Generalized Arcsine Laws for Fractional Brownian Motion.

Science.gov (United States)

Sadhu, Tridib; Delorme, Mathieu; Wiese, Kay Jörg

2018-01-26

The three arcsine laws for Brownian motion are a cornerstone of extreme-value statistics. For a Brownian B_{t} starting from the origin, and evolving during time T, one considers the following three observables: (i) the duration t_{+} the process is positive, (ii) the time t_{last} the process last visits the origin, and (iii) the time t_{max} when it achieves its maximum (or minimum). All three observables have the same cumulative probability distribution expressed as an arcsine function, thus the name arcsine laws. We show how these laws change for fractional Brownian motion X_{t}, a non-Markovian Gaussian process indexed by the Hurst exponent H. It generalizes standard Brownian motion (i.e., H=1/2). We obtain the three probabilities using a perturbative expansion in ϵ=H-1/2. While all three probabilities are different, this distinction can only be made at second order in ϵ. Our results are confirmed to high precision by extensive numerical simulations.

On some generalization of fractional Brownian motions

International Nuclear Information System (INIS)

Wang Xiaotian; Liang Xiangqian; Ren Fuyao; Zhang Shiying

2006-01-01

The multifractional Brownian motion (mBm) is a continuous Gaussian process that extends the classical fractional Brownian motion (fBm) defined by Barton and Vincent Poor [Barton RJ, Vincent Poor H. IEEE Trans Inform 1988;34(5):943] and Decreusefond and Ustuenel [Decreusefond L, Ustuenel AS. Potential Anal 1999;10:177]. In addition, an innovational representation of fBm is given

Fractional Brownian motion and long term clinical trial recruitment.

Science.gov (United States)

Zhang, Qiang; Lai, Dejian

2011-05-01

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

Biased and flow driven Brownian motion in periodic channels

Science.gov (United States)

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

2012-02-01

In this talk we will present an expansion of the common Fick-Jacobs approximation to hydrodynamically as well as by external forces driven Brownian transport in two-dimensional channels exhibiting smoothly varying periodic cross-section. We employ an asymptotic analysis to the components of the flow field and to stationary probability density for finding the particles within the channel in a geometric parameter. We demonstrate that the problem of biased Brownian dynamics in a confined 2D geometry can be replaced by Brownian motion in an effective periodic one-dimensional potential ψ(x) which takes the external bias, the change of the local channel width, and the flow velocity component in longitudinal direction into account. In addition, we study the influence of the external force magnitude, respectively, the pressure drop of the fluid on the particle transport quantities like the averaged velocity and the effective diffusion coefficient. The critical ratio between the external force and pressure drop where the average velocity equals zero is identified and the dependence of the latter on the channel geometry is derived. Analytic findings are confirmed by numerical simulations of the particle dynamics in a reflection symmetric sinusoidal channel.

Spherical particle Brownian motion in viscous medium as non-Markovian random process

International Nuclear Information System (INIS)

Morozov, Andrey N.; Skripkin, Alexey V.

2011-01-01

The Brownian motion of a spherical particle in an infinite medium is described by the conventional methods and integral transforms considering the entrainment of surrounding particles of the medium by the Brownian particle. It is demonstrated that fluctuations of the Brownian particle velocity represent a non-Markovian random process. The features of Brownian motion in short time intervals and in small displacements are considered. -- Highlights: → Description of Brownian motion considering the entrainment of medium is developed. → We find the equations for statistical characteristics of impulse fluctuations. → Brownian motion at small time intervals is considered. → Theoretical results and experimental data are compared.

Eigenfunction expansion for fractional Brownian motions

International Nuclear Information System (INIS)

Maccone, C.

1981-01-01

The fractional Brownian motions, a class of nonstationary stochastic processes defined as the Riemann-Liouville fractional integral/derivative of the Brownian motion, are studied. It is shown that these processes can be regarded as the output of a suitable linear system of which the input is the white noise. Their autocorrelation is then derived with a study of their standard-deviation curves. Their power spectra are found by resorting to the nonstationary spectral theory. And finally their eigenfunction expansion (Karhunen-Loeve expansion) is obtained: the eigenfunctions are proved to be suitable Bessel functions and the eigenvalues zeros of the Bessel functions. (author)

Area distribution of an elastic Brownian motion

International Nuclear Information System (INIS)

Rajabpour, M A

2009-01-01

We calculate the excursion and meander area distributions of the elastic Brownian motion by using the self-adjoint extension of the Hamiltonian of the free quantum particle on the half line. We also give some comments on the area of the Brownian motion bridge on the real line with the origin removed. We will focus on the power of self-adjoint extension to investigate different possible boundary conditions for the stochastic processes. We also discuss some possible physical applications.

Deep inelastic collisions viewed as Brownian motion

International Nuclear Information System (INIS)

Gross, D.H.E.; Freie Univ. Berlin

1980-01-01

Non-equilibrium transport processes like Brownian motion, are studied since perhaps 100 years and one should ask why does one not use these theories to explain deep inelastic collision data. These theories have reached a high standard of sophistication, experience, and precision that I believe them to be very usefull for our problem. I will try to sketch a possible form of an advanced theory of Brownian motion that seems to be suitable for low energy heavy ion collisions. (orig./FKS)

Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus

Directory of Open Access Journals (Sweden)

Yuquan Cang

2014-01-01

Full Text Available We study the asymptotic behavior of the sequence Sn=∑i=0n-1K(nαSiH1(Si+1H2-SiH2, as n tends to infinity, where SH1 and SH2 are two independent subfractional Brownian motions with indices H1 and H2, respectively. K is a kernel function and the bandwidth parameter α satisfies some hypotheses in terms of H1 and H2. Its limiting distribution is a mixed normal law involving the local time of the sub-fractional Brownian motion SH1. We mainly use the techniques of Malliavin calculus with respect to sub-fractional Brownian motion.

Manipulation and controlled amplification of Brownian motion of microcantilever sensors

International Nuclear Information System (INIS)

Mehta, Adosh; Cherian, Suman; Hedden, David; Thundat, Thomas

2001-01-01

Microcantilevers, such as those used in atomic force microscopy, undergo Brownian motion due to mechanical thermal noise. The root mean square amplitude of the Brownian motion of a cantilever typically ranges from 0.01--0.1 nm, which limits its use in practical applications. Here we describe a technique by which the Brownian amplitude and the Q factor in air and water can be amplified by three and two orders of magnitude, respectively. This technique is similar to a positive feedback oscillator, wherein the Brownian motion of the vibrating cantilever controls the frequency output of the oscillator. This technique can be exploited to improve sensitivity of microcantilever-based chemical and biological sensors, especially for sensors in liquid environments

Random motion and Brownian rotation

International Nuclear Information System (INIS)

Wyllie, G.

1980-01-01

The course is centred on the Brownian motion - the random movement of molecules arising from thermal fluctuations of the surrounding medium - and starts with the classical theory of A. Einstein, M.v. Smoluchowski and P. Langevin. The first part of this article is quite elementary, and several of the questions raised in it have been instructively treated in a much more sophisticated way in recent reviews by Pomeau and Resibois and by Fox. This simple material may nevertheless be helpful to some readers whose main interest lies in approaching the work on Brownian rotation reviewed in the latter part of the present article. The simplest, and most brutally idealised, problem in our field of interest is that of the random walk in one dimension of space. Its solution leads on, through the diffusivity-mobility relation of Einstein, to Langevin's treatment of the Brownian motion. The application of these ideas to the movement of a molecule in a medium of similar molecules is clearly unrealistic, and much energy has been devoted to finding a suitable generalisation. We shall discuss in particular ideas due to Green, Zwanzig and Mori. (orig./WL)

Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions

International Nuclear Information System (INIS)

Han Yuecai; Hu Yaozhong; Song Jian

2013-01-01

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.

Dissipation and decoherence in Brownian motion

Energy Technology Data Exchange (ETDEWEB)

Bellomo, Bruno [Dipartimento di Scienze Fisiche ed Astronomiche dell' Universita di Palermo, Via Archirafi, 36, 90123 Palermo (Italy); Barnett, Stephen M [Department of Physics, University of Strathclyde, Glasgow G4 0NG (United Kingdom); Jeffers, John [Department of Physics, University of Strathclyde, Glasgow G4 0NG (United Kingdom)

2007-05-15

We consider the evolution of a Brownian particle described by a measurement-based master equation. We derive the solution to this equation for general initial conditions and apply it to a Gaussian initial state. We analyse the effects of the diffusive terms, present in the master equation, and describe how these modify uncertainties and coherence length. This allows us to model dissipation and decoherence in quantum Brownian motion.

Non-colliding Brownian Motions and the Extended Tacnode Process

Science.gov (United States)

Johansson, Kurt

2013-04-01

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

Time rescaling and Gaussian properties of the fractional Brownian motions

International Nuclear Information System (INIS)

Maccone, C.

1981-01-01

The fractional Brownian motions are proved to be a class of Gaussian (normal) stochastic processes suitably rescaled in time. Some consequences affecting their eigenfunction expansion (Karhunen-Loeve expansion) are inferred. A known formula of Cameron and Martin is generalized. The first-passage time probability density is found. The partial differential equation of the fractional Brownian diffusion is obtained. And finally the increments of the fractional Brownian motions are proved to be independent for nonoverlapping time intervals. (author)

The Intersection Probability of Brownian Motion and SLEκ

Directory of Open Access Journals (Sweden)

Shizhong Zhou

2015-01-01

Full Text Available By using excursion measure Poisson kernel method, we obtain a second-order differential equation of the intersection probability of Brownian motion and SLEκ. Moreover, we find a transformation such that the second-order differential equation transforms into a hypergeometric differential equation. Then, by solving the hypergeometric differential equation, we obtain the explicit formula of the intersection probability for the trace of the chordal SLEκ and planar Brownian motion started from distinct points in an upper half-plane H-.

QUANTUM STOCHASTIC PROCESSES: BOSON AND FERMION BROWNIAN MOTION

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A.E.Kobryn

2003-01-01

Full Text Available Dynamics of quantum systems which are stochastically perturbed by linear coupling to the reservoir can be studied in terms of quantum stochastic differential equations (for example, quantum stochastic Liouville equation and quantum Langevin equation. In order to work it out one needs to define the quantum Brownian motion. As far as only its boson version has been known until recently, in the present paper we present the definition which makes it possible to consider the fermion Brownian motion as well.

Reflected Brownian motions in the KPZ universality class

CERN Document Server

Weiss, Thomas; Spohn, Herbert

2017-01-01

This book presents a detailed study of a system of interacting Brownian motions in one dimension. The interaction is point-like such that the n-th Brownian motion is reflected from the Brownian motion with label n-1. This model belongs to the Kardar-Parisi-Zhang (KPZ) universality class. In fact, because of the singular interaction, many universal properties can be established with rigor. They depend on the choice of initial conditions. Discussion addresses packed and periodic initial conditions (Chapter 5), stationary initial conditions (Chapter 6), and mixtures thereof (Chapter 7). The suitably scaled spatial process will be proven to converge to an Airy process in the long time limit. A chapter on determinantal random fields and another one on Airy processes are added to have the notes self-contained. These notes serve as an introduction to the KPZ universality class, illustrating the main concepts by means of a single model only. The notes will be of interest to readers from interacting diffusion processe...

Deterministic Brownian motion generated from differential delay equations.

Science.gov (United States)

Lei, Jinzhi; Mackey, Michael C

2011-10-01

This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential delay equation and then numerically investigate the probabilistic properties of chaotic solutions of the same equation. Our results show that solutions of the deterministic equation with randomly selected initial conditions display a Gaussian-like density for long time, but the densities are supported on an interval of finite measure. Using these chaotic solutions as velocities, we are able to produce Brownian-like motions, which show statistical properties akin to those of a classical Brownian motion over both short and long time scales. Several conjectures are formulated for the probabilistic properties of the solution of the differential delay equation. Numerical studies suggest that these conjectures could be "universal" for similar types of "chaotic" dynamics, but we have been unable to prove this.

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

Science.gov (United States)

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.

Survival probabilities for branching Brownian motion with absorption

OpenAIRE

Harris, John; Harris, Simon

2007-01-01

We study a branching Brownian motion (BBM) with absorption, in which particles move as Brownian motions with drift $-\\rho$, undergo dyadic branching at rate $\\beta>0$, and are killed on hitting the origin. In the case $\\rho>\\sqrt{2\\beta}$ the extinction time for this process, $\\zeta$, is known to be finite almost surely. The main result of this article is a large-time asymptotic formula for the survival probability $P^x(\\zeta>t)$ in the case $\\rho>\\sqrt{2\\beta}$, where $P^x$ is...

Evaluation of Underground Zinc Mine Investment Based on Fuzzy-Interval Grey System Theory and Geometric Brownian Motion

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Zoran Gligoric

2014-01-01

Full Text Available Underground mine projects are often associated with diverse sources of uncertainties. Having the ability to plan for these uncertainties plays a key role in the process of project evaluation and is increasingly recognized as critical to mining project success. To make the best decision, based on the information available, it is necessary to develop an adequate model incorporating the uncertainty of the input parameters. The model is developed on the basis of full discounted cash flow analysis of an underground zinc mine project. The relationships between input variables and economic outcomes are complex and often nonlinear. Fuzzy-interval grey system theory is used to forecast zinc metal prices while geometric Brownian motion is used to forecast operating costs over the time frame of the project. To quantify the uncertainty in the parameters within a project, such as capital investment, ore grade, mill recovery, metal content of concentrate, and discount rate, we have applied the concept of interval numbers. The final decision related to project acceptance is based on the net present value of the cash flows generated by the simulation over the time project horizon.

Under which conditions is quantum Brownian motion observable in a microscope?

International Nuclear Information System (INIS)

Helseth, L.E.

2010-01-01

We investigate under which conditions we can expect to observe quantum Brownian motion in a microscope. Using the fluctuation-dissipation theorem, we investigate quantum Brownian motion in an ohmic bath, and estimate temporal and spatial accuracy required to observe a crossover from classical to quantum behavior.

Microscopic derivation of open quantum Brownian motion: a particular example

International Nuclear Information System (INIS)

Sinayskiy, Ilya; Petruccione, Francesco

2015-01-01

The microscopic derivation of a new type of Brownian motion, namely open quantum Brownian motion (OQBM) is presented. The quantum master equation for OQBM is derived for a weakly driven system interacting with a decoherent environment. Examples of the dynamics for initial Gaussian and non-Gaussian distributions are presented. Both examples demonstrate convergence of the OQBM dynamics to Gaussian distributions. (topical article)

Brownian motion of tethered nanowires.

Science.gov (United States)

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

2014-05-01

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

Intrinsic and extrinsic measurement for Brownian motion

International Nuclear Information System (INIS)

Castro-Villarreal, Pavel

2014-01-01

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 〈δR 2 〉 on spheres and minimal surfaces, which are valid for all values of time. In the latter case, surprisingly, Brownian motion corresponds to the usual diffusion in flat geometries, albeit minimal surfaces have non-zero Gaussian curvature. Finally, the two-dimensional case is emphasized due to its close relation to surface self-diffusion in fluid membranes. (paper)

Brownian motion, martingales, and stochastic calculus

CERN Document Server

Le Gall, Jean-François

2016-01-01

This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested i...

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

Directory of Open Access Journals (Sweden)

Qing-Miao Nie

2014-04-01

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

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

Science.gov (United States)

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.

Brownian motion in Robertson-Walker spacetimes from electromagnetic vacuum fluctuations

International Nuclear Information System (INIS)

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

2009-01-01

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

Quantum Brownian motion model for the stock market

Science.gov (United States)

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

2016-06-01

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

On the definition of an admitted Lie group for stochastic differential equations with multi-Brownian motion

International Nuclear Information System (INIS)

Srihirun, B; Meleshko, S V; Schulz, E

2006-01-01

The definition of an admitted Lie group of transformations for stochastic differential equations has been already presented for equations with one-dimensional Brownian motion. The transformation of the dependent variables involves time as well, and it has been proven that Brownian motion is transformed to Brownian motion. In this paper, we will discuss this concept for stochastic differential equations involving multi-dimensional Brownian motion and present applications to a variety of stochastic differential equations

Estimation of the global regularity of a multifractional Brownian motion

DEFF Research Database (Denmark)

Lebovits, Joachim; Podolskij, Mark

This paper presents a new estimator of the global regularity index of a multifractional Brownian motion. Our estimation method is based upon a ratio statistic, which compares the realized global quadratic variation of a multifractional Brownian motion at two different frequencies. We show that a ...... that a logarithmic transformation of this statistic converges in probability to the minimum of the Hurst functional parameter, which is, under weak assumptions, identical to the global regularity index of the path....

Quantum equations from Brownian motions

International Nuclear Information System (INIS)

Rajput, B.S.

2011-01-01

Classical Schrodinger and Dirac equations have been derived from Brownian motions of a particle, it has been shown that the classical Schrodinger equation can be transformed to usual Schrodinger Quantum equation on applying Heisenberg uncertainty principle between position and momentum while Dirac Quantum equation follows it's classical counter part on applying Heisenberg uncertainly principle between energy and time without applying any analytical continuation. (author)

Brownian motion in a flowing fluid revisited

International Nuclear Information System (INIS)

Ramshaw, J.D.

1981-01-01

It is shown how the phenomenon of osmosis may be treated using the phenomenological theory of Brownian motion in a flowing fluid. The theory is also generalized to include viscous stresses in the particle and mixture momentum equations

Self-Intersection Local Times of Generalized Mixed Fractional Brownian Motion as White Noise Distributions

International Nuclear Information System (INIS)

Suryawan, Herry P.; Gunarso, Boby

2017-01-01

The generalized mixed fractional Brownian motion is defined by taking linear combinations of a finite number of independent fractional Brownian motions with different Hurst parameters. It is a Gaussian process with stationary increments, posseses self-similarity property, and, in general, is neither a Markov process nor a martingale. In this paper we study the generalized mixed fractional Brownian motion within white noise analysis framework. As a main result, we prove that for any spatial dimension and for arbitrary Hurst parameter the self-intersection local times of the generalized mixed fractional Brownian motions, after a suitable renormalization, are well-defined as Hida white noise distributions. The chaos expansions of the self-intersection local times in the terms of Wick powers of white noises are also presented. (paper)

Nuclear resonant scattering of synchrotron radiation from nuclei in the Brownian motion

International Nuclear Information System (INIS)

Razdan, Ashok

2003-01-01

The time evolution of the coherent forward scattering of the synchrotron radiation for resonant nuclei in Brownian motion is studied. Apart from target thickness, the appearance of the dynamical beats also depends on 'α' which is the ratio of the harmonic force constant to the damping force constant of harmonic oscillator undergoing Brownian motion

Synchronization and collective motion of globally coupled Brownian particles

International Nuclear Information System (INIS)

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

2014-01-01

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

Stochastic calculus for fractional Brownian motion and related processes

CERN Document Server

Mishura, Yuliya S

2008-01-01

The theory of fractional Brownian motion and other long-memory processes are addressed in this volume. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. Among these are results about Levy characterization of fractional Brownian motion, maximal moment inequalities for Wiener integrals including the values 0Brownian SDE. The author develops optimal filtering of mixed models including linear case, and studies financial applications and statistical inference with hypotheses testing and parameter estimation. She proves that the market with stock guided by the mixed model is arbitrage-free without any restriction on the dependence of the components and deduces different forms of the Black-Scholes equation for fractional mark...

Diffusion in one dimensional random medium and hyperbolic Brownian motion

International Nuclear Information System (INIS)

Comtet, A.; Monthus, C.; Paris-6 Univ., 75

1995-03-01

Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. This relationship is analyzed in detail and various distributions are studied using stochastic calculus and functional integration. (author) 17 refs

Brownian Motion of Boomerang Colloidal Particles

Science.gov (United States)

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

2014-03-01

We present experimental and theoretical studies on the Brownian motion of boomerang colloidal particles confined between two glass plates. Our experimental observations show that the mean displacements are biased towards the center of hydrodynamic stress (CoH), and that the mean-square displacements exhibit a crossover from short-time faster to long-time slower diffusion with the short-time diffusion coefficients dependent on the points used for tracking. A model based on Langevin theory elucidates that these behaviors are ascribed to the superposition of two diffusive modes: the ellipsoidal motion of the CoH and the rotational motion of the tracking point with respect to the CoH.

Brownian motion of solitons in a Bose-Einstein condensate.

Science.gov (United States)

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.

On the Generalized Brownian Motion and its Applications in Finance

DEFF Research Database (Denmark)

Høg, Esben; Frederiksen, Per; Schiemert, Daniel

This paper deals with dynamic term structure models (DTSMs) and proposes a new way to handle the limitation of the classical affine models. In particular, the paper expands the exibility of the DTSMs by applying generalized Brownian motions with dependent increments as the governing force...... of the state variables instead of standard Brownian motions. This is a new direction in pricing non defaultable bonds. By extending the theory developed by Dippon & Schiemert (2006a), the paper developes a bond market with memory, and proves the absence of arbitrage. The framework is readily extendable...

Brownian Motion of 2D Vacancy Islands by Adatom Terrace Diffusion

International Nuclear Information System (INIS)

Morgenstern, Karina; Laegsgaard, Erik; Besenbacher, Flemming

2001-01-01

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

The Pricing of Vulnerable Options in a Fractional Brownian Motion Environment

Directory of Open Access Journals (Sweden)

Chao Wang

2015-01-01

Full Text Available Under the assumption of the stock price, interest rate, and default intensity obeying the stochastic differential equation driven by fractional Brownian motion, the jump-diffusion model is established for the financial market in fractional Brownian motion setting. With the changes of measures, the traditional pricing method is simplified and the general pricing formula is obtained for the European vulnerable option with stochastic interest rate. At the same time, the explicit expression for it comes into being.

On correlations between certain random variables associated with first passage Brownian motion

International Nuclear Information System (INIS)

Kearney, Michael J; Pye, Andrew J; Martin, Richard J

2014-01-01

We analyse how the area swept out by a Brownian motion up to its first passage time correlates with the first passage time itself, obtaining several exact results in the process. Additionally, we analyse the relationship between the time average of a Brownian motion during a first passage and the maximum value attained. The results, which find various applications, are in excellent agreement with simulations. (paper)

On modeling animal movements using Brownian motion with measurement error.

Science.gov (United States)

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

2014-02-01

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

Cosmophysical Factors in the Fluctuation Amplitude Spectrum of Brownian Motion

Directory of Open Access Journals (Sweden)

Kaminsky A. V.

2010-04-01

Full Text Available Phenomenon of the regular variability of the fine structure of the fluctuation in the amplitude distributions (shapes of related histograms for the case of Brownian motion was investigated. We took an advantage of the dynamic light scattering method (DLS to get a stochastically fluctuated signal determined by Brownian motion. Shape of the histograms is most likely to vary, synchronous, in two proximally located independent cells containing Brownian particles. The synchronism persists in the cells distant at 2m from each other, and positioned meridionally. With a parallel-wise positioning of the cells, high probability of the synchronous variation in the shape of the histograms by local time has been observed. This result meets the previous conclusion about the dependency of histogram shapes ("fluctuation amplitudes" of the spectra of stochastic processes upon rotation of the Earth.

Cosmophysical Factors in the Fluctuation Amplitude Spectrum of Brownian Motion

Directory of Open Access Journals (Sweden)

Kaminsky A. V.

2010-07-01

Full Text Available Phenomenon of the regular variability of the fine structure of the fluctuation in the am- plitude distributions (shapes of related histograms for the case of Brownian motion was investigated. We took an advantage of the dynamic light scattering method (DLS to get a stochastically fluctuated signal determined by Brownian motion. Shape of the histograms is most likely to vary, synchronous, in two proximally located independent cells containing Brownian particles. The synchronism persists in the cells distant at 2 m from each other, and positioned meridionally. With a parallel-wise positioning of the cells, high probability of the synchronous variation in the shape of the histograms by local time has been observed. This result meets the previous conclusion about the dependency of histogram shapes (“fluctuation amplitudes” of the spectra of stochastic processes upon rotation of the Earth.

Modeling single-file diffusion with step fractional Brownian motion and a generalized fractional Langevin equation

International Nuclear Information System (INIS)

Lim, S C; Teo, L P

2009-01-01

Single-file diffusion behaves as normal diffusion at small time and as subdiffusion at large time. These properties can be described in terms of fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann–Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with a step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as a solution of the fractional Langevin equation with zero damping. Various kinds of fractional Langevin equations and their generalizations are then considered in order to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where the dissipative memory kernel is a Dirac delta function, a power-law function and a combination of these functions are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of a process that begins as ballistic motion

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

Science.gov (United States)

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

2017-09-01

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

Brownian motion and stochastic calculus

CERN Document Server

Karatzas, Ioannis

1998-01-01

This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large num...

Brownian motion model with stochastic parameters for asset prices

Science.gov (United States)

Ching, Soo Huei; Hin, Pooi Ah

2013-09-01

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

Directed motion of a Brownian motor in a temperature gradient

Science.gov (United States)

Liu, Yibing; Nie, Wenjie; Lan, Yueheng

2017-05-01

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

Finding viscosity of liquids from Brownian motion at students' laboratory

International Nuclear Information System (INIS)

Greczylo, Tomasz; Debowska, Ewa

2005-01-01

Brownian motion appears to be a good subject for investigation at advanced students' laboratory [1]. The paper presents such an investigation carried out in Physics Laboratory II at the Institute of Experimental Physics of Wroclaw University. The experiment has been designed to find viscosity of liquids from Brownian motion phenomenon. Authors use modern technology that helps to proceed with measurements and makes the procedure less time and effort consuming. Discussion of the process of setting up the experiment and the results obtained for three different solutions of glycerin in water are presented. Advantages and disadvantages of the apparatus are pointed out along with descriptions of possible future uses

Time-averaged MSD of Brownian motion

OpenAIRE

Andreanov, Alexei; Grebenkov, Denis

2012-01-01

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

Active Brownian motion models and applications to ratchets

Science.gov (United States)

Fiasconaro, A.; Ebeling, W.; Gudowska-Nowak, E.

2008-10-01

We give an overview over recent studies on the model of Active Brownian Motion (ABM) coupled to reservoirs providing free energy which may be converted into kinetic energy of motion. First, we present an introduction to a general concept of active Brownian particles which are capable to take up energy from the source and transform part of it in order to perform various activities. In the second part of our presentation we consider applications of ABM to ratchet systems with different forms of differentiable potentials. Both analytical and numerical evaluations are discussed for three cases of sinusoidal, staircaselike and Mateos ratchet potentials, also with the additional loads modelled by tilted potential structure. In addition, stochastic character of the kinetics is investigated by considering perturbation by Gaussian white noise which is shown to be responsible for driving the directionality of the asymptotic flux in the ratchet. This stochastically driven directionality effect is visualized as a strong nonmonotonic dependence of the statistics of the right versus left trajectories of motion leading to a net current of particles. Possible applications of the ratchet systems to molecular motors are also briefly discussed.

Functionals of Brownian motion, localization and metric graphs

International Nuclear Information System (INIS)

Comtet, Alain; Desbois, Jean; Texier, Christophe

2005-01-01

We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of Brownian motion arise in the study of electronic transport in weakly disordered metals (weak localization). Two aspects of the physics of the one-dimensional strong localization are reviewed: some properties of the scattering by a random potential (time delay distribution) and a study of the spectrum of a random potential on a bounded domain (the extreme value statistics of the eigenvalues). Then we mention several results concerning the diffusion on graphs, and more generally the spectral properties of the Schroedinger operator on graphs. The interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated. Finally, we consider a two-dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices. We recall the connection between spectral properties of this model and winding functionals of planar Brownian motion. (topical review)

Conformal geometry and invariants of 3-strand Brownian braids

International Nuclear Information System (INIS)

Nechaev, Sergei; Voituriez, Raphael

2005-01-01

We propose a simple geometrical construction of topological invariants of 3-strand Brownian braids viewed as world lines of 3 particles performing independent Brownian motions in the complex plane z. Our construction is based on the properties of conformal maps of doubly-punctured plane z to the universal covering surface. The special attention is paid to the case of indistinguishable particles. Our method of conformal maps allows us to investigate the statistical properties of the topological complexity of a bunch of 3-strand Brownian braids and to compute the expectation value of the irreducible braid length in the non-Abelian case

Analytical Solutions of a Model for Brownian Motion in the Double Well Potential

International Nuclear Information System (INIS)

Liu Ai-Jie; Zheng Lian-Cun; Zhang Xin-Xin; Ma Lian-Xi

2015-01-01

In this paper, the analytical solutions of Schrödinger equation for Brownian motion in a double well potential are acquired by the homotopy analysis method and the Adomian decomposition method. Double well potential for Brownian motion is always used to obtain the solutions of Fokker—Planck equation known as the Klein—Kramers equation, which is suitable for separation and additive Hamiltonians. In essence, we could study the random motion of Brownian particles by solving Schrödinger equation. The analytical results obtained from the two different methods agree with each other well. The double well potential is affected by two parameters, which are analyzed and discussed in details with the aid of graphical illustrations. According to the final results, the shapes of the double well potential have significant influence on the probability density function. (general)

Brownian gas models for extreme-value laws

International Nuclear Information System (INIS)

Eliazar, Iddo

2013-01-01

In this paper we establish one-dimensional Brownian gas models for the extreme-value laws of Gumbel, Weibull, and Fréchet. A gas model is a countable collection of independent particles governed by common diffusion dynamics. The extreme-value laws are the universal probability distributions governing the affine scaling limits of the maxima and minima of ensembles of independent and identically distributed one-dimensional random variables. Using the recently introduced concept of stationary Poissonian intensities, we construct two gas models whose global statistical structures are stationary, and yield the extreme-value laws: a linear Brownian motion gas model for the Gumbel law, and a geometric Brownian motion gas model for the Weibull and Fréchet laws. The stochastic dynamics of these gas models are studied in detail, and closed-form analytical descriptions of their temporal correlation structures, their topological phase transitions, and their intrinsic first-passage-time fluxes are presented. (paper)

Brownian motion in short range random potentials

International Nuclear Information System (INIS)

Romero, A.H.; Romero, A.H.; Sancho, J.M.

1998-01-01

A numerical study of Brownian motion of noninteracting particles in random potentials is presented. The dynamics are modeled by Langevin equations in the high friction limit. The random potentials are Gaussian distributed and short ranged. The simulations are performed in one and two dimensions. Different dynamical regimes are found and explained. Effective subdiffusive exponents are obtained and commented on. copyright 1998 The American Physical Society

Quantum Darwinism in Quantum Brownian Motion

Science.gov (United States)

Blume-Kohout, Robin; Zurek, Wojciech H.

2008-12-01

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

Algorithm for generating a Brownian motion on a sphere

International Nuclear Information System (INIS)

Carlsson, Tobias; Elvingson, Christer; Ekholm, Tobias

2010-01-01

We present a new algorithm for generation of a random walk on a two-dimensional sphere. The algorithm is obtained by viewing the 2-sphere as the equator in the 3-sphere surrounded by an infinitesimally thin band with boundary which reflects Brownian particles and then applying known effective methods for generating Brownian motion on the 3-sphere. To test the method, the diffusion coefficient was calculated in computer simulations using the new algorithm and, for comparison, also using a commonly used method in which the particle takes a Brownian step in the tangent plane to the 2-sphere and is then projected back to the spherical surface. The two methods are in good agreement for short time steps, while the method presented in this paper continues to give good results also for larger time steps, when the alternative method becomes unstable.

Frustrated Brownian Motion of Nonlocal Solitary Waves

International Nuclear Information System (INIS)

Folli, V.; Conti, C.

2010-01-01

We investigate the evolution of solitary waves in a nonlocal medium in the presence of disorder. By using a perturbational approach, we show that an increasing degree of nonlocality may largely hamper the Brownian motion of self-trapped wave packets. The result is valid for any kind of nonlocality and in the presence of nonparaxial effects. Analytical predictions are compared with numerical simulations based on stochastic partial differential equations.

Non-Markovian quantum Brownian motion in one dimension in electric fields

Science.gov (United States)

Shen, H. Z.; Su, S. L.; Zhou, Y. H.; Yi, X. X.

2018-04-01

Quantum Brownian motion is the random motion of quantum particles suspended in a field (or an effective field) resulting from their collision with fast-moving modes in the field. It provides us with a fundamental model to understand various physical features concerning open systems in chemistry, condensed-matter physics, biophysics, and optomechanics. In this paper, without either the Born-Markovian or rotating-wave approximation, we derive a master equation for a charged-Brownian particle in one dimension coupled with a thermal reservoir in electric fields. The effect of the reservoir and the electric fields is manifested as time-dependent coefficients and coherent terms, respectively, in the master equation. The two-photon correlation between the Brownian particle and the reservoir can induce nontrivial squeezing dynamics to the particle. We derive a current equation including the source from the driving fields, transient current from the system flowing into the environment, and the two-photon current caused by the non-rotating-wave term. The presented results then are compared with that given by the rotating-wave approximation in the weak-coupling limit, and these results are extended to a more general quantum network involving an arbitrary number of coupled-Brownian particles. The presented formalism might open a way to better understand exactly the non-Markovian quantum network.

Statistics of the first passage time of Brownian motion conditioned by maximum value or area

International Nuclear Information System (INIS)

Kearney, Michael J; Majumdar, Satya N

2014-01-01

We derive the moments of the first passage time for Brownian motion conditioned by either the maximum value or the area swept out by the motion. These quantities are the natural counterparts to the moments of the maximum value and area of Brownian excursions of fixed duration, which we also derive for completeness within the same mathematical framework. Various applications are indicated. (paper)

Brownian motion using video capture

International Nuclear Information System (INIS)

Salmon, Reese; Robbins, Candace; Forinash, Kyle

2002-01-01

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

Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

Directory of Open Access Journals (Sweden)

Xiao-Li Ding

2018-01-01

Full Text Available In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. Finally, we give three examples to demonstrate the applicability of our obtained results.

Occupation times distribution for Brownian motion on graphs

CERN Document Server

Desbois, J

2002-01-01

Considering a Brownian motion on a general graph, we study the joint law for the occupation times on all the bonds. In particular, we show that the Laplace transform of this distribution can be expressed as the ratio of two determinants. We give two formulations, with arc or vertex matrices, for this result and discuss a simple example. (letter to the editor)

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

Science.gov (United States)

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.

The open quantum Brownian motions

International Nuclear Information System (INIS)

Bauer, Michel; Bernard, Denis; Tilloy, Antoine

2014-01-01

Using quantum parallelism on random walks as the original seed, we introduce new quantum stochastic processes, the open quantum Brownian motions. They describe the behaviors of quantum walkers—with internal degrees of freedom which serve as random gyroscopes—interacting with a series of probes which serve as quantum coins. These processes may also be viewed as the scaling limit of open quantum random walks and we develop this approach along three different lines: the quantum trajectory, the quantum dynamical map and the quantum stochastic differential equation. We also present a study of the simplest case, with a two level system as an internal gyroscope, illustrating the interplay between the ballistic and diffusive behaviors at work in these processes. Notation H z : orbital (walker) Hilbert space, C Z in the discrete, L 2 (R) in the continuum H c : internal spin (or gyroscope) Hilbert space H sys =H z ⊗H c : system Hilbert space H p : probe (or quantum coin) Hilbert space, H p =C 2 ρ t tot : density matrix for the total system (walker + internal spin + quantum coins) ρ-bar t : reduced density matrix on H sys : ρ-bar t =∫dxdy ρ-bar t (x,y)⊗|x〉 z 〈y| ρ-hat t : system density matrix in a quantum trajectory: ρ-hat t =∫dxdy ρ-hat t (x,y)⊗|x〉 z 〈y|. If diagonal and localized in position: ρ-hat t =ρ t ⊗|X t 〉 z 〈X t | ρ t : internal density matrix in a simple quantum trajectory X t : walker position in a simple quantum trajectory B t : normalized Brownian motion ξ t , ξ t † : quantum noises (paper)

On the distribution of estimators of diffusion constants for Brownian motion

International Nuclear Information System (INIS)

Boyer, Denis; Dean, David S

2011-01-01

We discuss the distribution of various estimators for extracting the diffusion constant of single Brownian trajectories obtained by fitting the squared displacement of the trajectory. The analysis of the problem can be framed in terms of quadratic functionals of Brownian motion that correspond to the Euclidean path integral for simple Harmonic oscillators with time dependent frequencies. Explicit analytical results are given for the distribution of the diffusion constant estimator in a number of cases and our results are confirmed by numerical simulations.

Time-averaged MSD of Brownian motion

International Nuclear Information System (INIS)

Andreanov, Alexei; Grebenkov, Denis S

2012-01-01

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

Time-averaged MSD of Brownian motion

Science.gov (United States)

Andreanov, Alexei; Grebenkov, Denis S.

2012-07-01

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

Phase transition for absorbed Brownian motion with drift

International Nuclear Information System (INIS)

Ferrari, P.A.; Martinez, S.; San Martin, J.

