica, we confirm that its volatility properties reveal a strong nonlinear component in the time series for time scales of 5 - 200 kyr. The results suggest that temperature increments appear in clusters of big and small increments --- a big (positive or negative) climate change is most likely followed by a big (positive or negative) climate change and a small climate change is most likely followed by a small climate change.

  7. 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.

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

    PubMed

    Rougier, P; Caron, O

    2000-12-01

    The authors modeled the center of gravity vertical projection (CG(v)) and the difference, CP - CG(v), which, combined, constitute the center of pressure (CP) trajectory, as fractional Brownian motion in order to investigate their relative contributions and their spatiotemporal articulation. The results demonstrated that CG(v) and CP - CG(v) motions are both endowed in complementary fashion with strong stochastic and part-deterministic behaviors. In addition, if the temporal coordinates remain similar for all 3 trajectories by definition, the switch between the successive control mechanisms appears for shorter displacements for CP - CG(v) and CG(v) than for CP trajectories. Results deduced from both input (CG(v)) and muscular stiffness (CP - CG(v)) thus provide insight into the way the central nervous system regulates stance control and in particular how CG and CP - CG are controlled. PMID:11114233

  9. Brownian motion of graphene.

    PubMed

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

    2010-12-28

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

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

    NASA Astrophysics Data System (ADS)

    Neuman, S. P.

    2009-12-01

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

  11. Synergic co-activation of muscles in elbow flexion via fractional Brownian motion.

    PubMed

    Chang, Shyang; Hsyu, Ming-Chun; Cheng, Hsiu-Yao; Hsieh, Sheng-Hwu

    2008-12-31

    In reflex and volitional actions, co-activations of agonist and antagonist muscles are believed to be present. Recent studies indicate that such co-activations can be either synergic or dyssynergic. The aim of this paper is to investigate if the co-activations of biceps brachii, brachialis, and triceps brachii during volitional elbow flexion are in the synergic or dyssynergic state. In this study, two groups with each containing six healthy male volunteers participated. Each person of the first group performed 30 trials of volitional elbow flexion while each of the second group performed 30 trials of passive elbow flexion as control experiments. Based on the model of fractional Brownian motion, the intensity and frequency information of the surface electromyograms (EMGs) could be extracted simultaneously. No statistically significant changes were found in the control group. As to the other group, results indicated that the surface EMGs of all five muscle groups were temporally synchronized in frequencies with persistent intensities during each elbow flexion. In addition, the mean values of fractal dimensions for rest and volitional flexion states revealed significant differences with P < 0.01. The obtained positive results suggest that these muscle groups work together synergically to facilitate elbow flexion during the co-activations.

  12. 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.

  13. 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.

  14. 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.

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

    PubMed

    Sanders, Lloyd P; Ambjörnsson, Tobias

    2012-05-01

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

  16. Aging scaled Brownian motion.

    PubMed

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

    2015-04-01

    Scaled Brownian motion (SBM) is widely used to model anomalous diffusion of passive tracers in complex and biological systems. It is a highly nonstationary process governed by the Langevin equation for Brownian motion, however, with a power-law time dependence of the noise strength. Here we study the aging properties of SBM for both unconfined and confined motion. Specifically, we derive the ensemble and time averaged mean squared displacements and analyze their behavior in the regimes of weak, intermediate, and strong aging. A very rich behavior is revealed for confined aging SBM depending on different aging times and whether the process is sub- or superdiffusive. We demonstrate that the information on the aging factorizes with respect to the lag time and exhibits a functional form that is identical to the aging behavior of scale-free continuous time random walk processes. While SBM exhibits a disparity between ensemble and time averaged observables and is thus weakly nonergodic, strong aging is shown to effect a convergence of the ensemble and time averaged mean squared displacement. Finally, we derive the density of first passage times in the semi-infinite domain that features a crossover defined by the aging time. PMID:25974439

  17. 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.

  18. 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.

  19. An efficient, three-dimensional, anisotropic, fractional Brownian motion and truncated fractional Levy motion simulation algorithm based on successive random additions

    NASA Astrophysics Data System (ADS)

    Lu, Silong; Molz, Fred J.; Liu, Hui Hai

    2003-02-01

    Fluid flow and solute transport in the subsurface are known to be strongly influenced by the heterogeneity of aquifers. To simulate aquifer properties, such as logarithmic hydraulic conductivity (ln( K)) variations, fractional Brownian motion (fBm) and truncated fractional Levy motion (fLm) were suggested previously. In this paper, an efficient three-dimensional successive random additions (SRA) algorithm is presented to construct spatial ln( K) distributions. A convenient conditioning procedure using the inverse-distance-weighting method as a data interpolator, which forces the generated fBm or truncated fLm realization to go through known data points, is included also. The proposed method coded in the FORTRAN language, and a complementary code for verifying fractal structure in fBm realizations based on dispersional analysis, are validated carefully through numerical tests. These software packages allow one to go beyond the stationary stochastic process hydrology of the 1980s to the new geo-statistics of non-stationary stochastic processes with stationary increments, as embodied by the stochastic fractals fBm, fLm and their associated increments fGn and fLn.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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

  6. 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.

  7. Brownian motion of tethered nanowires.

    PubMed

    Ota, Sadao; Li, Tongcang; Li, Yimin; Ye, Ziliang; Labno, Anna; Yin, Xiaobo; Alam, Mohammad-Reza; Zhang, Xiang

    2014-05-01

    Brownian motion of slender particles near a boundary is ubiquitous in biological systems and in nanomaterial assembly, but the complex hydrodynamic interaction in those systems is still poorly understood. Here, we report experimental and computational studies of the Brownian motion of silicon nanowires tethered on a substrate. An optical interference method enabled direct observation of microscopic rotations of the slender bodies in three dimensions with high angular and temporal resolutions. This quantitative observation revealed anisotropic and angle-dependent hydrodynamic wall effects: rotational diffusivity in inclined and azimuth directions follows different power laws as a function of the length, ∼ L(-2.5) and ∼ L(-3), respectively, and is more hindered for smaller inclined angles. In parallel, we developed an implicit simulation technique that takes the complex wire-wall hydrodynamic interactions into account efficiently, the result of which agreed well with the experimentally observed angle-dependent diffusion. The demonstrated techniques provide a platform for studying the microrheology of soft condensed matters, such as colloidal and biological systems near interfaces, and exploring the optimal self-assembly conditions of nanostructures. PMID:25353883

  8. Brownian Motion--a Laboratory Experiment.

    ERIC Educational Resources Information Center

    Kruglak, Haym

    1988-01-01

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

  9. Nonisothermal fluctuating hydrodynamics and Brownian motion

    NASA Astrophysics Data System (ADS)

    Falasco, G.; Kroy, K.

    2016-03-01

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

  10. 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. Brownian motion - a laboratory experiment

    NASA Astrophysics Data System (ADS)

    Kruglak, Haym

    1988-09-01

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

  12. Tracer Brownian Motion in Complex Fluids

    NASA Astrophysics Data System (ADS)

    van Zanten, John; Amin, Samiul; Kloxin, Christopher

    2003-03-01

    The utility of tracer tracer Brownian motion in probing the structure and dynamics of complex fluids is gaining increasing recognition. This is primarily due to the significant advantages that so-called tracer microrheology provides over traditional mechanical rheometry such as gently probing a material's linear response over a wide frequency range and small sample volumes. The underlying basis of the technique relies on having a correct understanding of the connection between the Brownian or thermal motion of the probe particles and the viscoelastic response of the suspending media. Although this connection has been well established for simple viscous fluids it is still not well understood for viscoelastic media. This to primarily due to:(i) the presence of local heterogeneities in these complex systems, (ii) the possible perturbation of the local rheological properties brought about by the probe particles and (iii) the influence of longitudinal dynamical modes. Previous experimental investigations have primarily focused on aqueous biopolymer solutions where the above mentioned factors do not seem to play a significant role. Recent investigations indicate that the above-mentioned factors may significantly influence tracer Brownian motion. In order to gain a deeper understanding of the connection between the probe Brownian motion and the viscoelastic response of the suspending media, comprehensive studies of several polymer and surfactant solutions-semi-dilute PEO solutions, CTAB/KBr & CTAB/NaSal wormlike micelle solutions, Pluronic F108 micellar dispersions & FCC soft crystals-were undertaken. Tracer microrheology results are reported for both ensemble diffusing wave spectroscopy-based ensemble and one & two particle tracking measurements.

  13. 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.

  14. Simulations of magnetic nanoparticle Brownian motion

    NASA Astrophysics Data System (ADS)

    Reeves, Daniel B.; Weaver, John B.

    2012-12-01

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

  15. Intrinsic and extrinsic measurement for Brownian motion

    NASA Astrophysics Data System (ADS)

    Castro-Villarreal, Pavel

    2014-05-01

    Based upon the Smoluchowski equation on curved manifolds, three physical observables are considered for Brownian displacement, namely geodesic displacement s, Euclidean displacement δR, and projected displacement δR⊥. The Weingarten-Gauss equations are used to calculate the mean-square Euclidean displacements in the short-time regime. Our findings show that from an extrinsic point of view the geometry of the space affects the Brownian motion in such a way that the particle’s diffusion is decelerated, contrasting with the intrinsic point of view where dynamics is controlled by the sign of the Gaussian curvature (Castro-Villarreal, 2010 J. Stat. Mech. P08006). Furthermore, it is possible to give exact formulas for <δR> and <δR2> on spheres and minimal surfaces, which are valid for all values of time. In the latter case, surprisingly, Brownian motion corresponds to the usual diffusion in flat geometries, albeit minimal surfaces have non-zero Gaussian curvature. Finally, the two-dimensional case is emphasized due to its close relation to surface self-diffusion in fluid membranes.

  16. 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.

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

    SciTech Connect

    Katori, Makoto

    2011-12-15

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

  18. Quantum Darwinism in Quantum Brownian Motion

    NASA Astrophysics Data System (ADS)

    Blume-Kohout, Robin; Zurek, Wojciech H.

    2008-12-01

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

  19. Quantum Darwinism in quantum Brownian motion.

    PubMed

    Blume-Kohout, Robin; Zurek, Wojciech H

    2008-12-12

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

  20. Langevin theory of anomalous Brownian motion made simple

    NASA Astrophysics Data System (ADS)

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

    2011-05-01

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

  1. Brownian Motion and its Conditional Descendants

    NASA Astrophysics Data System (ADS)

    Garbaczewski, Piotr

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

  2. 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.

  3. 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)

  4. 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…

  5. 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.

  6. 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}.

  7. Suppressing Brownian motion of individual biomolecules in solution

    NASA Astrophysics Data System (ADS)

    Cohen, Adam E.; Moerner, W. E.

    2006-03-01

    Single biomolecules in free solution have long been of interest for detailed study by optical methods, but Brownian motion prevents the observation of one single molecule for extended periods. We have used an anti-Brownian electrokinetic (ABEL) trap to trap individual protein molecules in free solution, under ambient conditions, without requiring any attachment to beads or surfaces. We also demonstrate trapping and manipulation of single virus particles, lipid vesicles, and fluorescent semiconductor nanocrystals. anti | Brownian electrokinetic trap | electrophoresis | feedback | single molecule | trapping

  8. 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.

  9. 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.

  10. Noncolliding Brownian Motion and Determinantal Processes

    NASA Astrophysics Data System (ADS)

    Katori, Makoto; Tanemura, Hideki

    2007-12-01

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

  11. Langevin model for a Brownian system with directed motion

    NASA Astrophysics Data System (ADS)

    Ambía, Francisco; Híjar, Humberto

    2016-08-01

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

  12. 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.

  13. 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.

  14. 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.

  15. 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.

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

    PubMed

    Gitterman, M; Klyatskin, V I

    2010-05-01

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

  17. 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.

  18. Magnetic microstructures for regulating Brownian motion

    NASA Astrophysics Data System (ADS)

    Sooryakumar, Ratnasingham

    2013-03-01

    Nature has proven that it is possible to engineer complex nanoscale machines in the presence of thermal fluctuations. These biological complexes, which harness random thermal energy to provide functionality, yield a framework to develop related artificial, i.e., nonbiological, phenomena and devices. A major challenge to achieving positional control of fluid-borne submicron sized objects is regulating their Brownian fluctuations. In this talk a magnetic-field-based trap that regulates the thermal fluctuations of superparamagnetic beads in suspension will be presented. Local domain-wall fields originating from patterned magnetic wires, whose strength and profile are tuned by weak external fields, enable bead trajectories within the trap to be managed and easily varied between strong confinements and delocalized spatial excursions. Moreover, the frequency spectrum of the trapped bead responds to fields as a power-law function with a tunable, non-integer exponent. When extended to a cluster of particles, the trapping landscape preferentially stabilizes them into formations of 5-fold symmetry, while their Brownian fluctuations result in frequent transitions between different cluster configurations. The quantitative understanding of the Brownian dynamics together with the ability to tune the extent of the fluctuations enables the wire-based platform to serve as a model system to investigate the competition between random and deterministic forces. Funding from the U.S. Army Research Office under contract W911NF-10-1-0353 is acknowledged.

  19. 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

  20. Synchronization and collective motion of globally coupled Brownian particles

    NASA Astrophysics Data System (ADS)

    Sevilla, Francisco J.; Dossetti, Victor; Heiblum-Robles, Alexandro

    2014-12-01

    In this work, we study a system of passive Brownian (non-self-propelled) particles in two dimensions, interacting only through a social-like force (velocity alignment in this case) that resembles Kuramoto's coupling among phase oscillators. We show that the kinematical stationary states of the system go from a phase in thermal equilibrium with no net flux of particles, to far-from-equilibrium phases exhibiting collective motion by increasing the coupling among particles. The mechanism that leads to the instability of the equilibrium phase relies on the competition between two time scales, namely, the mean collision time of the Brownian particles in a thermal bath and the time it takes for a particle to orient its direction of motion along the direction of motion of the group. Our results show a clear connection between collective motion and the Kuramoto model for synchronization, in our case, for the direction of motion of the particles.

  1. 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.

  2. 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.

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

    SciTech Connect

    Gupta, D.

    1986-01-01

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

  4. 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

  5. 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.

  6. 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.

  7. 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.

  8. Coiled to diffuse: Brownian motion of a helical bacterium.

    PubMed

    Butenko, Alexander V; Mogilko, Emma; Amitai, Lee; Pokroy, Boaz; Sloutskin, Eli

    2012-09-11

    We employ real-time three-dimensional confocal microscopy to follow the Brownian motion of a fixed helically shaped Leptospira interrogans (LI) bacterium. We extract from our measurements the translational and the rotational diffusion coefficients of this bacterium. A simple theoretical model is suggested, perfectly reproducing the experimental diffusion coefficients, with no tunable parameters. An older theoretical model, where edge effects are neglected, dramatically underestimates the observed rates of translation. Interestingly, the coiling of LI increases its rotational diffusion coefficient by a factor of 5, compared to a (hypothetical) rectified bacterium of the same contour length. Moreover, the translational diffusion coefficients would have decreased by a factor of ~1.5, if LI were rectified. This suggests that the spiral shape of the spirochaete bacteria, in addition to being employed for their active twisting motion, may also increase the ability of these bacteria to explore the surrounding fluid by passive Brownian diffusion.

  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. 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.

  11. 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.

  12. From ballistic to brownian vortex motion in complex oscillatory media.

    PubMed

    Davidsen, Jörn; Erichsen, Ronaldo; Kapral, Raymond; Chaté, Hugues

    2004-07-01

    We show that the breaking of the rotation symmetry of spiral waves in two-dimensional complex (period-doubled or chaotic) oscillatory media by synchronization defect lines (SDLs) is accompanied by an intrinsic drift of the pattern. Single vortex motion changes from ballistic flights at a well-defined angle from the SDLs to Brownian-like diffusion when the turbulent character of the medium increases. It gives rise, in nonturbulent multispiral regimes, to a novel "vortex liquid."

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

    PubMed

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

    2016-01-01

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

  14. 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.

  15. 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

  16. Stochastic oscillator with random mass: New type of Brownian motion

    NASA Astrophysics Data System (ADS)

    Gitterman, M.

    2014-02-01

    The model of a stochastic oscillator subject to additive random force, which includes the Brownian motion, is widely used for analysis of different phenomena in physics, chemistry, biology, economics and social science. As a rule, by the appropriate choice of units one assumes that the particle’s mass is equal to unity. However, for the case of an additional multiplicative random force, the situation is more complicated. As we show in this review article, for the cases of random frequency or random damping, the mass cannot be excluded from the equations of motion, and, for example, besides the restriction of the size of Brownian particle, some restrictions exist also of its mass. In addition to these two types of multiplicative forces, we consider the random mass, which describes, among others, the Brownian motion with adhesion. The fluctuations of mass are modeled as a dichotomous noise, and the first two moments of coordinates show non-monotonic dependence on the parameters of oscillator and noise. In the presence of an additional periodic force an oscillator with random mass is characterized by the stochastic resonance phenomenon, when the appearance of noise increases the input signal.

  17. 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

  18. 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.

  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. 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.

  1. 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.

