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.
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...
Performance Estimation for Two-Dimensional Brownian Rotary Ratchet Systems
Tutu, Hiroki; Horita, Takehiko; Ouchi, Katsuya
2015-04-01
Within the context of the Brownian ratchet model, a molecular rotary system that can perform unidirectional rotations induced by linearly polarized ac fields and produce positive work under loads was studied. The model is based on the Langevin equation for a particle in a two-dimensional (2D) three-tooth ratchet potential of threefold symmetry. The performance of the system is characterized by the coercive torque, i.e., the strength of the load competing with the torque induced by the ac driving field, and the energy efficiency in force conversion from the driving field to the torque. We propose a master equation for coarse-grained states, which takes into account the boundary motion between states, and develop a kinetic description to estimate the mean angular momentum (MAM) and powers relevant to the energy balance equation. The framework of analysis incorporates several 2D characteristics and is applicable to a wide class of models of smooth 2D ratchet potential. We confirm that the obtained expressions for MAM, power, and efficiency of the model can enable us to predict qualitative behaviors. We also discuss the usefulness of the torque/power relationship for experimental analyses, and propose a characteristic for 2D ratchet systems.
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.
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.
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...
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.
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
Directory of Open Access Journals (Sweden)
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.
Beginning Introductory Physics with Two-Dimensional Motion
Huggins, Elisha
2009-01-01
During the session on "Introductory College Physics Textbooks" at the 2007 Summer Meeting of the AAPT, there was a brief discussion about whether introductory physics should begin with one-dimensional motion or two-dimensional motion. Here we present the case that by starting with two-dimensional motion, we are able to introduce a considerable…
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.
Generalized functionals of Brownian motion
Directory of Open Access Journals (Sweden)
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.
Combinatorial fractal Brownian motion model
Institute of Scientific and Technical Information of China (English)
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
Energy Technology Data Exchange (ETDEWEB)
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)
On some generalization of fractional Brownian motions
Energy Technology Data Exchange (ETDEWEB)
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.
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
DEFF Research Database (Denmark)
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...
The problem of friction in two-dimensional relative motion
Grech, D K; Grech, Dariusz; Mazur, Zygmunt
2000-01-01
We analyse a mechanical system in two-dimensional relative motion with friction. Although the system is simple, the peculiar interplay between two kinetic friction forces and gravity leads to the wide range of admissible solutions exceeding most intuitive expectations. In particular, the strong qualitative dependence between behaviour of the system, boundary conditions and parameters involved in its description is emphasised. The problem is intended to be discussed in theoretical framework and might be of interest for physics and mechanics students as well as for physics teachers.
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
Institute of Scientific and Technical Information of China (English)
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.
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
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.
Directory of Open Access Journals (Sweden)
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
(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...
Volumetric display containing multiple two-dimensional color motion pictures
Hirayama, R.; Shiraki, A.; Nakayama, H.; Kakue, T.; Shimobaba, T.; Ito, T.
2014-06-01
We have developed an algorithm which can record multiple two-dimensional (2-D) gradated projection patterns in a single three-dimensional (3-D) object. Each recorded pattern has the individual projected direction and can only be seen from the direction. The proposed algorithm has two important features: the number of recorded patterns is theoretically infinite and no meaningful pattern can be seen outside of the projected directions. In this paper, we expanded the algorithm to record multiple 2-D projection patterns in color. There are two popular ways of color mixing: additive one and subtractive one. Additive color mixing used to mix light is based on RGB colors and subtractive color mixing used to mix inks is based on CMY colors. We made two coloring methods based on the additive mixing and subtractive mixing. We performed numerical simulations of the coloring methods, and confirmed their effectiveness. We also fabricated two types of volumetric display and applied the proposed algorithm to them. One is a cubic displays constructed by light-emitting diodes (LEDs) in 8×8×8 array. Lighting patterns of LEDs are controlled by a microcomputer board. The other one is made of 7×7 array of threads. Each thread is illuminated by a projector connected with PC. As a result of the implementation, we succeeded in recording multiple 2-D color motion pictures in the volumetric displays. Our algorithm can be applied to digital signage, media art and so forth.
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'').
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.
Reflected Backward Stochastic Differential Equations Driven by Countable Brownian Motions
Directory of Open Access Journals (Sweden)
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
Directory of Open Access Journals (Sweden)
B. Berche
2012-12-01
Full Text Available The year 2012 marks the 140th birth anniversary of Marian Smoluchowski (28.05.1872-5.09.1917, a man who "made ground-breaking contribution to the theory of Brownian motion, the theory of sedimentation, the statistical nature of the Second Law, the theory and practice of density fluctuations (critical opalescence. During his final years of scientific creativity his pioneering theory of coagulation and diffusion-limited reaction rate appeared. These outstanding achievements present true gems which dominate the description of soft matter physics and chemical physics as well as the related areas up till now!" This quotation was taken from the lecture by Peter Hanggi given at international conference Statistical Physics: Modern Trends and Applications that took place in Lviv, Ukraine on July 3-6, 2012 (see conference web-page for more details and was dedicated to the commemoration of Smoluchowski's work. This and forthcoming issues of the Condensed Matter Physics contain papers presented at this conference.
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
Directory of Open Access Journals (Sweden)
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
DEFF Research Database (Denmark)
Lebovits, Joachim; Podolskij, Mark
This paper presents a new estimator of the global regularity index of a multifractional Brownian motion. Our estimation method is based upon a ratio statistic, which compares the realized global quadratic variation of a multifractional Brownian motion at two different frequencies. We show...... that a 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....
Femtosecond two-dimensional spectroscopy of molecular motion in liquids
Steffen, T; Duppen, K.
1996-01-01
Intermolecular motion in CS2 and benzene is investigated by femtosecond nonresonant four- and six-wave mixing. Impulsive stimulated six-wave mixing yields new information on dephasing of coherent nuclear motion, not accessible from four-wave mixing experiments. The results cannot be modeled by two i
Two dimensional fractional projectile motion in a resisting medium
Rosales, Juan; Guía, Manuel; Gómez, Francisco; Aguilar, Flor; Martínez, Juan
2014-07-01
In this paper we propose a fractional differential equation describing the behavior of a two dimensional projectile in a resisting medium. In order to maintain the dimensionality of the physical quantities in the system, an auxiliary parameter k was introduced in the derivative operator. This parameter has a dimension of inverse of seconds (sec)-1 and characterizes the existence of fractional time components in the given system. It will be shown that the trajectories of the projectile at different values of γ and different fixed values of velocity v 0 and angle θ, in the fractional approach, are always less than the classical one, unlike the results obtained in other studies. All the results obtained in the ordinary case may be obtained from the fractional case when γ = 1.
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
Institute of Scientific and Technical Information of China (English)
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.
Chaotic neural network applied to two-dimensional motion control.
Yoshida, Hiroyuki; Kurata, Shuhei; Li, Yongtao; Nara, Shigetoshi
2010-03-01
Chaotic dynamics generated in a chaotic neural network model are applied to 2-dimensional (2-D) motion control. The change of position of a moving object in each control time step is determined by a motion function which is calculated from the firing activity of the chaotic neural network. Prototype attractors which correspond to simple motions of the object toward four directions in 2-D space are embedded in the neural network model by designing synaptic connection strengths. Chaotic dynamics introduced by changing system parameters sample intermediate points in the high-dimensional state space between the embedded attractors, resulting in motion in various directions. By means of adaptive switching of the system parameters between a chaotic regime and an attractor regime, the object is able to reach a target in a 2-D maze. In computer experiments, the success rate of this method over many trials not only shows better performance than that of stochastic random pattern generators but also shows that chaotic dynamics can be useful for realizing robust, adaptive and complex control function with simple rules.
Brownian shape motion: Fission fragment mass distributions
Directory of Open Access Journals (Sweden)
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.
Supersymmetry and the constants of motion of the two-dimensional isotropic harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Torres del Castillo, G.F. [Departamento de Fisica Matematica, Instituto de Ciencias, Universidad Autonoma de Puebla, 72570 Puebla (Mexico); Tepper G, T. [Escuela de Ciencias, Departamento de Fisica y Matematicas, Universidad de Las Americas-Puebla, Santa Catarina Martir, 72820 Cholula, Puebla (Mexico)
2002-07-01
It is shown that the constants of motion of the two-dimensional isotropic harmonic oscillator not related to the rotational invariance of the Hamiltonian can be derived using the ideas of supersymmetric quantum mechanics. (Author)
Holographic Brownian motion and time scales in strongly coupled plasmas
Energy Technology Data Exchange (ETDEWEB)
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
Directory of Open Access Journals (Sweden)
Kaminsky A. V.
2010-07-01
Full Text Available Phenomenon of the regular variability of the fine structure of the fluctuation in the am- plitude distributions (shapes of related histograms for the case of Brownian motion was investigated. We took an advantage of the dynamic light scattering method (DLS to get a stochastically fluctuated signal determined by Brownian motion. Shape of the histograms is most likely to vary, synchronous, in two proximally located independent cells containing Brownian particles. The synchronism persists in the cells distant at 2 m from each other, and positioned meridionally. With a parallel-wise positioning of the cells, high probability of the synchronous variation in the shape of the histograms by local time has been observed. This result meets the previous conclusion about the dependency of histogram shapes (“fluctuation amplitudes” of the spectra of stochastic processes upon rotation of the Earth.
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.
Integrability of Nonlinear Equations of Motion on Two-Dimensional World Sheet Space-Time
Institute of Scientific and Technical Information of China (English)
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.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Mota, R.D. [Unidad Profesional Interdisciplinaria de Ingenieria y Tecnologias Avanzadas, Mexico DF (Mexico)]. E-mail: mota@gina.esfm.ipn.mx; ravelo@esfm.ipn.mx; Granados, V.D.; Queijeiro, A.; Garcia, J. [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Mexico DF (Mexico)
2002-03-29
For the quantum two-dimensional isotropic harmonic oscillator we show that the Infeld-Hull radial operators, as well as those of the supersymmetric approach for the radial equation, are contained in the constants of motion of the problem. (author)
Simulation of vortex motion in underdamped two-dimensional arrays of Josephson junctions
Energy Technology Data Exchange (ETDEWEB)
Bobbert, P.A. (Department of Applied Physics, Delft University of Technology, Lorentweg 1, 2628 CJ Delft (Netherlands) Department of Physics and Division of Applied Sciences, Harvard University, Cambridge, Massachusetts 02138 (United States))
1992-04-01
We report numerical simulations of classical vortex motion in two-dimensional arrays of underdamped Josephson junctions. A very efficient algorithm was developed, using a piecewise linear approximation for the Josephson current. We find no indication for ballistic motion, in square arrays nor in triangular arrays. Instead, in the limit of very low damping, there appears to be an effective viscosity due to excitation of the lattice behind the moving vortex.
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
DEFF Research Database (Denmark)
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.
Directory of Open Access Journals (Sweden)
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...
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.
Energy Technology Data Exchange (ETDEWEB)
Hollerbach, K.; Van Vorhis, R.L. [Lawrence Livermore National Lab., CA (United States); Hollister, A. [Louisiana State Univ., Shreveport, LA (United States)
1996-03-01
Wrist posture and rapid wrist movements are risk factors for work related musculoskeletal disorders. Measurement studies frequently involve optoelectronic methods in which markers are placed on the subject`s hand and wrist and the trajectories of the markers are tracked in three dimensional space. A goal of wrist posture measurements is to quantitatively establish wrist posture orientation. Accuracy and fidelity of the measurement data with respect to kinematic mechanisms are essential in wrist motion studies. Fidelity with the physical kinematic mechanism can be limited by the choice of kinematic modeling techniques and the representation of motion. Frequently, ergonomic studies involving wrist kinematics make use of two dimensional measurement and analysis techniques. Two dimensional measurement of human joint motion involves the analysis of three dimensional displacements in an obersver selected measurement plane. Accurate marker placement and alignment of joint motion plane with the observer plane are difficult. In nature, joint axes can exist at any orientation and location relative to an arbitrarily chosen global reference frame. An arbitrary axis is any axis that is not coincident with a reference coordinate. We calculate the errors that result from measuring joint motion about an arbitrary axis using two dimensional methods.
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
Institute of Scientific and Technical Information of China (English)
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
Institute of Scientific and Technical Information of China (English)
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
Institute of Scientific and Technical Information of China (English)
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.
Modeling strong motions produced by earthquakes with two-dimensional numerical codes
Helmberger, Donald V.; Vidale, John E.
1988-01-01
We present a scheme for generating synthetic point-source seismograms for shear dislocation sources using line source (two-dimensional) theory. It is based on expanding the complete three-dimensional solution of the wave equation expressed in cylindrical coordinates in an asymptotic form which provides for the separation of the motions into SH and P-SV systems. We evaluate the equations of motion with the aid of the Cagniard-de Hoop technique and derive close-formed expressions appropriate fo...
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
Energy Technology Data Exchange (ETDEWEB)
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
Energy Technology Data Exchange (ETDEWEB)
Wang, Gaoyuan; Battefeld, Thorsten [Institute for Astrophysics, University of Goettingen,Friedrich Hund Platz 1, D-37077 Goettingen (Germany)
2016-09-05
We develope a computationally efficient extension of the Dyson Brownian Motion (DBM) algorithm to generate random function in C{sup 2} locally. We further explain that random functions generated via DBM show an unstable growth as the traversed distance increases. This feature restricts the use of such functions considerably if they are to be used to model globally defined ones. The latter is the case if one uses random functions to model landscapes in string theory. We provide a concrete example, based on a simple axionic potential often used in cosmology, to highlight this problem and also offer an ad hoc modification of DBM that suppresses this growth to some degree.
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
Energy Technology Data Exchange (ETDEWEB)
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
Energy Technology Data Exchange (ETDEWEB)
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
Energy Technology Data Exchange (ETDEWEB)
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.
Description of Collective Motion in Two-Dimensional Nuclei; Tomonaga's Method Revisited
Nishiyama, Seiya
2014-01-01
Four decades ago, Tomonaga proposed the elementary theory of quantum mechanical collective motion of two-dimensional nuclei of N nucleons. The theory is based essentially on the neglect of 1/sqrtN against unity. Very recently we have given exact canonically conjugate momenta to quadrupole-type collective coordinates under some subsidiary conditions and have derived nuclear quadrupole-type collective Hamiltonian. Even in the case of simple two-dimensional nuclei, we have a subsidiary condition to obtain exact canonical variables. Particularly the structure of the collective subspace satisfying the subsidiary condition is studied in detail. This subsidiary condition is important to investigate what is a structure of the collective subspace.
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.
Karhunen-Loève Expansion for the Second Order Detrended Brownian Motion
Directory of Open Access Journals (Sweden)
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.
Contact position controlling for two-dimensional motion bodies by the boundary element method
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
An algorithm is presented for controlling two-dimensional motion contact bodies with conforming discretization. Since a kind of special boundary element is utilized in the algorithm, the displacement compatibility and traction equilibrium conditions at nodes can be satisfied simultaneously in arbitrary locations of the contact interface. In addition, a method is also proposed in which the contact boundary location can be moved flexibly on the possible contact boundary. This method is effective to deal with moving and rolling contact problems on a possible larger moving or rolling contact region. Numerical examples show effectiveness of the presented scheme.
Linear filtering with fractional Brownian motion in the signal and observation processes
Directory of Open Access Journals (Sweden)
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…
Reflecting Brownian motion in two dimensions: Exact asymptotics for the stationary distribution
Directory of Open Access Journals (Sweden)
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.
Two-dimensional convection and interchange motions in fluids and magnetized plasmas
DEFF Research Database (Denmark)
Garcia, O.E.; Bian, N.H.; Naulin, V.
2006-01-01
In this contribution some recent investigations of two- dimensional thermal convection relevant to ordinary fluids as well as magnetized plasmas are reviewed. An introductory discussion is given of the physical mechanism for baroclinic vorticity generation and convective motions in stratified...... fluids, emphasizing its relation to interchange motions of non- uniformly magnetized plasmas. This is followed by a review of the theories for the onset of convection and quasi-linear saturation in driven-dissipative systems. Non-linear numerical simulations which result in stationary convective states....... The global bursting is interpreted in terms of a predator-prey regulation from the point of view of energetics. Finally, a discussion is given of the relevance of these phenomena to a variety of magnetized plasma experiments....
Energy Technology Data Exchange (ETDEWEB)
Albert, Julian; Falge, Mirjam; Hildenbrand, Heiko; Engel, Volker [Universität Würzburg, Institut für Physikalische und Theoretische Chemie, Emil-Fischer-Str. 42, Campus Nord, Am Hubland, 97074 Würzburg (Germany); Gomez, Sandra; Sola, Ignacio R. [Departamento de Quimica Fisica, Universidad Complutense, 28040 Madrid (Spain)
2015-07-28
We theoretically investigate the photon-echo spectroscopy of coupled electron-nuclear quantum dynamics. Two situations are treated. In the first case, the Born-Oppenheimer (adiabatic) approximation holds. It is then possible to interpret the two-dimensional (2D) spectra in terms of vibrational motion taking place in different electronic states. In particular, pure vibrational coherences which are related to oscillations in the time-dependent third-order polarization can be identified. This concept fails in the second case, where strong non-adiabatic coupling leads to the breakdown of the Born-Oppenheimer-approximation. Then, the 2D-spectra reveal a complicated vibronic structure and vibrational coherences cannot be disentangled from the electronic motion.
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.
Brownian motion on Lie groups and open quantum systems
Energy Technology Data Exchange (ETDEWEB)
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
DEFF Research Database (Denmark)
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
Directory of Open Access Journals (Sweden)
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
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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.
Institute of Scientific and Technical Information of China (English)
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).
Two-dimensional simulation of red blood cell motion near a wall under a lateral force
Hariprasad, Daniel S.; Secomb, Timothy W.
2014-11-01
The motion of a red blood cell suspended in a linear shear flow adjacent to a fixed boundary subject to an applied lateral force directed toward the boundary is simulated. A two-dimensional model is used that represents the viscous and elastic properties of normal red blood cells. Shear rates in the range of 100 to 600 s-1 are considered, and the suspending medium viscosity is 1 cP. In the absence of a lateral force, the cell executes a tumbling motion. With increasing lateral force, a transition from tumbling to tank-treading is predicted. The minimum force required to ensure tank-treading increases nonlinearly with the shear rate. Transient swinging motions occur when the force is slightly larger than the transition value. The applied lateral force is balanced by a hydrodynamic lift force resulting from the positive orientation of the long axis of the cell with respect to the wall. In the case of cyclic tumbling motions, the orientation angle takes positive values through most of the cycle, resulting in lift generation. These results are used to predict the motion of a cell close to the outer edge of the cell-rich core region that is generated when blood flows in a narrow tube. In this case, the lateral force is generated by shear-induced dispersion, resulting from cell-cell interactions in a region with a concentration gradient. This force is estimated using previous data on shear-induced dispersion. The cell is predicted to execute tank-treading motions at normal physiological hematocrit levels, with the possibility of tumbling at lower hematocrit levels.
