A one-dimensional gravitationally interacting gas and the convex minorant of Brownian motion
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
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 ...
Quantum Brownian motion in a bath of parametric oscillators: A model for system-field interactions
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
Man'ko, V I
1993-01-01
Brownian motion may be embedded in the Fock space of bosonic free field in one dimension.Extending this correspondence to a family of creation and annihilation operators satisfying a q-deformed algebra, the notion of q-deformation is carried from the algebra to the domain of stochastic processes.The properties of q-deformed Brownian motion, in particular its non-Gaussian nature and cumulant structure,are established.
Brownian motion of tethered nanowires.
Ota, Sadao; Li, Tongcang; Li, Yimin; Ye, Ziliang; Labno, Anna; Yin, Xiaobo; Alam, Mohammad-Reza; Zhang, Xiang
2014-05-01
Brownian motion of slender particles near a boundary is ubiquitous in biological systems and in nanomaterial assembly, but the complex hydrodynamic interaction in those systems is still poorly understood. Here, we report experimental and computational studies of the Brownian motion of silicon nanowires tethered on a substrate. An optical interference method enabled direct observation of microscopic rotations of the slender bodies in three dimensions with high angular and temporal resolutions. This quantitative observation revealed anisotropic and angle-dependent hydrodynamic wall effects: rotational diffusivity in inclined and azimuth directions follows different power laws as a function of the length, ∼ L(-2.5) and ∼ L(-3), respectively, and is more hindered for smaller inclined angles. In parallel, we developed an implicit simulation technique that takes the complex wire-wall hydrodynamic interactions into account efficiently, the result of which agreed well with the experimentally observed angle-dependent diffusion. The demonstrated techniques provide a platform for studying the microrheology of soft condensed matters, such as colloidal and biological systems near interfaces, and exploring the optimal self-assembly conditions of nanostructures.
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...
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.
The open quantum Brownian motions
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)
Quantum equations from Brownian motions
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)
Microscopic derivation of open quantum Brownian motion: a particular example
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)
Random motion and Brownian rotation
Wyllie, G.
1980-01-01
The course is centred on the Brownian motion - the random movement of molecules arising from thermal fluctuations of the surrounding medium - and starts with the classical theory of A. Einstein, M.v. Smoluchowski and P. Langevin. The first part of this article is quite elementary, and several of the questions raised in it have been instructively treated in a much more sophisticated way in recent reviews by Pomeau and Resibois and by Fox. This simple material may nevertheless be helpful to some readers whose main interest lies in approaching the work on Brownian rotation reviewed in the latter part of the present article. The simplest, and most brutally idealised, problem in our field of interest is that of the random walk in one dimension of space. Its solution leads on, through the diffusivity-mobility relation of Einstein, to Langevin's treatment of the Brownian motion. The application of these ideas to the movement of a molecule in a medium of similar molecules is clearly unrealistic, and much energy has been devoted to finding a suitable generalisation. We shall discuss in particular ideas due to Green, Zwanzig and Mori. (orig./WL)
Brownian motion and stochastic calculus
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...
Constructive role of Brownian motion: Brownian motors and Stochastic Resonance
Hänggi, Peter
2005-03-01
Noise is usually thought of as the enemy of order rather as a constructive influence. For the phenomena of Stochastic Resonance [1] and Brownian motors [2], however, stochastic noise can play a beneficial role in enhancing detection and/or facilitating directed transmission of information in absence of biasing forces. Brownian motion assisted Stochastic Resonance finds useful applications in physical, technological, biological and biomedical contexts [1,3]. The basic principles that underpin Stochastic Resonance are elucidated and novel applications for nonlinear classical and quantum systems will be addressed. The presence of non-equilibrium disturbances enables to rectify Brownian motion so that quantum and classical objects can be directed around on a priori designed routes in biological and physical systems (Brownian motors). In doing so, the energy from the haphazard motion of (quantum) Brownian particles is extracted to perform useful work against an external load. This very concept together with first experimental realizations are discussed [2,4,5]. [1] L. Gammaitoni, P. Hä'nggi, P. Jung and F. Marchesoni, Stochastic Resonance, Rev. Mod. Phys. 70, 223 (1998).[2] R. D. Astumian and P. Hä'nggi, Brownian motors, Physics Today 55 (11), 33 (2002).[3] P. Hä'nggi, Stochastic Resonace in Physics and Biology, ChemPhysChem 3, 285 (2002).[4] H. Linke, editor, Special Issue on Brownian Motors, Applied Physics A 75, No. 2 (2002).[5] P. Hä'nggi, F. Marchesoni, F. Nori, Brownian motors, Ann. Physik (Leipzig) 14, xxx (2004); cond-mat/0410033.
Operator Fractional Brownian Motion and Martingale Differences
Hongshuai Dai
2014-01-01
Full Text Available It is well known that martingale difference sequences are very useful in applications and theory. On the other hand, the operator fractional Brownian motion as an extension of the well-known fractional Brownian motion also plays an important role in both applications and theory. In this paper, we study the relation between them. We construct an approximation sequence of operator fractional Brownian motion based on a martingale difference sequence.
Brownian motion using video capture
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)
Stock price prediction using geometric Brownian motion
Farida Agustini, W.; Restu Affianti, Ika; Putri, Endah RM
2018-03-01
Geometric Brownian motion is a mathematical model for predicting the future price of stock. The phase that done before stock price prediction is determine stock expected price formulation and determine the confidence level of 95%. On stock price prediction using geometric Brownian Motion model, the algorithm starts from calculating the value of return, followed by estimating value of volatility and drift, obtain the stock price forecast, calculating the forecast MAPE, calculating the stock expected price and calculating the confidence level of 95%. Based on the research, the output analysis shows that geometric Brownian motion model is the prediction technique with high rate of accuracy. It is proven with forecast MAPE value ≤ 20%.
Brownian motion in a flowing fluid revisited
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
On some generalization of fractional Brownian motions
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
Deep inelastic collisions viewed as Brownian motion
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)
Area distribution of an elastic Brownian motion
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.
A multiscale guide to Brownian motion
Grebenkov, Denis S; Belyaev, Dmitry; Jones, Peter W
2016-01-01
We revise the Lévy construction of Brownian motion as a simple though rigorous approach to operate with various Gaussian processes. A Brownian path is explicitly constructed as a linear combination of wavelet-based ‘geometrical features’ at multiple length scales with random weights. Such a wavelet representation gives a closed formula mapping of the unit interval onto the functional space of Brownian paths. This formula elucidates many classical results about Brownian motion (e.g., non-differentiability of its path), providing an intuitive feeling for non-mathematicians. The illustrative character of the wavelet representation, along with the simple structure of the underlying probability space, is different from the usual presentation of most classical textbooks. Similar concepts are discussed for the Brownian bridge, fractional Brownian motion, the Ornstein-Uhlenbeck process, Gaussian free fields, and fractional Gaussian fields. Wavelet representations and dyadic decompositions form the basis of many highly efficient numerical methods to simulate Gaussian processes and fields, including Brownian motion and other diffusive processes in confining domains. (topical review)
Dissipation and decoherence in Brownian motion
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.
Reflection Negative Kernels and Fractional Brownian Motion
Palle E. T. Jorgensen
2018-06-01
Full Text Available In this article we study the connection of fractional Brownian motion, representation theory and reflection positivity in quantum physics. We introduce and study reflection positivity for affine isometric actions of a Lie group on a Hilbert space E and show in particular that fractional Brownian motion for Hurst index 0 < H ≤ 1 / 2 is reflection positive and leads via reflection positivity to an infinite dimensional Hilbert space if 0 < H < 1 / 2 . We also study projective invariance of fractional Brownian motion and relate this to the complementary series representations of GL 2 ( R . We relate this to a measure preserving action on a Gaussian L 2 -Hilbert space L 2 ( E .
Eigenfunction expansion for fractional Brownian motions
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)
Brownian motion of solitons in a Bose-Einstein condensate.
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.
Brownian dynamics with hydrodynamic interactions
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
Rotational and translational Brownian motion
Coffey, W.T.; Salford Univ.
1980-01-01
In this review it is proposed to summarise the work on the theory of the translational and rotational Brownian movement which has been carried on over roughly the past 30 years. The review is intended to take the form of a tutorial paper rather than a list of the results obtained by the various investigators over the period in question. In this vein then it seems appropriate to firstly give a brief account of those parts of the theory of probability which are relevant to the problems under discussion. (orig.)
Generalized Arcsine Laws for Fractional Brownian Motion.
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.
Synchronization and collective motion of globally coupled Brownian particles
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)
Interacting Brownian Swarms: Some Analytical Results
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.
Brownian motion, martingales, and stochastic calculus
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...
Fractional Brownian motion with a reflecting wall
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.
Time-averaged MSD of Brownian motion
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...
Brownian motion in short range random potentials
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
Frustrated Brownian Motion of Nonlocal Solitary Waves
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.
Intrinsic and extrinsic measurement for Brownian motion
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)
Reflected Brownian motions in the KPZ universality class
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...
O'Connell's process as a vicious Brownian motion
Katori, Makoto
2011-01-01
Vicious Brownian motion is a diffusion scaling limit of Fisher's vicious walk model, which is a system of Brownian particles in one dimension such that if two motions meet they kill each other. We consider the vicious Brownian motions conditioned never to collide with each other and call it noncolliding Brownian motion. This conditional diffusion process is equivalent to the eigenvalue process of the Hermitian-matrix-valued Brownian motion studied by Dyson [J. Math. Phys. 3, 1191 (1962)]. Recently, O'Connell [Ann. Probab. (to be published)] introduced a generalization of the noncolliding Brownian motion by using the eigenfunctions (the Whittaker functions) of the quantum Toda lattice in order to analyze a directed polymer model in 1 + 1 dimensions. We consider a system of one-dimensional Brownian motions with a long-ranged killing term as a generalization of the vicious Brownian motion and construct the O'Connell process as a conditional process of the killing Brownian motions to survive forever.
Brownian Motion of Boomerang Colloidal Particles
Wei, Qi-Huo; Konya, Andrew; Wang, Feng; Selinger, Jonathan V.; Sun, Kai; Chakrabarty, Ayan
2014-03-01
We present experimental and theoretical studies on the Brownian motion of boomerang colloidal particles confined between two glass plates. Our experimental observations show that the mean displacements are biased towards the center of hydrodynamic stress (CoH), and that the mean-square displacements exhibit a crossover from short-time faster to long-time slower diffusion with the short-time diffusion coefficients dependent on the points used for tracking. A model based on Langevin theory elucidates that these behaviors are ascribed to the superposition of two diffusive modes: the ellipsoidal motion of the CoH and the rotational motion of the tracking point with respect to the CoH.
The relativistic Brownian motion: Interdisciplinary applications
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.
Time-averaged MSD of Brownian motion
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
Quantum Darwinism in Quantum Brownian Motion
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.
Time-averaged MSD of Brownian motion
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.
Langevin theory of anomalous Brownian motion made simple
Tothova, Jana; Vasziova, Gabriela; Lisy, VladimIr; Glod, Lukas
2011-01-01
During the century from the publication of the work by Einstein (1905 Ann. Phys. 17 549) Brownian motion has become an important paradigm in many fields of modern science. An essential impulse for the development of Brownian motion theory was given by the work of Langevin (1908 C. R. Acad. Sci., Paris 146 530), in which he proposed an 'infinitely more simple' description of Brownian motion than that by Einstein. The original Langevin approach has however strong limitations, which were rigorously stated after the creation of the hydrodynamic theory of Brownian motion (1945). Hydrodynamic Brownian motion is a special case of 'anomalous Brownian motion', now intensively studied both theoretically and in experiments. We show how some general properties of anomalous Brownian motion can be easily derived using an effective method that allows one to convert the stochastic generalized Langevin equation into a deterministic Volterra-type integro-differential equation for the mean square displacement of the particle. Within the Gibbs statistics, the method is applicable to linear equations of motion with any kind of memory during the evolution of the system. We apply it to memoryless Brownian motion in a harmonic potential well and to Brownian motion in fluids, taking into account the effects of hydrodynamic memory. Exploring the mathematical analogy between Brownian motion and electric circuits, which are at nanoscales also described by the generalized Langevin equation, we calculate the fluctuations of charge and current in RLC circuits that are in contact with the thermal bath. Due to the simplicity of our approach it could be incorporated into graduate courses of statistical physics. Once the method is established, it allows bringing to the attention of students and effectively solving a number of attractive problems related to Brownian motion.
Time rescaling and Gaussian properties of the fractional Brownian motions
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)
Greczylo, Tomasz; Debowska, Ewa
2007-01-01
The authors make comments and remarks on the papers by Salmon et al (2002 Eur. J. Phys. 23 249-53) and their own (2005 Eur. J. Phys. 26 827-33) concerning Brownian motion in two-dimensional space. New, corrected results of calculations and measurements for students' experiments on finding the viscosity of liquids from Brownian motion are presented. (letters and comments)
Brownian motion probe for water-ethanol inhomogeneous mixtures
Furukawa, Kazuki; Judai, Ken
2017-12-01
Brownian motion provides information regarding the microscopic geometry and motion of molecules, insofar as it occurs as a result of molecular collisions with a colloid particle. We found that the mobility of polystyrene beads from the Brownian motion in a water-ethanol mixture is larger than that predicted from the liquid shear viscosity. This indicates that mixing water and ethanol is inhomogeneous in micron-sized probe beads. The discrepancy between the mobility of Brownian motion and liquid mobility can be explained by the way the rotation of the beads in an inhomogeneous viscous solvent converts the translational movement.
Parallel Molecular Distributed Detection With Brownian Motion.
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.
Yukawa Potential, Panharmonic Measure and Brownian Motion
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.
Collective motion of active Brownian particles with polar alignment.
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.
Fractional Brownian motion and long term clinical trial recruitment.
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.
Diffusion in one dimensional random medium and hyperbolic Brownian motion
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
Estimation of the global regularity of a multifractional Brownian motion
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 STOCHASTIC PROCESSES: BOSON AND FERMION BROWNIAN MOTION
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.
From Brownian motion to power of fluctuations
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.
Manipulation and controlled amplification of Brownian motion of microcantilever sensors
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
Directed motion of a Brownian motor in a temperature gradient
Liu, Yibing; Nie, Wenjie; Lan, Yueheng
2017-05-01
Directed motion of mesoscopic systems in a non-equilibrium environment is of great interest to both scientists and engineers. Here, the translation and rotation of a Brownian motor is investigated under non-equilibrium conditions. An anomalous directed translation is found if the two heads of the Brownian motor are immersed in baths with different particle masses, which is hinted in the analytic computation and confirmed by the numerical simulation. Similar consideration is also used to find the directed movement in the single rotational and translational degree of freedom of the Brownian motor when residing in one thermal bath with a temperature gradient.
Willemsen, O.H.; Kuipers, L.; van der Werf, Kees; de Grooth, B.G.; Greve, Jan
2000-01-01
The thermal movement of an atomic force microscope (AFM) tip is used to reconstruct the tip-surface interaction potential. If a tip is brought into the vicinity of a surface, its movement is governed by the sum of the harmonic cantilever potential and the tip-surface interaction potential. By
Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus
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.
Non-colliding Brownian Motions and the Extended Tacnode Process
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.
Deterministic Brownian motion generated from differential delay equations.
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.
The Intersection Probability of Brownian Motion and SLEκ
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-.
On the Generalized Brownian Motion and its Applications in Finance
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...
Survival probabilities for branching Brownian motion with absorption
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...
Finding viscosity of liquids from Brownian motion at students' laboratory
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
Brownian motion, dynamical randomness and irreversibility
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
On modeling animal movements using Brownian motion with measurement error.
Pozdnyakov, Vladimir; Meyer, Thomas; Wang, Yu-Bo; Yan, Jun
2014-02-01
Modeling animal movements with Brownian motion (or more generally by a Gaussian process) has a long tradition in ecological studies. The recent Brownian bridge movement model (BBMM), which incorporates measurement errors, has been quickly adopted by ecologists because of its simplicity and tractability. We discuss some nontrivial properties of the discrete-time stochastic process that results from observing a Brownian motion with added normal noise at discrete times. In particular, we demonstrate that the observed sequence of random variables is not Markov. Consequently the expected occupation time between two successively observed locations does not depend on just those two observations; the whole path must be taken into account. Nonetheless, the exact likelihood function of the observed time series remains tractable; it requires only sparse matrix computations. The likelihood-based estimation procedure is described in detail and compared to the BBMM estimation.
Cosmophysical Factors in the Fluctuation Amplitude Spectrum of Brownian Motion
Kaminsky A. V.
2010-04-01
Full Text Available Phenomenon of the regular variability of the fine structure of the fluctuation in the amplitude distributions (shapes of related histograms for the case of Brownian motion was investigated. We took an advantage of the dynamic light scattering method (DLS to get a stochastically fluctuated signal determined by Brownian motion. Shape of the histograms is most likely to vary, synchronous, in two proximally located independent cells containing Brownian particles. The synchronism persists in the cells distant at 2m from each other, and positioned meridionally. With a parallel-wise positioning of the cells, high probability of the synchronous variation in the shape of the histograms by local time has been observed. This result meets the previous conclusion about the dependency of histogram shapes ("fluctuation amplitudes" of the spectra of stochastic processes upon rotation of the Earth.
Cosmophysical Factors in the Fluctuation Amplitude Spectrum of Brownian Motion
Kaminsky A. V.
2010-07-01
Full Text Available Phenomenon of the regular variability of the fine structure of the fluctuation in the am- plitude distributions (shapes of related histograms for the case of Brownian motion was investigated. We took an advantage of the dynamic light scattering method (DLS to get a stochastically fluctuated signal determined by Brownian motion. Shape of the histograms is most likely to vary, synchronous, in two proximally located independent cells containing Brownian particles. The synchronism persists in the cells distant at 2 m from each other, and positioned meridionally. With a parallel-wise positioning of the cells, high probability of the synchronous variation in the shape of the histograms by local time has been observed. This result meets the previous conclusion about the dependency of histogram shapes (“fluctuation amplitudes” of the spectra of stochastic processes upon rotation of the Earth.
Stochastic calculus for fractional Brownian motion and related processes
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 0
Quantum Brownian motion model for the stock market
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.
Spherical particle Brownian motion in viscous medium as non-Markovian random process
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.
Occupation times distribution for Brownian motion on graphs
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)
From a stochastic to a macroscopic approach to brownian motion
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)
Coupling of lever arm swing and biased Brownian motion in actomyosin.
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.
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.
Algorithm for generating a Brownian motion on a sphere
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.
Brownian motion with multiplicative noises revisited
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)
Study of two-dimensional Debye clusters using Brownian motion
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
Current fluctuations of interacting active Brownian particles
Pre, Trevor Grand; Limmer, David T.
2018-01-01
We derive the distribution function for particle currents for a system of interacting active Brownian particles in the long time limit using large deviation theory and a weighted many body expansion. We find the distribution is non-Gaussian, except in the limit of passive particles. The non-Gaussian fluctuations can be understood from the effective potential the particles experience when conditioned on a given current. This potential suppresses fluctuations of the particle's orientation, and ...
Exponential functionals of Brownian motion, I: Probability laws at fixed time
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.
Brownian motion model with stochastic parameters for asset prices
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.
Fuzzy Itand#244; Integral Driven by a Fuzzy Brownian Motion
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.
New methods for simulation of fractional Brownian motion
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
Phase transition for absorbed Brownian motion with drift
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
Bose polaron as an instance of quantum Brownian motion
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.
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.
Brownian Motion of Asymmetric Boomerang Colloidal Particles
Chakrabarty, Ayan; Konya, Andrew; Wang, Feng; Selinger, Jonathan; Sun, Kai; Wei, Qi-Huo
2014-03-01
We used video microscopy and single particle tracking to study the diffusion and local behaviors of asymmetric boomerang particles in a quasi-two dimensional geometry. The motion is biased towards the center of hydrodynamic stress (CoH) and the mean square displacements of the particles are linear at short and long times with different diffusion coefficients and in the crossover regime it is sub-diffusive. Our model based on Langevin theory shows that these behaviors arise from the non-coincidence of the CoH with the center of the body. Since asymmetric boomerangs represent a class of rigid bodies of more generals shape, therefore our findings are generic and true for any non-skewed particle in two dimensions. Both experimental and theoretical results will be discussed.
The Diffusion Process in Small Particles and Brownian Motion
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
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.
Undergraduate Labs for Biological Physics: Brownian Motion and Optical Trapping
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.
Active Brownian motion models and applications to ratchets
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.
Random functions via Dyson Brownian Motion: progress and problems
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
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.
Whitening filter and innovational representation of fractional Brownian motion
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.
Theory of Brownian motion with the Alder-Wainwright effect
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
Permutation entropy of fractional Brownian motion and fractional Gaussian noise
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
Functionals of Brownian motion, localization and metric graphs
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)
Nuclear resonant scattering of synchrotron radiation from nuclei in the Brownian motion
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
Under which conditions is quantum Brownian motion observable in a microscope?
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.
Statistics of the first passage time of Brownian motion conditioned by maximum value or area
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)
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
Brownian motion in complex fluids: venerable field and frontier of modern physics
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)
Optimal dividends in the Brownian motion risk model with interest
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.
Semicircular canals circumvent Brownian Motion overload of mechanoreceptor hair cells
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 (
Brownian motion of a nano-colloidal particle: the role of the solvent.
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
On the biased motion of a brownian particle for the pausing time behavior of the CTRW
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)
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.
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.
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
Second order limit laws for occupation times of the fractional Brownian motion
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.
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)
Asian Option Pricing with Monotonous Transaction Costs under Fractional Brownian Motion
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.
On correlations between certain random variables associated with first passage Brownian motion
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)
The Pricing of Vulnerable Options in a Fractional Brownian Motion Environment
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.
Characterizing Detrended Fluctuation Analysis of multifractional Brownian motion
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.
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
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
On the distribution of estimators of diffusion constants for Brownian motion
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.
Brownian motion in Robertson-Walker spacetimes from electromagnetic vacuum fluctuations
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.
Brownian Motion of 2D Vacancy Islands by Adatom Terrace Diffusion
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
Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions
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.
Entropic Ratchet transport of interacting active Brownian particles
Ai, Bao-Quan; He, Ya-Feng; Zhong, Wei-Rong
2014-01-01
Directed transport of interacting active (self-propelled) Brownian particles is numerically investigated in confined geometries (entropic barriers). The self-propelled velocity can break thermodynamical equilibrium and induce the directed transport. It is found that the interaction between active particles can greatly affect the ratchet transport. For attractive particles, on increasing the interaction strength, the average velocity first decreases to its minima, then increases, and finally decreases to zero. For repulsive particles, when the interaction is very weak, there exists a critical interaction at which the average velocity is minimal, nearly tends to zero, however, for the strong interaction, the average velocity is independent of the interaction
Entropic Ratchet transport of interacting active Brownian particles
Ai, Bao-Quan, E-mail: aibq@hotmail.com [Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, 510006 Guangzhou (China); He, Ya-Feng [College of Physics Science and Technology, Hebei University, 071002 Baoding (China); Zhong, Wei-Rong, E-mail: wrzhong@jnu.edu.cn [Department of Physics and Siyuan Laboratory, College of Science and Engineering, Jinan University, 510632 Guangzhou (China)
2014-11-21
Directed transport of interacting active (self-propelled) Brownian particles is numerically investigated in confined geometries (entropic barriers). The self-propelled velocity can break thermodynamical equilibrium and induce the directed transport. It is found that the interaction between active particles can greatly affect the ratchet transport. For attractive particles, on increasing the interaction strength, the average velocity first decreases to its minima, then increases, and finally decreases to zero. For repulsive particles, when the interaction is very weak, there exists a critical interaction at which the average velocity is minimal, nearly tends to zero, however, for the strong interaction, the average velocity is independent of the interaction.
Brownian motion, Minkowski space and principle of special relativity
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
Thermodynamic laws and equipartition theorem in relativistic Brownian motion.
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.
Analytical Solutions of a Model for Brownian Motion in the Double Well Potential
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)
Stochastic interactions of two Brownian hard spheres in the presence of depletants
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
3-d brownian motion simulator for high-sensitivity nanobiotechnological applications.
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.
Quantum work fluctuation theorem: Nonergodic Brownian motion case
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.
Anyonic partition functions and windings of planar Brownian motion
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
The first-passage area for drifted Brownian motion and the moments of the Airy distribution
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)
Time-changed geometric fractional Brownian motion and option pricing with transaction costs
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.
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.
An Extreme-Value Analysis of the LIL for Brownian Motion
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).
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
Brownian motion after Einstein and Smoluchowski: Some new applications and new experiments
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 ...
Non-intersecting Brownian motions leaving from and going to several points
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.
Conserved linear dynamics of single-molecule Brownian motion
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
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
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.
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.
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.
Non-Markovian quantum Brownian motion in one dimension in electric fields
Shen, H. Z.; Su, S. L.; Zhou, Y. H.; Yi, X. X.