  2. Tuning active Brownian motion with shot-noise energy pulses

    NASA Astrophysics Data System (ADS)

    Fiasconaro, Alessandro; Gudowska-Nowak, Ewa; Ebeling, Werner

    2009-01-01

    The main aim of this work is to explore the possibility of modeling the biological energy support mediated by absorption of ATP (adenosine triphosphate) as an energetic shot noise. We develop a general model with discrete input of energy pulses and study shot-noise-driven ratchets. We consider these ratchets as prototypes of Brownian motors driven by energy-rich ATP molecules. Our model is a stochastic machine able to acquire energy from the environment and convert it into kinetic energy of motion. We present characteristic features and demonstrate the possibility of tuning these motors by adapting the mean frequency of the discrete energy inputs, which are described as a special shot noise. In particular, the effect of stochastically driven directionality and uphill flux in systems acquiring energy from the shot noise is analyzed. As a possible application we consider the motion of kinesin on a microtubule under a constant load force.

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

    ERIC Educational Resources Information Center

    Parlar, Mahmut

    2004-01-01

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

  4. 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. 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.

  6. 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.

  7. Brownian motion near a liquid-gas interface

    NASA Astrophysics Data System (ADS)

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

    2016-09-01

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

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

    NASA Astrophysics Data System (ADS)

    Tuziemski, J.; Korbicz, J. K.

    2016-11-01

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

  9. 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.

  10. Nondiffusive Brownian motion of deformable particles: breakdown of the "long-time tail".

    PubMed

    Roldán-Vargas, Sándalo; Peláez-Fernández, Miguel; Barnadas-Rodríguez, Ramon; Quesada-Pérez, Manuel; Estelrich, Joan; Callejas-Fernández, José

    2009-08-01

    We study the nondiffusive Brownian motion of both rigid and deformable mesoscopic particles by cross-correlated dynamic light scattering with microsecond temporal resolution. Whereas rigid particles show the classical long-time tail prediction, the transition to diffusive motion of deformable particles presents a striking behavior not explained by the existing hydrodynamic treatments. This observation can be interpreted in terms of a damped oscillatory deformational motion on time scales of the order of the Brownian time. Finally, we show that the nondiffusive Brownian motion depends on the specific flexibility of the particles. PMID:19792120

  11. 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.

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

    PubMed

    Peng, Zheng; To, Kiwing

    2016-08-01

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

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

    PubMed

    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. PMID:27627375

  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. Higher Order Fractional Stable Motion: Hyperdiffusion with Heavy Tails

    NASA Astrophysics Data System (ADS)

    Kawai, Reiichiro

    2016-08-01

    We introduce the class of higher order fractional stable motions that can exhibit hyperdiffusive spreading with heavy tails. We define the class as a generalization of higher order fractional Brownian motion as well as a generalization of linear fractional stable motions. Higher order fractional stable motions are self-similar with Hurst index larger than one and non-Gaussian stable marginals with infinite variance and have stationary higher order increments. We investigate their sample path properties and asymptotic dependence structure on the basis of codifference. In particular, by incrementing or decrementing sample paths once under suitable conditions, the diffusion rate can be accelerated or decelerated by one order. With a view towards simulation study, we provide a ready-for-use sample path simulation recipe at discrete times along with error analysis. The proposed simulation scheme requires only elementary numerical operations and is robust to high frequency sampling, irregular spacing and super-sampling.

  17. Higher Order Fractional Stable Motion: Hyperdiffusion with Heavy Tails

    NASA Astrophysics Data System (ADS)

    Kawai, Reiichiro

    2016-10-01

    We introduce the class of higher order fractional stable motions that can exhibit hyperdiffusive spreading with heavy tails. We define the class as a generalization of higher order fractional Brownian motion as well as a generalization of linear fractional stable motions. Higher order fractional stable motions are self-similar with Hurst index larger than one and non-Gaussian stable marginals with infinite variance and have stationary higher order increments. We investigate their sample path properties and asymptotic dependence structure on the basis of codifference. In particular, by incrementing or decrementing sample paths once under suitable conditions, the diffusion rate can be accelerated or decelerated by one order. With a view towards simulation study, we provide a ready-for-use sample path simulation recipe at discrete times along with error analysis. The proposed simulation scheme requires only elementary numerical operations and is robust to high frequency sampling, irregular spacing and super-sampling.

  18. 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.

  19. 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.

  20. 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

  1. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2003-07-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-09-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-09-01

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

  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 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.

  7. 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.

  8. Brownian Motion of 2D Vacancy Islands by Adatom Terrace Diffusion

    SciTech Connect

    Morgenstern, Karina; L {ae}gsgaard, Erik; Besenbacher, Flemming

    2001-06-18

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

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

    ERIC Educational Resources Information Center

    Mishima, Nobuhiko; And Others

    1980-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Yu, Hongwei; Chen, Jun

    2004-12-01

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

  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.

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

    NASA Astrophysics Data System (ADS)

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

    1995-10-01

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

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

    NASA Astrophysics Data System (ADS)

    Li, Guanglai; Tang, Jay X.

    2009-08-01

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

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

    PubMed

    Li, Guanglai; Tang, Jay X

    2009-08-14

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

  16. 3-d brownian motion simulator for high-sensitivity nanobiotechnological applications.

    PubMed

    Toth, Arpád; Banky, Dániel; Grolmusz, Vince

    2011-12-01

    A wide variety of nanobiotechnologic applications are being developed for nanoparticle based in vitro diagnostic and imaging systems. Some of these systems make possible highly sensitive detection of molecular biomarkers. Frequently, the very low concentration of the biomarkers makes impossible the classical, partial differential equation-based mathematical simulation of the motion of the nanoparticles involved. We present a three-dimensional Brownian motion simulation tool for the prediction of the movement of nanoparticles in various thermal, viscosity, and geometric settings in a rectangular cuvette. For nonprofit users the server is freely available at the site http://brownian.pitgroup.org.

  17. Fission-Fragment Charge Yields in a Brownian Shape-Motion Model

    NASA Astrophysics Data System (ADS)

    Möller, P.; Randrup, J.

    2014-09-01

    We use a recent model for fission-fragment yield distributions based on Brownian shape motion on 5D potential-energy surfaces to calculate fission-fragment charge yields for the complete U and Th isotope chains observed in the seminal GSI experiment by K.H. Schmidt et al. Previously it was shown that this model describes the transition between symmetric and asymmetric fission in the light Th region; however in these studies the damping of shell corrections with energy was not taken into account. Here we use a generalized Brownian shape-motion model that includes damping of shell corrections with energy.

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

    PubMed

    Palanisami, Akilan; Miller, John H

    2010-10-01

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

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

    NASA Astrophysics Data System (ADS)

    Jiang, Xiaomeng; Li, Yong

    2016-10-01

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

  20. [Impact of Brownian motion and magnetic fields of erythrocytes on spin echo signal of blood protons].

    PubMed

    Zhernovoĭ, A I; Belorukova, M G; Nikolaeva, M N; Sharshina, L M

    2001-01-01

    A reduction in blood So2 and ESR is shown to lead to the decay of a spin echo signal. This effect is explained by the impact of red blood cell magnetic field fluctuations caused by the Brownian motion. The authors propose to use the effect to monitor red blood cell agglutination.

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

    NASA Astrophysics Data System (ADS)

    Jiang, Xiaomeng; Li, Yong

    2016-08-01

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

  2. 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.

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

    PubMed

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

    2013-08-01

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

  4. Path integral approach to Brownian motion driven with an ac force

    NASA Astrophysics Data System (ADS)

    Chen, L. Y.; Nash, P. L.

    2004-09-01

    Brownian motion in a periodic potential driven by an ac (oscillatory) force is investigated for the full range of damping constant from the overdamped limit to the underdamped limit. The path (functional) integral approach is advanced to produce formulas for the probability distribution function and for the current of the Brownian particle in response to an ac driving force. The negative friction Langevin dynamics technique is employed to evaluate the dc current for various parameters without invoking the overdamped or the underdamped approximation. The dc current is found to have nonlinear dependence upon the damping constant, the potential parameter, and the ac force magnitude and frequency.

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

    PubMed

    Turgeman, Lior; Carmi, Shai; Barkai, Eli

    2009-11-01

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

  6. 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.

  7. 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.

  8. 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.

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

    PubMed

    Kreft, Jennifer; Chen, Yeng-Long

    2007-08-01

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

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

    NASA Astrophysics Data System (ADS)

    Li, Guanglai; Tang, Jay

    2009-03-01

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

  11. 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.

  12. 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.

  13. 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.…

  14. 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…

  15. 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.

  16. 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.

  17. Brownian Motion Effects on Particle Pushing and Engulfment During Solidification in Metal-Matrix Composites

    NASA Astrophysics Data System (ADS)

    Ferguson, J. B.; Kaptay, George; Schultz, Benjamin F.; Rohatgi, Pradeep K.; Cho, Kyu; Kim, Chang-Soo

    2014-09-01

    Particle pushing and/or engulfment by the moving solidification front (SF) is important for the uniform distribution of reinforcement particles in metal-matrix composites (MMCs) synthesized from solidification processing, which can lead to a substantial increase in the strength of the composite materials. Previous theoretical models describing the interactions between particle and moving SF predict that large particles will be engulfed by SF while smaller particles including nanoparticles (NPs) will be pushed by it. However, there is evidence from metal-matrix nanocomposites (MMNCs) that NPs can sometimes be engulfed and distributed throughout the material rather than pushed and concentrated in the last regions to solidify. To address this disparity, in this work, an analytical model has been developed to account for Brownian motion effects. Computer simulations employing this model over a range of the SF geometries and time steps demonstrate that NPs are often engulfed rather than pushed. Based on our results, two distinct capture mechanisms were identified: (i) when a high random velocity is imparted to the particle by Brownian motion, large jumps allow the particle to overcome the repulsion of the SF, and (ii) when the net force acting on the particle is insufficient, the particle is not accelerated to a velocity high enough to outrun the advancing SF. This manuscript will quantitatively show the effect of particle size on the steady state or critical velocity of the SF when Brownian motion are taken into consideration. The statistical results incorporating the effects of Brownian motion based on the Al/Al2O3 MMNC system clearly show that ultrafine particles can be captured by the moving SF, which cannot be predicted by any of classical deterministic treatments.

  18. 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.

  19. Controlling Brownian motion of single protein molecules and single fluorophores in aqueous buffer.

    PubMed

    Cohen, Adam E; Moerner, W E

    2008-05-12

    We present an Anti-Brownian Electrokinetic trap (ABEL trap) capable of trapping individual fluorescently labeled protein molecules in aqueous buffer. The ABEL trap operates by tracking the Brownian motion of a single fluorescent particle in solution, and applying a time-dependent electric field designed to induce an electrokinetic drift that cancels the Brownian motion. The trapping strength of the ABEL trap is limited by the latency of the feedback loop. In previous versions of the trap, this latency was set by the finite frame rate of the camera used for video-tracking. In the present system, the motion of the particle is tracked entirely in hardware (without a camera or image-processing software) using a rapidly rotating laser focus and lock-in detection. The feedback latency is set by the finite rate of arrival of photons. We demonstrate trapping of individual molecules of the protein GroEL in buffer, and we show confinement of single fluorophores of the dye Cy3 in water.

  20. Noncolliding Brownian motion with drift and time-dependent Stieltjes-Wigert determinantal point process

    NASA Astrophysics Data System (ADS)

    Takahashi, Yuta; Katori, Makoto

    2012-10-01

    Using the determinantal formula of Biane, Bougerol, and O'Connell, we give multitime joint probability densities to the noncolliding Brownian motion with drift, where the number of particles is finite. We study a special case such that the initial positions of particles are equidistant with a period a and the values of drift coefficients are well-ordered with a scale σ. We show that, at each time t > 0, the single-time probability density of particle system is exactly transformed to the biorthogonal Stieltjes-Wigert matrix model in the Chern-Simons theory introduced by Dolivet and Tierz. Here, one-parameter extensions (θ-extensions) of the Stieltjes-Wigert polynomials, which are themselves q-extensions of the Hermite polynomials, play an essential role. The two parameters a and σ of the process combined with time t are mapped to the parameters q and θ of the biorthogonal polynomials. By the transformation of normalization factor of our probability density, the partition function of the Chern-Simons matrix model is readily obtained. We study the determinantal structure of the matrix model and prove that, at each time t > 0, the present noncolliding Brownian motion with drift is a determinantal point process, in the sense that any correlation function is given by a determinant governed by a single integral kernel called the correlation kernel. Using the obtained correlation kernel, we study time evolution of the noncolliding Brownian motion with drift.

  1. Superdiffusive Motion With Fractional Power-Law Exponents

    NASA Astrophysics Data System (ADS)

    Sajitz, M.; Metzner, C.; Raupach, C.; Fabry, B.

    2008-07-01

    The spontaneous random motion of microbeads bound to the actomyosin network of living cells is a non-Brownian process [1]. The mean-squared-displacement (MSD) of the bead shows a sub-to-superdiffusive transition, which has recently been traced back to the interplay of noise, dominating at short, and persistent traction forces dominating at long time scales [2]. The MSD increases at long times according to a powerlaw with fractional exponent between 1 and 2, which so far remained unexplained. We propose three different models of cytoskeletal dynamics producing such a fractional exponent. The traction forces are explained by the spontaneous formation and gradual self-assembly of stress fibers, attached to the microbead. While mature fibers constitute an elastic network for the bead, pre-mature fibers produce an increasing level of prestress with long-time powerlaw correlations. Our models focus on different biochemical mechanisms that give rise to such correlations.

  2. 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.

  3. 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

  4. 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

  5. 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.

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

    PubMed

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

    2014-12-23

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

  7. 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.

  8. Applications of statistical mechanics to non-Brownian random motion

    NASA Astrophysics Data System (ADS)

    Kutner, Ryszard; Wysocki, Krzysztof

    1999-12-01

    We analysed discrete and continuous Weierstrass-Mandelbrot representations of the Lévy flights occasionally interrupted by spatial localizations. We chose the discrete representation to easily detect by Monte Carlo simulation which stochastic quantity could be a candidate for describing the real processes. We found that the particle propagator is able to reveal surprisingly close, stable long-range algebraic tail. Unfortunately, long flights present in the system make, in practice, the particle mean-square displacement an irregular step-like function; such a behavior was expected since it is an experimental reminiscence of divergence of the mean-square displacement, predicted by the theory. We developed the continuous representation in the context of random motion of a particle in an amorphous environment; we established a correspondence between the stochastic quantities of both representations in which the latter quantities contain some material constants. The material constants appear due to the thermal average of the space-dependent stretch exponent which defines the probability of the particle passing a given distance. This averaging was performed for intermediate or even high temperatures, as well as for low or even intermediate internal friction regimes where long but not extremely long flights are readily able to construct a significant part of the Lévy distribution. This supplies a kind of self-cut-off of the length of flights. By way of example, we considered a possibility of observing the Lévy flights of hydrogen in amorphous low-concentration, high-temperature Pd 85Si 15H 7.5 phase; this conclusion is based on the results of a real experiment (Driesen et al., in: Janot et al. (Eds.), Atomic Transport and Defects in Metals by Neutron Scattering, Proceedings in Physics, Vol. 10, Springer, Berlin, 1986, p. 126; Richter et al., Phys. Rev. Lett. 57 (1986) 731; Driesen, Doctoral Thesis, Antwerpen University, 1987), performed by detecting the incoherent

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

    NASA Astrophysics Data System (ADS)

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

    2016-09-01

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

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

    NASA Astrophysics Data System (ADS)

    Lindenberg, Katja

    2015-03-01

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

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

    PubMed

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

    2010-04-27

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

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

    PubMed Central

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

    2013-01-01

    The Brownian motion of a nanoparticle in an incompressible Newtonian fluid (quiescent or fully developed Poiseuille flow) has been investigated with an arbitrary Lagrangian-Eulerian based finite element method. Results for the motion in a compressible fluid medium are estimated. Thermal fluctuations from the fluid are implemented using a fluctuating hydrodynamics approach. The instantaneous flow around the particle and the particle motion are fully resolved. Carriers of two different sizes with three different densities have been investigated (nearly neutrally buoyant). The numerical results show that (a) the calculated temperature of the nearly neutrally buoyant Brownian particle in a quiescent fluid satisfies the equipartition theorem; (b) the translational and rotational decay of the velocity autocorrelation functions result in algebraic tails, over long time; (c) the translational and rotational mean square displacements of the particle obeys Stokes-Einstein and Stokes-Einstein-Debye relations, respectively. Larger the particle, longer the time taken to attain this limit; and (d) the parallel and perpendicular diffusivities of the particle closer to the wall are consistent with the analytical results, where available. PMID:23950764

  13. 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.

  14. 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.

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

    PubMed

    Xie, Ping

    2009-09-16

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

  16. Influence of internal viscoelastic modes on the Brownian motion of a λ-DNA coated colloid.

    PubMed

    Yanagishima, Taiki; Laohakunakorn, Nadanai; Keyser, Ulrich F; Eiser, Erika; Tanaka, Hajime

    2014-03-21

    We study the influence of grafted polymers on the diffusive behaviour of a colloidal particle. Our work demonstrates how such additional degrees of freedom influence the Brownian motion of the particle, focusing on internal viscoelastic coupling between the polymer and colloid. Specifically, we study the mean-squared displacements (MSDs) of λ-DNA grafted colloids using Brownian dynamics simulation. Our simulations reveal the non-trivial effect of internal modes, which gives rise to a crossover from the short-time viscoelastic to long-time diffusional behaviour. We also show that basic features can be captured by a simple theoretical model considering the relative motion of a colloid to a part of the polymer corona. This model describes well a MSD calculated from an extremely long trajectory of a single λ-DNA coated colloid from experiment and allows characterisation of the λ-DNA hairs. Our study suggests that the access to the internal relaxation modes via the colloid trajectory offers a novel method for the characterisation of soft attachments to a colloid.

  17. 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.

