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 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.
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).
Active Brownian particles at interfaces: An effective equilibrium approach
Wittmann, René; Brader, Joseph M.
2016-06-01
A simple theoretical approach is used to investigate active colloids at the free interface and near repulsive substrates. We employ dynamical density functional theory to determine the steady-state density profiles in an effective equilibrium system (Farage T. F. F. et al., Phys. Rev. E, 91 (2015) 042310). In addition to the known accumulation at surfaces, we predict wetting and drying transitions at a flat repulsive wall and capillary condensation and evaporation in a slit pore. These new phenomena are closely related to the motility-induced phase separation (MIPS) in the bulk.
Brownian nanoimaging of interface dynamics and ligand-receptor binding at cell surfaces in 3-D.
Kuznetsov, Igor R; Evans, Evan A
2013-04-01
We describe a method for nanoimaging interfacial dynamics and ligand-receptor binding at surfaces of live cells in 3-D. The imaging probe is a 1-μm diameter glass bead confined by a soft laser trap to create a "cloud" of fluctuating states. Using a facile on-line method of video image analysis, the probe displacements are reported at ~10 ms intervals with bare precisions (±SD) of 4-6 nm along the optical axis (elevation) and 2 nm in the transverse directions. We demonstrate how the Brownian distributions are analyzed to characterize the free energy potential of each small probe in 3-D taking into account the blur effect of its motions during CCD image capture. Then, using the approach to image interactions of a labeled probe with lamellae of leukocytic cells spreading on cover-glass substrates, we show that deformations of the soft distribution in probe elevations provide both a sensitive long-range sensor for defining the steric topography of a cell lamella and a fast telemetry for reporting rare events of probe binding with its surface receptors. Invoking established principles of Brownian physics and statistical thermodynamics, we describe an off-line method of super resolution that improves precision of probe separations from a non-reactive steric boundary to ~1 nm.
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.
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.
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.
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.
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.
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.
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.
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 ...
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.
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.
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 ...
Anomalous Brownian refrigerator
Rana, Shubhashis; Pal, P. S.; Saha, Arnab; Jayannavar, A. M.
2016-02-01
We present a detailed study of a Brownian particle driven by Carnot-type refrigerating protocol operating between two thermal baths. Both the underdamped as well as the overdamped limits are investigated. The particle is in a harmonic potential with time-periodic strength that drives the system cyclically between the baths. Each cycle consists of two isothermal steps at different temperatures and two adiabatic steps connecting them. Besides working as a stochastic refrigerator, it is shown analytically that in the quasistatic regime the system can also act as stochastic heater, depending on the bath temperatures. Interestingly, in non-quasistatic regime, our system can even work as a stochastic heat engine for certain range of cycle time and bath temperatures. We show that the operation of this engine is not reliable. The fluctuations of stochastic efficiency/coefficient of performance (COP) dominate their mean values. Their distributions show power law tails, however the exponents are not universal. Our study reveals that microscopic machines are not the microscopic equivalent of the macroscopic machines that we come across in our daily life. We find that there is no one to one correspondence between the performance of our system under engine protocol and its reverse.
Martínez, I A; Roldán, É; Dinis, L; Petrov, D; Parrondo, J M R; Rica, R A
2016-01-01
The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths1. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors2 and some artificial micro-engines3-5 operate. As described by stochastic thermodynamics6,7, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit8. Here we report an experimental realization of a Carnot engine with a single optically trapped Brownian particle as the working substance. We present an exhaustive study of the energetics of the engine and analyse the fluctuations of the finite-time efficiency, showing that the Carnot bound can be surpassed for a small number of non-equilibrium cycles. As its macroscopic counterpart, the energetics of our Carnot device exhibits basic properties that one would expect to observe in any microscopic energy transducer operating with baths at different temperatures9-11. Our results characterize the sources of irreversibility in the engine and the statistical properties of the efficiency-an insight that could inspire new strategies in the design of efficient nano-motors.
Peruani, Fernando
2016-11-01
Bacteria, chemically-driven rods, and motility assays are examples of active (i.e. self-propelled) Brownian rods (ABR). The physics of ABR, despite their ubiquity in experimental systems, remains still poorly understood. Here, we review the large-scale properties of collections of ABR moving in a dissipative medium. We address the problem by presenting three different models, of decreasing complexity, which we refer to as model I, II, and III, respectively. Comparing model I, II, and III, we disentangle the role of activity and interactions. In particular, we learn that in two dimensions by ignoring steric or volume exclusion effects, large-scale nematic order seems to be possible, while steric interactions prevent the formation of orientational order at large scales. The macroscopic behavior of ABR results from the interplay between active stresses and local alignment. ABR exhibit, depending on where we locate ourselves in parameter space, a zoology of macroscopic patterns that ranges from polar and nematic bands to dynamic aggregates.