1997-01-01

We study one-dimensional Brownian motion with constant drift toward the origin and initial distribution concentrated in the strictly positive real line. We say that at the first time the process hits the origin, it is absorbed. We study the asymptotic behavior, as t → ∞, of m t , the conditional distribution at time zero of the process conditioned on survival up to time t and on the process having a fixed value at time t. We find that there is a phase transition in the decay rate of the initial condition. For fast decay rate (subcritical case) m t is localized, in the critical case m t is located around √t, and for slow rates (supercritical case) m, is located around t. The critical rate is given by the decay of the minimal quasistationary distribution of this process. We also study in each case the asymptotic distribution of the process, scaled by √t, conditioned as before. We prove that in the subcritical case this distribution is a Brownian excursion. In the critical case it is a Brownian bridge attaining 0 for the first time at time 1, with some initial distribution. In the supercritical case, after centering around the expected value-which is of the order of t we show that this process converges to a Brownian bridge arriving at 0 at time 1 and with a Gaussian initial distribution

New methods for simulation of fractional Brownian motion

International Nuclear Information System (INIS)

Yin, Z.M.

1996-01-01

We present new algorithms for simulation of fractional Brownian motion (fBm) which comprises a set of important random functions widely used in geophysical and physical modeling, fractal image (landscape) simulating, and signal processing. The new algorithms, which are both accurate and efficient, allow us to generate not only a one-dimensional fBm process, but also two- and three-dimensional fBm fields. 23 refs., 3 figs

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

International Nuclear Information System (INIS)

Yeh, L.

1993-01-01

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

An Extreme-Value Analysis of the LIL for Brownian Motion

OpenAIRE

Khoshnevisan, Davar; Levin, David; Shi, Zhan

2005-01-01

We use excursion theory and the ergodic theorem to present an extreme-value analysis of the classical law of the iterated logarithm (LIL) for Brownian motion. A simplified version of our method also proves, in a paragraph, the classical theorem of Darling and Erdős (1956).

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

Science.gov (United States)

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

2012-03-01

Consider n non-intersecting Brownian motions on R, depending on time t∈[0,1], with mi particles forced to leave from ai at time t=0, 1≤i≤q, and nj particles forced to end up at bj at time t=1, 1≤j≤p. For arbitrary p and q, it is not known if the distribution of the positions of the non-intersecting Brownian particles at a given time 0miracle! Unfortunately we were unable to find its explicit expression. The case p=q=2 will be discussed in the last section.

Brownian motion in complex fluids: venerable field and frontier of modern physics

International Nuclear Information System (INIS)

Vizcarra-Rendon, A.; Medina-Noyola, M.; Ruiz-Estrada, H.; Arauz-Lara, J.L.

1989-01-01

This paper reviews the current status of our understanding of tracer-diffusion phenomena in colloidal suspensions. This is the most direct observation of the Brownian motion executed by labelled Brownian particles interacting with the rest of colloidal particles in a suspension. The fundamental description of this phenomenon constitutes today one of the most relevant problems in the process of understanding the dynamic properties of this important class of complex fluids, from the experimental and theoretical perspective of physical research. This paper describes the recent developments in the extension of the classical theory of Brownian motion and its application to the description of the effects of direct and hydrodynamic interactions among colloidal particles. As a result, a coherent pictured has emerged in which the agreement between theory and experiment from nature fields of physics. The moral of the paper is that the use of well established concepts as statistical physics, assisted by modern experimental techniques, are contributing to transform complex fluids into a more amialbe class of materials from the point of view of the physicist. (Author)

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

OpenAIRE

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

2010-01-01

Various proteins are known to exhibit one-dimensional Brownian motion along charged rodlike polymers, such as microtubules (MTs), actin, and DNA. The electrostatic interaction between the proteins and the rodlike polymers appears to be crucial for one-dimensional Brownian motion, although the underlying mechanism has not been fully clarified. We examined the interactions of positively-charged nanoparticles composed of polyacrylamide gels with MTs. These hydrophilic nanoparticles bound to MTs ...

Characterization of turbulence stability through the identification of multifractional Brownian motions

Science.gov (United States)

Lee, K. C.

2013-02-01

Multifractional Brownian motions have become popular as flexible models in describing real-life signals of high-frequency features in geoscience, microeconomics, and turbulence, to name a few. The time-changing Hurst exponent, which describes regularity levels depending on time measurements, and variance, which relates to an energy level, are two parameters that characterize multifractional Brownian motions. This research suggests a combined method of estimating the time-changing Hurst exponent and variance using the local variation of sampled paths of signals. The method consists of two phases: initially estimating global variance and then accurately estimating the time-changing Hurst exponent. A simulation study shows its performance in estimation of the parameters. The proposed method is applied to characterization of atmospheric stability in which descriptive statistics from the estimated time-changing Hurst exponent and variance classify stable atmosphere flows from unstable ones.

Characterization of turbulence stability through the identification of multifractional Brownian motions

Directory of Open Access Journals (Sweden)

K. C. Lee

2013-02-01

Full Text Available Multifractional Brownian motions have become popular as flexible models in describing real-life signals of high-frequency features in geoscience, microeconomics, and turbulence, to name a few. The time-changing Hurst exponent, which describes regularity levels depending on time measurements, and variance, which relates to an energy level, are two parameters that characterize multifractional Brownian motions. This research suggests a combined method of estimating the time-changing Hurst exponent and variance using the local variation of sampled paths of signals. The method consists of two phases: initially estimating global variance and then accurately estimating the time-changing Hurst exponent. A simulation study shows its performance in estimation of the parameters. The proposed method is applied to characterization of atmospheric stability in which descriptive statistics from the estimated time-changing Hurst exponent and variance classify stable atmosphere flows from unstable ones.

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

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Björn Böttcher

Full Text Available 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.

Second order limit laws for occupation times of the fractional Brownian motion

OpenAIRE

Xu, Fangjun

2013-01-01

We prove second order limit laws for (additive) functionals of the $d$-dimensional fractional Brownian motion with Hurst index $H=\\frac{1}{d}$, using the method of moments, extending the Kallianpur-Robbins law.

Brownian entanglement

International Nuclear Information System (INIS)

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

2005-01-01

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

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

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

2015-07-15

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

The Diffusion Process in Small Particles and Brownian Motion

Science.gov (United States)

Khoshnevisan, M.

Albert Einstein in 1926 published his book entitled ''INVESTIGATIONS ON THE THEORY OF THE BROWNIAN MOVEMENT''. He investigated the process of diffusion in an undissociated dilute solution. The diffusion process is subject to Brownian motion. Furthermore, he elucidated the fact that the heat content of a substance will change the position of the single molecules in an irregular fashion. In this paper, I have shown that in order for the displacement of the single molecules to be proportional to the square root of the time, and for v/2 - v 1 Δ =dv/dx , (where v1 and v2 are the concentrations in two cross sections that are separated by a very small distance), ∫ - ∞ ∞ Φ (Δ) dΔ = I and I/τ ∫ - ∞ ∞Δ2/2 Φ (Δ) dΔ = D conditions to hold, then equation (7a) D =√{ 2 D }√{ τ} must be changed to Δ =√{ 2 D }√{ τ} . I have concluded that D =√{ 2 D }√{ τ} is an unintended error, and it has not been amended for almost 90 years in INVESTIGATIONS ON THE THEORY OF THE BROWNIAN MOVEMENT, 1926 publication.

The relativistic Brownian motion: Interdisciplinary applications

International Nuclear Information System (INIS)

Aragones-Munoz, A; Sandoval-Villalbazo, A

2010-01-01

Relativistic Brownian motion theory will be applied to the study of analogies between physical and economic systems, emphasizing limiting cases in which Gaussian distributions are no longer valid. The characteristic temperatures of the particles will be associated with the concept of variance, and this will allow us to choose whether the pertinent distribution is classical or relativistic, while working specific situations. The properties of particles can be interpreted as economic variables, in order to study the behavior of markets in terms of Levy financial processes, since markets behave as stochastic systems. As far as we know, the application of the Juettner distribution to the study of economic systems is a new idea.

Brownian motion under dynamic disorder: effects of memory on the decay of the non-Gaussianity parameter

Science.gov (United States)

Tyagi, Neha; Cherayil, Binny J.

2018-03-01

The increasingly widespread occurrence in complex fluids of particle motion that is both Brownian and non-Gaussian has recently been found to be successfully modeled by a process (frequently referred to as ‘diffusing diffusivity’) in which the white noise that governs Brownian diffusion is itself stochastically modulated by either Ornstein–Uhlenbeck dynamics or by two-state noise. But the model has so far not been able to account for an aspect of non-Gaussian Brownian motion that is also commonly observed: a non-monotonic decay of the parameter that quantifies the extent of deviation from Gaussian behavior. In this paper, we show that the inclusion of memory effects in the model—via a generalized Langevin equation—can rationalise this phenomenon.

Description of surface quadrupole oscillations of heated spherical nuclei in the Brownian-motion approximation

International Nuclear Information System (INIS)

Svin'in, I.R.

1982-01-01

The Brownian motion of a quadrupole quantum oscillator is considered as a model of surface quadrupole oscillations of heated spherical nuclei. The integrals of the motion related to energy and angular momentum conservation are constructed and the wave functions are obtained for states with definite values of these integrals of the motion in the phonon representation

Singularity spectra of fractional Brownian motions as a multi-fractal

International Nuclear Information System (INIS)

Kim, T.S.; Kim, S.

2004-01-01

Fractional Brownian motion acts as a random process with statistical self-similarity in time and self-affinity in shape. From these properties, the complicated patterns can be suitably represented by it with a minimal parameter and less memory. By considering its statistical property through the power spectrum density we can see that this process is not stationary, even though its differential motion is stationary. So in this paper, by taking the wavelet transform instead of Fourier transformation we investigate its multi-fractal spectrum as a multi-fractal model

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

International Nuclear Information System (INIS)

Yannouleas, C.

1984-05-01

From the purely quantal RPA description of the damped harmonic oscillator and of the corresponding Brownian Motion within the full space (phonon subspace plus reservoir), a master equation (as well as a Fokker-Planck equation) for the reduced density matrix (for the reduced Wigner function, respectively) within the phonon subspace is extracted. The RPA master equation agrees with the master equation derived by the time-dependent perturbative approaches which utilize Tamm-Dancoff Hilbert spaces and invoke the rotating wave approximation. Since the RPA yields a full, as well as a contracted description, it can account for both the kinetic and the unperturbed oscillator momenta. The RPA description of the quantal Brownian Motion contrasts with the descriptions provided by the time perturbative approaches whether they invoke or not the rotating wave approximation. The RPA description also contrasts with the phenomenological phase space quantization. (orig.)

Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

OpenAIRE

Xiao-Li Ding; Juan J. Nieto

2018-01-01

In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochast...

Natural convection in nano-fluids: Are the thermophoresis and Brownian motion effects significant in nano-fluid heat transfer enhancement?

International Nuclear Information System (INIS)

Haddad, Zoubida; Abu-Nada, Eiyad; Oztop, Hakan F.; Mataoui, Amina

2012-01-01

Natural convection heat transfer and fluid flow of CuO-Water nano-fluids is studied using the Rayleigh-Benard problem. A two component non-homogenous equilibrium model is used for the nano-fluid that incorporates the effects of Brownian motion and thermophoresis. Variable thermal conductivity and variable viscosity are taken into account in this work. Finite volume method is used to solve governing equations. Results are presented by streamlines, isotherms, nano-particle distribution, local and mean Nusselt numbers and nano-particle profiles at top and bottom side. Comparison of two cases as absence of Brownian and thermophoresis effects and presence of Brownian and thermophoresis effects showed that higher heat transfer is formed with the presence of Brownian and thermophoresis effect. In general, by considering the role of thermophoresis and Brownian motion, an enhancement in heat transfer is observed at any volume fraction of nano-particles. However, the enhancement is more pronounced at low volume fraction of nano-particles and the heat transfer decreases by increasing nano-particle volume fraction. On the other hand, by neglecting the role of thermophoresis and Brownian motion, deterioration in heat transfer is observed and this deterioration elevates by increasing the volume fraction of nano-particles. (authors)

Undergraduate Labs for Biological Physics: Brownian Motion and Optical Trapping

Science.gov (United States)

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.

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

DEFF Research Database (Denmark)

Dávid, Selmeczi; Tolic-Nørrelykke, S.F.; Schäffer, E.

2007-01-01

The first half of this review describes the development in mathematical models of Brownian motion after Einstein's and Smoluchowski's seminal papers and current applications to optical tweezers. This instrument of choice among single-molecule biophysicists is also an instrument of such precision ...

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

Science.gov (United States)

Lindenberg, Katja

2015-03-01

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

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

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Didier Kumwimba Seya

2015-11-01

Full Text Available In this paper we take into account the fuzzy stochastic integral driven by fuzzy Brownian motion. To define the metric between two fuzzy numbers and to take into account the limit of a sequence of fuzzy numbers, we invoke the Hausdorff metric. First this fuzzy stochastic integral is constructed for fuzzy simple stochastic functions, then the construction is done for fuzzy stochastic integrable functions.

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

Energy Technology Data Exchange (ETDEWEB)

Hiotelis, Nicos [1st Lyceum of Athens, Ipitou 15, Plaka, 10557, Athens (Greece); Popolo, Antonino Del, E-mail: adelpopolo@oact.inaf.it, E-mail: hiotelis@ipta.demokritos.gr [Dipartimento di Fisica e Astronomia, University Of Catania, Viale Andrea Doria 6, 95125, Catania (Italy)

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.

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

Science.gov (United States)

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

2010-04-21

Various proteins are known to exhibit one-dimensional Brownian motion along charged rodlike polymers, such as microtubules (MTs), actin, and DNA. The electrostatic interaction between the proteins and the rodlike polymers appears to be crucial for one-dimensional Brownian motion, although the underlying mechanism has not been fully clarified. We examined the interactions of positively-charged nanoparticles composed of polyacrylamide gels with MTs. These hydrophilic nanoparticles bound to MTs and displayed one-dimensional Brownian motion in a charge-dependent manner, which indicates that nonspecific electrostatic interaction is sufficient for one-dimensional Brownian motion. The diffusion coefficient decreased exponentially with an increasing particle charge (with the exponent being 0.10 kBT per charge), whereas the duration of the interaction increased exponentially (exponent of 0.22 kBT per charge). These results can be explained semiquantitatively if one assumes that a particle repeats a cycle of binding to and movement along an MT until it finally dissociates from the MT. During the movement, a particle is still electrostatically constrained in the potential valley surrounding the MT. This entire process can be described by a three-state model analogous to the Michaelis-Menten scheme, in which the two parameters of the equilibrium constant between binding and movement, and the rate of dissociation from the MT, are derived as a function of the particle charge density. This study highlights the possibility that the weak binding interactions between proteins and rodlike polymers, e.g., MTs, are mediated by a similar, nonspecific charge-dependent mechanism. Copyright 2010 Biophysical Society. Published by Elsevier Inc. All rights reserved.

On the biased motion of a brownian particle for the pausing time behavior of the CTRW

International Nuclear Information System (INIS)

Kim, K.S.

1982-01-01

The purpose of this paper is to discuss the biased Brownian motion with the absorbing barrier for the pausing time behavior of the CTRW (continuous-time random walk method), regarding a Brownian particle as a walker. For two pausing time density functions, the respective values for the transport averaged velocity and the dispersion are calculated as the time t becomes large. (KAERI)

Collective motion of active Brownian particles with polar alignment.

Science.gov (United States)

Martín-Gómez, Aitor; Levis, Demian; Díaz-Guilera, Albert; Pagonabarraga, Ignacio

2018-04-04

We present a comprehensive computational study of the collective behavior emerging from the competition between self-propulsion, excluded volume interactions and velocity-alignment in a two-dimensional model of active particles. We consider an extension of the active brownian particles model where the self-propulsion direction of the particles aligns with the one of their neighbors. We analyze the onset of collective motion (flocking) in a low-density regime (10% surface area) and show that it is mainly controlled by the strength of velocity-alignment interactions: the competition between self-propulsion and crowding effects plays a minor role in the emergence of flocking. However, above the flocking threshold, the system presents a richer pattern formation scenario than analogous models without alignment interactions (active brownian particles) or excluded volume effects (Vicsek-like models). Depending on the parameter regime, the structure of the system is characterized by either a broad distribution of finite-sized polar clusters or the presence of an amorphous, highly fluctuating, large-scale traveling structure which can take a lane-like or band-like form (and usually a hybrid structure which is halfway in between both). We establish a phase diagram that summarizes collective behavior of polar active brownian particles and propose a generic mechanism to describe the complexity of the large-scale structures observed in systems of repulsive self-propelled particles.

Parallel Molecular Distributed Detection With Brownian Motion.

Science.gov (United States)

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.

Theory of relativistic Brownian motion in the presence of electromagnetic field in (1+1) dimension

Science.gov (United States)

Mukhopadhyay, Annesh; Bandyopadhyay, M.; Bhamidipati, C.

2018-04-01

In this work, we consider the relativistic generalization of the theory of Brownian motion for the (1+1) dimensional case, which is again consistent with Einstein's special theory of relativity and reduces to standard Brownian motion in the Newtonian limit. All the generalizations are made considering Special theory of relativity into account. The particle under consideration has a velocity close to the speed of light and is a free Brownian particle suspended in a heat bath. With this generalization the velocity probability density functions are also obtained using Ito, Stratonovich and Hanggi-Klimontovich approach of pre-point, mid-point and post-point discretization rule. Subsequently, in our work, we have obtained the relativistic Langevin equations in the presence of an electromagnetic field. Finally, taking a special case of a constant vector potential and a constant electric field into account the Langevin equations are solved for the momentum and subsequently the velocity of the particle. Using a similar approach to the Fokker-planck equations of motion, the velocity distributions are also obtained in the presence of a constant vector potential and are plotted, which shows essential deviations from the one obtained without a potential. Our constant potential model can be realized in an optical potential.

Yukawa Potential, Panharmonic Measure and Brownian Motion

Directory of Open Access Journals (Sweden)

Antti Rasila

2018-05-01

Full Text Available This paper continues our earlier investigation, where a walk-on-spheres (WOS algorithm for Monte Carlo simulation of the solutions of the Yukawa and the Helmholtz partial differential equations (PDEs was developed by using the Duffin correspondence. In this paper, we investigate the foundations behind the algorithm for the case of the Yukawa PDE. We study the panharmonic measure, which is a generalization of the harmonic measure for the Yukawa PDE. We show that there are natural stochastic definitions for the panharmonic measure in terms of the Brownian motion and that the harmonic and the panharmonic measures are all mutually equivalent. Furthermore, we calculate their Radon–Nikodym derivatives explicitly for some balls, which is a key result behind the WOS algorithm.

Stochastic interest model driven by compound Poisson process andBrownian motion with applications in life contingencies

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Shilong Li

2018-03-01

Full Text Available In this paper, we introduce a class of stochastic interest model driven by a compoundPoisson process and a Brownian motion, in which the jumping times of force of interest obeyscompound Poisson process and the continuous tiny fluctuations are described by Brownian motion, andthe adjustment in each jump of interest force is assumed to be random. Based on the proposed interestmodel, we discuss the expected discounted function, the validity of the model and actuarial presentvalues of life annuities and life insurances under different parameters and distribution settings. Ournumerical results show actuarial values could be sensitive to the parameters and distribution settings,which shows the importance of introducing this kind interest model.

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

Science.gov (United States)

Wang, Jun; Liang, Jin-Rong; Lv, Long-Jin; Qiu, Wei-Yuan; Ren, Fu-Yao

2012-02-01

In this paper, we study the problem of continuous time option pricing with transaction costs by using the homogeneous subdiffusive fractional Brownian motion (HFBM) Z(t)=X(Sα(t)), 0transaction costs of replicating strategies. We also give the total transaction costs.

Quantum Brownian motion in a bath of parametric oscillators: A model for system-field interactions

International Nuclear Information System (INIS)

Hu, B.L.; Matacz, A.

1994-01-01

The quantum Brownian motion paradigm provides a unified framework where one can see the interconnection of some basic quantum statistical processes such as decoherence, dissipation, particle creation, noise, and fluctuation. The present paper continues the investigation begun in earlier papers on the quantum Brownian motion in a general environment via the influence functional formalism. Here, the Brownian particle is coupled linearly to a bath of the most general time-dependent quadratic oscillators. This bath of parametric oscillators minics a scalar field, while the motion of the Brownian particle modeled by a single oscillator could be used to depict the behavior of a particle detector, a quantum field mode, or the scale factor of the Universe. An important result of this paper is the derivation of the influence functional encompassing the noise and dissipation kernels in terms of the Bogolubov coefficients, thus setting the stage for the influence functional formalism treatment of problems in quantum field theory in curved spacetime. This method enables one to trace the source of statistical processes such as decoherence and dissipation to vacuum fluctuations and particle creation, and in turn impart a statistical mechanical interpretation of quantum field processes. With this result we discuss the statistical mechanical origin of quantum noise and thermal radiance from black holes and from uniformly accelerated observers in Minkowski space as well as from the de Sitter universe discovered by Hawking, Unruh, and Gibbons and Hawking. We also derive the exact evolution operator and master equation for the reduced density matrix of the system interacting with a parametric oscillator bath in an initial squeezed thermal state. These results are useful for decoherence and back reaction studies for systems and processes of interest in semiclassical cosmology and gravity. Our model and results are also expected to be useful for related problems in quantum optics

Special relativity and the Karhunen-Loeve expansion of Brownian motion

International Nuclear Information System (INIS)

Maccone, C.

1987-01-01

The connection between special relativity and the theory of the time-rescaled Gaussian stochastic processes is brought to light. It is given the general expression of the Karhunen-Loewe expansion for the Brownian motion whose variable is the proper time. The relevant eigenfunctions are proved to be Bessel functions, and their stability is discussed. The eigenvalues are shown to be the zeros of certain linear combinations of the Bessel functions and their partials. The energy distribution of such a class of processes is investigated, and it is given explicit formulae for both its mean value and variance. Finally it is studied in detail the Karhumen-Loeve expansion for a case of relativistic decelerated motion whose analysis is feasible in closed form

Maximizing the Mean Exit Time of a Brownian Motion from an Interval

Directory of Open Access Journals (Sweden)

Mario Lefebvre

2011-01-01

Full Text Available Let X(t be a controlled one-dimensional standard Brownian motion starting from x∈(−d,d. The problem of optimally controlling X(t until |X(t|=d for the first time is solved explicitly in a particular case. The maximal value that the instantaneous reward given for survival in (−d,d can take is determined.

Whitening filter and innovational representation of fractional Brownian motion

International Nuclear Information System (INIS)

Wang Xiaotian; Wu Min

2009-01-01

In this paper, by means of fractional differential-integral technique we give a new whitening filter formula for fractional Brownian motion defined by Mandelbrot and van Ness [Mandelbrot BB, van Ness JW. SIAM Rev 1968;10(4):422]. This new formula has potential use in time series analysis and in detecting signals as Barton and Vincent Poor [Barton RJ, Vincent Poor H. IEEE Trans Inform Theory 1988;34(5):943] have shown. Another potential application of it is behavioral finance, where the arbitrage opportunities that come from the reversal effect of stock returns, can be eliminated by such a formula.

Molecular dynamics test of the Brownian description of Na+ motion in water

International Nuclear Information System (INIS)

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

1985-01-01

The autocorrelation function of the velocity of an infinitely dilute Na + ion in aqueous solution, and the autocorrelation function of the force exerted on a stationary Na + under the same conditions are evaluated by molecular dynamics calculations. The results are used to test the accuracy of Brownian motion assumptions which are basic to hydrodynamic models of ion dynamics in solution. The self-diffusion coefficient of the Na + ion predicted by Brownian motion theory is (0.65 +- 0.1) x 10 -5 cm 2 /s. This value is about 60% greater than the one obtained for the proper dynamics of the finite mass ion, (0.4 +- 0.1) x 10 -5 cm 2 /s. The numerically correct velocity autocorrelation function is nonexponential, and the autocorrelation of the force on the stationary ion does not decay faster than the ion velocity autocorrelation function. Motivated by previous hydrodynamic modeling of friction kernels, we examine the approximation in which the memory function for the velocity autocorrelation function is identified with the autocorrelation function of the force on the stationary ion. The overall agreement between this approximation for the velocity autocorrelation function and the numerically correct answer is quite good

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

Science.gov (United States)

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.

Near-Field, On-Chip Optical Brownian Ratchets.

Science.gov (United States)

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

2016-08-10

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

Elliott wave principle and the corresponding fractional Brownian motion in stock markets: Evidence from Nikkei 225 index

International Nuclear Information System (INIS)

Ilalan, Deniz

2016-01-01

Highlights: • Hausdorff dimension of the Elliott Wave trajectories is computed. • Linkage between Elliott Wave principle and fractional Brownian motion is proposed. • Log-normality of stock returns is discussed from a fractal point of view. - Abstract: This paper examines one of the vital technical analysis indicators known as the Elliott wave principle. Since these waves have a fractal nature with patterns that are not exact, we first determine the dimension of them. Our second aim is to find a linkage between Elliott wave principle and fractional Brownian motion via comparing their Hausdorff dimensions. Thirdly, we consider the Nikkei 225 index during Japan asset price bubble, which is a perfect example of an Elliott wave.

Permutation entropy of fractional Brownian motion and fractional Gaussian noise

International Nuclear Information System (INIS)

Zunino, L.; Perez, D.G.; Martin, M.T.; Garavaglia, M.; Plastino, A.; Rosso, O.A.

2008-01-01

We have worked out theoretical curves for the permutation entropy of the fractional Brownian motion and fractional Gaussian noise by using the Bandt and Shiha [C. Bandt, F. Shiha, J. Time Ser. Anal. 28 (2007) 646] theoretical predictions for their corresponding relative frequencies. Comparisons with numerical simulations show an excellent agreement. Furthermore, the entropy-gap in the transition between these processes, observed previously via numerical results, has been here theoretically validated. Also, we have analyzed the behaviour of the permutation entropy of the fractional Gaussian noise for different time delays

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

Science.gov (United States)

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

2014-01-01

Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when foraging in resource-poor environments. Yet, empirical studies reveal animals moving in a Brownian fashion when resources are abundant. We demonstrate that Einstein's original theory of collision-induced Brownian motion in physics provides a parsimonious, mechanistic explanation for these observations. Here, Brownian motion results from frequent encounters between organisms in dense environments. In density-controlled experiments, movement patterns of mussels shifted from Lévy towards Brownian motion with increasing density. When the analysis was restricted to moves not truncated by encounters, this shift did not occur. Using a theoretical argument, we explain that any movement pattern approximates Brownian motion at high-resource densities, provided that movement is interrupted upon encounters. Hence, the observed shift to Brownian motion does not indicate a density-dependent change in movement strategy but rather results from frequent collisions. Our results emphasize the need for a more mechanistic use of Brownian motion in ecology, highlighting that especially in rich environments, Brownian motion emerges from ecological interactions, rather than being a default movement pattern. PMID:24225464

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

Science.gov (United States)

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.

Upside/Downside statistical mechanics of nonequilibrium Brownian motion. I. Distributions, moments, and correlation functions of a free particle

Science.gov (United States)

Craven, Galen T.; Nitzan, Abraham

2018-01-01

Statistical properties of Brownian motion that arise by analyzing, separately, trajectories over which the system energy increases (upside) or decreases (downside) with respect to a threshold energy level are derived. This selective analysis is applied to examine transport properties of a nonequilibrium Brownian process that is coupled to multiple thermal sources characterized by different temperatures. Distributions, moments, and correlation functions of a free particle that occur during upside and downside events are investigated for energy activation and energy relaxation processes and also for positive and negative energy fluctuations from the average energy. The presented results are sufficiently general and can be applied without modification to the standard Brownian motion. This article focuses on the mathematical basis of this selective analysis. In subsequent articles in this series, we apply this general formalism to processes in which heat transfer between thermal reservoirs is mediated by activated rate processes that take place in a system bridging them.

Random functions via Dyson Brownian Motion: progress and problems

International Nuclear Information System (INIS)

Wang, Gaoyuan; Battefeld, Thorsten

2016-01-01

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

Random functions via Dyson Brownian Motion: progress and problems

Energy Technology Data Exchange (ETDEWEB)

Wang, Gaoyuan; Battefeld, Thorsten [Institute for Astrophysics, University of Goettingen,Friedrich Hund Platz 1, D-37077 Goettingen (Germany)

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.

Theory of Brownian motion with the Alder-Wainwright effect

International Nuclear Information System (INIS)

Okabe, Y.

1986-01-01

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

A short note on the mean exit time of the Brownian motion

Science.gov (United States)

Cadeddu, Lucio; Farina, Maria Antonietta

We investigate the functional Ω↦ℰ(Ω) where Ω runs through the set of compact domains of fixed volume v in any Riemannian manifold (M,g) and where ℰ(Ω) is the mean exit time from Ω of the Brownian motion. We give an alternative analytical proof of a well-known fact on its critical points proved by McDonald: the critical points of ℰ(Ω) are harmonic domains.

Brownian modulated optical nanoprobes

International Nuclear Information System (INIS)

Behrend, C.J.; Anker, J.N.; Kopelman, R.

2004-01-01

Brownian modulated optical nanoprobes (Brownian MOONs) are fluorescent micro- and nanoparticles that resemble moons: one hemisphere emits a bright fluorescent signal, while an opaque metal darkens the other hemisphere. Brownian motion causes the particles to tumble and blink erratically as they rotate literally through the phases of the moon. The fluctuating probe signals are separated from optical and electronic backgrounds using principal components analysis or images analysis. Brownian MOONs enable microrheological measurements on size scales and timescales that are difficult to study with other methods. Local chemical concentrations can be measured simultaneously, using spectral characteristics of indicator dyes embedded within the MOONs

Vehicle ego-motion estimation with geometric algebra

NARCIS (Netherlands)

Mark, W. van der; Fontijne, D.; Dorst, L.; Groen, F.C.A.

2003-01-01

A method for estimating ego-motion with vehicle mounted stereo cameras is presented. This approach is based on finding corresponding features in stereo images and tracking them between succeeding stereo frames. Our approach estimates stereo ego-motion with geometric algebra techniques. Starting with

The effect of various conductivity and viscosity models considering Brownian motion on nanofluids mixed convection flow and heat transfer

Directory of Open Access Journals (Sweden)

H. R. Ehteram

2016-01-01

Full Text Available In this paper the effect of using various models for conductivity and viscosity considering Brownian motion of nanoparticles is investigated. This study is numerically conducted inside a cavity full of Water-Al2O3 nanofluid at the case of mixed convection heat transfer. The effect of some parameters such as the nanoparticle volume fraction, Rayleigh, Richardson and Reynolds numbers has been examined. The governing equations with specified boundary conditions has been solved using finite volume method. A computer code has been prepared for this purpose. The results are presented in form of stream functions, isotherms, Nusselt number and the flow power with and without the Brownian motion taken into consideration. The results show that for all the applied models the stream functions and isotherm have approximately same patterns and no considerable difference has been observed. In all the studied models when considering the Brownian motion, the average Nusselt number is higher than not taking this effect into account. The models of Koo-Kleinstreuer and Li-Kleinstreuer give almost same values for the maximum stream function and average Nusselt number. It is also true about the models of Vajjha-Das and Xiao et al.

Fractionalization of the complex-valued Brownian motion of order n using Riemann-Liouville derivative. Applications to mathematical finance and stochastic mechanics

International Nuclear Information System (INIS)

Jumarie, Guy

2006-01-01

The (complex-valued) Brownian motion of order n is defined as the limit of a random walk on the complex roots of the unity. Real-valued fractional noises are obtained as fractional derivatives of the Gaussian white noise (or order two). Here one combines these two approaches and one considers the new class of fractional noises obtained as fractional derivative of the complex-valued Brownian motion of order n. The key of the approach is the relation between differential and fractional differential provided by the fractional Taylor's series of analytic function f(z+h)=E α (h α D z α ).f(z), where E α is the Mittag-Leffler function on the one hand, and the generalized Maruyama's notation, on the other hand. Some questions are revisited such as the definition of fractional Brownian motion as integral w.r.t. (dt) α , and the exponential growth equation driven by fractional Brownian motion, to which a new solution is proposed. As a first illustrative example of application, in mathematical finance, one proposes a new approach to the optimal management of a stochastic portfolio of fractional order via the Lagrange variational technique applied to the state moment dynamical equations. In the second example, one deals with non-random Lagrangian mechanics of fractional order. The last example proposes a new approach to fractional stochastic mechanics, and the solution so obtained gives rise to the question as to whether physical systems would not have their own internal random times

Generalized Langevin Theory Of The Brownian Motion And The Dynamics Of Polymers In Solution

International Nuclear Information System (INIS)

Tothova, J.; Lisy, V.

2015-01-01

The review deals with a generalization of the Rouse and Zimm bead-spring models of the dynamics of flexible polymers in dilute solutions. As distinct from these popular theories, the memory in the polymer motion is taken into account. The memory naturally arises as a consequence of the fluid and bead inertia within the linearized Navier-Stokes hydrodynamics. We begin with a generalization of the classical theory of the Brownian motion, which forms the basis of any theory of the polymer dynamics. The random force driving the Brownian particles is not the white one as in the Langevin theory, but “colored”, i.e., statistically correlated in time, and the friction force on the particles depends on the history of their motion. An efficient method of solving the resulting generalized Langevin equations is presented and applied to the solution of the equations of motion of polymer beads. The memory effects lead to several peculiarities in the time correlation functions used to describe the dynamics of polymer chains. So, the mean square displacement of the polymer coils contains algebraic long-time tails and at short times it is ballistic. It is shown how these features reveal in the experimentally observable quantities, such as the dynamic structure factors of the scattering or the viscosity of polymer solutions. A phenomenological theory is also presented that describes the dependence of these quantities on the polymer concentration in solution. (author)

From Brownian motion to power of fluctuations

Directory of Open Access Journals (Sweden)

B. Berche

2012-12-01

Full Text Available The year 2012 marks the 140th birth anniversary of Marian Smoluchowski (28.05.1872-5.09.1917, a man who "made ground-breaking contribution to the theory of Brownian motion, the theory of sedimentation, the statistical nature of the Second Law, the theory and practice of density fluctuations (critical opalescence. During his final years of scientific creativity his pioneering theory of coagulation and diffusion-limited reaction rate appeared. These outstanding achievements present true gems which dominate the description of soft matter physics and chemical physics as well as the related areas up till now!" This quotation was taken from the lecture by Peter Hanggi given at international conference Statistical Physics: Modern Trends and Applications that took place in Lviv, Ukraine on July 3-6, 2012 (see conference web-page for more details and was dedicated to the commemoration of Smoluchowski's work. This and forthcoming issues of the Condensed Matter Physics contain papers presented at this conference.

A canonical process for estimation of convex functions : The "invelope" of integrated Brownian motion +t4

NARCIS (Netherlands)

Groeneboom, P.; Jongbloed, G.; Wellner, J.A.

2001-01-01

A process associated with integrated Brownian motion is introduced that characterizes the limit behavior of nonparametric least squares and maximum likelihood estimators of convex functions and convex densities, respectively. We call this process “the invelope” and show that it is an almost surely

Scaling laws for fractional Brownian motion with power-law clock

International Nuclear Information System (INIS)

O'Malley, Daniel; Cushman, John H; Johnson, Graham

2011-01-01

We study the mean first passage time (MFPT) for fractional Brownian motion (fBm) in a finite interval with absorbing boundaries at each end. Analytical arguments are used to suggest a simple scaling law for the MFPT and numerical experiments are performed to verify its accuracy. The same approach is used to derive a scaling law for fBm with a power-law clock (fBm-plc). The MFPT scaling laws are employed to develop scaling laws for the finite-size Lyapunov exponent (FSLE) of fBm and fBm-plc. We apply these results to diffusion of a large polymer in a region with absorbing boundaries. (letter)

Diffusion limit of Lévy-Lorentz gas is Brownian motion

Science.gov (United States)

Magdziarz, Marcin; Szczotka, Wladyslaw

2018-07-01

In this paper we analyze asymptotic behaviour of a stochastic process called Lévy-Lorentz gas. This process is aspecial kind of continuous-time random walk in which walker moves in the fixed environment composed of scattering points. Upon each collision the walker performs a flight to the nearest scattering point. This type of dynamics is observed in Lévy glasses or long quenched polymers. We show that the diffusion limit of Lévy-Lorentz gas with finite mean distance between scattering centers is the standard Brownian motion. Thus, for long times the behaviour of the Lévy-Lorentz gas is close to the diffusive regime.

A hydrodynamic formalism for Brownian systems

International Nuclear Information System (INIS)

Pina, E.; Rosales, M.A.

1981-01-01

A formal hydrodynamic approach to Brownian motion is presented and the corresponding equations are derived. Hydrodynamic quantities are expressed in terms of the physical variables characterizing the Brownian systems. Contact is made with the hydrodynamic model of Quantum Mechanics. (author)

Diffuse correlation tomography in the transport regime: A theoretical study of the sensitivity to Brownian motion

Science.gov (United States)

Tricoli, Ugo; Macdonald, Callum M.; Durduran, Turgut; Da Silva, Anabela; Markel, Vadim A.