Self-intersection local times and collision local times of bifractional Brownian motions
Institute of Scientific and Technical Information of China (English)
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.
Solution of Two-Dimensional Viscous Flow Driven by Motion of Flexible Walls
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Mohamed Gad-el-Hak
2010-03-01
Full Text Available An exact solution of the Navier–Stokes equations for a flow driven by motion of flexible wall is developed. A simple two-dimensional channel with deforming walls is considered as domain. The governing equations are linearized for low Reynolds number and large Womersley number Newtonian flows. Appropriate boundary conditions for general deformation are decomposed into harmonic excitations in space by Fourier series decomposition. A model of harmonic boundary deformation is considered and results are compared with computational fluid dynamics predictions. The results of velocity profiles across the channel and the centerline velocities of the channel are in good agreement with CFD solution. The analytical model developed provides quantitative descriptions of the flow field for a wide spectrum of actuating frequnecy and boundary conditions. The presented model can be used as an effective framework for preliminary design and optimization of displacement micropumps and other miniature applications.
Particle motion in unsteady two-dimensional peristaltic flow with application to the ureter
Jiménez-Lozano, Joel; Sen, Mihir; Dunn, Patrick F.
2009-04-01
Particle motion in an unsteady peristaltic fluid flow is analyzed. The fluid is incompressible and Newtonian in a two-dimensional planar geometry. A perturbation method based on a small ratio of wave height to wavelength is used to obtain a closed-form solution for the fluid velocity field. This analytical solution is used in conjunction with an equation of motion for a small rigid sphere in nonuniform flow taking Stokes drag, virtual mass, Faxén, Basset, and gravity forces into account. Fluid streamlines and velocity profiles are calculated. Theoretical values for pumping rates are compared with available experimental data. An application to ureteral peristaltic flow is considered since fluid flow in the ureter is sometimes accompanied by particles such as stones or bacteriuria. Particle trajectories for parameters that correspond to calcium oxalates for calculosis and Escherichia coli type for bacteria are analyzed. The findings show that retrograde or reflux motion of the particles is possible and bacterial transport can occur in the upper urinary tract when there is a partial occlusion of the wave. Dilute particle mixing is also investigated, and it is found that some of the particles participate in the formation of a recirculating bolus, and some of them are delayed in transit and eventually reach the walls. This can explain the failure of clearing residuals from the upper urinary tract calculi after successful extracorporeal shock wave lithotripsy. The results may also be relevant to the transport of other physiological fluids and industrial applications in which peristaltic pumping is used.
A Stability Result for Stochastic Differential Equations Driven by Fractional Brownian Motions
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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.
Understanding Ground Motion in Las Vegas: Insights from Data Analysis and Two-Dimensional Modeling
Energy Technology Data Exchange (ETDEWEB)
Rodgers, A; Tkalcic, H; McCallen, D
2004-02-05
Seismic ground motions are amplified in low velocity sedimentary basins relative to adjacent sites on high velocity hard rock. We used historical recordings of NTS nuclear explosions and earthquake recordings in Las Vegas Valley to quantify frequency-dependent basin amplification using Standard Spectral Ratios. We show that amplifications, referred to as site response, can reach a factor of 10 in the frequency band 0.4-2.0 Hz. Band-averaged site response between 0.4-2.0 Hz is strongly correlated with basin depth. However, it is also well known that site response is related to shallow shear-wave velocity structure. We simulated low frequency (f<1Hz) ground motion and site response with two-dimensional elastic finite difference simulations. We demonstrate that physically plausible models of the shallow subsurface, including low velocity sedimentary structure, can predict relative amplification as well as some of the complexity in the observed waveforms. This study demonstrates that site response can be modeled without invoking complex and computationally expensive three-dimensional structural models.
Moderate deviations for the quenched mean of the super-Brownian motion with random immigration
Institute of Scientific and Technical Information of China (English)
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
Institute of Scientific and Technical Information of China (English)
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
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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
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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
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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
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Di Pan
2013-01-01
Full Text Available Geometric-average Asian option pricing model with monotonous transaction cost rate under fractional Brownian motion was established. The method of partial differential equations was used to solve this model and the analytical expressions of the Asian option value were obtained. The numerical experiments show that Hurst exponent of the fractional Brownian motion and transaction cost rate have a significant impact on the option value.
Directory of Open Access Journals (Sweden)
L. Yılmazoğlu
2013-12-01
Full Text Available In this work, the surface ground motion that occurs during an earthquake in ground sections having different topographic forms has been examined with one and two dynamic site response analyses. One-dimensional analyses were undertaken using the Equivalent-Linear Earthquake Response Analysis program based on the equivalent linear analysis principle and the Deepsoil program which is able to make both equivalent linear and nonlinear analyses and two-dimensional analyses using the Plaxis software. The viscous damping parameters used in the dynamic site response analyses undertaken with the Plaxis software were obtained using the DeepSoil program. In the dynamic site response analyses, the synthetic acceleration over a 475 yr replication period representing the earthquakes in Istanbul was used as the basis of the bedrock ground motion. The peak ground acceleration obtained different depths of soils and acceleration spectrum values have been compared. The surface topography and layer boundaries in the 5-5' section were selected in order to examine the effect of the land topography and layer boundaries on the analysis results were flattened and compared with the actual status. The analysis results showed that the characteristics of the surface ground motion changes in relation to the varying local soil conditions and land topography.
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.
Three-dimensional liver motion tracking using real-time two-dimensional MRI
Energy Technology Data Exchange (ETDEWEB)
Brix, Lau, E-mail: lau.brix@stab.rm.dk [Department of Procurement and Clinical Engineering, Region Midt, Olof Palmes Allé 15, 8200 Aarhus N, Denmark and MR Research Centre, Aarhus University Hospital, Skejby, Brendstrupgaardsvej 100, 8200 Aarhus N (Denmark); Ringgaard, Steffen [MR Research Centre, Aarhus University Hospital, Skejby, Brendstrupgaardsvej 100, 8200 Aarhus N (Denmark); Sørensen, Thomas Sangild [Department of Computer Science, Aarhus University, Aabogade 34, 8200 Aarhus N, Denmark and Department of Clinical Medicine, Aarhus University, Brendstrupgaardsvej 100, 8200 Aarhus N (Denmark); Poulsen, Per Rugaard [Department of Clinical Medicine, Aarhus University, Brendstrupgaardsvej 100, 8200 Aarhus N, Denmark and Department of Oncology, Aarhus University Hospital, Nørrebrogade 44, 8000 Aarhus C (Denmark)
2014-04-15
Purpose: Combined magnetic resonance imaging (MRI) systems and linear accelerators for radiotherapy (MR-Linacs) are currently under development. MRI is noninvasive and nonionizing and can produce images with high soft tissue contrast. However, new tracking methods are required to obtain fast real-time spatial target localization. This study develops and evaluates a method for tracking three-dimensional (3D) respiratory liver motion in two-dimensional (2D) real-time MRI image series with high temporal and spatial resolution. Methods: The proposed method for 3D tracking in 2D real-time MRI series has three steps: (1) Recording of a 3D MRI scan and selection of a blood vessel (or tumor) structure to be tracked in subsequent 2D MRI series. (2) Generation of a library of 2D image templates oriented parallel to the 2D MRI image series by reslicing and resampling the 3D MRI scan. (3) 3D tracking of the selected structure in each real-time 2D image by finding the template and template position that yield the highest normalized cross correlation coefficient with the image. Since the tracked structure has a known 3D position relative to each template, the selection and 2D localization of a specific template translates into quantification of both the through-plane and in-plane position of the structure. As a proof of principle, 3D tracking of liver blood vessel structures was performed in five healthy volunteers in two 5.4 Hz axial, sagittal, and coronal real-time 2D MRI series of 30 s duration. In each 2D MRI series, the 3D localization was carried out twice, using nonoverlapping template libraries, which resulted in a total of 12 estimated 3D trajectories per volunteer. Validation tests carried out to support the tracking algorithm included quantification of the breathing induced 3D liver motion and liver motion directionality for the volunteers, and comparison of 2D MRI estimated positions of a structure in a watermelon with the actual positions. Results: Axial, sagittal
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.
Two-dimensional Fourier transform ESR in the slow-motional and rigid limits: 2D-ELDOR
Patyal, Baldev R.; Crepeau, Richard H.; Gamliel, Dan; Freed, Jack H.
1990-12-01
The two-dimensional Fourier transform ESP techniques of stimulated SECSY and 2D-ELDOR are shown to be powerful methods for the study of slow motions for nitroxides. Stimulated SECSY provides magnetization transfer rates, whereas 2D-ELDOR displays how the rotational motions spread the spins out from their initial spectral positions to new spectral positions, as a function of mixing time. The role of nuclear modulation in studies of structure and dynamics is also considered.
Brownian motion after Einstein and Smoluchowski: Some new applications and new experiments
DEFF Research Database (Denmark)
Dávid, Selmeczi; Tolic-Nørrelykke, S.F.; Schäffer, E.;
2007-01-01
The first half of this review describes the development in mathematical models of Brownian motion after Einstein's and Smoluchowski's seminal papers and current applications to optical tweezers. This instrument of choice among single-molecule biophysicists is also an instrument of such precision...... 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.
Coupling of lever arm swing and biased Brownian motion in actomyosin.
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Qing-Miao Nie
2014-04-01
Full Text Available An important unresolved problem associated with actomyosin motors is the role of Brownian motion in the process of force generation. On the basis of structural observations of myosins and actins, the widely held lever-arm hypothesis has been proposed, in which proteins are assumed to show sequential structural changes among observed and hypothesized structures to exert mechanical force. An alternative hypothesis, the Brownian motion hypothesis, has been supported by single-molecule experiments and emphasizes more on the roles of fluctuating protein movement. In this study, we address the long-standing controversy between the lever-arm hypothesis and the Brownian motion hypothesis through in silico observations of an actomyosin system. We study a system composed of myosin II and actin filament by calculating free-energy landscapes of actin-myosin interactions using the molecular dynamics method and by simulating transitions among dynamically changing free-energy landscapes using the Monte Carlo method. The results obtained by this combined multi-scale calculation show that myosin with inorganic phosphate (Pi and ADP weakly binds to actin and that after releasing Pi and ADP, myosin moves along the actin filament toward the strong-binding site by exhibiting the biased Brownian motion, a behavior consistent with the observed single-molecular behavior of myosin. Conformational flexibility of loops at the actin-interface of myosin and the N-terminus of actin subunit is necessary for the distinct bias in the Brownian motion. Both the 5.5-11 nm displacement due to the biased Brownian motion and the 3-5 nm displacement due to lever-arm swing contribute to the net displacement of myosin. The calculated results further suggest that the recovery stroke of the lever arm plays an important role in enhancing the displacement of myosin through multiple cycles of ATP hydrolysis, suggesting a unified movement mechanism for various members of the myosin family.
Finding viscosity of liquids from Brownian motion at students' laboratory
Energy Technology Data Exchange (ETDEWEB)
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.
Institute of Scientific and Technical Information of China (English)
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
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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
Institute of Scientific and Technical Information of China (English)
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
Institute of Scientific and Technical Information of China (English)
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
Institute of Scientific and Technical Information of China (English)
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
Institute of Scientific and Technical Information of China (English)
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
Energy Technology Data Exchange (ETDEWEB)
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
Directory of Open Access Journals (Sweden)
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
Institute of Scientific and Technical Information of China (English)
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.
Friction damping of two-dimensional motion and its application in vibration control
Menq, C.-H.; Chidamparam, P.; Griffin, J. H.
1991-01-01
This paper presents an approximate method for analyzing the two-dimensional friction contact problem so as to compute the dynamic response of a structure constrained by friction interfaces. The friction force at the joint is formulated based on the Coulomb model. The single-term harmonic balance scheme, together with the receptance approach of decoupling the effect of the friction force on the structure from those of the external forces has been utilized to obtain the steady state response. The computational efficiency and accuracy of the method are demonstrated by comparing the results with long-term time solutions.
Two-dimensional motion of unstable steps induced by flow in solution
Sato, Masahide
2011-01-01
By carrying out Monte Carlo simulation, we study step instabilities during crystal growth from solution. In previous studies [M. Sato. J. Phys. Soc. Jpn. 79 (2010) 064606; M. Sato, J. Cryst. Growth 318 (2011) 5; M. Sato. J. Phys. Soc. Jpn. 80 (2011) 024604], we used a one-dimensional model, so that we were unable to study another type of instability, step wandering. In this research, we use a two-dimensional model to study both step wandering and step bunching. When the flow of solutes is in ...
Second constant of motion for two-dimensional positronium in a magnetic field
Muñoz, G
2003-01-01
Recent numerical work indicates that the classical motion of positronium in a constant magnetic field does not exhibit chaotic behavior if the system is confined to two dimensions. One would therefore expect this system to possess a second constant of the motion in addition to the total energy. In this paper we construct a generalization of the Laplace-Runge-Lenz vector and show that a component of this vector is a constant of the motion.
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.
Errors in using two dimensional methods to measure motion about an offset revolute
Energy Technology Data Exchange (ETDEWEB)
Hollerbach, K. [Lawrence Livermore National Lab., CA (United States); Hollister, A. [Louisiana State Univ., Shreveport, LA (United States). Medical Center
1996-03-01
2D measurement of human joint motion involves analysis of 3D displacements in an observer selected measurement plane. Accurate marker placement and alignment of joint motion plane with the observer plane are difficult. Alignment of the two planes is essential for accurate recording and understanding of the joint mechanism and the movement about it. In nature, joint axes can exist at any orientation and location relative to a global reference frame. An aritrary axis is any axis that is not coincident with a reference coordinate. We calculate the errors resulting from measuring joint motion about an arbitrary axis using 2D methods.
Normal left ventricular wall motion measured with two-dimensional myocardial tagging
DEFF Research Database (Denmark)
Qi, P; Thomsen, C; Ståhlberg, F;
1993-01-01
Using a myocardial tagging technique, normal left ventricular wall motion was studied in 3 true short axis views and a double oblique 4-chamber view in 14 and 11 volunteers, respectively. Three orthogonal directions of left ventricular motion were observed throughout the systole; a concentric...... contraction towards the center of the left ventricle, a motion of the base of the heart towards the apex, and a rotation of the left ventricle around its long axis. The direction of left ventricular rotation changed from early systole to late systole. The base and middle levels of the left ventricle rotated...... that MR imaging with myocardial tagging is a method that can be used to study normal left ventricular wall motion, and that is promising for future use in patient groups....
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.
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.
Numerical solutions for a two-dimensional airfoil undergoing unsteady motion
Institute of Scientific and Technical Information of China (English)
WU Fu-bing; ZENG Nian-dong; ZHANG Liang; WU De-ming
2004-01-01
Continuous vorticity panels are used to model general unsteady inviscid, incompressible, and two-dimensional flows. The geometry of the airfoil is approximated by series of short straight segments having endpoints that lie on the actual surface. A piecewise linear, continuous distribution of vorticity over the airfoil surface is used to generate disturbance flow. The no-penetration condition is imposed at the midpoint of each segment and at discrete times. The wake is simulated by a system of point vortices, which move at local fluid velocity. At each time step, a new wake panel with uniform vorticity distribution is attached to the trailing edge, and the condition of eonstant circulation around the airfoil and wake is imposed. A new expression for Kutta condition is developed to study (i) the effect of thickness on the lift build-up of an impulsively started airfoil, (ii) the effects of reduced frequency and heave amplitude on the thrust production of flapping airfoils, and (iii) the vortex-airfoil interaction. This work presents some hydrodynamic results for tidalstreaim turbine.
DEFF Research Database (Denmark)
Dahl, Jens Peder; Schleich, W. P.
2009-01-01
For a closed quantum system the state operator must be a function of the Hamiltonian. When the state is degenerate, additional constants of the motion enter the play. But although it is the Weyl transform of the state operator, the Wigner function is not necessarily a function of the Weyl...
Sakuma, Ryusuke; Gunji, Atsuko; Goto, Takaaki; Kita, Yosuke; Koike, Toshihide; Kaga, Makiko; Inagaki, Masumi
2012-07-01
The current study sought to develop a new behavioral analysis methods to evaluate the effects of social skills training (SST). SST is known to be an effective method to improve the social skills of children with behavioral problems. However, current evaluation methods involve behavioral rating scales that are heavily dependent on evaluators' particular experiences they have had. To quantitatively examine the behavioral effects of SST, we examined subjects' head-movements related to social behavior, using a two-dimensional motion capture system (Kissei Comtec, Japan). Four children (three male, one female, 7-8 years of age) with pervasive developmental disorder (PDD) or attention deficit/hyperactivity disorder (AD/HD) participated in 16 sessions of SST. Before and after SST, head-coordinates on a two-dimensional plane were calculated using their behavior during a pair task, measured by four digital cameras. After SST, the number of communication behaviors was increased compared to before SST. In addition, children looked longer at another child within 30 degrees of the central visual field. Time-series analysis of the visual field during the detection of another child revealed significant auto-correlation from about -1.12 second. before to the beginning of communication behavior (p<0.05). The results suggested that our method can provide a quantitative index of characteristics related to skilled social behaviors. We conclude that a two-dimensional motion capture system would be useful for visualization of the interventional effects of SST, which would supplement assessments by the conventional observational strategies.
Iwaki, Sunao; Bonmassar, Giorgio; Belliveau, John W
2013-09-01
Recent neuroimaging studies implicate that both the dorsal and ventral visual pathways, as well as the middle temporal (MT) areas which are critical for the perception of visual motion, are involved in the perception of three-dimensional (3D) structure from two-dimensional (2D) motion (3D-SFM). However, the neural dynamics underlying the reconstruction of a 3D object from 2D optic flow is not known. Here we combined magnetoencephalography (MEG) and functional MRI (fMRI) measurements to investigate the spatiotemporal brain dynamics during 3D-SFM. We manipulated parametrically the coherence of randomly moving groups of dots to create different levels of 3D perception and to study the associated changes in brain activity. At different latencies, the posterior infero-temporal (pIT), the parieto-occipital (PO), and the intraparietal (IP) regions showed increased neural activity during highly coherent motion conditions in which subjects perceived a robust 3D object. Causality analysis between these regions indicated significant causal influence from IP to pIT and from pIT to PO only in conditions where subjects perceived a robust 3D object. Current results suggest that the perception of a 3D object from 2D motion includes integration of global motion and 3D mental image processing, as well as object recognition that are accomplished by interactions between the dorsal and ventral visual pathways.
