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.

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

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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

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.

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

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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

Non-colliding Brownian Motions and the Extended Tacnode Process

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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

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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...

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

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)

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)

Fractional Brownian motion with a reflecting wall

Science.gov (United States)

Wada, Alexander H. O.; Vojta, Thomas

2018-02-01

Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of Monte Carlo simulations. Whereas the mean-square displacement of the particle shows the expected anomalous diffusion behavior ˜tα , the interplay between the geometric confinement and the long-time memory leads to a highly non-Gaussian probability density function with a power-law singularity at the barrier. In the superdiffusive case α >1 , the particles accumulate at the barrier leading to a divergence of the probability density. For subdiffusion α implications of these findings, in particular, for applications that are dominated by rare events.

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.

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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)

Asian Option Pricing with Monotonous Transaction Costs under Fractional Brownian Motion

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Di Pan

2013-01-01

Full Text Available Geometric-average Asian option pricing model with monotonous transaction cost rate under fractional Brownian motion was established. The method of partial differential equations was used to solve this model and the analytical expressions of the Asian option value were obtained. The numerical experiments show that Hurst exponent of the fractional Brownian motion and transaction cost rate have a significant impact on the option value.

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)

Exponential functionals of Brownian motion, I: Probability laws at fixed time

OpenAIRE

Matsumoto, Hiroyuki; Yor, Marc

2005-01-01

This paper is the first part of our survey on various results about the distribution of exponential type Brownian functionals defined as an integral over time of geometric Brownian motion. Several related topics are also mentioned.

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...

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.

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 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.

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.

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

Science.gov (United States)

Toth, Arpád; Banky, Dániel; Grolmusz, Vince

2011-12-01

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

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.

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

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)

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)

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 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.

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

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.

Directory of Open Access Journals (Sweden)

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.

Science.gov (United States)

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.

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.

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

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)

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.

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.

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.

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.

Dynamical stability of the one-dimensional rigid Brownian rotator: the role of the rotator’s spatial size and shape

Science.gov (United States)

Jeknić-Dugić, Jasmina; Petrović, Igor; Arsenijević, Momir; Dugić, Miroljub

2018-05-01

We investigate dynamical stability of a single propeller-like shaped molecular cogwheel modelled as the fixed-axis rigid rotator. In the realistic situations, rotation of the finite-size cogwheel is subject to the environmentally-induced Brownian-motion effect that we describe by utilizing the quantum Caldeira-Leggett master equation. Assuming the initially narrow (classical-like) standard deviations for the angle and the angular momentum of the rotator, we investigate the dynamics of the first and second moments depending on the size, i.e. on the number of blades of both the free rotator as well as of the rotator in the external harmonic field. The larger the standard deviations, the less stable (i.e. less predictable) rotation. We detect the absence of the simple and straightforward rules for utilizing the rotator’s stability. Instead, a number of the size-related criteria appear whose combinations may provide the optimal rules for the rotator dynamical stability and possibly control. In the realistic situations, the quantum-mechanical corrections, albeit individually small, may effectively prove non-negligible, and also revealing subtlety of the transition from the quantum to the classical dynamics of the rotator. As to the latter, we detect a strong size-dependence of the transition to the classical dynamics beyond the quantum decoherence process.

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.

Rotational Fourier tracking of diffusing polygons.

Science.gov (United States)

Mayoral, Kenny; Kennair, Terry P; Zhu, Xiaoming; Milazzo, James; Ngo, Kathy; Fryd, Michael M; Mason, Thomas G

2011-11-01

We use optical microscopy to measure the rotational Brownian motion of polygonal platelets that are dispersed in a liquid and confined by depletion attractions near a wall. The depletion attraction inhibits out-of-plane translational and rotational Brownian fluctuations, thereby facilitating in-plane imaging and video analysis. By taking fast Fourier transforms (FFTs) of the images and analyzing the angular position of rays in the FFTs, we determine an isolated particle's rotational trajectory, independent of its position. The measured in-plane rotational diffusion coefficients are significantly smaller than estimates for the bulk; this difference is likely due to the close proximity of the particles to the wall arising from the depletion attraction.

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.

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.

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

Science.gov (United States)

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

2012-08-01

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

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.

Comment on “Time-changed geometric fractional Brownian motion and option pricing with transaction costs” by Hui Gu et al.

Science.gov (United States)

Guo, Zhidong; Song, Yukun; Zhang, Yunliang

2013-05-01

The purpose of this comment is to point out the inappropriate assumption of “3αH>1” and two problems in the proof of “Theorem 3.1” in section 3 of the paper “Time-changed geometric fractional Brownian motion and option pricing with transaction costs” by Hui Gu et al. [H. Gu, J.R. Liang, Y. X. Zhang, Time-changed geometric fractional Brownian motion and option pricing with transaction costs, Physica A 391 (2012) 3971-3977]. Then we show the two problems will be solved under our new assumption.

Rotational motion in nuclei

International Nuclear Information System (INIS)

Bohr, A.

1977-01-01

History is surveyed of the development of the theory of rotational states in nuclei. The situation in the 40's when ideas formed of the collective states of a nucleus is evoked. The general rotation theory and the relation between the single-particle and rotational motion are briefly discussed. Future prospects of the rotation theory development are indicated. (I.W.)

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.

Pendulum as a model system for driven rotation in molecular nanoscale machines

DEFF Research Database (Denmark)

Zolotaryuk, Yaroslav; Christiansen, Peter Leth; Nordén, B.

2000-01-01

We suggest a ratchet mechanism of rotatory (or translatory) motion of a Brownian rotator (or a particle) in a spatially symmetric periodic potential. The asymmetry that drives the ratchet motion is due to a special sequence of activation of catalytic sites arranged in space circularly and periodi...

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

Rotational motion in nuclei

International Nuclear Information System (INIS)

Bohr, A.

1976-01-01

Nuclear structure theories are reviewed concerned with nuclei rotational motion. The development of the deformed nucleus model facilitated a discovery of rotational spectra of nuclei. Comprehensive verification of the rotational scheme and a successful classification of corresponding spectra stimulated investigations of the rotational movement dynamics. Values of nuclear moments of inertia proved to fall between two marginal values corresponding to rotation of a solid and hydrodynamic pattern of an unrotating flow, respectively. The discovery of governing role of the deformation and a degree of a symmetry violence for determining rotational degrees of freedon is pointed out to pave the way for generalization of the rotational spectra

Brownian rotational relaxation and power absorption in magnetite nanoparticles

International Nuclear Information System (INIS)

Goya, G.F.; Fernandez-Pacheco, R.; Arruebo, M.; Cassinelli, N.; Ibarra, M.R.

2007-01-01

We present a study of the power absorption efficiency in several magnetite-based colloids, to asses their potential as magnetic inductive hyperthermia (MIH) agents. Relaxation times τ were measured through the imaginary susceptibility component χ ' '(T), and analyzed within Debye's theory of dipolar fluid. The results indicated Brownian rotational relaxation and allowed to calculate the hydrodynamic radius close to the values obtained from photon correlation. The study of the colloid performances as power absorbers showed no detectable increase of temperature for dextran-coated Fe 3 O 4 nanoparticles, whereas a second Fe 3 O 4 -based dispersion of similar concentration could be heated up to 12K after 30min under similar experimental conditions. The different power absorption efficiencies are discussed in terms of the magnetic structure of the nanoparticles

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 rotational relaxation and power absorption in magnetite nanoparticles

Energy Technology Data Exchange (ETDEWEB)

Goya, G.F. [Institute of Nanoscience of Aragon (INA), University of Zaragoza, 50009 Zaragoza (Spain)]. E-mail: goya@unizar.es; Fernandez-Pacheco, R. [Institute of Nanoscience of Aragon (INA), University of Zaragoza, 50009 Zaragoza (Spain); Arruebo, M. [Institute of Nanoscience of Aragon (INA), University of Zaragoza, 50009 Zaragoza (Spain); Cassinelli, N. [Electronics Division, Bauer and Associates, Buenos Aires (Argentina); Facultad de Ingenieria, UNLP (Argentina); Ibarra, M.R. [Institute of Nanoscience of Aragon (INA), University of Zaragoza, 50009 Zaragoza (Spain)

2007-09-15

We present a study of the power absorption efficiency in several magnetite-based colloids, to asses their potential as magnetic inductive hyperthermia (MIH) agents. Relaxation times {tau} were measured through the imaginary susceptibility component {chi}{sup '}'(T), and analyzed within Debye's theory of dipolar fluid. The results indicated Brownian rotational relaxation and allowed to calculate the hydrodynamic radius close to the values obtained from photon correlation. The study of the colloid performances as power absorbers showed no detectable increase of temperature for dextran-coated Fe{sub 3}O{sub 4} nanoparticles, whereas a second Fe{sub 3}O{sub 4}-based dispersion of similar concentration could be heated up to 12K after 30min under similar experimental conditions. The different power absorption efficiencies are discussed in terms of the magnetic structure of the nanoparticles.

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

Can walking motions improve visually induced rotational self-motion illusions in virtual reality?

Science.gov (United States)

Riecke, Bernhard E; Freiberg, Jacob B; Grechkin, Timofey Y

2015-02-04

Illusions of self-motion (vection) can provide compelling sensations of moving through virtual environments without the need for complex motion simulators or large tracked physical walking spaces. Here we explore the interaction between biomechanical cues (stepping along a rotating circular treadmill) and visual cues (viewing simulated self-rotation) for providing stationary users a compelling sensation of rotational self-motion (circular vection). When tested individually, biomechanical and visual cues were similarly effective in eliciting self-motion illusions. However, in combination they yielded significantly more intense self-motion illusions. These findings provide the first compelling evidence that walking motions can be used to significantly enhance visually induced rotational self-motion perception in virtual environments (and vice versa) without having to provide for physical self-motion or motion platforms. This is noteworthy, as linear treadmills have been found to actually impair visually induced translational self-motion perception (Ash, Palmisano, Apthorp, & Allison, 2013). Given the predominant focus on linear walking interfaces for virtual-reality locomotion, our findings suggest that investigating circular and curvilinear walking interfaces offers a promising direction for future research and development and can help to enhance self-motion illusions, presence and immersion in virtual-reality systems. © 2015 ARVO.

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

Simulating Stock Prices Using Geometric Brownian Motion: Evidence from Australian Companies

Directory of Open Access Journals (Sweden)

Krishna Reddy

2016-09-01

Full Text Available This study uses the geometric Brownian motion (GBM method to simulate stock price paths, and tests whether the simulated stock prices align with actual stock returns. The sample for this study was based on the large listed Australian companies listed on the S&P/ASX 50 Index. Daily stock price data was obtained from the Thomson One database over the period 1 January 2013 to 31 December 2014. The findings are slightly encouraging as results show that over all time horizons the chances of a stock price simulated using GBM moving in the same direction as real stock prices was a little greater than 50 percent. However, the results improved slightly when portfolios were formed.

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.

Motions on a rotating planet

Science.gov (United States)

Schröer, H.

In chapter 1 we want to describe the motion of a falling body on a rotating planet. The planet rotates with an arbitrary changable angular velocity and has a translational acceleration. We obtain 3 differential equations. For the general gravitational field an exact solution is possible, when the differential equation system is explicit solvable. Then we consider the case, if the angular velocity and the translational acceleration is constant. With a special transformation we get 3 partial differential equations of first order. Instead of a planet sphere we can choose a general body of rotation. Even general bodies are possible. Chapter 2 contains the motion in a local coordinate system on planet's surface. We have an inhomogeneous linear differential equation of first order. If the angular velocity is constant, we get a system with constant coefficients. There is an english and a german edition.

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)

Rotational Motion Control of a Spacecraft

DEFF Research Database (Denmark)

Wisniewski, Rafal; Kulczycki, P.

2001-01-01

The paper adopts the energy shaping method to control of rotational motion. A global representation of the rigid body motion is given in the canonical form by a quaternion and its conjugate momenta. A general method for motion control on a cotangent bundle to the 3-sphere is suggested. The design...... algorithm is validated for three-axis spacecraft attitude control...

Rotational motion control of a spacecraft

DEFF Research Database (Denmark)

Wisniewski, Rafal; Kulczycki, P.

2003-01-01

The paper adopts the energy shaping method to control of rotational motion. A global representation of the rigid body motion is given in the canonical form by a quaternion and its conjugate momenta. A general method for motion control on a cotangent bundle to the 3-sphere is suggested. The design...... algorithm is validated for three-axis spacecraft attitude control. Udgivelsesdato: APR...

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. 

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 ...

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

Autocorrelated process control: Geometric Brownian Motion approach versus Box-Jenkins approach

Science.gov (United States)

Salleh, R. M.; Zawawi, N. I.; Gan, Z. F.; Nor, M. E.

2018-04-01

Existing of autocorrelation will bring a significant effect on the performance and accuracy of process control if the problem does not handle carefully. When dealing with autocorrelated process, Box-Jenkins method will be preferred because of the popularity. However, the computation of Box-Jenkins method is too complicated and challenging which cause of time-consuming. Therefore, an alternative method which known as Geometric Brownian Motion (GBM) is introduced to monitor the autocorrelated process. One real case of furnace temperature data is conducted to compare the performance of Box-Jenkins and GBM methods in monitoring autocorrelation process. Both methods give the same results in terms of model accuracy and monitoring process control. Yet, GBM is superior compared to Box-Jenkins method due to its simplicity and practically with shorter computational time.

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.

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

Analysis of macroscopic and microscopic rotating motions in rotating jets: A direct numerical simulation

Directory of Open Access Journals (Sweden)

Xingtuan Yang

2015-05-01

Full Text Available A direct numerical simulation study of the characteristics of macroscopic and microscopic rotating motions in swirling jets confined in a rectangular flow domain is carried out. The different structures of vortex cores for different swirl levels are illustrated. It is found that the vortex cores of low swirl flows are of regular cylindrical-helix patterns, whereas those of the high swirl flows are characterized by the formation of the bubble-type vortex breakdown followed by the radiant processing vortex cores. The results of mean velocity fields show the general procedures of vortex origination. Moreover, the effects of macroscopic and microscopic rotating motions with respect to the mean and fluctuation fields of the swirling flows are evaluated. The microscopic rotating effects, especially the effects with respect to the turbulent fluctuation motion, are increasingly intermittent with the increase in the swirl levels. In contrast, the maximum value of the probability density functions with respect to the macroscopic rotating effects of the fluctuation motion occurs at moderate swirl levels since the macroscopic rotating effects are attenuated by the formation of the bubble vortex breakdown with a region of stagnant fluids at supercritical swirl levels.

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.

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 ...

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 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 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.

Relaxation processes in rotational motion

International Nuclear Information System (INIS)

Broglia, R.A.

1986-01-01

At few MeV above the yrast line the normally strong correlations among γ-ray energies in a rotational sequence become weaker. This observation can be interpreted as evidence for the damping of rotational motion in hot nuclei. It seems possible to relate the spreading width of the E2-rotational decay strength to the spread in frequency Δω 0 of rotational bands. The origin of these fluctuations is found in: (1) fluctuations in the occupation of special single-particle orbits which contribute a significant part of the total angular momentum; and (2) fluctuations in the moment of inertia induced by vibrations of the nuclear shape. Estimates of Δω 0 done making use of the hundred-odd known discrete rotational bands in the rare-earth region lead, for moderate spin and excitation energies (I ≅ 30 and U ≅ 3 to 4 MeV), to rotational spreading widths of the order of 60 to 160 keV in overall agreement with the data. 24 refs

Three-dimensional motion of the uncovertebral joint during head rotation.

Science.gov (United States)

Nagamoto, Yukitaka; Ishii, Takahiro; Iwasaki, Motoki; Sakaura, Hironobu; Moritomo, Hisao; Fujimori, Takahito; Kashii, Masafumi; Murase, Tsuyoshi; Yoshikawa, Hideki; Sugamoto, Kazuomi

2012-10-01

The uncovertebral joints are peculiar but clinically important anatomical structures of the cervical vertebrae. In the aged or degenerative cervical spine, osteophytes arising from an uncovertebral joint can cause cervical radiculopathy, often necessitating decompression surgery. Although these joints are believed to bear some relationship to head rotation, how the uncovertebral joints work during head rotation remains unclear. The purpose of this study is to elucidate 3D motion of the uncovertebral joints during head rotation. Study participants were 10 healthy volunteers who underwent 3D MRI of the cervical spine in 11 positions during head rotation: neutral (0°) and 15° increments to maximal head rotation on each side (left and right). Relative motions of the cervical spine were calculated by automatically superimposing a segmented 3D MR image of the vertebra in the neutral position over images of each position using the volume registration method. The 3D intervertebral motions of all 10 volunteers were standardized, and the 3D motion of uncovertebral joints was visualized on animations using data for the standardized motion. Inferred contact areas of uncovertebral joints were also calculated using a proximity mapping technique. The 3D animation of uncovertebral joints during head rotation showed that the joints alternate between contact and separation. Inferred contact areas of uncovertebral joints were situated directly lateral at the middle cervical spine and dorsolateral at the lower cervical spine. With increasing angle of rotation, inferred contact areas increased in the middle cervical spine, whereas areas in the lower cervical spine slightly decreased. In this study, the 3D motions of uncovertebral joints during head rotation were depicted precisely for the first time.

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)

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.

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.

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.

Principle and analysis of a rotational motion Fourier transform infrared spectrometer

Science.gov (United States)

Cai, Qisheng; Min, Huang; Han, Wei; Liu, Yixuan; Qian, Lulu; Lu, Xiangning

2017-09-01

Fourier transform infrared spectroscopy is an important technique in studying molecular energy levels, analyzing material compositions, and environmental pollutants detection. A novel rotational motion Fourier transform infrared spectrometer with high stability and ultra-rapid scanning characteristics is proposed in this paper. The basic principle, the optical path difference (OPD) calculations, and some tolerance analysis are elaborated. The OPD of this spectrometer is obtained by the continuously rotational motion of a pair of parallel mirrors instead of the translational motion in traditional Michelson interferometer. Because of the rotational motion, it avoids the tilt problems occurred in the translational motion Michelson interferometer. There is a cosine function relationship between the OPD and the rotating angle of the parallel mirrors. An optical model is setup in non-sequential mode of the ZEMAX software, and the interferogram of a monochromatic light is simulated using ray tracing method. The simulated interferogram is consistent with the theoretically calculated interferogram. As the rotating mirrors are the only moving elements in this spectrometer, the parallelism of the rotating mirrors and the vibration during the scan are analyzed. The vibration of the parallel mirrors is the main error during the rotation. This high stability and ultra-rapid scanning Fourier transform infrared spectrometer is a suitable candidate for airborne and space-borne remote sensing spectrometer.

Solar Magnetized Tornadoes: Rotational Motion in a Tornado-like Prominence

Science.gov (United States)

Su, Yang; Gömöry, Peter; Veronig, Astrid; Temmer, Manuela; Wang, Tongjiang; Vanninathan, Kamalam; Gan, Weiqun; Li, YouPing

2014-04-01

Su et al. proposed a new explanation for filament formation and eruption, where filament barbs are rotating magnetic structures driven by underlying vortices on the surface. Such structures have been noticed as tornado-like prominences when they appear above the limb. They may play a key role as the source of plasma and twist in filaments. However, no observations have successfully distinguished rotational motion of the magnetic structures in tornado-like prominences from other motions such as oscillation and counter-streaming plasma flows. Here we report evidence of rotational motions in a tornado-like prominence. The spectroscopic observations in two coronal lines were obtained from a specifically designed Hinode/EIS observing program. The data revealed the existence of both cold and million-degree-hot plasma in the prominence leg, supporting the so-called prominence-corona transition region. The opposite velocities at the two sides of the prominence and their persistent time evolution, together with the periodic motions evident in SDO/AIA dark structures, indicate a rotational motion of both cold and hot plasma with a speed of ~5 km s-1.

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."

Usage of stereoscopic visualization in the learning contents of rotational motion.