2018-02-01

Diffuse correlation tomography (DCT) uses the electric-field temporal autocorrelation function to measure the mean-square displacement of light-scattering particles in a turbid medium over a given exposure time. The movement of blood particles is here estimated through a Brownian-motion-like model in contrast to ordered motion as in blood flow. The sensitivity kernel relating the measurable field correlation function to the mean-square displacement of the particles can be derived by applying a perturbative analysis to the correlation transport equation (CTE). We derive an analytical expression for the CTE sensitivity kernel in terms of the Green's function of the radiative transport equation, which describes the propagation of the intensity. We then evaluate the kernel numerically. The simulations demonstrate that, in the transport regime, the sensitivity kernel provides sharper spatial information about the medium as compared with the correlation diffusion approximation. Also, the use of the CTE allows one to explore some additional degrees of freedom in the data such as the collimation direction of sources and detectors. Our results can be used to improve the spatial resolution of DCT, in particular, with applications to blood flow imaging in regions where the Brownian motion is dominant.

The colour of thermal noise in classical Brownian motion: a feasibility study of direct experimental observation

International Nuclear Information System (INIS)

Berg-Soerensen, Kirstine; Flyvbjerg, Henrik

2005-01-01

One hundred years after Einstein modelled Brownian motion, a central aspect of this motion in incompressible fluids has not been verified experimentally: the thermal noise that drives the Brownian particle, is not white, as in Einstein's simple theory. It is slightly coloured, due to hydrodynamics and the fluctuation-dissipation theorem. This theoretical result from the 1970s was prompted by computer simulation results in apparent violation of Einstein's theory. We discuss how a direct experimental observation of this colour might be carried out by using optical tweezers to separate the thermal noise from the particle's dynamic response to it. Since the thermal noise is almost white, very good statistics is necessary to resolve its colour. That requires stable equipment and long recording times, possibly making this experiment one for the future only. We give results for experimental requirements and for stochastic errors as functions of experimental window and measurement time, and discuss some potential sources of systematic errors

Random walks, Brownian motion, and interacting particle systems: a festschrift in honor of Frank Spitzer

National Research Council Canada - National Science Library

Durrett, Richard; Kesten, Harry; Spitzer, Frank

1991-01-01

..., made the transparency used in the printing process. STUDENTS OF FRANK SPITZERSTUDENTS OF FRANK SPITZER 1957 J. W. Lamperti, On the asymptotic behavior of recurrent and almostrecurrent events. 1964 W. W. Whitman, Some strong laws for random walks and Brownian motion. 1965 J. C. Mineka, The existence and uniqueness of positive solutions to the Wien...

The first-passage area for drifted Brownian motion and the moments of the Airy distribution

International Nuclear Information System (INIS)

Kearney, Michael J; Majumdar, Satya N; Martin, Richard J

2007-01-01

An exact expression for the distribution of the area swept out by a drifted Brownian motion till its first-passage time is derived. A study of the asymptotic behaviour confirms earlier conjectures and clarifies their range of validity. The analysis leads to a simple closed-form solution for the moments of the Airy distribution. (fast track communication)

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

Science.gov (United States)

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

2014-01-01

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

Brownian Optimal Stopping and Random Walks

International Nuclear Information System (INIS)

Lamberton, D.

2002-01-01

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

Semicircular canals circumvent Brownian Motion overload of mechanoreceptor hair cells

DEFF Research Database (Denmark)

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

2016-01-01

Vertebrate semicircular canals (SCC) first appeared in the vertebrates (i.e. ancestral fish) over 600 million years ago. In SCC the principal mechanoreceptors are hair cells, which as compared to cochlear hair cells are distinctly longer (70 vs. 7 μm), 10 times more compliant to bending (44 vs. 500...... nN/m), and have a 100-fold higher tip displacement threshold (hair cells where the bundle is approximated as a stiff, cylindrical elastic rod subject to friction and thermal agitation. Our models suggest that the above...... differences aid SCC hair cells in circumventing the masking effects of Brownian motion noise of about 70 nm, and thereby permit transduction of very low frequency (

A one-dimensional gravitationally interacting gas and the convex minorant of Brownian motion

International Nuclear Information System (INIS)

Suidan, T M

2001-01-01

The surprising connection between a one-dimensional gravitationally interacting gas of sticky particles and the convex minorant process generated by Brownian motion on [0,1] is studied. A study is made of the dynamics of this 1-D gas system by identifying three distinct clustering regimes and the time scales at which they occur. At the critical moment of time the mass distribution of the gas can be computed in terms of functionals of the convex minorant process

Quantum description of the Brownian movement in an external field

International Nuclear Information System (INIS)

Svin'in, I.R.

1976-01-01

The Schroedinger equation for brownian motion in an external field is obtained on the basis of the classical Langevin equation. The specific features of the approach proposed are illustrated by the example of the brownian motion of the quantum oscillator. The influence of the fluctuations on the various physical quantities is considered

From a stochastic to a macroscopic approach to brownian motion

International Nuclear Information System (INIS)

Bocquet, L.

1998-01-01

In this lecture, we examine the dynamics of suspensions of mesoscopic (Brownian) particles in a molecular fluid, starting from first principles. We introduce the technique of multiple time-scales to derive the Fokker-Planck equation for a single, or for a set of interacting Brownian particles, starting from the Liouville equation for the full system (Brownian particles and discrete bath). The limitations of the Fokker-Planck equation will then be emphasized. In particular, we shall point out that under ''standard'' experimental conditions, the Fokker-Planck description cannot be correct and that non-Markovian effects are expected. A microscopic description in the true experimental limit confirms this breakdown and leads to a ''generalized'' (non-Markovian and non-local in velocity space) Fokker-Planck equation, which describes the thermalization of the Brownian particle. (author)

Optimal dividends in the Brownian motion risk model with interest

Science.gov (United States)

Fang, Ying; Wu, Rong

2009-07-01

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

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

Science.gov (United States)

Puchkov, Evgeny O

2010-06-01

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

Characterizing Detrended Fluctuation Analysis of multifractional Brownian motion

Science.gov (United States)

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

2015-02-01

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

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

NARCIS (Netherlands)

de Jager, M.; Bartumeus, F.; Kölzsch, A.; Weissing, F.J.; Hengeveld, G.M.; Nolet, B.A.; Herman, P.M.J.; de Koppel, J.

2014-01-01

Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when

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

NARCIS (Netherlands)

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

2014-01-01

Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when

How superdiffusion gets arrested : Ecological encounters explain shift from Levy to Brownian movement

NARCIS (Netherlands)

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

2014-01-01

Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when

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

International Nuclear Information System (INIS)

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

2017-01-01

At present, many chaos-based image encryption algorithms have proved to be unsafe, few encryption schemes permute the plain images as three-dimensional (3D) bit matrices, and thus bits cannot move to any position, the movement range of bits are limited, and based on them, in this paper we present a novel image encryption algorithm based on 3D Brownian motion and chaotic systems. The architecture of confusion and diffusion is adopted. Firstly, the plain image is converted into a 3D bit matrix and split into sub blocks. Secondly, block confusion based on 3D Brownian motion (BCB3DBM) is proposed to permute the position of the bits within the sub blocks, and the direction of particle movement is generated by logistic-tent system (LTS). Furthermore, block confusion based on position sequence group (BCBPSG) is introduced, a four-order memristive chaotic system is utilized to give random chaotic sequences, and the chaotic sequences are sorted and a position sequence group is chosen based on the plain image, then the sub blocks are confused. The proposed confusion strategy can change the positions of the bits and modify their weights, and effectively improve the statistical performance of the algorithm. Finally, a pixel level confusion is employed to enhance the encryption effect. The initial values and parameters of chaotic systems are produced by the SHA 256 hash function of the plain image. Simulation results and security analyses illustrate that our algorithm has excellent encryption performance in terms of security and speed. (paper)

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

Science.gov (United States)

Gautestad, Arild O

2013-03-01

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

Study of two-dimensional Debye clusters using Brownian motion

International Nuclear Information System (INIS)

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

2006-01-01

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

On the motion of a Brownian particle with an asymmetric bias

International Nuclear Information System (INIS)

Kim, K.S.

1981-01-01

On the infinite three dimensional cubic lattice, the transport process of a Brownian particle biased on the direction (in the case of nearest-neighbor jumping) is discussed. The Brownian particle is considered as a walker of the random process. By introducing the theorem that the probability density P(l,t) becomes Gaussian for large t, P(l,t) is completely specified when the first and second moments of P(l,t) become known. The respective values for the transprot averaged velocity and dispersion of a biased Brownian particle are obtained. Finally as t becomes large we find Gaussian packets of a biased Brownian particle which propagate with a constant velocity and have a dispersion proportional to time t. (KAERI)

On Drift Parameter Estimation in Models with Fractional Brownian Motion by Discrete Observations

Directory of Open Access Journals (Sweden)

Yuliya Mishura

2014-06-01

Full Text Available We study a problem of an unknown drift parameter estimation in a stochastic differen- tial equation driven by fractional Brownian motion. We represent the likelihood ratio as a function of the observable process. The form of this representation is in general rather complicated. However, in the simplest case it can be simplified and we can discretize it to establish the a. s. convergence of the discretized version of maximum likelihood estimator to the true value of parameter. We also investigate a non-standard estimator of the drift parameter showing further its strong consistency. 

Entropy production of a Brownian ellipsoid in the overdamped limit.

Science.gov (United States)

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.

Irreversible Brownian Heat Engine

Science.gov (United States)

Taye, Mesfin Asfaw

2017-10-01

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

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

Energy Technology Data Exchange (ETDEWEB)

Dettmer, Simon L.; Keyser, Ulrich F.; Pagliara, Stefano [Cavendish Laboratory, University of Cambridge, 19 J J Thomson Avenue, Cambridge CB3 0HE (United Kingdom)

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.

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

Science.gov (United States)

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

2016-07-11

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

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

OpenAIRE

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

2014-01-01

Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when foraging in resource-poor environments. Yet, empirical studies reveal animals moving in a Brownian fashion when resources are abundant. We demonstrate that Einstein’s original theory ...

Oil prices. Brownian motion or mean reversion? A study using a one year ahead density forecast criterion

International Nuclear Information System (INIS)

Meade, Nigel

2010-01-01

For oil related investment appraisal, an accurate description of the evolving uncertainty in the oil price is essential. For example, when using real option theory to value an investment, a density function for the future price of oil is central to the option valuation. The literature on oil pricing offers two views. The arbitrage pricing theory literature for oil suggests geometric Brownian motion and mean reversion models. Empirically driven literature suggests ARMA-GARCH models. In addition to reflecting the volatility of the market, the density function of future prices should also incorporate the uncertainty due to price jumps, a common occurrence in the oil market. In this study, the accuracy of density forecasts for up to a year ahead is the major criterion for a comparison of a range of models of oil price behaviour, both those proposed in the literature and following from data analysis. The Kullbach Leibler information criterion is used to measure the accuracy of density forecasts. Using two crude oil price series, Brent and West Texas Intermediate (WTI) representing the US market, we demonstrate that accurate density forecasts are achievable for up to nearly two years ahead using a mixture of two Gaussians innovation processes with GARCH and no mean reversion. (author)

Oil prices. Brownian motion or mean reversion? A study using a one year ahead density forecast criterion

Energy Technology Data Exchange (ETDEWEB)

Meade, Nigel [Imperial College, Business School London (United Kingdom)

2010-11-15

For oil related investment appraisal, an accurate description of the evolving uncertainty in the oil price is essential. For example, when using real option theory to value an investment, a density function for the future price of oil is central to the option valuation. The literature on oil pricing offers two views. The arbitrage pricing theory literature for oil suggests geometric Brownian motion and mean reversion models. Empirically driven literature suggests ARMA-GARCH models. In addition to reflecting the volatility of the market, the density function of future prices should also incorporate the uncertainty due to price jumps, a common occurrence in the oil market. In this study, the accuracy of density forecasts for up to a year ahead is the major criterion for a comparison of a range of models of oil price behaviour, both those proposed in the literature and following from data analysis. The Kullbach Leibler information criterion is used to measure the accuracy of density forecasts. Using two crude oil price series, Brent and West Texas Intermediate (WTI) representing the US market, we demonstrate that accurate density forecasts are achievable for up to nearly two years ahead using a mixture of two Gaussians innovation processes with GARCH and no mean reversion. (author)

How superdiffusion gets arrested: Ecological encounters explain shift from Lévy to Brownian movement

NARCIS (Netherlands)

De Jager, M.; Bartumeus, F.; Kölzsch, A.; Weissing, F.J.; Hengeveld, G.M.; Nolet, B.A.; Herman, P.M.J.; Van de Koppel, J.

2014-01-01

Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when

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

NARCIS (Netherlands)

Jager, de M.; Bartumeus, F.; Kölzsch, A.; Weissing, F.J.; Hengeveld, G.M.; Nolet, B.A.; Herman, P.M.J.; Koppel, van de J.

2014-01-01

Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when

On the use of reverse Brownian motion to accelerate hybrid simulations

Energy Technology Data Exchange (ETDEWEB)

Bakarji, Joseph; Tartakovsky, Daniel M., E-mail: tartakovsky@stanford.edu

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.

Rotational and translational Brownian motion

International Nuclear Information System (INIS)

Coffey, W.T.; Salford Univ.

1980-01-01

In this review it is proposed to summarise the work on the theory of the translational and rotational Brownian movement which has been carried on over roughly the past 30 years. The review is intended to take the form of a tutorial paper rather than a list of the results obtained by the various investigators over the period in question. In this vein then it seems appropriate to firstly give a brief account of those parts of the theory of probability which are relevant to the problems under discussion. (orig.)

On the validity of Brownian assumptions in the spin van der Waals model

International Nuclear Information System (INIS)

Oh, Suhk Kun

1985-01-01

A simple Brownian motion theory of the spin van der Waals model, which can be stationary, Markoffian or Gaussian, is studied. By comparing the Brownian motion theory with an exact theory called the generalized Langevin equation theory, the validity of the Brownian assumptions is tested. Thereby, it is shown explicitly how the Markoffian and Gaussian properties are modified in the spin van der Waals model under the influence of quantum fluctuations and long range ordering. (Author)

NMR signals within the generalized Langevin model for fractional Brownian motion

Science.gov (United States)

Lisý, Vladimír; Tóthová, Jana

2018-03-01

The methods of Nuclear Magnetic Resonance belong to the best developed and often used tools for studying random motion of particles in different systems, including soft biological tissues. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard memoryless Langevin description of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spin-bearing particles in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in an exceedingly simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues. The effect of the trap is demonstrated by introducing a simple model for the generalized diffusion coefficient of the particle.

Brownian motion, dynamical randomness and irreversibility

International Nuclear Information System (INIS)

Gaspard, Pierre

2005-01-01

A relationship giving the entropy production as the difference between a time-reversed entropy per unit time and the standard one is applied to stochastic processes of diffusion of Brownian particles between two reservoirs at different concentrations. The entropy production in the nonequilibrium steady state is interpreted in terms of a time asymmetry in the dynamical randomness between the forward and backward paths of the diffusion process

Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field

Science.gov (United States)

Das, Joydip; Mondal, Shrabani; Bag, Bidhan Chandra

2017-10-01

In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.

Fractional Langevin Equation Model for Characterization of Anomalous Brownian Motion from NMR Signals

Science.gov (United States)

Lisý, Vladimír; Tóthová, Jana

2018-02-01

Nuclear magnetic resonance is often used to study random motion of spins in different systems. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard Langevin theory of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spins in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in a simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues.

Analyzing animal movements using Brownian bridges.

Science.gov (United States)

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

2007-09-01

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

Brownian movement and molecular reality

CERN Document Server

Perrin, Jean

2005-01-01

How do we know that molecules really exist? An important clue came from Brownian movement, a concept developed in 1827 by botanist Robert Brown, who noticed that tiny objects like pollen grains shook and moved erratically when viewed under a microscope. Nearly 80 years later, in 1905, Albert Einstein explained this ""Brownian motion"" as the result of bombardment by molecules. Einstein offered a quantitative explanation by mathematically estimating the average distance covered by the particles over time as a result of molecular bombardment. Four years later, Jean Baptiste Perrin wrote Brownia

Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders

Science.gov (United States)

Kanazawa, Kiyoshi; Sueshige, Takumi; Takayasu, Hideki; Takayasu, Misako

2018-03-01

A microscopic model is established for financial Brownian motion from the direct observation of the dynamics of high-frequency traders (HFTs) in a foreign exchange market. Furthermore, a theoretical framework parallel to molecular kinetic theory is developed for the systematic description of the financial market from microscopic dynamics of HFTs. We report first on a microscopic empirical law of traders' trend-following behavior by tracking the trajectories of all individuals, which quantifies the collective motion of HFTs but has not been captured in conventional order-book models. We next introduce the corresponding microscopic model of HFTs and present its theoretical solution paralleling molecular kinetic theory: Boltzmann-like and Langevin-like equations are derived from the microscopic dynamics via the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. Our model is the first microscopic model that has been directly validated through data analysis of the microscopic dynamics, exhibiting quantitative agreements with mesoscopic and macroscopic empirical results.

Spectral decomposition of optimal asset-liability management

NARCIS (Netherlands)

Decamps, M.; de Schepper, A.; Goovaerts, M.

2009-01-01

This paper concerns optimal asset-liability management when the assets and the liabilities are modeled by means of correlated geometric Brownian motions as suggested in Gerber and Shiu [2003. Geometric Brownian motion models for assets and liabilities: from pension funding to optimal dividends.

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

Science.gov (United States)

Xie, Ping

2009-09-16

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

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

International Nuclear Information System (INIS)

Xie Ping

2009-01-01

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

Entropic Approach to Brownian Movement.

Science.gov (United States)

Neumann, Richard M.

1980-01-01

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

Geometric Relations for CYLEX Test Tube-Wall Motion

Science.gov (United States)

Hill, Larry

2015-06-01

The CYLinder EXpansion (CYLEX) test is a (precision, instrumented, high-purity annealed copper) pipe bomb. Its essential measured quantities are detonation speed and tube-wall motion. Its main purpose is to calibrate detonation product equations of state (EOS) by measuring how product fluid pushes metal. In its full complexity, CYLEX is an integral test, for which EOS calibration requires the entire system to be computationally modeled and compared to salient data. Stripped to its essence, CYLEX is a non-integral test for which one may perform the inverse problem, to infer the EOS directly from data. CYLEX analysis can be simplified by the fact that the test constituents achieve a steady traveling wave structure; this allows derivation of several useful geometric relationships regarding tube wall motion. The first such treatment was by G.I. Taylor. Although his analysis was limited to small wall deflection angles, he asserted that the results remain valid for arbitrary ones. I confirm this attribute and present additional useful relationships. In the past decade, CYLEX wall-motion instrumentation has migrated almost entirely from streak camera to PDV, yet discrepancies remain between the two methods. I further present geometric relationships that shed light on this issue. Work supported by the U.S. DOE.

The verification of the Taylor-expansion moment method for the nanoparticle coagulation in the entire size regime due to Brownian motion

International Nuclear Information System (INIS)

Yu Mingzhou; Lin Jianzhong; Jin Hanhui; Jiang Ying

2011-01-01

The closure of moment equations for nanoparticle coagulation due to Brownian motion in the entire size regime is performed using a newly proposed method of moments. The equations in the free molecular size regime and the continuum plus near-continuum regime are derived separately in which the fractal moments are approximated by three-order Taylor-expansion series. The moment equations for coagulation in the entire size regime are achieved by the harmonic mean solution and the Dahneke’s solution. The results produced by the quadrature method of moments (QMOM), the Pratsinis’s log-normal moment method (PMM), the sectional method (SM), and the newly derived Taylor-expansion moment method (TEMOM) are presented and compared in accuracy and efficiency. The TEMOM method with Dahneke’s solution produces the most accurate results with a high efficiency than other existing moment models in the entire size regime, and thus it is recommended to be used in the following studies on nanoparticle dynamics due to Brownian motion.

A multiscale approach to Brownian motors

International Nuclear Information System (INIS)

Pavliotis, G.A.

2005-01-01

The problem of Brownian motion in a periodic potential, under the influence of external forcing, which is either random or periodic in time, is studied in this Letter. Multiscale techniques are used to derive general formulae for the steady state particle current and the effective diffusion tensor. These formulae are then applied to calculate the effective diffusion coefficient for a Brownian particle in a periodic potential driven simultaneously by additive Gaussian white and colored noise. Our theoretical findings are supported by numerical simulations

Self-induced temperature gradients in Brownian dynamics

Science.gov (United States)

Devine, Jack; Jack, M. W.

2017-12-01

Brownian systems often surmount energy barriers by absorbing and emitting heat to and from their local environment. Usually, the temperature gradients created by this heat exchange are assumed to dissipate instantaneously. Here we relax this assumption to consider the case where Brownian dynamics on a time-independent potential can lead to self-induced temperature gradients. In the same way that externally imposed temperature gradients can cause directed motion, these self-induced gradients affect the dynamics of the Brownian system. The result is a coupling between the local environment and the Brownian subsystem. We explore the resulting dynamics and thermodynamics of these coupled systems and develop a robust method for numerical simulation. In particular, by focusing on one-dimensional situations, we show that self-induced temperature gradients reduce barrier-crossing rates. We also consider a heat engine and a heat pump based on temperature gradients induced by a Brownian system in a nonequilibrium potential.

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

Science.gov (United States)

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.

Fractional Brownian motions via random walk in the complex plane and via fractional derivative. Comparison and further results on their Fokker-Planck equations

International Nuclear Information System (INIS)

Jumarie, Guy

2004-01-01

There are presently two different models of fractional Brownian motions available in the literature: the Riemann-Liouville fractional derivative of white noise on the one hand, and the complex-valued Brownian motion of order n defined by using a random walk in the complex plane, on the other hand. The paper provides a comparison between these two approaches, and in addition, takes this opportunity to contribute some complements. These two models are more or less equivalent on the theoretical standpoint for fractional order between 0 and 1/2, but their practical significances are quite different. Otherwise, for order larger than 1/2, the fractional derivative model has no counterpart in the complex plane. These differences are illustrated by an example drawn from mathematical finance. Taylor expansion of fractional order provides the expression of fractional difference in terms of finite difference, and this allows us to improve the derivation of Fokker-Planck equation and Kramers-Moyal expansion, and to get more insight in their relation with stochastic differential equations of fractional order. In the case of multi-fractal systems, the Fokker-Planck equation can be solved by using path integrals, and the fractional dynamic equations of the state moments of the stochastic system can be easily obtained. By combining fractional derivative and complex white noise of order n, one obtains a family of complex-valued fractional Brownian motions which exhibits long-range dependence. The conclusion outlines suggestions for further research, mainly regarding Lorentz transformation of fractional noises

Hydrodynamically Coupled Brownian Dynamics simulations for flow on non-Newtonian fluids

NARCIS (Netherlands)

Ahuja, Vishal Raju

2018-01-01

This thesis deals with model development for particle-based flow simulations of non-Newtonian fluids such as polymer solutions. A novel computational technique called Hydrodynamically Coupled Brownian Dynamics (HCBD) is presented in this thesis. This technique essentially couples the Brownian motion

Estimating the Counterparty Risk Exposure by Using the Brownian Motion Local Time

Directory of Open Access Journals (Sweden)

Bonollo Michele

2017-06-01

Full Text Available In recent years, the counterparty credit risk measure, namely the default risk in over-the-counter (OTC derivatives contracts, has received great attention by banking regulators, specifically within the frameworks of Basel II and Basel III. More explicitly, to obtain the related risk figures, one is first obliged to compute intermediate output functionals related to the mark-to-market position at a given time no exceeding a positive and finite time horizon. The latter implies an enormous amount of computational effort is needed, with related highly time consuming procedures to be carried out, turning out into significant costs. To overcome the latter issue, we propose a smart exploitation of the properties of the (local time spent by the Brownian motion close to a given value.

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

Science.gov (United States)

Chen, Yao; Wang, Xudong; Deng, Weihua

2017-10-01

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

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

Science.gov (United States)

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

2013-01-01

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

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

Directory of Open Access Journals (Sweden)

Ryo Kanada

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

Simple Brownian diffusion an introduction to the standard theoretical models

CERN Document Server

Gillespie, Daniel T

2013-01-01

Brownian diffusion, the motion of large molecules in a sea of very many much smaller molecules, is topical because it is one of the ways in which biologically important molecules move about inside living cells. This book presents the mathematical physics that underlies the four simplest models of Brownian diffusion.

Scale-free animal movement patterns: Levy walks outperform fractional Brownian motions and fractional Levy motions in random search scenarios

International Nuclear Information System (INIS)

Reynolds, A M

2009-01-01

The movement patterns of a diverse range of animals have scale-free characteristics. These characteristics provide necessary but not sufficient conditions for the presence of movement patterns that can be approximated by Levy walks. Nevertheless, it has been widely assumed that the occurrence of scale-free animal movements can indeed be attributed to the presence of Levy walks. This is, in part, because it is known that the super-diffusive properties of Levy walks can be advantageous in random search scenarios when searchers have little or no prior knowledge of target locations. However, fractional Brownian motions (fBms) and fractional Levy motions (fLms) are both scale-free and super-diffusive, and so it is possible that these motions rather than Levy walks underlie some or all occurrences of scale-free animal movement patterns. Here this possibility is examined in numerical simulations through a determination of the searching efficiencies of fBm and fLm searches. It is shown that these searches are less efficient than Levy walk searches. This finding does not rule out the possibility that some animals with scale-free movement patterns are executing fBm and fLm searches, but it does make Levy walk searches the more likely possibility.

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

Science.gov (United States)

Hyeon, Changbong; Hwang, Wonseok

2017-07-01

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

On the motion of matter in the geometrical gauge field theory

International Nuclear Information System (INIS)

Konopleva, N.P.

2005-01-01

In the geometrical gauge field theory, the motion equations of matter (elementary particles) are connected with the field equations. The problems arising from this connection are discussed. For the first time, such problems arose in Einstein's General Relativity. Einstein hoped that solution of these problems will allow explanation of elementary particles nature without making use of quantum mechanics. But, as it turned out, the situation is more difficult. Here the corresponding problems are formulated for the connection of equations of particle motion and field equations in the geometrical gauge field theory. It is shown that appearance of the problems under discussion is an inevitable effect of passage to relativism and local symmetries

On the Motion of Matter in the Geometrical Gauge Field Theory

CERN Document Server

Konopleva, N P

2005-01-01

In the geometrical gauge field theory, the motion equations of matter (elementary particles) are connected with the field equations. In the talk, the problems arising from this connection are discussed. For the first time, such problems arose in Einstein's General Relativity. Einstein hoped that solution of these problems will allow explanation of elementary particles nature without making use of quantum mechanics. But, as it turned out, the situation is more difficult. Here the corresponding problems are formulated for the connection of equations of particle motion and field equations in the geometrical gauge field theory. It is shown that appearance of the problems under discussion is an inevitable effect of passage to relativism and local symmetries.

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

Energy Technology Data Exchange (ETDEWEB)

McMullan, G., E-mail: gm2@mrc-lmb.cam.ac.uk; Vinothkumar, K.R.; Henderson, R.

2015-11-15

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{sup 2} for every incident 300 keV e{sup −}/Å{sup 2}. The induced motion leads to an optimal exposure with 300 keV electrons of 4.0 e{sup −}/Å{sup 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. - Highlights: • Thon rings can be seen from amorphous ice. • Radiation damage to amorphous ice randomly displaces water molecules. • Each incident 300 keV e{sup −}/Å{sup 2} displaces water molecules on average by ∼1 Å. • Macromolecules embedded in amorphous ice undergo beam induced Brownian motion.

Langevin equation method for the rotational Brownian motion and orientational relaxation in liquids: II. Symmetrical top molecules

CERN Document Server

Coffey, W T; Titov, S V

2003-01-01

A theory of orientational relaxation for the inertial rotational Brownian motion of a symmetric top molecule is developed using the Langevin equation rather than the Fokker-Planck equation. The infinite hierarchy of differential-recurrence relations for the orientational correlation functions for the relaxation behaviour is derived by averaging the corresponding Euler-Langevin equations. The solution of this hierarchy is obtained using matrix continued fractions allowing the calculation of the correlation times and the spectra of the orientational correlation functions for typical values of the model parameters.

Critique of the Brownian approximation to the generalized Langevin equation in lattice dynamics

International Nuclear Information System (INIS)

Diestler, D.J.; Riley, M.E.

1985-01-01

We consider the classical motion of a harmonic lattice in which only those atoms in a certain subset of the lattice (primary zone) may interact with an external force. The formally exact generalized Langevin equation (GLE) for the primary zone is an appropriate description of the dynamics. We examine a previously proposed Brownian, or frictional damping, approximation that reduces the GLE to a set of coupled ordinary Langevin equations for the primary atoms. It is shown that the solution of these equations can contain undamped motion if there is more than one atom in the primary zone. Such motion is explicitly demonstrated for a model that has been used to describe energy transfer in atom--surface collisions. The inability of the standard Brownian approximation to yield an acceptable, physically meaningful result for primary zones comprising more than one atom suggests that the Brownian approximation may introduce other spurious dynamical effects. Further work on damping of correlated motion in lattices is needed

The path integral formulation of fractional Brownian motion for the general Hurst exponent

International Nuclear Information System (INIS)

Calvo, I; Sanchez, R

2008-01-01

In 1995, Sebastian (1995 J. Phys. A: Math. Gen. 28 4305) gave a path integral computation of the propagator of subdiffusive fractional Brownian motion (fBm), i.e. fBm with a Hurst or self-similarity exponent H element of (0, 1/2). The extension of Sebastian's calculation to superdiffusion, H element of (1/2, 1], becomes however quite involved due to the appearance of additional boundary conditions on fractional derivatives of the path. In this communication, we address the construction of the path integral representation in a different fashion, which allows us to treat both subdiffusion and superdiffusion on an equal footing. The derivation of the propagator of fBm for the general Hurst exponent is then performed in a neat and unified way. (fast track communication)

Bose polaron as an instance of quantum Brownian motion

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Aniello Lampo

2017-09-01

Full Text Available We study the dynamics of a quantum impurity immersed in a Bose-Einstein condensate as an open quantum system in the framework of the quantum Brownian motion model. We derive a generalized Langevin equation for the position of the impurity. The Langevin equation is an integrodifferential equation that contains a memory kernel and is driven by a colored noise. These result from considering the environment as given by the degrees of freedom of the quantum gas, and thus depend on its parameters, e.g. interaction strength between the bosons, temperature, etc. We study the role of the memory on the dynamics of the impurity. When the impurity is untrapped, we find that it exhibits a super-diffusive behavior at long times. We find that back-flow in energy between the environment and the impurity occurs during evolution. When the particle is trapped, we calculate the variance of the position and momentum to determine how they compare with the Heisenberg limit. One important result of this paper is that we find position squeezing for the trapped impurity at long times. We determine the regime of validity of our model and the parameters in which these effects can be observed in realistic experiments.

Concurrent correction of geometric distortion and motion using the map-slice-to-volume method in EPI

Science.gov (United States)

Yeo, Desmond T. B.; Fessler, Jeffrey A.; Kim, Boklye

2014-01-01

The accuracy of measuring voxel intensity changes between stimulus and rest images in fMRI echo-planar imaging (EPI) data is severely degraded in the presence of head motion. In addition, EPI is sensitive to susceptibility-induced geometric distortions. Head motion causes image shifts and associated field map changes that induce different geometric distortion at different time points. Conventionally, geometric distortion is “corrected” with a static field map independently of image registration. That approach ignores all field map changes induced by head motion. This work evaluates the improved motion correction capability of mapping slice to volume (MSV) registration with concurrent iterative field corrected reconstruction using updated field maps derived from an initial static field map that has been spatially transformed and resampled. It accounts for motion-induced field map changes for translational and in-plane rotation motion. The results from simulated EPI time series data, in which motion, image intensity and activation ground truths are available, show improved accuracy in image registration, field corrected image reconstruction and activation detection. PMID:18280077

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

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T. Turiv

2015-06-01

Full Text Available As recently reported [Turiv T. et al., Science, 2013, Vol. 342, 1351], fluctuations in the orientation of the liquid crystal (LC director can transfer momentum from the LC to a colloid, such that the diffusion of the colloid becomes anomalous on a short time scale. Using video microscopy and single particle tracking, we investigate random thermal motion of colloidal particles in a nematic liquid crystal for the time scales shorter than the expected time of director fluctuations. At long times, compared to the characteristic time of the nematic director relaxation we observe typical anisotropic Brownian motion with the mean square displacement (MSD linear in time τ and inversly proportional to the effective viscosity of the nematic medium. At shorter times, however, the dynamics is markedly nonlinear with MSD growing more slowly (subdiffusion or faster (superdiffusion than τ. These results are discussed in the context of coupling of colloidal particle's dynamics to the director fluctuation dynamics.

Meandering Brownian Donkeys

Science.gov (United States)

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.

Meandering Brownian Donkeys

International Nuclear Information System (INIS)

Eichhorn, R.; Reimann, P.

2004-01-01

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. (author)

Brownian coagulation at high particle concentrations

NARCIS (Netherlands)

Trzeciak, T.M.

2012-01-01

The process of Brownian coagulation, whereby particles are brought together by thermal motion and grow by collisions, is one of the most fundamental processes influencing the final properties of particulate matter in a variety of technically important systems. It is of importance in colloids,

Optimal Exercise Boundary of American Fractional Lookback Option in a Mixed Jump-Diffusion Fractional Brownian Motion Environment

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Zhaoqiang Yang

2017-01-01

Full Text Available A new framework for pricing the American fractional lookback option is developed in the case where the stock price follows a mixed jump-diffusion fraction Brownian motion. By using Itô formula and Wick-Itô-Skorohod integral a new market pricing model is built. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given. Numerical simulation illustrates some notable features of American fractional lookback options.

Slow kinetics of Brownian maxima.

Science.gov (United States)

Ben-Naim, E; Krapivsky, P L

2014-07-18

We study extreme-value statistics of Brownian trajectories in one dimension. We define the maximum as the largest position to date and compare maxima of two particles undergoing independent Brownian motion. We focus on the probability P(t) that the two maxima remain ordered up to time t and find the algebraic decay P ∼ t(-β) with exponent β = 1/4. When the two particles have diffusion constants D(1) and D(2), the exponent depends on the mobilities, β = (1/π) arctan sqrt[D(2)/D(1)]. We also use numerical simulations to investigate maxima of multiple particles in one dimension and the largest extension of particles in higher dimensions.

Free convective MHD Cattaneo-Christov flow over three different geometries with thermophoresis and Brownian motion

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M. Jayachandra Babu

2017-12-01

Full Text Available The knowledge of heat and mass transfer of MHD flows over different geometries is very important for heat exchangers design, transpiration, fiber coating, etc. With this initiation, a mathematical model is proposed to investigate the two-dimensional flow, heat and mass transfer of magnetohydrodynamic flow over three different geometries (vertical cone, vertical wedge, and a vertical plate. Cattaneo-Christov heat flux with external magnetic field, thermophoresis and Brownian movement effect are introduced in the model. Runge-Kutta and Newton’s methods are employed to solve the altered governing nonlinear equations. The influences of the parameters of concern on the common profiles (velocity, temperature, and concentration are conversed (in three cases. By viewing the same parameters, skin friction coefficient, heat and mass transfer rates are discussed with the assistance of tables. It is discovered that the momentum and thermal boundary layers are non-uniform for the MHD flow over three geometries (vertical cone, wedge, and a plate. Thermal and solutal Grashof numbers regulate the temperature and concentration fields. The heat and mass transfer rates of the flow over a cone are highly influenced by the thermal relaxation parameter. Keywords: MHD, Cattaneo-Christov heat flux, Thermal relaxation, Thermophoresis, Brownian motion

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

International Nuclear Information System (INIS)

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

2011-01-01

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 c (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.

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

International Nuclear Information System (INIS)

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

2017-01-01

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

Brownian motion, Minkowski space and principle of special relativity

International Nuclear Information System (INIS)

Caubet, J.-P.

1977-01-01

From the assumption that the brownian diffusion locally behaves like an ideal gas (pressure being inversely proportional to volume according to Boyle's law) one can deduce the signature +++- of the Minkowski space, the Lorentz addition of velocities, and the principle of special relativity [fr

Concurrent correction of geometric distortion and motion using the map-slice-to-volume method in echo-planar imaging.

Science.gov (United States)

Yeo, Desmond T B; Fessler, Jeffrey A; Kim, Boklye

2008-06-01

The accuracy of measuring voxel intensity changes between stimulus and rest images in fMRI echo-planar imaging (EPI) data is severely degraded in the presence of head motion. In addition, EPI is sensitive to susceptibility-induced geometric distortions. Head motion causes image shifts and associated field map changes that induce different geometric distortion at different time points. Conventionally, geometric distortion is "corrected" with a static field map independently of image registration. That approach ignores all field map changes induced by head motion. This work evaluates the improved motion correction capability of mapping slice to volume with concurrent iterative field corrected reconstruction using updated field maps derived from an initial static field map that has been spatially transformed and resampled. It accounts for motion-induced field map changes for translational and in-plane rotation motion. The results from simulated EPI time series data, in which motion, image intensity and activation ground truths are available, show improved accuracy in image registration, field corrected image reconstruction and activation detection.

