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Sample records for fractional brownian motion

  1. 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.

  2. Extreme-value statistics of fractional Brownian motion bridges

    NASA Astrophysics Data System (ADS)

    Delorme, Mathieu; Wiese, Kay Jörg

    2016-11-01

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

  3. 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.

  4. 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.

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

    NASA Astrophysics Data System (ADS)

    Fuliński, A.

    2017-02-01

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

  6. 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.

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

    NASA Astrophysics Data System (ADS)

    Sikora, Grzegorz; Burnecki, Krzysztof; Wyłomańska, Agnieszka

    2017-03-01

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

  8. 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.

  9. 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)

  10. 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.

  11. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2013-09-01

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

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

    NASA Astrophysics Data System (ADS)

    Gu, Hui; Liang, Jin-Rong; Zhang, Yun-Xiu

    2012-08-01

    This paper deals with the problem of discrete time option pricing by a fractional subdiffusive Black-Scholes model. The price of the underlying stock follows a time-changed geometric fractional Brownian motion. By a mean self-financing delta-hedging argument, the pricing formula for the European call option in discrete time setting is obtained.

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

    DTIC Science & Technology

    2014-10-09

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

  15. Mackey-Glass equation driven by fractional Brownian motion

    NASA Astrophysics Data System (ADS)

    Nguyen, Dung Tien

    2012-11-01

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

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

    NASA Astrophysics Data System (ADS)

    Kamrani, Minoo; Jamshidi, Nahid

    2017-03-01

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

  17. 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.

  18. 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.

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

    NASA Astrophysics Data System (ADS)

    Eliazar, Iddo; Klafter, Joseph

    2009-02-01

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

  20. 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.

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

    PubMed

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

    2016-10-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-10-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2009-10-01

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

  4. 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.

  5. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-03-01

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

  7. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2017-02-01

    Many real time-series exhibit behavior adequate to long range dependent data. Additionally very often these time-series have constant time periods and also have characteristics similar to Gaussian processes although they are not Gaussian. Therefore there is need to consider new classes of systems to model these kinds of empirical behavior. Motivated by this fact in this paper we analyze two processes which exhibit long range dependence property and have additional interesting characteristics which may be observed in real phenomena. Both of them are constructed as the superposition of fractional Brownian motion (FBM) and other process. In the first case the internal process, which plays role of the time, is the gamma process while in the second case the internal process is its inverse. We present in detail their main properties paying main attention to the long range dependence property. Moreover, we show how to simulate these processes and estimate their parameters. We propose to use a novel method based on rescaled modified cumulative distribution function for estimation of parameters of the second considered process. This method is very useful in description of rounded data, like waiting times of subordinated processes delayed by inverse subordinators. By using the Monte Carlo method we show the effectiveness of proposed estimation procedures. Finally, we present the applications of proposed models to real time series.

  9. 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.

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

    PubMed

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

    2016-10-19

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

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

    NASA Astrophysics Data System (ADS)

    Hiotelis, Nicos; Del Popolo, Antonino

    2017-03-01

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

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

    NASA Astrophysics Data System (ADS)

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

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

  13. Relativistic Brownian motion

    NASA Astrophysics Data System (ADS)

    Dunkel, Jörn; Hänggi, Peter

    2009-02-01

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

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

    PubMed

    Taheriyoun, Ali R; Moghimbeygi, Meisam

    2017-02-14

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

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

    NASA Astrophysics Data System (ADS)

    Guo, Zhidong; Yuan, Hongjun

    2014-07-01

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

  16. A multiscale guide to Brownian motion

    NASA Astrophysics Data System (ADS)

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

    2016-01-01

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

  17. 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.

  18. p-adic Brownian motion

    NASA Astrophysics Data System (ADS)

    Zelenov, E. I.

    2016-12-01

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

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

    PubMed

    Rougier, P

    1999-05-14

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

  20. Superdiffusive trajectories in Brownian motion.

    PubMed

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

    2013-02-01

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

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

    NASA Astrophysics Data System (ADS)

    Hänggi, Peter

    2005-03-01

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

  2. 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.

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

    NASA Astrophysics Data System (ADS)

    Taheriyoun, Ali R.; Moghimbeygi, Meisam

    2017-02-01

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

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

    PubMed Central

    Taheriyoun, Ali R.; Moghimbeygi, Meisam

    2017-01-01

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

  5. Microscopic derivation of open quantum Brownian motion

    NASA Astrophysics Data System (ADS)

    Petruccione, Francesco; Sinayskiy, Ilya; UKZN Team

    2015-03-01

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

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

    PubMed

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

    2016-04-30

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

  7. Broadband boundary effects on Brownian motion

    NASA Astrophysics Data System (ADS)

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

    2015-12-01

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

  8. Monotone and boolean unitary Brownian motions

    NASA Astrophysics Data System (ADS)

    Hamdi, Tarek

    2015-06-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2009-03-01

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

  10. 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.

  11. Performance of Brownian-motion-generated universal portfolios

    NASA Astrophysics Data System (ADS)

    Tan, Choon Peng; Pang, Sook Theng

    2014-06-01

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

  12. Relativistic Brownian motion on a graphene chip

    NASA Astrophysics Data System (ADS)

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

    2012-10-01

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

  13. 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.

  14. 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.

  15. 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.

  16. 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.

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

    NASA Astrophysics Data System (ADS)

    Rauwerdink, Adam M.; Weaver, John B.

    2010-01-01

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

  18. 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…

  19. Parallel Molecular Distributed Detection With Brownian Motion.

    PubMed

    Rogers, Uri; Koh, Min-Sung

    2016-12-01

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

  20. Parallel Molecular Distributed Detection with Brownian Motion.

    PubMed

    Rogers, Uri; Koh, Min-Sung

    2016-12-05

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

  1. Lagrangian turbulence and the Brownian motion paradox

    NASA Astrophysics Data System (ADS)

    Viecelli, J. A.

    1991-11-01

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

  2. 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.

  3. Simulation of the active Brownian motion of a microswimmer

    NASA Astrophysics Data System (ADS)

    Volpe, Giorgio; Gigan, Sylvain; Volpe, Giovanni

    2014-07-01

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

  4. Dynamical and thermodynamical control of open quantum Brownian motion

    NASA Astrophysics Data System (ADS)

    Petruccione, Francesco; Sinayskiy, Ilya

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

  5. 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.

  6. 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.

  7. Transport properties of elastically coupled fractional Brownian motors

    NASA Astrophysics Data System (ADS)

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

    2015-11-01

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

  8. 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.

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

    PubMed

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

    2017-03-07

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

  10. 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.

  11. 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.

  12. Effect of interfaces on the nearby Brownian motion

    NASA Astrophysics Data System (ADS)

    Huang, Kai; Szlufarska, Izabela

    2015-10-01

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

  13. 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

  14. 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.

  15. 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

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

    NASA Astrophysics Data System (ADS)

    Gonzalez, Gabriela Ines

    1995-01-01

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

  17. 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.

  18. 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.

  19. On a nonstandard Brownian motion and its maximal function

    NASA Astrophysics Data System (ADS)

    Andrade, Bernardo B. de

    2015-07-01

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

  20. Convex hull of a Brownian motion in confinement.

    PubMed

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

    2015-05-01

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

  1. Convex hull of a Brownian motion in confinement

    NASA Astrophysics Data System (ADS)

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

    2015-05-01

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

  2. Relating Brownian motion to diffusion with superparamagnetic colloids

    NASA Astrophysics Data System (ADS)

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

    2017-04-01

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

  3. Free Energies and Fluctuations for the Unitary Brownian Motion

    NASA Astrophysics Data System (ADS)

    Dahlqvist, Antoine

    2016-12-01

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

  4. 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

  5. Brownian motion of a particle with arbitrary shape

    NASA Astrophysics Data System (ADS)

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

    2015-11-01

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

  6. Brownian motion: Absolute negative particle mobility

    NASA Astrophysics Data System (ADS)

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

    2005-08-01

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

  7. 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.

  8. 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.

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

    SciTech Connect

    Wang, Gaoyuan; Battefeld, Thorsten

    2016-09-05

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

  10. 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.

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

    NASA Astrophysics Data System (ADS)

    Ryan, Reade

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

  12. 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…

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

    NASA Astrophysics Data System (ADS)

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

    2015-12-01

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

  14. Observation of non-Markovian micromechanical Brownian motion

    PubMed Central

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

    2015-01-01

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

  15. Diffusion in different models of active Brownian motion

    NASA Astrophysics Data System (ADS)

    Lindner, B.; Nicola, E. M.

    2008-04-01

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

  16. 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.

  17. Non-Markovian expansion in quantum Brownian motion

    NASA Astrophysics Data System (ADS)

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

    2014-01-01

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

  18. 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.

  19. 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.

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

    NASA Astrophysics Data System (ADS)

    To, Kiwing; Peng, Zheng

    2016-11-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-07-01

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

  2. 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.

  3. A simple microviscometric approach based on Brownian motion tracking

    NASA Astrophysics Data System (ADS)

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

    2015-02-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2011-01-01

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

  5. 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.

  6. 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.

  7. 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.

  8. 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

  9. 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.

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

    PubMed

    Koide, T; Kodama, T

    2011-06-01

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

  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 of a circle swimmer in a harmonic trap

    NASA Astrophysics Data System (ADS)

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

    2017-02-01

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

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

    PubMed

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

    2017-02-01

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

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

    PubMed Central

    Li, Guanglai; Tang, Jay X.

    2009-01-01

    In this letter we propose a kinematic model to explain how collisions with a surface and rotational Brownian motion give rise to accumulation of micro-swimmers near a surface. In this model, an elongated microswimmer invariably travels parallel to the surface after hitting it from an oblique angle. It then swims away from the surface, facilitated by rotational Brownian motion. Simulations based on this model reproduce the density distributions measured for the small bacteria E. coli and Caulobacter crescentus, as well as for the much larger bull spermatozoa swimming between two walls. PMID:19792689

  16. 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.

  17. 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.

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

    NASA Astrophysics Data System (ADS)

    Das, Biswarup; Goswami, Debashish

    2012-01-01

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

  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. 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.

  1. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2006-11-01

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

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

    PubMed

    Turgeman, Lior; Carmi, Shai; Barkai, Eli

    2009-11-06

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

  4. 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.

  5. 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.

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

    NASA Astrophysics Data System (ADS)

    Sokolov, I. M.; Klafter, J.

    2005-06-01

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

  7. Arbitrage with fractional Gaussian processes

    NASA Astrophysics Data System (ADS)

    Zhang, Xili; Xiao, Weilin

    2017-04-01

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

  8. 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…

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

    NASA Astrophysics Data System (ADS)

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

    2012-12-01

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

  10. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-11-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

    Consider a one-dimensional branching Brownian motion and rescale the coordinate and time so that the rates of branching and diffusion are both equal to 1. If X1(t ) is the position of the rightmost particle of the branching Brownian motion at time t , the empirical velocity c of this rightmost particle is defined as c =X1(t ) /t . Using the Fisher-Kolmogorov-Petrovsky-Piscounov equation, we evaluate the probability distribution P (c ,t ) of this empirical velocity c in the long-time t limit for c >2 . It is already known that, for a single seed particle, P (c ,t ) ˜exp[-(c2/4 -1 ) t ] up to a prefactor that can depend on c and t . Here we show how to determine this prefactor. The result can be easily generalized to the case of multiple seed particles and to branching random walks associated with other traveling-wave equations.

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

    PubMed

    Cirovic, Ivana M

    2014-10-01

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

  14. Brownian motion of massive skyrmions in magnetic thin films

    SciTech Connect

    Troncoso, Roberto E.; Núñez, Álvaro S.

    2014-12-15

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

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

    DTIC Science & Technology

    1987-01-30

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

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

    PubMed Central

    Böttcher, Björn

    2010-01-01

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

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

    PubMed

    Böttcher, Björn

    2010-12-03

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

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

    NASA Astrophysics Data System (ADS)

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

    2004-03-01

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

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

    PubMed Central

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

    1991-01-01

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

  20. Relativistic Brownian motion: from a microscopic binary collision model to the Langevin equation.

    PubMed

    Dunkel, Jörn; Hänggi, Peter

    2006-11-01

    The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy pointlike Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, nonrelativistic LE is deduced from this model, by taking into account the nonrelativistic conservation laws for momentum and kinetic energy. Subsequently, this procedure is generalized to the relativistic case. There, it is found that the relativistic stochastic force is still delta correlated (white noise) but no longer corresponds to a Gaussian white noise process. Explicit results for the friction and momentum-space diffusion coefficients are presented and discussed.

  1. 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.

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

    PubMed Central

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

    2014-01-01

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

  3. 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.

  4. 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.

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

    PubMed

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

    2009-12-15

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

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

    PubMed Central

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

    2010-01-01

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

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

    PubMed

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

    2012-06-01

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

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

    NASA Astrophysics Data System (ADS)

    McCauley, Joseph L.

    1995-01-01

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

  9. 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

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

    NASA Astrophysics Data System (ADS)

    Silva, Antonio

    2005-03-01

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

  11. 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.

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

    NASA Astrophysics Data System (ADS)

    Randon-Furling, Julien; Wespi, Florian

    2017-03-01

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

  13. 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.

  14. 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.

  15. 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

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

    NASA Astrophysics Data System (ADS)

    Bakarji, Joseph; Tartakovsky, Daniel M.

    2017-04-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

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

  18. 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.

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

    PubMed

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

    2013-12-01

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

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

    NASA Astrophysics Data System (ADS)

    Derrida, Bernard; Shi, Zhan

    2016-06-01

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

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

    NASA Astrophysics Data System (ADS)

    Avan, Jean; Grosjean, Nicolas; Huillet, Thierry

    2015-04-01

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

  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.

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

    NASA Astrophysics Data System (ADS)

    Azuma, Ryuzo

    2002-10-01

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

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

    PubMed

    Minchew, Candace L; Didenko, Vladimir V

    2014-01-01

    We describe a new type of bio-nanomachine which runs on thermal noise. The machine is solely powered by the random motion of water molecules in its environment and does not ever require re-fuelling. The construct, which is made of DNA and vaccinia virus topoisomerase protein, can detect DNA damage by employing fluorescence. It uses Brownian motion as a cyclic motor to continually separate and bring together two types of fluorescent hairpins participating in FRET. This bio-molecular oscillator is a fast and specific sensor of 5'OH double-strand DNA breaks present in phagocytic phase of apoptosis. The detection takes 30 s in solution and 3 min in cell suspensions. The phagocytic phase is critical for the effective execution of apoptosis as it ensures complete degradation of the dying cells' DNA, preventing release of pathological, viral and tumor DNA and self-immunization. The construct can be used as a smart FRET probe in studies of cell death and phagocytosis.

  5. 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…

  6. 3D tracking the Brownian motion of colloidal particles using digital holographic microscopy and joint reconstruction.

    PubMed

    Verrier, Nicolas; Fournier, Corinne; Fournel, Thierry

    2015-06-01

    In-line digital holography is a valuable tool for sizing, locating, and tracking micro- or nano-objects in a volume. When a parametric imaging model is available, inverse problem approaches provide a straightforward estimate of the object parameters by fitting data with the model, thereby allowing accurate reconstruction. As recently proposed and demonstrated, combining pixel super-resolution techniques with inverse problem approaches improves the estimation of particle size and 3D position. Here, we demonstrate the accurate tracking of colloidal particles in Brownian motion. Particle size and 3D position are jointly optimized from video holograms acquired with a digital holographic microscopy setup based on a low-end microscope objective (×20, NA 0.5). Exploiting information redundancy makes it possible to characterize particles with a standard deviation of 15 nm in size and a theoretical resolution of 2×2×5  nm3 for position under additive white Gaussian noise assumption.

  7. 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.

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

    PubMed

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

    2016-12-23

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

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

    PubMed

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

    2013-12-15

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

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

    PubMed

    Nieuwenhuizen, Th M; Allahverdyan, A E

    2002-09-01

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

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

    PubMed Central

    Jakobsson, E; Chiu, S W

    1988-01-01

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

  12. 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

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

    PubMed

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

    2015-09-01

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

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

    PubMed

    de la Torre, J A; Español, Pep

    2011-09-21

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

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

    PubMed

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

    2009-10-02

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

  16. Quantum Brownian Motions and Navier-Stokes Weakly Turbulence — a Path Integral Study

    NASA Astrophysics Data System (ADS)

    Botelho, Luiz C. L.

    In this paper, we present a new method to solve exactly the Schrödinger Harmonic oscillator wave equation in the presence of time-dependent parameter. We also apply such technique to solve exactly the problem of random frequency averaged quantum propagator of a harmonic oscillator with white-noise statistics frequency. We still apply our technique to solve exactly the Brownian Quantum Oscillator in the presence of an electric field. Finally, we use these quantum mechanic techniques to solve exactly the Statistical-Turbulence of the Navier-Stokes in a region of fluid random stirring weakly (analytical) coupling through time-dependent Euclidean-Quantum oscillators path-integrals.

  17. 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.

  18. 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.

  19. 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.

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

    NASA Astrophysics Data System (ADS)

    Challis, K. J.

    2016-12-01

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

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

    PubMed

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

    2017-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2017-01-01

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

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

    PubMed

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

    2010-08-01

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

  4. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-11-01

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

  6. Inter-fraction variations in respiratory motion models.

    PubMed

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

    2011-01-07

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

  7. 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.

  8. 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.

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

    DOE PAGES

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

    2014-04-14

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

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

    PubMed Central

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

    2014-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

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

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

    NASA Astrophysics Data System (ADS)

    Azuma, Ryuzo; Takayama, Hajime

    2002-10-01

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

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

    PubMed

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

    2013-05-13

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

  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. 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.

  16. 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.

  17. 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.

  18. Fractional Levy stable motion for modeling speckle image

    NASA Astrophysics Data System (ADS)

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

    2008-03-01

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

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

    PubMed Central

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

    2013-01-01

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

  20. 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

  1. 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.

  2. 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}> .

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

    PubMed

    Hanasaki, Itsuo; Nagura, Ryo; Kawano, Satoyuki

    2015-03-14

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

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

    PubMed

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

    2017-02-01

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

  5. 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.

  6. 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.

  7. Brownian ratchets in physics and biology

    NASA Astrophysics Data System (ADS)

    Bier, Martin

    1997-06-01

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

  8. 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.

  9. Confined Brownian ratchets

    NASA Astrophysics Data System (ADS)

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

    2013-05-01

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

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

    DOE PAGES

    Moller, Peter; Ichikawa, Takatoshi

    2015-12-23

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

  11. 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.

  12. Brownian vortexes

    NASA Astrophysics Data System (ADS)

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

    2009-07-01

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

  13. Two dimensional fractional projectile motion in a resisting medium

    NASA Astrophysics Data System (ADS)

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

    2014-07-01

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

  14. Two dimensional fractional projectile motion in a resisting medium

    NASA Astrophysics Data System (ADS)

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

    2014-07-01

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

  15. 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

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

    PubMed

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

    2013-01-01

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

  17. 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.

  18. Brownian Motion, "Diverse and Undulating"

    NASA Astrophysics Data System (ADS)

    Duplantier, Bertrand

    Truly man is a marvelously vain, diverse, and undulating object. It is hard to found any constant and uniform judgment on him. Michel de Montaigne, Les Essais, Book I, Chapter 1: "By diverse means we arrive at the same end"; in The Complete Essays of Montaigne, Donald M. Frame transl., Stanford University Press (1958).

  19. Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell model

    NASA Astrophysics Data System (ADS)

    Wenchang, Tan; Mingyu, Xu

    2002-08-01

    The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. The flow near a wall suddenly set in motion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model. Exact solutions of velocity and stress are obtained by using the discrete inverse Laplace transform of the sequential fractional derivatives. It is found that the effect of the fractional orders in the constitutive relationship on the flow field is significant. The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate, for large times the viscoelastic effects become weak.

  20. Temporally Anticorrelated Motion of Nanoparticles at a Liquid Interface.

    PubMed

    Wang, Dapeng; Hu, Renfeng; Skaug, Michael J; Schwartz, Daniel K

    2015-01-02

    Quantum dots at the hexane-glycerol interface exhibited unexpected behavior including highly dynamic adsorption/desorption, where the lateral nanoparticle motion was anomalously fast immediately after adsorption and prior to desorption. At the interface, particles exhibited pseudo-Brownian lateral motion, in which the instantaneous diffusion coefficient was temporally anticorrelated, in agreement with our simulations involving fractional Brownian motion in the surface-normal direction. These phenomena suggest that, in contrast to the conventional picture for colloidal particles, nanoparticles explore a landscape of metastable interfacial positions, with different exposures to the two adjacent phases.

  1. Enhancing ejection fraction measurement through 4D respiratory motion compensation in cardiac PET imaging.

    PubMed

    Tang, Jing; Wang, Xinhui; Gao, Xiangzhen; Segars, Paul; Lodge, Martin; Rahmim, Arman

    2017-03-02

    ECG gated cardiac PET imaging measures functional parameters such as left ventricle (LV) ejection fraction (EF), providing diagnostic and prognostic information for management of patients with coronary artery disease (CAD). Respiratory motion degrades spatial resolution and affects the accuracy in measuring the LV volumes for EF calculation. The goal of this study is to systematically investigate the effect of respiratory motion correction on the estimation of end-diastolic volume (EDV), end-systolic volume (ESV), and EF, especially on the separation of normal and abnormal EFs. We developed a respiratory motion incorporated 4D PET image reconstruction technique which uses all gated-frame data to acquire a motion-suppressed image. Using the standard XCAT phantom and two individual-specific volunteer XCAT phantoms, we simulated dual-gated myocardial perfusion imaging data for normally and abnormally beating hearts. With and without respiratory motion correction, we measured the EDV, ESV, and EF from the cardiac gated reconstructed images. For all the phantoms, the estimated volumes increased and the biases significantly reduced with motion correction compared with those without. Furthermore, the improvement of ESV measurement in the abnormally beating heart led to better separation of normal and abnormal EFs. The simulation study demonstrated the significant effect of respiratory motion correction on cardiac imaging data with motion amplitude as small as 0.7 cm. The larger the motion amplitude the more improvement respiratory motion correction brought about on the measurement of EF. Using data-driven respiratory gating, we also demonstrated the effect of respiratory motion correction on estimation of the above functional parameters from list mode patient data. Respiratory motion correction is shown to improve the accuracy of EF measurement in clinical cardiac PET imaging.

  2. Ratcheted electrophoresis of Brownian particles

    NASA Astrophysics Data System (ADS)

    Kowalik, Mikołaj; Bishop, Kyle J. M.

    2016-05-01

    The realization of nanoscale machines requires efficient methods by which to rectify unbiased perturbations to perform useful functions in the presence of significant thermal noise. The performance of such Brownian motors often depends sensitively on their operating conditions—in particular, on the relative rates of diffusive and deterministic motions. In this letter, we present a type of Brownian motor that uses contact charge electrophoresis of a colloidal particle within a ratcheted channel to achieve directed transport or perform useful work against an applied load. We analyze the stochastic dynamics of this model ratchet to show that it functions under any operating condition—even in the limit of strong thermal noise and in contrast to existing ratchets. The theoretical results presented here suggest that ratcheted electrophoresis could provide a basis for electrochemically powered, nanoscale machines capable of transport and actuation of nanoscale components.

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

    PubMed

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

    2014-01-07

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

  4. 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.

  5. 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.

  6. 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

  7. 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.

  8. Generalized formulation of Brownian Vortexes

    NASA Astrophysics Data System (ADS)

    Moyses, Henrique; Bauer, Ross; Grier, David

    2013-03-01

    Brownian vortexes are stochastic noise driven machines that arise from the motion of particles subjected to static non conservative force fields. This motion is characterized by a toroidal circulation in the probability flux whose direction can be tuned by changing the temperature of the system. A discrete minimal model for Brownian Vortexes were described by previous work done by B.Sun, D.G.Grier and A.Y.Grosberg. Here we theoretically look for a continuous model in the form of a generalization of the equilibrium Boltzmann relation for the probability density in the case where the driven forces have a non conservative solenoidal component. This generalized relation features the temperature induced probability flux reversal. We further extend our theory to time dependent force fields and study the possibility of stochastic resonance in the characteristic frequency of circulation of the driven particle. This model is experimentally applied to investigate the motion of colloidal spheres in an optical trap whose intensity is oscillatory in time.