Lubaba, Caesar H; Hidano, Arata; Welburn, Susan C; Revie, Crawford W; Eisler, Mark C
2015-01-01
Two-dimensional motion sensors use electronic accelerometers to record the lying, standing and walking activity of cattle. Movement behaviour data collected automatically using these sensors over prolonged periods of time could be of use to stakeholders making management and disease control decisions in rural sub-Saharan Africa leading to potential improvements in animal health and production. Motion sensors were used in this study with the aim of monitoring and quantifying the movement behaviour of traditionally managed Angoni cattle in Petauke District in the Eastern Province of Zambia. This study was designed to assess whether motion sensors were suitable for use on traditionally managed cattle in two veterinary camps in Petauke District in the Eastern Province of Zambia. In each veterinary camp, twenty cattle were selected for study. Each animal had a motion sensor placed on its hind leg to continuously measure and record its movement behaviour over a two week period. Analysing the sensor data using principal components analysis (PCA) revealed that the majority of variability in behaviour among studied cattle could be attributed to their behaviour at night and in the morning. The behaviour at night was markedly different between veterinary camps; while differences in the morning appeared to reflect varying behaviour across all animals. The study results validate the use of such motion sensors in the chosen setting and highlight the importance of appropriate data summarisation techniques to adequately describe and compare animal movement behaviours if association to other factors, such as location, breed or health status are to be assessed.
National Research Council Canada - National Science Library
M. G. Kiselev; A. V. Drozdov; S. G. Monich; D. A. Yamnaya
2014-01-01
The purpose of the paper is to make an experimental impact assessment of parameters pertaining to blank two-dimensional circular blank motion on intensity of its cutting and quality of the machined surfaces...
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).
Directory of Open Access Journals (Sweden)
K. C. Lee
2013-02-01
Full Text Available Multifractional Brownian motions have become popular as flexible models in describing real-life signals of high-frequency features in geoscience, microeconomics, and turbulence, to name a few. The time-changing Hurst exponent, which describes regularity levels depending on time measurements, and variance, which relates to an energy level, are two parameters that characterize multifractional Brownian motions. This research suggests a combined method of estimating the time-changing Hurst exponent and variance using the local variation of sampled paths of signals. The method consists of two phases: initially estimating global variance and then accurately estimating the time-changing Hurst exponent. A simulation study shows its performance in estimation of the parameters. The proposed method is applied to characterization of atmospheric stability in which descriptive statistics from the estimated time-changing Hurst exponent and variance classify stable atmosphere flows from unstable ones.
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
Institute of Scientific and Technical Information of China (English)
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
Institute of Scientific and Technical Information of China (English)
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.
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.
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
Institute of Scientific and Technical Information of China (English)
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.
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...
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
Directory of Open Access Journals (Sweden)
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...
Directory of Open Access Journals (Sweden)
Guodong Liu
2013-01-01
Full Text Available Modular pebble-bed nuclear reactor (MPBNR technology is promising due to its attractive features such as high fuel performance and inherent safety. Particle motion of fuel and graphite pebbles is highly associated with the performance of pebbled-bed modular nuclear reactor. To understand the mechanism of pebble’s motion in the reactor, we numerically studied the influence of number ratio of fuel and graphite pebbles, funnel angle of the reactor, height of guide ring on the distribution of pebble position, and velocity by means of discrete element method (DEM in a two-dimensional MPBNR. Velocity distributions at different areas of the reactor as well as mixing characteristics of fuel and graphite pebbles were investigated. Both fuel and graphite pebbles moved downward, and a uniform motion was formed in the column zone, while pebbles motion in the cone zone was accelerated due to the decrease of the cross sectional flow area. The number ratio of fuel and graphite pebbles and the height of guide ring had a minor influence on the velocity distribution of pebbles, while the variation of funnel angle had an obvious impact on the velocity distribution. Simulated results agreed well with the work in the literature.
Brownian motion of massive skyrmions in magnetic thin films
Energy Technology Data Exchange (ETDEWEB)
Troncoso, Roberto E., E-mail: r.troncoso.c@gmail.com [Centro para el Desarrollo de la Nanociencia y la Nanotecnología, CEDENNA, Avda. Ecuador 3493, Santiago 9170124 (Chile); Núñez, Álvaro S., E-mail: alnunez@dfi.uchile.cl [Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago (Chile)
2014-12-15
We report on the thermal effects on the motion of current-driven massive magnetic skyrmions. The reduced equation for the motion of skyrmion has the form of a stochastic generalized Thiele’s equation. We propose an ansatz for the magnetization texture of a non-rigid single skyrmion that depends linearly with the velocity. By using this ansatz it is found that the skyrmion mass tensor is closely related to intrinsic skyrmion parameters, such as Gilbert damping, skyrmion-charge and dissipative force. We have found an exact expression for the average drift velocity as well as the mean-square velocity of the skyrmion. The longitudinal and transverse mobility of skyrmions for small spin-velocity of electrons is also determined and found to be independent of the skyrmion mass.
Dipole—Dipole Interaction and the Directional Motion of Brownian
Institute of Scientific and Technical Information of China (English)
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.
Two-Dimensional Wave Motion on the Charged Surface of a Viscous Liquid
Institute of Scientific and Technical Information of China (English)
LI Fang; YIN Xie-Yuan; YIN Xie-Zhen
2008-01-01
The wave motion on the charged surface of a viscous Newtonian liquid is solved as an initial-value problem. Both the leaky dielectric and perfect dielectric cases are considered. The amplitude of wave is assumed to be small. The electric field induced by surface charge is shown to have a generally destabilizing effect on surface wave. The neutral stability curve is drawn in the (G, N,e) plane (G: the gravitational bond number; Ne: the electrical Bond number). The Ohnesorge number, Taylor-Melcher number and permittivity ratio have little influence on the neutral stability curve. It is testified that the classical normal mode method cannot predict wave behaviour at small times.
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...
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.
Directory of Open Access Journals (Sweden)
Björn Böttcher
Full Text Available We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space dependent mixing of Lévy processes. Brownian Motion is one of the most frequently used continuous time Markov processes in applications. In recent years also Lévy processes, of which Brownian Motion is a special case, have become increasingly popular. Lévy processes are spatially homogeneous, but empirical data often suggest the use of spatially inhomogeneous processes. Thus it seems necessary to go to the next level of generalization: Feller processes. These include Lévy processes and in particular brownian motion as special cases but allow spatial inhomogeneities. Many properties of Feller processes are known, but proving the very existence is, in general, very technical. Moreover, an applicable framework for the generation of sample paths of a Feller process was missing. We explain, with practitioners in mind, how to overcome both of these obstacles. In particular our simulation technique allows to apply Monte Carlo methods to Feller processes.
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...
Enzensberger, Christian; Achterberg, Friederike; Degenhardt, Jan; Wolter, Aline; Graupner, Oliver; Herrmann, Johannes; Axt-Fliedner, Roland
2017-01-01
Objective The primary objective of this study was to determine the feasibility and reproducibility of 2-dimensional speckle tracking imaging based on the wall motion tracking (WMT) technique in fetal echocardiography. The secondary objective was to compare left and right ventricular global and segmental longitudinal peak strain values. Methods A prospective cross-sectional study was performed. Global and segmental longitudinal peak strain values of the left ventricle (LV) and right ventricle (RV) were assessed prospectively. Based on apical 4-chamber views, cine loops were acquired and digitally stored. Strain analysis was performed offline. Intra- and interobserver variabilities were analyzed. Results A total of 29 healthy fetuses with an echocardiogram performed between 19 and 37 weeks of gestation were included. Analysis was performed with a temporal resolution of 60 frames per second (fps). For both examiners, in all cases Cronbach’s alpha was>0.7. The interobserver variability showed a strong agreement in 50% of the segments (ICC 0.71–0.90). The global strain values for LV and RV were −16.34 and −14.65%, respectively. Segmental strain analysis revealed a basis to apex gradient with the lowest strain values in basal segments and the highest strain values in apical segments. Conclusion The assessment of fetal myocardial deformation parameters by 2D WMT is technically feasible with good reproducibility. PMID:28210715
Oliver, Thomas A A; Lewis, Nicholas H C; Fleming, Graham R
2014-07-15
Multidimensional nonlinear spectroscopy, in the electronic and vibrational regimes, has reached maturity. To date, no experimental technique has combined the advantages of 2D electronic spectroscopy and 2D infrared spectroscopy, monitoring the evolution of the electronic and nuclear degrees of freedom simultaneously. The interplay and coupling between the electronic state and vibrational manifold is fundamental to understanding ensuing nonradiative pathways, especially those that involve conical intersections. We have developed a new experimental technique that is capable of correlating the electronic and vibrational degrees of freedom: 2D electronic-vibrational spectroscopy (2D-EV). We apply this new technique to the study of the 4-(di-cyanomethylene)-2-methyl-6-p-(dimethylamino)styryl-4H-pyran (DCM) laser dye in deuterated dimethyl sulfoxide and its excited state relaxation pathways. From 2D-EV spectra, we elucidate a ballistic mechanism on the excited state potential energy surface whereby molecules are almost instantaneously projected uphill in energy toward a transition state between locally excited and charge-transfer states, as evidenced by a rapid blue shift on the electronic axis of our 2D-EV spectra. The change in minimum energy structure in this excited state nonradiative crossing is evident as the central frequency of a specific vibrational mode changes on a many-picoseconds timescale. The underlying electronic dynamics, which occur on the hundreds of femtoseconds timescale, drive the far slower ensuing nuclear motions on the excited state potential surface, and serve as a excellent illustration for the unprecedented detail that 2D-EV will afford to photochemical reaction dynamics.
RECTILINEAR AND BROWNIAN MOTION FROM A RANDOM POINT IN A CONVEX REGION
Directory of Open Access Journals (Sweden)
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.
Directory of Open Access Journals (Sweden)
Caesar H Lubaba
Full Text Available Two-dimensional motion sensors use electronic accelerometers to record the lying, standing and walking activity of cattle. Movement behaviour data collected automatically using these sensors over prolonged periods of time could be of use to stakeholders making management and disease control decisions in rural sub-Saharan Africa leading to potential improvements in animal health and production. Motion sensors were used in this study with the aim of monitoring and quantifying the movement behaviour of traditionally managed Angoni cattle in Petauke District in the Eastern Province of Zambia. This study was designed to assess whether motion sensors were suitable for use on traditionally managed cattle in two veterinary camps in Petauke District in the Eastern Province of Zambia. In each veterinary camp, twenty cattle were selected for study. Each animal had a motion sensor placed on its hind leg to continuously measure and record its movement behaviour over a two week period. Analysing the sensor data using principal components analysis (PCA revealed that the majority of variability in behaviour among studied cattle could be attributed to their behaviour at night and in the morning. The behaviour at night was markedly different between veterinary camps; while differences in the morning appeared to reflect varying behaviour across all animals. The study results validate the use of such motion sensors in the chosen setting and highlight the importance of appropriate data summarisation techniques to adequately describe and compare animal movement behaviours if association to other factors, such as location, breed or health status are to be assessed.
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
Dubinskii, Alexander A.; Maresch, Günter G.; Spiess, Hans-Wolfgang
1994-02-01
The combination of concepts of two-dimensional (2D) spectroscopy with the well-known field step electron-electron double resonance (ELDOR) method offers a practical route to recording 2D ELDOR spectra covering the full spectral range needed for electron paramagnetic resonance (EPR) of nitroxide spin labels in the solid state. The 2D ELDOR pattern provides information about molecular reorientation measured in real time, the anisotropies of electron phase, and electron spin-lattice relaxation as well as nuclear spin-lattice relaxation all of which are connected with the detailed geometry of the molecular reorientation. Thus, in 2D ELDOR the same electron spin probes the motional behavior over a wide range of correlation times from 10-4 to 10-12 s. An efficient algorithm for simulating 2D ELDOR spectra is derived, based on analytical solutions of the spin relaxation behavior for small-angle fluctuations and offers a means of quantitatively analyzing experimental data. As an example, the motion of nitroxide spin labels in a liquid-crystalline side-group polymer well below its glass transition is determined as a β-relaxation process with a mean angular amplitude of 5° and a distribution of correlation times with a mean correlation time of 0.9×10-10 s and a width of 2.5 decades.
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.
Directory of Open Access Journals (Sweden)
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
Directory of Open Access Journals (Sweden)
Yuliya Mishura
2014-06-01
Full Text Available We study a problem of an unknown drift parameter estimation in a stochastic differen- tial equation driven by fractional Brownian motion. We represent the likelihood ratio as a function of the observable process. The form of this representation is in general rather complicated. However, in the simplest case it can be simplified and we can discretize it to establish the a. s. convergence of the discretized version of maximum likelihood estimator to the true value of parameter. We also investigate a non-standard estimator of the drift parameter showing further its strong consistency.
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.
Energy Technology Data Exchange (ETDEWEB)
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.
Directory of Open Access Journals (Sweden)
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.
Jing, Fulong; Jiao, Shuhong; Hou, Changbo; Si, Weijian; Wang, Yu
2017-06-21
For targets with complex motion, such as ships fluctuating with oceanic waves and high maneuvering airplanes, azimuth echo signals can be modeled as multicomponent quadratic frequency modulation (QFM) signals after migration compensation and phase adjustment. For the QFM signal model, the chirp rate (CR) and the quadratic chirp rate (QCR) are two important physical quantities, which need to be estimated. For multicomponent QFM signals, the cross terms create a challenge for detection, which needs to be addressed. In this paper, by employing a novel multi-scale parametric symmetric self-correlation function (PSSF) and modified scaled Fourier transform (mSFT), an effective parameter estimation algorithm is proposed-referred to as the Two-Dimensional product modified Lv's distribution (2D-PMLVD)-for QFM signals. The 2D-PMLVD is simple and can be easily implemented by using fast Fourier transform (FFT) and complex multiplication. These measures are analyzed in the paper, including the principle, the cross term, anti-noise performance, and computational complexity. Compared to the other three representative methods, the 2D-PMLVD can achieve better anti-noise performance. The 2D-PMLVD, which is free of searching and has no identifiability problems, is more suitable for multicomponent situations. Through several simulations and analyses, the effectiveness of the proposed estimation algorithm is verified.
Directory of Open Access Journals (Sweden)
S. Van Niekerk
2008-02-01
Full Text Available Measuring upper quadrant posture and movement is a challenge to researchers and clinicians. A range of postural measurement tools is commonly used in the clinical setting and in research projects to evaluate postural align-ment, but information about the validity and reliability of these tools and thus as election of the optimal tool for a specific project is often uncertain. This reviewaims to make recommendations to clinicians and researchers regarding practical,valid and reliable tools to assess upper quadrant posture and range of motion.Electronic databases and key journals were searched. An adapted appraisal toolwas utilised to assess the methodology for each of the nine selected articles. Nine eligible articles reporting on thegoniometer, flexicurve and inclinometer were included. This review highlights the fact that a range of two-dimensional(2D posture measurement tools are being used in clinical practice and research. Although the findings for the reliability and validity of the tools included in this review appear to be promising, strong recommendations are limited by the imprecision of the results. Thus, the primary issue hampering the recommendation for the most reliable and valid tool to use in the clinical or research setting is due to the limitations pertaining the analysis of the data, and the interpretation thereof.
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
Indian Academy of Sciences (India)
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
Energy Technology Data Exchange (ETDEWEB)
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
Rao, Srisha M. V.; Jagadeesh, Gopalan
2014-03-01
Key features that drive the operation of a supersonic ejector are the complex gasdynamic interactions of the primary and secondary flows within a variable area duct and the phenomenon of compressible turbulent mixing between them, which have to be understood at a fundamental level. An experimental study has been carried out on the mixing characteristics of a two dimensional supersonic ejector with a supersonic primary flow (air) of Mach number 2.48 and the secondary flow (subsonic) which is induced from the ambient. The non-mixed length, which is the length within the ejector for which the primary and secondary flow remain visually distinct is used to characterize the mixing in the ejector. The operating pressures, flow rates and wall static pressures along the ejector have been measured. Two flow visualization tools have been implemented—time resolved schlieren and laser scattering flow visualization. An important contribution has been the development of in-house image processing algorithms on the MATLAB platform to detect the non-mixed length from the schlieren and laser scattering images. The ratio of mass flow rates of the secondary flow to primary flow (entrainment ratio) has been varied in a range of 0.15-0.69 for two locations of the primary nozzle in the ejector duct. Representative cases have been computed using commercial CFD tool (Fluent) to supplement the experiments. Significant outcomes of the study are—the non-mixed length quantified from the flow visualization images is observed to lie within 4.5 to 5.2 times the height of the mixing duct which is confirmed by the wall static pressure profiles. The flow through the supersonic ejector in the mixed regime is explained using corroborative evidences from different diagnostic tools. A reduction of the non-mixed length by 46.7% is observed at operating conditions when the nozzle is sufficiently overexpanded. The disturbance caused to the mixing layer due to unsteady shock-boundary layer interactions
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.
Institute of Scientific and Technical Information of China (English)
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.
DEFF Research Database (Denmark)
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...
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.
Institute of Scientific and Technical Information of China (English)
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...
Directory of Open Access Journals (Sweden)
Gayo Willy
2016-01-01
Full Text Available Philippine Stock Exchange Composite Index (PSEi is the main stock index of the Philippine Stock Exchange (PSE. PSEi is computed using a weighted mean of the top 30 publicly traded companies in the Philippines, called component stocks. It provides a single value by which the performance of the Philippine stock market is measured. Unfortunately, these weights, which may vary for every trading day, are not disclosed by the PSE. In this paper, we propose a model of forecasting the PSEi by estimating the weights based on historical data and forecasting each component stock using Monte Carlo simulation based on a Geometric Brownian Motion (GBM assumption. The model performance is evaluated and its forecast compared is with the results using a direct GBM forecast of PSEi over different forecast periods. Results showed that the forecasts using WGBM will yield smaller error compared to direct GBM forecast of PSEi.
Energy Technology Data Exchange (ETDEWEB)
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.
Franck, John M.; Chandrasekaran, Siddarth; Dzikovski, Boris; Dunnam, Curt R.; Freed, Jack H.