Science.gov (United States)

Matsuura, Shu

2013-01-01

Rotational motion plays an essential role in physics even at an introductory level. In addition, the stereoscopic display of three-dimensional graphics includes is advantageous for the presentation of rotational motions, particularly for depth recognition. However, the immersive visualization of rotational motion has been known to lead to dizziness and even nausea for some viewers. Therefore, the purpose of this study is to examine the onset of nausea and visual fatigue when learning rotational motion through the use of a stereoscopic display. The findings show that an instruction method with intermittent exposure of the stereoscopic display and a simplification of its visual components reduced the onset of nausea and visual fatigue for the viewers, which maintained the overall effect of instantaneous spatial recognition.

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.

The electrical MHD and Hall current impact on micropolar nanofluid flow between rotating parallel plates

Science.gov (United States)

Shah, Zahir; Islam, Saeed; Gul, Taza; Bonyah, Ebenezer; Altaf Khan, Muhammad

2018-06-01

The current research aims to examine the combined effect of magnetic and electric field on micropolar nanofluid between two parallel plates in a rotating system. The nanofluid flow between two parallel plates is taken under the influence of Hall current. The flow of micropolar nanofluid has been assumed in steady state. The rudimentary governing equations have been changed to a set of differential nonlinear and coupled equations using suitable similarity variables. An optimal approach has been used to acquire the solution of the modelled problems. The convergence of the method has been shown numerically. The impact of the Skin friction on velocity profile, Nusslet number on temperature profile and Sherwood number on concentration profile have been studied. The influences of the Hall currents, rotation, Brownian motion and thermophoresis analysis of micropolar nanofluid have been mainly focused in this work. Moreover, for comprehension the physical presentation of the embedded parameters that is, coupling parameter N1 , viscosity parameter Re , spin gradient viscosity parameter N2 , rotating parameter Kr , Micropolar fluid constant N3 , magnetic parameter M , Prandtl number Pr , Thermophoretic parameter Nt , Brownian motion parameter Nb , and Schmidt number Sc have been plotted and deliberated graphically.

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 .

Precise measurement of velocity dependent friction in rotational motion

Energy Technology Data Exchange (ETDEWEB)

Alam, Junaid; Hassan, Hafsa; Shamim, Sohaib; Mahmood, Waqas; Anwar, Muhammad Sabieh, E-mail: sabieh@lums.edu.pk [School of Science and Engineering, Lahore University of Management Sciences (LUMS), Opposite Sector U, D.H.A, Lahore 54792 (Pakistan)

2011-09-15

Frictional losses are experimentally determined for a uniform circular disc exhibiting rotational motion. The clockwise and anticlockwise rotations of the disc, that result when a hanger tied to a thread is released from a certain height, give rise to vertical oscillations of the hanger as the thread winds and unwinds over a pulley attached to the disc. It is thus observed how the maximum height is achieved by the hanger decrements in every bounce. From the decrements, the rotational frictional losses are measured. The precision is enhanced by correlating vertical motion with the angular motion. This method leads to a substantial improvement in precision. Furthermore, the frictional torque is shown to be proportional to the angular speed. The experiment has been successfully employed in the undergraduate lab setting.

SOLAR MAGNETIZED TORNADOES: ROTATIONAL MOTION IN A TORNADO-LIKE PROMINENCE

Energy Technology Data Exchange (ETDEWEB)

Su, Yang; Veronig, Astrid; Temmer, Manuela; Vanninathan, Kamalam [IGAM-Kanzelhöhe Observatory, Institute of Physics, University of Graz, Universitätsplatz 5, A-8010 Graz (Austria); Gömöry, Peter [Astronomical Institute of the Slovak Academy of Sciences, SK-05960 Tatranská Lomnica (Slovakia); Wang, Tongjiang [Department of Physics, the Catholic University of America, Washington, DC 20064 (United States); Gan, Weiqun; Li, YouPing, E-mail: yang.su@uni-graz.at [Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008 (China)

2014-04-10

Su et al. proposed a new explanation for filament formation and eruption, where filament barbs are rotating magnetic structures driven by underlying vortices on the surface. Such structures have been noticed as tornado-like prominences when they appear above the limb. They may play a key role as the source of plasma and twist in filaments. However, no observations have successfully distinguished rotational motion of the magnetic structures in tornado-like prominences from other motions such as oscillation and counter-streaming plasma flows. Here we report evidence of rotational motions in a tornado-like prominence. The spectroscopic observations in two coronal lines were obtained from a specifically designed Hinode/EIS observing program. The data revealed the existence of both cold and million-degree-hot plasma in the prominence leg, supporting the so-called prominence-corona transition region. The opposite velocities at the two sides of the prominence and their persistent time evolution, together with the periodic motions evident in SDO/AIA dark structures, indicate a rotational motion of both cold and hot plasma with a speed of ∼5 km s{sup –1}.

SOLAR MAGNETIZED TORNADOES: ROTATIONAL MOTION IN A TORNADO-LIKE PROMINENCE

International Nuclear Information System (INIS)

Su, Yang; Veronig, Astrid; Temmer, Manuela; Vanninathan, Kamalam; Gömöry, Peter; Wang, Tongjiang; Gan, Weiqun; Li, YouPing

2014-01-01

Su et al. proposed a new explanation for filament formation and eruption, where filament barbs are rotating magnetic structures driven by underlying vortices on the surface. Such structures have been noticed as tornado-like prominences when they appear above the limb. They may play a key role as the source of plasma and twist in filaments. However, no observations have successfully distinguished rotational motion of the magnetic structures in tornado-like prominences from other motions such as oscillation and counter-streaming plasma flows. Here we report evidence of rotational motions in a tornado-like prominence. The spectroscopic observations in two coronal lines were obtained from a specifically designed Hinode/EIS observing program. The data revealed the existence of both cold and million-degree-hot plasma in the prominence leg, supporting the so-called prominence-corona transition region. The opposite velocities at the two sides of the prominence and their persistent time evolution, together with the periodic motions evident in SDO/AIA dark structures, indicate a rotational motion of both cold and hot plasma with a speed of ∼5 km s –1

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.

Deformations and Rotational Ground Motions Inferred from Downhole Vertical Array Observations

Science.gov (United States)

Graizer, V.

2017-12-01

Only few direct reliable measurements of rotational component of strong earthquake ground motions are obtained so far. In the meantime, high quality data recorded at downhole vertical arrays during a number of earthquakes provide an opportunity to calculate deformations based on the differences in ground motions recorded simultaneously at different depths. More than twenty high resolution strong motion downhole vertical arrays were installed in California with primary goal to study site response of different geologic structures to strong motion. Deformation or simple shear strain with the rate γ is the combination of pure shear strain with the rate γ/2 and rotation with the rate of α=γ/2. Deformations and rotations were inferred from downhole array records of the Mw 6.0 Parkfield 2004, the Mw 7.2 Sierra El Mayor (Mexico) 2010, the Mw 6.5 Ferndale area in N. California 2010 and the two smaller earthquakes in California. Highest amplitude of rotation of 0.60E-03 rad was observed at the Eureka array corresponding to ground velocity of 35 cm/s, and highest rotation rate of 0.55E-02 rad/s associated with the S-wave was observed at a close epicentral distance of 4.3 km from the ML 4.2 event in Southern California at the La Cienega array. Large magnitude Sierra El Mayor earthquake produced long duration rotational motions of up to 1.5E-04 rad and 2.05E-03 rad/s associated with shear and surface waves at the El Centro array at closest fault distance of 33.4km. Rotational motions of such levels, especially tilting can have significant effect on structures. High dynamic range well synchronized and properly oriented instrumentation is necessary for reliable calculation of rotations from vertical array data. Data from the dense Treasure Island array near San Francisco demonstrate consistent change of shape of rotational motion with depth and material. In the frequency range of 1-15 Hz Fourier amplitude spectrum of vertical ground velocity is similar to the scaled tilt

Optical Torque Wrench: Angular Trapping, Rotation, and Torque Detection of Quartz Microparticles

Science.gov (United States)

La Porta, Arthur; Wang, Michelle D.

2004-05-01

We describe an apparatus that can measure the instantaneous angular displacement and torque applied to a quartz particle which is angularly trapped. Torque is measured by detecting the change in angular momentum of the transmitted trap beam. The rotational Brownian motion of the trapped particle and its power spectral density are used to determine the angular trap stiffness. The apparatus features a feedback control that clamps torque or other rotational quantities. The torque sensitivity demonstrated is ideal for the study of known biological molecular motors.

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

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

Rotational damping motion in nuclei

International Nuclear Information System (INIS)

Egido, J.L.; Faessler, A.

1991-01-01

The recently proposed model to explain the mechanism of the rotational motion damping in nuclei is exactly solved. When compared with the earlier approximative solution, we find significative differences in the low excitation energy limit (i.e. Γ μ 0 ). For the strength functions we find distributions going from the Wigner semicircle through gaussians to Breit-Wigner shapes. (orig.)

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

Directory of Open Access Journals (Sweden)

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.

Modeling and analyzing flow of third grade nanofluid due to rotating stretchable disk with chemical reaction and heat source

Science.gov (United States)

Hayat, T.; Ahmad, Salman; Khan, M. Ijaz; Alsaedi, A.

2018-05-01

This article addresses flow of third grade nanofluid due to stretchable rotating disk. Mass and heat transports are analyzed through thermophoresis and Brownian movement effects. Further the effects of heat generation and chemical reaction are also accounted. The obtained ODE's are tackled computationally by means of homotopy analysis method. Graphical outcomes are analyzed for the effects of different variables. The obtained results show that velocity reduces through Reynolds number and material parameters. Temperature and concentration increase with Brownian motion and these decrease by Reynolds number.

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

Directory of Open Access Journals (Sweden)

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.

Modeling Philippine Stock Exchange Composite Index Using Weighted Geometric Brownian Motion Forecasts

Directory of Open Access Journals (Sweden)

Gayo Willy

2016-01-01

Full Text Available Philippine Stock Exchange Composite Index (PSEi is the main stock index of the Philippine Stock Exchange (PSE. PSEi is computed using a weighted mean of the top 30 publicly traded companies in the Philippines, called component stocks. It provides a single value by which the performance of the Philippine stock market is measured. Unfortunately, these weights, which may vary for every trading day, are not disclosed by the PSE. In this paper, we propose a model of forecasting the PSEi by estimating the weights based on historical data and forecasting each component stock using Monte Carlo simulation based on a Geometric Brownian Motion (GBM assumption. The model performance is evaluated and its forecast compared is with the results using a direct GBM forecast of PSEi over different forecast periods. Results showed that the forecasts using WGBM will yield smaller error compared to direct GBM forecast of PSEi.

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

Directory of Open Access Journals (Sweden)

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

Directory of Open Access Journals (Sweden)

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.

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.

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.

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

Can earthquake source inversion benefit from rotational ground motion observations?

Science.gov (United States)

Igel, H.; Donner, S.; Reinwald, M.; Bernauer, M.; Wassermann, J. M.; Fichtner, A.

2015-12-01

With the prospects of instruments to observe rotational ground motions in a wide frequency and amplitude range in the near future we engage in the question how this type of ground motion observation can be used to solve seismic inverse problems. Here, we focus on the question, whether point or finite source inversions can benefit from additional observations of rotational motions. In an attempt to be fair we compare observations from a surface seismic network with N 3-component translational sensors (classic seismometers) with those obtained with N/2 6-component sensors (with additional colocated 3-component rotational motions). Thus we keep the overall number of traces constant. Synthetic seismograms are calculated for known point- or finite-source properties. The corresponding inverse problem is posed in a probabilistic way using the Shannon information content as a measure how the observations constrain the seismic source properties. The results show that with the 6-C subnetworks the source properties are not only equally well recovered (even that would be benefitial because of the substantially reduced logistics installing N/2 sensors) but statistically significant some source properties are almost always better resolved. We assume that this can be attributed to the fact the (in particular vertical) gradient information is contained in the additional rotational motion components. We compare these effects for strike-slip and normal-faulting type sources. Thus the answer to the question raised is a definite "yes". The challenge now is to demonstrate these effects on real data.

Single-particle motion in rapidly rotating nuclei

International Nuclear Information System (INIS)

Bengtsson, R.; Frisk, H.

1985-01-01

The motion of particles belonging to a single-j shell is described in terms of classical orbitals. The effects of rapid rotation and pairing correlations are discussed and the results are compared with the quantum mechanical orbitals. (orig.)

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.

Necessary conditions for tumbling in the rotational motion

Science.gov (United States)

Carrera, Danny H. Z.; Weber, Hans I.

2012-11-01

The goal of this work is the investigation of the necessary conditions for the possible existence of tumbling in rotational motion of rigid bodies. In a stable spinning satellite, tumbling may occur by sufficient strong action of external impulses, when the conical movement characteristic of the stable attitude is de-characterized. For this purpose a methodology is chosen to simplify the study of rotational motions with great amplitude, for example free bodies in space, allowing an extension of the analysis to non-conservative systems. In the case of a satellite in space, the projection of the angular velocity along the principal axes of inertia must be known, defining completely the initial conditions of motion for stability investigations. In this paper, the coordinate systems are established according to the initial condition in order to allow a simple analytical work on the equations of motion. Also it will be proposed the definition of a parameter, calling it tumbling coefficient, to measure the intensity of the tumbling and the amplitude of the motion when crossing limits of stability in the concept of Lyapunov. Tumbling in the motion of bodies in space is not possible when this coefficient is positive. Magnus Triangle representation will be used to represent the geometry of the body, establishing regions of stability/instability for possible initial conditions of motion. In the study of nonconservative systems for an oblate body, one sufficient condition will be enough to assure damped motion, and this condition is checked for a motion damped by viscous torques. This paper seeks to highlight the physical understanding of the phenomena and the influence of various parameters that are important in the process.

Benefits of rotational ground motions for planetary seismology

Science.gov (United States)

Donner, S.; Joshi, R.; Hadziioannou, C.; Nunn, C.; van Driel, M.; Schmelzbach, C.; Wassermann, J. M.; Igel, H.

2017-12-01

Exploring the internal structure of planetary objects is fundamental to understand the evolution of our solar system. In contrast to Earth, planetary seismology is hampered by the limited number of stations available, often just a single one. Classic seismology is based on the measurement of three components of translational ground motion. Its methods are mainly developed for a larger number of available stations. Therefore, the application of classical seismological methods to other planets is very limited. Here, we show that the additional measurement of three components of rotational ground motion could substantially improve the situation. From sparse or single station networks measuring translational and rotational ground motions it is possible to obtain additional information on structure and source. This includes direct information on local subsurface seismic velocities, separation of seismic phases, propagation direction of seismic energy, crustal scattering properties, as well as moment tensor source parameters for regional sources. The potential of this methodology will be highlighted through synthetic forward and inverse modeling experiments.

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.

Diffusing diffusivity: Rotational diffusion in two and three dimensions

Science.gov (United States)

Jain, Rohit; Sebastian, K. L.

2017-06-01

We consider the problem of calculating the probability distribution function (pdf) of angular displacement for rotational diffusion in a crowded, rearranging medium. We use the diffusing diffusivity model and following our previous work on translational diffusion [R. Jain and K. L. Sebastian, J. Phys. Chem. B 120, 3988 (2016)], we show that the problem can be reduced to that of calculating the survival probability of a particle undergoing Brownian motion, in the presence of a sink. We use the approach to calculate the pdf for the rotational motion in two and three dimensions. We also propose new dimensionless, time dependent parameters, αr o t ,2 D and αr o t ,3 D, which can be used to analyze the experimental/simulation data to find the extent of deviation from the normal behavior, i.e., constant diffusivity, and obtain explicit analytical expressions for them, within our model.

Correlation of glenohumeral internal rotation deficit and total rotational motion to shoulder injuries in professional baseball pitchers.

Science.gov (United States)

Wilk, Kevin E; Macrina, Leonard C; Fleisig, Glenn S; Porterfield, Ronald; Simpson, Charles D; Harker, Paul; Paparesta, Nick; Andrews, James R

2011-02-01

Glenohumeral internal rotation deficit (GIRD) indicates a 20° or greater loss of internal rotation of the throwing shoulder compared with the nondominant shoulder. To determine whether GIRD and a deficit in total rotational motion (external rotation + internal rotation) compared with the nonthrowing shoulder correlate with shoulder injuries in professional baseball pitchers. Case series; Level of evidence, 4. Over 3 competitive seasons (2005 to 2007), passive range of motion measurements were evaluated on the dominant and nondominant shoulders for 170 pitcher-seasons. This included 122 professional pitchers during the 3 seasons of data collection, in which some pitchers were measured during multiple seasons. Ranges of motion were measured with a bubble goniometer during the preseason, by the same examiner each year. External and internal rotation of the glenohumeral joint was assessed with the participant supine and the arm abducted 90° in the plane of the scapula, with the scapula stabilized anteriorly at the coracoid process. The reproducibility of the test methods had an intraclass correlation coefficient of .81. Days in which the player was unable to participate because of injury or surgery were recorded during the season by the medical staff of the team and defined as an injury. Pitchers with GIRD (n = 40) were nearly twice as likely to be injured as those without but without statistical significance (P = .17). Pitchers with total rotational motion deficit greater than 5° had a higher rate of injury. Minor league pitchers were more likely than major league pitchers to be injured. However, when players were injured, major league pitchers missed a significantly greater number of games than minor league pitchers. Compared with pitchers without GIRD, pitchers with GIRD appear to be at a higher risk for injury and shoulder surgery.

Digital tomosynthesis using a 35 mm X-ray cinematogram during an isocentric rotational motion

International Nuclear Information System (INIS)

Maeda, Hirofumi; Aikawa, Hisayuki; Maeda, Tohru; Miyake, Hidetoshi; Sugahara, Tetsuo.

1988-01-01

Digital tomosynthesis is performed using a 35 mm X-ray cinematogram obtained during an isocentric rotational motion of the cineangiographic apparatus. Formula of image shift for digital tomosynthesis using an isocentric rotational motion is induced by perspective projection and affine transformation. Images of desired layer are aligned at the same point in the image processor and summed. Resultant final image is displayed in sharp focus. We can set tomosynthetic factors on any desired projection, sweep angle and depth as concerns digital tomosynthesis using an isocentric rotational motion. Especially we emphasize that tomosynthesis tilted for central axis of isocentric rotational motion can be obtained, using shear transformation of image in the image processor. (author)

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

Isolating integrals of the motion for stellar orbits in a rotating galactic bar

International Nuclear Information System (INIS)

Vandervoort, P.O.

1979-01-01

The study of the equilibrium of a rotating galactic bar requires an enumeration of the isolating integrals of the motion of a star in the prevailing gravitational field. In general, Jacobi's integral is the only exact isolating integral known. This paper describes a search for an additional isolating integral for orbits confined to a plane perpendicular to the axis of the bar's rotation. It is shown that, in general, the equations of motion admit an additional integral exactly which is a nonhomogeneous quadratic form in the momenta of the star only if (1) the gravitational potential is axisymmetric, (2) the gravitational potential is harmonic, or (3) the bar does not rotate and the gravitational potential is separable in elliptic coordinates. A formal integral of the motion is constructed for orbits in a slightly anharmonic potential. Numerical solutions of the equations of motion for orbits in a slightly anharmonic potential behave as if there were indeed an additional isolating integral, and that behavior is represented very well in terms of the formal integral. If the rotation of the bar is rapid and/or the nonaxisymmetry of the bar is weak, then the additional integral restricts the motion of a star in much the same way that the angular momentum restricts motion in an axisymmetric potential. Conversely, if the rotation of the bar is slow and/or the nonaxisymmetry of the bar is strong, then the additional integral restricts the motion in much the same way that the difference of the separable energies would if the motion were separable in Cartesian coordinates

Nanoparticles in dilute solution : A numerical study of rotational diffusion

Energy Technology Data Exchange (ETDEWEB)

Evensen, Tom Richard

2008-06-15

This thesis is dedicated to Brownian dynamics simulations of rotational diffusion. A rotation dynamics engine has been implemented and tested. This engine will in the future be integrated as a part of a complete Brownian dynamics simulation tool. The special case, when translational motion can be ignored, has thoroughly been studied. Two choices of generalized coordinates describing angular orientation of the particles are used. The Euler angles, which constitute the classical choice, and the Cartesian components of the rotation vector, which was recently introduced as an alternative, are being compared with regards to computational efficiency. Results from both equilibrium and non-equilibrium simulations are presented. The consistency of two new algorithms is demonstrated on systems of free rigid particles with arbitrary surface topographies. The algorithms make use of only the principal values of the rotational mobility tensor, assuming the corresponding principal axes coincide with the body-fixed coordinate system. These three scalars contain all information about the particle surface topography relevant for rotational diffusion. The calculation of the mobility tensor can be performed in a pre-calculation step, which makes the algorithm itself highly efficient. Both choices of generalized coordinates correctly reproduce theoretical predictions, but we have found that the algorithm using the Cartesian components of the rotation vector as generalized coordinates outperform its counterpart using the Euler angles by up to a factor 1000 in extreme cases. The reason for this improvement is that the algorithm using the Cartesian components of the rotation vector is free of singularities. (Author). refs. figs

Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion

Science.gov (United States)

Zhang, Wei-Guo; Li, Zhe; Liu, Yong-Jun

2018-01-01

In this paper, we study the pricing problem of the continuously monitored fixed and floating strike geometric Asian power options in a mixed fractional Brownian motion environment. First, we derive both closed-form solutions and mixed fractional partial differential equations for fixed and floating strike geometric Asian power options based on delta-hedging strategy and partial differential equation method. Second, we present the lower and upper bounds of the prices of fixed and floating strike geometric Asian power options under the assumption that both risk-free interest rate and volatility are interval numbers. Finally, numerical studies are performed to illustrate the performance of our proposed pricing model.