  9. 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.

  10. 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

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

    PubMed

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

    2016-02-07

    In early-stage breast-cancer patients, accelerated partial-breast irradiation techniques (APBI) and hypofractionation are increasingly implemented after breast-conserving surgery (BCS). For a safe and effective radiation therapy (RT), the influence of intra-fraction motion during dose delivery becomes more important as associated fraction durations increase and targets become smaller. Current image-guidance techniques are insufficient to characterize local target movement in high temporal and spatial resolution for extended durations. Magnetic resonance imaging (MRI) can provide high soft-tissue contrast, allow fast imaging, and acquire images during longer periods. The goal of this study was to quantify intra-fraction motion using MRI scans from 21 breast-cancer patients, before and after BCS, in supine RT position, on two time scales. High-temporal 2-dimensional (2D) MRI scans (cine-MRI), acquired every 0.3 s during 2 min, and three 3D MRI scans, acquired over 20 min, were performed. The tumor (bed) and whole breast were delineated on 3D scans and delineations were transferred to the cine-MRI series. Consecutive scans were rigidly registered and delineations were transformed accordingly. Motion in sub-second time-scale (derived from cine-MRI) was generally regular and limited to a median of 2 mm. Infrequently, large deviations were observed, induced by deep inspiration, but these were temporary. Movement on multi-minute scale (derived from 3D MRI) varied more, although medians were restricted to 2.2 mm or lower. Large whole-body displacements (up to 14 mm over 19 min) were sparsely observed. The impact of motion on standard RT techniques is likely small. However, in novel hypofractionated APBI techniques, whole-body shifts may affect adequate RT delivery, given the increasing fraction durations and smaller targets. Motion management may thus be required. For this, on-line MRI guidance could be provided by a hybrid MRI/RT modality, such as the

  12. Motion detection using extended fractional Fourier transform and digital speckle photography.

    PubMed

    Bhaduri, Basanta; Tay, C J; Quan, C; Sheppard, Colin J R

    2010-05-24

    Digital speckle photography is a useful tool for measuring the motion of optically rough surfaces from the speckle shift that takes place at the recording plane. A simple correlation based digital speckle photographic system has been proposed that implements two simultaneous optical extended fractional Fourier transforms (EFRTs) of different orders using only a single lens and detector to simultaneously detect both the magnitude and direction of translation and tilt by capturing only two frames: one before and another after the object motion. The dynamic range and sensitivity of the measurement can be varied readily by altering the position of the mirror/s used in the optical setup. Theoretical analysis and experiment results are presented.

  13. 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…

  14. 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

  15. 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.

  16. Detection of Brownian Torque in a Magnetically-Driven Rotating Microsystem

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

    Thermal fluctuations significantly affect the behavior of microscale systems rotating in shear flow, such as microvortexes, microbubbles, rotating micromotors, microactuators and other elements of lab-on-a-chip devices. The influence of Brownian torque on the motion of individual magnetic microparticles in a rotating magnetic field is experimentally determined using optical tweezers. Rotational Brownian motion induces the flattening of the breakdown transition between the synchronous and asynchronous modes of microparticle rotation. The experimental findings regarding microparticle rotation in the presence of Brownian torque are compared with the results of numerical Brownian dynamics simulations.

  17. Three-dimensional tracking of Brownian motion of a particle trapped in optical tweezers with a pair of orthogonal tracking beams and the determination of the associated optical force constants.

    PubMed

    Wei, Ming-Tzo; Chiou, Arthur

    2005-07-25

    We report the first experimental results on quantitative mapping of three-dimensional optical force field on a silica micro-particle and on a Chinese hamster ovary cell trapped in optical tweezers by using a pair of orthogonal laser beams in conjunction with two quadrant photo-diodes to track the particle's (or the cell's) trajectory, analyze its Brownian motion, and calculate the optical force constants in a three-dimensional parabolic potential model. For optical tweezers with a 60x objective lens (NA = 0.85), a trapping beam wavelength lambda = 532nm, and a trapping optical power of 75mW, the optical force constants along the axial and the transverse directions (of the trapping beam) were measured to be approximately 1.1x10-8N/m and 1.3x10-7N/m, respectively, for a silica particle (diameter = 2.58microm), and 3.1x10-8 N/m and 2.3x10-7 N/m, respectively, for a Chinese hamster ovary cell (diameter ~ 10 microm to 15microm). The set of force constants (Kx, Ky, and Kz ) completely defines the optical force field E(x, y, z) = [Kx x2 + Ky y2 + Kz z2]/2 (in the parabolic potential approximation) on the trapped particle. Practical advantages and limitations of using a pair of orthogonal tracking beams are discussed.

  18. Brownian dynamics simulation of electrostatically interacting proteins

    NASA Astrophysics Data System (ADS)

    Ermakova, E.; Krushelnitsky, A. G.; Fedotov, V. D.

    Brownian dynamics simulation software has been developed to study the dynamics of proteins as a whole in solution. The proteins were modelled as spheres with point dipoles embedded in the centre of sphere. A set of Brownian dynamics simulations at different values of the dipole moments, protein concentration and translational diffusion coefficient was performed to investigate the influence of interprotein electrostatic interactions on dynamic protein behaviour in solution. It was shown that these interactions led to the slowing down of protein rotation and a complex non-exponential shape of the rotational correlation function. Analysis of the correlation functions was performed within the frame of the model of electrostatic interprotein interactions advanced earlier on the basis of NMR and dielectric spectroscopy data. This model assumes that, due to electrostatic interactions, protein Brownian rotation becomes anisotropic. The lifetime of this anisotropy is controlled mainly by translational diffusion of proteins. Thus, the correlation function can be decomposed into two components corresponding to anisotropic Brownian rotation and an isotropic motion of an external electric field vector produced by the surrounding proteins.

  19. Myosin V is a biological Brownian machine

    PubMed Central

    Fujita, Keisuke; Iwaki, Mitsuhiro

    2014-01-01

    Myosin V is a vesicle transporter that unidirectionally walks along cytoskeletal actin filaments by converting the chemical energy of ATP into mechanical work. Recently, it was found that myosin V force generation is a composition of two processes: a lever-arm swing, which involves a conformational change in the myosin molecule, and a Brownian search-and-catch, which involves a diffusive “search” by the motor domain that is followed by an asymmetric “catch” in the forward actin target such that Brownian motion is rectified. Here we developed a system that combines optical tweezers with DNA nano-material to show that the Brownian search-and-catch mechanism is the energetically dominant process at near stall force, providing 13 kBT of work compared to just 3 kBT by the lever-arm swing. Our result significantly reconsiders the lever-arm swinging model, which assumes the swing dominantly produces work (>10 kBT), and sheds light on the Brownian search-and-catch as a driving process. PMID:27493501

  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. Six-Dimensional Correction of Intra-Fractional Prostate Motion with CyberKnife Stereotactic Body Radiation Therapy.

    PubMed

    Lei, Siyuan; Piel, Nathaniel; Oermann, Eric K; Chen, Viola; Ju, Andrew W; Dahal, Kedar N; Hanscom, Heather N; Kim, Joy S; Yu, Xia; Zhang, Guowei; Collins, Brian T; Jha, Reena; Dritschilo, Anatoly; Suy, Simeng; Collins, Sean P

    2011-01-01

    Large fraction radiation therapy offers a shorter course of treatment and radiobiological advantages for prostate cancer treatment. The CyberKnife is an attractive technology for delivering large fraction doses based on the ability to deliver highly conformal radiation therapy to moving targets. In addition to intra-fractional translational motion (left-right, superior-inferior, and anterior-posterior), prostate rotation (pitch, roll, and yaw) can increase geographical miss risk. We describe our experience with six-dimensional (6D) intra-fraction prostate motion correction using CyberKnife stereotactic body radiation therapy (SBRT). Eighty-eight patients were treated by SBRT alone or with supplemental external radiation therapy. Trans-perineal placement of four gold fiducials within the prostate accommodated X-ray guided prostate localization and beam adjustment. Fiducial separation and non-overlapping positioning permitted the orthogonal imaging required for 6D tracking. Fiducial placement accuracy was assessed using the CyberKnife fiducial extraction algorithm. Acute toxicities were assessed using Common Toxicity Criteria v3. There were no Grade 3, or higher, complications and acute morbidity was minimal. Ninety-eight percent of patients completed treatment employing 6D prostate motion tracking with intra-fractional beam correction. Suboptimal fiducial placement limited treatment to 3D tracking in two patients. Our experience may guide others in performing 6D correction of prostate motion with CyberKnife SBRT.

  4. Paul Langevin's 1908 paper ``On the Theory of Brownian Motion'' [``Sur la théorie du mouvement brownien,'' C. R. Acad. Sci. (Paris) 146, 530-533 (1908)

    NASA Astrophysics Data System (ADS)

    Lemons, Don S.; Gythiel, Anthony

    1997-11-01

    We present a translation of Paul Langevin's landmark paper. In it Langevin successfully applied Newtonian dynamics to a Brownian particle and so invented an analytical approach to random processes which has remained useful to this day.

  5. 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.

  6. Fractional Fokker-Planck Equation and Black-Scholes Formula in Composite-Diffusive Regime

    NASA Astrophysics Data System (ADS)

    Liang, Jin-Rong; Wang, Jun; Lǔ, Long-Jin; Gu, Hui; Qiu, Wei-Yuan; Ren, Fu-Yao

    2012-01-01

    In statistical physics, anomalous diffusion plays an important role, whose applications have been found in many areas. In this paper, we introduce a composite-diffusive fractional Brownian motion X α, H ( t)= X H ( S α ( t)), 0< α, H<1, driven by anomalous diffusions as a model of asset prices and discuss the corresponding fractional Fokker-Planck equation and Black-Scholes formula. We obtain the fractional Fokker-Planck equation governing the dynamics of the probability density function of the composite-diffusive fractional Brownian motion and find the Black-Scholes differential equation driven by the stock asset X α, H ( t) and the corresponding Black-Scholes formula for the fair prices of European option.

  7. 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.

  8. Brownian Heat Engines -- from Leidenfrost Droplets to Nanowire Thermoelectrics

    NASA Astrophysics Data System (ADS)

    Linke, Heiner

    2007-03-01

    A Brownian heat engine is a system that rectifies the flow of Brownian particles to transform local temperature variations into directed motion (work). In the context of electronics, this is the principle of thermoelectric energy conversion. For a long time it was thought that Brownian heat engines (and thermoelectric devices) are inherently irreversible and would therefore necessarily fall short of the Carnot limit for the energy conversion efficiency. I will introduce the concept of a Brownian heat engine, and will discuss how quantum energy-filtering can in fact be used to design a Carnot efficient, Brownian heat engine [1]. I will then present two experimental systems. The first, heat-propelled Leidenfrost droplets [2], is not really `Brownian' but nevertheless a very entertaining and illustrative ratchet heat engine. The second is our experimental effort to demonstrate a near-Carnot efficient thermal-to-electric energy converter [3] based on a quantum dot embedded into a heterostructure nanowire [4]. The physics behind this novel thermoelectric system, and the status of experiments will be discussed. [1] T. E. Humphrey, R. Newbury, R. P. Taylor, H. Linke, Phys. Rev. Lett. 89, 116801 (2002). [2] H. Linke et al., Phys. Rev. Lett. 96, 154502 (2006). [3] M. O'Dwyer, T. E. Humphrey, H. Linke, Nanotechnology 17, S338 (2006). [4] M. T. Bj"ork et al., Nano Letters 2, 87 (2002).

  9. 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.

  10. Brownian Movement and Avogadro's Number: A Laboratory Experiment.

    ERIC Educational Resources Information Center

    Kruglak, Haym

    1988-01-01

    Reports an experimental procedure for studying Einstein's theory of Brownian movement using commercially available latex microspheres and a video camera. Describes how students can monitor sphere motions and determine Avogadro's number. Uses a black and white video camera, microscope, and TV. (ML)

  11. 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.

  12. 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.

  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. 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.

  15. Ultrasound tracking for intra-fractional motion compensation in radiation therapy.

    PubMed

    Schwaab, J; Prall, M; Sarti, C; Kaderka, R; Bert, C; Kurz, C; Parodi, K; Günther, M; Jenne, J

    2014-07-01

    Modern techniques as ion beam therapy or 4D imaging require precise target position information. However, target motion particularly in the abdomen due to respiration or patient movement is still a challenge and demands methods that detect and compensate this motion. Ultrasound represents a non-invasive, dose-free and model-independent alternative to fluoroscopy, respiration belt or optical tracking of the patient surface. Thus, ultrasound based motion tracking was integrated into irradiation with actively scanned heavy ions. In a first in vitro experiment, the ultrasound tracking system was used to compensate diverse sinusoidal target motions in two dimensions. A time delay of ∼200 ms between target motion and reported position data was compensated by a prediction algorithm (artificial neural network). The irradiated films proved feasibility of the proposed method. Furthermore, a practicable and reliable calibration workflow was developed to enable the transformation of ultrasound tracking data to the coordinates of the treatment delivery or imaging system - even if the ultrasound probe moves due to respiration. A first proof of principle experiment was performed during time-resolved positron emission tomography (4DPET) to test the calibration workflow and to show the accuracy of an ultrasound based motion tracking in vitro. The results showed that optical ultrasound tracking can reach acceptable accuracies and encourage further research.

  16. 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.

  17. Near-field optically driven Brownian motors (Conference Presentation)

    NASA Astrophysics Data System (ADS)

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

    2016-09-01

    Brownian ratchets are of fundamental interest in fields from statistical physics to molecular motors. The realization of Brownian ratchets in engineered systems opens up the potential to harness thermal energy for directed motion, with applications in transport and sorting of nanoparticles. Implementations based on optical traps provide a high degree of tunability along with precise spatiotemporal control. Near-field optical methods provide particular flexibility and ease of on-chip integration with other microfluidic components. Here, we demonstrate the first all-optical, near-field Brownian ratchet. Our approach uses an asymmetrically patterned photonic crystal and yields an ultra-stable trap stiffness of 253.6 pN/nm-W, 100x greater than conventional optical tweezers. By modulating the laser power, optical ratcheting with transport speed of 1 micron/s can be achieved, allowing a variety of dynamical lab-on-a-chip applications. The resulting transport speed matches well with the theoretical prediction.

  18. Power functional theory for Brownian dynamics.

    PubMed

    Schmidt, Matthias; Brader, Joseph M

    2013-06-07

    Classical density functional theory (DFT) provides an exact variational framework for determining the equilibrium properties of inhomogeneous fluids. We report a generalization of DFT to treat the non-equilibrium dynamics of classical many-body systems subject to Brownian dynamics. Our approach is based upon a dynamical functional consisting of reversible free energy changes and irreversible power dissipation. Minimization of this "free power" functional with respect to the microscopic one-body current yields a closed equation of motion. In the equilibrium limit the theory recovers the standard variational principle of DFT. The adiabatic dynamical density functional theory is obtained when approximating the power dissipation functional by that of an ideal gas. Approximations to the excess (over ideal) power dissipation yield numerically tractable equations of motion beyond the adiabatic approximation, opening the door to the systematic study of systems far from equilibrium.

  19. 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

  20. 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.

  1. Brownian transport controlled by dichotomic and thermal fluctuations

    NASA Astrophysics Data System (ADS)

    Kula, J.; Kostur, M.; Łuczka, J.

    1998-09-01

    We study transport of Brownian particles in spatially periodic structures, driven by both thermal equilibrium fluctuations and dichotomic noise of zero mean values. Introducing specific scaling, we show that the dimensionless Newton-Langevin type equation governing the motion of Brownian particles is very well approximated by the overdamped dynamics; inertial effects can be neglected because for generic systems dimensionless mass is many orders less than a dimensionless friction coefficient. An exact probability current, proportional to the mean drift velocity of particles, is obtained for a piecewise linear spatially periodic potential. We analyze in detail properties of the macroscopic averaged motion of particles. In dependence on statistics of both sources of fluctuations, the directed transport of particles exhibits such distinctive non-monotonic behavior as: bell-shaped dependence (there exists optimal statistics of fluctuations maximizing velocity) and reversal in the direction of macroscopic motion (there exists critical statistics at which the drift velocity is zero).

  2. 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.

  3. Active Brownian rods

    NASA Astrophysics Data System (ADS)

    Peruani, Fernando

    2016-11-01

    Bacteria, chemically-driven rods, and motility assays are examples of active (i.e. self-propelled) Brownian rods (ABR). The physics of ABR, despite their ubiquity in experimental systems, remains still poorly understood. Here, we review the large-scale properties of collections of ABR moving in a dissipative medium. We address the problem by presenting three different models, of decreasing complexity, which we refer to as model I, II, and III, respectively. Comparing model I, II, and III, we disentangle the role of activity and interactions. In particular, we learn that in two dimensions by ignoring steric or volume exclusion effects, large-scale nematic order seems to be possible, while steric interactions prevent the formation of orientational order at large scales. The macroscopic behavior of ABR results from the interplay between active stresses and local alignment. ABR exhibit, depending on where we locate ourselves in parameter space, a zoology of macroscopic patterns that ranges from polar and nematic bands to dynamic aggregates.

  4. 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

  5. Brownian Carnot engine.

    PubMed

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

    2016-01-01

    The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths1. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors2 and some artificial micro-engines3-5 operate. As described by stochastic thermodynamics6,7, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit8. Here we report an experimental realization of a Carnot engine with a single optically trapped Brownian particle as the working substance. We present an exhaustive study of the energetics of the engine and analyse the fluctuations of the finite-time efficiency, showing that the Carnot bound can be surpassed for a small number of non-equilibrium cycles. As its macroscopic counterpart, the energetics of our Carnot device exhibits basic properties that one would expect to observe in any microscopic energy transducer operating with baths at different temperatures9-11. Our results characterize the sources of irreversibility in the engine and the statistical properties of the efficiency-an insight that could inspire new strategies in the design of efficient nano-motors.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. Smoluchowski diffusion equation for active Brownian swimmers

    NASA Astrophysics Data System (ADS)

    Sevilla, Francisco J.; Sandoval, Mario

    2015-05-01

    We study the free diffusion in two dimensions of active Brownian swimmers subject to passive fluctuations on the translational motion and to active fluctuations on the rotational one. The Smoluchowski equation is derived from a Langevin-like model of active swimmers and analytically solved in the long-time regime for arbitrary values of the Péclet number; this allows us to analyze the out-of-equilibrium evolution of the positions distribution of active particles at all time regimes. Explicit expressions for the mean-square displacement and for the kurtosis of the probability distribution function are presented and the effects of persistence discussed. We show through Brownian dynamics simulations that our prescription for the mean-square displacement gives the exact time dependence at all times. The departure of the probability distribution from a Gaussian, measured by the kurtosis, is also analyzed both analytically and computationally. We find that for the inverse of Péclet numbers ≲0.1 , the distance from Gaussian increases as ˜t-2 at short times, while it diminishes as ˜t-1 in the asymptotic limit.

  11. Effective diffusivity in active Brownian suspensions

    NASA Astrophysics Data System (ADS)

    Burkholder, Eric; Brady, John

    2016-11-01

    We study the single-particle diffusion of a Brownian probe of size R in a suspension comprised of a Newtonian solvent and a dilute dispersion of active Brownian particles (ABPs) with size a, characteristic swim velocity U0, and a reorientation time τR. These ABPs, or "swimmers," have a run length l =U0τR , and a mechanical activity ksTs =ζaU02τR / 6 , where ζa is the Stokes drag coefficient of a swimmer. When the swimmers are inactive, collisions between the probe and the swimmers sterically hinder the probe's diffusive motion. When the activity of the swimmers is greater than the Boltzmann energy, ksTs >kB T , rather than being sterically hindered, the probe diffusivity is actually greater than its Stokes-Einstein-Sutherland diffusivity due to the mechanical energy imparted to the probe upon collisions with the swimmers. The active contribution to the effective diffusivity is a non-monotonic function of the swimmers' run length compared to the contact length between the probe and a swimmer: l / (R + a) . Comparisons are made to previous theoretical and experimental investigations of the hydrodynamic diffusion of a colloidal particle in a dilute suspension of swimming bacteria. NSF Grant No. CBET 1437570.

  12. 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.

  13. 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

  14. 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).

  15. 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…

  16. Motion.

    ERIC Educational Resources Information Center

    Gerhart, James B.; Nussbaum, Rudi H.

    This monograph was written for the Conference on the New Instructional Materials in Physics held at the University of Washington in summer, 1965. It is intended for use in an introductory course in college physics. It consists of an extensive qualitative discussion of motion followed by a detailed development of the quantitative methods needed to…

  17. Brownian Ratchets: Transport Controlled by Thermal Noise

    NASA Astrophysics Data System (ADS)

    Kula, J.; Czernik, T.; Łuczka, J.

    1998-02-01

    We analyze directed transport of overdamped Brownian particles in a 1D spatially periodic potential that are subjected to both zero-mean thermal equilibrium Nyquist noise and zero-mean exponentially correlated dichotomous fluctuations. We show that particles can reverse the direction of average motion upon a variation of noise parameters if two fundamental symmetries, namely, the reflection symmetry of the spatial periodic structure, and the statistical symmetry of dichotomous fluctuations, are broken. There is a critical thermal noise intensity Dc, or equivalently a critical temperature Tc, at which the mean velocity of particles is zero. Below Tc and above Tc particles move in opposite directions. At fixed temperature, there is a region of noise parameters in which particles of different linear size are transported in opposite directions.

  18. Molecular Motors: Power Strokes Outperform Brownian Ratchets.

    PubMed

    Wagoner, Jason A; Dill, Ken A

    2016-07-07

    Molecular motors convert chemical energy (typically from ATP hydrolysis) to directed motion and mechanical work. Their actions are often described in terms of "Power Stroke" (PS) and "Brownian Ratchet" (BR) mechanisms. Here, we use a transition-state model and stochastic thermodynamics to describe a range of mechanisms ranging from PS to BR. We incorporate this model into Hill's diagrammatic method to develop a comprehensive model of motor processivity that is simple but sufficiently general to capture the full range of behavior observed for molecular motors. We demonstrate that, under all conditions, PS motors are faster, more powerful, and more efficient at constant velocity than BR motors. We show that these differences are very large for simple motors but become inconsequential for complex motors with additional kinetic barrier steps.

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

    NASA Astrophysics Data System (ADS)

    Nishimura, Shin I.; Ueda, Masahiro; Sasai, Masaki

    2012-04-01

    Amoeboid cells such as Dictyostelium discoideum and Madin-Darby canine kidney cells show the non-Brownian dynamics of migration characterized by the superdiffusive increase of mean-squared displacement. In order to elucidate the physical mechanism of this non-Brownian dynamics, a computational model is developed which highlights a group of inhibitory molecules for actin polymerization. Based on this model, we propose a hypothesis that inhibitory molecules are sent backward in the moving cell to accumulate at the rear of cell. The accumulated inhibitory molecules at the rear further promote cell locomotion to form a slow positive feedback loop of the whole-cell scale. The persistent straightforward migration is stabilized with this feedback mechanism, but the fluctuation in the distribution of inhibitory molecules and the cell shape deformation concurrently interrupt the persistent motion to turn the cell into a new direction. A sequence of switching behaviors between persistent motions and random turns gives rise to the superdiffusive migration in the absence of the external guidance signal. In the complex environment with obstacles, this combined process of persistent motions and random turns drives the simulated amoebae to solve the maze problem in a highly efficient way, which suggests the biological advantage for cells to bear the non-Brownian dynamics.