Martínez, I. A.; Roldán, É.; Dinis, L.; Petrov, D.; Parrondo, J. M. R.; Rica, R. A.
2016-01-01
The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors and some artificial micro-engines operate. As described by stochastic thermodynamics, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit. Here we report an experimental realization of a Carnot engine with a single optically trapped Brownian particle as the working substance. We present an exhaustive study of the energetics of the engine and analyse the fluctuations of the finite-time efficiency, showing that the Carnot bound can be surpassed for a small number of non-equilibrium cycles. As its macroscopic counterpart, the energetics of our Carnot device exhibits basic properties that one would expect to observe in any microscopic energy transducer operating with baths at different temperatures. Our results characterize the sources of irreversibility in the engine and the statistical properties of the efficiency--an insight that could inspire new strategies in the design of efficient nano-motors.
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...
Harmonic functions on Walsh's Brownian motion
Jehring, Kristin Elizabeth
2009-01-01
In this dissertation we examine a variation of two- dimensional Brownian motion introduced in 1978 by Walsh. Walsh's Brownian motion can be described as a Brownian motion on the spokes of a (rimless) bicycle wheel. We will construct such a process by randomly assigning an angle to the excursions of a reflecting Brownian motion from 0. With this construction we see that Walsh's Brownian motion in R² behaves like one-dimensional Brownian motion away from the origin, but at the origin behaves di...
Brownian Motion 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...
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 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
Multiscale Reaction-Diffusion Algorithms: PDE-Assisted Brownian Dynamics
Franz, Benjamin
2013-06-19
Two algorithms that combine Brownian dynami cs (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use of a mean-field reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD simulations with PDEs by randomly creating new particles close to the interface, which partitions the domain, and by reincorporating particles into the continuum PDE-description when they cross the interface. The second PBD algorithm introduces an overlap region, where both descriptions exist in parallel. It is shown that the overlap region is required to accurately compute variances using PBD simulations. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented. © 2013 Society for Industrial and Applied Mathematics.
Multiscale reaction-diffusion algorithms: PDE-assisted Brownian dynamics
Franz, Benjamin; Chapman, S Jonathan; Erban, Radek
2012-01-01
Two algorithms that combine Brownian dynamics (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use of a mean-field reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD simulations with PDEs by randomly creating new particles close to the interface which partitions the domain and by reincorporating particles into the continuum PDE-description when they cross the interface. The second PBD algorithm introduces an overlap region, where both descriptions exist in parallel. It is shown that to accurately compute variances using the PBD simulation requires the overlap region. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented.
DEFF Research Database (Denmark)
Computerens interface eller grænseflade har spredt sig overalt. Mobiltelefoner, spilkonsoller, pc'er og storskærme indeholder computere – men computere indbygges også i tøj og andre hverdagslige genstande, så vi konstant har adgang til digitale data. Interface retter fokus mod, hvordan den digita...
Wu, Yu; Cheng, Tianhai; Zheng, Lijuan; Chen, Hao; Xu, Hui
2015-05-01
The optical properties of light absorbing soot aerosols generally change through interactions with weakly absorbing particles, resulting in complex mixing states, and have been highlighted as a major uncertainty in assessing their radiative forcing and climatic impact. The single scattering properties of soot aggregates partially embedded in the host sulfate particle (semi-embedded soot-containing mixtures) are investigated for two kinds of morphologies with intersecting and non-intersecting surfaces. The surfaces cannot be overlapped in the non-intersecting surface morphology, while the intersecting surface morphology is unconstrained. Based on the modified diffusion limited aggregation (DLA) algorithm, the models with non-intersecting surfaces are simulated and applied for the single scattering calculations of semi-embedded soot-containing mixtures using the superposition T-matrix (STM) method. For comparison, the models with intersecting surfaces are simulated with the same morphological parameters, but some soot monomers are intersected by the host sphere. Due to the limitation of current STM method, the optical properties of these models with intersecting surfaces are calculated using the discrete dipole approximation (DDA) method. The soot volume fractions outside sulfate host (Fs,out) are introduced and applied to characterize the mixing states of the soot-containing aerosols. These simulations show that the absorption cross-sections of those internally, deeply, half and slightly embedded mixed soot particles (Fs,out = 0.0, 0.2, 0.5, 0.8) are ~105%, ~65%, ~43% and ~14% larger than the semi-external mixtures (Fs,out = 1.0), respectively. The results also indicate that the differences of extinction cross-sections, single scattering albedo (SSA) and asymmetry parameter (ASY) between simulations with intersecting and non-intersecting surfaces are small (infrared wavelengths, the relative deviations of absorption cross-sections between these different
DEFF Research Database (Denmark)
Computerens interface eller grænseflade har spredt sig overalt. Mobiltelefoner, spilkonsoller, pc'er og storskærme indeholder computere – men computere indbygges også i tøj og andre hverdagslige genstande, så vi konstant har adgang til digitale data. Interface retter fokus mod, hvordan den digitale...... kunst og kultur skabes, spredes og opleves igennem interfaces. Forfatterne undersøger og diskuterer interfacets æstetik, ideologi og kultur – og analyserer aktuel interfacekunst på tværs af musik, kunst, litteratur og film. Bogen belyser interfacets oprindelse i den kolde krigs laboratorier og dets...