  18. 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

  19. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-07-01

    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.

  1. 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

  2. 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

  3. Brownian Motion Rectifier: Continuous Sorting of Macromolecules in a Microfabricated Sieve

    NASA Astrophysics Data System (ADS)

    Chou, C. F.; Duke, T. A. J.; Chan, S. S.; Bakajin, O. B.; Austin, R. H.; Cox, E. C.

    1998-03-01

    A new method for separating biological macromolecules according to size has been proposed by Duke and Austin (T.A.J. Duke and R.H. Austin, preprint (1997).). A fine stream of molecules is transported through a microfabricated sieve, etched from a silicon chip by photolithography. The sieve consists of a periodic array of oblong obstacles, oriented at an angle to the direction of flow. The spatial asymmetry and the broken time-reversal symmetry (imposed by the flow) cause the Brownian motion of the molecules to be rectified. Since the effect depends on the thermal motion, molecules with different diffusion coefficients are deflected by different amounts, and consequently a mixture of molecules is sorted according to size. Our preliminary results in sorting a mixture of DNA in such a sieve will be presented.

  4. Scaling and long-range dependence in option pricing II: Pricing European option with transaction costs under the mixed Brownian-fractional Brownian model

    NASA Astrophysics Data System (ADS)

    Wang, Xiao-Tian; Zhu, En-Hui; Tang, Ming-Ming; Yan, Hai-Gang

    2010-02-01

    This paper deals with the problem of discrete-time option pricing by the mixed Brownian-fractional Brownian model with transaction costs. By a mean-self-financing delta hedging argument in a discrete-time setting, a European call option pricing formula is obtained. In particular, the minimal pricing cmin(t,st) of an option under transaction costs is obtained, which shows that timestep δt and Hurst exponent H play an important role in option pricing with transaction costs. In addition, we also show that there exists fundamental difference between the continuous-time trade and discrete-time trade and that continuous-time trade assumption will result in underestimating the value of a European call option.

  5. 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.

  6. 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

  7. 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.

  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. 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

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

    PubMed

    Brenner, Howard

    2005-12-01

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

  11. 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.

  12. Intermittency in an interacting generalization of the geometric Brownian motion model

    NASA Astrophysics Data System (ADS)

    Kühn, Reimer; Neu, Peter

    2008-08-01

    We propose a minimal interacting generalization of the geometric Brownian motion model, which turns out to be formally equivalent to a model describing the dynamics of networks of analogue neurons. For sufficiently strong interactions, such systems may have many meta-stable states. Transitions between meta-stable states are associated with macroscopic reorganizations of the system, which can be triggered by random external forcing. Such a system will exhibit intermittent dynamics within a large part of its parameter space. We propose market dynamics as a possible application of this model, in which case random external forcing would correspond to the arrival of important information. The emergence of a model of interacting prices of the type considered here can be argued to follow naturally from a general argument based on integrating out all non-price degrees of freedom from the dynamics of a hypothetical complete description of economic dependences.

  13. 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.

  14. 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

  15. 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.

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

    NASA Astrophysics Data System (ADS)

    Herrmann, Markus; Otesteanu, Marius

    2016-11-01

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

  17. 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.

  18. Brownian motion of polyphosphate complexes in yeast vacuoles: characterization by fluorescence microscopy with image analysis.

    PubMed

    Puchkov, Evgeny O

    2010-06-01

    In the vacuoles of Saccharomyces cerevisiae yeast cells, vividly moving insoluble polyphosphate complexes (IPCs) <1 microm size, stainable by a fluorescent dye, 4',6-diamidino-2-phenylindole (DAPI), may appear under some growth conditions. The aim of this study was to quantitatively characterize the movement of the IPCs and to evaluate the viscosity in the vacuoles using the obtained data. Studies were conducted on S. cerevisiae cells stained by DAPI and fluorescein isothyocyanate-labelled latex microspheres, using fluorescence microscopy combined with computer image analysis (ImageJ software, NIH, USA). IPC movement was photorecorded and shown to be Brownian motion. On latex microspheres, a methodology was developed for measuring a fluorescing particle's two-dimensional (2D) displacements and its size. In four yeast cells, the 2D displacements and sizes of the IPCs were evaluated. Apparent viscosity values in the vacuoles of the cells, computed by the Einstein-Smoluchowski equation using the obtained data, were found to be 2.16 +/- 0.60, 2.52 +/- 0.63, 3.32 +/- 0.9 and 11.3 +/- 1.7 cP. The first three viscosity values correspond to 30-40% glycerol solutions. The viscosity value of 11.3 +/- 1.7 cP was supposed to be an overestimation, caused by the peculiarities of the vacuole structure and/or volume in this particular cell. This conclusion was supported by the particular quality of the Brownian motion trajectories set in this cell as compared to the other three cells.

  19. 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.

  20. 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).

  1. 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.

  2. 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

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

    SciTech Connect

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

    2009-01-01

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

  4. 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.

  5. Stereoscopic observation of the Brownian motion of a single dust particle

    NASA Astrophysics Data System (ADS)

    Schmidt, Christian; Piel, Alexander; Himpel, Michael; Melzer, André

    2013-10-01

    The Brownian motion of a single melamine-formaldehyde particle of 6.8 micron diameter is observed with 3 fast video cameras that are aligned in the xyz directions. The particle is trapped in the ``anodic plasma'' that forms in front of a small, positively DC-biased (0-300 V) additional electrode of 3 mm diameter embedded in the lower electrode of a parallel plate rf-discharge operated at 13.56 MHz, pargon = 10-20 Pa, Upp = 50-150 V. The random motion of the particle in 3D is analyzed in terms of the velocity distribution f(vx,vy,vz) and spatial distribution w(x,y,z). Systematic errors in deriving correct temperatures are discussed and compared with Langevin MD simulations. The eigenfrequencies of the potential trap are derived from FFT-spectra of the individual velocity components and are found consistent with the spatial distribution w(x,y,z). Funded by DFG within the Transregional Collaborative Research Center TR24, projects A2 and A3.

  6. 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

  7. 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…

  8. One-dimensional Brownian motion of charged nanoparticles along microtubules: a model system for weak binding interactions.

    PubMed

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

    2010-04-21

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

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

    PubMed

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

    2008-05-01

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

  10. Isotropic Brownian motions over complex fields as a solvable model for May-Wigner stability analysis

    NASA Astrophysics Data System (ADS)

    Ipsen, J. R.; Schomerus, H.

    2016-09-01

    We consider matrix-valued stochastic processes known as isotropic Brownian motions, and show that these can be solved exactly over complex fields. While these processes appear in a variety of questions in mathematical physics, our main motivation is their relation to a May-Wigner-like stability analysis, for which we obtain a stability phase diagram. The exact results establish the full joint probability distribution of the finite-time Lyapunov exponents, and may be used as a starting point for a more detailed analysis of the stability-instability phase transition. Our derivations rest on an explicit formulation of a Fokker-Planck equation for the Lyapunov exponents. This formulation happens to coincide with an exactly solvable class of models of the Calgero-Sutherland type, originally encountered for a model of phase-coherent transport. The exact solution over complex fields describes a determinantal point process of biorthogonal type similar to recent results for products of random matrices, and is also closely related to Hermitian matrix models with an external source.

  11. Auditory hair cell centrioles undergo confined Brownian motion throughout the developmental migration of the kinocilium.

    PubMed

    Lepelletier, Léa; de Monvel, Jacques Boutet; Buisson, Johanna; Desdouets, Chantal; Petit, Christine

    2013-07-01

    Planar polarization of the forming hair bundle, the mechanosensory antenna of auditory hair cells, depends on the poorly characterized center-to-edge displacement of a primary cilium, the kinocilium, at their apical surface. Taking advantage of the gradient of hair cell differentiation along the cochlea, we reconstituted a map of the kinocilia displacements in the mouse embryonic cochlea. We then developed a cochlear organotypic culture and video-microscopy approach to monitor the movements of the kinocilium basal body (mother centriole) and its daughter centriole, which we analyzed using particle tracking and modeling. We found that both hair cell centrioles undergo confined Brownian movements around their equilibrium positions, under the apparent constraint of a radial restoring force of ∼0.1 pN. This magnitude depended little on centriole position, suggesting nonlinear interactions with constraining, presumably cytoskeletal elements. The only dynamic change observed during the period of kinocilium migration was a doubling of the centrioles' confinement area taking place early in the process. It emerges from these static and dynamic observations that kinocilia migrate gradually in parallel with the organization of hair cells into rows during cochlear neuroepithelium extension. Analysis of the confined motion of hair cell centrioles under normal and pathological conditions should help determine which structures contribute to the restoring force exerting on them.

  12. Brownian motion or Lévy walk? Stepping towards an extended statistical mechanics for animal locomotion.

    PubMed

    Gautestad, Arild O

    2012-09-01

    Animals moving under the influence of spatio-temporal scaling and long-term memory generate a kind of space-use pattern that has proved difficult to model within a coherent theoretical framework. An extended kind of statistical mechanics is needed, accounting for both the effects of spatial memory and scale-free space use, and put into a context of ecological conditions. Simulations illustrating the distinction between scale-specific and scale-free locomotion are presented. The results show how observational scale (time lag between relocations of an individual) may critically influence the interpretation of the underlying process. In this respect, a novel protocol is proposed as a method to distinguish between some main movement classes. For example, the 'power law in disguise' paradox-from a composite Brownian motion consisting of a superposition of independent movement processes at different scales-may be resolved by shifting the focus from pattern analysis at one particular temporal resolution towards a more process-oriented approach involving several scales of observation. A more explicit consideration of system complexity within a statistical mechanical framework, supplementing the more traditional mechanistic modelling approach, is advocated.

  13. 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.

  14. 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.

  15. Agglomeration due to Brownian motion of fractal-structured combustion aerosols

    SciTech Connect

    Kaplan, C.H.

    1987-01-01

    A dynamic Monte-Carlo type lattice model has been developed to simulate the agglomeration of non-spherical chain-line aggregate combustion aerosols due to Brownian motion. Simulations are carried out in the free molecular and continuum regimes, for both initial monodisperse and initial log-normally distributed aerosols, with and without source mechanisms. Preservation of the chain-like structure of the aggregate is accomplished throughout the simulation by describing the agglomerate as fractal, that is, scale-invariant, self-similar with a noninteger dimensionality. Simulation results indicate that cluster growth is more rapid in the free molecular regime than in the continuum. Aerosols and log-normal distributions retain their log-normal characteristics even after long coagulation times. The effect of the clusters' fractal dimension on the cluster growth rate is determined; the rate of agglomeration increases when the structure of the agglomerate is more fragmented (lower fractal dimension). An analytical solution to the coagulation equation is obtained for log-normal aerosols by calculating moments of the distribution and solving sets of moment equations to determine the size distribution parameters. Condition numbers are employed to determine which moments should be calculated to most accurately determine these parameters. Excellent agreement is obtained between the simulations and the solution to the moment equations. Experimental measurements of soot particle velocity in a premixed methane/air flame are made using laser Doppler velocimetry.

  16. Evaluation of Proteins' Rotational Diffusion Coefficients from Simulations of Their Free Brownian Motion in Volume-Occupied Environments.

    PubMed

    Długosz, Maciej; Antosiewicz, Jan M

    2014-01-14

    We have investigated the rotational dynamics of hen egg white lysozyme in monodisperse aqueous solutions of concentrations up to 250 mg/mL, using a rigid-body Brownian dynamics method that accurately accounts for anisotropies of diffusing objects. We have examined the validity of the free diffusion concept in the analysis of computer simulations of volume-occupied molecular solutions. We have found that, when as the only intermolecular interaction, the excluded volume effect is considered, rotational diffusion of molecules adheres to the free diffusion model. Further, we present a method based on the exact (in the case of the free diffusion) analytic forms of autocorrelation functions of particular vectors rigidly attached to diffusing objects, which allows one to obtain from results of molecular simulations the three principal rotational diffusion coefficients characterizing rotational Brownian motion of an arbitrarily shaped rigid particle for an arbitrary concentration of crowders. We have applied this approach to trajectories resulting from Brownian dynamics simulations of hen egg white lysozyme solutions. We show that the apparent anisotropy of proteins' rotational motions increases with an increasing degree of crowding. Finally, we demonstrate that even if the hydrodynamic anisotropy of molecules is neglected and molecules are simulated using their average translational and rotational diffusion coefficients, excluded volume effects still lead to their anisotropic rotational dynamics.

  17. Biased Brownian motion mechanism for processivity and directionality of single-headed myosin-VI.

    PubMed

    Iwaki, Mitsuhiro; Iwane, Atsuko Hikikoshi; Ikebe, Mitsuo; Yanagida, Toshio

    2008-01-01

    Conventional form to function as a vesicle transporter is not a 'single molecule' but a coordinated 'two molecules'. The coordinated two molecules make it complicated to reveal its mechanism. To overcome the difficulty, we adopted a single-headed myosin-VI as a model protein. Myosin-VI is an intracellular vesicle and organelle transporter that moves along actin filaments in a direction opposite to most other known myosin classes. The myosin-VI was expected to form a dimer to move processively along actin filaments with a hand-over-hand mechanism like other myosin organelle transporters. However, wild-type myosin-VI was demonstrated to be monomer and single-headed, casting doubt on its processivity. Using single molecule techniques, we show that green fluorescent protein (GFP)-fused single-headed myosin-VI does not move processively. However, when coupled to a 200 nm polystyrene bead (comparable to an intracellular vesicle in size) at a ratio of one head per bead, single-headed myosin-VI moves processively with large (40 nm) steps. Furthermore, we found that a single-headed myosin-VI-bead complex moved more processively in a high-viscous solution (40-fold higher than water) similar to cellular environment. Because diffusion of the bead is 60-fold slower than myosin-VI heads alone in water, we propose a model in which the bead acts as a diffusional anchor for the myosin-VI, enhancing the head's rebinding following detachment and supporting processive movement of the bead-monomer complex. This investigation will help us understand how molecular motors utilize Brownian motion in cells.

  18. 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

  19. Marker-free detection of progenitor cell differentiation by analysis of Brownian motion in micro-wells.

    PubMed

    Sekhavati, Farzad; Endele, Max; Rappl, Susanne; Marel, Anna-Kristina; Schroeder, Timm; Rädler, Joachim O

    2015-02-01

    The kinetics of stem and progenitor cell differentiation at the single-cell level provides essential clues to the complexity of the underlying decision-making circuits. In many hematopoietic progenitor cells, differentiation is accompanied by the expression of lineage-specific markers and by a transition from a non-adherent to an adherent state. Here, using the granulocyte-macrophage progenitor (GMP) as a model, we introduce a label-free approach that allows one to follow the course of this transition in hundreds of single cells in parallel. We trap single cells in patterned arrays of micro-wells and use phase-contrast time-lapse movies to distinguish non-adherent from adherent cells by an analysis of Brownian motion. This approach allowed us to observe the kinetics of induced differentiation of primary bone-marrow-derived GMPs into macrophages. The time lapse started 2 hours after addition of the cytokine M-CSF, and nearly 80% of the population had accomplished the transition within the first 20 h. The analysis of Brownian motion proved to be a sensitive and robust tool for monitoring the transition, and thus provides a high-throughput method for the study of cell differentiation at the single-cell level. PMID:25514157

  20. 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

  1. Brownian needle in dire straits: Stochastic motion of a rod in very confined narrow domains

    NASA Astrophysics Data System (ADS)

    Holcman, D.; Schuss, Z.

    2012-01-01

    We study the mean turnaround time of a Brownian needle in a narrow planar strip. When the needle is only slightly shorter than the width of the strip, the computation becomes a nonstandard narrow escape problem. We develop a boundary layer method, based on a conformal mapping of cusplike narrow straits, to obtain an explicit asymptotic approximation to the mean turnaround time. Our result suggests that two-dimensional domains lying between parallel walls may play a significant role in DNA repair.

  2. Brownian motion and the hydrodynamic friction tensor for colloidal particles of complex shape.

    PubMed

    Kraft, Daniela J; Wittkowski, Raphael; ten Hagen, Borge; Edmond, Kazem V; Pine, David J; Löwen, Hartmut

    2013-11-01

    We synthesize colloidal particles with various anisotropic shapes and track their orientationally resolved Brownian trajectories using confocal microscopy. An analysis of appropriate short-time correlation functions provides direct access to the hydrodynamic friction tensor of the particles revealing nontrivial couplings between the translational and rotational degrees of freedom. The results are consistent with calculations of the hydrodynamic friction tensor in the low-Reynolds-number regime for the experimentally determined particle shapes.

  3. Local shear stress and its correlation with local volume fraction in concentrated non-Brownian suspensions: lattice Boltzmann simulation.

    PubMed

    Lee, Young Ki; Ahn, Kyung Hyun; Lee, Seung Jong

    2014-12-01

    The local shear stress of non-Brownian suspensions was investigated using the lattice Boltzmann method coupled with the smoothed profile method. Previous studies have only focused on the bulk rheology of complex fluids because the local rheology of complex fluids was not accessible due to technical limitations. In this study, the local shear stress of two-dimensional solid particle suspensions in Couette flow was investigated with the method of planes to correlate non-Newtonian fluid behavior with the structural evolution of concentrated particle suspensions. Shear thickening was successfully captured for highly concentrated suspensions at high particle Reynolds number, and both the local rheology and local structure of the suspensions were analyzed. It was also found that the linear correlation between the local particle stress and local particle volume fraction was dramatically reduced during shear thickening. These results clearly show how the change in local structure of suspensions influences the local and bulk rheology of the suspensions. PMID:25615103

  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. Direction reversal of fluctuation-induced biased Brownian motion on distorted ratchets.