  20. Microstructure from simulated Brownian suspension flows at large shear rate

    NASA Astrophysics Data System (ADS)

    Morris, Jeffrey F.; Katyal, Bhavana

    2002-06-01

    Pair microstructure of concentrated Brownian suspensions in simple-shear flow is studied by sampling of configurations from dynamic simulations by the Stokesian Dynamics technique. Simulated motions are three dimensional with periodic boundary conditions to mimic an infinitely extended suspension. Hydrodynamic interactions through Newtonian fluid and Brownian motion are the only physical influences upon the motion of the monodisperse hard-sphere particles. The dimensionless parameters characterizing the suspension are the particle volume fraction and Péclet number, defined, respectively, as φ=(4π/3)na3 with n the number density and a the sphere radius, and Pe=6πηγ˙a3/kT with η the fluid viscosity, γ˙ the shear rate, and kT the thermal energy. The majority of the results reported are from simulations at Pe=1000; results of simulations at Pe=1, 25, and 100 are also reported for φ=0.3 and φ=0.45. The pair structure is characterized by the pair distribution function, g(r)=P1|1(r)/n, where P1|1(r) is the conditional probability of finding a pair at a separation vector r. The structure under strong shearing exhibits an accumulation of pair probability at contact, and angular distortion (from spherical symmetry at Pe=0), with both effects increasing with Pe. Flow simulations were performed at Pe=1000 for eight volume fractions in the range 0.2⩽φ⩽0.585. For φ=0.2-0.3, the pair structure at contact, g(|r|=2)≡g(2), is found to exhibit a single region of strong correlation, g(2)≫1, at points around the axis of compression, with a particle-deficient wake in the extensional zones. A qualitative change in microstructure is observed between φ=0.3 and φ=0.37. For φ⩾0.37, the maximum g(2) lies at points in the shear plane nearly on the x axis of the bulk simple shear flow Ux=γ˙y, while at smaller φ, the maximum g(2) lies near the compressional axis; long-range string ordering is not observed. For φ=0.3 and φ=0.45, g(2)˜Pe0.7 for 1⩽Pe⩽1000, a

  1. 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.

  2. 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].

  3. Thermophoretically modified aerosol Brownian coagulation

    NASA Astrophysics Data System (ADS)

    Arias-Zugasti, Manuel; Rosner, Daniel E.

    2011-08-01

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

  4. 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.

  5. Mean distance of two Brownian particles trapped in a suspended droplet and its dependence on the Debye length

    NASA Astrophysics Data System (ADS)

    Goto, Kosuke; Sakata, Shinya; Moritani, Kousuke; Inui, Norio

    2017-01-01

    The Brownian motion of two particles confined near the bottom of a suspended droplet was considered in order to examine the electrical double-layer interaction between them. The mean distance between the particles was expressed as a function of the Debye screening length. We report the application of Brownian particle trajectories for the experimental determination of the Debye screening length between gold particles trapped within a water droplet. This was computed through a comparison of the mean distance measured by observing the Brownian motion with its theoretical value.

  6. 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.

  7. 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

  8. 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.

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

    PubMed Central

    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. Images FIGURE 4 PMID:8770190

  10. Fractional Diffusion, Low Exponent Lévy Stable Laws, and 'Slow Motion' Denoising of Helium Ion Microscope Nanoscale Imagery.

    PubMed

    Carasso, Alfred S; Vladár, András E

    2012-01-01

    Helium ion microscopes (HIM) are capable of acquiring images with better than 1 nm resolution, and HIM images are particularly rich in morphological surface details. However, such images are generally quite noisy. A major challenge is to denoise these images while preserving delicate surface information. This paper presents a powerful slow motion denoising technique, based on solving linear fractional diffusion equations forward in time. The method is easily implemented computationally, using fast Fourier transform (FFT) algorithms. When applied to actual HIM images, the method is found to reproduce the essential surface morphology of the sample with high fidelity. In contrast, such highly sophisticated methodologies as Curvelet Transform denoising, and Total Variation denoising using split Bregman iterations, are found to eliminate vital fine scale information, along with the noise. Image Lipschitz exponents are a useful image metrology tool for quantifying the fine structure content in an image. In this paper, this tool is applied to rank order the above three distinct denoising approaches, in terms of their texture preserving properties. In several denoising experiments on actual HIM images, it was found that fractional diffusion smoothing performed noticeably better than split Bregman TV, which in turn, performed slightly better than Curvelet denoising.

  11. 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.

  12. Phase Transitions in Brownian Pumps

    NASA Astrophysics Data System (ADS)

    Dierl, Marcel; Dieterich, Wolfgang; Einax, Mario; Maass, Philipp

    2014-04-01

    We study stochastic particle transport between two reservoirs along a channel, where the particles are pumped against a bias by a traveling wave potential. It is shown that phase transitions of period-averaged densities or currents occur inside the channel when exclusion interactions between the particles are taken into account. These transitions reflect those known for the asymmetric simple exclusion process. We argue that their occurrence is a generic feature of Brownian motors operating in open systems.

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

    NASA Astrophysics Data System (ADS)

    Cubero, David; Renzoni, Ferruccio

    2016-01-01

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

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

    PubMed

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

    2013-06-07

    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.

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

    NASA Astrophysics Data System (ADS)

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

    2013-06-01

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

  16. 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

  17. Exploring the Use of Slow Motion Animation (Slowmation) as a Teaching Strategy to Develop Year 4 Students' Understandings of Equivalent Fractions

    ERIC Educational Resources Information Center

    Kervin, Kristy

    2007-01-01

    In 2006, as a beginning teacher in a Western Sydney school, the author explored slow motion animation ("slowmation") as a strategy for teaching Year 4 students about equivalent fractions. She taught at this school five days a week, teaching Kindergarten, Year 4, and Year 5. Slowmation can be defined as a simplified version of claymation…

  18. Active Brownian particles with velocity-alignment and active fluctuations

    NASA Astrophysics Data System (ADS)

    Großmann, R.; Schimansky-Geier, L.; Romanczuk, P.

    2012-07-01

    We consider a model of active Brownian particles (ABPs) with velocity alignment in two spatial dimensions with passive and active fluctuations. Here, active fluctuations refers to purely non-equilibrium stochastic forces correlated with the heading of an individual active particle. In the simplest case studied here, they are assumed to be independent stochastic forces parallel (speed noise) and perpendicular (angular noise) to the velocity of the particle. On the other hand, passive fluctuations are defined by a noise vector independent of the direction of motion of a particle, and may account, for example, for thermal fluctuations. We derive a macroscopic description of the ABP gas with velocity-alignment interaction. Here, we start from the individual-based description in terms of stochastic differential equations (Langevin equations) and derive equations of motion for the coarse-grained kinetic variables (density, velocity and temperature) via a moment expansion of the corresponding probability density function. We focus here on the different impact of active and passive fluctuations on onset of collective motion and show how active fluctuations in the active Brownian dynamics can change the phase-transition behaviour of the system. In particular, we show that active angular fluctuations lead to an earlier breakdown of collective motion and to the emergence of a new bistable regime in the mean-field case.

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

    NASA Astrophysics Data System (ADS)

    Tóthová, Jana; Lisý, Vladimír

    2016-02-01

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

  20. TU-AB-303-06: Does Online Adaptive Radiation Therapy Mean Zero Margin for Intermediate-Risk Prostate Cancer? An Intra-Fractional Seminal Vesicles Motion Analysis

    SciTech Connect

    Sheng, Y; Li, T; Lee, W; Yin, F; Wu, Q

    2015-06-15

    Purpose: To provide benchmark for seminal vesicles (SVs) margin selection to account for intra-fractional motion; and to investigate the effectiveness of two motion surrogates in predicting intra-fractional SV underdosage. Methods: 9 prostate SBRT patients were studied; each has five pairs of pre-treatment and post-treatment cone-beam CTs (CBCTs). Each pair of CBCTs was registered based on fiducial markers in the prostate. To provide “ground truth” for coverage evaluation, all pre-treatment SVs were expanded with isotropic margin of 1,2,3,5 and 8mm, and their overlap with post-treatment SVs were used to quantify intra-fractional coverage. Two commonly used motion surrogates, the center-of-mass (COM) and the border of contour (the most distal points in SI/AP/LR directions) were evaluated using Receiver-Operating Characteristic (ROC) analyses for predicting SV underdosage due to intra-fractional motion. Action threshold of determining underdosage for each surrogate was calculated by selecting the optimal balancing between sensitivity and specificity. For comparison, margin for each surrogate was also calculated based on traditional margin recipe. Results: 90% post-treatment SV coverage can be achieved in 47%, 82%, 91%, 98% and 98% fractions for 1,2,3,5 and 8mm margins. 3mm margin ensured the 90% intra-fractional SV coverage in 90% fractions when prostate was aligned. The ROC analysis indicated the AUC for COM and border were 0.88 and 0.72. The underdosage threshold was 2.9mm for COM and 4.1mm for border. The Van Herk’s margin recipe recommended 0.5, 0 and 1.8mm margin in LR, AP and SI direction based on COM and for border, the corresponding margin was 2.1, 4.5 and 3mm. Conclusion: 3mm isotropic margin is the minimum required to mitigate the intra-fractional SV motion when prostate is aligned. ROC analysis reveals that both COM and border are acceptable predictors for SV underdosage with 2.9mm and 4.1mm action threshold. Traditional margin calculation is less

  1. Stochastically gated local and occupation times of a Brownian particle

    NASA Astrophysics Data System (ADS)

    Bressloff, Paul C.

    2017-01-01

    We generalize the Feynman-Kac formula to analyze the local and occupation times of a Brownian particle moving in a stochastically gated one-dimensional domain. (i) The gated local time is defined as the amount of time spent by the particle in the neighborhood of a point in space where there is some target that only receives resources from (or detects) the particle when the gate is open; the target does not interfere with the motion of the Brownian particle. (ii) The gated occupation time is defined as the amount of time spent by the particle in the positive half of the real line, given that it can only cross the origin when a gate placed at the origin is open; in the closed state the particle is reflected. In both scenarios, the gate randomly switches between the open and closed states according to a two-state Markov process. We derive a stochastic, backward Fokker-Planck equation (FPE) for the moment-generating function of the two types of gated Brownian functional, given a particular realization of the stochastic gate, and analyze the resulting stochastic FPE using a moments method recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment-generating function, averaged with respect to realizations of the stochastic gate.

  2. 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.

  3. Hydrodynamically enforced entropic Brownian pump

    NASA Astrophysics Data System (ADS)

    Ai, Bao-quan; He, Ya-feng; Li, Feng-guo; Zhong, Wei-rong

    2013-04-01

    Transport of overdamped Brownian particles in a finite hydrodynamical channel is investigated in the presence of the ac driving force and the pressure-driven flow. The system is bounded by two particle reservoirs. With the help of the Fick-Jacobs method, we obtain the directed current of Brownian particles and the pumping capacity of the system. The directed transport is determined by the competitions among the asymmetry of the channel, the ac driving force, the pressure-driven flow, and the concentration difference. Their interplays can exhibit the peculiar properties. Remarkably, the particles can be pumped through the channel from the lower concentration reservoir to the higher concentration one, or from the lower pressure side to the higher pressure one. In addition, due to the existence of the pressure drop, ac driving force still plays the significant role on directed transport even in a completely symmetric channel. Our results could be implemented in constrained structures with narrow channels or pores where the particles are suspended in a solvent.

  4. Dynamic light scattering arising from flowing Brownian particles: analytical model in optical coherence tomography conditions.

    PubMed

    Popov, Ivan; Weatherbee, Andrew S; Vitkin, I Alex

    2014-12-01

    The statistical model of scattered by flowing Brownian particles coherent radiation is suggested. The model includes the random Doppler shifts caused by particle Brownian motion and the speckle fluctuations caused primarily by the flow motion of particles. Analytical expressions are obtained for the correlation function, power spectrum, and spectral width of scattered radiation in the imaging geometry typically used in optical coherence tomography (OCT). It is shown that the spectral density has the Voigt shape, a well-known spectral profile from atomic and molecular spectroscopy. The approach enables the choice of the experimental regimes for the measurement of Brownian particle motion parameters even in the presence of flow. These regimes are characterized by the dominant contribution of Brownian motion in the spectral width of the flow-caused Doppler shift component. Further, the new formalism suggests that prior attempts to extract transverse flow velocity are only valid at near-perpendicular geometry. The impact of the small scattering volume contributing to the OCT signal is also discussed.

  5. Fractional kinetics emerging from ergodicity breaking in random media

    NASA Astrophysics Data System (ADS)

    Molina-García, Daniel; Pham, Tuan Minh; Paradisi, Paolo; Manzo, Carlo; Pagnini, Gianni

    2016-11-01

    We present a modeling approach for diffusion in a complex medium characterized by a random length scale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single-particle tracking experiments in living cells, such as ergodicity breaking, p variation, and aging. In particular, this approach recapitulates characteristic features previously described in part by the fractional Brownian motion and in part by the continuous-time random walk. Moreover, for a proper distribution of the length scale, a single parameter controls the ergodic-to-nonergodic transition and, remarkably, also drives the transition of the diffusion equation of the process from nonfractional to fractional, thus demonstrating that fractional kinetics emerges from ergodicity breaking.

  6. Random-order fractional bistable system and its stochastic resonance

    NASA Astrophysics Data System (ADS)

    Gao, Shilong; Zhang, Li; Liu, Hui; Kan, Bixia

    2017-01-01

    In this paper, the diffusion motion of Brownian particles in a viscous liquid suffering from stochastic fluctuations of the external environment is modeled as a random-order fractional bistable equation, and as a typical nonlinear dynamic behavior, the stochastic resonance phenomena in this system are investigated. At first, the derivation process of the random-order fractional bistable system is given. In particular, the random-power-law memory is deeply discussed to obtain the physical interpretation of the random-order fractional derivative. Secondly, the stochastic resonance evoked by random-order and external periodic force is mainly studied by numerical simulation. In particular, the frequency shifting phenomena of the periodical output are observed in SR induced by the excitation of the random order. Finally, the stochastic resonance of the system under the double stochastic excitations of the random order and the internal color noise is also investigated.

  7. Two-dimensional Brownian vortices

    NASA Astrophysics Data System (ADS)

    Chavanis, Pierre-Henri

    2008-12-01

    We introduce a stochastic model of 2D Brownian vortices associated with the canonical ensemble. The point vortices evolve through their usual mutual advection but they experience in addition a random velocity and a systematic drift generated by the system as a whole. The statistical equilibrium state of this stochastic model is the Gibbs canonical distribution. We consider a single species system and a system made of two types of vortices with positive and negative circulations. At positive temperatures, like-sign vortices repel each other (“plasma” case) and at negative temperatures, like-sign vortices attract each other (“gravity” case). We derive the stochastic equation satisfied by the exact vorticity field and the Fokker-Planck equation satisfied by the N-body distribution function. We present the BBGKY-like hierarchy of equations satisfied by the reduced distribution functions and close the hierarchy by considering an expansion of the solutions in powers of 1/N, where N is the number of vortices, in a proper thermodynamic limit. For spatially inhomogeneous systems, we derive the kinetic equations satisfied by the smooth vorticity field in a mean field approximation valid for N→+∞. For spatially homogeneous systems, we study the two-body correlation function, in a Debye-Hückel approximation valid at the order O(1/N). The results of this paper can also apply to other systems of random walkers with long-range interactions such as self-gravitating Brownian particles and bacterial populations experiencing chemotaxis. Furthermore, for positive temperatures, our study provides a kinetic derivation, from microscopic stochastic processes, of the Debye-Hückel model of electrolytes.

  8. TU-F-CAMPUS-J-01: Inference of Prostate PTV Margins in VMAT Delivery From Intra-Fraction Prostate Motion During SBRT Delivery

    SciTech Connect

    Thind, K; Wong, R; Gerdes, C; Chow, T; Wong, D

    2015-06-15

    Purpose: To retrospectively quantify the intra-fraction prostate motion during stereotactic body radiation therapy (SBRT) treatment using CyberKnife’s target tracking system, which may provide insight into expansion margins from GTV to PTV used in gantry-based treatments. CyberKnife is equipped with an active tracking system (InTempo) that tracks the four fiducials placed in the prostate gland. The system acquires intra-fraction orthogonal kV images at 45° and 315° in a sequential fashion. Methods: A total of 38 patients treated with SBRT using CyberKnife between 2011 and 2013 were studied. Dose-regime was 36.25 Gy in 5 fractions (7.25 Gy/fraction, twice per week) as per RTOG 0938 guidelines. The CyberKnife image tracking logs for all SBRT treatments using InTempo were examined. A total of 13663 images were examined for the superior/inferior (SI), anterior/posterior (AP) and left/right (LR) translation as well as roll, pitch and yaw rotations for the target position relative to the last known model position. Results: The mean ± 2 SD of intra-fraction motion was contained within 3 mm for SI and LR and 4.5 mm for AP directions at 5 minutes into the treatment delivery. It was contained within 4 mm for SI and LR and 5 mm for AP at 10 minutes. At 15 minutes into delivery, all translations were contained within 5 mm. The mean ± 2 SD of prostate roll, pitch and yaw increased with time but were contained within 5 degree at 5, 10 and 15 minutes into treatment. Additionally, target translations and rotations were within ± 1 mm and ± 1 degree for 90% and 78% of the time. Conclusion: The organ motion component of PTV margin for 10 minute VMAT delivery is contained within 4 mm in SI and LR direction and within 5 mm in the AP direction.

  9. A Brownian-ratchet DNA pump with applications to single-nucleotide polymorphism genotyping

    NASA Astrophysics Data System (ADS)

    Bader, J. S.; Deem, M. W.; Hammond, R. W.; Henck, S. A.; Simpson, J. W.; Rothberg, J. M.

    2002-08-01

    We have fabricated a micron-scale device capable of transporting DNA oligomers using Brownian ratchets. The ratchet potential is generated by applying a voltage difference to interdigitated electrodes. Cycling between the charged state and a discharged, free-diffusion state rectifies the Brownian motion of charged particles. The observed macroscopic transport properties agree with the transport rate predicted from microscopic parameters including the DNA diffusivity, the dimensions of the ratchet potential, and the cycling time. Applications to human genetics, primarily genotyping of single-nucleotide polymorphisms (SNPs), are discussed.

  10. Irreversible shear-activated aggregation in non-Brownian suspensions.

    PubMed

    Guery, J; Bertrand, E; Rouzeau, C; Levitz, P; Weitz, D A; Bibette, J

    2006-05-19

    We have studied the effect of shear on the stability of suspensions made of non-Brownian solid particles. We demonstrate the existence of an irreversible transition where the solid particles aggregate at remarkably low volume fractions (phi approximately 0.1). This shear-induced aggregation is dramatic and exhibits a very sudden change in the viscosity, which increases sharply after a shear-dependent induction time. We show that this induction time is related exponentially to the shear rate, reflecting the importance of the hydrodynamic forces in reducing the repulsive energy barrier that prevents the particles from aggregating.

  11. 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.

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

    NASA Astrophysics Data System (ADS)

    van Oudenaarden, Alexander

    2000-03-01

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

  13. Probing Brownian relaxation in water-glycerol mixtures using magnetic hyperthermia

    NASA Astrophysics Data System (ADS)

    Nemala, Humeshkar; Milgie, Michael; Wadehra, Anshu; Thakur, Jagdish; Naik, Vaman; Naik, Ratna

    2013-03-01

    Generation of heat by magnetic nanoparticles in the presence of an external oscillating magnetic field is known as magnetic hyperthermia (MHT). This heat is generated by two mechanisms: the Neel relaxation and Brownian relaxation. While the internal spin relaxation of the nanoparticles known as Neel relaxation is largely dependent on the magnetic properties of the nanoparticles, the physical motion of the particle or the Brownian relaxation is largely dependent on the viscous properties of the carrier liquid. The MHT properties of dextran coated iron oxide nanoparticles have been investigated at a frequency of 400KHz. To understand the influence of Brownian relaxation on heating, we probe the MHT properties of these ferrofluids in water-glycerol mixtures of varying viscosities. The heat generation is quantified using the specific absorption rate (SAR) and its maximum at a particular temperature is discussed with reference to the viscosity.

  14. 4D ultrasound speckle tracking of intra-fraction prostate motion: a phantom-based comparison with x-ray fiducial tracking using CyberKnife

    NASA Astrophysics Data System (ADS)

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

    2014-04-01

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

  15. 4D ultrasound speckle tracking of intra-fraction prostate motion: a phantom-based comparison with x-ray fiducial tracking using CyberKnife.

    PubMed

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

    2014-04-07

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

  16. Fluctuation relations for a driven Brownian particle.

    PubMed

    Imparato, A; Peliti, L

    2006-08-01

    We consider a driven Brownian particle, subject to both conservative and nonconservative applied forces, whose probability evolves according to the Kramers equation. We derive a general fluctuation relation, expressing the ratio of the probability of a given Brownian path in phase space with that of the time-reversed path, in terms of the entropy flux to the heat reservoir. This fluctuation relation implies those of Seifert, Jarzynski, and Gallavotti-Cohen in different special cases.

  17. Fluctuation relations for a driven Brownian particle

    NASA Astrophysics Data System (ADS)

    Imparato, A.; Peliti, L.

    2006-08-01

    We consider a driven Brownian particle, subject to both conservative and nonconservative applied forces, whose probability evolves according to the Kramers equation. We derive a general fluctuation relation, expressing the ratio of the probability of a given Brownian path in phase space with that of the time-reversed path, in terms of the entropy flux to the heat reservoir. This fluctuation relation implies those of Seifert, Jarzynski, and Gallavotti-Cohen in different special cases.

  18. The Asymmetric Exclusion Process and Brownian Excursions

    NASA Astrophysics Data System (ADS)

    Derrida, B.; Enaud, C.; Lebowitz, J. L.

    2004-04-01

    We consider the totally asymmetric exclusion process (TASEP) in one dimension in its maximal current phase. We show, by an exact calculation, that the non-Gaussian part of the fluctuations of density can be described in terms of the statistical properties of a Brownian excursion. Numerical simulations indicate that the description in terms of a Brownian excursion remains valid for more general one dimensional driven systems in their maximal current phase.

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

    NASA Astrophysics Data System (ADS)

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

    2014-11-01

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

  20. Controlling the motion and placement of micrometer-sized metal particles using patterned polymer brush surfaces.

    PubMed

    Dunderdale, Gary J; Howse, Jonathan R; Fairclough, J Patrick A

    2011-10-04

    In this paper, we show that silicon surfaces patterned with poly(methacrylic acid) brushes are able to control the Brownian motion of 2-3 μm iron particles, which sediment onto the surface in aqueous solution and experience differences in repulsive force depending upon their position. Differences in repulsion lead to different gravitational potential energies across the surface, which gives bias to the Brownian motion taking place. Three regimes have been identified depending upon the brush height: (i) no control of Brownian motion when the brush height is small, (ii) Brownian motion that is influenced by the polymer brush when the brush 17 height is intermediate, (iii) Brownian motion that is confined by polymer brush barriers when the brush height is greatest. The height of brush found necessary to significantly influence iron particle motion was small at 39 nm or 2% of the particle diameter.

  1. Intermediate scattering function of an anisotropic active Brownian particle

    NASA Astrophysics Data System (ADS)

    Kurzthaler, Christina; Leitmann, Sebastian; Franosch, Thomas

    2016-10-01

    Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations.

  2. 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

  3. Variational solutions and random dynamical systems to SPDEs perturbed by fractional Gaussian noise.

    PubMed

    Zeng, Caibin; Yang, Qigui; Cao, Junfei

    2014-01-01

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

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

    PubMed Central

    Zeng, Caibin; Yang, Qigui; Cao, Junfei

    2014-01-01

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

  5. Stochastic heating of a single Brownian particle by charge fluctuations in a radio-frequency produced plasma sheath.

    PubMed

    Schmidt, Christian; Piel, Alexander

    2015-10-01

    The Brownian motion of a single particle in the plasma sheath is studied to separate the effect of stochastic heating by charge fluctuations from heating by collective effects. By measuring the particle velocities in the ballistic regime and by carefully determining the particle mass from the Epstein drag it is shown that for a pressure of 10 Pa, which is typical of many experiments, the proper kinetic temperature of the Brownian particle remains close to the gas temperature and rises only slightly with particle size. This weak effect is confirmed by a detailed model for charging and charge fluctuations in the sheath. A substantial temperature rise is found for decreasing pressure, which approximately shows the expected scaling with p(-2). The system under study is an example for non-equilibrium Brownian motion under the influence of white noise without corresponding dissipation.