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.

Precise Measurement of Velocity Dependent Friction in Rotational Motion

Science.gov (United States)

Alam, Junaid; Hassan, Hafsa; Shamim, Sohaib; Mahmood, Waqas; Anwar, Muhammad Sabieh

2011-01-01

Frictional losses are experimentally determined for a uniform circular disc exhibiting rotational motion. The clockwise and anticlockwise rotations of the disc, that result when a hanger tied to a thread is released from a certain height, give rise to vertical oscillations of the hanger as the thread winds and unwinds over a pulley attached to the…

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

Modes of uncontrolled rotational motion of the Progress M-29M spacecraft

Science.gov (United States)

Belyaev, M. Yu.; Matveeva, T. V.; Monakhov, M. I.; Rulev, D. N.; Sazonov, V. V.

2018-01-01

We have reconstructed the uncontrolled rotational motion of the Progress M-29M transport cargo spacecraft in the single-axis solar orientation mode (the so-called sunward spin) and in the mode of the gravitational orientation of a rotating satellite. The modes were implemented on April 3-7, 2016 as a part of preparation for experiments with the DAKON convection sensor onboard the Progress spacecraft. The reconstruction was performed by integral statistical techniques using the measurements of the spacecraft's angular velocity and electric current from its solar arrays. The measurement data obtained in a certain time interval have been jointly processed using the least-squares method by integrating the equations of the spacecraft's motion relative to the center of mass. As a result of processing, the initial conditions of motion and parameters of the mathematical model have been estimated. The motion in the sunward spin mode is the rotation of the spacecraft with an angular velocity of 2.2 deg/s about the normal to the plane of solar arrays; the normal is oriented toward the Sun or forms a small angle with this direction. The duration of the mode is several orbit passes. The reconstruction has been performed over time intervals of up to 1 h. As a result, the actual rotational motion of the spacecraft relative to the Earth-Sun direction was obtained. In the gravitational orientation mode, the spacecraft was rotated about its longitudinal axis with an angular velocity of 0.1-0.2 deg/s; the longitudinal axis executed small oscillated relative to the local vertical. The reconstruction of motion relative to the orbital coordinate system was performed in time intervals of up to 7 h using only the angularvelocity measurements. The measurements of the electric current from solar arrays were used for verification.

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)

Effects of Rotational Motion in Robotic Needle Insertion

Science.gov (United States)

Ramezanpour, H.; Yousefi, H.; Rezaei, M.; Rostami, M.

2015-01-01

Background Robotic needle insertion in biological tissues has been known as one the most applicable procedures in sampling, robotic injection and different medical therapies and operations. Objective In this paper, we would like to investigate the effects of angular velocity in soft tissue insertion procedure by considering force-displacement diagram. Non-homogenous camel liver can be exploited as a tissue sample under standard compression test with Zwick/Roell device employing 1-D axial load-cell. Methods Effects of rotational motion were studied by running needle insertion experiments in 5, 50 and 200 mm/min in two types of with or without rotational velocity of 50, 150 and 300 rpm. On further steps with deeper penetrations, friction force of the insertion procedure in needle shaft was acquired by a definite thickness of the tissue. Results Designed mechanism of fixture for providing different frequencies of rotational motion is available in this work. Results for comparison of different force graphs were also provided. Conclusion Derived force-displacement graphs showed a significant difference between two procedures; however, tissue bleeding and disorganized micro-structure would be among unavoidable results. PMID:26688800

Interacting Brownian Swarms: Some Analytical Results

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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.

Protein brownian rotation at the glass transition temperature of a freeze-concentrated buffer probed by superparamagnetic nanoparticles.

Science.gov (United States)

Eloi, J-C; Okuda, M; Jones, S E Ward; Schwarzacher, W

2013-06-18

For applications from food science to the freeze-thawing of proteins it is important to understand the often complex freezing behavior of solutions of biomolecules. Here we use a magnetic method to monitor the Brownian rotation of a quasi-spherical cage-shaped protein, apoferritin, approaching the glass transition Tg in a freeze-concentrated buffer (Tris-HCl). The protein incorporates a synthetic magnetic nanoparticle (Co-doped Fe3O4 (magnetite)). We use the magnetic signal from the nanoparticles to monitor the protein orientation. As T decreases toward Tg of the buffer solution the protein's rotational relaxation time increases exponentially, taking values in the range from a few seconds up to thousands of seconds, i.e., orders of magnitude greater than usually accessed, e.g., by NMR. The longest relaxation times measured correspond to estimated viscosities >2 MPa s. As well as being a means to study low-temperature, high-viscosity environments, our method provides evidence that, for the cooling protocol used, the following applies: 1), the concentration of the freeze-concentrated buffer at Tg is independent of its initial concentration; 2), little protein adsorption takes place at the interface between ice and buffer; and 3), the protein is free to rotate even at temperatures as low as 207 K. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Nonlinear model of a rotating hub-beams structure: Equations of motion

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Warminski, Jerzy

2018-01-01

Dynamics of a rotating structure composed of a rigid hub and flexible beams is presented in the paper. A nonlinear model of a beam takes into account bending, extension and nonlinear curvature. The influence of geometric nonlinearity and nonconstant angular velocity on dynamics of the rotating structure is presented. The exact equations of motion and associated boundary conditions are derived on the basis of the Hamilton's principle. The simplification of the exact nonlinear mathematical model is proposed taking into account the second order approximation. The reduced partial differential equations of motion together with associated boundary conditions can be used to study natural or forced vibrations of a rotating structure considering constant or nonconstant angular speed of a rigid hub and an arbitrary number of flexible blades.

Oscillatory-rotational processes in the Earth motion about the center of mass: Interpolation and forecast

Science.gov (United States)

Akulenko, L. D.; Klimov, D. M.; Markov, Yu. G.; Perepelkin, V. V.

2012-11-01

The celestial-mechanics approach (the spatial version of the problem for the Earth-Moon system in the field of gravity of the Sun) is used to construct a mathematical model of the Earth's rotational-oscillatory motions. The fundamental aspects of the processes of tidal inhomogeneity in the Earth rotation and the Earth's pole oscillations are studied. It is shown that the presence of the perturbing component of gravitational-tidal forces, which is orthogonal to the Moon's orbit plane, also allows one to distinguish short-period perturbations in the Moon's motion. The obtained model of rotational-oscillatory motions of the nonrigid Earth takes into account both the basic perturbations of large amplitudes and the more complicated small-scale properties of the motion due to the Moon short-period perturbations with combination frequencies. The astrometric data of the International Earth Rotation and Reference Systems Service (IERS) are used to perform numerical simulation (interpolation and forecast) of the Earth rotation parameters (ERP) on various time intervals.

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

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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)

Semi-analytical study of the rotational motion stability of artificial satellites using quaternions

International Nuclear Information System (INIS)

Dos Santos, Josué C; Zanardi, Maria Cecília; Matos, Nicholas

2013-01-01

This study at aims performing the stability analysis of the rotational motion to artificial satellites using quaternions to describe the satellite attitude (orientation on the space). In the system of rotational motion equations, which is composed by four kinematic equations of the quaternions and by the three Euler equations in terms of the rotational spin components. The influence of the gravity gradient and the direct solar radiation pressure torques have been considered. Equilibrium points were obtained through numerical simulations using the softwares Matlab and Octave, which are then analyzed by the Routh-Hurwitz Stability Criterion

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

Vertical Axis Rotational Motion Cues in Hovering Flight Simulation

Science.gov (United States)

Schroeder, Jeffrey A.; Johnson, Walter W.; Showman, Robert D. (Technical Monitor)

1994-01-01

A previous study that examined how yaw motion affected a pilot's ability to perform realistic hovering flight tasks indicated that any amount of pure yaw motion had little-to-no effect on pilot performance or opinion. In that experiment, pilots were located at the vehicle's center of rotation; thus lateral or longitudinal accelerations were absent. The purpose of the new study described here was to investigate further these unanticipated results for additional flight tasks, but with the introduction of linear accelerations associated with yaw rotations when the pilot is not at the center of rotation. The question of whether a yaw motion degree-of-freedom is necessary or not is important to government regulators who specify what simulator motions are necessary according to prescribed levels of simulator sophistication. Currently, specifies two levels of motion sophistication for flight simulators: full 6-degree-of-freedom and 3-degree-of-freedom. For the less sophisticated simulator, the assumed three degrees of freedom are pitch, roll, and heave. If other degrees of freedom are selected, which are different f rom these three, they must be qualified on a case-by-case basis. Picking the assumed three axes is reasonable and based upon experience, but little empirical data are available to support the selection of critical axes. Thus, the research described here is aimed at answering this question. The yaw and lateral degrees of freedom were selected to be examined first, and maneuvers were defined to uncouple these motions from changes in the gravity vector with respect to the pilot. This approach simplifies the problem to be examined. For this experiment, the NASA Ames Vertical Motion Simulator was used in a comprehensive investigation. The math model was an AH-64 Apache in hover, which was identified from flight test data and had previously been validated by several AH-64 pilots. The pilot's head was located 4.5 ft in front of the vehicle center of gravity, which is

Structure-from-motion: dissociating perception, neural persistence, and sensory memory of illusory depth and illusory rotation.

Science.gov (United States)

Pastukhov, Alexander; Braun, Jochen

2013-02-01

In the structure-from-motion paradigm, physical motion on a screen produces the vivid illusion of an object rotating in depth. Here, we show how to dissociate illusory depth and illusory rotation in a structure-from-motion stimulus using a rotationally asymmetric shape and reversals of physical motion. Reversals of physical motion create a conflict between the original illusory states and the new physical motion: Either illusory depth remains constant and illusory rotation reverses, or illusory rotation stays the same and illusory depth reverses. When physical motion reverses after the interruption in presentation, we find that illusory rotation tends to remain constant for long blank durations (T (blank) ≥ 0.5 s), but illusory depth is stabilized if interruptions are short (T (blank) ≤ 0.1 s). The stability of illusory depth over brief interruptions is consistent with the effect of neural persistence. When this is curtailed using a mask, stability of ambiguous vision (for either illusory depth or illusory rotation) is disrupted. We also examined the selectivity of the neural persistence of illusory depth. We found that it relies on a static representation of an interpolated illusory object, since changes to low-level display properties had little detrimental effect. We discuss our findings with respect to other types of history dependence in multistable displays (sensory stabilization memory, neural fatigue, etc.). Our results suggest that when brief interruptions are used during the presentation of multistable displays, switches in perception are likely to rely on the same neural mechanisms as spontaneous switches, rather than switches due to the initial percept choice at the stimulus onset.

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.

Descriptive profile of hip rotation range of motion in elite tennis players and professional baseball pitchers.

Science.gov (United States)

Ellenbecker, Todd S; Ellenbecker, Gail A; Roetert, E Paul; Silva, Rogerio Teixeira; Keuter, Greg; Sperling, Fabio

2007-08-01

Repetitive loading to the hip joint in athletes has been reported as a factor in the development of degenerative joint disease and intra-articular injury. Little information is available on the bilateral symmetry of hip rotational measures in unilaterally dominant upper extremity athletes. Side-to-side differences in hip joint range of motion may be present because of asymmetrical loading in the lower extremities of elite tennis players and professional baseball pitchers. Cohort (cross-sectional) study (prevalence); Level of evidence, 1. Descriptive measures of hip internal and external rotation active range of motion were taken in the prone position of 64 male and 83 female elite tennis players and 101 male professional baseball pitchers using digital photos and computerized angle calculation software. Bilateral differences in active range of motion between the dominant and nondominant hip were compared using paired t tests and Bonferroni correction for hip internal, external, and total rotation range of motion. A Pearson correlation test was used to test the relationship between years of competition and hip rotation active range of motion. No significant bilateral difference (P > .005) was measured for mean hip internal or external rotation for the elite tennis players or the professional baseball pitchers. An analysis of the number of subjects in each group with a bilateral difference in hip rotation greater than 10 degrees identified 17% of the professional baseball pitchers with internal rotation differences and 42% with external rotation differences. Differences in the elite male tennis players occurred in only 15% of the players for internal rotation and 9% in external rotation. Female subjects had differences in 8% and 12% of the players for internal and external rotation, respectively. Statistical differences were found between the mean total arc of hip range of internal and external rotation in the elite tennis players with the dominant side being greater

Integration of Visual and Vestibular Information Used to Discriminate Rotational Self-Motion

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Florian Soyka

2011-10-01

Full Text Available Do humans integrate visual and vestibular information in a statistically optimal fashion when discriminating rotational self-motion stimuli? Recent studies are inconclusive as to whether such integration occurs when discriminating heading direction. In the present study eight participants were consecutively rotated twice (2s sinusoidal acceleration on a chair about an earth-vertical axis in vestibular-only, visual-only and visual-vestibular trials. The visual stimulus was a video of a moving stripe pattern, synchronized with the inertial motion. Peak acceleration of the reference stimulus was varied and participants reported which rotation was perceived as faster. Just-noticeable differences (JND were estimated by fitting psychometric functions. The visual-vestibular JND measurements are too high compared to the predictions based on the unimodal JND estimates and there is no JND reduction between visual-vestibular and visual-alone estimates. These findings may be explained by visual capture. Alternatively, the visual precision may not be equal between visual-vestibular and visual-alone conditions, since it has been shown that visual motion sensitivity is reduced during inertial self-motion. Therefore, measuring visual-alone JNDs with an underlying uncorrelated inertial motion might yield higher visual-alone JNDs compared to the stationary measurement. Theoretical calculations show that higher visual-alone JNDs would result in predictions consistent with the JND measurements for the visual-vestibular condition.

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)

A novel rotational invariants target recognition method for rotating motion blurred images

Science.gov (United States)

Lan, Jinhui; Gong, Meiling; Dong, Mingwei; Zeng, Yiliang; Zhang, Yuzhen

2017-11-01

The imaging of the image sensor is blurred due to the rotational motion of the carrier and reducing the target recognition rate greatly. Although the traditional mode that restores the image first and then identifies the target can improve the recognition rate, it takes a long time to recognize. In order to solve this problem, a rotating fuzzy invariants extracted model was constructed that recognizes target directly. The model includes three metric layers. The object description capability of metric algorithms that contain gray value statistical algorithm, improved round projection transformation algorithm and rotation-convolution moment invariants in the three metric layers ranges from low to high, and the metric layer with the lowest description ability among them is as the input which can eliminate non pixel points of target region from degenerate image gradually. Experimental results show that the proposed model can improve the correct target recognition rate of blurred image and optimum allocation between the computational complexity and function of region.

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...

Effects of translation-rotation coupling on the displacement probability distribution functions of boomerang colloidal particles

Science.gov (United States)

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

Prior studies have shown that low symmetry particles such as micro-boomerangs exhibit behaviour of Brownian motion rather different from that of high symmetry particles because convenient tracking points (TPs) are usually inconsistent with the center of hydrodynamic stress (CoH) where the translational and rotational motions are decoupled. In this paper we study the effects of the translation-rotation coupling on the displacement probability distribution functions (PDFs) of the boomerang colloid particles with symmetric arms. By tracking the motions of different points on the particle symmetry axis, we show that as the distance between the TP and the CoH is increased, the effects of translation-rotation coupling becomes pronounced, making the short-time 2D PDF for fixed initial orientation to change from elliptical to crescent shape and the angle averaged PDFs from ellipsoidal-particle-like PDF to a shape with a Gaussian top and long displacement tails. We also observed that at long times the PDFs revert to Gaussian. This crescent shape of 2D PDF provides a clear physical picture of the non-zero mean displacements observed in boomerangs particles.

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.

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.

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.

Potential of mechanical metamaterials to induce their own global rotational motion

Science.gov (United States)

Dudek, K. K.; Wojciechowski, K. W.; Dudek, M. R.; Gatt, R.; Mizzi, L.; Grima, J. N.

2018-05-01

The potential of several classes of mechanical metamaterials to induce their own overall rotational motion through the individual rotation of their subunits is examined. Using a theoretical approach, we confirm that for various rotating rigid unit systems, if by design the sum of angular momentum of subunits rotating in different directions is made to be unequal, then the system will experience an overall rotation, the extent of which may be controlled through careful choice of the geometric parameters defining these systems. This phenomenon of self-induced rotation is also confirmed experimentally. Furthermore, we discuss how these systems can be designed in a special way so as to permit extended rotations which allows them to overcome geometric lockage and the relevance of this concept in applications ranging from satellites to spacecraft and telescopes employed in space.

Historical Variations in Inner Core Rotation and Polar Motion at Decade Timescales

Science.gov (United States)

Dumberry, M.

2005-12-01

Exchanges of angular momentum between the mantle, the fluid core and the solid inner core result in changes in the Earth's rotation. Torques in the axial direction produce changes in amplitude, or changes in length of day, while torques in the equatorial direction lead to changes in orientation of the rotation vector with respect to the mantle, or polar motion. In this work, we explore the possibility that a combination of electromagnetic and gravitational torques on the inner core can reproduce the observed decadal variations in polar motion known as the Markowitz wobble. Torsional oscillations, which involve azimuthal motions in the fluid core with typical periods of decades, entrain the inner core by electromagnetic traction. When the inner core is axially rotated, its surfaces of constant density are no longer aligned with the gravitational potential from mantle density heterogeneities, and this results in a gravitational torque between the two. The axial component of this torque has been previously described and is believed to be partly responsible for decadal changes in length of day. In this work, we show that it has also an equatorial component, which produces a tilt of the inner core and results in polar motion. The polar motion produced by this mechanism depends on the density structure in the mantle, the rheology of the inner core, and the time-history of the angle of axial misalignment between the inner core and the mantle. We reconstruct the latter using a model of torsional oscillations derived from geomagnetic secular variation. From this time-history, and by using published models of mantle density structure, we show that we can reproduce the salient characteristics of the Markowitz wobble: an eccentric decadal polar motion of 30-50 milliarcsecs oriented along a specific longitude. We discuss the implications of this result, noting that a match in both amplitude and phase of the observed Markowitz wobble allows the recovery of the historical

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

Directory of Open Access Journals (Sweden)

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.

Adiabatic motion of charged dust grains in rotating magnetospheres

International Nuclear Information System (INIS)

Northrop, T.G.; Hill, J.R.