2015-06-01
The development, applications, and current challenges of the pulsed ESR technique of two-dimensional Electron-Electron Double Resonance (2D ELDOR) are described. This is a three-pulse technique akin to 2D Exchange Nuclear Magnetic Resonance, but involving electron spins, usually in the form of spin-probes or spin-labels. As a result, it required the extension to much higher frequencies, i.e., microwaves, and much faster time scales, with π/2 pulses in the 2-3 ns range. It has proven very useful for studying molecular dynamics in complex fluids, and spectral results can be explained by fitting theoretical models (also described) that provide a detailed analysis of the molecular dynamics and structure. We discuss concepts that also appear in other forms of 2D spectroscopy but emphasize the unique advantages and difficulties that are intrinsic to ESR. Advantages include the ability to tune the resonance frequency, in order to probe different motional ranges, while challenges include the high ratio of the detection dead time vs. the relaxation times. We review several important 2D ELDOR studies of molecular dynamics. (1) The results from a spin probe dissolved in a liquid crystal are followed throughout the isotropic → nematic → liquid-like smectic → solid-like smectic → crystalline phases as the temperature is reduced and are interpreted in terms of the slowly relaxing local structure model. Here, the labeled molecule is undergoing overall motion in the macroscopically aligned sample, as well as responding to local site fluctuations. (2) Several examples involving model phospholipid membranes are provided, including the dynamic structural characterization of the boundary lipid that coats a transmembrane peptide dimer. Additionally, subtle differences can be elicited for the phospholipid membrane phases: liquid disordered, liquid ordered, and gel, and the subtle effects upon the membrane, of antigen cross-linking of receptors on the surface of plasma membrane
Energy Technology Data Exchange (ETDEWEB)
Franck, John M.; Chandrasekaran, Siddarth; Dzikovski, Boris; Dunnam, Curt R.; Freed, Jack H., E-mail: jhf3@cornell.edu [Department of Chemistry and Chemical Biology and National Biomedical Center for Advanced ESR Technology, Cornell University, Ithaca, New York 14853 (United States)
2015-06-07
The development, applications, and current challenges of the pulsed ESR technique of two-dimensional Electron-Electron Double Resonance (2D ELDOR) are described. This is a three-pulse technique akin to 2D Exchange Nuclear Magnetic Resonance, but involving electron spins, usually in the form of spin-probes or spin-labels. As a result, it required the extension to much higher frequencies, i.e., microwaves, and much faster time scales, with π/2 pulses in the 2-3 ns range. It has proven very useful for studying molecular dynamics in complex fluids, and spectral results can be explained by fitting theoretical models (also described) that provide a detailed analysis of the molecular dynamics and structure. We discuss concepts that also appear in other forms of 2D spectroscopy but emphasize the unique advantages and difficulties that are intrinsic to ESR. Advantages include the ability to tune the resonance frequency, in order to probe different motional ranges, while challenges include the high ratio of the detection dead time vs. the relaxation times. We review several important 2D ELDOR studies of molecular dynamics. (1) The results from a spin probe dissolved in a liquid crystal are followed throughout the isotropic → nematic → liquid-like smectic → solid-like smectic → crystalline phases as the temperature is reduced and are interpreted in terms of the slowly relaxing local structure model. Here, the labeled molecule is undergoing overall motion in the macroscopically aligned sample, as well as responding to local site fluctuations. (2) Several examples involving model phospholipid membranes are provided, including the dynamic structural characterization of the boundary lipid that coats a transmembrane peptide dimer. Additionally, subtle differences can be elicited for the phospholipid membrane phases: liquid disordered, liquid ordered, and gel, and the subtle effects upon the membrane, of antigen cross-linking of receptors on the surface of plasma membrane
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.
Topological defects in two-dimensional crystals
Chen, Yong; Qi, Wei-Kai
2008-01-01
By using topological current theory, we study the inner topological structure of the topological defects in two-dimensional (2D) crystal. We find that there are two elementary point defects topological current in two-dimensional crystal, one for dislocations and the other for disclinations. The topological quantization and evolution of topological defects in two-dimensional crystals are discussed. Finally, We compare our theory with Brownian-dynamics simulations in 2D Yukawa systems.
布朗运动仿真实验的设计与实现%Simulation experiment of Brownian motion
Institute of Scientific and Technical Information of China (English)
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.
DEFF Research Database (Denmark)
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...
Energy Technology Data Exchange (ETDEWEB)
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
Institute of Scientific and Technical Information of China (English)
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
Institute of Scientific and Technical Information of China (English)
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.
Directory of Open Access Journals (Sweden)
Davide Mercadante
Full Text Available Pectin methylesterases (PMEs hydrolyze the methylester groups that are found on the homogalacturonan (HG chains of pectic polysaccharides in the plant cell wall. Plant and bacterial PMEs are especially interesting as the resulting de-methylesterified (carboxylated sugar residues are found to be arranged contiguously, indicating a so-called processive nature of these enzymes. Here we report the results of continuum electrostatics calculations performed along the molecular dynamics trajectory of a PME-HG-decasaccharide complex. In particular it was observed that, when the methylester groups of the decasaccharide were arranged in order to mimic the just-formed carboxylate product of de-methylesterification, a net unidirectional sliding of the model decasaccharide was subsequently observed along the enzyme's binding groove. The changes that occurred in the electrostatic binding energy and protein dynamics during this translocation provide insights into the mechanism by which the enzyme rectifies Brownian motions to achieve processivity. The free energy that drives these molecular motors is thus demonstrated to be incorporated endogenously in the methylesterified groups of the HG chains and is not supplied exogenously.
Guodong Liu; Yining Zhang; Huilin Lu; Ersheng You; Xiang Li
2013-01-01
Modular pebble-bed nuclear reactor (MPBNR) technology is promising due to its attractive features such as high fuel performance and inherent safety. Particle motion of fuel and graphite pebbles is highly associated with the performance of pebbled-bed modular nuclear reactor. To understand the mechanism of pebble’s motion in the reactor, we numerically studied the influence of number ratio of fuel and graphite pebbles, funnel angle of the reactor, height of guide ring on the distribution of pe...
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.
Directory of Open Access Journals (Sweden)
M. G. Kiselev
2014-01-01
Full Text Available The purpose of the paper is to make an experimental impact assessment of parameters pertaining to blank two-dimensional circular blank motion on intensity of its cutting and quality of the machined surfaces. Experimental data have been obtained that reveal efficiency in application of blank circular motion and improvement of its output cutting indices.A methodology has been developed for execution of comparative experimental investigations on cutting glass, nephrite and jasper specimens as under conventional conditions required for the operation so while transferring induced oscillations to boom suspension assembly that ensure specimen.The proposed methodology makes it possible to assess quantitatively intensity of specimen cutting and quality of its machined surface. The paper has shown that a positive impact of the specimen circular motion on quality improvement of its cross-cut surface is related to peculiar kinematics features pertaining to relative motion of disc side surface with cross-cut portions of the specimen surface. It has been shown that the intensifying impact of the specimen circular motion on the cutting process is primarily related to the changes in dynamic conditions of its interaction with the cutting edge of the disc. In contrast to conventional cutting when the process is going on under static pressure of contacting surfaces there is their periodical impact-frictional interaction due to transfer of circular motion to the specimen along elliptical trajectory. In this case the rate of the positive impact of the specimen circular motion on its cross-cut surface becomes higher while increasing vertical velocity component that concerns its sliding relative to disc side surface that is ensured by increasing oscillation frequency which is transferred to the boom suspension assembly. Moreover, the rate of positive impact of the specimen circulatory motion on the quality of its cross-cut surface becomes higher while increasing
Energy Technology Data Exchange (ETDEWEB)
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)
Directory of Open Access Journals (Sweden)
Zhaoqiang Yang
2017-01-01
Full Text Available A new framework for pricing the American fractional lookback option is developed in the case where the stock price follows a mixed jump-diffusion fraction Brownian motion. By using Itô formula and Wick-Itô-Skorohod integral a new market pricing model is built. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given. Numerical simulation illustrates some notable features of American fractional lookback options.
Song, Zhen; Moore, Kevin L.; Chen, YangQuan; Bahl, Vikas
2003-09-01
As an outgrowth of series of projects focused on mobility of unmanned ground vehicles (UGV), an omni-directional (ODV), multi-robot, autonomous mobile parking security system has been developed. The system has two types of robots: the low-profile Omni-Directional Inspection System (ODIS), which can be used for under-vehicle inspections, and the mid-sized T4 robot, which serves as a ``marsupial mothership'' for the ODIS vehicles and performs coarse resolution inspection. A key task for the T4 robot is license plate recognition (LPR). For a successful LPR task without compromising the recognition rate, the robot must be able to identify the bumper locations of vehicles in the parking area and then precisely position the LPR camera relative to the bumper. This paper describes a 2D-laser scanner based approach to bumper identification and laser servoing for the T4 robot. The system uses a gimbal-mounted scanning laser. As the T4 robot travels down a row of parking stalls, data is collected from the laser every 100ms. For each parking stall in the range of the laser during the scan, the data is matched to a ``bumper box'' corresponding to where a car bumper is expected, resulting in a point cloud of data corresponding to a vehicle bumper for each stall. Next, recursive line-fitting algorithms are used to determine a line for the data in each stall's ``bumper box.'' The fitting technique uses Hough based transforms, which are robust against segmentation problems and fast enough for real-time line fitting. Once a bumper line is fitted with an acceptable confidence, the bumper location is passed to the T4 motion controller, which moves to position the LPR camera properly relative to the bumper. The paper includes examples and results that show the effectiveness of the technique, including its ability to work in real-time.
Sompet, P.; Fung, Y. H.; Schwartz, E.; Hunter, M. D. J.; Phrompao, J.; Andersen, M. F.
2017-03-01
We combine near-deterministic preparation of a single atom with Raman sideband cooling, to create a push-button mechanism to prepare a single atom in the motional ground state of tightly focused optical tweezers. In the two-dimensional (2D) radial plane, we achieve a large ground-state fidelity for the entire procedure (loading and cooling) of ˜0.73 , while the ground-state occupancy is ˜0.88 for realizations with a single atom present. For 1D axial cooling, we attain a ground-state fraction of ˜0.52 . The combined 3D cooling provides a ground-state population of ˜0.11 . Our Raman sideband cooling variation is indifferent to magnetic field fluctuations, allowing widespread unshielded experimental implementations. Our work provides a pathway towards a range of coherent few-body experiments.
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
Institute of Scientific and Technical Information of China (English)
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。
Energy Technology Data Exchange (ETDEWEB)
Kang, Sang Mo; Mannoor, Madhusoodanan [Dong-A University, Busan (Korea, Republic of); Maniyeri, Ranjith Maniyeri [National Institute of Technology Karnataka, Mangalore (India)
2016-07-15
This paper presents two-dimensional direct numerical simulations to explore the effect of the Reynolds number on the Dielectrophoretic (DEP) motion of a pair of freely suspended particles in an unbounded viscous fluid under an external uniform electric field. Accordingly, the electric potential is obtained by solving the Maxwell'00s equation with a great sudden change in the electric conductivity at the particle-fluid interface and then the Maxwell stress tensor is integrated to determine the DEP force exerted on each particle. The fluid flow and particle movement, on the other hand, are predicted by solving the continuity and Navier-Stokes equations together with the kinetic equations. Numerical simulations are carried out using a finite volume approach, composed of a sharp interface method for the electric potential and a direct-forcing immersed-boundary method for the fluid flow. Through the simulations, it is found that both particles with the same sign of the conductivity revolve and eventually align themselves in a line with the electric field. With different signs, to the contrary, they revolve in the reverse way and eventually become lined up at a right angle with the electric field. The DEP motion also depends significantly on the Reynolds number defined based on the external electric field for all the combinations of the conductivity signs. When the Reynolds number is approximately below Re{sub cr} ≈ 0.1, the DEP motion becomes independent of the Reynolds number and thus can be exactly predicted by the no-inertia solver that neglects all the inertial and convective effects. With increasing Reynolds number above the critical number, on the other hand, the particles trace larger trajectories and thus take longer time during their revolution to the eventual in-line alignment.
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.
Directory of Open Access Journals (Sweden)
Fulong Jing
2017-06-01
Full Text Available For targets with complex motion, such as ships fluctuating with oceanic waves and high maneuvering airplanes, azimuth echo signals can be modeled as multicomponent quadratic frequency modulation (QFM signals after migration compensation and phase adjustment. For the QFM signal model, the chirp rate (CR and the quadratic chirp rate (QCR are two important physical quantities, which need to be estimated. For multicomponent QFM signals, the cross terms create a challenge for detection, which needs to be addressed. In this paper, by employing a novel multi-scale parametric symmetric self-correlation function (PSSF and modified scaled Fourier transform (mSFT, an effective parameter estimation algorithm is proposed—referred to as the Two-Dimensional product modified Lv’s distribution (2D-PMLVD—for QFM signals. The 2D-PMLVD is simple and can be easily implemented by using fast Fourier transform (FFT and complex multiplication. These measures are analyzed in the paper, including the principle, the cross term, anti-noise performance, and computational complexity. Compared to the other three representative methods, the 2D-PMLVD can achieve better anti-noise performance. The 2D-PMLVD, which is free of searching and has no identifiability problems, is more suitable for multicomponent situations. Through several simulations and analyses, the effectiveness of the proposed estimation algorithm is verified.
Kamali Tafreshi, Azadeh; Barış Top, Can; Güneri Gençer, Nevzat
2017-06-01
Harmonic motion microwave Doppler imaging (HMMDI) is a novel imaging modality for imaging the coupled electrical and mechanical properties of body tissues. In this paper, we used two experimental systems with different receiver configurations to obtain HMMDI images from tissue-mimicking phantoms at multiple vibration frequencies between 15 Hz and 35 Hz. In the first system, we used a spectrum analyzer to obtain the Doppler data in the frequency domain, while in the second one, we used a homodyne receiver that was designed to acquire time-domain data. The developed phantoms mimicked the elastic and dielectric properties of breast fat tissue, and included a 14~\\text{mm}× 9 mm cylindrical inclusion representing the tumor. A focused ultrasound probe was mechanically scanned in two lateral dimensions to obtain two-dimensional HMMDI images of the phantoms. The inclusions were resolved inside the fat phantom using both experimental setups. The image resolution increased with increasing vibration frequency. The designed receiver showed higher sensitivity than the spectrum analyzer measurements. The results also showed that time-domain data acquisition should be used to fully exploit the potential of the HMMDI method.
Saalmueller, J. W.; Long, H. W.; Maresch, G. G.; Spiess, H. W.
A practical route for obtaining two-dimensional electron double-resonance spectra of radicals in disordered solids is presented in detail. It involves narrow-band pulse excitation during a magnetic field step combined with echo detection after a mixing time. The equipment and experimental procedures are described, and factors affecting the performance of the field-jump coil, spectral resolution, and sensitivity are thoroughly discussed. Simulated spectra, which take into account distributions of correlation times, show the spectral features that can be observed with this technique. These simulations have been improved over previous work by taking into account g-tensor fluctuations, which is the dominant effect in determining the anisotropy of the electron spin-lattice relaxation. Data for nitroxide radicals in polycarbonate at 110 K are analyzed and an orientation averaged nuclear spin-lattice relaxation time of 82 ± 13 μs and an electron spin-lattice relaxation time for radicals oriented along the zdirection (slowest relaxation) of 23 ± 4 μs are measured. Simulations show that this relaxation is caused by highly restricted liberational motion with a distribution of correlation times having mean of 0.1 μs and a width of about 0.8 decades in combination with a very narrow mode having a correlation time of 10 ps.
Jing, Fulong; Jiao, Shuhong; Hou, Changbo; Si, Weijian; Wang, Yu
2017-01-01
For targets with complex motion, such as ships fluctuating with oceanic waves and high maneuvering airplanes, azimuth echo signals can be modeled as multicomponent quadratic frequency modulation (QFM) signals after migration compensation and phase adjustment. For the QFM signal model, the chirp rate (CR) and the quadratic chirp rate (QCR) are two important physical quantities, which need to be estimated. For multicomponent QFM signals, the cross terms create a challenge for detection, which needs to be addressed. In this paper, by employing a novel multi-scale parametric symmetric self-correlation function (PSSF) and modified scaled Fourier transform (mSFT), an effective parameter estimation algorithm is proposed—referred to as the Two-Dimensional product modified Lv’s distribution (2D-PMLVD)—for QFM signals. The 2D-PMLVD is simple and can be easily implemented by using fast Fourier transform (FFT) and complex multiplication. These measures are analyzed in the paper, including the principle, the cross term, anti-noise performance, and computational complexity. Compared to the other three representative methods, the 2D-PMLVD can achieve better anti-noise performance. The 2D-PMLVD, which is free of searching and has no identifiability problems, is more suitable for multicomponent situations. Through several simulations and analyses, the effectiveness of the proposed estimation algorithm is verified. PMID:28635640
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.
Energy Technology Data Exchange (ETDEWEB)
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.
Directory of Open Access Journals (Sweden)
Ryo Kanada
Full Text Available Kinesin is a family of molecular motors that move unidirectionally along microtubules (MT using ATP hydrolysis free energy. In the family, the conventional two-headed kinesin was experimentally characterized to move unidirectionally through "walking" in a hand-over-hand fashion by coordinated motions of the two heads. Interestingly a single-headed kinesin, a truncated KIF1A, still can generate a biased Brownian movement along MT, as observed by in vitro single molecule experiments. Thus, KIF1A must use a different mechanism from the conventional kinesin to achieve the unidirectional motions. Based on the energy landscape view of proteins, for the first time, we conducted a set of molecular simulations of the truncated KIF1A movements over an ATP hydrolysis cycle and found a mechanism exhibiting and enhancing stochastic forward-biased movements in a similar way to those in experiments. First, simulating stand-alone KIF1A, we did not find any biased movements, while we found that KIF1A with a large friction cargo-analog attached to the C-terminus can generate clearly biased Brownian movements upon an ATP hydrolysis cycle. The linked cargo-analog enhanced the detachment of the KIF1A from MT. Once detached, diffusion of the KIF1A head was restricted around the large cargo which was located in front of the head at the time of detachment, thus generating a forward bias of the diffusion. The cargo plays the role of a diffusional anchor, or cane, in KIF1A "walking."
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.
Two-dimensional optical thermal ratchets based on Fibonacci spirals.
Xiao, Ke; Roichman, Yael; Grier, David G
2011-07-01
An ensemble of symmetric potential energy wells arranged at the vertices of a Fibonacci spiral can serve as the basis for an irreducibly two-dimensional thermal ratchet. Periodic rotation of the potential energy landscape through a three-step cycle drives trapped Brownian particles along spiral trajectories through the pattern. Which spiral is selected depends on the angular displacement at each step, with transitions between selected spirals arising at rational proportions of the golden angle. Fibonacci spiral ratchets therefore display an exceptionally rich range of transport properties, including inhomogeneous states in which different parts of the pattern induce motion in different directions. Both the radial and angular components of these trajectories can undergo flux reversal as a function of the scale of the pattern or the rate of rotation.
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
Institute of Scientific and Technical Information of China (English)
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.
Energy Technology Data Exchange (ETDEWEB)
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.
Energy Technology Data Exchange (ETDEWEB)
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.
