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.
Array-induced collective transport in the Brownian motion of coupled nonlinear oscillator systems
Zheng, Zhigang; Hu, Bambi; Hu, Gang
1998-01-01
Brownian motion of an array of harmonically coupled particles subject to a periodic substrate potential and driven by an external bias is investigated. In the linear response limit (small bias), the coupling between particles may enhance the diffusion process, depending on the competition between the harmonic chain and the substrate potential. An analytical formula of the diffusion rate for the single-particle case is also obtained. In the nonlinear response regime, the moving kink may become...
Noncommutative Brownian motion
Santos, Willien O; Souza, Andre M C
2016-01-01
We investigate the Brownian motion of a particle in a two-dimensional noncommutative (NC) space. Using the standard NC algebra embodied by the sympletic Weyl-Moyal formalism we find that noncommutativity induces a non-vanishing correlation between both coordinates at different times. The effect itself stands as a signature of spatial noncommutativity and offers further alternatives to experimentally detect the phenomena.
Radiation Reaction on Brownian Motions
Seto, Keita
2016-01-01
Tracking the real trajectory of a quantum particle is one of the interpretation problem and it is expressed by the Brownian (stochastic) motion suggested by E. Nelson. Especially the dynamics of a radiating electron, namely, radiation reaction which requires us to track its trajectory becomes important in the high-intensity physics by PW-class lasers at present. It has been normally treated by the Furry picture in non-linear QED, but it is difficult to draw the real trajectory of a quantum particle. For the improvement of this, I propose the representation of a stochastic particle interacting with fields and show the way to describe radiation reaction on its Brownian motion.
Brownian Motion, "Diverse and Undulating"
Duplantier, Bertrand
2016-01-01
We describe in detail the history of Brownian motion, as well as the contributions of Einstein, Sutherland, Smoluchowski, Bachelier, Perrin and Langevin to its theory. The always topical importance in physics of the theory of Brownian motion is illustrated by recent biophysical experiments, where it serves, for instance, for the measurement of the pulling force on a single DNA molecule. In a second part, we stress the mathematical importance of the theory of Brownian motion, illustrated by two chosen examples. The by-now classic representation of the Newtonian potential by Brownian motion is explained in an elementary way. We conclude with the description of recent progress seen in the geometry of the planar Brownian curve. At its heart lie the concepts of conformal invariance and multifractality, associated with the potential theory of the Brownian curve itself.
Approximations of fractional Brownian motion
Li, Yuqiang; 10.3150/10-BEJ319
2012-01-01
Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the one-parameter fractional Brownian motion is constructed using a two-parameter Poisson process. The proof involves the tightness and identification of finite-dimensional distributions.
Brownian Motion Theory and Experiment
Basu, K; Basu, Kasturi; Baishya, Kopinjol
2003-01-01
Brownian motion is the perpetual irregular motion exhibited by small particles immersed in a fluid. Such random motion of the particles is produced by statistical fluctuations in the collisions they suffer with the molecules of the surrounding fluid. Brownian motion of particles in a fluid (like milk particles in water) can be observed under a microscope. Here we describe a simple experimental set-up to observe Brownian motion and a method of determining the diffusion coefficient of the Brownian particles, based on a theory due to Smoluchowski. While looking through the microscope we focus attention on a fixed small volume, and record the number of particles that are trapped in that volume, at regular intervals of time. This gives us a time-series data, which is enough to determine the diffusion coefficient of the particles to a good degree of accuracy.
Generalized functionals of Brownian motion
N. U. Ahmed
1994-01-01
Full Text Available In this paper we discuss some recent developments in the theory of generalized functionals of Brownian motion. First we give a brief summary of the Wiener-Ito multiple Integrals. We discuss some of their basic properties, and related functional analysis on Wiener measure space. then we discuss the generalized functionals constructed by Hida. The generalized functionals of Hida are based on L2-Sobolev spaces, thereby, admitting only Hs, s∈R valued kernels in the multiple stochastic integrals. These functionals are much more general than the classical Wiener-Ito class. The more recent development, due to the author, introduces a much more broad class of generalized functionals which are based on Lp-Sobolev spaces admitting kernels from the spaces p,s, s∈R. This allows analysis of a very broad class of nonlinear functionals of Brownian motion, which can not be handled by either the Wiener-Ito class or the Hida class. For s≤0, they represent generalized functionals on the Wiener measure space like Schwarz distributions on finite dimensional spaces. In this paper we also introduce some further generalizations, and construct a locally convex topological vector space of generalized functionals. We also present some discussion on the applications of these results.
Entropic forces in Brownian motion
Roos, Nico
2013-01-01
The interest in the concept of entropic forces has risen considerably since E. Verlinde proposed to interpret the force in Newton s second law and Gravity as entropic forces. Brownian motion, the motion of a small particle (pollen) driven by random impulses from the surrounding molecules, may be the first example of a stochastic process in which such forces are expected to emerge. In this note it is shown that at least two types of entropic motion can be identified in the case of 3D Brownian motion (or random walk). This yields simple derivations of known results of Brownian motion, Hook s law and, applying an external (nonradial) force, Curie s law and the Langevin-Debye equation.
Harmonic functions on Walsh's Brownian motion
Jehring, Kristin Elizabeth
2009-01-01
In this dissertation we examine a variation of two- dimensional Brownian motion introduced in 1978 by Walsh. Walsh's Brownian motion can be described as a Brownian motion on the spokes of a (rimless) bicycle wheel. We will construct such a process by randomly assigning an angle to the excursions of a reflecting Brownian motion from 0. With this construction we see that Walsh's Brownian motion in R² behaves like one-dimensional Brownian motion away from the origin, but at the origin behaves di...
Brownian motion from molecular dynamics
Shin, Hyun Kyung; Talkner, Peter; Lee, Eok Kyun
2010-01-01
Brownian motion of single particles with various masses M and diameters D is studied by molecular dynamics simulations. Besides the momentum auto-correlation function of the Brownian particle the memory function and the fluctuating force which enter the generalized Langevin equation of the Brownian particle are determined and their dependence on mass and diameter are investigated for two different fluid densities. Deviations of the fluctuating force distribution from a Gaussian form are observed for small particle diameters. For heavy particles the deviations of the fluctuating force from the total force acting on the Brownian particle decrease linearly with the mass ratio m/M where m denotes the mass of a fluid particle.
Brownian Motion and General Relativity
O'Hara, Paul
2013-01-01
We construct a model of Brownian Motion on a pseudo-Riemannian manifold associated with general relativity. There are two aspects of the problem: The first is to define a sequence of stopping times associated with the Brownian "kicks" or impulses. The second is to define the dynamics of the particle along geodesics in between the Brownian kicks. When these two aspects are taken together, we can associate various distributions with the motion. We will find that the statistics of space-time events will obey a temperature dependent four dimensional Gaussian distribution defined over the quaternions which locally can be identified with Minkowski space. Analogously, the statistics of the 4-velocities will obey a kind of Maxwell-Juttner distribution. In contrast to previous work, our processes are characterized by two independent proper time variables defined with respect to the laboratory frame: a discrete one corresponding to the stopping times when the impulses take place and a continuous one corresponding to th...
Generalization of Brownian Motion with Autoregressive Increments
Fendick, Kerry
2011-01-01
This paper introduces a generalization of Brownian motion with continuous sample paths and stationary, autoregressive increments. This process, which we call a Brownian ray with drift, is characterized by three parameters quantifying distinct effects of drift, volatility, and autoregressiveness. A Brownian ray with drift, conditioned on its state at the beginning of an interval, is another Brownian ray with drift over the interval, and its expected path over the interval is a ray with a slope that depends on the conditioned state. This paper shows how Brownian rays can be applied in finance for the analysis of queues or inventories and the valuation of options. We model a queue's net input process as a superposition of Brownian rays with drift and derive the transient distribution of the queue length conditional on past queue lengths and on past states of the individual Brownian rays comprising the superposition. The transient distributions of Regulated Brownian Motion and of the Regulated Brownian Bridge are...
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...
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 of helical flagella.
Hoshikawa, H; Saito, N
1979-07-01
We develops a theory of the Brownian motion of a rigid helical object such as bacterial flagella. The statistical properties of the random forces acting on the helical object are discussed and the coefficients of the correlations of the random forces are determined. The averages , and are also calculated where z and theta are the position along and angle around the helix axis respectively. Although the theory is limited to short time interval, direct comparison with experiment is possible by using the recently developed cinematography technique.
Combinatorial fractal Brownian motion model
朱炬波; 梁甸农
2000-01-01
To solve the problem of how to determine the non-scaled interval when processing radar clutter using fractal Brownian motion (FBM) model, a concept of combinatorial FBM model is presented. Since the earth (or sea) surface varies diversely with space, a radar clutter contains several fractal structures, which coexist on all scales. Taking the combination of two FBMs into account, via theoretical derivation we establish a combinatorial FBM model and present a method to estimate its fractal parameters. The correctness of the model and the method is proved by simulation experiments and computation of practial data. Furthermore, we obtain the relationship between fractal parameters when processing combinatorial model with a single FBM model. Meanwhile, by theoretical analysis it is concluded that when combinatorial model is observed on different scales, one of the fractal structures is more obvious.
de Boer, J.; Hubeny, V.E.; Rangamani, M.; Shigemori, M.
2009-01-01
We study Brownian motion and the associated Langevin equation in AdS/CFT. The Brownian particle is realized in the bulk spacetime as a probe fundamental string in an asymptotically AdS black hole background, stretching between the AdS boundary and the horizon. The modes on the string are excited by
Brownian Motion and its Conditional Descendants
Garbaczewski, Piotr
It happened before [1] that I have concluded my publication with a special dedication to John R. Klauder. Then, the reason was John's PhD thesis [2] and the questions (perhaps outdated in the eyes of the band-wagon jumpers, albeit still retaining their full vitality [3]): (i) What are the uses of the classical (c-number, non-Grassmann) spinor fields, especially nonlinear ones, what are they for at all ? (ii) What are, if any, the classical partners for Fermi models and fields in particular ? The present dedication, even if not as conspicuously motivated as the previous one by John's research, nevertheless pertains to investigations pursued by John through the years and devoted to the analysis of random noise. Sometimes, re-reading old papers and re-analysing old, frequently forgotten ideas might prove more rewarding than racing the fashions. Following this attitude, let us take as the departure point Schrödinger's original suggestion [4] of the existence of a special class of random processes, which have their origin in the Einstein-Smoluchowski theory of the Brownian motion and its Wiener's codification. The original analysis due to Schrodinger of the probabilistic significance of the heat equation and of its time adjoint in parallel, remained unnoticed by the physics community, and since then forgotten. It reappeared however in the mathematical literature as an inspiration to generalise the concept of Markovian diffusions to the case of Bernstein stochastic processes. But, it stayed without consequences for a deeper understanding of the possible physical phenomena which might underly the corresponding abstract formalism. Schrödinger's objective was to initiate investigations of possible links between quantum theory and the theory of Brownian motion, an attempt which culminated later in the so-called Nelson's stochastic mechanics [8] and its encompassing formalism [7] in which the issue of the Brownian implementation of quantum dynamics is placed in the
On some generalization of fractional Brownian motions
Wang Xiaotian [School of Management, Tianjin University, Tianjin 300072 (China); Liang Xiangqian [Department of Applied Mathematics, Shandong University of Science and Technology, Qingdao 266510, Shandong (China); Ren Fuyao [Institute of Mathematics, Fudan University, Shanghai 200433 (China); Zhang Shiying [School of Management, Tianjin University, Tianjin 300072 (China)]. E-mail: swa001@126.com
2006-05-15
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.
Blending Brownian motion and heat equation
Cristiani, Emiliano
2015-01-01
In this short communication we present an original way to couple the Brownian motion and the heat equation. More in general, we suggest a way for coupling the Langevin equation for a particle, which describes a single realization of its trajectory, with the associated Fokker-Planck equation, which instead describes the evolution of the particle's probability density function. Numerical results show that it is indeed possible to obtain a regularized Brownian motion and a Brownianized heat equation still preserving the global statistical properties of the solutions. The results also suggest that the more macroscale leads the dynamics the more one can reduce the microscopic degrees of freedom.
From fractional Brownian motion to multifractional and multistable motion
Falconer, Kenneth
2015-03-01
Fractional Brownian motion, introduced by Benoit Mandelbrot and John Van Ness in 1968, has had a major impact on stochastic processes and their applications. We survey a few of the many developments that have stemmed from their ideas. In particular we discuss the local structure of fractional and multifractional Brownian, stable and multistable processes, emphasising the `diagonal' construction of such processes. In all this, the ubiquity and centrality of fractional Brownian motion is striking.
Karhunen-Loève Expansion for the Second Order Detrended Brownian Motion
Yongchun Zhou
2014-01-01
Full Text Available Based on the norm in the Hilbert Space L2[0,1], the second order detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion into the space spanned by nonlinear function subspace. Karhunen-Loève expansion for this process is obtained together with the relationship of that of a generalized Brownian bridge. As applications, Laplace transform, large deviation, and small deviation are given.
On Kramers' general theory of Brownian motion
Brinkman, H.C.
1957-01-01
Kramer's general theory of Brownian motion 1) based on a diffusion equation in phase space is discussed from the standpoint of statistical thermodynamics. It is concluded that for particles moving in a medium in equilibrium the restrictions imposed by the second law of thermodynamics limit Kramer's
Fractional Brownian motion of director fluctuations in nematic ordering
Zhang, Z.; Mouritsen, Ole G.; Otnes, K.
1993-01-01
to determine the Hurst exponent H. Theory and experiment are in good agreement. A value of H congruent-to 1 was found for the nematic phase, characterizing fractional Brownian motion, whereas H congruent-to 0.5, reflecting ordinary Brownian motion, applies in the isotropic phase. Field-induced crossover from...... fractional to ordinary Brownian motion was observed in the nematic phase....
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...
Simulations of magnetic nanoparticle Brownian motion.
Reeves, Daniel B; Weaver, John B
2012-12-15
Magnetic nanoparticles are useful in many medical applications because they interact with biology on a cellular level thus allowing microenvironmental investigation. An enhanced understanding of the dynamics of magnetic particles may lead to advances in imaging directly in magnetic particle imaging or through enhanced MRI contrast and is essential for nanoparticle sensing as in magnetic spectroscopy of Brownian motion. Moreover, therapeutic techniques like hyperthermia require information about particle dynamics for effective, safe, and reliable use in the clinic. To that end, we have developed and validated a stochastic dynamical model of rotating Brownian nanoparticles from a Langevin equation approach. With no field, the relaxation time toward equilibrium matches Einstein's model of Brownian motion. In a static field, the equilibrium magnetization agrees with the Langevin function. For high frequency or low amplitude driving fields, behavior characteristic of the linearized Debye approximation is reproduced. In a higher field regime where magnetic saturation occurs, the magnetization and its harmonics compare well with the effective field model. On another level, the model has been benchmarked against experimental results, successfully demonstrating that harmonics of the magnetization carry enough information to infer environmental parameters like viscosity and temperature.
Performance of Brownian-motion-generated universal portfolios
Tan, Choon Peng; Pang, Sook Theng
2014-06-01
Investment in a market of m stocks is considered. Generating a universal portfolio using m independent Brownian motions is demonstrated. The asymptotic behaviour of a Brownian-motion-generated universal portfolio is described. The empirical performance of such portfolios on some selected three-stock data sets is analysed. Investment wealth can be increased by varying the drift coefficients or parameters of the Brownian motions.
The Isolation Time of Poisson Brownian motions
Peres, Yuval; Stauffer, Alexandre
2011-01-01
Let the nodes of a Poisson point process move independently in $\\R^d$ according to Brownian motions. We study the isolation time for a target particle that is placed at the origin, namely how long it takes until there is no node of the Poisson point process within distance $r$ of it. We obtain asymptotics for the tail probability which are tight up to constants in the exponent in dimension $d\\geq 3$ and tight up to logarithmic factors in the exponent for dimensions $d=1,2$.
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.
LINEAR SEARCH FOR A BROWNIAN TARGET MOTION
A. B. El-Rayes; Abd El-Moneim A. Mohamed; Hamdy M. Abou Gabal
2003-01-01
A target is assumed to move according to a Brownian motion on the real line.The searcher starts from the origin and moves in the two directions from the starting point.The object is to detect the target.The purpose of this paper is to find the conditions under which the expected value of the first meeting time of the searcher and the target is finite,and to show the existence of a search plan which made this expected value minimum.
Inducing Tropical Cyclones to Undergo Brownian Motion
Hodyss, D.; McLay, J.; Moskaitis, J.; Serra, E.
2014-12-01
Stochastic parameterization has become commonplace in numerical weather prediction (NWP) models used for probabilistic prediction. Here, a specific stochastic parameterization will be related to the theory of stochastic differential equations and shown to be affected strongly by the choice of stochastic calculus. From an NWP perspective our focus will be on ameliorating a common trait of the ensemble distributions of tropical cyclone (TC) tracks (or position), namely that they generally contain a bias and an underestimate of the variance. With this trait in mind we present a stochastic track variance inflation parameterization. This parameterization makes use of a properly constructed stochastic advection term that follows a TC and induces its position to undergo Brownian motion. A central characteristic of Brownian motion is that its variance increases with time, which allows for an effective inflation of an ensemble's TC track variance. Using this stochastic parameterization we present a comparison of the behavior of TCs from the perspective of the stochastic calculi of Itô and Stratonovich within an operational NWP model. The central difference between these two perspectives as pertains to TCs is shown to be properly predicted by the stochastic calculus and the Itô correction. In the cases presented here these differences will manifest as overly intense TCs, which, depending on the strength of the forcing, could lead to problems with numerical stability and physical realism.
Nonequilibrium Brownian motion beyond the effective temperature.
Andrea Gnoli
Full Text Available The condition of thermal equilibrium simplifies the theoretical treatment of fluctuations as found in the celebrated Einstein's relation between mobility and diffusivity for Brownian motion. Several recent theories relax the hypothesis of thermal equilibrium resulting in at least two main scenarios. With well separated timescales, as in aging glassy systems, equilibrium Fluctuation-Dissipation Theorem applies at each scale with its own "effective" temperature. With mixed timescales, as for example in active or granular fluids or in turbulence, temperature is no more well-defined, the dynamical nature of fluctuations fully emerges and a Generalized Fluctuation-Dissipation Theorem (GFDT applies. Here, we study experimentally the mixed timescale regime by studying fluctuations and linear response in the Brownian motion of a rotating intruder immersed in a vibro-fluidized granular medium. Increasing the packing fraction, the system is moved from a dilute single-timescale regime toward a denser multiple-timescale stage. Einstein's relation holds in the former and is violated in the latter. The violation cannot be explained in terms of effective temperatures, while the GFDT is able to impute it to the emergence of a strong coupling between the intruder and the surrounding fluid. Direct experimental measurements confirm the development of spatial correlations in the system when the density is increased.
The Fractional Langevin Equation: Brownian Motion Revisited
Mainardi, Francesco
2008-01-01
We have revisited the Brownian motion on the basis of the fractional Langevin equation which turns out to be a particular case of the generalized Langevin equation introduced by Kubo on 1966. The importance of our approach is to model the Brownian motion more realistically than the usual one based on the classical Langevin equation, in that it takes into account also the retarding effects due to hydrodynamic backflow, i.e. the added mass and the Basset memory drag. On the basis of the two fluctuation-dissipation theorems and of the techniques of the Fractional Calculus we have provided the analytical expressions of the correlation functions (both for the random force and the particle velocity) and of the mean squared particle displacement. The random force has been shown to be represented by a superposition of the usual white noise with a "fractional" noise. The velocity correlation function is no longer expressed by a simple exponential but exhibits a slower decay, proportional to $t^{-3/2}$ as $t \\to \\infty...
Optimal Control of Stochastic Systems Driven by Fractional Brownian Motions
2014-10-09
motions and other stochastic processes. For the control of both continuous time and discrete time finite dimensional linear systems with quadratic...problems for stochastic partial differential equations driven by fractional Brownian motions are explicitly solved. For the control of a continuous time...2010 30-Jun-2014 Approved for Public Release; Distribution Unlimited Final Report: Optimal Control of Stochastic Systems Driven by Fractional Brownian
Parallel Molecular Distributed Detection with Brownian Motion.
Rogers, Uri; Koh, Min-Sung
2016-12-05
This paper explores the in vivo distributed detection of an undesired biological agent's (BAs) biomarkers by a group of biological sized nanomachines in an aqueous medium under drift. The term distributed, indicates that the system information relative to the BAs presence is dispersed across the collection of nanomachines, where each nanomachine possesses limited communication, computation, and movement capabilities. Using Brownian motion with drift, a probabilistic detection and optimal data fusion framework, coined molecular distributed detection, will be introduced that combines theory from both molecular communication and distributed detection. Using the optimal data fusion framework as a guide, simulation indicates that a suboptimal fusion method exists, allowing for a significant reduction in implementation complexity while retaining BA detection accuracy.
Lecture Notes on Quantum Brownian Motion
Erdos, Laszlo
2010-01-01
Einstein's kinetic theory of the Brownian motion, based upon light water molecules continuously bombarding a heavy pollen, provided an explanation of diffusion from the Newtonian mechanics. Since the discovery of quantum mechanics it has been a challenge to verify the emergence of diffusion from the Schr\\"odinger equation. The first step in this program is to verify the linear Boltzmann equation as a certain scaling limit of a Schr\\"odinger equation with random potential. In the second step, one considers a longer time scale that corresponds to infinitely many Boltzmann collisions. The intuition is that the Boltzmann equation then converges to a diffusive equation similarly to the central limit theorem for Markov processes with sufficient mixing. In these lecture notes (prepared for the Les Houches summer school in 2010 August) we present the mathematical tools to rigorously justify this intuition. The new material relies on joint papers with H.-T. Yau and M. Salmhofer.
On Brownian motion in ideal gas and related principles
Kuzovlev, Yuriy E.
2008-01-01
Brownian motion of particle interacting with atoms of ideal gas is discussed as a key problem of kinetics lying at the border between ``dead'' systems like the Lorentz gas or formal constructs of conceptual Boltzmannian kinetics and actual ``alive'' systems like mere gas possessing scaleless (1/f) fluctuations in their kinetic characteristics (e.g. in diffusuvity and mobility of the ``Brownian particle'').
Reflected Backward Stochastic Differential Equations Driven by Countable Brownian Motions
Pengju Duan
2013-01-01
Full Text Available This paper deals with a new class of reflected backward stochastic differential equations driven by countable Brownian motions. The existence and uniqueness of the RBSDEs are obtained via Snell envelope and fixed point theorem.
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.
Brownian Motion of a Classical Particle in Quantum Environment
Tsekov, R.
2017-01-01
The Klein-Kramers equation, governing the Brownian motion of a classical particle in quantum environment under the action of an arbitrary external potential, is derived. Quantum temperature and friction operators are introduced and at large friction the corresponding Smoluchowski equation is obtained. Introducing the Bohm quantum potential, this Smoluchowski equation is extended to describe the Brownian motion of a quantum particle in quantum environment.
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.
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 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....
Non-Markovian expansion in quantum Brownian motion
Fraga, Eduardo S.; Krein, Gastão; Palhares, Letícia F.
2014-01-01
We consider the non-Markovian Langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism. After discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the most common choices, we derive an analytic expansion for the exact non-Markovian dissipation kernel and the corresponding colored noise in the general case that is consistent with the fluctuation-dissipation theorem and incorporates systematically non-local corrections. We illustrate the modifications to results obtained using the traditional (Markovian) Langevin approach in the case of the exponential kernel and analyze the case of the non-Markovian Brownian motion. We present detailed results for the free and the quadratic cases, which can be compared to exact solutions to test the convergence of the method, and discuss potentials of a general nonlinear form.
Langevin model for a Brownian system with directed motion
Ambía, Francisco; Híjar, Humberto
2016-08-01
We propose a model for an active Brownian system that exhibits one-dimensional directed motion. This system consists of two Brownian spherical particles that interact through an elastic potential and have time-dependent radii. We suggest an algorithm by which the sizes of the particles can be varied, such that the center of mass of the system is able to move at an average constant speed in one direction. The dynamics of the system is studied theoretically using a Langevin model, as well as from Brownian Dynamics simulations.
RESEARCH NOTES On the support of super-Brownian motion with super-Brownian immigration
洪文明; 钟惠芳
2001-01-01
The support properties of the super Brownian motion with random immigration Xρ1 are considered,where the immigration rate is governed by the trajectory of another super-Brownian motion ρ. When both the initial state Xρo of the process and the immigration rate process ρo are of finite measure and with compact supports, the probability of the support of the process Xρi dominated by a ball is given by the solutions of a singular elliptic boundary value problem.
Extreme-value statistics of fractional Brownian motion bridges.
Delorme, Mathieu; Wiese, Kay Jörg
2016-11-01
Fractional Brownian motion is a self-affine, non-Markovian, and translationally invariant generalization of Brownian motion, depending on the Hurst exponent H. Here we investigate fractional Brownian motion where both the starting and the end point are zero, commonly referred to as bridge processes. Observables are the time t_{+} the process is positive, the maximum m it achieves, and the time t_{max} when this maximum is taken. Using a perturbative expansion around Brownian motion (H=1/2), we give the first-order result for the probability distribution of these three variables and the joint distribution of m and t_{max}. Our analytical results are tested and found to be in excellent agreement, with extensive numerical simulations for both H>1/2 and H<1/2. This precision is achieved by sampling processes with a free end point and then converting each realization to a bridge process, in generalization to what is usually done for Brownian motion.
Brownian shape motion: Fission fragment mass distributions
Sierk Arnold J.
2012-02-01
Full Text Available It was recently shown that remarkably accurate fission-fragment mass distributions can be obtained by treating the nuclear shape evolution as a Brownian walk on previously calculated five-dimensional potential-energy surfaces; the current status of this novel method is described here.
Holographic Brownian motion and time scales in strongly coupled plasmas
Atmaja, Ardian Nata [Research Center for Physics, Indonesian Institute of Sciences (LIPI), Kompleks PUSPITEK Serpong, Tangerang 15310 (Indonesia); Indonesia Center for Theoretical and Mathematical Physics (ICTMP), Bandung 40132 (Indonesia); Boer, Jan de [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands); Shigemori, Masaki [Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502 (Japan); Hakubi Center, Kyoto University, Yoshida-Ushinomiyacho, Sakyo-ku, Kyoto 606-8501 (Japan)
2014-03-15
We study Brownian motion of a heavy quark in field theory plasma in the AdS/CFT setup and discuss the time scales characterizing the interaction between the Brownian particle and plasma constituents. Based on a simple kinetic theory, we first argue that the mean-free-path time is related to the connected 4-point function of the random force felt by the Brownian particle. Then, by holographically computing the 4-point function and regularizing the IR divergence appearing in the computation, we write down a general formula for the mean-free-path time, and apply it to the STU black hole which corresponds to plasma charged under three U(1)R-charges. The result indicates that the Brownian particle collides with many plasma constituents simultaneously.
Parameter Estimation for Generalized Brownian Motion with Autoregressive Increments
Fendick, Kerry
2011-01-01
This paper develops methods for estimating parameters for a generalization of Brownian motion with autoregressive increments called a Brownian ray with drift. We show that a superposition of Brownian rays with drift depends on three types of parameters - a drift coefficient, autoregressive coefficients, and volatility matrix elements, and we introduce methods for estimating each of these types of parameters using multidimensional times series data. We also cover parameter estimation in the contexts of two applications of Brownian rays in the financial sphere: queuing analysis and option valuation. For queuing analysis, we show how samples of queue lengths can be used to estimate the conditional expectation functions for the length of the queue and for increments in its net input and lost potential output. For option valuation, we show how the Black-Scholes-Merton formula depends on the price of the security on which the option is written through estimates not only of its volatility, but also of a coefficient ...
Brownian motion on random dynamical landscapes
Suñé Simon, Marc; Sancho, José María; Lindenberg, Katja
2016-03-01
We present a study of overdamped Brownian particles moving on a random landscape of dynamic and deformable obstacles (spatio-temporal disorder). The obstacles move randomly, assemble, and dissociate following their own dynamics. This landscape may account for a soft matter or liquid environment in which large obstacles, such as macromolecules and organelles in the cytoplasm of a living cell, or colloids or polymers in a liquid, move slowly leading to crowding effects. This representation also constitutes a novel approach to the macroscopic dynamics exhibited by active matter media. We present numerical results on the transport and diffusion properties of Brownian particles under this disorder biased by a constant external force. The landscape dynamics are characterized by a Gaussian spatio-temporal correlation, with fixed time and spatial scales, and controlled obstacle concentrations.
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.
Wrapping Brownian motion and heat kernels I: compact Lie groups
Maher, David G
2010-01-01
An important object of study in harmonic analysis is the heat equation. On a Euclidean space, the fundamental solution of the associated semigroup is known as the heat kernel, which is also the law of Brownian motion. Similar statements also hold in the case of a Lie group. By using the wrapping map of Dooley and Wildberger, we show how to wrap a Brownian motion to a compact Lie group from its Lie algebra (viewed as a Euclidean space) and find the heat kernel. This is achieved by considering It\\^o type stochastic differential equations and applying the Feynman-Ka\\v{c} theorem.
Effect of interfaces on the nearby Brownian motion
Huang, Kai
2016-01-01
Near-boundary Brownian motion is a classic hydrodynamic problem of great importance in a variety of fields, from biophysics to micro-/nanofluidics. However, due to challenges in experimental measurements of near-boundary dynamics, the effect of interfaces on Brownian motion has remained elusive. Here, we report a computational study of this effect using microsecond-long large-scale molecular dynamics simulations and our newly developed Green-Kubo relation for friction at the liquid-solid interface. Our computer experiment unambiguously reveals that the t^(-3/2) long-time decay of the velocity autocorrelation function of a Brownian particle in bulk liquid is replaced by a t^(-5/2) decay near a boundary. We discover a general breakdown of traditional no-slip boundary condition at short time scales and we show that this breakdown has a profound impact on the near-boundary Brownian motion. Our results demonstrate the potential of Brownian-particle based micro-/nano-sonar to probe the local wettability of liquid-s...
Brownian motion as a new probe of wettability
Mo, Jianyong; Simha, Akarsh; Raizen, Mark G.
2017-04-01
Understanding wettability is crucial for optimizing oil recovery, semiconductor manufacturing, pharmaceutical industry, and electrowetting. In this letter, we study the effects of wettability on Brownian motion. We consider the cases of a sphere in an unbounded fluid medium, as well as a sphere placed in the vicinity of a plane wall. For the first case, we show the effects of wettability on the statistical properties of the particles' motion, such as velocity autocorrelation, velocity, and thermal force power spectra over a large range of time scales. We also propose a new method to measure wettability based on the particles' Brownian motion. In addition, we compare the boundary effects on Brownian motion imposed by both no-slip and perfect-slip flat walls. We emphasize the surprising boundary effects on Brownian motion imposed by a perfect-slip wall in the parallel direction, such as a higher particle mobility parallel to a perfect flat wall compared to that in the absence of the wall, as well as compared to a particle near a no-slip flat wall.
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.
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.
Two-sided reflection of Markov-modulated Brownian motion
D'Auria, B.; Ivanovs, J.; Kella, O.; Mandjes, M.
2012-01-01
This article considers a Markov-modulated Brownian motion with a two-sided reflection. For this doubly-reflected process we compute the Laplace transform of the stationary distribution, as well as the average loss rates at both barriers. Our approach relies on spectral properties of the matrix polyn
Wrapping Brownian motion and heat kernels II: symmetric spaces
Maher, David G
2010-01-01
In this paper we extend our previous results on wrapping Brownian motion and heat kernels onto compact Lie groups to various symmetric spaces, where a global generalisation of Rouvi\\`ere's formula and the $e$-function are considered. Additionally, we extend some of our results to complex Lie groups, and certain non-compact symmetric spaces.
Distribution of maximum loss of fractional Brownian motion with drift
Çağlar, Mine; Vardar-Acar, Ceren
2013-01-01
In this paper, we find bounds on the distribution of the maximum loss of fractional Brownian motion with H >= 1/2 and derive estimates on its tail probability. Asymptotically, the tail of the distribution of maximum loss over [0, t] behaves like the tail of the marginal distribution at time t.
Integral representations and properties of operator fractional Brownian motions
Didier, Gustavo; 10.3150/10-BEJ259
2011-01-01
Operator fractional Brownian motions (OFBMs) are (i) Gaussian, (ii) operator self-similar and (iii) stationary increment processes. They are the natural multivariate generalizations of the well-studied fractional Brownian motions. Because of the possible lack of time-reversibility, the defining properties (i)--(iii) do not, in general, characterize the covariance structure of OFBMs. To circumvent this problem, the class of OFBMs is characterized here by means of their integral representations in the spectral and time domains. For the spectral domain representations, this involves showing how the operator self-similarity shapes the spectral density in the general representation of stationary increment processes. The time domain representations are derived by using primary matrix functions and taking the Fourier transforms of the deterministic spectral domain kernels. Necessary and sufficient conditions for OFBMs to be time-reversible are established in terms of their spectral and time domain representations. I...
The genealogy of extremal particles of Branching Brownian Motion
Arguin, Louis-Pierre; Kistler, Nicola
2010-01-01
Branching Brownian Motion describes a system of particles which diffuse in space and split into offsprings according to a certain random mechanism. In virtue of the groundbreaking work by M. Bramson on the convergence of solutions of the Fisher-KPP equation to traveling waves, the law of the rightmost particle in the limit of large times is rather well understood. In this work, we address the full statistics of the extremal particles (first-, second-, third- etc. largest). In particular, we prove that in the large $t-$limit, such particles descend with overwhelming probability from ancestors having split either within a distance of order one from time $0$, or within a distance of order one from time $t$. The approach relies on characterizing, up to a certain level of precision, the paths of the extremal particles. As a byproduct, a heuristic picture of Branching Brownian Motion ``at the edge'' emerges, which sheds light on the still unknown limiting extremal process.
Relating Brownian motion to diffusion with superparamagnetic colloids
Darras, A.; Fiscina, J.; Vandewalle, N.; Lumay, G.
2017-04-01
An original experiment is introduced that allows students to relate the Brownian motion of a set of superparamagnetic colloidal particles to their macroscopic diffusion. An external and constant magnetic field is first applied to the colloidal suspension so that the particles self-organize into chains. When the magnetic field is removed, the particles then freely diffuse from their positions in the chain, starting from the same coordinate on the axis perpendicular to the initial chain. This configuration thus enables an observer to study the one dimensional diffusion process, while also observing the underlying Brownian motion of the microscopic particles. Moreover, by studying the evolution of the particle distribution, a measurement of the diffusion coefficient can be obtained. In addition, by repeating this measurement with fluids of various viscosities, the Stokes-Einstein relation may be illustrated.
On a nonstandard Brownian motion and its maximal function
Andrade, Bernardo B. de
2015-07-01
This article uses Radically Elementary Probability Theory (REPT) to prove results about the Wiener walk (the radically elementary Brownian motion) without the technical apparatus required by stochastic integration. The techniques used replace measure-theoretic tools by discrete probability and the rigorous use of infinitesimals. Specifically, REPT is applied to the results in Palacios (The American Statistician, 2008) to calculate certain expectations related to the Wiener walk and its maximal function. Because Palacios uses mostly combinatorics and no measure theory his results carry over through REPT with minimal changes. The paper also presents a construction of the Wiener walk which is intended to mimic the construction of Brownian motion from "continuous" white noise. A brief review of the nonstandard model on which REPT is based is given in the Appendix in order to minimize the need for previous exposure to the subject.
Quantum mechanics and the square root of the Brownian motion
Frasca, Marco
2014-01-01
Using the Euler--Maruyama technique, we show that a class of Wiener processes exists that are obtained by computing an arbitrary positive power of them. This can be accomplished with a proper set of definitions that makes meaningful the realization at discrete times of these processes and make them computable. Then, we are able to show that quantum mechanics is not directly a stochastic process characterizing Brownian motion but rather its square root. Schr\\"odinger equation is immediately derived without further assumptions as the Fokker--Planck equation for this process. This generalizes without difficulty to a Clifford algebra that makes immediate the introduction of spin and a generalization to the Dirac equation. A relevant conclusion is that the introduction of spin is essential to recover the Brownian motion from its square root.
Coupling of Brownian motions and Perelman's L-functional
Kuwada, Kazumasa
2010-01-01
We show that on a manifold whose Riemannian metric evolves under backwards Ricci flow two Brownian motions can be coupled in such a way that the expectation of their normalized L-distance is non-increasing. As an immediate corollary we obtain a new proof of a recent result of Topping (J. reine angew. Math. 636 (2009), 93-122), namely that the normalized L-transportation cost between two solutions of the heat equation is non-increasing as well.
The frustrated Brownian motion of nonlocal solitary waves
Folli, Viola
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 non-paraxial effects. Analytical predictions are compared with numerical simulations based on stochastic partial differential equation
Quantum and classical correlations in quantum Brownian motion
Eisert, J; Plenio, M. B.
2001-01-01
We investigate the entanglement properties of the joint state of a distinguished quantum system and its environment in the quantum Brownian motion model. This model is a frequent starting point for investigations of environment-induced superselection. Using recent methods from quantum information theory, we show that there exists a large class of initial states for which no entanglement will be created at all times between the system of salient interest and the environment. If the distinguish...
Analytical studies of Spectrum Broadcast Structures in Quantum Brownian Motion
2016-01-01
Spectrum Broadcast Structures are a new and fresh concept in the quantum-to-classical transition, introduced recently in the context of decoherence and the appearance of objective features in quantum mechanics. These are specific quantum state structures, responsible for an apparent objectivity of a decohered state of a system. Recently they have been shown to appear in the well known Quantum Brownian Motion model, however the final analysis relied on numerics. Here, after a presentation of t...
On the Spectral Gap of Brownian Motion with Jump Boundary
Kolb, Martin
2011-01-01
In this paper we consider the Brownian motion with jump boundary and present a new proof of a recent result of Li, Leung and Rakesh concerning the exact convergence rate in the one-dimensional case. Our methods are different and mainly probabilistic relying on coupling methods adapted to the special situation under investigation. Moreover, we answer a question raised by Ben-Ari and Pinsky concerning the dependence of the spectral gap on the jump distribution in a multi-dimensional setting.
On the Generalized Brownian Motion and its Applications in Finance
Høg, Esben; Frederiksen, Per; Schiemert, Daniel
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...... to other markets or multi factors. As a complement the paper shows an example of how to derive the implied bond pricing parameters using the ordinary Kalman filter....
Free Energies and Fluctuations for the Unitary Brownian Motion
Dahlqvist, Antoine
2016-12-01
We show that the Laplace transforms of traces of words in independent unitary Brownian motions converge towards an analytic function on a non trivial disc. These results allow one to study the asymptotic behavior of Wilson loops under the unitary Yang-Mills measure on the plane with a potential. The limiting objects obtained are shown to be characterized by equations analogue to Schwinger-Dyson's ones, named here after Makeenko and Migdal.
Spatial Brownian motion in renormalized Poisson potential: A critical case
Chen, Xia
2011-01-01
Let $B_s$ be a three dimensional Brownian motion and $\\omega(dx)$ be an independent Poisson field on $\\mathbb{R}^3$. It is proved that for any $t>0$, conditionally on $\\omega(\\cdot)$, \\label{*} \\mathbb{E}_0 \\exp\\{\\theta \\int_0^t \\bar{V}(B_s) ds\\} \\ 1/16, where $\\bar{V}(x)$ is the renormalized Poisson potential
On moments of the integrated exponential Brownian motion
Caravelli, Francesco; Mansour, Toufik; Sindoni, Lorenzo; Severini, Simone
2016-07-01
We present new exact expressions for a class of moments of the geometric Brownian motion in terms of determinants, obtained using a recurrence relation and combinatorial arguments for the case of a Itô's Wiener process. We then apply the obtained exact formulas to computing averages of the solution of the logistic stochastic differential equation via a series expansion, and compare the results to the solution obtained via Monte Carlo.
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...
Fractional Brownian motions: memory, diffusion velocity, and correlation functions
Fuliński, A.
2017-02-01
Fractional Brownian motions (FBMs) have been observed recently in the measured trajectories of individual molecules or small particles in the cytoplasm of living cells and in other dense composite systems, among others. Various types of FBMs differ in a number of ways, including the strength, range and type of damping of the memory encoded in their definitions, but share several basic characteristics: distributions, non-ergodic properties, and scaling of the second moment, which makes it difficult to determine which type of Brownian motion (fractional or normal) the measured trajectory belongs to. Here, we show, by introducing FBMs with regulated range and strength of memory, that it is the structure of memory which determines their physical properties, including mean velocity of diffusion; therefore, the course and kinetics of several processes (including coagulation and some chemical reactions). We also show that autocorrelation functions possess characteristic features which enable identification of an observed FBM, and of the type of memory governing its trajectory. In memoriam Marian Smoluchowski, on the 100th anniversary of the publication of his seminal papers on Brownian motion and diffusion-limited kinetics.
Semicircular Canals Circumvent Brownian Motion Overload of Mechanoreceptor Hair Cells.
Mees Muller
Full Text Available Vertebrate semicircular canals (SCC first appeared in the vertebrates (i.e. ancestral fish over 600 million years ago. In SCC the principal mechanoreceptors are hair cells, which as compared to cochlear hair cells are distinctly longer (70 vs. 7 μm, 10 times more compliant to bending (44 vs. 500 nN/m, and have a 100-fold higher tip displacement threshold (< 10 μm vs. <400 nm. We have developed biomechanical models of vertebrate hair cells where the bundle is approximated as a stiff, cylindrical elastic rod subject to friction and thermal agitation. Our models suggest that the above differences aid SCC hair cells in circumventing the masking effects of Brownian motion noise of about 70 nm, and thereby permit transduction of very low frequency (<10 Hz signals. We observe that very low frequency mechanoreception requires increased stimulus amplitude, and argue that this is adaptive to circumvent Brownian motion overload at the hair bundles. We suggest that the selective advantage of detecting such low frequency stimuli may have favoured the evolution of large guiding structures such as semicircular canals and otoliths to overcome Brownian Motion noise at the level of the mechanoreceptors of the SCC.
A discrete impulsive model for random heating and Brownian motion
Ramshaw, John D.
2010-01-01
The energy of a mechanical system subjected to a random force with zero mean increases irreversibly and diverges with time in the absence of friction or dissipation. This random heating effect is usually encountered in phenomenological theories formulated in terms of stochastic differential equations, the epitome of which is the Langevin equation of Brownian motion. We discuss a simple discrete impulsive model that captures the essence of random heating and Brownian motion. The model may be regarded as a discrete analog of the Langevin equation, although it is developed ab initio. Its analysis requires only simple algebraic manipulations and elementary averaging concepts, but no stochastic differential equations (or even calculus). The irreversibility in the model is shown to be a consequence of a natural causal stochastic condition that is closely analogous to Boltzmann's molecular chaos hypothesis in the kinetic theory of gases. The model provides a simple introduction to several ostensibly more advanced topics, including random heating, molecular chaos, irreversibility, Brownian motion, the Langevin equation, and fluctuation-dissipation theorems.