  6. CNT based thermal Brownian motor to pump water in nanodevices

    NASA Astrophysics Data System (ADS)

    Oyarzua, Elton; Zambrano, Harvey; Walther, J. H.

    2016-11-01

    Brownian molecular motors are nanoscale machines that exploit thermal fluctuations for directional motion by employing mechanisms such as the Feynman-Smoluchowski ratchet. In this study, using Non Equilibrium Molecular Dynamics, we propose a novel thermal Brownian motor for pumping water through Carbon Nanotubes (CNTs). To achieve this we impose a thermal gradient along the axis of a CNT filled with water and impose, in addition, a spatial asymmetry by fixing specific zones on the CNT in order to modify the vibrational modes of the CNT. We find that the temperature gradient and imposed spatial asymmetry drive the water flow in a preferential direction. We systematically modified the magnitude of the applied thermal gradient and the axial position of the fixed points. The analysis involves measurement of the vibrational modes in the CNTs using a Fast Fourier Transform (FFT) algorithm. We observed water flow in CNTs of 0.94, 1.4 and 2.0 nm in diameter, reaching a maximum velocity of 5 m/s for a thermal gradient of 3.3 K/nm. The proposed thermal motor is capable of delivering a continuous flow throughout a CNT, providing a useful tool for driving liquids in nanofluidic devices by exploiting thermal gradients. We aknowledge partial support from Fondecyt project 11130559.

  7. Relaxation dynamics near nonequilibrium stationary states in Brownian ratchets

    NASA Astrophysics Data System (ADS)

    Woo, Hyung-June

    2009-02-01

    A comprehensive study of the static and dynamical properties of a representative stochastic model of Brownian ratchet effects for molecular motors is reported. The model describes Brownian motions on two periodic potentials under static and time-dependent forces, where there are two distinct locations of chemical reactions coupling the levels with reversible rates within a period. Complete stationary properties have been obtained analytically for arbitrary potentials under external force. Dynamical relaxation properties near nonequilibrium stationary states were examined by considering the response function of velocity upon time-dependent external force, expressed in terms of the conditional probability density of the model. The latter is fully calculated using a systematic numerical method using matrix diagonalization, which is easily generalized to more complicated models for studying both static and dynamical properties. The behavior of the time-dependent response examined for model potentials suggests that the characteristic relaxation time near stationary states generally decreases linearly with respect to increasing velocity as one goes away from equilibrium via an increase in chemical potential of fuel species, a prediction testable in single molecule experiments.

  8. Onsager coefficients of a Brownian Carnot cycle

    NASA Astrophysics Data System (ADS)

    Izumida, Y.; Okuda, K.

    2010-10-01

    We study a Brownian Carnot cycle introduced by Schmiedl and Seifert [Europhys. Lett. 81, 20003 (2008)] from a viewpoint of the linear irreversible thermodynamics. By considering the entropy production rate of this cycle, we can determine thermodynamic forces and fluxes of the cycle and calculate the Onsager coefficients for general protocols, that is, arbitrary schedules to change the potential confining the Brownian particle. We show that these Onsager coefficients contain the information of the protocol shape and they satisfy the tight-coupling condition irrespective of whatever protocol shape we choose. These properties may give an explanation why the Curzon-Ahlborn efficiency often appears in the finite-time heat engines.

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

    PubMed

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

    2011-11-21

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

  10. 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.

  11. 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.

  12. Brownian motion and polymer statistics on certain curved manifolds

    NASA Astrophysics Data System (ADS)

    Mondescu, Radu P.; Muthukumar, M.

    1998-04-01

    In this paper we have considered a Gaussian polymer chain of length L as an intrinsic object enclosed on a surface embedded in the Euclidean space. When the surfaces are the sphere SD-1 in D dimensions and the cylinder, the cone and the curved torus in R3, we have calculated analytically and numerically (using the diffusion equation and the path-integral approach) the probability distribution function G(R\\|R'L) of the end-to-end vector R-R' and the mean-square end-to-end distance <(R-R')2> of the polymer chain. Our findings are that the curvature of the surfaces induces a geometrical localization area; at short scales (L-->0) the polymer is locally flat and the mean-square end-to-end distance is just the Gaussian value Ll (l = Kuhn length), independent of the metric properties of the surface; at large scales (L-->∞), <(R-R')2> tends to a constant value in the sphere case, and it is linear in L for the cylinder and reaches different constant values (as a function of the geometry of the surface) for the curved torus. In the case of the cone, contraction of the chain is induced at all length scales by the presence of the vertex, as a function of the opening angle 2α and the end position R' of the chain. Explicit crossover formulas are derived for G(R\\|R'L) and <(R-R')2>.

  13. Nonlinear Neural Networks, Motion Sensing and Fractional Charge Detection with Silicon P-I Structures at 4.2 K.

    NASA Astrophysics Data System (ADS)

    Betarbet, Sandeep Raghunandan

    A model has been constructed to predict interpulse time intervals (IPTI) of current spikes of spontaneous pulsing Si p-i-n diodes at 4.2K. The model yields an iterative formula of the form T_{n+1} = f(T_{n}, beta, gamma), where f is the transfer function, T_{n } is the n^{th} IPTI and beta and gamma are the feedback and noise factors respectively. The transfer function has been shown to be similar to a sigmoid neural transfer function under small signal conditions, with gamma/beta equivalent to the voltage bias. A diode produces a nonlinear 2-D return map of the IPTI's when driven by a second diode through a filter circuit. Increasing the bias on the first diode produces a Hopf bifurcation from a fixed point to a limit cycle both in the experimental output and the model. Circuits which can both detect transient light signals and also show lateral inhibition and integration of temporal signals, have been constructed with spontaneously pulsing Si p-i-n diodes. The experimental output of these circuits agree with a model based on simple circuit equations. The circuits have been shown to have equivalent units in the lamina and medulla of the fly eye. A search has been conducted for unconfined primordial fractional charges (FCP) and FCP's created during high energy collisions. The search is based on fractional charge impurity energy level predictions of Chaudhuri et al., (P. R. L. 1374, 45 1980) in Si p-i-n diodes and (for the created FCP's) those properties described by A. De Rujula et al. (Phys. Rev. D, 285, 17 (1978)). An upper limit (95% C.L.) of 2.3 times 10 ^{-20} fractional charges per atom is obtained for primordial FCP's. The diode readout technique uses a combination of an IR photoionization and a field ionization technique. This optoelectronic approach has the advantage of giving an estimate for the concentration of fractional charges. The production experiment had Al as a target, where the FCP's would be created. A stack of 20 diodes contiguous to the target

  14. 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

  15. 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.

  16. Diffusion in crowded biological environments: applications of Brownian dynamics

    PubMed Central

    2011-01-01

    Biochemical reactions in living systems occur in complex, heterogeneous media with total concentrations of macromolecules in the range of 50 - 400 mgml. Molecular species occupy a significant fraction of the immersing medium, up to 40% of volume. Such complex and volume-occupied environments are generally termed 'crowded' and/or 'confined'. In crowded conditions non-specific interactions between macromolecules may hinder diffusion - a major process determining metabolism, transport, and signaling. Also, the crowded media can alter, both qualitatively and quantitatively, the reactions in vivo in comparison with their in vitro counterparts. This review focuses on recent developments in particle-based Brownian dynamics algorithms, their applications to model diffusive transport in crowded systems, and their abilities to reproduce and predict the behavior of macromolecules under in vivo conditions. PMID:21595998

  17. Propagating interfaces in mixtures of active and passive Brownian particles

    NASA Astrophysics Data System (ADS)

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

    2016-12-01

    The emergent collective dynamics in phase-separated mixtures of isometric active and passive Brownian particles is studied numerically in two-dimensions. A novel steady-state of well-defined propagating interfaces is observed, where the interface between the dense and the dilute phase propagates and the bulk of both phases is (nearly) at rest. Two kind of interfaces, advancing and receding, are formed by spontaneous symmetry breaking, induced by an instability of a planar interface due to the formation of localized vortices. The propagation arises due to flux imbalance at the interface, resembling the growth behavior of rough surfaces far from equilibrium. Above a threshold, the interface velocity decreases linearly with increasing fraction of active particles.

  18. 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.

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

    PubMed

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

    2014-06-07

    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.

  20. 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.

  1. Ising model for a Brownian donkey

    NASA Astrophysics Data System (ADS)

    Cleuren, B.; Van den Broeck, C.

    2001-04-01

    We introduce a thermal engine consisting of N interacting Brownian particles moving in a periodic potential, featuring an alternation of hot and cold symmetric peaks. A discretized Ising-like version is solved analytically. In response to an external force, absolute negative mobility is observed for N >= 4. For N → ∞ a nonequilibrium phase transition takes place with a spontaneous symmetry breaking entailing the appearance of a current in the absence of an external force.

  2. A unified framework for non-Brownian suspension flows and soft amorphous solids

    PubMed Central

    Lerner, Edan; Düring, Gustavo; Wyart, Matthieu

    2012-01-01

    While the rheology of non-Brownian suspensions in the dilute regime is well understood, their behavior in the dense limit remains mystifying. As the packing fraction of particles increases, particle motion becomes more collective, leading to a growing length scale and scaling properties in the rheology as the material approaches the jamming transition. There is no accepted microscopic description of this phenomenon. However, in recent years it has been understood that the elasticity of simple amorphous solids is governed by a critical point, the unjamming transition where the pressure vanishes, and where elastic properties display scaling and a diverging length scale. The correspondence between these two transitions is at present unclear. Here we show that for a simple model of dense flow, which we argue captures the essential physics near the jamming threshold, a formal analogy can be made between the rheology of the flow and the elasticity of simple networks. This analogy leads to a new conceptual framework to relate microscopic structure to rheology. It enables us to define and compute numerically normal modes and a density of states. We find striking similarities between the density of states in flow, and that of amorphous solids near unjamming: both display a plateau above some frequency scale ω∗ ∼ |zc - z|, where z is the coordination of the network of particle in contact, zc = 2D where D is the spatial dimension. However, a spectacular difference appears: the density of states in flow displays a single mode at another frequency scale ωmin ≪ ω∗ governing the divergence of the viscosity. PMID:22392976

  3. 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.

  4. Dynamics of non-Brownian rodlike particles in a nonuniform elongational flow

    NASA Astrophysics Data System (ADS)

    Cloitre, M.; Mongruel, A.

    1999-04-01

    This paper deals with the orientation of non-Brownian rodlike particles in a nonuniform elongational flow at low-Reynolds number. Experimentally, an elongational flow is created by introducing a small circular orifice into a cylindrical channel. The flow field is studied using a tracer anemometry technique. On the axis of symmetry, the deformation field is that of a pure elongation with a nonuniform elongation rate. It is well described by the analytical solution obtained for an infinite contraction ratio. This flow is used to study the dynamics of non-Brownian rodlike particles subject to nonuniform elongation. The orientation dynamics of a particle depends on the history of the deformation that it has experienced. The effects of small perturbations existing in the vicinity of the orifice are greatly amplified downstream. Consequently, particle motion does not exhibit the symmetry with respect to the orifice which is expected at low-Reynolds number.

  5. Brownian motor with competing spatial and temporal asymmetry of potential energy.

    PubMed

    Rozenbaum, V M; Korochkova, T Ye; Chernova, A A; Dekhtyar, M L

    2011-05-01

    A Brownian motor is considered which operates due to asymmetric dichotomic fluctuations of the spatially periodic asymmetric potential energy. As shown, the motion direction and stopping points of this motor are dictated by the competition between the spatial and temporal asymmetry of the potential energy (or solely by temporal asymmetry in the case that the potential energy sign fluctuates). For an asymmetric sawtooth potential, the Brownian-particle average velocity is calculated numerically as a function of certain parameters of the model, whereas the low-frequency and low-energy approximations allow the corresponding analytical relationships to be derived for an arbitrarily shaped potential profile. It is shown that temporal asymmetry is not necessary for stopping point occurrence provided that the potential profile fluctuates not only in amplitude but in shape as well. This inference is illustrated by photoinduced fluctuations of the potential energy for a number of substituted arylpyrene molecules on a substrate with symmetrically distributed charge density.

  6. 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"

  7. Decreases in Molecular Diffusion, Perfusion Fraction and Perfusion-Related Diffusion in Fibrotic Livers: A Prospective Clinical Intravoxel Incoherent Motion MR Imaging Study

    PubMed Central

    Lu, Pu-Xuan; Huang, Hua; Yuan, Jing; Zhao, Feng; Chen, Zhi-Yi; Zhang, Qinwei; Ahuja, Anil T.; Zhou, Bo-Ping; Wáng, Yì-Xiáng J.

    2014-01-01

    Purpose This study was aimed to determine whether pure molecular-based diffusion coefficient (D) and perfusion-related diffusion parameters (perfusion fraction f, perfusion-related diffusion coefficient D*) differ in healthy livers and fibrotic livers through intra-voxel incoherent motion (IVIM) MR imaging. Material and Methods 17 healthy volunteers and 34 patients with histopathologically confirmed liver fibrosis patients (stage 1 = 14, stage 2 = 8, stage 3& 4 = 12, METAVIR grading) were included. Liver MR imaging was performed at 1.5-T. IVIM diffusion weighted imaging sequence was based on standard single-shot DW spin echo-planar imaging, with ten b values of 10, 20, 40, 60, 80, 100, 150, 200, 400, 800 sec/mm2 respectively. Pixel-wise realization and regions-of-interest based quantification of IVIM parameters were performed. Results D, f, and D* in healthy volunteer livers and patient livers were 1.096±0.155 vs 0.917±0.152 (10−3 mm2/s, p = 0.0015), 0.164±0.021 vs 0.123±0.029 (p<0.0001), and 13.085±2.943 vs 9.423±1.737 (10−3 mm2/s, p<0.0001) respectively, all significantly lower in fibrotic livers. As the fibrosis severity progressed, D, f, and D* values decreased, with a trend significant for f and D*. Conclusion Fibrotic liver is associated with lower pure molecular diffusion, lower perfusion volume fraction, and lower perfusion-related diffusion. The decrease of f and D* in the liver is significantly associated liver fibrosis severity. PMID:25436458

  8. Controlling enantiomeric populations in fluctuating Brownian monolayers of chiral colloids.

    PubMed

    Rossi, L; Mason, T G

    2015-03-28

    An ideal parallelogram platelet, although achiral in 3D, has an identifiable chirality when confined in a 2D monolayer. We lithographically fabricate microscale parallelogram platelets, disperse them in an aqueous surfactant solution, and allow them to settle towards a lower glass wall. To reduce the thermal-gravitational height, we add polystyrene nanospheres as a depletion agent to create a depletion attraction between the parallelograms and the wall. Surprisingly, by increasing the volume fraction of the depletion agent, we show that a nearly enantiopure monolayer can be created. We explain this by developing a model of 2D monolayer formation based on anisotropic facial attractions; one face of a platelet is more strongly attracted to the wall than the other as a consequence of an anisotropy introduced by the lithographic process. We study enantiopure Brownian systems of parallelograms as a function of particle area fraction and show that oblique chiral crystals form at high densities. By mixing parallelogram platelets printed in opposite senses, we also dictate the chiral ratio in the monolayer over the entire possible range. This approach is not limited to parallelograms and provides a means for tuning the chiral ratio in fluctuating 2D monolayers composed of a wide variety of chiral shapes.

  9. 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.

  10. Effective diffusion of confined active Brownian swimmers

    NASA Astrophysics Data System (ADS)

    Sandoval, Mario; Dagdug, Leonardo

    2014-11-01

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

  11. Two Time Distribution in Brownian Directed Percolation

    NASA Astrophysics Data System (ADS)

    Johansson, Kurt

    2017-04-01

    In the zero temperature Brownian semi-discrete directed polymer we study the joint distribution of two last-passage times at positions ordered in the time-like direction. This is the situation when we have the slow de-correlation phenomenon. We compute the limiting joint distribution function in a scaling limit. This limiting distribution is given by an expansion in determinants that is not a Fredholm expansion. A somewhat similar looking formula was derived non-rigorously in a related model by Dotsenko.

  12. 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

  13. 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.

  14. 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.

  15. Relation between cooperative molecular motors and active Brownian particles

    NASA Astrophysics Data System (ADS)

    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.

  16. 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.

  17. 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.

  18. Asymmetric exclusion process in a system of interacting Brownian particles.

    PubMed

    Eduardo de Oliveira Rodrigues, José; Dickman, Ronald

    2010-06-01

    We study a continuous-space version of the totally asymmetric simple exclusion process (TASEP), consisting of interacting Brownian particles subject to a driving force in a periodic array of potential wells. Particles are inserted into the leftmost well at rate α, hop to the right at unit rate, and are removed at the rightmost well at rate β. Our study is motivated by recent experiments on colloidal particles in a periodic potential generated by an optical tweezers array. Particles spend most of the time near potential minima, approximating the situation on the lattice; a short-range repulsive interaction prevents two particles from occupying the same potential well. A constant driving force, representing Stokes drag on particles suspended in a moving fluid, leads to biased motion. Our results for the density profile and current, obtained via numerical integration of the Langevin equation and dynamic Monte Carlo simulations, indicate that the continuous-space model exhibits phase transitions analogous to those observed in the lattice TASEP. The correspondence is not exact, however, due to the lack of particle-hole symmetry in our model.

  19. 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.

  20. 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 \

  1. NMR measurement and Brownian movement in the short-time limit

    NASA Astrophysics Data System (ADS)

    Stepišnik, Janez

    1994-05-01

    This study is carried out to find relations between the time-dependent molecular self-diffusion and the attenuation of NMR spin-echo. Two cases of diffusion are considered: the Brownian motion in Ornstein's short-time limit and the random walk with memory [13]. The friction and the correlation time describe the mechanism of entrapping interactions between molecules or their bonding to macromolecule chains. The obtained formula for the self-diffusion attenuation is valid at short times and it develops into the well-known Torrey's result in the long-time limit. It fits very efficiently into the NMR data from Refs. [19-20].

  2. Brownian dynamics simulations of amelogenin microribbons formation

    NASA Astrophysics Data System (ADS)

    Li, Wei; Perez Lopez, Anthony; Liu, Ya; Chakrabarti, Amit; Gunton, James

    2011-03-01

    Recent advances in chemical particle synthesis have emphasized the fundamental role of surface colloidal heterogeneities and their detailed chemical composition, which is particularly significant for an important subclass of colloidal systems, namely, proteins. Recently, the process of self-assembly of amelogenin monomers with a hydrophobic/hydrophilic bipolar nature into ordered ribbon structures has been studied experimentally. In this work, we study this dynamical process by means of a Brownian dynamic simulation of a simple model which represents the bipolar character of the globular amelogenin molecule and the hydrophilic C-terminal tail. We monitor the kinetics of self-assembly through a study of the structure factor. We also calculate the phase diagram of the model using Gibbs ensemble Monte Carlo simulation and thermodynamic perturbation theory. This work is supported by grants from the NSF and Mathers Foundation.

  3. Communication: Memory effects and active Brownian diffusion

    NASA Astrophysics Data System (ADS)

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

    2015-12-01

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

  4. Communication: Memory effects and active Brownian diffusion.

    PubMed

    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.

  5. 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.

  6. 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

  7. Centrifugal instability of semidilute non-Brownian fiber suspensions

    NASA Astrophysics Data System (ADS)

    Gupta, V. K.; Sureshkumar, R.; Khomami, B.; Azaiez, J.

    2002-06-01

    Linear stability of the Taylor-Couette (TC) flow of semidilute non-Brownian suspension is investigated by utilizing the fiber orientation model developed by Hinch and Leal [J. Fluid Mech. 76, 187 (1976)] in conjunction with a quadratic and hybrid closure proposed by Advani and Tucker [J. Rheol. 34, 367 (1990)]. It is found that irrespective of the closure approximation used the fiber additives suppress the centrifugal TC instability, i.e., the critical Reynolds number (Re) increases with the fiber volume fraction and aspect ratio as well as the interfiber interaction coefficient. This increase in the critical Re is significantly larger than that in the total viscosity, except for very small values of the volume fraction and the interaction coefficient. The enhanced stabilization can be attributed to the fact that the suspension develops negative first and second normal stresses in the TC flow when the inner cylinder rotates and the outer one is stationary, i.e., the fluid is in a state of compression. Moreover, the interfiber interactions result in alignment of the fiber orientation tensor with respect to the rate of deformation tensor. This coupling enhances the ability of the fluid elements to resist the amplification of radial velocity disturbances that give rise to the centrifugal instability. This mechanism is substantiated based on a rigorous energy analysis, demonstrating that the coupling between the fiber orientation and perturbation radial velocities gives rise to fiber-induced perturbation shear stresses that are dissipative. Specifically, the coupling of fiber-induced perturbation shear stresses with the base flow velocity leads to a compressive force that dissipates energy leading to the suppression of the centrifugal instability.

  8. MSB estimation of bound fraction: bias from binding energy uncertainty

    NASA Astrophysics Data System (ADS)

    Weaver, John B.

    2012-03-01

    Magnetic spectroscopy of nanoparticle Brownian motion, MSB, uses the magnetization produced by magnetic nanoparticles in a sinusoidal magnetic field, which can be observed remotely at low enough concentrations to enable it to be used for "molecular imaging". The MSB signal is sensitive to chemical binding, temperature and viscosity. If the MSB signals from nanoparticles in multiple bound states are known, a mixture model can be used to find the concentration of nanoparticles in each bound state. The accuracy has been shown to be high for two and three bound states. However, if the bound states are not accurately known, as is often the case in vivo, the model is perturbed significantly. Using simulations of two bound states based on the effective field approximation to the Fokker-Planck equations, we show that the error in the bound fraction is roughly proportional to the error in the bound state relaxation time. The errors in bound fraction were roughly proportional to the error in the relaxation time for the bound state used in the mixture model. The largest errors occurred for short relaxation time bound states. But for all bound state relaxation times, 10% errors in the relaxation time of the bound state resulted in errors in the bound fraction of less than 10%.

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

    PubMed Central

    2012-01-01

    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. PMID:22353343

  10. Rotational Brownian dynamics simulations of clathrin cage formation.

    PubMed

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

    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.

  11. 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.

  12. 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.

  13. 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

  14. Response of Brownian Fluctuations to External Forces

    NASA Astrophysics Data System (ADS)

    Laub, Jeffrey William

    Millikan's law of particle fall is an empirical result which shows the dependence of particle fall rate in a gas on particle radius and host gas density. The size of submicron particles in gases has long been determined by Millikan's law. The dominant factor is Stokes' law with a correction added to account for the physics of slip. However, it was recently shown by Kim and Fedele that Brownian fluctuations affect the fall rate while showing no anomalies in the density dependence of the rms displacement. The effect was an enhancement of the fall rate of small particles as the density of the host gas is increased. This enhancement showed a size dependence in the form of a smooth transition from the one of decreasing fall rate with increasing density for large particles (~0.4 μm radius) to another of increasing fall rate with increasing gas density for small particles ( ~0.15mum radius). The magnitude of the anomaly is determined by how the rms Brownian velocity compares with its fall rate. In an effort to understand the effect of Brownian fluctuations coupling with gravity, a new experiment has been carried out where an AC field was applied to force particles to fluctuate more in the vertical direction on one hand and where a constant DC field was applied to change the effective force of gravity on the other. These fields were applied to a charged oil drop in the 0.2 to 0.3 μm radius range falling in a nitrogen environment. Displacements over a 4 second time interval were repeatedly measured in both the vertical and horizontal directions. The original experimental apparatus was used with some modifications. The modifications included computer automation of particle control and data taking to allow for longer use of the same particle, up to 120 hours, and to facilitate application of the additional fields. The objective was to make large particles appear to be smaller via forced oscillations and make them fall faster or slower via the DC bias to effect the change in

  15. Relaxation of Brownian particles in a gravitational field

    NASA Astrophysics Data System (ADS)

    Saka, Halil; Bengtson, Roger D.; Reichl, Linda E.