Directory of Open Access Journals (Sweden)
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Meade, Nigel [Imperial College, Business School London (United Kingdom)
2010-11-15
For oil related investment appraisal, an accurate description of the evolving uncertainty in the oil price is essential. For example, when using real option theory to value an investment, a density function for the future price of oil is central to the option valuation. The literature on oil pricing offers two views. The arbitrage pricing theory literature for oil suggests geometric Brownian motion and mean reversion models. Empirically driven literature suggests ARMA-GARCH models. In addition to reflecting the volatility of the market, the density function of future prices should also incorporate the uncertainty due to price jumps, a common occurrence in the oil market. In this study, the accuracy of density forecasts for up to a year ahead is the major criterion for a comparison of a range of models of oil price behaviour, both those proposed in the literature and following from data analysis. The Kullbach Leibler information criterion is used to measure the accuracy of density forecasts. Using two crude oil price series, Brent and West Texas Intermediate (WTI) representing the US market, we demonstrate that accurate density forecasts are achievable for up to nearly two years ahead using a mixture of two Gaussians innovation processes with GARCH and no mean reversion. (author)
Directory of Open Access Journals (Sweden)
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
Institute of Scientific and Technical Information of China (English)
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.
Energy Technology Data Exchange (ETDEWEB)
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.
Choi, Changmok; Na, Youngjin; Rim, Byeongcheol; Kim, Youngkyung; Kang, Sangkuk; Kim, Jung
2013-06-01
We developed an alternative computer interface using surface electromyography (sEMG) for individuals with spinal cord injuries (SCI) to access a computer. We designed this interface to make a cursor move on a two-dimensional screen and to click using only three muscles for each subject. In addition, a user can voluntarily control cursor movement speed by modulating muscle contraction levels. Three SCI patients and 10 healthy subjects volunteered to evaluate the performance of this interface using Fitts' law test in a two-dimensional testing setup. The throughputs (TP) of our interface were 0.1962±0.0562 b/s for the SCI patients and 0.4356±0.0706 b/s for the healthy subjects. This interface could help SCI patients handle a wider range of activities such as browsing the Internet and communicating with others.
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 ...
运动人体检测和二维关键点提取%Two-dimensional human motion detection and key points extration
Institute of Scientific and Technical Information of China (English)
宫宇
2012-01-01
A method based on video sequence of moving body and corresponding two-dimensional key points are presented.Firstly,frame difference method to initialize and update background is represented.And then substraction background is to detect two-dimensional moving body.At last,according to the moving body dectection,using the idea of APAR area extracts two-dimensional key points of human body.%给出了一种运动人体区域的检测及其对应的二维关键点的提取方法。首先运用帧差法构建一个自适应的背景模型以达到背景初始化和背景更新的目的。接着用减背景法实现二维运动人体区域的检测。最后将检测到的运动人体区域,通过运用APAR（anti-paralle lines）区域法实现对运动人体关键点的提取。
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.
Directory of Open Access Journals (Sweden)
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.
Osserman, Robert
2011-01-01
The basic component of several-variable calculus, two-dimensional calculus is vital to mastery of the broader field. This extensive treatment of the subject offers the advantage of a thorough integration of linear algebra and materials, which aids readers in the development of geometric intuition. An introductory chapter presents background information on vectors in the plane, plane curves, and functions of two variables. Subsequent chapters address differentiation, transformations, and integration. Each chapter concludes with problem sets, and answers to selected exercises appear at the end o
Juday, Richard D. (Inventor)
1992-01-01
A two-dimensional vernier scale is disclosed utilizing a cartesian grid on one plate member with a polar grid on an overlying transparent plate member. The polar grid has multiple concentric circles at a fractional spacing of the spacing of the cartesian grid lines. By locating the center of the polar grid on a location on the cartesian grid, interpolation can be made of both the X and Y fractional relationship to the cartesian grid by noting which circles coincide with a cartesian grid line for the X and Y direction.
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 ...
Carling; Williams; Bowtell
1998-12-01
Anguilliform swimming has been investigated by using a computational model combining the dynamics of both the creature's movement and the two-dimensional fluid flow of the surrounding water. The model creature is self-propelled; it follows a path determined by the forces acting upon it, as generated by its prescribed changing shape. The numerical solution has been obtained by applying coordinate transformations and then using finite difference methods. Results are presented showing the flow around the creature as it accelerates from rest in an enclosed tank. The kinematics and dynamics associated with the creature's centre of mass are also shown. For a particular set of body shape parameters, the final mean swimming speed is found to be 0.77 times the speed of the backward-travelling wave. The corresponding movement amplitude envelope is shown. The magnitude of oscillation in the net forward force has been shown to be approximately twice that in the lateral force. The importance of allowing for acceleration and deceleration of the creature's body (rather than imposing a constant swimming speed) has been demonstrated. The calculations of rotational movement of the body and the associated moment of forces about the centre of mass have also been included in the model. The important role of viscous forces along and around the creature's body and in the growth and dissolution of the vortex structures has been illustrated.
Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun
2014-12-07
Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.
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).
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.
Chang, Hing-Chiu; Chen, Nan-Kuei
2016-09-01
Diffusion-weighted imaging (DWI) obtained with interleaved echo-planar imaging (EPI) pulse sequence has great potential of characterizing brain tissue properties at high spatial-resolution. However, interleaved EPI based DWI data may be corrupted by various types of aliasing artifacts. First, inconsistencies in k-space data obtained with opposite readout gradient polarities result in Nyquist artifact, which is usually reduced with 1D phase correction in post-processing. When there exist eddy current cross terms (e.g., in oblique-plane EPI), 2D phase correction is needed to effectively reduce Nyquist artifact. Second, minuscule motion induced phase inconsistencies in interleaved DWI scans result in image-domain aliasing artifact, which can be removed with reconstruction procedures that take shot-to-shot phase variations into consideration. In existing interleaved DWI reconstruction procedures, Nyquist artifact and minuscule motion-induced aliasing artifact are typically removed subsequently in two stages. Although the two-stage phase correction generally performs well for non-oblique plane EPI data obtained from well-calibrated system, the residual artifacts may still be pronounced in oblique-plane EPI data or when there exist eddy current cross terms. To address this challenge, here we report a new composite 2D phase correction procedure, which effective removes Nyquist artifact and minuscule motion induced aliasing artifact jointly in a single step. Our experimental results demonstrate that the new 2D phase correction method can much more effectively reduce artifacts in interleaved EPI based DWI data as compared with the existing two-stage artifact correction procedures. The new method robustly enables high-resolution DWI, and should prove highly valuable for clinical uses and research studies of DWI.
Energy Technology Data Exchange (ETDEWEB)
Bietenholz, Wolfgang, E-mail: wolbi@nucleares.unam.mx; Chryssomalakos, Chryssomalis, E-mail: chryss@nucleares.unam.mx; Salgado, Marcelo, E-mail: marcelo@nucleares.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, México D.F. 04510, México (Mexico)
2015-10-15
We comment on a fatal flaw in the analysis contained in the work of Martínez-y-Romero et al., [J. Math. Phys. 54, 053509 (2013)], which concerns the motion of a point particle in an inverse square potential, and show that most conclusions reached there are wrong. In particular, the manifestly senseless claim that, in the attractive potential case, no bounded orbits exist for negative energies, is traced to a sign error. Several more mistakes, both in the classical and the quantum cases, are pointed out.
Two-dimensional optical spectroscopy
Cho, Minhaeng
2009-01-01
Discusses the principles and applications of two-dimensional vibrational and optical spectroscopy techniques. This book provides an account of basic theory required for an understanding of two-dimensional vibrational and electronic spectroscopy.
Directory of Open Access Journals (Sweden)
Woochul Nam
Full Text Available Kinesins are molecular motors which walk along microtubules by moving their heads to different binding sites. The motion of kinesin is realized by a conformational change in the structure of the kinesin molecule and by a diffusion of one of its two heads. In this study, a novel model is developed to account for the 2D diffusion of kinesin heads to several neighboring binding sites (near the surface of microtubules. To determine the direction of the next step of a kinesin molecule, this model considers the extension in the neck linkers of kinesin and the dynamic behavior of the coiled-coil structure of the kinesin neck. Also, the mechanical interference between kinesins and obstacles anchored on the microtubules is characterized. The model predicts that both the kinesin velocity and run length (i.e., the walking distance before detaching from the microtubule are reduced by static obstacles. The run length is decreased more significantly by static obstacles than the velocity. Moreover, our model is able to predict the motion of kinesin when other (several motors also move along the same microtubule. Furthermore, it suggests that the effect of mechanical interaction/interference between motors is much weaker than the effect of static obstacles. Our newly developed model can be used to address unanswered questions regarding degraded transport caused by the presence of excessive tau proteins on microtubules.
Pan, Tsorng-Whay
2016-01-01
In this article we present a numerical study of the dynamics of two disks settling in a narrow vertical channel filled with Oldroyd-B fluid. Two kinds of particle dynamics are obtained: (i) periodic interaction between two disks and (ii) the chain formation of two disks. For the periodic interaction of two disks, two different motions are obtained: (a) two disks stay far apart and interact periodically and (b) two disks interact closely and then far apart in a periodic way, like the drafting, kissing and tumbling of two disks sedimenting in Newtonian fluid, due to the lack of strong enough elastic force. For the formation of two disk chain occurred at higher values of the elasticity number, it is either a tilted chain or a vertical chain. The tilted chain can be obtained for either that the elasticity number is less than the critical value for having the vertical chain or that the Mach number is greater than the critical value for a long body to fall broadside-on. Hence the values of the elasticity number and...
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.
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
Institute of Scientific and Technical Information of China (English)
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.
DEFF Research Database (Denmark)
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...
DEFF Research Database (Denmark)
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).
Brela, Mateusz; Stare, Jernej; Pirc, Gordana; Sollner-Dolenc, Marija; Boczar, Marek; Wójcik, Marek J; Mavri, Janez
2012-04-19
The nature of medium strong intra- and intermolecular hydrogen bonding in 2-hydroxy-5-nitrobenzamide in the crystal phase was examined by infrared spectroscopy and Car-Parrinello molecular dynamics simulation. The focal point of our study was the part of the infrared spectra associated with the O-H and N-H stretching modes that are very sensitive to the strength of hydrogen bonding. For spectra calculations we used an isolated dimer and the fully periodic crystal environment. We calculated the spectra by using harmonic approximation, the time course of the dipole moment function as obtained from the Car-Parrinello simulation, and the quantization of the nuclear motion of the proton for an instantaneous snapshot of the structures in one and two dimensions. Although quantitative assessment of the agreement between the computed and experimental band contour is difficult due to the fact that the experimental band is very broad, we feel that the most reasonable qualitative agreement with the experiment is obtained from snapshot structures and two-dimensional quantization of the proton motion. We have also critically examined the methods of constructing the one-dimensional proton potential. Perspectives are given for the treatment of nuclear quantum effects in biocatalysis.
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.
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
Institute of Scientific and Technical Information of China (English)
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.
Institute of Scientific and Technical Information of China (English)
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。
Jun, Brian; Giarra, Matthew; Golz, Brian; Main, Russell; Vlachos, Pavlos
2016-11-01
We present a methodology to mitigate the major sources of error associated with two-dimensional confocal laser scanning microscopy (CLSM) images of nanoparticles flowing through a microfluidic channel. The correlation-based velocity measurements from CLSM images are subject to random error due to the Brownian motion of nanometer-sized tracer particles, and a bias error due to the formation of images by raster scanning. Here, we develop a novel ensemble phase correlation with dynamic optimal filter that maximizes the correlation strength, which diminishes the random error. In addition, we introduce an analytical model of CLSM measurement bias error correction due to two-dimensional image scanning of tracer particles. We tested our technique using both synthetic and experimental images of nanoparticles flowing through a microfluidic channel. We observed that our technique reduced the error by up to a factor of ten compared to ensemble standard cross correlation (SCC) for the images tested in the present work. Subsequently, we will assess our framework further, by interrogating nanoscale flow in the cell culture environment (transport within the lacunar-canalicular system) to demonstrate our ability to accurately resolve flow measurements in a biological system.
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.
Theory of two-dimensional transformations
Kanayama, Yutaka J.; Krahn, Gary W.
1998-01-01
The article of record may be found at http://dx.doi.org/10.1109/70.720359 Robotics and Automation, IEEE Transactions on This paper proposes a new "heterogeneous" two-dimensional (2D) transformation group ___ to solve motion analysis/planning problems in robotics. In this theory, we use a 3×1 matrix to represent a transformation as opposed to a 3×3 matrix in the homogeneous formulation. First, this theory is as capable as the homogeneous theory, Because of the minimal size, its implement...
Dynamics of film. [two dimensional continua theory
Zak, M.
1979-01-01
The general theory of films as two-dimensional continua are elaborated upon. As physical realizations of such a model this paper examines: inextensible films, elastic films, and nets. The suggested dynamic equations have enabled us to find out the characteristic speeds of wave propagation of the invariants of external and internal geometry and formulate the criteria of instability of their shape. Also included herein is a detailed account of the equation describing the film motions beyond the limits of the shape stability accompanied by the formation of wrinkles. The theory is illustrated by examples.
Two-dimensional liquid chromatography
DEFF Research Database (Denmark)
Græsbøll, Rune
of this thesis is on online comprehensive two-dimensional liquid chromatography (online LC×LC) with reverse phase in both dimensions (online RP×RP). Since online RP×RP has not been attempted before within this research group, a significant part of this thesis consists of knowledge and experience gained...
Institute of Scientific and Technical Information of China (English)
章晨; 孙寅光; 朱佳; 黄洁; 王琳; 葛卫力; 唐礼江
2012-01-01
目的 研究正常人心肌机械运动特性.方法 研究对象为60例正常志愿者,男34例,年龄(42.0±13.0)岁；女26例,年龄(37.0±10.0)岁,应用超声心动图二维斑点成像技术评价左心室纵向、径向和圆周向运动的心肌机械运动参数,包括收缩应变、收缩应变率和舒张应变率及其达峰时间.结果左心室收缩应变纵向运动和圆周向表现出自基底部至心尖部收缩应变的绝对值递增,纵向运动基底部、中间部至心尖部收缩应变的绝对值分别为:20.2±4.2,20.4±4.3,22.5±6.4(P＜0.05)；圆周向运动基底部、中间部至心尖部收缩应变的绝对值分别为:20.1±7.7,23.4±8.1,27.1±7.1(P＜0.01),而径向运动的表现则不同,基底部、中间部与心尖部收缩应变的绝对值分别为40.9±17.4,41.8±17.6,28.8±17.1(P＜0.01)；3个方向的收缩应变率表现完全不一致,没有明显规律.3个方向舒张早期应变率均表现为自基底部至心尖部递增的趋势.重复性检验提示纵向收缩峰值应变,重复性最佳.结论心肌机械运动是一个极其复杂的过程,二维应变超声心动图有助于揭示生理和病理状态下心肌运动特性.%Objective To study myocardial characteristics of mechanical motion in normal subjects. Methods Sixty healthy volunteers were included,male 34 cases,aged (42. 0±13. 0) years;female 26 cases,aged (37. 0± 10, 0) years,two- dimensional speckle imaging technique was used to measure the left ventricular myocardial longitudinal, radial and circumferential movement of mechanical motion parameters including systolic strain,systolic strain rate and diatolic strain rates,as well as time-to-peak. Results The performance of left ventricular radial motion was different in absolute strain value, compared to longitudinal and circumferential systolic strains which increased from the base to the apex. The absolute value of longitudinal strain from base to apex respectively was 20. 2±4. 2,20. 4±4
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
Institute of Scientific and Technical Information of China (English)
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.
Two dimensional unstable scar statistics.
Energy Technology Data Exchange (ETDEWEB)
Warne, Larry Kevin; Jorgenson, Roy Eberhardt; Kotulski, Joseph Daniel; Lee, Kelvin S. H. (ITT Industries/AES Los Angeles, CA)
2006-12-01
This report examines the localization of time harmonic high frequency modal fields in two dimensional cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This paper examines the enhancements for these unstable orbits when the opposing mirrors are both convex and concave. In the latter case the construction includes the treatment of interior foci.
Juday, Richard D.
1992-01-01
Modified vernier scale gives accurate two-dimensional coordinates from maps, drawings, or cathode-ray-tube displays. Movable circular overlay rests on fixed rectangular-grid overlay. Pitch of circles nine-tenths that of grid and, for greatest accuracy, radii of circles large compared with pitch of grid. Scale enables user to interpolate between finest divisions of regularly spaced rule simply by observing which mark on auxiliary vernier rule aligns with mark on primary rule.
Two-dimensional liquid chromatography
DEFF Research Database (Denmark)
Græsbøll, Rune
Two-dimensional liquid chromatography has received increasing interest due to the rise in demand for analysis of complex chemical mixtures. Separation of complex mixtures is hard to achieve as a simple consequence of the sheer number of analytes, as these samples might contain hundreds or even...... dimensions. As a consequence of the conclusions made within this thesis, the research group has, for the time being, decided against further development of online LC×LC systems, since it was not deemed ideal for the intended application, the analysis of the polar fraction of oil. Trap-and...
Two-dimensional capillary origami
Energy Technology Data Exchange (ETDEWEB)
Brubaker, N.D., E-mail: nbrubaker@math.arizona.edu; Lega, J., E-mail: lega@math.arizona.edu
2016-01-08
We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid. - Highlights: • Full solution set of the two-dimensional capillary origami problem. • Fluid does not necessarily wet the entire plate. • Global energy approach provides exact differential equations satisfied by minimizers. • Bifurcation diagrams highlight three different regimes. • Conditions for spontaneous encapsulation are identified.
Two-dimensional gauge theoretic supergravities
Cangemi, D.; Leblanc, M.
1994-05-01
We investigate two-dimensional supergravity theories, which can be built from a topological and gauge invariant action defined on an ordinary surface. One is the N = 1 supersymmetric extension of the Jackiw-Teitelboim model presented by Chamseddine in a superspace formalism. We complement the proof of Montano, Aoaki and Sonnenschein that this extension is topological and gauge invariant, based on the graded de Sitter algebra. Not only do the equations of motion correspond to the supergravity ones and do gauge transformations encompass local supersymmetries, but we also identify the ∫-theory with the superfield formalism action written by Chamseddine. Next, we show that the N = 1 supersymmetric extension of string-inspired two-dimensional dilaton gravity put forward by Park and Strominger cannot be written as a ∫-theory. As an alternative, we propose two topological and gauge theories that are based on a graded extension of the extended Poincaré algebra and satisfy a vanishing-curvature condition. Both models are supersymmetric extensions of the string-inspired dilaton gravity.
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
Energy Technology Data Exchange (ETDEWEB)
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
Two-dimensional quantum repeaters
Wallnöfer, J.; Zwerger, M.; Muschik, C.; Sangouard, N.; Dür, W.