Stochastic Calculus with respect to multifractional Brownian motion
Lebovits, Joachim
2011-01-01
Stochastic calculus with respect to fractional Brownian motion (fBm) has attracted a lot of interest in recent years, motivated in particular by applications in finance and Internet traffic modeling. Multifractional Brownian motion (mBm) is a Gaussian extension of fBm that allows to control the pointwise regularity of the paths of the process and to decouple it from its long range dependence properties. This generalization is obtained by replacing the constant Hurst parameter H of fBm by a function h(t). Multifractional Brownian motion has proved useful in many applications, including the ones just mentioned. In this work we extend to mBm the construction of a stochastic integral with respect to fBm. This stochastic integral is based on white noise theory, as originally proposed in [15], [6], [4] and in [5]. In that view, a multifractional white noise is defined, which allows to integrate with respect to mBm a large class of stochastic processes using Wick products. It\\^o formulas (both for tempered distribut...
Impurity driven Brownian motion of solitons in elongated Bose-Einstein Condensates
Aycock, L M; Genkina, D; Lu, H -I; Galitski, V; Spielman, I B
2016-01-01
Solitons, spatially-localized, mobile excitations resulting from an interplay between nonlinearity and dispersion, are ubiquitous in physical systems from water channels and oceans to optical fibers and Bose-Einstein condensates (BECs). For the first time, we observed and controlled the Brownian motion of solitons. We launched long-lived dark solitons in highly elongated $^{87}\\rm{Rb}$ 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 (1-D), 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-1-D scattering theory of impurity atoms interacting with a soliton, giving diffusion coefficients consistent with experiment.
Transient aging in fractional Brownian and Langevin-equation motion.
Kursawe, Jochen; Schulz, Johannes; Metzler, Ralf
2013-12-01
Stochastic processes driven by stationary fractional Gaussian noise, that is, fractional Brownian motion and fractional Langevin-equation motion, are usually considered to be ergodic in the sense that, after an algebraic relaxation, time and ensemble averages of physical observables coincide. Recently it was demonstrated that fractional Brownian motion and fractional Langevin-equation motion under external confinement are transiently nonergodic-time and ensemble averages behave differently-from the moment when the particle starts to sense the confinement. Here we show that these processes also exhibit transient aging, that is, physical observables such as the time-averaged mean-squared displacement depend on the time lag between the initiation of the system at time t=0 and the start of the measurement at the aging time t(a). In particular, it turns out that for fractional Langevin-equation motion the aging dependence on t(a) is different between the cases of free and confined motion. We obtain explicit analytical expressions for the aged moments of the particle position as well as the time-averaged mean-squared displacement and present a numerical analysis of this transient aging phenomenon.
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.
When fractional Brownian motion does not behave as a continuous function with bounded variation?
Azmoodeh, Ehsan; Valkeila, Esko
2010-01-01
If we compose a smooth function g with fractional Brownian motion B with Hurst index H > 1/2, then the resulting change of variables formula [or It/^o- formula] has the same form as if fractional Brownian motion would be a continuous function with bounded variation. In this note we prove a new integral representation formula for the running maximum of a continuous function with bounded variation. Moreover we show that the analogue to fractional Brownian motion fails.
Convergence in Law to Operator Fractional Brownian Motion of Riemann-Liouville Type
Hong Shuai DAI
2013-01-01
In this paper,we extend the well-studied fractional Brownian motion of Riemann-Liouville type to the multivariate case,and the corresponding processes are called operator fractional Brownian motions of Riemann-Liouville type.We also provide two results on approximation to operator fractional Brownian motions of Riemann-Liouville type.The first approximation is based on a Poisson process,and the second one is based on a sequence of I.I.D.random variables.
Self-intersection local times and collision local times of bifractional Brownian motions
2009-01-01
In this paper, we consider the local time and the self-intersection local time for a bifractional Brownian motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the existence and smoothness of the self-intersection local time and the collision local time, through the strong local nondeterminism of bifractional Brownian motion, L2 convergence and Chaos expansion.
Hausdorff measures of the image, graph and level set of bifractional Brownian motion
无
2010-01-01
Let BH,K = {BH,K(t), t ∈ R+} be a bifractional Brownian motion in Rd. This process is a selfsimilar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of fractional Brownian motion (which is obtained for K = 1). The exact Hausdorff measures of the image, graph and the level set of BH,K are investigated. The results extend the corresponding results proved by Talagrand and Xiao for fractional Brownian motion.
Active Brownian motion of an asymmetric rigid particle
Mammadov, Gulmammad
2012-01-01
Individual movements of a rod-like self-propelled particle on a flat substrate are quantified. Biological systems that fit into this description may be the Gram-negative delta-proteobacterium Myxococcus xanthus, Gram-negative bacterium Escherichia coli, and Mitochondria. There are also non-living analogues such as vibrated polar granulates and self-driven anisotropic colloidal particles. For that we study the Brownian motion of an asymmetric rod-like rigid particle self-propelled at a fixed speed along its long axis in two dimensions. The motion of such a particle in a uniform external potential field is also considered. The theoretical model presented here is anticipated to better describe individual cell motion as well as intracellular transport in 2D than previous models.
Role of Brownian Motion Hydrodynamics on Nanofluid Thermal Conductivity
W Evans, J Fish, P Keblinski
2005-11-14
We use a simple kinetic theory based analysis of heat flow in fluid suspensions of solid nanoparticles (nanofluids) to demonstrate that the hydrodynamics effects associated with Brownian motion have a minor effect on the thermal conductivity of the nanofluid. Our conjecture is supported by the results of molecular dynamics simulations of heat flow in a model nanofluid with well-dispersed particles. Our findings are consistent with the predictions of the effective medium theory as well as with recent experimental results on well dispersed metal nanoparticle suspensions.
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.
Random functions via Dyson Brownian Motion: progress and problems
Wang, Gaoyuan; Battefeld, Thorsten
2016-09-01
We develope a computationally efficient extension of the Dyson Brownian Motion (DBM) algorithm to generate random function in C2 locally. We further explain that random functions generated via DBM show an unstable growth as the traversed distance increases. This feature restricts the use of such functions considerably if they are to be used to model globally defined ones. The latter is the case if one uses random functions to model landscapes in string theory. We provide a concrete example, based on a simple axionic potential often used in cosmology, to highlight this problem and also offer an ad hoc modification of DBM that suppresses this growth to some degree.
Random Functions via Dyson Brownian Motion: Progress and Problems
Wang, Gaoyuan
2016-01-01
We develope a computationally efficient extension of the Dyson Brownian Motion (DBM) algorithm to generate random function in C2 locally. We further explain that random functions generated via DBM show an unstable growth as the traversed distance increases. This feature restricts the use of such functions considerably if they are to be used to model globally defined ones. The latter is the case if one used 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.
Isolated zeros for Brownian motion with variable drift
Antunović, Tonći; Peres, Yuval; Ruscher, Julia
2010-01-01
It is well known that standard one-dimensional Brownian motion B(t) has no isolated zeros almost surely. We show that for any alpha<1/2 there are alpha-H\\"older continuous functions f(t) for which the process B(t)-f(t) has isolated zeros with positive probability. We also prove that for any f(t), the zero set of B(t)-f(t) has Hausdorff dimension at least 1/2 with positive probability, and 1/2 is an upper bound if f(t) is 1/2-H\\"older continuous or of bounded variation.
Permutation entropy of fractional Brownian motion and fractional Gaussian noise
Zunino, L. [Centro de Investigaciones Opticas, C.C. 124 Correo Central, 1900 La Plata (Argentina); Departamento de Ciencias Basicas, Facultad de Ingenieria, Universidad Nacional de La Plata (UNLP), 1900 La Plata (Argentina); Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 1900 La Plata (Argentina)], E-mail: lucianoz@ciop.unlp.edu.ar; Perez, D.G. [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso (PUCV), 23-40025 Valparaiso (Chile)], E-mail: dario.perez@ucv.cl; Martin, M.T. [Instituto de Fisica (IFLP), Facultad de Ciencias Exactas, Universidad Nacional de La Plata and Argentina' s National Council (CCT-CONICET), C.C. 727, 1900 La Plata (Argentina)], E-mail: mtmartin@fisica.unlp.edu.ar; Garavaglia, M. [Centro de Investigaciones Opticas, C.C. 124 Correo Central, 1900 La Plata (Argentina); Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 1900 La Plata (Argentina)], E-mail: garavagliam@ciop.unlp.edu.ar; Plastino, A. [Instituto de Fisica (IFLP), Facultad de Ciencias Exactas, Universidad Nacional de La Plata and Argentina' s National Council (CCT-CONICET), C.C. 727, 1900 La Plata (Argentina)], E-mail: plastino@fisica.unlp.edu.ar; Rosso, O.A. [Centre for Bioinformatics, Biomarker Discovery and Information-Based Medicine, School of Electrical Engineering and Computer Science, The University of Newcastle, University Drive, Callaghan NSW 2308 (Australia); Chaos and Biology Group, Instituto de Calculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellon II, Ciudad Universitaria, 1428 Ciudad de Buenos Aires (Argentina)], E-mail: oarosso@fibertel.com.ar
2008-06-30
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.
Cavity-enhanced optical detection of carbon nanotube Brownian motion
Stapfner, S; Hunger, D; Weig, E M; Reichel, J; Favero, I
2012-01-01
Optical cavities with small mode volume are well-suited to detect the vibration of sub-wavelength sized objects. Here we employ a fiber-based, high-finesse optical microcavity to detect the Brownian motion of a freely suspended carbon nanotube at room temperature under vacuum. The optical detection resolves deflections of the oscillating tube down to 50pm/Hz^1/2. A full vibrational spectrum of the carbon nanotube is obtained and confirmed by characterization of the same device in a scanning electron microscope. Our work successfully extends the principles of high-sensitivity optomechanical detection to molecular scale nanomechanical systems.
Non-Markovian quantum Brownian motion of a harmonic oscillator
Tang, J.
1994-02-01
We apply the density-matrix method to the study of quantum Brownian motion of a harmonic oscillator coupled to a heat bath, a system investigated previously by Caldeira and Leggett using a different method. Unlike the earlier work, in our derivation of the master equation the non-Markovian terms are maintained. Although the same model of interaction is used, discrepancy is found between their results and our equation in the Markovian limit. We also point out that the particular interaction model used by both works cannot lead to the phenomenological generalized Langevin theory of Kubo.
Whitening filter and innovational representation of fractional Brownian motion
Wang Xiaotian [School of Mathematical sciences, South China University of Technology, Guangzhou 510640 (China)], E-mail: swa001@126.com; Wu Min [School of Mathematical sciences, South China University of Technology, Guangzhou 510640 (China)
2009-03-15
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.
Suspended particle transport through constriction channel with Brownian motion
Hanasaki, Itsuo; Walther, Jens H.
2017-08-01
It is well known that translocation events of a polymer or rod through pores or narrower parts of micro- and nanochannels have a stochastic nature due to the Brownian motion. However, it is not clear whether the objects of interest need to have a larger size than the entrance to exhibit the deviation from the dynamics of the surrounding fluid. We show by numerical analysis that the particle injection into the narrower part of the channel is affected by thermal fluctuation, where the particles have spherical symmetry and are smaller than the height of the constriction. The Péclet number (Pe) is the order parameter that governs the phenomena, which clarifies the spatio-temporal significance of Brownian motion compared to hydrodynamics. Furthermore, we find that there exists an optimal condition of Pe to attain the highest flow rate of particles relative to the dispersant fluid flow. Our finding is important in science and technology from nanopore DNA sequencers and lab-on-a-chip devices to filtration by porous materials and chromatography.
Dinarvand, S.; Hosseini, R.; Tamim, H.; Damangir, E.; Pop, I.
2015-07-01
An unsteady three-dimensional stagnation-point flow of a nanofluid past a circular cylinder with sinusoidal radius variation is investigated numerically. By introducing new similarity transformations for the velocity, temperature, and nanoparticle volume fraction, the basic equations governing the flow and heat and mass transfer are reduced to highly nonlinear ordinary differential equations. The resulting nonlinear system is solved numerically by the fourth-order Runge-Kutta method with the shooting technique. The thermophoresis and Brownian motion effects occur in the transport equations. The velocity, temperature, and nanoparticle concentration profiles are analyzed with respect to the involved parameters of interest, namely, unsteadiness parameter, Brownian motion parameter, thermophoresis parameter, Prandtl number, and Lewis number. Numerical values of the friction coefficient, diffusion mass flux, and heat flux are computed. It is found that the friction coefficient and heat transfer rate increase with increasing unsteadiness parameter (the highest heat transfer rate at the surface occurs if the thermophoresis and Brownian motion effects are absent) and decrease with increasing both thermophoresis and Brownian motion parameters. The present results are found to be in good agreement with previously published results.
Greczylo, Tomasz; Debowska, Ewa [Institute of Experimental Physics, Wroclaw University, pl. Maxa Borna 9, 50-204 Wroclaw (Poland)
2007-09-15
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)
Linear filtering with fractional Brownian motion in the signal and observation processes
M. L. Kleptsyna
1999-01-01
Full Text Available Integral equations for the mean-square estimate are obtained for the linear filtering problem, in which the noise generating the signal is a fractional Brownian motion with Hurst index h∈(3/4,1 and the noise in the observation process includes a fractional Brownian motion as well as a Wiener process.
Parlar, Mahmut
2004-01-01
Brownian motion is an important stochastic process used in modelling the random evolution of stock prices. In their 1973 seminal paper--which led to the awarding of the 1997 Nobel prize in Economic Sciences--Fischer Black and Myron Scholes assumed that the random stock price process is described (i.e., generated) by Brownian motion. Despite its…
Brownian motion on Lie groups and open quantum systems
Aniello, P; Marmo, G; Ventriglia, F [Dipartimento di Scienze Fisiche dell' Universita di Napoli ' Federico II' and Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, I-80126 Napoli (Italy); Kossakowski, A, E-mail: paolo.aniello@na.infn.i, E-mail: kossak@fyzika.umk.p, E-mail: marmo@na.infn.i, E-mail: ventriglia@na.infn.i [MECENAS, Universita di Napoli ' Federico II' , via Mezzocannone 8, I-80134 Napoli (Italy)
2010-07-02
We study the twirling semigroups of (super) operators, namely certain quantum dynamical semigroups that are associated, in a natural way, with the pairs formed by a projective representation of a locally compact group and a convolution semigroup of probability measures on this group. The link connecting this class of semigroups of operators with (classical) Brownian motion is clarified. It turns out that every twirling semigroup associated with a finite-dimensional representation is a random unitary semigroup, and, conversely, every random unitary semigroup arises as a twirling semigroup. Using standard tools of the theory of convolution semigroups of measures and of convex analysis, we provide a complete characterization of the infinitesimal generator of a twirling semigroup associated with a finite-dimensional unitary representation of a Lie group.
Brownian motion on Lie groups and open quantum systems
Aniello, P.; Kossakowski, A.; Marmo, G.; Ventriglia, F.
2010-07-01
We study the twirling semigroups of (super) operators, namely certain quantum dynamical semigroups that are associated, in a natural way, with the pairs formed by a projective representation of a locally compact group and a convolution semigroup of probability measures on this group. The link connecting this class of semigroups of operators with (classical) Brownian motion is clarified. It turns out that every twirling semigroup associated with a finite-dimensional representation is a random unitary semigroup, and, conversely, every random unitary semigroup arises as a twirling semigroup. Using standard tools of the theory of convolution semigroups of measures and of convex analysis, we provide a complete characterization of the infinitesimal generator of a twirling semigroup associated with a finite-dimensional unitary representation of a Lie group.
Brownian motion on Lie groups and open quantum systems
Aniello, P; Marmo, G; Ventriglia, F
2010-01-01
We study the twirling semigroups of (super)operators, namely, certain quantum dynamical semigroups that are associated, in a natural way, with the pairs formed by a projective representation of a locally compact group and a convolution semigroup of probability measures on this group. The link connecting this class of semigroups of operators with (classical) Brownian motion is clarified. It turns out that every twirling semigroup associated with a finite-dimensional representation is a random unitary semigroup, and, conversely, every random unitary semigroup arises as a twirling semigroup. Using standard tools of the theory of convolution semigroups of measures and of convex analysis, we provide a complete characterization of the infinitesimal generator of a twirling semigroup associated with a finite-dimensional unitary representation of a Lie group.
Analytical studies of spectrum broadcast structures in quantum Brownian motion
Tuziemski, J.; Korbicz, J. K.
2016-11-01
Spectrum broadcast structures are a new and fresh concept in the quantum-to-classical transition, introduced recently in the context of decoherence and the appearance of objective features in quantum mechanics. These are specific quantum state structures, responsible for the objectivization of the decohered state of a system. Recently, they have been demonstrated by means of the well-known quantum Brownian motion model of the recoilless limit (infinitely massive central system), as the principal interest lies in information transfer from the system to the environment. However, a final analysis relied on numerics. Here, after a presentation of the main concepts, we perform analytical studies of the model, showing the timescales and the efficiency of the spectrum broadcast structure formation. We consider a somewhat simplified environment, being random with a uniform distribution of frequencies.
Semicircular canals circumvent Brownian Motion overload of mechanoreceptor hair cells
Muller, Mees; Heeck, Kier; Elemans, Coen P H
2016-01-01
nN/m), and have a 100-fold higher tip displacement threshold (cells where the bundle is approximated as a stiff, cylindrical elastic rod subject to friction and thermal agitation. Our models suggest that the above......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...... 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 (
The genealogy of branching Brownian motion with absorption
Berestycki, Julien; Schweinsberg, Jason
2010-01-01
We consider a system of particles which perform branching Brownian motion with negative drift and are killed upon reaching zero, in the near-critical regime where the total population stays roughly constant with approximately N particles. We show that the characteristic time scale for the evolution of this population is of order (log N)^3, in the sense that when time is measured in these units, the scaled number of particles converges to a variant of Neveu's continuous-state branching process. Furthermore, the genealogy of the particles is then governed by a coalescent process known as the Bolthausen-Sznitman coalescent. This validates the non-rigorous predictions by Brunet, Derrida, Muller, and Munier for a closely related model.
Probabilities on the Heisenberg group limit theorems and Brownian motion
Neuenschwander, Daniel
1996-01-01
The Heisenberg group comes from quantum mechanics and is the simplest non-commutative Lie group. While it belongs to the class of simply connected nilpotent Lie groups, it turns out that its special structure yields many results which (up to now) have not carried over to this larger class. This book is a survey of probabilistic results on the Heisenberg group. The emphasis lies on limit theorems and their relation to Brownian motion. Besides classical probability tools, non-commutative Fourier analysis and functional analysis (operator semigroups) comes in. The book is intended for probabilists and analysts interested in Lie groups, but given the many applications of the Heisenberg group, it will also be useful for theoretical phycisists specialized in quantum mechanics and for engineers.
Quantum Brownian motion near a point-like reflecting boundary
De Lorenci, V A; Silva, M M
2014-01-01
The Brownian motion of a test particle interacting with a quantum scalar field in the presence of a perfectly reflecting boundary is studied in (1 + 1)-dimensional flat spacetime. Particularly, the expressions for dispersions in velocity and position of the particle are explicitly derived and their behaviors examined. The results are similar to those corresponding to an electric charge interacting with a quantum electromagnetic field near a reflecting plane boundary, mainly regarding the divergent behavior of the dispersions at the origin (where the boundary is placed), and at the time interval corresponding to a round trip of a light pulse between the particle and the boundary. We close by addressing some effects of allowing the position of the particle to fluctuate.
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.
Brownian Motion in Non-Commutative Super-Yang-Mills
Fischler, Willy; Garcia, Walter Tangarife
2012-01-01
Using the gauge/gravity correspondence, we study the dynamics of a heavy quark in strongly-coupled non-commutative Super-Yang-Mills at finite temperature. We propose a Langevin equation that accounts for the effects of non-commutativity and resembles the structure of Brownian motion in the presence of a magnetic field. As expected, fluctuations along non-commutative directions are generically correlated. Our results show that the viscosity of the plasma is smaller than the commutative case and that the diffusion properties of the quark are unaffected by non-commutativity. Finally, we compute the random force autocorrelator and verify that the fluctuation-dissipation theorem holds in the presence of non-commutativity.
Effects of Brownian motion on freezing of PCM containing nanoparticles
Abdollahzadeh Jamalabadi M.Y.
2016-01-01
Full Text Available Enhancement of thermal and heat transfer capabilities of phase change materials with addition of nanoparticles is reported. The mixed nanofluid of phase change material and nanoparticles presents a high thermal conductivity and low heat capacity and latent heat, in comparison with the base fluid. In order to present the thermophysical effects of nanoparticles, a solidification of nanofluid in a rectangular enclosure with natural convection induced by different wall temperatures is considered. The results show that the balance between the solidification acceleration by nanoparticles and slowing-down by phase change material gives rise to control the medium temperature. It indicates that this kind of mixture has great potential in various applications which requires temperature regulation. Also, the Brownian motion of nanoparticles enhances the convective heat transfer much more than the conductive transfer.
Mean-squared-displacement statistical test for fractional Brownian motion
Sikora, Grzegorz; Burnecki, Krzysztof; Wyłomańska, Agnieszka
2017-03-01
Anomalous diffusion in crowded fluids, e.g., in cytoplasm of living cells, is a frequent phenomenon. A common tool by which the anomalous diffusion of a single particle can be classified is the time-averaged mean square displacement (TAMSD). A classical mechanism leading to the anomalous diffusion is the fractional Brownian motion (FBM). A validation of such process for single-particle tracking data is of great interest for experimentalists. In this paper we propose a rigorous statistical test for FBM based on TAMSD. To this end we analyze the distribution of the TAMSD statistic, which is given by the generalized chi-squared distribution. Next, we study the power of the test by means of Monte Carlo simulations. We show that the test is very sensitive for changes of the Hurst parameter. Moreover, it can easily distinguish between two models of subdiffusion: FBM and continuous-time random walk.
Brownian motion near a liquid-gas interface
Benavides-Parra, Juan Carlos; Jacinto-Méndez, Damián; Brotons, Guillaume; Carbajal-Tinoco, Mauricio D.
2016-09-01
By using digital video microscopy, we study the three-dimensional displacement of fluorescent colloidal particles that are located close to a water-air interface. Our technique takes advantage of the diffraction pattern generated by fluorescent spheres that are found below the focal plane of the microscope objective. By means of image analysis software, we are able to determine the spatial location of a few beads in a sequence of digital images, which allows us to reconstruct their trajectories. From their corresponding mean square displacements, we get the diffusion coefficients in the directions parallel and perpendicular to the interface. We find a qualitatively different kind of diffusion between the two directions, in agreement with theoretical predictions that are obtained from established models as well as our own proposals. Quite interesting, we observe the enhanced Brownian motion in the parallel direction.
On the first-passage time of integrated Brownian motion
Christian H. Hesse
2005-01-01
Full Text Available Let (Bt;t≥0 be a Brownian motion process starting from B0=ν and define Xν(t=∫0tBsds. For a≥0, set τa,ν:=inf{t:Xν(t=a} (with inf φ=∞. We study the conditional moments of τa,ν given τa,ν<∞. Using martingale methods, stopping-time arguments, as well as the method of dominant balance, we obtain, in particular, an asymptotic expansion for the conditional mean E(τa,ν|τa,ν<∞ as ν→∞. Through a series of simulations, it is shown that a truncation of this expansion after the first few terms provides an accurate approximation to the unknown true conditional mean even for small ν.
Xu Sheng-Hua; Sun Zhi-Wei; Li Xu; Jin Tong Wang
2012-01-01
Simultaneous orthokinetic and perikinetic coagulations(SOPCs)are studied for small and large Peclet numbers(Pe)using Brownian dynamics simulation.The results demonstrate that the contributions of the Brownian motion and the shear flow to the overall coagulation rate are basically not additive.At the early stages of coagulation with small Peclet numbers,the ratio of overall coagulation rate to the rate of pure perikinetic coagulation is proportional to Pe1/2,while with high Peclet numbers,the ratio of overall coagulation rate to the rate of pure orthokinetic coagulation is proportional to pe-1/2.Moreover,our results show that the aggregation rate generally changes with time for the SOPC,which is different from that for pure preikinetic and pure orthokinetic coagulations.By comparing the SOPC with pure preikinetic and pure orthokinetic coagulations,we show that the redistribution of particles due to Brownian motion can play a very important role in the SOPC.In addition,the effects of redistribution in the directions perpendicular and parallel to the shear flow direction are different.This perspective explains the behavior of coagulation due to the joint effects of the Brownian motion(perikinetic)and the fluid motion(orthokinetic).
Self-intersection local times and collision local times of bifractional Brownian motions
JIANG YiMing; WANG YongJin
2009-01-01
In this paper, we consider the local time and the self-intersection local time for a bifrac-tional Brownish motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the existence and smoothness of the self-intersection local time and the collision local time, through the strong local nondeterminism of bifractional Brownian motion, L2 convergence and Chaos expansion.
Biased Brownian motion in narrow channels with asymmetry and anisotropy
To, Kiwing; Peng, Zheng
2016-11-01
We study Brownian motion of a single millimeter size bead confined in a quasi-two-dimensional horizontal channel with built-in anisotropy and asymmetry. Channel asymmetry is implemented by ratchet walls while anisotropy is introduced using a channel base that is grooved along the channel axis so that a bead can acquire a horizontal impulse perpendicular to the longitudinal direction when it collides with the base. When energy is injected to the channel by vertical vibration, the combination of asymmetric walls and anisotropic base induces an effective force which drives the bead into biased diffusive motion along the channel axis with diffusivity and drift velocity increase with vibration strength. The magnitude of this driving force, which can be measured in experiments of tilted channel, is found to be consistent to those obtained from dynamic mobility and position probability distribution measurements. These results are explained by a simple collision model that suggests the random kinetic energies transfer between different translational degrees of freedom may be turned into useful work in the presence of asymmetry and anisotropy.
A Stability Result for Stochastic Differential Equations Driven by Fractional Brownian Motions
Bruno Saussereau
2012-01-01
Full Text Available We study the stability of the solutions of stochastic differential equations driven by fractional Brownian motions with Hurst parameter greater than half. We prove that when the initial conditions, the drift, and the diffusion coefficients as well as the fractional Brownian motions converge in a suitable sense, then the sequence of the solutions of the corresponding equations converge in Hölder norm to the solution of a stochastic differential equation. The limit equation is driven by the limit fractional Brownian motion and its coefficients are the limits of the sequence of the coefficients.
A simple model for Brownian motion leading to the Langevin equation
Grooth, de Bart G.
1999-01-01
A simple one-dimensional model is presented for the motion of a Brownian particle. It is shown how the collisions between a Brownian particle and its surrounding molecules lead to the Langevin equation, the power spectrum of the stochastic force, and the equipartition of kinetic energy.
Moderate deviations for the quenched mean of the super-Brownian motion with random immigration
2008-01-01
Moderate deviations for the quenched mean of the super-Brownian motion with random immigration are proved for 3≤d≤6, which fills in the gap between central limit theorem(CLT)and large deviation principle(LDP).
On the weak convergence of super-Brownian motion with immigration
2009-01-01
We prove fluctuation limit theorems for the occupation times of super-Brownian motion with immigration. The weak convergence of the processes is established, which improves the results in references. The limiting processes are Gaussian processes.
Fan, Xi-Liang
2012-01-01
In the paper, Harnack inequalities are established for stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H<1/2$. As applications, strong Feller property, log-Harnack inequality and entropy-cost inequality are given.
Stochastic Volterra Equation Driven by Wiener Process and Fractional Brownian Motion
Zhi Wang
2013-01-01
Full Text Available For a mixed stochastic Volterra equation driven by Wiener process and fractional Brownian motion with Hurst parameter H>1/2, we prove an existence and uniqueness result for this equation under suitable assumptions.
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.
Error Assessment in Modeling with Fractal Brownian Motions
Qiao, Bingqiang
2013-01-01
To model a given time series $F(t)$ with fractal Brownian motions (fBms), it is necessary to have appropriate error assessment for related quantities. Usually the fractal dimension $D$ is derived from the Hurst exponent $H$ via the relation $D=2-H$, and the Hurst exponent can be evaluated by analyzing the dependence of the rescaled range $\\langle|F(t+\\tau)-F(t)|\\rangle$ on the time span $\\tau$. For fBms, the error of the rescaled range not only depends on data sampling but also varies with $H$ due to the presence of long term memory. This error for a given time series then can not be assessed without knowing the fractal dimension. We carry out extensive numerical simulations to explore the error of rescaled range of fBms and find that for $0
Beyond multifractional Brownian motion: new stochastic models for geophysical modelling
J. Lévy Véhel
2013-09-01
Full Text Available Multifractional Brownian motion (mBm has proved to be a useful tool in various areas of geophysical modelling. Although a versatile model, mBm is of course not always an adequate one. We present in this work several other stochastic processes which could potentially be useful in geophysics. The first alternative type is that of self-regulating processes: these are models where the local regularity is a function of the amplitude, in contrast to mBm where it is tuned exogenously. We demonstrate the relevance of such models for digital elevation maps and for temperature records. We also briefly describe two other types of alternative processes, which are the counterparts of mBm and of self-regulating processes when the intensity of local jumps is considered in lieu of local regularity: multistable processes allow one to prescribe the local intensity of jumps in space/time, while this intensity is governed by the amplitude for self-stabilizing processes.
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.
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.
Brownian motion and gambling: from ratchets to paradoxical games
Parrondo, J M R
2014-01-01
Two losing gambling games, when alternated in a periodic or random fashion, can produce a winning game. This paradox has been inspired by certain physical systems capable of rectifying fluctuations: the so-called Brownian ratchets. In this paper we review this paradox, from Brownian ratchets to the most recent studies on collective games, providing some intuitive explanations of the unexpected phenomena that we will find along the way.
Quantum power source: putting in order of a Brownian motion without Maxwell's demon
Aristov, Vitaly V.; Nikulov, A. V.
2003-07-01
The problem of possible violation of the second law of thermodynamics is discussed. It is noted that the task of the well known challenge to the second law called Maxwell's demon is put in order a chaotic perpetual motion and if any ordered Brownian motion exists then the second law can be broken without this hypothetical intelligent entity. The postulate of absolute randomness of any Brownian motion saved the second law in the beginning of the 20th century when it was realized as perpetual motion. This postulate can be proven in the limits of classical mechanics but is not correct according to quantum mechanics. Moreover some enough known quantum phenomena, such as the persistent current at non-zero resistance, are an experimental evidence of the non-chaotic Brownian motion with non-zero average velocity. An experimental observation of a dc quantum power soruce is interperted as evidence of violation of the second law.
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...... that it requires an understanding of Brownian motion beyond Einstein's and Smoluchowski's for its calibration, and can measure effects not present in their theories. This is illustrated with some applications, current and potential. It is also shown how addition of a controlled forced motion on the nano...
The reduction in the brownian motion of electrometers
Milatz, J.M.W.; Zolingen, J.J. van; Iperen, B.B. van
1953-01-01
A method is described to reduce the Brownian deflections of electrometer systems. This is achieved by replacing the air damping by a special type of artificial damping. The latter is realised by means of a photoelectric amplifier containing a differentiating circuit, comp. fig. 1. The amount of ligh
Thermodynamic Laws and Equipartition Theorem in Relativistic Brownian Motion
Koide, T.; Kodama, T.
2011-01-01
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.
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.
Brownian motion of a charged test particle in vacuum between two conducting plates
Yu, Hongwei; Chen, Jun
2004-12-01
The Brownian motion of a charged test particle caused by quantum electromagnetic vacuum fluctuations between two perfectly conducting plates is examined and the mean squared fluctuations in the velocity and position of the test particle are calculated. Our results show that the Brownian motion in the direction normal to the plates is reinforced in comparison to that in the single plate case. The effective temperature associated with this normal Brownian motion could be three times as large as that in the single plate case. However, the negative dispersions for the velocity and position in the longitudinal directions, which could be interpreted as reducing the quantum uncertainties of the particle, acquire positive corrections due to the presence of the second plate, and are thus weakened.
Brownian motion of a charged test particle in vacuum between two conducting plates
Yu, H; Yu, Hongwei; Chen, Jun
2004-01-01
The Brownian motion of a charged test particle caused by quantum electromagnetic vacuum fluctuations between two perfectly conducting plates is examined and the mean squared fluctuations in the velocity and position of the test particle are calculated. Our results show that the Brownian motion in the direction normal to the plates is reinforced in comparison to that in the single-plate case. The effective temperature associated with this normal Brownian motion could be three times as large as that in the single-plate case. However, the negative dispersions for the velocity and position in the longitudinal directions, which could be interpreted as reducing the quantum uncertainties of the particle, acquire positive corrections due to the presence of the second plate, and are thus weakened.
(Quantum) Fractional Brownian Motion and Multifractal Processes under the Loop of a Tensor Networks
Descamps, Benoît
2016-01-01
We derive fractional Brownian motion and stochastic processes with multifractal properties using a framework of network of Gaussian conditional probabilities. This leads to the derivation of new representations of fractional Brownian motion. These constructions are inspired from renormalization. The main result of this paper consists of constructing each increment of the process from two-dimensional gaussian noise inside the light-cone of each seperate increment. Not only does this allows us to derive fractional Brownian motion, we can introduce extensions with multifractal flavour. In another part of this paper, we discuss the use of the multi-scale entanglement renormalization ansatz (MERA), introduced in the study critical systems in quantum spin lattices, as a method for sampling integrals with respect to such multifractal processes. After proper calibration, a MERA promises the generation of a sample of size $N$ of a multifractal process in the order of $O(N\\log(N))$, an improvement over the known method...
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.
Finding viscosity of liquids from Brownian motion at students' laboratory
Greczylo, Tomasz; Debowska, Ewa [Institute of Experimental Physics, Wroclaw University, pl. Maxa Borna 9, 50-204 Wroclaw (Poland)
2005-09-01
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.
Accumulation of Microswimmers near a Surface Mediated by Collision and Rotational Brownian Motion
Li, Guanglai; Tang, Jay X.
2009-08-01
In this Letter we propose a kinematic model to explain how collisions with a surface and rotational Brownian motion give rise to accumulation of microswimmers near a surface. In this model, an elongated microswimmer invariably travels parallel to the surface after hitting it from an oblique angle. It then swims away from the surface, facilitated by rotational Brownian motion. Simulations based on this model reproduce the density distributions measured for the small bacteria E. coli and Caulobacter crescentus, as well as for the much larger bull spermatozoa swimming between two walls.
ZHANG Jia-Lin; YU Hong-Wei
2005-01-01
@@ We show that the velocity and position dispersions of a test particle with a nonzero constant classical velocity undergoing Brownian motion caused by electromagnetic vacuum fluctuations in a space with plane boundaries can be obtained from those of the static case by Lorentz transformation. We explicitly derive the Lorentz transformations relating the dispersions of the two cases and then apply them to the case of the Brownian motion of a test particle with a constant classical velocity parallel to the boundary between two conducting planes. Our results show that the influence of a nonzero initial velocity is negligible for nonrelativistic test particles.
Brownian motion in a singular potential and a fractal renewal process
Ouyang, H. F.; Huang, Z. Q.; Ding, E. J.
1995-10-01
We have proposed a model for the one-dimensional Brownian motion of a single particle in a singular potential field in our previous paper [Phys. Rev. E 50, 2491 (1994)]. In this Brief Report, we further discuss this model and show that, in some special cases, the Brownian motion can be considered as a finite-valued alternating renewal process, which has been investigated by Lowen and Teich [Phys. Rev. E 47, 992 (1993)]. The numerical results here are in agreement with those drawn by Lowen and Teich.
Survival probability of mutually killing Brownian motions and the O'Connell process
Katori, Makoto
2011-01-01
Recently O'Connell introduced an interacting diffusive particle system in order to study a directed polymer model in 1+1 dimensions. The infinitesimal generator of the process is a harmonic transform of the quantum Toda-lattice Hamiltonian by the Whittaker function. As a physical interpretation of this construction, we show that the O'Connell process without drift is realized as a system of mutually killing Brownian motions conditioned that all particles survive forever. When the characteristic length of interaction killing other particles goes to zero, the process is reduced to the noncolliding Brownian motion (the Dyson model).
Holographic Brownian Motion in Three-Dimensional Gödel Black Hole
J. Sadeghi
2014-01-01
Full Text Available By using the AdS/CFT correspondence and Gödel black hole background, we study the dynamics of heavy quark under a rotating plasma. In that case we follow Atmaja (2013 about Brownian motion in BTZ black hole. In this paper we receive some new results for the case of α2l2≠1. In this case, we must redefine the angular velocity of string fluctuation. We obtain the time evolution of displacement square and angular velocity and show that it behaves as a Brownian particle in non relativistic limit. In this plasma, it seems that relating the Brownian motion to physical observables is rather a difficult work. But our results match with Atmaja work in the limit α2l2→1.
Quantum Brownian motion representation for the quantum field modes
Arteaga, Daniel
2007-01-01
Any pair of modes of opposite momentum of any interacting quantum field theory can be regarded as an open quantum system. Provided that the state of the field is stationary, homogeneous and isotropic, under a Gaussian approximation the two-mode system can be equivalently represented in terms of a pair of quantum Brownian oscillators, namely, by two identical harmonic oscillators linearly coupled to an effective environment. The precise details of the correspondence are explained, and its usefulness is commented. As an example of application, the interpretation of the imaginary part of the retarded self-energy in a general background state is rederived.
Time integration for particle Brownian motion determined through fluctuating hydrodynamics
Delmotte, Blaise
2015-01-01
Fluctuating hydrodynamics has been successfully combined with several computational methods to rapidly compute the correlated random velocities of Brownian particles. In the overdamped limit where both particle and fluid inertia are ignored, one must also account for a Brownian drift term in order to successfully update the particle positions. In this paper, we introduce and study a midpoint time integration scheme we refer to as the drifter-corrector (DC) that resolves the drift term for fluctuating hydrodynamics-based methods even when constraints are imposed on the fluid flow to obtain higher-order corrections to the particle hydrodynamic interactions. We explore this scheme in the context of the fluctuating force-coupling method (FCM) where the constraint is imposed on the rate-of-strain averaged over the volume occupied by the particle. For the DC, the constraint need only be imposed once per time step, leading to a significant reduction in computational cost with respect to other schemes. In fact, for f...
Moderate Deviation for the Single Point Catalytic Super-Brownian Motion
Xu YANG; Mei ZHANG
2012-01-01
We establish the moderate deviation for the density process of the single point catalytic super-Brownian motion.The main tools are the abstract G(a)rtner-Ellis theorem,Dawson-G(a)rtner theorem and the contraction principle.The rate function is expressed by the Fenchel-Legendre transform of log-exponential moment generation function.
Pricing Perpetual American Put Option in theMixed Fractional Brownian Motion
2015-01-01
Under the assumption of the underlying asset is driven by the mixed fractional Brownian motion, we obtain the mixed fractionalBlack-Scholes partial differential equation by fractional Ito formula, and the pricing formula of perpetual American put option bythis partial differential equation theory.
The tail of the maximum of Brownian motion minus a parabola
P. Groeneboom; N.M. Temme (Nico)
2011-01-01
textabstractWe analyze the tail behavior of the maximum $N$ of $\\{W(t)-t^2:t\\ge0\\}$, where $W$ is standard Brownian motion on $[0,\\infty)$ and give an asymptotic expansion for $\\mathbb P\\{N\\ge x\\}$, as $x\\to\\infty$. This extends a first order result on the tail behavior, which can be deduced from H\\
Brownian Motion on a Pseudo Sphere in Minkowski Space R^l_v
Jiang, Xiaomeng; Li, Yong
2016-10-01
For a Brownian motion moving on a pseudo sphere in Minkowski space R^l_v of radius r starting from point X, we obtain the distribution of hitting a fixed point on this pseudo sphere with l≥ 3 by solving Dirichlet problems. The proof is based on the method of separation of variables and the orthogonality of trigonometric functions and Gegenbauer polynomials.
Some Properties of Stochastic Differential Equations Driven by the G-Brownian Motion
Qian LIN
2013-01-01
In this paper,we study the property of continuous dependence on the parameters of stochastic integrals and solutions of stochastic differential equations driven by the G-Brownian motion.In addition,the uniqueness and comparison theorems for those stochastic differential equations with non-Lipschitz coefficients are obtained.
The tail of the maximum of Brownian motion minus a parabola
P. Groeneboom; N.M. Temme (Nico)
2011-01-01
textabstractWe analyze the tail behavior of the maximum $N$ of $\\{W(t)-t^2:t\\ge0\\}$, where $W$ is standard Brownian motion on $[0,\\infty)$ and give an asymptotic expansion for $\\mathbb P\\{N\\ge x\\}$, as $x\\to\\infty$. This extends a first order result on the tail behavior, which can be deduced from
Some scaled limit theorems for an immigration super-Brownian motion
ZHANG Mei
2008-01-01
In this paper, the small time limit behaviors for an immigration super-Brownian motion are studied, where the immigration is determined by Lebesgue measure. We first prove a functional central limit theorem, and then study the large and moderate deviations associated with this central tendency.
Brownian motion with variable drift: 0-1 laws, hitting probabilities and Hausdorff dimension
Peres, Yuval
2010-01-01
By the Cameron--Martin theorem, if a function $f$ is in the Dirichlet space $D$, then $B+f$ has the same a.s. properties as standard Brownian motion, $B$. In this paper we examine properties of $B+f$ when $f \
The first-passage area for drifted Brownian motion and the moments of the Airy distribution
Kearney, Michael J [Faculty of Engineering and Physical Sciences, University of Surrey, Guildford, Surrey, GU2 7XH (United Kingdom); Majumdar, Satya N [Laboratoire de Physique Theorique et Modeles Statistique, Universite Paris-Sud. Bat. 100 91405, Orsay Cedex (France); Martin, Richard J [Quantitative Credit Strategy Group, Credit Suisse, One Cabot Square, London, E14 4QJ (United Kingdom)
2007-09-07
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)
Successive Approximation of SFDEs with Finite Delay Driven by G-Brownian Motion
Litan Yan
2013-01-01
Full Text Available We consider the stochastic functional differential equations with finite delay driven by G-Brownian motion. Under the global Carathéodory conditions we prove the existence and uniqueness, and as an application, we price the European call option when the underlying asset's price follows such an equation.
Some scaled limit theorems for an immigration super-Brownian motion
2008-01-01
In this paper,the small time limit behaviors for an immigration super-Brownian motion are studied,where the immigration is determined by Lebesgue measure.We first prove a functional central limit theorem,and then study the large and moderate deviations associated with this central tendency.
Brownian motion and parabolic Anderson model in a renormalized Poisson potential
Chen, Xia; Kulik, Alexey M.
2012-01-01
A method known as renormalization is proposed for constructing some more physically realistic random potentials in a Poisson cloud. The Brownian motion in the renormalized random potential and related parabolic Anderson models are modeled. With the renormalization, for example, the models consistent to Newton’s law of universal attraction can be rigorously constructed.
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.
Local times and excursion theory for Brownian motion a tale of Wiener and Itô measures
Yen, Ju-Yi
2013-01-01
This monograph discusses the existence and regularity properties of local times associated to a continuous semimartingale, as well as excursion theory for Brownian paths. Realizations of Brownian excursion processes may be translated in terms of the realizations of a Wiener process under certain conditions. With this aim in mind, the monograph presents applications to topics which are not usually treated with the same tools, e.g.: arc sine law, laws of functionals of Brownian motion, and the Feynman-Kac formula.