    PubMed

    Yan, B; Miura, R M; Chen, Y D

    2001-05-21

    The biased movement of Brownian particles on a fluctuating two-state periodic potential made of identical distorted ratchets is studied. The purpose is to investigate how the direction of the particle movement is related to the asymmetry of the potential. In general, distorting one of the two linear arms of a regular symmetric ratchet (with equal arm lengths) can create a driving force for the Brownian particle to execute biased movement. The direction of the induced biased movement depends on the type of the distortion. It has been found that if one linear arm is kinked into two linear sub-arms, the direction of the movement can be either positive or negative depending on the frequency of the fluctuation and the location and the degree of the kink. In contrast, if one arm of the symmetric ratchet is replaced by a continuous nonlinear sinusoidal function, the movement is always unidirectional. Thus, for the latter case to generate the direction reversal phenomenon, the ratchets have to have an additional asymmetry. We also have found that two potentials with different distorted ratchets can generate identical fluxes if the distortions are polar symmetric about the mid-point of the arm(s) of the basic linear two-arm ratchet. The results are useful for designing experimental apparatuses for the separation of protein particles based on their sizes and charges and the viscosity of the medium.

  6. 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.

  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. 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.

  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.

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

    NASA Astrophysics Data System (ADS)

    Banerjee, Arindam; Kihm, Kenneth D.

    2005-10-01

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

  12. 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.

  13. 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

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

    PubMed

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

    2013-01-01

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

  15. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-11-01

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

  17. Calibration of optical tweezers with non-spherical probes via high-resolution detection of Brownian motion

    NASA Astrophysics Data System (ADS)

    Butykai, A.; Mor, F. M.; Gaál, R.; Domínguez-García, P.; Forró, L.; Jeney, S.

    2015-11-01

    Optical tweezers are commonly used and powerful tools to perform force measurements on the piconewton scale and to detect nanometer-scaled displacements. However, the precision of these instruments relies to a great extent on the accuracy of the calibration method. A well-known calibration procedure is to record the stochastic motion of the trapped particle and compare its statistical behavior with the theory of the Brownian motion in a harmonic potential. Here we present an interactive calibration software which allows for the simultaneous fitting of three different statistical observables (power spectral density, mean square displacement and velocity autocorrelation function) calculated from the trajectory of the probe to enhance fitting accuracy. The fitted theory involves the hydrodynamic interactions experimentally observable at high sampling rates. Furthermore, a qualitative extension is included in our model to handle the thermal fluctuations in the orientation of optically trapped asymmetric objects. The presented calibration methodology requires no prior knowledge of the bead size and can be applied to non-spherical probes as well. The software was validated on synthetic and experimental data.

  18. Efficient numerical solution of the time fractional diffusion equation by mapping from its Brownian counterpart

    NASA Astrophysics Data System (ADS)

    Stokes, Peter W.; Philippa, Bronson; Read, Wayne; White, Ronald D.

    2015-02-01

    The solution of a Caputo time fractional diffusion equation of order 0 < α < 1 is expressed in terms of the solution of a corresponding integer order diffusion equation. We demonstrate a linear time mapping between these solutions that allows for accelerated computation of the solution of the fractional order problem. In the context of an N-point finite difference time discretisation, the mapping allows for an improvement in time computational complexity from O (N2) to O (Nα), given a precomputation of O (N 1 + α ln ⁡ N). The mapping is applied successfully to the least squares fitting of a fractional advection-diffusion model for the current in a time-of-flight experiment, resulting in a computational speed up in the range of one to three orders of magnitude for realistic problem sizes.

  19. Translational and Brownian motion in laser-Doppler flowmetry of large tissue volumes.

    PubMed

    Binzoni, T; Leung, T S; Seghier, M L; Delpy, D T

    2004-12-21

    This study reports the derivation of a precise mathematical relationship existing between the different p-moments of the power spectrum of the photoelectric current, obtained from a laser-Doppler flowmeter (LDF), and the red blood cell speed. The main purpose is that both the Brownian (defining the 'biological zero') and the translational movements are taken into account, clarifying in this way what the exact contribution of each parameter is to the LDF derived signals. The derivation of the equations is based on the quasi-elastic scattering theory and holds for multiple scattering (i.e. measurements in large tissue volumes and/or very high red blood cell concentration). The paper also discusses why experimentally there exists a range in which the relationship between the first moment of the power spectrum and the average red blood cells speed may be considered as 'linear' and what are the physiological determinants that can result in nonlinearity. A correct way to subtract the biological zero from the LDF data is also proposed. The findings should help in the design of improved LDF instruments and in the interpretation of experimental data.

  20. 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

  1. 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.

  2. 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.

  3. 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.

  4. 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.

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

    ERIC Educational Resources Information Center

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

    1970-01-01

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

  6. 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.

  7. 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.

  8. 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.

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

    PubMed

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

    2014-05-01

    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.

  10. 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.

  11. 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.

  12. Scaling of the space-time correlation function of particle currents in a suspension of hard-sphere-like particles: exposing when the motion of particles is Brownian.

    PubMed

    van Megen, W; Martinez, V A; Bryant, G

    2009-12-18

    The current correlation function is determined from dynamic light scattering measurements of a suspension of particles with hard spherelike interactions. For suspensions in thermodynamic equilibrium we find scaling of the space and time variables of the current correlation function. This finding supports the notion that the movement of suspended particles can be described in terms of uncorrelated Brownian encounters. However, in the metastable fluid, at volume fractions above freezing, this scaling fails.

  13. Brownian motion in a designer force field: dynamical effects of negative refraction on nanoparticles.

    PubMed

    Cuche, A; Stein, B; Canaguier-Durand, A; Devaux, E; Genet, C; Ebbesen, T W

    2012-08-01

    Photonic crystals (PC) have demonstrated unique features that have renewed the fields of classical and quantum optics. Although holding great promises, associated mechanical effects have proven challenging to observe. We demonstrate for the first time that one of the most salient properties of PC, namely negative refraction, can induce specific forces on metal nanoparticles. By integrating a periodically patterned metal film in a fluidic cell, we show that near-field optical forces associated with negatively refracted surface plasmons are capable of controlling particle trajectories. Coupling particle motions to PC band structures draws new approaches and strategies for parallel and high resolution all-optical control of particle flows with applications for micro- and nanofluidic systems.

  14. 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.

  15. 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

  16. 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.

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

    PubMed

    Felderhof, B U

    2011-05-28

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

  18. 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}> .

  19. Lévy meets poisson: a statistical artifact may lead to erroneous recategorization of Lévy walk as Brownian motion.

    PubMed

    Gautestad, Arild O

    2013-03-01

    The flow of GPS data on animal space is challenging old paradigms, such as the issue of the scale-free Lévy walk versus scale-specific Brownian motion. Since these movement classes often require different protocols with respect to ecological analyses, further theoretical development in this field is important. I describe central concepts such as scale-specific versus scale-free movement and the difference between mechanistic and statistical-mechanical levels of analysis. Next, I report how a specific sampling scheme may have produced much confusion: a Lévy walk may be wrongly categorized as Brownian motion if the duration of a move, or bout, is used as a proxy for step length and a move is subjectively defined. Hence, the categorization and recategorization of movement class compliance surrounding the Lévy walk controversy may have been based on a statistical artifact. This issue may be avoided by collecting relocations at a fixed rate at a temporal scale that minimizes over- and undersampling.

  20. Displacement correlation as an indicator of collective motion in one-dimensional and quasi-one-dimensional systems of repulsive Brownian particles

    NASA Astrophysics Data System (ADS)

    Ooshida, Takeshi; Goto, Susumu; Matsumoto, Takeshi; Otsuki, Michio

    2015-12-01

    While the slow dynamics in glassy liquids are known to be accompanied by collective motions undetectable with static structure factor and requiring four-point space-time correlations for their detection, it is usually difficult to calculate such correlations analytically. In the present study, a system of Brownian particles in a (quasi-)one-dimensional passageway is taken as an example to demonstrate the usefulness of displacement correlation. In the purely one-dimensional case (known as the single-file diffusion) with overtaking forbidden, the diffusion slows down and collective motion is captured by displacement correlation both calculated here numerically and analytically. On the other hand, displacement correlation vanishes if overtaking is allowed, which leads to normal diffusion.

  1. 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

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

    PubMed

    Antonopoulos, Markos; Stamatakos, Georgios

    2015-01-01

    Intensive glioma tumor infiltration into the surrounding normal brain tissues is one of the most critical causes of glioma treatment failure. To quantitatively understand and mathematically simulate this phenomenon, several diffusion-based mathematical models have appeared in the literature. The majority of them ignore the anisotropic character of diffusion of glioma cells since availability of pertinent truly exploitable tomographic imaging data is limited. Aiming at enriching the anisotropy-enhanced glioma model weaponry so as to increase the potential of exploiting available tomographic imaging data, we propose a Brownian motion-based mathematical analysis that could serve as the basis for a simulation model estimating the infiltration of glioblastoma cells into the surrounding brain tissue. The analysis is based on clinical observations and exploits diffusion tensor imaging (DTI) data. Numerical simulations and suggestions for further elaboration are provided. PMID:26309390

  3. 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.

  4. 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

  5. Brownian Emitters

    NASA Astrophysics Data System (ADS)

    Tsekov, Roumen

    2016-06-01

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

  6. 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.

  7. 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.

  8. 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

  9. Entropic Approach to Brownian Movement.

    ERIC Educational Resources Information Center

    Neumann, Richard M.

    1980-01-01

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

  10. Comment on “Mössbauer studies of harmonically bound oscillators in Brownian motion: a quantum approach”

    NASA Astrophysics Data System (ADS)

    Tewari, S. P.; Silotia, Poonam

    1994-05-01

    It is argued that the recent claim of Kumar [Phys. Lett. A 154 (1991) 461], that assuming the protein specific modes in a deoxymyoglobin crystal to be described by a quantum mechanical overdamped oscillator can explain the sudden sharp decrease, above a characteristic temperature, of the Lamb-Mössbauer recoilles fraction of the 57Fe atom in the protein crystal, is not teenable.

  11. Brownian vortexes.

    PubMed

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

    2009-07-01

    Mechanical equilibrium at zero temperature does not necessarily imply thermodynamic equilibrium at finite temperature for a particle confined by a static but nonconservative force field. Instead, the diffusing particle can enter into a steady state characterized by toroidal circulation in the probability flux, which we call a Brownian vortex. The circulatory bias in the particle's thermally driven trajectory is not simply a deterministic response to the solenoidal component of the force but rather reflects interplay between advection and diffusion in which thermal fluctuations extract work from the nonconservative force field. As an example of this previously unrecognized class of stochastic heat engines, we consider a colloidal sphere diffusing in a conventional optical tweezer. We demonstrate both theoretically and experimentally that nonconservative optical forces bias the particle's fluctuations into toroidal vortexes whose circulation can reverse direction with temperature or laser power. PMID:19658638

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

    PubMed

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

    2015-01-21

    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 (r(2) = 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

  13. 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

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. Brownian motion under annihilation dynamics.

    PubMed

    García de Soria, María Isabel; Maynar, Pablo; Trizac, Emmanuel

    2008-12-01

    The behavior of a heavy tagged intruder immersed in a bath of particles evolving under ballistic annihilation dynamics is investigated. The Fokker-Planck equation for this system is derived and the peculiarities of the corresponding diffusive behavior are worked out. In the long time limit, the intruder velocity distribution function approaches a Gaussian form, but with a different temperature from its bath counterpart. As a consequence of the continuous decay of particles in the bath, the mean-squared displacement increases exponentially in the collision per particle time scale. Analytical results are finally successfully tested against Monte Carlo numerical simulations. PMID:19256805

  20. 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.

  1. 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

  2. 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.

  3. 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.

  4. 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

  5. Strategies for reducing intra-fraction motion induced dosimetric effects in proton therapy

    NASA Astrophysics Data System (ADS)

    Zhao, Li

    Intra-fraction respiration motion during radiation delivery presents a major challenge to radiation therapy. There has been a growing effort to characterize and manage internal organ motion in radiation therapy, however very few studies focus on tackling this issue in proton therapy. Current practice for treating lung tumors in proton therapy is still to apply population-based margins to account for internal tumor motion, which can lead to target underdosage and normal tissue overdosage. This thesis explores the intra-fraction motion induced dosimetric effects from both computational treatment planning and experimental studies. Four-dimensional CT scans are used to analyze the patient-specific tumor motion characteristics. A feasible method to design the range compensator by using the maximum intensity projection (MIP) images is proposed. Results demonstrate that this MIP approach ensures adequate tumor coverage throughout the entire respiratory cycle whilst maintaining normal tissue dose under clinical constraints. Based on 4D-CT scans, dose convolution is used for assessing the accuracy of Gaussian probability density function for modeling the patient-specific respiratory motion on dose distribution. Non-negligible dose discrepancy is observed in comparisons of convolved dose distributions, and patient-specific respiration PDF is advocated. In addition, an experimental phantom study primarily focusing on the interplay effect between target motion and the scanning beam motion is implemented in two proton beam delivery systems: double scattering and uniform scanning. Measurement results suggest that dose blurring effect is dominant, and interplay effect is trivial in the uniform scanning system due to dose repainting.

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

    PubMed

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

    2014-01-01

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

  7. Detecting Non-Brownian Trait Evolution in Adaptive Radiations

    PubMed Central

    Freckleton, Robert P; Harvey, Paul H

    2006-01-01

    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

  8. 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

  9. 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.

  10. Tempered fractional Feynman-Kac equation: Theory and examples.

    PubMed

    Wu, Xiaochao; Deng, Weihua; Barkai, Eli

    2016-03-01

    Functionals of Brownian and non-Brownian motions have diverse applications and attracted a lot of interest among scientists. This paper focuses on deriving the forward and backward fractional Feynman-Kac equations describing the distribution of the functionals of the space and time-tempered anomalous diffusion, belonging to the continuous time random walk class. Several examples of the functionals are explicitly treated, including the occupation time in half-space, the first passage time, the maximal displacement, the fluctuations of the occupation fraction, and the fluctuations of the time-averaged position.

  11. Tempered fractional Feynman-Kac equation: Theory and examples.

    PubMed

    Wu, Xiaochao; Deng, Weihua; Barkai, Eli

    2016-03-01

    Functionals of Brownian and non-Brownian motions have diverse applications and attracted a lot of interest among scientists. This paper focuses on deriving the forward and backward fractional Feynman-Kac equations describing the distribution of the functionals of the space and time-tempered anomalous diffusion, belonging to the continuous time random walk class. Several examples of the functionals are explicitly treated, including the occupation time in half-space, the first passage time, the maximal displacement, the fluctuations of the occupation fraction, and the fluctuations of the time-averaged position. PMID:27078336

  12. 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.

  13. Quantification of intra-fraction motion in breast radiotherapy using supine magnetic resonance imaging.

    PubMed

    van Heijst, Tristan C F; Philippens, Mariëlle E P; Charaghvandi, Ramona K; den Hartogh, Mariska D; Lagendijk, Jan J W; van den Bongard, H J G Desirée; van Asselen, Bram

    2016-02-01

    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

  14. 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

  15. Near-Field, On-Chip Optical Brownian Ratchets.

    PubMed

    Wu, Shao-Hua; Huang, Ningfeng; Jaquay, Eric; Povinelli, Michelle L

    2016-08-10

    Nanoparticles in aqueous solution are subject to collisions with solvent molecules, resulting in random, Brownian motion. By breaking the spatiotemporal symmetry of the system, the motion can be rectified. In nature, Brownian ratchets leverage thermal fluctuations to provide directional motion of proteins and enzymes. In man-made systems, Brownian ratchets have been used for nanoparticle sorting and manipulation. Implementations based on optical traps provide a high degree of tunability along with precise spatiotemporal control. Here, we demonstrate an optical Brownian ratchet based on the near-field traps of an asymmetrically patterned photonic crystal. The system yields over 25 times greater trap stiffness than conventional optical tweezers. Our technique opens up new possibilities for particle manipulation in a microfluidic, lab-on-chip environment. PMID:27403605

  16. Controllable 3D atomic Brownian motor in optical lattices

    NASA Astrophysics Data System (ADS)

    Dion, C. M.; Sjölund, P.; Petra, S. J. H.; Jonsell, S.; Nylén, M.; Sanchez-Palencia, L.; Kastberg, A.

    2008-06-01

    We study a Brownian motor, based on cold atoms in optical lattices, where atomic motion can be induced in a controlled manner in an arbitrary direction, by rectification of isotropic random fluctuations. In contrast with ratchet mechanisms, our Brownian motor operates in a potential that is spatially and temporally symmetric, in apparent contradiction to the Curie principle. Simulations, based on the Fokker-Planck equation, allow us to gain knowledge on the qualitative behaviour of our Brownian motor. Studies of Brownian motors, and in particular ones with unique control properties, are of fundamental interest because of the role they play in protein motors and their potential applications in nanotechnology. In particular, our system opens the way to the study of quantum Brownian motors.