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

Science.gov (United States)

Berry, Hugues; Chaté, Hugues

2014-02-01

In vivo measurements of the passive movements of biomolecules or vesicles in cells consistently report "anomalous diffusion," where mean-squared displacements scale as a power law of time with exponent αmovement hindrance by obstacles is often invoked. However, our understanding of how hindered diffusion leads to subdiffusion is based on diffusion amidst randomly located immobile obstacles. Here, we have used Monte Carlo simulations to investigate transient subdiffusion due to mobile obstacles with various modes of mobility. Our simulations confirm that the anomalous regimes rapidly disappear when the obstacles move by Brownian motion. By contrast, mobile obstacles with more confined displacements, e.g., Orstein-Ulhenbeck motion, are shown to preserve subdiffusive regimes. The mean-squared displacement of tracked protein displays convincing power laws with anomalous exponent α that varies with the density of Orstein-Ulhenbeck (OU) obstacles or the relaxation time scale of the OU process. In particular, some of the values we observed are significantly below the universal value predicted for immobile obstacles in two dimensions. Therefore, our results show that subdiffusion due to mobile obstacles with OU type of motion may account for the large variation range exhibited by experimental measurements in living cells and may explain that some experimental estimates are below the universal value predicted for immobile obstacles.

Geometrical-integrability constraints and equations of motion in four plus extended super spaces

International Nuclear Information System (INIS)

Chau, L.L.

1987-01-01

It is pointed out that many equations of motion in physics, including gravitational and Yang-Mills equations, have a common origin: i.e. they are the results of certain geometrical integrability conditions. These integrability conditions lead to linear systems and conservation laws that are important in integrating these equations of motion

Brownian dynamic simulations and experiments of MR fluids

International Nuclear Information System (INIS)

Segovia-Gutiérrez, J P; Vicente, J de; Hidalgo, R; Puertas, A M

2013-01-01

The use of computational techniques in magnetorheology is not new. I general, these approaches assume dipolar magnetic interactions, hard sphere repulsions, and no-slip conditions. In this contribution we focus on the dynamics of the equilibrium state in the presence of uniaxial DC fields. To achieve this goal we make use of Brownian Dynamic Simulations. We highlight the importance of the Brownian forces versus magnetic dipolar interaction in the range of low magnetic field strengths. We monitor the formation of columnar structures and their dynamics, in competition with the Brownian motion, until a hexatic crystal phase appears at high field strengths for monodisperse systems. The shear viscosity is computed from the Einstein relation and eventually compared with experimental data at very low-shear rates. A reasonably good agreement between both data sets is observed.

Experimental Studies of the Brownian Diffusion of Boomerang Colloidal Particle in a Confined Geometry

Science.gov (United States)

Chakrabarty, Ayan; Wang, Feng; Joshi, Bhuwan; Wei, Qi-Huo

2011-03-01

Recent studies shows that the boomerang shaped molecules can form various kinds of liquid crystalline phases. One debated topic related to boomerang molecules is the existence of biaxial nematic liquid crystalline phase. Developing and optical microscopic studies of colloidal systems of boomerang particles would allow us to gain better understanding of orientation ordering and dynamics at ``single molecule'' level. Here we report the fabrication and experimental studies of the Brownian motion of individual boomerang colloidal particles confined between two glass plates. We used dark-field optical microscopy to directly visualize the Brownian motion of the single colloidal particles in a quasi two dimensional geometry. An EMCCD was used to capture the motion in real time. An indigenously developed imaging processing algorithm based on MatLab program was used to precisely track the position and orientation of the particles with sub-pixel accuracy. The experimental finding of the Brownian diffusion of a single boomerang colloidal particle will be discussed.

Dynamic tracking of a nano-particle in fluids under Brownian motions

International Nuclear Information System (INIS)

Wu, X C; Zhang, W J; Sammynaiken, R

2008-01-01

Most previous studies on H 2 S were devoted to its toxic effects. However, recently there have been increasing evidences which show that endogenously generated H 2 S in specific mammalian tissues has certain significant positive physiological effects such as a neuromodulator and vasorelaxant in a membrane receptor-independent manner. In order to know the functions of endogenous H 2 S, low concentration and high accuracy measurement of H 2 S is a must. Furthermore, this measurement is desired to be real-time and non-invasive. It is reported that low concentration and nano quantity of H 2 S can be detected in water solutions and sera using carbon nanotubes with the fluorescence by confocal laser scanning microscopy. However, because of the Brownian motion of the small particle (carbon nanotube), a control system must be developed to track the movement of the particle in fluids. In this paper, we present a study to track a carbon nanotube which absorbs H 2 S in water or serum using a Raman microscope or confocal laser scanning microscope. In particular, we developed a novel control system for this task. Simulation has shown that our system works very well.

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

Science.gov (United States)

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

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

Science.gov (United States)

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)

Brownian motion with multiplicative noises revisited

International Nuclear Information System (INIS)

Kuroiwa, T; Miyazaki, K

2014-01-01

The Langevin equation with multiplicative noise and a state-dependent transport coefficient should always complemented with the proper interpretation rule of the noise, such as the Itô and Stratonovich conventions. Although the mathematical relationship between the different rules and how to translate from one rule to another are well established, the subject of which is a more physically natural rule still remains controversial. In this communication, we derive the overdamped Langevin equation with multiplicative noise for Brownian particles, by systematically eliminating the fast degrees of freedom of the underdamped Langevin equation. The Langevin equations obtained here vary depending on the choice of the noise conventions but they are different representations for an identical phenomenon. The results apply to multi-variable, nonequilibrium, non-stationary systems, and other general settings. (fast track communication)

Quantum work fluctuation theorem: Nonergodic Brownian motion case

International Nuclear Information System (INIS)

Bai, Zhan-Wu

2014-01-01

The work fluctuations of a quantum Brownian particle driven by an external force in a general nonergodic heat bath are studied under a general initial state. The exact analytical expression of the work probability distribution function is derived. Results show the existence of a quantum asymptotic fluctuation theorem, which is in general not a direct generalization of its classical counterpart. The form of this theorem is dependent on the structure of the heat bath and the specified initial condition.

Geometrical determination of the constant of motion in General Relativity

International Nuclear Information System (INIS)

Catoni, F.; Cannata, R.; Zampetti, P.

2009-01-01

In recent time a theorem, due to E. Beltrami, through which the integration of the geodesic equations of a curved manifold is obtained by means of a merely geometric method, has been revisited. This way of dealing with the problem is well in accordance with the geometric spirit of the Theory of General Relativity. In this paper we show another relevant consequence of this method. Actually, the constants of the motion, introduced in this geometrical way that is completely independent of Newton theory, are related to the conservation laws for test particles in the Einstein theory. These conservation laws may be compared with the conservation laws of Newton. In particular, by the conservation of energy (E) and the L z component of angular momentum, the equivalence of the conservation laws for the Schwarzschild field is verified and the difference between Newton and Einstein theories for the rotating bodies (Kerr metric) is obtained in a straightforward way.

Thermodynamic laws and equipartition theorem in relativistic Brownian motion.

Science.gov (United States)

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.

Relaxation property of the fractional Brownian particle

International Nuclear Information System (INIS)

Wang Litan; Lung, C.W.

1988-08-01

Dynamic susceptibility of a diffusion system associated with the fractional Brownian motion (fBm) was examined for the fractal property of the Non-Debye relaxation process. The comparisons between fBm and other approaches were made. Anomalous diffusion and the Non-Debye relaxation processes were discussed with this approach. (author). 8 refs, 1 fig

The single- and double-particle properties and the current reversal of coupled Brownian motors

International Nuclear Information System (INIS)

Li, Chen-Pu; Chen, Hong-Bin; Zheng, Zhi-Gang; Fan, Hong; Shen, Wen-Mei

2017-01-01

In this paper, we investigate the directed transport of coupled Brownian motors composed of two identical particles which is individually subject to a time-symmetric rocking force in spatially-symmetric periodic potentials. We find that both the coupling free length and the coupling strength can induce the reversed motion of the coupled Brownian motors, the essence of which is the coupled Brownian motors can exhibit completely different single- or double-particle properties under certain conditions. Namely, the current reversal is the result of the mutual conversion between the single- and double-particle properties of the coupled Brownian motors. Moreover, the directed current of coupled Brownian motors can be optimized and manipulated by adjusting the strength, the period, the phase difference of the rocking forces, and the noise intensity. (paper)

Interacting Brownian Swarms: Some Analytical Results

Directory of Open Access Journals (Sweden)

Guillaume Sartoretti

2016-01-01

Full Text Available We consider the dynamics of swarms of scalar Brownian agents subject to local imitation mechanisms implemented using mutual rank-based interactions. For appropriate values of the underlying control parameters, the swarm propagates tightly and the distances separating successive agents are iid exponential random variables. Implicitly, the implementation of rank-based mutual interactions, requires that agents have infinite interaction ranges. Using the probabilistic size of the swarm’s support, we analytically estimate the critical interaction range below that flocked swarms cannot survive. In the second part of the paper, we consider the interactions between two flocked swarms of Brownian agents with finite interaction ranges. Both swarms travel with different barycentric velocities, and agents from both swarms indifferently interact with each other. For appropriate initial configurations, both swarms eventually collide (i.e., all agents interact. Depending on the values of the control parameters, one of the following patterns emerges after collision: (i Both swarms remain essentially flocked, or (ii the swarms become ultimately quasi-free and recover their nominal barycentric speeds. We derive a set of analytical flocking conditions based on the generalized rank-based Brownian motion. An extensive set of numerical simulations corroborates our analytical findings.

Bivariate Gaussian bridges: directional factorization of diffusion in Brownian bridge models.

Science.gov (United States)

Kranstauber, Bart; Safi, Kamran; Bartumeus, Frederic

2014-01-01

In recent years high resolution animal tracking data has become the standard in movement ecology. The Brownian Bridge Movement Model (BBMM) is a widely adopted approach to describe animal space use from such high resolution tracks. One of the underlying assumptions of the BBMM is isotropic diffusive motion between consecutive locations, i.e. invariant with respect to the direction. Here we propose to relax this often unrealistic assumption by separating the Brownian motion variance into two directional components, one parallel and one orthogonal to the direction of the motion. Our new model, the Bivariate Gaussian bridge (BGB), tracks movement heterogeneity across time. Using the BGB and identifying directed and non-directed movement within a trajectory resulted in more accurate utilisation distributions compared to dynamic Brownian bridges, especially for trajectories with a non-isotropic diffusion, such as directed movement or Lévy like movements. We evaluated our model with simulated trajectories and observed tracks, demonstrating that the improvement of our model scales with the directional correlation of a correlated random walk. We find that many of the animal trajectories do not adhere to the assumptions of the BBMM. The proposed model improves accuracy when describing the space use both in simulated correlated random walks as well as observed animal tracks. Our novel approach is implemented and available within the "move" package for R.

GEOMETRIC PROPERTIES OF A MECHANICAL FORWARD MOTION COMPENSATION SYSTEM CONTROLLED BY A PIEZOELECTRIC DRIVE

Directory of Open Access Journals (Sweden)

F. Collette

2012-07-01

Full Text Available Forward Motion Compensation (FMC systems have been designed to ensure the radiometric quality of motion acquisition in airborne cameras. If the radiometric benefits of FMC have been acknowledged, what are its effects on the geometrical properties of the camera? This paper demonstrates that FMC significantly improves geometrical properties of a camera. Aspects of FMC theory are discussed, with a focus on the near-lossless implementation of this technology into digital aerial camera systems. Among mechanical FMC technologies, the piezoelectric drive is proving to excel in dynamic positioning in both accuracy and repeatability. The patented piezoelectric drive integrated into Optech aerial camera systems allows for continuous and precise sensor motion to ensure exact compensation of the aircraft's forward motion. This paper presents findings that demonstrate the validity of this assertion. The paper also discusses the physical principles involved in motion acquisition. Equations are included that define the motion effect at image level and illustrate how FMC acts to prevent motion effects. The residual motion effect or compensation error is formulated and a practical computation applied to the more restrictive camera case. The assessment concludes that, in the range of airborne camera utilization, the mechanical FMC technique is free of "visible" error at both human eye and computer assessment level. Lastly, the paper proceeds to a detailed technical discussion of piezoelectric drives and why they have proven to be so effective as nanopositioning devices for optical applications. The effectiveness of the patented piezoelectric drives used to achieve FMC in Optech cameras is conclusively demonstrated.

Processive pectin methylesterases: the role of electrostatic potential, breathing motions and bond cleavage in the rectification of Brownian motions.

Directory of Open Access Journals (Sweden)

Davide Mercadante

Full Text Available Pectin methylesterases (PMEs hydrolyze the methylester groups that are found on the homogalacturonan (HG chains of pectic polysaccharides in the plant cell wall. Plant and bacterial PMEs are especially interesting as the resulting de-methylesterified (carboxylated sugar residues are found to be arranged contiguously, indicating a so-called processive nature of these enzymes. Here we report the results of continuum electrostatics calculations performed along the molecular dynamics trajectory of a PME-HG-decasaccharide complex. In particular it was observed that, when the methylester groups of the decasaccharide were arranged in order to mimic the just-formed carboxylate product of de-methylesterification, a net unidirectional sliding of the model decasaccharide was subsequently observed along the enzyme's binding groove. The changes that occurred in the electrostatic binding energy and protein dynamics during this translocation provide insights into the mechanism by which the enzyme rectifies Brownian motions to achieve processivity. The free energy that drives these molecular motors is thus demonstrated to be incorporated endogenously in the methylesterified groups of the HG chains and is not supplied exogenously.

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

International Nuclear Information System (INIS)

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

2014-01-01

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

Coupling motion of colloidal particles in quasi-two-dimensional confinement

International Nuclear Information System (INIS)

Ma, Jun; Jing, Guangyin

2014-01-01

The Brownian motion of colloidal particles in quasi-two-dimensional (q2D) confinement displays a distinct kinetic character from that in bulk. Here we experimentally report dynamic coupling motion of Brownian particles in a relatively long process (∼100 h), which displays a quasi-equilibrium state in the q2D system. In the quasi-equilibrium state, the q2D confinement results in the coupling of particle motions, which slowly damps the motion and interaction of particles until the final equilibrium state is reached. The process of approaching the equilibrium is a random relaxation of a many-body interaction system of Brownian particles. As the relaxation proceeds for ∼100 h, the system reaches the equilibrium state in which the energy gained by the particles from the stochastic collision in the whole system is counteracted by the dissipative energy resulting from the collision. The relaxation time of this stochastic q2D system is 17.7 h. The theory is developed to explain coupling motions of Brownian particles in q2D confinement. (paper)

Brownian relaxation of an inelastic sphere in air

Energy Technology Data Exchange (ETDEWEB)

Bird, G. A., E-mail: gab@gab.com.au [University of Sydney, Sydney, NSW 2006 (Australia)

2016-06-15

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

Anyonic partition functions and windings of planar Brownian motion

International Nuclear Information System (INIS)

Desbois, J.; Heinemann, C.; Ouvry, S.

1995-01-01

The computation of the N-cycle Brownian paths contribution F N (α) to the N-anyon partition function is addressed. A detailed numerical analysis based on a random walk on a lattice indicates that F N 0 (α)=product k=1 N-1 [1-(N/k)α]. In the paramount three-anyon case, one can show that F 3 (α) is built by linear states belonging to the bosonic, fermionic, and mixed representations of S 3

Active Brownian particles with velocity-alignment and active fluctuations

International Nuclear Information System (INIS)

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

2012-01-01

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. (paper)

Quantum dynamical framework for Brownian heat engines

Science.gov (United States)

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.

Semiclassical Klein-Kramers and Smoluchowski equations for the Brownian motion of a particle in an external potential

International Nuclear Information System (INIS)

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

2007-01-01

The quantum Brownian motion of a particle in an external potential V(x) is treated using the master equation for the Wigner distribution function W(x, p, t) in phase space (x, p). A heuristic method of determination of diffusion coefficients in the master equation is proposed. The time evolution equation so obtained contains explicit quantum correction terms up to o(ℎ 4 ) and in the classical limit, ℎ → 0, reduces to the Klein-Kramers equation. For a quantum oscillator, the method yields an evolution equation for W(x, p, t) coinciding with that of Agarwal (1971 Phys. Rev. A 4 739). In the non-inertial regime, by applying the Brinkman expansion of the momentum distribution in Weber functions (Brinkman 1956 Physica 22 29), the corresponding semiclassical Smoluchowski equation is derived. (fast track communication)

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

International Nuclear Information System (INIS)

Ni Xiaohui; Jiang Zhiqiang; Zhou Weixing

2009-01-01

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.

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

CERN Document Server

Berzin, Corinne; León, José R

2014-01-01

This book is devoted to a number of stochastic models that display scale invariance. It primarily focuses on three issues: probabilistic properties, statistical estimation and simulation of the processes considered. It will be of interest to probability specialists, who will find here an uncomplicated presentation of statistics tools, and to those statisticians who wants to tackle the most recent theories in probability in order to develop Central Limit Theorems in this context; both groups will also benefit from the section on simulation. Algorithms are described in great detail, with a focus on procedures that is not usually found in mathematical treatises. The models studied are fractional Brownian motions and processes that derive from them through stochastic differential equations. Concerning the proofs of the limit theorems, the “Fourth Moment Theorem” is systematically used, as it produces rapid and helpful proofs that can serve as models for the future. Readers will also find elegant and new proof...

Real-Time Correction By Optical Tracking with Integrated Geometric Distortion Correction for Reducing Motion Artifacts in fMRI

Science.gov (United States)

Rotenberg, David J.

Artifacts caused by head motion are a substantial source of error in fMRI that limits its use in neuroscience research and clinical settings. Real-time scan-plane correction by optical tracking has been shown to correct slice misalignment and non-linear spin-history artifacts, however residual artifacts due to dynamic magnetic field non-uniformity may remain in the data. A recently developed correction technique, PLACE, can correct for absolute geometric distortion using the complex image data from two EPI images, with slightly shifted k-space trajectories. We present a correction approach that integrates PLACE into a real-time scan-plane update system by optical tracking, applied to a tissue-equivalent phantom undergoing complex motion and an fMRI finger tapping experiment with overt head motion to induce dynamic field non-uniformity. Experiments suggest that including volume by volume geometric distortion correction by PLACE can suppress dynamic geometric distortion artifacts in a phantom and in vivo and provide more robust activation maps.

Triangular Geometrized Sampling Heuristics for Fast Optimal Motion Planning

Directory of Open Access Journals (Sweden)

Ahmed Hussain Qureshi

2015-02-01

Full Text Available Rapidly-exploring Random Tree (RRT-based algorithms have become increasingly popular due to their lower computational complexity as compared with other path planning algorithms. The recently presented RRT* motion planning algorithm improves upon the original RRT algorithm by providing optimal path solutions. While RRT determines an initial collision-free path fairly quickly, RRT* guarantees almost certain convergence to an optimal, obstacle-free path from the start to the goal points for any given geometrical environment. However, the main limitations of RRT* include its slow processing rate and high memory consumption, due to the large number of iterations required for calculating the optimal path. In order to overcome these limitations, we present another improvement, i.e, the Triangular Geometerized-RRT* (TG-RRT* algorithm, which utilizes triangular geometrical methods to improve the performance of the RRT* algorithm in terms of the processing time and a decreased number of iterations required for an optimal path solution. Simulations comparing the performance results of the improved TG-RRT* with RRT* are presented to demonstrate the overall improvement in performance and optimal path detection.

Directed transport of confined Brownian particles with torque

Science.gov (United States)

Radtke, Paul K.; Schimansky-Geier, Lutz

2012-05-01

We investigate the influence of an additional torque on the motion of Brownian particles confined in a channel geometry with varying width. The particles are driven by random fluctuations modeled by an Ornstein-Uhlenbeck process with given correlation time τc. The latter causes persistent motion and is implemented as (i) thermal noise in equilibrium and (ii) noisy propulsion in nonequilibrium. In the nonthermal process a directed transport emerges; its properties are studied in detail with respect to the correlation time, the torque, and the channel geometry. Eventually, the transport mechanism is traced back to a persistent sliding of particles along the even boundaries in contrast to scattered motion at uneven or rough ones.

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

Science.gov (United States)

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.

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

Science.gov (United States)

Grančič, Peter; Štěpánek, František

2012-07-01

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

Correlation Properties of (Discrete Fractional Gaussian Noise and Fractional Brownian Motion

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Didier Delignières

2015-01-01

Full Text Available The fractional Gaussian noise/fractional Brownian motion framework (fGn/fBm has been widely used for modeling and interpreting physiological and behavioral data. The concept of 1/f noise, reflecting a kind of optimal complexity in the underlying systems, is of central interest in this approach. It is generally considered that fGn and fBm represent a continuum, punctuated by the boundary of “ideal” 1/f noise. In the present paper, we focus on the correlation properties of discrete-time versions of these processes (dfGn and dfBm. We especially derive a new analytical expression of the autocorrelation function (ACF of dfBm. We analyze the limit behavior of dfGn and dfBm when they approach their upper and lower limits, respectively. We show that, as H approaches 1, the ACF of dfGn tends towards 1 at all lags, suggesting that dfGn series tend towards straight line. Conversely, as H approaches 0, the ACF of dfBm tends towards 0 at all lags, suggesting that dfBm series tend towards white noise. These results reveal a severe breakdown of correlation properties around the 1/f boundary and challenge the idea of a smooth transition between dfGn and dfBm processes. We discuss the implications of these findings for the application of the dfGn/dfBm model to experimental series, in terms of theoretical interpretation and modeling.

Description os surface quadrupole oscillations of heateU spherical nuclei in the Brownian movement approximation

International Nuclear Information System (INIS)

Svin'in, I.R.

1982-01-01

Description of collective phenomena in heated nuclei within the framework of the Brownian approximation may be conditionally divided into two parts: 1) solution of the problem for some realization of a random force, 2) averaging in a set of all the possible realizations. Results of the present work are setted the first part of the problem in the case of surface quadrupole oscillations of spherical heated nuclei. Quadrupole surface oscillations of heated spherical nuclei are considered in the Brownian motion approximation. The integrals of motion are constructed taking into account the energy and angular momentum conservations for the nucleus in the process of relaxation of the collective excitations. Wave functions are obtained for states having definite values of the integrals of motion in the phonon representation. It is noted that the description scheme developed is easily used with respect to other multipolarity oscillations

Non-cooperative Brownian donkeys: A solvable 1D model

Science.gov (United States)

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 (absolute negative mobility). Under suitable conditions, the system approaches 100% efficiency when working against the external force F.

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

Science.gov (United States)

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

2016-06-01

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

The Onsager reciprocity relation and generalized efficiency of a thermal Brownian motor

International Nuclear Information System (INIS)

Tian-Fu, Gao; Jin-Can, Chen; Yue, Zhang

2009-01-01

Based on a general model of Brownian motors, the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically. It is found that the Onsager reciprocity relation holds and the Onsager coefficients are not affected by the kinetic energy change due to the particle's motion. Only when the heat leak in the system is negligible can the determinant of the Onsager matrix vanish. Moreover, the influence of the main parameters characterizing the model on the generalized efficiency of the Brownian motor is discussed in detail. The characteristic curves of the generalized efficiency varying with these parameters are presented, and the maximum generalized efficiency and the corresponding optimum parameters are determined. The results obtained here are of general significance. They are used to analyze the performance characteristics of the Brownian motors operating in the three interesting cases with zero heat leak, zero average drift velocity or a linear response relation, so that some important conclusions in current references are directly included in some limit cases of the present paper. (general)

Conception of Brownian coil

OpenAIRE

Zhang, Jiayuan

2018-01-01

This article proposes a conception of Brownian coil. Brownian coil is a tiny coil with the same size of pollen. Once immersed into designed magnetic field and liquid, the coil will be moved and deformed macroscopically, due to the microscopic thermodynamic molecular collisions. Such deformation and movement will change the magnetic flux through the coil, by which an ElectroMotive Force (EMF) is produced. In this work, Brownian heat exchanger and Brownian generator are further designed to tran...

Intermittency and multifractional Brownian character of geomagnetic time series

Directory of Open Access Journals (Sweden)

G. Consolini

2013-07-01

Full Text Available The Earth's magnetosphere exhibits a complex behavior in response to the solar wind conditions. This behavior, which is described in terms of mutifractional Brownian motions, could be the consequence of the occurrence of dynamical phase transitions. On the other hand, it has been shown that the dynamics of the geomagnetic signals is also characterized by intermittency at the smallest temporal scales. Here, we focus on the existence of a possible relationship in the geomagnetic time series between the multifractional Brownian motion character and the occurrence of intermittency. In detail, we investigate the multifractional nature of two long time series of the horizontal intensity of the Earth's magnetic field as measured at L'Aquila Geomagnetic Observatory during two years (2001 and 2008, which correspond to different conditions of solar activity. We propose a possible double origin of the intermittent character of the small-scale magnetic field fluctuations, which is related to both the multifractional nature of the geomagnetic field and the intermittent character of the disturbance level. Our results suggest a more complex nature of the geomagnetic response to solar wind changes than previously thought.

Non-Markovian Effects on the Brownian Motion of a Free Particle

OpenAIRE

Bolivar, A. O.

2010-01-01

Non-Markovian effects upon the Brownian movement of a free particle in the presence as well as in the absence of inertial force are investigated within the framework of Fokker-Planck equations (Rayleigh and Smoluchowski equations). More specifically, it is predicted that non-Markovian features can enhance the values of the mean square displacement and momentum, thereby assuring the mathematical property of differentiability of the these physically observable quantities.

Entropic noises-induced resonance in a geometrically confined system

International Nuclear Information System (INIS)

Zeng, Chunhua; Gong, Ailing; Wang, Hua

2012-01-01

We consider the motion of Brownian particles through a narrow tube of varying cross-section in a geometrically confined system subjected to a sinusoidal oscillating force. The varying cross-section of the confinement results in an effective purely entropic potential in reduced dimension. Besides an additive Langevin force, one external additive and another multiplicative noise are acting along the x-direction. We demonstrate that the presence of a periodic input may give rise to a maximum and a minimum of the spectral amplification at corresponding optimal values of the noise strength, and therefore to the appearance of the purely entropic stochastic resonance and reverse-resonance phenomena. Furthermore, we show that the cross-correlation between two noises leads to a decrease of the spectral amplification, i.e., we observe the cross-correlation between two noises weakening the resonance. Mechanisms for the cross-correlation weakening the resonance are explained from the point of view of the effective purely entropic potential. (paper)

Conserved linear dynamics of single-molecule Brownian motion

KAUST Repository

Serag, Maged F.

2017-06-06

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

Conserved linear dynamics of single-molecule Brownian motion

Science.gov (United States)

Serag, Maged F.; Habuchi, Satoshi

2017-06-01

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

Conserved linear dynamics of single-molecule Brownian motion

KAUST Repository

Serag, Maged F.; Habuchi, Satoshi

2017-01-01

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

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

International Nuclear Information System (INIS)

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

2015-01-01

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. - Highlights: • Temperature rises when Brownian motion and thermophoresis effects intensify. • Temperature profile increases when thermal slip parameter increases. • Concentration field is a decreasing function of concentration slip parameter. • Temperature decreases whereas concentration increases for Hartman number

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

Energy Technology Data Exchange (ETDEWEB)

Hayat, T. [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, King Abdulaziz University, P.O. Box 80257, Jeddah 21589 (Saudi Arabia); Nisar, Z. [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Ahmad, B. [Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, King Abdulaziz University, P.O. Box 80257, Jeddah 21589 (Saudi Arabia); Yasmin, H., E-mail: qau2011@gmail.com [Department of Mathematics, COMSATS Institute of Information Technology, G.T. Road, Wah Cantt 47040 (Pakistan)

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. - Highlights: • Temperature rises when Brownian motion and thermophoresis effects intensify. • Temperature profile increases when thermal slip parameter increases. • Concentration field is a decreasing function of concentration slip parameter. • Temperature decreases whereas concentration increases for Hartman number.

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

Science.gov (United States)

Gautestad, Arild O

2012-09-07

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

The reduction of motion artifacts in digital subtraction angiography by geometrical image transformation

International Nuclear Information System (INIS)

Fitzpatrick, J.M.; Pickens, D.R.; Mandava, V.R.; Grefenstette, J.J.

1988-01-01

In the diagnosis of arteriosclerosis, radio-opaque dye is injected into the interior of the arteries to make them visible. Because of its increased contrast sensitivity, digital subtraction angiography has the potential for providing diagnostic images of arteries with reduced dye volumes. In the conventional technique, a mask image, acquired before the introduction of the dye, is subtracted from the contrast image, acquired after the dye is introduced, to produce a difference image in which only the dye in the arteries is visible. The usefulness of this technique has been severely limited by the image degradation caused by patient motion during image acquisition. This motion produces artifacts in the difference image that obscure the arteries. One technique for dealing with the problem is to reduce the degradation by means of image registration. The registration is carried out by means of a geometrical transformation of the mask image before subtraction so that it is in registration with the contrast image. This paper describes a technique for determining an optimal transformation. The authors employ a one-to-one elastic mapping and the Jacobian of that mapping to produce a geometrical image transformation. They choose a parameterized class of such mappings and use a heuristic search algorithm to optimize the parameters to minimize the severity of the motion artifacts. To increase the speed of the optimization process they use a statistical image comparison technique that provides a quick approximate evaluation of each image transformation. They present the experimental results of the application of their registration system to mask-contrast pairs, for images acquired from a specially designed phantom, and for clinical images

CNT based thermal Brownian motor to pump water in nanodevices

DEFF Research Database (Denmark)

Oyarzua, Elton; Zambrano, Harvey; Walther, Jens Honore

2016-01-01

asymmetry drive the water ow 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......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 flxing specific zones on the CNT in order to modify the vibrational modes of the CNT. We find that the temperature gradient and imposed spatial...

Modified Feynman ratchet with velocity-dependent fluctuations

Directory of Open Access Journals (Sweden)

Jack Denur

2004-03-01

Full Text Available Abstract: The randomness of Brownian motion at thermodynamic equilibrium can be spontaneously broken by velocity-dependence of fluctuations, i.e., by dependence of values or probability distributions of fluctuating properties on Brownian-motional velocity. Such randomness-breaking can spontaneously obtain via interaction between Brownian-motional Doppler effects --- which manifest the required velocity-dependence --- and system geometrical asymmetry. A non random walk is thereby spontaneously superposed on Brownian motion, resulting in a systematic net drift velocity despite thermodynamic equilibrium. The time evolution of this systematic net drift velocity --- and of velocity probability density, force, and power output --- is derived for a velocity-dependent modification of Feynman's ratchet. We show that said spontaneous randomness-breaking, and consequent systematic net drift velocity, imply: bias from the Maxwellian of the system's velocity probability density, the force that tends to accelerate it, and its power output. Maximization, especially of power output, is discussed. Uncompensated decreases in total entropy, challenging the second law of thermodynamics, are thereby implied.

On the Humble Origins of the Brownian Entropic Force

OpenAIRE

Neumann, Richard M.

2015-01-01

Recognition that certain forces arising from the averaging of the multiple impacts of a solute particle by the surrounding solvent particles undergoing random thermal motion can be of an entropic nature has led to the incorporation of these forces and their related entropies into theoretical protocols ranging from molecular-dynamics simulations to the modeling of quarkonium suppression in particle physics. Here we present a rigorous derivation of this Brownian entropic force by means of the c...

An electricity price model with consideration to load and gas price effects.

Science.gov (United States)

Huang, Min-xiang; Tao, Xiao-hu; Han, Zhen-xiang

2003-01-01

Some characteristics of the electricity load and prices are studied, and the relationship between electricity prices and gas (fuel) prices is analyzed in this paper. Because electricity prices are strongly dependent on load and gas prices, the authors constructed a model for electricity prices based on the effects of these two factors; and used the Geometric Mean Reversion Brownian Motion (GMRBM) model to describe the electricity load process, and a Geometric Brownian Motion(GBM) model to describe the gas prices; deduced the price stochastic process model based on the above load model and gas price model. This paper also presents methods for parameters estimation, and proposes some methods to solve the model.

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

International Nuclear Information System (INIS)

McKane, Alan

2003-01-01

This is a book about the modelling of complex systems and, unlike many books on this subject, concentrates on the discussion of specific systems and gives practical methods for modelling and simulating them. This is not to say that the author does not devote space to the general philosophy and definition of complex systems and agent-based modelling, but the emphasis is definitely on the development of concrete methods for analysing them. This is, in my view, to be welcomed and I thoroughly recommend the book, especially to those with a theoretical physics background who will be very much at home with the language and techniques which are used. The author has developed a formalism for understanding complex systems which is based on the Langevin approach to the study of Brownian motion. This is a mesoscopic description; details of the interactions between the Brownian particle and the molecules of the surrounding fluid are replaced by a randomly fluctuating force. Thus all microscopic detail is replaced by a coarse-grained description which encapsulates the essence of the interactions at the finer level of description. In a similar way, the influences on Brownian agents in a multi-agent system are replaced by stochastic influences which sum up the effects of these interactions on a finer scale. Unlike Brownian particles, Brownian agents are not structureless particles, but instead have some internal states so that, for instance, they may react to changes in the environment or to the presence of other agents. Most of the book is concerned with developing the idea of Brownian agents using the techniques of statistical physics. This development parallels that for Brownian particles in physics, but the author then goes on to apply the technique to problems in biology, economics and the social sciences. This is a clear and well-written book which is a useful addition to the literature on complex systems. It will be interesting to see if the use of Brownian agents becomes

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

Science.gov (United States)

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. Copyright © 2015 The Authors. Published by Elsevier B.V. All rights reserved.

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

Czech Academy of Sciences Publication Activity Database

Filip, R.; Zemánek, Pavel

2016-01-01

Roč. 18, č. 6 (2016), 065401:1-8 ISSN 2040-8978 R&D Projects: GA ČR GB14-36681G Institutional support: RVO:68081731 Keywords : optically trapped particles * Brownian motion * optomechanics Subject RIV: BH - Optics, Masers, Lasers Impact factor: 1.741, year: 2016

System for simultaneously measuring 6DOF geometric motion errors using a polarization maintaining fiber-coupled dual-frequency laser.

Science.gov (United States)

Cui, Cunxing; Feng, Qibo; Zhang, Bin; Zhao, Yuqiong

2016-03-21

A novel method for simultaneously measuring six degree-of-freedom (6DOF) geometric motion errors is proposed in this paper, and the corresponding measurement instrument is developed. Simultaneous measurement of 6DOF geometric motion errors using a polarization maintaining fiber-coupled dual-frequency laser is accomplished for the first time to the best of the authors' knowledge. Dual-frequency laser beams that are orthogonally linear polarized were adopted as the measuring datum. Positioning error measurement was achieved by heterodyne interferometry, and other 5DOF geometric motion errors were obtained by fiber collimation measurement. A series of experiments was performed to verify the effectiveness of the developed instrument. The experimental results showed that the stability and accuracy of the positioning error measurement are 31.1 nm and 0.5 μm, respectively. For the straightness error measurements, the stability and resolution are 60 and 40 nm, respectively, and the maximum deviation of repeatability is ± 0.15 μm in the x direction and ± 0.1 μm in the y direction. For pitch and yaw measurements, the stabilities are 0.03″ and 0.04″, the maximum deviations of repeatability are ± 0.18″ and ± 0.24″, and the accuracies are 0.4″ and 0.35″, respectively. The stability and resolution of roll measurement are 0.29″ and 0.2″, respectively, and the accuracy is 0.6″.

Unlikely Fluctuations and Non-Equilibrium Work Theorems-A Simple Example.

Science.gov (United States)

Muzikar, Paul

2016-06-30

An exciting development in statistical mechanics has been the elucidation of a series of surprising equalities involving the work done during a nonequilibrium process. Astumian has presented an elegant example of such an equality, involving a colloidal particle undergoing Brownian motion in the presence of gravity. We analyze this example; its simplicity, and its link to geometric Brownian motion, allows us to clarify the inner workings of the equality. Our analysis explicitly shows the important role played by large, unlikely fluctuations.

Continuous state branching processes in random environment: The Brownian case

OpenAIRE

Palau, Sandra; Pardo, Juan Carlos

2015-01-01

We consider continuous state branching processes that are perturbed by a Brownian motion. These processes are constructed as the unique strong solution of a stochastic differential equation. The long-term extinction and explosion behaviours are studied. In the stable case, the extinction and explosion probabilities are given explicitly. We find three regimes for the asymptotic behaviour of the explosion probability and, as in the case of branching processes in random environment, we find five...