Accumulation of microswimmers near surface due to steric confinement and rotational Brownian motion
Li, Guanglai; Tang, Jay
2009-03-01
Microscopic swimmers display some intriguing features dictated by Brownian motion, low Reynolds number fluid mechanics, and boundary confinement. We re-examine the reported accumulation of swimming bacteria or bull spermatozoa near the boundaries of a fluid chamber, and propose a kinematic model to explain how collision with surface, confinement and rotational Brownian motion give rise to the accumulation of micro-swimmers near a surface. In this model, an elongated microswimmer invariably travels parallel to the surface after hitting it from any incident angle. It then takes off and swims away from the surface after some time due to rotational Brownian motion. Based on this analysis, we obtain through computer simulation steady state density distributions that reproduce the ones measured for the small bacteria E coli and Caulobacter crescentus, as well as for the much larger bull spermatozoa swimming near surfaces. These results suggest strongly that Brownian dynamics and surface confinement are the dominant factors for the accumulation of microswimmers near a surface.
Molecular dynamics test of the Brownian description of Na(+) motion in water
Wilson, M. A.; Pohorille, A.; Pratt, L. R.
1985-01-01
The present paper provides the results of molecular dynamics calculations on a Na(+) ion in aqueous solution. Attention is given to the sodium-oxygen and sodium-hydrogen radial distribution functions, the velocity autocorrelation function for the Na(+) ion, the autocorrelation function of the force on the stationary ion, and the accuracy of Brownian motion assumptions which are basic to hydrodynamic models of ion dyanmics in solution. It is pointed out that the presented calculations provide accurate data for testing theories of ion dynamics in solution. The conducted tests show that it is feasible to calculate Brownian friction constants for ions in aqueous solutions. It is found that for Na(+) under the considered conditions the Brownian mobility is in error by only 60 percent.
Molecular dynamics test of the Brownian description of Na(+) motion in water
Wilson, M. A.; Pohorille, A.; Pratt, L. R.
1985-01-01
The present paper provides the results of molecular dynamics calculations on a Na(+) ion in aqueous solution. Attention is given to the sodium-oxygen and sodium-hydrogen radial distribution functions, the velocity autocorrelation function for the Na(+) ion, the autocorrelation function of the force on the stationary ion, and the accuracy of Brownian motion assumptions which are basic to hydrodynamic models of ion dyanmics in solution. It is pointed out that the presented calculations provide accurate data for testing theories of ion dynamics in solution. The conducted tests show that it is feasible to calculate Brownian friction constants for ions in aqueous solutions. It is found that for Na(+) under the considered conditions the Brownian mobility is in error by only 60 percent.
Mirror coupling of reflecting Brownian motion and an application to Chavel's conjecture
Pascu, Mihai N
2010-01-01
In a series of papers, Burdzy et. al. introduced the \\emph{mirror coupling} of reflecting Brownian motions in a smooth bounded domain $D\\subset \\mathbb{R}^{d}$, and used it to prove certain properties of eigenvalues and eigenfunctions of the Neumann Laplaceian on $D$. In the present paper we show that the construction of the mirror coupling can be extended to the case when the two Brownian motions live in different domains $D_{1},D_{2}\\subset \\mathbb{R}^{d}$. As an application of the construction, we derive a unifying proof of the two main results concerning the validity of Chavel's conjecture on the domain monotonicity of the Neumann heat kernel, due to I. Chavel (\\cite{Chavel}), respectively W. S. Kendall (\\cite{Kendall}).
Appuhamillage, Thilanka; Thomann, Enrique; Waymire, Edward; Wood, Brian
2010-01-01
Advective skew dispersion is a natural Markov process defined by a diffusion with drift across an interface of jump discontinuity in a piecewise constant diffusion coefficient. In the absence of drift, this process may be represented as a function of $\\alpha$-skew Brownian motion for a uniquely determined value of $\\alpha=\\alpha^*$; see Ramirez et al. (2006). In the present paper, the analysis is extended to the case of nonzero drift. A determination of the (joint) distributions of key functionals of standard skew Brownian motion together with some associated probabilistic semigroup and local time theory is given for these purposes. An application to the dispersion of a solute concentration across an interface is provided that explains certain symmetries and asymmetries in recently reported laboratory experiments conducted at Lawrence-Livermore Berkeley Labs by Berkowitz et al. (2009).
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.
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.
Derrida, Bernard; Meerson, Baruch; Sasorov, Pavel V.
2016-04-01
Consider a one-dimensional branching Brownian motion and rescale the coordinate and time so that the rates of branching and diffusion are both equal to 1. If X1(t ) is the position of the rightmost particle of the branching Brownian motion at time t , the empirical velocity c of this rightmost particle is defined as c =X1(t ) /t . Using the Fisher-Kolmogorov-Petrovsky-Piscounov equation, we evaluate the probability distribution P (c ,t ) of this empirical velocity c in the long-time t limit for c >2 . It is already known that, for a single seed particle, P (c ,t ) ˜exp[-(c2/4 -1 ) t ] up to a prefactor that can depend on c and t . Here we show how to determine this prefactor. The result can be easily generalized to the case of multiple seed particles and to branching random walks associated with other traveling-wave equations.
The exact Hausdorff measures for the graph and image of a multidimensional iterated Brownian motion
2007-01-01
Let {W(t),t∈R}, {B(t),t∈R+} be two independent Brownian motions on R with W(0) = B(0) = 0. In this paper, we shall consider the exact Hausdorff measures for the image and graph sets of the d-dimensional iterated Brownian motion X(t), where X(t) = (Xi(t),... ,Xd(t)) and X1(t),... ,Xd(t) are d independent copies of Y(t) = W(B(t)). In particular, for any Borel set Q (?) (0,∞), the exact Hausdorff measures of the image X(Q) = {X(t) : t∈Q} and the graph GrX(Q) = {(t, X(t)) :t∈Q}are established.
The exact Hausdorff measures for the graph and image of a multidimensional iterated Brownian motion
Rong-mao ZHANG; Zheng-yan LIN
2007-01-01
Let {W(t),t ∈ R}, {B(t),t ∈ R+} be two independent Brownian motions on R with W(0) = B(0) = 0. In this paper, we shall consider the exact Hausdorff measures for the image and graph sets of the d-dimensional iterated Brownian motion X(t), where X(t) = (X1(t),..., Xd(t))and X1(t),... ,Xd(t) are d independent copies of Y(t) = W(B(t)). In particular, for any Borel set Q (∈) (0, oo), the exact Hausdorff measures of the image X(Q) = {X(t) ∶ t ∈ Q} and the graph GrX(Q) = {(t, X(t))∶ t ∈ Q} are established.
Chen, Xia; Rosinski, Jan; Shao, Qi-Man
2009-01-01
In this paper we prove exact forms of large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes. We also show that a fractional Brownian motion and the related Riemann-Liouville process behave like constant multiples of each other with regard to large deviations for their local and intersection local times. As a consequence of our large deviation estimates, we derive laws of iterated logarithm for the corresponding local times. The key points of our methods: (1) logarithmic superadditivity of a normalized sequence of moments of exponentially randomized local time of a fractional Brownian motion; (2) logarithmic subadditivity of a normalized sequence of moments of exponentially randomized intersection local time of Riemann-Liouville processes; (3) comparison of local and intersection local times based on embedding of a part of a fractional Brownian motion into the reproducing kernel Hilbert space of the Riemann-Liouville process.
Stability of Linear Stochastic Differential Equations with Respect to Fractional Brownian Motion
SHU Hui-sheng; CHEN Chun-li; WEI Guo-liang
2009-01-01
This paper is concerned with the stochastically stability for the m -dimensional linear stochastic differential equations with respect to fractional Brownian motion (FBM) with Hurst parameter H∈ (1/2, 1). On the basis of the pioneering work of Duncan and Hu, a Ito's formula is given.An improved derivative operator to Lyapunov functions is constructed, and the sufficient conditions for the stochastically stability of linear stochastic differential equations driven by FBM are established. These extend the stochastic Lyapunov stability theories.
Implicit Euler approximation of stochastic evolution equations with fractional Brownian motion
Kamrani, Minoo; Jamshidi, Nahid
2017-03-01
This work was intended as an attempt to motivate the approximation of quasi linear evolution equations driven by infinite-dimensional fractional Brownian motion with Hurst parameter H >1/2 . The spatial approximation method is based on Galerkin and the temporal approximation is based on implicit Euler scheme. An error bound and the convergence of the numerical method are given. The numerical results show usefulness and accuracy of the method.
Saussereau, Bruno
2012-01-01
We establish Talagrand's $T_1$ and $T_2$ inequalities for the law of the solution of a stochastic differential equation driven by a fractional Brownian motion with Hurst parameter $H>1/2$. We use the $L^2$ metric and the uniform metric on the path space of continuous functions on $[0,T]$. These results are applied to study small-time and large-time asymptotics for the solutions of such equations by means of a Hoeffding-type inequality.
Study of Submicron Particle Size Distribution by Laser Doppler Measurement of Brownian Motion.
1987-01-30
regime considered here, heat transfer from the submicron particles by forced convection and natural convection are negligible due to the extremely small...physical processes begin to influence the Brownian motion characteristics at high laser beam intensity. An analysis of the effects of thermophoresis and...photon pressure was carried out. The effect of thermophoresis due to the uneven heating of the particle by the laser beam was found to be a major
Random variables as pathwise integrals with respect to fractional Brownian motion
Mishura, Yuliya; Valkeila, Esko
2011-01-01
We show that a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand $g$ can have any prescribed distribution, moreover, we give both necessary and sufficient conditions when random variables can be represented in this form. We also prove that any random variable is a value of such integral in some improper sense. We discuss some applications of these results, in particular, to fractional Black--Scholes model of financial market.
Simulation paradoxes related to a fractional Brownian motion with small Hurst index
Makogin, Vitalii
2016-01-01
We consider the simulation of sample paths of a fractional Brownian motion with small values of the Hurst index and estimate the behavior of the expected maximum. We prove that, for each fixed $N$, the error of approximation $\\mathbf {E}\\max_{t\\in[0,1]}B^H(t)-\\mathbf {E}\\max_{i=\\overline{1,N}}B^H(i/N)$ grows rapidly to $\\infty$ as the Hurst index tends to 0.
An Averaging Principle for Stochastic Differential Delay Equations with Fractional Brownian Motion
Yong Xu
2014-01-01
Full Text Available An averaging principle for a class of stochastic differential delay equations (SDDEs driven by fractional Brownian motion (fBm with Hurst parameter in (1/2,1 is considered, where stochastic integration is convolved as the path integrals. The solutions to the original SDDEs can be approximated by solutions to the corresponding averaged SDDEs in the sense of both convergence in mean square and in probability, respectively. Two examples are carried out to illustrate the proposed averaging principle.
Intersection local times of independent Brownian motions as generalized white noise functionals
Albeverio, Sergio; Oliveira, Maria João; Streit, Ludwig
2001-01-01
The original publication is available at http://www.springerlink.com/content/14jtbl19nh37ggtx/fulltext.pdf A "chaos expansion" of the intersection local time functional of two independent Brownian motions in Rd is given. The expansion is in terms of normal products of white noise (corresponding to multiple Wiener integrals). As a consequence of the local structure of the normal products, the kernel functions in the expansion are explicitly given and exhibit clearly the dimension depende...
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.
Dipole—Dipole Interaction and the Directional Motion of Brownian
YUHui; ZHAOTong－Jun; 等
2002-01-01
The electric field of the microtubule is calculated according to its dipole distribution.The conformational change of a molecular motor is described by the rotation of a dipole which interacts with the microtubule.The numerical simulation for the particle currend shows that this interaction helps to produce a directional motion along the microtubule.And the average displacement executes step changes that resemble the experimental result for kinesin motors.
Vertices of the least concave majorant of Brownian motion with parabolic drift
Groeneboom, Piet
2010-01-01
It was shown in Groeneboom (1983) that the least concave majorant of one-sided Brownian motion without drift can be characterized by a jump process with independent increments, which is the inverse of the process of slopes of the least concave majorant. This result can be used to prove the result of Sparre Andersen (1954) that the number of vertices of the smallest concave majorant of the empirical distribution function of a sample of size n from the uniform distribution on [0,1] is asymptotically normal, with an asymptotic expectation and variance which are both of order log n. A similar (Markovian) inverse jump process was introduced in Groeneboom (1989), in an analysis of the least concave majorant of two-sided Brownian motion with a parabolic drift. This process is quite different from the process for one-sided Brownian motion without drift: the number of vertices in a (corresponding slopes) interval has an expectation proportional to the length of the interval and the variance of the number of vertices i...
Fractional Brownian motion, the Matérn process, and stochastic modeling of turbulent dispersion
Lilly, Jonathan M.; Sykulski, Adam M.; Early, Jeffrey J.; Olhede, Sofia C.
2017-08-01
Stochastic processes exhibiting power-law slopes in the frequency domain are frequently well modeled by fractional Brownian motion (fBm), with the spectral slope at high frequencies being associated with the degree of small-scale roughness or fractal dimension. However, a broad class of real-world signals have a high-frequency slope, like fBm, but a plateau in the vicinity of zero frequency. This low-frequency plateau, it is shown, implies that the temporal integral of the process exhibits diffusive behavior, dispersing from its initial location at a constant rate. Such processes are not well modeled by fBm, which has a singularity at zero frequency corresponding to an unbounded rate of dispersion. A more appropriate stochastic model is a much lesser-known random process called the Matérn process, which is shown herein to be a damped version of fractional Brownian motion. This article first provides a thorough introduction to fractional Brownian motion, then examines the details of the Matérn process and its relationship to fBm. An algorithm for the simulation of the Matérn process in O(NlogN) operations is given. Unlike fBm, the Matérn process is found to provide an excellent match to modeling velocities from particle trajectories in an application to two-dimensional fluid turbulence.
Bessel processes and hyperbolic Brownian motions stopped at different random times
D'Ovidio, Mirko
2010-01-01
Iterated Bessel processes R^\\gamma(t), t>0, \\gamma>0 and their counterparts on hyperbolic spaces, i.e. hyperbolic Brownian motions B^{hp}(t), t>0 are examined and their probability laws derived. The higher-order partial differential equations governing the distributions of I_R(t)=_1R^\\gamma(_2R^\\gamma(t)), t>0 and J_R(t) =_1R^\\gamma(|_2R^\\gamma(t)|^2), t>0 are obtained and discussed. Processes of the form R^\\gamma(T_t), t>0, B^{hp}(T_t), t>0 where T_t=\\inf{s: B(s)=t} are examined and numerous probability laws derived, including the Student law, the arcsin laws (also their asymmetric versions), the Lamperti distribution of the ratio of independent positively skewed stable random variables and others. For the process R^{\\gamma}(T^\\mu_t), t>0 (where T^\\mu_t = \\inf{s: B^\\mu(s)=t} and B^\\mu is a Brownian motion with drift \\mu) the explicit probability law and the governing equation are obtained. For the hyperbolic Brownian motions on the Poincar\\'e half-spaces H^+_2, H^+_3 we study B^{hp}(T_t), t>0 and the corresp...
Feller processes: the next generation in modeling. Brownian motion, Levy 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.
Feller processes: the next generation in modeling. Brownian motion, Lévy processes and beyond.
Böttcher, Björn
2010-12-03
We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space dependent mixing of Lévy processes. Brownian Motion is one of the most frequently used continuous time Markov processes in applications. In recent years also Lévy processes, of which Brownian Motion is a special case, have become increasingly popular. Lévy processes are spatially homogeneous, but empirical data often suggest the use of spatially inhomogeneous processes. Thus it seems necessary to go to the next level of generalization: Feller processes. These include Lévy processes and in particular brownian motion as special cases but allow spatial inhomogeneities. Many properties of Feller processes are known, but proving the very existence is, in general, very technical. Moreover, an applicable framework for the generation of sample paths of a Feller process was missing. We explain, with practitioners in mind, how to overcome both of these obstacles. In particular our simulation technique allows to apply Monte Carlo methods to Feller processes.
Fractional Brownian motion, the Matern process, and stochastic modeling of turbulent dispersion
Lilly, J M; Early, J J; Olhede, S C
2016-01-01
Stochastic process exhibiting power-law slopes in the frequency domain are frequently well modeled by fractional Brownian motion (fBm). In particular, the spectral slope at high frequencies is associated with the degree of small-scale roughness or fractal dimension. However, a broad class of real-world signals have a high-frequency slope, like fBm, but a plateau in the vicinity of zero frequency. This low-frequency plateau, it is shown, implies that the temporal integral of the process exhibits diffusive behavior, dispersing from its initial location at a constant rate. Such processes are not well modeled by fBm, which has a singularity at zero frequency corresponding to an unbounded rate of dispersion. A more appropriate stochastic model is a much lesser-known random process called the Matern process, which is shown herein to be a damped version of fractional Brownian motion. This article first provides a thorough introduction to fractional Brownian motion, then examines the details of the Matern process and...
RECTILINEAR AND BROWNIAN MOTION FROM A RANDOM POINT IN A CONVEX REGION
Peter Ehlers
2011-05-01
Full Text Available A particle is projected from a point P in a subset E of a convex region H to a point Q in a uniformly random direction. The probability that Q lies in the interior of H at time t is obtained for two types of motion of the particle, rectilinear (i.e. straight-line and Brownian. In the case of rectilinear motion, the first passage time through the boundary of H is considered. Results are obtained in terms of the generalized overlap function for embedded bodies.
Relativistic Brownian motion: from a microscopic binary collision model to the Langevin equation.
Dunkel, Jörn; Hänggi, Peter
2006-11-01
The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy pointlike Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, nonrelativistic LE is deduced from this model, by taking into account the nonrelativistic conservation laws for momentum and kinetic energy. Subsequently, this procedure is generalized to the relativistic case. There, it is found that the relativistic stochastic force is still delta correlated (white noise) but no longer corresponds to a Gaussian white noise process. Explicit results for the friction and momentum-space diffusion coefficients are presented and discussed.
Probing short-range protein Brownian motion in the cytoplasm of living cells
di Rienzo, Carmine; Piazza, Vincenzo; Gratton, Enrico; Beltram, Fabio; Cardarelli, Francesco
2014-12-01
The translational motion of molecules in cells deviates from what is observed in dilute solutions. Theoretical models provide explanations for this effect but with predictions that drastically depend on the nanoscale organization assumed for macromolecular crowding agents. A conclusive test of the nature of the translational motion in cells is missing owing to the lack of techniques capable of probing crowding with the required temporal and spatial resolution. Here we show that fluorescence-fluctuation analysis of raster scans at variable timescales can provide this information. By using green fluorescent proteins in cells, we measure protein motion at the unprecedented timescale of 1 μs, unveiling unobstructed Brownian motion from 25 to 100 nm, and partially suppressed diffusion above 100 nm. Furthermore, experiments on model systems attribute this effect to the presence of relatively immobile structures rather than to diffusing crowding agents. We discuss the implications of these results for intracellular processes.
Probing short-range protein Brownian motion in the cytoplasm of living cells.
Di Rienzo, Carmine; Piazza, Vincenzo; Gratton, Enrico; Beltram, Fabio; Cardarelli, Francesco
2014-12-23
The translational motion of molecules in cells deviates from what is observed in dilute solutions. Theoretical models provide explanations for this effect but with predictions that drastically depend on the nanoscale organization assumed for macromolecular crowding agents. A conclusive test of the nature of the translational motion in cells is missing owing to the lack of techniques capable of probing crowding with the required temporal and spatial resolution. Here we show that fluorescence-fluctuation analysis of raster scans at variable timescales can provide this information. By using green fluorescent proteins in cells, we measure protein motion at the unprecedented timescale of 1 μs, unveiling unobstructed Brownian motion from 25 to 100 nm, and partially suppressed diffusion above 100 nm. Furthermore, experiments on model systems attribute this effect to the presence of relatively immobile structures rather than to diffusing crowding agents. We discuss the implications of these results for intracellular processes.
Applications of statistical mechanics to non-Brownian random motion
Kutner, Ryszard; Wysocki, Krzysztof
1999-12-01
We analysed discrete and continuous Weierstrass-Mandelbrot representations of the Lévy flights occasionally interrupted by spatial localizations. We chose the discrete representation to easily detect by Monte Carlo simulation which stochastic quantity could be a candidate for describing the real processes. We found that the particle propagator is able to reveal surprisingly close, stable long-range algebraic tail. Unfortunately, long flights present in the system make, in practice, the particle mean-square displacement an irregular step-like function; such a behavior was expected since it is an experimental reminiscence of divergence of the mean-square displacement, predicted by the theory. We developed the continuous representation in the context of random motion of a particle in an amorphous environment; we established a correspondence between the stochastic quantities of both representations in which the latter quantities contain some material constants. The material constants appear due to the thermal average of the space-dependent stretch exponent which defines the probability of the particle passing a given distance. This averaging was performed for intermediate or even high temperatures, as well as for low or even intermediate internal friction regimes where long but not extremely long flights are readily able to construct a significant part of the Lévy distribution. This supplies a kind of self-cut-off of the length of flights. By way of example, we considered a possibility of observing the Lévy flights of hydrogen in amorphous low-concentration, high-temperature Pd 85Si 15H 7.5 phase; this conclusion is based on the results of a real experiment (Driesen et al., in: Janot et al. (Eds.), Atomic Transport and Defects in Metals by Neutron Scattering, Proceedings in Physics, Vol. 10, Springer, Berlin, 1986, p. 126; Richter et al., Phys. Rev. Lett. 57 (1986) 731; Driesen, Doctoral Thesis, Antwerpen University, 1987), performed by detecting the incoherent
Brownian motion of massive black hole binaries and the final parsec problem
Bortolas, E.; Gualandris, A.; Dotti, M.; Spera, M.; Mapelli, M.
2016-09-01
Massive black hole binaries (BHBs) are expected to be one of the most powerful sources of gravitational waves in the frequency range of the pulsar timing array and of forthcoming space-borne detectors. They are believed to form in the final stages of galaxy mergers, and then harden by slingshot ejections of passing stars. However, evolution via the slingshot mechanism may be ineffective if the reservoir of interacting stars is not readily replenished, and the binary shrinking may come to a halt at roughly a parsec separation. Recent simulations suggest that the departure from spherical symmetry, naturally produced in merger remnants, leads to efficient loss cone refilling, preventing the binary from stalling. However, current N-body simulations able to accurately follow the evolution of BHBs are limited to very modest particle numbers. Brownian motion may artificially enhance the loss cone refilling rate in low-N simulations, where the binary encounters a larger population of stars due its random motion. Here we study the significance of Brownian motion of BHBs in merger remnants in the context of the final parsec problem. We simulate mergers with various particle numbers (from 8k to 1M) and with several density profiles. Moreover, we compare simulations where the BHB is fixed at the centre of the merger remnant with simulations where the BHB is free to random walk. We find that Brownian motion does not significantly affect the evolution of BHBs in simulations with particle numbers in excess of one million, and that the hardening measured in merger simulations is due to collisionless loss cone refilling.
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.
Jing, Shuai
2010-01-01
We study the existence of a unique solution to semilinear fractional backward doubly stochastic differential equation driven by a Brownian motion and a fractional Brownian motion with Hurst parameter less than 1/2. Here the stochastic integral with respect to the fractional Brownian motion is the extended divergence operator and the one with respect to Brownian motion is It\\^o's backward integral. For this we use the technique developed by R.Buckdahn to analyze stochastic differential equations on the Wiener space, which is based on the Girsanov theorem and the Malliavin calculus, and we reduce the backward doubly stochastic differential equation to a backward stochastic differential equation driven by the Brownian motion. We also prove that the solution of semilinear fractional backward doubly stochastic differential equation defines the unique stochastic viscosity solution of a semilinear stochastic partial differential equation driven by a fractional Brownian motion.
Kevin D. Brewer
2012-11-01
Full Text Available This paper presents some Excel-based simulation exercises that are suitable for use in financial modeling courses. Such exercises are based on a stochastic process of stock price movements, called geometric Brownian motion, that underlies the derivation of the Black-Scholes option pricing model. Guidance is provided in assigning appropriate values of the drift parameter in the stochastic process for such exercises. Some further simulation exercises are also suggested. As the analytical underpinning of the materials involved is provided, this paper is expected to be of interest also to instructors and students of investment courses.
A Milstein-type scheme without Levy area terms for SDEs driven by fractional Brownian motion
Deya, Aurélien; Tindel, Samy
2010-01-01
In this article, we study the numerical approximation of stochastic differential equations driven by a multidimensional fractional Brownian motion (fBm) with Hurst parameter greater than 1/3. We introduce an implementable scheme for these equations, which is based on a second order Taylor expansion, where the usual Levy area terms are replaced by products of increments of the driving fBm. The convergence of our scheme is shown by means of a combination of rough paths techniques and error bounds for the discretisation of the Levy area terms.
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.
Slower deviations of the branching Brownian motion and of branching random walks
Derrida, Bernard; Shi, Zhan
2017-08-01
We have shown recently how to calculate the large deviation function of the position X\\max(t) of the rightmost particle of a branching Brownian motion at time t. This large deviation function exhibits a phase transition at a certain negative velocity. Here we extend this result to more general branching random walks and show that the probability distribution of X\\max(t) has, asymptotically in time, a prefactor characterized by a non trivial power law. Dedicated to John Cardy on the occasion of his 70th birthday.
The fractional Brownian motion property of the turbulent refractive within Geometric Optics
Pérez, D G
2003-01-01
We introduce fractional Brownian motion processes (fBm) as an alternative model for the turbulent index of refraction. These processes allow to reconstruct most of the refractive index properties, but they are not differentiable. We overcome the apparent impossibility of their use within the Ray Optics approximation introducing a Stochastic Calculus. Afterwards, we successfully provide a solution for the stochastic ray-equation; moreover, its implications in the statistical analysis of experimental data is discussed. In particular, we analyze the dependence of the averaged solution against the characteristic variables of a simple propagation problem.
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.
Second order asymptotics for Brownian motion among a heavy tailed Poissonian potential
Fukushima, Ryoki
2010-01-01
We consider the Feynman-Kac functional associated with a Brownian motion among a random potential. The potential is defined by attaching a heavy tailed positive potential around the Poisson point process. This model was first considered by Pastur~(1977) and the first order term of the moment asymptotics was determined. In this paper, both moment and almost sure asymptotics are determined up to the second order. As an application, we also derive the second order asymptotics of the integrated density of states of the corresponding random Schr\\"{o}dinger operator.
Macedo-Junior, A.F. [Departamento de Fisica, Laboratorio de Fisica Teorica e Computacional, Universidade Federal de Pernambuco, 50670-901 Recife, PE (Brazil)]. E-mail: ailton@df.ufpe.br; Macedo, A.M.S. [Departamento de Fisica, Laboratorio de Fisica Teorica e Computacional, Universidade Federal de Pernambuco, 50670-901 Recife, PE (Brazil)
2006-09-25
We study a class of Brownian-motion ensembles obtained from the general theory of Markovian stochastic processes in random-matrix theory. The ensembles admit a complete classification scheme based on a recent multivariable generalization of classical orthogonal polynomials and are closely related to Hamiltonians of Calogero-Sutherland-type quantum systems. An integral transform is proposed to evaluate the n-point correlation function for a large class of initial distribution functions. Applications of the classification scheme and of the integral transform to concrete physical systems are presented in detail.
Jean-Francois Coeurjolly
2000-09-01
Full Text Available We present a non exhaustive bibliographical and comparative study of the problem of simulation and identification of the fractional Brownian motion. The discussed implementation is realized within the software S-plus 3.4. A few simulations illustrate this work. Furthermore, we propose a test based on the asymptotic behavior of a self-similarity parameter's estimator to explore the quality of different generators. This procedure, easily computable, allows us to extract an efficient method of simulation. In the Appendix are described the S-plus scripts related to simulation and identification methods of the fBm.
Complex motions and chaos in nonlinear systems
Machado, José; Zhang, Jiazhong
2016-01-01
This book brings together 10 chapters on a new stream of research examining complex phenomena in nonlinear systems—including engineering, physics, and social science. Complex Motions and Chaos in Nonlinear Systems provides readers a particular vantage of the nature and nonlinear phenomena in nonlinear dynamics that can develop the corresponding mathematical theory and apply nonlinear design to practical engineering as well as the study of other complex phenomena including those investigated within social science.
Limitation of the Least Square Method in the Evaluation of Dimension of Fractal Brownian Motions
Qiao, Bingqiang; Zeng, Houdun; Li, Xiang; Dai, Benzhong
2015-01-01
With the standard deviation for the logarithm of the re-scaled range $\\langle |F(t+\\tau)-F(t)|\\rangle$ of simulated fractal Brownian motions $F(t)$ given in a previous paper \\cite{q14}, the method of least squares is adopted to determine the slope, $S$, and intercept, $I$, of the log$(\\langle |F(t+\\tau)-F(t)|\\rangle)$ vs $\\rm{log}(\\tau)$ plot to investigate the limitation of this procedure. It is found that the reduced $\\chi^2$ of the fitting decreases with the increase of the Hurst index, $H$ (the expectation value of $S$), which may be attributed to the correlation among the re-scaled ranges. Similarly, it is found that the errors of the fitting parameters $S$ and $I$ are usually smaller than their corresponding standard deviations. These results show the limitation of using the simple least square method to determine the dimension of a fractal time series. Nevertheless, they may be used to reinterpret the fitting results of the least square method to determine the dimension of fractal Brownian motions more...
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.
Muniandy, S V; Lim, S C
2001-04-01
Fractional Brownian motion (FBM) is widely used in the modeling of phenomena with power spectral density of power-law type. However, FBM has its limitation since it can only describe phenomena with monofractal structure or a uniform degree of irregularity characterized by the constant Holder exponent. For more realistic modeling, it is necessary to take into consideration the local variation of irregularity, with the Holder exponent allowed to vary with time (or space). One way to achieve such a generalization is to extend the standard FBM to multifractional Brownian motion (MBM) indexed by a Holder exponent that is a function of time. This paper proposes an alternative generalization to MBM based on the FBM defined by the Riemann-Liouville type of fractional integral. The local properties of the Riemann-Liouville MBM (RLMBM) are studied and they are found to be similar to that of the standard MBM. A numerical scheme to simulate the locally self-similar sample paths of the RLMBM for various types of time-varying Holder exponents is given. The local scaling exponents are estimated based on the local growth of the variance and the wavelet scalogram methods. Finally, an example of the possible applications of RLMBM in the modeling of multifractal time series is illustrated.
Weak convergence of the past and future of Brownian motion given the present
K B Athreya; B Rajeev
2017-02-01
In this paper, we show that for $t > 0$, the joint distribution of the past $\\{W_{t−s} : 0 \\leq s \\leq t\\}$ and the future $\\{W_{t+s} : s \\geq 0\\}$ of a $d$-dimensional standard Brownian motion $(W_s)$, conditioned on $\\{W_t\\in U\\}$, where $U$ is a bounded open set in $\\mathbb{R}^d$, converges weakly in $C[0,\\infty)\\times C[0, \\infty)$ as $t\\rightarrow\\infty$. The limiting distribution is that of a pair of coupled processes $Y + B^1$, $Y + B^2$ where $Y$, $B^1$, $B^2$ are independent, $Y$ is uniformly distributed on $U$ and $B^1$, $B^2$ are standard $d$-dimensional Brownian motions. Let $\\sigma_t$, $d_t$ be respectively, the last entrance time before time $t$ into the set $U$ and the first exit time after $t$ from $U$. When the boundary of $U$ is regular, we use the continuous mapping theorem to show that the limiting distribution as $t\\rightarrow\\infty$ of the four dimensional vector with components $(W_{\\sigma_t}, t − \\sigma_t, W_{d_t}, d_t − t)$, conditioned on $\\{W_t\\in U\\}$, is the same as that of the four dimensional vector whose components are the place and time of first exit from $U$ of the processes $Y + B^1$ and $Y + B^2$ respectively.
Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion
Bodrova, Anna S.; Chechkin, Aleksei V.; Cherstvy, Andrey G.; Safdari, Hadiseh; Sokolov, Igor M.; Metzler, Ralf
2016-07-01
It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.
Supercritical super-Brownian motion with a general branching mechanism and travelling waves
Kyprianou, A E; Murillo-Salas, A; Ren, Y -X
2010-01-01
We consider the classical problem of existence, uniqueness and asymptotics of monotone solutions to the travelling wave equation associated to the parabolic semi-group equation of a super-Brownian motion with a general branching mechanism. Whilst we are strongly guided by the probabilistic reasoning of Kyprianou (2004) for branching Brownian motion, the current paper offers a number of new insights. Our analysis incorporates the role of Seneta-Heyde norming which, in the current setting, draws on classical work of Grey (1974). We give a pathwise explanation of Evans' immortal particle picture (the spine decomposition) which uses the Dynkin-Kuznetsov N-measure as a key ingredient. Moreover, in the spirit of Neveu's stopping lines we make repeated use of Dynkin's exit measures. Additional complications arise from the general nature of the branching mechanism. As a consequence of the analysis we also offer an exact X(log X)^2 moment dichotomy for the almost sure convergence of the so-called derivative martingale...
Silva, Antonio
2005-03-01
It is well-known that the mathematical theory of Brownian motion was first developed in the Ph. D. thesis of Louis Bachelier for the French stock market before Einstein [1]. In Ref. [2] we studied the so-called Heston model, where the stock-price dynamics is governed by multiplicative Brownian motion with stochastic diffusion coefficient. We solved the corresponding Fokker-Planck equation exactly and found an analytic formula for the time-dependent probability distribution of stock price changes (returns). The formula interpolates between the exponential (tent-shaped) distribution for short time lags and the Gaussian (parabolic) distribution for long time lags. The theoretical formula agrees very well with the actual stock-market data ranging from the Dow-Jones index [2] to individual companies [3], such as Microsoft, Intel, etc. [] [1] Louis Bachelier, ``Th'eorie de la sp'eculation,'' Annales Scientifiques de l''Ecole Normale Sup'erieure, III-17:21-86 (1900).[] [2] A. A. Dragulescu and V. M. Yakovenko, ``Probability distribution of returns in the Heston model with stochastic volatility,'' Quantitative Finance 2, 443--453 (2002); Erratum 3, C15 (2003). [cond-mat/0203046] [] [3] A. C. Silva, R. E. Prange, and V. M. Yakovenko, ``Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact,'' Physica A 344, 227--235 (2004). [cond-mat/0401225
Brownian motion of massive black hole binaries and the final parsec problem
Bortolas, E; Dotti, M; Spera, M; Mapelli, M
2016-01-01
Massive black hole binaries (BHBs) are expected to be one of the most powerful sources of gravitational waves (GWs) in the frequency range of the pulsar timing array and of forthcoming space-borne detectors. They are believed to form in the final stages of galaxy mergers, and then harden by slingshot ejections of passing stars. However, evolution via the slingshot mechanism may be ineffective if the reservoir of interacting stars is not readily replenished, and the binary shrinking may come to a halt at roughly a parsec separation. Recent simulations suggest that the departure from spherical symmetry, naturally produced in merger remnants, leads to efficient loss cone refilling, preventing the binary from stalling. However, current N-body simulations able to accurately follow the evolution of BHBs are limited to very modest particle numbers. Brownian motion may artificially enhance the loss cone refilling rate in low-N simulations, where the binary encounters a larger population of stars due its random motion...
Quantum harmonic Brownian motion in a general environment: A modified phase-space approach
Yeh, L. [Univ. of California, Berkeley, CA (United States). Dept. of Physics]|[Lawrence Berkeley Lab., CA (United States)
1993-06-23
After extensive investigations over three decades, the linear-coupling model and its equivalents have become the standard microscopic models for quantum harmonic Brownian motion, in which a harmonically bound Brownian particle is coupled to a quantum dissipative heat bath of general type modeled by infinitely many harmonic oscillators. The dynamics of these models have been studied by many authors using the quantum Langevin equation, the path-integral approach, quasi-probability distribution functions (e.g., the Wigner function), etc. However, the quantum Langevin equation is only applicable to some special problems, while other approaches all involve complicated calculations due to the inevitable reduction (i.e., contraction) operation for ignoring/eliminating the degrees of freedom of the heat bath. In this dissertation, the author proposes an improved methodology via a modified phase-space approach which employs the characteristic function (the symplectic Fourier transform of the Wigner function) as the representative of the density operator. This representative is claimed to be the most natural one for performing the reduction, not only because of its simplicity but also because of its manifestation of geometric meaning. Accordingly, it is particularly convenient for studying the time evolution of the Brownian particle with an arbitrary initial state. The power of this characteristic function is illuminated through a detailed study of several physically interesting problems, including the environment-induced damping of quantum interference, the exact quantum Fokker-Planck equations, and the relaxation of non-factorizable initial states. All derivations and calculations axe shown to be much simplified in comparison with other approaches. In addition to dynamical problems, a novel derivation of the fluctuation-dissipation theorem which is valid for all quantum linear systems is presented.
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
Byczkowski, Tomasz; Graczyk, Piotr; Malecki, Jacek
2011-01-01
The purpose of the paper is to provide integral representations of the Poisson kernel for a half-space and balls for hyperbolic Brownian motion and for the classical Ornstein-Uhlenbeck process. The method of proof is based on Girsanov's theorem and yields more complete results as those based on Feynmann-Kac technique.
Acharya, R.C.; Dijke, van M.I.J.; Sorbie, K.S.; Zee, van der S.E.A.T.M.; Leijnse, A.
2007-01-01
We present a 3D network model with particle tracking to upscale 3D Brownian motion of non-reactive tracer particles subjected to a velocity field in the network bonds, representing both local diffusion and convection. At the intersections of the bonds (nodes) various jump conditions are implemented.
2009-01-01
This is a survey on normal distributions and the related central limit theorem under sublinear expectation.We also present Brownian motion under sublinear expectations and the related stochastic calculus of It?’s type.The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk,statistics and other industrial problems.
DuPré, Donald B.; Chapoy, L. Lawrence
1980-01-01
The effect of rotational Brownian motion on measurements of orientational distribution functions in uniaxial liquid crystals is discussed. The comments of Naqvi1 on the authors previously published2,3 papers are answered.(AIP) The Journal of Chemical Physics is copyrighted by The American Institute...
PENG ShiGe
2009-01-01
This is a survey on normal distributions and the related central limit theorem under sublinear expectation. We also present Brownian motion under sublinear expectations and the related stochastic calculus of Ito's type. The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk, statistics and other industrial problems.
A MAP estimator based on geometric Brownian motion for sample distances of laser triangulation data
Herrmann, Markus; Otesteanu, Marius
2016-11-01
The proposed algorithm is designed to enhance the line-detection stability in laser-stripe sensors. Despite their many features and capabilities, these sensors become unstable when measuring in dark or strongly-reflective environments. Ambiguous points within a camera image can appear on dark surfaces and be confused with noise when the laser-reflection intensity approaches noise level. Similar problems arise when strong reflections within the sensor image have intensities comparable to that of the laser. In these circumstances, it is difficult to determine the most probable point for the laser line. Hence, the proposed algorithm introduces a maximum a posteriori estimator, based on geometric Brownian motion, to provide a range estimate for the expected location of the reflected laser line.
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...
Verrier, Nicolas; Fournel, Thierry
2015-01-01
In-line digital holography is a valuable tool for sizing, locating and tracking micro- or nano-objects in a volume. When a parametric imaging model is available, Inverse Problems approaches provide a straightforward estimate of the object parameters by fitting data with the model, thereby allowing accurate reconstruction. As recently proposed and demonstrated, combining pixel super-resolution techniques with Inverse Problems approaches improves the estimation of particle size and 3D-position. Here we demonstrate the accurate tracking of colloidal particles in Brownian motion. Particle size and 3D-position are jointly optimized from video holograms acquired with a digital holographic microscopy set up based on a "low-end" microscope objective ($\\times 20$, $\\rm NA\\ 0.5$). Exploiting information redundancy makes it possible to characterize particles with a standard deviation of 15 nm in size and a theoretical resolution of 2 x 2 x 5 nm$^3$ for position under additive white Gaussian noise assumption.
Large Deviations for the Branching Brownian Motion in Presence of Selection or Coalescence
Derrida, Bernard; Shi, Zhan
2016-06-01
The large deviation function has been known for a long time in the literature for the displacement of the rightmost particle in a branching random walk (BRW), or in a branching Brownian motion (BBM). More recently a number of generalizations of the BBM and of the BRW have been considered where selection or coalescence mechanisms tend to limit the exponential growth of the number of particles. Here we try to estimate the large deviation function of the position of the rightmost particle for several such generalizations: the L-BBM, the N-BBM, and the coalescing branching random walk (CBRW) which is closely related to the noisy FKPP equation. Our approach allows us to obtain only upper bounds on these large deviation functions. One noticeable feature of our results is their non analytic dependence on the parameters (such as the coalescence rate in the CBRW).
On the use of reverse Brownian motion to accelerate hybrid simulations
Bakarji, Joseph; Tartakovsky, Daniel M.
2017-04-01
Multiscale and multiphysics simulations are two rapidly developing fields of scientific computing. Efficient coupling of continuum (deterministic or stochastic) constitutive solvers with their discrete (stochastic, particle-based) counterparts is a common challenge in both kinds of simulations. We focus on interfacial, tightly coupled simulations of diffusion that combine continuum and particle-based solvers. The latter employs the reverse Brownian motion (rBm), a Monte Carlo approach that allows one to enforce inhomogeneous Dirichlet, Neumann, or Robin boundary conditions and is trivially parallelizable. We discuss numerical approaches for improving the accuracy of rBm in the presence of inhomogeneous Neumann boundary conditions and alternative strategies for coupling the rBm solver with its continuum counterpart. Numerical experiments are used to investigate the convergence, stability, and computational efficiency of the proposed hybrid algorithm.
Challis, K J; Jack, Michael W
2013-05-01
We present a theoretical treatment of overdamped Brownian motion on a multidimensional tilted periodic potential that is analogous to the tight-binding model of quantum mechanics. In our approach, we expand the continuous Smoluchowski equation in the localized Wannier states of the periodic potential to derive a discrete master equation. This master equation can be interpreted in terms of hopping within and between Bloch bands, and for weak tilting and long times we show that a single-band description is valid. In the limit of deep potential wells, we derive a simple functional dependence of the hopping rates and the lowest band eigenvalues on the tilt. We also derive formal expressions for the drift and diffusion in terms of the lowest band eigenvalues.
Dettmer, Simon L; Pagliara, Stefano
2014-01-01
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...
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.
Super-Brownian motion: Lp-convergence of martingales through the pathwise spine decomposition
Murillo-Salas, A E Kyprianou A
2011-01-01
Evans (1992) described the semi-group of a superprocess with quadratic branching mechanism under a martingale change of measure in terms of the semi-group of an immortal particle and the semigroup of the superprocess prior to the change of measure. This result, commonly referred to as the spine decomposition, alludes to a pathwise decomposition in which independent copies of the original process `immigrate' along the path of the immortal particle. For branching particle diffusions the analogue of this decomposition has already been demonstrated in the pathwise sense, see for example Hardy and Harris (2009). The purpose of this short note is to exemplify a new {\\it pathwise} spine decomposition for supercritical super-Brownian motion with general branching mechanism (cf. Kyprianou et al. (2010)) by studying $L^p$ convergence of naturally underlying additive martingales in the spirit of analogous arguments for branching particle diffusions due to Hardys and Harris (2009). Amongst other ingredients, the Dynkin-K...