    2009-03-01

    We describe an upper level undergraduate experiment on the time-dependent behavior of a suspension of Brownian particles under gravitational attraction. We employed the Fokker-Planck equation in the strong friction limit and measured the time-evolution of the probability distribution for 1.0μm diameter latex Brownian particles in water at room temperature and pressure. The experiment provides evidence of the atomic nature of water.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

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

    SciTech Connect

    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. 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.

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

    DOE PAGES

    Stingaciu, Laura R.; Ivanova, Oxana; Ohl, Michael; ...

    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

  2. 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

  3. Engineered Swift Equilibration of a Brownian particle

    PubMed Central

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

    2016-01-01

    A fundamental and intrinsic property of any device or natural system is its relaxation time relax, which is the time it takes to return to equilibrium after the sudden change of a control parameter [1]. 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 driving have been recently demonstrated [2, 3], for isolated quantum and classical systems [4–9]. 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 times faster than the natural equilibration rate. We also estimate the increase of the dissipated energy needed to get such a time reduction. The method paves the way for applications in micro and nano devices, where the reduction of operation time represents as substantial a challenge as miniaturization [10]. PMID:27610190

  4. Cost and Precision of Brownian Clocks

    NASA Astrophysics Data System (ADS)

    Barato, Andre C.; Seifert, Udo

    2016-10-01

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

  5. 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)].

  6. 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.

  7. Brownian dynamics simulation of DNA condensation.

    PubMed Central

    Sottas, P E; Larquet, E; Stasiak, A; Dubochet, J

    1999-01-01

    DNA condensation observed in vitro with the addition of polyvalent counterions is due to intermolecular attractive forces. We introduce a quantitative model of these forces in a Brownian dynamics simulation in addition to a standard mean-field Poisson-Boltzmann repulsion. The comparison of a theoretical value of the effective diameter calculated from the second virial coefficient in cylindrical geometry with some experimental results allows a quantitative evaluation of the one-parameter attractive potential. We show afterward that with a sufficient concentration of divalent salt (typically approximately 20 mM MgCl(2)), supercoiled DNA adopts a collapsed form where opposing segments of interwound regions present zones of lateral contact. However, under the same conditions the same plasmid without torsional stress does not collapse. The condensed molecules present coexisting open and collapsed plectonemic regions. Furthermore, simulations show that circular DNA in 50% methanol solutions with 20 mM MgCl(2) aggregates without the requirement of torsional energy. This confirms known experimental results. Finally, a simulated DNA molecule confined in a box of variable size also presents some local collapsed zones in 20 mM MgCl(2) above a critical concentration of the DNA. Conformational entropy reduction obtained either by supercoiling or by confinement seems thus to play a crucial role in all forms of condensation of DNA. PMID:10512808

  8. Robustness of multidimensional Brownian ratchets as directed transport mechanisms

    NASA Astrophysics Data System (ADS)

    González-Candela, Ernesto; Romero-Rochín, Víctor; Del Río, Fernando

    2011-08-01

    Brownian ratchets have recently been considered as models to describe the ability of certain systems to locate very specific states in multidimensional configuration spaces. This directional process has particularly been proposed as an alternative explanation for the protein folding problem, in which the polypeptide is driven toward the native state by a multidimensional Brownian ratchet. Recognizing the relevance of robustness in biological systems, in this work we analyze such a property of Brownian ratchets by pushing to the limits all the properties considered essential to produce directed transport. Based on the results presented here, we can state that Brownian ratchets are able to deliver current and locate funnel structures under a wide range of conditions. As a result, they represent a simple model that solves the Levinthal's paradox with great robustness and flexibility and without requiring any ad hoc biased transition probability. The behavior of Brownian ratchets shown in this article considerably enhances the plausibility of the model for at least part of the structural mechanism behind protein folding process.

  9. Improved search for elementary particles with fractional electric charge

    NASA Astrophysics Data System (ADS)

    Mar, Nancy M.; Lee, Eric R.; Fleming, George R.; Casey, Brendan C. K.; Perl, Martin L.; Garwin, Edward L.; Hendricks, Charles D.; Lackner, Klaus S.; Shaw, Gordon 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 5 974 941 drops and found no evidence for fractional charges in 1.07 mg of oil. With 95% confidence, the concentration of isolated quarks with +/-1/3e or +/-2/3e in silicone oil is less than one per 2.14×1020 nucleons.

  10. 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.

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

    PubMed

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

    2016-05-10

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

  12. 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.

  13. 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.

  14. Effect of external periodic regulations on Brownian motor

    NASA Astrophysics Data System (ADS)

    Yu, Lilong; Chen, Ruyin; Nie, Linru

    2015-01-01

    Effect of external periodic regulations on a symmetric Brownian motor performing between two temperature sources was investigated. By means of numerical calculations, we found that: (i) The regulations can control magnitude and direction of the motor's current to a large degree. As one of the motor's compartments is regulated, the motor's current can be both inversed and maximized, dependent on amplitude and frequency of the periodic driving force. If two periodic driving forces with identical amplitudes and frequencies are employed to regulate respectively two compartments of the Brownian motor, the current's magnitude and direction will make periodic oscillations with phase difference between them. In addition, the external periodic regulation can also change direction of thermal rectifier of the system as a switch. (ii) Optimal regulating parameters of the external periodic forces can enhance pronouncedly conversion efficiency of energy of the Brownian motor.

  15. 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.

  16. 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.

  17. Memory effects for a trapped Brownian particle in viscoelastic shear flows

    NASA Astrophysics Data System (ADS)

    Mankin, Romi; Laas, Katrin; Lumi, Neeme

    2013-10-01

    The long-time limit behavior of the positional distribution for an underdamped Brownian particle in a fluctuating harmonic potential well, which is simultaneously exposed to an oscillatory viscoelastic shear flow is investigated using the generalized Langevin equation with a power-law-type memory kernel. The influence of a fluctuating environment is modeled by a multiplicative white noise (fluctuations of the stiffness of the trapping potential) and by an additive internal fractional Gaussian noise. The exact expressions of the second-order moments of the fluctuating position for the Brownian particle in the shear plane have been calculated. Also, shear-induced cross correlation between particle fluctuations along orthogonal directions as well as the angular momentum are found. It is shown that interplay of shear flow, memory, and multiplicative noise can generate a variety of cooperation effects, such as energetic instability, multiresonance versus the shear frequency, and memory-induced anomalous diffusion in the direction of the shear flow. Particularly, two different critical memory exponents have been found, which mark dynamical transitions from a stationary regime to a subdiffusive (or superdiffusive) regime of the system. Similarities and differences between the behaviors of the models with oscillatory and nonoscillatory shear flow are also discussed.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  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. 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.

  4. Accurate method for the Brownian dynamics simulation of spherical particles with hard-body interactions

    NASA Astrophysics Data System (ADS)

    Barenbrug, Theo M. A. O. M.; Peters, E. A. J. F. (Frank); Schieber, Jay D.

    2002-11-01

    In Brownian Dynamics simulations, the diffusive motion of the particles is simulated by adding random displacements, proportional to the square root of the chosen time step. When computing average quantities, these Brownian contributions usually average out, and the overall simulation error becomes proportional to the time step. A special situation arises if the particles undergo hard-body interactions that instantaneously change their properties, as in absorption or association processes, chemical reactions, etc. The common "naı̈ve simulation method" accounts for these interactions by checking for hard-body overlaps after every time step. Due to the simplification of the diffusive motion, a substantial part of the actual hard-body interactions is not detected by this method, resulting in an overall simulation error proportional to the square root of the time step. In this paper we take the hard-body interactions during the time step interval into account, using the relative positions of the particles at the beginning and at the end of the time step, as provided by the naı̈ve method, and the analytical solution for the diffusion of a point particle around an absorbing sphere. Öttinger used a similar approach for the one-dimensional case [Stochastic Processes in Polymeric Fluids (Springer, Berlin, 1996), p. 270]. We applied the "corrected simulation method" to the case of a simple, second-order chemical reaction. The results agree with recent theoretical predictions [K. Hyojoon and Joe S. Kook, Phys. Rev. E 61, 3426 (2000)]. The obtained simulation error is proportional to the time step, instead of its square root. The new method needs substantially less simulation time to obtain the same accuracy. Finally, we briefly discuss a straightforward way to extend the method for simulations of systems with additional (deterministic) forces.

  5. 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.

  6. Brownian gyrator: a minimal heat engine on the nanoscale.

    PubMed

    Filliger, Roger; Reimann, Peter

    2007-12-07

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

  7. 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.

  8. Robust Biased Brownian Dynamics for Rate Constant Calculation

    PubMed Central

    Zou, Gang; Skeel, Robert D.

    2003-01-01

    A reaction probability is required to calculate the rate constant of a diffusion-dominated reaction. Due to the complicated geometry and potentially high dimension of the reaction probability problem, it is usually solved by a Brownian dynamics simulation, also known as a random walk or path integral method, instead of solving the equivalent partial differential equation by a discretization method. Building on earlier work, this article completes the development of a robust importance sampling algorithm for Brownian dynamics—i.e., biased Brownian dynamics with weight control—to overcome the high energy and entropy barriers in biomolecular association reactions. The biased Brownian dynamics steers sampling by a bias force, and the weight control algorithm controls sampling by a target weight. This algorithm is optimal if the bias force and the target weight are constructed from the solution of the reaction probability problem. In reality, an approximate reaction probability has to be used to construct the bias force and the target weight. Thus, the performance of the algorithm depends on the quality of the approximation. Given here is a method to calculate a good approximation, which is based on the selection of a reaction coordinate and the variational formulation of the reaction probability problem. The numerically approximated reaction probability is shown by computer experiments to give a factor-of-two speedup over the use of a purely heuristic approximation. Also, the fully developed method is compared to unbiased Brownian dynamics. The tests for human superoxide dismutase, Escherichia coli superoxide dismutase, and antisweetener antibody NC6.8, show speedups of 17, 35, and 39, respectively. The test for reactions between two model proteins with orientations shows speedups of 2578 for one set of configurations and 3341 for another set of configurations. PMID:14507681

  9. 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.

  10. Brownian microswimmer in a Poiseuille Flow

    NASA Astrophysics Data System (ADS)

    Apaza-Pilco, Leonardo; Sandoval, Mario

    We study the two and three dimensional dynamics of a microswimmer at low-Reynolds-number in a Poiseuille flow and subject to thermal fluctuations. A deterministic analysis is also performed, and we find that under certain conditions the swimmer becomes hydrodynamically trapped thus performing periodic orbits. We provide an analytical expression where this trapping occur. A numerical solution for the coupled system of stochastic differential equations based on two parameters, the Peclet number and the ratio of the swimming velocity and the flow velocity, is also obtained. Based on this parameter space, it is found that the mean-square displacement (MSD) along the longitudinal axis (flow direction) is always quadratic in time, whereas along the transversal direction the mean-square displacement achieves a constant value due to the presence of physical boundaries. A comparison among the 2D and 3D MSD results are also discussed. Finally, the effect of the Poiseuille flow on the angular probability distribution for the two-dimensional motion is also computationally shown.

  11. Exact master equation for a noncommutative Brownian particle

    SciTech Connect

    Costa Dias, Nuno Nuno Prata, Joao

    2009-01-15

    We derive the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators on the plane with spatial noncommutativity. The results obtained are exact to all orders in the noncommutative parameter. As a by-product we derive some miscellaneous results such as the equilibrium Wigner distribution for the reservoir of noncommutative oscillators, the weak coupling limit of the master equation and a set of sufficient conditions for strict purity decrease of the Brownian particle. Finally, we consider a high-temperature Ohmic model and obtain an estimate for the time scale of the transition from noncommutative to ordinary quantum mechanics. This scale is considerably smaller than the decoherence scale.

  12. A Brownian dynamics algorithm for colloids in curved manifolds.

    PubMed

    Castro-Villarreal, Pavel; Villada-Balbuena, Alejandro; Méndez-Alcaraz, José Miguel; Castañeda-Priego, Ramón; Estrada-Jiménez, Sendic

    2014-06-07

    The many-particle Langevin equation, written in local coordinates, is used to derive a Brownian dynamics simulation algorithm to study the dynamics of colloids moving on curved manifolds. The predictions of the resulting algorithm for the particular case of free particles diffusing along a circle and on a sphere are tested against analytical results, as well as with simulation data obtained by means of the standard Brownian dynamics algorithm developed by Ermak and McCammon [J. Chem. Phys. 69, 1352 (1978)] using explicitly a confining external field. The latter method allows constraining the particles to move in regions very tightly, emulating the diffusion on the manifold. Additionally, the proposed algorithm is applied to strong correlated systems, namely, paramagnetic colloids along a circle and soft colloids on a sphere, to illustrate its applicability to systems made up of interacting particles.

  13. Pressure and phase equilibria in interacting active brownian spheres.

    PubMed

    Solon, Alexandre P; Stenhammar, Joakim; Wittkowski, Raphael; Kardar, Mehran; Kafri, Yariv; Cates, Michael E; Tailleur, Julien

    2015-05-15

    We derive a microscopic expression for the mechanical pressure P in a system of spherical active Brownian particles at density ρ. Our exact result relates P, defined as the force per unit area on a bounding wall, to bulk correlation functions evaluated far away from the wall. It shows that (i) P(ρ) is a state function, independent of the particle-wall interaction; (ii) interactions contribute two terms to P, one encoding the slow-down that drives motility-induced phase separation, and the other a direct contribution well known for passive systems; and (iii) P is equal in coexisting phases. We discuss the consequences of these results for the motility-induced phase separation of active Brownian particles and show that the densities at coexistence do not satisfy a Maxwell construction on P.

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

    SciTech Connect

    Radiom, Milad Ducker, William; Robbins, Brian; Paul, Mark

    2015-02-15

    The hydrodynamic interaction of two closely spaced micron-scale spheres undergoing Brownian motion was measured as a function of their separation. Each sphere was attached to the distal end of a different atomic force microscopy cantilever, placing each sphere in a stiff one-dimensional potential (0.08 Nm{sup −1}) with a high frequency of thermal oscillations (resonance at 4 kHz). As a result, the sphere’s inertial and restoring forces were significant when compared to the force due to viscous drag. We explored interparticle gap regions where there was overlap between the two Stokes layers surrounding each sphere. Our experimental measurements are the first of their kind in this parameter regime. The high frequency of oscillation of the spheres means that an analysis of the fluid dynamics would include the effects of fluid inertia, as described by the unsteady Stokes equation. However, we find that, for interparticle separations less than twice the thickness of the wake of the unsteady viscous boundary layer (the Stokes layer), the hydrodynamic interaction between the Brownian particles is well-approximated by analytical expressions that neglect the inertia of the fluid. This is because elevated frictional forces at narrow gaps dominate fluid inertial effects. The significance is that interparticle collisions and concentrated suspensions at this condition can be modeled without the need to incorporate fluid inertia. We suggest a way to predict when fluid inertial effects can be ignored by including the gap-width dependence into the frequency number. We also show that low frequency number analysis can be used to determine the microrheology of mixtures at interfaces.

  15. Brownian dynamics study of ion transport in the vestibule of membrane channels.

    PubMed

    Li, S C; Hoyles, M; Kuyucak, S; Chung, S H

    1998-01-01

    Brownian dynamics simulations have been carried out to study the transport of ions in a vestibular geometry, which offers a more realistic shape for membrane channels than cylindrical tubes. Specifically, we consider a torus-shaped channel, for which the analytical solution of Poisson's equation is possible. The system is composed of the toroidal channel, with length and radius of the constricted region of 80 A and 4 A, respectively, and two reservoirs containing 50 sodium ions and 50 chloride ions. The positions of each of these ions executing Brownian motion under the influence of a stochastic force and a systematic electric force are determined at discrete time steps of 50 fs for up to 2.5 ns. All of the systematic forces acting on an ion due to the other ions, an external electric field, fixed charges in the channel protein, and the image charges induced at the water-protein boundary are explicitly included in the calculations. We find that the repulsive dielectric force arising from the induced surface charges plays a dominant role in channel dynamics. It expels an ion from the vestibule when it is deliberately put in it. Even in the presence of an applied electric potential of 100 mV, an ion cannot overcome this repulsive force and permeate the channel. Only when dipoles of a favorable orientation are placed along the sides of the transmembrane segment can an ion traverse the channel under the influence of a membrane potential. When the strength of the dipoles is further increased, an ion becomes detained in a potential well, and the driving force provided by the applied field is not sufficient to drive the ion out of the well. The trajectory of an ion navigating across the channel mostly remains close to the central axis of the pore lumen. Finally, we discuss the implications of these findings for the transport of ions across the membrane.

  16. Pseudo-random number generation for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU devices

    SciTech Connect

    Phillips, Carolyn L.; Anderson, Joshua A.; Glotzer, Sharon C.

    2011-08-10

    Highlights: {yields} Molecular Dynamics codes implemented on GPUs have achieved two-order of magnitude computational accelerations. {yields} Brownian Dynamics and Dissipative Particle Dynamics simulations require a large number of random numbers per time step. {yields} We introduce a method for generating small batches of pseudorandom numbers distributed over many threads of calculations. {yields} With this method, Dissipative Particle Dynamics is implemented on a GPU device without requiring thread-to-thread communication. - Abstract: Brownian Dynamics (BD), also known as Langevin Dynamics, and Dissipative Particle Dynamics (DPD) are implicit solvent methods commonly used in models of soft matter and biomolecular systems. The interaction of the numerous solvent particles with larger particles is coarse-grained as a Langevin thermostat is applied to individual particles or to particle pairs. The Langevin thermostat requires a pseudo-random number generator (PRNG) to generate the stochastic force applied to each particle or pair of neighboring particles during each time step in the integration of Newton's equations of motion. In a Single-Instruction-Multiple-Thread (SIMT) GPU parallel computing environment, small batches of random numbers must be generated over thousands of threads and millions of kernel calls. In this communication we introduce a one-PRNG-per-kernel-call-per-thread scheme, in which a micro-stream of pseudorandom numbers is generated in each thread and kernel call. These high quality, statistically robust micro-streams require no global memory for state storage, are more computationally efficient than other PRNG schemes in memory-bound kernels, and uniquely enable the DPD simulation method without requiring communication between threads.

  17. Work fluctuations for a Brownian particle between two thermostats

    NASA Astrophysics Data System (ADS)

    Visco, Paolo

    2006-06-01

    We explicitly determine the large deviation function of the energy flow of a Brownian particle coupled to two heat baths at different temperatures. This toy model, initially introduced by Derrida and Brunet (2005, Einstein aujourd'hui (Les Ulis: EDP Sciences)), not only allows us to sort out the influence of initial conditions on large deviation functions but also allows us to pinpoint various restrictions bearing upon the range of validity of the Fluctuation Relation.

  18. Analysis of a Brownian heat engine with ecological criteria

    NASA Astrophysics Data System (ADS)

    Açıkkalp, Emin

    2016-12-01

    The purpose of this study is to investigate the Brownian heat engine with thermo-ecological function ( ECF) and ecological coefficient of performance ( ECOP). Potential and kinetic heat flows are taken into account. Different parameters are considered in the analyses. Beside the thermo-ecological function and ecological coefficient of performance, the basic thermodynamics parameters involving power output and efficiency are investigated. Results are presented numerically and the optimum points of the system are determined.

  19. Algorithms for Brownian first-passage-time estimation.

    PubMed

    Adib, Artur B

    2009-09-01

    A class of algorithms in discrete space and continuous time for Brownian first-passage-time estimation is considered. A simple algorithm is derived that yields exact mean first-passage times (MFPTs) for linear potentials in one dimension, regardless of the lattice spacing. When applied to nonlinear potentials and/or higher spatial dimensions, numerical evidence suggests that this algorithm yields MFPT estimates that either outperform or rival Langevin-based (discrete time and continuous space) estimates.

  20. Ellipsoidal Brownian self-driven particles in a magnetic field

    NASA Astrophysics Data System (ADS)

    Fan, Wai-Tong Louis; Pak, On Shun; Sandoval, Mario

    2017-03-01

    We study the two-dimensional Brownian dynamics of an ellipsoidal paramagnetic microswimmer moving at a low Reynolds number and subject to a magnetic field. Its corresponding mean-square displacement, showing the effect of a particles's shape, activity, and magnetic field on the microswimmer's diffusion, is analytically obtained. Comparison between analytical and computational results shows good agreement. In addition, the effect of self-propulsion on the transition time from anisotropic to isotropic diffusion of the ellipse is investigated.

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

    PubMed

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

    2015-06-12

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

  2. Generation of microswimmers from passive Brownian particles in a spherically aberrated optical trap.

    PubMed

    Mondal, Argha; Roy, Basudev; Banerjee, Ayan

    2015-03-23

    We induce spontaneous motion that is both directed and complex in micron-sized asymmetric Brownian particles in a spherically aberrated optical trap to generate microswimmers. The aberrated optical trap is prepared in a slightly modified optical tweezers configuration where we use a refractive index mismatched cover slip leading to the formation of an annular intensity distribution near the trap focal plane. Asymmetric scattering from a micro-particle trapped in this annular trap gives rise to a net tangential force on the particle causing it to revolve spontaneously in the intensity ring. The rate of revolution can be controlled from sub-Hz to a few Hz by changing the intensity of the trapping light. Theoretical simulations performed using finite-difference time-domain method verify the experimental observations. We also experimentally demonstrate simultaneous spin and revolution of a micro-swimmer which shows that complex motion can be achieved by designing a suitable shape of a micro-swimmer in the optical potential.

  3. Stability and convergence of an implicit numerical method for the space and time fractional Bloch-Torrey equation.

    PubMed

    Yu, Qiang; Liu, Fawang; Turner, Ian; Burrage, Kevin

    2013-05-13

    Fractional-order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brownian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As magnetic resonance imaging is applied with increasing temporal and spatial resolution, the spin dynamics is being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here, the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments, where processes are often anisotropic. Anomalous diffusion in the human brain using fractional-order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional-order calculus with respect to time and space. However, effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) in both fractional Laplacian and Riesz derivative form is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE in fractional Laplacian form with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE based on the Riesz form, and the stability and convergence of the INM are investigated. We prove that the INM for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.

  4. Fractional dissipative standard map.

    PubMed

    Tarasov, Vasily E; Edelman, M

    2010-06-01

    Using kicked differential equations of motion with derivatives of noninteger orders, we obtain generalizations of the dissipative standard map. The main property of these generalized maps, which are called fractional maps, is long-term memory. The memory effect in the fractional maps means that their present state of evolution depends on all past states with special forms of weights. Already a small deviation of the order of derivative from the integer value corresponding to the regular dissipative standard map (small memory effects) leads to the qualitatively new behavior of the corresponding attractors. The fractional dissipative standard maps are used to demonstrate a new type of fractional attractors in the wide range of the fractional orders of derivatives.

  5. Direct tests of muscle cross-bridge theories: predictions of a Brownian dumbbell model for position-dependent cross-bridge lifetimes and step sizes with an optically trapped actin filament.

    PubMed Central

    Smith, D A

    1998-01-01

    Force and displacement events from a single myosin molecule interacting with an actin filament suspended between optically trapped beads (Finer, J. T., R. M. Simmons, and J. A. Spudich. 1994. Nature. 368:113-119) can be interpreted in terms of a generalized cross-bridge model that includes the effects of Brownian forces on the beads. Steady-state distributions of force and displacement can be obtained directly from a generalized Smoluchowski equation for Brownian motion of the actin-bead "dumbbell," and time series from Monte Carlo simulations of the corresponding Langevin equation. When the frequency spectrum of Brownian motion extends beyond cross-bridge transition rates, the inverse mean lifetimes of force/displacement pulses are given by cross-bridge rate constants averaged over a Boltzmann distribution of Brownian noise. These averaged rate constants reflect the strain-dependence of the rate constants for the stationary filament, most faithfully at high trap stiffness. Hence, measurements of the lifetimes and displacements of single events as a function of the resting position of the dumbbell can provide a direct test of different cross-bridge theories of muscle contraction. Quantitative demonstrations are given for Huxley models with 1) faster binding or 2) slower dissociation at positive cross-bridge strain. Predictions for other models can be inferred from the averaging procedure. PMID:9826619

  6. The effects of temperature, volume fraction and vibration time on the thermo-physical properties of a carbon nanotube suspension (carbon nanofluid).