Evaluating correlation between geometrical relationship and dose difference caused by respiratory motion using statistical analysis

Energy Technology Data Exchange (ETDEWEB)

Shin, Dong Seok; Kim, Dong Su; Kim, Tae Ho; Kim, Kyeong Hyeon; Yoon, Do Kun; Suh, Tae Suk [The Catholic University of Korea, Seoul (Korea, Republic of); Kang, Seong Hee [Seoul National University Hospital, Seoul (Korea, Republic of); Cho, Min Seok [Asan Medical Center, Seoul (Korea, Republic of); Noh, Yu Yoon [Eulji University Hospital, Daejeon (Korea, Republic of)

2017-04-15

Three-dimensional dose (3D dose) can consider coverage of moving target, however it is difficult to provide dosimetric effect which occurs by respiratory motions. Four-dimensional dose (4D dose) which uses deformable image registration (DIR) algorithm from four-dimensional computed tomography (4DCT) images can consider dosimetric effect by respiratory motions. The dose difference between 3D dose and 4D dose can be varied according to the geometrical relationship between a planning target volume (PTV) and an organ at risk (OAR). The purpose of this study is to evaluate the correlation between the overlap volume histogram (OVH), which quantitatively shows the geometrical relationship between the PTV and OAR, and the dose differences. In conclusion, no significant statistical correlation was found between the OVH and dose differences. However, it was confirmed that a higher difference between the 3D and 4D doses could occur in cases that have smaller OVH value. No significant statistical correlation was found between the OVH and dose differences. However, it was confirmed that a higher difference between the 3D and 4D doses could occur in cases that have smaller OVH value.

Effects of temperature gradient induced nanoparticle motion on conduction and convection of fluid

International Nuclear Information System (INIS)

Zhou Leping; Peterson, George P.; Yoda, Minani; Wang Buxuan

2012-01-01

The role of temperature gradient induced nanoparticle motion on conduction and convection was investigated. Possible mechanisms for variations resulting from variations in the thermophysical properties are theoretically and experimentally discussed. The effect of the nanoparticle motion on conduction is demonstrated through thermal conductivity measurement of deionized water with suspended CuO nanoparticles (50 nm in diameter) and correlated with the contributions of Brownian diffusion, thermophoresis, etc. The tendencies observed is that the magnitude of and the variation in the thermal conductivity increases with increasing volume fraction for a given temperature, which is due primarily to the Brownian diffusion of the nanoparticles. Using dimensional analysis, the thermal conductivity is correlated and both the interfacial thermal resistance and near-field radiation are found to be essentially negligible. A modification term that incorporates the contributions of Brownian motion and thermophoresis is proposed. The effect of nanoscale convection is illustrated through an experimental investigation that utilized fluorescent polystyrene nanoparticle tracers (200 nm in diameter) and multilayer nanoparticle image velocimetry. The results indicate that both the magnitude and the deviation of the fluid motion increased with increasing heat flux in the near-wall region. Meanwhile, the fluid motion tended to decrease with the off-wall distance for a given heating power. A corresponding numerical study of convection of pure deionized water shows that the velocity along the off-wall direction is several orders of magnitude lower than that of deionized water, which indicates that Brownian motion in the near-wall region is crucial for fluid with suspended nanoparticles in convection.

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

Science.gov (United States)

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

2008-01-01

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

The Lévy flight foraging hypothesis: forgetting about memory may lead to false verification of Brownian motion.

Science.gov (United States)

Gautestad, Arild O; Mysterud, Atle

2013-01-01

The Lévy flight foraging hypothesis predicts a transition from scale-free Lévy walk (LW) to scale-specific Brownian motion (BM) as an animal moves from resource-poor towards resource-rich environment. However, the LW-BM continuum implies a premise of memory-less search, which contradicts the cognitive capacity of vertebrates. We describe methods to test if apparent support for LW-BM transitions may rather be a statistical artifact from movement under varying intensity of site fidelity. A higher frequency of returns to previously visited patches (stronger site fidelity) may erroneously be interpreted as a switch from LW towards BM. Simulations of scale-free, memory-enhanced space use illustrate how the ratio between return events and scale-free exploratory movement translates to varying strength of site fidelity. An expanded analysis of GPS data of 18 female red deer, Cervus elaphus, strengthens previous empirical support of memory-enhanced and scale-free space use in a northern forest ecosystem. A statistical mechanical model architecture that describes foraging under environment-dependent variation of site fidelity may allow for higher realism of optimal search models and movement ecology in general, in particular for vertebrates with high cognitive capacity.

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

Science.gov (United States)

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

2013-07-02

Planar polarization of the forming hair bundle, the mechanosensory antenna of auditory hair cells, depends on the poorly characterized center-to-edge displacement of a primary cilium, the kinocilium, at their apical surface. Taking advantage of the gradient of hair cell differentiation along the cochlea, we reconstituted a map of the kinocilia displacements in the mouse embryonic cochlea. We then developed a cochlear organotypic culture and video-microscopy approach to monitor the movements of the kinocilium basal body (mother centriole) and its daughter centriole, which we analyzed using particle tracking and modeling. We found that both hair cell centrioles undergo confined Brownian movements around their equilibrium positions, under the apparent constraint of a radial restoring force of ∼0.1 pN. This magnitude depended little on centriole position, suggesting nonlinear interactions with constraining, presumably cytoskeletal elements. The only dynamic change observed during the period of kinocilium migration was a doubling of the centrioles' confinement area taking place early in the process. It emerges from these static and dynamic observations that kinocilia migrate gradually in parallel with the organization of hair cells into rows during cochlear neuroepithelium extension. Analysis of the confined motion of hair cell centrioles under normal and pathological conditions should help determine which structures contribute to the restoring force exerting on them. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Efficient Brownian Dynamics of rigid colloids in linear flow fields based on the grand mobility matrix

Science.gov (United States)

Palanisamy, Duraivelan; den Otter, Wouter K.

2018-05-01

We present an efficient general method to simulate in the Stokesian limit the coupled translational and rotational dynamics of arbitrarily shaped colloids subject to external potential forces and torques, linear flow fields, and Brownian motion. The colloid's surface is represented by a collection of spherical primary particles. The hydrodynamic interactions between these particles, here approximated at the Rotne-Prager-Yamakawa level, are evaluated only once to generate the body's (11 × 11) grand mobility matrix. The constancy of this matrix in the body frame, combined with the convenient properties of quaternions in rotational Brownian Dynamics, enables an efficient simulation of the body's motion. Simulations in quiescent fluids yield correct translational and rotational diffusion behaviour and sample Boltzmann's equilibrium distribution. Simulations of ellipsoids and spherical caps under shear, in the absence of thermal fluctuations, yield periodic orbits in excellent agreement with the theories by Jeffery and Dorrepaal. The time-varying stress tensors provide the Einstein coefficient and viscosity of dilute suspensions of these bodies.

The Brownian loop soup

OpenAIRE

Lawler, Gregory F.; Werner, Wendelin

2003-01-01

We define a natural conformally invariant measure on unrooted Brownian loops in the plane and study some of its properties. We relate this measure to a measure on loops rooted at a boundary point of a domain and show how this relation gives a way to ``chronologically add Brownian loops'' to simple curves in the plane.

Effective Brownian ratchet separation by a combination of molecular filtering and a self-spreading lipid bilayer system.

Science.gov (United States)

Motegi, Toshinori; Nabika, Hideki; Fu, Yingqiang; Chen, Lili; Sun, Yinlu; Zhao, Jianwei; Murakoshi, Kei

2014-07-01

A new molecular manipulation method in the self-spreading lipid bilayer membrane by combining Brownian ratchet and molecular filtering effects is reported. The newly designed ratchet obstacle was developed to effectively separate dye-lipid molecules. The self-spreading lipid bilayer acted as both a molecular transport system and a manipulation medium. By controlling the size and shape of ratchet obstacles, we achieved a significant increase in the separation angle for dye-lipid molecules compared to that with the previous ratchet obstacle. A clear difference was observed between the experimental results and the simple random walk simulation that takes into consideration only the geometrical effect of the ratchet obstacles. This difference was explained by considering an obstacle-dependent local decrease in molecular diffusivity near the obstacles, known as the molecular filtering effect at nanospace. Our experimental findings open up a novel controlling factor in the Brownian ratchet manipulation that allow the efficient separation of molecules in the lipid bilayer based on the combination of Brownian ratchet and molecular filtering effects.

Modelling and measuring the irrational behaviour of agents in financial markets: Discovering the psychological soliton

International Nuclear Information System (INIS)

Dhesi, Gurjeet; Ausloos, Marcel

2016-01-01

Following a Geometrical Brownian Motion extension into an Irrational fractional Brownian Motion model, we re-examine agent behaviour reacting to time dependent news on the log-returns thereby modifying a financial market evolution. We specifically discuss the role of financial news or economic information positive or negative feedback of such irrational (or contrarian) agents upon the price evolution. We observe a kink-like effect reminiscent of soliton behaviour, suggesting how analysts' forecasts errors induce stock prices to adjust accordingly, thereby proposing a measure of the irrational force in a market.

Brownian motion in a field of force and the diffusion theory of chemical reactions. II

NARCIS (Netherlands)

Brinkman, H.C.

1956-01-01

H. A. Kramers has studied the rate of chemical reactions in view of the Brownian forces caused by a surrounding medium in temperature equilibrium. In a previous paper 3) the author gave a solution of Kramers' diffusion equation in phase space by systematic development. In this paper the general

Change of particle size distribution during Brownian coagulation

International Nuclear Information System (INIS)

Lee, K.W.

1984-01-01

Change in particle size distribution due to Brownian coagulation in the continuum regime has been stuied analytically. A simple analytic solution for the size distribution of an initially lognormal distribution is obtained based on the assumption that the size distribution during the coagulation process attains or can, at least, be represented by a time dependent lognormal function. The results are found to be in a form that corrects Smoluchowski's solution for both polydispersity and size-dependent kernel. It is further shown that regardless of whether the initial distribution is narrow or broad, the spread of the distribution is characterized by approaching a fixed value of the geometric standard deviation. This result has been compared with the self-preserving distribution obtained by similarity theory. (Author)

Generalized Kerr spacetime with an arbitrary mass quadrupole moment: geometric properties versus particle motion

International Nuclear Information System (INIS)

Bini, Donato; Geralico, Andrea; Luongo, Orlando; Quevedo, Hernando

2009-01-01

An exact solution of Einstein's field equations in empty space first found in 1985 by Quevedo and Mashhoon is analyzed in detail. This solution generalizes Kerr spacetime to include the case of matter with an arbitrary mass quadrupole moment and is specified by three parameters, the mass M, the angular momentum per unit mass a and the quadrupole parameter q. It reduces to the Kerr spacetime in the limiting case q = 0 and to the Erez-Rosen spacetime when the specific angular momentum a vanishes. The geometrical properties of such a solution are investigated. Causality violations, directional singularities and repulsive effects occur in the region close to the source. Geodesic motion and accelerated motion are studied on the equatorial plane which, due to the reflection symmetry property of the solution, also turns out to be a geodesic plane.

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

Directory of Open Access Journals (Sweden)

F. Mabood

Full Text Available 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. Keywords: Nanofluid, MHD, Chemical reaction, Rotating stretching sheet, Radiation

Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials.

Science.gov (United States)

Dechant, A; Lutz, E; Kessler, D A; Barkai, E

2012-05-01

We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and the fluctuations of the time-averaged position of the particle for large but finite times. We characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential, and we support our predictions with extensive Langevin simulations. While the Boltzmann measure is used to obtain stationary correlation functions, we show how the non-normalizable infinite covariant density is related to the superaging behavior.

Thermodynamic and Quantum Thermodynamic Analyses of Brownian Movement

OpenAIRE

Gyftopoulos, Elias P.

2006-01-01

Thermodynamic and quantum thermodynamic analyses of Brownian movement of a solvent and a colloid passing through neutral thermodynamic equilibrium states only. It is shown that Brownian motors and E. coli do not represent Brownian movement.

Fractional Brownian motion run with a multi-scaling clock mimics diffusion of spherical colloids in microstructural fluids.

Science.gov (United States)

Park, Moongyu; Cushman, John Howard; O'Malley, Dan

2014-09-30

The collective molecular reorientations within a nematic liquid crystal fluid bathing a spherical colloid cause the colloid to diffuse anomalously on a short time scale (i.e., as a non-Brownian particle). The deformations and fluctuations of long-range orientational order in the liquid crystal profoundly influence the transient diffusive regimes. Here we show that an anisotropic fractional Brownian process run with a nonlinear multiscaling clock effectively mimics this collective and transient phenomenon. This novel process has memory, Gaussian increments, and a multiscale mean square displacement that can be chosen independently from the fractal dimension of a particle trajectory. The process is capable of modeling multiscale sub-, super-, or classical diffusion. The finite-size Lyapunov exponents for this multiscaling process are defined for future analysis of related mixing processes.

Properties of Brownian Image Models in Scale-Space

DEFF Research Database (Denmark)

Pedersen, Kim Steenstrup

2003-01-01

Brownian images) will be discussed in relation to linear scale-space theory, and it will be shown empirically that the second order statistics of natural images mapped into jet space may, within some scale interval, be modeled by the Brownian image model. This is consistent with the 1/f 2 power spectrum...... law that apparently governs natural images. Furthermore, the distribution of Brownian images mapped into jet space is Gaussian and an analytical expression can be derived for the covariance matrix of Brownian images in jet space. This matrix is also a good approximation of the covariance matrix......In this paper it is argued that the Brownian image model is the least committed, scale invariant, statistical image model which describes the second order statistics of natural images. Various properties of three different types of Gaussian image models (white noise, Brownian and fractional...

Species and Scale Dependence of Bacterial Motion Dynamics

Science.gov (United States)

Sund, N. L.; Yang, X.; Parashar, R.; Plymale, A.; Hu, D.; Kelly, R.; Scheibe, T. D.

2017-12-01

Many metal reducing bacteria are motile with their motion characteristics described by run-and-tumble behavior exhibiting series of flights (jumps) and waiting (residence) time spanning a wide range of values. Accurate models of motility allow for improved design and evaluation of in-situ bioremediation in the subsurface. While many bioremediation models neglect the motion of the bacteria, others treat motility using an advection dispersion equation, which assumes that the motion of the bacteria is Brownian.The assumption of Brownian motion to describe motility has enormous implications on predictive capabilities of bioremediation models, yet experimental evidence of this assumption is mixed [1][2][3]. We hypothesize that this is due to the species and scale dependence of the motion dynamics. We test our hypothesis by analyzing videos of motile bacteria of five different species in open domains. Trajectories of individual cells ranging from several seconds to few minutes in duration are extracted in neutral conditions (in the absence of any chemical gradient). The density of the bacteria is kept low so that the interaction between the bacteria is minimal. Preliminary results show a transition from Fickian (Brownian) to non-Fickian behavior for one species of bacteria (Pelosinus) and persistent Fickian behavior of another species (Geobacter).Figure: Video frames of motile bacteria with the last 10 seconds of their trajectories drawn in red. (left) Pelosinus and (right) Geobacter.[1] Ariel, Gil, et al. "Swarming bacteria migrate by Lévy Walk." Nature Communications 6 (2015).[2] Saragosti, Jonathan, Pascal Silberzan, and Axel Buguin. "Modeling E. coli tumbles by rotational diffusion. Implications for chemotaxis." PloS one 7.4 (2012): e35412.[3] Wu, Mingming, et al. "Collective bacterial dynamics revealed using a three-dimensional population-scale defocused particle tracking technique." Applied and Environmental Microbiology 72.7 (2006): 4987-4994.

Behavior of aerosols undergoing Brownian coagulation, Brownian diffusion and gravitational settling in a closed chamber

International Nuclear Information System (INIS)

Okuyama, Kikuo; Kousaka, Yasuo; Yoshida, Tetsuo

1976-01-01

The behavior of aerosols undergoing Brownian coagulation. Brownian diffusion and gravitational settling in a closed chamber was studied by solving the basic equation, the so-called population balance equation, numerically for a polydisperse aerosol system and analytically for a monodisperse system, and then the results were examined by experiment. In solving the basic equation, two dimensionless parameters, which are determined by the initial properties of an aerosol and the chamber dimension and also characterize the relative effects of Brownian coagulation and Brownian diffusion to gravitational settling, were introduced in order to generalize the behavior under arbitrary conditions. The calculated results, the time-dependent changes in particle number concentration and particle size distribution for a polydisperse system, were presented graphically by using the above two parameters. And further using these parameters, the domains of the three controlling factors were mapped to show the extent of each effect of these factors under various conditions for a monodisperse system. Some of the calculated results were compared with the experimental results obtained by the ultramicroscopic size analysis previously developed by the authors. (auth.)

Stochastic processes from physics to finance

CERN Document Server

Paul, Wolfgang

2013-01-01

This book introduces the theory of stochastic processes with applications taken from physics and finance. Fundamental concepts like the random walk or Brownian motion but also Levy-stable distributions are discussed. Applications are selected to show the interdisciplinary character of the concepts and methods. In the second edition of the book a discussion of extreme events ranging from their mathematical definition to their importance for financial crashes was included. The exposition of basic notions of probability theory and the Brownian motion problem as well as the relation between conservative diffusion processes and quantum mechanics is expanded. The second edition also enlarges the treatment of financial markets. Beyond a presentation of geometric Brownian motion and the Black-Scholes approach to option pricing as well as the econophysics analysis of the stylized facts of financial markets, an introduction to agent based modeling approaches is given.

Electromagnetic radiation of charged particles in stochastic motion

Energy Technology Data Exchange (ETDEWEB)

Harko, Tiberiu [Babes-Bolyai University, Department of Physics, Cluj-Napoca (Romania); University College London, Department of Mathematics, London (United Kingdom); Mocanu, Gabriela [Astronomical Institute of the Romanian Academy, Cluj-Napoca (Romania)

2016-03-15

The study of the Brownian motion of a charged particle in electric and magnetic fields has many important applications in plasma and heavy ions physics, as well as in astrophysics. In the present paper we consider the electromagnetic radiation properties of a charged non-relativistic particle in the presence of electric and magnetic fields, of an exterior non-electromagnetic potential, and of a friction and stochastic force, respectively. We describe the motion of the charged particle by a Langevin and generalized Langevin type stochastic differential equation. We investigate in detail the cases of the Brownian motion with or without memory in a constant electric field, in the presence of an external harmonic potential, and of a constant magnetic field. In all cases the corresponding Langevin equations are solved numerically, and a full description of the spectrum of the emitted radiation and of the physical properties of the motion is obtained. The power spectral density of the emitted power is also obtained for each case, and, for all considered oscillating systems, it shows the presence of peaks, corresponding to certain intervals of the frequency. (orig.)

Correlational approach to study interactions between dust Brownian particles in a plasma

Science.gov (United States)

Lisin, E. A.; Vaulina, O. S.; Petrov, O. F.

2018-01-01

A general approach to the correlational analysis of Brownian motion of strongly coupled particles in open dissipative systems is described. This approach can be applied to the theoretical description of various non-ideal statistically equilibrium systems (including non-Hamiltonian systems), as well as for the analysis of experimental data. In this paper, we consider an application of the correlational approach to the problem of experimental exploring the wake-mediated nonreciprocal interactions in complex plasmas. We derive simple analytic equations, which allows one to calculate the gradients of forces acting on a microparticle due to each of other particles as well as the gradients of external field, knowing only the information on time-averaged correlations of particles displacements and velocities. We show the importance of taking dissipative and random processes into account, without which consideration of a system with a nonreciprocal interparticle interaction as linearly coupled oscillators leads to significant errors in determining the characteristic frequencies in a system. In the examples of numerical simulations, we demonstrate that the proposed original approach could be an effective instrument in exploring the longitudinal wake structure of a microparticle in a plasma. Unlike the previous attempts to study the wake-mediated interactions in complex plasmas, our method does not require any external perturbations and is based on Brownian motion analysis only.

On the joint residence time of N independent two-dimensional Brownian motions

International Nuclear Information System (INIS)

Benichou, O; Coppey, M; Klafter, J; Moreau, M; Oshanin, G

2003-01-01

We study the behaviour of several joint residence times of N independent Brownian particles in a disc of radius R in two dimensions. We consider: (i) the time T N (t) spent by all N particles simultaneously in the disc within the time interval [0, t], (ii) the time T (m) N (t) which at least m out of N particles spend together in the disc within the time interval [0, t], and (iii) the time T-tilde (m) N (t) which exactly m out of N particles spend together in the disc within the time interval [0, t]. We obtain very simple exact expressions for the expectations of these three residence times in the limit t → ∞

Brownian dynamics with hydrodynamic interactions

International Nuclear Information System (INIS)

Ermak, D.L.; McCammon, J.A.

1978-01-01

A method for simulating the Brownian dynamics of N particles with the inclusion of hydrodynamic interactions is described. The particles may also be subject to the usual interparticle or external forces (e.g., electrostatic) which have been included in previous methods for simulating Brownian dynamics of particles in the absence of hydrodynamic interactions. The present method is derived from the Langevin equations for the N particle assembly, and the results are shown to be consistent with the corresponding Fokker--Planck results. Sample calculations on small systems illustrate the importance of including hydrodynamic interactions in Brownian dynamics simulations. The method should be useful for simulation studies of diffusion limited reactions, polymer dynamics, protein folding, particle coagulation, and other phenomena in solution

Probability laws related to the Jacobi theta and Riemann zeta function and Brownian excursions

OpenAIRE

Biane, P.; Pitman, J.; Yor, M.

1999-01-01

This paper reviews known results which connect Riemann's integral representations of his zeta function, involving Jacobi's theta function and its derivatives, to some particular probability laws governing sums of independent exponential variables. These laws are related to one-dimensional Brownian motion and to higher dimensional Bessel processes. We present some characterizations of these probability laws, and some approximations of Riemann's zeta function which are related to these laws.

Maximum of an Airy process plus Brownian motion and memory in Kardar-Parisi-Zhang growth

Science.gov (United States)

Le Doussal, Pierre

2017-12-01

We obtain several exact results for universal distributions involving the maximum of the Airy2 process minus a parabola and plus a Brownian motion, with applications to the one-dimensional Kardar-Parisi-Zhang (KPZ) stochastic growth universality class. This allows one to obtain (i) the universal limit, for large time separation, of the two-time height correlation for droplet initial conditions, e.g., C∞=limt2/t1→+∞h(t1) h (t2)¯c/h(t1)2¯c, with C∞≈0.623 , as well as conditional moments, which quantify ergodicity breaking in the time evolution; (ii) in the same limit, the distribution of the midpoint position x (t1) of a directed polymer of length t2; and (iii) the height distribution in stationary KPZ with a step. These results are derived from the replica Bethe ansatz for the KPZ continuum equation, with a "decoupling assumption" in the large time limit. They agree and confirm, whenever they can be compared, with (i) our recent tail results for two-time KPZ with the work by de Nardis and Le Doussal [J. Stat. Mech. (2017) 053212, 10.1088/1742-5468/aa6bce], checked in experiments with the work by Takeuchi and co-workers [De Nardis et al., Phys. Rev. Lett. 118, 125701 (2017), 10.1103/PhysRevLett.118.125701] and (ii) a recent result of Maes and Thiery [J. Stat. Phys. 168, 937 (2017), 10.1007/s10955-017-1839-2] on midpoint position.

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

Science.gov (United States)

Antonopoulos, Markos; Stamatakos, Georgios

2015-01-01

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

Spatio-Temporal Constrained Human Trajectory Generation from the PIR Motion Detector Sensor Network Data: A Geometric Algebra Approach

Directory of Open Access Journals (Sweden)

Zhaoyuan Yu

2015-12-01

Full Text Available Passive infrared (PIR motion detectors, which can support long-term continuous observation, are widely used for human motion analysis. Extracting all possible trajectories from the PIR sensor networks is important. Because the PIR sensor does not log location and individual information, none of the existing methods can generate all possible human motion trajectories that satisfy various spatio-temporal constraints from the sensor activation log data. In this paper, a geometric algebra (GA-based approach is developed to generate all possible human trajectories from the PIR sensor network data. Firstly, the representation of the geographical network, sensor activation response sequences and the human motion are represented as algebraic elements using GA. The human motion status of each sensor activation are labeled using the GA-based trajectory tracking. Then, a matrix multiplication approach is developed to dynamically generate the human trajectories according to the sensor activation log and the spatio-temporal constraints. The method is tested with the MERL motion database. Experiments show that our method can flexibly extract the major statistical pattern of the human motion. Compared with direct statistical analysis and tracklet graph method, our method can effectively extract all possible trajectories of the human motion, which makes it more accurate. Our method is also likely to provides a new way to filter other passive sensor log data in sensor networks.

Spatio-Temporal Constrained Human Trajectory Generation from the PIR Motion Detector Sensor Network Data: A Geometric Algebra Approach.

Science.gov (United States)

Yu, Zhaoyuan; Yuan, Linwang; Luo, Wen; Feng, Linyao; Lv, Guonian

2015-12-30

Passive infrared (PIR) motion detectors, which can support long-term continuous observation, are widely used for human motion analysis. Extracting all possible trajectories from the PIR sensor networks is important. Because the PIR sensor does not log location and individual information, none of the existing methods can generate all possible human motion trajectories that satisfy various spatio-temporal constraints from the sensor activation log data. In this paper, a geometric algebra (GA)-based approach is developed to generate all possible human trajectories from the PIR sensor network data. Firstly, the representation of the geographical network, sensor activation response sequences and the human motion are represented as algebraic elements using GA. The human motion status of each sensor activation are labeled using the GA-based trajectory tracking. Then, a matrix multiplication approach is developed to dynamically generate the human trajectories according to the sensor activation log and the spatio-temporal constraints. The method is tested with the MERL motion database. Experiments show that our method can flexibly extract the major statistical pattern of the human motion. Compared with direct statistical analysis and tracklet graph method, our method can effectively extract all possible trajectories of the human motion, which makes it more accurate. Our method is also likely to provides a new way to filter other passive sensor log data in sensor networks.

Development of a simple system for simultaneously measuring 6DOF geometric motion errors of a linear guide.

Science.gov (United States)

Qibo, Feng; Bin, Zhang; Cunxing, Cui; Cuifang, Kuang; Yusheng, Zhai; Fenglin, You

2013-11-04

A simple method for simultaneously measuring the 6DOF geometric motion errors of the linear guide was proposed. The mechanisms for measuring straightness and angular errors and for enhancing their resolution are described in detail. A common-path method for measuring the laser beam drift was proposed and it was used to compensate the errors produced by the laser beam drift in the 6DOF geometric error measurements. A compact 6DOF system was built. Calibration experiments with certain standard measurement meters showed that our system has a standard deviation of 0.5 µm in a range of ± 100 µm for the straightness measurements, and standard deviations of 0.5", 0.5", and 1.0" in the range of ± 100" for pitch, yaw, and roll measurements, respectively.

Active motions of Brownian particles in a generalized energy-depot model

International Nuclear Information System (INIS)

Zhang Yong; Koo Kim, Chul; Lee, Kong-Ju-Bock

2008-01-01

We present a generalized energy-depot model in which the rate of conversion of the internal energy into motion can be dependent on the position and velocity of a particle. When the conversion rate is a general function of the velocity, the active particle exhibits diverse patterns of motion, including a braking mechanism and a stepping motion. The phase trajectories of the motion are investigated in a systematic way. With a particular form of the conversion rate dependent on the position and velocity, the particle shows a spontaneous oscillation characterizing a negative stiffness. These types of active behaviors are compared with similar phenomena observed in biology, such as the stepping motion of molecular motors and amplification in the hearing mechanism. Hence, our model can provide a generic understanding of the active motion related to the energy conversion and also a new control mechanism for nano-robots. We also investigate the effect of noise, especially on the stepping motion, and observe random walk-like behavior as expected.

Large scale Brownian dynamics of confined suspensions of rigid particles

Science.gov (United States)

Sprinkle, Brennan; Balboa Usabiaga, Florencio; Patankar, Neelesh A.; Donev, Aleksandar

2017-12-01

We introduce methods for large-scale Brownian Dynamics (BD) simulation of many rigid particles of arbitrary shape suspended in a fluctuating fluid. Our method adds Brownian motion to the rigid multiblob method [F. Balboa Usabiaga et al., Commun. Appl. Math. Comput. Sci. 11(2), 217-296 (2016)] at a cost comparable to the cost of deterministic simulations. We demonstrate that we can efficiently generate deterministic and random displacements for many particles using preconditioned Krylov iterative methods, if kernel methods to efficiently compute the action of the Rotne-Prager-Yamakawa (RPY) mobility matrix and its "square" root are available for the given boundary conditions. These kernel operations can be computed with near linear scaling for periodic domains using the positively split Ewald method. Here we study particles partially confined by gravity above a no-slip bottom wall using a graphical processing unit implementation of the mobility matrix-vector product, combined with a preconditioned Lanczos iteration for generating Brownian displacements. We address a major challenge in large-scale BD simulations, capturing the stochastic drift term that arises because of the configuration-dependent mobility. Unlike the widely used Fixman midpoint scheme, our methods utilize random finite differences and do not require the solution of resistance problems or the computation of the action of the inverse square root of the RPY mobility matrix. We construct two temporal schemes which are viable for large-scale simulations, an Euler-Maruyama traction scheme and a trapezoidal slip scheme, which minimize the number of mobility problems to be solved per time step while capturing the required stochastic drift terms. We validate and compare these schemes numerically by modeling suspensions of boomerang-shaped particles sedimented near a bottom wall. Using the trapezoidal scheme, we investigate the steady-state active motion in dense suspensions of confined microrollers, whose

Inchworm movement of two rings switching onto a thread by biased Brownian diffusion represent a three-body problem.

Science.gov (United States)

Benson, Christopher R; Maffeo, Christopher; Fatila, Elisabeth M; Liu, Yun; Sheetz, Edward G; Aksimentiev, Aleksei; Singharoy, Abhishek; Flood, Amar H

2018-05-07

The coordinated motion of many individual components underpins the operation of all machines. However, despite generations of experience in engineering, understanding the motion of three or more coupled components remains a challenge, known since the time of Newton as the "three-body problem." Here, we describe, quantify, and simulate a molecular three-body problem of threading two molecular rings onto a linear molecular thread. Specifically, we use voltage-triggered reduction of a tetrazine-based thread to capture two cyanostar macrocycles and form a [3]pseudorotaxane product. As a consequence of the noncovalent coupling between the cyanostar rings, we find the threading occurs by an unexpected and rare inchworm-like motion where one ring follows the other. The mechanism was derived from controls, analysis of cyclic voltammetry (CV) traces, and Brownian dynamics simulations. CVs from two noncovalently interacting rings match that of two covalently linked rings designed to thread via the inchworm pathway, and they deviate considerably from the CV of a macrocycle designed to thread via a stepwise pathway. Time-dependent electrochemistry provides estimates of rate constants for threading. Experimentally derived parameters (energy wells, barriers, diffusion coefficients) helped determine likely pathways of motion with rate-kinetics and Brownian dynamics simulations. Simulations verified intercomponent coupling could be separated into ring-thread interactions for kinetics, and ring-ring interactions for thermodynamics to reduce the three-body problem to a two-body one. Our findings provide a basis for high-throughput design of molecular machinery with multiple components undergoing coupled motion.

A mean-variance frontier in discrete and continuous time

NARCIS (Netherlands)

Bekker, Paul A.

2004-01-01

The paper presents a mean-variance frontier based on dynamic frictionless investment strategies in continuous time. The result applies to a finite number of risky assets whose price process is given by multivariate geometric Brownian motion with deterministically varying coefficients. The derivation

A bipedal DNA Brownian motor with coordinated legs.

Science.gov (United States)

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

2009-04-03

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

First passage Brownian functional properties of snowmelt dynamics

Science.gov (United States)

Dubey, Ashutosh; Bandyopadhyay, Malay

2018-04-01

In this paper, we model snow-melt dynamics in terms of a Brownian motion (BM) with purely time dependent drift and difusion and examine its first passage properties by suggesting and examining several Brownian functionals which characterize the lifetime and reactivity of such stochastic processes. We introduce several probability distribution functions (PDFs) associated with such time dependent BMs. For instance, for a BM with initial starting point x0, we derive analytical expressions for : (i) the PDF P(tf|x0) of the first passage time tf which specify the lifetime of such stochastic process, (ii) the PDF P(A|x0) of the area A till the first passage time and it provides us numerous valuable information about the total fresh water availability during melting, (iii) the PDF P(M) associated with the maximum size M of the BM process before the first passage time, and (iv) the joint PDF P(M; tm) of the maximum size M and its occurrence time tm before the first passage time. These P(M) and P(M; tm) are useful in determining the time of maximum fresh water availability and in calculating the total maximum amount of available fresh water. These PDFs are examined for the power law time dependent drift and diffusion which matches quite well with the available data of snowmelt dynamics.

Reversibility and switching options values in the geological disposal of radioactive waste

International Nuclear Information System (INIS)

Ionescu, Oana; Spaeter, Sandrine

2011-07-01

This article offers some economic insights for the debate on the reversible geological disposal of radioactive waste. Irreversibility due to large sunk costs, an important degree of flexibility and several sources of uncertainty are taken into account in the decision process relative to the radioactive waste disposal. We draw up a stochastic model in a continuous time framework to study the decision problem of a reversible repository project for the radioactive waste, with multiple disposal stages. We consider that the value of reversibility, related to the radioactive waste packages, is jointly affected by economic and technological uncertainty. These uncertainties are modeled, first, by a 2-Dimensional Geometric Brownian Motion, and, second, by a Geometric Brownian Motion with a Poisson jump process. A numerical analysis and a sensitivity study of various parameters are also proposed. Switching options values in the geological disposal of radioactive waste. (authors)

Double-temperature ratchet model and current reversal of coupled Brownian motors

Science.gov (United States)

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

2017-12-01

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

On designing geometric motion planners to solve regulating and trajectory tracking problems for robotic locomotion systems

Energy Technology Data Exchange (ETDEWEB)

Asnafi, Alireza [Hydro-Aeronautical Research Center, Shiraz University, Shiraz, 71348-13668 (Iran, Islamic Republic of); Mahzoon, Mojtaba [Department of Mechanical Engineering, School of Engineering, Shiraz University, Shiraz, 71348-13668 (Iran, Islamic Republic of)

2011-09-15

Based on a geometric fiber bundle structure, a generalized method to solve both regulation and trajectory tracking problems for locomotion systems is presented. The method is especially applied to two case studies of robotic locomotion systems; a three link articulated fish-like robot as a prototype of locomotion systems with symmetry, and the snakeboard as a prototype of mixed locomotion systems. Our results show that although these motion planners have an open loop structure, due to their generalities, they can steer case studies with negligible errors for almost any complicated path.

On designing geometric motion planners to solve regulating and trajectory tracking problems for robotic locomotion systems

International Nuclear Information System (INIS)

Asnafi, Alireza; Mahzoon, Mojtaba

2011-01-01

Based on a geometric fiber bundle structure, a generalized method to solve both regulation and trajectory tracking problems for locomotion systems is presented. The method is especially applied to two case studies of robotic locomotion systems; a three link articulated fish-like robot as a prototype of locomotion systems with symmetry, and the snakeboard as a prototype of mixed locomotion systems. Our results show that although these motion planners have an open loop structure, due to their generalities, they can steer case studies with negligible errors for almost any complicated path.

Decision Making in Incomplete Markets with Ambiguity : a case study of a gas field acquisition

NARCIS (Netherlands)

Zhao, Lin; van Wijnbergen, S.

2017-01-01

We apply utility indifference pricing to solve a contingent claim problem, valuing a connected pair of gas fields where the underlying process is not standard Geometric Brownian Motion and the assumption of complete markets is not fulfilled. First, empirical data are often characterized by

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

DEFF Research Database (Denmark)

Shillcock, Julian C.

2009-01-01

Brownian dynamics simulations are used to study the dynamical process of self-assembly of actin monomers into long filaments containing up to 1000 actin protomers. In order to overcome the large separation of time scales between the diffusive motion of the freemonomers and the relatively slow....../detachment events. When a single filament is allowed to grow in a bath of constant concentration of free ADP-actin monomers, its growth rate increases linearly with the free monomer concentration in quantitative agreement with in vitro experiments. Theresults also show that the waiting time is governed by...

Conformal correlation functions in the Brownian loop soup

Science.gov (United States)

Camia, Federico; Gandolfi, Alberto; Kleban, Matthew

2016-01-01

We define and study a set of operators that compute statistical properties of the Brownian loop soup, a conformally invariant gas of random Brownian loops (Brownian paths constrained to begin and end at the same point) in two dimensions. We prove that the correlation functions of these operators have many of the properties of conformal primaries in a conformal field theory, and compute their conformal dimension. The dimensions are real and positive, but have the novel feature that they vary continuously as a periodic function of a real parameter. We comment on the relation of the Brownian loop soup to the free field, and use this relation to establish that the central charge of the loop soup is twice its intensity.