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.
Ni Xiaohui [School of Business, East China University of Science and Technology, Shanghai 200237 (China)] [School of Science, East China University of Science and Technology, Shanghai 200237 (China)] [Research Center for Econophysics, East China University of Science and Technology, Shanghai 200237 (China); Jiang Zhiqiang [School of Business, East China University of Science and Technology, Shanghai 200237 (China)] [School of Science, East China University of Science and Technology, Shanghai 200237 (China)] [Research Center for Econophysics, East China University of Science and Technology, Shanghai 200237 (China)] [Chair of Entrepreneurial Risks, D-MTEC, ETH Zurich, Kreuplatz 5, CH-8032 Zurich (Switzerland); Zhou Weixing, E-mail: wxzhou@ecust.edu.c [School of Business, East China University of Science and Technology, Shanghai 200237 (China)] [School of Science, East China University of Science and Technology, Shanghai 200237 (China)] [Research Center for Econophysics, East China University of Science and Technology, Shanghai 200237 (China)] [Engineering Research Center of Process Systems Engineering (Ministry of Education), East China University of Science and Technology, Shanghai 200237 (China)] [Research Center on Fictitious Economics and Data Science, Chinese Academy of Sciences, Beijing 100080 (China)
2009-10-12
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 alpha 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 alphaapproxH linear relationship.
He, Hui; Zhou, Xiaowen
2009-01-01
This paper concerns the almost sure time dependent local extinction behavior for super-coalescing Brownian motion $X$ with $(1+\\beta)$-stable branching and Lebesgue initial measure on $\\bR$. We first give a representation of $X$ using excursions of a continuous state branching process and Arratia's coalescing Brownian flow. For any nonnegative, nondecreasing and right continuous function $g$, put \\tau:=\\sup \\{t\\geq 0: X_t([-g(t),g(t)])>0 \\}. We prove that $\\bP\\{\\tau=\\infty\\}=0$ or 1 according as the integral $\\int_1^\\infty g(t)t^{-1-1/\\beta} dt$ is finite or infinite.
Cristian Rodriguez Rivero
2016-03-01
Full Text Available A new predictor algorithm based on Bayesian enhanced approach (BEA for long-term chaotic time series using artificial neural networks (ANN is presented. The technique based on stochastic models uses Bayesian inference by means of Fractional Brownian Motion as model data and Beta model as prior information. However, the need of experimental data for specifying and estimating causal models has not changed. Indeed, Bayes method provides another way to incorporate prior knowledge in forecasting models; the simplest representations of prior knowledge in forecasting models are hard to beat in many forecasting situations, either because prior knowledge is insufficient to improve on models or because prior knowledge leads to the conclusion that the situation is stable. This work contributes with long-term time series prediction, to give forecast horizons up to 18 steps ahead. Thus, the forecasted values and validation data are presented by solutions of benchmark chaotic series such as Mackey-Glass, Lorenz, Henon, Logistic, Rössler, Ikeda, Quadratic one-dimensional map series and monthly cumulative rainfall collected from Despeñaderos, Cordoba, Argentina. The computational results are evaluated against several non-linear ANN predictors proposed before on high roughness series that shows a better performance of Bayesian Enhanced approach in long-term forecasting.
布朗运动仿真实验的设计与实现%Simulation experiment of Brownian motion
丁望峰
2014-01-01
介绍了布朗运动仿真实验的设计与实现方法，利用“位置朗之万方程”的数值离散化，最大程度还原真实的布朗运动。通过对仿真实验数据的定量分析，并计算出了阿伏加德罗常量的近似值。%The design and implement method of Brownian motion simulation experiment were in-troduced .The characteristics of real Brownian motion was maximally retained by the numerial discret-ization of position of Langevin equation .By quantitative analyzing of the motion traces ,a close ap-proximation of Avogadro constant was obtained .
Minchew, Candace L.; Didenko, Vladimir V.
2014-01-01
We describe a new type of bio-nanomachine which runs on thermal noise. The machine is solely powered by the random motion of water molecules in its environment and does not ever require re-fuelling. The construct, which is made of DNA and vaccinia virus topoisomerase protein, can detect DNA damage by employing fluorescence. It uses Brownian motion as a cyclic motor to continually separate and bring together two types of fluorescent hairpins participating in FRET. This bio-molecular oscillator is a fast and specific sensor of 5′OH double-strand DNA breaks present in phagocytic phase of apoptosis. The detection takes 30 s in solution and 3 min in cell suspensions. The phagocytic phase is critical for the effective execution of apoptosis as it ensures complete degradation of the dying cells’ DNA, preventing release of pathological, viral and tumor DNA and self-immunization. The construct can be used as a smart FRET probe in studies of cell death and phagocytosis. PMID:25268504
Palyulin, Vladimir V.; Chechkin, Aleksei V.; Klages, Rainer; Metzler, Ralf
2016-09-01
A combined dynamics consisting of Brownian motion and Lévy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of doing so economically of such dynamics thus poses an important problem. Here we model this dynamics by a one-dimensional fractional Fokker-Planck equation combining unbiased Brownian motion and Lévy flights. By solving this equation both analytically and numerically we show that the superposition of recurrent Brownian motion and Lévy flights with stable exponent α \\lt 1, by itself implying zero probability of hitting a point on a line, leads to transient motion with finite probability of hitting any point on the line. We present results for the exact dependence of the values of both the search reliability and the search efficiency on the distance between the starting and target positions as well as the choice of the scaling exponent α of the Lévy flight component.
D'Auria, Bernardo
2011-01-01
In this paper we study a reflected Markov-modulated Brownian motion with a two sided reflection in which the drift, diffusion coefficient and the two boundaries are (jointly) modulated by a finite state space irreducible continuous time Markov chain. The goal is to compute the stationary distribution of this Markov process, which in addition to the complication of having a stochastic boundary can also include jumps at state change epochs of the underlying Markov chain because of the boundary changes. We give the general theory and then specialize to the case where the underlying Markov chain has two states. Moreover, motivated by an application of optimal dividend strategies, we consider the case where the lower barrier is zero and the upper barrier is subject to control. In this case we generalized earlier results from the case of a reflected Brownian motion to the Markov modulated case.
Burdzy, Krzysztof; Pal, Soumik
2010-01-01
We prove that the distance between two reflected Brownian motions outside a sphere in a 3-dimensional flat torus does not converge to 0, a.s., if the radius of the sphere is sufficiently small, relative to the size of the torus.
Chapoy, Larry Lawrence; DuPré, Donald B.
1978-01-01
An expression is derived for the anisotropic fluorescent emission in uniaxial liquid crystals where fluorescent sites governed by an initial nonrandom distribution of orientations are subject to rotational Brownian motion. The possibility of nonparallelism of absorption and emission oscillators...
Michalet, Xavier
2010-01-01
We examine the capability of mean square displacement analysis to extract reliable values of the diffusion coefficient D of single particle undergoing Brownian motion in an isotropic medium in the presence of localization uncertainty. The theoretical results, supported by simulations, show that a simple unweighted least square fit of the MSD curve can provide the best estimate of D provided an optimal number of MSD points is used for the fit. We discuss the practical implications of these res...
Mackey, Michael C. [Departments of Physiology, Physics and Mathematics and Centre for Nonlinear Dynamics, McGill University, 3655 Promenade Sir William Osler, Montreal, QC, H3G 1Y6 (Canada)]. E-mail: mackey@cnd.mcgill.ca; Tyran-Kaminska, Marta [Institute of Mathematics, Silesian University, ul. Bankowa 14, 40-007 Katowice (Poland)]. E-mail: mtyran@us.edu.pl
2006-01-15
Here we review and extend central limit theorems for chaotic deterministic semi-dynamical discrete time systems. We then apply these results to show how Brownian motion-like behavior can be recovered and how an Ornstein-Uhlenbeck process can be constructed within a totally deterministic framework. These results illustrate that under certain circumstances the contamination of experimental data by 'noise' may be alternately interpreted as the signature of an underlying chaotic process.
Fractional Brownian Motion and Geodesic Rao Distance for Bone X-ray Image Characterization.
El Hassouni, Mohammed; Tafraouti, Abdessamad; Toumi, Hechmi; Lespessailles, Eric; Jennane, Rachid
2016-10-19
Osteoporosis diagnosis has attracted particular attention in recent decades. Textured images from the microarchitecture of osteoporotic and healthy subjects show a high degree of similarity, increasing the difficulty of classifying such textures. Thus, the evaluation of osteoporosis from bone X-ray images presents a major challenge for pattern recognition and medical applications. The purpose of this paper is to use the fractional Brownian motion (fBm) model and the Probability Density Function (PDF) of its increments to compute a similarity measure with the Rao geodesic distance to classify trabecular bone X-ray images. When evaluated on synthetic fBm images (test vectors) with the well-known Hurst parameter H, the proposed method met our expectations in that a good classification of the synthetic images was achieved. A clinical study was conducted on textured bone X-ray images from two different female populations of osteoporotic patients (fracture cases) and control subjects. Using the proposed method, an Area Under Curve (AUC) rate of 97% was achieved.
Tulzer, Gerhard; Heitzinger, Clemens
2016-04-22
In this work, we develop a 2D algorithm for stochastic reaction-diffusion systems describing the binding and unbinding of target molecules at the surfaces of affinity-based sensors. In particular, we simulate the detection of DNA oligomers using silicon-nanowire field-effect biosensors. Since these devices are uniform along the nanowire, two dimensions are sufficient to capture the kinetic effects features. The model combines a stochastic ordinary differential equation for the binding and unbinding of target molecules as well as a diffusion equation for their transport in the liquid. A Brownian-motion based algorithm simulates the diffusion process, which is linked to a stochastic-simulation algorithm for association at and dissociation from the surface. The simulation data show that the shape of the cross section of the sensor yields areas with significantly different target-molecule coverage. Different initial conditions are investigated as well in order to aid rational sensor design. A comparison of the association/hybridization behavior for different receptor densities allows optimization of the functionalization setup depending on the target-molecule density.
Fractional Brownian motion time-changed by gamma and inverse gamma process
Kumar, A.; Wyłomańska, A.; Połoczański, R.; Sundar, S.
2017-02-01
Many real time-series exhibit behavior adequate to long range dependent data. Additionally very often these time-series have constant time periods and also have characteristics similar to Gaussian processes although they are not Gaussian. Therefore there is need to consider new classes of systems to model these kinds of empirical behavior. Motivated by this fact in this paper we analyze two processes which exhibit long range dependence property and have additional interesting characteristics which may be observed in real phenomena. Both of them are constructed as the superposition of fractional Brownian motion (FBM) and other process. In the first case the internal process, which plays role of the time, is the gamma process while in the second case the internal process is its inverse. We present in detail their main properties paying main attention to the long range dependence property. Moreover, we show how to simulate these processes and estimate their parameters. We propose to use a novel method based on rescaled modified cumulative distribution function for estimation of parameters of the second considered process. This method is very useful in description of rounded data, like waiting times of subordinated processes delayed by inverse subordinators. By using the Monte Carlo method we show the effectiveness of proposed estimation procedures. Finally, we present the applications of proposed models to real time series.
Finite time extinction of super-Brownian motions with deterministic catalyst
REN; Yanxia(任艳霞); WANG; Yongjin(王永进)
2003-01-01
In this paper we consider a super-Brownian motion X with branching mechanism k(x)za, where k(x) ＞ 0 is a bounded Holder continuous function on Rd and infx∈Rd k(x) = 0. We prove that if k(x) ≥‖x‖-1(0 ≤ l ＜∞) for sufficiently large x, then X has compact support property, and for dimension d = 1, if k(x) ≥ exp(-l‖x‖)(0 ≤ l ＜∞) for sufficiently large x, then X also has compact support property. The maximal order of k(x) for finite time extinction is different between d = 1, d = 2 and d ≥3: it is O(‖x‖-(a+1))in one dimension, O(‖x‖-2(log ‖x‖)-(a+1)) in two dimensions, and O(‖x‖2) in higher dimensions. These growth orders also turn out to be the maximum order for the nonexistence of a positive solution for 1/2△u =k(x)uα.
Scale Relativistic signature in the Brownian motion of micro-spheres in optical traps
Lebohec, Stephan
2017-09-01
The development of mechanics of nondifferentiable paths36 suggested by Scale Relativity31,32 results in a foundation of Quantum Mechanics30,37 including Schrödinger’s equation and all the other axioms under the assumption the path nondifferentiability can be described as a Wiener process at the resolution-scale of observation. This naturally brings under question the possibility that the statistics of the dynamics of macroscopic systems fulfilling this hypothesis could fall under a quantum-like description with the Planck constant replaced with some other constant, possibly system specific, and corresponding to a diffusion coefficient. The observation of such a quantum-like dynamics would establish if the Scale Relativistic principle is implemented in macroscopic complex or chaotic systems. This would have major implications for the study of structure formation dynamics in various research fields. In this paper, I investigate the possibility for the detection of such an effect in the Brownian motion of a micro-sphere in an optical trap. I find that, if it exists, the observation of the transition to a quantum-like regime is within reach of modern experiments.
Detection of two-sided alternatives in a Brownian motion model
Hadjiliadis, Olympia
2007-01-01
This work examines the problem of sequential detection of a change in the drift of a Brownian motion in the case of two-sided alternatives. Applications to real life situations in which two-sided changes can occur are discussed. Traditionally, 2-CUSUM stopping rules have been used for this problem due to their asymptotically optimal character as the mean time between false alarms tends to $\\infty$. In particular, attention has focused on 2-CUSUM harmonic mean rules due to the simplicity in calculating their first moments. In this paper, we derive closed-form expressions for the first moment of a general 2-CUSUM stopping rule. We use these expressions to obtain explicit upper and lower bounds for it. Moreover, we derive an expression for the rate of change of this first moment as one of the threshold parameters changes. Based on these expressions we obtain explicit upper and lower bounds to this rate of change. Using these expressions we are able to find the best 2-CUSUM stopping rule with respect to the exten...
The generalization of a class of impulse stochastic control models of a geometric Brownian motion
LIU XiaoPeng; LIU KunHui
2009-01-01
Recently, international academic circles advanced a class of new stochastic control models of a geometric Brownian motion which is an important kind of impulse control models whose cost structure is different from the others before, and it has a broad applying background and important theoretical significance in financial control and management of investment. This paper generalizes substantially the above stochastic control models under quite extensive conditions and describes the models more exactly under more normal theoretical system of stochastic process. By establishing a set of proper variational equations and proving the existence of its solution, and applying the means of stochastic analysis, this paper proves that the generalized stochastic control models have optimal controls.Meanwhile, we also analyze the structure of optimal controls carefully. Besides, we study the solution function of variational equations in a relatively deep-going way, which constitutes the value function of control models to some extent. Because the analysis methods of this paper are greatly different from those of original reference, this paper possesses considerable originality to some extent. In addition,this paper gives the strict proof to the part of original reference which is not fairly well-knit in analyses,and makes analyses and discussions of the model have the exactitude of mathematical sense.
From Brownian motion to operational risk: Statistical physics and financial markets
Voit, Johannes
2003-04-01
High-frequency returns of the DAX German blue chip stock index are used to test geometric Brownian motion, the standard model for financial time series. Even on a 15-s time scale, the linear correlations of DAX returns have a zero-time delta function which carries 90% of the weight, while the remaining 10% are positively correlated with a decay time of 53 s and negatively correlated on a 9.4-min scale. The probability density of the returns possesses fat tails with power laws whose exponents continuously increase with time scales. It is suggested that hydrodynamic turbulence may provide a phenomenological framework for the description of these data, and at the same time, open a way to use them for risk-management purposes, e.g. option pricing and hedging. Option pricing also is the cornerstone of credit valuation, an area of much practical importance not considered explicitly in most other physics-inspired papers on finance. Finally, operational risk is introduced as a new risk category currently emphasized by regulators, which will become important in many banks in the near future.
Isotropic Brownian motions over complex fields as a solvable model for May-Wigner stability analysis
Ipsen, J. R.; Schomerus, H.
2016-09-01
We consider matrix-valued stochastic processes known as isotropic Brownian motions, and show that these can be solved exactly over complex fields. While these processes appear in a variety of questions in mathematical physics, our main motivation is their relation to a May-Wigner-like stability analysis, for which we obtain a stability phase diagram. The exact results establish the full joint probability distribution of the finite-time Lyapunov exponents, and may be used as a starting point for a more detailed analysis of the stability-instability phase transition. Our derivations rest on an explicit formulation of a Fokker-Planck equation for the Lyapunov exponents. This formulation happens to coincide with an exactly solvable class of models of the Calgero-Sutherland type, originally encountered for a model of phase-coherent transport. The exact solution over complex fields describes a determinantal point process of biorthogonal type similar to recent results for products of random matrices, and is also closely related to Hermitian matrix models with an external source.
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.
Suksmono, Andriyan Bayu
2011-01-01
This paper proposes a new fBm (fractional Brownian motion) interpolation/reconstruction method from partially known samples based on CS (Compressive Sampling). Since 1/f property implies power law decay of the fBm spectrum, the fBm signals should be sparse in frequency domain. This property motivates the adoption of CS in the development of the reconstruction method. Hurst parameter H that occurs in the power law determines the sparsity level, therefore the CS reconstruction quality of an fBm signal for a given number of known subsamples will depend on H. However, the proposed method does not require the information of H to reconstruct the fBm signal from its partial samples. The method employs DFT (Discrete Fourier Transform) as the sparsity basis and a random matrix derived from known samples positions as the projection basis. Simulated fBm signals with various values of H are used to show the relationship between the Hurst parameter and the reconstruction quality. Additionally, US-DJIA (Dow Jones Industria...
Brownian-motion based simulation of stochastic reaction-diffusion systems for affinity based sensors
Tulzer, Gerhard; Heitzinger, Clemens
2016-04-01
In this work, we develop a 2D algorithm for stochastic reaction-diffusion systems describing the binding and unbinding of target molecules at the surfaces of affinity-based sensors. In particular, we simulate the detection of DNA oligomers using silicon-nanowire field-effect biosensors. Since these devices are uniform along the nanowire, two dimensions are sufficient to capture the kinetic effects features. The model combines a stochastic ordinary differential equation for the binding and unbinding of target molecules as well as a diffusion equation for their transport in the liquid. A Brownian-motion based algorithm simulates the diffusion process, which is linked to a stochastic-simulation algorithm for association at and dissociation from the surface. The simulation data show that the shape of the cross section of the sensor yields areas with significantly different target-molecule coverage. Different initial conditions are investigated as well in order to aid rational sensor design. A comparison of the association/hybridization behavior for different receptor densities allows optimization of the functionalization setup depending on the target-molecule density.
Fractional Brownian motion time-changed by gamma and inverse gamma process
Kumar, A; Połoczański, R; Sundar, S
2016-01-01
Many real time-series exhibit behavior adequate to long range dependent data. Additionally very often these time-series have constant time periods and also have characteristics similar to Gaussian processes although they are not Gaussian. Therefore there is need to consider new classes of systems to model these kind of empirical behavior. Motivated by this fact in this paper we analyze two processes which exhibit long range dependence property and have additional interesting characteristics which may be observed in real phenomena. Both of them are constructed as the superposition of fractional Brownian motion (FBM) and other process. In the first case the internal process, which plays role of the time, is the gamma process while in the second case the internal process is its inverse. We present in detail their main properties paying main attention to the long range dependence property. Moreover, we show how to simulate these processes and estimate their parameters. We propose to use a novel method based on re...
Yu, Zu-Guo; Zhang, Huan; Huang, Da-Wen; Lin, Yong; Anh, Vo
2016-03-01
Many studies have shown that additional information can be gained on time series by investigating their associated complex networks. In this work, we investigate the multifractal property and Laplace spectrum of the horizontal visibility graphs (HVGs) constructed from fractional Brownian motions. We aim to identify via simulation and curve fitting the form of these properties in terms of the Hurst index H. First, we use the sandbox algorithm to study the multifractality of these HVGs. It is found that multifractality exists in these HVGs. We find that the average fractal dimension of HVGs approximately satisfies the prominent linear formula =2-H ; while the average information dimension and average correlation dimension are all approximately bi-linear functions of H when H≥slant 0.15 . Then, we calculate the spectrum and energy for the general Laplacian operator and normalized Laplacian operator of these HVGs. We find that, for the general Laplacian operator, the average logarithm of second-smallest eigenvalue , the average logarithm of third-smallest eigenvalue , and the average logarithm of maximum eigenvalue of these HVGs are approximately linear functions of H; while the average Laplacian energy is approximately a quadratic polynomial function of H. For the normalized Laplacian operator, and of these HVGs approximately satisfy linear functions of H; while and are approximately a 4th and cubic polynomial function of H respectively.
Hiotelis, Nicos; Del Popolo, Antonino
2017-03-01
We construct an integral equation for the first crossing distributions for fractional Brownian motion in the case of a constant barrier and we present an exact analytical solution. Additionally we present first crossing distributions derived by simulating paths from fractional Brownian motion. We compare the results of the analytical solutions with both those of simulations and those of some approximated solutions which have been used in the literature. Finally, we present multiplicity functions for dark matter structures resulting from our analytical approach and we compare with those resulting from N-body simulations. We show that the results of analytical solutions are in good agreement with those of path simulations but differ significantly from those derived from approximated solutions. Additionally, multiplicity functions derived from fractional Brownian motion are poor fits of the those which result from N-body simulations. We also present comparisons with other models which are exist in the literature and we discuss different ways of improving the agreement between analytical results and N-body simulations.
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.
Nonlinear optomechanical measurement of mechanical motion
Brawley, G.A.; Vanner, M R; Larsen, Peter Emil
2016-01-01
Precision measurement of nonlinear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing...... with otherwise linear interactions. In cavity optomechanics much progress has been made using linear interactions and measurement, but observation of nonlinear mechanical degrees-of-freedom remains outstanding. Here we report the observation of displacement-squared thermal motion of a micro-mechanical resonator...... by exploiting the intrinsic nonlinearity of the radiation-pressure interaction. Using this measurement we generate bimodal mechanical states of motion with separations and feature sizes well below 100 pm. Future improvements to this approach will allow the preparation of quantum superposition states, which can...
Ground motion estimation and nonlinear seismic analysis
McCallen, D.B.; Hutchings, L.J.
1995-08-14
Site specific predictions of the dynamic response of structures to extreme earthquake ground motions are a critical component of seismic design for important structures. With the rapid development of computationally based methodologies and powerful computers over the past few years, engineers and scientists now have the capability to perform numerical simulations of many of the physical processes associated with the generation of earthquake ground motions and dynamic structural response. This paper describes application of a physics based, deterministic, computational approach for estimation of earthquake ground motions which relies on site measurements of frequently occurring small (i.e. M < 3 ) earthquakes. Case studies are presented which illustrate application of this methodology for two different sites, and nonlinear analyses of a typical six story steel frame office building are performed to illustrate the potential sensitivity of nonlinear response to site conditions and proximity to the causative fault.
First passage times for a tracer particle in single file diffusion and fractional Brownian motion.
Sanders, Lloyd P; Ambjörnsson, Tobias
2012-05-01
We investigate the full functional form of the first passage time density (FPTD) of a tracer particle in a single-file diffusion (SFD) system whose population is: (i) homogeneous, i.e., all particles having the same diffusion constant and (ii) heterogeneous, with diffusion constants drawn from a heavy-tailed power-law distribution. In parallel, the full FPTD for fractional Brownian motion [fBm-defined by the Hurst parameter, H ∈ (0, 1)] is studied, of interest here as fBm and SFD systems belong to the same universality class. Extensive stochastic (non-Markovian) SFD and fBm simulations are performed and compared to two analytical Markovian techniques: the method of images approximation (MIA) and the Willemski-Fixman approximation (WFA). We find that the MIA cannot approximate well any temporal scale of the SFD FPTD. Our exact inversion of the Willemski-Fixman integral equation captures the long-time power-law exponent, when H ≥ 1/3, as predicted by Molchan [Commun. Math. Phys. 205, 97 (1999)] for fBm. When H systems are compared to their fBm counter parts; and in the homogeneous system both scaled FPTDs agree on all temporal scales including also, the result by Molchan, thus affirming that SFD and fBm dynamics belong to the same universality class. In the heterogeneous case SFD and fBm results for heterogeneity-averaged FPTDs agree in the asymptotic time limit. The non-averaged heterogeneous SFD systems display a lack of self-averaging. An exponential with a power-law argument, multiplied by a power-law pre-factor is shown to describe well the FPTD for all times for homogeneous SFD and sub-diffusive fBm systems.
Reflecting Brownian motion in two dimensions: Exact asymptotics for the stationary distribution
Jim Dai
2011-01-01
Full Text Available We consider a two-dimensional semimartingale reflecting Brownian motion (SRBM in the nonnegative quadrant. The data of the SRBM consists of a two-dimensional drift vector, a 2 × 2 positive definite covariance matrix, and a 2 × 2 reflection matrix. Assuming the SRBM is positive recurrent, we are interested in tail asymptotic of its marginal stationary distribution along each direction in the quadrant. For a given direction, the marginal tail distribution has the exact asymptotic of the form bxκ exp(–αx as x goes to infinity, where α and b are positive constants and κ takes one of the values –3/2, –1/2, 0, or 1; both the decay rate α and the power κ can be computed explicitly from the given direction and the SRBM data.A key tool in our proof is a relationship governing the moment generating function of the two-dimensional stationary distribution and two moment generating functions of the associated one-dimensional boundary measures. This relationship allows us to characterize the convergence domain of the two-dimensional moment generating function. For a given direction c, the line in this direction intersects the boundary of the convergence domain at one point, and that point uniquely determines the decay rate α. The one-dimensional moment generating function of the marginal distribution along direction c has a singularity at α. Using analytic extension in complex analysis, we characterize the precise nature of the singularity there. Using that characterization and complex inversion techniques, we obtain the exact asymptotic of the marginal tail distribution.
Haddad, Zoubida [Department of Mechanical Engineering, Technology Faculty, Firat University, TR-23119, Elazig (Turkey); Department of Fluid Mechanics, Faculty of Physics, University of Sciences and Technology-Houari Boumediene, Algiers (Algeria); Abu-Nada, Eiyad [Department of Mechanical Engineering, King Faisal University, Al-Ahsa 31982 (Saudi Arabia); Oztop, Hakan F. [Department of Mechanical Engineering, Technology Faculty, Firat University, TR-23119, Elazig (Turkey); Mataoui, Amina [Department of Fluid Mechanics, Faculty of Physics, University of Sciences and Technology-Houari Boumediene, Algiers (Algeria)
2012-07-15
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)
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.
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 prob
Feller－Brown 运动的游程与 Tanaka 公式%Excursions and Tananka Formula of Feller-Brownian Motions
杜海霞; 谢栋梁; 李永凤
2013-01-01
The excursion theory of Feller-Brownian motions about the state of 0 was discussed.All the Feller-Brownian motions were structured by using the excursion theory and the Tanaka formula of this kind of processes were given.% 讨论了 Feller－Brown 运动关于状态0的游程理论，利用游程理论构造了所有的 Feller－Brown 运动，并给出了这类过程的 Tanaka 公式。
Nonlinear dynamical characteristics of bed load motion
BAI; Yuchuan; XU; Haijue; XU; Dong
2006-01-01
Bed forms of various kinds that evolve naturally on the bottom of sandy coasts and rivers are a result of the kinematics of bed load transport. Based on the group motion of particles in the bed load within the bottom layer, a study on the nonlinear dynamics of bed load transport is presented in this paper. It is found that some development stages, such as the initiation, the equilibrium sediment transport, and the transition from a smooth bed to sand dunes, can be accounted for by different states in the nonlinear system of the bed load transport. It is verified by comparison with experimental data reported by Laboratoire Nationae D'Hydraulique, Chatou, France, that the evolution from a smooth bed to sand dunes is determined by mutation in the bed load transport. This paper presents results that may offer theoretical explanations to the experimental observations. It is also an attempt to apply the state-of-the-art nonlinear science to the classical sediment transport mechanics.
OpenCL/OpenGL aproach for studying active Brownian motion
Żabicki, Michał A
2011-01-01
This work presents a methodology for studying active Brownian dynamics on ratchet potentials using interoperating OpenCL and OpenGL frameworks. Programing details along with optimization issues are discussed, followed by a comparison of performance on different devices. Time of visualization using OpenGL sharing buffer with OpenCL has been tested against another technique which, while using OpenGL, does not share memory buffer with OpenCL. Both methods has been compared with visualizing data to external software - gnuplot. OpenCL/OpenGL interoperating method has been found the most appropriate to visualize large set of data for which calculation itself is not very long.
Quantum Brownian Motions and Navier-Stokes Weakly Turbulence — a Path Integral Study
Botelho, Luiz C. L.
In this paper, we present a new method to solve exactly the Schrödinger Harmonic oscillator wave equation in the presence of time-dependent parameter. We also apply such technique to solve exactly the problem of random frequency averaged quantum propagator of a harmonic oscillator with white-noise statistics frequency. We still apply our technique to solve exactly the Brownian Quantum Oscillator in the presence of an electric field. Finally, we use these quantum mechanic techniques to solve exactly the Statistical-Turbulence of the Navier-Stokes in a region of fluid random stirring weakly (analytical) coupling through time-dependent Euclidean-Quantum oscillators path-integrals.
Brownian regime of finite-N corrections to particle motion in the XY Hamiltonian mean field model
Ribeiro, Bruno V.; Amato, Marco A.; Elskens, Yves
2016-08-01
We study the dynamics of the N-particle system evolving in the XY Hamiltonian mean field (HMF) model for a repulsive potential, when no phase transition occurs. Starting from a homogeneous distribution, particles evolve in a mean field created by the interaction with all others. This interaction does not change the homogeneous state of the system, and particle motion is approximately ballistic with small corrections. For initial particle data approaching a waterbag, it is explicitly proved that corrections to the ballistic velocities are in the form of independent Brownian noises over a time scale diverging not slower than {N}2/5 as N\\to ∞ , which proves the propagation of molecular chaos. Molecular dynamics simulations of the XY-HMF model confirm our analytical findings.
Brownian regime of finite-N corrections to particle motion in the XY hamiltonian mean field model
Ribeiro, Bruno V; Elskens, Yves
2016-01-01
We study the dynamics of the N-particle system evolving in the XY hamiltonian mean field (HMF) model for a repulsive potential, when no phase transition occurs. Starting from a homogeneous distribution, particles evolve in a mean field created by the interaction with all others. This interaction does not change the homogeneous state of the system, and particle motion is approximately ballistic with small corrections. For initial particle data approaching a waterbag, it is explicitly proved that corrections to the ballistic velocities are in the form of independent brownian noises over a time scale diverging not slower than $N^{2/5}$ as $N \\to \\infty$, which proves the propagation of molecular chaos. Molecular dynamics simulations of the XY-HMF model confirm our analytical findings.
Randrup, Jørgen; Möller, Peter
2011-04-01
Although nuclear fission can be understood qualitatively as an evolution of the nuclear shape, a quantitative description has proven to be very elusive. In particular, until now, there existed no model with demonstrated predictive power for the fission-fragment mass yields. Exploiting the expected strongly damped character of nuclear dynamics, we treat the nuclear shape evolution in analogy with Brownian motion and perform random walks on five-dimensional fission potential-energy surfaces which were calculated previously and are the most comprehensive available. Test applications give good reproduction of highly variable experimental mass yields. This novel general approach requires only a single new global parameter, namely, the critical neck size at which the mass split is frozen in, and the results are remarkably insensitive to its specific value.
Challis, K. J.
2016-12-01
We present a numerical study of the tight-binding approach to overdamped Brownian motion on a tilted periodic potential. In the tight-binding method the probability density is expanded on a basis of Wannier states to transform the Smoluchowski equation to a discrete master equation that can be interpreted in terms of thermal hopping between potential minima. We calculate the Wannier states and hopping rates for a variety of potentials, including tilted cosine and ratchet potentials. For deep potential minima the Wannier states are well localized and the hopping rates between nearest-neighbor states are qualitatively well described by Kramers' escape rate. The next-nearest-neighbor hopping rates are negative and must be negligible compared to the nearest-neighbor rates for the discrete master equation treatment to be valid. We find that the validity of the master equation extends beyond the quantitative applicability of Kramers' escape rate.
Tejedor, V; Benichou, O; Voituriez, R [Laboratoire de Physique Theorique de la Matiere Condensee (UMR 7600), Universite Pierre et Marie Curie, 4 Place Jussieu, 75255 Paris Cedex (France); Metzler, Ralf, E-mail: voiturie@lptmc.jussieu.fr [Physics Department, Technical University of Munich, James Franck Strasse, 85747 Garching (Germany)
2011-06-24
We derive a functional equation for the mean first-passage time (MFPT) of a generic self-similar Markovian continuous process to a target in a one-dimensional domain and obtain its exact solution. We show that the obtained expression of the MFPT for continuous processes is actually different from the large system size limit of the MFPT for discrete jump processes allowing leapovers. In the case considered here, the asymptotic MFPT admits non-vanishing corrections, which we call residual MFPT. The case of Levy flights with diverging variance of jump lengths is investigated in detail, in particular, with respect to the associated leapover behavior. We also show numerically that our results apply with good accuracy to fractional Brownian motion, despite its non-Markovian nature.
Randrup, Jorgen
2011-01-01
Although nuclear fission can be understood qualitatively as an evolution of the nuclear shape, a quantitative description has proven to be very elusive. In particular, until now, there exists no model with demonstrated predictive power for the fission fragment mass yields. Exploiting the expected strongly damped character of nuclear dynamics, we treat the nuclear shape evolution in analogy with Brownian motion and perform random walks on five-dimensional fission potential-energy surfaces which were calculated previously and are the most comprehensive available. Test applications give good reproduction of highly variable experimental mass yields. This novel general approach requires only a single new global parameter, namely the critical neck size at which the mass split is frozen in, and the results are remarkably insensitive to its specific value.
Safdari, Hadiseh; Cherstvy, Andrey G.; Chechkin, Aleksei V.; Bodrova, Anna; Metzler, Ralf
2017-01-01
We investigate both analytically and by computer simulations the ensemble- and time-averaged, nonergodic, and aging properties of massive particles diffusing in a medium with a time dependent diffusivity. We call this stochastic diffusion process the (aging) underdamped scaled Brownian motion (UDSBM). We demonstrate how the mean squared displacement (MSD) and the time-averaged MSD of UDSBM are affected by the inertial term in the Langevin equation, both at short, intermediate, and even long diffusion times. In particular, we quantify the ballistic regime for the MSD and the time-averaged MSD as well as the spread of individual time-averaged MSD trajectories. One of the main effects we observe is that, both for the MSD and the time-averaged MSD, for superdiffusive UDSBM the ballistic regime is much shorter than for ordinary Brownian motion. In contrast, for subdiffusive UDSBM, the ballistic region extends to much longer diffusion times. Therefore, particular care needs to be taken under what conditions the overdamped limit indeed provides a correct description, even in the long time limit. We also analyze to what extent ergodicity in the Boltzmann-Khinchin sense in this nonstationary system is broken, both for subdiffusive and superdiffusive UDSBM. Finally, the limiting case of ultraslow UDSBM is considered, with a mixed logarithmic and power-law dependence of the ensemble- and time-averaged MSDs of the particles. In the limit of strong aging, remarkably, the ordinary UDSBM and the ultraslow UDSBM behave similarly in the short time ballistic limit. The approaches developed here open ways for considering other stochastic processes under physically important conditions when a finite particle mass and aging in the system cannot be neglected.
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."
Restoration of nonlinear motion-distorted composite frame
Yitzhaky, Yitzhak; Stern, Adrian; Kopeika, Norman S.
2000-12-01
A composite frame image is an interlaced composition of two sub-image odd and even fields. Such image type is common in many imaging systems that produce video sequences. When relative motion between the camera and the scene occurs during the imaging process, two types of distortion degrade the image: the edge 'staircase effect' due to the shifted appearances of the objects in successive fields, and blur due to the scene motion during each field exposure. This paper deals with restoration of composite frame images degraded by motion. In contrast to other previous works that dealt with only uniform velocity motion, here we consider a more general case of nonlinear motion. Since conventional motion identification techniques used in other works can not be employed in the case of nonlinear motion, a new method for identification of the motion from each field is used. Results of motion identification and image restoration for various motion types are presented.
Yu, Hsiu-Yu; Eckmann, David M; Ayyaswamy, Portonovo S; Radhakrishnan, Ravi
2015-05-01
We present a composite generalized Langevin equation as a unified framework for bridging the hydrodynamic, Brownian, and adhesive spring forces associated with a nanoparticle at different positions from a wall, namely, a bulklike regime, a near-wall regime, and a lubrication regime. The particle velocity autocorrelation function dictates the dynamical interplay between the aforementioned forces, and our proposed methodology successfully captures the well-known hydrodynamic long-time tail with context-dependent scaling exponents and oscillatory behavior due to the binding interaction. Employing the reactive flux formalism, we analyze the effect of hydrodynamic variables on the particle trajectory and characterize the transient kinetics of a particle crossing a predefined milestone. The results suggest that both wall-hydrodynamic interactions and adhesion strength impact the particle kinetics.
Non-Markovian Brownian motion in a magnetic field and time-dependent force fields
Hidalgo-Gonzalez, J. C.; Jiménez-Aquino, J. I.; Romero-Bastida, M.
2016-11-01
This work focuses on the derivation of the velocity and phase-space generalized Fokker-Planck equations for a Brownian charged particle embedded in a memory thermal bath and under the action of force fields: a constant magnetic field and arbitrary time-dependent force fields. To achieve the aforementioned goal we use a Gaussian but non-Markovian generalized Langevin equation with an arbitrary friction memory kernel. In a similar way, the generalized diffusion equation in the zero inertia limit is also derived. Additionally we show, in the absence of the time-dependent external forces, that, if the fluctuation-dissipation relation of the second kind is valid, then the generalized Langevin dynamics associated with the charged particle reaches a stationary state in the large-time limit. The consistency of our theoretical results is also verified when they are compared with those derived in the absence of the force fields and in the Markovian case.
Characterization of Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes
2016-04-20
Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 62601F...AFRL-RV-PS- AFRL-RV-PS- TR-2015-0182 TR-2015-0182 CHARACTERIZATION OF NON-LINEARIZED SPACECRAFT RELATIVE MOTION USING NONLINEAR NORMAL MODES Eric...STATEMENT. THOMAS LOVELL PAUL HAUSGEN, Ph.D. Program Manager Technical Advisor, Spacecraft Component Technology JOHN BEAUCHEMIN Chief Engineer
Ikeda, Tatsushi; Tanimura, Yoshitaka
2015-01-01
We explore and describe the roles of inter-molecular vibrations in terms of a Brownian oscillator (BO) model with linear-linear (LL) and square-linear (SL) system-bath interactions, which we use to analyze two-dimensional (2D) THz-Raman spectra obtained by means of molecular dynamics (MD) simulations. In addition to linear absorption (1D IR), we calculate 2D Raman-THz-THz, THz-Raman-THz, and THz-THz-Raman signals for liquid formamide, water, and methanol using an equilibrium non-equilibrium hybrid MD simulation. The calculated 1D IR and 2D THz-Raman signals are then accounted by the LL+SL BO model with the use of the hierarchal Fokker-Planck equations for a non-perturbative and non-Markovian noise. All of the characteristic 2D profiles of the simulated signals are reproduced using the LL+SL BO model, indicating that the present model captures the essential features of the inter-molecular motion. We analyze the fitted the 2D profiles in terms of anharmonicity, nonlinear polarizability, and dephasing time. The ...
Eka Putri, Irana; Gita Redhyka, Grace
2017-07-01
Micro-air-bubble has a high potential contribution in waste water, farming, and fishery treatment. In this research, submicron scale of micro-air-bubble was observed to determine its stability in H2O solvent. By increasing its stability, it can be used for several applications, such as bio-preservative for medical and food transport. The micro-air-bubble was assumed in spherical shape that in incompressible gas boundary condition. So, the random motion of particle (Brownian motion) can be solved by using Stokes-Einstein approximation. But, Hadamard and Rybczynski equation is promoted to solve for larger bubble (micro scale). While, the effect of physical properties (e.g. diffusion coefficient, density, and flow rate) have taken important role in its characteristics in water. According to the theoretical investigation that have been done, decreasing of bubble velocity indicates that the bubble dissolves away or shrinking to the surface. To obtain longevity bubble in pure water medium, it is recomended to apply some surfactant molecules (e.g. NaCl) in micro-air-bubble medium.
On the weak convergence of super-Brownian mo-tion with immigration
ZHANG Mei
2009-01-01
We prove fluctuation limit theorems for the occupation times of super-Brownish motion with immigration. The weak convergence of the processes is established, which improves the results in references. The limiting processes are Gaussian processes.
A Second-Order Stochastic Leap-Frog Algorithm for Multiplicative Noise Brownian Motion
Qiang, J; Qiang, Ji; Habib, Salman
1999-01-01
A stochastic leap-frog algorithm for the numerical integration of Brownianmotion stochastic differential equations with multiplicative noise is proposedand tested. The algorithm has a second-order convergence of moments in a finitetime interval and requires the sampling of only one uniformly distributedrandom variable per time step. The noise may be white or colored. We apply thealgorithm to a study of the approach towards equilibrium of an oscillatorcoupled nonlinearly to a heat bath and investigate the effect of themultiplicative noise (arising from the nonlinear coupling) on the relaxationtime. This allows us to test the regime of validity of the energy-envelopeapproximation method.
Roura, Albert [Los Alamos National Laboratory; Fleming, C H [UNIV OF MARYLAND; Hu, B L [UNIV OF MARYLAND
2008-01-01
We revisit the model of a system made up of a Brownian quantum oscillator linearly coupled to an environment made up of many quantum oscillators at finite temperature. We show that the HPZ master equation for the reduced density matrix derived earlier [B.L. Hu, J.P. Paz, Y. Zhang, Phys. Rev. D 45, 2843 (1992)] has incorrectly specified coefficients for the case of nonlocal dissipation. We rederive the QBM master equation, correctly specifying all coefficients, and determine the position uncertainty to be free of excessive cutoff sensitivity. Our coefficients and solutions are reduced entirely to contour integration for analytic spectra at arbitrary temperature, coupling strength, and cut-off. As an illustration we calculate the master equation coefficients and solve the master equation for ohmic coupling (with finite cutoff) and example supra-ohmic and sub-ohmic spectral densities. We determine the effect of an external force on the quantum oscillator and also show that our representation of the master equation and solutions naturally extends to a system of multiple oscillators bilinearly coupled to themselves and the bath in arbitrary fashion. This produces a formula for investigating the standard quantum limit which is central to addressing many theoretical issues in macroscopic quantum phenomena and experimental concerns related to low temperature precision measurements. We find that in a dissipative environment, all initial states settle down to a Gaussian density matrix whose covariance is determined by the thermal reservoir and whose mean is determined by the external force. We specify the thermal covariance for the spectral densities we explore.
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.
An exactly solvable model for Brownian motion : I. Derivation of the Langevin equation
Ullersma, P.