    PubMed

    Amrollahi, A; Hamidi, A A; Rashidi, A M

    2008-08-06

    In this investigation, nanofluids of carbon nanotubes are prepared and the thermal conductivity and volumetric heat capacity of these fluids are measured using a thin layer technique as a function of time of ultrasonication, temperature, and volume fraction. It has been observed that after using the ultrasonic disrupter, the size of agglomerated particles and number of primary particles in a particle cluster was significantly decreased and that the thermal conductivity increased with elapsed ultrasonication time. The clustering of carbon nanotubes was also confirmed microscopically. The strong dependence of the effective thermal conductivity on temperature and volume fraction of nanofluids was attributed to Brownian motion and the interparticle potential, which influences the particle motion. The effect of temperature will become much more evident with an increase in the volume fraction and the agglomeration of the nanoparticles, as observed experimentally. The data obtained from this work have been compared with those of other studies and also with mathematical models at present proven for suspensions. Using a 2.5% volumetric concentration of carbon nanotubes resulted in a 20% increase in the thermal conductivity of the base fluid (ethylene glycol).The volumetric heat capacity also showed a pronounced increase with respect to that of the pure base fluid.

  7. I. Statistical mechanics of bubbly liquids. II. Behavior of sheared suspensions of non-Brownian particles

    NASA Astrophysics Data System (ADS)

    Yurkovetsky, Yevgeny

    I. The dynamics of bubbles at high Reynolds numbers is studied from the viewpoint of statistical mechanics. Individual bubbles are treated as dipoles in potential flow. A virtual mass matrix of the system of bubbles is introduced, which depends on the instantaneous positions of the bubbles, and is used to calculate the energy of the bubbly flow as a quadratic form of the bubbles' velocities. The energy is shown to be the system's Hamiltonian and is used to construct a canonical ensemble partition function, which explicitly includes the total impulse of the suspension along with its energy. The Hamiltonian is decomposed into an effective potential due to the bubbles' collective motion and a kinetic term due to the random motion about the mean. An effective bubble temperature-a measure of the relative importance of the bubbles' relative to collective motion-is derived with the help of the impulse-dependent partition function. Two effective potentials are shown to operate: one, due to the mean motion of the bubbles, dominates at low bubble temperatures where it leads to their grouping in flat clusters normal to the direction of the collective motion, while the other, temperature invariant, is due to the bubbles' position-dependent virtual mass and results in their mutual repulsion. Numerical evidence is presented for the existence of the effective potentials, the condensed and dispersed phases and a phase transition. II. Suspensions of non-Brownian particles in simple shear flow of a Newtonian solvent in the range of particle phase concentration, φ, from 0.05 to 0.52, are studied numerically by Stokesian Dynamics. The simulations are a function of φ and the dimensionless shear rate, γ*, which measures the relative importance of the shear and short-ranged interparticle forces. The pair-distribution functions, shear viscosity, normal stress differences, suspension pressure, long-time self-diffusion coefficients, and mean square of the particle velocity fluctuations

  8. Local Nanomechanical Motion In Single Cells.

    NASA Astrophysics Data System (ADS)

    Pelling, Andrew; Gimzewski, James

    2004-03-01

    We present new evidence that the nanoscale motion of the cell wall of Saccharomyces cerevisiae exhibits local bionanomechanical motion at characteristic frequencies and which is not caused by random or Brownian processes. This motion is measured with the AFM tip which acts as a nanomechanical sensor, permitting the motion of the cell wall to be recorded as a function of time, applied force, etc. We present persuasive evidence which shows that the local nanomechanical motion is characteristic of metabolic processes taking place inside the cell. This is demonstrated by clear differences between living cells and living cells treated with a metabolic inhibitor. This inhibitor specifically targets cytochrome oxidase inside the mitochondria and inhibits ATP production. The cells observed in this study display characteristic local cell wall motion with amplitudes between 1 and 3 nm and frequencies between 500 and 1700 Hz. The motion is temperature dependant which also suggests the mechanism for the observed motion has biological origins. In addition to a stringent series of control experiments we also discuss local measurements of the cell's mechanical properties and their influence on the observed bionanomechanical motion.

  9. Singular perturbation theory for predicting extravasation of Brownian particles

    PubMed Central

    Shah, Preyas; Fitzgibbon, Sean; Narsimhan, Vivek; Shaqfeh, Eric S. G.

    2013-01-01

    Motivated by recent studies on tumor treatments using the drug delivery of nanoparticles, we provide a singular perturbation theory and perform Brownian dynamics simulations to quantify the extravasation rate of Brownian particles in a shear flow over a circular pore with a lumped mass transfer resistance. The analytic theory we present is an expansion in the limit of a vanishing Péclet number (P), which is the ratio of convective fluxes to diffusive fluxes on the length scale of the pore. We state the concentration of particles near the pore and the extravasation rate (Sherwood number) to O(P1/2). This model improves upon previous studies because the results are valid for all values of the particle mass transfer coefficient across the pore, as modeled by the Damköhler number (κ), which is the ratio of the reaction rate to the diffusive mass transfer rate at the boundary. Previous studies focused on the adsorption-dominated regime (i.e., κ → ∞). Specifically, our work provides a theoretical basis and an interpolation-based approximate method for calculating the Sherwood number (a measure of the extravasation rate) for the case of finite resistance [κ ~ O(1)] at small Péclet numbers, which are physiologically important in the extravasation of nanoparticles. We compare the predictions of our theory and an approximate method to Brownian dynamics simulations with reflection–reaction boundary conditions as modeled by κ. They are found to agree well at small P and for the κ ≪ 1 and κ ≫ 1 asymptotic limits representing the diffusion-dominated and adsorption-dominated regimes, respectively. Although this model neglects the finite size effects of the particles, it provides an important first step toward understanding the physics of extravasation in the tumor vasculature. PMID:24563548

  10. Control of dynamical self-assembly of strongly Brownian nanoparticles through convective forces induced by ultrafast laser

    NASA Astrophysics Data System (ADS)

    Ilday, Serim; Akguc, Gursoy B.; Tokel, Onur; Makey, Ghaith; Yavuz, Ozgun; Yavuz, Koray; Pavlov, Ihor; Ilday, F. Omer; Gulseren, Oguz

    We report a new dynamical self-assembly mechanism, where judicious use of convective and strong Brownian forces enables effective patterning of colloidal nanoparticles that are almost two orders of magnitude smaller than the laser beam. Optical trapping or tweezing effects are not involved, but the laser is used to create steep thermal gradients through multi-photon absorption, and thereby guide the colloids through convective forces. Convective forces can be thought as a positive feedback mechanism that helps to form and reinforce pattern, while Brownian motion act as a competing negative feedback mechanism to limit the growth of the pattern, as well as to increase the possibilities of bifurcation into different patterns, analogous to the competition observed in reaction-diffusion systems. By steering stochastic processes through these forces, we are able to gain control over the emergent pattern such as to form-deform-reform of a pattern, to change its shape and transport it spatially within seconds. This enables us to dynamically initiate and control large patterns comprised of hundreds of colloids. Further, by not relying on any specific chemical, optical or magnetic interaction, this new method is, in principle, completely independent of the material type being assembled.

  11. A Fractional PDE Approach to Turbulent Mixing; Part I: an Anomalous Transport Theory

    NASA Astrophysics Data System (ADS)

    Zayernouri, Mohsen; Samiee, Mehdi

    2016-11-01

    It has been experimentally and theoretically shown that even in the most ideal cases of homogeneous and isotropic turbulence, the statistical distributions are asymmetric and heavy-tailed. Similar observations, in addition to high peaks, have been made in grid turbulence and atmospheric boundary layer. In the aforementioned problems, the skewness, as a measure of asymmetry, is non-zero and negative, also the flatness (kurtosis), as a notion of the tail heaviness in the distribution, significantly exceeds the Gaussian value 3, reflecting a strong non-Gaussianity. In this talk, we demonstrate that the existence of such anomalous characteristics e.g., heavy tails, asymmetric distributions, and high peaks can naturally put the phenomenology of Taylor, Richardson, and Kolmogorov in broader framework, where the generalizing fractional Brownian motions and stochastic Lévy jump processes (or Lévy flights), investigated in the context of fractional PDEs in the fluid limit, can physically and mathematically explain, hence, predict the notion of anomalously enhanced (sub-to-super) diffusion and self-similar features in passive scalar turbulence. Assistant Professor, Department Computational Mathematics, Science, and Engineering, & Department of Mechanical Engineering.

  12. Additivity, density fluctuations, and nonequilibrium thermodynamics for active Brownian particles

    NASA Astrophysics Data System (ADS)

    Chakraborti, Subhadip; Mishra, Shradha; Pradhan, Punyabrata

    2016-05-01

    Using an additivity property, we study particle-number fluctuations in a system of interacting self-propelled particles, called active Brownian particles (ABPs), which consists of repulsive disks with random self-propulsion velocities. From a fluctuation-response relation, a direct consequence of additivity, we formulate a thermodynamic theory which captures the previously observed features of nonequilibrium phase transition in the ABPs from a homogeneous fluid phase to an inhomogeneous phase of coexisting gas and liquid. We substantiate the predictions of additivity by analytically calculating the subsystem particle-number distributions in the homogeneous fluid phase away from criticality where analytically obtained distributions are compatible with simulations in the ABPs.

  13. Continuum Theory of Phase Separation Kinetics for Active Brownian Particles

    NASA Astrophysics Data System (ADS)

    Stenhammar, Joakim; Tiribocchi, Adriano; Allen, Rosalind J.; Marenduzzo, Davide; Cates, Michael E.

    2013-10-01

    Active Brownian particles (ABPs), when subject to purely repulsive interactions, are known to undergo activity-induced phase separation broadly resembling an equilibrium (attraction-induced) gas-liquid coexistence. Here we present an accurate continuum theory for the dynamics of phase-separating ABPs, derived by direct coarse graining, capturing leading-order density gradient terms alongside an effective bulk free energy. Such gradient terms do not obey detailed balance; yet we find coarsening dynamics closely resembling that of equilibrium phase separation. Our continuum theory is numerically compared to large-scale direct simulations of ABPs and accurately accounts for domain growth kinetics, domain topologies, and coexistence densities.

  14. Entropic Ratchet transport of interacting active Brownian particles

    SciTech Connect

    Ai, Bao-Quan; He, Ya-Feng; Zhong, Wei-Rong

    2014-11-21

    Directed transport of interacting active (self-propelled) Brownian particles is numerically investigated in confined geometries (entropic barriers). The self-propelled velocity can break thermodynamical equilibrium and induce the directed transport. It is found that the interaction between active particles can greatly affect the ratchet transport. For attractive particles, on increasing the interaction strength, the average velocity first decreases to its minima, then increases, and finally decreases to zero. For repulsive particles, when the interaction is very weak, there exists a critical interaction at which the average velocity is minimal, nearly tends to zero, however, for the strong interaction, the average velocity is independent of the interaction.

  15. A parity breaking Ising chain Hamiltonian as a Brownian motor

    NASA Astrophysics Data System (ADS)

    Cornu, F.; Hilhorst, H. J.

    2014-10-01

    We consider the translationally invariant but parity (left-right symmetry) breaking Ising chain Hamiltonian {\\cal H} =-{U_2}\\sumk sksk+1 - {U_3}\\sumk sksk+1sk+3 and let this system evolve by Kawasaki spin exchange dynamics. Monte Carlo simulations show that perturbations forcing this system off equilibrium make it act as a Brownian molecular motor which, in the lattice gas interpretation, transports particles along the chain. We determine the particle current under various different circumstances, in particular as a function of the ratio {U_3}/{U_2} and of the conserved magnetization M=\\sum_ksk . The symmetry of the U3 term in the Hamiltonian is discussed.

  16. Fractional randomness

    NASA Astrophysics Data System (ADS)

    Tapiero, Charles S.; Vallois, Pierre

    2016-11-01

    The premise of this paper is that a fractional probability distribution is based on fractional operators and the fractional (Hurst) index used that alters the classical setting of random variables. For example, a random variable defined by its density function might not have a fractional density function defined in its conventional sense. Practically, it implies that a distribution's granularity defined by a fractional kernel may have properties that differ due to the fractional index used and the fractional calculus applied to define it. The purpose of this paper is to consider an application of fractional calculus to define the fractional density function of a random variable. In addition, we provide and prove a number of results, defining the functional forms of these distributions as well as their existence. In particular, we define fractional probability distributions for increasing and decreasing functions that are right continuous. Examples are used to motivate the usefulness of a statistical approach to fractional calculus and its application to economic and financial problems. In conclusion, this paper is a preliminary attempt to construct statistical fractional models. Due to the breadth and the extent of such problems, this paper may be considered as an initial attempt to do so.

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

    NASA Astrophysics Data System (ADS)

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

    2015-06-01

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

  18. Nonlinear Behavior of Magnetic Fluid in Brownian Relaxation

    SciTech Connect

    Yoshida, Takashi; Ogawa, Koutaro; Bhuiya, Anwarul K.; Enpuku, Keiji

    2010-12-02

    This study investigated the nonlinear behavior of magnetic fluids under high excitation fields due to nonlinear Brownian relaxation. As a direct indication of nonlinear behavior, we characterized the higher harmonics of the magnetization signal generated by the magnetic fluid. The amplitudes of the fundamental to the ninth harmonic of the magnetization signal were measured as a function of the external field. The experimental results were compared with numerical simulations based on the Fokker-Planck equation, which describes nonlinear Brownian relaxation. To allow a quantitative comparison, we estimated the size distribution and size dependence of the magnetic moment in the sample. In the present magnetic fluid, composed of agglomerates of Fe{sub 3}O{sub 4} particles, the magnetic moment was estimated to be roughly proportional to the diameter of the particles, in contrast to the case of single-domain particles. When the size distribution and the size dependence of the magnetic moment were taken into account, there was good quantitative agreement between the experiment and simulation.

  19. Fractional Schrödinger equation in optics.

    PubMed

    Longhi, Stefano

    2015-03-15

    In quantum mechanics, the space-fractional Schrödinger equation provides a natural extension of the standard Schrödinger equation when the Brownian trajectories in Feynman path integrals are replaced by Levy flights. Here an optical realization of the fractional Schrödinger equation, based on transverse light dynamics in aspherical optical cavities, is proposed. As an example, a laser implementation of the fractional quantum harmonic oscillator is presented in which dual Airy beams can be selectively generated under off-axis longitudinal pumping.

  20. Shuttling heat across one-dimensional homogenous nonlinear lattices with a Brownian heat motor

    NASA Astrophysics Data System (ADS)

    Li, Nianbei; Zhan, Fei; Hänggi, Peter; Li, Baowen

    2009-07-01

    We investigate directed thermal heat flux across one-dimensional homogenous nonlinear lattices when no net thermal bias is present on average. A nonlinear lattice of Fermi-Pasta-Ulam-type or Lennard-Jones-type system is connected at both ends to thermal baths which are held at the same temperature on temporal average. We study two different modulations of the heat bath temperatures, namely: (i) a symmetric, harmonic ac driving of temperature of one heat bath only and (ii) a harmonic mixing drive of temperature acting on both heat baths. While for case (i) an adiabatic result for the net heat transport can be derived in terms of the temperature-dependent heat conductivity of the nonlinear lattice a similar such transport approach fails for the harmonic mixing case (ii). Then, for case (ii), not even the sign of the resulting Brownian motion induced heat flux can be predicted a priori. A nonvanishing heat flux (including a nonadiabatic reversal of flux) is detected which is the result of an induced dynamical symmetry breaking mechanism in conjunction with the nonlinearity of the lattice dynamics. Computer simulations demonstrate that the heat flux is robust against an increase of lattice sizes. The observed ratchet effect for such directed heat currents is quite sizable for our studied class of homogenous nonlinear lattice structures, thereby making this setup accessible for experimental implementation and verification.

  1. Non-equilibrium sedimentation of colloids: confocal microscopy and Brownian dynamics simulations

    NASA Astrophysics Data System (ADS)

    Schmidt, Matthias; Royall, C. Patrick; van Blaaderen, Alfons; Dzubiella, Joachim

    2008-12-01

    Experimental and computational details are presented for an investigation of the transient time evolution of colloidal dispersions confined in a horizontal slit pore and under the influence of gravity (Royall et al 2007 Phys. Rev. Lett. 98 188304). We demonstrate that the interparticle interactions can be well described by those of effective hard spheres by comparing experimental results for the pair distribution function obtained in the homogeneous part of the settling system to the theoretical result for hard spheres in equilibrium. Using an effective hard sphere diameter that is 10% larger than that obtained by static light scattering takes account of the (screened) electrostatic repulsion between particles. As a simple computational model, we use Brownian dynamics computer simulations with hard sphere pair interactions and investigate the time evolution of the one-body density profile during sedimentation. We show that an 'intrinsic clock', that ticks only when trial moves are accepted, facilitates high accuracy of the time evolution of the density profile, even when using relatively large integration time steps for the Langevin equations of motion.

  2. Translocation of a Polymer Chain across a Nanopore: A Brownian Dynamics Simulation Study

    NASA Technical Reports Server (NTRS)

    Tian, Pu; Smith, Grant D.

    2003-01-01

    We carried out Brownian dynamics simulation studies of the translocation of single polymer chains across a nanosized pore under the driving of an applied field (chemical potential gradient). The translocation process can be either dominated by the entropic barrier resulted from restricted motion of flexible polymer chains or by applied forces (or chemical gradient across the wall), we focused on the latter case in our studies. Calculation of radius of gyrations at the two opposite sides of the wall shows that the polymer chains are not in equilibrium during the translocation process. Despite this fact, our results show that the one-dimensional diffusion and the nucleation model provide an excellent description of the dependence of average translocation time on the chemical potential gradients, the polymer chain length and the solvent viscosity. In good agreement with experimental results and theoretical predictions, the translocation time distribution of our simple model shows strong non-Gaussian characteristics. It is observed that even for this simple tubelike pore geometry, more than one peak of translocation time distribution can be generated for proper pore diameter and applied field strengths. Both repulsive Weeks-Chandler-Anderson and attractive Lennard-Jones polymer-nanopore interaction were studied, attraction facilitates the translocation process by shortening the total translocation time and dramatically improve the capturing of polymer chain. The width of the translocation time distribution was found to decrease with increasing temperature, increasing field strength, and decreasing pore diameter.

  3. Conformation and translational diffusion of a xanthan polyelectrolyte chain: Brownian dynamics simulation and single molecule tracking

    NASA Astrophysics Data System (ADS)

    Chun, Myung-Suk; Kim, Chongyoup; Lee, Duck E.

    2009-05-01

    In our recent Brownian dynamics (BD) simulation study, the structure and dynamics of anionic polyelectrolyte xanthan in bulk solution as well as confined spaces of slitlike channel were examined by applying a coarse-grained model with nonlinear bead-spring discretization of a whole chain [J. Jeon and M.-S. Chun, J. Chem. Phys. 126, 154904 (2007)]. This model goes beyond other simulations as they did not consider both long-range electrostatic and hydrodynamic interactions between pairs of beads. Simulation parameters are obtained from the viscometric method of rheology data on the native and sonicated xanthan polysaccharides, which have a contour length less than 1μm . The size of the semiflexible polyelectrolyte can be well described by the wormlike chain model once the electrostatic effects are taken into account by the persistence length measured at a long length scale. For experimental verifications, single molecule visualization was performed on fluorescein-labeled xanthan using an inverted fluorescence microscope, and the motion of an individual molecule was quantified. Experimental results on the conformational changes in xanthan chain in the electrolyte solution have a reasonable trend to agree with the prediction by BD simulations. In the translational diffusion induced by the Debye screening effect, the simulation prediction reveals slightly higher values compared to those of our measurements, although it agrees with the literature data. Considering the experimental restrictions, our BD simulations are verified to model the single polyelectrolyte well.

  4. Experimental study of the stochastic heating of a single Brownian particle by charge fluctuations

    NASA Astrophysics Data System (ADS)

    Schmidt, Christian; Piel, Alexander

    2016-08-01

    The Brownian motion of a micro-particle, which is suspended in the sheath of a radio-frequency discharge, is studied by high-speed video microscopy. In this environment, stochastic heating by charge fluctuations is expected, which should lead to an anisotropic kinetic temperature of the particle with a preferential heating in the direction of the mean electric field in the sheath. The stochastic heating should become more effective at low gas pressures where cooling by the neutral gas becomes ineffective. Our refined experiments confirm the anisotropic heating and the temperature rise for diminishing pressure. Particle-in-cell simulations have guided us in modifying the gap width of the discharge and to specify the dependence of the plasma density on gas pressure as n i ∝ p 1 / 2 . Since the stochastic heating rate also depends on the life-time of charge fluctuations, a temperature scaling T kin ∝ p 3 / 2 results, which is in agreement with the experimental data. The experimental procedure to eliminate other spurious heating mechanisms is described in detail.

  5. From Random Walks to Brownian Motion, from Diffusion to Entropy: Statistical Principles in Introductory Physics

    NASA Astrophysics Data System (ADS)

    Reeves, Mark

    2014-03-01

    Entropy changes underlie the physics that dominates biological interactions. Indeed, introductory biology courses often begin with an exploration of the qualities of water that are important to living systems. However, one idea that is not explicitly addressed in most introductory physics or biology textbooks is dominant contribution of the entropy in driving important biological processes towards equilibrium. From diffusion to cell-membrane formation, to electrostatic binding in protein folding, to the functioning of nerve cells, entropic effects often act to counterbalance deterministic forces such as electrostatic attraction and in so doing, allow for effective molecular signaling. A small group of biology, biophysics and computer science faculty have worked together for the past five years to develop curricular modules (based on SCALEUP pedagogy) that enable students to create models of stochastic and deterministic processes. Our students are first-year engineering and science students in the calculus-based physics course and they are not expected to know biology beyond the high-school level. In our class, they learn to reduce seemingly complex biological processes and structures to be described by tractable models that include deterministic processes and simple probabilistic inference. The students test these models in simulations and in laboratory experiments that are biologically relevant. The students are challenged to bridge the gap between statistical parameterization of their data (mean and standard deviation) and simple model-building by inference. This allows the students to quantitatively describe realistic cellular processes such as diffusion, ionic transport, and ligand-receptor binding. Moreover, the students confront ``random'' forces and traditional forces in problems, simulations, and in laboratory exploration throughout the year-long course as they move from traditional kinematics through thermodynamics to electrostatic interactions. This talk will present a number of these exercises, with particular focus on the hands-on experiments done by the students, and will give examples of the tangible material that our students work with throughout the two-semester sequence of their course on introductory physics with a bio focus. Supported by NSF DUE.

  6. Newton's method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion.

    PubMed

    Leszczynski, Henryk; Wrzosek, Monika

    2017-02-01

    We consider nonlinear stochastic wave equations driven by one-dimensional white noise with respect to time. The existence of solutions is proved by means of Picard iterations. Next we apply Newton's method. Moreover, a second-order convergence in a probabilistic sense is demonstrated.

  7. An image encryption scheme based on three-dimensional Brownian motion and chaotic system

    NASA Astrophysics Data System (ADS)

    Chai, Xiu-Li; Gan, Zhi-Hua; Yuan, Ke; Lu, Yang; Chen, Yi-Ran

    2017-02-01

    Not Available Project supported by the National Natural Science Foundation of China (Grant Nos. 41571417 and 61305042), the National Science Foundation of the United States (Grant Nos. CNS-1253424 and ECCS-1202225), the Science and Technology Foundation of Henan Province, China (Grant No. 152102210048), the Foundation and Frontier Project of Henan Province, China (Grant No. 162300410196), China Postdoctoral Science Foundation (Grant No. 2016M602235), the Natural Science Foundation of Educational Committee of Henan Province, China (Grant No. 14A413015), and the Research Foundation of Henan University, China (Grant No. xxjc20140006).