Conformal correlation functions in the Brownian loop soup

Energy Technology Data Exchange (ETDEWEB)

Camia, Federico, E-mail: federico.camia@nyu.edu [New York University Abu Dhabi (United Arab Emirates); VU University, Amsterdam (Netherlands); Gandolfi, Alberto, E-mail: albertogandolfi@nyu.edu [New York University Abu Dhabi (United Arab Emirates); Università di Firenze (Italy); Kleban, Matthew, E-mail: kleban@nyu.edu [New York University Abu Dhabi (United Arab Emirates); Center for Cosmology and Particle Physics, Department of Physics, New York University (United States)

2016-01-15

We define and study a set of operators that compute statistical properties of the Brownian loop soup, a conformally invariant gas of random Brownian loops (Brownian paths constrained to begin and end at the same point) in two dimensions. We prove that the correlation functions of these operators have many of the properties of conformal primaries in a conformal field theory, and compute their conformal dimension. The dimensions are real and positive, but have the novel feature that they vary continuously as a periodic function of a real parameter. We comment on the relation of the Brownian loop soup to the free field, and use this relation to establish that the central charge of the loop soup is twice its intensity.

Conformal correlation functions in the Brownian loop soup

Directory of Open Access Journals (Sweden)

Federico Camia

2016-01-01

Full Text Available We define and study a set of operators that compute statistical properties of the Brownian loop soup, a conformally invariant gas of random Brownian loops (Brownian paths constrained to begin and end at the same point in two dimensions. We prove that the correlation functions of these operators have many of the properties of conformal primaries in a conformal field theory, and compute their conformal dimension. The dimensions are real and positive, but have the novel feature that they vary continuously as a periodic function of a real parameter. We comment on the relation of the Brownian loop soup to the free field, and use this relation to establish that the central charge of the loop soup is twice its intensity.

Schroedinger operators - geometric estimates in terms of the occupation time

International Nuclear Information System (INIS)

Demuth, M.; Kirsch, W.; McGillivray, I.

1995-01-01

The difference of Schroedinger and Dirichlet semigroups is expressed in terms of the Laplace transform of the Brownian motion occupation time. This implies quantitative upper and lower bounds for the operator norms of the corresponding resolvent differences. One spectral theoretical consequence is an estimate for the eigenfunction for a Schroedinger operator in a ball where the potential is given as a cone indicator function. 12 refs

Symmetries of stochastic differential equations: A geometric approach

Energy Technology Data Exchange (ETDEWEB)

De Vecchi, Francesco C., E-mail: francesco.devecchi@unimi.it; Ugolini, Stefania, E-mail: stefania.ugolini@unimi.it [Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, Milano (Italy); Morando, Paola, E-mail: paola.morando@unimi.it [DISAA, Università degli Studi di Milano, via Celoria 2, Milano (Italy)

2016-06-15

A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence between an algebra of weak symmetries for a given SDE and an algebra of strong symmetries for a modified SDE is proved under suitable regularity assumptions. This general approach is applied to a stochastic version of a two dimensional symmetric ordinary differential equation and to the case of two dimensional Brownian motion.

Biological impact of geometric uncertainties: what margin is needed for intra-hepatic tumors?

International Nuclear Information System (INIS)

Kuo, Hsiang-Chi; Liu, Wen-Shan; Wu, Andrew; Mah, Dennis; Chuang, Keh-Shih; Hong, Linda; Yaparpalvi, Ravi; Guha, Chandan; Kalnicki, Shalom

2010-01-01

To evaluate and compare the biological impact on different proposed margin recipes for the same geometric uncertainties for intra-hepatic tumors with different tumor cell types or clinical stages. Three different margin recipes based on tumor motion were applied to sixteen IMRT plans with a total of twenty two intra-hepatic tumors. One recipe used the full amplitude of motion measured from patients to generate margins. A second used 70% of the full amplitude of motion, while the third had no margin for motion. The biological effects of geometric uncertainty in these three situations were evaluated with Equivalent Uniform Doses (EUD) for various survival fractions at 2 Gy (SF 2 ). There was no significant difference in the biological impact between the full motion margin and the 70% motion margin. Also, there was no significant difference between different tumor cell types. When the margin for motion was eliminated, the difference of the biological impact was significant among different cell types due to geometric uncertainties. Elimination of the motion margin requires dose escalation to compensate for the biological dose reduction due to the geometric misses during treatment. Both patient-based margins of full motion and of 70% motion are sufficient to prevent serious dosimetric error. Clinical implementation of margin reduction should consider the tumor sensitivity to radiation

Infinite-mode squeezed coherent states and non-equilibrium statistical mechanics (phase-space-picture approach)

International Nuclear Information System (INIS)

Yeh, L.

1992-01-01

The phase-space-picture approach to quantum non-equilibrium statistical mechanics via the characteristic function of infinite- mode squeezed coherent states is introduced. We use quantum Brownian motion as an example to show how this approach provides an interesting geometrical interpretation of quantum non-equilibrium phenomena

Estimation of a Non-homogeneous Poisson Model: An Empirical ...

African Journals Online (AJOL)

This article aims at applying the Nonhomogeneous Poisson process to trends of economic development. For this purpose, a modified Nonhomogeneous Poisson process is derived when the intensity rate is considered as a solution of stochastic differential equation which satisfies the geometric Brownian motion. The mean ...

A practical application of the geometrical theory on fibered manifolds to an autonomous bicycle motion in mechanical system with nonholonomic constraints

Science.gov (United States)

Haddout, Soufiane

2018-01-01

The equations of motion of a bicycle are highly nonlinear and rolling of wheels without slipping can only be expressed by nonholonomic constraint equations. A geometrical theory of general nonholonomic constrained systems on fibered manifolds and their jet prolongations, based on so-called Chetaev-type constraint forces, was proposed and developed in the last decade by O. Krupková (Rossi) in 1990's. Her approach is suitable for study of all kinds of mechanical systems-without restricting to Lagrangian, time-independent, or regular ones, and is applicable to arbitrary constraints (holonomic, semiholonomic, linear, nonlinear or general nonholonomic). The goal of this paper is to apply Krupková's geometric theory of nonholonomic mechanical systems to study a concrete problem in nonlinear nonholonomic dynamics, i.e., autonomous bicycle. The dynamical model is preserved in simulations in its original nonlinear form without any simplifying. The results of numerical solutions of constrained equations of motion, derived within the theory, are in good agreement with measurements and thus they open the possibility of direct application of the theory to practical situations.

Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.

Science.gov (United States)

Arrieta, Jorge; Cartwright, Julyan H E; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan

2015-01-01

Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.

Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.

Directory of Open Access Journals (Sweden)

Jorge Arrieta

Full Text Available Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.

Decay ratio for third order Brownian oscillators

International Nuclear Information System (INIS)

Konno, H.; Kanemoto, S.

1998-01-01

We have obtained the analytical expressions of the decay ratios for two types of third order Brownian oscillators which are generalizations of the second order Brownian oscillator driven by the Gaussian-white noise. The resulting expressions will provide us useful baseline information for more complicated practical problems and their applications

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

International Nuclear Information System (INIS)

Plyukhin, A.V.

2013-01-01

A model of an autonomous isothermal Brownian motor with an internal propulsion mechanism is considered. The motor is a Brownian particle which is semi-transparent for molecules of surrounding ideal gas. Molecular passage through the particle is controlled by a potential similar to that in the transition rate theory, i.e. characterized by two stationary states with a finite energy difference separated by a potential barrier. The internal potential drop maintains the diode-like asymmetry of molecular fluxes through the particle, which results in the particle's stationary drift.

Brownian motion of massive skyrmions in magnetic thin films

International Nuclear Information System (INIS)

Troncoso, Roberto E.; Núñez, Álvaro S.

2014-01-01

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

Brownian motion of massive skyrmions in magnetic thin films

Energy Technology Data Exchange (ETDEWEB)

Troncoso, Roberto E., E-mail: r.troncoso.c@gmail.com [Centro para el Desarrollo de la Nanociencia y la Nanotecnología, CEDENNA, Avda. Ecuador 3493, Santiago 9170124 (Chile); Núñez, Álvaro S., E-mail: alnunez@dfi.uchile.cl [Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago (Chile)

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.

Bounds for the American perpetual put on a stock index

OpenAIRE

Paulsen, V.

2001-01-01

Let us consider n stocks with dependent price processes each following a geometric Brownian motion. We want to investigate the American perpetual put on an index of those stocks. We will provide inner and outer boundaries for its early exercise region by using a decomposition technique for optimal stopping.

Brownian quasi-particles in statistical physics

International Nuclear Information System (INIS)

Tellez-Arenas, A.; Fronteau, J.; Combis, P.

1979-01-01

The idea of a Brownian quasi-particle and the associated differentiable flow (with nonselfadjoint forces) are used here in the context of a stochastic description of the approach towards statistical equilibrium. We show that this quasi-particle flow acquires, at equilibrium, the principal properties of a conservative Hamiltonian flow. Thus the model of Brownian quasi-particles permits us to establish a link between the stochastic description and the Gibbs description of statistical equilibrium

Static structure of active Brownian hard disks

Science.gov (United States)

de Macedo Biniossek, N.; Löwen, H.; Voigtmann, Th; Smallenburg, F.

2018-02-01

We explore the changes in static structure of a two-dimensional system of active Brownian particles (ABP) with hard-disk interactions, using event-driven Brownian dynamics simulations. In particular, the effect of the self-propulsion velocity and the rotational diffusivity on the orientationally-averaged fluid structure factor is discussed. Typically activity increases structural ordering and generates a structure factor peak at zero wave vector which is a precursor of motility-induced phase separation. Our results provide reference data to test future statistical theories for the fluid structure of active Brownian systems. This manuscript was submitted for the special issue of the Journal of Physics: Condensed Matter associated with the Liquid Matter Conference 2017.

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

Science.gov (United States)

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

2012-07-01

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

Catalytic micromotor generating self-propelled regular motion through random fluctuation

Science.gov (United States)

Yamamoto, Daigo; Mukai, Atsushi; Okita, Naoaki; Yoshikawa, Kenichi; Shioi, Akihisa

2013-07-01

Most of the current studies on nano/microscale motors to generate regular motion have adapted the strategy to fabricate a composite with different materials. In this paper, we report that a simple object solely made of platinum generates regular motion driven by a catalytic chemical reaction with hydrogen peroxide. Depending on the morphological symmetry of the catalytic particles, a rich variety of random and regular motions are observed. The experimental trend is well reproduced by a simple theoretical model by taking into account of the anisotropic viscous effect on the self-propelled active Brownian fluctuation.

Rapid sampling of stochastic displacements in Brownian dynamics simulations with stresslet constraints

Science.gov (United States)

Fiore, Andrew M.; Swan, James W.

2018-01-01

Brownian Dynamics simulations are an important tool for modeling the dynamics of soft matter. However, accurate and rapid computations of the hydrodynamic interactions between suspended, microscopic components in a soft material are a significant computational challenge. Here, we present a new method for Brownian dynamics simulations of suspended colloidal scale particles such as colloids, polymers, surfactants, and proteins subject to a particular and important class of hydrodynamic constraints. The total computational cost of the algorithm is practically linear with the number of particles modeled and can be further optimized when the characteristic mass fractal dimension of the suspended particles is known. Specifically, we consider the so-called "stresslet" constraint for which suspended particles resist local deformation. This acts to produce a symmetric force dipole in the fluid and imparts rigidity to the particles. The presented method is an extension of the recently reported positively split formulation for Ewald summation of the Rotne-Prager-Yamakawa mobility tensor to higher order terms in the hydrodynamic scattering series accounting for force dipoles [A. M. Fiore et al., J. Chem. Phys. 146(12), 124116 (2017)]. The hydrodynamic mobility tensor, which is proportional to the covariance of particle Brownian displacements, is constructed as an Ewald sum in a novel way which guarantees that the real-space and wave-space contributions to the sum are independently symmetric and positive-definite for all possible particle configurations. This property of the Ewald sum is leveraged to rapidly sample the Brownian displacements from a superposition of statistically independent processes with the wave-space and real-space contributions as respective covariances. The cost of computing the Brownian displacements in this way is comparable to the cost of computing the deterministic displacements. The addition of a stresslet constraint to the over-damped particle

Optimal portfolio strategies under a shortfall constraint | Akume ...

African Journals Online (AJOL)

We impose dynamically, a shortfall constraint in terms of Tail Conditional Expectation on the portfolio selection problem in continuous time, in order to obtain optimal strategies. The nancial market is assumed to comprise n risky assets driven by geometric Brownian motion and one risk-free asset. The method of Lagrange ...

Crossover of two power laws in the anomalous diffusion of a two lipid membrane.

Science.gov (United States)

Bakalis, Evangelos; Höfinger, Siegfried; Venturini, Alessandro; Zerbetto, Francesco

2015-06-07

Molecular dynamics simulations of a bi-layer membrane made by the same number of 1-palmitoyl-2-oleoyl-glycero-3-phospho-ethanolamine and palmitoyl-oleoyl phosphatidylserine lipids reveal sub-diffusional motion, which presents a crossover between two different power laws. Fractional Brownian motion is the stochastic mechanism that governs the motion in both regimes. The location of the crossover point is justified with simple geometrical arguments and is due to the activation of the mechanism of circumrotation of lipids about each other.

Crossover of two power laws in the anomalous diffusion of a two lipid membrane

Energy Technology Data Exchange (ETDEWEB)

Bakalis, Evangelos, E-mail: ebakalis@gmail.com, E-mail: francesco.zerbetto@unibo.it; Höfinger, Siegfried; Zerbetto, Francesco, E-mail: ebakalis@gmail.com, E-mail: francesco.zerbetto@unibo.it [Dipartimento di Chimica “G. Ciamician”, Universita’ di Bologna, Via F. Selmi 2, 40126 Bologna (Italy); Venturini, Alessandro [Institute for the Organic Synthesis and Photoreactivity, National Research Council of Italy, Via Gobetti 101, 40129 Bologna (Italy)

2015-06-07

Molecular dynamics simulations of a bi-layer membrane made by the same number of 1-palmitoyl-2-oleoyl-glycero-3-phospho-ethanolamine and palmitoyl-oleoyl phosphatidylserine lipids reveal sub-diffusional motion, which presents a crossover between two different power laws. Fractional Brownian motion is the stochastic mechanism that governs the motion in both regimes. The location of the crossover point is justified with simple geometrical arguments and is due to the activation of the mechanism of circumrotation of lipids about each other.

Instantaneous ballistic velocity of suspended Brownian nanocrystals measured by upconversion nanothermometry

Science.gov (United States)

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.

Brownian Motion of Asymmetric Boomerang Colloidal Particles

Science.gov (United States)

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

2014-03-01

We used video microscopy and single particle tracking to study the diffusion and local behaviors of asymmetric boomerang particles in a quasi-two dimensional geometry. The motion is biased towards the center of hydrodynamic stress (CoH) and the mean square displacements of the particles are linear at short and long times with different diffusion coefficients and in the crossover regime it is sub-diffusive. Our model based on Langevin theory shows that these behaviors arise from the non-coincidence of the CoH with the center of the body. Since asymmetric boomerangs represent a class of rigid bodies of more generals shape, therefore our findings are generic and true for any non-skewed particle in two dimensions. Both experimental and theoretical results will be discussed.

On geometrized gravitation theories

International Nuclear Information System (INIS)

Logunov, A.A.; Folomeshkin, V.N.

1977-01-01

General properties of the geometrized gravitation theories have been considered. Geometrization of the theory is realized only to the extent that by necessity follows from an experiment (geometrization of the density of the matter Lagrangian only). Aor a general case the gravitation field equations and the equations of motion for matter are formulated in the different Riemann spaces. A covariant formulation of the energy-momentum conservation laws is given in an arbitrary geometrized theory. The noncovariant notion of ''pseudotensor'' is not required in formulating the conservation laws. It is shown that in the general case (i.e., when there is an explicit dependence of the matter Lagrangian density on the covariant derivatives) a symmetric energy-momentum tensor of the matter is explicitly dependent on the curvature tensor. There are enlisted different geometrized theories that describe a known set of the experimental facts. The properties of one of the versions of the quasilinear geometrized theory that describes the experimental facts are considered. In such a theory the fundamental static spherically symmetrical solution has a singularity only in the coordinate origin. The theory permits to create a satisfactory model of the homogeneous nonstationary Universe

On the Brownian motion of a massive sphere suspended in a hard-sphere fluid. II. Molecular dynamics estimates of the friction coefficient

International Nuclear Information System (INIS)

Bocquet, L.; Hansen, J.P.; Piasecki, J.

1994-01-01

The friction coefficient γ exerted by a hard-sphere fluid on an infinitely massive Brownian sphere is calculated for several size ratios Σ/σ where Σ and σ are the diameters of the Brownian and fluid spheres, respectively. The exact microscopic expression derived in part I of this work from kinetic theory is transformed and shown to be proportional to the time integral of the autocorrelation function of the momentum transferred from the fluid to the Brownian sphere during instantaneous collisions. Three different methods are described to extract the friction coefficient from molecular dynamics simulations carried out on finite systems. The three independent methods lead to estimates of γ which agree within statistical errors (typically 5%). The results are compared to the predictions of Enskog theory and of the hydrodynamic Stokes law. The former breaks down as the size ratio and/or the packing fraction of the fluid increase. Somewhat surprisingly, Stokes' law is found to hold with stick boundary conditions, in the range 1 ≤ Σ/σ ≤ 4.5 explored in the present simulations, with a hydrodynamic diameter d=Σ. The analysis of the molecular dynamics data on the basis of Stokes' law with slip boundary conditions is less conclusive, although the right trend is found as Σ/σ increases

BROWNIAN HEAT TRANSFER ENHANCEMENT IN THE TURBULENT REGIME

Directory of Open Access Journals (Sweden)

Suresh Chandrasekhar

2016-08-01

Full Text Available The paper presents convection heat transfer of a turbulent flow Al2O3/water nanofluid in a circular duct. The duct is a under constant and uniform heat flux. The paper computationally investigates the system’s thermal behavior in a wide range of Reynolds number and also volume concentration up to 6%. To obtain the nanofluid thermophysical properties, the Hamilton-Crosser model along with the Brownian motion effect are utilized. Then the thermal performance of the system with the nanofluid is compared to the conventional systems which use water as the working fluid. The results indicate that the use of nanofluid of 6% improves the heat transfer rate up to 36.8% with respect to pure water. Therefore, using the Al2O3/water nanofluid instead of water can be a great choice when better heat transfer is needed.

Biased Brownian dynamics for rate constant calculation.

OpenAIRE

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

2000-01-01

An enhanced sampling method-biased Brownian dynamics-is developed for the calculation of diffusion-limited biomolecular association reaction rates with high energy or entropy barriers. Biased Brownian dynamics introduces a biasing force in addition to the electrostatic force between the reactants, and it associates a probability weight with each trajectory. A simulation loses weight when movement is along the biasing force and gains weight when movement is against the biasing force. The sampl...

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

Energy Technology Data Exchange (ETDEWEB)

Dubina, Sean Hyun, E-mail: sdubin2@uic.edu; Wedgewood, Lewis Edward, E-mail: wedge@uic.edu [Department of Chemical Engineering, University of Illinois at Chicago, 810 S. Clinton St. (MC 110), Chicago, Illinois 60607-4408 (United States)

2016-07-15

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.

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

International Nuclear Information System (INIS)

Dubina, Sean Hyun; Wedgewood, Lewis Edward

2016-01-01

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.

Optimum analysis of a Brownian refrigerator.

Science.gov (United States)

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

2013-02-01

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

Lyapunov vs. geometrical stability analysis of the Kepler and the restricted three body problems

International Nuclear Information System (INIS)

Yahalom, A.; Levitan, J.; Lewkowicz, M.; Horwitz, L.

2011-01-01

In this Letter we show that although the application of standard Lyapunov analysis predicts that completely integrable Kepler motion is unstable, the geometrical analysis of Horwitz et al. predicts the observed stability. This seems to us to provide evidence for both the incompleteness of the standard Lyapunov analysis and the strength of the geometrical analysis. Moreover, we apply this approach to the three body problem in which the third body is restricted to move on a circle of large radius which induces an adiabatic time dependent potential on the second body. This causes the second body to move in a very interesting and intricate but periodic trajectory; however, the standard Lyapunov analysis, as well as methods based on the parametric variation of curvature associated with the Jacobi metric, incorrectly predict chaotic behavior. The geometric approach predicts the correct stable motion in this case as well. - Highlights: → Lyapunov analysis predicts Kepler motion to be unstable. → Geometrical analysis predicts the observed stability. → Lyapunov analysis predicts chaotic behavior in restricted three body problem. → The geometric approach predicts the correct stable motion in restricted three body problem.

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

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

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

2004-01-01

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

Fast orthogonal transforms and generation of Brownian paths.

Science.gov (United States)

Leobacher, Gunther

2012-04-01

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

Using Temporal Covariance of Motion and Geometric Features via Boosting for Human Fall Detection.

Science.gov (United States)

Ali, Syed Farooq; Khan, Reamsha; Mahmood, Arif; Hassan, Malik Tahir; Jeon, And Moongu

2018-06-12

Fall induced damages are serious incidences for aged as well as young persons. A real-time automatic and accurate fall detection system can play a vital role in timely medication care which will ultimately help to decrease the damages and complications. In this paper, we propose a fast and more accurate real-time system which can detect people falling in videos captured by surveillance cameras. Novel temporal and spatial variance-based features are proposed which comprise the discriminatory motion, geometric orientation and location of the person. These features are used along with ensemble learning strategy of boosting with J48 and Adaboost classifiers. Experiments have been conducted on publicly available standard datasets including Multiple Cameras Fall ( with 2 classes and 3 classes ) and UR Fall Detection achieving percentage accuracies of 99.2, 99.25 and 99.0, respectively. Comparisons with nine state-of-the-art methods demonstrate the effectiveness of the proposed approach on both datasets.

Secular Extragalactic Parallax and Geometric Distances with Gaia Proper Motions

Science.gov (United States)

Paine, Jennie; Darling, Jeremiah K.

2018-06-01

The motion of the Solar System with respect to the cosmic microwave background (CMB) rest frame creates a well measured dipole in the CMB, which corresponds to a linear solar velocity of about 78 AU/yr. This motion causes relatively nearby extragalactic objects to appear to move compared to more distant objects, an effect that can be measured in the proper motions of nearby galaxies. An object at 1 Mpc and perpendicular to the CMB apex will exhibit a secular parallax, observed as a proper motion, of 78 µas/yr. The relatively large peculiar motions of galaxies make the detection of secular parallax challenging for individual objects. Instead, a statistical parallax measurement can be made for a sample of objects with proper motions, where the global parallax signal is modeled as an E-mode dipole that diminishes linearly with distance. We present preliminary results of applying this model to a sample of nearby galaxies with Gaia proper motions to detect the statistical secular parallax signal. The statistical measurement can be used to calibrate the canonical cosmological “distance ladder.”

Mathematical interpretation of Brownian motor model: Limit cycles and directed transport phenomena

Science.gov (United States)

Yang, Jianqiang; Ma, Hong; Zhong, Suchuang

2018-03-01

In this article, we first suggest that the attractor of Brownian motor model is one of the reasons for the directed transport phenomenon of Brownian particle. We take the classical Smoluchowski-Feynman (SF) ratchet model as an example to investigate the relationship between limit cycles and directed transport phenomenon of the Brownian particle. We study the existence and variation rule of limit cycles of SF ratchet model at changing parameters through mathematical methods. The influences of these parameters on the directed transport phenomenon of a Brownian particle are then analyzed through numerical simulations. Reasonable mathematical explanations for the directed transport phenomenon of Brownian particle in SF ratchet model are also formulated on the basis of the existence and variation rule of the limit cycles and numerical simulations. These mathematical explanations provide a theoretical basis for applying these theories in physics, biology, chemistry, and engineering.

100 years of Einstein's Theory of Brownian Motion: From Pollen ...

Indian Academy of Sciences (India)

complex form. Recall that the rotational motion of a ... blocked and they retain the memory of the direction of the earth's .... In other words, the system works as a rectifier where the ... This is easy to understand using a picture simi- lar to the ...

Numerical investigation of the effects of geometric parameters on transverse motion with slanted-groove micro-mixers

Energy Technology Data Exchange (ETDEWEB)

Baik, Seung Joo; Cho, Jae Yong; Choi, Se Bin; Lee, Joon Sang [School of Mechanical Engineering, Yonsei University, Seoul (Korea, Republic of)

2016-08-15

We investigated hydrodynamic phenomena inside several passive microfluidic mixers using a Lattice Boltzmann method (LBM) based on particle mesoscopic kinetic equations. Mixing processes were simulated in a Slanted grooved micro-mixer (SGM), a Staggered herringbone grooved micro-mixer (SHM), and a Bi-layered staggered herringbone grooved micro-mixer (BSHM). Then, the effects of six geometric mixer parameters (i.e., groove height to channel height ratio, groove width to groove pitch length ratio, groove pitch to groove height ratio, groove intersection angle, herringbone groove asymmetric ratio and bi-layered groove asymmetric ratio) on mixing were investigated using computed cross-flow velocity and helicity density distributions in the flow cross-section. We demonstrated that helicity density provides sufficient information to analyze micro helical motion within a micro-mixer, allowing for micro-mixer design optimization.

Geometric control theory and sub-Riemannian geometry

CERN Document Server

Boscain, Ugo; Gauthier, Jean-Paul; Sarychev, Andrey; Sigalotti, Mario

2014-01-01

This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as  sub-Riemannian, Finslerian  geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods  has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group  of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.

The Role of Motion Concepts in Understanding Non-Motion Concepts

Directory of Open Access Journals (Sweden)

Omid Khatin-Zadeh

2017-12-01

Full Text Available This article discusses a specific type of metaphor in which an abstract non-motion domain is described in terms of a motion event. Abstract non-motion domains are inherently different from concrete motion domains. However, motion domains are used to describe abstract non-motion domains in many metaphors. Three main reasons are suggested for the suitability of motion events in such metaphorical descriptions. Firstly, motion events usually have high degrees of concreteness. Secondly, motion events are highly imageable. Thirdly, components of any motion event can be imagined almost simultaneously within a three-dimensional space. These three characteristics make motion events suitable domains for describing abstract non-motion domains, and facilitate the process of online comprehension throughout language processing. Extending the main point into the field of mathematics, this article discusses the process of transforming abstract mathematical problems into imageable geometric representations within the three-dimensional space. This strategy is widely used by mathematicians to solve highly abstract and complex problems.

Breaking the symmetry of a Brownian motor with symmetric potentials

International Nuclear Information System (INIS)

Hagman, H; Zelan, M; Dion, C M

2011-01-01

The directed transport of Brownian particles requires a system with an asymmetry and with non-equilibrium noise. Here we investigate numerically alternative ways of fulfilling these requirements for a two-state Brownian motor, realized with Brownian particles alternating between two phase-shifted, symmetric potentials. We show that, besides the previously known spatio-temporal asymmetry based on unequal transfer rates between the potentials, inequalities in the potential depths, the frictions, or the equilibrium temperatures of the two potentials also generate the required asymmetry. We also show that the effects of the thermal noise and the noise of the transfer's randomness depend on the way the asymmetry is induced.

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

Science.gov (United States)

Mezzasalma, Stefano A

2007-03-15

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

Stochastic flows in the Brownian web and net

Czech Academy of Sciences Publication Activity Database

Schertzer, E.; Sun, R.; Swart, Jan M.

2014-01-01

Roč. 227, č. 1065 (2014), s. 1-160 ISSN 0065-9266 R&D Projects: GA ČR GA201/07/0237; GA ČR GA201/09/1931 Institutional support: RVO:67985556 Keywords : Brownian web * Brownian net * stochastic flow of kernels * measure-valued process * Howitt-Warren flow * linear system * random walk in random environment * finite graph representation Subject RIV: BA - General Mathematics Impact factor: 1.727, year: 2014 http://library.utia.cas.cz/separaty/2013/SI/swart-0396636.pdf

A comparison of two clinical correlation models used for real-time tumor tracking of semi-periodic motion: A focus on geometrical accuracy in lung and liver cancer patients

International Nuclear Information System (INIS)

Poels, Kenneth; Dhont, Jennifer; Verellen, Dirk; Blanck, Oliver; Ernst, Floris; Vandemeulebroucke, Jef; Depuydt, Tom; Storme, Guy; De Ridder, Mark

2015-01-01

Purpose: A head-to-head comparison of two clinical correlation models with a focus on geometrical accuracy for internal tumor motion estimation during real-time tumor tracking (RTTT). Methods and materials: Both the CyberKnife (CK) and the Vero systems perform RTTT with a correlation model that is able to describe hysteresis in the breathing motion. The CK dual-quadratic (DQ) model consists of two polynomial functions describing the trajectory of the tumor for inhale and exhale breathing motion, respectively. The Vero model is based on a two-dimensional (2D) function depending on position and speed of the external breathing signal to describe a closed-loop tumor trajectory. In this study, 20 s of internal motion data, using an 11 Hz (on average) full fluoroscopy (FF) sequence, was used for training of the CK and Vero models. Further, a subsampled set of 15 internal tumor positions (15p) equally spread over the different phases of the breathing motion was used for separate training of the CK DQ model. Also a linear model was trained using 15p and FF tumor motion data. Fifteen liver and lung cancer patients, treated on the Vero system with RTTT, were retrospectively evaluated comparing the CK FF, CK 15p and Vero FF models using an in-house developed simulator. The distance between estimated target position and the tumor position localized by X-ray imaging was measured in the beams-eye view (BEV) to calculate the 95th percentile BEV modeling errors (ME 95,BEV ). Additionally, the percentage of ME 95,BEV smaller than 5 mm (P 5mm ) was determined for all correlation models. Results: In general, no significant difference (p > 0.05, paired t-test) was found between the CK FF and Vero models. Based on patient-specific evaluation of the geometrical accuracy of the linear, CK DQ and Vero correlation models, no statistical necessity (p > 0.05, two-way ANOVA) of including hysteresis in correlation models was proven, although during inhale breathing motion, the linear model

Distribution and spectrum of fluctuations of a Brownian particle in a potential well with reflecting walls

International Nuclear Information System (INIS)

Soskin, S.M.

1987-01-01

The authors examine Brownian motion in a square well with reflecting walls. An exact solution is obtained for the corresponding Einstein-Fokker-Planck equation, which is used to find the coordinate correlation function in explicit form. The correlation function, normalized to the square of the distance between the walls, typically exhibits a similarity property: its behavior as a function of time, friction, temperature, and wall separation reduces to a function of one simple combination of those four quantities. The limiting cases of low and high friction are investigated in detail, with explicit expressions being derived for the spectrum

Modelling anisotropic covariance using stochastic development and sub-Riemannian frame bundle geometry

DEFF Research Database (Denmark)

Sommer, Stefan Horst; Svane, Anne Marie

2017-01-01

distributions. We discuss a factorization of the frame bundle projection map through this bundle, the natural sub-Riemannian structure of the frame bundle, the effect of holonomy, and the existence of subbundles where the Hormander condition is satisfied such that the Brownian motions have smooth transition......We discuss the geometric foundation behind the use of stochastic processes in the frame bundle of a smooth manifold to build stochastic models with applications in statistical analysis of non-linear data. The transition densities for the projection to the manifold of Brownian motions developed...... in the frame bundle lead to a family of probability distributions on the manifold. We explain how data mean and covariance can be interpreted as points in the frame bundle or, more precisely, in the bundle of symmetric positive definite 2-tensors analogously to the parameters describing Euclidean normal...

Friction between Two Brownian Particles in a Lennard-Jones Solvent: A Molecular Dynamics Simulation Study

International Nuclear Information System (INIS)

Lee, Song Hi

2010-01-01

We presented a molecular dynamics (MD) simulation study of friction behavior between two very massive Brownian particles (BPs) oriented along the z axis with BP centers at -R 12 /2 and R 12 /2 in a Lennard-Jones solvent as a function of the inter-particle separation, R 12 . In order to fix the BPs in space an MD simulation method with the mass of the BP as 10 90 g/mol was employed in which the total momentum of the system was conserved. The cross friction coefficients of x- and y-components are nearly insensitive to R 12 but that of z-component varies with R 12 in good accord with the simple hydrodynamic approximation. On the other hand, the self-friction coefficients are estimated as a very small difference from the single particle friction coefficients, ξ 0 , at all inter-particle separations which agrees with the simple hydrodynamic approximation. Consequently ξ (-) xx is nearly independent of R 12 and equal to its asymptotic value of twice the single particle friction coefficient, and the other relative friction, ξ (-) zz , is in good agreement with the simple hydrodynamic approximation. Molecular theory of Brownian motion of a single heavy particle in a fluid had received a considerable attention in earlier years. After molecular dynamics (MD) simulation technique was utilized, this subject has been widely studied by a variety of MD simulation methods. The common issues here were about the long time behavior of the force and velocity autocorrelation functions, the system size dependent friction coefficient of a massive Brownian particle, and test of the Stokes-Einstein law

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

Science.gov (United States)

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.

A very efficient approach for pricing barrier options on an underlying described by the mixed fractional Brownian motion

International Nuclear Information System (INIS)

Ballestra, Luca Vincenzo; Pacelli, Graziella; Radi, Davide

2016-01-01

We deal with the problem of pricing barrier options on an underlying described by the mixed fractional Brownian model. To this aim, we consider the initial-boundary value partial differential problem that yields the option price and we derive an integral representation of it in which the integrand functions must be obtained solving Volterra equations of the first kind. In addition, we develop an ad-hoc numerical procedure to solve the integral equations obtained. Numerical simulations reveal that the proposed method is extremely accurate and fast, and performs significantly better than the finite difference method.

Brownian dynamics of a protein-polymer chain complex in a solid-state nanopore

Science.gov (United States)

Wells, Craig C.; Melnikov, Dmitriy V.; Gracheva, Maria E.

2017-08-01

We study the movement of a polymer attached to a large protein inside a nanopore in a thin silicon dioxide membrane submerged in an electrolyte solution. We use Brownian dynamics to describe the motion of a negatively charged polymer chain of varying lengths attached to a neutral protein modeled as a spherical bead with a radius larger than that of the nanopore, allowing the chain to thread the nanopore but preventing it from translocating. The motion of the protein-polymer complex within the pore is also compared to that of a freely translocating polymer. Our results show that the free polymer's standard deviations in the direction normal to the pore axis is greater than that of the protein-polymer complex. We find that restrictions imposed by the protein, bias, and neighboring chain segments aid in controlling the position of the chain in the pore. Understanding the behavior of the protein-polymer chain complex may lead to methods that improve molecule identification by increasing the resolution of ionic current measurements.

Symmetries and conserved quantities in geodesic motion

International Nuclear Information System (INIS)

Hojman, S.; Nunez, L.; Patino, A.; Rago, H.

1986-01-01

Recently obtained results linking several constants of motion to one (non-Noetherian) symmetry to the problem of geodesic motion in Riemannian space-times are applied. The construction of conserved quantities in geodesic motion as well as the deduction of geometrical statements about Riemannian space-times are achieved

Directed Transport of Brownian Particles in a Periodic Channel

International Nuclear Information System (INIS)

Jiang Jie; Ai Bao-Quan; Wu Jian-Chun

2015-01-01

The transport of Brownian particles in the infinite channel within an external force along the axis of the channel has been studied. In this paper, we study the transport of Brownian particle in the infinite channel within an external force along the axis of the channel and an external force in the transversal direction. In this more sophisticated situation, some property is similar to the simple situation, but some interesting property also appears. (paper)

What Can We Learn from a Cross-Section of Returns? An Investigation of Idiosyncratic Volatility Range

OpenAIRE

Serguey Khovansky; Zhylyevskyy, Oleksandr

2011-01-01

We investigate empirical properties of idiosyncratic volatility using cross-sections of stock returns in the standard framework of geometric Brownian motion price dynamics. Knowledge of the sign and magnitude of idiosyncratic volatility characteristics may help us better understand the role of idiosyncratic risk in asset pricing. This knowledge may also help practitioners devise innovative investment strategies to exploit profitable investment opportunities that have not been eliminated becau...

Geometric optimization and sums of algebraic functions

KAUST Repository

Vigneron, Antoine E.

2014-01-01

We present a new optimization technique that yields the first FPTAS for several geometric problems. These problems reduce to optimizing a sum of nonnegative, constant description complexity algebraic functions. We first give an FPTAS for optimizing such a sum of algebraic functions, and then we apply it to several geometric optimization problems. We obtain the first FPTAS for two fundamental geometric shape-matching problems in fixed dimension: maximizing the volume of overlap of two polyhedra under rigid motions and minimizing their symmetric difference. We obtain the first FPTAS for other problems in fixed dimension, such as computing an optimal ray in a weighted subdivision, finding the largest axially symmetric subset of a polyhedron, and computing minimum-area hulls.