1966-01-01
The motion of an elastically bound particle, linearly coupled with a bath of N harmonic oscillators is calculated exactly. The interaction is assumed to be rather weak and to vary slowly as function of the frequencies of the oscillators. The bath is chosen at the initial time in thermal equilibrium.
Jumarie, Guy [Department of Mathematics, University of Quebec at Montreal, P.O. Box 8888, Downtown Station, Montreal, QC, H3C 3P8 (Canada)]. E-mail: jumarie.guy@uqam.ca
2006-06-15
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{sub {alpha}}(h{sup {alpha}}D{sub z}{sup {alpha}}).f(z), where E{sub {alpha}} 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){sup {alpha}}, 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.
Li, Chien-Cheng; Hau, Nga Yu; Wang, Yuechen; Soh, Ai Kah; Feng, Shien-Ping
2016-06-01
Ethanol-based nanofluids have attracted much attention due to the enhancement in heat transfer and their potential applications in nanofluid-type fuels and thermal storage. Most research has been conducted on ethanol-based nanofluids containing various nanoparticles in low mass fraction; however, to-date such studies based on high weight fraction of nanoparticles are limited due to the poor stability problem. In addition, very little existing work has considered the inevitable water content in ethanol for the change of thermal conductivity. In this paper, the highly stable and well-dispersed TiO2-ethanol nanofluids of high weight fraction of up to 3 wt% can be fabricated by stirred bead milling, which enables the studies of thermal conductivity of TiO2-ethanol nanofluids over a wide range of operating temperatures. Our results provide evidence that the enhanced thermal conductivity is mainly contributed by the percolation network of nanoparticles at low temperatures, while it is in combination with both Brownian motion and local percolation of nanoparticle clustering at high temperatures.
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)
De-Lei Sheng
2014-01-01
Full Text Available This paper investigates the excess-of-loss reinsurance and investment problem for a compound Poisson jump-diffusion risk process, with the risk asset price modeled by a constant elasticity of variance (CEV model. It aims at obtaining the explicit optimal control strategy and the optimal value function. Applying stochastic control technique of jump diffusion, a Hamilton-Jacobi-Bellman (HJB equation is established. Moreover, we show that a closed-form solution for the HJB equation can be found by maximizing the insurer’s exponential utility of terminal wealth with the independence of two Brownian motions W(t and W1(t. A verification theorem is also proved to verify that the solution of HJB equation is indeed a solution of this optimal control problem. Then, we quantitatively analyze the effect of different parameter impacts on optimal control strategy and the optimal value function, which show that optimal control strategy is decreasing with the initial wealth x and decreasing with the volatility rate of risk asset price. However, the optimal value function V(t;x;s is increasing with the appreciation rate μ of risk asset.
Dipole-Dipole Interaction and the Directional Motion of Brownian Motors
YU Hui; ZHAO TongJun; JI Qing; SONG YanLi; WANG YongHong; ZHAN Yong
2002-01-01
The electric field of the microtubule is calculated according to its dipole distribution. The conformationalchange of a molecular motor is described by the rotation ofa dipole which interacts with the microtubulc. The mricalsimulation for the particle current shows that this interaction helps to produce a directional motion along the microtubule.And tte average displacement executes step changes that resemble the experimental result for kinesin motors.
Jumarie, Guy E-mail: jumarie.guy@uqam.ca
2004-11-01
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.
Characterizing N-dimensional anisotropic Brownian motion by the distribution of diffusivities
Heidernätsch, Mario; Radons, Günter
2013-01-01
Anisotropic diffusion processes emerge in various fields such as transport in biological tissue and diffusion in liquid crystals. In such systems, the motion is described by a diffusion tensor. For a proper characterization of processes with more than one diffusion coefficient an average description by the mean squared displacement is often not sufficient. Hence, in this paper, we use the distribution of diffusivities to study diffusion in a homogeneous anisotropic environment. We derive analytical expressions of the distribution and relate its properties to an anisotropy measure in order to distinguish between isotropic and anisotropic processes. We further discuss the influence on the analysis of projected trajectories, which are typically accessible in experiments. For the experimentally relevant cases of two- and three-dimensional anisotropic diffusion we derive the specific expressions, determine the diffusion tensor, characterize the anisotropy, and demonstrate the applicability for simulated trajectori...
Motion of a nano-ellipsoid in a cylindrical vessel flow: Brownian and hydrodynamic interactions
Ramakrishnan, N; Eckmann, D M; Ayyaswamy, P S; Radhakrishnan, Ravi
2016-01-01
We present comprehensive numerical studies of the motion of a buoyant or a nearly neutrally buoyant nano-sized ellipsoidal particle in a fluid filled cylindrical tube without or with the presence of imposed pressure gradient (weak Poiseuille flow). The Fluctuating hydrodynamics approach and the Deterministic method are both employed. We ensure that the fluctuation-dissipation relation and the principle of thermal equipartition of energy are both satisfied. The major focus is on the effect of the confining boundary. Results for the velocity and angular velocity autocorrelations (VACF and AVACF), diffusivities, and drag and lift forces as functions of shape, aspect ratio, inclination angle, and proximity to the wall are presented. For the parameters considered, the boundary modifies the VACF and AVACF such that three distinct regimes are discernible --- an initial exponential decay, followed by an algebraic decay culminating in a second exponential decay. The first is due to thermal noise, the algebraic regime ...
A Coupled Analysis of Nonlinear Sloshing and Ship Motion
Shuo Huang; Wenyang Duan; Hao Zhang
2012-01-01
Nonlinear interactions among incident wave,tank-sloshing and floating body coupling motion are investigated.The fully nonlinear sloshing and body-surface nonlinear free surface hydrodynamics is simulated using a Non-Uniform Rational B-Spline (NURBS) higher-order panel method in time domain based on the potential theory.A robust and stable improved iterative procedure (Yan and Ma,2007) for floating bodies is used for calculating the time derivative of velocity potential and floating body motion.An energy dissipation condition based on linear theory adopted by Huang (2011) is developed to consider flow viscosity effects of sloshing flow in nonlinear model.A two-dimensional tank model test was performed to identify its validity.The present nonlinear coupling sway motion results are subsequently compared with the corresponding Rognebakke and Faltinsen (2003)'s experimental results,showing fair agreement.Thus,the numerical approach presented in this paper is expected to be very efficient and realistic in evaluating the coupling effects of nonlinear sloshing and body motion.
Taheriyoun, Ali R.; Moghimbeygi, Meisam
2017-02-01
An approximation of the fractional Brownian motion based on the Ornstein-Uhlenbeck process is used to obtain an asymptotic likelihood function. Two estimators of the Hurst index are then presented in the likelihood approach. The first estimator is produced according to the observed values of the sample path; while the second one employs the likelihood function of the incremental process. We also employ visual roughness of realization to restrict the parameter space and to obtain prior information in Bayesian approach. The methods are then compared with three contemporary estimators and an experimental data set is studied.
Mohammad Ferdows
2015-01-01
Full Text Available Natural convective boundary-layer flow of a nanofluid on a heated vertical cylinder embedded in a nanofluid-saturated porous medium is studied. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. Lie groups analysis is used to get the similarity transformations, which transform the governing partial differential equations to a system of ordinary differential equations. Two groups of similarity transformations are obtained. Numerical solutions of the resulting ordinary differential systems are obtained and discussed for various values of the governing parameters.
Archimedes' principle for Brownian liquid
Burdzy, Krzysztof; Pal, Soumik
2009-01-01
We consider a family of hard core objects moving as independent Brownian motions confined to a vessel by reflection. These are subject to gravitational forces modeled by drifts. The stationary distribution for the process has many interesting implications, including an illustration of the Archimedes' principle. The analysis rests on constructing reflecting Brownian motion with drift in a general open connected domain and studying its stationary distribution. In dimension two we utilize known results about sphere packing.
Archimedes' principle for Brownian liquid
Burdzy, Krzysztof; Chen, Zhen-Qing; Pal, Soumik
2009-01-01
We consider a family of hard core objects moving as independent Brownian motions confined to a vessel by reflection. These are subject to gravitational forces modeled by drifts. The stationary distribution for the process has many interesting implications, including an illustration of the Archimedes’ principle. The analysis rests on constructing reflecting Brownian motion with drift in a general open connected domain and studying its stationary distribution. In dimension two we utilize known ...
Method and system for non-linear motion estimation
Lu, Ligang (Inventor)
2011-01-01
A method and system for extrapolating and interpolating a visual signal including determining a first motion vector between a first pixel position in a first image to a second pixel position in a second image, determining a second motion vector between the second pixel position in the second image and a third pixel position in a third image, determining a third motion vector between one of the first pixel position in the first image and the second pixel position in the second image, and the second pixel position in the second image and the third pixel position in the third image using a non-linear model, determining a position of the fourth pixel in a fourth image based upon the third motion vector.
Hanasaki, Itsuo; Nagura, Ryo; Kawano, Satoyuki
2015-03-14
The Brownian motion of a particle in a fluid is often described by the linear Langevin equation, in which it is assumed that the mass of the particle is sufficiently large compared to the surrounding fluid molecules. This assumption leads to a diffusion coefficient that is independent of the particle mass. The Stokes-Einstein equation indicates that the diffusion coefficient depends solely on the particle size, but the concept of size can be ambiguous when close to the molecular scale. We first examine the Brownian motion of simple model particles based on short-range interactions in water by the molecular dynamics method and show that the diffusion coefficient can vary with mass when this mass is comparable to that of the solvent molecules, and that this effect is evident when the solute particle size is sufficiently small. We then examine the properties of a water molecule considered as a solute in the bulk solvent consisting of the remainder of the water. A comparison with simple solute models is used to clarify the role of force fields. The long-range Coulomb interaction between water molecules is found to lead to a Gaussian force distribution in spite of a mass ratio and nominal size ratio of unity, such that solutes with short-range interactions exhibit non-Gaussian force distribution. Thus, the range of the interaction distance determines the effective size even if it does not represent the volume excluded by the repulsive force field.
Switching of myosin-V motion between the lever-arm swing and brownian search-and-catch.
Fujita, Keisuke; Iwaki, Mitsuhiro; Iwane, Atsuko H; Marcucci, Lorenzo; Yanagida, Toshio
2012-07-17
Motor proteins are force-generating nanomachines that are highly adaptable to their ever-changing biological environments and have a high energy conversion efficiency. Here we constructed an imaging system that uses optical tweezers and a DNA handle to visualize elementary mechanical processes of a nanomachine under load. We apply our system to myosin-V, a well-known motor protein that takes 72 nm 'hand-over-hand' steps composed of a 'lever-arm swing' and a 'brownian search-and-catch'. We find that the lever-arm swing generates a large proportion of the force at low load (high load (1.9 pN), however, the contribution of the brownian search-and-catch increases to dominate, reaching 13 k(B)T of work. We believe the ability to switch between these two force-generation modes facilitates myosin-V function at high efficiency while operating in a dynamic intracellular environment.
New Evidence for Nonlinearity in Strong Ground Motion
Beroza, G. C.; Schaff, D. P.
2001-12-01
Dynamic strains associated with the strong ground motion of large earthquakes are well within the regime found to show nonlinearity in the laboratory; however, evidence for nonlinearity in recorded seismic waves is often ambiguous and controversial. We present new and independent evidence that nonlinearity in strong ground motion may be widespread. The evidence consists of velocity changes measured by repeating microearthquakes in the aftermath of the 1984 M=6.2 Morgan Hill and 1989 M=6.9 Loma Prieta events. We have identified over 20 sets of repeating earthquakes in the aftershock zones of these mainshocks that contain up to 40 repeats of the same event. Waveform analysis reveals clearly detectable delays of arrivals from events after the Loma Prieta earthquake, compared with events before, of as much as 3.5% in the early S-wave coda. Source array analysis and waveform similarity over a wide range of source-receiver distances both suggest that the early coda is generated by scattering in the shallow crust near the receiver. We find that the magnitude of the velocity change decreases logarithmically in time following the Loma Prieta mainshock. We have not yet recovered repeating earthquake seismograms from before the Morgan Hill earthquake; however, we observe a clear post-seismic increase in velocity, again with a logarithmic time dependence, suggesting that the same effect accompanied both events. Recent experiments indicate that velocity decreases followed by logarithmic recovery in time accompany recoverable nonlinearity in laboratory samples at ambient conditions [Ten Cate et al., 2000]. Thus, we believe that we have detected the lingering effects of nonlinear mainshock strong ground motion in the time-varying wave propagation characteristics of the Earth's crust. The changes are strongly concentrated near the rupture zones of the two mainshocks; however, the effect is also observed at more distant stations. We use our observations to illuminate the possible
分支依赖于人口总数的具有交互作用的超布朗运动%Interacting Super-Brownian Motions Depending on Population Size
陈丽; 闫国军
2008-01-01
In this paper,we investigate the interacting super-Brownian motion depending on population size.This process can be viewed as the high density limit of a sequence of particle systems with branching mechanism depending on their population size.We will construct a limit function-valued dual process.
Zhu, Jie
There exist dual-listed stocks which are issued by the same company in some stock markets. Although these stocks bare the same firm-specific risk and enjoy identical dividends and voting policies, they are priced differently. Some previous studies show this seeming deviation from the law of one...... price can be solved due to different ex- pected return and market price of risk for investors holding heterogeneous beliefs. This paper provides empirical evidence for that argument by testing the expected return and market price of risk between Chinese A and B shares listed in Shanghai and Shenzhen...... stock markets. Models with dynamic of Geometric Brownian Motion are adopted, multivariate GARCH models are also introduced to capture the feature of time-varying volatility in stock returns. The results suggest that the different pric- ing can be explained by the difference in expected returns between...
Zhu, Jie
There exist dual-listed stocks which are issued by the same company in some stock markets. Although these stocks bare the same firm-specific risk and enjoy identical dividends and voting policies, they are priced differently. Some previous studies show this seeming deviation from the law of one...... price can be solved due to different ex- pected return and market price of risk for investors holding heterogeneous beliefs. This paper provides empirical evidence for that argument by testing the expected return and market price of risk between Chinese A and B shares listed in Shanghai and Shenzhen...... stock markets. Models with dynamic of Geometric Brownian Motion are adopted, multivariate GARCH models are also introduced to capture the feature of time-varying volatility in stock returns. The results suggest that the different pric- ing can be explained by the difference in expected returns between...
Brownian ratchets in physics and biology
Bier, Martin
1997-06-01
Thirty years ago Feynman et al. presented a paradox in the Lectures on Physics: an imagined device could let Brownian motion do work by allowing it in one direction and blocking it in the opposite direction. In the chapter Feynman et al. eventually show that such ratcheting can only be achieved if there is, in compliance with the basic conservation laws, some energy input from an external source. Now that technology is going into ever smaller dimensions, ratcheting Brownian motion seems to be a real possibility in nanotechnological applications. Furthermore, Brownian motion plays an essential role in the action of motor proteins (individual molecules that convert chemical energy into motion).
Realising traceable electrostatic forces despite non-linear balance motion
Stirling, Julian; Shaw, Gordon A.
2017-05-01
Direct realisation of force, traceable to fundamental constants via electromagnetic balances, is a key goal of the proposed redefinition of the international system of units (SI). This will allow small force metrology to be performed using an electrostatic force balance (EFB) rather than subdivision of larger forces. Such a balance uses the electrostatic force across a capacitor to balance an external force. In this paper we model the capacitance of a concentric cylinder EFB design as a function of the displacement of its free electrode, accounting for the arcuate motion produced by parallelogram linkages commonly used in EFB mechanisms. From this model we suggest new fitting procedures to reduce uncertainties arising from non-linear motion as well as methods to identify misalignment of the mechanism. Experimental studies on both a test capacitor and the NIST EFB validate the model.
Simplified Methods Applied to Nonlinear Motion of Spar Platforms
Haslum, Herbjoern Alf
2000-07-01
Simplified methods for prediction of motion response of spar platforms are presented. The methods are based on first and second order potential theory. Nonlinear drag loads and the effect of the pumping motion in a moon-pool are also considered. Large amplitude pitch motions coupled to extreme amplitude heave motions may arise when spar platforms are exposed to long period swell. The phenomenon is investigated theoretically and explained as a Mathieu instability. It is caused by nonlinear coupling effects between heave, surge, and pitch. It is shown that for a critical wave period, the envelope of the heave motion makes the pitch motion unstable. For the same wave period, a higher order pitch/heave coupling excites resonant heave response. This mutual interaction largely amplifies both the pitch and the heave response. As a result, the pitch/heave instability revealed in this work is more critical than the previously well known Mathieu's instability in pitch which occurs if the wave period (or the natural heave period) is half the natural pitch period. The Mathieu instability is demonstrated both by numerical simulations with a newly developed calculation tool and in model experiments. In order to learn more about the conditions for this instability to occur and also how it may be controlled, different damping configurations (heave damping disks and pitch/surge damping fins) are evaluated both in model experiments and by numerical simulations. With increased drag damping, larger wave amplitudes and more time are needed to trigger the instability. The pitch/heave instability is a low probability of occurrence phenomenon. Extreme wave periods are needed for the instability to be triggered, about 20 seconds for a typical 200m draft spar. However, it may be important to consider the phenomenon in design since the pitch/heave instability is very critical. It is also seen that when classical spar platforms (constant cylindrical cross section and about 200m draft
Radially Symmetric Motions of Nonlinearly Viscoelastic Bodies Under Live Loads
Stepanov, Alexey B.; Antman, Stuart S.
2017-08-01
This paper treats radially symmetric motions of nonlinearly viscoelastic circular-cylindrical and spherical shells subjected to the live loads of centrifugal force and (time-dependent) hydrostatic pressures. The governing equations are exact versions of those for 3-dimensional continuum mechanics (so shell does not connote an approximate via some shell theory). These motions are governed by quasilinear third-order parabolic-hyperbolic equations having but one independent spatial variable. The principal part of such a partial differential equation is determined by a general family of nonlinear constitutive equations. The presence of strains in two orthogonal directions requires a careful treatment of constitutive restrictions that are physically natural and support the analysis. The interaction of geometrically exact formulations, the compatible use of general constitutive equations for material response, and the presence of live loads show how these factors play crucial roles in the behavior of solutions. In particular, for different kinds of live loads there are thresholds separating materials that produce qualitatively different dynamical behavior. The analysis (using classical methods) covers infinite-time blowup for cylindrical shells subject to centrifugal forces, infinite-time blowup for cylindrical shells subject to steady and time-dependent hydrostatic pressures, finite-time blowup for spherical shells subject to steady and time-dependent hydrostatic pressures, and the preclusion of total compression. This paper concludes with a sketch (using some modern methods) of the existence of regular solutions until the time of blowup.
Tsekov, Roumen
2016-06-01
A Brownian harmonic oscillator, which dissipates energy either by friction or via emission of electromagnetic radiation, is considered. This Brownian emitter is driven by the surrounding thermo-quantum fluctuations, which are theoretically described by the fluctuation-dissipation theorem. It is shown how the Abraham-Lorentz force leads to dependence of the half-width on the peak frequency of the oscillator amplitude spectral density. It is found that for the case of a charged particle moving in vacuum at zero temperature, its root-mean-square velocity fluctuation is a universal constant, equal to roughly 1/18 of the speed of light. The relevant Fokker-Planck and Smoluchowski equations are also derived.
Malgaretti, Paolo; Pagonabarraga, Ignacio; Rubi, J Miguel
2013-05-21
We analyze the dynamics of Brownian ratchets in a confined environment. The motion of the particles is described by a Fick-Jakobs kinetic equation in which the presence of boundaries is modeled by means of an entropic potential. The cases of a flashing ratchet, a two-state model, and a ratchet under the influence of a temperature gradient are analyzed in detail. We show the emergence of a strong cooperativity between the inherent rectification of the ratchet mechanism and the entropic bias of the fluctuations caused by spatial confinement. Net particle transport may take place in situations where none of those mechanisms leads to rectification when acting individually. The combined rectification mechanisms may lead to bidirectional transport and to new routes to segregation phenomena. Confined Brownian ratchets could be used to control transport in mesostructures and to engineer new and more efficient devices for transport at the nanoscale.
A nonlinear piezoelectric energy harvester for various mechanical motions
Fan, Kangqi, E-mail: kangqifan@gmail.com [School of Mechano-Electronic Engineering, Xidian University, Xi' an 710071 (China); Department of Electrical and Computer Engineering, University of Alberta, Edmonton T6G 2V4 (Canada); Chang, Jianwei; Liu, Zhaohui; Zhu, Yingmin [School of Mechano-Electronic Engineering, Xidian University, Xi' an 710071 (China); Pedrycz, Witold [Department of Electrical and Computer Engineering, University of Alberta, Edmonton T6G 2V4 (Canada)
2015-06-01
This study presents a nonlinear piezoelectric energy harvester with intent to scavenge energy from diverse mechanical motions. The harvester consists of four piezoelectric cantilever beams, a cylindrical track, and a ferromagnetic ball, with magnets integrated to introduce the magnetic coupling between the ball and the beams. The experimental results demonstrate that the harvester is able to collect energy from various directions of vibrations. For the vibrations perpendicular to the ground, the maximum peak voltage is increased by 3.2 V and the bandwidth of the voltage above 4 V is increased by more than 4 Hz compared to the results obtained when using a conventional design. For the vibrations along the horizontal direction, the frequency up-conversion is realized through the magnetic coupling. Moreover, the proposed design can harvest energy from the sway motion around different directions on the horizontal plane. Harvesting energy from the rotation motion is also achieved with an operating bandwidth of approximately 6 Hz.
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 fora
FU Xiang-Yun; YU Hong-Wei
2007-01-01
We study the random motion of a charged test particle with a normal classical constant velocity in a spacetime with a perfectly reflecting plane boundary and calculate both the velocity and position dispersions of the test particle. Our results show that the dispersions in the normal direction are weakened while those in the parallel directions are strengthened as compared to the classical static case when the test particle classically moves away from the boundary.However, if the classical motion reverses its direction, then the dispersions in the normal direction are reinforced while those in the parallel directions get weakened.
苗杰
2013-01-01
Under the fractional brownian motion, we supposes that risk-free rate, dividend rate, anticipated returns ratio and fluctuating rate of the stock all are the definite continue function of time. By the equal qusi-martingale measure method, we discuss the pricing of the convertible bond with dividend-paying under the fractional Brownian motion and obtain pricing formula of the convertible bond.%在分数布朗运动环境下，假设股票的预期收益率、波动率、红利率和无风险利率都是时间的确定性连续函数，用通过等价概率测度变换，用拟鞅的方法，得到了分数布朗运动下有红利支付的可转换债券的定价公式。
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
Sun, Bo; Lin, Jiayi; Darby, Ellis; Grosberg, Alexander Y.; Grier, David G.
2009-07-01
Mechanical equilibrium at zero temperature does not necessarily imply thermodynamic equilibrium at finite temperature for a particle confined by a static but nonconservative force field. Instead, the diffusing particle can enter into a steady state characterized by toroidal circulation in the probability flux, which we call a Brownian vortex. The circulatory bias in the particle’s thermally driven trajectory is not simply a deterministic response to the solenoidal component of the force but rather reflects interplay between advection and diffusion in which thermal fluctuations extract work from the nonconservative force field. As an example of this previously unrecognized class of stochastic heat engines, we consider a colloidal sphere diffusing in a conventional optical tweezer. We demonstrate both theoretically and experimentally that nonconservative optical forces bias the particle’s fluctuations into toroidal vortexes whose circulation can reverse direction with temperature or laser power.
NONLINEAR DYNAMICAL BIFURCATION AND CHAOTIC MOTION OF SHALLOW CONICAL LATTICE SHELL
WANG Xin-zhi; HAN Ming-jun; ZHAO Yan-ying; ZHAO Yong-gang
2006-01-01
The nonlinear dynamical equations of axle symmetry are established by the method of quasi-shells for three-dimensional shallow conical single-layer lattice shells. The compatible equations are given in geometrical nonlinear range. A nonlinear differential equation containing the second and the third order nonlinear items is derived under the boundary conditions of fixed and clamped edges by the method of Galerkin. The problem of bifurcation is discussed by solving the Floquet exponent. In order to study chaotic motion, the equations of free oscillation of a kind of nonlinear dynamics system are solved. Then an exact solution to nonlinear free oscillation of the shallow conical single-layer lattice shell is found as well. The critical conditions of chaotic motion are obtained by solving Melnikov functions, some phase planes are drawn by using digital simulation proving the existence of chaotic motion.
Application and prediction of geometric Brownian motion on Matlab%基于Matlab的几何运动布朗模型的应用与预测
冯晓龙
2013-01-01
介绍了Matlab计量经济学工具箱在随机微分方程方面的应用.叙述了几何布朗运动模型的定义以及该系统的离散化过程.利用Matlab计量经济学工具箱对某地区证券交易所10年综合指数进行模拟,阐述了随机模型分析数据的步骤,比较了真实值与Euler逼近值之间的误差.最后使用Euler数值方法离散后的方程,以最终的原始数据预测之后20天的综合指数,并与实际值进行了比较.研究结果表明几何布朗运动模型的应用与预测效果良好.%In this paper,the application of econometrics toolbox of Matlab in Stochastic Differential Equation (SDE) was introduced firstly,the definition for Geometric Brownian Motion (GBM) and discrete approximation of this model were discussed.Then,the method and steps of composite index analysis over 10 years of one stock exchange by using econometrics toolbox were showed,and the error between analytic solution and numerical solution of Euler method was displayed.Finally,the values of composite index in this stock exchange were predicted by using the equation of Euler method and initial values of the ending numbers on raw data.The result shows that the application and prediction of GBM are satisfactory.
Li, Jin
2011-01-01
In this paper we consider the Stochastic isothermal, nonlinear, incompressible bipolar viscous fluids driven by a genuine cylindrical fractional Bronwnian motion with Hurst parameter $H \\in (1/4,1/2)$ under Dirichlet boundary condition on 2D square domain. First we prove the existence and regularity of the stochastic convolution corresponding to the stochastic non-Newtonian fluids. Then we obtain the existence and uniqueness results for the stochastic non-Newtonian fluids. Under certain condition, the random dynamical system generated by non-Newtonian fluids has a random attractor.
Nonlinear Doob-Meyer Decomposition with Jumps
Qing Quan LIN
2003-01-01
Concepts of g-supersolution, g-martingale, g-supermartingale are introduced, which arerelated to BSDE with Brownian motion and Poisson point process. A strict comparison theorem,monotonic limit theorem related to this type of BSDE are also discussed. As an application of theseresults, a nonlinear Doob-Meyer decomposition theorem is obtained.
Zhang Wei [College of Mechanical Engineering, Beijing University of Technology, Beijing 100022 (China)] e-mail: sandyzhang0@yahoo.com
2005-11-01
This paper presents an analysis of the chaotic motion and its control for the nonlinear nonplanar oscillations of a cantilever beam subjected to a harmonic axial excitation and transverse excitations at the free end. A new method of controlling chaotic motion for the nonlinear nonplanar oscillations of the cantilever beam, refereed as to the force control approach, is proposed for the first time. The governing nonlinear equations of nonplanar motion under combined parametric and external excitations are obtained. The Galerkin procedure is applied to the governing equation to obtain a two-degree-of-freedom nonlinear system under combined parametric and forcing excitations for the in-plane and out-of-plane modes. The work is focused on the case of 2:1 internal resonance, principal parametric resonance-1/2 subharmonic resonance for the in-plane mode and fundamental parametric resonance-primary resonance for the out-of-plane mode. The method of multiple scales is used to transform the parametrically and externally excited system to the averaged equations which have a constant perturbation force. Based on the averaged equations obtained here, numerical simulation is utilized to discover the periodic and chaotic motions for the nonlinear nonplanar oscillations of the cantilever beam. The numerical results indicate that the transverse excitation in the z direction at the free end can control the chaotic motion to a period n motion or a static state for the nonlinear nonplanar oscillations of the cantilever beam. The methodology of controlling chaotic motion by using the transverse excitation is proposed. The transverse excitation in the z direction at the free end may be thought about to be an open-loop control. For the problem investigated in this paper, this approach is an effective methodology of controlling chaotic motion to a period n motion or a static state for the nonlinear nonplanar oscillations of the cantilever beam.
Integrability of Nonlinear Equations of Motion on Two-Dimensional World Sheet Space-Time
YAN Jun
2005-01-01
The integrability character of nonlinear equations of motion of two-dimensional gravity with dynamical torsion and bosonic string coupling is studied in this paper. The space-like and time-like first integrals of equations of motion are also found.
A new solution procedure for a nonlinear infinite beam equation of motion
Jang, T. S.
2016-10-01
Our goal of this paper is of a purely theoretical question, however which would be fundamental in computational partial differential equations: Can a linear solution-structure for the equation of motion for an infinite nonlinear beam be directly manipulated for constructing its nonlinear solution? Here, the equation of motion is modeled as mathematically a fourth-order nonlinear partial differential equation. To answer the question, a pseudo-parameter is firstly introduced to modify the equation of motion. And then, an integral formalism for the modified equation is found here, being taken as a linear solution-structure. It enables us to formulate a nonlinear integral equation of second kind, equivalent to the original equation of motion. The fixed point approach, applied to the integral equation, results in proposing a new iterative solution procedure for constructing the nonlinear solution of the original beam equation of motion, which consists luckily of just the simple regular numerical integration for its iterative process; i.e., it appears to be fairly simple as well as straightforward to apply. A mathematical analysis is carried out on both natures of convergence and uniqueness of the iterative procedure by proving a contractive character of a nonlinear operator. It follows conclusively,therefore, that it would be one of the useful nonlinear strategies for integrating the equation of motion for a nonlinear infinite beam, whereby the preceding question may be answered. In addition, it may be worth noticing that the pseudo-parameter introduced here has double roles; firstly, it connects the original beam equation of motion with the integral equation, second, it is related with the convergence of the iterative method proposed here.
Impulse Control of Brownian Motion.
1981-11-01
convert some of his cash into securities, and for this he pays a fixed transaction cost K plus a proportional cost of k times the transaction size...securities, incurring a transaction cost of K+kq. (le never liquidates securities except when it is necessary to maintain a positive cash balance.) On the...and incurring a total transaction cost of L+1s. (If the initial cash balance exceeds S, the controller imediately buys enough securities to reduce
Brownian Motion in Planetary Migration
Murray-Clay, R A; Murray-Clay, Ruth A.; Chiang, Eugene I.
2006-01-01
A residual planetesimal disk of mass 10-100 Earth masses remained in the outer solar system following the birth of the giant planets, as implied by the existence of the Oort cloud, coagulation requirements for Pluto, and inefficiencies in planet formation. Upon gravitationally scattering planetesimal debris, planets migrate. Orbital migration can lead to resonance capture, as evidenced here in the Kuiper and asteroid belts, and abroad in extra-solar systems. Finite sizes of planetesimals render migration stochastic ("noisy"). At fixed disk mass, larger (fewer) planetesimals generate more noise. Extreme noise defeats resonance capture. We employ order-of-magnitude physics to construct an analytic theory for how a planet's orbital semi-major axis fluctuates in response to random planetesimal scatterings. To retain a body in resonance, the planet's semi-major axis must not random walk a distance greater than the resonant libration width. We translate this criterion into an analytic formula for the retention effi...
Brownian motion of interacting particles
Ackerson, B.J.
1976-01-01
Guided by the descriptions which are used to describe noninteracting particles, it is argued that the generalized Smoluchowski equation, including the hydrodynamic interaction and corrections for ion cloud effects may be used to describe interacting particles for the temporal and spatial regimes probed by light beating spectroscopy. This equation is then used to find cumulants of decay of the intermediate scattering function. The generalized Smoluchowski equation is reduced to a simple diffusion equation. The resulting diffusion constant depends upon the interparticle forces and is reminiscent of some early descriptions for interacting systems. The generalized Smoluchowski equation is solved for the model system of a linear chain of colloidal particles interacting via nearest neighbor harmonic couplings. The results for the intermediate scattering function and the static structure factor are very reminiscent of corresponding measurements made for interacting colloidal systems. (GHT)
Brownian particles in supramolecular polymer solutions
Gucht, van der J.; Besseling, N.A.M.; Knoben, W.; Bouteiller, L.; Cohen Stuart, M.A.
2003-01-01
The Brownian motion of colloidal particles embedded in solutions of hydrogen-bonded supramolecular polymers has been studied using dynamic light scattering. At short times, the motion of the probe particles is diffusive with a diffusion coefficient equal to that in pure solvent. At intermediate time
Brownian particles in supramolecular polymer solutions
Gucht, van der J.; Besseling, N.A.M.; Knoben, W.; Bouteiller, L.; Cohen Stuart, M.A.
2003-01-01
The Brownian motion of colloidal particles embedded in solutions of hydrogen-bonded supramolecular polymers has been studied using dynamic light scattering. At short times, the motion of the probe particles is diffusive with a diffusion coefficient equal to that in pure solvent. At intermediate time
On intrinsic nonlinear particle motion in compact synchrotrons
Hwang, Kyung Ryun
Due to the low energy and small curvature characteristics of compact synchrotrons, there can be unexpected features that were not present or negligible in high energy accelerators. Nonlinear kinetics, fringe field effect, and space charge effect are those features which become important for low energy and small curvature accelerators. Nonlinear kinematics can limit the dynamics aperture for compact machine even if it consists of all linear elements. The contribution of the nonlinear kinematics on nonlinear optics parameters are first derived. As the dipole bending radius become smaller, the dipole fringe field effect become stronger. Calculation of the Lie map generator and corresponding mapping equation of dipole fringe field is presented. It is found that the higher order nonlinear potential is inverse proportional to powers of fringe field extent and correction to focusing and low order nonlinear potential is proportional to powers of fringe field extent. The fringe field also found to cause large closed orbit deviation for compact synchrotrons. The 2:1 and 4:1 space charge resonances are known to cause beam loss, emittance growth and halo formation for low energy high intensity beams. By numerical simulations, we observe a higher order 6:2 space charge resonance, which can successfully be understood by the concatenation of 2:1 and 4:1 resonances via canonical perturbation. We also develop an explicit symplectic tracking method for compact electrostatic storage rings and explore the feasibility of electric dipole moment (EDM) measurements.
Stochastic Analysis of Nonlinear Coupled Heave-Pitch Motion for the Truss Spar Platform
Wenjun Shen; Yougang Tang
2011-01-01
Considering the static stability and the change of the displacement volume,including the influences of higher order nonlinear terms and the instantaneous wave surface,the nonlinear coupled heave-pitch motion was established in stochastic waves.The responses of heave-pitch coupling motion for the Truss Spar platform were investigated.It was found that,when the characteristic frequency of a stochastic wave is close to the natural heave frequency,the large amplitude pitch motion is induced under the parametric-forced excitation,which is called the Mathieu instability.It was observed that the heave mode energy is transferred to pitch mode when the heave motion amplitude exceeds a certain extent.In addition,the probability of internal resonant heave-pitch motion is greatly reduced while the characteristic wave frequency is away from the natural heave frequency.
Ratcheted electrophoresis of Brownian particles
Kowalik, Mikołaj; Bishop, Kyle J. M.
2016-05-01
The realization of nanoscale machines requires efficient methods by which to rectify unbiased perturbations to perform useful functions in the presence of significant thermal noise. The performance of such Brownian motors often depends sensitively on their operating conditions—in particular, on the relative rates of diffusive and deterministic motions. In this letter, we present a type of Brownian motor that uses contact charge electrophoresis of a colloidal particle within a ratcheted channel to achieve directed transport or perform useful work against an applied load. We analyze the stochastic dynamics of this model ratchet to show that it functions under any operating condition—even in the limit of strong thermal noise and in contrast to existing ratchets. The theoretical results presented here suggest that ratcheted electrophoresis could provide a basis for electrochemically powered, nanoscale machines capable of transport and actuation of nanoscale components.
Approximate solutions of non-linear circular orbit relative motion in curvilinear coordinates
Bombardelli, Claudio; Gonzalo, Juan Luis; Roa, Javier
2016-07-01
A compact, time-explicit, approximate solution of the highly non-linear relative motion in curvilinear coordinates is provided under the assumption of circular orbit for the chief spacecraft. The rather compact, three-dimensional solution is obtained by algebraic manipulation of the individual Keplerian motions in curvilinear, rather than Cartesian coordinates, and provides analytical expressions for the secular, constant and periodic terms of each coordinate as a function of the initial relative motion conditions or relative orbital elements. Numerical test cases are conducted to show that the approximate solution can be effectively employed to extend the classical linear Clohessy-Wiltshire solution to include non-linear relative motion without significant loss of accuracy up to a limit of 0.4-0.45 in eccentricity and 40-45° in relative inclination for the follower. A very simple, quadratic extension of the classical Clohessy-Wiltshire solution in curvilinear coordinates is also presented.
Approximate solutions of non-linear circular orbit relative motion in curvilinear coordinates
Bombardelli, Claudio; Gonzalo, Juan Luis; Roa, Javier
2017-01-01
A compact, time-explicit, approximate solution of the highly non-linear relative motion in curvilinear coordinates is provided under the assumption of circular orbit for the chief spacecraft. The rather compact, three-dimensional solution is obtained by algebraic manipulation of the individual Keplerian motions in curvilinear, rather than Cartesian coordinates, and provides analytical expressions for the secular, constant and periodic terms of each coordinate as a function of the initial relative motion conditions or relative orbital elements. Numerical test cases are conducted to show that the approximate solution can be effectively employed to extend the classical linear Clohessy-Wiltshire solution to include non-linear relative motion without significant loss of accuracy up to a limit of 0.4-0.45 in eccentricity and 40-45° in relative inclination for the follower. A very simple, quadratic extension of the classical Clohessy-Wiltshire solution in curvilinear coordinates is also presented.
张晨; 彭婷; 刘宇佳
2015-01-01
文章将广义自回归条件异方差（generalized autoregressive conditional heteroskedasticity ，GARCH ）模型和分形布朗运动结合引入碳金融期权定价研究中。通过对欧洲碳排放配额（European Union Allowance ， EUA）期货收盘价的样本数据检验，发现其存在尖峰厚尾、条件异方差性和分形特征；采用GARCH模型拟合并预测碳价收益率波动率；将预测的波动率作为输入值代入分形布朗运动期权定价方法，运用蒙特卡罗模拟对EUA期货期权进行定价，并与B‐S期权定价法（Black‐Scholes Option Pricing Model）比较。结果表明，基于GARCH分形布朗运动模型的碳期权定价法预测精度有显著提高。%This paper introduces the idea of combining generalized autoregressive conditional heteroskedasticity (GARCH) model and fractional Brownian motion into carbon option pricing .Firstly ,the test results from closing price of European Union Allowance (EUA) Futures show that obvious peak and fat tails ,heterosce‐dasticity and fractal feature reside in the data .Secondly ,the GARCH model is used to fit the volatility of EUA Futures price ,which can reasonably describe and forecast the time‐varying volatility .With the forecas‐ted volatility being the input in fractional Brownian motion carbon option pricing ,the Monte Carlo simulation is used to simulate the pricing of EUA Futures options ,and then the pricing result is compared with that of Black‐Scholes option pricing model .The result shows that carbon option pricing based on fractional Brownian motion combined with GARCH model can improve the pricing accuracy .
Prediction of Ship Unsteady Maneuvering in Calm Water by a Fully Nonlinear Ship Motion Model
Ray-Qing Lin
2012-01-01
Full Text Available This is the continuation of our research on development of a fully nonlinear, dynamically consistent, numerical ship motion model (DiSSEL. In this study we will report our results in predicting ship motions in unsteady maneuvering in calm water. During the unsteady maneuvering, both the rudder angle, and ship forward speed vary with time. Therefore, not only surge, sway, and yaw motions occur, but roll, pitch and heave motions will also occur even in calm water as heel, trim, and sinkage, respectively. When the rudder angles and ship forward speed vary rapidly with time, the six degrees-of-freedom ship motions and their interactions become strong. To accurately predict the six degrees-of-freedom ship motions in unsteady maneuvering, a universal method for arbitrary ship hull requires physics-based fully-nonlinear models for ship motion and for rudder forces and moments. The numerical simulations will be benchmarked by experimental data of the Pre-Contract DDG51 design and an Experimental Hull Form. The benchmarking shows a good agreement between numerical simulations by the enhancement DiSSEL and experimental data. No empirical parameterization is used, except for the influence of the propeller slipstream on the rudder, which is included using a flow acceleration factor.
RESEARCH OF THE PERIODIC MOTION AND STABILITY OF TWO-DEGREE-OF-FREEDOM NONLINEAR OSCILLATING SYSTEMS
刘俊
2002-01-01
The periodic motion and stability for a class of two-degree-of freedom nonlinear oscillating systems are studied by using the method of Liapunov function.The sufficient conditions which guarantee the existence, uniqueness and asymptotic stability of the periodic solutions are obtained.
Poincaré-MacMillan Equations of Motion for a Nonlinear Nonholonomic Dynamical System
Amjad Hussain; Syed Tauseef Mohyud-Din; Ahmet Yildirim
2012-01-01
MacMillan's equations are extended to Poincaré's formalism,and MacMillan's equations for nonlinear nonholonomic systems are obtained in terms of Poincaré parameters.The equivalence of the results obtained here with other forms of equations of motion is demonstrated.An illustrative example of the theory is provided as well.
The Vestibular System Implements a Linear–Nonlinear Transformation In Order to Encode Self-Motion
Massot, Corentin; Schneider, Adam D.; Chacron, Maurice J.; Cullen, Kathleen E.
2012-01-01
Although it is well established that the neural code representing the world changes at each stage of a sensory pathway, the transformations that mediate these changes are not well understood. Here we show that self-motion (i.e. vestibular) sensory information encoded by VIIIth nerve afferents is integrated nonlinearly by post-synaptic central vestibular neurons. This response nonlinearity was characterized by a strong (∼50%) attenuation in neuronal sensitivity to low frequency stimuli when presented concurrently with high frequency stimuli. Using computational methods, we further demonstrate that a static boosting nonlinearity in the input-output relationship of central vestibular neurons accounts for this unexpected result. Specifically, when low and high frequency stimuli are presented concurrently, this boosting nonlinearity causes an intensity-dependent bias in the output firing rate, thereby attenuating neuronal sensitivities. We suggest that nonlinear integration of afferent input extends the coding range of central vestibular neurons and enables them to better extract the high frequency features of self-motion when embedded with low frequency motion during natural movements. These findings challenge the traditional notion that the vestibular system uses a linear rate code to transmit information and have important consequences for understanding how the representation of sensory information changes across sensory pathways. PMID:22911113
The vestibular system implements a linear-nonlinear transformation in order to encode self-motion.
Massot, Corentin; Schneider, Adam D; Chacron, Maurice J; Cullen, Kathleen E
2012-01-01
Although it is well established that the neural code representing the world changes at each stage of a sensory pathway, the transformations that mediate these changes are not well understood. Here we show that self-motion (i.e. vestibular) sensory information encoded by VIIIth nerve afferents is integrated nonlinearly by post-synaptic central vestibular neurons. This response nonlinearity was characterized by a strong (~50%) attenuation in neuronal sensitivity to low frequency stimuli when presented concurrently with high frequency stimuli. Using computational methods, we further demonstrate that a static boosting nonlinearity in the input-output relationship of central vestibular neurons accounts for this unexpected result. Specifically, when low and high frequency stimuli are presented concurrently, this boosting nonlinearity causes an intensity-dependent bias in the output firing rate, thereby attenuating neuronal sensitivities. We suggest that nonlinear integration of afferent input extends the coding range of central vestibular neurons and enables them to better extract the high frequency features of self-motion when embedded with low frequency motion during natural movements. These findings challenge the traditional notion that the vestibular system uses a linear rate code to transmit information and have important consequences for understanding how the representation of sensory information changes across sensory pathways.