2018-04-01
Quantum Brownian motion is the random motion of quantum particles suspended in a field (or an effective field) resulting from their collision with fast-moving modes in the field. It provides us with a fundamental model to understand various physical features concerning open systems in chemistry, condensed-matter physics, biophysics, and optomechanics. In this paper, without either the Born-Markovian or rotating-wave approximation, we derive a master equation for a charged-Brownian particle in one dimension coupled with a thermal reservoir in electric fields. The effect of the reservoir and the electric fields is manifested as time-dependent coefficients and coherent terms, respectively, in the master equation. The two-photon correlation between the Brownian particle and the reservoir can induce nontrivial squeezing dynamics to the particle. We derive a current equation including the source from the driving fields, transient current from the system flowing into the environment, and the two-photon current caused by the non-rotating-wave term. The presented results then are compared with that given by the rotating-wave approximation in the weak-coupling limit, and these results are extended to a more general quantum network involving an arbitrary number of coupled-Brownian particles. The presented formalism might open a way to better understand exactly the non-Markovian quantum network.
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.
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
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.
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.
Quantal Brownian Motion from RPA dynamics: The master and Fokker-Planck equations
Yannouleas, C.
1984-05-01
From the purely quantal RPA description of the damped harmonic oscillator and of the corresponding Brownian Motion within the full space (phonon subspace plus reservoir), a master equation (as well as a Fokker-Planck equation) for the reduced density matrix (for the reduced Wigner function, respectively) within the phonon subspace is extracted. The RPA master equation agrees with the master equation derived by the time-dependent perturbative approaches which utilize Tamm-Dancoff Hilbert spaces and invoke the rotating wave approximation. Since the RPA yields a full, as well as a contracted description, it can account for both the kinetic and the unperturbed oscillator momenta. The RPA description of the quantal Brownian Motion contrasts with the descriptions provided by the time perturbative approaches whether they invoke or not the rotating wave approximation. The RPA description also contrasts with the phenomenological phase space quantization. (orig.)
Correlational approach to study interactions between dust Brownian particles in a plasma
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.
A short note on the mean exit time of the Brownian motion
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.
Maximizing the Mean Exit Time of a Brownian Motion from an Interval
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.
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...
100 years of Einstein's Theory of Brownian Motion: From Pollen ...
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 ...
Feller processes: the next generation in modeling. Brownian motion, Lévy processes and beyond.
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.
Theory of relativistic Brownian motion in the presence of electromagnetic field in (1+1) dimension
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.
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.
Brownian motion of massive skyrmions in magnetic thin films
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.
Brownian motion of massive skyrmions in magnetic thin films
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
Singularity spectra of fractional Brownian motions as a multi-fractal
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
Brownian motion of spins; generalized spin Langevin equation
Jayannavar, A.M.
1990-03-01
We derive the Langevin equations for a spin interacting with a heat bath, starting from a fully dynamical treatment. The obtained equations are non-Markovian with multiplicative fluctuations and concomitant dissipative terms obeying the fluctuation-dissipation theorem. In the Markovian limit our equations reduce to the phenomenological equations proposed by Kubo and Hashitsume. The perturbative treatment on our equations lead to Landau-Lifshitz equations and to other known results in the literature. (author). 16 refs
Generalized Langevin Theory Of The Brownian Motion And The Dynamics Of Polymers In Solution
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)
Brownian motion, old and new, and Irwin's role in my academic life
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.
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.
Diffusion limit of Lévy-Lorentz gas is Brownian motion
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.
Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion.
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.
On Drift Parameter Estimation in Models with Fractional Brownian Motion by Discrete Observations
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.
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.
An image encryption scheme based on three-dimensional Brownian motion and chaotic system
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)
Molecular dynamics test of the Brownian description of Na+ motion in water
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
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.
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.
Fornés, José A
2010-01-15
We use the Brownian dynamics with hydrodynamic interactions simulation in order to describe the movement of a elastically coupled dimer Brownian motor in a ratchet potential. The only external forces considered in our system were the load, the random thermal noise and an unbiased thermal fluctuation. For a given set of parameters we observe direct movement against the load force if hydrodynamic interactions were considered.
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.
Special relativity and the Karhunen-Loeve expansion of Brownian motion
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
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.
Quantum harmonic Brownian motion in a general environment: A modified phase-space approach
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
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.
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.
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 .
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 Newtonâs 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
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
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
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...
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.
Brownian motion properties of optoelectronic random bit generators based on laser chaos.
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.
Estimating the Counterparty Risk Exposure by Using the Brownian Motion Local Time
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.
Simulating Stock Prices Using Geometric Brownian Motion: Evidence from Australian Companies
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.
Scaling laws for fractional Brownian motion with power-law clock
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)
Autocorrelated process control: Geometric Brownian Motion approach versus Box-Jenkins approach
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.
Localization and Ballistic Diffusion for the Tempered Fractional Brownian-Langevin Motion
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.
The path integral formulation of fractional Brownian motion for the general Hurst exponent
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)
On the use of reverse Brownian motion to accelerate hybrid simulations
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.
Radiom, Milad; Ducker, William; Robbins, Brian; Paul, Mark
2015-01-01
The hydrodynamic interaction of two closely spaced micron-scale spheres undergoing Brownian motion was measured as a function of their separation. Each sphere was attached to the distal end of a different atomic force microscopy cantilever, placing each sphere in a stiff one-dimensional potential (0.08 Nm −1 ) with a high frequency of thermal oscillations (resonance at 4 kHz). As a result, the sphere’s inertial and restoring forces were significant when compared to the force due to viscous drag. We explored interparticle gap regions where there was overlap between the two Stokes layers surrounding each sphere. Our experimental measurements are the first of their kind in this parameter regime. The high frequency of oscillation of the spheres means that an analysis of the fluid dynamics would include the effects of fluid inertia, as described by the unsteady Stokes equation. However, we find that, for interparticle separations less than twice the thickness of the wake of the unsteady viscous boundary layer (the Stokes layer), the hydrodynamic interaction between the Brownian particles is well-approximated by analytical expressions that neglect the inertia of the fluid. This is because elevated frictional forces at narrow gaps dominate fluid inertial effects. The significance is that interparticle collisions and concentrated suspensions at this condition can be modeled without the need to incorporate fluid inertia. We suggest a way to predict when fluid inertial effects can be ignored by including the gap-width dependence into the frequency number. We also show that low frequency number analysis can be used to determine the microrheology of mixtures at interfaces
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.
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.
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.
NMR signals within the generalized Langevin model for fractional Brownian motion
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.
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.
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.
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.
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.
Correlation Properties of (Discrete Fractional Gaussian Noise and Fractional Brownian Motion
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.
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.
Dynamic tracking of a nano-particle in fluids under Brownian motions
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.
Numerically pricing American options under the generalized mixed fractional Brownian motion model
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.
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.
How superdiffusion gets arrested: ecological encounters explain shift from Lévy to Brownian movement
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
The mode coupling theory in the FDR-preserving field theory of interacting Brownian particles
Kim, Bongsoo; Kawasaki, Kyozi
2007-01-01
We develop a renormalized perturbation theory for the dynamics of interacting Brownian particles, which preserves the fluctuation-dissipation relation order by order. We then show that the resulting one-loop theory gives a closed equation for the density correlation function, which is identical with that in the standard mode coupling theory. (fast track communication)
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.
On the motion of a Brownian particle with an asymmetric bias
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)
Biased Brownian motion mechanism for processivity and directionality of single-headed myosin-VI.
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.
Maximum of an Airy process plus Brownian motion and memory in Kardar-Parisi-Zhang growth
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.
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)
Coffey, W T; Titov, S V
2003-01-01
A theory of orientational relaxation for the inertial rotational Brownian motion of a symmetric top molecule is developed using the Langevin equation rather than the Fokker-Planck equation. The infinite hierarchy of differential-recurrence relations for the orientational correlation functions for the relaxation behaviour is derived by averaging the corresponding Euler-Langevin equations. The solution of this hierarchy is obtained using matrix continued fractions allowing the calculation of the correlation times and the spectra of the orientational correlation functions for typical values of the model parameters.
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.
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 motion in a field of force and the diffusion theory of chemical reactions. II
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
Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field
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.
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.
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.
Non-Markovian Effects on the Brownian Motion of a Free Particle
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.
Brownian modulated optical nanoprobes
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
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)
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
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.
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)
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."
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."
On the joint residence time of N independent two-dimensional Brownian motions
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 → ∞
Miao, Linling; Young, Charles D.; Sing, Charles E.
2017-07-01
Brownian Dynamics (BD) simulations are a standard tool for understanding the dynamics of polymers in and out of equilibrium. Quantitative comparison can be made to rheological measurements of dilute polymer solutions, as well as direct visual observations of fluorescently labeled DNA. The primary computational challenge with BD is the expensive calculation of hydrodynamic interactions (HI), which are necessary to capture physically realistic dynamics. The full HI calculation, performed via a Cholesky decomposition every time step, scales with the length of the polymer as O(N3). This limits the calculation to a few hundred simulated particles. A number of approximations in the literature can lower this scaling to O(N2 - N2.25), and explicit solvent methods scale as O(N); however both incur a significant constant per-time step computational cost. Despite this progress, there remains a need for new or alternative methods of calculating hydrodynamic interactions; large polymer chains or semidilute polymer solutions remain computationally expensive. In this paper, we introduce an alternative method for calculating approximate hydrodynamic interactions. Our method relies on an iterative scheme to establish self-consistency between a hydrodynamic matrix that is averaged over simulation and the hydrodynamic matrix used to run the simulation. Comparison to standard BD simulation and polymer theory results demonstrates that this method quantitatively captures both equilibrium and steady-state dynamics after only a few iterations. The use of an averaged hydrodynamic matrix allows the computationally expensive Brownian noise calculation to be performed infrequently, so that it is no longer the bottleneck of the simulation calculations. We also investigate limitations of this conformational averaging approach in ring polymers.
Active motions of Brownian particles in a generalized energy-depot model
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.
Translational and Brownian motion in laser-Doppler flowmetry of large tissue volumes
Binzoni, T; Leung, T S; Seghier, M L; Delpy, D T
2004-01-01
This study reports the derivation of a precise mathematical relationship existing between the different p-moments of the power spectrum of the photoelectric current, obtained from a laser-Doppler flowmeter (LDF), and the red blood cell speed. The main purpose is that both the Brownian (defining the 'biological zero') and the translational movements are taken into account, clarifying in this way what the exact contribution of each parameter is to the LDF derived signals. The derivation of the equations is based on the quasi-elastic scattering theory and holds for multiple scattering (i.e. measurements in large tissue volumes and/or very high red blood cell concentration). The paper also discusses why experimentally there exists a range in which the relationship between the first moment of the power spectrum and the average red blood cells speed may be considered as 'linear' and what are the physiological determinants that can result in nonlinearity. A correct way to subtract the biological zero from the LDF data is also proposed. The findings should help in the design of improved LDF instruments and in the interpretation of experimental data
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.
A hydrodynamic formalism for Brownian systems
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)
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
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.
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.
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.
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
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)
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)
Butler, Jason E.; Shaqfeh, Eric S. G.
2005-01-01
Using methods adapted from the simulation of suspension dynamics, we have developed a Brownian dynamics algorithm with multibody hydrodynamic interactions for simulating the dynamics of polymer molecules. The polymer molecule is modeled as a chain composed of a series of inextensible, rigid rods with constraints at each joint to ensure continuity of the chain. The linear and rotational velocities of each segment of the polymer chain are described by the slender-body theory of Batchelor [J. Fluid Mech. 44, 419 (1970)]. To include hydrodynamic interactions between the segments of the chain, the line distribution of forces on each segment is approximated by making a Legendre polynomial expansion of the disturbance velocity on the segment, where the first two terms of the expansion are retained in the calculation. Thus, the resulting linear force distribution is specified by a center of mass force, couple, and stresslet on each segment. This method for calculating the hydrodynamic interactions has been successfully used to simulate the dynamics of noncolloidal suspensions of rigid fibers [O. G. Harlen, R. R. Sundararajakumar, and D. L. Koch, J. Fluid Mech. 388, 355 (1999); J. E. Butler and E. S. G. Shaqfeh, J. Fluid Mech. 468, 204 (2002)]. The longest relaxation time and center of mass diffusivity are among the quantities calculated with the simulation technique. Comparisons are made for different levels of approximation of the hydrodynamic interactions, including multibody interactions, two-body interactions, and the "freely draining" case with no interactions. For the short polymer chains studied in this paper, the results indicate a difference in the apparent scaling of diffusivity with polymer length for the multibody versus two-body level of approximation for the hydrodynamic interactions.
Hoda, Nazish; Kumar, Satish
2007-12-01
The adsorption of single polyelectrolyte molecules in shear flow is studied using Brownian dynamics simulations with hydrodynamic interaction (HI). Simulations are performed with bead-rod and bead-spring chains, and electrostatic interactions are incorporated through a screened Coulombic potential with excluded volume accounted for by the repulsive part of a Lennard-Jones potential. A correction to the Rotne-Prager-Yamakawa tensor is derived that accounts for the presence of a planar wall. The simulations show that migration away from an uncharged wall, which is due to bead-wall HI, is enhanced by increases in the strength of flow and intrachain electrostatic repulsion, consistent with kinetic theory predictions. When the wall and polyelectrolyte are oppositely charged, chain behavior depends on the strength of electrostatic screening. For strong screening, chains get depleted from a region close to the wall and the thickness of this depletion layer scales as N1/3Wi2/3 at high Wi, where N is the chain length and Wi is the Weissenberg number. At intermediate screening, bead-wall electrostatic attraction competes with bead-wall HI, and it is found that there is a critical Weissenberg number for desorption which scales as N-1/2κ-3(lB∣σq∣)3/2, where κ is the inverse screening length, lB is the Bjerrum length, σ is the surface charge density, and q is the bead charge. When the screening is weak, adsorbed chains are observed to align in the vorticity direction at low shear rates due to the effects of repulsive intramolecular interactions. At higher shear rates, the chains align in the flow direction. The simulation method and results of this work are expected to be useful for a number of applications in biophysics and materials science in which polyelectrolyte adsorption plays a key role.
Brownian motion of classical spins: Anomalous dissipation and generalized Langevin equation
Bandyopadhyay, Malay; Jayannavar, A. M.
2017-10-01
In this work, we derive the Langevin equation (LE) of a classical spin interacting with a heat bath through momentum variables, starting from the fully dynamical Hamiltonian description. The derived LE with anomalous dissipation is analyzed in detail. The obtained LE is non-Markovian with multiplicative noise terms. The concomitant dissipative terms obey the fluctuation-dissipation theorem. The Markovian limit correctly produces the Kubo and Hashitsume equation. The perturbative treatment of our equations produces the Landau-Lifshitz equation and the Seshadri-Lindenberg equation. Then we derive the Fokker-Planck equation corresponding to LE and the concept of equilibrium probability distribution is analyzed.
Reeves, Mark
2014-03-01
Entropy changes underlie the physics that dominates biological interactions. Indeed, introductory biology courses often begin with an exploration of the qualities of water that are important to living systems. However, one idea that is not explicitly addressed in most introductory physics or biology textbooks is dominant contribution of the entropy in driving important biological processes towards equilibrium. From diffusion to cell-membrane formation, to electrostatic binding in protein folding, to the functioning of nerve cells, entropic effects often act to counterbalance deterministic forces such as electrostatic attraction and in so doing, allow for effective molecular signaling. A small group of biology, biophysics and computer science faculty have worked together for the past five years to develop curricular modules (based on SCALEUP pedagogy) that enable students to create models of stochastic and deterministic processes. Our students are first-year engineering and science students in the calculus-based physics course and they are not expected to know biology beyond the high-school level. In our class, they learn to reduce seemingly complex biological processes and structures to be described by tractable models that include deterministic processes and simple probabilistic inference. The students test these models in simulations and in laboratory experiments that are biologically relevant. The students are challenged to bridge the gap between statistical parameterization of their data (mean and standard deviation) and simple model-building by inference. This allows the students to quantitatively describe realistic cellular processes such as diffusion, ionic transport, and ligand-receptor binding. Moreover, the students confront ``random'' forces and traditional forces in problems, simulations, and in laboratory exploration throughout the year-long course as they move from traditional kinematics through thermodynamics to electrostatic interactions. This talk
van Megen, W; Martinez, V A; Bryant, G
2009-12-18
The current correlation function is determined from dynamic light scattering measurements of a suspension of particles with hard spherelike interactions. For suspensions in thermodynamic equilibrium we find scaling of the space and time variables of the current correlation function. This finding supports the notion that the movement of suspended particles can be described in terms of uncorrelated Brownian encounters. However, in the metastable fluid, at volume fractions above freezing, this scaling fails.
Motion Model Employment using interacting Motion Model Algorithm
Hussain, Dil Muhammad Akbar
2006-01-01
The paper presents a simulation study to track a maneuvering target using a selective approach in choosing Interacting Multiple Models (IMM) algorithm to provide a wider coverage to track such targets. Initially, there are two motion models in the system to track a target. Probability of each m...
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.
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.
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.
Interactive inverse kinematics for human motion estimation
Engell-Nørregård, Morten Pol; Hauberg, Søren; Lapuyade, Jerome
2009-01-01
We present an application of a fast interactive inverse kinematics method as a dimensionality reduction for monocular human motion estimation. The inverse kinematics solver deals efficiently and robustly with box constraints and does not suffer from shaking artifacts. The presented motion...... to significantly speed up the particle filtering. It should be stressed that the observation part of the system has not been our focus, and as such is described only from a sense of completeness. With our approach it is possible to construct a robust and computationally efficient system for human motion estimation....
Brownian dynamic simulations and experiments of MR fluids
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.
Ballestra, Luca Vincenzo; Pacelli, Graziella; Radi, Davide
2016-01-01
We deal with the problem of pricing barrier options on an underlying described by the mixed fractional Brownian model. To this aim, we consider the initial-boundary value partial differential problem that yields the option price and we derive an integral representation of it in which the integrand functions must be obtained solving Volterra equations of the first kind. In addition, we develop an ad-hoc numerical procedure to solve the integral equations obtained. Numerical simulations reveal that the proposed method is extremely accurate and fast, and performs significantly better than the finite difference method.
Irreversible Brownian Heat Engine
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.
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
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.
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)
Critique of the Brownian approximation to the generalized Langevin equation in lattice dynamics
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
Brownian Optimal Stopping and Random Walks
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
How superdiffusion gets arrested: Ecological encounters explain shift from Lévy to Brownian movement
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 Levy to Brownian movement
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 Lévy to Brownian movement
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
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
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
Financial Brownian Particle in the Layered Order-Book Fluid and Fluctuation-Dissipation Relations
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.
Intelligent Motion and Interaction Within Virtual Environments
Ellis, Stephen R. (Editor); Slater, Mel (Editor); Alexander, Thomas (Editor)
2007-01-01
What makes virtual actors and objects in virtual environments seem real? How can the illusion of their reality be supported? What sorts of training or user-interface applications benefit from realistic user-environment interactions? These are some of the central questions that designers of virtual environments face. To be sure simulation realism is not necessarily the major, or even a required goal, of a virtual environment intended to communicate specific information. But for some applications in entertainment, marketing, or aspects of vehicle simulation training, realism is essential. The following chapters will examine how a sense of truly interacting with dynamic, intelligent agents may arise in users of virtual environments. These chapters are based on presentations at the London conference on Intelligent Motion and Interaction within a Virtual Environments which was held at University College, London, U.K., 15-17 September 2003.
Entropic Approach to Brownian Movement.
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)
Brownian movement and molecular reality
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
Quantum description of the Brownian movement in an external field
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
Laws of motion for interacting Yang-Mills particles
Fuchs, H.
1988-01-01
Our recent Lagrangian approach to the equations of motion for test particles with internal structure can be enlarged to the laws of motion for interacting particles, at least in principle. As an example we consider the interaction of point particles endowed with a pole-dipole structure of the non-abelian charge. (author)
Visual-vestibular interaction in motion perception
Hosman, Ruud J A W; Cardullo, Frank M.; Bos, Jelte E.
2011-01-01
Correct perception of self motion is of vital importance for both the control of our position and posture when moving around in our environment. With the development of human controlled vehicles as bicycles, cars and aircraft motion perception became of interest for the understanding of vehicle
A multiscale approach to Brownian motors
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
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...
Brownian relaxation of an inelastic sphere in air
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.
INTERACTIVE MOTION PLATFORMS AND VIRTUAL REALITY FOR VEHICLE SIMULATORS
Evžen Thöndel
2017-12-01
Full Text Available Interactive motion platforms are intended for vehicle simulators, where the direct interaction of the human body is used for controlling the simulated vehicle (e.g. bicycle, motorbike or other sports vehicles. The second use of interactive motion platforms is for entertainment purposes or fitness. The development of interactive motion platforms reacts to recent calls in the simulation industry to provide a device, which further enhances the virtual reality experience, especially with connection to the new and very fast growing business in virtual reality glasses. The paper looks at the design and control of an interactive motion platform with two degrees of freedom to be used in virtual reality applications. The paper provides the description of the control methods and new problems related to the virtual reality sickness are discussed here.
Interactive motion tracing for Rowing Training
Dai, Zheng
2011-01-01
This paper studies motion tracking and team coordination for the training of rowers. The design research is drawn upon the division of contribution between the designers input and the user input in a design process. We built a training system that can record and show the action of a rower’s hand....... Designer proposed solutions for both a fundamental problem and a very advanced problem. Users guided the design direction, and spoke what they expected or what they disliked. As the result, our design provided a real-time recording tool for rowers and coaches to discuss and analyze the motion. The coach...... can correct the path immediately and save the corrected path for the rower to try to imitate and train. The members in a rowing team train with the same path from to coordinate and synchronize their actions for the best performance. The training system was developed through a user-centered design...
Simple Brownian diffusion an introduction to the standard theoretical models
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.
Slow kinetics of Brownian maxima.
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.
Active Brownian particles with velocity-alignment and active fluctuations
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)
Bocquet, L.; Hansen, J.P.; Piasecki, J.
1994-01-01
The friction coefficient γ exerted by a hard-sphere fluid on an infinitely massive Brownian sphere is calculated for several size ratios Σ/σ where Σ and σ are the diameters of the Brownian and fluid spheres, respectively. The exact microscopic expression derived in part I of this work from kinetic theory is transformed and shown to be proportional to the time integral of the autocorrelation function of the momentum transferred from the fluid to the Brownian sphere during instantaneous collisions. Three different methods are described to extract the friction coefficient from molecular dynamics simulations carried out on finite systems. The three independent methods lead to estimates of γ which agree within statistical errors (typically 5%). The results are compared to the predictions of Enskog theory and of the hydrodynamic Stokes law. The former breaks down as the size ratio and/or the packing fraction of the fluid increase. Somewhat surprisingly, Stokes' law is found to hold with stick boundary conditions, in the range 1 ≤ Σ/σ ≤ 4.5 explored in the present simulations, with a hydrodynamic diameter d=Σ. The analysis of the molecular dynamics data on the basis of Stokes' law with slip boundary conditions is less conclusive, although the right trend is found as Σ/σ increases
Induced motion of domain walls in multiferroics with quadratic interaction
Gerasimchuk, Victor S., E-mail: viktor.gera@gmail.com [National Technical University of Ukraine “Kyiv Polytechnic Institute”, Peremohy Avenue 37, 03056 Kiev (Ukraine); Shitov, Anatoliy A., E-mail: shitov@mail.ru [Donbass National Academy of Civil Engineering, Derzhavina Street 2, 86123 Makeevka, Donetsk Region (Ukraine)
2013-10-15
We theoretically study the dynamics of 180-degree domain wall of the ab-type in magnetic materials with quadratic magnetoelectric interaction in external alternating magnetic and electric fields. The features of the oscillatory and translational motions of the domain walls and stripe structures depending on the parameters of external fields and characteristics of the multiferroics are discussed. The possibility of the domain walls drift in a purely electric field is established. - Highlights: • We study DW and stripe DS in multiferroics with quadratic magnetoelectric interaction. • We build up the theory of oscillatory and translational (drift) DW and DS motion. • DW motion can be caused by crossed alternating electric and magnetic fields. • DW motion can be caused by alternating “pure” electric field. • DW drift velocity is formed by the AFM and Dzyaloshinskii interaction terms.
Relaxation property of the fractional Brownian particle
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
Brownian coagulation at high particle concentrations
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,
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.
Arm Motion Recognition and Exercise Coaching System for Remote Interaction
Hong Zeng
2016-01-01
Full Text Available Arm motion recognition and its related applications have become a promising human computer interaction modal due to the rapid integration of numerical sensors in modern mobile-phones. We implement a mobile-phone-based arm motion recognition and exercise coaching system that can help people carrying mobile-phones to do body exercising anywhere at any time, especially for the persons that have very limited spare time and are constantly traveling across cities. We first design improved k-means algorithm to cluster the collecting 3-axis acceleration and gyroscope data of person actions into basic motions. A learning method based on Hidden Markov Model is then designed to classify and recognize continuous arm motions of both learners and coaches, which also measures the action similarities between the persons. We implement the system on MIUI 2S mobile-phone and evaluate the system performance and its accuracy of recognition.
Interaction between electromagnetic waves and plasma waves in motional plasma
Chen, S. Y.; Gao, M.; Tang, C. J.; Peng, X. D.