1983-01-01

Dust grains in the ring systems and rapidly rotating magnetospheres of the outer planets such as Jupiter and Saturn may be sufficiently charged that the magnetic and electric forces on them are comparable with the gravitational force. The adiabatic theory of charged particle motion has previously been applied to electrons and atomic size particles. But it is also applicable to these charged dust grains in the micrometer and smaller size range. We derive here the guiding center equation of motion, drift velocity, and parallel equation of motion for these grains in a rotating magnetosphere. The effects of periodic grain charge-discharge have not been treated previously and have been included in this analysis. Grain charge is affected by the surrounding plasma properties and by the grain plasma velocity (among other factors), both of which may vary over the gyrocircle. The resulting charge-discharge process at the gyrofrequency destroys the invariance of the magnetic moment and causes a grain to move radially. The magnetic moment may increase or decrease, depending on the gyrophase of the charge variation. If it decreases, the motion is always toward synchronous radius for an equatorial grain. But the orbit becomes circular before the grain reaches synchronous radius, a conclusion that follows from an exact constant of the motion. This circularization can be viewed as a consequence of the gradual reduction in the magnetic moment. This circularization also suggests that dust grains leaving Io could not reach the region of the Jovian ring, but several effects could change that conclusion. Excellent qualitative and quantitative agreement is obtained between adiabatic theory and detailed numerical orbit integrations

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.

Early Versus Delayed Motion After Rotator Cuff Repair: A Systematic Review of Overlapping Meta-analyses.

Science.gov (United States)

Houck, Darby A; Kraeutler, Matthew J; Schuette, Hayden B; McCarty, Eric C; Bravman, Jonathan T

2017-10-01

Previous meta-analyses have been conducted to compare outcomes of early versus delayed motion after rotator cuff repair. To conduct a systematic review of overlapping meta-analyses comparing early versus delayed motion rehabilitation protocols after rotator cuff repair to determine which meta-analyses provide the best available evidence. Systematic review. A systematic review was performed by searching PubMed and Cochrane Library databases. Search terms included "rotator cuff repair," "early passive motion," "immobilization," "rehabilitation protocol," and "meta-analysis." Results were reviewed to determine study eligibility. Patient outcomes and structural healing were extracted from these meta-analyses. Meta-analysis quality was assessed using the Oxman-Guyatt and Quality of Reporting of Meta-analyses (QUOROM) systems. The Jadad decision algorithm was then used to determine which meta-analyses provided the best level of evidence. Seven meta-analyses containing a total of 5896 patients met the eligibility criteria (1 Level I evidence, 4 Level II evidence, 2 Level III evidence). None of these meta-analyses found immobilization to be superior to early motion; however, most studies suggested that early motion would increase range of motion (ROM), thereby reducing time of recovery. Three of these studies suggested that tear size contributed to the choice of rehabilitation to ensure proper healing of the shoulder. A study by Chan et al in 2014 received the highest QUOROM and Oxman-Guyatt scores, and therefore this meta-analysis appeared to have the highest level of evidence. Additionally, a study by Riboh and Garrigues in 2014 was selected as the highest quality study in this systematic review according to the Jadad decision algorithm. The current, best available evidence suggests that early motion improves ROM after rotator cuff repair but increases the risk of rotator cuff retear. Lower quality meta-analyses indicate that tear size may provide a better strategy in

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.

Gating-by-rotation: a solution to the problem of intratreatment motion in helical tomotherapy

International Nuclear Information System (INIS)

Kapatoes, J.M.; Olivera, G.H.; Schloesser, E.A.; Pearson, D.W.; Balog, J.P.; Ruchala, K.J.; Schmidt, R.; Reckwerdt, P.J.; Mehta, M.P.; Mackie, T.R.

2001-01-01

Purpose: To assess the feasibility of addressing intratreatment motion issues in helical tomotherapy by gating the treatments by rotation. Intratreatment motion is a problem common to all IMRT techniques. Traditional methods of gating in conformal radiotherapy and some forms of IMRT are not applicable to helical tomotherapy due to the continuous rotation of the gantry. An alternative method is presented. Materials and Methods: Rotation-gating in helical tomotherapy is the process in which one rotation of treatment is immediately followed by a rotation of non-treatment. This on-off strategy is repeated for the full treatment volume. During the treatment rotations, the patient is required to hold their breath while the intensity-modulated fan beam deposits dose. For the non-treatment rotations, the patient is allowed to breathe freely as all leaves of the MLC will be closed, the accelerator disabled, or both. The couch indexes normally for treatment rotations and holds the patient stationary during non-treatment rotations. An investigation was conducted to assess the feasibility of rotation-gating. Film was placed between two hemispheres of a water phantom and a continuous helical delivery was carried out with all leaves opened. The film was replaced and another treatment was performed employing rotation-gating. The two films were compared to assess the process. The films were irradiated to dose levels within the linear region of the film response curve (maximum film dose ∼35 cGy). Films were also acquired with all leaves closed to quantify leakage dose through the collimation systems. Results: Central profiles for the inferior-superior direction (parallel to the direction of translation) for both films are displayed in Figure 1. The profiles agree very well, illustrating that a rotation-gated treatment closely mimics a continuous helical delivery. The only significant discrepancy lay in the tails of the profiles: a higher film dose is seen for the rotation

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)

Equations of motion for free-flight systems of rotating-translating bodies

International Nuclear Information System (INIS)

Hodapp, A.E. Jr.

1976-09-01

General vector differential equations of motion are developed for a system of rotating-translating, unbalanced, constant mass bodies. Complete flexibility is provided in placement of the reference coordinates within the system of bodies and in placement of body fixed axes within each body. Example cases are presented to demonstrate the ease in reduction of these equations to the equations of motion for systems of interest

Perception of self motion during and after passive rotation of the body around an earth-vertical axis.

Science.gov (United States)

Sinha, N; Zaher, N; Shaikh, A G; Lasker, A G; Zee, D S; Tarnutzer, A A

2008-01-01

We investigated the perception of self-rotation using constant-velocity chair rotations. Subjects signalled self motion during three independent tasks (1) by pushing a button when rotation was first sensed, when velocity reached a peak, when velocity began to decrease, and when velocity reached zero, (2) by rotating a disc to match the perceived motion of the body, or (3) by changing the static position of the dial such that a bigger change in its position correlated with a larger perceived velocity. All three tasks gave a consistent quantitative measure of perceived angular velocity. We found a delay in the time at which peak velocity of self-rotation was perceived (2-5 s) relative to the beginning or to the end of chair rotation. In addition the decay of the perception of self-rotation was preceded by a sensed constant-velocity interval or plateau (9-14 s). This delay in the rise of self-motion perception, and the plateau for the maximum perceived velocity, contrasts with the rapid rise and the immediate decay of the angular vestibuloocular reflex (aVOR). This difference suggests that the sensory signal from the semicircular canals undergoes additional neural processing, beyond the contribution of the velocity-storage mechanism of the aVOR, to compute the percept of self-motion.

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...

Relative Attitude Estimation for a Uniform Motion and Slowly Rotating Noncooperative Spacecraft

Directory of Open Access Journals (Sweden)

Liu Zhang

2017-01-01

Full Text Available This paper presents a novel relative attitude estimation approach for a uniform motion and slowly rotating noncooperative spacecraft. It is assumed that the uniform motion and slowly rotating noncooperative chief spacecraft is in failure or out of control and there is no a priori rotation rate information. We utilize a very fast binary descriptor based on binary robust independent elementary features (BRIEF to obtain the features of the target, which are rotational invariance and resistance to noise. And then, we propose a novel combination of single candidate random sample consensus (RANSAC with extended Kalman filter (EKF that makes use of the available prior probabilistic information from the EKF in the RANSAC model hypothesis stage. The advantage of this combination obviously reduces the sample size to only one, which results in large computational savings without the loss of accuracy. Experimental results from real image sequence of a real model target show that the relative angular error is about 3.5% and the mean angular velocity error is about 0.1 deg/s.

Chemically Dissected Rotation Curves of the Galactic Bulge from Main-sequence Proper Motions

Science.gov (United States)

Clarkson, William I.; Calamida, Annalisa; Sahu, Kailash C.; Brown, Thomas M.; Gennaro, Mario; Avila, Roberto J.; Valenti, Jeff; Debattista, Victor P.; Rich, R. Michael; Minniti, Dante; Zoccali, Manuela; Aufdemberge, Emily R.

2018-05-01

We report results from an exploratory study implementing a new probe of Galactic evolution using archival Hubble Space Telescope imaging observations. Precise proper motions are combined with photometric relative metallicity and temperature indices, to produce the proper-motion rotation curves of the Galactic bulge separately for metal-poor and metal-rich main-sequence samples. This provides a “pencil-beam” complement to large-scale wide-field surveys, which to date have focused on the more traditional bright giant branch tracers. We find strong evidence that the Galactic bulge rotation curves drawn from “metal-rich” and “metal-poor” samples are indeed discrepant. The “metal-rich” sample shows greater rotation amplitude and a steeper gradient against line-of-sight distance, as well as possibly a stronger central concentration along the line of sight. This may represent a new detection of differing orbital anisotropy between metal-rich and metal-poor bulge objects. We also investigate selection effects that would be implied for the longitudinal proper-motion cut often used to isolate a “pure-bulge” sample. Extensive investigation of synthetic stellar populations suggests that instrumental and observational artifacts are unlikely to account for the observed rotation curve differences. Thus, proper-motion-based rotation curves can be used to probe chemodynamical correlations for main-sequence tracer stars, which are orders of magnitude more numerous in the Galactic bulge than the bright giant branch tracers. We discuss briefly the prospect of using this new tool to constrain detailed models of Galactic formation and evolution. Based on observations made with the NASA/ESA Hubble Space Telescope and obtained from the data archive at the Space Telescope Science Institute. STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.

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.

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.

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.

The effect of postoperative passive motion on rotator cuff healing in a rat model.

Science.gov (United States)

Peltz, Cathryn D; Dourte, Leann M; Kuntz, Andrew F; Sarver, Joseph J; Kim, Soung-Yon; Williams, Gerald R; Soslowsky, Louis J

2009-10-01

Surgical repairs of torn rotator cuff tendons frequently fail. Immobilization has been shown to improve tissue mechanical properties in an animal model of rotator cuff repair, and passive motion has been shown to improve joint mechanics in animal models of flexor tendon repair. Our objective was to determine if daily passive motion would improve joint mechanics in comparison with continuous immobilization in a rat rotator cuff repair model. We hypothesized that daily passive motion would result in improved passive shoulder joint mechanics in comparison with continuous immobilization initially and that there would be no differences in passive joint mechanics or insertion site mechanical properties after four weeks of remobilization. A supraspinatus injury was created and was surgically repaired in sixty-five Sprague-Dawley rats. Rats were separated into three postoperative groups (continuous immobilization, passive motion protocol 1, and passive motion protocol 2) for two weeks before all underwent a remobilization protocol for four weeks. Serial measurements of passive shoulder mechanics (internal and external range of motion and joint stiffness) were made before surgery and at two and six weeks after surgery. After the animals were killed, collagen organization and mechanical properties of the tendon-to-bone insertion site were determined. Total range of motion for both passive motion groups (49% and 45% of the pre-injury values) was less than that for the continuous immobilization group (59% of the pre-injury value) at two weeks and remained significantly less following four weeks of remobilization exercise. Joint stiffness at two weeks was increased for both passive motion groups in comparison with the continuous immobilization group. At both two and six weeks after repair, internal range of motion was significantly decreased whereas external range of motion was not. There were no differences between the groups in terms of collagen organization or mechanical

Computations for nanofluid flow near a stretchable rotating disk with axial magnetic field and convective conditions

Science.gov (United States)

Mushtaq, A.; Mustafa, M.

In this paper, the classical Von Kármán problem of infinite disk is extended when an electrically conducting nanofluid fills the space above the rotating disk which also stretches uniformly in the radial direction. Buongiorno model is considered in order to incorporate the novel Brownian motion and thermophoresis effects. Heat transport mechanism is modeled through more practically feasible convective conditions while Neumann type condition for nanoparticle concentration is adopted. Modified Von Kármán transformations are utilized to obtain self-similar differential system which is treated through a numerical method. Stretching phenomenon yields an additional parameter c which compares the stretch rate with the swirl rate. The effect of parameter c is to reduce the temperature and nanoparticle concentration profiles. Torque required to main steady rotation of the disk increases for increasing values of c while an improvement in cooling rate is anticipated in case of radial stretching, which is important in engineering processes. Brownian diffusion does not influence the heat flux from the stretching wall. Moreover, the wall heat flux has the maximum value for the situation in which thermoporetic force is absent.

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.

Brownian dynamics and dynamic Monte Carlo simulations of isotropic and liquid crystal phases of anisotropic colloidal particles: a comparative study.

Science.gov (United States)

Patti, Alessandro; Cuetos, Alejandro

2012-07-01

We report on the diffusion of purely repulsive and freely rotating colloidal rods in the isotropic, nematic, and smectic liquid crystal phases to probe the agreement between Brownian and Monte Carlo dynamics under the most general conditions. By properly rescaling the Monte Carlo time step, being related to any elementary move via the corresponding self-diffusion coefficient, with the acceptance rate of simultaneous trial displacements and rotations, we demonstrate the existence of a unique Monte Carlo time scale that allows for a direct comparison between Monte Carlo and Brownian dynamics simulations. To estimate the validity of our theoretical approach, we compare the mean square displacement of rods, their orientational autocorrelation function, and the self-intermediate scattering function, as obtained from Brownian dynamics and Monte Carlo simulations. The agreement between the results of these two approaches, even under the condition of heterogeneous dynamics generally observed in liquid crystalline phases, is excellent.

Inversion of ground-motion data from a seismometer array for rotation using a modification of Jaeger's method

Science.gov (United States)

Chi, Wu-Cheng; Lee, W.H.K.; Aston, J.A.D.; Lin, C.J.; Liu, C.-C.

2011-01-01

We develop a new way to invert 2D translational waveforms using Jaeger's (1969) formula to derive rotational ground motions about one axis and estimate the errors in them using techniques from statistical multivariate analysis. This procedure can be used to derive rotational ground motions and strains using arrayed translational data, thus providing an efficient way to calibrate the performance of rotational sensors. This approach does not require a priori information about the noise level of the translational data and elastic properties of the media. This new procedure also provides estimates of the standard deviations of the derived rotations and strains. In this study, we validated this code using synthetic translational waveforms from a seismic array. The results after the inversion of the synthetics for rotations were almost identical with the results derived using a well-tested inversion procedure by Spudich and Fletcher (2009). This new 2D procedure can be applied three times to obtain the full, three-component rotations. Additional modifications can be implemented to the code in the future to study different features of the rotational ground motions and strains induced by the passage of seismic waves.

Self-assembly of robotic micro- and nanoswimmers using magnetic nanoparticles

Energy Technology Data Exchange (ETDEWEB)

Cheang, U. Kei; Kim, Min Jun, E-mail: mkim@coe.drexel.edu [Drexel University, Department of Mechanical Engineering & Mechanics (United States)

2015-03-15

Micro- and nanoscale robotic swimmers are very promising to significantly enhance the performance of particulate drug delivery by providing high accuracy at extremely small scales. Here, we introduce micro- and nanoswimmers fabricated using self-assembly of nanoparticles and control via magnetic fields. Nanoparticles self-align into parallel chains under magnetization. The swimmers exhibit flexibility under a rotating magnetic field resulting in chiral structures upon deformation, thereby having the prerequisite for non-reciprocal motion to move about at low Reynolds number. The swimmers are actuated wirelessly using an external rotating magnetic field supplied by approximate Helmholtz coils. By controlling the concentration of the suspended magnetic nanoparticles, the swimmers can be modulated into different sizes. Nanoscale swimmers are largely influenced by Brownian motion, as observed from their jerky trajectories. The microswimmers, which are roughly three times larger, are less vulnerable to the effects from Brownian motion. In this paper, we demonstrate responsive directional control of micro- and nanoswimmers and compare their respective diffusivities and trajectories to characterize the implications of Brownian disturbance on the motions of small and large swimmers. We then performed a simulation using a kinematic model for the magnetic swimmers including the stochastic nature of Brownian motion.

Self-assembly of robotic micro- and nanoswimmers using magnetic nanoparticles

Science.gov (United States)

Cheang, U. Kei; Kim, Min Jun

2015-03-01

Micro- and nanoscale robotic swimmers are very promising to significantly enhance the performance of particulate drug delivery by providing high accuracy at extremely small scales. Here, we introduce micro- and nanoswimmers fabricated using self-assembly of nanoparticles and control via magnetic fields. Nanoparticles self-align into parallel chains under magnetization. The swimmers exhibit flexibility under a rotating magnetic field resulting in chiral structures upon deformation, thereby having the prerequisite for non-reciprocal motion to move about at low Reynolds number. The swimmers are actuated wirelessly using an external rotating magnetic field supplied by approximate Helmholtz coils. By controlling the concentration of the suspended magnetic nanoparticles, the swimmers can be modulated into different sizes. Nanoscale swimmers are largely influenced by Brownian motion, as observed from their jerky trajectories. The microswimmers, which are roughly three times larger, are less vulnerable to the effects from Brownian motion. In this paper, we demonstrate responsive directional control of micro- and nanoswimmers and compare their respective diffusivities and trajectories to characterize the implications of Brownian disturbance on the motions of small and large swimmers. We then performed a simulation using a kinematic model for the magnetic swimmers including the stochastic nature of Brownian motion.

Self-assembly of robotic micro- and nanoswimmers using magnetic nanoparticles

International Nuclear Information System (INIS)

Cheang, U. Kei; Kim, Min Jun

2015-01-01

Micro- and nanoscale robotic swimmers are very promising to significantly enhance the performance of particulate drug delivery by providing high accuracy at extremely small scales. Here, we introduce micro- and nanoswimmers fabricated using self-assembly of nanoparticles and control via magnetic fields. Nanoparticles self-align into parallel chains under magnetization. The swimmers exhibit flexibility under a rotating magnetic field resulting in chiral structures upon deformation, thereby having the prerequisite for non-reciprocal motion to move about at low Reynolds number. The swimmers are actuated wirelessly using an external rotating magnetic field supplied by approximate Helmholtz coils. By controlling the concentration of the suspended magnetic nanoparticles, the swimmers can be modulated into different sizes. Nanoscale swimmers are largely influenced by Brownian motion, as observed from their jerky trajectories. The microswimmers, which are roughly three times larger, are less vulnerable to the effects from Brownian motion. In this paper, we demonstrate responsive directional control of micro- and nanoswimmers and compare their respective diffusivities and trajectories to characterize the implications of Brownian disturbance on the motions of small and large swimmers. We then performed a simulation using a kinematic model for the magnetic swimmers including the stochastic nature of Brownian motion

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.

Beyond RPA in nuclear rotation and wobbling motion at high spin

International Nuclear Information System (INIS)

Kaneko, Kazunari

1991-01-01

A quantum mechanical method of the nuclear rotation and the wobbling motion at high spin beyond the small-oscillation approximation is represented within the framework of time-dependent mean-field theory with some constraints. The constraints which determine the choice of the rotating reference frame are considered in the spin-orientation frame and the principal-axis frame. The quantization under such constraints is performed by making use of the Dirac bracket. Then the commutation relations of the angular momentum are derived. (orig.)

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.

Nucleation of rotating crystals by Thiovulum majus bacteria

Science.gov (United States)

Petroff, A. P.; Libchaber, A.

2018-01-01

Thiovulum majus self-organize on glass surfaces into active two-dimensional crystals of rotating cells. Unlike classical crystals, these bacterial crystallites continuously rotate and reorganize as the power of rotating cells is dissipated by the surrounding flow. In this article, we describe the earliest stage of crystallization, the attraction of two bacteria into a hydrodynamically-bound dimer. This process occurs in three steps. First a free-swimming cell collides with the wall and becomes hydrodynamically bound to the two-dimensional surface. We present a simple model to understand how viscous forces localize cells near the chamber walls. Next, the cell diffuses over the surface for an average of 63+/- 6 s before escaping to the bulk fluid. The diffusion coefficient {D}{{eff}}=7.98 +/- 0.1 μ {{{m}}}2 {{{s}}}-1 of these 8.5 μ {{m}} diameter cells corresponds to a temperature of (4.16+/- 0.05)× {10}4 K, and thus cannot be explained by equilibrium fluctuations. Finally, two cells coalesce into a rotating dimer when the convergent flow created by each cell overwhelms their active Brownian motion. This occurs when cells diffuse to within a distance of 13.3 ± 0.2 μm of each other.

Cyclic fatigue resistance of RaCe and Mtwo rotary files in continuous rotation and reciprocating motion.