  8. From local to hydrodynamic friction in Brownian motion: A multiparticle collision dynamics simulation study.

    PubMed

    Theers, Mario; Westphal, Elmar; Gompper, Gerhard; Winkler, Roland G

    2016-03-01

    The friction and diffusion coefficients of rigid spherical colloidal particles dissolved in a fluid are determined from velocity and force autocorrelation functions by mesoscale hydrodynamic simulations. Colloids with both slip and no-slip boundary conditions are considered, which are embedded in fluids modeled by multiparticle collision dynamics with and without angular momentum conservation. For no-slip boundary conditions, hydrodynamics yields the well-known Stokes law, while for slip boundary conditions the lack of angular momentum conservation leads to a reduction of the hydrodynamic friction coefficient compared to the classical result. The colloid diffusion coefficient is determined by integration of the velocity autocorrelation function, where the numerical result at shorter times is combined with the theoretical hydrodynamic expression for longer times. The suitability of this approach is confirmed by simulations of sedimenting colloids. In general, we find only minor deviations from the Stokes-Einstein relation, which even disappear for larger colloids. Importantly, for colloids with slip boundary conditions, our simulation results contradict the frequently assumed additivity of local and hydrodynamic diffusion coefficients.

  9. Littelmann path model for geometric crystals, Whittaker functions on Lie groups and Brownian motion

    NASA Astrophysics Data System (ADS)

    Chhaibi, Reda

    2013-02-01

    Generally speaking, this thesis focuses on the interplay between the representations of Lie groups and probability theory. It subdivides into essentially three parts. In a first rather algebraic part, we construct a path model for geometric crystals in the sense of Berenstein and Kazhdan, for complex semi-simple Lie groups. We will mainly describe the algebraic structure, its natural morphisms and parameterizations. The theory of total positivity will play a particularly important role. Then, we anticipate on the probabilistic part by exhibiting a canonical measure on geometric crystals. It uses as ingredients the superpotential for the flag manifold and a measure invariant under the crystal actions. The image measure under the weight map plays the role of Duistermaat-Heckman measure. Its Laplace transform defines Whittaker functions, providing an interesting formula for all Lie groups. Then it appears clearly that Whittaker functions are to geometric crystals, what characters are to combinatorial crystals. The Littlewood-Richardson rule is also exposed. Finally we present the probabilistic approach that allows to find the canonical measure. It is based on the fundamental idea that the Wiener measure will induce the adequate measure on the algebraic structures through the path model. In the last chapter, we show how our geometric model degenerates to the continuous classical Littelmann path model and thus recover known results. For example, the canonical measure on a geometric crystal of highest weight degenerates into a uniform measure on a polytope, and recovers the parameterizations of continuous crystals.

  10. Visualizing the Motion of Graphene Nanodrums.

    PubMed

    Davidovikj, Dejan; Slim, Jesse J; Cartamil-Bueno, Santiago J; van der Zant, Herre S J; Steeneken, Peter G; Venstra, Warner J

    2016-04-13

    Membranes of suspended two-dimensional materials show a large variability in mechanical properties, in part due to static and dynamic wrinkles. As a consequence, experiments typically show a multitude of nanomechanical resonance peaks, which make an unambiguous identification of the vibrational modes difficult. Here, we probe the motion of graphene nanodrum resonators with spatial resolution using a phase-sensitive interferometer. By simultaneously visualizing the local phase and amplitude of the driven motion, we show that unexplained spectral features represent split degenerate modes. When taking these into account, the resonance frequencies up to the eighth vibrational mode agree with theory. The corresponding displacement profiles, however, are remarkably different from theory, as small imperfections increasingly deform the nodal lines for the higher modes. The Brownian motion, which is used to calibrate the local displacement, exhibits a similar mode pattern. The experiments clarify the complicated dynamic behavior of suspended two-dimensional materials, which is crucial for reproducible fabrication and applications.

  11. Average hydrodynamic correction for the Brownian dynamics calculation of flocculation rates in concentrated dispersions

    NASA Astrophysics Data System (ADS)

    Urbina-Villalba, German; García-Sucre, Máximo; Toro-Mendoza, Jhoan

    2003-12-01

    In order to account for the hydrodynamic interaction (HI) between suspended particles in an average way, Honig et al. [J. Colloid Interface Sci. 36, 97 (1971)] and more recently Heyes [Mol. Phys. 87, 287 (1996)] proposed different analytical forms for the diffusion constant. While the formalism of Honig et al. strictly applies to a binary collision, the one from Heyes accounts for the dependence of the diffusion constant on the local concentration of particles. However, the analytical expression of the latter approach is more complex and depends on the particular characteristics of each system. Here we report a combined methodology, which incorporates the formula of Honig et al. at very short distances and a simple local volume-fraction correction at longer separations. As will be shown, the flocculation behavior calculated from Brownian dynamics simulations employing the present technique, is found to be similar to that of Batchelor’s tensor [J. Fluid. Mech. 74, 1 (1976); 119, 379 (1982)]. However, it corrects the anomalous coalescence found in concentrated systems as a result of the overestimation of many-body HI.

  12. A new analysis methodology for the motion of self-propelled particles and its application

    NASA Astrophysics Data System (ADS)

    Byun, Young-Moo; Lammert, Paul; Crespi, Vincent

    2011-03-01

    The self-propelled particle (SPP) on the microscale in the solution is a growing field of study, which has a potential to be used for nanomedicine and nanorobots. However, little detailed quantitative analysis on the motion of the SPP has been performed so far because its self-propelled motion is strongly coupled to Brownian motion, which makes the extraction of intrinsic propulsion mechanisms problematic, leading to inconsistent conclusions. Here, we present a novel way to decompose the motion of the SPP into self-propelled and Brownian components; accurate values for self-propulsion speed and diffusion coefficients of the SPP are obtained for the first time. Then, we apply our analysis methodology to ostensible chemotaxis of SPP, and reveal the actual (non-chemotactic) mechanism of the phenomenon, demonstrating that our analysis methodology is a powerful and reliable tool.

  13. Plate motion

    SciTech Connect

    Gordon, R.G. )

    1991-01-01

    The motion of tectonic plates on the earth is characterized in a critical review of U.S. research from the period 1987-1990. Topics addressed include the NUVEL-1 global model of current plate motions, diffuse plate boundaries and the oceanic lithosphere, the relation between plate motions and distributed deformations, accelerations and the steadiness of plate motions, the distribution of current Pacific-North America motion across western North America and its margin, plate reconstructions and their uncertainties, hotspots, and plate dynamics. A comprehensive bibliography is provided. 126 refs.

  14. Crystallization and melting of bacteria colonies and Brownian bugs.

    PubMed

    Ramos, Francisco; López, Cristóbal; Hernández-García, Emilio; Muñoz, Miguel A

    2008-02-01

    Motivated by the existence of remarkably ordered cluster arrays of bacteria colonies growing in Petri dishes and related problems, we study the spontaneous emergence of clustering and patterns in a simple nonequilibrium system: the individual-based interacting Brownian bug model. We map this discrete model into a continuous Langevin equation which is the starting point for our extensive numerical analyses. For the two-dimensional case we report on the spontaneous generation of localized clusters of activity as well as a melting-freezing transition from a disordered or isotropic phase to an ordered one characterized by hexagonal patterns. We study in detail the analogies and differences with the well-established Kosterlitz-Thouless-Halperin-Nelson-Young theory of equilibrium melting, as well as with another competing theory. For that, we study translational and orientational correlations and perform a careful defect analysis. We find a nonstandard one-stage, defect-mediated transition whose nature is only partially elucidated.

  15. Electric-field-induced rotation of Brownian metal nanowires.

    PubMed

    Arcenegui, Juan J; García-Sánchez, Pablo; Morgan, Hywel; Ramos, Antonio

    2013-09-01

    We describe the physical mechanism responsible for the rotation of Brownian metal nanowires suspended in an electrolyte exposed to a rotating electric field. The electric field interacts with the induced charge in the electrical double layer at the metal-electrolyte interface, causing rotation due to the torque on the induced dipole and to the induced-charge electro-osmotic flow around the particle. Experiments demonstrate that the primary driving mechanism is the former of these two. Our analysis contrasts with previous work describing the electrical manipulation of metallic particles with electric fields, which neglected the electrical double layer. Theoretical values for the rotation speed are calculated and good agreement with experiments is found.

  16. Brownian ratchets: How stronger thermal noise can reduce diffusion

    NASA Astrophysics Data System (ADS)

    Spiechowicz, Jakub; Kostur, Marcin; Łuczka, Jerzy

    2017-02-01

    We study diffusion properties of an inertial Brownian motor moving on a ratchet substrate, i.e., a periodic structure with broken reflection symmetry. The motor is driven by an unbiased time-periodic symmetric force that takes the system out of thermal equilibrium. For selected parameter sets, the system is in a non-chaotic regime in which we can identify a non-monotonic dependence of the diffusion coefficient on temperature: for low temperature, it initially increases as the temperature grows, passes through its local maximum, next starts to diminish reaching its local minimum, and finally it monotonically increases in accordance with the Einstein linear relation. Particularly interesting is the temperature interval in which diffusion is suppressed by the thermal noise, and we explain this effect in terms of transition rates of a three-state stochastic model.

  17. Brownian dynamics simulation of fission yeast mitotic spindle formation

    NASA Astrophysics Data System (ADS)

    Edelmaier, Christopher

    2014-03-01

    The mitotic spindle segregates chromosomes during mitosis. The dynamics that establish bipolar spindle formation are not well understood. We have developed a computational model of fission-yeast mitotic spindle formation using Brownian dynamics and kinetic Monte Carlo methods. Our model includes rigid, dynamic microtubules, a spherical nuclear envelope, spindle pole bodies anchored in the nuclear envelope, and crosslinkers and crosslinking motor proteins. Crosslinkers and crosslinking motor proteins attach and detach in a grand canonical ensemble, and exert forces and torques on the attached microtubules. We have modeled increased affinity for crosslinking motor attachment to antiparallel microtubule pairs, and stabilization of microtubules in the interpolar bundle. We study parameters controlling the stability of the interpolar bundle and assembly of a bipolar spindle from initially adjacent spindle-pole bodies.

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

    NASA Astrophysics Data System (ADS)

    Salgado-García, R.

    2016-07-01

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

  19. Brownian dynamics simulation of sickle hemoglobin bundle formation

    NASA Astrophysics Data System (ADS)

    Liu, Ya; Gunton, James; Chakrabarti, Amit

    2010-03-01

    The physical properties of biopolymer fibers, such as their stability and degree of aggregation, are implicated in many diseases, including sickle cell anemia. The natural chirality of protofilaments plays a crucial role in the formation of sickle hemoglobin fiber which leads to the permanent blockage of microvessels. We use Brownian dynamics to investigate the kinetics of fiber aggregation. The geometrical helical structure and chirality of the filaments are modeled by anisotropic patch-like interactions. We present the kinetics of fiber formation and study the possibility of a finite critical fiber bundle size. We compare our results with various experimental and theoretical results. This work is supported by grants from the NSF and the G. Harold and Leila Y. Mathers Foundation.

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

    SciTech Connect

    Pan, Y.; Powell, C. V.; Balocco, C.; Song, A. M.

    2014-12-22

    We experimentally demonstrated the operation of a rectenna for harvesting thermal (blackbody) radiation and converting it into dc electric power. The device integrates an ultrafast rectifier, the self-switching nanodiode, with a wideband log-periodic spiral microantenna. The radiation from the thermal source drives the rectenna out of thermal equilibrium, permitting the rectification of the excess thermal fluctuations from the antenna. The power conversion efficiency increases with the source temperatures up to 0.02% at 973 K. The low efficiency is attributed mainly to the impedance mismatch between antenna and rectifier, and partially to the large field of view of the antenna. Our device not only opens a potential solution for harvesting thermal energy but also provides a platform for experimenting with Brownian ratchets.

  1. Processing Motion Signals in Complex Environments

    NASA Technical Reports Server (NTRS)

    Verghese, Preeti

    2000-01-01

    Motion information is critical for human locomotion and scene segmentation. Currently we have excellent neurophysiological models that are able to predict human detection and discrimination of local signals. Local motion signals are insufficient by themselves to guide human locomotion and to provide information about depth, object boundaries and surface structure. My research is aimed at understanding the mechanisms underlying the combination of motion signals across space and time. A target moving on an extended trajectory amidst noise dots in Brownian motion is much more detectable than the sum of signals generated by independent motion energy units responding to the trajectory segments. This result suggests that facilitation occurs between motion units tuned to similar directions, lying along the trajectory path. We investigated whether the interaction between local motion units along the motion direction is mediated by contrast. One possibility is that contrast-driven signals from motion units early in the trajectory sequence are added to signals in subsequent units. If this were the case, then units later in the sequence would have a larger signal than those earlier in the sequence. To test this possibility, we compared contrast discrimination thresholds for the first and third patches of a triplet of sequentially presented Gabor patches, aligned along the motion direction. According to this simple additive model, contrast increment thresholds for the third patch should be higher than thresholds for the first patch.The lack of a measurable effect on contrast thresholds for these various manipulations suggests that the pooling of signals along a trajectory is not mediated by contrast-driven signals. Instead, these results are consistent with models that propose that the facilitation of trajectory signals is achieved by a second-level network that chooses the strongest local motion signals and combines them if they occur in a spatio-temporal sequence consistent

  2. First passage time of multiple Brownian particles on networks with applications

    NASA Astrophysics Data System (ADS)

    Wang, Shao-Ping; Pei, Wen-Jiang

    2008-07-01

    In this article, we study some theoretical and technological problems with relation to multiple Brownian particles on networks. We are especially interested in the behavior of the first arriving Brownian particle when all the Brownian particles start out from the source s simultaneously and head to the destination h randomly. We analyze the first passage time (FPT) Y(z) and the mean first passage time (MFPT) of multiple Brownian particles on complex networks. Equations of Y(z) and are obtained. On a variety of commonly encountered networks, we observe first passage properties of multiple Brownian particles from different aspects. We find that drops substantially when particle number z increases at the first stage, and converges to d, the distance between the source and the destination when z→∞. The distribution of FPT Prob{Y(z)=t},t=0,1,2,… is also analyzed in these networks. The distribution curve peaks up towards t=d when z increases. Consequently, if particle number z is set appropriately large, the first arriving Brownian particle will go along the shortest or near shortest paths between the source and the destination with high probability. Simulations confirm our analysis. Based on theoretical studies, we also investigate some practical problems using multiple Brownian particles, such as communication on P2P networks, optimal routing in small world networks, phenomenon of asymmetry in scale-free networks, information spreading in social networks, pervasion of viruses on the Internet, and so on. Our analytic and experimental results on multiple Brownian particles provide useful evidence for further understanding and properly tackling these problems.

  3. Understanding Multiplication of Fractions.

    ERIC Educational Resources Information Center

    Sweetland, Robert D.

    1984-01-01

    Discussed the use of Cuisenaire rods in teaching the multiplication of fractions. Considers whole number times proper fraction, proper fraction multiplied by proper fraction, mixed number times proper fraction, and mixed fraction multiplied by mixed fractions. (JN)

  4. Brownian Dynamics Simulation of Protein Solutions: Structural and Dynamical Properties

    PubMed Central

    Mereghetti, Paolo; Gabdoulline, Razif R.; Wade, Rebecca C.

    2010-01-01

    The study of solutions of biomacromolecules provides an important basis for understanding the behavior of many fundamental cellular processes, such as protein folding, self-assembly, biochemical reactions, and signal transduction. Here, we describe a Brownian dynamics simulation procedure and its validation for the study of the dynamic and structural properties of protein solutions. In the model used, the proteins are treated as atomically detailed rigid bodies moving in a continuum solvent. The protein-protein interaction forces are described by the sum of electrostatic interaction, electrostatic desolvation, nonpolar desolvation, and soft-core repulsion terms. The linearized Poisson-Boltzmann equation is solved to compute electrostatic terms. Simulations of homogeneous solutions of three different proteins with varying concentrations, pH, and ionic strength were performed. The results were compared to experimental data and theoretical values in terms of long-time self-diffusion coefficients, second virial coefficients, and structure factors. The results agree with the experimental trends and, in many cases, experimental values are reproduced quantitatively. There are no parameters specific to certain protein types in the interaction model, and hence the model should be applicable to the simulation of the behavior of mixtures of macromolecules in cell-like crowded environments. PMID:21112303

  5. Entanglement of Semiflexiible Polymers: A Brownian Dynamics Study

    NASA Astrophysics Data System (ADS)

    Ramanathan, Shriram

    2005-03-01

    We report extensive Brownian dynamics simulations of very tightly entangled solutions of semiflexible rods, of length L comparable to their persistence length Lp, at concentrations comparable to those in recent experiments on Fd-virus and filamentous actin. We find a clear crossover with increasing number concentration c from a regime of loosely entangled rods, in which rotational diffusion is hindered by topological constraints but transverse bending fluctuations are not, to a tightly entangled regime in which bending fluctuations are also restricted, and can relax only by reptation along a wormlike tube. This crossover occurs at a dimensionless concentration c^**L^3 ˜500 for chains with L = Lp. The tube radius Re is found to depend upon c and Lp with the predicted scaling relation Rec-3/5 Lp-1/5 for c > c^**. The dynamic modulus G(t) has been obtained from simulations of the relaxation of stress after a small amplitude step extension of the simulation unit cell. An elastic plateau in G(t) that is absent at lower concentrations also appears for c >=c^**.

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

    NASA Astrophysics Data System (ADS)

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

    2016-08-01

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

  7. Fractional variational calculus in terms of Riesz fractional derivatives

    NASA Astrophysics Data System (ADS)

    Agrawal, O. P.

    2007-06-01

    This paper presents extensions of traditional calculus of variations for systems containing Riesz fractional derivatives (RFDs). Specifically, we present generalized Euler-Lagrange equations and the transversality conditions for fractional variational problems (FVPs) defined in terms of RFDs. We consider two problems, a simple FVP and an FVP of Lagrange. Results of the first problem are extended to problems containing multiple fractional derivatives, functions and parameters, and to unspecified boundary conditions. For the second problem, we present Lagrange-type multiplier rules. For both problems, we develop the Euler-Lagrange-type necessary conditions which must be satisfied for the given functional to be extremum. Problems are considered to demonstrate applications of the formulations. Explicitly, we introduce fractional momenta, fractional Hamiltonian, fractional Hamilton equations of motion, fractional field theory and fractional optimal control. The formulations presented and the resulting equations are similar to the formulations for FVPs given in Agrawal (2002 J. Math. Anal. Appl. 272 368, 2006 J. Phys. A: Math. Gen. 39 10375) and to those that appear in the field of classical calculus of variations. These formulations are simple and can be extended to other problems in the field of fractional calculus of variations.

  8. Mystery Fractions

    ERIC Educational Resources Information Center

    Bhattacharyya, Sonalee; Namakshi, Nama; Zunker, Christina; Warshauer, Hiroko K.; Warshauer, Max

    2016-01-01

    Making math more engaging for students is a challenge that every teacher faces on a daily basis. These authors write that they are constantly searching for rich problem-solving tasks that cover the necessary content, develop critical-thinking skills, and engage student interest. The Mystery Fraction activity provided here focuses on a key number…

  9. Pitch Fractionation.

    DTIC Science & Technology

    1981-12-15

    13 3. Solvent Fractionation Experiments .................................... 15 4. Fourier Transform Infrared Spectra for A240 Petrolem Pitch AG 12...34 and Mesophase Pitch AG 164B ............................... 21 5. Fourier Transform Infrared Spectra ................................... 23 6...compared by Fourier transform infrared (FTIR) analysis using a Digilab Model FTS 14 spectrophotometer (Rockwell International, Anaheim, California

  10. Circular Motion.

    ERIC Educational Resources Information Center

    Lee, Paul D.

    1995-01-01

    Provides a period-long activity using battery powered cars rolling in a circular motion on a tile floor. Students measure the time and distance as the car moves to derive the equation for centripetal acceleration. (MVL)

  11. Three-dimensional Brownian diffusion of rod-like macromolecules in the presence of randomly distributed spherical obstacles: molecular dynamics simulation.

    PubMed

    Sakha, Farzaneh; Fazli, Hossein

    2010-12-21

    Brownian diffusion of rod-like polymers in the presence of randomly distributed spherical obstacles is studied using molecular dynamics simulations. It is observed that dependence of the reduced diffusion coefficient of these macromolecules on the available volume fraction can be described reasonably by a power law function. Despite the case of obstructed diffusion of flexible polymers in which reduced diffusion coefficient has a weak dependence on the polymer length, this dependence is noticeably strong in the case of rod-like polymers. Diffusion of these macromolecules in the presence of obstacles is observed that is anomalous at short time scales and normal at long times. Duration time of the anomalous diffusion regime is found that increases very rapidly with increasing both the polymer length and the obstructed volume fraction. Dynamics of diffusion of these polymers is observed that crosses over from Rouse to reptation type with increasing the density of obstacles.

  12. Permeation of ions across the potassium channel: Brownian dynamics studies.

    PubMed

    Chung, S H; Allen, T W; Hoyles, M; Kuyucak, S

    1999-11-01

    The physical mechanisms underlying the transport of ions across a model potassium channel are described. The shape of the model channel corresponds closely to that deduced from crystallography. From electrostatic calculations, we show that an ion permeating the channel, in the absence of any residual charges, encounters an insurmountable energy barrier arising from induced surface charges. Carbonyl groups along the selectivity filter, helix dipoles near the oval chamber, and mouth dipoles near the channel entrances together transform the energy barrier into a deep energy well. Two ions are attracted to this well, and their presence in the channel permits ions to diffuse across it under the influence of an electric field. Using Brownian dynamics simulations, we determine the magnitude of currents flowing across the channel under various conditions. The conductance increases with increasing dipole strength and reaches its maximum rapidly; a further increase in dipole strength causes a steady decrease in the channel conductance. The current also decreases systematically when the effective dielectric constant of the channel is lowered. The conductance with the optimal choice of dipoles reproduces the experimental value when the dielectric constant of the channel is assumed to be 60. The current-voltage relationship obtained with symmetrical solutions is linear when the applied potential is less than approximately 100 mV but deviates from Ohm's law at a higher applied potential. The reversal potentials obtained with asymmetrical solutions are in agreement with those predicted by the Nernst equation. The conductance exhibits the saturation property observed experimentally. We discuss the implications of these findings for the transport of ions across the potassium channels and membrane channels in general.

  13. Modeling diverse range of potassium channels with Brownian dynamics.

    PubMed Central

    Chung, Shin-Ho; Allen, Toby W; Kuyucak, Serdar

    2002-01-01

    Using the experimentally determined KcsA structure as a template, we propose a plausible explanation for the diversity of potassium channels seen in nature. A simplified model of KcsA is constructed from its atomic resolution structure by smoothing out the protein-water boundary and representing the atoms forming the channel protein as a homogeneous, low dielectric medium. The properties of the simplified and atomic-detail models, deduced from electrostatic calculations and Brownian dynamics simulations, are shown to be qualitatively similar. We then study how the current flowing across the simplified model channel changes as the shape of the intrapore region is modified. This is achieved by increasing the radius of the intracellular pore systematically from 1.5 to 5 A while leaving the dimensions of the selectivity filter and inner chamber unaltered. The strengths of the dipoles located near the entrances of the channel, the carbonyl groups lining the selectivity filter, and the helix macrodipoles are kept constant. The channel conductance increases steadily as the radius of the intracellular pore is increased. The rate-limiting step for both the outward and inward current is the time it takes for an ion to cross the residual energy barrier located in the intrapore region. The current-voltage relationship obtained with symmetrical solutions is linear when the applied potential is less than approximately 100 mV but deviates slightly from Ohm's law at higher applied potentials. The nonlinearity in the current-voltage curve becomes less pronounced as the radius of the intracellular pore is increased. When the strengths of the dipoles near the intracellular entrance are reduced, the channel shows a pronounced inward rectification. Finally, the conductance exhibits the saturation property observed experimentally. We discuss the implications of these findings on the transport of ions across the potassium channels and membrane channels in general. PMID:12080118

  14. A Brownian Dynamics Approach to ESR Line Shape Calculations

    NASA Astrophysics Data System (ADS)

    Wright, Matthew P.