  17. Displacements Of Brownian Particles In Terms Of Marian Von Smoluchowski's Heuristic Model

    ERIC Educational Resources Information Center

    Klein, Hermann; Woermann, Dietrich

    2005-01-01

    Albert Einstein's theory of the Brownian motion, Marian von Smoluchowski's heuristic model, and Perrin's experimental results helped to bring the concept of molecules from a state of being a useful hypothesis in chemistry to objects existing in reality. Central to the theory of Brownian motion is the relation between mean particle displacement and…

  18. Right ventricular ejection fraction is better reflected by transverse rather than longitudinal wall motion in pulmonary hypertension

    PubMed Central

    2010-01-01

    Background Longitudinal wall motion of the right ventricle (RV), generally quantified as tricuspid annular systolic excursion (TAPSE), has been well studied in pulmonary hypertension (PH). In contrast, transverse wall motion has been examined less. Therefore, the aim of this study was to evaluate regional RV transverse wall motion in PH, and its relation to global RV pump function, quantified as RV ejection fraction (RVEF). Methods In 101 PH patients and 29 control subjects cardiovascular magnetic resonance was performed. From four-chamber cine imaging, RV transverse motion was quantified as the change of the septum-free-wall (SF) distance between end-diastole and end-systole at seven levels along an apex-to-base axis. For each level, regional absolute and fractional transverse distance change (SFD and fractional-SFD) were computed and related to RVEF. Longitudinal measures, including TAPSE and fractional tricuspid-annulus-apex distance change (fractional-TAAD) were evaluated for comparison. Results Transverse wall motion was significantly reduced at all levels compared to control subjects (p < 0.001). For all levels, fractional-SFD and SFD were related to RVEF, with the strongest relation at mid RV (R2 = 0.70, p < 0.001 and R2 = 0.62, p < 0.001). For TAPSE and fractional-TAAD, weaker relations with RVEF were found (R2 = 0.21, p < 0.001 and R2 = 0.27, p < 0.001). Conclusions Regional transverse wall movements provide important information of RV function in PH. Compared to longitudinal motion, transverse motion at mid RV reveals a significantly stronger relationship with RVEF and thereby might be a better predictor for RV function. PMID:20525337

  19. 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.

  20. Fractional motion model for characterization of anomalous diffusion from NMR signals.

    PubMed

    Fan, Yang; Gao, Jia-Hong

    2015-07-01

    Measuring molecular diffusion has been used to characterize the properties of living organisms and porous materials. NMR is able to detect the diffusion process in vivo and noninvasively. The fractional motion (FM) model is appropriate to describe anomalous diffusion phenomenon in crowded environments, such as living cells. However, no FM-based NMR theory has yet been established. Here, we present a general formulation of the FM-based NMR signal under the influence of arbitrary magnetic field gradient waveforms. An explicit analytic solution of the stretched exponential decay format for NMR signals with finite-width Stejskal-Tanner bipolar pulse magnetic field gradients is presented. Signals from a numerical simulation matched well with the theoretical prediction. In vivo diffusion-weighted brain images were acquired and analyzed using the proposed theory, and the resulting parametric maps exhibit remarkable contrasts between different brain tissues.

  1. Fractional motion model for characterization of anomalous diffusion from NMR signals

    NASA Astrophysics Data System (ADS)

    Fan, Yang; Gao, Jia-Hong

    2015-07-01

    Measuring molecular diffusion has been used to characterize the properties of living organisms and porous materials. NMR is able to detect the diffusion process in vivo and noninvasively. The fractional motion (FM) model is appropriate to describe anomalous diffusion phenomenon in crowded environments, such as living cells. However, no FM-based NMR theory has yet been established. Here, we present a general formulation of the FM-based NMR signal under the influence of arbitrary magnetic field gradient waveforms. An explicit analytic solution of the stretched exponential decay format for NMR signals with finite-width Stejskal-Tanner bipolar pulse magnetic field gradients is presented. Signals from a numerical simulation matched well with the theoretical prediction. In vivo diffusion-weighted brain images were acquired and analyzed using the proposed theory, and the resulting parametric maps exhibit remarkable contrasts between different brain tissues.

  2. 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.

  3. 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

  4. 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.

  5. 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.

  6. 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.

  7. Fractional Levy motion as an Alternative Model for Apparent Multiaffinity in Solar Wind Time Series

    NASA Astrophysics Data System (ADS)

    Credgington, D.; Watkins, N. W.; Freeman, M. P.; Hnat, B.; Chapman, S. C.

    2006-12-01

    One widely used technique in the testing of multifractal theories of turbulence has been the the multiaffinity plot of ζ(q) versus q, where ζ is the exponent of the q^{th} order structure function, provided that has already been found to be a power law. However, it is not obvious that the most economical description of all derived solar wind quantities, for example the Poynting flux or the ɛ function, must also be a multifractal. We have elsewhere argued that it is also instructive to capture the "stylised facts" of the scaling behaviour of auroral indices and solar wind quantities in simpler phenomenological models. To make this idea more concrete we here consider the use of fractional Lévy motion as a model for solar wind time series. fLm has only three parameters, the Lévy exponent μ, the persistence exponent β and the selfsimilarity exponent H which depends additively on the other two. By making the fLm hypothesis we explore how experimentally measured quantities, in particular the growth of variance, the scaling of the first return probability, and the multiaffinity plot depend on the fLm model's parameters. Comparison of these predictions with data is then used to assess the usefulness of fLm as an alternative model for solar wind time series.

  8. Analyzing animal movements using Brownian bridges.

    PubMed

    Horne, Jon S; Garton, Edward O; Krone, Stephen M; Lewis, Jesse S

    2007-09-01

    By studying animal movements, researchers can gain insight into many of the ecological characteristics and processes important for understanding population-level dynamics. We developed a Brownian bridge movement model (BBMM) for estimating the expected movement path of an animal, using discrete location data obtained at relatively short time intervals. The BBMM is based on the properties of a conditional random walk between successive pairs of locations, dependent on the time between locations, the distance between locations, and the Brownian motion variance that is related to the animal's mobility. We describe two critical developments that enable widespread use of the BBMM, including a derivation of the model when location data are measured with error and a maximum likelihood approach for estimating the Brownian motion variance. After the BBMM is fitted to location data, an estimate of the animal's probability of occurrence can be generated for an area during the time of observation. To illustrate potential applications, we provide three examples: estimating animal home ranges, estimating animal migration routes, and evaluating the influence of fine-scale resource selection on animal movement patterns.

  9. Real-time prostate motion assessment: image-guidance and the temporal dependence of intra-fraction motion

    PubMed Central

    2013-01-01

    Background The rapid adoption of image-guidance in prostate intensity-modulated radiotherapy (IMRT) results in longer treatment times, which may result in larger intrafraction motion, thereby negating the advantage of image-guidance. This study aims to qualify and quantify the contribution of image-guidance to the temporal dependence of intrafraction motion during prostate IMRT. Methods One-hundred and forty-three patients who underwent conventional IMRT (n=67) or intensity-modulated arc therapy (IMAT/RapidArc, n=76) for localized prostate cancer were evaluated. Intrafraction motion assessment was based on continuous RL (lateral), SI (longitudinal), and AP (vertical) positional detection of electromagnetic transponders at 10 Hz. Daily motion amplitudes were reported as session mean, median, and root-mean-square (RMS) displacements. Temporal effect was evaluated by categorizing treatment sessions into 4 different classes: IMRTc (transponder only localization), IMRTcc (transponder + CBCT localization), IMATc (transponder only localization), or IMATcc (transponder + CBCT localization). Results Mean/median session times were 4.15/3.99 min (IMATc), 12.74/12.19 min (IMATcc), 5.99/5.77 min (IMRTc), and 12.98/12.39 min (IMRTcc), with significant pair-wise difference (p<0.0001) between all category combinations except for IMRTcc vs. IMATcc (p>0.05). Median intrafraction motion difference between CBCT and non-CBCT categories strongly correlated with time for RMS (t-value=17.29; p<0.0001), SI (t-value=−4.25; p<0.0001), and AP (t-value=2.76; p<0.0066), with a weak correlation for RL (t-value=1.67; p=0.0971). Treatment time reduction with non-CBCT treatment categories showed reductions in the observed intrafraction motion: systematic error (Σ)<0.6 mm and random error (σ)<1.2 mm compared with ≤0.8 mm and <1.6 mm, respectively, for CBCT-involved treatment categories. Conclusions For treatment durations >4-6 minutes, and without any intrafraction motion mitigation protocol

  10. Chaotic Behavior of a Brownian Particle in a Periodic Potential

    NASA Astrophysics Data System (ADS)

    Fang, Jian-Shu; Liu, Wing-Ki; Zhan, Li-Xin

    2005-07-01

    The classical deterministic dynamics of a Brownian particle with a time-dependent periodic perturbation in a spatially periodic potential is investigated. We have constructed a perturbed chaotic solution near the heteroclinic orbit of the nonlinear dynamics system by using the Constant-Variation method. Theoretical analysis and numerical result show that the motion of the Brownian particle is a kind of chaotic motion. The corresponding chaotic region in parameter space is obtained analytically and numerically. The project supported by the Natural Science Foundation of Hunan Educational Bureau of China under Grant No. 04C063

  11. 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.

  12. Bioassay-guided fractionation of antifouling compounds using computer-assisted motion analysis of brown algal spore swimming.

    PubMed

    Greer, Stephen P; Iken, Katrin; McClintock, James B; Amsler, Charles D

    2006-01-01

    Antifouling extracts from the sea stars Astropecten articulatus and Luidia clathrata and from the brittle star Astrocyclus caecilia were fractionated by solid phase extraction and high performance liquid chromatography. Bioactive fractions were identified with the use of computer-assisted motion analysis-based bioassays utilising previously described Hincksia irregularis spore swimming behaviour parameters. Quantified parameters of spore movement were rate of change of direction (RCD) and speed (SPEE). The methods used initially required only 10 microg equivalent amounts of total crude extract and each resultant resolving step (normalised to 1 mg ml(-1) of crude, unfractionated extract) required far less material. Statistical analyses of RCD and ratios of RCD:SPEE values in experiments comparing swimming in the presence of extract fractions to controls revealed that both parameters were useful individually and in combination for efficiently following compound bioactivity throughout the fractionation procedure. This technique was also able to detect synergistic or additive interactions between compounds.

  13. SU-E-J-135: An Investigation of Ultrasound Imaging for 3D Intra-Fraction Prostate Motion Estimation

    SciTech Connect

    O'Shea, T; Harris, E; Bamber, J; Evans, P

    2014-06-01

    Purpose: This study investigates the use of a mechanically swept 3D ultrasound (US) probe to estimate intra-fraction motion of the prostate during radiation therapy using an US phantom and simulated transperineal imaging. Methods: A 3D motion platform was used to translate an US speckle phantom while simulating transperineal US imaging. Motion patterns for five representative types of prostate motion, generated from patient data previously acquired with a Calypso system, were using to move the phantom in 3D. The phantom was also implanted with fiducial markers and subsequently tracked using the CyberKnife kV x-ray system for comparison. A normalised cross correlation block matching algorithm was used to track speckle patterns in 3D and 2D US data. Motion estimation results were compared with known phantom translations. Results: Transperineal 3D US could track superior-inferior (axial) and anterior-posterior (lateral) motion to better than 0.8 mm root-mean-square error (RMSE) at a volume rate of 1.7 Hz (comparable with kV x-ray tracking RMSE). Motion estimation accuracy was poorest along the US probe's swept axis (right-left; RL; RMSE < 4.2 mm) but simple regularisation methods could be used to improve RMSE (< 2 mm). 2D US was found to be feasible for slowly varying motion (RMSE < 0.5 mm). 3D US could also allow accurate radiation beam gating with displacement thresholds of 2 mm and 5 mm exhibiting a RMSE of less than 0.5 mm. Conclusion: 2D and 3D US speckle tracking is feasible for prostate motion estimation during radiation delivery. Since RL prostate motion is small in magnitude and frequency, 2D or a hybrid (2D/3D) US imaging approach which also accounts for potential prostate rotations could be used. Regularisation methods could be used to ensure the accuracy of tracking data, making US a feasible approach for gating or tracking in standard or hypo-fractionated prostate treatments.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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)

  19. 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.

  20. 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.

  1. 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.

  2. The regulation of the cold neutral gas mass fraction by turbulent motions

    NASA Astrophysics Data System (ADS)

    Gazol, A.; Villagran, M. A.

    2016-10-01

    We present results from hydrodynamic simulations with forced turbulence at a scale of 50 pc and cooling functions adapted to describe the thermal conditions at four different Galactocentric distances: 8.5, 11, 15, and 18 kpc. These experiments are aimed to study the effects of varying the turbulent velocity vrms on the cold gas mass fraction. With realistic vrms we obtain average one-dimensional cold gas mass fractions which are comparable with the observed values. Our simulations can also lead to an approximately constant cold gas mass fraction for distances ≥11 kpc when considering subsonic perturbations for 15 and 18 kpc. We also find that the average one dimensional cold gas mass fraction and the volumetric cold gas mass fraction do not follow the same radial trends.

  3. 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

  4. Monte Carlo calculation of VMAT and helical tomotherapy dose distributions for lung stereotactic treatments with intra-fraction motion

    NASA Astrophysics Data System (ADS)

    Belec, J.; Clark, B. G.

    2013-05-01

    The aim of this study is to calculate realistic dose distributions that include the continuous deformation of organs and continuous motion of machine using 4D Monte Carlo methods for both volumetric modulated arc therapy and helical tomotherapy treatments. As part of a previous study, we presented a method to perform position-probability-sampled Monte Carlo dose calculations in the BEAMnrc and DOSXZYnrc user codes of EGSnrc. In this study, the DOSXYZnrc user code was further modified to account for the continuous intra-fraction deformation of the patient geometry. We implemented in the user code a method to update the transport grid densities as a function of time and map the energy deposited in the time dependent transport grid back to a reference grid. We provide information on the measurements performed to validate the implementation of this method and present an example of the application of the method for lung stereotactic treatments with intra-fraction motion. The results show that breathing motion is properly addressed with the internal target volume method for the cases studied.

  5. 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.

  6. 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.

  7. Highly Parallel Fractional Motion Estimation Engine for Super Hi-Vision 4k×4k@60fps

    NASA Astrophysics Data System (ADS)

    Huang, Yiqing; Ikenaga, Takeshi

    One Super Hi-Vision (SHV) 4k×4k@60fps fractional motion estimation (FME) engine is proposed in our paper. Firstly, two complexity reduction schemes are proposed in the algorithm level. By analyzing the integer motion cost of sub blocks in each inter mode, the mode reduction based mode pre-filtering scheme can achieve 48% clock cycle saving compared with previous algorithm. By further check the motion cost of search points around best integer candidate, the motion cost oriented directional one-pass scheme can provide 50% clock cycle saving and 36% reduction in the number of processing units (PU). Secondly, in the hardware level, two parallel improved schemes namely 16-Pel processing and MB-parallel scheme are given out in our paper, which reduces design effort to only 145MHz for SHV FME processing. Also, quarter sub-sampling is adopted in our design and 75% hardware cost is reduced for each PU. Thirdly, one unified pixel block loading scheme is proposed. About 28.67% to 86.39% pixels are reused and the related memory access is saved. Furthermore, we also give out one parity pixel organization scheme to solve memory access conflict of MB-parallel scheme. By using TSMC 0.18µm technology in worst work conditions (1.62V, 125°C), our FME engine can achieve real-time processing for SHV 4k×4k@60fps with 412k gates hardware.

  8. Minimal model for Brownian vortexes.

    PubMed

    Sun, Bo; Grier, David G; Grosberg, Alexander Y

    2010-08-01

    A Brownian vortex is a noise-driven machine that uses thermal fluctuations to extract a steady-state flow of work from a static force field. Its operation is characterized by loops in a probability current whose topology and direction can change with changes in temperature. We present discrete three- and four-state minimal models for Brownian vortexes that can be solved exactly with a master-equation formalism. These models elucidate conditions required for flux reversal in Brownian vortexes and provide insights into their thermodynamic efficiency through the rate of entropy production. PMID:20866791

  9. 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.

  10. 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.

  11. 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

  12. 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.

  13. Persistence of a Brownian particle in a time-dependent potential.

    PubMed

    Chakraborty, D

    2012-05-01

    We investigate the persistence probability of a Brownian particle in a harmonic potential, which decays to zero at long times, leading to an unbounded motion of the Brownian particle. We consider two functional forms for the decay of the confinement, an exponential decay and an algebraic decay. Analytical calculations and numerical simulations show that for the case of the exponential relaxation, the dynamics of Brownian particle at short and long times are independent of the parameters of the relaxation. On the contrary, for the algebraic decay of the confinement, the dynamics at long times is determined by the exponent of the decay. Finally, using the two-time correlation function for the position of the Brownian particle, we construct the persistence probability for the Brownian walker in such a scenario.

  14. 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.

  15. 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

  16. 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

  17. 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

  18. 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.

  19. 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.

  20. 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

  1. 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…

  2. Demonstration of a Controllable Three-Dimensional Brownian Motor in Symmetric Potentials

    SciTech Connect

    Sjoelund, P.; Petra, S.J.H.; Dion, C.M.; Jonsell, S.; Nylen, M.; Kastberg, A.; Sanchez-Palencia, L.

    2006-05-19

    We demonstrate a Brownian motor, based on cold atoms in optical lattices, where isotropic random fluctuations are rectified in order to induce controlled atomic motion in arbitrary directions. In contrast to earlier demonstrations of ratchet effects, our Brownian motor operates in potentials that are spatially and temporally symmetric, but where spatiotemporal symmetry is broken by a phase shift between the potentials and asymmetric transfer rates between them. The Brownian motor is demonstrated in three dimensions and the noise-induced drift is controllable in our system.