Science.gov (United States)

Vadhana, Sekar; SaravanaKarthikeyan, Balasubramanian; Nandini, Suresh; Velmurugan, Natanasabapathy

2014-07-01

The purpose of this study was to evaluate and compare the cyclic fatigue resistance of RaCe (FKG Dentaire, La Chaux-de-Fonds, Switzerland) and Mtwo (VDW, Munich, Germany) rotary files in continuous rotation and reciprocating motion. A total of 60 new rotary Mtwo and RaCe files (ISO size = 25, taper = 0.06, length = 25 mm) were selected and randomly divided into 4 groups (n = 15 each): Mtc (Mtwo NiTi files in continuous rotation), Rc (RaCe NiTi files in continuous rotation), Mtr (Mtwo NiTi files in reciprocating motion), and Rr (RaCe NiTi files in reciprocating motion). A cyclic fatigue testing device was fabricated with a 60° angle of curvature and a 5-mm radius. All instruments were rotated or reciprocated until fracture occurred. The time taken for each instrument to fracture and the length of the broken fragments were recorded. All the fractured files were analyzed under a scanning electron microscope to detect the mode of fracture. The Kolmogorov-Smirnov test was used to assess the normality of samples distribution, and statistical analysis was performed using the independent sample t test. The time taken for the instruments of the Mtr and Rr groups to fail under cyclic loading was significantly longer compared with the Mtc and Rc groups (P ductile mode of fracture. The length of the fractured segments was between 5 and 6 mm, which was not statistically significant among the experimental groups. Mtwo and RaCe rotary instruments showed a significantly higher cyclic fatigue resistance in reciprocating motion compared with continuous rotation motion. Copyright © 2014 American Association of Endodontists. Published by Elsevier Inc. All rights reserved.

Differential contribution of visual and auditory information to accurately predict the direction and rotational motion of a visual stimulus.

Science.gov (United States)

Park, Seoung Hoon; Kim, Seonjin; Kwon, MinHyuk; Christou, Evangelos A

2016-03-01

Vision and auditory information are critical for perception and to enhance the ability of an individual to respond accurately to a stimulus. However, it is unknown whether visual and auditory information contribute differentially to identify the direction and rotational motion of the stimulus. The purpose of this study was to determine the ability of an individual to accurately predict the direction and rotational motion of the stimulus based on visual and auditory information. In this study, we recruited 9 expert table-tennis players and used table-tennis service as our experimental model. Participants watched recorded services with different levels of visual and auditory information. The goal was to anticipate the direction of the service (left or right) and the rotational motion of service (topspin, sidespin, or cut). We recorded their responses and quantified the following outcomes: (i) directional accuracy and (ii) rotational motion accuracy. The response accuracy was the accurate predictions relative to the total number of trials. The ability of the participants to predict the direction of the service accurately increased with additional visual information but not with auditory information. In contrast, the ability of the participants to predict the rotational motion of the service accurately increased with the addition of auditory information to visual information but not with additional visual information alone. In conclusion, this finding demonstrates that visual information enhances the ability of an individual to accurately predict the direction of the stimulus, whereas additional auditory information enhances the ability of an individual to accurately predict the rotational motion of stimulus.

Observations of Near-Field Rotational Motions from Oklahoma Seismicity using Applied Technology Associate Sensors

Science.gov (United States)

Ringler, A. T.; Anthony, R. E.; Holland, A. A.; Wilson, D. C.

2017-12-01

Characterizing rotational motions from moderate-sized earthquakes in the near-field has the potential to improve earthquake engineering and seismic gradiometry by better characterizing the rotational component of the seismic wavefield, but has remained challenging due to the limited development of portable, low-noise rotational sensors. Here, we test Applied Technology Associate (ATA) Proto-Seismic Magnetohydrodynamic (SMHD) three-component rotational rate sensors at Albuquerque Seismological Laboratory (ASL) for self-noise and sensitivity before deploying them at U.S. Geological Survey (USGS) temporary aftershock station OK38 in Waynoka, Oklahoma. The sensors have low self-noise levels below 2 Hz, making them ideal to record local rotations. From April 11, 2017 to June 6, 2017 we recorded the translational and rotational motions of over 155 earthquakes of ML≥2.0 within 2 degrees of the station. Using the recorded events we compare Peak Ground Velocity (PGV) with Peak Ground Rotation Rate (PG). For example, we measured a maximal PG of 0.00211 radians/s and 0.00186 radians/s for the horizontal components of the two rotational sensors during the Mwr=4.2 event on May 13, 2017 which was 0.5 km from that station. Similarly, our PG for the vertical rotational components were 0.00112 radians/s and 0.00085 radians/s. We also measured Peak Ground Rotations (PGω) as a function of seismic moment, as well as mean vertical Power Spectral Density (PSD) with mean horizontal PSD power levels. We compute apparent phase velocity directly from the rotational data, which may have may improve estimates of local site effects. Finally, by comparing various rotational and translational components we look at potential implications for estimating local event source parameters, which may help in identifying phenomena such as repeating earthquakes by using differences in the rotational components correlation.

Motion Controllers for Learners to Manipulate and Interact with 3D Objects for Mental Rotation Training

Science.gov (United States)

Yeh, Shih-Ching; Wang, Jin-Liang; Wang, Chin-Yeh; Lin, Po-Han; Chen, Gwo-Dong; Rizzo, Albert

2014-01-01

Mental rotation is an important spatial processing ability and an important element in intelligence tests. However, the majority of past attempts at training mental rotation have used paper-and-pencil tests or digital images. This study proposes an innovative mental rotation training approach using magnetic motion controllers to allow learners to…

Rotational motion of an artificial satellite perturbed by solar radiation pressure

International Nuclear Information System (INIS)

Moraes, R.V. de; Zanardi, M.C.

1988-01-01

The motion of a satellite about its center of mass is studied using a semi-analytical method. Torques produced by conservative and non conservative forces are considered. An analytical model is proposed for solar radiation torques. Andoyer variables are used to describe the rotational motion. Analytical equations are used to transform osculating to a mean set of differential equations. Since the mean equations are more slowly varying, a numerical integration using large step size can be performed to obtain the mean state at a later time. (author) [pt

Robotic real-time translational and rotational head motion correction during frameless stereotactic radiosurgery

Energy Technology Data Exchange (ETDEWEB)

Liu, Xinmin; Belcher, Andrew H.; Grelewicz, Zachary; Wiersma, Rodney D., E-mail: rwiersma@uchicago.edu [Department of Radiation and Cellular Oncology, The University of Chicago, Chicago, Illinois 60637 (United States)

2015-06-15

Purpose: To develop a control system to correct both translational and rotational head motion deviations in real-time during frameless stereotactic radiosurgery (SRS). Methods: A novel feedback control with a feed-forward algorithm was utilized to correct for the coupling of translation and rotation present in serial kinematic robotic systems. Input parameters for the algorithm include the real-time 6DOF target position, the frame pitch pivot point to target distance constant, and the translational and angular Linac beam off (gating) tolerance constants for patient safety. Testing of the algorithm was done using a 4D (XY Z + pitch) robotic stage, an infrared head position sensing unit and a control computer. The measured head position signal was processed and a resulting command was sent to the interface of a four-axis motor controller, through which four stepper motors were driven to perform motion compensation. Results: The control of the translation of a brain target was decoupled with the control of the rotation. For a phantom study, the corrected position was within a translational displacement of 0.35 mm and a pitch displacement of 0.15° 100% of the time. For a volunteer study, the corrected position was within displacements of 0.4 mm and 0.2° over 98.5% of the time, while it was 10.7% without correction. Conclusions: The authors report a control design approach for both translational and rotational head motion correction. The experiments demonstrated that control performance of the 4D robotic stage meets the submillimeter and subdegree accuracy required by SRS.

Robotic real-time translational and rotational head motion correction during frameless stereotactic radiosurgery

International Nuclear Information System (INIS)

Liu, Xinmin; Belcher, Andrew H.; Grelewicz, Zachary; Wiersma, Rodney D.

2015-01-01

Purpose: To develop a control system to correct both translational and rotational head motion deviations in real-time during frameless stereotactic radiosurgery (SRS). Methods: A novel feedback control with a feed-forward algorithm was utilized to correct for the coupling of translation and rotation present in serial kinematic robotic systems. Input parameters for the algorithm include the real-time 6DOF target position, the frame pitch pivot point to target distance constant, and the translational and angular Linac beam off (gating) tolerance constants for patient safety. Testing of the algorithm was done using a 4D (XY Z + pitch) robotic stage, an infrared head position sensing unit and a control computer. The measured head position signal was processed and a resulting command was sent to the interface of a four-axis motor controller, through which four stepper motors were driven to perform motion compensation. Results: The control of the translation of a brain target was decoupled with the control of the rotation. For a phantom study, the corrected position was within a translational displacement of 0.35 mm and a pitch displacement of 0.15° 100% of the time. For a volunteer study, the corrected position was within displacements of 0.4 mm and 0.2° over 98.5% of the time, while it was 10.7% without correction. Conclusions: The authors report a control design approach for both translational and rotational head motion correction. The experiments demonstrated that control performance of the 4D robotic stage meets the submillimeter and subdegree accuracy required by SRS

Microbiorobots for Manipulation and Sensing

Science.gov (United States)

2016-04-19

interaction  A net thrust on the microsturcture causing rotational and/or translational movement • Self-actuation of BPM...summary  There are variance on Brownian motion due to measurement noise.  The bacterial carpet generates much stronger flow field than Brownian ...16 μm 22 μm Brownian motion 20 18 16 12 2 10 8 6 4 14 Height (μm) t = 0.00s t = 1.00s t = 2.00s Dalton 2004 0 2 4 6 8 10 12 14 16 18

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...

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.

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...

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

4D rotational x-ray imaging of wrist joint dynamic motion

International Nuclear Information System (INIS)

Carelsen, Bart; Bakker, Niels H.; Strackee, Simon D.; Boon, Sjirk N.; Maas, Mario; Sabczynski, Joerg; Grimbergen, Cornelis A.; Streekstra, Geert J.

2005-01-01

Current methods for imaging joint motion are limited to either two-dimensional (2D) video fluoroscopy, or to animated motions from a series of static three-dimensional (3D) images. 3D movement patterns can be detected from biplane fluoroscopy images matched with computed tomography images. This involves several x-ray modalities and sophisticated 2D to 3D matching for the complex wrist joint. We present a method for the acquisition of dynamic 3D images of a moving joint. In our method a 3D-rotational x-ray (3D-RX) system is used to image a cyclically moving joint. The cyclic motion is synchronized to the x-ray acquisition to yield multiple sets of projection images, which are reconstructed to a series of time resolved 3D images, i.e., four-dimensional rotational x ray (4D-RX). To investigate the obtained image quality parameters the full width at half maximum (FWHM) of the point spread function (PSF) via the edge spread function and the contrast to noise ratio between air and phantom were determined on reconstructions of a bullet and rod phantom, using 4D-RX as well as stationary 3D-RX images. The CNR in volume reconstructions based on 251 projection images in the static situation and on 41 and 34 projection images of a moving phantom were 6.9, 3.0, and 2.9, respectively. The average FWHM of the PSF of these same images was, respectively, 1.1, 1.7, and 2.2 mm orthogonal to the motion and parallel to direction of motion 0.6, 0.7, and 1.0 mm. The main deterioration of 4D-RX images compared to 3D-RX images is due to the low number of projection images used and not to the motion of the object. Using 41 projection images seems the best setting for the current system. Experiments on a postmortem wrist show the feasibility of the method for imaging 3D dynamic joint motion. We expect that 4D-RX will pave the way to improved assessment of joint disorders by detection of 3D dynamic motion patterns in joints

Simultaneous characterization of rotational and translational diffusion of optically anisotropic particles by optical microscopy

International Nuclear Information System (INIS)

Giavazzi, Fabio; Cerbino, Roberto; Haro-Pérez, Catalina

2016-01-01

We probe the roto-translational Brownian motion of optically anisotropic particles suspended in water with a simple and straightforward optical microscopy experiment that does not require positional or rotational particle tracking. We acquire a movie of the suspension placed between two polarizing elements and we extract the translational diffusion coefficient D T and the rotational diffusion coefficient D R from the analysis of the temporal correlation properties of the spatial Fourier modes of the intensity fluctuations in the movie. Our method is successfully tested with a dilute suspension of birefringent spherical colloidal particles obtained by polymerizing an emulsion of droplets of liquid crystal in a nematic phase, whose roto-translational dynamics is found to be well described by theory. The simplicity of our approach makes our method a viable alternative to particle tracking and depolarized dynamic light scattering. (paper)

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.

The unsteady flow of a nanofluid in the stagnation point region of a time-dependent rotating sphere

Directory of Open Access Journals (Sweden)

Malvandi Amir

2015-01-01

Full Text Available This paper deals with the unsteady boundary layer flow and heat transfer of nanofluid over a time-dependent rotating sphere where the free stream velocity varies continuously with time. The boundary layer equations were normalized via similarity variables and solved numerically. Best accuracy of the results has been obtained for regular fluid with previous studies. The nanofluid is treated as a two-component mixture (base fluid+nanoparticles that incorporates the effects of Brownian diffusion and thermophoresis simultaneously as the two most important mechanisms of slip velocity in laminar flows. Our outcomes indicated that as A and λ increase, surface shear stresses, heat transfer and concentration rates, climb up. Also, Increasing the thermophoresis Nt is found to decrease in the both values of heat transfer and concentration rates. This decrease supresses for higher thermophoresis number. In addition, it was observed that unlike the heat transfer rate, a rise in Brownian motion Nb, leads to an increase in concentration rate.

Rotational and Translational Components of Motion Parallax: Observers' Sensitivity and Implications for Three-Dimensional Computer Graphics

Science.gov (United States)

Kaiser, Mary K.; Montegut, Michael J.; Proffitt, Dennis R.

1995-01-01

The motion of objects during motion parallax can be decomposed into 2 observer-relative components: translation and rotation. The depth ratio of objects in the visual field is specified by the inverse ratio of their angular displacement (from translation) or equivalently by the inverse ratio of their rotations. Despite the equal mathematical status of these 2 information sources, it was predicted that observers would be far more sensitive to the translational than rotational component. Such a differential sensitivity is implicitly assumed by the computer graphics technique billboarding, in which 3-dimensional (3-D) objects are drawn as planar forms (i.e., billboards) maintained normal to the line of sight. In 3 experiments, observers were found to be consistently less sensitive to rotational anomalies. The implications of these findings for kinetic depth effect displays and billboarding techniques are discussed.

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

Random forcing of geostrophic motion in rotating stratified turbulence

Science.gov (United States)

Waite, Michael L.

2017-12-01

Random forcing of geostrophic motion is a common approach in idealized simulations of rotating stratified turbulence. Such forcing represents the injection of energy into large-scale balanced motion, and the resulting breakdown of quasi-geostrophic turbulence into inertia-gravity waves and stratified turbulence can shed light on the turbulent cascade processes of the atmospheric mesoscale. White noise forcing is commonly employed, which excites all frequencies equally, including frequencies much higher than the natural frequencies of large-scale vortices. In this paper, the effects of these high frequencies in the forcing are investigated. Geostrophic motion is randomly forced with red noise over a range of decorrelation time scales τ, from a few time steps to twice the large-scale vortex time scale. It is found that short τ (i.e., nearly white noise) results in about 46% more gravity wave energy than longer τ, despite the fact that waves are not directly forced. We argue that this effect is due to wave-vortex interactions, through which the high frequencies in the forcing are able to excite waves at their natural frequencies. It is concluded that white noise forcing should be avoided, even if it is only applied to the geostrophic motion, when a careful investigation of spontaneous wave generation is needed.

Effects of asymptomatic rotator cuff pathology on in vivo shoulder motion and clinical outcomes.

Science.gov (United States)

Baumer, Timothy G; Dischler, Jack; Mende, Veronica; Zauel, Roger; van Holsbeeck, Marnix; Siegal, Daniel S; Divine, George; Moutzouros, Vasilios; Bey, Michael J

2017-06-01

The incidence of asymptomatic rotator cuff tears has been reported to range from 15% to 39%, but the influence of asymptomatic rotator cuff pathology on shoulder function is not well understood. This study assessed the effects of asymptomatic rotator cuff pathology on shoulder kinematics, strength, and patient-reported outcomes. A clinical ultrasound examination was performed in 46 asymptomatic volunteers (age: 60.3 ± 7.5 years) with normal shoulder function to document the condition of their rotator cuff. The ultrasound imaging identified the participants as healthy (n = 14) or pathologic (n = 32). Shoulder motion was measured with a biplane x-ray imaging system, strength was assessed with a Biodex (Biodex Medical Systems, Inc., Shirley, NY, USA), and patient-reported outcomes were assessed using the Western Ontario Rotator Cuff Index and visual analog scale pain scores. Compared with healthy volunteers, those with rotator cuff pathology had significantly less abduction (P = .050) and elevation (P = .041) strength, their humerus was positioned more inferiorly on the glenoid (P = .018), and the glenohumeral contact path length was longer (P = .007). No significant differences were detected in the Western Ontario Rotator Cuff Index, visual analog scale, range of motion, or acromiohumeral distance. The differences observed between the healthy volunteers and those with asymptomatic rotator cuff pathology lend insight into the changes in joint mechanics, shoulder strength, and conventional clinical outcomes associated with the early stages of rotator cuff pathology. Furthermore, these findings suggest a plausible mechanical progression of kinematic and strength changes associated with the development of rotator cuff pathology. Copyright © 2016 Journal of Shoulder and Elbow Surgery Board of Trustees. Published by Elsevier Inc. All rights reserved.

Prosthesis alignment affects axial rotation motion after total knee replacement: a prospective in vivo study combining computed tomography and fluoroscopic evaluations

Directory of Open Access Journals (Sweden)

Harman Melinda K

2012-10-01

Full Text Available Abstract Background Clinical consequences of alignment errors in total knee replacement (TKR have led to the rigorous evaluation of surgical alignment techniques. Rotational alignment in the transverse plane has proven particularly problematic, with errors due to component malalignment relative to bone anatomic landmarks and an overall mismatch between the femoral and tibial components’ relative positions. Ranges of nominal rotational alignment are not well defined, especially for the tibial component and for relative rotational mismatch, and some studies advocate the use of mobile-bearing TKR to accommodate the resulting small rotation errors. However, the relationships between prosthesis rotational alignment and mobile-bearing polyethylene insert motion are poorly understood. This prospective, in vivo study evaluates whether component malalignment and mismatch affect axial rotation motions during passive knee flexion after TKR. Methods Eighty patients were implanted with mobile-bearing TKR. Rotational alignment of the femoral and tibial components was measured from postoperative CT scans. All TKR were categorized into nominal or outlier groups based on defined norms for surgical rotational alignment relative to bone anatomic landmarks and relative rotational mismatch between the femoral and tibial components. Axial rotation motion of the femoral, tibial and polyethylene bearing components was measured from fluoroscopic images acquired during passive knee flexion. Results Axial rotation motion was generally accomplished in two phases, dominated by polyethylene bearing rotation on the tibial component in early to mid-flexion and then femoral component rotation on the polyethylene articular surface in later flexion. Opposite rotations of the femur-bearing and bearing-baseplate articulations were evident at flexion greater than 80°. Knees with outlier alignment had lower magnitudes of axial rotation and distinct transitions from external to

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...

CHAOTIC MOTION OF CHARGED PARTICLES IN AN ELECTROMAGNETIC FIELD SURROUNDING A ROTATING BLACK HOLE

International Nuclear Information System (INIS)

Takahashi, Masaaki; Koyama, Hiroko

2009-01-01

The observational data from some black hole candidates suggest the importance of electromagnetic fields in the vicinity of a black hole. Highly magnetized disk accretion may play an importance rule, and large-scale magnetic field may be formed above the disk surface. Then, we expect that the nature of the black hole spacetime would be revealed by magnetic phenomena near the black hole. We will start investigating the motion of a charged test particle which depends on the initial parameter setting in the black hole dipole magnetic field, which is a test field on the Kerr spacetime. Particularly, we study the spin effects of a rotating black hole on the motion of the charged test particle trapped in magnetic field lines. We make detailed analysis for the particle's trajectories by using the Poincare map method, and show the chaotic properties that depend on the black hole spin. We find that the dragging effects of the spacetime by a rotating black hole weaken the chaotic properties and generate regular trajectories for some sets of initial parameters, while the chaotic properties dominate on the trajectories for slowly rotating black hole cases. The dragging effects can generate the fourth adiabatic invariant on the particle motion approximately.