2016-11-01
The endeavor to develop quantum networks gave rise to a rapidly developing field with far-reaching applications such as secure communication and the realization of distributed computing tasks. This ultimately calls for the creation of flexible multiuser structures that allow for quantum communication between arbitrary pairs of parties in the network and facilitate also multiuser applications. To address this challenge, we propose a two-dimensional quantum repeater architecture to establish long-distance entanglement shared between multiple communication partners in the presence of channel noise and imperfect local control operations. The scheme is based on the creation of self-similar multiqubit entanglement structures at growing scale, where variants of entanglement swapping and multiparty entanglement purification are combined to create high-fidelity entangled states. We show how such networks can be implemented using trapped ions in cavities.
Two-dimensional capillary origami
Brubaker, N. D.; Lega, J.
2016-01-01
We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid.
Two-dimensional cubic convolution.
Reichenbach, Stephen E; Geng, Frank
2003-01-01
The paper develops two-dimensional (2D), nonseparable, piecewise cubic convolution (PCC) for image interpolation. Traditionally, PCC has been implemented based on a one-dimensional (1D) derivation with a separable generalization to two dimensions. However, typical scenes and imaging systems are not separable, so the traditional approach is suboptimal. We develop a closed-form derivation for a two-parameter, 2D PCC kernel with support [-2,2] x [-2,2] that is constrained for continuity, smoothness, symmetry, and flat-field response. Our analyses, using several image models, including Markov random fields, demonstrate that the 2D PCC yields small improvements in interpolation fidelity over the traditional, separable approach. The constraints on the derivation can be relaxed to provide greater flexibility and performance.
Zero sound in a two-dimensional dipolar Fermi gas
Lu, Z.K.; Matveenko, S.I.; Shlyapnikov, G.V.
2013-01-01
We study zero sound in a weakly interacting two-dimensional (2D) gas of single-component fermionic dipoles (polar molecules or atoms with a large magnetic moment) tilted with respect to the plane of their translational motion. It is shown that the propagation of zero sound is provided by both mean-f
Two-dimensional static black holes with pointlike sources
Melis, M
2004-01-01
We study the static black hole solutions of generalized two-dimensional dilaton-gravity theories generated by pointlike mass sources, in the hypothesis that the matter is conformally coupled. We also discuss the motion of test particles. Due to conformal coupling, these follow the geodesics of a metric obtained by rescaling the canonical metric with the dilaton.
SAR Processing Based On Two-Dimensional Transfer Function
Chang, Chi-Yung; Jin, Michael Y.; Curlander, John C.
1994-01-01
Exact transfer function, ETF, is two-dimensional transfer function that constitutes basis of improved frequency-domain-convolution algorithm for processing synthetic-aperture-radar, SAR data. ETF incorporates terms that account for Doppler effect of motion of radar relative to scanned ground area and for antenna squint angle. Algorithm based on ETF outperforms others.
Two-dimensional model of elastically coupled molecular motors
Institute of Scientific and Technical Information of China (English)
Zhang Hong-Wei; Wen Shu-Tang; Chen Gai-Rong; Li Yu-Xiao; Cao Zhong-Xing; Li Wei
2012-01-01
A flashing ratchet model of a two-headed molecular motor in a two-dimensional potential is proposed to simulate the hand-over-hand motion of kinesins.Extensive Langevin simulations of the model are performed.We discuss the dependences of motion and efficiency on the model parameters,including the external force and the temperature.A good qualitative agreement with the expected behavior is observed.
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.
Classifying Two-dimensional Hyporeductive Triple Algebras
Issa, A Nourou
2010-01-01
Two-dimensional real hyporeductive triple algebras (h.t.a.) are investigated. A classification of such algebras is presented. As a consequence, a classification of two-dimensional real Lie triple algebras (i.e. generalized Lie triple systems) and two-dimensional real Bol algebras is given.
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.
Two-dimensional function photonic crystals
Wu, Xiang-Yao; Liu, Xiao-Jing; Liang, Yu
2016-01-01
In this paper, we have firstly proposed two-dimensional function photonic crystals, which the dielectric constants of medium columns are the functions of space coordinates $\\vec{r}$, it is different from the two-dimensional conventional photonic crystals constituting by the medium columns of dielectric constants are constants. We find the band gaps of two-dimensional function photonic crystals are different from the two-dimensional conventional photonic crystals, and when the functions form of dielectric constants are different, the band gaps structure should be changed, which can be designed into the appropriate band gaps structures by the two-dimensional function photonic crystals.
Singular analysis of two-dimensional bifurcation system
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Bifurcation properties of two-dimensional bifurcation system are studied in this paper.Universal unfolding and transition sets of the bifurcation equations are obtained.The whole parametric plane is divided into several different persistent regions according to the type of motion,and the different qualitative bifurcation diagrams in different persistent regions are given.The bifurcation properties of the two-dimensional bifurcation system are compared with its reduced one-dimensional system.It is found that the system which is reduced to one dimension has lost many bifurcation properties.
Quasinormal frequencies of asymptotically flat two-dimensional black holes
Lopez-Ortega, A
2011-01-01
We discuss whether the minimally coupled massless Klein-Gordon and Dirac fields have well defined quasinormal modes in single horizon, asymptotically flat two-dimensional black holes. To get the result we solve the equations of motion in the massless limit and we also calculate the effective potentials of Schrodinger type equations. Furthermore we calculate exactly the quasinormal frequencies of the Dirac field propagating in the two-dimensional uncharged Witten black hole. We compare our results on its quasinormal frequencies with other already published.
Hamiltonian formalism of two-dimensional Vlasov kinetic equation.
Pavlov, Maxim V
2014-12-08
In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.
Institute of Scientific and Technical Information of China (English)
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 .
General criteria for determining rotation or oscillation in a two-dimensional axisymmetric system
Koyano, Yuki; Yoshinaga, Natsuhiko; Kitahata, Hiroyuki
2015-07-01
A self-propelled particle in a two-dimensional axisymmetric system, such as a particle in a central force field or confined in a circular region, may show rotational or oscillatory motion. These motions do not require asymmetry of the particle or the boundary, but arise through spontaneous symmetry breaking. We propose a generic model for a self-propelled particle in a two-dimensional axisymmetric system. A weakly nonlinear analysis establishes criteria for determining rotational or oscillatory motion.
Hadamard States and Two-dimensional Gravity
Salehi, H
2001-01-01
We have used a two-dimensional analog of the Hadamard state-condition to study the local constraints on the two-point function of a linear quantum field conformally coupled to a two-dimensional gravitational background. We develop a dynamical model in which the determination of the state of the quantum field is essentially related to the determination of a conformal frame. A particular conformal frame is then introduced in which a two-dimensional gravitational equation is established.
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.
Institute of Scientific and Technical Information of China (English)
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
Institute of Scientific and Technical Information of China (English)
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.
Strongly interacting two-dimensional Dirac fermions
Lim, L.K.; Lazarides, A.; Hemmerich, Andreas; de Morais Smith, C.
2009-01-01
We show how strongly interacting two-dimensional Dirac fermions can be realized with ultracold atoms in a two-dimensional optical square lattice with an experimentally realistic, inherent gauge field, which breaks time reversal and inversion symmetries. We find remarkable phenomena in a temperature
Topology optimization of two-dimensional waveguides
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard; Sigmund, Ole
2003-01-01
In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss.......In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss....
沟道二维泥石流运动和冲淤数值模型研究%Two-dimensional numerical model for debris flow motion and gully bed evolution
Institute of Scientific and Technical Information of China (English)
张万顺; 赵琰鑫; 崔鹏; 彭虹; 陈雪娇
2012-01-01
以水沙混合流模型为基础,采用混合流沙量动态变化模式,提出泥石流运动控制方程组,建立适用于模拟泥石流在天然沟道中的运动和冲淤过程的二维数值模型.模型基于水动力学理论、水沙两相混合流理论和宾汉体模型理论,考虑了泥石流运动、泥沙输移、沟床变形、泥石流宾汉体流变特性等主要动力学过程.将模型应用于云南东川蒋家沟实测泥石流过程的模拟研究,结果较好地反映了泥石流运动不连续性的特征和泥石流沟道冲淤随时间演变的实际规律.%A two-dimensional mathematical model of debris flow in natural gully is developed. Based on the hydrodynamic theory, the water-sediments two-phase flow theory and the Bingham rheological theory, the dynamic processes of debris flow movement, sediment transport, bed evolution and rheological properties of the debris flow are considered. The model is applied to simulate debris flow event in Jiangjia Gully, Yunnan Province and predict the flow pattern and bed erosion-deposition processes. The results show the effectiveness of the proposed model.
Acoustic Bloch oscillations in a two-dimensional phononic crystal.
He, Zhaojian; Peng, Shasha; Cai, Feiyan; Ke, Manzhu; Liu, Zhengyou
2007-11-01
We report the observation of acoustic Bloch oscillations at megahertz frequency in a two-dimensional phononic crystal. By creating periodically arrayed cavities with a decreasing gradient in width along one direction in the phononic crystal, acoustic Wannier-Stark ladders are created in the frequency domain. The oscillatory motion of an incident Gaussian pulse inside the sample is demonstrated by both simulation and experiment.
Quantum entanglement in a two-dimensional ion trap
Institute of Scientific and Technical Information of China (English)
王成志; 方卯发
2003-01-01
In this paper, we investigate the quantum entanglement in a two-dimensional ion trap system. We discuss the quantum entanglement between the ion and phonons by using reduced entropy, and that between two degrees of freedom of the vibrational motion along x and y directions by using quantum relative entropy. We discuss also the influence of initial state of the system on the quantum entanglement and the relation between two entanglements in the trapped ion system.
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.
Effective diffusion of confined active Brownian swimmers
Sandoval, Mario; Dagdug, Leonardo
2014-11-01
We find theoretically the effect of confinement and thermal fluctuations, on the diffusivity of a spherical active swimmer moving inside a two-dimensional narrow cavity of general shape. The explicit formulas for the effective diffusion coefficient of a swimmer moving inside two particular cavities are presented. We also compare our analytical results with Brownian Dynamics simulations and we obtain excellent agreement. L.D. thanks Consejo Nacional de Ciencia y Tecnologia (CONACyT) Mexico, for partial support by Grant No. 176452. M. S. thanks CONACyT and Programa de Mejoramiento de Profesorado (PROMEP) for partially funding this work under Grant No. 103.5/13/6732.
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.
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.
Two Dimensional Plasmonic Cavities on Moire Surfaces
Balci, Sinan; Kocabas, Askin; Karabiyik, Mustafa; Kocabas, Coskun; Aydinli, Atilla
2010-03-01
We investigate surface plasmon polariton (SPP) cavitiy modes on two dimensional Moire surfaces in the visible spectrum. Two dimensional hexagonal Moire surface can be recorded on a photoresist layer using Interference lithography (IL). Two sequential exposures at slightly different angles in IL generate one dimensional Moire surfaces. Further sequential exposure for the same sample at slightly different angles after turning the sample 60 degrees around its own axis generates two dimensional hexagonal Moire cavity. Spectroscopic reflection measurements have shown plasmonic band gaps and cavity states at all the azimuthal angles (omnidirectional cavity and band gap formation) investigated. The plasmonic band gap edge and the cavity states energies show six fold symmetry on the two dimensional Moire surface as measured in reflection measurements.
Two-dimensional function photonic crystals
Liu, Xiao-Jing; Liang, Yu; Ma, Ji; Zhang, Si-Qi; Li, Hong; Wu, Xiang-Yao; Wu, Yi-Heng
2017-01-01
In this paper, we have studied two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , that can become true easily by electro-optical effect and optical kerr effect. We calculated the band gap structures of TE and TM waves, and found the TE (TM) wave band gaps of function photonic crystals are wider (narrower) than the conventional photonic crystals. For the two-dimensional function photonic crystals, when the dielectric constant functions change, the band gaps numbers, width and position should be changed, and the band gap structures of two-dimensional function photonic crystals can be adjusted flexibly, the needed band gap structures can be designed by the two-dimensional function photonic crystals, and it can be of help to design optical devices.
Two-Dimensional Planetary Surface Lander
Hemmati, H.; Sengupta, A.; Castillo, J.; McElrath, T.; Roberts, T.; Willis, P.
2014-06-01
A systems engineering study was conducted to leverage a new two-dimensional (2D) lander concept with a low per unit cost to enable scientific study at multiple locations with a single entry system as the delivery vehicle.
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...
Institute of Scientific and Technical Information of China (English)
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.
Interpolation by two-dimensional cubic convolution
Shi, Jiazheng; Reichenbach, Stephen E.
2003-08-01
This paper presents results of image interpolation with an improved method for two-dimensional cubic convolution. Convolution with a piecewise cubic is one of the most popular methods for image reconstruction, but the traditional approach uses a separable two-dimensional convolution kernel that is based on a one-dimensional derivation. The traditional, separable method is sub-optimal for the usual case of non-separable images. The improved method in this paper implements the most general non-separable, two-dimensional, piecewise-cubic interpolator with constraints for symmetry, continuity, and smoothness. The improved method of two-dimensional cubic convolution has three parameters that can be tuned to yield maximal fidelity for specific scene ensembles characterized by autocorrelation or power-spectrum. This paper illustrates examples for several scene models (a circular disk of parametric size, a square pulse with parametric rotation, and a Markov random field with parametric spatial detail) and actual images -- presenting the optimal parameters and the resulting fidelity for each model. In these examples, improved two-dimensional cubic convolution is superior to several other popular small-kernel interpolation methods.
TWO-DIMENSIONAL TOPOLOGY OF COSMOLOGICAL REIONIZATION
Energy Technology Data Exchange (ETDEWEB)
Wang, Yougang; Xu, Yidong; Chen, Xuelei [Key Laboratory of Computational Astrophysics, National Astronomical Observatories, Chinese Academy of Sciences, Beijing, 100012 China (China); Park, Changbom [School of Physics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722 (Korea, Republic of); Kim, Juhan, E-mail: wangyg@bao.ac.cn, E-mail: cbp@kias.re.kr [Center for Advanced Computation, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722 (Korea, Republic of)
2015-11-20
We study the two-dimensional topology of the 21-cm differential brightness temperature for two hydrodynamic radiative transfer simulations and two semi-numerical models. In each model, we calculate the two-dimensional genus curve for the early, middle, and late epochs of reionization. It is found that the genus curve depends strongly on the ionized fraction of hydrogen in each model. The genus curves are significantly different for different reionization scenarios even when the ionized faction is the same. We find that the two-dimensional topology analysis method is a useful tool to constrain the reionization models. Our method can be applied to the future observations such as those of the Square Kilometre Array.
Two dimensional topology of cosmological reionization
Wang, Yougang; Xu, Yidong; Chen, Xuelei; Kim, Juhan
2015-01-01
We study the two-dimensional topology of the 21-cm differential brightness temperature for two hydrodynamic radiative transfer simulations and two semi-numerical models. In each model, we calculate the two dimensional genus curve for the early, middle and late epochs of reionization. It is found that the genus curve depends strongly on the ionized fraction of hydrogen in each model. The genus curves are significantly different for different reionization scenarios even when the ionized faction is the same. We find that the two-dimensional topology analysis method is a useful tool to constrain the reionization models. Our method can be applied to the future observations such as those of the Square Kilometer Array.
Two-dimensional x-ray diffraction
He, Bob B
2009-01-01
Written by one of the pioneers of 2D X-Ray Diffraction, this useful guide covers the fundamentals, experimental methods and applications of two-dimensional x-ray diffraction, including geometry convention, x-ray source and optics, two-dimensional detectors, diffraction data interpretation, and configurations for various applications, such as phase identification, texture, stress, microstructure analysis, crystallinity, thin film analysis and combinatorial screening. Experimental examples in materials research, pharmaceuticals, and forensics are also given. This presents a key resource to resea
Matching Two-dimensional Gel Electrophoresis' Spots
DEFF Research Database (Denmark)
Dos Anjos, António; AL-Tam, Faroq; Shahbazkia, Hamid Reza
2012-01-01
This paper describes an approach for matching Two-Dimensional Electrophoresis (2-DE) gels' spots, involving the use of image registration. The number of false positive matches produced by the proposed approach is small, when compared to academic and commercial state-of-the-art approaches. This ar......This paper describes an approach for matching Two-Dimensional Electrophoresis (2-DE) gels' spots, involving the use of image registration. The number of false positive matches produced by the proposed approach is small, when compared to academic and commercial state-of-the-art approaches...
Mobility anisotropy of two-dimensional semiconductors
Lang, Haifeng; Zhang, Shuqing; Liu, Zhirong
2016-12-01
The carrier mobility of anisotropic two-dimensional semiconductors under longitudinal acoustic phonon scattering was theoretically studied using deformation potential theory. Based on the Boltzmann equation with the relaxation time approximation, an analytic formula of intrinsic anisotropic mobility was derived, showing that the influence of effective mass on mobility anisotropy is larger than those of deformation potential constant or elastic modulus. Parameters were collected for various anisotropic two-dimensional materials (black phosphorus, Hittorf's phosphorus, BC2N , MXene, TiS3, and GeCH3) to calculate their mobility anisotropy. It was revealed that the anisotropic ratio is overestimated by the previously described method.
Towards two-dimensional search engines
Ermann, Leonardo; Chepelianskii, Alexei D.; Shepelyansky, Dima L.
2011-01-01
We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of ingoing links, while CheiRank orders nodes proportionally to a number of outgoing links. In this way the ranking of nodes becomes two-dimensional that paves the way for development of two-dimensional search engines of new type. Statistical properties of inf...
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.
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.
A two-dimensional approach to relativistic positioning systems
Coll, B; Morales, J A; Coll, Bartolom\\'{e}; Ferrando, Joan Josep; Morales, Juan Antonio
2006-01-01
A relativistic positioning system is a physical realization of a coordinate system consisting in four clocks in arbitrary motion broadcasting their proper times. The basic elements of the relativistic positioning systems are presented in the two-dimensional case. This simplified approach allow to explain and to analyze the properties and interest of these new systems. The positioning system defined by geodesic emitters in flat metric is developed in detail. The information that the data generated by a relativistic positioning system give on the space-time metric interval is analyzed, and the interest of these results in gravimetry is pointed out.
Smoothed Particle Hydrodynamics Method for Two-dimensional Stefan Problem
Tarwidi, Dede
2016-01-01
Smoothed particle hydrodynamics (SPH) is developed for modelling of melting and solidification. Enthalpy method is used to solve heat conduction equations which involved moving interface between phases. At first, we study the melting of floating ice in the water for two-dimensional system. The ice objects are assumed as solid particles floating in fluid particles. The fluid and solid motion are governed by Navier-Stokes equation and basic rigid dynamics equation, respectively. We also propose a strategy to separate solid particles due to melting and solidification. Numerical results are obtained and plotted for several initial conditions.
Institute of Scientific and Technical Information of China (English)
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.