The vestibular system implements a linear-nonlinear transformation in order to encode self-motion.
Corentin Massot
Full Text Available Although it is well established that the neural code representing the world changes at each stage of a sensory pathway, the transformations that mediate these changes are not well understood. Here we show that self-motion (i.e. vestibular sensory information encoded by VIIIth nerve afferents is integrated nonlinearly by post-synaptic central vestibular neurons. This response nonlinearity was characterized by a strong (~50% attenuation in neuronal sensitivity to low frequency stimuli when presented concurrently with high frequency stimuli. Using computational methods, we further demonstrate that a static boosting nonlinearity in the input-output relationship of central vestibular neurons accounts for this unexpected result. Specifically, when low and high frequency stimuli are presented concurrently, this boosting nonlinearity causes an intensity-dependent bias in the output firing rate, thereby attenuating neuronal sensitivities. We suggest that nonlinear integration of afferent input extends the coding range of central vestibular neurons and enables them to better extract the high frequency features of self-motion when embedded with low frequency motion during natural movements. These findings challenge the traditional notion that the vestibular system uses a linear rate code to transmit information and have important consequences for understanding how the representation of sensory information changes across sensory pathways.
Modeling the Nonlinear Motion of the Rat Central Airways.
Ibrahim, G; Rona, A; Hainsworth, S V
2016-01-01
Advances in volumetric medical imaging techniques allowed the subject-specific modeling of the bronchial flow through the first few generations of the central airways using computational fluid dynamics (CFD). However, a reliable CFD prediction of the bronchial flow requires modeling of the inhomogeneous deformation of the central airways during breathing. This paper addresses this issue by introducing two models of the central airways motion. The first model utilizes a node-to-node mapping between the discretized geometries of the central airways generated from a number of successive computed tomography (CT) images acquired dynamically (without breath hold) over the breathing cycle of two Sprague-Dawley rats. The second model uses a node-to-node mapping between only two discretized airway geometries generated from the CT images acquired at end-exhale and at end-inhale along with the ventilator measurement of the lung volume change. The advantage of this second model is that it uses just one pair of CT images, which more readily complies with the radiation dosage restrictions for humans. Three-dimensional computer aided design geometries of the central airways generated from the dynamic-CT images were used as benchmarks to validate the output from the two models at sampled time-points over the breathing cycle. The central airway geometries deformed by the first model showed good agreement to the benchmark geometries within a tolerance of 4%. The central airway geometry deformed by the second model better approximated the benchmark geometries than previous approaches that used a linear or harmonic motion model.
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, emulsi
Magnen, Jacques; Unterberger, Jérémie
2012-03-01
{Let $B=(B_1(t),...,B_d(t))$ be a $d$-dimensional fractional Brownian motion with Hurst index $\\alphacalculus with respect to $B$, or to solving differential equations driven by $B$. We intend to show in a series of papers how to desingularize iterated integrals by a weak, singular non-Gaussian perturbation of the Gaussian measure defined by a limit in law procedure. Convergence is proved by using "standard" tools of constructive field theory, in particular cluster expansions and renormalization. These powerful tools allow optimal estimates, and call for an extension of Gaussian tools such as for instance the Malliavin calculus. After a first introductory paper \\cite{MagUnt1}, this one concentrates on the details of the constructive proof of convergence for second-order iterated integrals, also known as L\\'evy area.
王剑君
2011-01-01
In this paper, a new kind of hybrid model is presented. Under the hypothesis of underlying asset price submitting to multidimensional fractional Brownian motions and Poisson processes, the pricing formulas of two kinds of exotic options are obtained by means of the generalized pricing formula of European contingent claim of the model.%文章假设标的资产价格服从受分数布朗运动和泊松过程共同驱动的一类混合模型,通过这一模型的欧式未定权益的一般定价公式,求出了2种奇异期权的定价公式.
在分数布朗运动下权益指数年金的定价%On Pricing of Equity-Indexed Annuities in Fractional Brownian Motion
郭峰涛
2012-01-01
假设标的资产价格服从几何分数布朗运动,在标的资产有红利支付且红利率和无风险利率为非随机函数的情况下,给出了不同方法下权益指数年金的定价公式.%In this paper, the underlying asset is supposed to be subject to Geometric Fractional Brownian Motion with payment of dividends. The risk-free interest rate and dividend yield are non-random functions. The pricing formulas of Equity-Indexed Annuities under different methods are given. In addition, a-nalysis of sensitivity has also been made.
Nonlinear seismic behavior of a CANDU containment building subjected to near-field ground motions
Choi, In Kil; Ahn, Seong Moon; Choun, Young Sun; Seo, Jeong Moon [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
2004-07-01
The standard response spectrum proposed by US NRC has been used as a design earthquake for the design of Korean nuclear power plant structures. A survey on some of the Quaternary fault segments near Korean nuclear power plants is ongoing. It is likely that these faults will be identified as active ones. If the faults are confirmed as active ones, it will be necessary to reevaluate the seismic safety of the nuclear power plants located near the fault. Near-fault ground motions are the ground motions that occur near an earthquake fault. In general, the near-fault ground motion records exhibit a distinctive long period pulse like time history with very high peak velocities. These features are induced by the slip of the earthquake fault. Near-fault ground motions, which have caused much of the damage in recent major earthquakes, can be characterized by a pulse-like motion that exposes the structure to a high input energy at the beginning of the motion. In this study, nonlinear dynamic time-history analyses were performed to investigate the seismic behavior of a CANDU containment structure subjected to various earthquake ground motions including the near-field ground motions.
Tamburini, F; Bianchini, A
1999-01-01
A time-correlated EPR pairs protocol is analized, based on detection of fractal correlated signals into a statistical mixture of EPR correlated pairs: an approximated alpha-Fractional Brownian Motion (FBM) is induced on the group of EPR pairs (e.g. by sender-third party eavesdropper-like interactions as in Ekert quantum cryptography), to be detected by the receiver using a non - orthogonal wavelet filter, able to characterize the FBM from a noisy enviroment by formalizing a nonlinear optimization problem for the FBM alpha-characteristic parameter extimation.
Zhou Di; Zhou Jingyang
2007-01-01
The slewing motion control of a truss arm driven by a V-gimbaled control-moment-gyro (CMG) is a nonlinear control problem.The V-gimbaled CMG consists of a pair of gyros that must precess synchronously. The moment of inertia of the system, the angular momentum of the gyros and the external disturbances are not exactly known. With the help of feedback linearization and recursive Lyapunov design method, an adaptive nonlinear controller is designed to deal with the unknown items. Performance of the proposed controller is verified by simulation.
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.
Fan Liang
2013-01-01
Full Text Available Off‐pump coronary artery bypass graft surgery outperforms the traditional on‐pump surgery because the assisted robotic tools can cancel the relative motion between the beating heart and the robotic tools, which reduces post‐surgery complications for patients. The challenge for the robot assisted tool when tracking the beating heart is the abrupt change caused by the nonlinear nature of heart motion and high precision surgery requirements. A characteristic analysis of 3D heart motion data through bi‐spectral analysis demonstrates the quadratic nonlinearity in heart motion. Therefore, it is necessary to introduce nonlinear heart motion prediction into the motion tracking control procedures. In this paper, the heart motion tracking problem is transformed into a heart motion model following problem by including the adaptive heart motion model into the controller. Moreover, the model following algorithm with the nonlinear heart motion model embedded inside provides more accurate future reference by the quadratic term of sinusoid series, which could enhance the tracking accuracy of sharp change point and approximate the motion with sufficient detail. The experiment results indicate that the proposed algorithm outperforms the linear prediction‐based model following controller in terms of tracking accuracy (root mean square.
van den Broek, M; Van den Broeck, C
2008-04-04
We present the exact analysis of a chiral Brownian motor and heat pump. Optimization of the construction predicts, for a nanoscale device, frequencies of the order of kHz and cooling rates of the order of femtojoule per second.
Van Den Broek, Martijn; Van Den Broeck, Christian
2007-01-01
We present the exact analysis of a chiral Brownian motor and heat pump. Optimization of the construction predicts, for a nanoscale device, frequencies of the order of kHz and cooling rates of the order of femtojoule per second.
How superdiffusion gets arrested: ecological encounters explain shift from Lévy to Brownian movement
de Jager, Monique; Bartumeus, Frederic; Kölzsch, Andrea; Franz J. Weissing; 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-induc...
A. Malvandi
2014-01-01
Full Text Available Steady two-dimensional boundary layer flow of a nanofluid past a nonlinear stretching sheet is investigated analytically using the Homotopy Analysis Method (HAM. The employed model for nanofluid includes twocomponent four-equation non-homogeneous equilibrium model that incorporates the effects of Brownian motion ( Nb , thermophoresis ( Nt and Lewis number ( Le simultaneously. The basic partial boundary layer equations have been reduced to a two-point boundary value problem via the similarity variables. Analytical results are in best agreements with those existing in the literatures. The outcomes signify the decreasing trend of heat transfer rate with thermophoresis, Brownian motion and Lewis number. However, concentration rate has a sensitive behavior with parameters, especially the Brownian motion and thermophoresis parameters. Also, the weak points of numerical methods in such problems have been mentioned and the efficiency of HAM, as an alternative approach, in solving these kinds of nonlinear coupled problems has been shown.
Kinetic treatment of nonlinear magnetized plasma motions - General geometry and parallel waves
Khabibrakhmanov, I. KH.; Galinskii, V. L.; Verheest, F.
1992-01-01
The expansion of kinetic equations in the limit of a strong magnetic field is presented. This gives a natural description of the motions of magnetized plasmas, which are slow compared to the particle gyroperiods and gyroradii. Although the approach is 3D, this very general result is used only to focus on the parallel propagation of nonlinear Alfven waves. The derivative nonlinear Schroedinger-like equation is obtained. Two new terms occur compared to earlier treatments, a nonlinear term proportional to the heat flux along the magnetic field line and a higher-order dispersive term. It is shown that kinetic description avoids the singularities occurring in magnetohydrodynamic or multifluid approaches, which correspond to the degenerate case of sound speeds equal to the Alfven speed, and that parallel heat fluxes cannot be neglected, not even in the case of low parallel plasma beta. A truly stationary soliton solution is derived.
桑利恒; 杜雪樵
2012-01-01
利用分数布朗运动研究了一种强路径依赖型期权—回望期权的定价问题.首先列出了有关的定义和引理;其次利用该定义和引理建立了分数布朗运动情况下的价格模型,通过鞅方法,得到了回望期权价格所满足的方程;最后分别给出了看跌回望期权和看涨回望期权的定价公式的显式解.%This paper mainly deals with the pricing problem of the look-back option using the fractional Berownian motion, which is a kind of path dependent option. First of all the paper Lists in the definition and lemma; and secondly by the use of the definition and lemma established under fractional Brownian motion model of the price, look-back options pricing has been met by the differential equation; the final shows look-back put option and look-back call option pricing formula of the explicit solution respectively by using the random differential equation and the martingale methods.
Bifurcation and Resonance of a Mathematical Model for Non-Linear Motion of a Flooded Ship in Waves
Murashige, S.; Aihara, K.; Komuro, M.
1999-02-01
A flooded ship can exhibit undesirable non-linear roll motion even in waves of moderate amplitude. In order to understand the mechanism of this non-linear phenomenon, the non-linearly coupled dynamics of a ship and flood water are considered using a mathematical model for the simplified motion of a flooded ship in regular beam waves. This paper describes bifurcation and resonance of this coupled system. A bifurcation diagram shows that large-amplitude subharmonic motion exists in a wide range of parameters, and that the Hopf bifurcation is observed due to the dynamic effects of flood water. Resonance frequencies can be determined by linearization of this model. Comparison between the resonant points and the bifurcation curves suggests that non-linear resonance of this model can bring about large-amplitude subharmonic motion, even if it is in the non-resonate state of the linearized system.
Flow and Heat Transfer to Sisko Nanofluid over a Nonlinear Stretching Sheet.
Masood Khan
Full Text Available The two-dimensional boundary layer flow and heat transfer to Sisko nanofluid over a non-linearly stretching sheet is scrutinized in the concerned study. Our nanofluid model incorporates the influences of the thermophoresis and Brownian motion. The convective boundary conditions are taken into account. Implementation of suitable transformations agreeing with the boundary conditions result in reduction of the governing equations of motion, energy and concentration into non-linear ordinary differential equations. These coupled non-linear ordinary differential equations are solved analytically by using the homotopy analysis method (HAM and numerically by the shooting technique. The effects of the thermophoresis and Brownian motion parameters on the temperature and concentration fields are analyzed and graphically presented. The secured results make it clear that the temperature distribution is an increasing function of the thermophoresis and Brownian motion parameters and concentration distribution increases with the thermophoresis parameter but decreases with the Brownian motion parameter. To see the validity of the present work, we made a comparison with the numerical results as well as previously published work with an outstanding compatibility.
Flow and Heat Transfer to Sisko Nanofluid over a Nonlinear Stretching Sheet.
Khan, Masood; Malik, Rabia; Munir, Asif; Khan, Waqar Azeem
2015-01-01
The two-dimensional boundary layer flow and heat transfer to Sisko nanofluid over a non-linearly stretching sheet is scrutinized in the concerned study. Our nanofluid model incorporates the influences of the thermophoresis and Brownian motion. The convective boundary conditions are taken into account. Implementation of suitable transformations agreeing with the boundary conditions result in reduction of the governing equations of motion, energy and concentration into non-linear ordinary differential equations. These coupled non-linear ordinary differential equations are solved analytically by using the homotopy analysis method (HAM) and numerically by the shooting technique. The effects of the thermophoresis and Brownian motion parameters on the temperature and concentration fields are analyzed and graphically presented. The secured results make it clear that the temperature distribution is an increasing function of the thermophoresis and Brownian motion parameters and concentration distribution increases with the thermophoresis parameter but decreases with the Brownian motion parameter. To see the validity of the present work, we made a comparison with the numerical results as well as previously published work with an outstanding compatibility.
Fuzzy robust nonlinear control approach for electro-hydraulic flight motion simulator
Han Songshan
2015-02-01
Full Text Available A fuzzy robust nonlinear controller for hydraulic rotary actuators in flight motion simulators is proposed. Compared with other three-order models of hydraulic rotary actuators, the proposed controller based on first-order nonlinear model is more easily applied in practice, whose control law is relatively simple. It not only does not need high-order derivative of desired command, but also does not require the feedback signals of velocity, acceleration and jerk of hydraulic rotary actuators. Another advantage is that it does not rely on any information of friction, inertia force and external disturbing force/torque, which are always difficult to resolve in flight motion simulators. Due to the special composite vane seals of rectangular cross-section and goalpost shape used in hydraulic rotary actuators, the leakage model is more complicated than that of traditional linear hydraulic cylinders. Adaptive multi-input single-output (MISO fuzzy compensators are introduced to estimate nonlinear uncertain functions about leakage and bulk modulus. Meanwhile, the decomposition of the uncertainties is used to reduce the total number of fuzzy rules. Different from other adaptive fuzzy compensators, a discontinuous projection mapping is employed to guarantee the estimation process to be bounded. Furthermore, with a sufficient number of fuzzy rules, the controller theoretically can guarantee asymptotic tracking performance in the presence of the above uncertainties, which is very important for high-accuracy tracking control of flight motion simulators. Comparative experimental results demonstrate the effectiveness of the proposed algorithm, which can guarantee transient performance and better final accurate tracking in the presence of uncertain nonlinearities and parametric uncertainties.
Fuzzy robust nonlinear control approach for electro-hydraulic flight motion simulator
Han Songshan; Jiao Zongxia; Wang Chengwen; Shang Yaoxing
2015-01-01
A fuzzy robust nonlinear controller for hydraulic rotary actuators in flight motion sim-ulators is proposed. Compared with other three-order models of hydraulic rotary actuators, the proposed controller based on first-order nonlinear model is more easily applied in practice, whose control law is relatively simple. It not only does not need high-order derivative of desired command, but also does not require the feedback signals of velocity, acceleration and jerk of hydraulic rotary actuators. Another advantage is that it does not rely on any information of friction, inertia force and external disturbing force/torque, which are always difficult to resolve in flight motion simula-tors. Due to the special composite vane seals of rectangular cross-section and goalpost shape used in hydraulic rotary actuators, the leakage model is more complicated than that of traditional linear hydraulic cylinders. Adaptive multi-input single-output (MISO) fuzzy compensators are introduced to estimate nonlinear uncertain functions about leakage and bulk modulus. Meanwhile, the decom-position of the uncertainties is used to reduce the total number of fuzzy rules. Different from other adaptive fuzzy compensators, a discontinuous projection mapping is employed to guarantee the estimation process to be bounded. Furthermore, with a sufficient number of fuzzy rules, the control-ler theoretically can guarantee asymptotic tracking performance in the presence of the above uncer-tainties, which is very important for high-accuracy tracking control of flight motion simulators. Comparative experimental results demonstrate the effectiveness of the proposed algorithm, which can guarantee transient performance and better final accurate tracking in the presence of uncertain nonlinearities and parametric uncertainties.
Li Jie; Liu Zhangjun; Chen Jianbing
2009-01-01
This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method (PDEM) is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described, An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.
Roynette, Bernard
2009-01-01
Penalising a process is to modify its distribution with a limiting procedure, thus defining a new process whose properties differ somewhat from those of the original one. We are presenting a number of examples of such penalisations in the Brownian and Bessel processes framework. The Martingale theory plays a crucial role. A general principle for penalisation emerges from these examples. In particular, it is shown in the Brownian framework that a positive sigma-finite measure takes a large class of penalisations into account.
Poole, L. R.
1972-01-01
A computer program is presented by which the effects of nonlinear suspension-system elastic characteristics on parachute inflation loads and motions can be investigated. A mathematical elastic model of suspension-system geometry is coupled to the planar equations of motion of a general vehicle and canopy. Canopy geometry and aerodynamic drag characteristics and suspension-system elastic properties are tabular inputs. The equations of motion are numerically integrated by use of an equivalent fifth-order Runge-Kutta technique.
Radiation Reaction for a Charged Brownian Particle
Vlasov, A A
2002-01-01
As it is known a model of a charged particle with finite size is a good tool to consider the effects of self- action and backreaction, caused by electromagnetic radiation. In this work the "size" of a charged particle is induced by its stochastic Brownian vibration. Appropriate equation of particle's motion with radiation force is derived. It is shown that the solutions of this equation correctly describe the effects of radiation reaction.
Directed motion generated by heat bath nonlinearly driven by external noise
Chaudhuri, J Ray [Department of Physics, Katwa College, Katwa, Burdwan 713 130, West Bengal (India); Barik, D [Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032 (India); Banik, S K [Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0435 (United States)
2007-12-07
Based on the heat bath system approach where the bath is nonlinearly modulated by an external Gaussian random force, we propose a new microscopic model to study directed motion in the overdamped limit for a nonequilibrium open system. Making use of the coupling between the heat bath and the external modulation as a small perturbation, we construct a Langevin equation with multiplicative noise- and space-dependent dissipation and the corresponding Fokker-Planck-Smoluchowski equation in the overdamped limit. We examine the thermodynamic consistency condition and explore the possibility of observing a phase-induced current as a consequence of state-dependent diffusion and, necessarily, nonlinear driving of the heat bath by the external noise.
杨朝强
2013-01-01
利用混合分数布朗运动的Itó公式和复合泊松过程驱动的随机微分方程,建立了一类混合跳-扩散分数布朗运动环境下的价格模型,在Merton假设条件下对其随机微分方程的Cauchy初值问题采用迭代法作了估计,得到了混合跳-扩散模型下的欧式看跌期权定价的Merton公式,从而给出了混合跳-扩散分数布朗运动欧式浮动履约价的看涨回望期权和看跌回望期权定价公式.%The mixed jump-diffusion fractional Brownian motion model under the Itó formula and fractional diffusion process with non-homogeneous Poisson process was proposed.By using the iterative method,the Cauchy initial problem of stochastic differential equations were estimated under the conditions of Merton assumptions.Then the pricing Merton-formula of European option that meets the pricing model for the European floating strike price of the lookback option was obtained.Finally the pricing formulas of floating strike lookback call option and lookback put option were proofed.
Nonlinear Motion Control of a Rotary Wing Vehicle Powered by Four Rotors
S. Araujo–Estrada
2009-10-01
Full Text Available This paper presents a solution to the motion control problem for a rotary wing vehicle powered by four rotors. It is considered that the rotary wing vehicle performs an indoor low speed flight mission so that aerodynamic effects are not taken into account. The proposed controller is based on a combination of the well–known backstepping nonlinear control design technique and bounded controllers. It is shown that the resulting closed—loop dynamics evolves inside a set where singularities are avoided. Numerical simulations show the performance of the proposed controller.
Brownian molecular rotors: Theoretical design principles and predicted realizations
Schönborn, Jan Boyke; Herges, Rainer; Hartke, Bernd
2009-06-01
We propose simple design concepts for molecular rotors driven by Brownian motion and external photochemical switching. Unidirectionality and efficiency of the motion is measured by explicit simulations. Two different molecular scaffolds are shown to yield viable molecular rotors when decorated with suitable substituents.
Xiao-Feng Pang
2008-01-01
The properties and rules of motion of superconductive electrons in steady and time-dependent non-equilibrium states of superconductors are studied by using the Ginzberg-Landau (GL) equations and nonlinear quantum theory. In the absence of external fields, the superconductive electrons move in the solitons with certain energy and velocity in a uniform system, The superconductive electron is still a soliton under action of an electromagnetic field, but its amplitude, phase and shape are changed. Thus we conclude that super- conductivity is a result of motion of soliton of superconductive electrons. Since soliton has the feature of motion for retaining its energy and form, thus a permanent current occurs in superconductor. From these solutions of GL equations under action of an electromagnetic field, we gain the structure of vortex lines-magnetic flux lines observed experimentally in type-II superconductors. In the time-dependent non- equilibrium states of superconductor, the motions of superconductive electrons exhibit still the soliton features, but the shape and amplitude have changed. In an invariant electric-field, it moves in a constant acceleration. In the medium with dissipation, the superconductive electron behaves still like a soliton, although its form, amplitude, and velocity are altered. Thus we have to convince that the superconductive electron is essentially a soliton in both non-equilibrium and equilibrium superconductors.
Nonlinear effect of elastic vortexlike motion on the dynamic stress state of solids
Shilko, Evgeny V.; Grinyaev, Yurii V.; Popov, Mikhail V.; Popov, Valentin L.; Psakhie, Sergey G.
2016-05-01
We present a theoretical analysis of the dynamic stress-strain state of regions in a solid body that are involved in a collective elastic vortexlike motion. It is shown that the initiation of elastic vortexlike motion in the material is accompanied by the appearance of dilatancy and equivalent strain, the magnitudes of which are proportional to the square of the ratio of linear velocity on the periphery of the elastic vortex to the velocity of longitudinal elastic waves (P wave). Under conditions of dynamic loading the described dynamic effects are able to initiate inelastic deformation or destruction of the material at loading speeds of a few percent of the P -wave speed. The obtained analytical estimates suggest that dynamic nonlinear strains can make a significant contribution in a number of widely studied nonlinear dynamic phenomena in solids. Among them are the effect of acoustic (dynamic) dilatancy in solids and granular media, which leads to the generation of longitudinal elastic waves by transverse waves [V. Tournat et al., Phys. Rev. Lett. 92, 085502 (2004), 10.1103/PhysRevLett.92.085502] and the formation of an array of intense "hot spots" (reminiscent of shear-induced hydrodynamic instabilities in fluids) in adiabatic shear bands [P. R. Guduru et al., Phys. Rev. E 64, 036128 (2001), 10.1103/PhysRevE.64.036128].
Cooperative rectification in confined Brownian ratchets.
Malgaretti, Paolo; Pagonabarraga, Ignacio; Rubí, J Miguel
2012-01-01
We analyze the rectified motion of a Brownian particle in a confined environment. We show the emergence of strong cooperativity between the inherent rectification of the ratchet mechanism and the entropic bias of the fluctuations caused by spatial confinement. Net particle transport may develop even in situations where separately the ratchet and the geometric restrictions do not give rise to particle motion. The combined rectification effects can lead to bidirectional transport depending on particle size, resulting in a different route for segregation. The reported mechanism can be used to control transport in mesostructures and nanodevices in which particles move in a reduced space.
Anomalous Brownian Refrigerator
Rana, Shubhashis; Pal, P. S.; Saha, Arnab; Jayannavar, A. M.
2015-01-01
We present a detailed study of a Brownian particle driven by Carnot-type refrigerating protocol operating between two thermal baths. Both the underdamped as well as the overdamped limits are investigated. The particle is in a harmonic potential with time-periodic strength that drives the particle cyclically between the baths. Each cycle consists of two isothermal steps at different temperatures and two adiabatic steps connecting them. Besides working as a stochastic refrigerator, it is shown ...
Eliazar, Iddo I., E-mail: eliazar@post.tau.ac.il [Holon Institute of Technology, P.O. Box 305, Holon 58102 (Israel); Shlesinger, Michael F., E-mail: mike.shlesinger@navy.mil [Office of Naval Research, Code 30, 875 N. Randolph St., Arlington, VA 22203 (United States)
2013-06-10
Brownian motion is the archetypal model for random transport processes in science and engineering. Brownian motion displays neither wild fluctuations (the “Noah effect”), nor long-range correlations (the “Joseph effect”). The quintessential model for processes displaying the Noah effect is Lévy motion, the quintessential model for processes displaying the Joseph effect is fractional Brownian motion, and the prototypical model for processes displaying both the Noah and Joseph effects is fractional Lévy motion. In this paper we review these four random-motion models–henceforth termed “fractional motions” –via a unified physical setting that is based on Langevin’s equation, the Einstein–Smoluchowski paradigm, and stochastic scaling limits. The unified setting explains the universal macroscopic emergence of fractional motions, and predicts–according to microscopic-level details–which of the four fractional motions will emerge on the macroscopic level. The statistical properties of fractional motions are classified and parametrized by two exponents—a “Noah exponent” governing their fluctuations, and a “Joseph exponent” governing their dispersions and correlations. This self-contained review provides a concise and cohesive introduction to fractional motions.
Stochastic description of quantum Brownian dynamics
Yan, Yun-An; Shao, Jiushu
2016-08-01
Classical Brownian motion has well been investigated since the pioneering work of Einstein, which inspired mathematicians to lay the theoretical foundation of stochastic processes. A stochastic formulation for quantum dynamics of dissipative systems described by the system-plus-bath model has been developed and found many applications in chemical dynamics, spectroscopy, quantum transport, and other fields. This article provides a tutorial review of the stochastic formulation for quantum dissipative dynamics. The key idea is to decouple the interaction between the system and the bath by virtue of the Hubbard-Stratonovich transformation or Itô calculus so that the system and the bath are not directly entangled during evolution, rather they are correlated due to the complex white noises introduced. The influence of the bath on the system is thereby defined by an induced stochastic field, which leads to the stochastic Liouville equation for the system. The exact reduced density matrix can be calculated as the stochastic average in the presence of bath-induced fields. In general, the plain implementation of the stochastic formulation is only useful for short-time dynamics, but not efficient for long-time dynamics as the statistical errors go very fast. For linear and other specific systems, the stochastic Liouville equation is a good starting point to derive the master equation. For general systems with decomposable bath-induced processes, the hierarchical approach in the form of a set of deterministic equations of motion is derived based on the stochastic formulation and provides an effective means for simulating the dissipative dynamics. A combination of the stochastic simulation and the hierarchical approach is suggested to solve the zero-temperature dynamics of the spin-boson model. This scheme correctly describes the coherent-incoherent transition (Toulouse limit) at moderate dissipation and predicts a rate dynamics in the overdamped regime. Challenging problems
Longitudinal/Lateral Stability Analysis of Vehicle Motion in the Nonlinear Region
Keji Chen
2016-01-01
Full Text Available We focus on the study of motion stability of vehicle nonlinear dynamics. The dynamic model combining with Burckhardt tire model is firstly derived. By phase portrait method, the vehicle stability differences of three cases, front wheels steering/four-wheel steering case, front/rear/four-wheel braking case, and high/low road friction case, are characterized. With the Jacobian matrix, the stable equilibrium point is found and stable areas are calculated out. Similarly, the stability boundaries corresponding to different working conditions are also captured. With vehicle braking or accelerating in the steering process, the relationship between front/rear wheel slippage and the stable area is examined. Comparing with current literatures, the research method and its results present the novelty and provide a guideline for new vehicle controller design.
Deyuan Meng
2014-05-01
Full Text Available The dynamics of pneumatic systems are highly nonlinear, and there normally exists a large extent of model uncertainties; the precision motion trajectory tracking control of pneumatic cylinders is still a challenge. In this paper, two typical nonlinear controllers—adaptive controller and deterministic robust controller—are constructed firstly. Considering that they have both benefits and limitations, an adaptive robust controller (ARC is further proposed. The ARC is a combination of the first two controllers; it employs online recursive least squares estimation (RLSE to reduce the extent of parametric uncertainties, and utilizes the robust control method to attenuate the effects of parameter estimation errors, unmodeled dynamics, and disturbances. In order to solve the conflicts between the robust control design and the parameter adaption law design, the projection mapping is used to condition the RLSE algorithm so that the parameter estimates are kept within a known bounded convex set. Theoretically, ARC possesses the advantages of the adaptive control and the deterministic robust control, and thus an even better tracking performance can be expected. Extensive comparative experimental results are presented to illustrate the achievable performance of the three proposed controllers and their performance robustness to the parameter variations and sudden disturbance.
Non-linear station motions in the DGFI realization of the ITRF2014
Seitz, Manuela; Bloßfeld, Mathis; Angermann, Detlef; Schmid, Ralf
2016-04-01
The DGFI Terrestrial Reference Frame DTRF2014 is the most recent realization of the International Terrestrial Reference System computed by DGFI-TUM. It comprises 3-dimensional station coordinates and velocities which are estimated in a common adjustment together with Earth orientation parameters (EOP). The input data for the DTRF2014 are observations of the four fundamental space geodetic techniques (GNSS, VLBI, SLR and DORIS) from 1979 until 2015 as well as terrestrial difference vectors (local ties) between the technique-specific reference points. In previous ITRS realizations, the motions of the crust-fixed reference points were approximated through linear velocities. Un-modeled and/or residual non-linear station motions were neglected and, therefore, deteriorated station coordinates, velocities as well as commonly adjusted EOP. For the DTRF2014, geophysical non-tidal loading corrections provided by the IERS Global Geophysical Fluids Center (IERS-GGFC) which account for atmospheric and hydrological effects were considered. In this study, we present the strategy to apply non-tidal loading corrections at the normal equation level of the Gauss-Markov model. We compare DTRF2014 solutions with and without non-tidal loading corrections and investigate their impact on TRF parameters (station coordinates, velocities, geodetic datum) and EOP. Furthermore, a validation of different DTRF2014 solutions with independent ITRS realizations computed by other institutions is shown.
Brownian dynamics simulations with hard-body interactions: Spherical particles
Behringer, Hans; 10.1063/1.4761827
2012-01-01
A novel approach to account for hard-body interactions in (overdamped) Brownian dynamics simulations is proposed for systems with non-vanishing force fields. The scheme exploits the analytically known transition probability for a Brownian particle on a one-dimensional half-line. The motion of a Brownian particle is decomposed into a component that is affected by hard-body interactions and into components that are unaffected. The hard-body interactions are incorporated by replacing the affected component of motion by the evolution on a half-line. It is discussed under which circumstances this approach is justified. In particular, the algorithm is developed and formulated for systems with space-fixed obstacles and for systems comprising spherical particles. The validity and justification of the algorithm is investigated numerically by looking at exemplary model systems of soft matter, namely at colloids in flow fields and at protein interactions. Furthermore, a thorough discussion of properties of other heurist...
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.
Yonghwan Kim
2011-03-01
Full Text Available The present paper introduced a computer program, called WISH, which is based on a time-domain Rankine panel method. The WISH has been developed for practical use to predict the linear and nonlinear ship motion and structural loads in waves. The WISH adopts three different levels of seakeeping analysis: linear, weakly-nonlinear and weak-scatterer approaches. Later, WISH-FLEX has been developed to consider hydroelasticity effects on hull-girder structure. This program can solve the springing and whipping problems by coupling between the hydrodynamic and structural problems. More recently this development has been continued to more diverse problems, including the motion responses of multiple adjacent bodies, the effects of seakeeping in ship maneuvering, and the floating-body motion in finite-depth domain with varying bathymetry. This paper introduces a brief theoretical and numerical background of the WISH package, and some validation results. Also several applications to real ships and offshore structures are shown.
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.
Single potassium niobate nano/microsized particles as local mechano-optical Brownian probes
Mor, Flavio M.; Sienkiewicz, Andrzej; Magrez, Arnaud; Forró, László; Jeney, Sylvia
2016-03-01
Perovskite alkaline niobates, due to their strong nonlinear optical properties, including birefringence and the capability to produce second-harmonic generation (SHG) signals, attract a lot of attention as potential candidates for applications as local nano/microsized mechano-optical probes. Here, we report on an implementation of photonic force microscopy (PFM) to explore the Brownian motion and optical trappability of monocrystalline potassium niobate (KNbO3) nano/microsized particles having sizes within the range of 50 to 750 nm. In particular, we exploit the anisotropic translational diffusive regime of the Brownian motion to quantify thermal fluctuations and optical forces of singly-trapped KNbO3 particles within the optical trapping volume of a PFM microscope. We also show that, under near-infrared (NIR) excitation of the highly focused laser beam of the PFM microscope, a single optically-trapped KNbO3 particle reveals a strong SHG signal manifested by a narrow peak (λem = 532 nm) at half the excitation wavelength (λex = 1064 nm). Moreover, we demonstrate that the thus induced SHG emission can be used as a local light source that is capable of optically exciting molecules of an organic dye, Rose Bengal (RB), which adhere to the particle surface, through the mechanism of luminescence energy transfer (LET).Perovskite alkaline niobates, due to their strong nonlinear optical properties, including birefringence and the capability to produce second-harmonic generation (SHG) signals, attract a lot of attention as potential candidates for applications as local nano/microsized mechano-optical probes. Here, we report on an implementation of photonic force microscopy (PFM) to explore the Brownian motion and optical trappability of monocrystalline potassium niobate (KNbO3) nano/microsized particles having sizes within the range of 50 to 750 nm. In particular, we exploit the anisotropic translational diffusive regime of the Brownian motion to quantify thermal
唐振华; 喻祖国
2012-01-01
最近发展了一些将时间序列转化为复杂网络的方法,从而可以通过研究网络的拓扑性质来分析原始时间序列的性质.本文用递归图方法将分数布朗运动(FBM)时间序列转化为复杂网络,并研究其对应递归网络的拓扑性质.我们发现,对固定的Hurst指数H,在网络连通率首次增长到1之前,随着递归图的参数阈值的增大,网络的平均路径长度L也随之递增,之后反而递减.我们也发现由FBM时间序列转化得到的网络是无标度网络.我们采用节点覆盖盒计数法分析发现FBM的递归网络为分形网络,具有自相似特性,其分形维数dB随Hurst指数H的增大而减小,特别当H≥0.4时,有近似关系dB=H2 - 2.1×H+2.%Some methods have been proposed recently to convert a single time series to a complex network so that the properties of the original time series can be understood by investigating the topological properties of the network. Here we convert fractional Brownian motion (FBM) time series to complex networks using recurrence plot method, and then we investigate the topological properties of the corresponding recurrence networks. It is found that for fixed Hurst exponent H, before the connectivity rate of corresponding networks increases to about 1 for the first time, the average length L of the shortest paths increases with the increase of parameter threshold in the recurrence plot, and then decreases. It is also found that the converted networks from FBM time series are scale-free. The analysis using the node-covering box-counting method shows that the recurrence networks are fractals with self-similarity property, and the fractal dimension dB decreases with Hurst index H. Especially, when H ≥ 0.4, there is a approximately relationship dB = H2 - 2.1 × H + 2.
On Optimal Control of a Brownian Motion.
1982-06-01
barriers. Puterman [9] uses diffusion processes to model production and inventory processes. In both cases they assume the existence of a stationary... Puterman , A diffusion model for a storage system, Logistic, M. Geisler ed., North-Holland 197S. [101 J. Rath, The optimal policy for a controlled
Yong Zhao
1997-01-01
Full Text Available A nonlinear three dimensional (3D single rack model and a nonlinear 3D whole pool multi-rack model are developed for the spent fuel storage racks of a nuclear power plant (NPP to determine impacts and frictional motion responses when subjected to 3D excitations from the supporting building floor. The submerged free standing rack system and surrounding water are coupled due to hydrodynamic fluid-structure interaction (FSI using potential theory. The models developed have features that allow consideration of geometric and material nonlinearities including (1 the impacts of fuel assemblies to rack cells, a rack to adjacent racks or pool walls, and rack support legs to the pool floor; (2 the hydrodynamic coupling of fuel assemblies with their storing racks, and of a rack with adjacent racks, pool walls, and the pool floor; and (3 the dynamic motion behavior of rocking, twisting, and frictional sliding of rack modules. Using these models 3D nonlinear time history dynamic analyses are performed per the U.S. Nuclear Regulatory Commission (USNRC criteria. Since few such modeling, analyses, and results using both the 3D single and whole pool multiple rack models are available in the literature, this paper emphasizes description of modeling and analysis techniques using the SOLVIA general purpose nonlinear finite element code. Typical response results with different Coulomb friction coefficients are presented and discussed.
Fully Nonlinear Simulations of Wave Resonance by An Array of Cylinders in Vertical Motions
HUANG Hao-cai; WANG Chi-zhong; LENG Jian-xing
2013-01-01
The finite element method (FEM) is employed to analyze the resonant oscillations of the liquid confined within multiple or an array of floating bodies with fully nonlinear boundary conditions on the free surface and the body surface in two dimensions.The velocity potentials at each time step are obtained through the FEM with 8-node quadratic shape functions.The finite element linear system is solved by the conjugate gradient (CG) method with a symmetric successive overelaxlation (SSOR) preconditioner.The waves at the open boundary are absorbed by the combination of the damping zone method and the Sommerfeld-Orlanski equation.Numerical examples are given by an array of floating wedgeshaped cylinders and rectangular cylinders.Results are provided for heave motions including wave elevations,profiles and hydrodynamic forces.Comparisons are made in several cases with the results obtained from the second order solution in the time domain.It is found that the wave amplitude in the middle region of the array is larger than those in other places,and the hydrodynamic force on a cylinder increases with the cylinder closing to the middle of the array.
Territory Covered by N Self-Propelled Brownian Agents in 2 dimensions
Sevilla, Francisco J.; Gómez Nava, Luis Alberto
2014-03-01
We consider the problem of the territory covered by N non-interacting self-propelled Brownian agents where self-propulsion is modeled by a non-linear friction term in the Langevin-like equations of motion for each agent. Our study generalizes, to a continuous time and space description, the well known problem of the territory explored by N Random Walkers. Numerical and analytical approaches are presented to exhibit the effects of self-propulsion on the many independent agents exploring two dimensional homogenous regions. Our results may have a wide range of applications in a variaty of non-equilibrium systems. FJSP and LAGN aknowledge PAPIIT-IN113114 and PAEP-PCF-UNAM.
非线性粘弹性梁的混沌运动%Chaotic Motions of Nonlinear Viscoelastic Beams
陈立群; 程昌; 张能辉
2000-01-01
The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams with geometric and material nonlinearities is established. The material of the beams obeys the Leaderman nonlinear constitutive relation. In the case of simple supported ends, the Galerkin method is applied to simplify the integro-partial-differential equation to a integro -differential equation. The equation is further simplified to a set of ordinary differential equations by introducing an additional variable. Finally, the numerical method is applied to investigate the dynamical behavior of the beam, and results show that chaos occurs in the motion of the beam.
非线性粘弹性梁的混沌运动%Chaotic Motions of Nonlinear Viscoelastic Beams
陈立群; 程昌; 张能辉
2001-01-01
The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams with geometric and material nonlinearities is established. The material of the beams obeys the Leaderman nonlinear constitutive relation. In the case of simple supported ends, the Galerkin method is applied to simplify the integro-partial-differential equation to a integro -differential equation. The equation is further simplified to a set of ordinary differential equations by introducing an additional variable. Finally, the numerical method is applied to investigate the dynamical behavior of the beam, and results show that chaos occurs in the motion of the beam.
Abdikarimov, R.; Bykovtsev, A.; Khodzhaev, D.; Research Team Of Geotechnical; Structural Engineers
2010-12-01
Long-period earthquake ground motions (LPEGM) with multiple oscillations have become a crucial consideration in seismic hazard assessment because of the rapid increase of tall buildings and special structures (SP).Usually, SP refers to innovative long-span structural systems. More specifically, they include many types of structures, such as: geodesic showground; folded plates; and thin shells. As continuation of previous research (Bykovtsev, Abdikarimov, Khodzhaev 2003, 2010) analysis of nonlinear vibrations (NV) and dynamic stability of SP simulated as shells with variable rigidity in geometrically nonlinear statement will be presented for two cases. The first case will represent NV example of a viscoelastic orthotropic cylindrical shell with radius R, length L and variable thickness h=h(x,y). The second case will be NV example of a viscoelastic shell with double curvature, variable thickness, and bearing the concentrated masses. In both cases we count, that the SP will be operates under seismic load generated by LPEGM with multiple oscillations. For different seismic loads simulations, Bykovtsev’s Model and methodology was used for generating LPEGM time history. The methodology for synthesizing LPEGM from fault with multiple segmentations was developed by Bykovtev (1978-2010) and based on 3D-analytical solutions by Bykovtsev-Kramarovskii (1987&1989) constructed for faults with multiple segmentations. This model is based on a kinematics description of displacement function on the fault and included in consideration of all possible combinations of 3 components of vector displacement (two slip vectors and one tension component). The opportunities to take into consideration fault segmentations with both shear and tension vector components of displacement on the fault plane provide more accurate LPEGM evaluations. Radiation patterns and directivity effects were included in the model and more physically realistic results for simulated LPEGM were considered. The
Brownian rod scheme in microenvironment sensing
Ian Gralinski
2012-03-01
Full Text Available Fluctuations of freely translating spherical particles via Brownian motion should provide inexhaustible information about the micro-environment, but is beset by the problem of particles drifting away from the venue of measurement as well as colliding with other particles. We propose a scheme here to circumvent this in which a Brownian rod that lies in proximity to a cylindrical pillar is drawn in by a tuneable attractive force from the pillar. The force is assumed to act through the centre of each body and the motion exclusive to the x-y plane. Simulation studies show two distinct states, one in which the rod is moving freely (state I and the other in which the rod contacts the cylinder surface (state II. Information about the micro-environment could be obtained by tracking the rotational diffusion coefficient Dθ populating in either of these two states. However, the magnitude of the normalized charge product in excess of 6.3x104 was found necessary for a rod of 6.81 × 0.93 μm2 (length × diameter and 10μm diameter cylindrical pillar to minimize deviation errors. It was also found that the extent of spatial sensing coverage could be controlled by varying the charge level. The conditions needed to ascertain the rotational sampling for angle determination through the Hough transform were also discussed.