  3. Dynamics and efficiency of Brownian rotors.

    PubMed

    Bauer, Wolfgang R; Nadler, Walter

    2008-12-14

    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.

  4. Accelerated Stokesian Dynamics: Brownian Suspensions

    NASA Astrophysics Data System (ADS)

    Banchio, Adolfo J.; Brady, John F.

    2001-11-01

    A new Stokesian Dynamics (SD) algorithm for Brownian suspensions is presented. This implementation is based on the recently developed Accelerated Stokesian Dynamics (ASD) simulation method(Sierou, A and Brady, J. F.; J. Fluid Mech., accepted for publication.) for non-Brownian particles. As in ASD, the many-body long-range hydrodynamic interactions are computed using Fast Fourier Transforms and the resistance matrix is inverted iteratively, in order to keep the computational cost of O(N log N). A fast method for computing the Brownian forces acting on the particles is applied by splitting them into near-field and far-field contributions. For the near-field part the forces can be represented as a sum of pairwise contributions with a cost of O(N); and for the far-field part using a Chebyshev polynomial approximation for the inverse of the square root of the mobility matrix results in an order O(N^1.25 log N) computational cost. The overall scaling of the method is roughly of O(N^1.25 log N) and makes possible the simulation of larger systems, necessary for studying dynamical properties and/or polydispersity effects in colloidal suspensions. Also a faster approximate method is presented in which the far-field hydrodynamic contribution to the Brownian forces are treated in a mean-field-like fashion. The accuracy of the approximation is discussed, and results for the dynamics and rheology of Brownian suspensions are presented.

  5. Active Brownian particles escaping a channel in single file.

    PubMed

    Locatelli, Emanuele; Baldovin, Fulvio; Orlandini, Enzo; Pierno, Matteo

    2015-02-01

    Active particles may happen to be confined in channels so narrow that they cannot overtake each other (single-file conditions). This interesting situation reveals nontrivial physical features as a consequence of the strong interparticle correlations developed in collective rearrangements. We consider a minimal two-dimensional model for active Brownian particles with the aim of studying the modifications introduced by activity with respect to the classical (passive) single-file picture. Depending on whether their motion is dominated by translational or rotational diffusion, we find that active Brownian particles in single file may arrange into clusters that are continuously merging and splitting (active clusters) or merely reproduce passive-motion paradigms, respectively. We show that activity conveys to self-propelled particles a strategic advantage for trespassing narrow channels against external biases (e.g., the gravitational field).

  6. Active Brownian particles escaping a channel in single file

    NASA Astrophysics Data System (ADS)

    Locatelli, Emanuele; Baldovin, Fulvio; Orlandini, Enzo; Pierno, Matteo

    2015-02-01

    Active particles may happen to be confined in channels so narrow that they cannot overtake each other (single-file conditions). This interesting situation reveals nontrivial physical features as a consequence of the strong interparticle correlations developed in collective rearrangements. We consider a minimal two-dimensional model for active Brownian particles with the aim of studying the modifications introduced by activity with respect to the classical (passive) single-file picture. Depending on whether their motion is dominated by translational or rotational diffusion, we find that active Brownian particles in single file may arrange into clusters that are continuously merging and splitting (active clusters) or merely reproduce passive-motion paradigms, respectively. We show that activity conveys to self-propelled particles a strategic advantage for trespassing narrow channels against external biases (e.g., the gravitational field).

  7. 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.

  8. 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

  9. 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.

  10. 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

  11. 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.

  12. Non-Brownian dynamics and strategy of amoeboid cell locomotion.

    PubMed

    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.

  13. 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

  14. Thermophoretically modified aerosol brownian coagulation.

    PubMed

    Arias-Zugasti, Manuel; Rosner, Daniel E

    2011-08-01

    A theory of aerosol coagulation rates resulting from continuum-regime brownian coagulation in the presence of size-dependent particle thermophoresis is developed and explored here. We are motivated by a wide variety of applications in which particle brownian coagulation occurs in a nonisothermal gas where differential thermophoretic drift contributes to, but does not dominate, the encounter frequency between suspended spherical particles (e.g., mist droplets) of different sizes. We employ a Smoluchowski-like population-balance to demonstrate the relative roles of brownian diffusion and thermophoresis in shaping the short and long time (asymptotic or "coagulation-aged") mist-droplet size distribution (DSD) function. To carry out these combined-mechanism DSD-evolution calculations we developed a rational "coupled" coagulation rate constant (allowing for simultaneous brownian diffusion and relative thermophoretic drift) rather than simply adding the relevant individual coagulation "kernels." Dimensionless criteria are provided to facilitate precluding other coagulation mechanisms not considered here (such as simultaneous sedimentation or Marangoni-flow-induced mist-droplet phoresis) and potential complications not included in the present model [as finite-rate coalescence, initial departures from the continuum (Stokes drag-) limit, and even dense (nonideal) vapor effects]. PMID:21928988

  15. 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.

  16. Thermophoretically modified aerosol brownian coagulation.

    PubMed

    Arias-Zugasti, Manuel; Rosner, Daniel E

    2011-08-01

    A theory of aerosol coagulation rates resulting from continuum-regime brownian coagulation in the presence of size-dependent particle thermophoresis is developed and explored here. We are motivated by a wide variety of applications in which particle brownian coagulation occurs in a nonisothermal gas where differential thermophoretic drift contributes to, but does not dominate, the encounter frequency between suspended spherical particles (e.g., mist droplets) of different sizes. We employ a Smoluchowski-like population-balance to demonstrate the relative roles of brownian diffusion and thermophoresis in shaping the short and long time (asymptotic or "coagulation-aged") mist-droplet size distribution (DSD) function. To carry out these combined-mechanism DSD-evolution calculations we developed a rational "coupled" coagulation rate constant (allowing for simultaneous brownian diffusion and relative thermophoretic drift) rather than simply adding the relevant individual coagulation "kernels." Dimensionless criteria are provided to facilitate precluding other coagulation mechanisms not considered here (such as simultaneous sedimentation or Marangoni-flow-induced mist-droplet phoresis) and potential complications not included in the present model [as finite-rate coalescence, initial departures from the continuum (Stokes drag-) limit, and even dense (nonideal) vapor effects].

  17. 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

  18. 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.

  19. Weighted-ensemble Brownian dynamics simulations for protein association reactions.

    PubMed

    Huber, G A; Kim, S

    1996-01-01

    A new method, weighted-ensemble Brownian dynamics, is proposed for the simulation of protein-association reactions and other events whose frequencies of outcomes are constricted by free energy barriers. The method features a weighted ensemble of trajectories in configuration space with energy levels dictating the proper correspondence between "particles" and probability. Instead of waiting a very long time for an unlikely event to occur, the probability packets are split, and small packets of probability are allowed to diffuse almost immediately into regions of configuration space that are less likely to be sampled. The method has been applied to the Northrup and Erickson (1992) model of docking-type diffusion-limited reactions and yields reaction rate constants in agreement with those obtained by direct Brownian simulation, but at a fraction of the CPU time (10(-4) to 10(-3), depending on the model). Because the method is essentially a variant of standard Brownian dynamics algorithms, it is anticipated that weighted-ensemble Brownian dynamics, in conjunction with biophysical force models, can be applied to a large class of association reactions of interest to the biophysics community.

  20. 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

  1. Discontinuous shear thickening in Brownian suspensions by dynamic simulation.

    PubMed

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

    2015-12-15

    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

  2. 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

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

    PubMed

    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.

  4. 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.

  5. 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.

  6. 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

  7. 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.

  8. 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.

  9. Constrained diffusion or immobile fraction on cell surfaces: a new interpretation.

    PubMed Central

    Feder, T J; Brust-Mascher, I; Slattery, J P; Baird, B; Webb, W W

    1996-01-01

    Protein lateral mobility in cell membranes is generally measured using fluorescence photobleaching recovery (FPR). Since the development of this technique, the data have been interpreted by assuming free Brownian diffusion of cell surface receptors in two dimensions, an interpretation that requires that a subset of the diffusing species remains immobile. The origin of this so-called immobile fraction remains a mystery. In FPR, the motions of thousands of particles are inherently averaged, inevitably masking the details of individual motions. Recently, tracking of individual cell surface receptors has identified several distinct types of motion (Gross and Webb, 1988; Ghosh and Webb, 1988, 1990, 1994; Kusumi et al. 1993; Qian et al. 1991; Slattery, 1995), thereby calling into question the classical interpretation of FPR data as free Brownian motion of a limited mobile fraction. We have measured the motion of fluorescently labeled immunoglobulin E complexed to high affinity receptors (Fc epsilon RI) on rat basophilic leukemia cells using both single particle tracking and FPR. As in previous studies, our tracking results show that individual receptors may diffuse freely, or may exhibit restricted, time-dependent (anomalous) diffusion. Accordingly, we have analyzed FPR data by a new model to take this varied motion into account, and we show that the immobile fraction may be due to particles moving with the anomalous subdiffusion associated with restricted lateral mobility. Anomalous subdiffusion denotes random molecular motion in which the mean square displacements grow as a power law in time with a fractional positive exponent less than one. These findings call for a new model of cell membrane structure. PMID:8744314

  10. Non-conservative optical forces and Brownian vortexes

    NASA Astrophysics Data System (ADS)

    Sun, Bo

    Optical manipulation using optical tweezers has been widely adopted in physics, chemical engineering and biology. While most applications and fundamental studies of optical trapping have focused on optical forces resulting from intensity gradients, we have also explored the role of radiation pressure, which is directed by phase gradients in beams of light. Interestingly, radiation pressure turns out to be a non-conservative force and drives trapped objects out of thermodynamic equilibrium with their surrounding media. We have demonstrated the resulting nonequilibrium effects experimentally by tracking the thermally driven motions of optically trapped colloidal spheres using holographic video microscopy. Rather than undergoing equilibrium thermal fluctuations, as has been assumed for more than a quarter century, a sphere in an optical tweezer enters into a stochastic steady-state characterized by closed loops in its probability current density. These toroidal vortexes constitute a bias in the particle's otherwise random thermal fluctuations arising at least indirectly from a solenoidal component in the optical force. This surprising effect is a particular manifestation of a more general class of noise-driven machines that we call Brownian vortexes. This previously unrecognized class of stochastic heat engines operates on qualitatively different principles from such extensively studied nonequilibrium systems as thermal ratchets and Brownian motors. Among its interesting properties, a Brownian vortex can reverse its direction with changes in temperature or equivalent control parameters.

  11. 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.

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. 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

  17. Asymmetric pores in a silicon membrane acting as massively parallel brownian ratchets.

    PubMed

    Matthias, Sven; Müller, Frank

    2003-07-01

    The brownian motion of mesoscopic particles is ubiquitous and usually random. But in systems with periodic asymmetric barriers to movement, directed or 'rectified' motion can arise and may even modulate some biological processes. In man-made devices, brownian ratchets and variants based on optical or quantum effects have been exploited to induce directed motion, and the dependence of the amplitude of motion on particle size has led to the size-dependent separation of biomolecules. Here we demonstrate that the one-dimensional pores of a macroporous silicon membrane, etched to exhibit a periodic asymmetric variation in pore diameter, can act as massively parallel and multiply stacked brownian ratchets that are potentially suitable for large-scale particle separations. We show that applying a periodic pressure profile with a mean value of zero to a basin separated by such a membrane induces a periodic flow of water and suspended particles through the pores, resulting in a net motion of the particles from one side of the membrane to the other without moving the liquid itself. We find that the experimentally observed pressure dependence of the particle transport, including an inversion of the transport direction, agrees with calculations of the transport properties in the type of ratchet devices used here.

  18. 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

  19. 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.

  20. 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

  1. Fractionated Lung IMPT Treatments: Sensitivity to Setup Uncertainties and Motion Effects Based on Single-Field Homogeneity.

    PubMed

    Dowdell, Stephen; Grassberger, Clemens; Sharp, Greg; Paganetti, Harald

    2016-10-01

    Treatment uncertainties in radiotherapy are either systematic or random. This study evaluates the sensitivity of fractionated intensity-modulated proton therapy (IMPT) lung treatments to systematic and random setup uncertainties. Treatments in which single-field homogeneity was restricted to within ±20% (IMPT20%) were compared to full IMPT (IMPTfull) for 10 patients with lung cancer. Four-dimensional Monte Carlo calculations were performed using patient computed tomography geometries with ±5 mm systematic or random setup uncertainties applied over a 35 × 2.5Gy(RBE) treatment course. Fifty fractionated courses were simulated for each patient using both IMPT delivery methods with random setup uncertainties applied each fraction and for 3 energy-dependent spot sizes (big spots, σ≈18-9 mm; intermediate spots, σ≈11-5 mm; and small spots, σ≈4-2 mm). These results were compared to Monte Carlo recalculations of the original treatment plan assuming zero setup uncertainty. Results are presented as the difference in equivalent uniform dose (ΔEUD), V95 (ΔV95), and target dose homogeneity (ΔD1-D99). Over the whole patient cohort, the ΔEUD was 2.0 ± 0.5 (big spots), 1.9 ± 0.7 (intermediate spots), and 1.3 ± 0.4 (small spots) times more sensitive to ±5 mm systematic setup uncertainties in IMPTfull compared to IMPT20% IMPTfull is 1.9 ± 0.9 (big spots), 2.1 ± 1.1 (intermediate spots), and 1.5 ± 0.6 (small spots) times more sensitive to random setup uncertainties than IMPT20% over a fractionated treatment course. The ΔV95 is at least 1.4 times more sensitive to systematic and random setup uncertainties for IMPTfull for all spot sizes considered. The ΔD1-D99 values coincided within uncertainty limits for both IMPT delivery methods for the 3 spot sizes considered, with higher mean values always observed for IMPTfull The paired t-test indicated that variations observed between IMPTfull and IMPT20% were significantly different for the majority of scenarios

  2. 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.

  3. 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

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

    NASA Astrophysics Data System (ADS)

    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.

  5. 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.

  6. 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

  7. 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.

  8. 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.

  9. Rectification efficiency of a Brownian motor.

    PubMed

    Suzuki, Daisuke; Munakata, Toyonori

    2003-08-01

    The energy balance of a Brownian motor is discussed based on a Langevin equation without the overdamped approximation. Energetics of the system suggests that the frictional dissipation energy associated with the unidirectional movement should be counted as a part of the useful energy for the rectification process of a Brownian motor. This leads to a new definition of the efficiency, which is applicable, contrary to the conventional one, even if the external load is absent. For the so-called flashing ratchet model, we numerically solve the Langevin equation for various situations and discuss both the temperature and the friction strength dependence of the rectification efficiency and the role of the duty ratio.

  10. 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.

  11. 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

  12. 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.

  13. 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

  14. 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.

  15. Diffusion of Brownian Particles under Oscillatory Shear Flow

    NASA Astrophysics Data System (ADS)

    Takikawa, Yoshinori; Orihara, Hiroshi

    2012-12-01

    Brownian motion has been investigated in oscillatory flows. A number of polystyrene spheres dispersed in water were traced with a confocal scanning laser microscope, and the time dependences of their coordinates were obtained. From the trajectories of the particles observed, mean-square displacements (MSDs) were calculated. We found that although the MSD in the vorticity direction is independent of the amplitude of shear strain, that of MSD in the flow direction increases as the amplitude of shear strain is increased, and that the effective diffusion constant depends on both the amplitude and initial phase of the applied sinusoidal shear strains. All experimental results are in good agreement with the theoretical results derived from the Langevin equation.

  16. 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

  17. Dynamics of a trapped Brownian particle in shear flows

    NASA Astrophysics Data System (ADS)

    Holzer, Lukas; Bammert, Jochen; Rzehak, Roland; Zimmermann, Walter

    2010-04-01

    The Brownian motion of a particle in a harmonic potential, which is simultaneously exposed either to a linear shear flow or to a plane Poiseuille flow is investigated. In the shear plane of both flows the probability distribution of the particle becomes anisotropic and the dynamics is changed in a characteristic manner compared to a trapped particle in a quiescent fluid. The particle distribution takes either an elliptical or a parachute shape or a superposition of both depending on the mean particle position in the shear plane. Simultaneously, shear-induced cross-correlations between particle fluctuations along orthogonal directions in the shear plane are found. They are asymmetric in time. In Poiseuille flow thermal particle fluctuations perpendicular to the flow direction in the shear plane induce a shift of the particle’s mean position away from the potential minimum. Two complementary methods are suggested to measure shear-induced cross-correlations between particle fluctuations along orthogonal directions.

  18. 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.

  19. Note: From reaction-diffusion systems to confined Brownian motion

    NASA Astrophysics Data System (ADS)

    Martens, S.

    2016-07-01

    In this note, we demonstrated for the first time that one can derive an expression for the effective diffusion coefficient, equal to the Lifson-Jackson formula, using a subsequent homogenization of the 1D reaction-diffusion-advection equation. The latter has been derived by applying asymptotic perturbation analysis to the underlying 3D reaction-diffusion equation with spatially dependent no-flux boundary conditions and incorporates the effects of boundary interactions on the reactants via a boundary-induced advection term [S. Martens et al, Phys. Rev. E 91, 022902 (2015)].

  20. 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

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

    NASA Astrophysics Data System (ADS)

    Yazdi, Anoosheh; Sperl, Matthias

    2016-09-01

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

  2. Phase transition in non-brownian fiber suspensions

    NASA Astrophysics Data System (ADS)

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

    2012-11-01

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

  3. 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.

  4. 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.

  5. 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"

  6. 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.

  7. 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.