    The work presented in this thesis uses a Monte Carlo technique to simulate spectra for 14N spin-labels and 15N spin labels. The algorithm presented here also has the capability to produce simulated spectra for any admixture of 14N and 15N. The algorithm makes use of `iterative loops' to model Brownian rotational diffusion and for the repeated evaluation of the spectral correlation function (relaxation function). The method described in this work starts with a derivation of an angular dependent "Spin Hamiltonian" that when diagonalized yields orientation dependent eigenvalues. The resulting eigenvalue equations are later used to calculate the energy trajectories of a nitroxide spin-label undergoing rotational diffusion. The energy trajectories are then used to evaluate the relaxation function. The absorption spectrum is obtained by applying a Fourier transform to the relaxation function. However, the application of the Fourier transform to the relaxation function produces "leakage" effects that manifest as spurious peaks in the first derivative spectrum. To counter "leakage" effects a data windowing function was applied to the relaxation function prior to the Fourier transform. In order to test the accuracy of this algorithm, simulated spectra for 14N, and 15N spin labels diffusing in a glycerol-water mixture as well as a 14N-15N admixture diffusing in the same solvent were produced and compared to experimental spectra. An attempt to quantify the level of agreement was made by calculating the mean square residual of the simulated and experimental spectra. The main spectral features were reproduced with reasonable fidelity by the simulated spectra.

  15. Effects of Matrix Viscoelasticity on Rheology of Dilute and Semi-Dilute Suspensions of Non Brownian Rigid Spheres

    NASA Astrophysics Data System (ADS)

    Grizzuti, Nino; Pasquino, Rossana

    2008-07-01

    The rheology of non-Brownian, inertialess rigid spheres suspended in viscoelastic fluids was investigated in the dilute and semi-dilute regimes (volume fractions up to 10%), where interparticle interactions become increasingly relevant. PMMA spherical particles were suspended in viscoelastic Polydimethylsiloxanes (PDMS). A Newtonian fluid (Polyisobutilene, PIB) was also used as a reference system. As expected, both the viscosity and the viscoelastic moduli increased with increasing solid volume fraction. The rheological parameters showed a simple scaling behaviour when their normalized values (with respect to the pure fluid) were considered. Viscosity and moduli were found to be independent upon shear rate and frequency, respectively. Following Batchelor's approach for non-dilute Newtonian suspensions, a second order polynomial dependency for the rheological properties was assumed. While the Newtonian reference fluid was found to obey well Batchelor's theoretical predictions, the viscoelastic suspensions showed more pronounced deviations from the linear dilute behavior, resulting in a second order polynomial coefficient substantially larger than that predicted by Batchelor for Newtonian systems. It was also found that the same concentration dependence was followed by both elastic and loss modulus.

  16. Fraction Reduction through Continued Fractions

    ERIC Educational Resources Information Center

    Carley, Holly

    2011-01-01

    This article presents a method of reducing fractions without factoring. The ideas presented may be useful as a project for motivated students in an undergraduate number theory course. The discussion is related to the Euclidean Algorithm and its variations may lead to projects or early examples involving efficiency of an algorithm.

  17. Motion contrast using optical coherence tomography

    NASA Astrophysics Data System (ADS)

    Fingler, Jeffrey Paul

    Diagnosis of ophthalmic diseases like age-related macular degeneration is very important for treatment of the disease as well as the development of future treatments. Optical coherence tomography (OCT) is an optical interference technique which can measure the three-dimensional structural information of the reflecting layers within a sample. In retinal imaging, OCT is used as the primary diagnostic tool for structural abnormalities such as retinal holes and detachments. The contrast within the images of this technique is based upon reflectivity changes from different regions of the retina. This thesis demonstrates the developments of methods used to produce additional contrast to the structural OCT images based on the tiny fluctuations of motion experienced by the mobile scatterers within a sample. Motion contrast was observed for motions smaller than 50 nm in images of a variety of samples. Initial contrast method demonstrations used Brownian motion differences to separate regions of a mobile Intralipid solution from a static agarose gel, chosen in concentration to minimize reflectivity contrast. Zebrafish embryos in the range of 3-4 days post fertilization were imaged using several motion contrast methods to determine the capabilities of identifying regions of vascular flow. Vasculature identification was demonstrated in zebrafish for blood vessels of all orientations as small as 10 microns in diameter. Mouse retinal imaging utilized the same motion contrast methods to determine the contrast capabilities for motions associated with vasculature within the retina. Improved contrast imaging techniques demonstrated comparable images to fluorescein angiography, the gold standard of retinal vascular imaging. Future studies can improve the demonstrated contrast analysis techniques and apply them towards human retinal motion contrast imaging for ophthalmic diagnostic purposes.

  18. Isotope fractionation

    NASA Astrophysics Data System (ADS)

    Bell, Peter M.

    A rash of new controversy has emerged around the subject of mass-independent isotope fractionation effects, particularly in the case of the oxygen isotopes. To be sure, the controversy has been around for awhile, but it has been given new impetus by the results of a recent study by Mark H. Thiemens and John E. Heidenreich III of the University of California, San Diego (Science, March 4, 1983).Gustav Arrhenius has been trying to convince the planetary science community that chemical effects in isotope fractionation processes could explain observations in meteorites that appear to be outside of the traditionally understood mass-dependent fractionations (G. Arrhenius, J . L. McCrumb, and N. F. Friedman, Astrophys. Space Sci, 65, 297, 1974). Robert Clayton had made the basic observations of oxygen in carbonaceous chondrites that the slope of the δ17 versus δ18 line was 1 instead of the slope of ½ characteristic of terrestrial rocks and lunar samples (Ann. Rev. Nucl. Part. Sci., 28, 501, 1978). The mass-independent effects were ascribed to the apparent contribution of an ancient presolar system component of O16.

  19. A fractional Dirac equation and its solution

    NASA Astrophysics Data System (ADS)

    Muslih, Sami I.; Agrawal, Om P.; Baleanu, Dumitru

    2010-02-01

    This paper presents a fractional Dirac equation and its solution. The fractional Dirac equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives. By applying the variational principle to a fractional action S, we obtain the fractional Euler-Lagrange equations of motion. We present a Lagrangian and a Hamiltonian for the fractional Dirac equation of order α. We also use a fractional Klein-Gordon equation to obtain the fractional Dirac equation which is the same as that obtained using the fractional variational principle. Eigensolutions of this equation are presented which follow the same approach as that for the solution of the standard Dirac equation. We also provide expressions for the path integral quantization for the fractional Dirac field which, in the limit α → 1, approaches to the path integral for the regular Dirac field. It is hoped that the fractional Dirac equation and the path integral quantization of the fractional field will allow further development of fractional relativistic quantum mechanics.

  20. Real-time monitoring and visualization of the multi-dimensional motion of an anisotropic nanoparticle.

    PubMed

    Go, Gi-Hyun; Heo, Seungjin; Cho, Jong-Hoi; Yoo, Yang-Seok; Kim, MinKwan; Park, Chung-Hyun; Cho, Yong-Hoon

    2017-03-08

    As interest in anisotropic particles has increased in various research fields, methods of tracking such particles have become increasingly desirable. Here, we present a new and intuitive method to monitor the Brownian motion of a nanowire, which can construct and visualize multi-dimensional motion of a nanowire confined in an optical trap, using a dual particle tracking system. We measured the isolated angular fluctuations and translational motion of the nanowire in the optical trap, and determined its physical properties, such as stiffness and torque constants, depending on laser power and polarization direction. This has wide implications in nanoscience and nanotechnology with levitated anisotropic nanoparticles.

  1. Real-time monitoring and visualization of the multi-dimensional motion of an anisotropic nanoparticle

    PubMed Central

    Go, Gi-Hyun; Heo, Seungjin; Cho, Jong-Hoi; Yoo, Yang-Seok; Kim, MinKwan; Park, Chung-Hyun; Cho, Yong-Hoon

    2017-01-01

    As interest in anisotropic particles has increased in various research fields, methods of tracking such particles have become increasingly desirable. Here, we present a new and intuitive method to monitor the Brownian motion of a nanowire, which can construct and visualize multi-dimensional motion of a nanowire confined in an optical trap, using a dual particle tracking system. We measured the isolated angular fluctuations and translational motion of the nanowire in the optical trap, and determined its physical properties, such as stiffness and torque constants, depending on laser power and polarization direction. This has wide implications in nanoscience and nanotechnology with levitated anisotropic nanoparticles. PMID:28272445

  2. Real-time monitoring and visualization of the multi-dimensional motion of an anisotropic nanoparticle

    NASA Astrophysics Data System (ADS)

    Go, Gi-Hyun; Heo, Seungjin; Cho, Jong-Hoi; Yoo, Yang-Seok; Kim, Minkwan; Park, Chung-Hyun; Cho, Yong-Hoon

    2017-03-01

    As interest in anisotropic particles has increased in various research fields, methods of tracking such particles have become increasingly desirable. Here, we present a new and intuitive method to monitor the Brownian motion of a nanowire, which can construct and visualize multi-dimensional motion of a nanowire confined in an optical trap, using a dual particle tracking system. We measured the isolated angular fluctuations and translational motion of the nanowire in the optical trap, and determined its physical properties, such as stiffness and torque constants, depending on laser power and polarization direction. This has wide implications in nanoscience and nanotechnology with levitated anisotropic nanoparticles.

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

    NASA Astrophysics Data System (ADS)

    Zhang, Yunxin

    2009-07-01

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

  4. A Fractional Variational Approach to the Fractional Basset-Type Equation

    NASA Astrophysics Data System (ADS)

    Baleanu, Dumitru; Garra, Roberto; Petras, Ivo

    2013-08-01

    In this paper we discuss an application of fractional variational calculus to the Basset-type fractional equations. It is well known that the unsteady motion of a sphere immersed in a Stokes fluid is described by an integro-differential equation involving derivative of real order. Here we study the inverse problem, i.e. we consider the problem from a Lagrangian point of view in the framework of fractional variational calculus. In this way we find an application of fractional variational methods to a classical physical model, finding a Basset-type fractional equation starting from a Lagrangian depending on derivatives of fractional order.

  5. Motion Sickness

    MedlinePlus

    ... but it is more common in children, pregnant women, and people taking certain medicines. Motion sickness can start suddenly, with a queasy feeling and cold sweats. It can then lead to dizziness and nausea and vomiting. Your brain senses movement by getting signals from your inner ears, eyes, ...

  6. Design of a fractional order PID controller using GBMO algorithm for load-frequency control with governor saturation consideration.

    PubMed

    Zamani, Abbasali; Barakati, S Masoud; Yousofi-Darmian, Saeed

    2016-09-01

    Load-frequency control is one of the most important issues in power system operation. In this paper, a Fractional Order PID (FOPID) controller based on Gases Brownian Motion Optimization (GBMO) is used in order to mitigate frequency and exchanged power deviation in two-area power system with considering governor saturation limit. In a FOPID controller derivative and integrator parts have non-integer orders which should be determined by designer. FOPID controller has more flexibility than PID controller. The GBMO algorithm is a recently introduced search method that has suitable accuracy and convergence rate. Thus, this paper uses the advantages of FOPID controller as well as GBMO algorithm to solve load-frequency control. However, computational load will higher than conventional controllers due to more complexity of design procedure. Also, a GBMO based fuzzy controller is designed and analyzed in detail. The performance of the proposed controller in time domain and its robustness are verified according to comparison with other controllers like GBMO based fuzzy controller and PI controller that used for load-frequency control system in confronting with model parameters variations.

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

    SciTech Connect

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

    2015-03-21

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

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

    PubMed

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

    2015-03-21

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

  9. Nonequilibrium statistical mechanics of the heat bath for two Brownian particles.

    PubMed

    De Bacco, Caterina; Baldovin, Fulvio; Orlandini, Enzo; Sekimoto, Ken

    2014-05-09

    We propose a new look at the heat bath for two Brownian particles, in which the heat bath as a "system" is both perturbed and sensed by the Brownian particles. Nonlocal thermal fluctuations give rise to bath-mediated static forces between the particles. Based on the general sum rule of the linear response theory, we derive an explicit relation linking these forces to the friction kernel describing the particles' dynamics. The relation is analytically confirmed in the case of two solvable models and could be experimentally challenged. Our results point out that the inclusion of the environment as a part of the whole system is important for micron- or nanoscale physics.

  10. Stochastic electrodynamics with particle structure Part I: Zero-point induced Brownian behavior

    NASA Astrophysics Data System (ADS)

    Rueda, A.

    1993-02-01

    If ordinary views on particle structure are introduced in a simple classical particle model in replacement of the point particles of standard use in stochastic electrodynamics, it can be shown that an internal Zitterbewegung induced by the zero-point field background gives rise to a Brownian movement for the whole particle with a diffusion constant of the form D = ħ/2mD , where mD is a modeldependent mass. Since the days of Madeleung and Fuhr brownian behaviour has often been associated with quantization. We discuss this from the viewpoint of stochastic electrodynamics.

  11. MHD Mixed Convective Peristaltic Motion of Nanofluid with Joule Heating and Thermophoresis Effects

    PubMed Central

    Shehzad, Sabir Ali; Abbasi, Fahad Munir; Hayat, Tasawar; Alsaadi, Fuad

    2014-01-01

    The primary objective of present investigation is to introduce the novel aspect of thermophoresis in the mixed convective peristaltic transport of viscous nanofluid. Viscous dissipation and Joule heating are also taken into account. Problem is modeled using the lubrication approach. Resulting system of equations is solved numerically. Effects of sundry parameters on the velocity, temperature, concentration of nanoparticles and heat and mass transfer rates at the wall are studied through graphs. It is noted that the concentration of nanoparticles near the boundaries is enhanced for larger thermophoresis parameter. However reverse situation is observed for an increase in the value of Brownian motion parameter. Further, the mass transfer rate at the wall significantly decreases when Brownian motion parameter is assigned higher values. PMID:25391147

  12. MHD mixed convective peristaltic motion of nanofluid with Joule heating and thermophoresis effects.

    PubMed

    Shehzad, Sabir Ali; Abbasi, Fahad Munir; Hayat, Tasawar; Alsaadi, Fuad

    2014-01-01

    The primary objective of present investigation is to introduce the novel aspect of thermophoresis in the mixed convective peristaltic transport of viscous nanofluid. Viscous dissipation and Joule heating are also taken into account. Problem is modeled using the lubrication approach. Resulting system of equations is solved numerically. Effects of sundry parameters on the velocity, temperature, concentration of nanoparticles and heat and mass transfer rates at the wall are studied through graphs. It is noted that the concentration of nanoparticles near the boundaries is enhanced for larger thermophoresis parameter. However reverse situation is observed for an increase in the value of Brownian motion parameter. Further, the mass transfer rate at the wall significantly decreases when Brownian motion parameter is assigned higher values.

  13. Stochastic thermodynamics with a Brownian particle in an optical trap (Presentation Recording)

    NASA Astrophysics Data System (ADS)

    Martinez, Ignacio A.; Roldán, Édgar; Dinis, Luis; Mestres, Pau; Parrondo, Juan M. R.; Rica, Raúl A.

    2015-08-01

    Stochastic thermodynamics [1,2] is a recently developed framework to deal with the thermodynamics at the microscope, where thermal fluctuations strongly influence their behaviour. Typical such systems are colloids and biomolecules or cells. These thermal fluctuations do not only lead to Brownian motion, but to a continuous and unavoidable heat exchange between the suspending medium and the particles, leading to a very interesting phenomenology. In order to explore such phenomenology and to test theoretical results obtained from stochastic thermodynamics, we developed an "experimental simulator" of thermodynamic devices in the microscale with an optically trapped bead that is subject to an external noise that mimics a controllable thermal bath. The noise is applied by means of electric fields acting on the charge of the trapped particle. In this talk, I will present some of the results we obtained with this simulator, demonstrating excellent control over the effective temperature of the system and a control parameter. This allows us to perform a variety of equilibrium and non-equilibrium thermodynamic processes [3-5]. In particular, we were able to realize microadiabatic processes, where no heat is exchanged on average between the particle and the medium [6]. This achievement allowed us to implement a Carnot microengine as a concatenation of isothermal and adiabatic processes [7], whose theoretical study is playing a key role in the foundations of stochastic thermodynamics. References [1] K Sekimoto; Lecture Notes in Physics (Springer, Berlin, 2010), Vol. 799. [2] U Seifert; Rep. Prog. Phys. 75 (2012) 126001 [3] IA Martínez, E Roldan, JMR Parrondo, D Petrov; Phys. Rev. E 87 (2013) 032159 [4] É Roldán, IA Martínez, L Dinis, RA Rica; Appl. Phys. Lett. 104 (2014) 234103 [5] P Mestres, IA Martinez, A Ortiz-Ambriz, RA Rica, E Roldan; Phys. Rev. E 90 (2014) 032116 [6] IA Martínez, E Roldan, L Dinis, D Petrov, RA Rica; Phys. Rev. Lett. (2015) In press [7] IA Martinez

  14. Anti-Brownian ELectrokinetic (ABEL) trapping of single β2-adrenergic receptors in the absence and presence of agonist

    NASA Astrophysics Data System (ADS)

    Bockenhauer, Samuel; Fuerstenberg, Alexandre; Yao, Xiao Jie; Kobilka, Brian K.; Moerner, W. E.

    2012-02-01

    The ABEL trap allows trapping of single biomolecules in solution for extended observation without immobilization. The essential idea combines fluorescence-based position estimation with fast electrokinetic feedback in a microfluidic geometry to counter the Brownian motion of a single nanoscale object, hence maintaining its position in the field of view for hundreds of milliseconds to seconds. Such prolonged observation of single proteins allows access to slow dynamics, as probed by any available photophysical observables. We have used the ABEL trap to study conformational dynamics of the β2-adrenergic receptor, a key G-protein coupled receptor and drug target, in the absence and presence of agonist. A single environment-sensitive dye reports on the receptor microenvironment, providing a real-time readout of conformational change for each trapped receptor. The focus of this paper will be a quantitative comparison of the ligandfree and agonist-bound receptor data from our ABEL trap experiments. We observe a small but clearly detectable shift in conformational equilibria and a lengthening of fluctuation timescales upon binding of agonist. In order to quantify the shift in state distributions and timescales, we apply nonparametric statistical tests to place error bounds on the resulting single-molecule distributions.

  15. Brownian cluster dynamics with short range patchy interactions: Its application to polymers and step-growth polymerization

    NASA Astrophysics Data System (ADS)

    Prabhu, A.; Babu, S. B.; Dolado, J. S.; Gimel, J.-C.

    2014-07-01

    We present a novel simulation technique derived from Brownian cluster dynamics used so far to study the isotropic colloidal aggregation. It now implements the classical Kern-Frenkel potential to describe patchy interactions between particles. This technique gives access to static properties, dynamics and kinetics of the system, even far from the equilibrium. Particle thermal motions are modeled using billions of independent small random translations and rotations, constrained by the excluded volume and the connectivity. This algorithm, applied to a single polymer chain leads to correct static and dynamic properties, in the framework where hydrodynamic interactions are ignored. By varying patch angles, various local chain flexibilities can be obtained. We have used this new algorithm to model step-growth polymerization under various solvent qualities. The polymerization reaction is modeled by an irreversible aggregation between patches while an isotropic finite square-well potential is superimposed to mimic the solvent quality. In bad solvent conditions, a competition between a phase separation (due to the isotropic interaction) and polymerization (due to patches) occurs. Surprisingly, an arrested network with a very peculiar structure appears. It is made of strands and nodes. Strands gather few stretched chains that dip into entangled globular nodes. These nodes act as reticulation points between the strands. The system is kinetically driven and we observe a trapped arrested structure. That demonstrates one of the strengths of this new simulation technique. It can give valuable insights about mechanisms that could be involved in the formation of stranded gels.

  16. Salt effects on the structure and internal dynamics of superhelical DNAs studied by light scattering and Brownian dynamics.

    PubMed Central

    Hammermann, M; Steinmaier, C; Merlitz, H; Kapp, U; Waldeck, W; Chirico, G; Langowski, J

    1997-01-01

    Using laser light scattering, we have measured the static and dynamic structure factor of two different superhelical DNAs, p1868 (1868 bp) and simian virus 40 (SV40) (5243 bp), in dilute aqueous solution at salt concentrations between 1 mM and 3 M NaCl. For both DNA molecules, Brownian dynamics (BD) simulations were also performed, using a previously described model. A Fourier mode decomposition procedure was used to compute theoretical light scattering autocorrelation functions (ACFs) from the BD trajectories. Both measured and computed autocorrelation functions were then subjected to the same multiexponential decomposition procedure. Simulated and measured relaxation times as a function of scattering angle were in very good agreement. Similarly, computed and measured static structure factors and radii of gyration agreed within experimental error. One main result of this study is that the amplitudes of the fast-relaxing component in the ACF show a peak at 1 M salt concentration. This nonmonotonic behavior might be caused by an initial increase in the amplitudes of internal motions due to diminishing long-range electrostatic repulsions, followed by a decrease at higher salt concentration due to a compaction of the structure. PMID:9370461

  17. Segregation and phase inversion of strongly and weakly fluctuating Brownian particle mixtures and a chain of such particle mixtures in spherical containers

    NASA Astrophysics Data System (ADS)

    Awazu, Akinori

    2014-10-01

    We investigate the segregation pattern formation of strongly and weakly fluctuating Brownian particle mixtures confined in a three-dimensional spherical container. We consider systems where the particle motion is restricted by the harmonic external trapping potential and the container edge wall. In such systems, two segregation patterns are observed. When the container radius is sufficiently large, more weakly fluctuating particles accumulate near the center of the container than strongly fluctuating particles. On the other hand, the distributions of the strongly and weakly fluctuating particles are inverted when the container radius is small. With no external trapping potentials, we find similar segregation and phase inversion if the particles construct a chain (heterofluctuating polymer) and are confined in a three-dimensional spherical container. We could apply these phenomena in the study of biopolymer behavior, such as chromosomes in the cell nucleus.

  18. [Motion sickness].

    PubMed

    Taillemite, J P; Devaulx, P; Bousquet, F

    1997-01-01

    Motion sickness is a general term covering sea-sickness, car-sickness, air-sickness, and space-sickness. Symptoms can occur when a person is exposed to unfamiliar movement whether real or simulated. Despite progress in the technology and comfort of modern transportation (planes, boats, and overland vehicles), a great number of travelers still experience motion sickness. Bouts are characterized by an initial phase of mild discomfort followed by neurologic and gastro-intestinal manifestations. The delay in onset depends on specific circumstances and individual susceptibility. Attacks are precipitated by conflicting sensory, visual, and vestibular signals but the underlying mechanism is unclear. Most medications used for prevention and treatment (e.g. anticholinergics and antihistamines) induce unwanted sedation. Furthermore no one drug is completely effective or preventive under all conditions.

  19. Brownian-dynamics simulation studies of a charge-stabilized colloidal suspension under shear flow

    SciTech Connect

    Chakrabarti, J. ); Sood, A.K.; Krishnamurthy, H.R. Jawaharlal Nehru Center for Advanced Scientific Research, Indian Institute of Science campus, Bangalore 560012 )

    1994-11-01

    We have carried out Brownian-dynamics simulations of a charged colloidal suspension under oscillatory shear flow with both Couette and Poiseuille velocity profiles. We show that in the steady-shear'' limit, for both of the velocity profiles, the enhancement of the self-diffusion coefficient in directions transverse to the flow shows a crossover from a [dot [gamma

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

    USGS Publications Warehouse

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

    2015-01-01

    The dynamic Brownian bridge movement model improves our understanding of flyways by estimating relative use of regions in the flyway while providing detailed, quantitative information on migration timing and population connectivity including uncertainty between locations. This model effectively quantifies the relative importance of different migration corridors and stopover sites and may help prioritize specific areas in flyways for conservation of waterbird populations.