Brownian Dynamics of charged particles in a constant magnetic field
Hou, L J; Piel, A; Shukla, P K
2009-01-01
Numerical algorithms are proposed for simulating the Brownian dynamics of charged particles in an external magnetic field, taking into account the Brownian motion of charged particles, damping effect and the effect of magnetic field self-consistently. Performance of these algorithms is tested in terms of their accuracy and long-time stability by using a three-dimensional Brownian oscillator model with constant magnetic field. Step-by-step recipes for implementing these algorithms are given in detail. It is expected that these algorithms can be directly used to study particle dynamics in various dispersed systems in the presence of a magnetic field, including polymer solutions, colloidal suspensions and, particularly complex (dusty) plasmas. The proposed algorithms can also be used as thermostat in the usual molecular dynamics simulation in the presence of magnetic field.
Near-field optically driven Brownian motors (Conference Presentation)
Wu, Shao-Hua; Huang, Ningfeng; Jaquay, Eric; Povinelli, Michelle L.
2016-09-01
Brownian ratchets are of fundamental interest in fields from statistical physics to molecular motors. The realization of Brownian ratchets in engineered systems opens up the potential to harness thermal energy for directed motion, with applications in transport and sorting of nanoparticles. Implementations based on optical traps provide a high degree of tunability along with precise spatiotemporal control. Near-field optical methods provide particular flexibility and ease of on-chip integration with other microfluidic components. Here, we demonstrate the first all-optical, near-field Brownian ratchet. Our approach uses an asymmetrically patterned photonic crystal and yields an ultra-stable trap stiffness of 253.6 pN/nm-W, 100x greater than conventional optical tweezers. By modulating the laser power, optical ratcheting with transport speed of 1 micron/s can be achieved, allowing a variety of dynamical lab-on-a-chip applications. The resulting transport speed matches well with the theoretical prediction.
Brownian versus Newtonian devitrification of hard-sphere glasses
Montero de Hijes, Pablo; Rosales-Pelaez, Pablo; Valeriani, Chantal; Pusey, Peter N.; Sanz, Eduardo
2017-08-01
In a recent molecular dynamics simulation work it has been shown that glasses composed of hard spheres crystallize via cooperative, stochastic particle displacements called avalanches [E. Sanz et al., Proc. Natl. Acad. Sci. USA 111, 75 (2014), 10.1073/pnas.1308338110]. In this Rapid Communication we investigate if such a devitrification mechanism is also present when the dynamics is Brownian rather than Newtonian. The research is motivated in part by the fact that colloidal suspensions, an experimental realization of hard-sphere systems, undergo Brownian motion. We find that Brownian hard-sphere glasses do crystallize via avalanches with very similar characteristics to those found in the Newtonian case. We briefly discuss the implications of these findings for experiments on colloids.
Graybill, George
2007-01-01
Take the mystery out of motion. Our resource gives you everything you need to teach young scientists about motion. Students will learn about linear, accelerating, rotating and oscillating motion, and how these relate to everyday life - and even the solar system. Measuring and graphing motion is easy, and the concepts of speed, velocity and acceleration are clearly explained. Reading passages, comprehension questions, color mini posters and lots of hands-on activities all help teach and reinforce key concepts. Vocabulary and language are simplified in our resource to make them accessible to str
Brownian transport controlled by dichotomic and thermal fluctuations
Kula, J.; Kostur, M.; Łuczka, J.
1998-09-01
We study transport of Brownian particles in spatially periodic structures, driven by both thermal equilibrium fluctuations and dichotomic noise of zero mean values. Introducing specific scaling, we show that the dimensionless Newton-Langevin type equation governing the motion of Brownian particles is very well approximated by the overdamped dynamics; inertial effects can be neglected because for generic systems dimensionless mass is many orders less than a dimensionless friction coefficient. An exact probability current, proportional to the mean drift velocity of particles, is obtained for a piecewise linear spatially periodic potential. We analyze in detail properties of the macroscopic averaged motion of particles. In dependence on statistics of both sources of fluctuations, the directed transport of particles exhibits such distinctive non-monotonic behavior as: bell-shaped dependence (there exists optimal statistics of fluctuations maximizing velocity) and reversal in the direction of macroscopic motion (there exists critical statistics at which the drift velocity is zero).
Bhatti, M. M.; Zeeshan, A.; Ellahi, R.
2016-09-01
In this article, heat transfer with nonlinear thermal radiation on sinusoidal motion of magnetic solid particles in a dust Jeffrey fluid has been studied. The effects of Magnetohydrodynamic (MHD) and hall current are also taken under consideration. The governing equation of motion and energy equation are modelled with help of Ohms law for fluid and dust phases. The solutions of the resulting ordinary coupled partial differential equations are solved analytically. The impact of all the physical parameters of interest such as Hartmann number, slip parameter, Hall parameter, radiation parameter, Prandtl number, Eckert number and particle volume fraction are demonstrated mathematically and graphically. Trapping mechanism is also discussed in detail by drawing contour lines. The present analysis affirms many interesting behaviours, which permit further study on solid particles motion with heat and mass transfer.
Anomalous Brownian refrigerator
Rana, Shubhashis; Pal, P. S.; Saha, Arnab; Jayannavar, A. M.
2016-02-01
We present a detailed study of a Brownian particle driven by Carnot-type refrigerating protocol operating between two thermal baths. Both the underdamped as well as the overdamped limits are investigated. The particle is in a harmonic potential with time-periodic strength that drives the system cyclically between the baths. Each cycle consists of two isothermal steps at different temperatures and two adiabatic steps connecting them. Besides working as a stochastic refrigerator, it is shown analytically that in the quasistatic regime the system can also act as stochastic heater, depending on the bath temperatures. Interestingly, in non-quasistatic regime, our system can even work as a stochastic heat engine for certain range of cycle time and bath temperatures. We show that the operation of this engine is not reliable. The fluctuations of stochastic efficiency/coefficient of performance (COP) dominate their mean values. Their distributions show power law tails, however the exponents are not universal. Our study reveals that microscopic machines are not the microscopic equivalent of the macroscopic machines that we come across in our daily life. We find that there is no one to one correspondence between the performance of our system under engine protocol and its reverse.
Martínez, I A; Roldán, É; Dinis, L; Petrov, D; Parrondo, J M R; Rica, R A
2016-01-01
The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths1. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors2 and some artificial micro-engines3-5 operate. As described by stochastic thermodynamics6,7, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit8. Here we report an experimental realization of a Carnot engine with a single optically trapped Brownian particle as the working substance. We present an exhaustive study of the energetics of the engine and analyse the fluctuations of the finite-time efficiency, showing that the Carnot bound can be surpassed for a small number of non-equilibrium cycles. As its macroscopic counterpart, the energetics of our Carnot device exhibits basic properties that one would expect to observe in any microscopic energy transducer operating with baths at different temperatures9-11. Our results characterize the sources of irreversibility in the engine and the statistical properties of the efficiency-an insight that could inspire new strategies in the design of efficient nano-motors.
Peruani, Fernando
2016-11-01
Bacteria, chemically-driven rods, and motility assays are examples of active (i.e. self-propelled) Brownian rods (ABR). The physics of ABR, despite their ubiquity in experimental systems, remains still poorly understood. Here, we review the large-scale properties of collections of ABR moving in a dissipative medium. We address the problem by presenting three different models, of decreasing complexity, which we refer to as model I, II, and III, respectively. Comparing model I, II, and III, we disentangle the role of activity and interactions. In particular, we learn that in two dimensions by ignoring steric or volume exclusion effects, large-scale nematic order seems to be possible, while steric interactions prevent the formation of orientational order at large scales. The macroscopic behavior of ABR results from the interplay between active stresses and local alignment. ABR exhibit, depending on where we locate ourselves in parameter space, a zoology of macroscopic patterns that ranges from polar and nematic bands to dynamic aggregates.
Martínez, I. A.; Roldán, É.; Dinis, L.; Petrov, D.; Parrondo, J. M. R.; Rica, R. A.
2016-01-01
The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors and some artificial micro-engines operate. As described by stochastic thermodynamics, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit. Here we report an experimental realization of a Carnot engine with a single optically trapped Brownian particle as the working substance. We present an exhaustive study of the energetics of the engine and analyse the fluctuations of the finite-time efficiency, showing that the Carnot bound can be surpassed for a small number of non-equilibrium cycles. As its macroscopic counterpart, the energetics of our Carnot device exhibits basic properties that one would expect to observe in any microscopic energy transducer operating with baths at different temperatures. Our results characterize the sources of irreversibility in the engine and the statistical properties of the efficiency--an insight that could inspire new strategies in the design of efficient nano-motors.
Extinction and persistence of a stochastic nonlinear SIS epidemic model with jumps
Ge, Qing; Ji, Guilin; Xu, Jiabo; Fan, Xiaolin
2016-11-01
In this paper, Brownian motion and L e ´ vy jumps are introduced to a SIS type epidemic model with nonlinear incidence rate. The dynamical behavior of the considered model is investigated. In order to reveal the extinction and permanence of the disease, two threshold values R˜0 ,R¯0 are showed. We find that if R˜0 1, the disease may be persistent. Finally, the numerical simulations are presented to illustrate our mathematical results.
Superdiffusions and positive solutions of non-linear partial differential equations
Dynkin, E B [Cornell University, New York (United States)
2004-02-28
By using super-Brownian motion, all positive solutions of the non-linear differential equation {delta}u=u{sup {alpha}} with 1<{alpha}{<=}2 in a bounded smooth domain E are characterized by their (fine) traces on the boundary. This solves a problem posed by the author a few years ago. The special case {alpha}=2 was treated by B. Mselati in 2002.
Altamimi, Zuheir; Rebischung, Paul; Métivier, Laurent; Collilieux, Xavier
2016-08-01
For the first time in the International Terrestrial Reference Frame (ITRF) history, the ITRF2014 is generated with an enhanced modeling of nonlinear station motions, including seasonal (annual and semiannual) signals of station positions and postseismic deformation for sites that were subject to major earthquakes. Using the full observation history of the four space geodetic techniques (very long baseline interferometry (VLBI), satellite laser ranging (SLR), Global Navigation Satellite Systems (GNSS), and Doppler orbitography and radiopositioning integrated by satellite (DORIS)), the corresponding international services provided reprocessed time series (weekly from SLR and DORIS, daily from GNSS, and 24 h session-wise from VLBI) of station positions and daily Earth Orientation Parameters. ITRF2014 is demonstrated to be superior to past ITRF releases, as it precisely models the actual station trajectories leading to a more robust secular frame and site velocities. The ITRF2014 long-term origin coincides with the Earth system center of mass as sensed by SLR observations collected on the two LAGEOS satellites over the time span between 1993.0 and 2015.0. The estimated accuracy of the ITRF2014 origin, as reflected by the level of agreement with the ITRF2008 (both origins are defined by SLR), is at the level of less than 3 mm at epoch 2010.0 and less than 0.2 mm/yr in time evolution. The ITRF2014 scale is defined by the arithmetic average of the implicit scales of SLR and VLBI solutions as obtained by the stacking of their respective time series. The resulting scale and scale rate differences between the two solutions are 1.37 (±0.10) ppb at epoch 2010.0 and 0.02 (±0.02) ppb/yr. While the postseismic deformation models were estimated using GNSS/GPS data, the resulting parametric models at earthquake colocation sites were applied to the station position time series of the three other techniques, showing a very high level of consistency which enforces more the link
He, Tiancheng; Xue, Zhong; Alvarado, Miguel Valdivia y.; Wong, Kelvin K.; Xie, Weixin; Wong, Stephen T. C.
2013-01-01
Fluorescence microendoscopy can potentially be a powerful modality in minimally invasive percutaneous intervention for cancer diagnosis because it has an exceptional ability to provide micron-scale resolution images in tissues inaccessible to traditional microscopy. After targeting the tumor with guidance by macroscopic images such as computed tomorgraphy or magnetic resonance imaging, fluorescence microendoscopy can help select the biopsy spots or perform an on-site molecular imaging diagnosis. However, one challenge of this technique for percutaneous lung intervention is that the respiratory and hemokinesis motion often renders instability of the sequential image visualization and results in inaccurate quantitative measurement. Motion correction on such serial microscopy image sequences is, therefore, an important post-processing step. We propose a nonlinear motion compensation algorithm using a cubature Kalman filter (NMC-CKF) to correct these periodic spatial and intensity changes, and validate the algorithm using preclinical imaging experiments. The algorithm integrates a longitudinal nonlinear system model using the CKF in the serial image registration algorithm for robust estimation of the longitudinal movements. Experiments were carried out using simulated and real microendoscopy videos captured from the CellVizio 660 system in rabbit VX2 cancer intervention. The results show that the NMC-CKF algorithm yields more robust and accurate alignment results.
Salama, M.; Trubert, M.
1979-01-01
A formulation is given for the second order nonlinear equations of motion for spinning line-elements having little or no intrinsic structural stiffness. Such elements have been employed in recent studies of structural concepts for future large space structures such as the Heliogyro solar sailer. The derivation is based on Hamilton's variational principle and includes the effect of initial geometric imperfections (axial, curvature, and twist) on the line-element dynamics. For comparison with previous work, the nonlinear equations are reduced to a linearized form frequently found in the literature. The comparison has revealed several new spin-stiffening terms that have not been previously identified and/or retained. They combine geometric imperfections, rotary inertia, Coriolis, and gyroscopic terms.
Nonlinear Synchronization for Automatic Learning of 3D Pose Variability in Human Motion Sequences
Mozerov M
2010-01-01
Full Text Available A dense matching algorithm that solves the problem of synchronizing prerecorded human motion sequences, which show different speeds and accelerations, is proposed. The approach is based on minimization of MRF energy and solves the problem by using Dynamic Programming. Additionally, an optimal sequence is automatically selected from the input dataset to be a time-scale pattern for all other sequences. The paper utilizes an action specific model which automatically learns the variability of 3D human postures observed in a set of training sequences. The model is trained using the public CMU motion capture dataset for the walking action, and a mean walking performance is automatically learnt. Additionally, statistics about the observed variability of the postures and motion direction are also computed at each time step. The synchronized motion sequences are used to learn a model of human motion for action recognition and full-body tracking purposes.
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...
Molecular Motors: Power Strokes Outperform Brownian Ratchets.
Wagoner, Jason A; Dill, Ken A
2016-07-07
Molecular motors convert chemical energy (typically from ATP hydrolysis) to directed motion and mechanical work. Their actions are often described in terms of "Power Stroke" (PS) and "Brownian Ratchet" (BR) mechanisms. Here, we use a transition-state model and stochastic thermodynamics to describe a range of mechanisms ranging from PS to BR. We incorporate this model into Hill's diagrammatic method to develop a comprehensive model of motor processivity that is simple but sufficiently general to capture the full range of behavior observed for molecular motors. We demonstrate that, under all conditions, PS motors are faster, more powerful, and more efficient at constant velocity than BR motors. We show that these differences are very large for simple motors but become inconsequential for complex motors with additional kinetic barrier steps.
Brownian Ratchets: Transport Controlled by Thermal Noise
Kula, J.; Czernik, T.; Łuczka, J.
1998-02-01
We analyze directed transport of overdamped Brownian particles in a 1D spatially periodic potential that are subjected to both zero-mean thermal equilibrium Nyquist noise and zero-mean exponentially correlated dichotomous fluctuations. We show that particles can reverse the direction of average motion upon a variation of noise parameters if two fundamental symmetries, namely, the reflection symmetry of the spatial periodic structure, and the statistical symmetry of dichotomous fluctuations, are broken. There is a critical thermal noise intensity Dc, or equivalently a critical temperature Tc, at which the mean velocity of particles is zero. Below Tc and above Tc particles move in opposite directions. At fixed temperature, there is a region of noise parameters in which particles of different linear size are transported in opposite directions.
Thermal equilibrium of two quantum Brownian particles
Valente, D M
2009-01-01
The influence of the environment in the thermal equilibrium properties of a bipartite continuous variable quantum system is studied. The problem is treated within a system-plus-reservoir approach. The considered model reproduces the conventional Brownian motion when the two particles are far apart and induces an effective interaction between them, depending on the choice of the spectral function of the bath. The coupling between the system and the environment guarantees the translational invariance of the system in the absence of an external potential. The entanglement between the particles is measured by the logarithmic negativity, which is shown to monotonically decrease with the increase of the temperature. A range of finite temperatures is found in which entanglement is still induced by the reservoir.
王剑君; 廖芳芳
2011-01-01
In this paper a new kind of hybrid process is presented. Under the hypothesis of underlying asset price submitting to multidimensional Fractional Brownian Motions and Poisson Processes, by applying equivalent martingale measure, we obtain the pricing formulas of several kinds of European power options by means of the generalized pricing formula of European contingent claim.%假设标的资产价格服从受多维分数布朗运动和泊松过程共同驱动的一类混合模型，在等价鞅测度下，通过这一模型的欧式未定权益的一般定价公式，求出了几种欧式幂型期权的定价公式．
Kalkan, Erol; ,
2012-01-01
Building codes in the U.S. require at least two horizontal ground motion components for three-dimensional (3D) response history analysis (RHA) of structures. For sites within 5 km of an active fault, these records should be rotated to fault-normal/fault-parallel (FN/FP) directions, and two RHA analyses should be performed separately (when FN and then FP are aligned with transverse direction of the structural axes). It is assumed that this approach will lead to two sets of responses that envelope the range of possible responses over all non-redundant rotation angles. This assumption is examined here using 3D computer models of a single-story structure having symmetric (that is, torsionally-stiff) and asymmetric (that is, torsionally flexible) layouts subjected to an ensemble of bi-directional near-fault strong ground motions with and without apparent velocity pulses. In this parametric study, the elastic vibration period of the structures is varied from 0.2 to 5 seconds, and yield strength reduction factors R is varied from a value that leads to linear-elastic design to 3 and 5. The influence that the rotation angle of the ground motion has on several engineering demand parameters (EDPs) is examined in linear-elastic and nonlinear-inelastic domains to form a benchmark for evaluating the use of the FN/FP directions as well as the maximum-direction (MD) ground motion, a new definition of horizontal ground motions for use in the seismic design of structures according to the 2009 NEHRP Provisions and Commentary.
曹玉松
2013-01-01
针对标的资产服从几何布朗运动的期权价格风险问题，通过购买看跌风险降低股票风险，将市场分为风险市场和无风险市场，建立服从几何布朗运动的资本运营过程，使其更加贴近实际情况。讨论了风险市场和无风险市场资本运营的情况，利用随机过程相关知识给出了购买过看跌期权后的期末最终资本的市场价格期望、最终资本的市场价格超过给定值的概率及期末最终损失的期望。所得结论对预防股票风险具有一定的指导意义。% On account of the problem that option price risk of which the underline asset follows the geometric Brownian, the problem of stock hedging through buying a put option is concerned, this paper divided the market into risky market and the risk free market, and built the process of capital operation which follows the geometric Brownian. The model reflects the realities. The problem about capital operation in risky market and the risk free market is studied. Using stochastic process knowledge, the paper obtained the expectation of the final market price of the portfolio, the probability of the final market price of the portfolio which exceeds a give threshold and the expectation of the final risk. This study is useful to prevent the risk of stock.
An analytical solution to the equation of motion for the damped nonlinear pendulum
Johannessen, Kim
2014-01-01
An analytical approximation of the solution to the differential equation describing the oscillations of the damped nonlinear pendulum at large angles is presented. The solution is expressed in terms of the Jacobi elliptic functions by including a parameter-dependent elliptic modulus. The analytical...... of the damped nonlinear pendulum is presented, and it is shown that the period of oscillation is dependent on time. It is established that, in general, the period is longer than that of a linearized model, asymptotically approaching the period of oscillation of a damped linear pendulum....
A Flashing Model for Transport of Brownian Motors
赵同军; 展永; 吴建海; 王永宏
2002-01-01
A flashing coloured noise model is proposed to describe the motion of a molecular motor. In this model,the overdamped Brownian particle moves in an asymmetric periodic potential with a tashing Ornstein-Ulenbeck coloured noise. The relationship between the current and the parameters-such as the intensity, the correlation time of coloured noise and the flip rate of the noise-is discussed using the Monte Carlo simulation method.Current reversal occurs with the change of the correlation time and the flip rate of coloured noise, which may be related to the directed motion and the current reversal of molecular motors.
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.
Nonlinear Optical Response of Disordered J Aggregates in the Motional Narrowing Limit
Knoester, Jasper
1995-01-01
We discuss the theory of nonlinear optical response of molecular aggregates with frequency disorder. In contrast to the usual modeling, we allow for spatial correlations in the disorder. We show that the joint distribution of all multi-exciton frequencies can be determined analytically to first orde
Nonlinear research of an image motion stabilization system embedded in a space land-survey telescope
Somov, Yevgeny; Butyrin, Sergey; Siguerdidjane, Houria
2017-01-01
We consider an image motion stabilization system embedded into a space telescope for a scanning optoelectronic observation of terrestrial targets. Developed model of this system is presented taking into account physical hysteresis of piezo-ceramic driver and a time delay at a forming of digital control. We have presented elaborated algorithms for discrete filtering and digital control, obtained results on analysis of the image motion velocity oscillations in the telescope focal plane, and also methods for terrestrial and in-flight verification of the system.
Normalized gradient fields for nonlinear motion correction of DCE-MRI time series.
Hodneland, Erlend; Lundervold, Arvid; Rørvik, Jarle; Munthe-Kaas, Antonella Z
2014-04-01
Dynamic MR image recordings (DCE-MRI) of moving organs using bolus injections create two different types of dynamics in the images: (i) spatial motion artifacts due to patient movements, breathing and physiological pulsations that we want to counteract and (ii) signal intensity changes during contrast agent wash-in and wash-out that we want to preserve. Proper image registration is needed to counteract the motion artifacts and for a reliable assessment of physiological parameters. In this work we present a partial differential equation-based method for deformable multimodal image registration using normalized gradients and the Fourier transform to solve the Euler-Lagrange equations in a multilevel hierarchy. This approach is particularly well suited to handle the motion challenges in DCE-MRI time series, being validated on ten DCE-MRI datasets from the moving kidney. We found that both normalized gradients and mutual information work as high-performing cost functionals for motion correction of this type of data. Furthermore, we demonstrated that normalized gradients have improved performance compared to mutual information as assessed by several performance measures. We conclude that normalized gradients can be a viable alternative to mutual information regarding registration accuracy, and with promising clinical applications to DCE-MRI recordings from moving organs.
Nonlinear Nanofluid Flow over Heated Vertical Surface with Sinusoidal Wall Temperature Variations
S. S. Motsa
2014-01-01
Full Text Available The nonlinear density temperature variations in two-dimensional nanofluid flow over heated vertical surface with a sinusoidal wall temperature are investigated. The model includes the effects of Brownian motion and thermophoresis. Using the boundary layer approximation, the two-dimensional momentum, heat, and mass transfer equations are transferred to nonlinear partial differential equations form and solved numerically using a new method called spectral local linearisation method. The effects of the governing parameters on the fluid properties and on the heat and nanomass transfer coefficients are determined and shown graphically.
Brownian relaxation of an inelastic sphere in air
Bird, G. A.
2016-06-01
The procedures that are used to calculate the forces and moments on an aerodynamic body in the rarefied gas of the upper atmosphere are applied to a small sphere of the size of an aerosol particle at sea level. While the gas-surface interaction model that provides accurate results for macroscopic bodies may not be appropriate for bodies that are comprised of only about a thousand atoms, it provides a limiting case that is more realistic than the elastic model. The paper concentrates on the transfer of energy from the air to an initially stationary sphere as it acquires Brownian motion. Individual particle trajectories vary wildly, but a clear relaxation process emerges from an ensemble average over tens of thousands of trajectories. The translational and rotational energies in equilibrium Brownian motion are determined. Empirical relationships are obtained for the mean translational and rotational relaxation times, the mean initial power input to the particle, the mean rates of energy transfer between the particle and air, and the diffusivity. These relationships are functions of the ratio of the particle mass to an average air molecule mass and the Knudsen number, which is the ratio of the mean free path in the air to the particle diameter. The ratio of the molecular radius to the particle radius also enters as a correction factor. The implications of Brownian relaxation for the second law of thermodynamics are discussed.
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.
Efficiency of Brownian heat engines.
Derényi, I; Astumian, R D
1999-06-01
We study the efficiency of one-dimensional thermally driven Brownian ratchets or heat engines. We identify and compare the three basic setups characterized by the type of the connection between the Brownian particle and the two heat reservoirs: (i) simultaneous, (ii) alternating in time, and (iii) position dependent. We make a clear distinction between the heat flow via the kinetic and the potential energy of the particle, and show that the former is always irreversible and it is only the third setup where the latter is reversible when the engine works quasistatically. We also show that in the third setup the heat flow via the kinetic energy can be reduced arbitrarily, proving that even for microscopic heat engines there is no fundamental limit of the efficiency lower than that of a Carnot cycle.
R. P. Pogrebnyak
2017-08-01
Full Text Available Purpose. The article is aimed to determine the conditions of a dynamic error formation of contour machine cutting of surface of the real railway wheel flange by the cup-tip tool and propose the ways of reducing the errors. Methodology. The problem was solved by the creation of dynamic nonlinear and elastic calculation model with further modeling of its loading by the external force factors. The values of forces were obtained by analytical and experimental methods. The calculation scheme of the equilibrium support is a nonlinear two-mass system, a dynamic model of slide - single-mass with one degree of freedom. The basis of the mathematical description of technological loads is the results of factory experiments, as well as analytical generalizations obtained as a result of the comparison of several schemes of the formation of the wheel flange. Analytical determination of the components of the cutting force takes into account the changes in the kinematic parameters of the cutting mode when the profiling is done using a shaped tool. Findings. During processing of the wheel flange the radial and axial components of the cutting forces that load slide and slide-block of machine are alternating. There are conditions in drive of slide and slide-block when the gaps appear, and it is possible at any profile geometry of the wheel. The peculiarities of loading of the slide and slide-block forming a flange (with biharmonic allowance cause the occurrence of the processing areas where the gaps increase many times in drives of mechanical transmissions and error of forms increases. The dynamic system of the drive is quite tough and high-frequency and it is sensitive to the presence of gaps. Originality. The author created elastic nonlinear dynamic models of support and slide. In accordance with the model it is written and solved equations of motion of the masses and loading of the connections. The conditions of the stable motion were found. Practical value. It
Bi-Hamiltonian Structure of a Third-Order Nonlinear Evolution Equation on Plane Curve Motions
无
2007-01-01
In the present paper, we identify the integrability of the third-order nonlinear evolution equation ut = (1/2)((uxx + u)-2)x in a Hamiltonian viewpoint. We prove that the recursion operator obtained by S. Yu. Sakovich is hereditary, and then deduce a bi-Hamiltonian structure of the equation by using some decomposition of the hereditary operator. A hierarchy associated to the equation is also shown.
FU Jing-Li; FU Hao
2008-01-01
We deai with the generalization of the field method to weakly non-linear mechanico-electricai coupling systems.The field co-ordinates and field momenta approaches are combined with the method of multiple time scales in order to obtain the amplitudes and phase of oscillations in the frst approximation. An example in mechanico-electrical coupling systems is given to illustrate this method.
Westergaard, Philip G; Tieri, David; Matin, Rastin; Cooper, John; Holland, Murray; Ye, Jun; Thomsen, Jan W
2014-01-01
As an alternative to state-of-the-art laser frequency stabilisation using ultra-stable cavities, it has been proposed to exploit the non-linear effects from coupling of atoms with a narrow atomic transition to an optical cavity. Here we have constructed such a system and observed non-linear phase shifts of a narrow optical line by strong coupling of a sample of strontium-88 atoms to an optical cavity. The sample temperature of a few mK provides a domain where the Doppler energy scale is several orders of magnitude larger than the narrow linewidth of the optical transition. This makes the system sensitive to velocity dependent multi-photon scattering events (Dopplerons) that affect the cavity transmission significantly while leaving the phase signature relatively unaffected. By varying the number of atoms and the intra-cavity power we systematically study this non-linear phase signature which displays roughly the same features as for much lower temperature samples. This demonstration in a relatively simple sys...
CNT based thermal Brownian motor to pump water in nanodevices
Oyarzua, Elton; Zambrano, Harvey; Walther, Jens Honore
2016-01-01
Brownian molecular motors are nanoscale machines that exploit thermal fluctuations for directional motion by employing mechanisms such as the Feynman-Smoluchowski ratchet. In this study, using Non Equilibrium Molecular Dynamics, we propose a novel thermal Brownian motor for pumping water through...... Carbon Nanotubes (CNTs). To achieve this we impose a thermal gradient along the axis of a CNT filled with water and impose, in addition, a spatial asymmetry by 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...... 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...
Accurate 3D maps from depth images and motion sensors via nonlinear Kalman filtering
Hervier, Thibault; Goulette, François
2012-01-01
This paper investigates the use of depth images as localisation sensors for 3D map building. The localisation information is derived from the 3D data thanks to the ICP (Iterative Closest Point) algorithm. The covariance of the ICP, and thus of the localization error, is analysed, and described by a Fisher Information Matrix. It is advocated this error can be much reduced if the data is fused with measurements from other motion sensors, or even with prior knowledge on the motion. The data fusion is performed by a recently introduced specific extended Kalman filter, the so-called Invariant EKF, and is directly based on the estimated covariance of the ICP. The resulting filter is very natural, and is proved to possess strong properties. Experiments with a Kinect sensor and a three-axis gyroscope prove clear improvement in the accuracy of the localization, and thus in the accuracy of the built 3D map.
Nonlinear Effects of the Magnetotail Particle Motion in Time—dependent Electric Field
QiugangZONG; SuiyanFU; 等
1996-01-01
The Motion of charged particle in magnetotail-like reversal field with time dependent electric field is studied analytically and numerically using a test particle approach.Variations in the solar wind magnetic and/or velocity can induce a time-dependent electric field in the magnetotail.Interaction of the magnetotail particles with this electric field can give rise to stochasticity.Energy coupling from the field to the plasma is due to stochastic motion of the particles and is termed “Stochastic heating” or “stochastic acceleration”,The stochasticity can lead to heating of the plasma and to strong particle acceleration.The process can provide an explanation to the difference between ion and electron temperatures in the plasma sheet.
The theory of asynchronous relative motion I: time transformations and nonlinear corrections
Roa, Javier; Peláez, Jesús
2017-03-01
Using alternative independent variables in lieu of time has important advantages when propagating the partial derivatives of the trajectory. This paper focuses on spacecraft relative motion, but the concepts presented here can be extended to any problem involving the variational equations of orbital motion. A usual approach for modeling the relative dynamics is to evaluate how the reference orbit changes when modifying the initial conditions slightly. But when the time is a mere dependent variable, changes in the initial conditions will result in changes in time as well: a time delay between the reference and the neighbor solution will appear. The theory of asynchronous relative motion shows how the time delay can be corrected to recover the physical sense of the solution and, more importantly, how this correction can be used to improve significantly the accuracy of the linear solutions to relative motion found in the literature. As an example, an improved version of the Clohessy-Wiltshire (CW) solution is presented explicitly. The correcting terms are extremely compact, and the solution proves more accurate than the second and even third order CW equations for long propagations. The application to the elliptic case is also discussed. The theory is not restricted to Keplerian orbits, as it holds under any perturbation. To prove this statement, two examples of realistic trajectories are presented: a pair of spacecraft orbiting the Earth and perturbed by a realistic force model; and two probes describing a quasi-periodic orbit in the Jupiter-Europa system subject to third-body perturbations. The numerical examples show that the new theory yields reductions in the propagation error of several orders of magnitude, both in position and velocity, when compared to the linear approach.
The theory of asynchronous relative motion I: time transformations and nonlinear corrections
Roa, Javier; Peláez, Jesús
2016-09-01
Using alternative independent variables in lieu of time has important advantages when propagating the partial derivatives of the trajectory. This paper focuses on spacecraft relative motion, but the concepts presented here can be extended to any problem involving the variational equations of orbital motion. A usual approach for modeling the relative dynamics is to evaluate how the reference orbit changes when modifying the initial conditions slightly. But when the time is a mere dependent variable, changes in the initial conditions will result in changes in time as well: a time delay between the reference and the neighbor solution will appear. The theory of asynchronous relative motion shows how the time delay can be corrected to recover the physical sense of the solution and, more importantly, how this correction can be used to improve significantly the accuracy of the linear solutions to relative motion found in the literature. As an example, an improved version of the Clohessy-Wiltshire (CW) solution is presented explicitly. The correcting terms are extremely compact, and the solution proves more accurate than the second and even third order CW equations for long propagations. The application to the elliptic case is also discussed. The theory is not restricted to Keplerian orbits, as it holds under any perturbation. To prove this statement, two examples of realistic trajectories are presented: a pair of spacecraft orbiting the Earth and perturbed by a realistic force model; and two probes describing a quasi-periodic orbit in the Jupiter-Europa system subject to third-body perturbations. The numerical examples show that the new theory yields reductions in the propagation error of several orders of magnitude, both in position and velocity, when compared to the linear approach.
Ali Akbar Akbari
2014-08-01
Full Text Available Introduction In order to improve the quality of life of amputees, biomechatronic researchers and biomedical engineers have been trying to use a combination of various techniques to provide suitable rehabilitation systems. Diverse biomedical signals, acquired from a specialized organ or cell system, e.g., the nervous system, are the driving force for the whole system. Electromyography(EMG, as an experimental technique,is concerned with the development, recording, and analysis of myoelectric signals. EMG-based research is making progress in the development of simple, robust, user-friendly, and efficient interface devices for the amputees. Materials and Methods Prediction of muscular activity and motion patterns is a common, practical problem in prosthetic organs. Recurrent neural network (RNN models are not only applicable for the prediction of time series, but are also commonly used for the control of dynamical systems. The prediction can be assimilated to identification of a dynamic process. An architectural approach of RNN with embedded memory is Nonlinear Autoregressive Exogenous (NARX model, which seems to be suitable for dynamic system applications. Results Performance of NARX model is verified for several chaotic time series, which are applied as input for the neural network. The results showed that NARX has the potential to capture the model of nonlinear dynamic systems. The R-value and MSE are and , respectively. Conclusion EMG signals of deltoid and pectoralis major muscles are the inputs of the NARX network. It is possible to obtain EMG signals of muscles in other arm motions to predict the lost functions of the absent arm in above-elbow amputees, using NARX model.
Deborah Apthorp
Full Text Available Visually-induced illusions of self-motion (vection can be compelling for some people, but they are subject to large individual variations in strength. Do these variations depend, at least in part, on the extent to which people rely on vision to maintain their postural stability? We investigated by comparing physical posture measures to subjective vection ratings. Using a Bertec balance plate in a brightly-lit room, we measured 13 participants' excursions of the centre of foot pressure (CoP over a 60-second period with eyes open and with eyes closed during quiet stance. Subsequently, we collected vection strength ratings for large optic flow displays while seated, using both verbal ratings and online throttle measures. We also collected measures of postural sway (changes in anterior-posterior CoP in response to the same visual motion stimuli while standing on the plate. The magnitude of standing sway in response to expanding optic flow (in comparison to blank fixation periods was predictive of both verbal and throttle measures for seated vection. In addition, the ratio between eyes-open and eyes-closed CoP excursions during quiet stance (using the area of postural sway significantly predicted seated vection for both measures. Interestingly, these relationships were weaker for contracting optic flow displays, though these produced both stronger vection and more sway. Next we used a non-linear analysis (recurrence quantification analysis, RQA of the fluctuations in anterior-posterior position during quiet stance (both with eyes closed and eyes open; this was a much stronger predictor of seated vection for both expanding and contracting stimuli. Given the complex multisensory integration involved in postural control, our study adds to the growing evidence that non-linear measures drawn from complexity theory may provide a more informative measure of postural sway than the conventional linear measures.
Apthorp, Deborah; Nagle, Fintan; Palmisano, Stephen
2014-01-01
Visually-induced illusions of self-motion (vection) can be compelling for some people, but they are subject to large individual variations in strength. Do these variations depend, at least in part, on the extent to which people rely on vision to maintain their postural stability? We investigated by comparing physical posture measures to subjective vection ratings. Using a Bertec balance plate in a brightly-lit room, we measured 13 participants' excursions of the centre of foot pressure (CoP) over a 60-second period with eyes open and with eyes closed during quiet stance. Subsequently, we collected vection strength ratings for large optic flow displays while seated, using both verbal ratings and online throttle measures. We also collected measures of postural sway (changes in anterior-posterior CoP) in response to the same visual motion stimuli while standing on the plate. The magnitude of standing sway in response to expanding optic flow (in comparison to blank fixation periods) was predictive of both verbal and throttle measures for seated vection. In addition, the ratio between eyes-open and eyes-closed CoP excursions during quiet stance (using the area of postural sway) significantly predicted seated vection for both measures. Interestingly, these relationships were weaker for contracting optic flow displays, though these produced both stronger vection and more sway. Next we used a non-linear analysis (recurrence quantification analysis, RQA) of the fluctuations in anterior-posterior position during quiet stance (both with eyes closed and eyes open); this was a much stronger predictor of seated vection for both expanding and contracting stimuli. Given the complex multisensory integration involved in postural control, our study adds to the growing evidence that non-linear measures drawn from complexity theory may provide a more informative measure of postural sway than the conventional linear measures.
Imitation learning of Non-Linear Point-to-Point Robot Motions using Dirichlet Processes
Krüger, Volker; Tikhanoff, Vadim; Natale, Lorenzo
2012-01-01
In this paper we discuss the use of the infinite Gaussian mixture model and Dirichlet processes for learning robot movements from demonstrations. Starting point of this work is an earlier paper where the authors learn a non-linear dynamic robot movement model from a small number of observations....... The model in that work is learned using a classical finite Gaussian mixture model (FGMM) where the Gaussian mixtures are appropriately constrained. The problem with this approach is that one needs to make a good guess for how many mixtures the FGMM should use. In this work, we generalize this approach...
Olmez, O.; Ozbulut, M.; Yildiz, M.; Goren, O.
2016-06-01
The present study investigates the vortical and nonlinear effects in the roll motion of a 2-D body with square cross-sections by using Smoothed Particle Hydrodynamics (SPH). A 2-D rigid body with square cross-section is taken into account for the benchmark study and subjected to the oscillatory roll motion with a given angular frequency. The governing equations are continuity equation and Euler's equation with artificial viscosity term. Weakly Compressible SPH (WCSPH) scheme is employed for the discretization of the governing equations. Velocities of the fluid particles are updated by means of XSPH+Artificial Particle Displacement (VXSPH+APD) algorithm. In this method only the free surface fluid particles are subjected to VXSPH algorithm while the APD algorithm is employed for the fully populated flow regions. The hybrid usage of numerical treatment keeps free surface particles together by creating an artificial surface tension on the free surface. VXSPH+APD is a proven numerical treatment to provide the most accurate results for this type of free surface flows (Ozbulut et al. 2014). The results of the present study are compared with those of the experimental studies as well as with those of the numerical methods obtained from the current literature.
Schaub, Hanspeter
1998-12-01
Novel sets of attitude coordinates called the Stereographic Parameters (SPs) and configuration quasivelocity coordinates called the Eigenfactor Quasivelocities (EQVs) are discussed. The SPs are generated through stereographic projections of the Euler parameter constraint hypersphere onto hyperplanes. SP sets are non-unique and have distinct alternate sets referred to as shadow sets. They abide by the same differential kinematic equation, but generally display a different singular behavior. Explicit expressions are developed that map the original SP set to the shadow set and thus avoid any singularities. Both symmetric SPs such as the classical and Modified Rodrigues Parameters (MRPs), as well as asymmetric SPs are discussed. A globally asymptotically stable MRP feedback law which tracks any reference trajectory is presented. Both unsaturated and saturated control cases are discussed. Further, an MRP costate switching condition is developed that allows both original and shadow MRPs to be used simultaneously in optimal control problems. The Lagrange equations of motion in terms of the n-dimensional EQV vector are developed. The EQV formulation has an identity mass matrix which results in no matrix inverse being taken in numerical simulations. An explicit expression is presented that incorporates Pfaffian non-holonomic constraints into the EQV formulation without increasing the system order. Unfortunately, the use of EQV in numerical simulations only proved beneficial in selected cases. Generally the computational burden proved too high. However, the EQVs are found to be valuable when used as velocity feedback coordinates. EQV feedback laws have an exponentially decaying kinetic energy, superior performance to traditional state velocity feedback laws and are found to decouple the motion of multi-link robotic systems. The equations of motion and steering laws of spacecraft containing Variable Speed Control Moment Gyroscopes (VSCMGs) are developed. Contrary to classical
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.
Statistical Properties of Thermal Noise Driving the Brownian Particles in Fluids
Tóthová Jana
2016-01-01
Full Text Available In several recent works high-resolution interferometric detection allowed to study the Brownian motion of optically trapped microparticles in air and fluids. The observed positional fluctuations of the particles are well described by the generalized Langevin equation with the Boussinesq-Basset “history force” instead of the Stokes friction, which is valid only for the steady motion. Recently, also the time correlation function of the thermal random force Fth driving the Brownian particles through collisions with the surrounding molecules has been measured. In the present contribution we propose a method to describe the statistical properties of Fth in incompressible fluids. Our calculations show that the time decay of the correlator 〈Fth(tFth(0〉 is significantly slower than that found in the literature. It is also shown how the “color” of the thermal noise can be determined from the measured positions of the Brownian particles.
N·安布泽志昂; K·斯里尼瓦桑; K·钱德拉塞卡兰; R·坎达沙密; 海治
2012-01-01
The problem of laminar fluid flow resulted from the stretching of a vertical surface with variable stream conditions in a nanofluid due to solar energ was investigated numerically.The model used for the nanofluid incorporated the effects of Brownian motion and thermophoresis in the presence of thermal stratification.The symmetry groups admitted by the corresponding boundary value problem were obtained by using a special form of Lie group transformations viz.scaling group of transformations.An exact solution was obtained for translation symmetry and numerical solutions for scaling symmetry.This solution depended on a Lewis number,Brownian motion parameter,thermal stratification parameter and thermophoretic parameter.The conclusion was drawn that the flow field and temperature and nanoparticle volume fraction profiles were significantly influenced by these parameters.Nanofluids were shown to increase the thermal conductivity and convective heat transfer performance of the base liquids.Nanoparticles in the base fluid also offered the potential of improving the radiative properties of the liquids,leading to an increase in the efficiency of direct absorption solar collectors.%在太阳辐射下的纳米流体中,数值地研究竖向延伸壁面具有可变流条件时的层流运动.使用的纳米流体模型为,在热分层中综合考虑了Brown运动和热泳的影响.应用一个特殊形式的Lie群变换,即缩放群变换,得到相应边值问题的对称群.对平移对称群得到一个精确解,对缩放对称群得到数值解.数值解依赖于Lewis数、Brown运动参数、热分层参数和热泳参数.得到结论:上述参数明显地影响着流场、温度和纳米粒子体积率的分布.显示出纳米流体提高了基流体热传导率和对流的热交换性能,基流体中的纳米粒子还具有改善液体辐射性能的作用,直接提高了太阳能集热器的吸热效率.