2009-01-01
The electromagnetic wave (EM wave) behavior and the electromagnetic instability caused by the interaction between an EM wave and a plasma wave in motional plasma are studied. The dispersion relation of EM waves and the dielectric tensor of motional plasma are derived by magnetohydrodynamics, and the wave phenomenon in motional plasma is displayed. As a result, the electromagnetic instability, which is excited by the interaction between the EM waves and the plasma waves, is revealed. The mechanism of the instability is the coupling between high frequency electromagnetic field and the transverse electron oscillation derived from the deflection of longitudinal electron oscillation due to self-magnetic field. The present research is useful with regard to the new type of plasma radiation source, ion-focusing accelerator, and plasma diagnostic technique.
Spatial Attention and Audiovisual Interactions in Apparent Motion
Sanabria, Daniel; Soto-Faraco, Salvador; Spence, Charles
2007-01-01
In this study, the authors combined the cross-modal dynamic capture task (involving the horizontal apparent movement of visual and auditory stimuli) with spatial cuing in the vertical dimension to investigate the role of spatial attention in cross-modal interactions during motion perception. Spatial attention was manipulated endogenously, either…
Near-Field, On-Chip Optical Brownian Ratchets.
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.
Brownian Agents and Active Particles: Collective Dynamics in the Natural and Social Sciences
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
On the validity of Brownian assumptions in the spin van der Waals model
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)
How superdiffusion gets arrested: ecological encounters explain shift from Lévy to Brownian movement
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 ...
Inquiry style interactive virtual experiments: a case on circular motion
Zhou Shaona; Wang Xiaojun; Xiao Hua; Han Jing; Pelz, Nathaniel; Peng Liangyu; Bao Lei
2011-01-01
Interest in computer-based learning, especially in the use of virtual reality simulations is increasing rapidly. While there are good reasons to believe that technologies have the potential to improve teaching and learning, how to utilize the technology effectively in teaching specific content difficulties is challenging. To help students develop robust understandings of correct physics concepts, we have developed interactive virtual experiment simulations that have the unique feature of enabling students to experience force and motion via an analogue joystick, allowing them to feel the applied force and simultaneously see its effects. The simulations provide students learning experiences that integrate both scientific representations and low-level sensory cues such as haptic cues under a single setting. In this paper, we introduce a virtual experiment module on circular motion. A controlled study has been conducted to evaluate the impact of using this virtual experiment on students' learning of force and motion in the context of circular motion. The results show that the interactive virtual experiment method is preferred by students and is more effective in helping students grasp the physics concepts than the traditional education method such as problem-solving practices. Our research suggests that well-developed interactive virtual experiments can be useful tools in teaching difficult concepts in science.
Inquiry style interactive virtual experiments: a case on circular motion
Zhou Shaona; Wang Xiaojun; Xiao Hua [School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006 (China); Han Jing; Pelz, Nathaniel; Peng Liangyu; Bao Lei, E-mail: xiaoh@scnu.edu.cn, E-mail: lbao@mps.ohio-state.edu [Department of Physics, Ohio State University, Columbus, OH 43210 (United States)
2011-11-15
Interest in computer-based learning, especially in the use of virtual reality simulations is increasing rapidly. While there are good reasons to believe that technologies have the potential to improve teaching and learning, how to utilize the technology effectively in teaching specific content difficulties is challenging. To help students develop robust understandings of correct physics concepts, we have developed interactive virtual experiment simulations that have the unique feature of enabling students to experience force and motion via an analogue joystick, allowing them to feel the applied force and simultaneously see its effects. The simulations provide students learning experiences that integrate both scientific representations and low-level sensory cues such as haptic cues under a single setting. In this paper, we introduce a virtual experiment module on circular motion. A controlled study has been conducted to evaluate the impact of using this virtual experiment on students' learning of force and motion in the context of circular motion. The results show that the interactive virtual experiment method is preferred by students and is more effective in helping students grasp the physics concepts than the traditional education method such as problem-solving practices. Our research suggests that well-developed interactive virtual experiments can be useful tools in teaching difficult concepts in science.
Self-induced temperature gradients in Brownian dynamics
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.
Motion-to-Motion Gauge for the Electroweak Interaction of Leptons
Tselnik F.
2015-01-01
Full Text Available Comprised of rods and clocks, a reference system is a mere intermediary between the motion that is of interest in the problem and the motions of auxiliary test bodies the reference system is to be gauged with. However, a theory base d on such reference sys- tems might hide some features of this actual motion-to-motion correspondence, thus leaving these features incomprehensible. It is therefore d esirable to consider this corre- spondence explicitly, if only to substantiate a particular scheme. To this end, the very existence of a (local top-speed signal is shown to be sufficient to explain some peculiar- ities of the weak interaction using symmetrical configurations of auxiliary trajectories as a means for the gauge. In particular, the unification of the electromagnetic and weak interactions, parity violation, SU(2 L × U(1 group structure with the values of its cou- pling constants, and the intermediate vector boson are found to be a direct consequence of this gauge procedure.
Unreal Interactive Puppet Game Development Using Leap Motion
Huang, An-Pin; Huang, Fay; Jhu, Jing-Siang
2018-04-01
This paper proposed a novel puppet play method utilizing recent technology. An interactive puppet game has been developed based on the theme of a famous Chinese classical novel. This project was implemented using Unreal Engine, which is a leading software of integrated tools for developers to design and build games. On the other hand, Leap Motion Controller is a sensor device for recognizing hand movements and gestures. It is commonly used in systems which require close-range finger-based user interaction. In order to manipulate puppets’ movements, the developed program employs the Leap Motion SDK, which provides a friendly way to add motion-controlled 3D hands to an Unreal game. The novelty of our project is to replace 3D model of rigged hands by two 3D humanoid rigged characters. The challenges of this task are two folds. First, the skeleton structure of a human hand and a humanoid character (i.e., puppets) are totally different. Making the puppets to follow the hand poses of the user and yet ensuring reasonable puppets’ movements has not been discussed in the literatures nor in the developer forums. Second, there are only a limited number of built-in recognizable hand gestures. More recognizable hand gestures need to be created for the interactive game. This paper reports the proposed solutions to these challenges.
Conformal geometry and invariants of 3-strand Brownian braids
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
Magnetic interactions, bonding, and motion of positive muons in magnetite
Boekema, C.; Lichti, R.L.; Brabers, V.A.M.; Denison, A.B.; Cooke, D.W.; Heffner, R.H.; Hutson, R.L.; Leon, M.; Schillaci, M.E.
1985-01-01
Positive-muon behavior in magnetite is investigated by the muon-spin-rotation technique. The observed muon relaxation rate in zero applied field, in conjunction with the measured local field, allows us to separate muon-motion effects from phase transitions associated with magnetite. The local magnetic field is observed to be 4.02 kOe directed along the axis, the easy axis of magnetization. Possible origins of this field are discussed in terms which include local muon diffusion and a supertransfer hyperfine interaction resulting from muon-oxygen bonding. An anomaly in the muon hyperfine interactions is observed at 247 K
Video stereolization: combining motion analysis with user interaction.
Liao, Miao; Gao, Jizhou; Yang, Ruigang; Gong, Minglun
2012-07-01
We present a semiautomatic system that converts conventional videos into stereoscopic videos by combining motion analysis with user interaction, aiming to transfer as much as possible labeling work from the user to the computer. In addition to the widely used structure from motion (SFM) techniques, we develop two new methods that analyze the optical flow to provide additional qualitative depth constraints. They remove the camera movement restriction imposed by SFM so that general motions can be used in scene depth estimation-the central problem in mono-to-stereo conversion. With these algorithms, the user's labeling task is significantly simplified. We further developed a quadratic programming approach to incorporate both quantitative depth and qualitative depth (such as these from user scribbling) to recover dense depth maps for all frames, from which stereoscopic view can be synthesized. In addition to visual results, we present user study results showing that our approach is more intuitive and less labor intensive, while producing 3D effect comparable to that from current state-of-the-art interactive algorithms.
Jafarimoghaddam, Amin; Aberoumand, Sadegh
2017-01-01
The present study aims to experimentally investigate heat transfer performance of rectangular and semicircular tubes in the presence of Ag / water nanofluids. The nanoparticles of Ag (silver) were used in seven different volume concentrations of 0.03%, 0.07%, 0.1%, 0.2%, 0.4%, 1% and 2%. The experiment was conducted in relatively low Reynolds numbers of 301 to 740. A heater with the power of 200 W was used to keep the outer surface of the tubes under a constant heat flux condition. In addition, the rectangular tube has been designed within the same length as the semicircular one and also within the same hydraulic diameter. Moreover, the average nanoparticles size was 20 nm. The outcome results of the present empirical work indicate that, for all the examined Reynolds numbers, the semicircular tube has higher convective heat transfer coefficient for all the utilized volume concentrations of Ag nanoparticles. The possible reasons behind this advantage are discussed through the present work mainly by taking the boundary effect on Brownian motions into account. Coming to this point that the conventional design for cooling system of photovoltaic cells is a heat sink with the rectangular graves, it is discussed that using a semicircular design may have the advantage over the rectangular one in convective heat transfer coefficient enhancement and hence a better cooling performance for these solar cells.
Moeller, Peter [Los Alamos National Laboratory, Theoretical Division, Los Alamos, NM (United States); Ichikawa, Takatoshi [Kyoto University, Yukawa Institute for Theoretical Physics, Kyoto (Japan)
2015-12-15
We propose a method to calculate the two-dimensional (2D) fission-fragment yield Y(Z,N) versus both proton and neutron number, with inclusion of odd-even staggering effects in both variables. The approach is to use the Brownian shape-motion on a macroscopic-microscopic potential-energy surface which, for a particular compound system is calculated versus four shape variables: elongation (quadrupole moment Q{sub 2}), neck d, left nascent fragment spheroidal deformation ε{sub f1}, right nascent fragment deformation ε{sub f2} and two asymmetry variables, namely proton and neutron numbers in each of the two fragments. The extension of previous models 1) introduces a method to calculate this generalized potential-energy function and 2) allows the correlated transfer of nucleon pairs in one step, in addition to sequential transfer. In the previous version the potential energy was calculated as a function of Z and N of the compound system and its shape, including the asymmetry of the shape. We outline here how to generalize the model from the ''compound-system'' model to a model where the emerging fragment proton and neutron numbers also enter, over and above the compound system composition. (orig.)
Amin Jafarimoghaddam
Full Text Available The present study aims to experimentally investigate heat transfer performance of rectangular and semicircular tubes in the presence of Ag / water nanofluids. The nanoparticles of Ag (silver were used in seven different volume concentrations of 0.03%, 0.07%, 0.1%, 0.2%, 0.4%, 1% and 2%. The experiment was conducted in relatively low Reynolds numbers of 301 to 740. A heater with the power of 200 W was used to keep the outer surface of the tubes under a constant heat flux condition. In addition, the rectangular tube has been designed within the same length as the semicircular one and also within the same hydraulic diameter. Moreover, the average nanoparticles size was 20 nm. The outcome results of the present empirical work indicate that, for all the examined Reynolds numbers, the semicircular tube has higher convective heat transfer coefficient for all the utilized volume concentrations of Ag nanoparticles. The possible reasons behind this advantage are discussed through the present work mainly by taking the boundary effect on Brownian motions into account. Coming to this point that the conventional design for cooling system of photovoltaic cells is a heat sink with the rectangular graves, it is discussed that using a semicircular design may have the advantage over the rectangular one in convective heat transfer coefficient enhancement and hence a better cooling performance for these solar cells.
Static structure of active Brownian hard disks
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.
Human motion behavior while interacting with an industrial robot.
Bortot, Dino; Ding, Hao; Antonopolous, Alexandros; Bengler, Klaus
2012-01-01
Human workers and industrial robots both have specific strengths within industrial production. Advantageously they complement each other perfectly, which leads to the development of human-robot interaction (HRI) applications. Bringing humans and robots together in the same workspace may lead to potential collisions. The avoidance of such is a central safety requirement. It can be realized with sundry sensor systems, all of them decelerating the robot when the distance to the human decreases alarmingly and applying the emergency stop, when the distance becomes too small. As a consequence, the efficiency of the overall systems suffers, because the robot has high idle times. Optimized path planning algorithms have to be developed to avoid that. The following study investigates human motion behavior in the proximity of an industrial robot. Three different kinds of encounters between the two entities under three robot speed levels are prompted. A motion tracking system is used to capture the motions. Results show, that humans keep an average distance of about 0,5m to the robot, when the encounter occurs. Approximation of the workbenches is influenced by the robot in ten of 15 cases. Furthermore, an increase of participants' walking velocity with higher robot velocities is observed.
Analyzing animal movements using Brownian bridges.
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.
Hydrodynamically Coupled Brownian Dynamics simulations for flow on non-Newtonian fluids
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
Interactions Controlling the Slow Dynamic Conformational Motions of Ubiquitin
Soichiro Kitazawa
2017-08-01
Full Text Available Rational mutation of proteins based on their structural and dynamic characteristics is a useful strategy for amplifying specific fluctuations in proteins. Here, we show the effects of mutation on the conformational fluctuations and thermodynamic stability of ubiquitin. In particular, we focus on the salt bridge between K11 and E34 and the hydrogen bond between I36 and Q41, which are predicted to control the fluctuation between the basic folded state, N1, and the alternatively folded state, N2, of the protein, using high-pressure NMR spectroscopy. The E34A mutation, which disrupts the salt bridge, did not alter picosecond–to–nanosecond, microsecond–to–millisecond dynamic motions, and stability of the protein, while the Q41N mutation, which destabilizes the hydrogen bond, specifically amplified the N1–N2 conformational fluctuation and decreased stability. Based on the observed thermodynamic stabilities of the various conformational states, we showed that in the Q41N mutant, the N1 state is more significantly destabilized than the N2 state, resulting in an increase in the relative population of N2. Identifying the interactions controlling specific motions of a protein will facilitate molecular design to achieve functional dynamics beyond native state dynamics.
Lin, P L; Huang, P W; Huang, P Y; Hsu, H C
2015-10-01
Periodontitis involves progressive loss of alveolar bone around the teeth. Hence, automatic alveolar bone-loss (ABL) measurement in periapical radiographs can assist dentists in diagnosing such disease. In this paper, we propose an effective method for ABL area localization and denote it as ABLIfBm. ABLIfBm is a threshold segmentation method that uses a hybrid feature fused of both intensity and texture measured by the H-value of fractional Brownian motion (fBm) model, where the H-value is the Hurst coefficient in the expectation function of a fBm curve (intensity change) and is directly related to the value of fractal dimension. Adopting leave-one-out cross validation training and testing mechanism, ABLIfBm trains weights for both features using Bayesian classifier and transforms the radiograph image into a feature image obtained from a weighted average of both features. Finally, by Otsu's thresholding, it segments the feature image into normal and bone-loss regions. Experimental results on 31 periodontitis radiograph images in terms of mean true positive fraction and false positive fraction are about 92.5% and 14.0%, respectively, where the ground truth is provided by a dentist. The results also demonstrate that ABLIfBm outperforms (a) the threshold segmentation method using either feature alone or a weighted average of the same two features but with weights trained differently; (b) a level set segmentation method presented earlier in literature; and (c) segmentation methods based on Bayesian, K-NN, or SVM classifier using the same two features. Our results suggest that the proposed method can effectively localize alveolar bone-loss areas in periodontitis radiograph images and hence would be useful for dentists in evaluating degree of bone-loss for periodontitis patients. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.
Brownian gas models for extreme-value laws
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)
Anthropomorphic Robot Design and User Interaction Associated with Motion
Ellis, Stephen R.
2016-01-01
Though in its original concept a robot was conceived to have some human-like shape, most robots now in use have specific industrial purposes and do not closely resemble humans. Nevertheless, robots that resemble human form in some way have continued to be introduced. They are called anthropomorphic robots. The fact that the user interface to all robots is now highly mediated means that the form of the user interface is not necessarily connected to the robots form, human or otherwise. Consequently, the unique way the design of anthropomorphic robots affects their user interaction is through their general appearance and the way they move. These robots human-like appearance acts as a kind of generalized predictor that gives its operators, and those with whom they may directly work, the expectation that they will behave to some extent like a human. This expectation is especially prominent for interactions with social robots, which are built to enhance it. Often interaction with them may be mainly cognitive because they are not necessarily kinematically intricate enough for complex physical interaction. Their body movement, for example, may be limited to simple wheeled locomotion. An anthropomorphic robot with human form, however, can be kinematically complex and designed, for example, to reproduce the details of human limb, torso, and head movement. Because of the mediated nature of robot control, there remains in general no necessary connection between the specific form of user interface and the anthropomorphic form of the robot. But their anthropomorphic kinematics and dynamics imply that the impact of their design shows up in the way the robot moves. The central finding of this report is that the control of this motion is a basic design element through which the anthropomorphic form can affect user interaction. In particular, designers of anthropomorphic robots can take advantage of the inherent human-like movement to 1) improve the users direct manual control over
Quantum dynamical framework for Brownian heat engines
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.
Brownian Movement and Avogadro's Number: A Laboratory Experiment.
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)
Entropy production of a Brownian ellipsoid in the overdamped limit.
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.
Non-cooperative Brownian donkeys: A solvable 1D model
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.
Coupling motion of colloidal particles in quasi-two-dimensional confinement
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)
Lectures from Markov processes to Brownian motion
Chung, Kai Lai
1982-01-01
This book evolved from several stacks of lecture notes written over a decade and given in classes at slightly varying levels. In transforming the over lapping material into a book, I aimed at presenting some of the best features of the subject with a minimum of prerequisities and technicalities. (Needless to say, one man's technicality is another's professionalism. ) But a text frozen in print does not allow for the latitude of the classroom; and the tendency to expand becomes harder to curb without the constraints of time and audience. The result is that this volume contains more topics and details than I had intended, but I hope the forest is still visible with the trees. The book begins at the beginning with the Markov property, followed quickly by the introduction of option al times and martingales. These three topics in the discrete parameter setting are fully discussed in my book A Course In Probability Theory (second edition, Academic Press, 1974). The latter will be referred to throughout this book ...
Proteins as micro viscosimeters: Brownian motion revisited.
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
Active Brownian motion in a narrow channel
Ao, X.; Ghosh, P. K.; Li, Y.; Schmid, G.; Hänggi, P.; Marchesoni, F.
2014-12-01
We review recent advances in rectification control of artificial microswimmers, also known as Janus particles, diffusing along narrow, periodically corrugated channels. The swimmer self-propulsion mechanism is modeled so as to incorporate a nonzero torque (propulsion chirality). We first summarize the effects of chirality on the autonomous current of microswimmers freely diffusing in channels of different geometries. In particular, left-right and upside-down asymmetric channels are shown to exhibit different transport properties. We then report new results on the dependence of the diffusivity of chiral microswimmers on the channel geometry and their own self-propulsion mechanism. The self-propulsion torque turns out to play a key role as a transport control parameter.
The single- and double-particle properties and the current reversal of coupled Brownian motors
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)
Double-temperature ratchet model and current reversal of coupled Brownian motors
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.
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.
Stochastic motion from a forced plasma-maser interaction
Honjo, Haruo; Nambu, Mitsuhiro
1986-01-01
A model of forced plasma-maser effects is examined numerically. The model represents a conservative system and reduces to the forced type of the original Lotka-Volterra equation. A stochastic motion is found to occur when the density of a cold ion beam becomes larger. (author)
Magnetic interactions, bonding, and motion of positive muons in magnetite
Boekema, C.; Lichti, R.L.; Brabers, V.A.M.; Denison, A.B.; Cooke, D.W.; Heffner, R.H.; Hutson, R.L.; Leon, M.; Schillaci, M.E.
1985-01-01
Positive-muon behavior in magnetite is investigated by the muon-spin-rotation technique. The observed muon relaxation rate in zero applied field, in conjunction with the measured local field, allows us to separate muon-motion effects from phase transitions associated with magnetite. The local
Composing Interactive Dance Pieces for the MotionComposer, a device for Persons with Disabilities
Bergsland, Andreas; Wechsler, Robert
2015-01-01
The authors have developed a new hardware/software device for persons with disabilities (the MotionComposer), and in the process created a number of interactive dance pieces for non- disabled professional dancers. The paper briefly describes the hardware and motion tracking software of the device before going into more detail concerning the mapping strategies and sound design applied to three interactive dance pieces. The paper concludes by discussing a particular philosophy championing trans...
Fiore, Andrew M.; Swan, James W.
2018-01-01
Brownian Dynamics simulations are an important tool for modeling the dynamics of soft matter. However, accurate and rapid computations of the hydrodynamic interactions between suspended, microscopic components in a soft material are a significant computational challenge. Here, we present a new method for Brownian dynamics simulations of suspended colloidal scale particles such as colloids, polymers, surfactants, and proteins subject to a particular and important class of hydrodynamic constraints. The total computational cost of the algorithm is practically linear with the number of particles modeled and can be further optimized when the characteristic mass fractal dimension of the suspended particles is known. Specifically, we consider the so-called "stresslet" constraint for which suspended particles resist local deformation. This acts to produce a symmetric force dipole in the fluid and imparts rigidity to the particles. The presented method is an extension of the recently reported positively split formulation for Ewald summation of the Rotne-Prager-Yamakawa mobility tensor to higher order terms in the hydrodynamic scattering series accounting for force dipoles [A. M. Fiore et al., J. Chem. Phys. 146(12), 124116 (2017)]. The hydrodynamic mobility tensor, which is proportional to the covariance of particle Brownian displacements, is constructed as an Ewald sum in a novel way which guarantees that the real-space and wave-space contributions to the sum are independently symmetric and positive-definite for all possible particle configurations. This property of the Ewald sum is leveraged to rapidly sample the Brownian displacements from a superposition of statistically independent processes with the wave-space and real-space contributions as respective covariances. The cost of computing the Brownian displacements in this way is comparable to the cost of computing the deterministic displacements. The addition of a stresslet constraint to the over-damped particle
P3-23: Center/Surround Motion Interactions Measured Using a Nulling Procedure
Soo Hyun Park
2012-10-01
Full Text Available Many direction-selective neurons have a receptive field structure that promotes suppressive interactions between center and surround regions. These interactions sculpt the overall pattern of activity among those neurons and, therefore, presumably impact perceived direction of motion. To test this conjecture, we have assessed the effect of motion signals produced by a moving stimulus on perceived motion within a neighboring region. On each trial a vertical bar (inducer appeared at 8 eccentricity in the upper visual field, moving either leftward or rightward, and a circular shaped random dot kinematogram (test appeared at 4 eccentricity. The test dots moved randomly except when the inducer passed nearby the test, at which time a pulse of coherent motion occurred in one of the two directions within the test. Coherence strength was adjusted by QUEST to maintain equal likelihood (point of subjective equality: PSE of leftward and rightward reports of perceived direction during this motion pulse. The inducer caused a substantial shift in PSE: it was necessary for the test to contain 50% coherent motion in the same direction as that of the inducer to nullify the illusory motion within the test caused by the inducer. The effect of the inducer could also be offset by simultaneously presenting a second inducer moving in the opposite direction. This pattern of results implies substantial suppressive interactions between neighboring moving stimuli, interactions whose strength and direction can be assessed psychophysically using nulling procedures.
Dubina, Sean Hyun, E-mail: sdubin2@uic.edu; Wedgewood, Lewis Edward, E-mail: wedge@uic.edu [Department of Chemical Engineering, University of Illinois at Chicago, 810 S. Clinton St. (MC 110), Chicago, Illinois 60607-4408 (United States)
2016-07-15
Ferrofluids are often favored for their ability to be remotely positioned via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally simulated using the Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely, Maxwell’s equations. An iterative constraint method was developed to satisfy Maxwell’s equations when a uniform magnetic field is imposed on ferrofluids in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters in a mesoscale particle collection. This was accomplished by allowing a particulate system in a simple shear flow to advance by a time step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint method applied over sub-volume length scales until Maxwell’s equations were satisfied. The resultant ferrofluid model with constraints demonstrates that the magnetoviscosity contribution is not as substantial when compared to homogeneous simulations that assume the material’s magnetism is a direct response to the external magnetic field. This was detected across varying intensities of particle-particle interaction, Brownian motion, and shear flow. Ferroparticle aggregation was still extensively present but less so than typically observed.
Dubina, Sean Hyun; Wedgewood, Lewis Edward
2016-01-01
Ferrofluids are often favored for their ability to be remotely positioned via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally simulated using the Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely, Maxwell’s equations. An iterative constraint method was developed to satisfy Maxwell’s equations when a uniform magnetic field is imposed on ferrofluids in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters in a mesoscale particle collection. This was accomplished by allowing a particulate system in a simple shear flow to advance by a time step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint method applied over sub-volume length scales until Maxwell’s equations were satisfied. The resultant ferrofluid model with constraints demonstrates that the magnetoviscosity contribution is not as substantial when compared to homogeneous simulations that assume the material’s magnetism is a direct response to the external magnetic field. This was detected across varying intensities of particle-particle interaction, Brownian motion, and shear flow. Ferroparticle aggregation was still extensively present but less so than typically observed.
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.