Geometric phases for nonlinear coherent and squeezed states

International Nuclear Information System (INIS)

Yang Dabao; Chen Ying; Chen Jingling; Zhang Fulin

2011-01-01

The geometric phases for standard coherent states which are widely used in quantum optics have attracted considerable attention. Nevertheless, few physicists consider the counterparts of nonlinear coherent states, which are useful in the description of the motion of a trapped ion. In this paper, the non-unitary and non-cyclic geometric phases for two nonlinear coherent and one squeezed states are formulated, respectively. Moreover, some of their common properties are discussed, such as gauge invariance, non-locality and nonlinear effects. The nonlinear functions have dramatic impacts on the evolution of the corresponding geometric phases. They speed the evolution up or down. So this property may have an application in controlling or measuring geometric phase. For the squeezed case, when the squeezed parameter r → ∞, the limiting value of the geometric phase is also determined by a nonlinear function at a given time and angular velocity. In addition, the geometric phases for standard coherent and squeezed states are obtained under a particular condition. When the time evolution undergoes a period, their corresponding cyclic geometric phases are achieved as well. And the distinction between the geometric phases of the two coherent states may be regarded as a geometric criterion.

Presentation of quantum Brownian movement in the collective coordinate method

International Nuclear Information System (INIS)

Oksak, A.I.; Sukhanov, A.D.

2003-01-01

Two explicitly solved models of quantum randomized processes described by the Langevin equation, i. e. a free quantum Brownian particle and a quantum Brownian harmonic oscillator, are considered. The Hamiltonian (string) realization of the models reveals soliton-like structure of classical solutions. Accordingly, the method of zero mode collective coordinate is an adequate means for describing the models quantum dynamics [ru

Interpretation of NMR relaxation properties of Pin1, a two-domain protein, based on Brownian dynamic simulations

International Nuclear Information System (INIS)

Bernado, Pau; Fernandes, Miguel X.; Jacobs, Doris M.; Fiebig, Klaus; Garcia de la Torre, Jose; Pons, Miquel

2004-01-01

Many important proteins contain multiple domains connected by flexible linkers. Inter-domain motion is suggested to play a key role in many processes involving molecular recognition. Heteronuclear NMR relaxation is sensitive to motions in the relevant time scales and could provide valuable information on the dynamics of multi-domain proteins. However, the standard analysis based on the separation of global tumbling and fast local motions is no longer valid for multi-domain proteins undergoing internal motions involving complete domains and that take place on the same time scale than the overall motion.The complexity of the motions experienced even for the simplest two-domain proteins are difficult to capture with simple extensions of the classical Lipari-Szabo approach. Hydrodynamic effects are expected to dominate the motion of the individual globular domains, as well as that of the complete protein. Using Pin1 as a test case, we have simulated its motion at the microsecond time scale, at a reasonable computational expense, using Brownian Dynamic simulations on simplified models. The resulting trajectories provide insight on the interplay between global and inter-domain motion and can be analyzed using the recently published method of isotropic Reorientational Mode Dynamics which offer a way of calculating their contribution to heteronuclear relaxation rates. The analysis of trajectories computed with Pin1 models of different flexibility provides a general framework to understand the dynamics of multi-domain proteins and explains some of the observed features in the relaxation rate profile of free Pin1

Interpretation of NMR relaxation properties of Pin1, a two-domain protein, based on Brownian dynamic simulations

Energy Technology Data Exchange (ETDEWEB)

Bernado, Pau [Institut de Biologie Structurale, Jean Pierre Ebel (France); Fernandes, Miguel X. [Universidad de Murcia, Departamento de Quimica Fisica, Facultad de Quimica (Spain); Jacobs, Doris M. [Johann Wolfgang Goethe-Universitaet Frankfurt, Institut fuer Organische Chemie und Chemische Biologie (Germany); Fiebig, Klaus [Affinium Pharmaceuticals (Canada); Garcia de la Torre, Jose [Universidad de Murcia, Departamento de Quimica Fisica, Facultad de Quimica (Spain); Pons, Miquel [Laboratori de RMN de Biomolecules, Parc Cientific de Barcelona (Spain)], E-mail: mpons@ub.edu

2004-05-15

Many important proteins contain multiple domains connected by flexible linkers. Inter-domain motion is suggested to play a key role in many processes involving molecular recognition. Heteronuclear NMR relaxation is sensitive to motions in the relevant time scales and could provide valuable information on the dynamics of multi-domain proteins. However, the standard analysis based on the separation of global tumbling and fast local motions is no longer valid for multi-domain proteins undergoing internal motions involving complete domains and that take place on the same time scale than the overall motion.The complexity of the motions experienced even for the simplest two-domain proteins are difficult to capture with simple extensions of the classical Lipari-Szabo approach. Hydrodynamic effects are expected to dominate the motion of the individual globular domains, as well as that of the complete protein. Using Pin1 as a test case, we have simulated its motion at the microsecond time scale, at a reasonable computational expense, using Brownian Dynamic simulations on simplified models. The resulting trajectories provide insight on the interplay between global and inter-domain motion and can be analyzed using the recently published method of isotropic Reorientational Mode Dynamics which offer a way of calculating their contribution to heteronuclear relaxation rates. The analysis of trajectories computed with Pin1 models of different flexibility provides a general framework to understand the dynamics of multi-domain proteins and explains some of the observed features in the relaxation rate profile of free Pin1.

Adiabatic Processes Realized with a Trapped Brownian Particle

Science.gov (United States)

Martínez, Ignacio A.; Roldán, Édgar; Dinis, Luis; Petrov, Dmitri; Rica, Raúl A.

2015-03-01

The ability to implement adiabatic processes in the mesoscale is of key importance in the study of artificial or biological micro- and nanoengines. Microadiabatic processes have been elusive to experimental implementation due to the difficulty in isolating Brownian particles from their fluctuating environment. Here we report on the experimental realization of a microscopic quasistatic adiabatic process employing a trapped Brownian particle. We circumvent the complete isolation of the Brownian particle by designing a protocol where both characteristic volume and temperature of the system are changed in such a way that the entropy of the system is conserved along the process. We compare the protocols that follow from either the overdamped or underdamped descriptions, demonstrating that the latter is mandatory in order to obtain a vanishing average heat flux to the particle. We provide analytical expressions for the distributions of the fluctuating heat and entropy and verify them experimentally. Our protocols could serve to implement the first microscopic engine that is able to attain the fundamental limit for the efficiency set by Carnot.

Thermally induced micro-motion by inflection in optical potential

Czech Academy of Sciences Publication Activity Database

Šiler, Martin; Jákl, Petr; Brzobohatý, Oto; Ryabov, A.; Filip, R.; Zemánek, Pavel

2017-01-01

Roč. 7, MAY (2017), s. 1-8, č. článku 1697. ISSN 2045-2322 R&D Projects: GA ČR GB14-36681G; GA MŠk(CZ) LO1212; GA MŠk ED0017/01/01 Institutional support: RVO:68081731 Keywords : molecular motors * brownian-motion * manipulation * efficiency * tweezers Subject RIV: BH - Optics, Masers, Lasers OBOR OECD: Optics (including laser optics and quantum optics) Impact factor: 4.259, year: 2016

A Diffusion Approximation Based on Renewal Processes with Applications to Strongly Biased Run-Tumble Motion.

Science.gov (United States)

Thygesen, Uffe Høgsbro

2016-03-01

We consider organisms which use a renewal strategy such as run-tumble when moving in space, for example to perform chemotaxis in chemical gradients. We derive a diffusion approximation for the motion, applying a central limit theorem due to Anscombe for renewal-reward processes; this theorem has not previously been applied in this context. Our results extend previous work, which has established the mean drift but not the diffusivity. For a classical model of tumble rates applied to chemotaxis, we find that the resulting chemotactic drift saturates to the swimming velocity of the organism when the chemical gradients grow increasingly steep. The dispersal becomes anisotropic in steep gradients, with larger dispersal across the gradient than along the gradient. In contrast to one-dimensional settings, strong bias increases dispersal. We next include Brownian rotation in the model and find that, in limit of high chemotactic sensitivity, the chemotactic drift is 64% of the swimming velocity, independent of the magnitude of the Brownian rotation. We finally derive characteristic timescales of the motion that can be used to assess whether the diffusion limit is justified in a given situation. The proposed technique for obtaining diffusion approximations is conceptually and computationally simple, and applicable also when statistics of the motion is obtained empirically or through Monte Carlo simulation of the motion.

Volume of the domain visited by N spherical Brownian particles

International Nuclear Information System (INIS)

Berezhkovskii, A.M.

1994-01-01

The average value and variance of the volume of the domain visited in time t by N spherical Brownian particles starting initially at the same point are presented as quadratures of the solutions of simple diffusion problems of the survival of a point Brownian particle in the presence of one and two spherical traps. As an illustration, explicit time dependences are obtained for the average volume in one and three dimensions

On the Black-Scholes European Option Pricing Model Robustness and Generality

Science.gov (United States)

Takada, Hellinton Hatsuo; de Oliveira Siqueira, José

2008-11-01

The common presentation of the widely known and accepted Black-Scholes European option pricing model explicitly imposes some restrictions such as the geometric Brownian motion assumption for the underlying stock price. In this paper, these usual restrictions are relaxed using maximum entropy principle of information theory, Pearson's distribution system, market frictionless and risk-neutrality theories to the calculation of a unique risk-neutral probability measure calibrated with market parameters.

The Relationship between the Stochastic Maximum Principle and the Dynamic Programming in Singular Control of Jump Diffusions

Directory of Open Access Journals (Sweden)

Farid Chighoub

2014-01-01

the stochastic calculus of jump diffusions and some properties of singular controls. Then, we give, under smoothness conditions, a useful verification theorem and we show that the solution of the adjoint equation coincides with the spatial gradient of the value function, evaluated along the optimal trajectory of the state equation. Finally, using these theoretical results, we solve explicitly an example, on optimal harvesting strategy, for a geometric Brownian motion with jumps.

Thermally activated dislocation motion including inertial effects in solid solutions

International Nuclear Information System (INIS)

Isaac, R.D.

1977-01-01

Dislocation motion through an array of obstacles is considered in terms of the potential energy of the dislocation as it moves through the array. The obstacles form a series of potential wells and barriers which can trap the dislocations. The effect of thermal fluctuations and of a viscous drag on the motion of the dislocation is investigated by analogy with Brownian motion in a field of force. The rate of escape of a trapped dislocation is found to depend on the damping coefficient only for a large viscous drag. The probability that a dislocation will be trapped by a well or barrier is found to depend on the damping coefficient for a small viscous drag. This inertial effect determines how far a dislocation will travel after breaking away from an obstacle

Achieving swift equilibration of a Brownian particle using flow-fields

Science.gov (United States)

Patra, Ayoti; Jarzynski, Christopher

Can a system be driven to a targeted equilibrium state on a timescale that is much shorter than its natural equilibration time? In a recent experiment, the swift equilibration of an overdamped Brownian particle was achieved by use of an appropriately designed, time-dependent optical trap potential. Motivated by these results, we develop a general theoretical approach for guiding an ensemble of Brownian particles to track the instantaneous equilibrium distribution of a desired potential U (q , t) . In our approach, we use flow-fields associated with the parametric evolution of the targeted equilibrium state to construct an auxiliary potential U (q , t) , such that dynamics under the composite potential U (t) + U (t) achieves the desired evolution. Our results establish a close connection between the swift equilibration of Brownian particles, quantum shortcuts to adiabaticity, and the dissipationless driving of a classical, Hamiltonian system.

An information geometric approach to least squares minimization

Science.gov (United States)

Transtrum, Mark; Machta, Benjamin; Sethna, James

2009-03-01

Parameter estimation by nonlinear least squares minimization is a ubiquitous problem that has an elegant geometric interpretation: all possible parameter values induce a manifold embedded within the space of data. The minimization problem is then to find the point on the manifold closest to the origin. The standard algorithm for minimizing sums of squares, the Levenberg-Marquardt algorithm, also has geometric meaning. When the standard algorithm fails to efficiently find accurate fits to the data, geometric considerations suggest improvements. Problems involving large numbers of parameters, such as often arise in biological contexts, are notoriously difficult. We suggest an algorithm based on geodesic motion that may offer improvements over the standard algorithm for a certain class of problems.

Geometric calibration between PET scanner and structured light scanner

DEFF Research Database (Denmark)

Kjer, Hans Martin; Olesen, Oline Vinter; Paulsen, Rasmus Reinhold

2011-01-01

Head movements degrade the image quality of high resolution Positron Emission Tomography (PET) brain studies through blurring and artifacts. Manny image reconstruction methods allows for motion correction if the head position is tracked continuously during the study. Our method for motion tracking...... is a structured light scanner placed just above the patient tunnel on the High Resolution Research Tomograph (HRRT, Siemens). It continuously registers point clouds of a part of the patient's face. The relative motion is estimated as the rigid transformation between frames. A geometric calibration between...

Single particle nonlocality, geometric phases and time-dependent boundary conditions

Science.gov (United States)

Matzkin, A.

2018-03-01

We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We discuss earlier claims according to which the quantum state of a particle remaining localized at the center of an infinite well with moving walls would be specifically modified by the change in boundary conditions due to the wall’s motion. We first prove that the evolution of an initially localized Gaussian state is not affected nonlocally by a linearly moving wall: as long as the quantum state has negligible amplitude near the wall, the boundary motion has no effect. This result is further extended to related confined time-dependent oscillators in which the boundary’s motion is known to give rise to geometric phases: for a Gaussian state remaining localized far from the boundaries, the effect of the geometric phases is washed out and the particle dynamics shows no traces of a nonlocal influence that would be induced by the moving boundaries.

The Geometric Phase of Stock Trading.

Science.gov (United States)

Altafini, Claudio

2016-01-01

Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote.

Exact master equation for a noncommutative Brownian particle

International Nuclear Information System (INIS)

Costa Dias, Nuno; Nuno Prata, Joao

2009-01-01

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

Brownian dynamics of self-regulated particles with additional degrees of freedom: Symmetry breaking and homochirality

Science.gov (United States)

Bhattacharyya, Debankur; Paul, Shibashis; Ghosh, Shyamolina; Ray, Deb Shankar

2018-04-01

We consider the Brownian motion of a collection of particles each with an additional degree of freedom. The degree of freedom of a particle (or, in general, a molecule) can assume distinct values corresponding to certain states or conformations. The time evolution of the additional degree of freedom of a particle is guided by those of its neighbors as well as the temperature of the system. We show that the local averaging over these degrees of freedom results in emergence of a collective order in the dynamics in the form of selection or dominance of one of the isomers leading to a symmetry-broken state. Our statistical model captures the basic features of homochirality, e.g., autocatalysis and chiral inhibition.

The Building Game: From Enumerative Combinatorics to Conformational Diffusion

Science.gov (United States)

Johnson-Chyzhykov, Daniel; Menon, Govind

2016-08-01

We study a discrete attachment model for the self-assembly of polyhedra called the building game. We investigate two distinct aspects of the model: (i) enumerative combinatorics of the intermediate states and (ii) a notion of Brownian motion for the polyhedral linkage defined by each intermediate that we term conformational diffusion. The combinatorial configuration space of the model is computed for the Platonic, Archimedean, and Catalan solids of up to 30 faces, and several novel enumerative results are generated. These represent the most exhaustive computations of this nature to date. We further extend the building game to include geometric information. The combinatorial structure of each intermediate yields a systems of constraints specifying a polyhedral linkage and its moduli space. We use a random walk to simulate a reflected Brownian motion in each moduli space. Empirical statistics of the random walk may be used to define the rates of transition for a Markov process modeling the process of self-assembly.

A mean-variance frontier in discrete and continuous time

OpenAIRE

Bekker, Paul A.

2004-01-01

The paper presents a mean-variance frontier based on dynamic frictionless investment strategies in continuous time. The result applies to a finite number of risky assets whose price process is given by multivariate geometric Brownian motion with deterministically varying coefficients. The derivation is based on the solution for the frontier in discrete time. Using the same multiperiod framework as Li and Ng (2000), I provide an alternative derivation and an alternative formulation of the solu...

Brownian ratchets from statistical physics to bio and nano-motors

CERN Document Server

Cubero, David

2016-01-01

Illustrating the development of Brownian ratchets, from their foundations, to their role in the description of life at the molecular scale and in the design of artificial nano-machinery, this text will appeal to both advanced graduates and researchers entering the field. Providing a self-contained introduction to Brownian ratchets, devices which rectify microscopic fluctuations, Part I avoids technicalities and sets out the broad range of physical systems where the concept of ratchets is relevant. Part II supplies a single source for a complete and modern theoretical analysis of ratchets in regimes such as classical vs quantum and stochastic vs deterministic, and in Part III readers are guided through experimental developments in different physical systems, each highlighting a specific unique feature of ratchets. The thorough and systematic approach to the topic ensures that this book provides a complete guide to Brownian ratchets for newcomers and established researchers in physics, biology and biochemistry.

Dual-frequency magnetic particle imaging of the Brownian particle contribution

Energy Technology Data Exchange (ETDEWEB)

Viereck, Thilo, E-mail: t.viereck@tu-bs.de; Kuhlmann, Christian; Draack, Sebastian; Schilling, Meinhard; Ludwig, Frank

2017-04-01

Magnetic particle imaging (MPI) is an emerging medical imaging modality based on the non-linear response of magnetic nanoparticles to an exciting magnetic field. MPI has been recognized as a fast imaging technique with high spatial resolution in the mm range. For some applications of MPI, especially in the field of functional imaging, the determination of the particle mobility (Brownian rotation) is of great interest, as it enables binding detection in MPI. It also enables quantitative imaging in the presence of Brownian-dominated particles, which is otherwise implausible. Discrimination of different particle responses in MPI is possible via the joint reconstruction approach. In this contribution, we propose a dual-frequency acquisition scheme to enhance sensitivity and contrast in the detection of different particle mobilities compared to a standard single-frequency MPI protocol. The method takes advantage of the fact, that the magnetization response of the tracer is strongly frequency-dependent, i.e. for low excitation frequencies a stronger Brownian contribution is observed.

Algebraic Description of Motion

Science.gov (United States)

Davidon, William C.

1974-01-01

An algebraic definition of time differentiation is presented and used to relate independent measurements of position and velocity. With this, students can grasp certain essential physical, geometric, and algebraic properties of motion and differentiation before undertaking the study of limits. (Author)

Dynamics of a Brownian particle in a plasma in the long-time limit

International Nuclear Information System (INIS)

Dickman, R.; Varley, R.L.

1981-01-01

The velocity autocorrelation function (VAF) of a Brownian particle in a plasma is calculated in the long-time limit. The Brownian particle VAF exhibits the same qualitative behavior as the electron VAF in a one-component plasma: oscillations at the plasma frequency and decay approx. t -3 sup(/) 2 . (orig.)

The probability of an encounter of two Brownian particles before escape

International Nuclear Information System (INIS)

Holcman, D; Kupka, I

2009-01-01

We study the probability of meeting of two Brownian particles before one of them exits a finite interval. We obtain an explicit expression for the probability as a function of the initial distance between the two particles using the Weierstrass elliptic function. We also find the law of the meeting location. Brownian simulations show the accuracy of our analysis. Finally, we discuss some applications to the probability that a double-strand DNA break repairs in confined environments.

Motion contrast using optical coherence tomography

Science.gov (United States)

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.

From Levy to Brownian: a computational model based on biological fluctuation.

Directory of Open Access Journals (Sweden)

Surya G Nurzaman

Full Text Available BACKGROUND: Theoretical studies predict that Lévy walks maximizes the chance of encountering randomly distributed targets with a low density, but Brownian walks is favorable inside a patch of targets with high density. Recently, experimental data reports that some animals indeed show a Lévy and Brownian walk movement patterns when forage for foods in areas with low and high density. This paper presents a simple, Gaussian-noise utilizing computational model that can realize such behavior. METHODOLOGY/PRINCIPAL FINDINGS: We extend Lévy walks model of one of the simplest creature, Escherichia coli, based on biological fluctuation framework. We build a simulation of a simple, generic animal to observe whether Lévy or Brownian walks will be performed properly depends on the target density, and investigate the emergent behavior in a commonly faced patchy environment where the density alternates. CONCLUSIONS/SIGNIFICANCE: Based on the model, animal behavior of choosing Lévy or Brownian walk movement patterns based on the target density is able to be generated, without changing the essence of the stochastic property in Escherichia coli physiological mechanism as explained by related researches. The emergent behavior and its benefits in a patchy environment are also discussed. The model provides a framework for further investigation on the role of internal noise in realizing adaptive and efficient foraging behavior.

Rotation and migration of nanoparticles for heat transfer augmentation in nanofluids by molecular dynamics simulation

Directory of Open Access Journals (Sweden)

Wenzheng Cui

2015-09-01

Full Text Available Nanofluids are a new generation of high-efficiency refrigerant with abnormal increased thermal conductivity and convective heat transfer properties. In view of the paucity of research work on the contribution of nanoparticle Brownian motion for the thermal conductivity augmentation, the present paper carries out a series of MD simulations to explorer the order of magnitude of nanoparticle Brownian motion and discusses the effect of nanoparticle Brownian motion for thermal conductivity enhancement of nanofluids. Various influence factors including nanoparticle shapes, sizes, and materials are considered. The Brownian motion of nanoparticles is decomposed into rotation and migration and calculated by MD simulation. By means of Peclet number, the effect of nanoparticle Brownian motion for thermal conductivity enhancement of nanofluids is discussed.

Multiscale Reaction-Diffusion Algorithms: PDE-Assisted Brownian Dynamics

KAUST Repository

Franz, Benjamin

2013-06-19

Two algorithms that combine Brownian dynami cs (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use of a mean-field reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD simulations with PDEs by randomly creating new particles close to the interface, which partitions the domain, and by reincorporating particles into the continuum PDE-description when they cross the interface. The second PBD algorithm introduces an overlap region, where both descriptions exist in parallel. It is shown that the overlap region is required to accurately compute variances using PBD simulations. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented. © 2013 Society for Industrial and Applied Mathematics.

Stochastic pump effect and geometric phases in dissipative and stochastic systems

Energy Technology Data Exchange (ETDEWEB)

Sinitsyn, Nikolai [Los Alamos National Laboratory

2008-01-01

The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).

An efficient formulation for linear and geometric non-linear membrane elements

Directory of Open Access Journals (Sweden)

Mohammad Rezaiee-Pajand

Full Text Available Utilizing the straingradient notation process and the free formulation, an efficient way of constructing membrane elements will be proposed. This strategy can be utilized for linear and geometric non-linear problems. In the suggested formulation, the optimization constraints of insensitivity to distortion, rotational invariance and not having parasitic shear error are employed. In addition, the equilibrium equations will be established based on some constraints among the strain states. The authors' technique can easily separate the rigid body motions, and those belong to deformational motions. In this article, a novel triangular element, named SST10, is formulated. This element will be used in several plane problems having irregular mesh and complicated geometry with linear and geometrically nonlinear behavior. The numerical outcomes clearly demonstrate the efficiency of the new formulation.

From Lévy to Brownian: a computational model based on biological fluctuation.

Science.gov (United States)

Nurzaman, Surya G; Matsumoto, Yoshio; Nakamura, Yutaka; Shirai, Kazumichi; Koizumi, Satoshi; Ishiguro, Hiroshi

2011-02-03

Theoretical studies predict that Lévy walks maximizes the chance of encountering randomly distributed targets with a low density, but Brownian walks is favorable inside a patch of targets with high density. Recently, experimental data reports that some animals indeed show a Lévy and Brownian walk movement patterns when forage for foods in areas with low and high density. This paper presents a simple, Gaussian-noise utilizing computational model that can realize such behavior. We extend Lévy walks model of one of the simplest creature, Escherichia coli, based on biological fluctuation framework. We build a simulation of a simple, generic animal to observe whether Lévy or Brownian walks will be performed properly depends on the target density, and investigate the emergent behavior in a commonly faced patchy environment where the density alternates. Based on the model, animal behavior of choosing Lévy or Brownian walk movement patterns based on the target density is able to be generated, without changing the essence of the stochastic property in Escherichia coli physiological mechanism as explained by related researches. The emergent behavior and its benefits in a patchy environment are also discussed. The model provides a framework for further investigation on the role of internal noise in realizing adaptive and efficient foraging behavior.

Geometrical primitives reconstruction from image sequence in an interactive context

International Nuclear Information System (INIS)

Monchal, L.; Aubry, P.

1995-01-01

We propose a method to recover 3D geometrical shape from image sequence, in a context of man machine co-operation. The human operator has to point out the edges of an object in the first image and choose a corresponding geometrical model. The algorithm tracks each relevant 2D segments describing surface discontinuities or limbs, in the images. Then, knowing motion of the camera between images, the positioning and the size of the virtual object are deduced by minimising a function. The function describes how well the virtual objects is linked to the extracted segments of the sequence, its geometrical model and pieces of information given by the operator. (author). 13 refs., 7 figs., 8 tabs

Feedback control of two-headed Brownian motors in flashing ratchet potential

International Nuclear Information System (INIS)

Zhao A-Ke; Zhang Hong-Wei; Li Yu-Xiao

2010-01-01

We presented a detailed investigation on the movement of two-headed Brownian motors in an asymmetric potential under a feedback control. By numerical simulations the direct current is obtained. The current is periodic in the initial length of spring. There is an optimal value of the spring constant. And the dependence of the current on the opposing force is reversed. Then we found that when the change of the temperature and the opposing force have optimal values, the Brownian motors can also obtain the optimal efficiency

Stable Lévy motion with inverse Gaussian subordinator

Science.gov (United States)

Kumar, A.; Wyłomańska, A.; Gajda, J.

2017-09-01

In this paper we study the stable Lévy motion subordinated by the so-called inverse Gaussian process. This process extends the well known normal inverse Gaussian (NIG) process introduced by Barndorff-Nielsen, which arises by subordinating ordinary Brownian motion (with drift) with inverse Gaussian process. The NIG process found many interesting applications, especially in financial data description. We discuss here the main features of the introduced subordinated process, such as distributional properties, existence of fractional order moments and asymptotic tail behavior. We show the connection of the process with continuous time random walk. Further, the governing fractional partial differential equations for the probability density function is also obtained. Moreover, we discuss the asymptotic distribution of sample mean square displacement, the main tool in detection of anomalous diffusion phenomena (Metzler et al., 2014). In order to apply the stable Lévy motion time-changed by inverse Gaussian subordinator we propose a step-by-step procedure of parameters estimation. At the end, we show how the examined process can be useful to model financial time series.

The Zoom Lens: A Case Study in Geometrical Optics.

Science.gov (United States)

Cheville, Alan; Scepanovic, Misa

2002-01-01

Introduces a case study on a motion picture company considering the purchase of a newly developed zoom lens in which students act as the engineers designing the zoom lens based on the criteria of company's specifications. Focuses on geometrical optics. Includes teaching notes and classroom management strategies. (YDS)

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

Science.gov (United States)

Sims, David W; Humphries, Nicolas E; Bradford, Russell W; Bruce, Barry D

2012-03-01

1. Search processes play an important role in physical, chemical and biological systems. In animal foraging, the search strategy predators should use to search optimally for prey is an enduring question. Some models demonstrate that when prey is sparsely distributed, an optimal search pattern is a specialised random walk known as a Lévy flight, whereas when prey is abundant, simple Brownian motion is sufficiently efficient. These predictions form part of what has been termed the Lévy flight foraging hypothesis (LFF) which states that as Lévy flights optimise random searches, movements approximated by optimal Lévy flights may have naturally evolved in organisms to enhance encounters with targets (e.g. prey) when knowledge of their locations is incomplete. 2. Whether free-ranging predators exhibit the movement patterns predicted in the LFF hypothesis in response to known prey types and distributions, however, has not been determined. We tested this using vertical and horizontal movement data from electronic tagging of an apex predator, the great white shark Carcharodon carcharias, across widely differing habitats reflecting different prey types. 3. Individual white sharks exhibited movement patterns that predicted well the prey types expected under the LFF hypothesis. Shark movements were best approximated by Brownian motion when hunting near abundant, predictable sources of prey (e.g. seal colonies, fish aggregations), whereas movements approximating truncated Lévy flights were present when searching for sparsely distributed or potentially difficult-to-detect prey in oceanic or shelf environments, respectively. 4. That movement patterns approximated by truncated Lévy flights and Brownian behaviour were present in the predicted prey fields indicates search strategies adopted by white sharks appear to be the most efficient ones for encountering prey in the habitats where such patterns are observed. This suggests that C. carcharias appears capable of exhibiting

Experimental and numerical response of rigid slender blocks with geometrical defects under seismic excitation

Directory of Open Access Journals (Sweden)

Mathey Charlie

2015-01-01

Full Text Available The present work investigates on the influence of small geometrical defects on the behavior of slender rigid blocks. A comprehensive experimental campaign was carried out on one of the shake tables of CEA/Saclay in France. The tested model was a massive steel block with standard manufacturing quality. Release, free oscillations tests as well as shake table tests revealed a non-negligible out-of-plane motion even in the case of apparently plane initial conditions or excitations. This motion exhibits a highly reproducible part for a short duration that was used to calibrate a numerical geometrically asymmetrical model. The stability of this model when subjected to 2 000 artificial seismic horizontal bidirectional signals was compared to the stability of a symmetrical one. This study showed that the geometrical imperfections slightly increase the rocking and overturning probabilities under bidirectional seismic excitations in a narrow range of peak ground acceleration.

High-precision tracking of brownian boomerang colloidal particles confined in quasi two dimensions.

Science.gov (United States)

Chakrabarty, Ayan; Wang, Feng; Fan, Chun-Zhen; Sun, Kai; Wei, Qi-Huo

2013-11-26

In this article, we present a high-precision image-processing algorithm for tracking the translational and rotational Brownian motion of boomerang-shaped colloidal particles confined in quasi-two-dimensional geometry. By measuring mean square displacements of an immobilized particle, we demonstrate that the positional and angular precision of our imaging and image-processing system can achieve 13 nm and 0.004 rad, respectively. By analyzing computer-simulated images, we demonstrate that the positional and angular accuracies of our image-processing algorithm can achieve 32 nm and 0.006 rad. Because of zero correlations between the displacements in neighboring time intervals, trajectories of different videos of the same particle can be merged into a very long time trajectory, allowing for long-time averaging of different physical variables. We apply this image-processing algorithm to measure the diffusion coefficients of boomerang particles of three different apex angles and discuss the angle dependence of these diffusion coefficients.

Remarks on a financial inverse problem by means of Monte Carlo Methods

Science.gov (United States)

Cuomo, Salvatore; Di Somma, Vittorio; Sica, Federica

2017-10-01

Estimating the price of a barrier option is a typical inverse problem. In this paper we present a numerical and statistical framework for a market with risk-free interest rate and a risk asset, described by a Geometric Brownian Motion (GBM). After approximating the risk asset with a numerical method, we find the final option price by following an approach based on sequential Monte Carlo methods. All theoretical results are applied to the case of an option whose underlying is a real stock.

Quantum no-singularity theorem from geometric flows

Science.gov (United States)

Alsaleh, Salwa; Alasfar, Lina; Faizal, Mir; Ali, Ahmed Farag

2018-04-01

In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.

Friction tensor for a pair of Brownian particles: Spurious finite-size effects and molecular dynamics estimates

International Nuclear Information System (INIS)

Bocquet, L.; Hansen, J.P.; Piasecki, J.

1997-01-01

In this work, we show that in any finite system, the binary friction tenser for two Brownian particles cannot be directly estimated from an evaluation of the microscopic Green Kubo formula, involving the time integral of force-force autocorrelation functions. This pitfall is associated with a subtle inversion of the thermodynamic and long-time limits and leads to spurious results for the estimates of the friction matrix based on molecular dynamics simulations. Starting from a careful analysis of the coupled Langevin equations for two interacting Brownian particles, we derive a method to circumvent these effects and extract the binary friction tenser from the correlation function matrix of the instantaneous forces exerted by the bath particles on the fixed Brownian particles, and from the relaxation of the total momentum of the bath in a finite system. The general methodology is applied to the case of two hard or soft Brownian spheres in a bath of light particles. Numerical estimates of the relevant correlation functions and of the resulting self and mutual components of the matrix of friction tensors are obtained by molecular dynamics simulations for various spacings between the Brownian particles

Geometrical Determinants of Neuronal Actin Waves

OpenAIRE

Tomba, Caterina; Bra?ni, C?line; Bugnicourt, Ghislain; Cohen, Floriane; Friedrich, Benjamin M.; Gov, Nir S.; Villard, Catherine

2017-01-01

Hippocampal neurons produce in their early stages of growth propagative, actin-rich dynamical structures called actin waves. The directional motion of actin waves from the soma to the tip of neuronal extensions has been associated with net forward growth, and ultimately with the specification of neurites into axon and dendrites. Here, geometrical cues are used to control actin wave dynamics by constraining neurons on adhesive stripes of various widths. A key observable, the average time betwe...

Performance Estimation for Two-Dimensional Brownian Rotary Ratchet Systems

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

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

2011-01-01

Highlights: → Molecular Dynamics codes implemented on GPUs have achieved two-order of magnitude computational accelerations. → Brownian Dynamics and Dissipative Particle Dynamics simulations require a large number of random numbers per time step. → We introduce a method for generating small batches of pseudorandom numbers distributed over many threads of calculations. → 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.

A geometric rationale for invariance, covariance and constitutive relations

Science.gov (United States)

Romano, Giovanni; Barretta, Raffaele; Diaco, Marina

2018-01-01

There are, in each branch of science, statements which, expressed in ambiguous or even incorrect but seemingly friendly manner, were repeated for a long time and eventually became diffusely accepted. Objectivity of physical fields and of their time rates and frame indifference of constitutive relations are among such notions. A geometric reflection on the description of frame changes as spacetime automorphisms, on induced push-pull transformations and on proper physico-mathematical definitions of material, spatial and spacetime tensor fields and of their time-derivatives along the motion, is here carried out with the aim of pointing out essential notions and of unveiling false claims. Theoretical and computational aspects of nonlinear continuum mechanics, and especially those pertaining to constitutive relations, involving material fields and their time rates, gain decisive conceptual and operative improvement from a proper geometric treatment. Outcomes of the geometric analysis are frame covariance of spacetime velocity, material stretching and material spin. A univocal and frame-covariant tool for evaluation of time rates of material fields is provided by the Lie derivative along the motion. The postulate of frame covariance of material fields is assessed to be a natural physical requirement which cannot interfere with the formulation of constitutive laws, with claims of the contrary stemming from an improper imposition of equality in place of equivalence.

How fast do stock prices adjust to market efficiency? Evidence from a detrended fluctuation analysis

Science.gov (United States)

Reboredo, Juan C.; Rivera-Castro, Miguel A.; Miranda, José G. V.; García-Rubio, Raquel

2013-04-01

In this paper we analyse price fluctuations with the aim of measuring how long the market takes to adjust prices to weak-form efficiency, i.e., how long it takes for prices to adjust to a fractional Brownian motion with a Hurst exponent of 0.5. The Hurst exponent is estimated for different time horizons using detrended fluctuation analysis-a method suitable for non-stationary series with trends-in order to identify at which time scale the Hurst exponent is consistent with the efficient market hypothesis. Using high-frequency share price, exchange rate and stock data, we show how price dynamics exhibited important deviations from efficiency for time periods of up to 15 min; thereafter, price dynamics was consistent with a geometric Brownian motion. The intraday behaviour of the series also indicated that price dynamics at trade opening and close was hardly consistent with efficiency, which would enable investors to exploit price deviations from fundamental values. This result is consistent with intraday volume, volatility and transaction time duration patterns.

Geometrical theory of spin motion

International Nuclear Information System (INIS)

Halpern, L.

1983-01-01

A discussion of the fundamental interrelation of geometry and physical laws with Lie groups leads to a reformulation and heuristic modification of the principle of inertia and the principle of equivalence, which is based on the simple De Sitter group instead of the Poincare group. The resulting law of motion allows a unified formulation for structureless and spinning test particles. A metrical theory of gravitation is constructed with the modified principle, which is structured after the geometry of the manifold of the De Sitter group. The theory is equivalent to a particular Kaluza-Klein theory in ten dimensions with the Lorentz group as gauge group. A restricted version of this theory excludes torsion. It is shown by a reformulation of the energy momentum complex that this version is equivalent to general relativity with a cosmologic term quadratic in the curvature tensor and in which the existence of spinning particle fields is inherent from first principles. The equations of the general theory with torsion are presented and it is shown in a special case how the boundary conditions for the torsion degree of freedom have to be chosen such as to treat orbital and spin angular momenta on an equal footing. The possibility of verification of the resulting anomalous spin-spin interaction is mentioned and a model imposed by the group topology of SO(3, 2) is outlined in which the unexplained discrepancy between the magnitude of the discrete valued coupling constants and the gravitational constant in Kaluza-Klein theories is resolved by the identification of identical fermions as one orbit. The mathematical structure can be adapted to larger groups to include other degrees of freedom. 41 references

Geometrical approach to fluid models

International Nuclear Information System (INIS)

Kuvshinov, B.N.; Schep, T.J.