Piezoelectricity in Two-Dimensional Materials
Wu, Tao
2015-02-25
Powering up 2D materials: Recent experimental studies confirmed the existence of piezoelectricity - the conversion of mechanical stress into electricity - in two-dimensional single-layer MoS2 nanosheets. The results represent a milestone towards embedding low-dimensional materials into future disruptive technologies. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA.
Kronecker Product of Two-dimensional Arrays
Institute of Scientific and Technical Information of China (English)
Lei Hu
2006-01-01
Kronecker sequences constructed from short sequences are good sequences for spread spectrum communication systems. In this paper we study a similar problem for two-dimensional arrays, and we determine the linear complexity of the Kronecker product of two arrays. Our result shows that similar good property on linear complexity holds for Kronecker product of arrays.
Two-Dimensional Toda-Heisenberg Lattice
Directory of Open Access Journals (Sweden)
Vadim E. Vekslerchik
2013-06-01
Full Text Available We consider a nonlinear model that is a combination of the anisotropic two-dimensional classical Heisenberg and Toda-like lattices. In the framework of the Hirota direct approach, we present the field equations of this model as a bilinear system, which is closely related to the Ablowitz-Ladik hierarchy, and derive its N-soliton solutions.
A novel two dimensional particle velocity sensor
Pjetri, Olti; Wiegerink, Remco J.; Lammerink, Theo S.; Krijnen, Gijs J.
2013-01-01
In this paper we present a two wire, two-dimensional particle velocity sensor. The miniature sensor of size 1.0x2.5x0.525 mm, consisting of only two crossed wires, shows excellent directional sensitivity in both directions, thus requiring no directivity calibration, and is relatively easy to fabrica
Two-dimensional microstrip detector for neutrons
Energy Technology Data Exchange (ETDEWEB)
Oed, A. [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)
1997-04-01
Because of their robust design, gas microstrip detectors, which were developed at ILL, can be assembled relatively quickly, provided the prefabricated components are available. At the beginning of 1996, orders were received for the construction of three two-dimensional neutron detectors. These detectors have been completed. The detectors are outlined below. (author). 2 refs.
Two-dimensional magma-repository interactions
Bokhove, O.
2001-01-01
Two-dimensional simulations of magma-repository interactions reveal that the three phases --a shock tube, shock reflection and amplification, and shock attenuation and decay phase-- in a one-dimensional flow tube model have a precursor. This newly identified phase ``zero'' consists of the impact of
Two-dimensional subwavelength plasmonic lattice solitons
Ye, F; Hu, B; Panoiu, N C
2010-01-01
We present a theoretical study of plasmonic lattice solitons (PLSs) formed in two-dimensional (2D) arrays of metallic nanowires embedded into a nonlinear medium with Kerr nonlinearity. We analyze two classes of 2D PLSs families, namely, fundamental and vortical PLSs in both focusing and defocusing media. Their existence, stability, and subwavelength spatial confinement are studied in detai
A two-dimensional Dirac fermion microscope
DEFF Research Database (Denmark)
Bøggild, Peter; Caridad, Jose; Stampfer, Christoph
2017-01-01
in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2...
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.
Two-dimensional Imaging Velocity Interferometry: Technique and Data Analysis
Energy Technology Data Exchange (ETDEWEB)
Erskine, D J; Smith, R F; Bolme, C; Celliers, P; Collins, G
2011-03-23
We describe the data analysis procedures for an emerging interferometric technique for measuring motion across a two-dimensional image at a moment in time, i.e. a snapshot 2d-VISAR. Velocity interferometers (VISAR) measuring target motion to high precision have been an important diagnostic in shockwave physics for many years Until recently, this diagnostic has been limited to measuring motion at points or lines across a target. We introduce an emerging interferometric technique for measuring motion across a two-dimensional image, which could be called a snapshot 2d-VISAR. If a sufficiently fast movie camera technology existed, it could be placed behind a traditional VISAR optical system and record a 2d image vs time. But since that technology is not yet available, we use a CCD detector to record a single 2d image, with the pulsed nature of the illumination providing the time resolution. Consequently, since we are using pulsed illumination having a coherence length shorter than the VISAR interferometer delay ({approx}0.1 ns), we must use the white light velocimetry configuration to produce fringes with significant visibility. In this scheme, two interferometers (illuminating, detecting) having nearly identical delays are used in series, with one before the target and one after. This produces fringes with at most 50% visibility, but otherwise has the same fringe shift per target motion of a traditional VISAR. The 2d-VISAR observes a new world of information about shock behavior not readily accessible by traditional point or 1d-VISARS, simultaneously providing both a velocity map and an 'ordinary' snapshot photograph of the target. The 2d-VISAR has been used to observe nonuniformities in NIF related targets (polycrystalline diamond, Be), and in Si and Al.
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.
Gesture Recognition Using Character Recognition Techniques on Two-dimensional Eigenspace
大野, 宏; 山本, 正信; Ohno, Hiroshi; Yamamoto, Masanobu
1999-01-01
This paper describes a novel method for gesture recognition using character recognition techniques on two-dimensional eigenspace. An image-based approach can capture human body poses in 3D motion from multiple image sequences. The sequence of poses can be reduced into a trajectory on the two-dimensional eigenspace with preserving the main features in gesture, so that the gesture recognition equals the character recognition. Experiments for the gesture recognition using some character recognit...
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.
Electronics based on two-dimensional materials.
Fiori, Gianluca; Bonaccorso, Francesco; Iannaccone, Giuseppe; Palacios, Tomás; Neumaier, Daniel; Seabaugh, Alan; Banerjee, Sanjay K; Colombo, Luigi
2014-10-01
The compelling demand for higher performance and lower power consumption in electronic systems is the main driving force of the electronics industry's quest for devices and/or architectures based on new materials. Here, we provide a review of electronic devices based on two-dimensional materials, outlining their potential as a technological option beyond scaled complementary metal-oxide-semiconductor switches. We focus on the performance limits and advantages of these materials and associated technologies, when exploited for both digital and analog applications, focusing on the main figures of merit needed to meet industry requirements. We also discuss the use of two-dimensional materials as an enabling factor for flexible electronics and provide our perspectives on future developments.
Two-dimensional ranking of Wikipedia articles
Zhirov, A. O.; Zhirov, O. V.; Shepelyansky, D. L.
2010-10-01
The Library of Babel, described by Jorge Luis Borges, stores an enormous amount of information. The Library exists ab aeterno. Wikipedia, a free online encyclopaedia, becomes a modern analogue of such a Library. Information retrieval and ranking of Wikipedia articles become the challenge of modern society. While PageRank highlights very well known nodes with many ingoing links, CheiRank highlights very communicative nodes with many outgoing links. In this way the ranking becomes two-dimensional. Using CheiRank and PageRank we analyze the properties of two-dimensional ranking of all Wikipedia English articles and show that it gives their reliable classification with rich and nontrivial features. Detailed studies are done for countries, universities, personalities, physicists, chess players, Dow-Jones companies and other categories.
Two-Dimensional NMR Lineshape Analysis
Waudby, Christopher A.; Ramos, Andres; Cabrita, Lisa D.; Christodoulou, John
2016-04-01
NMR titration experiments are a rich source of structural, mechanistic, thermodynamic and kinetic information on biomolecular interactions, which can be extracted through the quantitative analysis of resonance lineshapes. However, applications of such analyses are frequently limited by peak overlap inherent to complex biomolecular systems. Moreover, systematic errors may arise due to the analysis of two-dimensional data using theoretical frameworks developed for one-dimensional experiments. Here we introduce a more accurate and convenient method for the analysis of such data, based on the direct quantum mechanical simulation and fitting of entire two-dimensional experiments, which we implement in a new software tool, TITAN (TITration ANalysis). We expect the approach, which we demonstrate for a variety of protein-protein and protein-ligand interactions, to be particularly useful in providing information on multi-step or multi-component interactions.
Towards two-dimensional search engines
Ermann, Leonardo; Shepelyansky, Dima L
2011-01-01
We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of ingoing links, while CheiRank orders nodes proportionally to a number of outgoing links. In this way the ranking of nodes becomes two-dimensional that paves the way for development of two-dimensional search engines of new type. Information flow properties on PageRank-CheiRank plane are analyzed for networks of British, French and Italian Universities, Wikipedia, Linux Kernel, gene regulation and other networks. Methods of spam links control are also analyzed.
Toward two-dimensional search engines
Ermann, L.; Chepelianskii, A. D.; Shepelyansky, D. L.
2012-07-01
We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of ingoing links, while CheiRank orders nodes proportionally to a number of outgoing links. In this way, the ranking of nodes becomes two dimensional which paves the way for the development of two-dimensional search engines of a new type. Statistical properties of information flow on the PageRank-CheiRank plane are analyzed for networks of British, French and Italian universities, Wikipedia, Linux Kernel, gene regulation and other networks. A special emphasis is done for British universities networks using the large database publicly available in the UK. Methods of spam links control are also analyzed.
A two-dimensional Dirac fermion microscope
Bøggild, Peter; Caridad, José M.; Stampfer, Christoph; Calogero, Gaetano; Papior, Nick Rübner; Brandbyge, Mads
2017-06-01
The electron microscope has been a powerful, highly versatile workhorse in the fields of material and surface science, micro and nanotechnology, biology and geology, for nearly 80 years. The advent of two-dimensional materials opens new possibilities for realizing an analogy to electron microscopy in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges, terminations and defects, as well as interfaces, including external nanoscale structures such as adsorbed molecules, nanoparticles or quantum dots.
A two-dimensional Dirac fermion microscope.
Bøggild, Peter; Caridad, José M; Stampfer, Christoph; Calogero, Gaetano; Papior, Nick Rübner; Brandbyge, Mads
2017-06-09
The electron microscope has been a powerful, highly versatile workhorse in the fields of material and surface science, micro and nanotechnology, biology and geology, for nearly 80 years. The advent of two-dimensional materials opens new possibilities for realizing an analogy to electron microscopy in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges, terminations and defects, as well as interfaces, including external nanoscale structures such as adsorbed molecules, nanoparticles or quantum dots.
Two-Dimensional Scheduling: A Review
Directory of Open Access Journals (Sweden)
Zhuolei Xiao
2013-07-01
Full Text Available In this study, we present a literature review, classification schemes and analysis of methodology for scheduling problems on Batch Processing machine (BP with both processing time and job size constraints which is also regarded as Two-Dimensional (TD scheduling. Special attention is given to scheduling problems with non-identical job sizes and processing times, with details of the basic algorithms and other significant results.
Two dimensional fermions in four dimensional YM
Narayanan, R
2009-01-01
Dirac fermions in the fundamental representation of SU(N) live on a two dimensional torus flatly embedded in $R^4$. They interact with a four dimensional SU(N) Yang Mills vector potential preserving a global chiral symmetry at finite $N$. As the size of the torus in units of $\\frac{1}{\\Lambda_{SU(N)}}$ is varied from small to large, the chiral symmetry gets spontaneously broken in the infinite $N$ limit.
Two-dimensional Kagome photonic bandgap waveguide
DEFF Research Database (Denmark)
Nielsen, Jens Bo; Søndergaard, Thomas; Libori, Stig E. Barkou;
2000-01-01
The transverse-magnetic photonic-bandgap-guidance properties are investigated for a planar two-dimensional (2-D) Kagome waveguide configuration using a full-vectorial plane-wave-expansion method. Single-moded well-localized low-index guided modes are found. The localization of the optical modes...... is investigated with respect to the width of the 2-D Kagome waveguide, and the number of modes existing for specific frequencies and waveguide widths is mapped out....
String breaking in two-dimensional QCD
Hornbostel, K J
1999-01-01
I present results of a numerical calculation of the effects of light quark-antiquark pairs on the linear heavy-quark potential in light-cone quantized two-dimensional QCD. I extract the potential from the Q-Qbar component of the ground-state wavefunction, and observe string breaking at the heavy-light meson pair threshold. I briefly comment on the states responsible for the breaking.
Two-dimensional supramolecular electron spin arrays.
Wäckerlin, Christian; Nowakowski, Jan; Liu, Shi-Xia; Jaggi, Michael; Siewert, Dorota; Girovsky, Jan; Shchyrba, Aneliia; Hählen, Tatjana; Kleibert, Armin; Oppeneer, Peter M; Nolting, Frithjof; Decurtins, Silvio; Jung, Thomas A; Ballav, Nirmalya
2013-05-07
A bottom-up approach is introduced to fabricate two-dimensional self-assembled layers of molecular spin-systems containing Mn and Fe ions arranged in a chessboard lattice. We demonstrate that the Mn and Fe spin states can be reversibly operated by their selective response to coordination/decoordination of volatile ligands like ammonia (NH3). Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Two dimensional echocardiographic detection of intraatrial masses.
DePace, N L; Soulen, R L; Kotler, M N; Mintz, G S
1981-11-01
With two dimensional echocardiography, a left atrial mass was detected in 19 patients. Of these, 10 patients with rheumatic mitral stenosis had a left atrial thrombus. The distinctive two dimensional echocardiographic features of left atrial thrombus included a mass of irregular nonmobile laminated echos within an enlarged atrial cavity, usually with a broad base of attachment to the posterior left atrial wall. Seven patients had a left atrial myxoma. Usually, the myxoma appeared as a mottled ovoid, sharply demarcated mobile mass attached to the interatrial septum. One patient had a right atrial angiosarcoma that appeared as a nonmobile mass extending from the inferior vena caval-right atrial junction into the right atrial cavity. One patient had a left atrial leiomyosarcoma producing a highly mobile mass attached to the lateral wall of the left atrium. M mode echocardiography detected six of the seven myxomas, one thrombus and neither of the other tumors. Thus, two dimensional echocardiography appears to be the technique of choice in the detection, localization and differentiation of intraatrial masses.
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 ...
Energy Technology Data Exchange (ETDEWEB)
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.
Weakly disordered two-dimensional Frenkel excitons
Boukahil, A.; Zettili, Nouredine
2004-03-01
We report the results of studies of the optical properties of weakly disordered two- dimensional Frenkel excitons in the Coherent Potential Approximation (CPA). An approximate complex Green's function for a square lattice with nearest neighbor interactions is used in the self-consistent equation to determine the coherent potential. It is shown that the Density of States is very much affected by the logarithmic singularities in the Green's function. Our CPA results are in excellent agreement with previous investigations by Schreiber and Toyozawa using the Monte Carlo simulation.
Two-dimensional photonic crystal surfactant detection.
Zhang, Jian-Tao; Smith, Natasha; Asher, Sanford A
2012-08-07
We developed a novel two-dimensional (2-D) crystalline colloidal array photonic crystal sensing material for the visual detection of amphiphilic molecules in water. A close-packed polystyrene 2-D array monolayer was embedded in a poly(N-isopropylacrylamide) (PNIPAAm)-based hydrogel film. These 2-D photonic crystals placed on a mirror show intense diffraction that enables them to be used for visual determination of analytes. Binding of surfactant molecules attaches ions to the sensor that swells the PNIPAAm-based hydrogel. The resulting increase in particle spacing red shifts the 2-D diffracted light. Incorporation of more hydrophobic monomers increases the sensitivity to surfactants.
Two-dimensional ranking of Wikipedia articles
Zhirov, A O; Shepelyansky, D L
2010-01-01
The Library of Babel, described by Jorge Luis Borges, stores an enormous amount of information. The Library exists {\\it ab aeterno}. Wikipedia, a free online encyclopaedia, becomes a modern analogue of such a Library. Information retrieval and ranking of Wikipedia articles become the challenge of modern society. We analyze the properties of two-dimensional ranking of all Wikipedia English articles and show that it gives their reliable classification with rich and nontrivial features. Detailed studies are done for countries, universities, personalities, physicists, chess players, Dow-Jones companies and other categories.
Mobility anisotropy of two-dimensional semiconductors
Lang, Haifeng; Liu, Zhirong
2016-01-01
The carrier mobility of anisotropic two-dimensional (2D) semiconductors under longitudinal acoustic (LA) phonon scattering was theoretically studied with the deformation potential theory. Based on Boltzmann equation with relaxation time approximation, an analytic formula of intrinsic anisotropic mobility was deduced, which shows that the influence of effective mass to the mobility anisotropy is larger than that of deformation potential constant and elastic modulus. Parameters were collected for various anisotropic 2D materials (black phosphorus, Hittorf's phosphorus, BC$_2$N, MXene, TiS$_3$, GeCH$_3$) to calculate their mobility anisotropy. It was revealed that the anisotropic ratio was overestimated in the past.
Sums of two-dimensional spectral triples
DEFF Research Database (Denmark)
Christensen, Erik; Ivan, Cristina
2007-01-01
construct a sum of two dimensional modules which reflects some aspects of the topological dimensions of the compact metric space, but this will only give the metric back approximately. At the end we make an explicit computation of the last module for the unit interval in. The metric is recovered exactly......, the Dixmier trace induces a multiple of the Lebesgue integral but the growth of the number of eigenvalues is different from the one found for the standard differential operator on the unit interval....
Binding energy of two-dimensional biexcitons
DEFF Research Database (Denmark)
Singh, Jai; Birkedal, Dan; Vadim, Lyssenko;
1996-01-01
Using a model structure for a two-dimensional (2D) biexciton confined in a quantum well, it is shown that the form of the Hamiltonian of the 2D biexciton reduces into that of an exciton. The binding energies and Bohr radii of a 2D biexciton in its various internal energy states are derived...... analytically using the fractional dimension approach. The ratio of the binding energy of a 2D biexciton to that of a 2D exciton is found to be 0.228, which agrees very well with the recent experimental value. The results of our approach are compared with those of earlier theories....
Effects of finite laser pulse width on two-dimensional electronic spectroscopy
Leng, Xuan; Yue, Shuai; Weng, Yu-Xiang; Song, Kai; Shi, Qiang
2017-01-01
We combine the hierarchical equations of motion method and the equation-of-motion phase-matching approach to calculate two-dimensional electronic spectra of model systems. When the laser pulse is short enough, the current method reproduces the results based on third-order response function calculations in the impulsive limit. Finite laser pulse width is found to affect both the peak positions and shapes, as well as the time evolution of diagonal and cross peaks. Simulations of the two-color two-dimensional electronic spectra also show that, to observe quantum beats in the diagonal and cross peaks, it is necessary to excite the related excitonic states simultaneously.
Two-Dimensional Theory of Scientific Representation
Directory of Open Access Journals (Sweden)
A Yaghmaie
2013-03-01
Full Text Available Scientific representation is an interesting topic for philosophers of science, many of whom have recently explored it from different points of view. There are currently two competing approaches to the issue: cognitive and non-cognitive, and each of them claims its own merits over the other. This article tries to provide a hybrid theory of scientific representation, called Two-Dimensional Theory of Scientific Representation, which has the merits of the two accounts and is free of their shortcomings. To do this, we will argue that although scientific representation needs to use the notion of intentionality, such a notion is defined and realized in a simply structural form contrary to what cognitive approach says about intentionality. After a short introduction, the second part of the paper is devoted to introducing theories of scientific representation briefly. In the third part, the structural accounts of representation will be criticized. The next step is to introduce the two-dimensional theory which involves two key components: fixing and structural fitness. It will be argued that fitness is an objective and non-intentional relation, while fixing is intentional.