Luco, J E; Wong, H L [Structural and Earthquake Engineering Consultants, Inc., Sierra Madre, CA (United States); Chang, C -Y; Power, M S; Idriss, I M [Woodward-Clyde Consultants, Walnut Creek, CA (United States)
1986-08-01
This report presents the results of part of a two-task study on the engineering characterization of earthquake ground motion for nuclear power plant design. The overall objective of this research program sponsored by the U.S. Nuclear Regulatory Commission (USNRC) is to develop recommendations for methods for selecting design response spectra or acceleration time histories to be used to characterize motion at the foundation level of nuclear power plants. Task I of the study, which is presented in Vol. 1 of NUREG/CR-3805, developed a basis for selecting design response spectra taking into account the characteristics of free-field ground motion found to be significant in causing structural damage. Task II incorporates additional considerations of effects of spatial variations of ground motions and soil-structure interaction on foundation motions and structural response. The results of Task II are presented in Vols. 2 through of NUREG/CR-3805 as follows: Vol. 2 effects of ground motion characteristics on structural response considering localized structural nonlinearities and soil-structure interaction effects; Vol. 3 observational data on spatial variations of earthquake ground motions; Vol. 4 soil-structure interaction effects on structural response; and Vol. 5, summary based on Tasks I and II studies. This report presents the results of the Vol. 4 studies.
Continuous state branching processes in random environment: The Brownian case
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...
On the Humble Origins of the Brownian Entropic Force
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...
Communicative interactions improve visual detection of biological motion.
Valeria Manera
Full Text Available BACKGROUND: In the context of interacting activities requiring close-body contact such as fighting or dancing, the actions of one agent can be used to predict the actions of the second agent. In the present study, we investigated whether interpersonal predictive coding extends to interactive activities--such as communicative interactions--in which no physical contingency is implied between the movements of the interacting individuals. METHODOLOGY/PRINCIPAL FINDINGS: Participants observed point-light displays of two agents (A and B performing separate actions. In the communicative condition, the action performed by agent B responded to a communicative gesture performed by agent A. In the individual condition, agent A's communicative action was substituted with a non-communicative action. Using a simultaneous masking detection task, we demonstrate that observing the communicative gesture performed by agent A enhanced visual discrimination of agent B. CONCLUSIONS/SIGNIFICANCE: Our finding complements and extends previous evidence for interpersonal predictive coding, suggesting that the communicative gestures of one agent can serve as a predictor for the expected actions of the respondent, even if no physical contact between agents is implied.
Combining coordination of motion actuators with driver steering interaction.
Tagesson, Kristoffer; Laine, Leo; Jacobson, Bengt
2015-01-01
A new method is suggested for coordination of vehicle motion actuators; where driver feedback and capabilities become natural elements in the prioritization. The method is using a weighted least squares control allocation formulation, where driver characteristics can be added as virtual force constraints. The approach is in particular suitable for heavy commercial vehicles that in general are over actuated. The method is applied, in a specific use case, by running a simulation of a truck applying automatic braking on a split friction surface. Here the required driver steering angle, to maintain the intended direction, is limited by a constant threshold. This constant is automatically accounted for when balancing actuator usage in the method. Simulation results show that the actual required driver steering angle can be expected to match the set constant well. Furthermore, the stopping distance is very much affected by this set capability of the driver to handle the lateral disturbance, as expected. In general the capability of the driver to handle disturbances should be estimated in real-time, considering driver mental state. By using the method it will then be possible to estimate e.g. stopping distance implied from this. The setup has the potential of even shortening the stopping distance, when the driver is estimated as active, this compared to currently available systems. The approach is feasible for real-time applications and requires only measurable vehicle quantities for parameterization. Examples of other suitable applications in scope of the method would be electronic stability control, lateral stability control at launch and optimal cornering arbitration.
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.
Sandlund, Marlene; Dock, Katarina; Häger, Charlotte K; Waterworth, Eva Lindh
2012-01-01
To explore parents' perceptions of using low-cost motion interactive video games as home training for their children with mild/moderate cerebral palsy. Semi-structured interviews were carried out with parents from 15 families after participation in an intervention where motion interactive games were used daily in home training for their child. A qualitative content analysis approach was applied. The parents' perception of the training was very positive. They expressed the view that motion interactive video games may promote positive experiences of physical training in rehabilitation, where the social aspects of gaming were especially valued. Further, the parents experienced less need to take on coaching while gaming stimulated independent training. However, there was a desire for more controlled and individualized games to better challenge the specific rehabilitative need of each child. Low-cost motion interactive games may provide increased motivation and social interaction to home training and promote independent training with reduced coaching efforts for the parents. In future designs of interactive games for rehabilitation purposes, it is important to preserve the motivational and social features of games while optimizing the individualized physical exercise.
Advanced and natural interaction system for motion-impaired users
Manresa Yee, Cristina Suemay
2009-01-01
Human-computer interaction is an important area that searches for better and more comfortable systems to promote communication between humans and machines. Vision-based interfaces can offer a more natural and appealing way of communication. Moreover, it can help in the e-accessibility component of the e-inclusion. The aim is to develop a usable system, that is, the end-user must consider the use of this device effective, efficient and satisfactory. The research's main contribution is SINA, a ...
Maskalick, D.G.
1984-01-01
It is expected that the internal motions of amino acid side chains and protein backbone segments influence and are in turn affected by charge-charge and related interactions, steric constraints, hydrophobic forces, and hydrogen bonding. As an initial test of this theory 13 C-enriched glycine, alanine, and isoleucine have been substituted for the amino terminal valine of sperm whale myoglobin using semisynthetic techniques. 13 C-NMR has been used to analyze the motions of the side chain and the protonation state of the alpha amino group as a function of pH. The addition of a single methyl group to the side chain can alter the alpha amino pK value by as much as 0.3 pH units indicating a delicately balanced set of change-charge interactions between the alpha amino group and the rest of the protein. Further evidence in support of the state theory was found upon examination of the internal motions of seven of nine isoleucine vectors. These motions were extracted from natural abundance 13 C-NMR relaxation data. The results suggest a strong possibility that concerted motions are important. Also, an increase in temperature from 32 0 C to 52 0 C leads to an electrostatically driven tightening of the myoglobin structure as evidenced by no significant increase in motion amplitude of most of the vectors
Ion Motion in a Plasma Interacting with Strong Magnetic Fields
Weingarten, A.; Grabowski, C.; Chakrabarti, N.; Maron, Y.; Fruchtmant, A.
1999-01-01
The interaction of a plasma with strong magnetic fields takes place in many laboratory experiments and astrophysical plasmas. Applying a strong magnetic field to the plasma may result in plasma displacement, magnetization, or the formation of instabilities. Important phenomena in plasma, such as the energy transport and the momentum balance, take a different form in each case. We study this interaction in a plasma that carries a short-duration (80-ns) current pulse, generating a magnetic field of up to 17 kG. The evolution of the magnetic field, plasma density, ion velocities, and electric fields are determined before and during the current pulse. The dependence of the plasma limiting current on the plasma density and composition are studied and compared to theoretical models based on the different phenomena. When the plasma collisionality is low, three typical velocities should be taken into consideration: the proton and heavier-ion Alfven velocities (v A p and v A h , respectively) and the EMHD magnetic-field penetration velocity into the plasma (v EMHD ). If both Alfven velocities are larger than v EMHD the plasma is pushed ahead of the magnetic piston and the magnetic field energy is dissipated into ion kinetic energy. If v EMHD is the largest of three velocities, the plasma become magnetized and the ions acquire a small axial momentum only. Different ion species may drift in different directions along the current lines. In this case, the magnetic field energy is probably dissipated into electron thermal energy. When vs > V EMHD > vi, as in the case of one of our experiments, ion mass separation occurs. The protons are pushed ahead of the piston while the heavier-ions become magnetized. Since the plasma electrons are unmagnetized they cannot cross the piston, and the heavy ions are probably charge-neutralized by electrons originating from the cathode that are 'born' magnetized
Egmose, Ida; Varni, Giovanna; Cordes, Katharina; Smith-Nielsen, Johanne; Væver, Mette S; Køppe, Simo; Cohen, David; Chetouani, Mohamed
2017-01-01
Bodily movements are an essential component of social interactions. However, the role of movement in early mother-infant interaction has received little attention in the research literature. The aim of the present study was to investigate the relationship between automatically extracted motion features and interaction quality in mother-infant interactions at 4 and 13 months. The sample consisted of 19 mother-infant dyads at 4 months and 33 mother-infant dyads at 13 months. The coding system Coding Interactive Behavior (CIB) was used for rating the quality of the interactions. Kinetic energy of upper-body, arms and head motion was calculated and used as segmentation in order to extract coarse- and fine-grained motion features. Spearman correlations were conducted between the composites derived from the CIB and the coarse- and fine-grained motion features. At both 4 and 13 months, longer durations of maternal arm motion and infant upper-body motion were associated with more aversive interactions, i.e., more parent-led interactions and more infant negativity. Further, at 4 months, the amount of motion silence was related to more adaptive interactions, i.e., more sensitive and child-led interactions. Analyses of the fine-grained motion features showed that if the mother coordinates her head movements with her infant's head movements, the interaction is rated as more adaptive in terms of less infant negativity and less dyadic negative states. We found more and stronger correlations between the motion features and the interaction qualities at 4 compared to 13 months. These results highlight that motion features are related to the quality of mother-infant interactions. Factors such as infant age and interaction set-up are likely to modify the meaning and importance of different motion features.
Overveld, van C.W.A.M.
1991-01-01
A method is presented for approximating the motions of linked 3-dimensional rigid body systems that may be applied in the context of interactive motion specification for computer animation. The method is based on decoupling the ballistic (free) component of the motion of the points that constitute
CNT based thermal Brownian motor to pump water in nanodevices
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...
Equations of motion of a particle interacting with a scalar field
Sato, N.K.
1984-01-01
The equations of motion of a particle (nucleon) interacting with a escalar (mesonic) field are derived by the energy momentum tensor moments method of Papapetrou. After a detailed study of the mesonic radiation field the expression of the reactive radiation force of the field upon the particle is established. (Author) [pt
Mancisidor, Aitziber; Zubizarreta, Asier; Cabanes, Itziar; Bengoa, Pablo; Jung, Je Hyung
2017-07-01
In order to enhance the performance of rehabilitation robots, it is imperative to know both force and motion caused by the interaction between user and robot. However, common direct measurement of both signals through force and motion sensors not only increases the complexity of the system but also impedes affordability of the system. As an alternative of the direct measurement, in this work, we present new force and motion estimators for the proper control of the upper-limb rehabilitation Universal Haptic Pantograph (UHP) robot. The estimators are based on the kinematic and dynamic model of the UHP and the use of signals measured by means of common low-cost sensors. In order to demonstrate the effectiveness of the estimators, several experimental tests were carried out. The force and impedance control of the UHP was implemented first by directly measuring the interaction force using accurate extra sensors and the robot performance was compared to the case where the proposed estimators replace the direct measured values. The experimental results reveal that the controller based on the estimators has similar performance to that using direct measurement (less than 1 N difference in root mean square error between two cases), indicating that the proposed force and motion estimators can facilitate implementation of interactive controller for the UHP in robotmediated rehabilitation trainings.
Commercial Motion Sensor Based Low-Cost and Convenient Interactive Treadmill
Jonghyun Kim
2015-09-01
Full Text Available Interactive treadmills were developed to improve the simulation of overground walking when compared to conventional treadmills. However, currently available interactive treadmills are expensive and inconvenient, which limits their use. We propose a low-cost and convenient version of the interactive treadmill that does not require expensive equipment and a complicated setup. As a substitute for high-cost sensors, such as motion capture systems, a low-cost motion sensor was used to recognize the subject’s intention for speed changing. Moreover, the sensor enables the subject to make a convenient and safe stop using gesture recognition. For further cost reduction, the novel interactive treadmill was based on an inexpensive treadmill platform and a novel high-level speed control scheme was applied to maximize performance for simulating overground walking. Pilot tests with ten healthy subjects were conducted and results demonstrated that the proposed treadmill achieves similar performance to a typical, costly, interactive treadmill that contains a motion capture system and an instrumented treadmill, while providing a convenient and safe method for stopping.
Deliberate utilization of interaction torques brakes elbow extension in a fast throwing motion.
Hore, Jon; Debicki, Derek B; Gribble, Paul L; Watts, Sherry
2011-05-01
We tested the hypothesis that in fast arm movements the CNS deliberately utilizes interaction torques to decelerate (brake) joint rotations. Twelve subjects performed fast 2-D overarm throws in which large elbow extension velocities occurred. Joint motions were computed from recordings made with search coils; joint torques were calculated using inverse dynamics. After ball release, a large follow-through shoulder extension acceleration occurred that was initiated by shoulder extensor muscle torque. This shoulder acceleration produced a flexor interaction torque at the elbow that initiated elbow deceleration (braking). An instantaneous mechanical interaction of passive torques then occurred between elbow and shoulder, i.e., elbow extension deceleration produced a large shoulder extensor interaction torque that contributed to the shoulder extension acceleration which, simultaneously, produced a large elbow flexor interaction torque that contributed to elbow extension deceleration, and so on. Late elbow flexor muscle torque also contributed to elbow deceleration. The interaction of passive torques between shoulder and elbow was braked by shoulder flexor muscle torque. In this mechanism, shoulder musculature contributed to braking elbow extension in two ways: shoulder extensors initiated the mechanical interaction of passive torques between shoulder and elbow and shoulder flexors dissipated kinetic energy from elbow braking. It is concluded that, in fast 2-D throws, the CNS deliberately utilizes powerful interaction torques between shoulder and elbow to brake motion at the elbow.
Thermodynamic and Quantum Thermodynamic Analyses of Brownian Movement
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.
Detecting Biological Motion for Human–Robot Interaction: A Link between Perception and Action
Alessia Vignolo
2017-06-01
Full Text Available One of the fundamental skills supporting safe and comfortable interaction between humans is their capability to understand intuitively each other’s actions and intentions. At the basis of this ability is a special-purpose visual processing that human brain has developed to comprehend human motion. Among the first “building blocks” enabling the bootstrapping of such visual processing is the ability to detect movements performed by biological agents in the scene, a skill mastered by human babies in the first days of their life. In this paper, we present a computational model based on the assumption that such visual ability must be based on local low-level visual motion features, which are independent of shape, such as the configuration of the body and perspective. Moreover, we implement it on the humanoid robot iCub, embedding it into a software architecture that leverages the regularities of biological motion also to control robot attention and oculomotor behaviors. In essence, we put forth a model in which the regularities of biological motion link perception and action enabling a robotic agent to follow a human-inspired sensory-motor behavior. We posit that this choice facilitates mutual understanding and goal prediction during collaboration, increasing the pleasantness and safety of the interaction.
Noise-to-signal transition of a Brownian particle in the cubic potential: I. general theory
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
Directed transport of confined Brownian particles with torque
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.
Decay ratio for third order Brownian oscillators
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
Nuclear electric quadrupole interactions in liquids entrapped in cavities
Furman, Gregory B., E-mail: gregoryf@bgu.ac.il; Meerovich, Victor M.; Sokolovsky, Vladimir L. [Ben Gurion University of the Negev, Physics Department (Israel)
2016-12-15
Liquids entrapped in cavities and containing quadrupole nuclei are considered. The interaction of the quadrupole moment of a nucleus with the electric field gradient is studied. In such a system, molecules are in both rotational and translational Brownian motions which are described by the diffusion equation. Solving this equation, we show that the intra- and intermolecular nuclear quadrupole interactions are averaged to zero in cavities with the size larger than several angstroms.
Cross-sensory facilitation reveals neural interactions between visual and tactile motion in humans
Monica eGori
2011-04-01
Full Text Available Many recent studies show that the human brain integrates information across the different senses and that stimuli of one sensory modality can enhance the perception of other modalities. Here we study the processes that mediate cross-modal facilitation and summation between visual and tactile motion. We find that while summation produced a generic, non-specific improvement of thresholds, probably reflecting higher-order interaction of decision signals, facilitation reveals a strong, direction-specific interaction, which we believe reflects sensory interactions. We measured visual and tactile velocity discrimination thresholds over a wide range of base velocities and conditions. Thresholds for both visual and tactile stimuli showed the characteristic dipper function, with the minimum thresholds occurring at a given pedestal speed. When visual and tactile coherent stimuli were combined (summation condition the thresholds for these multi-sensory stimuli also showed a dipper function with the minimum thresholds occurring in a similar range to that for unisensory signals. However, the improvement of multisensory thresholds was weak and not directionally specific, well predicted by the maximum likelihood estimation model (agreeing with previous research. A different technique (facilitation did, however, reveal direction-specific enhancement. Adding a non-informative pedestal motion stimulus in one sensory modality (vision or touch selectively lowered thresholds in the other, by the same amount as pedestals in the same modality. Facilitation did not occur for neutral stimuli like sounds (that would also have reduced temporal uncertainty, nor for motion in opposite direction, even in blocked trials where the subjects knew that the motion was in the opposite direction showing that the facilitation was not under subject control. Cross-sensory facilitation is strong evidence for functionally relevant cross-sensory integration at early levels of sensory
Xie, Weihong; Yu, Yang
2017-01-01
Robot-assisted motion compensated beating heart surgery has the advantage over the conventional Coronary Artery Bypass Graft (CABG) in terms of reduced trauma to the surrounding structures that leads to shortened recovery time. The severe nonlinear and diverse nature of irregular heart rhythm causes enormous difficulty for the robot to realize the clinic requirements, especially under arrhythmias. In this paper, we propose a fusion prediction framework based on Interactive Multiple Model (IMM) estimator, allowing each model to cover a distinguishing feature of the heart motion in underlying dynamics. We find that, at normal state, the nonlinearity of the heart motion with slow time-variant changing dominates the beating process. When an arrhythmia occurs, the irregularity mode, the fast uncertainties with random patterns become the leading factor of the heart motion. We deal with prediction problem in the case of arrhythmias by estimating the state with two behavior modes which can adaptively “switch” from one to the other. Also, we employed the signal quality index to adaptively determine the switch transition probability in the framework of IMM. We conduct comparative experiments to evaluate the proposed approach with four distinguished datasets. The test results indicate that the new proposed approach reduces prediction errors significantly. PMID:29124062
Fan Liang
2017-01-01
Full Text Available Robot-assisted motion compensated beating heart surgery has the advantage over the conventional Coronary Artery Bypass Graft (CABG in terms of reduced trauma to the surrounding structures that leads to shortened recovery time. The severe nonlinear and diverse nature of irregular heart rhythm causes enormous difficulty for the robot to realize the clinic requirements, especially under arrhythmias. In this paper, we propose a fusion prediction framework based on Interactive Multiple Model (IMM estimator, allowing each model to cover a distinguishing feature of the heart motion in underlying dynamics. We find that, at normal state, the nonlinearity of the heart motion with slow time-variant changing dominates the beating process. When an arrhythmia occurs, the irregularity mode, the fast uncertainties with random patterns become the leading factor of the heart motion. We deal with prediction problem in the case of arrhythmias by estimating the state with two behavior modes which can adaptively “switch” from one to the other. Also, we employed the signal quality index to adaptively determine the switch transition probability in the framework of IMM. We conduct comparative experiments to evaluate the proposed approach with four distinguished datasets. The test results indicate that the new proposed approach reduces prediction errors significantly.
Nagpal, A.K.
1978-01-01
Contrary to the prevalent belief, it is shown here that for the spin-3/2 Rarita-Schwinger field in the presence of a fully quantized interaction, the (anti) commutation relations are compatible with the Heisenberg equations of motion. The latter are indeed the same as the Lagrangian equations of motion. Further, it is shown that the validity of the Heisenberg equations of motion does not depend upon the choice of the canonical variables
Effect of Interaction and Rocking Motion on The Earthquake Response of Buildings
Gholamreza Havaei
2015-03-01
Full Text Available Usually structures are designed under codes based on the assumption that the soil stiffness is infinite, so the foundation rests firmly on the soil. In many cases, the overturning moment due to the lateral forces may exceed the resisting moment due to the gravity forces. Thus, this may cause a foundation uplift because in reality the soil stiffness is not infinite and the structure stands up under gravity forces. The phenomenon of foundation uplifting and its impact on the soil are known as the rocking motion.This study investigates the influence of the rocking motion and interaction by the yielding base plates on the nonlinear behavior of steel structures under dynamic analysis. More specifically, Three- five and seven -storied structuresare designed with ordinary ductility, then the structuresare analyzed in rigid and deformable base plate cases with using the ABAQUS software.The results show that the rocking motion and Interaction decrease the response of buildings such as the base shear, the axial force of columns and the strain energy but also increase the natural period.
Species and Scale Dependence of Bacterial Motion Dynamics
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.
Non-intersecting Brownian walkers and Yang-Mills theory on the sphere
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.
Unidirectional Magnon-Driven Domain Wall Motion due to Interfacial Dzyaloshinskii-Moriya Interaction
Lee, Seo-Won
2018-03-28
We theoretically study magnon-driven motion of a tranverse domain wall in the presence of interfacial Dzyaloshinskii-Moriya interaction (DMI). Contrary to previous studies, the domain wall moves along the same direction regardless of the magnon-flow direction. Our symmetry analysis reveals that the odd order DMI contributions to the domain wall velocity are independent of the magnon-flow direction. Corresponding DMI-induced asymmetric transitions from a spin-wave state to another give rise to a large momentum transfer to the domain wall without nonreciprocity and much reflection. This counterintuitive unidirectional motion occurs not only for a spin wave with a single wavevector but also for thermal magnons with distributed wavevectors.
Unidirectional Magnon-Driven Domain Wall Motion due to Interfacial Dzyaloshinskii-Moriya Interaction
Lee, Seo-Won; Kim, Kyoung-Whan; Moon, Jung-Hwan; Go, Gyungchoon; Manchon, Aurelien; Lee, Hyun-Woo; Everschor-Sitte, Karin; Lee, Kyung-Jin
2018-01-01
We theoretically study magnon-driven motion of a tranverse domain wall in the presence of interfacial Dzyaloshinskii-Moriya interaction (DMI). Contrary to previous studies, the domain wall moves along the same direction regardless of the magnon-flow direction. Our symmetry analysis reveals that the odd order DMI contributions to the domain wall velocity are independent of the magnon-flow direction. Corresponding DMI-induced asymmetric transitions from a spin-wave state to another give rise to a large momentum transfer to the domain wall without nonreciprocity and much reflection. This counterintuitive unidirectional motion occurs not only for a spin wave with a single wavevector but also for thermal magnons with distributed wavevectors.
Ilday, Serim; Akguc, Gursoy B.; Tokel, Onur; Makey, Ghaith; Yavuz, Ozgun; Yavuz, Koray; Pavlov, Ihor; Ilday, F. Omer; Gulseren, Oguz
We report a new dynamical self-assembly mechanism, where judicious use of convective and strong Brownian forces enables effective patterning of colloidal nanoparticles that are almost two orders of magnitude smaller than the laser beam. Optical trapping or tweezing effects are not involved, but the laser is used to create steep thermal gradients through multi-photon absorption, and thereby guide the colloids through convective forces. Convective forces can be thought as a positive feedback mechanism that helps to form and reinforce pattern, while Brownian motion act as a competing negative feedback mechanism to limit the growth of the pattern, as well as to increase the possibilities of bifurcation into different patterns, analogous to the competition observed in reaction-diffusion systems. By steering stochastic processes through these forces, we are able to gain control over the emergent pattern such as to form-deform-reform of a pattern, to change its shape and transport it spatially within seconds. This enables us to dynamically initiate and control large patterns comprised of hundreds of colloids. Further, by not relying on any specific chemical, optical or magnetic interaction, this new method is, in principle, completely independent of the material type being assembled.
Motion of Rydberg atoms with strong permanent-electric-dipole interactions
Gonçalves, Luís Felipe; Thaicharoen, Nithiwadee; Raithel, Georg
2016-01-01
Using classical trajectories simulations, we investigate the dynamics of a cold sample of Rydberg atoms with high permanent electric dipole moments. The dipolar state can be created using an adiabatic passage through an avoided crossing between an S-like state and a linear Stark state. The simulations yield the pair-correlation functions (PCF) of the atom samples, which allow us to extract the motion of Rydberg-atom pairs in the many-body system. The results reveal the strength and the anisotropic character of the underlying interaction. The simulation is employed to test the suitability of experimental methods designed to derive interaction parameters from PCF. Insight is obtained about the stability of the method against variation of experimentally relevant parameters. Transient correlations due to interaction-induced heating are observed. (paper)
Swarming behavior of gradient-responsive Brownian particles in a porous medium
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.
An adjustable Brownian heat engine
Asfaw, Mesfin; Bekele, Mulugeta
2002-09-01
A microscopic heat engine is modeled as a Brownian particle in a sawtooth potential (with load) moving through a highly viscous medium driven by the thermal kick it gets from alternately placed hot and cold heat reservoirs. We found a closed form expression for the current as a function of the parameters characterizing the model. Depending on the values these model parameters take, the engine is also found to function as a refrigerator. Expressions for the efficiency as well as for the refrigerator performance are also reported. Study of how these quantities depend on the model parameters enabled us in identifying the points in the parameter space where the engine performs either with maximum power or with optimized efficiency. The corresponding efficiencies of the engine are then compared with those of the endoreversible and Carnot engines. (author)
Intermittency and multifractional Brownian character of geomagnetic time series
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.