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.

High-resolution simulations of unstable cylindrical gravity currents undergoing wandering and splitting motions in a rotating system

Science.gov (United States)

Dai, Albert; Wu, Ching-Sen

2018-02-01

High-resolution simulations of unstable cylindrical gravity currents when wandering and splitting motions occur in a rotating system are reported. In this study, our attention is focused on the situation of unstable rotating cylindrical gravity currents when the ratio of Coriolis to inertia forces is larger, namely, 0.5 ≤ C ≤ 2.0, in comparison to the stable ones when C ≤ 0.3 as investigated previously by the authors. The simulations reproduce the major features of the unstable rotating cylindrical gravity currents observed in the laboratory, i.e., vortex-wandering or vortex-splitting following the contraction-relaxation motion, and good agreement is found when compared with the experimental results on the outrush radius of the advancing front and on the number of bulges. Furthermore, the simulations provide energy budget information which could not be attained in the laboratory. After the heavy fluid is released, the heavy fluid collapses and a contraction-relaxation motion is at work for approximately 2-3 revolutions of the system. During the contraction-relaxation motion of the heavy fluid, the unstable rotating cylindrical gravity currents behave similar to the stable ones. Towards the end of the contraction-relaxation motion, the dissipation rate in the system reaches a local minimum and a quasi-geostrophic equilibrium state is reached. After the quasi-geostrophic equilibrium state, vortex-wandering or vortex-splitting may occur depending on the ratio of Coriolis to inertia forces. The vortex-splitting process begins with non-axisymmetric bulges and, as the bulges grow, the kinetic energy increases at the expense of decreasing potential energy in the system. The completion of vortex-splitting is accompanied by a local maximum of dissipation rate and a local maximum of kinetic energy in the system. A striking feature of the unstable rotating cylindrical gravity currents is the persistent upwelling and downwelling motions, which are observed for both the

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.

Pros and cons of rotating ground motion records to fault-normal/parallel directions for response history analysis of buildings

Science.gov (United States)

Kalkan, Erol; Kwong, Neal S.

2014-01-01

According to the regulatory building codes in the United States (e.g., 2010 California Building Code), at least two horizontal ground motion components are required for three-dimensional (3D) response history analysis (RHA) of building structures. For sites within 5 km of an active fault, these records should be rotated to fault-normal/fault-parallel (FN/FP) directions, and two RHAs should be performed separately (when FN and then FP are aligned with the transverse direction of the structural axes). It is assumed that this approach will lead to two sets of responses that envelope the range of possible responses over all nonredundant rotation angles. This assumption is examined here, for the first time, using a 3D computer model of a six-story reinforced-concrete instrumented building subjected to an ensemble of bidirectional near-fault ground motions. Peak values of engineering demand parameters (EDPs) were computed for rotation angles ranging from 0 through 180° to quantify the difference between peak values of EDPs over all rotation angles and those due to FN/FP direction rotated motions. It is demonstrated that rotating ground motions to FN/FP directions (1) does not always lead to the maximum responses over all angles, (2) does not always envelope the range of possible responses, and (3) does not provide maximum responses for all EDPs simultaneously even if it provides a maximum response for a specific EDP.

Motion of a Rigid Body Supported at One Point by a Rotating Arm

Directory of Open Access Journals (Sweden)

Jeffrey D. Stoen

1993-01-01

Full Text Available This article details a scheme for evaluating the stability of motions of a system consisting of a rigid body connected at one point to a rotating arm. The nonlinear equations of motion for the system are formulated, and a method for finding exact solutions representing motions that resemble a state of rest is presented. The equations are then linearized and roots of the eigensystem are classified and used to construct stability diagrams that facilitate the assessment of effects of varying the body's mass properties and system geometry, changing the position of the attachment joint, and adding energy dissipation in the joint.

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.

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

Directory of Open Access Journals (Sweden)

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.

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.

Velocity-dependent changes of rotational axes in the non-visual control of unconstrained 3D arm motions.

Science.gov (United States)

Isableu, B; Rezzoug, N; Mallet, G; Bernardin, D; Gorce, P; Pagano, C C

2009-12-29

We examined the roles of inertial (e(3)), shoulder-centre of mass (SH-CM) and shoulder-elbow articular (SH-EL) rotation axes in the non-visual control of unconstrained 3D arm rotations. Subjects rotated the arm in elbow configurations that yielded either a constant or variable separation between these axes. We hypothesized that increasing the motion frequency and the task complexity would result in the limbs' rotational axis to correspond to e(3) in order to minimize rotational resistances. Results showed two velocity-dependent profiles wherein the rotation axis coincided with the SH-EL axis for S and I velocities and then in the F velocity shifted to either a SH-CM/e(3) trade-off axis for one profile, or to no preferential axis for the other. A third profile was velocity-independent, with the SH-CM/e(3) trade-off axis being adopted. Our results are the first to provide evidence that the rotational axis of a multi-articulated limb may change from a geometrical axis of rotation to a mass or inertia based axis as motion frequency increases. These findings are discussed within the framework of the minimum inertia tensor model (MIT), which shows that rotations about e(3) reduce the amount of joint muscle torque that must be produced by employing the interaction torque to assist movement.

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.

Three-dimensional organization of vestibular related eye movements to rotational motion in pigeons

Science.gov (United States)

Dickman, J. D.; Beyer, M.; Hess, B. J.

2000-01-01

During rotational motions, compensatory eye movement adjustments must continually occur in order to maintain objects of visual interest as stable images on the retina. In the present study, the three-dimensional organization of the vestibulo-ocular reflex in pigeons was quantitatively examined. Rotations about different head axes produced horizontal, vertical, and torsional eye movements, whose component magnitude was dependent upon the cosine of the stimulus axis relative to the animal's visual axis. Thus, the three-dimensional organization of the VOR in pigeons appears to be compensatory for any direction of head rotation. Frequency responses of the horizontal, vertical, and torsional slow phase components exhibited high pass filter properties with dominant time constants of approximately 3 s.

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

Rotational motions from the 2016, Central Italy seismic sequence, as observed by an underground ring laser gyroscope

Science.gov (United States)

Simonelli, A.; Igel, H.; Wassermann, J.; Belfi, J.; Di Virgilio, A.; Beverini, N.; De Luca, G.; Saccorotti, G.

2018-05-01

We present the analysis of rotational and translational ground motions from earthquakes recorded during October/November, 2016, in association with the Central Italy seismic-sequence. We use co-located measurements of the vertical ground rotation rate from a large ring laser gyroscope (RLG), and the three components of ground velocity from a broadband seismometer. Both instruments are positioned in a deep underground environment, within the Gran Sasso National Laboratories (LNGS) of the Istituto Nazionale di Fisica Nucleare (INFN). We collected dozens of events spanning the 3.5-5.9 Magnitude range, and epicentral distances between 30 km and 70 km. This data set constitutes an unprecedented observation of the vertical rotational motions associated with an intense seismic sequence at local distance. Under the plane wave approximation we process the data set in order to get an experimental estimation of the events back azimuth. Peak values of rotation rate (PRR) and horizontal acceleration (PGA) are markedly correlated, according to a scaling constant which is consistent with previous measurements from different earthquake sequences. We used a prediction model in use for Italy to calculate the expected PGA at the recording site, obtaining consequently predictions for PRR. Within the modeling uncertainties, predicted rotations are consistent with the observed ones, suggesting the possibility of establishing specific attenuation models for ground rotations, like the scaling of peak velocity and peak acceleration in empirical ground-motion prediction relationships. In a second step, after identifying the direction of the incoming wave-field, we extract phase velocity data using the spectral ratio of the translational and rotational components.. This analysis is performed over time windows associated with the P-coda, S-coda and Lg phase. Results are consistent with independent estimates of shear-wave velocities in the shallow crust of the Central Apennines.

Reconstructing plate-motion changes in the presence of finite-rotations noise.

Science.gov (United States)

Iaffaldano, Giampiero; Bodin, Thomas; Sambridge, Malcolm

2012-01-01

Understanding lithospheric plate motions is of paramount importance to geodynamicists. Much effort is going into kinematic reconstructions featuring progressively finer temporal resolution. However, the challenge of precisely identifying ocean-floor magnetic lineations, and uncertainties in geomagnetic reversal timescales result in substantial finite-rotations noise. Unless some type of temporal smoothing is applied, the scenario arising at the native temporal resolution is puzzling, as plate motions vary erratically and significantly over short periods (<1 Myr). This undermines our ability to make geodynamic inferences, as the rates at which forces need to be built upon plates to explain these kinematics far exceed the most optimistic estimates. Here we show that the largest kinematic changes reconstructed across the Atlantic, Indian and South Pacific ridges arise from data noise. We overcome this limitation using a trans-dimensional hierarchical Bayesian framework. We find that plate-motion changes occur on timescales no shorter than a few million years, yielding simpler kinematic patterns and more plausible dynamics.

Shoulder Dynamic Control Ratio and Rotation Range of Motion in Female Junior Elite Handball Players and Controls.

Science.gov (United States)

van Cingel, Robert; Habets, Bas; Willemsen, Linn; Staal, Bart

2018-03-01

To compare glenohumeral range of motion and shoulder rotator muscle strength in healthy female junior elite handball players and controls. Cross-sectional case-control study. Sports medical center. Forty elite female handball players and 30 controls active in nonoverhead sports participated in this study. Passive external rotator (ER), internal rotator (IR), and total range of motion (TROM) of the dominant and nondominant arm were examined with a goniometer. An isokinetic dynamometer was used to evaluate concentric and eccentric rotator muscle strength at 60 and 120 degrees/s with dynamic control ratio (DCR = ERecc:IRcon) as the main outcome parameter. Except for the ER range of motion in the nondominant arm, no significant differences were found between groups for IR, ER of the dominant arm, and the TROM. Within the handball group, the side-to-side difference for IR of the dominant arm was -1.4 degrees. The ER and the TROM of the dominant arm were significantly larger, 6.3 and 4.9 degrees, respectively. For both groups, the DCR values were above 1 and no significant differences were found between the dominant and nondominant arm. The DCR values in the handball group were significantly lower than in the control group. Based on the adopted definitions for muscle imbalance, glenohumeral internal range of motion deficit and TROM deficit our elite female handball players seem not at risk for shoulder injuries. Prospective studies are needed to support the belief that a DCR below 1 places the shoulder at risk for injury.

Improved finite-source inversion through joint measurements of rotational and translational ground motions: a numerical study

Science.gov (United States)

Reinwald, Michael; Bernauer, Moritz; Igel, Heiner; Donner, Stefanie

2016-10-01

With the prospects of seismic equipment being able to measure rotational ground motions in a wide frequency and amplitude range in the near future, we engage in the question of how this type of ground motion observation can be used to solve the seismic source inverse problem. In this paper, we focus on the question of whether finite-source inversion can benefit from additional observations of rotational motion. Keeping the overall number of traces constant, we compare observations from a surface seismic network with 44 three-component translational sensors (classic seismometers) with those obtained with 22 six-component sensors (with additional three-component rotational motions). Synthetic seismograms are calculated for known finite-source properties. The corresponding inverse problem is posed in a probabilistic way using the Shannon information content to measure how the observations constrain the seismic source properties. We minimize the influence of the source receiver geometry around the fault by statistically analyzing six-component inversions with a random distribution of receivers. Since our previous results are achieved with a regular spacing of the receivers, we try to answer the question of whether the results are dependent on the spatial distribution of the receivers. The results show that with the six-component subnetworks, kinematic source inversions for source properties (such as rupture velocity, rise time, and slip amplitudes) are not only equally successful (even that would be beneficial because of the substantially reduced logistics installing half the sensors) but also statistically inversions for some source properties are almost always improved. This can be attributed to the fact that the (in particular vertical) gradient information is contained in the additional motion components. We compare these effects for strike-slip and normal-faulting type sources and confirm that the increase in inversion quality for kinematic source parameters is

Vibrational motions in rotating nuclei studied by Coulomb excitations

Energy Technology Data Exchange (ETDEWEB)

Shimizu, Yoshifumi R [Kyushu Univ., Fukuoka (Japan). Dept. of Physics

1998-03-01

As is well-known Coulomb excitation is an excellent tool to study the nuclear collective motions. Especially the vibrational excitations in rotating nuclei, which are rather difficult to access by usual heavy-ion fusion reactions, can be investigated in detail. Combined with the famous 8{pi}-Spectrometer, which was one of the best {gamma}-ray detector and had discovered some of superdeformed bands, such Coulomb excitation experiments had been carried out at Chalk River laboratory just before it`s shutdown of physics division. In this meeting some of the experimental data are presented and compared with the results of theoretical investigations. (author)

Proteins as micro viscosimeters: Brownian motion revisited.

NARCIS (Netherlands)

Lavalette, D.; Hink, M.A.; Torbez, M.; Tetreau, C.; Visser, A.J.W.G.

2006-01-01

Translational and rotational diffusion coefficients of proteins in solution strongly deviate from the Stokes-Einstein laws when the ambient viscosity is induced by macromolecular co-solutes rather than by a solvent of negligible size as was assumed by A. Einstein one century ago for deriving the

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.

Relationship between massive chronic rotator cuff tear pattern and loss of active shoulder range of motion.

Science.gov (United States)

Collin, Philippe; Matsumura, Noboru; Lädermann, Alexandre; Denard, Patrick J; Walch, Gilles

2014-08-01

Management of massive chronic rotator cuff tears remains controversial, with no clearly defined clinical presentation as yet. The purpose of the study was to evaluate the effect of tear size and location on active motion in patients with chronic and massive rotator cuff tears with severe muscle degeneration. One hundred patients with massive rotator cuff tears accompanied by muscle fatty infiltration beyond Goutallier stage 3 were prospectively included in this study. All patients were divided into 5 groups on the basis of tear pattern (supraspinatus, superior subscapularis, inferior subscapularis, infraspinatus, and teres minor). Active range of shoulder motion was assessed in each group and differences were analyzed. Active elevation was significantly decreased in patients with 3 tear patterns involved. Pseudoparalysis was found in 80% of the cases with supraspinatus and complete subscapularis tears and in 45% of the cases with tears involving the supraspinatus, infraspinatus, and superior subscapularis. Loss of active external rotation was related to tears involving the infraspinatus and teres minor; loss of active internal rotation was related to tears of the subscapularis. This study revealed that dysfunction of the entire subscapularis and supraspinatus or 3 rotator cuff muscles is a risk factor for pseudoparalysis. For function to be preserved in patients with massive chronic rotator cuff tears, it may be important to avoid fatty infiltration with anterior extension into the lower subscapularis or involvement of more than 2 rotator cuff muscles. Copyright © 2014 Journal of Shoulder and Elbow Surgery Board of Trustees. Published by Mosby, Inc. All rights reserved.

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.

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)

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...

Optimisation of NMR dynamic models II. A new methodology for the dual optimisation of the model-free parameters and the Brownian rotational diffusion tensor

International Nuclear Information System (INIS)

D'Auvergne, Edward J.; Gooley, Paul R.

2008-01-01

Finding the dynamics of an entire macromolecule is a complex problem as the model-free parameter values are intricately linked to the Brownian rotational diffusion of the molecule, mathematically through the autocorrelation function of the motion and statistically through model selection. The solution to this problem was formulated using set theory as an element of the universal set U-the union of all model-free spaces (d'Auvergne EJ and Gooley PR (2007) Mol BioSyst 3(7), 483-494). The current procedure commonly used to find the universal solution is to initially estimate the diffusion tensor parameters, to optimise the model-free parameters of numerous models, and then to choose the best model via model selection. The global model is then optimised and the procedure repeated until convergence. In this paper a new methodology is presented which takes a different approach to this diffusion seeded model-free paradigm. Rather than starting with the diffusion tensor this iterative protocol begins by optimising the model-free parameters in the absence of any global model parameters, selecting between all the model-free models, and finally optimising the diffusion tensor. The new model-free optimisation protocol will be validated using synthetic data from Schurr JM et al. (1994) J Magn Reson B 105(3), 211-224 and the relaxation data of the bacteriorhodopsin (1-36)BR fragment from Orekhov VY (1999) J Biomol NMR 14(4), 345-356. To demonstrate the importance of this new procedure the NMR relaxation data of the Olfactory Marker Protein (OMP) of Gitti R et al. (2005) Biochem 44(28), 9673-9679 is reanalysed. The result is that the dynamics for certain secondary structural elements is very different from those originally reported

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.)

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.

Atoms

International Nuclear Information System (INIS)

Fuchs, Alain; Villani, Cedric; Guthleben, Denis; Leduc, Michele; Brenner, Anastasios; Pouthas, Joel; Perrin, Jean

2014-01-01

Completed by recent contributions on various topics (atoms and the Brownian motion, the career of Jean Perrin, the evolution of atomic physics since Jean Perrin, relationship between scientific atomism and philosophical atomism), this book is a reprint of a book published at the beginning of the twentieth century in which the author addressed the relationship between atomic theory and chemistry (molecules, atoms, the Avogadro hypothesis, molecule structures, solutes, upper limits of molecular quantities), molecular agitation (molecule velocity, molecule rotation or vibration, molecular free range), the Brownian motion and emulsions (history and general features, statistical equilibrium of emulsions), the laws of the Brownian motion (Einstein's theory, experimental control), fluctuations (the theory of Smoluchowski), light and quanta (black body, extension of quantum theory), the electricity atom, the atom genesis and destruction (transmutations, atom counting)

Event-based motion correction for PET transmission measurements with a rotating point source

International Nuclear Information System (INIS)

Zhou, Victor W; Kyme, Andre Z; Meikle, Steven R; Fulton, Roger

2011-01-01

Accurate attenuation correction is important for quantitative positron emission tomography (PET) studies. When performing transmission measurements using an external rotating radioactive source, object motion during the transmission scan can distort the attenuation correction factors computed as the ratio of the blank to transmission counts, and cause errors and artefacts in reconstructed PET images. In this paper we report a compensation method for rigid body motion during PET transmission measurements, in which list mode transmission data are motion corrected event-by-event, based on known motion, to ensure that all events which traverse the same path through the object are recorded on a common line of response (LOR). As a result, the motion-corrected transmission LOR may record a combination of events originally detected on different LORs. To ensure that the corresponding blank LOR records events from the same combination of contributing LORs, the list mode blank data are spatially transformed event-by-event based on the same motion information. The number of counts recorded on the resulting blank LOR is then equivalent to the number of counts that would have been recorded on the corresponding motion-corrected transmission LOR in the absence of any attenuating object. The proposed method has been verified in phantom studies with both stepwise movements and continuous motion. We found that attenuation maps derived from motion-corrected transmission and blank data agree well with those of the stationary phantom and are significantly better than uncorrected attenuation data.

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

Rotation sequence to report humerothoracic kinematics during 3D motion involving large horizontal component: application to the tennis forehand drive.

Science.gov (United States)

Creveaux, Thomas; Sevrez, Violaine; Dumas, Raphaël; Chèze, Laurence; Rogowski, Isabelle

2018-03-01

The aim of this study was to examine the respective aptitudes of three rotation sequences (Y t X f 'Y h '', Z t X f 'Y h '', and X t Z f 'Y h '') to effectively describe the orientation of the humerus relative to the thorax during a movement involving a large horizontal abduction/adduction component: the tennis forehand drive. An optoelectronic system was used to record the movements of eight elite male players, each performing ten forehand drives. The occurrences of gimbal lock, phase angle discontinuity and incoherency in the time course of the three angles defining humerothoracic rotation were examined for each rotation sequence. Our results demonstrated that no single sequence effectively describes humerothoracic motion without discontinuities throughout the forehand motion. The humerothoracic joint angles can nevertheless be described without singularities when considering the backswing/forward-swing and the follow-through phases separately. Our findings stress that the sequence choice may have implications for the report and interpretation of 3D joint kinematics during large shoulder range of motion. Consequently, the use of Euler/Cardan angles to represent 3D orientation of the humerothoracic joint in sport tasks requires the evaluation of the rotation sequence regarding singularity occurrence before analysing the kinematic data, especially when the task involves a large shoulder range of motion in the horizontal plane.