Two-dimensional shape memory graphene oxide
Chang, Zhenyue; Deng, Junkai; Chandrakumara, Ganaka G.; Yan, Wenyi; Liu, Jefferson Zhe
2016-06-01
Driven by the increasing demand for micro-/nano-technologies, stimuli-responsive shape memory materials at nanoscale have recently attracted great research interests. However, by reducing the size of conventional shape memory materials down to approximately nanometre range, the shape memory effect diminishes. Here, using density functional theory calculations, we report the discovery of a shape memory effect in a two-dimensional atomically thin graphene oxide crystal with ordered epoxy groups, namely C8O. A maximum recoverable strain of 14.5% is achieved as a result of reversible phase transition between two intrinsically stable phases. Our calculations conclude co-existence of the two stable phases in a coherent crystal lattice, giving rise to the possibility of constructing multiple temporary shapes in a single material, thus, enabling highly desirable programmability. With an atomic thickness, excellent shape memory mechanical properties and electric field stimulus, the discovery of a two-dimensional shape memory graphene oxide opens a path for the development of exceptional micro-/nano-electromechanical devices.
Institute of Scientific and Technical Information of China (English)
XU Quan; TIAN Qiang
2007-01-01
Two-dimensional compact-like discrete breathers in discrete two-dimensional monatomic square lattices are investigated by discussing a generafized discrete two-dimensional monatomic model.It is proven that the twodimensional compact-like discrete breathers exist not only in two-dimensional soft Ф4 potentials but also in hard two-dimensional Ф4 potentials and pure two-dimensional K4 lattices.The measurements of the two-dimensional compact-like discrete breather cores in soft and hard two-dimensional Ф4 potential are determined by coupling parameter K4,while those in pure two-dimensional K4 lattices have no coupling with parameter K4.The stabilities of the two-dimensional compact-like discrete breathers correlate closely to the coupling parameter K4 and the boundary condition of lattices.
Commensurability oscillations in a two-dimensional lateral superlattice
Davies, John; Long, Andrew; Grant, David; Chowdhury, Suja
2000-03-01
We have calculated and measured conduction in a two-dimensional electron gas subject to a weak two-dimensional periodic potential and a normal magnetic field. Simulations with a potential Vx \\cos(2π x/a) + Vy \\cos(2π y/a) show the usual commensurability oscillations in ρ_xx(B) with Vx alone. The introduction of Vy suppresses these oscillations, rather than introducing the additional oscillations in ρ_yy(B) expected from previous perturbation theories. We explain this in terms of drift of the guiding center of cyclotron motion along contours of an effective potential: open orbits of the guiding center contribute to conduction but closed orbits do not. All orbits are closed in a symmetric superlattice with |V_x| = |V_y| and commensurability oscillations are therefore quenched. Experiments on etched superlattices confirm this picture. Conventional lattice-matched samples give a symmetric potential and weak oscillations; the symmetry is broken by the piezoelectric effect in stressed samples, leading to strong oscillations. Periodic modulation of the magnetic field can be treated in the same way, which explains previous experimental results.
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...
All or nothing: On the small fluctuations of two-dimensional string theoretic black holes
Energy Technology Data Exchange (ETDEWEB)
Gilbert, Gerald [Univ. of Maryland, College Park, MD (United States); Raiten, Eric [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
1992-10-01
A comprehensive analysis of small fluctuations about two-dimensional string-theoretic and string-inspired black holes is presented. It is shown with specific examples that two-dimensional black holes behave in a radically different way from all known black holes in four dimensions. For both the SL(2,R)/U(1) black hole and the two-dimensional black hole coupled to a massive dilaton with constant field strength, it is shown that there are a {\\it continuous infinity} of solutions to the linearized equations of motion, which are such that it is impossible to ascertain the classical linear response. It is further shown that the two-dimensional black hole coupled to a massive, linear dilaton admits {\\it no small fluctuations at all}. We discuss possible implications of our results for the Callan-Giddings-Harvey-Strominger black hole.
Epi-two-dimensional flow and generalized enstrophy
Yoshida, Zensho
2016-01-01
The conservation of the enstrophy ($L^2$ norm of the vorticity $\\omega$) plays an essential role in the physics and mathematics of two-dimensional (2D) Euler fluids. Generalizing to compressible ideal (inviscid and barotropic) fluids, the generalized enstrophy $\\int_{\\Sigma(t)} f(\\omega/\\rho)\\rho\\, d^2 x$, ($f$ an arbitrary smooth function, $\\rho$ the density, and $\\Sigma(t)$ an arbitrary 2D domain co-moving with the fluid) is a constant of motion, and plays the same role. On the other hand, for the three-dimensional (3D) ideal fluid, the helicity $\\int_{M} {V}\\cdot\\omega\\,d^3x$, ($V$ the flow velocity, $\\omega=\
Structure and computation of two-dimensional incompressible extended MHD
Grasso, D; Abdelhamid, H M; Morrison, P J
2016-01-01
A comprehensive study of a reduced version of Lust's equations, the extended magnetohydrodynamic (XMHD) model obtained from the two-fluid theory for electrons and ions with the enforcement of quasineutrality, is given. Starting from the Hamiltonian structure of the fully three-dimensional theory, a Hamiltonian two-dimensional incompressible four-field model is derived. In this way energy conservation along with four families of Casimir invariants are naturally obtained. The construction facilitates various limits leading to the Hamiltonian forms of Hall, inertial, and ideal MHD, with their conserved energies and Casimir invariants. Basic linear theory of the four-field model is treated, and the growth rate for collisionless reconnection is obtained. Results from nonlinear simulations of collisionless tearing are presented and interpreted using, in particular normal fields, a product of the Hamiltonian theory that gives rise to simplified equations of motion.
Structure and computation of two-dimensional incompressible extended MHD
Grasso, D.; Tassi, E.; Abdelhamid, H. M.; Morrison, P. J.
2017-01-01
A comprehensive study of the extended magnetohydrodynamic model obtained from the two-fluid theory for electrons and ions with the enforcement of quasineutrality is given. Starting from the Hamiltonian structure of the fully three-dimensional theory, a Hamiltonian two-dimensional incompressible four-field model is derived. In this way, the energy conservation along with four families of Casimir invariants is naturally obtained. The construction facilitates various limits leading to the Hamiltonian forms of Hall, inertial, and ideal MHD, with their conserved energies and Casimir invariants. Basic linear theory of the four-field model is treated, and the growth rate for collisionless reconnection is obtained. Results from nonlinear simulations of collisionless tearing are presented and interpreted using, in particular, normal fields, a product of the Hamiltonian theory that gives rise to simplified equations of motion.
Interacting Brownian Swarms: Some Analytical Results
Directory of Open Access Journals (Sweden)
Guillaume Sartoretti
2016-01-01
Full Text Available We consider the dynamics of swarms of scalar Brownian agents subject to local imitation mechanisms implemented using mutual rank-based interactions. For appropriate values of the underlying control parameters, the swarm propagates tightly and the distances separating successive agents are iid exponential random variables. Implicitly, the implementation of rank-based mutual interactions, requires that agents have infinite interaction ranges. Using the probabilistic size of the swarm’s support, we analytically estimate the critical interaction range below that flocked swarms cannot survive. In the second part of the paper, we consider the interactions between two flocked swarms of Brownian agents with finite interaction ranges. Both swarms travel with different barycentric velocities, and agents from both swarms indifferently interact with each other. For appropriate initial configurations, both swarms eventually collide (i.e., all agents interact. Depending on the values of the control parameters, one of the following patterns emerges after collision: (i Both swarms remain essentially flocked, or (ii the swarms become ultimately quasi-free and recover their nominal barycentric speeds. We derive a set of analytical flocking conditions based on the generalized rank-based Brownian motion. An extensive set of numerical simulations corroborates our analytical findings.
Intermittency measurement in two-dimensional bacterial turbulence
Qiu, Xiang; Ding, Long; Huang, Yongxiang; Chen, Ming; Lu, Zhiming; Liu, Yulu; Zhou, Quan
2016-06-01
In this paper, an experimental velocity database of a bacterial collective motion, e.g., Bacillus subtilis, in turbulent phase with volume filling fraction 84 % provided by Professor Goldstein at Cambridge University (UK), was analyzed to emphasize the scaling behavior of this active turbulence system. This was accomplished by performing a Hilbert-based methodology analysis to retrieve the scaling property without the β -limitation. A dual-power-law behavior separated by the viscosity scale ℓν was observed for the q th -order Hilbert moment Lq(k ) . This dual-power-law belongs to an inverse-cascade since the scaling range is above the injection scale R , e.g., the bacterial body length. The measured scaling exponents ζ (q ) of both the small-scale (k >kν ) and large-scale (k
Optimal excitation of two dimensional Holmboe instabilities
Constantinou, Navid C
2010-01-01
Highly stratified shear layers are rendered unstable even at high stratifications by Holmboe instabilities when the density stratification is concentrated in a small region of the shear layer. These instabilities may cause mixing in highly stratified environments. However these instabilities occur in tongues for a limited range of parameters. We perform Generalized Stability analysis of the two dimensional perturbation dynamics of an inviscid Boussinesq stratified shear layer and show that Holmboe instabilities at high Richardson numbers can be excited by their adjoints at amplitudes that are orders of magnitude larger than by introducing initially the unstable mode itself. We also determine the optimal growth that obtains for parameters for which there is no instability. We find that there is potential for large transient growth regardless of whether the background flow is exponentially stable or not and that the characteristic structure of the Holmboe instability asymptotically emerges for parameter values ...
Phonon hydrodynamics in two-dimensional materials.
Cepellotti, Andrea; Fugallo, Giorgia; Paulatto, Lorenzo; Lazzeri, Michele; Mauri, Francesco; Marzari, Nicola
2015-03-06
The conduction of heat in two dimensions displays a wealth of fascinating phenomena of key relevance to the scientific understanding and technological applications of graphene and related materials. Here, we use density-functional perturbation theory and an exact, variational solution of the Boltzmann transport equation to study fully from first-principles phonon transport and heat conductivity in graphene, boron nitride, molybdenum disulphide and the functionalized derivatives graphane and fluorographene. In all these materials, and at variance with typical three-dimensional solids, normal processes keep dominating over Umklapp scattering well-above cryogenic conditions, extending to room temperature and more. As a result, novel regimes emerge, with Poiseuille and Ziman hydrodynamics, hitherto typically confined to ultra-low temperatures, characterizing transport at ordinary conditions. Most remarkably, several of these two-dimensional materials admit wave-like heat diffusion, with second sound present at room temperature and above in graphene, boron nitride and graphane.
Probabilistic Universality in two-dimensional Dynamics
Lyubich, Mikhail
2011-01-01
In this paper we continue to explore infinitely renormalizable H\\'enon maps with small Jacobian. It was shown in [CLM] that contrary to the one-dimensional intuition, the Cantor attractor of such a map is non-rigid and the conjugacy with the one-dimensional Cantor attractor is at most 1/2-H\\"older. Another formulation of this phenomenon is that the scaling structure of the H\\'enon Cantor attractor differs from its one-dimensional counterpart. However, in this paper we prove that the weight assigned by the canonical invariant measure to these bad spots tends to zero on microscopic scales. This phenomenon is called {\\it Probabilistic Universality}. It implies, in particular, that the Hausdorff dimension of the canonical measure is universal. In this way, universality and rigidity phenomena of one-dimensional dynamics assume a probabilistic nature in the two-dimensional world.
Two-dimensional position sensitive neutron detector
Indian Academy of Sciences (India)
A M Shaikh; S S Desai; A K Patra
2004-08-01
A two-dimensional position sensitive neutron detector has been developed. The detector is a 3He + Kr filled multiwire proportional counter with charge division position readout and has a sensitive area of 345 mm × 345 mm, pixel size 5 mm × 5 mm, active depth 25 mm and is designed for efficiency of 70% for 4 Å neutrons. The detector is tested with 0.5 bar 3He + 1.5 bar krypton gas mixture in active chamber and 2 bar 4He in compensating chamber. The pulse height spectrum recorded at an anode potential of 2000 V shows energy resolution of ∼ 25% for the 764 keV peak. A spatial resolution of 8 mm × 6 mm is achieved. The detector is suitable for SANS studies in the range of 0.02–0.25 Å-1.
Two-dimensional heterostructures for energy storage
Pomerantseva, Ekaterina; Gogotsi, Yury
2017-07-01
Two-dimensional (2D) materials provide slit-shaped ion diffusion channels that enable fast movement of lithium and other ions. However, electronic conductivity, the number of intercalation sites, and stability during extended cycling are also crucial for building high-performance energy storage devices. While individual 2D materials, such as graphene, show some of the required properties, none of them can offer all properties needed to maximize energy density, power density, and cycle life. Here we argue that stacking different 2D materials into heterostructured architectures opens an opportunity to construct electrodes that would combine the advantages of the individual building blocks while eliminating the associated shortcomings. We discuss characteristics of common 2D materials and provide examples of 2D heterostructured electrodes that showed new phenomena leading to superior electrochemical performance. We also consider electrode fabrication approaches and finally outline future steps to create 2D heterostructured electrodes that could greatly expand current energy storage technologies.
Rationally synthesized two-dimensional polymers.
Colson, John W; Dichtel, William R
2013-06-01
Synthetic polymers exhibit diverse and useful properties and influence most aspects of modern life. Many polymerization methods provide linear or branched macromolecules, frequently with outstanding functional-group tolerance and molecular weight control. In contrast, extending polymerization strategies to two-dimensional periodic structures is in its infancy, and successful examples have emerged only recently through molecular framework, surface science and crystal engineering approaches. In this Review, we describe successful 2D polymerization strategies, as well as seminal research that inspired their development. These methods include the synthesis of 2D covalent organic frameworks as layered crystals and thin films, surface-mediated polymerization of polyfunctional monomers, and solid-state topochemical polymerizations. Early application targets of 2D polymers include gas separation and storage, optoelectronic devices and membranes, each of which might benefit from predictable long-range molecular organization inherent to this macromolecular architecture.
Janus Spectra in Two-Dimensional Flows
Liu, Chien-Chia; Cerbus, Rory T.; Chakraborty, Pinaki
2016-09-01
In large-scale atmospheric flows, soap-film flows, and other two-dimensional flows, the exponent of the turbulent energy spectra, α , may theoretically take either of two distinct values, 3 or 5 /3 , but measurements downstream of obstacles have invariably revealed α =3 . Here we report experiments on soap-film flows where downstream of obstacles there exists a sizable interval in which α transitions from 3 to 5 /3 for the streamwise fluctuations but remains equal to 3 for the transverse fluctuations, as if two mutually independent turbulent fields of disparate dynamics were concurrently active within the flow. This species of turbulent energy spectra, which we term the Janus spectra, has never been observed or predicted theoretically. Our results may open up new vistas in the study of turbulence and geophysical flows.
Local doping of two-dimensional materials
Wong, Dillon; Velasco, Jr, Jairo; Ju, Long; Kahn, Salman; Lee, Juwon; Germany, Chad E.; Zettl, Alexander K.; Wang, Feng; Crommie, Michael F.
2016-09-20
This disclosure provides systems, methods, and apparatus related to locally doping two-dimensional (2D) materials. In one aspect, an assembly including a substrate, a first insulator disposed on the substrate, a second insulator disposed on the first insulator, and a 2D material disposed on the second insulator is formed. A first voltage is applied between the 2D material and the substrate. With the first voltage applied between the 2D material and the substrate, a second voltage is applied between the 2D material and a probe positioned proximate the 2D material. The second voltage between the 2D material and the probe is removed. The first voltage between the 2D material and the substrate is removed. A portion of the 2D material proximate the probe when the second voltage was applied has a different electron density compared to a remainder of the 2D material.
Two-dimensional fourier transform spectrometer
Energy Technology Data Exchange (ETDEWEB)
DeFlores, Lauren; Tokmakoff, Andrei
2016-10-25
The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.
Two-dimensional fourier transform spectrometer
DeFlores, Lauren; Tokmakoff, Andrei
2013-09-03
The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.
FACE RECOGNITION USING TWO DIMENSIONAL LAPLACIAN EIGENMAP
Institute of Scientific and Technical Information of China (English)
Chen Jiangfeng; Yuan Baozong; Pei Bingnan
2008-01-01
Recently,some research efforts have shown that face images possibly reside on a nonlinear sub-manifold. Though Laplacianfaces method considered the manifold structures of the face images,it has limits to solve face recognition problem. This paper proposes a new feature extraction method,Two Dimensional Laplacian EigenMap (2DLEM),which especially considers the manifold structures of the face images,and extracts the proper features from face image matrix directly by using a linear transformation. As opposed to Laplacianfaces,2DLEM extracts features directly from 2D images without a vectorization preprocessing. To test 2DLEM and evaluate its performance,a series of ex-periments are performed on the ORL database and the Yale database. Moreover,several experiments are performed to compare the performance of three 2D methods. The experiments show that 2DLEM achieves the best performance.
Equivalency of two-dimensional algebras
Energy Technology Data Exchange (ETDEWEB)
Santos, Gildemar Carneiro dos; Pomponet Filho, Balbino Jose S. [Universidade Federal da Bahia (UFBA), BA (Brazil). Inst. de Fisica
2011-07-01
Full text: Let us consider a vector z = xi + yj over the field of real numbers, whose basis (i,j) satisfy a given algebra. Any property of this algebra will be reflected in any function of z, so we can state that the knowledge of the properties of an algebra leads to more general conclusions than the knowledge of the properties of a function. However structural properties of an algebra do not change when this algebra suffers a linear transformation, though the structural constants defining this algebra do change. We say that two algebras are equivalent to each other whenever they are related by a linear transformation. In this case, we have found that some relations between the structural constants are sufficient to recognize whether or not an algebra is equivalent to another. In spite that the basis transform linearly, the structural constants change like a third order tensor, but some combinations of these tensors result in a linear transformation, allowing to write the entries of the transformation matrix as function of the structural constants. Eventually, a systematic way to find the transformation matrix between these equivalent algebras is obtained. In this sense, we have performed the thorough classification of associative commutative two-dimensional algebras, and find that even non-division algebra may be helpful in solving non-linear dynamic systems. The Mandelbrot set was used to have a pictorial view of each algebra, since equivalent algebras result in the same pattern. Presently we have succeeded in classifying some non-associative two-dimensional algebras, a task more difficult than for associative one. (author)
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.