Bending-Twisting Motions and Main Interactions in Nucleoplasmin Nuclear Import.
Marcos Tadeu Geraldo
Full Text Available Alpha solenoid proteins play a key role in regulating the classical nuclear import pathway, recognizing a target protein and transporting it into the nucleus. Importin-α (Impα is the solenoid responsible for cargo protein recognition, and it has been extensively studied by X-ray crystallography to understand the binding specificity. To comprehend the main motions of Impα and to extend the information about the critical interactions during carrier-cargo recognition, we surveyed different conformational states based on molecular dynamics (MD and normal mode (NM analyses. Our model of study was a crystallographic structure of Impα complexed with the classical nuclear localization sequence (cNLS from nucleoplasmin (Npl, which was submitted to multiple 100 ns of MD simulations. Representative conformations were selected for calculating the 87 lowest frequencies NMs of vibration, and a displacement approach was applied along each NM. Based on geometric criteria, using the radius of curvature and inter-repeat angles as the reference metrics, the main motions of Impα were described. Moreover, we determined the salt bridges, hydrogen bonds and hydrophobic interactions in the Impα-NplNLS interface. Our results show the bending and twisting motions participating in the recognition of nuclear proteins, allowing the accommodation and adjustment of a classical bipartite NLS sequence. The essential contacts for the nuclear import were also described and were mostly in agreement with previous studies, suggesting that the residues in the cNLS linker region establish important contacts with Impα adjusting the cNLS backbone. The MD simulations combined with NM analysis can be applied to the Impα-NLS system to help understand interactions between Impα and cNLSs and the analysis of non-classic NLSs.
Phillips, Carolyn L.; Anderson, Joshua A.; Glotzer, Sharon C.
2011-01-01
Highlights: → Molecular Dynamics codes implemented on GPUs have achieved two-order of magnitude computational accelerations. → Brownian Dynamics and Dissipative Particle Dynamics simulations require a large number of random numbers per time step. → We introduce a method for generating small batches of pseudorandom numbers distributed over many threads of calculations. → With this method, Dissipative Particle Dynamics is implemented on a GPU device without requiring thread-to-thread communication. - Abstract: Brownian Dynamics (BD), also known as Langevin Dynamics, and Dissipative Particle Dynamics (DPD) are implicit solvent methods commonly used in models of soft matter and biomolecular systems. The interaction of the numerous solvent particles with larger particles is coarse-grained as a Langevin thermostat is applied to individual particles or to particle pairs. The Langevin thermostat requires a pseudo-random number generator (PRNG) to generate the stochastic force applied to each particle or pair of neighboring particles during each time step in the integration of Newton's equations of motion. In a Single-Instruction-Multiple-Thread (SIMT) GPU parallel computing environment, small batches of random numbers must be generated over thousands of threads and millions of kernel calls. In this communication we introduce a one-PRNG-per-kernel-call-per-thread scheme, in which a micro-stream of pseudorandom numbers is generated in each thread and kernel call. These high quality, statistically robust micro-streams require no global memory for state storage, are more computationally efficient than other PRNG schemes in memory-bound kernels, and uniquely enable the DPD simulation method without requiring communication between threads.
Interaction and collective effects in classical-equations-of-motion calculations
Bodmer, A.R.
1981-01-01
We discuss results obtained with the classical-equations-of-motion (CEOM) approach, with particular reference to interaction (potential energy) and collective effects in central collisions of equal mass nuclei. The essence of the CEOM approach is the classical calculation of all A = A/sub P/ + A/sub T/ trajectories using a 2-body potential V between all pairs of nucleons; V = V/sub short/ + V/sub long/ has a short range repulsion and a longer range attractive tail. In contrast to hydrodynamics, the CEOM approach is microscopic and includes transparency and nonequilibrium effects
Equations of motion of interacting massless fields of all spins as a free differential algebra
Vasiliev, M A
1988-08-11
It is argued that the equations of motion of interacting massless fields of all spins s=0, 1, ..., infinity can naturally be formulated in terms of a free differential algebra (FDA) constructed from one-forms and zero-forms that belong both to the adjoint representation of the infinite-dimensional superalgebra of higher spins and auxiliary fields proposed previously. This FDA is found explicitly in the first non-trivial order in the zero-forms. Various properties of the proposed FDA are discussed including the ways for incorporating internal (Yang-Mills) gauge symmetries via associative algebras.
Current R and D status on material motion and interactions relevant to core disruptive accidents
Kondo, Satoru [Safety Engineering Division, O-arai Engineering Center, Power Reactor and Nuclear Fuel Development Corporation, O-arai, Ibaraki (Japan)
1994-07-01
In this paper, the current status of research and development activities are briefly reviewed on evaluation of material-coolant interactions and material movement and relocation relevant to the safety of liquid-metal fast reactors. Since the status of European activities are well summarized in other papers submitted to the present meeting, the activities in Japan and the United States are highlighted in this paper. The review includes: out-of-pile experiments, in-pile experiments and relevant computer code development. It is emphasized that improved understanding on material motion has contributed to establishing more realistic and rational safety evaluation methods, where various mitigation mechanisms are inherently effective. (author)
Erees Queen B. Macabebe
2017-04-01
Full Text Available To assess effectively the influence of peer discussion in understandingconcepts, and to evaluate if the conceptual understanding through Interactive Lecture Demonstrations (ILD and collaborative learning can be translated to actual situations, ten (10 questions on human and carts in motion were presented to 151 university students comprising mostly of science majors but of different year levels. Individual and group predictions were conducted to assess the students’ pre-conceptual understanding of motion graphs. During the ILD, real-time motion graphs were obtained and analysed after each demonstration and an assessment that integrates the ten situations into two scenarios was given to evaluate the conceptual understanding of the students. Collaborative learning produced a positive effect on the prediction scores of the students and the ILD with real-time measurement allowed the students to validate their prediction. However, when the given situations were incorporated to create a scenario, it posted a challenge to the students. The results of this activity identified the area where additional instruction and emphasis is necessary.
Design of a compact low-power human-computer interaction equipment for hand motion
Wu, Xianwei; Jin, Wenguang
2017-01-01
Human-Computer Interaction (HCI) raises demand of convenience, endurance, responsiveness and naturalness. This paper describes a design of a compact wearable low-power HCI equipment applied to gesture recognition. System combines multi-mode sense signals: the vision sense signal and the motion sense signal, and the equipment is equipped with the depth camera and the motion sensor. The dimension (40 mm × 30 mm) and structure is compact and portable after tight integration. System is built on a module layered framework, which contributes to real-time collection (60 fps), process and transmission via synchronous confusion with asynchronous concurrent collection and wireless Blue 4.0 transmission. To minimize equipment's energy consumption, system makes use of low-power components, managing peripheral state dynamically, switching into idle mode intelligently, pulse-width modulation (PWM) of the NIR LEDs of the depth camera and algorithm optimization by the motion sensor. To test this equipment's function and performance, a gesture recognition algorithm is applied to system. As the result presents, general energy consumption could be as low as 0.5 W.
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
Biased Brownian dynamics for rate constant calculation.
Zou, G; Skeel, R D; Subramaniam, S
2000-01-01
An enhanced sampling method-biased Brownian dynamics-is developed for the calculation of diffusion-limited biomolecular association reaction rates with high energy or entropy barriers. Biased Brownian dynamics introduces a biasing force in addition to the electrostatic force between the reactants, and it associates a probability weight with each trajectory. A simulation loses weight when movement is along the biasing force and gains weight when movement is against the biasing force. The sampl...
Brownian quasi-particles in statistical physics
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
Genre, technology and embodied interaction: The evolution of digital game genres and motion gaming
Andreas Gregersen
2011-11-01
Full Text Available Technology has been given relatively little attention in genre theory, but this article argues that material technologies can be important components in genre development. The argument is based on a historically informed analysis of digital games, with special attention paid to home console video games and recent genre developments within this domain commonly referred to as motion gaming. The main point is that digital game genres imply structured embodied activity. A constitutive element of digital game mediation is a control interface geared to player embodiment, and I propose the concept of ‘interaction modes’ to describe the coupling of technology and player embodiment and show how this can be integrated with genre theory. The resulting framework allows for increased attention to continuity and change in game and communication genres, material and digital technologies, and the related interaction modes.
Lin, Chern-Sheng; Chen, Chia-Tse; Shei, Hung-Jung; Lay, Yun-Long; Chiu, Chuang-Chien
2012-09-01
This study develops a body motion interactive system with computer vision technology. This application combines interactive games, art performing, and exercise training system. Multiple image processing and computer vision technologies are used in this study. The system can calculate the characteristics of an object color, and then perform color segmentation. When there is a wrong action judgment, the system will avoid the error with a weight voting mechanism, which can set the condition score and weight value for the action judgment, and choose the best action judgment from the weight voting mechanism. Finally, this study estimated the reliability of the system in order to make improvements. The results showed that, this method has good effect on accuracy and stability during operations of the human-machine interface of the sports training system.
Magnon–magnon interactions in O(3) ferromagnets and equations of motion for spin operators
Radošević, Slobodan M.
2015-01-01
The method of equations of motion for spin operators in the case of O(3) Heisenberg ferromagnet is systematically analyzed starting from the effective Lagrangian. It is shown that the random phase approximation and the Callen approximation can be understood in terms of perturbation theory for type B magnons. Also, the second order approximation of Kondo and Yamaji for one dimensional ferromagnet is reduced to the perturbation theory for type A magnons. An emphasis is put on the physical picture, i.e. on magnon–magnon interactions and symmetries of the Heisenberg model. Calculations demonstrate that all three approximations differ in manner in which the magnon–magnon interactions arising from the Wess–Zumino term are treated, from where specific features and limitations of each of them can be deduced.
Magnon–magnon interactions in O(3) ferromagnets and equations of motion for spin operators
Radošević, Slobodan M., E-mail: slobodan@df.uns.ac.rs
2015-11-15
The method of equations of motion for spin operators in the case of O(3) Heisenberg ferromagnet is systematically analyzed starting from the effective Lagrangian. It is shown that the random phase approximation and the Callen approximation can be understood in terms of perturbation theory for type B magnons. Also, the second order approximation of Kondo and Yamaji for one dimensional ferromagnet is reduced to the perturbation theory for type A magnons. An emphasis is put on the physical picture, i.e. on magnon–magnon interactions and symmetries of the Heisenberg model. Calculations demonstrate that all three approximations differ in manner in which the magnon–magnon interactions arising from the Wess–Zumino term are treated, from where specific features and limitations of each of them can be deduced.
Thermal motion in proteins: Large effects on the time-averaged interaction energies
Goethe, Martin; Rubi, J. Miguel; Fita, Ignacio
2016-01-01
As a consequence of thermal motion, inter-atomic distances in proteins fluctuate strongly around their average values, and hence, also interaction energies (i.e. the pair-potentials evaluated at the fluctuating distances) are not constant in time but exhibit pronounced fluctuations. These fluctuations cause that time-averaged interaction energies do generally not coincide with the energy values obtained by evaluating the pair-potentials at the average distances. More precisely, time-averaged interaction energies behave typically smoother in terms of the average distance than the corresponding pair-potentials. This averaging effect is referred to as the thermal smoothing effect. Here, we estimate the strength of the thermal smoothing effect on the Lennard-Jones pair-potential for globular proteins at ambient conditions using x-ray diffraction and simulation data of a representative set of proteins. For specific atom species, we find a significant smoothing effect where the time-averaged interaction energy of a single atom pair can differ by various tens of cal/mol from the Lennard-Jones potential at the average distance. Importantly, we observe a dependency of the effect on the local environment of the involved atoms. The effect is typically weaker for bulky backbone atoms in beta sheets than for side-chain atoms belonging to other secondary structure on the surface of the protein. The results of this work have important practical implications for protein software relying on free energy expressions. We show that the accuracy of free energy expressions can largely be increased by introducing environment specific Lennard-Jones parameters accounting for the fact that the typical thermal motion of protein atoms depends strongly on their local environment.
Thermal motion in proteins: Large effects on the time-averaged interaction energies
Goethe, Martin, E-mail: martingoethe@ub.edu; Rubi, J. Miguel [Departament de Física Fonamental, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona (Spain); Fita, Ignacio [Institut de Biologia Molecular de Barcelona, Baldiri Reixac 10, 08028 Barcelona (Spain)
2016-03-15
As a consequence of thermal motion, inter-atomic distances in proteins fluctuate strongly around their average values, and hence, also interaction energies (i.e. the pair-potentials evaluated at the fluctuating distances) are not constant in time but exhibit pronounced fluctuations. These fluctuations cause that time-averaged interaction energies do generally not coincide with the energy values obtained by evaluating the pair-potentials at the average distances. More precisely, time-averaged interaction energies behave typically smoother in terms of the average distance than the corresponding pair-potentials. This averaging effect is referred to as the thermal smoothing effect. Here, we estimate the strength of the thermal smoothing effect on the Lennard-Jones pair-potential for globular proteins at ambient conditions using x-ray diffraction and simulation data of a representative set of proteins. For specific atom species, we find a significant smoothing effect where the time-averaged interaction energy of a single atom pair can differ by various tens of cal/mol from the Lennard-Jones potential at the average distance. Importantly, we observe a dependency of the effect on the local environment of the involved atoms. The effect is typically weaker for bulky backbone atoms in beta sheets than for side-chain atoms belonging to other secondary structure on the surface of the protein. The results of this work have important practical implications for protein software relying on free energy expressions. We show that the accuracy of free energy expressions can largely be increased by introducing environment specific Lennard-Jones parameters accounting for the fact that the typical thermal motion of protein atoms depends strongly on their local environment.
Engineering Autonomous Chemomechanical Nanomachines Using Brownian Ratchets
Lavella, Gabriel
Nanoscale machines which directly convert chemical energy into mechanical work are ubiquitous in nature and are employed to perform a diverse set of tasks such as transporting molecules, maintaining molecular gradients, and providing motion to organisms. Their widespread use in nature suggests that large technological rewards can be obtained by designing synthetic machines that use similar mechanisms. This thesis addresses the technological adaptation of a specific mechanism known as the Brownian ratchet for the design of synthetic autonomous nanomachines. My efforts were focused more specifically on synthetic chemomechanical ratchets which I deem will be broadly applicable in the life sciences. In my work I have theoretically explored the biophysical mechanisms and energy landscapes that give rise to the ratcheting phenomena and devised devices that operate off these principles. I demonstrate two generations of devices that produce mechanical force/deformation in response to a user specified ligand. The first generation devices, fabricatied using a combination nanoscale lithographic processes and bioconjugation techniques, were used to provide evidence that the proposed ratcheting phenomena can be exploited in synthetic architectures. Second generation devices fabricated using self-assembled DNA/hapten motifs were constructed to gain a precise understanding of ratcheting dynamics and design constraints. In addition, the self-assembled devices enabled fabrication en masse, which I feel will alleviate future experimental hurdles in analysis and facilitate its adaptation to technologies. The product of these efforts is an architecture that has the potential to enable numerous technologies in biosensing and drug delivery. For example, the coupling of molecule-specific actuation to the release of drugs or signaling molecules from nanocapsules or porous materials could be transformative. Such architectures could provide possible avenues to pressing issues in biology and
Vamsi Kiran Adhikarla
2015-04-01
Full Text Available This paper reports on the design and evaluation of direct 3D gesture interaction with a full horizontal parallax light field display. A light field display defines a visual scene using directional light beams emitted from multiple light sources as if they are emitted from scene points. Each scene point is rendered individually resulting in more realistic and accurate 3D visualization compared to other 3D displaying technologies. We propose an interaction setup combining the visualization of objects within the Field Of View (FOV of a light field display and their selection through freehand gesture tracked by the Leap Motion Controller. The accuracy and usefulness of the proposed interaction setup was also evaluated in a user study with test subjects. The results of the study revealed high user preference for free hand interaction with light field display as well as relatively low cognitive demand of this technique. Further, our results also revealed some limitations and adjustments of the proposed setup to be addressed in future work.
Adhikarla, Vamsi Kiran; Sodnik, Jaka; Szolgay, Peter; Jakus, Grega
2015-04-14
This paper reports on the design and evaluation of direct 3D gesture interaction with a full horizontal parallax light field display. A light field display defines a visual scene using directional light beams emitted from multiple light sources as if they are emitted from scene points. Each scene point is rendered individually resulting in more realistic and accurate 3D visualization compared to other 3D displaying technologies. We propose an interaction setup combining the visualization of objects within the Field Of View (FOV) of a light field display and their selection through freehand gesture tracked by the Leap Motion Controller. The accuracy and usefulness of the proposed interaction setup was also evaluated in a user study with test subjects. The results of the study revealed high user preference for free hand interaction with light field display as well as relatively low cognitive demand of this technique. Further, our results also revealed some limitations and adjustments of the proposed setup to be addressed in future work.
Pan, Wen Fu
2017-01-01
The objective of this study was to test whether the Kinect motion-sensing interactive system (KMIS) enhanced students' English vocabulary learning, while also comparing the system's effectiveness against a traditional computer-mouse interface. Both interfaces utilized an interactive game with a questioning strategy. One-hundred and twenty…
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.
Okruszek, Ł; Wordecha, M; Jarkiewicz, M; Kossowski, B; Lee, J; Marchewka, A
2017-11-27
Recognition of communicative interactions is a complex social cognitive ability which is associated with a specific neural activity in healthy individuals. However, neural correlates of communicative interaction processing from whole-body motion have not been known in patients with schizophrenia (SCZ). Therefore, the current study aims to examine the neural activity associated with recognition of communicative interactions in SCZ by using displays of the dyadic interactions downgraded to minimalistic point-light presentations. Twenty-six healthy controls (HC) and 25 SCZ were asked to judge whether two agents presented only by point-light displays were communicating or acting independently. Task-related activity and functional connectivity of brain structures were examined with General Linear Model and Generalized Psychophysiological Interaction approach, respectively. HC were significantly more efficient in recognizing each type of action than SCZ. At the neural level, the activity of the right posterior superior temporal sulcus (pSTS) was observed to be higher in HC compared with SCZ for communicative v. individual action processing. Importantly, increased connectivity of the right pSTS with structures associated with mentalizing (left pSTS) and mirroring networks (left frontal areas) was observed in HC, but not in SCZ, during the presentation of social interactions. Under-recruitment of the right pSTS, a structure known to have a pivotal role in social processing, may also be of importance for higher-order social cognitive deficits in SCZ. Furthermore, decreased task-related connectivity of the right pSTS may result in reduced use of additional sources of information (for instance motor resonance signals) during social cognitive processing in schizophrenia.
Interactive motion-controlled games in the neurorehabilitation of adult post-stroke patients
Emilia Mikołajewska
2015-08-01
Emilia Mikołajewska Rehabilitation Clinic Military Clinical Hospital No. 10 and Polyclinic Bydgoszcz, Poland e-mail: e.mikolajewska@wp.pl, emiliam@cm.umk.pl www: http://emikolajewska.netstrefa.eu Keywords: neurorehabilitation; physiotherapy; stroke; neurological deficit; therapeutic game. Abstract Despite efforts of scientists and clinicians stroke still constitutes one of the major causes of disability worldwide. Motion-controlled video games become increasingly common adjunct to the traditional physical therapy. Such games are usually available, low-cost, fun, and functional ways to increase everyday treatment possibilities, both in hospital, ambulatory and home settings. Research and scientific publications concerning this issue are still rare. Assessment how interactive motion-controlled games can be incorporated into current guidelines of the eclectic approach within neurorehabilitation of adult post-stroke survivors is key issue within contemporary neurorehabilitation of adults. Complementary use of such games may constitute another breakthrough both in in-patient and out-patient rehabilitation and care. This review aims at potential of aforementioned solutions and modalities for the rehabilitation of function in cases of stroke.
Collective motion of groups of self-propelled particles following interacting leaders
Ferdinandy, B.; Ozogány, K.; Vicsek, T.
2017-08-01
In order to keep their cohesiveness during locomotion gregarious animals must make collective decisions. Many species boast complex societies with multiple levels of communities. A common case is when two dominant levels exist, one corresponding to leaders and the other consisting of followers. In this paper we study the collective motion of such two-level assemblies of self-propelled particles. We present a model adapted from one originally proposed to describe the movement of cells resulting in a smoothly varying coherent motion. We shall use the terminology corresponding to large groups of some mammals where leaders and followers form a group called a harem. We study the emergence (self-organization) of sub-groups within a herd during locomotion by computer simulations. The resulting processes are compared with our prior observations of a Przewalski horse herd (Hortobágy, Hungary) which we use as results from a published case study. We find that the model reproduces key features of a herd composed of harems moving on open ground, including fights for followers between leaders and bachelor groups (group of leaders without followers). One of our findings, however, does not agree with the observations. While in our model the emerging group size distribution is normal, the group size distribution of the observed herd based on historical data have been found to follow lognormal distribution. We argue that this indicates that the formation (and the size) of the harems must involve a more complex social topology than simple spatial-distance based interactions.
Motion Intention Analysis-Based Coordinated Control for Amputee-Prosthesis Interaction
Fei Wang
2010-01-01
Full Text Available To study amputee-prosthesis (AP interaction, a novel reconfigurable biped robot was designed and fabricated. In homogeneous configuration, two identical artificial legs (ALs were used to simulate the symmetrical lower limbs of a healthy person. Linear inverted pendulum model combining with ZMP stability criterion was used to generate the gait trajectories of ALs. To acquire interjoint coordination for healthy gait, rate gyroscopes were mounted on CoGs of thigh and shank of both legs. By employing principal component analysis, the measured angular velocities were processed and the motion synergy was obtained in the final. Then, one of two ALs was replaced by a bionic leg (BL, and the biped robot was changed into heterogeneous configuration to simulate the AP coupling system. To realize symmetrical stable walking, master/slave coordinated control strategy is proposed. According to information acquired by gyroscopes, BL recognized the motion intention of AL and reconstructed its kinematic variables based on interjoint coordination. By employing iterative learning control, gait tracking of BL to AL was archived. Real environment robot walking experiments validated the correctness and effectiveness of the proposed scheme.
Kim, Jae Kwan; Lee, J. S.; Yang, T. S.; Cho, J. R.; R, H. [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1997-09-01
In order to establish a correct correlation between them, mechanical characteristics of the ancient structures need to be investigated. Since sedimentary basins are preferred dwelling sites in ancient times, it is necessary to perform SSI analysis to derive correct correlation between the damage and ground motion intensity. Contents of Project are as follows: (1) Generation of stochastic earthquake ground motion considering source mechanism and site effects. (2) Analysis of seismic response of sedimentary basin. (3) Soil-structure interaction analysis of ancient structures (4) Investigation of dynamic response characteristics of ancient structure considering soil-structure interaction effects. A procedure is presented for generation of stochastic earthquake ground motion considering source mechanism and site effects. The simulation method proposed by Boore is used to generate the outcropping rock motion. The free field motion at the soil site is obtained by a convolution analysis. And for the study of wood structures, a nonlinear SDOF model is developed. The effects of soil-structure interaction on the behavior of the wood structures are found to be very minor. But the response can be significantly affected due to the intensity and frequency contents of the input motion. 13 refs., 6 tabs., 31 figs. (author)
First passage Brownian functional properties of snowmelt dynamics
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.
The interaction of grammatical aspect and temporal distance in motion descriptions
Sarah eAnderson
2013-07-01
Full Text Available Grammatical aspect is known to shape event understanding. However, little is known about how it interacts with other important temporal information, such as recent and distant past. The current work uses computer-mouse tracking (Spivey, Grosjean, & Knoblich, 2005 to explore the interaction of aspect and temporal context. Participants in our experiment listened to past motion event descriptions that varied according to aspect (simple past, past progressive and temporal distance (recent past, distant past while viewing scenes with paths and implied destinations. Participants used a computer mouse to place characters into the scene to match event descriptions. Our results indicated that aspect and temporal context interact in interesting ways. When aspect placed emphasis on the ongoing details of the event and the temporal context was recent (thus, making fine details available in memory, this match between conditions elicited smoother and faster computer mouse movements than when conditions mismatched. Likewise, when aspect placed emphasis on the less-detailed end state of the event and temporal context was in the distant past (thus making fine details less available, this match between conditions also elicited smoother and faster computer mouse movements.