  8. 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

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

    PubMed

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

    2014-06-01

    A quantitative analysis is presented for the stochastic interactions of a pair of Brownian hard spheres in non-adsorbing polymer solutions. The hard spheres are hypothetically trapped by optical tweezers and allowed for random motion near the trapped positions. The investigation focuses on the long-time correlated Brownian motion. The mobility tensor altered by the polymer depletion effect is computed by the boundary integral method, and the corresponding random displacement is determined by the fluctuation-dissipation theorem. From our computations it follows that the presence of depletion layers around the hard spheres has a significant effect on the hydrodynamic interactions and particle dynamics as compared to pure solvent and uniform polymer solution cases. The probability distribution functions of random walks of the two interacting hard spheres that are trapped clearly shift due to the polymer depletion effect. The results show that the reduction of the viscosity in the depletion layers around the spheres and the entropic force due to the overlapping of depletion zones have a significant influence on the correlated Brownian interactions. PMID:24908040

  10. 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.

  11. A bipedal DNA Brownian motor with coordinated legs.

    PubMed

    Omabegho, Tosan; Sha, Ruojie; Seeman, Nadrian C

    2009-04-01

    A substantial challenge in engineering molecular motors is designing mechanisms to coordinate the motion between multiple domains of the motor so as to bias random thermal motion. For bipedal motors, this challenge takes the form of coordinating the movement of the biped's legs so that they can move in a synchronized fashion. To address this problem, we have constructed an autonomous DNA bipedal walker that coordinates the action of its two legs by cyclically catalyzing the hybridization of metastable DNA fuel strands. This process leads to a chemically ratcheted walk along a directionally polar DNA track. By covalently cross-linking aliquots of the walker to its track in successive walking states, we demonstrate that this Brownian motor can complete a full walking cycle on a track whose length could be extended for longer walks. We believe that this study helps to uncover principles behind the design of unidirectional devices that can function without intervention. This device should be able to fulfill roles that entail the performance of useful mechanical work on the nanometer scale.

  12. Trajectories of the ribosome as a Brownian nanomachine.

    PubMed

    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

    2014-12-01

    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.

  13. Evaluation of Brownian warps for shape alignment

    NASA Astrophysics Data System (ADS)

    Nielsen, Mads

    2007-03-01

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

  14. Optimum analysis of a Brownian refrigerator.

    PubMed

    Luo, X G; Liu, N; He, J Z

    2013-02-01

    A Brownian refrigerator with the cold and hot reservoirs alternating along a space coordinate is established. The heat flux couples with the movement of the Brownian particles due to an external force in the spatially asymmetric but periodic potential. After using the Arrhenius factor to describe the behaviors of the forward and backward jumps of the particles, the expressions for coefficient of performance (COP) and cooling rate are derived analytically. Then, through maximizing the product of conversion efficiency and heat flux flowing out, a new upper bound only depending on the temperature ratio of the cold and hot reservoirs is found numerically in the reversible situation, and it is a little larger than the so-called Curzon and Ahlborn COP ε(CA)=(1/√[1-τ])-1. After considering the irreversible factor owing to the kinetic energy change of the moving particles, we find the optimized COP is smaller than ε(CA) and the external force even does negative work on the Brownian particles when they jump from a cold to hot reservoir.

  15. Dynamics of Brownian motors in deformable medium

    NASA Astrophysics Data System (ADS)

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

    2016-10-01

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

  16. Bimolecular reaction simulation using Weighted Ensemble Brownian dynamics and the University of Houston Brownian Dynamics program.

    PubMed

    Rojnuckarin, A; Livesay, D R; Subramaniam, S

    2000-08-01

    We discuss here the implementation of the Weighted Ensemble Brownian (WEB) dynamics algorithm of Huber and Kim in the University of Houston Brownian Dynamics (UHBD) suite of programs and its application to bimolecular association problems. WEB dynamics is a biased Brownian dynamics (BD) algorithm that is more efficient than the standard Northrup-Allison-McCammon (NAM) method in cases where reaction events are infrequent because of intervening free energy barriers. Test cases reported here include the Smoluchowski rate for association of spheres, the association of the enzyme copper-zinc superoxide dismutase with superoxide anion, and the binding of the superpotent sweetener N-(p-cyanophenyl)-N'-(diphenylmethyl)-guanidinium acetic acid to a monoclonal antibody fragment, NC6.8. Our results show that the WEB dynamics algorithm is a superior simulation method for enzyme-substrate reaction encounters with large free energy barriers.

  17. 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.

  18. 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

  19. 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

  20. Fractional Feynman-Kac equation for weak ergodicity breaking.

    PubMed

    Carmi, Shai; Barkai, Eli

    2011-12-01

    The continuous-time random walk (CTRW) is a model of anomalous subdiffusion in which particles are immobilized for random times between successive jumps. A power-law distribution of the waiting times, ψ(τ) ~ τ(-(1+α)), leads to subdiffusion (x(2) ~ t(α)) for 0 < α < 1. In closed systems, the long stagnation periods cause time averages to divert from the corresponding ensemble averages, which is a manifestation of weak ergodicity breaking. The time average of a general observable U(t) = 1/t ∫(0)(t) U[x(τ)]dτ is a functional of the path and is described by the well-known Feynman-Kac equation if the motion is Brownian. Here, we derive forward and backward fractional Feynman-Kac equations for functionals of CTRW in a binding potential. We use our equations to study two specific time averages: the fraction of time spent by a particle in half-box, and the time average of the particle's position in a harmonic field. In both cases, we obtain the probability density function of the time averages for t → ∞ and the first two moments. Our results show that both the occupation fraction and the time-averaged position are random variables even for long times, except for α = 1, when they are identical to their ensemble averages. Using our fractional Feynman-Kac equation, we also study the dynamics leading to weak ergodicity breaking, namely the convergence of the fluctuations to their asymptotic values.

  1. Perpetual Motion with Maxwell's Demon

    NASA Astrophysics Data System (ADS)

    Gordon, Lyndsay G. M.

    2002-11-01

    A method for producing a temperature gradient by Brownian motion in an equilibrated isolated system composed of two fluid compartments and a separating adiabatic membrane is discussed. This method requires globular protein molecules, partially embedded in the membrane, to alternate between two conformations which lie on opposite sides of the membrane. The greater part of each conformer is bathed by one of the fluids and rotates in Brownian motion around its axis, perpendicular to the membrane. Rotational energy is transferred through the membrane during conformational changes. Angular momentum is conserved during the transitions. The energy flow becomes asymmetrical when the conformational changes of the protein are sterically hindered by two of its side-chains, the positions of which are affected by the angular velocity of the rotor. The heat flow increases the temperature gradient in contravention of the Second Law. A second hypothetical model which illustrates solute transfer at variance with the Second Law is also discussed.

  2. Reversible quantum brownian heat engines for electrons.

    PubMed

    Humphrey, T E; Newbury, R; Taylor, R P; Linke, H

    2002-09-01

    Brownian heat engines use local temperature gradients in asymmetric potentials to move particles against an external force. The energy efficiency of such machines is generally limited by irreversible heat flow carried by particles that make contact with different heat baths. Here we show that, by using a suitably chosen energy filter, electrons can be transferred reversibly between reservoirs that have different temperatures and electrochemical potentials. We apply this result to propose heat engines based on mesoscopic semiconductor ratchets, which can quasistatically operate arbitrarily close to Carnot efficiency.

  3. 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

  4. 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.

  5. Brownian friction coefficient of Kr/graphite.

    NASA Astrophysics Data System (ADS)

    Boutchko, R.

    1998-03-01

    Calculations of the Brownian friction coefficient of fluid Kr/graphite are described. The phonon frequencies and polarization vectors are calculated for a thick graphite slab using the Benedek-Onida bond charge model(G. Benedek and G. Onida, Phys. Rev. B 47), 16471 (1993). The fluctuating forces on the adatom from the substrate are expressed in terms of the graphite fluctuation spectrum. The friction coefficient is expressed in terms of a spectral density to be derived from the slab calculations. The relation of the results to diffusive processes in monolayer fluids(F. Y. Hansen, L. W. Bruch, and H. Taub, Phys. Rev. B 54), 14077 (1996). is discussed.

  6. 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.

  7. Self-propelled Brownian spinning top: dynamics of a biaxial swimmer at low Reynolds numbers.

    PubMed

    Wittkowski, Raphael; Löwen, Hartmut

    2012-02-01

    Recently the Brownian dynamics of self-propelled (active) rodlike particles was explored to model the motion of colloidal microswimmers, catalytically driven nanorods, and bacteria. Here we generalize this description to biaxial particles with arbitrary shape and derive the corresponding Langevin equation for a self-propelled Brownian spinning top. The biaxial swimmer is exposed to a hydrodynamic Stokes friction force at low Reynolds numbers, to fluctuating random forces and torques as well as to an external and an internal (effective) force and torque. The latter quantities control its self-propulsion. Due to biaxiality and hydrodynamic translational-rotational coupling, the Langevin equation can only be solved numerically. In the special case of an orthotropic particle in the absence of external forces and torques, the noise-free (zero-temperature) trajectory is analytically found to be a circular helix. This trajectory is confirmed numerically to be more complex in the general case of an arbitrarily shaped particle under the influence of arbitrary forces and torques involving a transient irregular motion before ending up in a simple periodic motion. By contrast, if the external force vanishes, no transient regime is found, and the particle moves on a superhelical trajectory. For orthotropic particles, the noise-averaged trajectory is a generalized concho-spiral. We furthermore study the reduction of the model to two spatial dimensions and classify the noise-free trajectories completely finding circles, straight lines with and without transients, as well as cycloids and arbitrary periodic trajectories.

  8. 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.

  9. Long-time Average of Field Measured by a Two-Dimensional Brownian Wanderer

    NASA Astrophysics Data System (ADS)

    Ezawa, Hiroshi; Nakamura, Toru; Watanabe, Keiji; Wiegel, Frederik W.

    2003-10-01

    For a 2-dimensional Brownian motion ω(t) starting from x0 at t = 0 and for a given function V(x), x\\in\\mathbb{R}^2, we determine (i) a normalization factor ν(T) such that the random variable, X[ω] = \\limT \\to ∞ ν(T)-1\\int_0T V(ω(t))dt, converges in law to have a nontrivial statistical distribution and (ii) the distribution itself. Assuming that \\int\\mathbb{R^2}V(x)d^2x \

  10. Brownian Dynamics Simulation for Suspension of Oblate Spheroidal Particles in Simple Shear Flow

    NASA Astrophysics Data System (ADS)

    Yamamoto, Takehiro; Suga, Takanori; Mori, Noriyasu

    2004-04-01

    Brownian dynamics simulations have been carried out for suspensions of oblate spheroidal particles interacting via the Gay-Berne potential. The system changed from isotropic phase to nematic one with increasing the particle concentration. In addition, the behavior of particles in simple shear flows was simulated; the shear was imposed on the systems in nematic phase at rest. The systems exhibited various motions of the director depending on the shear rate, e.g. continuous rotations of director at low shear rates and flow aligning at high shear rates.

  11. 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.

  12. 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.

  13. Relation between cooperative molecular motors and active Brownian particles.

    PubMed

    Touya, Clément; Schwalger, Tilo; Lindner, Benjamin

    2011-05-01

    Active Brownian particles (ABPs), obeying a nonlinear Langevin equation with speed-dependent drift and noise amplitude, are well-known models used to describe self-propelled motion in biology. In this paper we study a model describing the stochastic dynamics of a group of coupled molecular motors (CMMs). Using two independent numerical methods, one based on the stationary velocity distribution of the motors and the other one on the local increments (also known as the Kramers-Moyal coefficients) of the velocity, we establish a connection between the CMM and the ABP models. The parameters extracted for the ABP via the two methods show good agreement for both symmetric and asymmetric cases and are independent of N, the number of motors, provided that N is not too small. This indicates that one can indeed describe the CMM problem with a simpler ABP model. However, the power spectrum of velocity fluctuations in the CMM model reveals a peak at a finite frequency, a peak which is absent in the velocity spectrum of the ABP model. This implies richer dynamic features of the CMM model which cannot be captured by an ABP model.

  14. 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.

  15. Effective mass of holographic Brownian particle in rotating plasma

    NASA Astrophysics Data System (ADS)

    Atmaja, A. Nata; Kassim, H. Abu; Yusof, N.

    2015-04-01

    The dynamics of string fluctuations under a rotating Bañados-Teitelboim-Zanelli black hole is studied using the method developed in Son and Teaney [J. High Energy Phys. 07 (2009) 021]. We compare our result with the one computed previously in Atmaja [J. High Energy Phys. 02 (2013) 021], using a different method as developed in de Boer et al. [J. High Energy Phys. 07 (2009) 094] for the case of a corotating string. The result supports the claim made in Atmaja [J. High Energy Phys. 02 (2013) 021] that the end of the string, which is identified as an external quark at the boundary, behaves as a Brownian particle with the mass is given by an effective mass parameter Meff equals to the zero-temperature mass of an external quark M0 times the cube of a Lorentz factor γ . Furthermore, we extend the computation to a higher dimensional rotating AdS black hole, where the metric is effectively asymptotic to AdS3 and the fluctuation is taken only along the corotating motion. It turns out that the effective mass of the external quark has a universal form of Meff=γ3M0 .

  16. Brownian simulations and unidirectional flux in diffusion

    NASA Astrophysics Data System (ADS)

    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/γ of the Langevin equation. We find that the probability of Brownian trajectories that cross an interface in one direction in unit time Δt equals that of the probability of the corresponding Langevin trajectories if γΔt=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 unidirectional flux

  17. 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

  18. 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.

  19. From molecular dynamics to Brownian dynamics

    PubMed Central

    Erban, Radek

    2014-01-01

    Three coarse-grained molecular dynamics (MD) models are investigated with the aim of developing and analysing multi-scale methods which use MD simulations in parts of the computational domain and (less detailed) Brownian dynamics (BD) simulations in the remainder of the domain. The first MD model is formulated in one spatial dimension. It is based on elastic collisions of heavy molecules (e.g. proteins) with light point particles (e.g. water molecules). Two three-dimensional MD models are then investigated. The obtained results are applied to a simplified model of protein binding to receptors on the cellular membrane. It is shown that modern BD simulators of intracellular processes can be used in the bulk and accurately coupled with a (more detailed) MD model of protein binding which is used close to the membrane. PMID:25002825

  20. 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.

  1. 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

  2. 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.

  3. Kinetic nanofriction: a mechanism transition from quasi-continuous to ballistic-like Brownian regime.

    PubMed

    Jafary-Zadeh, Mehdi; Reddy, Chilla Damodara; Sorkin, Viacheslav; Zhang, Yong-Wei

    2012-02-21

    Surface diffusion of mobile adsorbates is not only the key to control the rate of dynamical processes on solid surfaces, e.g. epitaxial growth, but also of fundamental importance for recent technological applications, such as nanoscale electro-mechanical, tribological, and surface probing devices. Though several possible regimes of surface diffusion have been suggested, the nanoscale surface Brownian motion, especially in the technologically important low friction regimes, remains largely unexplored. Using molecular dynamics simulations, we show for the first time, that a C60 admolecule on a graphene substrate exhibits two distinct regimes of nanoscale Brownian motion: a quasi-continuous and a ballistic-like. A crossover between these two regimes is realized by changing the temperature of the system. We reveal that the underlying physical origin for this crossover is a mechanism transition of kinetic nanofriction arising from distinctive ways of interaction between the admolecule and the graphene substrate in these two regimes due to the temperature change. Our findings provide insight into surface mass transport and kinetic friction control at the nanoscale.

  4. 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

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

    PubMed

    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 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.

  6. 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

  7. 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

  8. 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

  9. 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

  10. Boltzmann distribution in a nonequilibrium steady state: measuring local potential by granular Brownian particles.

    PubMed

    To, Kiwing

    2014-06-01

    We investigate experimentally the steady state motion of a millimeter-sized granular polyhedral object on vertically vibrating platforms of flat, conical, and parabolic surfaces. We find that the position distribution of the granular object is related to the shape of the platform, just like that of a Brownian particle trapped in a potential at equilibrium, even though the granular object is intrinsically not at equilibrium due to inelastic collisions with the platform. From the collision dynamics, we derive the Langevin equation which describes the motion of the object under an effective potential that equals the gravitational potential along the platform surface. The potential energy is found to agree with the equilibrium equipartition theorem while the kinetic energy does not. Furthermore, the granular temperature is found to be higher than the effective temperature associated with the average potential energy, suggesting the presence of heat transfer from the kinetic part to the potential part of the granular object.

  11. Optimal tuning of a confined Brownian information engine.

    PubMed

    Park, Jong-Min; Lee, Jae Sung; Noh, Jae Dong

    2016-03-01

    A Brownian information engine is a device extracting mechanical work from a single heat bath by exploiting the information on the state of a Brownian particle immersed in the bath. As for engines, it is important to find the optimal operating condition that yields the maximum extracted work or power. The optimal condition for a Brownian information engine with a finite cycle time τ has been rarely studied because of the difficulty in finding the nonequilibrium steady state. In this study, we introduce a model for the Brownian information engine and develop an analytic formalism for its steady-state distribution for any τ. We find that the extracted work per engine cycle is maximum when τ approaches infinity, while the power is maximum when τ approaches zero.

  12. 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.

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

    NASA Astrophysics Data System (ADS)

    Domínguez-García, P.; Forró, László; Jeney, Sylvia

    2016-10-01

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

  14. 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.