1997-01-01

Differential geometry based upon the Cartan calculus of differential forms is applied to investigate invariant properties of equations that describe the motion of continuous media. The main feature of this approach is that physical quantities are treated as geometrical objects. The geometrical notion of invariance is introduced in terms of Lie derivatives and a general procedure for the construction of local and integral fluid invariants is presented. The solutions of the equations for invariant fields can be written in terms of Lagrange variables. A generalization of the Hamiltonian formalism for finite-dimensional systems to continuous media is proposed. Analogously to finite-dimensional systems, Hamiltonian fluids are introduced as systems that annihilate an exact two-form. It is shown that Euler and ideal, charged fluids satisfy this local definition of a Hamiltonian structure. A new class of scalar invariants of Hamiltonian fluids is constructed that generalizes the invariants that are related with gauge transformations and with symmetries (Noether). copyright 1997 American Institute of Physics

Evaluation of the geometric accuracy of surrogate-based gated VMAT using intrafraction kilovoltage x-ray images

International Nuclear Information System (INIS)

Li Ruijiang; Mok, Edward; Han, Bin; Koong, Albert; Xing Lei

2012-01-01

Purpose: To evaluate the geometric accuracy of beam targeting in external surrogate-based gated volumetric modulated arc therapy (VMAT) using kilovoltage (kV) x-ray images acquired during dose delivery. Methods: Gated VMAT treatments were delivered using a Varian TrueBeam STx Linac for both physical phantoms and patients. Multiple gold fiducial markers were implanted near the target. The reference position was created for each implanted marker, representing its correct position at the gating threshold. The gating signal was generated from the RPM system. During the treatment, kV images were acquired immediately before MV beam-on at every breathing cycle, using the on-board imaging system. All implanted markers were detected and their 3D positions were estimated using in-house developed software. The positioning error of a marker is defined as the distance of the marker from its reference position for each frame of the images. The overall error of the system is defined as the average over all markers. For the phantom study, both sinusoidal motion (1D and 3D) and real human respiratory motion was simulated for the target and surrogate. In the baseline case, the two motions were synchronized for the first treatment fraction. To assess the effects of surrogate-target correlation on the geometric accuracy, a phase shift of 5% and 10% between the two motions was introduced. For the patient study, intrafraction kV images of five stereotactic body radiotherapy (SBRT) patients were acquired for one or two fractions. Results: For the phantom study, a high geometric accuracy was achieved in the baseline case (average error: 0.8 mm in the superior-inferior or SI direction). However, the treatment delivery is prone to geometric errors if changes in the target-surrogate relation occur during the treatment: the average error was increased to 2.3 and 4.7 mm for the phase shift of 5% and 10%, respectively. Results obtained with real human respiratory curves show a similar trend

The escape of brownian particle over potential barriers

International Nuclear Information System (INIS)

Zhong Yunxiao

1985-01-01

A convenient method is introduced to calculate the rate of escape of Brownian particle over potential barriers by exact solution of Smoluchowskian equation. This method is applied to calculate the nuclear fission probabilities. The results for four different cases are compared with the results of other theories

Geometric transitions on non-Kaehler manifolds

International Nuclear Information System (INIS)

Knauf, A.

2007-01-01

We study geometric transitions on the supergravity level using the basic idea of an earlier paper (M. Becker et al., 2004), where a pair of non-Kaehler backgrounds was constructed, which are related by a geometric transition. Here we embed this idea into an orientifold setup. The non-Kaehler backgrounds we obtain in type IIA are non-trivially fibered due to their construction from IIB via T-duality with Neveu-Schwarz flux. We demonstrate that these non-Kaehler manifolds are not half-flat and show that a symplectic structure exists on them at least locally. We also review the construction of new non-Kaehler backgrounds in type I and heterotic theory. They are found by a series of T- and S-duality and can be argued to be related by geometric transitions as well. A local toy model is provided that fulfills the flux equations of motion in IIB and the torsional relation in heterotic theory, and that is consistent with the U-duality relating both theories. For the heterotic theory we also propose a global solution that fulfills the torsional relation because it is similar to the Maldacena-Nunez background. (Abstract Copyright [2007], Wiley Periodicals, Inc.)

Inflation and dark energy arising from geometrical tachyons

International Nuclear Information System (INIS)

Panda, Sudhakar; Sami, M.; Tsujikawa, Shinji

2006-01-01

We study the motion of a Bogomol'nyi-Prasad-Sommerfield D3-brane in the NS5-brane ring background. The radion field becomes tachyonic in this geometrical setup. We investigate the potential of this geometrical tachyon in the cosmological scenario for inflation as well as dark energy. We evaluate the spectra of scalar and tensor perturbations generated during tachyon inflation and show that this model is compatible with recent observations of cosmic microwave background due to an extra freedom of the number of NS5-branes. It is not possible to explain the origin of both inflation and dark energy by using a single tachyon field, since the energy density at the potential minimum is not negligibly small because of the amplitude of scalar perturbations set by cosmic microwave background anisotropies. However, the geometrical tachyon can account for dark energy when the number of NS5-branes is large, provided that inflation is realized by another scalar field

Information Geometric Complexity of a Trivariate Gaussian Statistical Model

Directory of Open Access Journals (Sweden)

Domenico Felice

2014-05-01

Full Text Available We evaluate the information geometric complexity of entropic motion on low-dimensional Gaussian statistical manifolds in order to quantify how difficult it is to make macroscopic predictions about systems in the presence of limited information. Specifically, we observe that the complexity of such entropic inferences not only depends on the amount of available pieces of information but also on the manner in which such pieces are correlated. Finally, we uncover that, for certain correlational structures, the impossibility of reaching the most favorable configuration from an entropic inference viewpoint seems to lead to an information geometric analog of the well-known frustration effect that occurs in statistical physics.

Hierarchical Motion Planning for Autonomous Aerial and Terrestrial Vehicles

Science.gov (United States)

Cowlagi, Raghvendra V.

Autonomous mobile robots---both aerial and terrestrial vehicles---have gained immense importance due to the broad spectrum of their potential military and civilian applications. One of the indispensable requirements for the autonomy of a mobile vehicle is the vehicle's capability of planning and executing its motion, that is, finding appropriate control inputs for the vehicle such that the resulting vehicle motion satisfies the requirements of the vehicular task. The motion planning and control problem is inherently complex because it involves two disparate sub-problems: (1) satisfaction of the vehicular task requirements, which requires tools from combinatorics and/or formal methods, and (2) design of the vehicle control laws, which requires tools from dynamical systems and control theory. Accordingly, this problem is usually decomposed and solved over two levels of hierarchy. The higher level, called the geometric path planning level, finds a geometric path that satisfies the vehicular task requirements, e.g., obstacle avoidance. The lower level, called the trajectory planning level, involves sufficient smoothening of this geometric path followed by a suitable time parametrization to obtain a reference trajectory for the vehicle. Although simple and efficient, such hierarchical decomposition suffers a serious drawback: the geometric path planner has no information of the kinematical and dynamical constraints of the vehicle. Consequently, the geometric planner may produce paths that the trajectory planner cannot transform into a feasible reference trajectory. Two main ideas appear in the literature to remedy this problem: (a) randomized sampling-based planning, which eliminates the geometric planner altogether by planning in the vehicle state space, and (b) geometric planning supported by feedback control laws. The former class of methods suffer from a lack of optimality of the resultant trajectory, while the latter class of methods makes a restrictive assumption

Geometric Mechanics Reveals Optimal Complex Terrestrial Undulation Patterns

Science.gov (United States)

Gong, Chaohui; Astley, Henry; Schiebel, Perrin; Dai, Jin; Travers, Matthew; Goldman, Daniel; Choset, Howie; CMU Team; GT Team

Geometric mechanics offers useful tools for intuitively analyzing biological and robotic locomotion. However, utility of these tools were previously restricted to systems that have only two internal degrees of freedom and in uniform media. We show kinematics of complex locomotors that make intermittent contacts with substrates can be approximated as a linear combination of two shape bases, and can be represented using two variables. Therefore, the tools of geometric mechanics can be used to analyze motions of locomotors with many degrees of freedom. To demonstrate the proposed technique, we present studies on two different types of snake gaits which utilize combinations of waves in the horizontal and vertical planes: sidewinding (in the sidewinder rattlesnake C. cerastes) and lateral undulation (in the desert specialist snake C. occipitalis). C. cerastes moves by generating posteriorly traveling body waves in the horizontal and vertical directions, with a relative phase offset equal to +/-π/2 while C. occipitalismaintains a π/2 offset of a frequency doubled vertical wave. Geometric analysis reveals these coordination patterns enable optimal movement in the two different styles of undulatory terrestrial locomotion. More broadly, these examples demonstrate the utility of geometric mechanics in analyzing realistic biological and robotic locomotion.

Hydrodynamic interactions induce movement against an external load in a ratchet dimer Brownian motor.

Science.gov (United States)

Fornés, José A

2010-01-15

We use the Brownian dynamics with hydrodynamic interactions simulation in order to describe the movement of a elastically coupled dimer Brownian motor in a ratchet potential. The only external forces considered in our system were the load, the random thermal noise and an unbiased thermal fluctuation. For a given set of parameters we observe direct movement against the load force if hydrodynamic interactions were considered.

Constructing a completely integrable system via algebro-geometric data

Science.gov (United States)

Piovan, Luis A.

2001-03-01

We use the algebro-geometric data given by a genus-2 Jacobian, a curve and a line bundle on the Jacobian, and the action of a group of translates on the theta sections of this line bundle, to reconstruct an integrable system: the geodesic motion on {SO}(4), metric II (so termed after Adler and van Moerbeke).

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

Energy Technology Data Exchange (ETDEWEB)

Moeller, Peter [Los Alamos National Laboratory, Theoretical Division, Los Alamos, NM (United States); Ichikawa, Takatoshi [Kyoto University, Yukawa Institute for Theoretical Physics, Kyoto (Japan)

2015-12-15

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 Q{sub 2}), neck d, left nascent fragment spheroidal deformation ε{sub f1}, right nascent fragment deformation ε{sub f2} and two asymmetry variables, namely proton and neutron numbers in each of the two fragments. The extension of previous models 1) introduces a method to calculate this generalized potential-energy function and 2) allows the correlated transfer of nucleon pairs in one step, in addition to sequential transfer. In the previous version the potential energy was calculated as a function of Z and N of the compound system and its shape, including the asymmetry of the shape. We outline here how to generalize the model from the ''compound-system'' model to a model where the emerging fragment proton and neutron numbers also enter, over and above the compound system composition. (orig.)

Geometrical dynamics of Born-Infeld objects

Energy Technology Data Exchange (ETDEWEB)

Cordero, Ruben [Departamento de Fisica, Escuela Superior de Fisica y Matematicas del I.P.N., Unidad Adolfo Lopez Mateos, Edificio 9, 07738 Mexico, D.F. (Mexico); Molgado, Alberto [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Col. Villas San Sebastian, Colima (Mexico); Rojas, Efrain [Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico)

2007-03-21

We present a geometrically inspired study of the dynamics of Dp-branes. We focus on the usual non-polynomial Dirac-Born-Infeld action for the worldvolume swept out by the brane in its evolution in general background spacetimes. We emphasize the form of the resulting equations of motion which are quite simple and resemble Newton's second law, complemented with a conservation law for a worldvolume bicurrent. We take a closer look at the classical Hamiltonian analysis which is supported by the ADM framework of general relativity. The constraints and their algebra are identified as well as the geometrical role they play in phase space. In order to illustrate our results, we review the dynamics of a D1-brane immersed in a AdS{sub 3} x S{sup 3} background spacetime. We exhibit the mechanical properties of Born-Infeld objects paving the way to a consistent quantum formulation.

Geometrical dynamics of Born-Infeld objects

International Nuclear Information System (INIS)

Cordero, Ruben; Molgado, Alberto; Rojas, Efrain

2007-01-01

We present a geometrically inspired study of the dynamics of Dp-branes. We focus on the usual non-polynomial Dirac-Born-Infeld action for the worldvolume swept out by the brane in its evolution in general background spacetimes. We emphasize the form of the resulting equations of motion which are quite simple and resemble Newton's second law, complemented with a conservation law for a worldvolume bicurrent. We take a closer look at the classical Hamiltonian analysis which is supported by the ADM framework of general relativity. The constraints and their algebra are identified as well as the geometrical role they play in phase space. In order to illustrate our results, we review the dynamics of a D1-brane immersed in a AdS 3 x S 3 background spacetime. We exhibit the mechanical properties of Born-Infeld objects paving the way to a consistent quantum formulation

Geometrically biased random walks in bacteria-driven micro-shuttles

International Nuclear Information System (INIS)

Angelani, Luca; Di Leonardo, Roberto

2010-01-01

Micron-sized objects having asymmetric boundaries can rectify the chaotic motions of an active bacterial suspension and perform geometrically biased random walks. Using numerical simulations in a planar geometry, we show that arrow-shaped micro-shuttles, constrained to move in one dimension (1D) in a bath of self-propelled micro-organisms, spontaneously perform unidirectional translational motions with a strongly shape-dependent speed. Relaxing the 1D constraint, a random motion in the whole plane sets in at long times, due to random changes in shuttle orientation caused by bacterial collisions. The complex dynamics arising from the mechanical interactions between bacteria and the object boundaries can be described by a Gaussian stochastic force with a shape-dependent mean and a self-correlation decaying exponentially on the timescale of seconds.

On uses, misuses and potential abuses of fractal analysis in zooplankton behavioral studies: A review, a critique and a few recommendations

Science.gov (United States)

Seuront, Laurent

2015-08-01

Fractal analysis is increasingly used to describe, and provide further understanding to, zooplankton swimming behavior. This may be related to the fact that fractal analysis and the related fractal dimension D have the desirable properties to be independent of measurement scale and to be very sensitive to even subtle behavioral changes that may be undetectable to other behavioral variables. As early claimed by Coughlin et al. (1992), this creates "the need for fractal analysis" in behavioral studies, which has hence the potential to become a valuable tool in zooplankton behavioral ecology. However, this paper stresses that fractal analysis, as well as the more elaborated multifractal analysis, is also a risky business that may lead to irrelevant results, without paying extreme attention to a series of both conceptual and practical steps that are all likely to bias the results of any analysis. These biases are reviewed and exemplified on the basis of the published literature, and remedial procedures are provided not only for geometric and stochastic fractal analyses, but also for the more complicated multifractal analysis. The concept of multifractals is finally introduced as a direct, objective and quantitative tool to identify models of motion behavior, such as Brownian motion, fractional Brownian motion, ballistic motion, Lévy flight/walk and multifractal random walk. I finally briefly review the state of this emerging field in zooplankton behavioral research.

Geometric and numerical foundations of movements

CERN Document Server

Mansard, Nicolas; Lasserre, Jean-Bernard

2017-01-01

This book aims at gathering roboticists, control theorists, neuroscientists, and mathematicians, in order to promote a multidisciplinary research on movement analysis. It follows the workshop “ Geometric and Numerical Foundations of Movements ” held at LAAS-CNRS in Toulouse in November 2015[1]. Its objective is to lay the foundations for a mutual understanding that is essential for synergetic development in motion research. In particular, the book promotes applications to robotics --and control in general-- of new optimization techniques based on recent results from real algebraic geometry.

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

DEFF Research Database (Denmark)

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

2012-01-01

We present on-chip Brownian relaxation measurements on a logarithmic dilution series of 40 nm beads dispersed in water with bead concentrations between 16 mu g/ml and 4000 mu g/ml. The measurements are performed using a planar Hall effect bridge sensor at frequencies up to 1 MHz. No external fields...... are needed as the beads are magnetized by the field generated by the applied sensor bias current. We show that the Brownian relaxation frequency can be extracted from fitting the Cole-Cole model to measurements for bead concentrations of 64 mu g/ml or higher and that the measured dynamic magnetic response...... is proportional to the bead concentration. For bead concentrations higher than or equal to 500 mu g/ml, we extract a hydrodynamic diameter of 47(1) nm for the beads, which is close to the nominal bead size of 40 nm. Furthermore, we study the signal vs. bead concentration at a fixed frequency close to the Brownian...

Stochastic production planning for a biofuel supply chain under demand and price uncertainties

International Nuclear Information System (INIS)

Awudu, Iddrisu; Zhang, Jun

2013-01-01

Highlights: ► The proposed stochastic model outperforms the deterministic model. ► The price of biofuel is modeled as Geometric Brownian Motion (GBM). ► The proposed model can be applied in any biofuel supply chain. -- Abstract: In this paper, we propose a stochastic production planning model for a biofuel supply chain under demand and price uncertainties. The supply chain consists of biomass suppliers, biofuel refinery plants and distribution centers. A stochastic linear programming model is proposed within a single-period planning framework to maximize the expected profit. Decisions such as the amount of raw materials purchased, the amount of raw materials consumed and the amount of products produced are considered. Demands of end products are uncertain with known probability distributions. The prices of end products follow Geometric Brownian Motion (GBM). Benders decomposition (BD) with Monte Carlo simulation technique is applied to solve the proposed model. To demonstrate the effectiveness of the proposed stochastic model and the decomposition algorithm, a representative supply chain for an ethanol plant in North Dakota is considered. To investigate the results of the proposed model, a simulation framework is developed to compare the performances of deterministic model and proposed stochastic model. The results from the simulation indicate the proposed model obtain higher expected profit than the deterministic model under different uncertainty settings. Sensitivity analyses are performed to gain management insight on how profit changes due to the uncertainties affect the model developed.

Simple wealth distribution model causing inequality-induced crisis without external shocks

Science.gov (United States)

Benisty, Henri

2017-05-01

We address the issue of the dynamics of wealth accumulation and economic crisis triggered by extreme inequality, attempting to stick to most possibly intrinsic assumptions. Our general framework is that of pure or modified multiplicative processes, basically geometric Brownian motions. In contrast with the usual approach of injecting into such stochastic agent models either specific, idiosyncratic internal nonlinear interaction patterns or macroscopic disruptive features, we propose a dynamic inequality model where the attainment of a sizable fraction of the total wealth by very few agents induces a crisis regime with strong intermittency, the explicit coupling between the richest and the rest being a mere normalization mechanism, hence with minimal extrinsic assumptions. The model thus harnesses the recognized lack of ergodicity of geometric Brownian motions. It also provides a statistical intuition to the consequences of Thomas Piketty's recent "r >g " (return rate > growth rate) paradigmatic analysis of very-long-term wealth trends. We suggest that the "water-divide" of wealth flow may define effective classes, making an objective entry point to calibrate the model. Consistently, we check that a tax mechanism associated to a few percent relative bias on elementary daily transactions is able to slow or stop the build-up of large wealth. When extreme fluctuations are tamed down to a stationary regime with sizable but steadier inequalities, it should still offer opportunities to study the dynamics of crisis and the inner effective classes induced through external or internal factors.

An explicit local uniform large deviation bound for Brownian bridges

NARCIS (Netherlands)

Wittich, O.

2005-01-01

By comparing curve length in a manifold and a standard sphere, we prove a local uniform bound for the exponent in the Large Deviation formula that describes the concentration of Brownian bridges to geodesics.

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

CERN Document Server

Schweitzer, Frank

2007-01-01

""This book lays out a vision for a coherent framework for understanding complex systems"" (from the foreword by J. Doyne Farmer). By developing the genuine idea of Brownian agents, the author combines concepts from informatics, such as multiagent systems, with approaches of statistical many-particle physics. This way, an efficient method for computer simulations of complex systems is developed which is also accessible to analytical investigations and quantitative predictions. The book demonstrates that Brownian agent models can be successfully applied in many different contexts, ranging from

Geometrical and topological formulation of local gauge and supergauge theories

International Nuclear Information System (INIS)

Macrae, K.I.

1976-01-01

A geometrical and topological formulation of local gauge and supergauge invariance is presented. Analysis of experiments of the type described by Bohm and Aharanov and in the attempt to understand immersed submanifolds such as the string with internal symmetry, in a geometric setting, are led to the introduction of fiber bundles, superspaces. Many exact classical solutions to the equations of motion were considered for these gauge theories with specific choices of gauge group such as SU 4 . We describe some exact soliton solutions to these theories which have linear Regge trajectories, i.e., their angular momentum is a linear function of their mass squared. Next one discusses the actions and equations of motion for gauge theories whose base manifolds can have arbitrarily dimensioned submanifolds excised from them, manifolds with holes were discussed. These holes can have fractional quark charges when the structure group is, for example, SU 3 or SU 4 . By extending the concept of conservation of energy to include the excised submanifolds, their actions, and their equations of motion were derived showing that they can act as charged particles. Using the fractionality of the quark charges, are led to suggest a topological confinement mechanism for these particles. One also derives the actions and equations of motion for the string from this viewpoint. Some new Lie algebras which have anticommuting elements are introduced. Their gauge theories are described, and the possibility of fermionic actions for the anticommuting pieces is examined. Supersymmetric strings and their supergauge transformations were discussed and an extension was suggested of supersymmetry to immersed minimal submanifolds other than the string. Both quarklike and vectorlike fermions are included. Finally the invariance of both the equations of motion and the gauge conditions under supersymmetry transformations for these submanifolds were described

The quantum brownian particle and memory effects

International Nuclear Information System (INIS)

Britani, J.R.; Mizrahi, S.S.; Pimentel, B.M.

1991-01-01

The Quantum Brownian particle, immersed in a heat bath, is described by a statistical operator whose evolution is ruled by a Generalized Master Equation (GME). The heat bath degrees of freedom are considered to be either white noise or coloured noise correlated,while the GME is considered under either the Markov or Non-Markov approaches. The comparison between these considerations are fully developed and their physical meaning is discussed. (author)

Optimally eating a stochastic cake. A recursive utility approach

International Nuclear Information System (INIS)

Epaulard, Anne; Pommeret, Aude

2003-01-01

In this short paper, uncertainties on resource stock and on technical progress are introduced into an intertemporal equilibrium model of optimal extraction of a non-renewable resource. The representative consumer maximizes a recursive utility function which disentangles between intertemporal elasticity of substitution and risk aversion. A closed-form solution is derived for both the optimal extraction and price paths. The value of the intertemporal elasticity of substitution relative to unity is then crucial in understanding extraction. Moreover, this model leads to a non-renewable resource price following a geometric Brownian motion

From Cannibalism to Active Motion of Groups

Science.gov (United States)

Romanczuk, Pawel; Schimansky-Geier, Lutz

2008-03-01

The detailed mechanisms leading to collective dynamics in groups of animals and insect are still poorly understood. A recent study by Simpson et. al. suggests cannibalism as a driving mechanism for coordinated migration of mormon crickets [1]. Based on this result we propose a simple generic model of brownian particles interacting by asymmetric, non-conservative collisions accounting for cannibalistic behavior and the corresponding avoidance strategy. We discuss our model in one and two dimensions and show that a certain type of collisions drives the system out of equilibrium and leads to coordinated active motion of groups.[1] Stephen J. Simpson, Gregory A. Sword, Patrick D. Lorch and Iain D. Couzin: Cannibal crickets on a forced march for protein and salt, PNAS, 103:4152-4156, 2006

Geometrical approach to the dynamics of the relativistic string

International Nuclear Information System (INIS)

Barbashov, B.M.; Koshkarov, A.L.

1979-01-01

The dynamics of the relativistic string is considered from the point of view of the gaussian theory of two-dimensional surfaces in the three-dimensional pseudoeuclidean space-epsilon 3 1 according to which the surface is characterized by its first and second quadratic forms. The geometrical approach possesses an advantage which gives the possibility to solve manifestly additional conditions on the vector describing the coordinates of the string world surface. The equations of motion and boundary conditions are written out for the cases of a string with massive ends and a closed string. The basic equations are formulated for the coefficients of the first and second quadratic forms of the string world surface, which represent the known geometric conditions of integration of Gauss and Weingarten derivation formulas. By means of integration of the derivation formulas the representation is obtained for the form of the string world surface in a certain basis, which satisfies the equations of motion as well as additional conditions. A new relativistic invariant gauge is suggested which fixes the second quadratic form of the surface. This representation can be extended to the case of arbitrary dimensional space

Asset pricing puzzles explained by incomplete Brownian equilibria

DEFF Research Database (Denmark)

Christensen, Peter Ove; Larsen, Kasper

We examine a class of Brownian based models which produce tractable incomplete equilibria. The models are based on finitely many investors with heterogeneous exponential utilities over intermediate consumption who receive partially unspanned income. The investors can trade continuously on a finit...... markets. Consequently, our model can simultaneously help explaining the risk-free rate and equity premium puzzles....

Ecole d'été de probabilités de Saint-Flour XLIII

CERN Document Server

Burdzy, Krzysztof

2014-01-01

These lecture notes provide an introduction to the applications of Brownian motion to analysis and, more generally, connections between Brownian motion and analysis. Brownian motion is a well-suited model for a wide range of real random phenomena, from chaotic oscillations of microscopic objects, such as flower pollen in water, to stock market fluctuations. It is also a purely abstract mathematical tool which can be used to prove theorems in "deterministic" fields of mathematics. The notes include a brief review of Brownian motion and a section on probabilistic proofs of classical theorems in analysis. The bulk of the notes are devoted to recent (post-1990) applications of stochastic analysis to Neumann eigenfunctions, Neumann heat kernel and the heat equation in time-dependent domains.

Non-linear time series analysis on flow instability of natural circulation under rolling motion condition

International Nuclear Information System (INIS)

Zhang, Wenchao; Tan, Sichao; Gao, Puzhen; Wang, Zhanwei; Zhang, Liansheng; Zhang, Hong

2014-01-01

Highlights: • Natural circulation flow instabilities in rolling motion are studied. • The method of non-linear time series analysis is used. • Non-linear evolution characteristic of flow instability is analyzed. • Irregular complex flow oscillations are chaotic oscillations. • The effect of rolling parameter on the threshold of chaotic oscillation is studied. - Abstract: Non-linear characteristics of natural circulation flow instabilities under rolling motion conditions were studied by the method of non-linear time series analysis. Experimental flow time series of different dimensionless power and rolling parameters were analyzed based on phase space reconstruction theory. Attractors which were reconstructed in phase space and the geometric invariants, including correlation dimension, Kolmogorov entropy and largest Lyapunov exponent, were determined. Non-linear characteristics of natural circulation flow instabilities under rolling motion conditions was studied based on the results of the geometric invariant analysis. The results indicated that the values of the geometric invariants first increase and then decrease as dimensionless power increases which indicated the non-linear characteristics of the system first enhance and then weaken. The irregular complex flow oscillation is typical chaotic oscillation because the value of geometric invariants is at maximum. The threshold of chaotic oscillation becomes larger as the rolling frequency or rolling amplitude becomes big. The main influencing factors that influence the non-linear characteristics of the natural circulation system under rolling motion are thermal driving force, flow resistance and the additional forces caused by rolling motion. The non-linear characteristics of the natural circulation system under rolling motion changes caused by the change of the feedback and coupling degree among these influencing factors when the dimensionless power or rolling parameters changes

Ventricular dyssynchrony assessed by gated myocardial perfusion SPECT using a geometrical approach: a feasibility study

International Nuclear Information System (INIS)

Veen, Berlinda J. van der; Younis, Imad Al; Ajmone-Marsan, Nina; Bax, Jeroen J.; Westenberg, Jos J.M.; Roos, Albert de; Stokkel, Marcel P.M.

2012-01-01

Left ventricular dyssynchrony may predict response to cardiac resynchronization therapy and may well predict adverse cardiac events. Recently, a geometrical approach for dyssynchrony analysis of myocardial perfusion scintigraphy (MPS) was introduced. In this study the feasibility of this geometrical method to detect dyssynchrony was assessed in a population with a normal MPS and in patients with documented ventricular dyssynchrony. For the normal population 80 patients (40 men and 40 women) with normal perfusion (summed stress score ≤2 and summed rest score ≤2) and function (left ventricular ejection fraction 55-80%) on MPS were selected; 24 heart failure patients with proven dyssynchrony on MRI were selected for comparison. All patients underwent a 2-day stress/rest MPS protocol. Perfusion, function and dyssynchrony parameters were obtained by the Corridor4DM software package (Version 6.1). For the normal population time to peak motion was 42.8 ± 5.1% RR cycle, SD of time to peak motion was 3.5 ± 1.4% RR cycle and bandwidth was 18.2 ± 6.0% RR cycle. No significant gender-related differences or differences between rest and post-stress acquisition were found for the dyssynchrony parameters. Discrepancies between the normal and abnormal populations were most profound for the mean wall motion (p value <0.001), SD of time to peak motion (p value <0.001) and bandwidth (p value <0.001). It is feasible to quantify ventricular dyssynchrony in MPS using the geometrical approach as implemented by Corridor4DM. (orig.)

Laser light scattering in Brownian medium

International Nuclear Information System (INIS)

Suwono; Santoso, Budi; Baiquni, A.

1983-01-01

The principle of laser light scattering in Brownian medium and photon correlation spectroscopy are described in detail. Their application to the study of the behaviour of a polystyrene latex solution are discussed. The auto-correlation function of light scattered by the polystyrene latex solution in various angle, various temperature and in various sample times, have been measured. Information on the translation diffusion coefficient and size on the particle can be obtained from the auto-correlation function. Good agreement between the available data and experiment is shown. (author)

Modeling of Geometric Error in Linear Guide Way to Improved the vertical three-axis CNC Milling machine’s accuracy

Science.gov (United States)

Kwintarini, Widiyanti; Wibowo, Agung; Arthaya, Bagus M.; Yuwana Martawirya, Yatna

2018-03-01

The purpose of this study was to improve the accuracy of three-axis CNC Milling Vertical engines with a general approach by using mathematical modeling methods of machine tool geometric errors. The inaccuracy of CNC machines can be caused by geometric errors that are an important factor during the manufacturing process and during the assembly phase, and are factors for being able to build machines with high-accuracy. To improve the accuracy of the three-axis vertical milling machine, by knowing geometric errors and identifying the error position parameters in the machine tool by arranging the mathematical modeling. The geometric error in the machine tool consists of twenty-one error parameters consisting of nine linear error parameters, nine angle error parameters and three perpendicular error parameters. The mathematical modeling approach of geometric error with the calculated alignment error and angle error in the supporting components of the machine motion is linear guide way and linear motion. The purpose of using this mathematical modeling approach is the identification of geometric errors that can be helpful as reference during the design, assembly and maintenance stages to improve the accuracy of CNC machines. Mathematically modeling geometric errors in CNC machine tools can illustrate the relationship between alignment error, position and angle on a linear guide way of three-axis vertical milling machines.

Lie group model neuromorphic geometric engine for real-time terrain reconstruction from stereoscopic aerial photos

Science.gov (United States)

Tsao, Thomas R.; Tsao, Doris

1997-04-01

In the 1980's, neurobiologist suggested a simple mechanism in primate visual cortex for maintaining a stable and invariant representation of a moving object. The receptive field of visual neurons has real-time transforms in response to motion, to maintain a stable representation. When the visual stimulus is changed due to motion, the geometric transform of the stimulus triggers a dual transform of the receptive field. This dual transform in the receptive fields compensates geometric variation in the stimulus. This process can be modelled using a Lie group method. The massive array of affine parameter sensing circuits will function as a smart sensor tightly coupled to the passive imaging sensor (retina). Neural geometric engine is a neuromorphic computing device simulating our Lie group model of spatial perception of primate's primal visual cortex. We have developed the computer simulation and experimented on realistic and synthetic image data, and performed a preliminary research of using analog VLSI technology for implementation of the neural geometric engine. We have benchmark tested on DMA's terrain data with their result and have built an analog integrated circuit to verify the computational structure of the engine. When fully implemented on ANALOG VLSI chip, we will be able to accurately reconstruct a 3D terrain surface in real-time from stereoscopic imagery.

Algorithms for Brownian first-passage-time estimation

Science.gov (United States)

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.

Current fluctuations of interacting active Brownian particles

OpenAIRE

Pre, Trevor Grand; Limmer, David T.

2018-01-01

We derive the distribution function for particle currents for a system of interacting active Brownian particles in the long time limit using large deviation theory and a weighted many body expansion. We find the distribution is non-Gaussian, except in the limit of passive particles. The non-Gaussian fluctuations can be understood from the effective potential the particles experience when conditioned on a given current. This potential suppresses fluctuations of the particle's orientation, and ...

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

International Nuclear Information System (INIS)

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

2015-01-01

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

From Brownian Dynamics to Markov Chain: An Ion Channel Example

KAUST Repository

Chen, Wan; Erban, Radek; Chapman, S. Jonathan

2014-01-01

is illustrated with a two-ion one-well channel. The stationary probability of states is compared with that from both Brownian dynamics simulation and the hierarchical Fokker-Planck equations. The conductivity of the channel is also studied, and the optimal

Eigenfunction statistics of Wishart Brownian ensembles

International Nuclear Information System (INIS)

Shukla, Pragya

2017-01-01

We theoretically analyze the eigenfunction fluctuation measures for a Hermitian ensemble which appears as an intermediate state of the perturbation of a stationary ensemble by another stationary ensemble of Wishart (Laguerre) type. Similar to the perturbation by a Gaussian stationary ensemble, the measures undergo a diffusive dynamics in terms of the perturbation parameter but the energy-dependence of the fluctuations is different in the two cases. This may have important consequences for the eigenfunction dynamics as well as phase transition studies in many areas of complexity where Brownian ensembles appear. (paper)

Conduction properties of KcsA measured using brownian dynamics with flexible carbonyl groups in the selectivity filter.

Science.gov (United States)

Chung, Shin-Ho; Corry, Ben

2007-07-01

In the narrow segment of an ion conducting pathway, it is likely that a permeating ion influences the positions of the nearby atoms that carry partial or full electronic charges. Here we introduce a method of incorporating the motion of charged atoms lining the pore into Brownian dynamics simulations of ion conduction. The movements of the carbonyl groups in the selectivity filter of the KcsA channel are calculated explicitly, allowing their bond lengths, bond angles, and dihedral angels to change in response to the forces acting upon them. By systematically changing the coefficients of bond stretching and of angle bending, the carbon and oxygen atoms can be made to fluctuate from their fixed positions by varying mean distances. We show that incorporating carbonyl motion in this way does not alter the mechanism of ion conduction and only has a small influence on the computed current. The slope conductance of the channel increases by approximately 25% when the root mean-square fluctuations of the carbonyl groups are increased from 0.01 to 0.61 A. The energy profiles and the number of resident ions in the channel remain unchanged. The method we utilized here can be extended to allow the movement of glutamate or aspartate side chains lining the selectivity filters of other ionic channels.

Single-particle tracking: applications to membrane dynamics.

Science.gov (United States)

Saxton, M J; Jacobson, K

1997-01-01

Measurements of trajectories of individual proteins or lipids in the plasma membrane of cells show a variety of types of motion. Brownian motion is observed, but many of the particles undergo non-Brownian motion, including directed motion, confined motion, and anomalous diffusion. The variety of motion leads to significant effects on the kinetics of reactions among membrane-bound species and requires a revision of existing views of membrane structure and dynamics.

An extended geometric criterion for chaos in the Dicke model

International Nuclear Information System (INIS)

Li Jiangdan; Zhang Suying

2010-01-01

We extend HBLSL's (Horwitz, Ben Zion, Lewkowicz, Schiffer and Levitan) new Riemannian geometric criterion for chaotic motion to Hamiltonian systems of weak coupling of potential and momenta by defining the 'mean unstable ratio'. We discuss the Dicke model of an unstable Hamiltonian system in detail and show that our results are in good agreement with that of the computation of Lyapunov characteristic exponents.

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

Science.gov (United States)

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

2009-12-18

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

Management of three-dimensional intrafraction motion through real-time DMLC tracking

International Nuclear Information System (INIS)

Sawant, Amit; Venkat, Raghu; Srivastava, Vikram; Carlson, David; Povzner, Sergey; Cattell, Herb; Keall, Paul

2008-01-01

Tumor tracking using a dynamic multileaf collimator (DMLC) represents a promising approach for intrafraction motion management in thoracic and abdominal cancer radiotherapy. In this work, we develop, empirically demonstrate, and characterize a novel 3D tracking algorithm for real-time, conformal, intensity modulated radiotherapy (IMRT) and volumetric modulated arc therapy (VMAT)-based radiation delivery to targets moving in three dimensions. The algorithm obtains real-time information of target location from an independent position monitoring system and dynamically calculates MLC leaf positions to account for changes in target position. Initial studies were performed to evaluate the geometric accuracy of DMLC tracking of 3D target motion. In addition, dosimetric studies were performed on a clinical linac to evaluate the impact of real-time DMLC tracking for conformal, step-and-shoot (S-IMRT), dynamic (D-IMRT), and VMAT deliveries to a moving target. The efficiency of conformal and IMRT delivery in the presence of tracking was determined. Results show that submillimeter geometric accuracy in all three dimensions is achievable with DMLC tracking. Significant dosimetric improvements were observed in the presence of tracking for conformal and IMRT deliveries to moving targets. A gamma index evaluation with a 3%-3 mm criterion showed that deliveries without DMLC tracking exhibit between 1.7 (S-IMRT) and 4.8 (D-IMRT) times more dose points that fail the evaluation compared to corresponding deliveries with tracking. The efficiency of IMRT delivery, as measured in the lab, was observed to be significantly lower in case of tracking target motion perpendicular to MLC leaf travel compared to motion parallel to leaf travel. Nevertheless, these early results indicate that accurate, real-time DMLC tracking of 3D tumor motion is feasible and can potentially result in significant geometric and dosimetric advantages leading to more effective management of intrafraction motion