Interacting with target tracking algorithms in a gaze-enhanced motion video analysis system
Hild, Jutta; Krüger, Wolfgang; Heinze, Norbert; Peinsipp-Byma, Elisabeth; Beyerer, Jürgen
2016-05-01
Motion video analysis is a challenging task, particularly if real-time analysis is required. It is therefore an important issue how to provide suitable assistance for the human operator. Given that the use of customized video analysis systems is more and more established, one supporting measure is to provide system functions which perform subtasks of the analysis. Recent progress in the development of automated image exploitation algorithms allow, e.g., real-time moving target tracking. Another supporting measure is to provide a user interface which strives to reduce the perceptual, cognitive and motor load of the human operator for example by incorporating the operator's visual focus of attention. A gaze-enhanced user interface is able to help here. This work extends prior work on automated target recognition, segmentation, and tracking algorithms as well as about the benefits of a gaze-enhanced user interface for interaction with moving targets. We also propose a prototypical system design aiming to combine both the qualities of the human observer's perception and the automated algorithms in order to improve the overall performance of a real-time video analysis system. In this contribution, we address two novel issues analyzing gaze-based interaction with target tracking algorithms. The first issue extends the gaze-based triggering of a target tracking process, e.g., investigating how to best relaunch in the case of track loss. The second issue addresses the initialization of tracking algorithms without motion segmentation where the operator has to provide the system with the object's image region in order to start the tracking algorithm.
Haering, Diane; Raison, Maxime; Begon, Mickael
2014-08-01
The shoulder is the most mobile joint of the human body due to bony constraint scarcity and soft tissue function unlocking several degrees of freedom (DOF). Clinical evaluation of the shoulder range of motion (RoM) is often limited to a few monoplanar measurements where each DOF varies independently. The main objective of this study was to provide a method and its experimental approach to assess shoulder 3D RoM with DOF interactions. Sixteen participants performed four series of active arm movements with maximal amplitude consisting in (1) elevations with fixed arm axial rotations (elevation series), (2) axial rotations at different elevations (rotation series), both in five planes of elevation, (3) free arm movements with the instruction to fill the largest volume in space while varying hand orientation (random series), and (4) a combination of elevation and rotation series (overall series). A motion analysis system combined with an upper limb kinematic model was used to estimate the 3D joint kinematics. Thoracohumeral Euler angles with correction were chosen to represent rotations. The angle-time-histories were treated altogether to analyze their 3D interaction. Then, all 3D angular poses were included into a nonconvex hull representing the RoM space accounting for DOF interactions. The effect of series of movements (n = 4) on RoM volumes was tested with a one-way repeated-measures ANOVA followed by Bonferroni posthoc analysis. A normalized 3D RoM space was defined by including 3D poses common to a maximal number of participants into a hull of average volume. A significant effect of the series of movements (p measured the largest RoM with an average volume of 3.46 ± 0.89 million cubic degrees. The main difference between the series of movements was due to axial rotation. A normalized RoM hull with average volume was found by encompassing arm poses common to more than 50% of the participants. In general, the results confirmed and characterized the complex 3D
Interactions between motion and form processing in the human visual system.
Mather, George; Pavan, Andrea; Bellacosa Marotti, Rosilari; Campana, Gianluca; Casco, Clara
2013-01-01
The predominant view of motion and form processing in the human visual system assumes that these two attributes are handled by separate and independent modules. Motion processing involves filtering by direction-selective sensors, followed by integration to solve the aperture problem. Form processing involves filtering by orientation-selective and size-selective receptive fields, followed by integration to encode object shape. It has long been known that motion signals can influence form processing in the well-known Gestalt principle of common fate; texture elements which share a common motion property are grouped into a single contour or texture region. However, recent research in psychophysics and neuroscience indicates that the influence of form signals on motion processing is more extensive than previously thought. First, the salience and apparent direction of moving lines depends on how the local orientation and direction of motion combine to match the receptive field properties of motion-selective neurons. Second, orientation signals generated by "motion-streaks" influence motion processing; motion sensitivity, apparent direction and adaptation are affected by simultaneously present orientation signals. Third, form signals generated by human body shape influence biological motion processing, as revealed by studies using point-light motion stimuli. Thus, form-motion integration seems to occur at several different levels of cortical processing, from V1 to STS.
Interactions between motion and form processing in the human visual system
George eMather
2013-05-01
Full Text Available The predominant view of motion and form processing in the human visual system assumes that these two attributes are handled by separate and independent modules. Motion processing involves filtering by direction-selective sensors, followed by integration to solve the aperture problem. Form processing involves filtering by orientation-selective and size-selective receptive fields, followed by integration to encode object shape. It has long been known that motion signals can influence form processing in the well-known Gestalt principle of common fate; texture elements which share a common motion property are grouped into a single contour or texture region. However recent research in psychophysics and neuroscience indicates that the influence of form signals on motion processing is more extensive than previously thought. First, the salience and apparent direction of moving lines depends on how the local orientation and direction of motion combine to match the receptive field properties of motion-selective neurons. Second, orientation signals generated by ‘motion-streaks’ influence motion processing; motion sensitivity, apparent direction and adaptation are affected by simultaneously present orientation signals. Third, form signals generated by human body shape influence biological motion processing, as revealed by studies using point-light motion stimuli. Thus form-motion integration seems to occur at several different levels of cortical processing, from V1 to STS.
Probability laws related to the Jacobi theta and Riemann zeta function and Brownian excursions
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.
Skyrme's interaction beyond the mean-field. The DGCM+GOA Hamiltonian of nuclear quadrupole motion
Kluepfel, Peter
2008-01-01
This work focuses on the microscopic description of nuclear collective quadrupole motion within the framework of the dynamic Generator-Coordinate-Method(DGCM)+Gaussian-Overlap-Approximation(GOA). Skyrme-type effective interactions are used as the fundamental many-particle interaction. Starting from a rotational invariant, polynomial and topologic consistent formulation of the GCM+GOA Hamiltonian an interpolation scheme for the collective masses and potential is developed. It allows to define the collective Hamiltonian of fully triaxial collective quadrupole dynamics from a purely axial symmetric configuration space. The substantial gain in performance allows the self-consistent evaluation of the dynamic quadrupole mass within the ATDHF-cranking model. This work presents the first large-scale analysis of quadrupole correlation energies and lowlying collective states within the DGCM+GOA model. Different Skyrme- and pairing interactions are compared from old standards up to more recent parameterizations. After checking the validity of several approximations to the DGCM+GOA model - both on the mean-field and the collective level - we proceed with a detailed investigation of correlation effects along the chains of semi-magic isotopes and isotones. This finally allows to define a set of observables which are hardly affected by collective correlations. Those observables were used for a refit of a Skyrme-type effective interaction which is expected to cure most of the problems of the recent parameterizations. Preparing further work, estimates for the correlated ground state energy are proposed which can be evaluated directly from the mean-field model. (orig.)
Skyrme's interaction beyond the mean-field. The DGCM+GOA Hamiltonian of nuclear quadrupole motion
Kluepfel, Peter
2008-07-29
This work focuses on the microscopic description of nuclear collective quadrupole motion within the framework of the dynamic Generator-Coordinate-Method(DGCM)+Gaussian-Overlap-Approximation(GOA). Skyrme-type effective interactions are used as the fundamental many-particle interaction. Starting from a rotational invariant, polynomial and topologic consistent formulation of the GCM+GOA Hamiltonian an interpolation scheme for the collective masses and potential is developed. It allows to define the collective Hamiltonian of fully triaxial collective quadrupole dynamics from a purely axial symmetric configuration space. The substantial gain in performance allows the self-consistent evaluation of the dynamic quadrupole mass within the ATDHF-cranking model. This work presents the first large-scale analysis of quadrupole correlation energies and lowlying collective states within the DGCM+GOA model. Different Skyrme- and pairing interactions are compared from old standards up to more recent parameterizations. After checking the validity of several approximations to the DGCM+GOA model - both on the mean-field and the collective level - we proceed with a detailed investigation of correlation effects along the chains of semi-magic isotopes and isotones. This finally allows to define a set of observables which are hardly affected by collective correlations. Those observables were used for a refit of a Skyrme-type effective interaction which is expected to cure most of the problems of the recent parameterizations. Preparing further work, estimates for the correlated ground state energy are proposed which can be evaluated directly from the mean-field model. (orig.)
Ito, Tomohiro; Fujiwara, Yoshihiro; Shintani, Atsuhiko; Nakagaw, Chihiro; Furuta, Kazuhisa
2012-01-01
The cask-canister system is a coaxial circular cylindrical structure in which several spent fuels are installed. This system is a free-standing structure thus, it is very important to reduce sliding motion for very large seismic excitations. In this study, we propose a mitigation method for sliding motion. Water is installed in an annular region between a cask and a canister. The equations of motion are derived taking fluid-structure interaction into consideration for nonlinear sliding motion analyses. Based on these equations, mitigation effects of sliding motions are studied analytically. Furthermore, a fundamental test model of a cask-canister system is fabricated and shaking table tests are conducted. From the analytical and test results, sliding motion mitigation effects are investigated. In this paper, the sliding motion of the cask-canister system subjected to a horizontal base excitation is studied and the effectiveness of water filled in the annular region between the cask and the canister is evaluated. This water brings inertia force coupling effect which is proportional to acceleration of the cask and the canister. Therefore, due to this fluid coupling, the cask and canister system couples through 3 types of forces, i.e., spring force, damping force and inertia force of the liquid. Equations of motion for the sliding motion are derived based on the fluid-structure coupling effects formulated by Fritz. Based on these equations of motion, nonlinear sliding motion of the cask-canister system is analyzed and the sliding suppression effects are investigated numerically. Furthermore, a fundamental test model of a cask-canister system is fabricated and the shaking table tests are conducted. From these analytical and test results, the sliding motion suppression effects due to fluid-structure coupling effects are investigated. As a result, it is confirmed that the inertia coupling effects due to water filled in the annular region are relatively large, and the
BROWNIAN HEAT TRANSFER ENHANCEMENT IN THE TURBULENT REGIME
Suresh Chandrasekhar
2016-08-01
Full Text Available The paper presents convection heat transfer of a turbulent flow Al2O3/water nanofluid in a circular duct. The duct is a under constant and uniform heat flux. The paper computationally investigates the system’s thermal behavior in a wide range of Reynolds number and also volume concentration up to 6%. To obtain the nanofluid thermophysical properties, the Hamilton-Crosser model along with the Brownian motion effect are utilized. Then the thermal performance of the system with the nanofluid is compared to the conventional systems which use water as the working fluid. The results indicate that the use of nanofluid of 6% improves the heat transfer rate up to 36.8% with respect to pure water. Therefore, using the Al2O3/water nanofluid instead of water can be a great choice when better heat transfer is needed.
Bivariate Gaussian bridges: directional factorization of diffusion in Brownian bridge models.
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.
Browndye: A software package for Brownian dynamics
Huber, Gary A.; McCammon, J. Andrew
2010-11-01
A new software package, Browndye, is presented for simulating the diffusional encounter of two large biological molecules. It can be used to estimate second-order rate constants and encounter probabilities, and to explore reaction trajectories. Browndye builds upon previous knowledge and algorithms from software packages such as UHBD, SDA, and Macrodox, while implementing algorithms that scale to larger systems. Program summaryProgram title: Browndye Catalogue identifier: AEGT_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGT_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: MIT license, included in distribution No. of lines in distributed program, including test data, etc.: 143 618 No. of bytes in distributed program, including test data, etc.: 1 067 861 Distribution format: tar.gz Programming language: C++, OCaml ( http://caml.inria.fr/) Computer: PC, Workstation, Cluster Operating system: Linux Has the code been vectorised or parallelized?: Yes. Runs on multiple processors with shared memory using pthreads RAM: Depends linearly on size of physical system Classification: 3 External routines: uses the output of APBS [1] ( http://www.poissonboltzmann.org/apbs/) as input. APBS must be obtained and installed separately. Expat 2.0.1, CLAPACK, ocaml-expat, Mersenne Twister. These are included in the Browndye distribution. Nature of problem: Exploration and determination of rate constants of bimolecular interactions involving large biological molecules. Solution method: Brownian dynamics with electrostatic, excluded volume, van der Waals, and desolvation forces. Running time: Depends linearly on size of physical system and quadratically on precision of results. The included example executes in a few minutes.
The Onsager reciprocity relation and generalized efficiency of a thermal Brownian motor
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)
Large scale Brownian dynamics of confined suspensions of rigid particles
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
Phillips, Carolyn L.; Anderson, Joshua A.; Glotzer, Sharon C.
2011-08-01
Brownian Dynamics (BD), also known as Langevin Dynamics, and Dissipative Particle Dynamics (DPD) are implicit solvent methods commonly used in models of soft matter and biomolecular systems. The interaction of the numerous solvent particles with larger particles is coarse-grained as a Langevin thermostat is applied to individual particles or to particle pairs. The Langevin thermostat requires a pseudo-random number generator (PRNG) to generate the stochastic force applied to each particle or pair of neighboring particles during each time step in the integration of Newton's equations of motion. In a Single-Instruction-Multiple-Thread (SIMT) GPU parallel computing environment, small batches of random numbers must be generated over thousands of threads and millions of kernel calls. In this communication we introduce a one-PRNG-per-kernel-call-per-thread scheme, in which a micro-stream of pseudorandom numbers is generated in each thread and kernel call. These high quality, statistically robust micro-streams require no global memory for state storage, are more computationally efficient than other PRNG schemes in memory-bound kernels, and uniquely enable the DPD simulation method without requiring communication between threads.
Brownian Motion as a Limit to Physical Measuring Processes
Niss, Martin
2016-01-01
In this paper, we examine the history of the idea that noise presents a fundamental limit to physical measuring processes. This idea had its origins in research aimed at improving the accuracy of instruments for electrical measurements. Out of these endeavors, the Swedish physicist Gustaf A. Ising...
Relativistic Brownian motion and the foundations of quantum mechanics
Roy, S.
1979-01-01
Within the context of the generalized stochastic interpretation of quantum mechanics it is possible to deduce the quantum principles as well as to resolve the EPR paradox. Moreover, the postulates of the stochastic space-time as proposed by Frederick et al. can be deduced in a consistent way. A new possibility arises of rethinking of the existence of hidden variables in quantum mechanics. (author)
Relativistic Brownian motion and the foundations of quantum mechanics
Roy, S.
1979-01-01
Within the context of the generalized stochastic interpretation of quantum mechanics it is possible to deduce the quantum principles as well as to resolve the EPR paradox. Moreover, the postulates of the stochastic space-time as proposed by Frederick et al. can be deduced in a consistent way. A new possibility arises of rethinking of the existence of hidden variables in quantum mechanics
Beyond Brownian Motion: A Levy Flight in Magic Boots -50 ...
in the scientific community to observe molecular aggregates which travel at times .... tional Institutes of health analysed the time intervals between heart beats. ... mental and numerical methods to study a leaking tap. They found that the time ...
Brownian Motion Problem: Random Walk and Beyond -RE ...
by their continuous bombardment by the surrounding molecules of much smaller size (Figure 1). This effect .... of continuous impacts of the randomly moving surround- ing molecules of the fluid (the 'npise'); (ii) these ..... ually increasing range of values due to integration and, thus, keeping it alive. Consequently, the observed ...
Parameter inference from hitting times for perturbed Brownian motion
Tamborrino, Massimiliano; Ditlevsen, Susanne; Lansky, Peter
2015-01-01
.g. the political conflict finishes, the industrial component breaks down or the person dies. Imagine an intervention, e.g., a political decision, maintenance of a component or a medical treatment, is initiated to the process before the event occurs. How can we evaluate whether the intervention had an effect......A latent internal process describes the state of some system, e.g. the social tension in a political conflict, the strength of an industrial component or the health status of a person. When this process reaches a predefined threshold, the process terminates and an observable event occurs, e......? To answer this question we describe the effect of the intervention through parameter changes of the law governing the internal process. Then, the time interval between the start of the process and the final event is divided into two subintervals: the time from the start to the instant of intervention...
Brownian Motion Problem: Random Walk and Beyond -RE ...
was subjected to various killing treatments, liquids other .... This phrase is used for the systems rectifying the inescapable thermal noise to produce unidirectional current of particles in the .... with dispersion 2Dt (Figure 2) implying spread of the.
Brownian motion and the heat equation on superspace and anyspace
Majid, S.; Rodriguez-Plaza, M.J.
1993-01-01
We use random walks to study diffusion on anyspace. Anyspace is characterized by co-ordinate ξ with ξ N =0 and statistics ξξ'=e 2πi/N ξ'ξ between independent copies. Anyonic integration and anyonic Dirac δ-functions are introduced, and reduce to familiar results for supersymmetry when N=2. These ingredients are then used to formulate and solve the resulting anyonic diffusion equation. (oirg.)
Quantum electrodynamical torques in the presence of Brownian motion
Munday, J. N.; Iannuzzi, D.; Capasso, F.
2006-01-01
Quantum fluctuations of the electromagnetic field give rise to a zero-point energy that persists even in the absence of electromagnetic sources. One striking consequence of the zero-point energy is manifested in the Casimir force, which causes two electrically neutral metallic plates to attract in
A simple microviscometric approach based on Brownian motion tracking
Hnyluchová, Z.; Bjalončikova, P.; Karas, P.; Mravec, F.; Halasová, T.; Pekar, M.; Kubala, Lukáš; Víteček, Jan
2015-01-01
Roč. 86, č. 2 (2015) ISSN 0034-6748 R&D Projects: GA ČR(CZ) GCP305/12/J038 Grant - others:GA MŠk(CZ) ED1.100/02/0123 Institutional support: RVO:68081707 Keywords : MULTIPLE-PARTICLE TRACKING * MICRORHEOLOGY * IMAGE Subject RIV: BO - Biophysics Impact factor: 1.336, year: 2015
Parameter inference from hitting times for perturbed Brownian motion
Tamborrino, M.; Ditlevsen, S.; Lánský, Petr
2015-01-01
Roč. 21, č. 3 (2015), s. 331-352 ISSN 1380-7870 Institutional support: RVO:67985823 Keywords : first passage times * maximum likelihood estimation * Wiener proces * degradation proces * effect of intervention * survival analysis Subject RIV: BD - Theory of Information Impact factor: 0.810, year: 2015
Theoretical predictions of diffusion from Brownian motion in superstrong polymers
Dowell, F.
1991-01-01
This paper presents a summary of unique highly nonlinear static and dynamic theories for chain molecules (actually, for almost any kind of organic molecule), including the first superstrong polymers. These theories have been used to predict and explain (1) the physical self-assembly (self-ordering) of specific kinds of molecules into liquid crystalline (LC) phases (i.e., partially ordered phases) and (2) the diffusion of these molecules in various LC phases and the isotropic (I) liquid phase
Two derivations of the master equation of quantum Brownian motion
Halliwell, J J [Blackett Laboratory, Imperial College, London SW7 2BZ (United Kingdom)
2007-03-23
Central to many discussion of decoherence is a master equation for the reduced density matrix of a massive particle experiencing scattering from its surrounding environment, such as that of Joos and Zeh. Such master equations enjoy a close relationship with spontaneous localization models, like the GRW model. The aim of this paper is to present two derivations of the master equation. The first derivation is a pedagogical model designed to illustrate the origins of the master equation as simply as possible, focusing on physical principles and without the complications of S-matrix theory. This derivation may serve as a useful tutorial example for students attempting to learn this subject area. The second is the opposite: a very general derivation using non-relativistic many-body field theory. It reduces to the equation of the type given by Joos and Zeh in the one-particle sector, but correcting certain numerical factors which have recently become significant in connection with experimental tests of decoherence. This master equation also emphasizes the role of local number density as the 'preferred basis' for decoherence in this model.
Brownian motion approximations for stock control and tankage assessment
R.A.J.J. Nieboer; R. Dekker (Rommert)
1995-01-01
textabstractThis paper presents a model for refinery tankage assessment. Special characteristics covered are a hybrid demand process and a periodic-review target-stock policy for production control. The demand is assumed to be in two forms: as large parcels, collected at fixed intervals, and as many
Two derivations of the master equation of quantum Brownian motion
Halliwell, J J
2007-01-01
Central to many discussion of decoherence is a master equation for the reduced density matrix of a massive particle experiencing scattering from its surrounding environment, such as that of Joos and Zeh. Such master equations enjoy a close relationship with spontaneous localization models, like the GRW model. The aim of this paper is to present two derivations of the master equation. The first derivation is a pedagogical model designed to illustrate the origins of the master equation as simply as possible, focusing on physical principles and without the complications of S-matrix theory. This derivation may serve as a useful tutorial example for students attempting to learn this subject area. The second is the opposite: a very general derivation using non-relativistic many-body field theory. It reduces to the equation of the type given by Joos and Zeh in the one-particle sector, but correcting certain numerical factors which have recently become significant in connection with experimental tests of decoherence. This master equation also emphasizes the role of local number density as the 'preferred basis' for decoherence in this model
Chen, C.H.-T.
1980-10-01
A unified description of the following classes of nuclear collective states in terms of an interacting sp-boson model is proposed: (i) Low-lying collective states in the light nuclei, both odd-odd and even-even; (ii) Giant multipole resonances (GMR), and (iii) pairing collective motions. (Author) [pt
Elkhoraibi, T.; Hashemi, A.; Ostadan, F.
2014-01-01
Soil-structure interaction (SSI) is a major step for seismic design of massive and stiff structures typical of the nuclear facilities and civil infrastructures such as tunnels, underground stations, dams and lock head structures. Currently most SSI analyses are performed deterministically, incorporating limited range of variation in soil and structural properties and without consideration of the ground motion incoherency effects. This often leads to overestimation of the seismic response particularly the In-Structure-Response Spectra (ISRS) with significant impositions of design and equipment qualification costs, especially in the case of high-frequency sensitive equipment at stiff soil or rock sites. The reluctance to incorporate a more comprehensive probabilistic approach is mainly due to the fact that the computational cost of performing probabilistic SSI analysis even without incoherency function considerations has been prohibitive. As such, bounding deterministic approaches have been preferred by the industry and accepted by the regulatory agencies. However, given the recently available and growing computing capabilities, the need for a probabilistic-based approach to the SSI analysis is becoming clear with the advances in performance-based engineering and the utilization of fragility analysis in the decision making process whether by the owners or the regulatory agencies. This paper demonstrates the use of both probabilistic and deterministic SSI analysis techniques to identify important engineering demand parameters in the structure. A typical nuclear industry structure is used as an example for this study. The system is analyzed for two different site conditions: rock and deep soil. Both deterministic and probabilistic SSI analysis approaches are performed, using the program SASSI, with and without ground motion incoherency considerations. In both approaches, the analysis begins at the hard rock level using the low frequency and high frequency hard rock
Elkhoraibi, T., E-mail: telkhora@bechtel.com; Hashemi, A.; Ostadan, F.
2014-04-01
Soil-structure interaction (SSI) is a major step for seismic design of massive and stiff structures typical of the nuclear facilities and civil infrastructures such as tunnels, underground stations, dams and lock head structures. Currently most SSI analyses are performed deterministically, incorporating limited range of variation in soil and structural properties and without consideration of the ground motion incoherency effects. This often leads to overestimation of the seismic response particularly the In-Structure-Response Spectra (ISRS) with significant impositions of design and equipment qualification costs, especially in the case of high-frequency sensitive equipment at stiff soil or rock sites. The reluctance to incorporate a more comprehensive probabilistic approach is mainly due to the fact that the computational cost of performing probabilistic SSI analysis even without incoherency function considerations has been prohibitive. As such, bounding deterministic approaches have been preferred by the industry and accepted by the regulatory agencies. However, given the recently available and growing computing capabilities, the need for a probabilistic-based approach to the SSI analysis is becoming clear with the advances in performance-based engineering and the utilization of fragility analysis in the decision making process whether by the owners or the regulatory agencies. This paper demonstrates the use of both probabilistic and deterministic SSI analysis techniques to identify important engineering demand parameters in the structure. A typical nuclear industry structure is used as an example for this study. The system is analyzed for two different site conditions: rock and deep soil. Both deterministic and probabilistic SSI analysis approaches are performed, using the program SASSI, with and without ground motion incoherency considerations. In both approaches, the analysis begins at the hard rock level using the low frequency and high frequency hard rock
From Cannibalism to Active Motion of Groups
Romanczuk, Pawel; Schimansky-Geier, Lutz
2008-03-01
The detailed mechanisms leading to collective dynamics in groups of animals and insect are still poorly understood. A recent study by Simpson et. al. suggests cannibalism as a driving mechanism for coordinated migration of mormon crickets [1]. Based on this result we propose a simple generic model of brownian particles interacting by asymmetric, non-conservative collisions accounting for cannibalistic behavior and the corresponding avoidance strategy. We discuss our model in one and two dimensions and show that a certain type of collisions drives the system out of equilibrium and leads to coordinated active motion of groups.[1] Stephen J. Simpson, Gregory A. Sword, Patrick D. Lorch and Iain D. Couzin: Cannibal crickets on a forced march for protein and salt, PNAS, 103:4152-4156, 2006
Interactions between motion and form processing in the human visual system
Mather, G.; Pavan, A.; Bellacosa Marotti, R.; Campana, G.; Casco, C.
2013-01-01
The predominant view of motion and form processing in the human visual system assumes that these two attributes are handled by separate and independent modules. Motion processing involves filtering by direction-selective sensors, followed by integration to solve the aperture problem. Form processing involves filtering by orientation-selective and size-selective receptive fields, followed by integration to encode object shape. It has long been known that motion signals can influence form proce...