  15. Improved search for elementary particles with fractional electric charge

    SciTech Connect

    Mar, N.M.; Lee, E.R.; Fleming, G.R.; Casey, B.C.; Perl, M.L.; Garwin, E.L.; Hendricks, C.D.; Lackner, K.S.; Shaw, G.L.

    1996-06-01

    We have devised and demonstrated the successful operation of a low-cost, high-mass throughput technique capable of performing bulk matter searches for fractionally charged particles based on an improved Millikan liquid drop method. The method uses a stroboscopic lamp and a charge coupled device video camera to image the trajectories of silicone oil drops falling through air in the presence of a vertical, alternating electric field. The images of the trajectories are computer processed in real time, the electric charge on a drop being measured with an rms error of 0.025 of an electron charge. This error is dominated by Brownian motion. In the first use of this method, we have looked at 5974941 drops and found no evidence for fractional charges in 1.07 mg of oil. With 95{percent} confidence, the concentration of isolated quarks with {plus_minus}1/3{ital e} or {plus_minus}2/3{ital e} in silicone oil is less than one per 2.14{times}10{sup 20} nucleons. {copyright} {ital 1996 The American Physical Society.}

  16. Using artificial microswimmers for controlling the motion of passive colloidal particles in straight and asymmetric channels

    NASA Astrophysics Data System (ADS)

    Misko, Vyacheslav R.

    2015-03-01

    Artificial self-propelled microswimmers capable of autonomous navigation through complex environments provide appealing opportunities for localization, pick-up and delivery of micro-and nanoscopic objects. Such self-driven microswimmers show not only the ability to navigate through the environment but also modify the environment. Using numerical simulations, we investigate active Brownian motion of self-propelled overdamped microswimmers, i.e., Janus spheres illuminated by light, in straight and corrugated channels. We demonstrated that a small fraction of active microswimmers injected in a system of passive colloids are capable of rectifying the passive species (i.e., in asymmetric channels) or separating various species (i.e., in a mixture of passive species). We analyze the effect of autonomous pumping of passive species by active microswimmers in various corrugated channels.

  17. Engineered swift equilibration of a Brownian particle

    NASA Astrophysics Data System (ADS)

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

    2016-09-01

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

  18. 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.

  19. 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)].

  20. 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

  1. 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.

  2. Statistical correlation of fractional oscillator response by complex spectral moments and state variable expansion

    NASA Astrophysics Data System (ADS)

    Pinnola, Francesco Paolo

    2016-10-01

    The statistical characterization of the oscillator response with non-integer order damping under Gaussian noise represents an important challenge in the modern stochastic mechanics. In fact, this kind of problem appears in several issues of different type (wave propagation in viscoelastic media, Brownian motion, fluid dynamics, RLC circuit, etc.). The aim of this paper is to provide a stochastic characterization of the stationary response of linear fractional oscillator forced by normal white noise. In particular, this paper shows a new method to obtain the correlation function by exact complex spectral moments. These complex quantities contain all the information to describe the random processes but in the considered case their analytical evaluation needs some mathematical manipulations. For this reason such complex spectral moment characterization is used in conjunction with a fractional-order state variable analysis. This kind of analysis permits to find the exact expression of complex spectral moments, and the correlation function by using the Mellin transform. Moreover, the proposed approach provides an analytical expression of the response variance of the fractional oscillator. Capability and efficiency of the present method are shown in the numerical examples in which correlation and variance of fractional oscillator response are found and compared with those obtained by Monte Carlo simulations.

  3. Instantaneous ballistic velocity of suspended Brownian nanocrystals measured by upconversion nanothermometry

    NASA Astrophysics Data System (ADS)

    Brites, Carlos D. S.; Xie, Xiaoji; Debasu, Mengistie L.; Qin, Xian; Chen, Runfeng; Huang, Wei; Rocha, João; Liu, Xiaogang; Carlos, Luís D.

    2016-10-01

    Brownian motion is one of the most fascinating phenomena in nature. Its conceptual implications have a profound impact in almost every field of science and even economics, from dissipative processes in thermodynamic systems, gene therapy in biomedical research, artificial motors and galaxy formation to the behaviour of stock prices. However, despite extensive experimental investigations, the basic microscopic knowledge of prototypical systems such as colloidal particles in a fluid is still far from being complete. This is particularly the case for the measurement of the particles' instantaneous velocities, elusive due to the rapid random movements on extremely short timescales. Here, we report the measurement of the instantaneous ballistic velocity of Brownian nanocrystals suspended in both aqueous and organic solvents. To achieve this, we develop a technique based on upconversion nanothermometry. We find that the population of excited electronic states in NaYF4:Yb/Er nanocrystals at thermal equilibrium can be used for temperature mapping of the nanofluid with great thermal sensitivity (1.15% K‑1 at 296 K) and a high spatial resolution (<1 μm). A distinct correlation between the heat flux in the nanofluid and the temporal evolution of Er3+ emission allows us to measure the instantaneous velocity of nanocrystals with different sizes and shapes.

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

    PubMed

    Kuznetsov, Igor R; Evans, Evan A

    2013-04-01

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

  5. 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

  6. 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.

  7. 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

  8. 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.

  9. 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.

  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. Brownian dynamics of emulsion film formation and droplet coalescence

    NASA Astrophysics Data System (ADS)

    Toro-Mendoza, Jhoan; Petsev, Dimiter N.

    2010-05-01

    We analyze the evolution in thickness and radius of the film formed during the collision of two deformable emulsion Brownian droplets. These variables exhibit random fluctuations due to thermal disturbances from the continuous liquid phase. As a result, the system probes a random trajectory in the configurational space until it reaches a critical film thickness, at which point the droplets coalesce. Therefore, the film is modeled as a disk with thicknesses and radi that can fluctuate. Our analysis is based on a Langevin-Brownian dynamics approach, which accounts for the thermodynamic and hydrodynamic interactions in the lubrication approximation. We examine the effect of parameters such as droplet size, interfacial mobility, and electrolyte concentration on the coalescence of small Brownian droplets. The results suggest that the coalescence times depend on a complex interplay between the thermodynamic and hydrodynamic interactions.

  12. Applicability of effective pair potentials for active Brownian particles.

    PubMed

    Rein, Markus; Speck, Thomas

    2016-09-01

    We have performed a case study investigating a recently proposed scheme to obtain an effective pair potential for active Brownian particles (Farage et al., Phys. Rev. E 91, 042310 (2015)). Applying this scheme to the Lennard-Jones potential, numerical simulations of active Brownian particles are compared to simulations of passive Brownian particles interacting by the effective pair potential. Analyzing the static pair correlations, our results indicate a limited range of activity parameters (speed and orientational correlation time) for which we obtain quantitative, or even qualitative, agreement. Moreover, we find a qualitatively different behavior for the virial pressure even for small propulsion speeds. Combining these findings we conclude that beyond linear response active particles exhibit genuine non-equilibrium properties that cannot be captured by effective pair interaction alone. PMID:27628695

  13. Unidirectional Flux In Brownian And Langevin Simulations Of Diffusion

    NASA Astrophysics Data System (ADS)

    Singer, A.; Schuss, Z.; Nadler, B.

    2005-11-01

    Brownian and Langevin simulations of ions in solution require the maintenance of average fixed concentrations at the interface between the simulation volume and the surrounding continuum. This requires the injection of new trajectories into the simulation, which creates a unidirectional flux at the interface. The Wiener path integral splits the net diffusion flux into infinite unidirectional fluxes, whose difference is finite, as in classical diffusion theory. The infinite unidirectional flux is an artifact of the diffusion approximation to Langevin's equation, which fails on time scales shorter than the relaxation time 1/γ. The probability of Brownian trajectories that cross a point in one direction per unit time Δt equals that of Langevin trajectories if γΔt = 2. This result is relevant to Brownian dynamics simulation of particles in a finite volume inside a large bath.

  14. 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

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

    NASA Astrophysics Data System (ADS)

    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), 10.1021/jacs.5b10549], we show that mobile two-particle predictions of the probability of dimerization Pdimer, equilibrium constant K , and 2D osmotic pressure Π2 D as a function of the particle area fraction ϕA 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.

  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. Finite-element approach to Brownian dynamics of polymers.

    PubMed

    Cyron, Christian J; Wall, Wolfgang A

    2009-12-01

    In the last decades simulation tools for Brownian dynamics of polymers have attracted more and more interest. Such simulation tools have been applied to a large variety of problems and accelerated the scientific progress significantly. However, the currently most frequently used explicit bead models exhibit severe limitations, especially with respect to time step size, the necessity of artificial constraints and the lack of a sound mathematical foundation. Here we present a framework for simulations of Brownian polymer dynamics based on the finite-element method. This approach allows simulating a wide range of physical phenomena at a highly attractive computational cost on the basis of a far-developed mathematical background.

  18. Powering a burnt bridges Brownian ratchet: a model for an extracellular motor driven by proteolysis of collagen.

    PubMed

    Saffarian, Saveez; Qian, Hong; Collier, Ivan; Elson, Elliot; Goldberg, Gregory

    2006-04-01

    Biased diffusion of collagenase on collagen fibrils may represent the first observed adenosine triphosphate-independent extracellular molecular motor. The magnitude of force generated by the enzyme remains unclear. We propose a propulsion mechanism based on a burnt bridges Brownian ratchet model with a varying degree of coupling of the free energy from collagen proteolysis to the enzyme motion. When constrained by experimental observations, our model predicts 0.1 pN stall force for individual collagenase molecules. A dimer, surprisingly, can generate a force in the range of 5 pN, suggesting that the motor can be of biological significance.

  19. 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.

  20. Brownian dynamics of a self-propelled particle in shear flow.

    PubMed

    ten Hagen, Borge; Wittkowski, Raphael; Löwen, Hartmut

    2011-09-01

    Brownian dynamics of a self-propelled particle in linear shear flow is studied analytically by solving the Langevin equation and in simulation. The particle has a constant propagation speed along a fluctuating orientation and is additionally subjected to a constant torque. In two spatial dimensions, the mean trajectory and the mean square displacement (MSD) are calculated as functions of time t analytically. In general, the mean trajectories are cycloids that are modified by finite temperature effects. With regard to the MSD, different regimes are identified where the MSD scales with t(ν) with ν=0,1,2,3,4. In particular, an accelerated (ν=4) motion emerges if the particle is self-propelled along the gradient direction of the shear flow.

  1. 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.

  2. 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

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

    NASA Astrophysics Data System (ADS)

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

    2010-03-01

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

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

    PubMed

    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

  6. Aggregate size distribution evolution for Brownian coagulation-sensitivity to an improved rate constant.

    PubMed

    Zurita-Gotor, M; Rosner, D E

    2004-06-15

    Brownian motion causes small aggregates to encounter one another and grow in gaseous environments, often under conditions in which the coalescence rate (say, spheroidization by "sintering") cannot compete. The polydisperse nature of the aerosol population formed by this mechanism is typically accounted for by formulating an evolution equation for the joint PDF of the state variables needed for describing individual particles. In the simple case of fractal-like aggregates (prescribed morphology and state, characterized just by the number of aggregated spherules, or total aggregate volume), we use the quadrature method of moments and Monte Carlo simulations to show that recent improvements in the laws governing free molecule regime coagulation frequency (rate "constant") of these aggregates cause systematic changes in the shape of the asymptotic aggregate size distribution, with significant implications for the light-scattering power and inertial impaction behavior of such aggregate populations.

  7. 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.

  8. The stochastic dynamics of a Brownian particle in a viscoelastic (VE) medium

    NASA Astrophysics Data System (ADS)

    Azese, Martin; Bhattacharya, Sukalyan

    2012-02-01

    The stochastic dynamics of a Brownian particle in a viscoelastic (VE) medium is an important phenomenon from micro-rheological perspective. In micro-rheology, the main question is how to predict the rheological properties by observing the Brownian motion in the it without using a rheometer, as the sample is too precious to be structurally destroyed in a macro-scale experiment. Thus, several theoretical studies tried to relate the features of the stochastic motion to the VE property. However, it seems that none of these theories is complete because their formulations invariably involve heuristic assumptions inherited from the classical results for purely viscous fluid. In this talk, we will present a theory which is devoid of any such arbitrary assumption. Accordingly, we will first generalize the fluctuation-dissipation theorem for VE medium to obtain the velocity correlation function (VCF) for given velocity-response function (VRF) which describes the temporal dependence of velocity of the particle initially driven by an impulse. Our generalized theorem proves VCF and VRF to be unequal, and shows the corresponding equality in classical result for purely viscous fluid as a special case. We will re-examine the validity of Green-Kubo relation so that mean square displacement(MSD) can be associated with VCF. Finally, the linearized hydrodynamic equation for general VE medium will be solved to provide the required VRF. As a result, the property of the medium which is represented by VRF would be revealed by both time-dependence of the VCF and MSD.

  9. 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

  10. 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.

  11. Single-particle motion in three-dimensional vibrofluidized granular beds

    NASA Astrophysics Data System (ADS)

    Wildman, R. D.; Huntley, J. M.; Hansen, J.-P.; Parker, D. J.; Allen, D. A.

    2000-09-01

    A technique to probe the interior of three-dimensional dynamic granular systems is presented. Positron emission particle tracking (PEPT) allows a single tracer particle to be followed around a three dimensional vibrofluidized granular bed for periods up to six hours. At present the technique is able to resolve the position of the grains to +/-4 mm, with an average temporal resolution of about 7 ms. Packing fraction profiles are calculated by making use of the ergodicity of the system, and granular temperature profiles are obtained, in the dilute case, from the short time behavior of the mean squared displacement. At longer times, the mean squared displacement shows a range of behavior which can be explained by the presence of strong gradients in the packing fraction. Convection currents were observed, but were sufficiently small in magnitude to be ignored during the analysis of grain motion. The system was modeled using the Smoluchowski equation, which was solved numerically, and the results compared with the experimentally determined displacement probability density functions. Good agreement between experiment and numerical results was achieved using Brownian motion relationships modified to accommodate differences between granular systems and thermal systems.

  12. 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.

  13. 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.

  14. Heterogeneity and the role of normal stresses during the extensional thinning of non-Brownian shear-thickening fluids.

    PubMed

    Roché, Matthieu; Kellay, Hamid; Stone, Howard A

    2011-09-23

    We contrast the extensional and shear dynamics of non-Brownian suspensions as a function of particle concentration. We show that the thinning rate selected during the viscoelastic pinch-off of a liquid bridge is related to the shear rate at which normal stresses become positive, which differs from the shear rate at the onset of shear thickening. By tracking particles, we demonstrate that the extensional flow is heterogeneous, with local variations of the volume fraction consistent with self-dilution. This nonuniform structure is the cause of the buckling of the threads formed after breakup. PMID:22026859

  15. 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

  16. Simultaneous effects of slip and wall properties on MHD peristaltic motion of nanofluid with Joule heating

    NASA Astrophysics Data System (ADS)

    Hayat, T.; Nisar, Z.; Ahmad, B.; Yasmin, H.

    2015-12-01

    This paper is devoted to the magnetohydrodynamic (MHD) peristaltic transport of nanofluid in a channel with wall properties. Flow analysis is addressed in the presence of viscous dissipation, partial slip and Joule heating effects. Mathematical modelling also includes the salient features of Brownian motion and thermophoresis. Both analytic and numerical solutions are provided. Comparison between the solutions is shown in a very good agreement. Attention is focused to the Brownian motion parameter, thermophoresis parameter, Hartman number, Eckert number and Prandtl number. Influences of various parameters on skin friction coefficient, Nusselt and Sherwood numbers are also investigated. It is found that both the temperature and nanoparticles concentration are increasing functions of Brownian motion and thermophoresis parameters.

  17. Non-Gaussian statistics for the motion of self-propelled Janus particles: experiment versus theory.

    PubMed

    Zheng, Xu; Ten Hagen, Borge; Kaiser, Andreas; Wu, Meiling; Cui, Haihang; Silber-Li, Zhanhua; Löwen, Hartmut

    2013-09-01

    Spherical Janus particles are one of the most prominent examples for active Brownian objects. Here, we study the diffusiophoretic motion of such microswimmers in experiment and in theory. Three stages are found: simple Brownian motion at short times, superdiffusion at intermediate times, and finally diffusive behavior again at long times. These three regimes observed in the experiments are compared with a theoretical model for the Langevin dynamics of self-propelled particles with coupled translational and rotational motion. Besides the mean square displacement also higher displacement moments are addressed. In particular, theoretical predictions regarding the non-Gaussian behavior of self-propelled particles are verified in the experiments. Furthermore, the full displacement probability distribution is analyzed, where in agreement with Brownian dynamics simulations either an extremely broadened peak or a pronounced double-peak structure is found, depending on the experimental conditions.

  18. An invariance principle for reversible Markov processes. Applications to random motions in random environments

    SciTech Connect

    De Masi, A.; Ferrari, P.A.; Goldstein, S.; Wick, W.D. )

    1989-05-01

    The authors present an invariance principle for antisymmetric functions of a reversible Markov process which immediately implies convergence to Brownian motion for a wide class of random motions in random environments. They apply it to establish convergence to Brownian motion (i) for a walker moving in the infinite cluster of the two-dimensional bond percolation model, (ii) for a d-dimensional walker moving in a symmetric random environment under very mild assumptions on the distribution of the environment, (iii) for a tagged particle in a d-dimensional symmetric lattice gas which allows interchanges, (iv) for a tagged particle in a d-dimensional system of interacting Brownian particles. Their formulation also leads naturally to bounds on the diffusion constant.

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

    NASA Astrophysics Data System (ADS)

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

    2008-12-01

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

  20. 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....