王栋; 唐长庆; 田宝国; 曲亮生; 张金春; 狄增如
2014-01-01
循环竞争博弈常被用来研究物种多样性。以前有关循环竞争博弈的研究工作所考虑的相互作用距离模式包括最近邻、取固定距离或一定距离以内的随机值，这与实际情况不相符。考虑到实际生物系统中物种个体做列维飞行与布朗运动的情况广泛存在，综合考虑了最近邻相互作用模式和列维飞行(布朗运动)长程相互作用模式，对循环竞争博弈及保持物种多样性的条件进行了研究。得到了最大飞行距离与选择概率的临界关系(包括Logistic式和指数式关系)，进一步得到了幂指数与选择概率的临界关系，以及保持物种共存的条件。%Cyclical game is often used to study the biodiversity in ecosystem. However, the interaction distance mode con-sidered in previous studies of cyclical game is only the interaction between nearest neighbors, a fixed distance, or a random value of fixed distance among the individuals of species. This is not consistent with the actual situation. In this paper, considering the fact that Levy flight and Brownian motion widespreadly exist in ecosystem, and comprehensively considering the nearest-neighbor-interaction and long-range-interaction given by Levy flight and Brownian motion, the cyclical game and conditions of maintaining biodiversity are investigated. The critical relation of maximal step length of flight versus choosing probability is presented, including Logistic and exponent relations. Further the critical relation between power-law exponent and choosing probability is found. The condition of maintaining species coexistence is also found.
Katsuichiro eGoda
2015-06-01
Full Text Available This study investigates the effects of earthquake types, magnitudes, and hysteretic behavior on the peak and residual ductility demands of inelastic single-degree-of-freedom systems and evaluates the effects of major aftershocks on the nonlinear structural responses. An extensive dataset of real mainshock-aftershock sequences for Japanese earthquakes is developed. The constructed dataset is large, compared with previous datasets of similar kinds, and includes numerous sequences from the 2011 Tohoku earthquake, facilitating an investigation of spatial aspects of the aftershock effects. The empirical assessment of peak and residual ductility demands of numerous inelastic systems having different vibration periods, yield strengths, and hysteretic characteristics indicates that the increase in seismic demand measures due to aftershocks occurs rarely but can be significant. For a large mega-thrust subduction earthquake, a critical factor for major aftershock damage is the spatial occurrence process of aftershocks.
Non-linear water waves generated by impulsive motion of submerged obstacle
N. I. Makarenko
2013-12-01
Full Text Available Fully nonlinear problem on unsteady water waves generated by impulsively moving obstacle is studied analytically. Our method involves the reduction of Euler equations to the integral-differential system for the wave elevation together with normal and tangential fluid velocities at the free surface. Exact model equations are derived in explicit form in the case when the isolated obstacle is presented by totally submerged elliptic cylinder. Small-time asymptotic solution is constructed for the cylinder which starts with constant acceleration from rest. It is demonstrated that the leading-order solution terms describe several wave regimes such as the formation of non-stationary splash jets by vertical rising or vertical submersion of the obstacle, as well as the generation of diverging waves is observed.
Brownian dynamics without Green's functions
Delong, Steven; Donev, Aleksandar, E-mail: donev@courant.nyu.edu [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States); Usabiaga, Florencio Balboa; Delgado-Buscalioni, Rafael [Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Univeridad Autónoma de Madrid, Madrid 28049 (Spain); Griffith, Boyce E. [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States); Leon H. Charney Division of Cardiology, Department of Medicine, New York University School of Medicine, New York, New York 10016 (United States)
2014-04-07
We develop a Fluctuating Immersed Boundary (FIB) method for performing Brownian dynamics simulations of confined particle suspensions. Unlike traditional methods which employ analytical Green's functions for Stokes flow in the confined geometry, the FIB method uses a fluctuating finite-volume Stokes solver to generate the action of the response functions “on the fly.” Importantly, we demonstrate that both the deterministic terms necessary to capture the hydrodynamic interactions among the suspended particles, as well as the stochastic terms necessary to generate the hydrodynamically correlated Brownian motion, can be generated by solving the steady Stokes equations numerically only once per time step. This is accomplished by including a stochastic contribution to the stress tensor in the fluid equations consistent with fluctuating hydrodynamics. We develop novel temporal integrators that account for the multiplicative nature of the noise in the equations of Brownian dynamics and the strong dependence of the mobility on the configuration for confined systems. Notably, we propose a random finite difference approach to approximating the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. Through comparisons with analytical and existing computational results, we numerically demonstrate the ability of the FIB method to accurately capture both the static (equilibrium) and dynamic properties of interacting particles in flow.
Non-conservative optical forces and Brownian vortexes
Sun, Bo
Optical manipulation using optical tweezers has been widely adopted in physics, chemical engineering and biology. While most applications and fundamental studies of optical trapping have focused on optical forces resulting from intensity gradients, we have also explored the role of radiation pressure, which is directed by phase gradients in beams of light. Interestingly, radiation pressure turns out to be a non-conservative force and drives trapped objects out of thermodynamic equilibrium with their surrounding media. We have demonstrated the resulting nonequilibrium effects experimentally by tracking the thermally driven motions of optically trapped colloidal spheres using holographic video microscopy. Rather than undergoing equilibrium thermal fluctuations, as has been assumed for more than a quarter century, a sphere in an optical tweezer enters into a stochastic steady-state characterized by closed loops in its probability current density. These toroidal vortexes constitute a bias in the particle's otherwise random thermal fluctuations arising at least indirectly from a solenoidal component in the optical force. This surprising effect is a particular manifestation of a more general class of noise-driven machines that we call Brownian vortexes. This previously unrecognized class of stochastic heat engines operates on qualitatively different principles from such extensively studied nonequilibrium systems as thermal ratchets and Brownian motors. Among its interesting properties, a Brownian vortex can reverse its direction with changes in temperature or equivalent control parameters.
Mustafa, M.; Khan, Junaid Ahmad
2015-07-01
Present work deals with the magneto-hydro-dynamic flow and heat transfer of Casson nanofluid over a non-linearly stretching sheet. Non-linear temperature distribution across the sheet is considered. More physically acceptable model of passively controlled wall nanoparticle volume fraction is accounted. The arising mathematical problem is governed by interesting parameters which include Casson fluid parameter, magnetic field parameter, power-law index, Brownian motion parameter, thermophoresis parameter, Prandtl number and Schmidt number. Numerical solutions are computed through fourth-fifth-order-Runge-Kutta integration approach combined with the shooting technique. Both temperature and nanoparticle volume fraction are increasing functions of Casson fluid parameter.
Stevanella, Marco; Votta, Emiliano; Redaelli, Alberto
2009-12-01
Finite element modeling represents an established method for the comprehension of the mitral function and for the simulation of interesting clinical scenarios. However, current models still do not include all the key aspects of the real system. We implemented a new structural finite element model that considers (i) an accurate morphological description of the valve, (ii) a description of the tissues' mechanical properties that accounts for anisotropy and nonlinearity, and (iii) dynamic boundary conditions that mimic annulus and papillary muscles' contraction. The influence of such contraction on valve biomechanics was assessed by comparing the computed results with the ones obtained through an auxiliary model with fixed annulus and papillary muscles. At the systolic peak, the leaflets' maximum principal stress contour showed peak values in the anterior leaflet at the strut chordae insertion zone (300 kPa) and near the annulus (200-250 kPa), while much lower values were detected in the posterior leaflet. Both leaflets underwent larger tensile strains in the longitudinal direction, while in the circumferential one the anterior leaflet experienced nominal tensile strains up to 18% and the posterior one experienced compressive strains up to 23% associated with the folding of commissures and paracommissures, consistently with tissue redundancy. The force exerted by papillary muscles at the systolic peak was equal to 4.11 N, mainly borne by marginal chordae (76% of the force). Local reaction forces up to 45 mN were calculated on the annulus, leading to tensions of 89 N/m and 54 N/m for its anterior and posterior tracts, respectively. The comparison with the results of the auxiliary model showed that annular contraction mainly affects the leaflets' circumferential strains. When it was suppressed, no more compressive strains could be observed and peak strain values were located in the belly of the anterior leaflet. Computational results agree to a great extent with
Mechanical radiation detection via sub-Brownian lever deflections
Hammig, Mark David
2005-07-01
A micromechanical lever that deflects in response to the impacts of charged particles is proposed as a means of improving upon the capabilities of existing radiation detection technology. When a particle strikes an object, momentum is transferred to the impacted body. The resulting body motion can be correlated to the energy of the incident particle. The momentum detector offers promise as a highly discriminating, high-resolution tool for ion sensing. Advances required to successfully realize a spectroscopic capability have been completed; specifically, techniques for reproducibly fabricating micromechanical structures have been optimized, and an instrument that measures miniscule deflections has been developed. Even absent substantial refinement efforts, the novel coupled-cavity optical detector can resolve lever motions on the order of 1--10 picometers. A method by which the Brownian motion of the lever can be stilled has been proven which elicits reductions sufficient to measure heavy-ion impact, the deflections from which may be several orders of magnitude below the thermal vibration amplitude. Using active forcing techniques, the Brownian vibration of the microlevers has been reduced from room temperature (288 K) to sub-Kelvin temperatures, for levers vibrating in air. The mechanical factors that limit the noise reduction magnitude are discussed and methods of surmounting those limitations are identified.
Trajectories of Brownian particles with space-correlated noise
EDOARDO MILOTTI
2017-07-01
The Langevin equation used to model Brownian motion includes a stochastic process that is routinely assumed to be a Gaussian white noise. Spatial correlations of the noise are usually ruled out, and the paths traced by the random walkers are statistically independent. In this study, I consider instead noise which is white in time and has a Gaussian correlation in space, and by means of numerical simulation, I show how the spatial correlation determines the time evolution of the spatial separation of random walkers.
Minimal Cost of a Brownian Risk without Ruin
Luo, Shangzhen
2011-01-01
In this paper, we study a risk process modeled by a Brownian motion with drift (the diffusion approximation model). The insurance entity can purchase reinsurance to lower its risk and receive cash injections at discrete times to avoid ruin. Proportional reinsurance and excess-of-loss reinsurance are considered. The objective is to find the optimal reinsurance and cash injection strategy that minimizes the total cost to keep the company's surplus process non-negative, i.e. without ruin, where the cost function is defined as the total discounted value of the injections. The optimal solution is found explicitly by solving the according quasi-variational inequalities (QVIs).
熊海灵; 杨志敏; 李航
2015-01-01
The cluster-cluster aggregation (CCA) model bridges the study of colloid aggregation by computer simulation and laboratory experiment. Two distinct and limiting regimes of irreversible colloid aggregation have been identified by computer simulation with the CCA model. One regime is diffusion-limited cluster aggregation (DLCA) corresponding to the rapid colloid aggregation. The other is reaction-limited cluster aggregation (RLCA) corresponding to the slow colloid aggregation. The simulations of the two regimes are both start with N non-overlapping identical particles distributed randomly in a cubic box with side-lengths of L. A three dimensional array, hypothetically named Cube[L][L][L], was usually used to represent the cubic box. Each particle in the cubic box occupies an element of the three dimensional array and are labeled with a different integer. When particles and/or clusters collide and aggregate, all particles in the resulting cluster are modified with the same label (one of them). The progression of Brownian movement and aggregation are realized by updating the labels of the corresponding array elements. However, a critical issue in this kind of simulation is how to efficiently distinguish all of the particles in any selected cluster only based on the three dimensional array Cube[L][L][L] when the cluster is to be moved. Similarly, there are difficulties in the process of collision detection to locate all neighboring positions of the cluster. The traditional method must perform exhaustive search in the whole system, what’s more, this kind of exhaustive search will repeated over and over again in the simulation progression. In this paper, the traditional on-lattice CCA algorithm is optimized by improving the storage structure to reduce the time complexity, in which the simulation system is represented by a three dimensional array, while the clusters in the system are simultaneously stored by the linked lists respectively in programming. Another one
罗平平; 王兰甫; 范波; 张芳
2012-01-01
In order to study the influence of aperture distribution on the infiltration in a single fracture, based on the fractal theory of multi-fractional Brownian motion（MBM）, four groups of fracture surfaces at different regularization dimensions are constructed, all of which more realistically reflect the asymptotic self-similarity of aperture distribution of natural fracture surface. From the numerical simulation of grouting in a single random aperture fracture, it is indicated that pressure contours show twists and turns spreading over time, which reflects the distinct non-uniform characteristics. The distribution of closed area has a tendency that is from dot-like scatter to focused plane with the regularization dimensions tending to reduce, and its spatial location has obvious influence on the pressure and grouting time. As the development of percolation, there appears a tendency that the node pressure is from monotonically rapid increase to stepwise stability, and the more the node approaching the percolation border, the shorter the grouting time used in the case of reaching the steady pressure. Moreover, there is a power relationship between the node pressure and the grouting time. In view of this rule, empirical equations with different parameters are also obtained by fitting curves.%为了研究单裂隙面隙宽分布对浆液渗透的影响,基于多重分数布朗运动（MBM）分形理论构建出4种不同规则维数下的随机隙宽单裂隙几何模型,从而较真实的反应了天然裂隙面隙宽分布的局部渐进自相似性。通过注浆数值模拟研究发现,压力等值线随时间延续呈现曲折扩散形式,反映了其非均匀渗透特征。裂隙面闭合区分布形态随规则维数降低由点状散布趋向面状集中,其空间位置对浆液后期渗透压力和全程注浆时间影响很大;并且随着浆液入渗发展,节点压力由前期的较快单调增长到后期逐步趋于稳定,越靠近入渗边界的节点
Hayat, T. [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia); Muhammad, Taseer, E-mail: taseer_qau@yahoo.com [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Alsaedi, A.; Alhuthali, M.S. [Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia)
2015-07-01
Magnetohydrodynamic (MHD) three-dimensional flow of couple stress nanofluid in the presence of thermophoresis and Brownian motion effects is analyzed. Energy equation subject to nonlinear thermal radiation is taken into account. The flow is generated by a bidirectional stretching surface. Fluid is electrically conducting in the presence of a constant applied magnetic field. The induced magnetic field is neglected for a small magnetic Reynolds number. Mathematical formulation is performed using boundary layer analysis. Newly proposed boundary condition requiring zero nanoparticle mass flux is employed. The governing nonlinear mathematical problems are first converted into dimensionless expressions and then solved for the series solutions of velocities, temperature and nanoparticles concentration. Convergence of the constructed solutions is verified. Effects of emerging parameters on the temperature and nanoparticles concentration are plotted and discussed. Skin friction coefficients and Nusselt number are also computed and analyzed. It is found that the thermal boundary layer thickness is an increasing function of radiative effect. - Highlights: • Three-dimensional boundary layer flow of viscoelastic nanofluid is examined. • Nonlinear thermal radiation is analyzed. • Brownian motion and thermophoresis effects are present. • Recently developed condition requiring zero nanoparticle mass flux is implemented. • Construction of convergent solutions of nonlinear flow is possible.
On magnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet
Hayat, Tasawar [Department of Mathematics, Quaid-I-Azam University, Islamabad 44000 (Pakistan); Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia); Aziz, Arsalan [Department of Mathematics, Quaid-I-Azam University, Islamabad 44000 (Pakistan); Muhammad, Taseer, E-mail: taseer_qau@yahoo.com [Department of Mathematics, Quaid-I-Azam University, Islamabad 44000 (Pakistan); Ahmad, Bashir [Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia)
2016-06-15
This research article addresses the magnetohydrodynamic (MHD) flow of second grade nanofluid over a nonlinear stretching sheet. Heat and mass transfer aspects are investigated through the thermophoresis and Brownian motion effects. Second grade fluid is assumed electrically conducting through a non-uniform applied magnetic field. Mathematical formulation is developed subject to small magnetic Reynolds number and boundary layer assumptions. Newly constructed condition having zero mass flux of nanoparticles at the boundary is incorporated. Transformations have been invoked for the reduction of partial differential systems into the set of nonlinear ordinary differential systems. The governing nonlinear systems have been solved for local behavior. Graphical results of different influential parameters are studied and discussed in detail. Computations for skin friction coefficient and local Nusselt number have been carried out. It is observed that the effects of thermophoresis parameter on the temperature and nanoparticles concentration distributions are qualitatively similar. The temperature and nanoparticles concentration distributions are enhanced for the larger magnetic parameter. - Highlights: • Constitutive relation for second grade fluid is employed. • Flow is caused by a nonlinear stretching surface. • Magnetic field applied is in transverse direction. • Nanofluid model consists of Brownian motion and thermophoresis. • Magnetic Reynolds number is assumed small.
Francisco L. Silva-González
2014-01-01
Full Text Available A non-Gaussian stochastic equivalent linearization (NSEL method for estimating the non-Gaussian response of inelastic non-linear structural systems subjected to seismic ground motions represented as nonstationary random processes is presented. Based on a model that represents the time evolution of the joint probability density function (PDF of the structural response, mathematical expressions of equivalent linearization coefficients are derived. The displacement and velocity are assumed jointly Gaussian and the marginal PDF of the hysteretic component of the displacement is modeled by a mixed PDF which is Gaussian when the structural behavior is linear and turns into a bimodal PDF when the structural behavior is hysteretic. The proposed NSEL method is applied to calculate the response of hysteretic single-degree-of-freedom systems with different vibration periods and different design displacement ductility values. The results corresponding to the proposed method are compared with those calculated by means of Monte Carlo simulation, as well as by a Gaussian equivalent linearization method. It is verified that the NSEL approach proposed herein leads to maximum structural response standard deviations similar to those obtained with Monte Carlo technique. In addition, a brief discussion about the extension of the method to muti-degree-of-freedom systems is presented.
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.
Brownian Ratchets in Biophysics: from Diffusing Phospholipids to Polymerizing Actin Filaments
van Oudenaarden, Alexander
2000-03-01
In the 'Feynman Lectures on Physics' Feynman introduces a mechanical ratchet and pawl subjected to thermal fluctuations to demonstrate the impossibility to violate the second law of thermodynamics. Since this introduction the Brownian ratchet has evolved from Gedanken experiments to real experiments in the interdisciplinary sciences such as biophysics and biochemistry. In this symposium I will present two experiments in which the concept Brownian ratchet is of key importance. The first experiment addresses a so-called geometrical Brownian ratchet [1]. This ratchet consists of a two-dimensional microfabricated periodic array of asymmetric diffusion barriers. As an experimental realization of a two-dimensional fluid of Brownian particles, a bilayer of phospholipid molecules is used. I will demonstrate that the geometrical Brownian ratchet can be used as a molecular sieve to separate mixtures of membrane molecules without the need to extract them from the membrane. In the second experiment I explore the spontaneous symmetry breaking of polymerizing actin networks [2]. Small submicron size beads coated uniformly with a protein that catalyzes actin polymerization, are initially surrounded by a symmetrical cloud of actin filaments. This symmetry can be broken spontaneously after which the beads undergo directional motion with constant velocity. I will present a simple stochastic theory, in which each filament is modeled as an elastic Brownian ratchet that qualitatively reproduces the experimental results. The presence of the bead couples the dynamics of different filaments which results in a complex collective system of interacting Brownian ratchets that exhibits an emergent symmetry breaking behavior. [1] A. van Oudenaarden and S. G. Boxer, Science 285, 1046 (1999). [2] A. van Oudenaarden and J. A. Theriot, Nature Cell Biology 1, 493 (1999).
Steady nanofluid flow between parallel plates considering thermophoresis and Brownian effects
M. Sheikholeslami
2016-10-01
Full Text Available In this article, heat and mass transfer behavior of steady nanofluid flow between parallel plates in the presence of uniform magnetic field is studied. The important effect of Brownian motion and thermophoresis has been included in the model of nanofluid. The governing equations are solved via the Differential Transformation Method. The validity of this method was verified by comparison of previous work which is done for viscous fluid. The analysis is carried out for different parameters namely: viscosity parameter, Magnetic parameter, thermophoretic parameter and Brownian parameter. Results reveal that skin friction coefficient enhances with rise of viscosity and Magnetic parameters. Also it can be found that Nusselt number augments with an increase of viscosity parameters but it decreases with augment of Magnetic parameter, thermophoretic parameter and Brownian parameter.
Probing Brownian relaxation in water-glycerol mixtures using magnetic hyperthermia
Nemala, Humeshkar; Milgie, Michael; Wadehra, Anshu; Thakur, Jagdish; Naik, Vaman; Naik, Ratna
2013-03-01
Generation of heat by magnetic nanoparticles in the presence of an external oscillating magnetic field is known as magnetic hyperthermia (MHT). This heat is generated by two mechanisms: the Neel relaxation and Brownian relaxation. While the internal spin relaxation of the nanoparticles known as Neel relaxation is largely dependent on the magnetic properties of the nanoparticles, the physical motion of the particle or the Brownian relaxation is largely dependent on the viscous properties of the carrier liquid. The MHT properties of dextran coated iron oxide nanoparticles have been investigated at a frequency of 400KHz. To understand the influence of Brownian relaxation on heating, we probe the MHT properties of these ferrofluids in water-glycerol mixtures of varying viscosities. The heat generation is quantified using the specific absorption rate (SAR) and its maximum at a particular temperature is discussed with reference to the viscosity.
The Asymmetric Exclusion Process and Brownian Excursions
Derrida, B.; Enaud, C.; Lebowitz, J. L.
2004-04-01
We consider the totally asymmetric exclusion process (TASEP) in one dimension in its maximal current phase. We show, by an exact calculation, that the non-Gaussian part of the fluctuations of density can be described in terms of the statistical properties of a Brownian excursion. Numerical simulations indicate that the description in terms of a Brownian excursion remains valid for more general one dimensional driven systems in their maximal current phase.
Fluctuation relations for a driven Brownian particle
Imparato, A.; Peliti, L.
2006-08-01
We consider a driven Brownian particle, subject to both conservative and nonconservative applied forces, whose probability evolves according to the Kramers equation. We derive a general fluctuation relation, expressing the ratio of the probability of a given Brownian path in phase space with that of the time-reversed path, in terms of the entropy flux to the heat reservoir. This fluctuation relation implies those of Seifert, Jarzynski, and Gallavotti-Cohen in different special cases.
Dijkstra, Arend G
2015-01-01
We study hole, electron and exciton transport in a charge transfer system in the presence of underdamped vibrational motion. We analyze the signature of these processes in the linear and third-, and fifth-order nonlinear electronic spectra. Calculations are performed with a numerically exact hierarchical equations of motion method for an underdamped Brownian oscillator spectral density. We find that combining electron, hole and exciton transfer can lead to non-trivial spectra with more structure than with excitonic coupling alone. Traces taken during the waiting time of a two-dimensional spectrum are dominated by vibrational motion and do not reflect the electron, hole, and exciton dynamics directly. We find that the fifth-order nonlinear response is particularly sensitive to the charge transfer process. While third-order 2D spectroscopy detects the correlation between two coherences, fifth-order 2D spectroscopy (2D population spectroscopy) is here designed to detect correlations between the excited states du...
Liu, Shuxiao; Tang, Yougang; Li, Wei
2016-06-01
In this study, we consider first- and second-order random wave loads and the effects of time-varying displacement volume and transient wave elevation to establish motion equations of the Spar platform's coupled heave-pitch. We generated random wave loads based on frequency-domain wave load transfer functions and the Joint North Sea Wave Project (JONSWAP) wave spectrum, designed program codes to solve the motion equations, and then simulated the coupled heave-pitch motion responses of the platform in the time domain. We then calculated and compared the motion responses in different sea conditions and separately investigated the effects of second-order random wave loads and transient wave elevation. The results show that the coupled heave-pitch motion responses of the platform are primarily dominated by wave height and the characteristic wave period, the latter of which has a greater impact. Second-order mean wave loads mainly affect the average heave value. The platform's pitch increases after the second-order low frequency wave loads are taken into account. The platform's heave is underestimated if the transient wave elevation term in the motion equations is neglected.
1/f noise from the nonlinear transformations of the variables
Kaulakys, B; Ruseckas, J
2015-01-01
The origin of the low-frequency noise with power spectrum $1/f^\\beta$ (also known as $1/f$ fluctuations or flicker noise) remains a challenge. Recently, the nonlinear stochastic differential equations for modeling $1/f^\\beta$ noise have been proposed and analyzed. Here we use the self-similarity properties of this model with respect to the nonlinear transformations of the variable of these equations and show that $1/f^\\beta$ noise of the observable may yield from the power-law transformations of well-known standard processes, like the Brownian motion, Bessel and similar stochastic processes. Analytical and numerical investigations of such techniques for modeling processes with $1/f^\\beta$ fluctuations is presented.
Intermediate scattering function of an anisotropic active Brownian particle
Kurzthaler, Christina; Leitmann, Sebastian; Franosch, Thomas
2016-10-01
Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations.
Derras, Boumédiène; Bard, Pierre-Yves; Cotton, Fabrice
2017-09-01
The aim of this paper is to investigate the ability of various site-condition proxies (SCPs) to reduce ground-motion aleatory variability and evaluate how SCPs capture nonlinearity site effects. The SCPs used here are time-averaged shear-wave velocity in the top 30 m ( V S30), the topographical slope (slope), the fundamental resonance frequency ( f 0) and the depth beyond which V s exceeds 800 m/s ( H 800). We considered first the performance of each SCP taken alone and then the combined performance of the 6 SCP pairs [ V S30- f 0], [ V S30- H 800], [ f 0-slope], [ H 800-slope], [ V S30-slope] and [ f 0- H 800]. This analysis is performed using a neural network approach including a random effect applied on a KiK-net subset for derivation of ground-motion prediction equations setting the relationship between various ground-motion parameters such as peak ground acceleration, peak ground velocity and pseudo-spectral acceleration PSA ( T), and M w, R JB, focal depth and SCPs. While the choice of SCP is found to have almost no impact on the median ground-motion prediction, it does impact the level of aleatory uncertainty. V S30 is found to perform the best of single proxies at short periods ( T < 0.6 s), while f 0 and H 800 perform better at longer periods; considering SCP pairs leads to significant improvements, with particular emphasis on [ V S30- H 800] and [ f 0-slope] pairs. The results also indicate significant nonlinearity on the site terms for soft sites and that the most relevant loading parameter for characterising nonlinear site response is the "stiff" spectral ordinate at the considered period.[Figure not available: see fulltext.
Thermal equilibrium of a Brownian particle in a fluctuating fluid: a numerical study
Liu, Yi; Nie, Deming
2017-07-01
In this work the fluctuating lattice Boltzmann method was adopted to simulate the motion of a Brownian particle in a fluid in two dimensions. The temperatures characterizing the translation motion and rotational motion of the particle were calculated to evaluate the thermal equilibrium between the particle and the fluid. Furthermore, the effects of the fluid temperature and viscosity on the fluid pressure fluctuation were investigated. The linear relationships were observed in a log-log coordinate. Besides, the slopes of the linear relation were obtained, which keeps constant for all cases studied.
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.
CNT based thermal Brownian motor to pump water in nanodevices
Oyarzua, Elton; Zambrano, Harvey; Walther, J. H.
2016-11-01
Brownian molecular motors are nanoscale machines that exploit thermal fluctuations for directional motion by employing mechanisms such as the Feynman-Smoluchowski ratchet. In this study, using Non Equilibrium Molecular Dynamics, we propose a novel thermal Brownian motor for pumping water through Carbon Nanotubes (CNTs). To achieve this we impose a thermal gradient along the axis of a CNT filled with water and impose, in addition, a spatial asymmetry by fixing specific zones on the CNT in order to modify the vibrational modes of the CNT. We find that the temperature gradient and imposed spatial asymmetry drive the water flow in a preferential direction. We systematically modified the magnitude of the applied thermal gradient and the axial position of the fixed points. The analysis involves measurement of the vibrational modes in the CNTs using a Fast Fourier Transform (FFT) algorithm. We observed water flow in CNTs of 0.94, 1.4 and 2.0 nm in diameter, reaching a maximum velocity of 5 m/s for a thermal gradient of 3.3 K/nm. The proposed thermal motor is capable of delivering a continuous flow throughout a CNT, providing a useful tool for driving liquids in nanofluidic devices by exploiting thermal gradients. We aknowledge partial support from Fondecyt project 11130559.
On magnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet
Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Ahmad, Bashir
2016-06-01
This research article addresses the magnetohydrodynamic (MHD) flow of second grade nanofluid over a nonlinear stretching sheet. Heat and mass transfer aspects are investigated through the thermophoresis and Brownian motion effects. Second grade fluid is assumed electrically conducting through a non-uniform applied magnetic field. Mathematical formulation is developed subject to small magnetic Reynolds number and boundary layer assumptions. Newly constructed condition having zero mass flux of nanoparticles at the boundary is incorporated. Transformations have been invoked for the reduction of partial differential systems into the set of nonlinear ordinary differential systems. The governing nonlinear systems have been solved for local behavior. Graphical results of different influential parameters are studied and discussed in detail. Computations for skin friction coefficient and local Nusselt number have been carried out. It is observed that the effects of thermophoresis parameter on the temperature and nanoparticles concentration distributions are qualitatively similar. The temperature and nanoparticles concentration distributions are enhanced for the larger magnetic parameter.
A surface-bound molecule that undergoes optically biased Brownian rotation
Hutchison, James A.; Uji-I, Hiroshi; Deres, Ania; Vosch, Tom; Rocha, Susana; Müller, Sibylle; Bastian, Andreas A.; Enderlein, Jörg; Nourouzi, Hassan; Li, Chen; Herrmann, Andreas; Müllen, Klaus; de Schryver, Frans; Hofkens, Johan
2014-02-01
Developing molecular systems with functions analogous to those of macroscopic machine components, such as rotors, gyroscopes and valves, is a long-standing goal of nanotechnology. However, macroscopic analogies go only so far in predicting function in nanoscale environments, where friction dominates over inertia. In some instances, ratchet mechanisms have been used to bias the ever-present random, thermally driven (Brownian) motion and drive molecular diffusion in desired directions. Here, we visualize the motions of surface-bound molecular rotors using defocused fluorescence imaging, and observe the transition from hindered to free Brownian rotation by tuning medium viscosity. We show that the otherwise random rotations can be biased by the polarization of the excitation light field, even though the associated optical torque is insufficient to overcome thermal fluctuations. The biased rotation is attributed instead to a fluctuating-friction mechanism in which photoexcitation of the rotor strongly inhibits its diffusion rate.
Carasso, Alfred S
2013-01-01
Identifying sources of ground water pollution, and deblurring nanoscale imagery as well as astronomical galaxy images, are two important applications involving numerical computation of parabolic equations backward in time. Surprisingly, very little is known about backward continuation in nonlinear parabolic equations. In this paper, an iterative procedure originating in spectroscopy in the 1930's, is adapted into a useful tool for solving a wide class of 2D nonlinear backward parabolic equations. In addition, previously unsuspected difficulties are uncovered that may preclude useful backward continuation in parabolic equations deviating too strongly from the linear, autonomous, self adjoint, canonical model. This paper explores backward continuation in selected 2D nonlinear equations, by creating fictitious blurred images obtained by using several sharp images as initial data in these equations, and capturing the corresponding solutions at some positive time T. Successful backward continuation from t=T to t = 0, would recover the original sharp image. Visual recognition provides meaningful evaluation of the degree of success or failure in the reconstructed solutions. Instructive examples are developed, illustrating the unexpected influence of certain types of nonlinearities. Visually and statistically indistinguishable blurred images are presented, with vastly different deblurring results. These examples indicate that how an image is nonlinearly blurred is critical, in addition to the amount of blur. The equations studied represent nonlinear generalizations of Brownian motion, and the blurred images may be interpreted as visually expressing the results of novel stochastic processes.
Brownian semistationary processes and conditional full support
Pakkanen, Mikko S
2010-01-01
In this note, we study the infinite-dimensional conditional laws of Brownian semistationary processes. Motivated by the fact that these processes are typically not semimartingales, we present sufficient conditions ensuring that a Brownian semistationary process has conditional full support, a property introduced by Guasoni, R\\'asonyi, and Schachermayer [Ann. Appl. Probab., 18 (2008) pp. 491--520]. By the results of Guasoni, R\\'asonyi, and Schachermayer, this property has two important implications. It ensures, firstly, that the process admits no free lunches under proportional transaction costs, and secondly, that it can be approximated pathwise (in the sup norm) by semimartingales that admit equivalent martingale measures.
Diffusion of torqued active Brownian particles
Sevilla, Francisco J.
An analytical approach is used to study the diffusion of active Brownian particles that move at constant speed in three-dimensional space, under the influence of passive (external) and active (internal) torques. The Smoluchowski equation for the position distribution of the particles is obtained from the Kramer-Fokker-Planck equation corresponding to Langevin equations for active Brownian particles subject to torques. In addition of giving explicit formulas for the mean square-displacement, the non-Gaussian behavior is analyzed through the kurtosis of the position distribution that exhibits an oscillatory behavior in the short-time limit. FJS acknowledges support from PAPIIT-UNAM through the grant IN113114
Momentum conserving Brownian dynamics propagator for complex soft matter fluids
Padding, J. T. [Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven (Netherlands); Briels, W. J. [Computational Biophysics, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands)
2014-12-28
We present a Galilean invariant, momentum conserving first order Brownian dynamics scheme for coarse-grained simulations of highly frictional soft matter systems. Friction forces are taken to be with respect to moving background material. The motion of the background material is described by locally averaged velocities in the neighborhood of the dissolved coarse coordinates. The velocity variables are updated by a momentum conserving scheme. The properties of the stochastic updates are derived through the Chapman-Kolmogorov and Fokker-Planck equations for the evolution of the probability distribution of coarse-grained position and velocity variables, by requiring the equilibrium distribution to be a stationary solution. We test our new scheme on concentrated star polymer solutions and find that the transverse current and velocity time auto-correlation functions behave as expected from hydrodynamics. In particular, the velocity auto-correlation functions display a long time tail in complete agreement with hydrodynamics.
Temporal Correlations of the Running Maximum of a Brownian Trajectory
Bénichou, Olivier; Krapivsky, P. L.; Mejía-Monasterio, Carlos; Oshanin, Gleb
2016-08-01
We study the correlations between the maxima m and M of a Brownian motion (BM) on the time intervals [0 ,t1] and [0 ,t2], with t2>t1. We determine the exact forms of the distribution functions P (m ,M ) and P (G =M -m ), and calculate the moments E {(M-m ) k} and the cross-moments E {mlMk} with arbitrary integers l and k . We show that correlations between m and M decay as √{t1/t2 } when t2/t1→∞ , revealing strong memory effects in the statistics of the BM maxima. We also compute the Pearson correlation coefficient ρ (m ,M ) and the power spectrum of Mt, and we discuss a possibility of extracting the ensemble-averaged diffusion coefficient in single-trajectory experiments using a single realization of the maximum process.
Blowup and Conditionings of $\\psi$-super Brownian Exit Measures
Athreya, Siva R
2011-01-01
We extend earlier results on conditioning of super-Brownian motion to general branching rules. We obtain representations of the conditioned process, both as an $h$-transform, and as an unconditioned superprocess with immigration along a branching tree. Unlike the finite-variance branching setting, these trees are no longer binary, and strictly positive mass can be created at branch points. This construction is singular in the case of stable branching. We analyze this singularity first by approaching the stable branching function via analytic approximations. In this context the singularity of the stable case can be attributed to blow up of the mass created at the first branch of the tree. Other ways of approaching the stable case yield a branching tree that is different in law. To explain this anomaly we construct a family of martingales whose backbones have multiple limit laws.
Momentum conserving Brownian dynamics propagator for complex soft matter fluids.
Padding, J T; Briels, W J
2014-12-28
We present a Galilean invariant, momentum conserving first order Brownian dynamics scheme for coarse-grained simulations of highly frictional soft matter systems. Friction forces are taken to be with respect to moving background material. The motion of the background material is described by locally averaged velocities in the neighborhood of the dissolved coarse coordinates. The velocity variables are updated by a momentum conserving scheme. The properties of the stochastic updates are derived through the Chapman-Kolmogorov and Fokker-Planck equations for the evolution of the probability distribution of coarse-grained position and velocity variables, by requiring the equilibrium distribution to be a stationary solution. We test our new scheme on concentrated star polymer solutions and find that the transverse current and velocity time auto-correlation functions behave as expected from hydrodynamics. In particular, the velocity auto-correlation functions display a long time tail in complete agreement with hydrodynamics.
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.
Magnetization direction in the Heisenberg model exhibiting fractional Brownian motion
Zhang, Zhengping; Mouritsen, Ole G.; Zuckermann, Martin J.
1993-01-01
The temporal magnetization-direction fluctuations in the three-dimensional classical ferromagnetic Heisenberg model have been generated by Monte Carlo simulation and analyzed by the rescaled-range method to yield the Hurst exponent H. A value of H congruent-to 1 has been found to apply...
Brownian Motion as a Limit to Physical Measuring Processes
Niss, Martin
2016-01-01
and received widespread recognition, but his way of modeling the system was contested by his contemporaries. With the more embracing notion of noise that developed during and after World War II, Ising’s conclusion was reinterpreted as showing that noise puts a limit on physical measurement processes. Hence...
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 (4
Semicircular Canals Circumvent Brownian Motion Overload of Mechanoreceptor Hair Cells
Muller, Mees; Heeck, Kier
2016-01-01
Vertebrate semicircular canals (SCC) first appeared in the vertebrates (i.e. ancestral fish) over 600 million years ago. In SCC the principal mechanoreceptors are hair cells, which as compared to cochlear hair cells are distinctly longer (70 vs. 7 μm), 10 times more compliant to bending (44 vs. 500 nN/m), and have a 100-fold higher tip displacement threshold (mechanoreceptors of the SCC. PMID:27448330
Parameter inference from hitting times for perturbed Brownian motion
Tamborrino, Massimiliano; Ditlevsen, Susanne; Lansky, Peter
2015-01-01
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.g. th....... Also covariates and handling of censored observations are incorporated into the statistical model, and the method is illustrated on lung cancer data........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...
EFFECTIVE DIFFUSION AND EFFECTIVE DRAG COEFFICIENT OF A BROWNIAN PARTICLE IN A PERIODIC POTENTIAL
Hongyun Wang
2011-01-01
We study the stochastic motion of a Brownian particle driven by a constant force over a static periodic potential.We show that both the effective diffusion and the effective drag coefficient are mathematically well-defined and we derive analytic expressions for these two quantities.We then investigate the asymptotic behaviors of the effective diffusion and the effective drag coefficient,respectively,for small driving force and for large driving force.In the case of small driving force,the effective diffusion is reduced from its Brownian value by a factor that increases exponentially with the amplitude of the potential.The effective drag coefficient is increased by approximately the same factor.As a result,the Einstein relation between the diffusion coefficient and the drag coefficient is approximately valid when the driving force is small.For moderately large driving force,both the effective diffusion and the effective drag coefficient are increased from their Brownian values,and the Einstein relation breaks down. In the limit of very large driving force,both the effective diffusion and the effective drag coefficient converge to their Brownian values and the Einstein relation is once again valid.
Brownian machinery in physics and biology
Hänggi, Peter
2001-01-01
Brownian machinery in physics and biology. - In: Noise in physical systems and 1/f fluctuations : proceedings of the 16th internat. conference, Gainesville, Fl., 22-25 Oct. 2001 / Ed.: Gijs Bosman. - New Jersey u.a. : World Scientific, 2001. - S. 397-399
Glassy dynamics of Brownian particles with velocity-dependent friction
Yazdi, Anoosheh; Sperl, Matthias
2016-09-01
We consider a two-dimensional model system of Brownian particles in which slow particles are accelerated while fast particles are damped. The motion of the individual particles is described by a Langevin equation with Rayleigh-Helmholtz velocity-dependent friction. In the case of noninteracting particles, the time evolution equations lead to a non-Gaussian velocity distribution. The velocity-dependent friction allows negative values of the friction or energy intakes by slow particles, which we consider active motion, and also causes breaking of the fluctuation dissipation relation. Defining the effective temperature proportional to the second moment of velocity, it is shown that for a constant effective temperature the higher the noise strength, the lower the number of active particles in the system. Using the Mori-Zwanzig formalism and the mode-coupling approximation, the equations of motion for the density autocorrelation function are derived. The equations are solved using the equilibrium structure factors. The integration-through-transients approach is used to derive a relation between the structure factor in the stationary state considering the interacting forces, and the conventional equilibrium static structure factor.
Fannin, PC; Charles, SW; Kopcansky, P; Timko, M; Ocelik, [No Value; Koneracka, M; Tomco, L; Turek, F; Stelina, J; Musil, C; Ocelik, Vaclav
Two methods, the Toroidal Technique and the Forced Rayleigh Scattering (FRS) method, were used in the determination of the size of magnetic particles and their aggregates in magnetic fluids. The toroidal technique was used in the determination of the complex, frequency dependent magnetic
Fannin, PC; Charles, SW; Kopcansky, P; Timko, M; Ocelik, [No Value; Koneracka, M; Tomco, L; Turek, F; Stelina, J; Musil, C; Ocelik, Vaclav
2001-01-01
Two methods, the Toroidal Technique and the Forced Rayleigh Scattering (FRS) method, were used in the determination of the size of magnetic particles and their aggregates in magnetic fluids. The toroidal technique was used in the determination of the complex, frequency dependent magnetic susceptibil
Do, K. D.
2017-02-01
Equations of motion of extensible and shearable slender beams with large translational and rotational motions under external loads in three-dimensional space are first derived in a vector form. Boundary feedback controllers are then designed to ensure that the beams are practically K∞-exponentially stable at the equilibrium. The control design, well-posedness, and stability analysis are based on two Lyapunov-type theorems developed for a class of evolution systems in Hilbert space. Numerical simulations on a slender beam immersed in sea water are included to illustrate the effectiveness of the proposed control design.
Communication: Impact of inertia on biased Brownian transport in confined geometries
Martens, S.; Sokolov, I. M.; Schimansky-Geier, L.
2012-03-01
We consider the impact of inertia on biased Brownian motion of point-size particles in a two-dimensional channel with sinusoidally varying width. If the time scales of the problem separate, the adiabatic elimination of the transverse degrees of freedom leads to an effective description for the motion along the channel given by the potential of mean force. The possibility of such description is intimately connected with equipartition. Numerical simulations show that in the presence of external bias the equipartition may break down leading to non-monotonic dependence of mobility on external force and several other interesting effects.
Suppression of a Brownian noise in a hole-type sensor due to induced-charge electro-osmosis
Sugioka, Hideyuki
2016-03-01
Noise reduction is essential for a single molecular sensor. Thus, we propose a novel noise reduction mechanism using a hydrodynamic force due to induced-charge electro-osmosis (ICEO) in a hole-type sensor and numerically examine the performance. By the boundary element method that considers both a Brownian motion and an ICEO flow of a polarizable particle, we find that the Brownian noise in a current signal is suppressed significantly in a converging channel because of the ICEO flow around the particle in the presence of an electric field. Further, we propose a simple model that explains a numerically obtained threshold voltage of the suppression of the Brownian noise due to ICEO. We believe that our findings contribute greatly to developments of a single molecular sensor.