Infrared tomographic PIV and 3D motion tracking system applied to aquatic predator–prey interaction
Adhikari, Deepak; Longmire, Ellen K
2013-01-01
Infrared tomographic PIV and 3D motion tracking are combined to measure evolving volumetric velocity fields and organism trajectories during aquatic predator–prey interactions. The technique was used to study zebrafish foraging on both non-evasive and evasive prey species. Measurement volumes of 22.5 mm × 10.5 mm × 12 mm were reconstructed from images captured on a set of four high-speed cameras. To obtain accurate fluid velocity vectors within each volume, fish were first masked out using an automated visual hull method. Fish and prey locations were identified independently from the same image sets and tracked separately within the measurement volume. Experiments demonstrated that fish were not influenced by the infrared laser illumination or the tracer particles. Results showed that the zebrafish used different strategies, suction and ram feeding, for successful capture of non-evasive and evasive prey, respectively. The two strategies yielded different variations in fluid velocity between the fish mouth and the prey. In general, the results suggest that the local flow field, the direction of prey locomotion with respect to the predator and the relative accelerations and speeds of the predator and prey may all be significant in determining predation success. (paper)
Centelles, L; Assaiante, C; Etchegoyhen, K; Bouvard, M; Schmitz, C
2012-06-01
Autism spectrum disorders (ASD) are characterized by difficulties in social interaction and verbal and non verbal reciprocal communication. Face and gaze direction, which participate in non verbal communication, are described as atypical in ASD. Also body movements carry multiple social cues. Under certain circumstances, for instance when seeing two persons from far, they constitute the only support that allows the grasping of a social content. Here, we investigated the contribution of whole-body motion processing in social understanding. The aim of the study was to evaluate whether children with ASD make use of information carried by body motion to categorize dynamic visual scenes that portrayed social interactions. In 1973, Johansson devised a technique for studying the perception of biological motion that minimizes static form information from the stimulus, but retains motion information. In these point-light displays, the movement figure, such as a body, is represented by a small number of illuminated dots positioned to highlight the motion of the body parts. We used Johansson's model to explore the ability of children with ASD to understand social interactions based on human movement analysis. Three-second silent point-light displays were created by videotaping two actors. The two actors were either interacting together or moving side by side without interacting. A large range of social interaction displays were used to cover social scenes depicting social norms (conventional gestures and courteous attitudes), emotional situations (carrying positive or negative valences) and scenes from games (sports, dance, etc.). Children were asked to carefully watch the stimuli and to classify them according to the question "Are the two persons communicating or not?". Four sessions of 3 minutes were performed by each child. Children with ASD were compared with typically developing control children matched with either non verbal mental age or chronological age. Response and
Dendro-dendritic interactions between motion-sensitive large-field neurons in the fly.
Haag, Juergen; Borst, Alexander
2002-04-15
For visual course control, flies rely on a set of motion-sensitive neurons called lobula plate tangential cells (LPTCs). Among these cells, the so-called CH (centrifugal horizontal) cells shape by their inhibitory action the receptive field properties of other LPTCs called FD (figure detection) cells specialized for figure-ground discrimination based on relative motion. Studying the ipsilateral input circuitry of CH cells by means of dual-electrode and combined electrical-optical recordings, we find that CH cells receive graded input from HS (large-field horizontal system) cells via dendro-dendritic electrical synapses. This particular wiring scheme leads to a spatial blur of the motion image on the CH cell dendrite, and, after inhibiting FD cells, to an enhancement of motion contrast. This could be crucial for enabling FD cells to discriminate object from self motion.
K. Hacıefendioğlu
2012-04-01
Full Text Available The deconvolution effect of the near-fault earthquake ground motions on the stochastic dynamic response of tunnel-soil deposit interaction systems are investigated by using the finite element method. Two different earthquake input mechanisms are used to consider the deconvolution effects in the analyses: the standard rigid-base input and the deconvolved-base-rock input model. The Bolu tunnel in Turkey is chosen as a numerical example. As near-fault ground motions, 1999 Kocaeli earthquake ground motion is selected. The interface finite elements are used between tunnel and soil deposit. The mean of maximum values of quasi-static, dynamic and total responses obtained from the two input models are compared with each other.
Sarig Bahat, Hilla; Chen, Xiaoqi; Reznik, David; Kodesh, Einat; Treleaven, Julia
2015-04-01
Chronic neck pain has been consistently shown to be associated with impaired kinematic control including reduced range, velocity and smoothness of cervical motion, that seem relevant to daily function as in quick neck motion in response to surrounding stimuli. The objectives of this study were: to compare interactive cervical kinematics in patients with neck pain and controls; to explore the new measures of cervical motion accuracy; and to find the sensitivity, specificity, and optimal cutoff values for defining impaired kinematics in those with neck pain. In this cross-section study, 33 patients with chronic neck pain and 22 asymptomatic controls were assessed for their cervical kinematic control using interactive virtual reality hardware and customized software utilizing a head mounted display with built-in head tracking. Outcome measures included peak and mean velocity, smoothness (represented by number of velocity peaks (NVP)), symmetry (represented by time to peak velocity percentage (TTPP)), and accuracy of cervical motion. Results demonstrated significant and strong effect-size differences in peak and mean velocities, NVP and TTPP in all directions excluding TTPP in left rotation, and good effect-size group differences in 5/8 accuracy measures. Regression results emphasized the high clinical value of neck motion velocity, with very high sensitivity and specificity (85%-100%), followed by motion smoothness, symmetry and accuracy. These finding suggest cervical kinematics should be evaluated clinically, and screened by the provided cut off values for identification of relevant impairments in those with neck pain. Such identification of presence or absence of kinematic impairments may direct treatment strategies and additional evaluation when needed. Copyright © 2014 Elsevier Ltd. All rights reserved.
van den Broeck, C.; Cleuren, B.; Kawai, R.; Kambon, M.
A previously introduced model (B. Cleuren and C. Van den Broeck, Europhys. Lett. 54, 1 (2001)) is studied numerically. Pure negative mobility is found for the minimum number of three interacting walkers.
Tseng, Wen S., E-mail: wen.tseng@rizzoassoc.com [Paul C. Rizzo Associates, Inc., Western Region, 2201 Broadway, Suite 400, Oakland, CA 94612 (United States); Lilhanand, Kiat; Hamasaki, Don; Garcia, Julio A. [Paul C. Rizzo Associates, Inc., Western Region, 2201 Broadway, Suite 400, Oakland, CA 94612 (United States); Srinivasan, Ram [AREVA, NP, Inc., 6399 San Ignacio Avenue, San Jose, CA 95119 (United States)
2014-04-01
This paper presents a case study of seismic soil-structure interaction (SSI) analysis with consideration of spatial incoherence of seismic input ground motions. The SSI analyses were performed using the SASSI computer program for the Auxiliary Control Building (ACB) structure of an existing nuclear power plant on a hard rock site located in the Center and Eastern United States (CEUS) region. The incoherent seismic input motions for the hard rock site used for the analyses were generated using the computer program INCOH that works together with SASSI. The objective of the analyses was to generate maximum seismic response parameters for assessment of potential impact of newly developed site-specific (ground motion) response spectra (SSRS) on the seismic design of the ACB and potential benefits that could be gained by considering spatial incoherence of seismic input motions. Maximum seismic response values for selected response parameters of interest were generated with both SSRS-compatible coherent and incoherent seismic input motions. Comparisons were made of the corresponding maximum response parameter values and in-structure (acceleration) response spectra (ISRS) generated for both the coherent and incoherent motion inputs. These comparisons indicate that, by incorporating incoherence of ground motions in the seismic input, the maximum response values reduces and the ISRS peak amplitudes in the high frequency range (>10 Hz) also reduce from the corresponding response values resulting from the coherent motion input. The amount of ISRS-amplitude reduction increases as the spectral frequency increases, as expected. Such reductions can be as much as 20–50%. This case study demonstrates that, for a CEUS hard rock site where relatively high high-frequency in the seismic input response spectra exist, consideration of spatial incoherence of input motions would result in substantial benefits in reducing the high-frequency seismic responses. Such benefits are especially
Mostafa Farajian
2017-03-01
Full Text Available Soil-structure interaction (SSI could affect the seismic response of structures. Since liquid storage tanks are vital structures and must continue their operation under severe earthquakes, their seismic behavior should be studied. Accordingly, the seismic response of two types of steel liquid storage tanks (namely, broad and slender, with aspect ratios of height to radius equal to 0.6 and 1.85 founded on half-space soil is scrutinized under different earthquake ground motions. For a better comparison, the six considered ground motions are classified, based on their pulse-like characteristics, into two groups, named far and near fault ground motions. To model the liquid storage tanks, the simplified mass-spring model is used and the liquid is modeled as two lumped masses known as sloshing and impulsive, and the interaction of fluid and structure is considered using two coupled springs and dashpots. The SSI effect, also, is considered using a coupled spring and dashpot. Additionally, four types of soils are used to consider a wide variety of soil properties. To this end, after deriving the equations of motion, MATLAB programming is employed to obtain the time history responses. Results show that although the SSI effect leads to a decrease in the impulsive displacement, overturning moment, and normalized base shear, the sloshing (or convective displacement is not affected by such effects due to its long period.
Freed, K.F.; Herman, M.F.; Yeager, D.L.
1980-01-01
A description is provided of the common conceptual origins of many-body equations of motion and Green's function methods in Liouville operator formulations of the quantum mechanics of atomic and molecular electronic structure. Numerical evidence is provided to show the inadequacies of the traditional strictly perturbative approaches to these methods. Nonperturbative methods are introduced by analogy with techniques developed for handling large configuration interaction calculations and by evaluating individual matrix elements to higher accuracy. The important role of higher excitations is exhibited by the numerical calculations, and explicit comparisons are made between converged equations of motion and configuration interaction calculations for systems where a fundamental theorem requires the equality of the energy differences produced by these different approaches. (Auth.)
Sandlund, Marlene; Domellöf, Erik; Grip, Helena; Rönnqvist, Louise; Häger, Charlotte K
2014-10-01
The main aim of this study was to evaluate the quality of goal-directed arm movements in 15 children with cerebral palsy (CP) following four weeks of home-based training with motion interactive video games. A further aim was to investigate the applicability and characteristics of kinematic parameters in a virtual context in comparison to a physical context. Kinematics and kinetics were captured while the children performed arm movements directed towards both virtual and physical targets. The children's movement precision improved, their centre of pressure paths decreased, as did the variability in maximal shoulder angles when reaching for virtual objects. Transfer to a situation with physical targets was mainly indicated by increased movement smoothness. Training with motion interactive games seems to improve arm motor control in children with CP. The results highlight the importance of considering both the context and the task itself when investigating kinematic parameters.
A bipedal DNA Brownian motor with coordinated legs.
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.
The quantum brownian particle and memory effects
Britani, J.R.; Mizrahi, S.S.; Pimentel, B.M.
1991-01-01
The Quantum Brownian particle, immersed in a heat bath, is described by a statistical operator whose evolution is ruled by a Generalized Master Equation (GME). The heat bath degrees of freedom are considered to be either white noise or coloured noise correlated,while the GME is considered under either the Markov or Non-Markov approaches. The comparison between these considerations are fully developed and their physical meaning is discussed. (author)
Heisenberg equations of motion for the spin-3/2 field in the presence of an interaction
Nagpal, A.K.
1977-01-01
The Rarita-Schwinger spin-3/2 field interacting with a Dirac field and a scalar field (external) is found to satisfy the Heisenberg equations of motion, in the weak-field limit. This is analogous to the result, for the case of spin-3/2 field minimally coupled with external electromagnetic field, recently obtained by Mainland and Sudarshan (Phys. Rev. D. 8:1088 (1973)). (author)
Optimum analysis of a Brownian refrigerator.
Luo, X G; Liu, N; He, J Z
2013-02-01
A Brownian refrigerator with the cold and hot reservoirs alternating along a space coordinate is established. The heat flux couples with the movement of the Brownian particles due to an external force in the spatially asymmetric but periodic potential. After using the Arrhenius factor to describe the behaviors of the forward and backward jumps of the particles, the expressions for coefficient of performance (COP) and cooling rate are derived analytically. Then, through maximizing the product of conversion efficiency and heat flux flowing out, a new upper bound only depending on the temperature ratio of the cold and hot reservoirs is found numerically in the reversible situation, and it is a little larger than the so-called Curzon and Ahlborn COP ε(CA)=(1/√[1-τ])-1. After considering the irreversible factor owing to the kinetic energy change of the moving particles, we find the optimized COP is smaller than ε(CA) and the external force even does negative work on the Brownian particles when they jump from a cold to hot reservoir.
Properties of Brownian Image Models in Scale-Space
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...
Shit, Anindita; Chattopadhyay, Sudip; Chaudhuri, Jyotipratim Ray
2012-01-01
Graphical abstract: By invoking physically motivated coordinate transformation into quantum Smoluchowski equation, we have presented a transparent treatment for the determination of the effective diffusion coefficient and current of a quantum Brownian particle. Substantial enhancement in the efficiency of the diffusive transport is envisaged due to the quantum correction effects. Highlights:: ► Transport of a quantum Brownian particle in a periodic potential has been addressed. ► Governing quantum Smoluchowski equation (QSE) includes state dependent diffusion. ► A coordinate transformation is used to recast QSE with constant diffusion. ► Transport properties increases in comparison to the corresponding classical result. ► This enhancement is purely a quantum effect. - Abstract: The transport property of a quantum Brownian particle that interacts strongly with a bath (in which a typical damping constant by far exceeds a characteristic frequency of the isolated system) under the influence of a tilted periodic potential has been studied by solving quantum Smoluchowski equation (QSE). By invoking physically motivated coordinate transformation into QSE, we have presented a transparent treatment for the determination of the effective diffusion coefficient of a quantum Brownian particle and the current (the average stationary velocity). Substantial enhancement in the efficiency of the diffusive transport is envisaged due to the quantum correction effects only if the bath temperature hovers around an appropriate range of intermediate values. Our findings also confirm the results obtained in the classical cases.
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.
Hybrid finite element and Brownian dynamics method for charged particles
Huber, Gary A., E-mail: ghuber@ucsd.edu; Miao, Yinglong [Howard Hughes Medical Institute, University of California San Diego, La Jolla, California 92093-0365 (United States); Zhou, Shenggao [Department of Mathematics and Mathematical Center for Interdiscipline Research, Soochow University, 1 Shizi Street, Suzhou, 215006 Jiangsu (China); Li, Bo [Department of Mathematics and Quantitative Biology Graduate Program, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112 (United States); McCammon, J. Andrew [Howard Hughes Medical Institute, University of California San Diego, La Jolla, California 92093 (United States); Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093-0365 (United States); Department of Pharmacology, University of California San Diego, La Jolla, California 92093-0636 (United States)
2016-04-28
Diffusion is often the rate-determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. A previous study introduced a new hybrid diffusion method that couples the strengths of each of these two methods, but was limited by the lack of interactions among the particles; the force on each particle had to be from an external field. This study further develops the method to allow charged particles. The method is derived for a general multidimensional system and is presented using a basic test case for a one-dimensional linear system with one charged species and a radially symmetric system with three charged species.
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.
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
Chen, Duxin; Xu, Bowen; Zhu, Tao; Zhou, Tao; Zhang, Hai-Tao
2017-08-01
Coordination shall be deemed to the result of interindividual interaction among natural gregarious animal groups. However, revealing the underlying interaction rules and decision-making strategies governing highly coordinated motion in bird flocks is still a long-standing challenge. Based on analysis of high spatial-temporal resolution GPS data of three pigeon flocks, we extract the hidden interaction principle by using a newly emerging machine learning method, namely the sparse Bayesian learning. It is observed that the interaction probability has an inflection point at pairwise distance of 3-4 m closer than the average maximum interindividual distance, after which it decays strictly with rising pairwise metric distances. Significantly, the density of spatial neighbor distribution is strongly anisotropic, with an evident lack of interactions along individual velocity. Thus, it is found that in small-sized bird flocks, individuals reciprocally cooperate with a variational number of neighbors in metric space and tend to interact with closer time-varying neighbors, rather than interacting with a fixed number of topological ones. Finally, extensive numerical investigation is conducted to verify both the revealed interaction and decision-making principle during circular flights of pigeon flocks.
Kottonau, Johannes
2011-01-01
Effectively teaching the concepts of osmosis to college-level students is a major obstacle in biological education. Therefore, a novel computer model is presented that allows students to observe the random nature of particle motion simultaneously with the seemingly directed net flow of water across a semipermeable membrane during osmotic…
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…
Moving along the Mental Number Line: Interactions between Whole-Body Motion and Numerical Cognition
Hartmann, Matthias; Grabherr, Luzia; Mast, Fred W.
2012-01-01
Active head turns to the left and right have recently been shown to influence numerical cognition by shifting attention along the mental number line. In the present study, we found that passive whole-body motion influences numerical cognition. In a random-number generation task (Experiment 1), leftward and downward displacement of participants…
Interaction between stope support and ground motion in the hangingwall and footwall Project.
Cichowicz, A
2002-07-01
Full Text Available and limitations were verified by detailed testing with the strong ground motion data. The support response may be simulated using SDOF model when PGA is in the range 18 - 100 m/s2 ; for this data model shows that the maximal value of the stiffness is 120,000 k...
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.)
Baddoura, Ritta; Venture, Gentiane
2014-01-01
During an unannounced encounter between two humans and a proactive humanoid (NAO, Aldebaran Robotics), we study the dependencies between the human partners' affective experience (measured via the answers to a questionnaire) particularly regarding feeling familiar and feeling frightened, and their arm and head motion [frequency and smoothness using Inertial Measurement Units (IMU)]. NAO starts and ends its interaction with its partners by non-verbally greeting them hello (bowing) and goodbye (moving its arm). The robot is invested with a real and useful task to perform: handing each participant an envelope containing a questionnaire they need to answer. NAO's behavior varies from one partner to the other (Smooth with X vs. Resisting with Y). The results show high positive correlations between feeling familiar while interacting with the robot and: the frequency and smoothness of the human arm movement when waving back goodbye, as well as the smoothness of the head during the whole encounter. Results also show a negative dependency between feeling frightened and the frequency of the human arm movement when waving back goodbye. The principal component analysis (PCA) suggests that, in regards to the various motion measures examined in this paper, the head smoothness and the goodbye gesture frequency are the most reliable measures when it comes to considering the familiar experienced by the participants. The PCA also points out the irrelevance of the goodbye motion frequency when investigating the participants' experience of fear in its relation to their motion characteristics. The results are discussed in light of the major findings of studies on body movements and postures accompanying specific emotions.
Bocquet, L.; Hansen, J.P.; Piasecki, J.
1997-01-01
In this work, we show that in any finite system, the binary friction tenser for two Brownian particles cannot be directly estimated from an evaluation of the microscopic Green Kubo formula, involving the time integral of force-force autocorrelation functions. This pitfall is associated with a subtle inversion of the thermodynamic and long-time limits and leads to spurious results for the estimates of the friction matrix based on molecular dynamics simulations. Starting from a careful analysis of the coupled Langevin equations for two interacting Brownian particles, we derive a method to circumvent these effects and extract the binary friction tenser from the correlation function matrix of the instantaneous forces exerted by the bath particles on the fixed Brownian particles, and from the relaxation of the total momentum of the bath in a finite system. The general methodology is applied to the case of two hard or soft Brownian spheres in a bath of light particles. Numerical estimates of the relevant correlation functions and of the resulting self and mutual components of the matrix of friction tensors are obtained by molecular dynamics simulations for various spacings between the Brownian particles
Shukla, Pragya
2004-01-01
We find that the statistics of levels undergoing metal-insulator transition in systems with multi-parametric Gaussian disorders and non-interacting electrons behaves in a way similar to that of the single parametric Brownian ensembles \\cite{dy}. The latter appear during a Poisson $\\to$ Wigner-Dyson transition, driven by a random perturbation. The analogy provides the analytical evidence for the single parameter scaling of the level-correlations in disordered systems as well as a tool to obtai...
Effective diffusion of confined active Brownian swimmers
Sandoval, Mario; Dagdug, Leonardo
2014-11-01
We find theoretically the effect of confinement and thermal fluctuations, on the diffusivity of a spherical active swimmer moving inside a two-dimensional narrow cavity of general shape. The explicit formulas for the effective diffusion coefficient of a swimmer moving inside two particular cavities are presented. We also compare our analytical results with Brownian Dynamics simulations and we obtain excellent agreement. L.D. thanks Consejo Nacional de Ciencia y Tecnologia (CONACyT) Mexico, for partial support by Grant No. 176452. M. S. thanks CONACyT and Programa de Mejoramiento de Profesorado (PROMEP) for partially funding this work under Grant No. 103.5/13/6732.
Eigenfunction statistics of Wishart Brownian ensembles
Shukla, Pragya
2017-01-01
We theoretically analyze the eigenfunction fluctuation measures for a Hermitian ensemble which appears as an intermediate state of the perturbation of a stationary ensemble by another stationary ensemble of Wishart (Laguerre) type. Similar to the perturbation by a Gaussian stationary ensemble, the measures undergo a diffusive dynamics in terms of the perturbation parameter but the energy-dependence of the fluctuations is different in the two cases. This may have important consequences for the eigenfunction dynamics as well as phase transition studies in many areas of complexity where Brownian ensembles appear. (paper)
Laser light scattering in Brownian medium
Suwono; Santoso, Budi; Baiquni, A.
1983-01-01
The principle of laser light scattering in Brownian medium and photon correlation spectroscopy are described in detail. Their application to the study of the behaviour of a polystyrene latex solution are discussed. The auto-correlation function of light scattered by the polystyrene latex solution in various angle, various temperature and in various sample times, have been measured. Information on the translation diffusion coefficient and size on the particle can be obtained from the auto-correlation function. Good agreement between the available data and experiment is shown. (author)
Presentation of quantum Brownian movement in the collective coordinate method
Oksak, A.I.; Sukhanov, A.D.
2003-01-01
Two explicitly solved models of quantum randomized processes described by the Langevin equation, i. e. a free quantum Brownian particle and a quantum Brownian harmonic oscillator, are considered. The Hamiltonian (string) realization of the models reveals soliton-like structure of classical solutions. Accordingly, the method of zero mode collective coordinate is an adequate means for describing the models quantum dynamics [ru
Self-assembly of actin monomers into long filaments: Brownian Dynamics simulations
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...
Soskin, S.M.
1987-01-01
The authors examine Brownian motion in a square well with reflecting walls. An exact solution is obtained for the corresponding Einstein-Fokker-Planck equation, which is used to find the coordinate correlation function in explicit form. The correlation function, normalized to the square of the distance between the walls, typically exhibits a similarity property: its behavior as a function of time, friction, temperature, and wall separation reduces to a function of one simple combination of those four quantities. The limiting cases of low and high friction are investigated in detail, with explicit expressions being derived for the spectrum
Zelan, M; Hagman, H; Labaigt, G; Jonsell, S; Dion, C M
2011-02-01
The rectification of noise into directed movement or useful energy is utilized by many different systems. The peculiar nature of the energy source and conceptual differences between such Brownian motor systems makes a characterization of the performance far from straightforward. In this work, where the Brownian motor consists of atoms interacting with dissipative optical lattices, we adopt existing theory and present experimental measurements for both the efficiency and the transport coherence. We achieve up to 0.3% for the efficiency and 0.01 for the Péclet number.
Experiential Learning in Vehicle Dynamics Education via Motion Simulation and Interactive Gaming
Hulme, Kevin; Kasprzak, Edward; English, Ken; Moore-Russo, Deborah; Lewis, Kemper
2009-01-01
Creating active, student-centered learning situations in postsecondary education is an ongoing challenge for engineering educators. Contemporary students familiar with visually engaging and fast-paced games can find traditional classroom methods of lecture and guided laboratory experiments limiting. This paper presents a methodology that incorporates driving simulation, motion simulation, and educational practices into an engaging, gaming-inspired simulation framework for a vehicle dynamics c...
Wozniak, Peter; Vauderwange, Oliver; Mandal, Avikarsha; Javahiraly, Nicolas; Curticapean, Dan
2016-09-01
Practical exercises are a crucial part of many curricula. Even simple exercises can improve the understanding of the underlying subject. Most experimental setups require special hardware. To carry out e. g. a lens experiments the students need access to an optical bench, various lenses, light sources, apertures and a screen. In our previous publication we demonstrated the use of augmented reality visualization techniques in order to let the students prepare with a simulated experimental setup. Within the context of our intended blended learning concept we want to utilize augmented or virtual reality techniques for stationary laboratory exercises. Unlike applications running on mobile devices, stationary setups can be extended more easily with additional interfaces and thus allow for more complex interactions and simulations in virtual reality (VR) and augmented reality (AR). The most significant difference is the possibility to allow interactions beyond touching a screen. The LEAP Motion controller is a small inexpensive device that allows for the tracking of the user's hands and fingers in three dimensions. It is conceivable to allow the user to interact with the simulation's virtual elements by the user's very hand position, movement and gesture. In this paper we evaluate possible applications of the LEAP Motion controller for simulated experiments in augmented and virtual reality. We pay particular attention to the devices strengths and weaknesses and want to point out useful and less useful application scenarios.
Bocian, M.; Brownjohn, J. M. W.; Racic, V.; Hester, D.; Quattrone, A.; Gilbert, L.; Beasley, R.