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

On connection of rotation and internal motion in deformed nuclei

International Nuclear Information System (INIS)

Krutov, V.A.

1979-01-01

In the semiphenomenological nuclear madel (SPNM) the problem of ''overestimate of Coriolis interaction'' is shown to be easily solved. The rotation and internal motion coupling operator H(rot/in) is used. Overdetermination of the operator H(rot/in) has been generalized and extended into schemes of strong and weak coupling. In this case both schemes of coupling are transformed from approximate into precise ones and become applicable for any nuclear deformation. As examples of application of the theory considered are the matrix elements of the E2-transitions and inertia parameters of a 235 U nucleus

Modeling direction discrimination thresholds for yaw rotations around an earth-vertical axis for arbitrary motion profiles.

Science.gov (United States)

Soyka, Florian; Giordano, Paolo Robuffo; Barnett-Cowan, Michael; Bülthoff, Heinrich H

2012-07-01

Understanding the dynamics of vestibular perception is important, for example, for improving the realism of motion simulation and virtual reality environments or for diagnosing patients suffering from vestibular problems. Previous research has found a dependence of direction discrimination thresholds for rotational motions on the period length (inverse frequency) of a transient (single cycle) sinusoidal acceleration stimulus. However, self-motion is seldom purely sinusoidal, and up to now, no models have been proposed that take into account non-sinusoidal stimuli for rotational motions. In this work, the influence of both the period length and the specific time course of an inertial stimulus is investigated. Thresholds for three acceleration profile shapes (triangular, sinusoidal, and trapezoidal) were measured for three period lengths (0.3, 1.4, and 6.7 s) in ten participants. A two-alternative forced-choice discrimination task was used where participants had to judge if a yaw rotation around an earth-vertical axis was leftward or rightward. The peak velocity of the stimulus was varied, and the threshold was defined as the stimulus yielding 75 % correct answers. In accordance with previous research, thresholds decreased with shortening period length (from ~2 deg/s for 6.7 s to ~0.8 deg/s for 0.3 s). The peak velocity was the determining factor for discrimination: Different profiles with the same period length have similar velocity thresholds. These measurements were used to fit a novel model based on a description of the firing rate of semi-circular canal neurons. In accordance with previous research, the estimates of the model parameters suggest that velocity storage does not influence perceptual thresholds.

CHROMOSPHERIC MASS MOTIONS AND INTRINSIC SUNSPOT ROTATIONS FOR NOAA ACTIVE REGIONS 10484, 10486, AND 10488 USING ISOON DATA

International Nuclear Information System (INIS)

Hardersen, Paul S.; Balasubramaniam, K. S.; Shkolyar, Svetlana

2013-01-01

This work utilizes Improved Solar Observing Optical Network continuum (630.2 nm) and Hα (656.2 nm) data to: (1) detect and measure intrinsic sunspot rotations occurring in the photosphere and chromosphere, (2) identify and measure chromospheric filament mass motions, and (3) assess any large-scale photospheric and chromospheric mass couplings. Significant results from 2003 October 27-29, using the techniques of Brown et al., indicate significant counter-rotation between the two large sunspots in NOAA AR 10486 on October 29, as well as discrete filament mass motions in NOAA AR 10484 on October 27 that appear to be associated with at least one C-class solar flare

Rotating Wavepackets

Science.gov (United States)

Lekner, John

2008-01-01

Any free-particle wavepacket solution of Schrodinger's equation can be converted by differentiations to wavepackets rotating about the original direction of motion. The angular momentum component along the motion associated with this rotation is an integral multiple of [h-bar]. It is an "intrinsic" angular momentum: independent of origin and…

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.

On the application of the theory of the translational Brownian movement to the calculation of the differential cross-sections for the incoherent scattering of slow neutrons

International Nuclear Information System (INIS)

Coffey, W.T.

1978-01-01

It is shown how three models (based on the theory of the Brownian movement) for the translational motion of an atom in a fluid may be used to calculate explicitly the intermediate scattering functions and differential cross-sections for the incoherent scattering of slow neutrons. In the first model the translational motion of the atom is represented by the motion of a particle in space subjected to no forces other than those arising from the thermal motion of its surroundings. The differential scattering cross-section for this model is then obtained as a continued fraction similar to that given by Sack (Proc. Phys. Soc.; B70:402 and 414 (1957)) for the electric polarisability in his investigation of the role of inertial effects in dielectric relaxation. The second model is a corrected version of the itinerant oscillator model of Sears (Proc. Phys. Soc.; 86:953 (1965)). Here the differential cross-section is obtained in the form of a series and a closed-form expression is found for the intermediate scattering function. The last model to be considered is the harmonically bound particle where again a closed form expression is obtained for the intermediate scattering function. In each case the intermediate scattering function has a mathematical form which is similar to the after-effect function describing the decay of electric polarisation for the rotational versions of the models. (author)

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

Shoulder-Rotator Strength, Range of Motion, and Acromiohumeral Distance in Asymptomatic Adolescent Volleyball Attackers.

Science.gov (United States)

Harput, Gulcan; Guney, Hande; Toprak, Ugur; Kaya, Tunca; Colakoglu, Fatma Filiz; Baltaci, Gul

2016-09-01

Sport-specific adaptations at the glenohumeral joint could occur in adolescent athletes because they start participating in high-performance sports in early childhood. To investigate shoulder-rotator strength, internal-rotation (IR) and external-rotation (ER) range of motion (ROM), and acromiohumeral distance (AHD) in asymptomatic adolescent volleyball attackers to determine if they have risk factors for injury. Cross-sectional study. University laboratory. Thirty-nine adolescent high school-aged volleyball attackers (22 boys, 17 girls; age = 16.0 ± 1.4 years, height = 179.2 ± 9.0 cm, mass = 67.1 ± 10.9 kg, body mass index = 20.7 ± 2.6 kg/m 2 ). Shoulder IR and ER ROM, total-rotation ROM, glenohumeral IR deficit, AHD, and concentric and eccentric strength of the shoulder internal and external rotators were tested bilaterally. External-rotation ROM was greater (t 38 = 4.92, P 18°). We observed greater concentric internal-rotator (t 38 = 2.89, P = .006) and eccentric external-rotator (t 38 = 2.65, P = .01) strength in the dominant than in the nondominant shoulder. The AHD was less in the dominant shoulder (t 38 = -3.60, P volleyball attackers demonstrated decreased IR ROM, total ROM, and AHD and increased ER ROM in their dominant shoulder. Therefore, routine screening of adolescent athletes and designing training programs for hazardous adaptive changes could be important in preventing shoulder injuries.

Assessment of shoulder external rotation range-of-motion on throwing athletes: the effects of testing end-range determination (active versus passive).

Science.gov (United States)

Ribeiro, A; Pascoal, A

2015-07-01

The purpose of this study was to compare the effects of active or passive end-range determination (supine position) for external rotation range of motion (ROM) in overhead throwing athletes and verify if athletes' ROM is similar to non-athletes. Kinematic data from the dominant shoulder of 24 healthy male subjects, divided into two groups (12 athletes and 12 non-athletes) were recorded at end-range external rotation, thoracohumeral and glenohumeral external rotation angles were compared and a 2-way repeated-measures ANOVA was used to calculate the effects of end-range determination (passive versus active) across groups (athlete and non-athlete). A significant main effect (p external end-range angles was observed while the highest end-range determination values were associated with passive motion. No differences were observed between the athletic or non-athletic groups for either thoracohumeral (p = 0.784) or glenohumeral (p = 0.364) motion.

THE CONTRACTION OF OVERLYING CORONAL LOOP AND THE ROTATING MOTION OF A SIGMOID FILAMENT DURING ITS ERUPTION

Energy Technology Data Exchange (ETDEWEB)

Yan, X. L.; Qu, Z. Q.; Xue, Z. K.; Deng, L. H.; Ma, L.; Kong, D. F. [National Astronomical Observatories/Yunnan Astronomical Observatory, Chinese Academy of Sciences, Kunming 650011 (China); Pan, G. M. [College of Mathematics Physics and Information Engineering, Jiaxing University, Jiaxing 314001 (China); Liu, J. H. [Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012 (China)

2013-06-15

We present an observation of overlying coronal loop contraction and rotating motion of the sigmoid filament during its eruption on 2012 May 22 observed by the Solar Dynamics Observatory (SDO). Our results show that the twist can be transported into the filament from the lower atmosphere to the higher atmosphere. The successive contraction of the coronal loops was due to a suddenly reduced magnetic pressure underneath the filament, which was caused by the rising of the filament. Before the sigmoid filament eruption, there was a counterclockwise flow in the photosphere at the right feet of the filament and the contraction loops and a convergence flow at the left foot of the filament. The hot and cool materials have inverse motion along the filament before the filament eruption. Moreover, two coronal loops overlying the filament first experienced brightening, expansion, and contraction successively. At the beginning of the rising and rotation of the left part of the filament, the second coronal loop exhibited rapid contraction. The top of the second coronal loop also showed counterclockwise rotation during the contraction process. After the contraction of the second loop, the left part of the filament rotated counterclockwise and expanded toward the right of NOAA AR 11485. During the filament expansion, the right part of the filament also exhibited counterclockwise rotation like a tornado.

Collective circular motion in synchronized and balanced formations with second-order rotational dynamics

Science.gov (United States)

Jain, Anoop; Ghose, Debasish

2018-01-01

This paper considers collective circular motion of multi-agent systems in which all the agents are required to traverse different circles or a common circle at a prescribed angular velocity. It is required to achieve these collective motions with the heading angles of the agents synchronized or balanced. In synchronization, the agents and their centroid have a common velocity direction, while in balancing, the movement of agents causes the location of the centroid to become stationary. The agents are initially considered to move at unit speed around individual circles at different angular velocities. It is assumed that the agents are subjected to limited communication constraints, and exchange relative information according to a time-invariant undirected graph. We present suitable feedback control laws for each of these motion coordination tasks by considering a second-order rotational dynamics of the agent. Simulations are given to illustrate the theoretical findings.

Optimization of voltage output of energy harvesters with continuous mechanical rotation extracted from human motion (Conference Presentation)

Science.gov (United States)

Rashid, Evan; Hamidi, Armita; Tadesse, Yonas

2017-04-01

With increasing popularity of portable devices for outdoor activities, portable energy harvesting devices are coming into spot light. The next generation energy harvester which is called hybrid energy harvester can employ more than one mechanism in a single device to optimize portion of the energy that can be harvested from any source of waste energy namely motion, vibration, heat and etc. In spite of few recent attempts for creating hybrid portable devices, the level of output energy still needs to be improved with the intention of employing them in commercial electronic systems or further applications. Moreover, implementing a practical hybrid energy harvester in different application for further investigation is still challenging. This proposal is projected to incorporate a novel approach to maximize and optimize the voltage output of hybrid energy harvesters to achieve a greater conversion efficiency normalized by the total mass of the hybrid device than the simple arithmetic sum of the individual harvesting mechanisms. The energy harvester model previously proposed by Larkin and Tadesse [1] is used as a baseline and a continuous unidirectional rotation is incorporated to maximize and optimize the output. The device harvest mechanical energy from oscillatory motion and convert it to electrical energy through electromagnetic and piezoelectric systems. The new designed mechanism upgrades the device in a way that can harvest energy from both rotational and linear motions by using magnets. Likewise, the piezoelectric section optimized to harvest at least 10% more energy. To the end, the device scaled down for tested with different sources of vibrations in the immediate environment, including machinery operation, bicycle, door motion while opening and closing and finally, human motions. Comparing the results from literature proved that current device has capability to be employed in commercial small electronic devices for enhancement of battery usage or as a backup

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 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.

Rotational Seismology: AGU Session, Working Group, and Website

Science.gov (United States)

Lee, William H.K.; Igel, Heiner; Todorovska, Maria I.; Evans, John R.

2007-01-01

Introduction Although effects of rotational motions due to earthquakes have long been observed (e. g., Mallet, 1862), nevertheless Richter (1958, p. 213) stated that: 'Perfectly general motion would also involve rotations about three perpendicular axes, and three more instruments for these. Theory indicates, and observation confirms, that such rotations are negligible.' However, Richter provided no references for this claim. Seismology is based primarily on the observation and modeling of three-component translational ground motions. Nevertheless, theoretical seismologists (e.g., Aki and Richards, 1980, 2002) have argued for decades that the rotational part of ground motions should also be recorded. It is well known that standard seismometers are quite sensitive to rotations and therefore subject to rotation-induced errors. The paucity of observations of rotational motions is mainly the result of a lack, until recently, of affordable rotational sensors of sufficient resolution. Nevertheless, in the past decade, a number of authors have reported direct observations of rotational motions and rotations inferred from rigid-body rotations in short baseline accelerometer arrays, creating a burgeoning library of rotational data. For example, ring laser gyros in Germany and New Zealand have led to the first significant and consistent observations of rotational motions from distant earthquakes (Igel et al., 2005, 2007). A monograph on Earthquake Source Asymmetry, Structural Media and Rotation Effects was published recently as well by Teisseyre et al. (2006). Measurement of rotational motions has implications for: (1) recovering the complete ground-displacement history from seismometer recordings; (2) further constraining earthquake rupture properties; (3) extracting information about subsurface properties; and (4) providing additional ground motion information to earthquake engineers for seismic design. A special session on Rotational Motions in Seismology was convened by H

Successive X-class Flares and Coronal Mass Ejections Driven by Shearing Motion and Sunspot Rotation in Active Region NOAA 12673

Science.gov (United States)

Yan, X. L.; Wang, J. C.; Pan, G. M.; Kong, D. F.; Xue, Z. K.; Yang, L. H.; Li, Q. L.; Feng, X. S.

2018-03-01

We present a clear case study on the occurrence of two successive X-class flares, including a decade-class flare (X9.3) and two coronal mass ejections (CMEs) triggered by shearing motion and sunspot rotation in active region NOAA 12673 on 2017 September 6. A shearing motion between the main sunspots with opposite polarities began on September 5 and lasted even after the second X-class flare on September 6. Moreover, the main sunspot with negative polarity rotated around its umbral center, and another main sunspot with positive polarity also exhibited a slow rotation. The sunspot with negative polarity at the northwest of the active region also began to rotate counterclockwise before the onset of the first X-class flare, which is related to the formation of the second S-shaped structure. The successive formation and eruption of two S-shaped structures were closely related to the counterclockwise rotation of the three sunspots. The existence of a flux rope is found prior to the onset of two flares by using nonlinear force-free field extrapolation based on the vector magnetograms observed by Solar Dynamics Observatory/Helioseismic and Magnetic Image. The first flux rope corresponds to the first S-shaped structures mentioned above. The second S-shaped structure was formed after the eruption of the first flux rope. These results suggest that a shearing motion and sunspot rotation play an important role in the buildup of the free energy and the formation of flux ropes in the corona that produces solar flares and CMEs.

Evaluation of fault-normal/fault-parallel directions rotated ground motions for response history analysis of an instrumented six-story building

Science.gov (United States)

Kalkan, Erol; Kwong, Neal S.

2012-01-01

According to regulatory building codes in United States (for example, 2010 California Building Code), at least two horizontal ground-motion components are required for three-dimensional (3D) response history analysis (RHA) of buildings. For sites within 5 km of an active fault, these records should be rotated to fault-normal/fault-parallel (FN/FP) directions, and two RHA analyses should be performed separately (when FN and then FP are aligned with the transverse direction of the structural axes). It is assumed that this approach will lead to two sets of responses that envelope the range of possible responses over all nonredundant rotation angles. This assumption is examined here using a 3D computer model of a six-story reinforced-concrete instrumented building subjected to an ensemble of bidirectional near-fault ground motions. Peak responses of engineering demand parameters (EDPs) were obtained for rotation angles ranging from 0° through 180° for evaluating the FN/FP directions. It is demonstrated that rotating ground motions to FN/FP directions (1) does not always lead to the maximum responses over all angles, (2) does not always envelope the range of possible responses, and (3) does not provide maximum responses for all EDPs simultaneously even if it provides a maximum response for a specific EDP.

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.

Effects of solar radiation pressure torque on the rotational motion of an artificial satellite

Science.gov (United States)

Zanardi, Maria Cecilia F. P. S.; Vilhenademoraes, Rodolpho

1992-01-01

The motion of an artificial satellite about its center of mass is studied considering torques due to the gravity gradient and direct solar radiation pressure. A model for direct solar radiation torque is derived for a circular cylindrical satellite. An analytical solution is obtained by the method of variation of the parameters. This solution shows that the angular variables have secular variation but that the modulus of the rotational angular momentum, the projection of rotational angular momentum on the z axis of the moment of inertia and inertial axis z, suffer only periodic variations. Considering a hypothetical artificial satellite, a numerical application is demonstrated.

[Efficiency of a postoperative treatment after rotator cuff repair with a continuous passive motion device (CPM)].

Science.gov (United States)

Michael, J W-P; König, D P; Imhoff, A B; Martinek, V; Braun, S; Hübscher, M; Koch, C; Dreithaler, B; Bernholt, J; Preis, S; Loew, M; Rickert, M; Speck, M; Bös, L; Bidner, A; Eysel, P

2005-01-01

The main objective of this study was to prove that a postoperative combined continuous passive motion (CPM) and physiotherapy treatment protocol (CPM group) can achieve 90 degrees active abduction in the shoulder joint earlier than physiotherapy alone (PT group). The indication was a complete tear of the rotator cuff. The study was conducted under in-patient and out-patient conditions. 55 patients were included in this study. The prospective, randomized multicenter study design complies with DIN EN 540. The primary endpoint was the time span until 90 degrees active abduction was achieved by the patients. Patients in the CPM group reached the primary endpoint on average 12 days earlier than the control group. This difference was statistically significant (p = 0.0292). Analyzing the secondary endpoints, e. g., pain and disablement, the results in the CPM group showed again advantages of the combined treatment protocol (CPM + physiotherapy). The postoperative treatment of a total tear of the rotator cuff with a combined continuous passive motion and physiotherapy protocol provided a significantly earlier range of motion in the shoulder joint than physiotherapy alone. There was no report of CPM-related adverse effects.

Influence of Visual Motion, Suggestion, and Illusory Motion on Self-Motion Perception in the Horizontal Plane.

Science.gov (United States)

Rosenblatt, Steven David; Crane, Benjamin Thomas

2015-01-01

A moving visual field can induce the feeling of self-motion or vection. Illusory motion from static repeated asymmetric patterns creates a compelling visual motion stimulus, but it is unclear if such illusory motion can induce a feeling of self-motion or alter self-motion perception. In these experiments, human subjects reported the perceived direction of self-motion for sway translation and yaw rotation at the end of a period of viewing set visual stimuli coordinated with varying inertial stimuli. This tested the hypothesis that illusory visual motion would influence self-motion perception in the horizontal plane. Trials were arranged into 5 blocks based on stimulus type: moving star field with yaw rotation, moving star field with sway translation, illusory motion with yaw, illusory motion with sway, and static arrows with sway. Static arrows were used to evaluate the effect of cognitive suggestion on self-motion perception. Each trial had a control condition; the illusory motion controls were altered versions of the experimental image, which removed the illusory motion effect. For the moving visual stimulus, controls were carried out in a dark room. With the arrow visual stimulus, controls were a gray screen. In blocks containing a visual stimulus there was an 8s viewing interval with the inertial stimulus occurring over the final 1s. This allowed measurement of the visual illusion perception using objective methods. When no visual stimulus was present, only the 1s motion stimulus was presented. Eight women and five men (mean age 37) participated. To assess for a shift in self-motion perception, the effect of each visual stimulus on the self-motion stimulus (cm/s) at which subjects were equally likely to report motion in either direction was measured. Significant effects were seen for moving star fields for both translation (p = 0.001) and rotation (pperception was shifted in the direction consistent with the visual stimulus. Arrows had a small effect on self-motion

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...