2018-05-01
A multi-scale and multi-object interaction phenomena can arise when a group of walking pedestrians crosses a structure capable of exhibiting dynamic response. This is because each pedestrian is an autonomous dynamic system capable of displaying intricate behaviour affected by social, psychological, biomechanical and environmental factors, including adaptations to the structural motion. Despite a wealth of mathematical models attempting to describe and simulate coupled crowd-structure system, their applicability can generally be considered uncertain. This can be assigned to a number of assumptions made in their development and the scarcity or unavailability of data suitable for their validation, in particular those associated with pedestrian-pedestrian and pedestrian-structure interaction. To alleviate this problem, data on behaviour of individual pedestrians within groups of six walkers with different spatial arrangements are gathered simultaneously with data on dynamic structural response of a footbridge, from a series of measurements utilising wireless motion monitors. Unlike in previous studies on coordination of pedestrian behaviour, the collected data can serve as a proxy for pedestrian vertical force, which is of critical importance from the point of view of structural stability. A bivariate analysis framework is proposed and applied to these data, encompassing wavelet transform, synchronisation measures based on Shannon entropy and circular statistics. A topological pedestrian map is contrived showing the strength and directionality of between-subjects interactions. It is found that the coordination in pedestrians' vertical force depends on the spatial collocation within a group, but it is generally weak. The relationship between the bridge and pedestrian behaviour is also analysed, revealing stronger propensity for pedestrians to coordinate their force with the structural motion rather than with each other.
Shaking table test and analysis of embedded structure soil interaction considering input motion
Matsushima, Y.; Mizuno, H.; Machida, N.; Sato, K.; Okano, H.
1987-01-01
The dynamic interaction between soil and structure is decomposed into inertial interaction (II) and kinematic interaction (KI). II denotes the interaction due to inertial force applied on foundations. KI denotes the interaction of massless foundations subjected to seismic waves. Forced vibration tests by exciters are not enough to evaluate the complete soil-structure interaction due to the lack of KI. To clarify the effects of KI on the seismic response of structure, the authors intended to carry out shaking table tests of the interaction between the soil and the embedded structure. A method to decompose II and KI is introduced which reveals the construction of embedment effects. Finally, the authors discuss the validity of three kinds of simulation analyses, that is, two-dimensional, approximate three-dimensional and rigorous three-dimensional analyses, comparing with the test results
Itai, K.
1987-02-01
Two models which describe one-dimensional hopping motion of a heavy particle interacting with phonons are discussed. Model A corresponds to hopping in 1D metals or to the polaron problem. In model B the momentum dependence of the particle-phonon coupling is proportional to k-1/2. The scaling equations show that only in model B does localization occur for a coupling larger than a critical value. In the localization region this model shows close analogy to the Caldeira-Leggett model for macroscopic quantum tunneling.
More on equations of motion for interacting massless field of all spins in 3+1 dimensions
Vasiliev, M A [Inst. of Theoretical Physics, Goteborg (Sweden)
1992-07-09
We establish the simple link between the recently proposed equations of motion for interacting massless fields of all spins 0{<=}s<{infinity} in 3+1 dimensions and conventional formulations of free higher-spin dynamics. In addition, we discuss various types of formal generalizations of the system of equations of Vasiliev which may give rise to interesting relativistic systems in 2+1 and 3+1 dimensions. In particular, it is shown that there exists a class of equations generalizing Vasiliev's system, parametrized by an arbitrary function of one variable. Self-dual higher-spin equations are discussed briefly. (orig.).
Performance Estimation for Two-Dimensional Brownian Rotary Ratchet Systems
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.
Linear response approach to active Brownian particles in time-varying activity fields
Merlitz, Holger; Vuijk, Hidde D.; Brader, Joseph; Sharma, Abhinav; Sommer, Jens-Uwe
2018-05-01
In a theoretical and simulation study, active Brownian particles (ABPs) in three-dimensional bulk systems are exposed to time-varying sinusoidal activity waves that are running through the system. A linear response (Green-Kubo) formalism is applied to derive fully analytical expressions for the torque-free polarization profiles of non-interacting particles. The activity waves induce fluxes that strongly depend on the particle size and may be employed to de-mix mixtures of ABPs or to drive the particles into selected areas of the system. Three-dimensional Langevin dynamics simulations are carried out to verify the accuracy of the linear response formalism, which is shown to work best when the particles are small (i.e., highly Brownian) or operating at low activity levels.
Sundaramoorthi, Ganesh
2012-09-13
This paper presents a novel medical image registration algorithm that explicitly models the physical constraints imposed by objects or sub-structures of objects that have differing material composition and border each other, which is the case in most medical registration applications. Typical medical image registration algorithms ignore these constraints and therefore are not physically viable, and to incorporate these constraints would require prior segmentation of the image into regions of differing material composition, which is a difficult problem in itself. We present a mathematical model and algorithm for incorporating these physical constraints into registration / motion and deformation estimation that does not require a segmentation of different material regions. Our algorithm is a joint estimation of different material regions and the motion/deformation within these regions. Therefore, the segmentation of different material regions is automatically provided in addition to the image registration satisfying the physical constraints. The algorithm identifies differing material regions (sub-structures or objects) as regions where the deformation has different characteristics. We demonstrate the effectiveness of our method on the analysis of cardiac MRI which includes the detection of the left ventricle boundary and its deformation. The experimental results indicate the potential of the algorithm as an assistant tool for the quantitative analysis of cardiac functions in the diagnosis of heart disease.
A Single Camera Motion Capture System for Human-Computer Interaction
Okada, Ryuzo; Stenger, Björn
This paper presents a method for markerless human motion capture using a single camera. It uses tree-based filtering to efficiently propagate a probability distribution over poses of a 3D body model. The pose vectors and associated shapes are arranged in a tree, which is constructed by hierarchical pairwise clustering, in order to efficiently evaluate the likelihood in each frame. Anew likelihood function based on silhouette matching is proposed that improves the pose estimation of thinner body parts, i. e. the limbs. The dynamic model takes self-occlusion into account by increasing the variance of occluded body-parts, thus allowing for recovery when the body part reappears. We present two applications of our method that work in real-time on a Cell Broadband Engine™: a computer game and a virtual clothing application.
Experiential Learning in Vehicle Dynamics Education via Motion Simulation and Interactive Gaming
Kevin Hulme
2009-01-01
Full Text Available Creating active, student-centered learning situations in postsecondary education is an ongoing challenge for engineering educators. Contemporary students familiar with visually engaging and fast-paced games can find traditional classroom methods of lecture and guided laboratory experiments limiting. This paper presents a methodology that incorporates driving simulation, motion simulation, and educational practices into an engaging, gaming-inspired simulation framework for a vehicle dynamics curriculum. The approach is designed to promote active student participation in authentic engineering experiences that enhance learning about road vehicle dynamics. The paper presents the student use of physical simulation and large-scale visualization to discover the impact that design decisions have on vehicle design using a gaming interface. The approach is evaluated using two experiments incorporated into a sequence of two upper level mechanical engineering courses.
Breaking the symmetry of a Brownian motor with symmetric potentials
Hagman, H; Zelan, M; Dion, C M
2011-01-01
The directed transport of Brownian particles requires a system with an asymmetry and with non-equilibrium noise. Here we investigate numerically alternative ways of fulfilling these requirements for a two-state Brownian motor, realized with Brownian particles alternating between two phase-shifted, symmetric potentials. We show that, besides the previously known spatio-temporal asymmetry based on unequal transfer rates between the potentials, inequalities in the potential depths, the frictions, or the equilibrium temperatures of the two potentials also generate the required asymmetry. We also show that the effects of the thermal noise and the noise of the transfer's randomness depend on the way the asymmetry is induced.
Stecklein, Jason Jeffrey
The utilization of interactive technologies will affect learning in science classrooms of the future. And although these technologies have improved in form and function, their effective employment in university science classrooms has lagged behind the rapid development of new constructivist pedagogies and means of instruction. This dissertation examines the enlistment of instructional technologies, in particular tablet PCs and DyKnow Interactive Software, in a technologically enhanced, university-level, introductory physics course. Results of this qualitative case study of three university students indicate that (1) the use of interactive technology positively affects both student learning within force and motion and self-reported beliefs about physics, (2) ad hoc use of instructional technologies may not sufficient for effective learning in introductory physics, (3) student learners dictate the leveraging of technology in any classroom, and (4) that purposeful teacher structuring of classroom activities with technologies are essential for student construction of knowledge. This includes designing activities to elicit attention and make knowledge visible for low-level content, while augmenting student interactions and modelling procedural steps for higher-level content.
Zoltán Rusák
2014-01-01
Full Text Available Motor interaction in virtual sculpting, dance trainings, and physiological rehabilitation requires close virtual proximity of users, which may be hindered by low resolution of images and system latency. This paper reports on the results of our investigation aiming to explore the pros and cons of using ultrahigh 4K resolution displays (4096 × 2160 pixels in remote motor interaction. 4K displays are able to overcome the problem of visible pixels and they are able to show more accurate image details on the level of textures, shadows, and reflections. It was our assumption that such image details can not only satisfy visual comfort of the users, but also provide detailed visual cues and improve the reaction time of users in motor interaction. To validate this hypothesis, we explored the relationships between the reaction time of subjects responding to a series of action-reaction type of games and resolution of the image used in an experiment. The results of our experiment showed that the subjects’ reaction time is significantly shorter in 4K images than in HD or VGA images in motor interaction with small motion envelope.
Communication: Memory effects and active Brownian diffusion
Ghosh, Pulak K. [Department of Chemistry, Presidency University, Kolkata 700073 (India); Li, Yunyun, E-mail: yunyunli@tongji.edu.cn [Center for Phononics and Thermal Energy Science, Tongji University, Shanghai 200092 (China); Marchegiani, Giampiero [Dipartimento di Fisica, Università di Camerino, I-62032 Camerino (Italy); Marchesoni, Fabio [Center for Phononics and Thermal Energy Science, Tongji University, Shanghai 200092 (China); Dipartimento di Fisica, Università di Camerino, I-62032 Camerino (Italy)
2015-12-07
A self-propelled artificial microswimmer is often modeled as a ballistic Brownian particle moving with constant speed aligned along one of its axis, but changing direction due to random collisions with the environment. Similarly to thermal noise, its angular randomization is described as a memoryless stochastic process. Here, we speculate that finite-time correlations in the orientational dynamics can affect the swimmer’s diffusivity. To this purpose, we propose and solve two alternative models. In the first one, we simply assume that the environmental fluctuations governing the swimmer’s propulsion are exponentially correlated in time, whereas in the second one, we account for possible damped fluctuations of the propulsion velocity around the swimmer’s axis. The corresponding swimmer’s diffusion constants are predicted to get, respectively, enhanced or suppressed upon increasing the model memory time. Possible consequences of this effect on the interpretation of the experimental data are discussed.
Factorization Procedure for Harmonically Bound Brownian Particle
Omolo, JK.
2006-01-01
The method of factorization to solve the problem of the one-dimensional harmonically bound Brownian particle was applied. Assuming the the rapidily fluctuating random force is Gaussian and has an infinitely short correlation time, explicit expressions for the position-position,velocity-velocity, and the position-velocity correlation functions, which are also use to write down appropriate distribution functions were used. The correlation and distribution functions for the complex quantity (amplititude) which provides the expressions for the position and velocity of the particle are calculated. Finally, Fokker-Planck equations for the joint probability distribution functions for the amplititude and it's complex conjugate as well as for the position and velocity of the particle are obtained. (author)
Uzhinskij, V.V.; Shmakov, S.Yu.
1988-01-01
A method is suggested which enables one to take unto account the Fermi motion of nuclear nucleons in Monte-Carlo simulation of exclusive states in hadron-nucleus and nucleus-nucleus interactions and, in hadron-hadron interaction simulation, to take into account the quark transverse momentum without violation of the energy-momentum conservation law
Theory of molecular crowding in Brownian hard-sphere liquids.
Zaccone, Alessio; Terentjev, Eugene M
2012-06-01
We derive an analytical pair potential of mean force for Brownian molecules in the liquid state. Our approach accounts for many-particle correlations of crowding particles of the liquid and for diffusive transport across the spatially modulated local density of crowders in the dense environment. Focusing on the limit of equal-size particles, we show that this diffusive transport leads to additional density- and structure-dependent terms in the interaction potential and to a much stronger attraction (by a factor of ≈4 at average volume fraction of crowders φ{0}=0.25) than in the standard depletion interaction where the diffusive effects are neglected. As an illustration of the theory, we use it to study the size of a polymer chain in a solution of inert crowders. Even in the case of an athermal background solvent, when a classical chain should be fully swollen, we find a sharp coil-globule transition of the ideal chain collapsing at a critical value of the crowder volume fraction φ{c}≈0.145.
Interactive modeling activities in the classroom—rotational motion and smartphone gyroscopes
Pörn, Ray; Braskén, Mats
2016-11-01
The wide-spread availability of smartphones makes them a valuable addition to the measurement equipment in both the physics classroom and the instructional laboratory, encouraging an active interaction between measurements and modeling activities. In this paper we illustrate this interaction by making use of the internal gyroscope of a smartphone to study and measure the rotational dynamics of objects rotating about a fixed axis. The workflow described in this paper has been tested in a classroom setting and found to encourage an exploratory approach to both data collecting and modeling.
Munro, R. J.
2012-02-01
Experiments were performed to analyse the interaction between a vortex ring and a sloped sediment layer. Attention focussed on interactions under "critical" conditions, in which sediment motion was only just induced by the ring's flow field. Both hydraulically smooth and hydraulically rough bedforms were analysed, using near-spherical monodisperse sediments with relative densities of 1.2 and 2.5 and mean diameters (dp) ranging between 80 and 1087 μm. Measurements of the vortex-ring flow field were obtained, during the interaction, using two-dimensional particle imaging velocimetry. The threshold conditions for incipient sediment motion were analysed in terms of the critical Shields parameter (Nc), defined in terms of the peak tangential velocity measured adjacent to the bed surface. Bed-slope effects were investigated by tilting the sediment layer at various angles between the horizontal and the repose limit for the sediment. In all cases, the propagation axis of the vortex ring was aligned normal to the bed surface. The measured values of Nc were compared with a force-balance model based on the conditions for incipient grain motion on a sloping bed. For hydraulically smooth bedforms, where the bed roughness is small compared to the boundary-layer depth, the model was derived to account for how viscous stresses affect the drag and lift forces acting on the near surface sediment. For hydraulically rough bedforms, where this viscous-damping effect is not present, the model assumes the drag and lift forces scale with the square of the near-bed (inviscid) velocity scale. In both cases, the model predicts that bedforms become more mobile as the bed slope is increased. However, the damping effect of the viscous sublayer acts as a stabilizing influence for hydraulically smooth bedforms, to reduce the rate at which the bed mobility increases with bed slope. The measured values of Nc were in agreement with the trends predicted by this model, and exhibit a transition in
Katherine S Young
2015-02-01
Full Text Available Background: Impaired social functioning is a well-established feature of depression. Evidence to date suggests that disrupted processing of emotional cues may constitute part of this impairment. Beyond processing of emotional cues, fluent social interactions require that people physically move in synchronised, contingent ways. Disruptions to physical movements are a diagnostic feature of depression (psychomotor disturbance but have not previously been assessed in the context of social functioning. Here we investigated the impact of psychomotor disturbance in depression on physical responsive behaviour in both an experimental and observational setting.Methods: In Experiment 1, we examined motor disturbance in depression in response to salient emotional sounds, using a laboratory-based effortful motor task. In Experiment 2, we explored whether psychomotor disturbance was apparent in real-life social interactions. Using mother-infant interactions as a model affective social situation, we compared physical behaviours of mothers with and without postnatal depression (PND.Results: We found impairments in precise, controlled psychomotor performance in adults with depression relative to healthy adults (Experiment 1. Despite this disruption, all adults showed enhanced performance following exposure to highly salient emotional cues (infant cries. Examining real-life interactions, we found differences in physical movements, namely reduced affective touching, in mothers with PND responding to their infants, compared to healthy mothers (Experiment 2.Conclusions: Together, these findings suggest that psychomotor disturbance may be an important feature of depression that can impair social functioning. Future work investigating whether improvements in physical movement in depression could have a positive impact on social interactions would be of much interest.
Conformal correlation functions in the Brownian loop soup
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
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
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.
An explicit local uniform large deviation bound for Brownian bridges
Wittich, O.
2005-01-01
By comparing curve length in a manifold and a standard sphere, we prove a local uniform bound for the exponent in the Large Deviation formula that describes the concentration of Brownian bridges to geodesics.
Kivotides, Demosthenes, E-mail: demosthenes.kivotides@strath.ac.uk
2017-02-12
An asymptotically exact method for the direct computation of turbulent polymeric liquids that includes (a) fully resolved, creeping microflow fields due to hydrodynamic interactions between chains, (b) exact account of (subfilter) residual stresses, (c) polymer Brownian motion, and (d) direct calculation of chain entanglements, is formulated. Although developed in the context of polymeric fluids, the method is equally applicable to turbulent colloidal dispersions and aerosols. - Highlights: • An asymptotically exact method for the computation of polymer and colloidal fluids is developed. • The method is valid for all flow inertia and all polymer volume fractions. • The method models entanglements and hydrodynamic interactions between polymer chains.
Directed Transport of Brownian Particles in a Periodic Channel
Jiang Jie; Ai Bao-Quan; Wu Jian-Chun
2015-01-01
The transport of Brownian particles in the infinite channel within an external force along the axis of the channel has been studied. In this paper, we study the transport of Brownian particle in the infinite channel within an external force along the axis of the channel and an external force in the transversal direction. In this more sophisticated situation, some property is similar to the simple situation, but some interesting property also appears. (paper)
Volume of the domain visited by N spherical Brownian particles
Berezhkovskii, A.M.
1994-01-01
The average value and variance of the volume of the domain visited in time t by N spherical Brownian particles starting initially at the same point are presented as quadratures of the solutions of simple diffusion problems of the survival of a point Brownian particle in the presence of one and two spherical traps. As an illustration, explicit time dependences are obtained for the average volume in one and three dimensions
Fast orthogonal transforms and generation of Brownian paths.
Leobacher, Gunther
2012-04-01
We present a number of fast constructions of discrete Brownian paths that can be used as alternatives to principal component analysis and Brownian bridge for stratified Monte Carlo and quasi-Monte Carlo. By fast we mean that a path of length [Formula: see text] can be generated in [Formula: see text] floating point operations. We highlight some of the connections between the different constructions and we provide some numerical examples.
AirDraw: Leveraging Smart Watch Motion Sensors for Mobile Human Computer Interactions
Sajjadi, Seyed A; Moazen, Danial; Nahapetian, Ani
2017-01-01
Wearable computing is one of the fastest growing technologies today. Smart watches are poised to take over at least of half the wearable devices market in the near future. Smart watch screen size, however, is a limiting factor for growth, as it restricts practical text input. On the other hand, wearable devices have some features, such as consistent user interaction and hands-free, heads-up operations, which pave the way for gesture recognition methods of text entry. This paper proposes a new...
Skyrme's interaction beyond the mean-field. The DGCM+GOA Hamiltonian of nuclear quadrupole motion
Kluepfel, Peter
2008-07-29
This work focuses on the microscopic description of nuclear collective quadrupole motion within the framework of the dynamic Generator-Coordinate-Method(DGCM)+Gaussian-Overlap-Approximation(GOA). Skyrme-type effective interactions are used as the fundamental many-particle interaction. Starting from a rotational invariant, polynomial and topologic consistent formulation of the GCM+GOA Hamiltonian an interpolation scheme for the collective masses and potential is developed. It allows to define the collective Hamiltonian of fully triaxial collective quadrupole dynamics from a purely axial symmetric configuration space. The substantial gain in performance allows the self-consistent evaluation of the dynamic quadrupole mass within the ATDHF-cranking model. This work presents the first large-scale analysis of quadrupole correlation energies and lowlying collective states within the DGCM+GOA model. Different Skyrme- and pairing interactions are compared from old standards up to more recent parameterizations. After checking the validity of several approximations to the DGCM+GOA model - both on the mean-field and the collective level - we proceed with a detailed investigation of correlation effects along the chains of semi-magic isotopes and isotones. This finally allows to define a set of observables which are hardly affected by collective correlations. Those observables were used for a refit of a Skyrme-type effective interaction which is expected to cure most of the problems of the recent parameterizations. Preparing further work, estimates for the correlated ground state energy are proposed which can be evaluated directly from the mean-field model. (orig.)
Lee, Song Hi
2010-01-01
We presented a molecular dynamics (MD) simulation study of friction behavior between two very massive Brownian particles (BPs) oriented along the z axis with BP centers at -R 12 /2 and R 12 /2 in a Lennard-Jones solvent as a function of the inter-particle separation, R 12 . In order to fix the BPs in space an MD simulation method with the mass of the BP as 10 90 g/mol was employed in which the total momentum of the system was conserved. The cross friction coefficients of x- and y-components are nearly insensitive to R 12 but that of z-component varies with R 12 in good accord with the simple hydrodynamic approximation. On the other hand, the self-friction coefficients are estimated as a very small difference from the single particle friction coefficients, ξ 0 , at all inter-particle separations which agrees with the simple hydrodynamic approximation. Consequently ξ (-) xx is nearly independent of R 12 and equal to its asymptotic value of twice the single particle friction coefficient, and the other relative friction, ξ (-) zz , is in good agreement with the simple hydrodynamic approximation. Molecular theory of Brownian motion of a single heavy particle in a fluid had received a considerable attention in earlier years. After molecular dynamics (MD) simulation technique was utilized, this subject has been widely studied by a variety of MD simulation methods. The common issues here were about the long time behavior of the force and velocity autocorrelation functions, the system size dependent friction coefficient of a massive Brownian particle, and test of the Stokes-Einstein law
Faghihi, M. J.; Tavassoly, M. K.; Hatami, M.
In this paper, a model by which we study the interaction between a motional three-level atom and two-mode field injected simultaneously in a bichromatic cavity is considered; the three-level atom is assumed to be in a Λ-type configuration. As a result, the atom-field and the field-field interaction (parametric down conversion) will be appeared. It is shown that, by applying a canonical transformation, the introduced model can be reduced to a well-known form of the generalized Jaynes-Cummings model. Under particular initial conditions, which may be prepared for the atom and the field, the time evolution of state vector of the entire system is analytically evaluated. Then, the dynamics of atom by considering ‘atomic population inversion’ and two different measures of entanglement, i.e., ‘von Neumann entropy’ and ‘idempotency defect’ is discussed, in detail. It is deduced from the numerical results that, the duration and the maximum amount of the considered physical quantities can be suitably tuned by selecting the proper field-mode structure parameter p and the detuning parameters.
Brownian dynamics simulations of insulin microspheres formation
Li, Wei; Chakrabarti, Amit; Gunton, James
2010-03-01
Recent experiments have indicated a novel, aqueous process of microsphere insulin fabrication based on controlled phase separation of protein from water-soluble polymers. We investigate the insulin microsphere crystal formation from insulin-PEG-water systems via 3D Brownian Dynamics simulations. We use the two component Asakura-Oosawa model to simulate the kinetics of this colloid polymer mixture. We first perform a deep quench below the liquid-crystal boundary that leads to fractal formation. We next heat the system to obtain a break-up of the fractal clusters and subsequently cool the system to obtain a spherical aggregation of droplets with a relatively narrow size distribution. We analyze the structure factor S(q) to identify the cluster dimension. S(q) crosses over from a power law q dependence of 1.8 (in agreement with DLCA) to 4 as q increases, which shows the evolution from fractal to spherical clusters. By studying the bond-order parameters, we find the phase transition from liquid-like droplets to crystals which exhibit local HCP and FCC order. This work is supported by grants from the NSF and Mathers Foundation.
Bernado, Pau; Fernandes, Miguel X.; Jacobs, Doris M.; Fiebig, Klaus; Garcia de la Torre, Jose; Pons, Miquel
2004-01-01
Many important proteins contain multiple domains connected by flexible linkers. Inter-domain motion is suggested to play a key role in many processes involving molecular recognition. Heteronuclear NMR relaxation is sensitive to motions in the relevant time scales and could provide valuable information on the dynamics of multi-domain proteins. However, the standard analysis based on the separation of global tumbling and fast local motions is no longer valid for multi-domain proteins undergoing internal motions involving complete domains and that take place on the same time scale than the overall motion.The complexity of the motions experienced even for the simplest two-domain proteins are difficult to capture with simple extensions of the classical Lipari-Szabo approach. Hydrodynamic effects are expected to dominate the motion of the individual globular domains, as well as that of the complete protein. Using Pin1 as a test case, we have simulated its motion at the microsecond time scale, at a reasonable computational expense, using Brownian Dynamic simulations on simplified models. The resulting trajectories provide insight on the interplay between global and inter-domain motion and can be analyzed using the recently published method of isotropic Reorientational Mode Dynamics which offer a way of calculating their contribution to heteronuclear relaxation rates. The analysis of trajectories computed with Pin1 models of different flexibility provides a general framework to understand the dynamics of multi-domain proteins and explains some of the observed features in the relaxation rate profile of free Pin1