Rotational motions from the 2016, Central Italy seismic sequence, as observed by an underground ring laser gyroscope

Science.gov (United States)

Simonelli, Andreino; Belfi, Jacopo; Beverini, Nicolò; Di Virgilio, Angela; Maccioni, Enrico; De Luca, Gaetano; Saccorotti, Gilberto; Wassermann, Joachim; Igel, Heiner

2017-04-01

We present analyses of rotational and translational ground motions from earthquakes recorded during October-November, 2016, in association with the Central Italy seismic-sequence. We use co-located measurements of the vertical ground rotation rate from a large ring laser gyroscope (RLG), and the three components of ground velocity from a broadband seismometer. Both instruments are positioned in a deep underground environment, within the Gran Sasso National Laboratories (LNGS) of the Istituto Nazionale di Fisica Nucleare (INFN). We collected dozen of events spanning the 3.5-5.9 Magnitude range, and epicentral distances between 40 km and 80 km. This data set constitutes an unprecedented observation of the vertical rotational motions associated with an intense seismic sequence at local distance. In theory - assuming plane wave propagation - the ratio between the vertical rotation rate and the transverse acceleration permits, in a single station approach, the estimation of apparent phase velocity in the case of SH arrivals or real phase velocity in the case of Love surface waves. This is a standard approach for the analysis of earthquakes at teleseismic distances, and the results reported by the literature are compatible with the expected phase velocities from the PREM model. Here we extend the application of the same approach to local events, thus exploring higher frequency ranges and larger rotation rate amplitudes. We use a novel approach to joint rotation/acceleration analysis based on the continuous wavelet transform (CWT). Wavelet coherence (WTC) is used as a filter for identifying those regions of the time-period plane where the rotation rate and transverse acceleration signals exhibit significant coherence. This allows retrieving estimates of phase velocities over the period range spanned by correlated arrivals. Coherency among ground rotation and translation is also observed throughout the coda of the P-wave arrival, an observation which is interpreted in

The effect of a rotator cuff tear and its size on three-dimensional shoulder motion.

Science.gov (United States)

Kolk, Arjen; Henseler, Jan Ferdinand; de Witte, Pieter Bas; van Zwet, Erik W; van der Zwaal, Peer; Visser, Cornelis P J; Nagels, Jochem; Nelissen, Rob G H H; de Groot, Jurriaan H

2017-06-01

Rotator cuff-disease is associated with changes in kinematics, but the effect of a rotator cuff-tear and its size on shoulder kinematics is still unknown in-vivo. In this cross-sectional study, glenohumeral and scapulothoracic kinematics of the affected shoulder were evaluated using electromagnetic motion analysis in 109 patients with 1) subacromial pain syndrome (n=34), 2) an isolated supraspinatus tear (n=21), and 3) a massive rotator cuff tear involving the supraspinatus and infraspinatus (n=54). Mixed models were applied for the comparisons of shoulder kinematics between the three groups during abduction and forward flexion. In the massive rotator cuff-tear group, we found reduced glenohumeral elevation compared to the subacromial pain syndrome (16°, 95% CI [10.5, 21.2], protator cuff tears coincides with an increase in scapulothoracic lateral rotation compared to subacromial pain syndrome (11°, 95% CI [6.5, 15.2], protator cuff-tear group had substantially less glenohumeral elevation and more scapulothoracic lateral rotation compared to the other groups. These observations suggest that the infraspinatus is essential to preserve glenohumeral elevation in the presence of a supraspinatus tear. Shoulder kinematics are associated with rotator cuff-tear size and may have diagnostic potential. Copyright © 2017 Elsevier Ltd. All rights reserved.

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.

Self-motion perception and vestibulo-ocular reflex during whole body yaw rotation in standing subjects: the role of head position and neck proprioception.

Science.gov (United States)

Panichi, Roberto; Botti, Fabio Massimo; Ferraresi, Aldo; Faralli, Mario; Kyriakareli, Artemis; Schieppati, Marco; Pettorossi, Vito Enrico

2011-04-01

Self-motion perception and vestibulo-ocular reflex (VOR) were studied during whole body yaw rotation in the dark at different static head positions. Rotations consisted of four cycles of symmetric sinusoidal and asymmetric oscillations. Self-motion perception was evaluated by measuring the ability of subjects to manually track a static remembered target. VOR was recorded separately and the slow phase eye position (SPEP) was computed. Three different head static yaw deviations (active and passive) relative to the trunk (0°, 45° to right and 45° to left) were examined. Active head deviations had a significant effect during asymmetric oscillation: the movement perception was enhanced when the head was kept turned toward the side of body rotation and decreased in the opposite direction. Conversely, passive head deviations had no effect on movement perception. Further, vibration (100 Hz) of the neck muscles splenius capitis and sternocleidomastoideus remarkably influenced perceived rotation during asymmetric oscillation. On the other hand, SPEP of VOR was modulated by active head deviation, but was not influenced by neck muscle vibration. Through its effects on motion perception and reflex gain, head position improved gaze stability and enhanced self-motion perception in the direction of the head deviation. Copyright © 2010 Elsevier B.V. All rights reserved.

Grain boundary motion and grain rotation in aluminum bicrystals: recent experiments and simulations

International Nuclear Information System (INIS)

Molodov, D A; Barrales-Mora, L A; Brandenburg, J-E

2015-01-01

The results of experimental and computational efforts over recent years to study the motion of geometrically different grain boundaries and grain rotation under various driving forces are briefly reviewed. Novel in-situ measuring techniques based on orientation contrast imaging and applied simulation techniques are described. The experimental results obtained on specially grown aluminum bicrystals are presented and discussed. Particularly, the faceting and migration behavior of low angle grain boundaries under the curvature force is addressed. In contrast to the pure tilt boundaries, which remained flat/faceted and immobile during annealing at elevated temperatures, mixed tilt-twist boundaries readily assumed a curved shape and steadily moved under the capillary force. Computational analysis revealed that this behavior is due to the inclinational anisotropy of grain boundary energy, which in turn depends on boundary geometry. The shape evolution and shrinkage kinetics of cylindrical grains with different tilt and mixed boundaries were studied by molecular dynamics simulations. The mobility of low angle <100> boundaries with misorientation angles higher than 10°, obtained by both the experiments and simulations, was found not to differ from that of the high angle boundaries, but decreases essentially with further decrease of misorientation. The shape evolution of the embedded grains in simulations was found to relate directly to results of the energy computations. Further simulation results revealed that the shrinkage of grains with pure tilt boundaries is accompanied by grain rotation. In contrast, grains with the tilt-twist boundaries composed of dislocations with the mixed edge-screw character do not rotate during their shrinkage. Stress driven boundary migration in aluminium bicrystals was observed to be coupled to a tangential translation of the grains. The activation enthalpy of high angle boundary migration was found to vary non-monotonically with

Rotating drum tests of particle suspensions within a fines dispersion

Science.gov (United States)

Cabrera, Miguel Angel; Gollin, Devis; Kaitna, Roland; Wu, Wei

2014-05-01

Natural flows like mudflows, debris flow, and hyperconcentrated flows are commonly composed by a matrix of particles suspended in a viscous fluid. The nature of the interactions between particles immersed in a fluid is related to its size. While coarse particles (sand, gravel, and boulders) interact with each other or with the surrounding fluid, a dispersion of fine particles interacts with each other through colloidal forces or Brownian motion effects (Coussot and Piau, 1995, and Ancey and Jorrot, 2001). The predominance of one of the previous interactions defines the rheology of the flow. On this sense, experimental insight is required to validate the limits where the rheology of a dispersion of fines is valid. For this purpose, an experimental program in a rotating drum is performed over samples of sand, loess, and kaolin. The solid concentration and angular velocity of the rotating drum are varied. Height and normal loads are measured during flow. High-speed videos are performed to obtain the flow patterns of the mixtures. The experiments provide new laboratory evidence of granular mixture behaviour within an increased viscous fluid phase and its characterization. The results show an apparent threshold in terms of solid concentration, in which the mixtures started to behave as a shear-dependent material.

The analysis of influence of field of co-rotation on motion of submicronic particles in the Earth's plasmasphere

Science.gov (United States)

Yakovlev, A. B.

2018-05-01

The analysis of the motion of micro-particles with radii of several dozens of nanometers in the Earth's plasmasphere has confirmed that the earlier proved statement about conservation of the form for an orbit of a particle with constant electric charge which moves in superposition of the central gravitational field and the field of a magnetic dipole is true also for the case of a quasi-equilibrium electric charge. For a wide range of altitudes and the sizes of micro-particles other forces that act on the charged grain make considerably smaller impact on its motion. On the basis of numerical simulation it has been shown that for motion in an equatorial plane the field of co-rotation leads to very small monotonous growth of the semimajor axis and an orbit eccentricity, and for not-equatorial orbits there are fluctuations of the semimajor axis, an eccentricity and an inclination of an orbit with the period that considerably exceeds the period of orbital motion. In this paper, on the basis of the analysis of the canonical equations of the motion of a micro-particle in superposition of the central gravitational field and the field of co-rotation the explanation of the time dependences obtained numerically for the basic characteristics of an orbit of a micro-particle is proposed.

Design and experimental investigation of a magnetically coupled vibration energy harvester using two inverted piezoelectric cantilever beams for rotational motion

International Nuclear Information System (INIS)

Zou, Hong-Xiang; Zhang, Wen-ming; Li, Wen-Bo; Wei, Ke-Xiang; Gao, Qiu-Hua; Peng, Zhi-Ke; Meng, Guang

2017-01-01

Highlights: • A magnetically coupled two-degree-of-freedom harvester for rotation is proposed. • The electromechanical coupling model is developed and validated experimentally. • The harvester can generate high voltage at low rotating speeds. • The harvester can harvest vibration energy in multiple frequency bands. - Abstract: Energy can be harvested from rotational motion for powering wireless autonomous electronic devices. The paper presents a magnetically coupled two-degree-of-freedom vibration energy harvester for rotary motion applications. The design consists of two inverted piezoelectric cantilever beams whose free ends point to the rotating shaft. The centrifugal force of the inverted cantilever beam is beneficial to producing large amplitude in a low speed range. The electromechanical coupling dynamical model is developed by the energy method from Hamilton’s principle and validated experimentally. The experimental results indicate that the presented harvester is suitable for low speed rotation and can harvest vibration energy in multiple frequency bands. The first and second resonant behaviors of voltage can be obtained at 420 r/min and 550 r/min, and the average output powers are 564 μW and 535.3 μW, respectively.

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

EVIDENCE FOR ROTATIONAL MOTIONS IN THE FEET OF A QUIESCENT SOLAR PROMINENCE

International Nuclear Information System (INIS)

Orozco Suárez, D.; Asensio Ramos, A.; Trujillo Bueno, J.

2012-01-01

We present observational evidence of apparent plasma rotational motions in the feet of a solar prominence. Our study is based on spectroscopic observations taken in the He I 1083.0 nm multiplet with the Tenerife Infrared Polarimeter attached to the German Vacuum Tower Telescope. We recorded a time sequence of spectra with 34 s cadence placing the slit of the spectrograph almost parallel to the solar limb and crossing two feet of an intermediate size, quiescent hedgerow prominence. The data show opposite Doppler shifts, ±6 km s –1 , at the edges of the prominence feet. We argue that these shifts may be interpreted as prominence plasma rotating counterclockwise around the vertical axis to the solar surface as viewed from above. The evolution of the prominence seen in EUV images taken with the Solar Dynamics Observatory provided us with clues to interpret the results as swirling motions. Moreover, time-distance images taken far from the central wavelength show plasma structures moving parallel to the solar limb with velocities of about 10-15 km s –1 . Finally, the shapes of the observed intensity profiles suggest the presence of, at least, two components at some locations at the edges of the prominence feet. One of them is typically Doppler shifted (up to ∼20 km s –1 ) with respect to the other, thus suggesting the existence of supersonic counter-streaming flows along the line of sight.

Signal Processing in Cold Atom Interferometry-Based INS

Science.gov (United States)

2014-03-27

angular rotation. Additionally, because of their particle nature, the atoms may be treated as inertial masses and their movement is used to determine the...G(τ)δβ(τ) = Φ(∆t)xi + wdi where β(t) is a Brownian motion process with dispersion Q, andΦ is the discrete-time state transition matrix [14]. That is...identity matrix, I. βA and βG are 3 × 1 vectors of independent, unity Brownian motions, that is, βA(t) ∼ N (0, t · I) and βG(t) ∼ N (0, t · I). The rate

Dynamic strain and rotation ground motions of the 2011 Tohoku earthquake from dense high-rate GPS observations in Taiwan

Science.gov (United States)

Huang, B. S.; Rau, R. J.; Lin, C. J.; Kuo, L. C.

2017-12-01

Seismic waves generated by the 2011 Mw 9.0 Tohoku, Japan earthquake were well recorded by continuous GPS in Taiwan. Those GPS were operated in one hertz sampling rate and densely distributed in Taiwan Island. Those continuous GPS observations and the precise point positioning technique provide an opportunity to estimate spatial derivatives from absolute ground motions of this giant teleseismic event. In this study, we process and investigate more than one and half hundred high-rate GPS displacements and its spatial derivatives, thus strain and rotations, to compare to broadband seismic and rotational sensor observations. It is shown that continuous GPS observations are highly consistent with broadband seismic observations during its surface waves across Taiwan Island. Several standard Geodesy and seismic array analysis techniques for spatial gradients have been applied to those continuous GPS time series to determine its dynamic strain and rotation time histories. Results show that those derivate GPS vertical axis ground rotations are consistent to seismic array determined rotations. However, vertical rotation-rate observations from the R1 rotational sensors have low resolutions and could not compared with GPS observations for this special event. For its dese spatial distribution of GPS stations in Taiwan Island, not only wavefield gradient time histories at individual site was obtained but also 2-D spatial ground motion fields were determined in this study also. In this study, we will report the analyzed results of those spatial gradient wavefields of the 2011 Tohoku earthquake across Taiwan Island and discuss its geological implications.

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.

Comment on "The motion of an arbitrarily rotating spherical projectile and its application to ball games"

DEFF Research Database (Denmark)

Jensen, Jens Højgaard

2014-01-01

In a recent paper (Robinson G and Robinson I 2013 Phys. Scr. 88 018101) the authors developed the differential equations which govern the motion of a spherical projectile rotating about an arbitrary axis in the presence of an arbitrary wind, assuming that both the drag force and the lift force...

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

On the relative rotational motion between rigid fibers and fluid in turbulent channel flow

Energy Technology Data Exchange (ETDEWEB)

Marchioli, C. [Department of Electrical, Management and Mechanical Engineering, University of Udine, 33100 Udine (Italy); Zhao, L., E-mail: lihao.zhao@ntnu.no [Department of Energy and Process Engineering, Norwegian University of Science and Technology, 7491 Trondheim (Norway); Andersson, H. I. [Department of Electrical, Management and Mechanical Engineering, University of Udine, 33100 Udine (Italy); Department of Energy and Process Engineering, Norwegian University of Science and Technology, 7491 Trondheim (Norway)

2016-01-15

In this study, the rotation of small rigid fibers relative to the surrounding fluid in wall-bounded turbulence is examined by means of direct numerical simulations coupled with Lagrangian tracking. Statistics of the relative (fiber-to-fluid) angular velocity, referred to as slip spin in the present study, are evaluated by modelling fibers as prolate spheroidal particles with Stokes number, St, ranging from 1 to 100 and aspect ratio, λ, ranging from 3 to 50. Results are compared one-to-one with those obtained for spherical particles (λ = 1) to highlight effects due to fiber length. The statistical moments of the slip spin show that differences in the rotation rate of fibers and fluid are influenced by inertia, but depend strongly also on fiber length: Departures from the spherical shape, even when small, are associated with an increase of rotational inertia and prevent fibers from passively following the surrounding fluid. An increase of fiber length, in addition, decouples the rotational dynamics of a fiber from its translational dynamics suggesting that the two motions can be modelled independently only for long enough fibers (e.g., for aspect ratios of order ten or higher in the present simulations)

A COMPARATIVE STUDY OF PASSIVE SHOULDER ROTATION RANGE OF MOTION, ISOMETRIC ROTATION STRENGTH AND SERVE SPEED BETWEEN ELITE TENNIS PLAYERS WITH AND WITHOUT HISTORY OF SHOULDER PAIN.

Science.gov (United States)

Moreno-Pérez, V; Elvira, Jll; Fernandez-Fernandez, J; Vera-Garcia, F J

2018-02-01

Glenohumeral internal rotation deficit and external rotation strength have been associated with the development of shoulder pain in overhead athletes. To examine the bilateral passive shoulder rotational range of motion (ROM), the isometric rotational strength and unilateral serve speed in elite tennis players with and without shoulder pain history (PH and NPH, respectively) and compare between dominant and non-dominant limbs and between groups. Cohort study. Fifty-eight elite tennis players were distributed into the PH group (n = 20) and the NPH group (n = 38). Serve velocity, dominant and non-dominant passive shoulder external and internal rotation (ER and IR) ROM, total arc of motion (TAM: the sum of IR and ER ROM), ER and IR isometric strength, bilateral deficits and ER/IR strength ratio were measured in both groups. Questionnaires were administered in order to classify characteristics of shoulder pain. The dominant shoulder showed significantly reduced IR ROM and TAM, and increased ER ROM compared to the non-dominant shoulder in both groups. Isometric ER strength and ER/IR strength ratio were significantly lower in the dominant shoulder in the PH group when compared with the NPH group. No significant differences between groups were found for serve speed. These data show specific adaptations in the IR, TAM and ER ROM in the dominant shoulder in both groups. Isometric ER muscle weakness and ER/IR strength ratio deficit appear to be associated with history of shoulder injuries in elite tennis players. It would be advisable for clinicians to use the present information to design injury prevention programs. 2.

Rotation of vertically oriented objects during earthquakes

Science.gov (United States)

Hinzen, Klaus-G.

2012-10-01

Vertically oriented objects, such as tombstones, monuments, columns, and stone lanterns, are often observed to shift and rotate during earthquake ground motion. Such observations are usually limited to the mesoseismal zone. Whether near-field rotational ground motion components are necessary in addition to pure translational movements to explain the observed rotations is an open question. We summarize rotation data from seven earthquakes between 1925 and 2009 and perform analog and numeric rotation testing with vertically oriented objects. The free-rocking motion of a marble block on a sliding table is disturbed by a pulse in the direction orthogonal to the rocking motion. When the impulse is sufficiently strong and occurs at the `right' moment, it induces significant rotation of the block. Numeric experiments of a free-rocking block show that the initiation of vertical block rotation by a cycloidal acceleration pulse applied orthogonal to the rocking axis depends on the amplitude of the pulse and its phase relation to the rocking cycle. Rotation occurs when the pulse acceleration exceeds the threshold necessary to provoke rocking of a resting block, and the rocking block approaches its equilibrium position. Experiments with blocks subjected to full 3D strong motion signals measured during the 2009 L'Aquila earthquake confirm the observations from the tests with analytic ground motions. Significant differences in the rotational behavior of a monolithic block and two stacked blocks exist.

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.

Numerical analysis of MHD Casson Navier's slip nanofluid flow yield by rigid rotating disk

Science.gov (United States)

Rehman, Khalil Ur; Malik, M. Y.; Zahri, Mostafa; Tahir, M.

2018-03-01

An exertion is perform to report analysis on Casson liquid equipped above the rigid disk for z bar > 0 as a semi-infinite region. The flow of Casson liquid is achieve through rotation of rigid disk with constant angular frequency Ω bar . Magnetic interaction is consider by applying uniform magnetic field normal to the axial direction. The nanosized particles are suspended in the Casson liquid and rotation of disk is manifested with Navier's slip condition, heat generation/absorption and chemical reaction effects. The obtain flow narrating differential equations subject to MHD Casson nanofluid are transformed into ordinary differential system. For this purpose the Von Karman way of scheme is executed. To achieve accurate trends a computational algorithm is develop rather than to go on with usual build-in scheme. The effects logs of involved parameters, namely magnetic field parameter, Casson fluid parameter, slip parameter, thermophoresis and Brownian motion parameters on radial, tangential velocities, temperature, nanoparticles concentration, Nusselt and Sherwood numbers are provided by means of graphical and tabular structures. It is observed that both tangential and radial velocities are decreasing function of Casson fluid parameter.

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.