Efficiency of Brownian heat engines.
Derényi, I; Astumian, R D
1999-06-01
We study the efficiency of one-dimensional thermally driven Brownian ratchets or heat engines. We identify and compare the three basic setups characterized by the type of the connection between the Brownian particle and the two heat reservoirs: (i) simultaneous, (ii) alternating in time, and (iii) position dependent. We make a clear distinction between the heat flow via the kinetic and the potential energy of the particle, and show that the former is always irreversible and it is only the third setup where the latter is reversible when the engine works quasistatically. We also show that in the third setup the heat flow via the kinetic energy can be reduced arbitrarily, proving that even for microscopic heat engines there is no fundamental limit of the efficiency lower than that of a Carnot cycle.
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.
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...
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.
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.
Thermodynamic and Quantum Thermodynamic Analyses of Brownian Movement
Gyftopoulos, Elias P.
2006-01-01
Thermodynamic and quantum thermodynamic analyses of Brownian movement of a solvent and a colloid passing through neutral thermodynamic equilibrium states only. It is shown that Brownian motors and E. coli do not represent Brownian movement.
Directory of Open Access Journals (Sweden)
Dipayan Sanyal
2005-01-01
macroscopic conservation equations with an order parameter which can account for the solid, liquid, and the mushy zones with the help of a phase function defined on the basis of the liquid fraction, the Gibbs relation, and the phase diagram with local approximations. Using the above formalism for alloy solidification, the width of the diffuse interface (mushy zone was computed rather accurately for iron-carbon and ammonium chloride-water binary alloys and validated against experimental data from literature.
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.
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
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.
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).
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.
The Asymmetric Exclusion Process and Brownian Excursions
Derrida, B.; Enaud, C.; Lebowitz, J. L.
2004-04-01
We consider the totally asymmetric exclusion process (TASEP) in one dimension in its maximal current phase. We show, by an exact calculation, that the non-Gaussian part of the fluctuations of density can be described in terms of the statistical properties of a Brownian excursion. Numerical simulations indicate that the description in terms of a Brownian excursion remains valid for more general one dimensional driven systems in their maximal current phase.
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.
Fluctuation relations for a driven Brownian particle
Imparato, A.; Peliti, L.
2006-08-01
We consider a driven Brownian particle, subject to both conservative and nonconservative applied forces, whose probability evolves according to the Kramers equation. We derive a general fluctuation relation, expressing the ratio of the probability of a given Brownian path in phase space with that of the time-reversed path, in terms of the entropy flux to the heat reservoir. This fluctuation relation implies those of Seifert, Jarzynski, and Gallavotti-Cohen in different special cases.
Coupling of lever arm swing and biased Brownian motion in actomyosin.
Directory of Open Access Journals (Sweden)
Qing-Miao Nie
2014-04-01
Full Text Available An important unresolved problem associated with actomyosin motors is the role of Brownian motion in the process of force generation. On the basis of structural observations of myosins and actins, the widely held lever-arm hypothesis has been proposed, in which proteins are assumed to show sequential structural changes among observed and hypothesized structures to exert mechanical force. An alternative hypothesis, the Brownian motion hypothesis, has been supported by single-molecule experiments and emphasizes more on the roles of fluctuating protein movement. In this study, we address the long-standing controversy between the lever-arm hypothesis and the Brownian motion hypothesis through in silico observations of an actomyosin system. We study a system composed of myosin II and actin filament by calculating free-energy landscapes of actin-myosin interactions using the molecular dynamics method and by simulating transitions among dynamically changing free-energy landscapes using the Monte Carlo method. The results obtained by this combined multi-scale calculation show that myosin with inorganic phosphate (Pi and ADP weakly binds to actin and that after releasing Pi and ADP, myosin moves along the actin filament toward the strong-binding site by exhibiting the biased Brownian motion, a behavior consistent with the observed single-molecular behavior of myosin. Conformational flexibility of loops at the actin-interface of myosin and the N-terminus of actin subunit is necessary for the distinct bias in the Brownian motion. Both the 5.5-11 nm displacement due to the biased Brownian motion and the 3-5 nm displacement due to lever-arm swing contribute to the net displacement of myosin. The calculated results further suggest that the recovery stroke of the lever arm plays an important role in enhancing the displacement of myosin through multiple cycles of ATP hydrolysis, suggesting a unified movement mechanism for various members of the myosin family.
Brownian semistationary processes and conditional full support
Pakkanen, Mikko S
2010-01-01
In this note, we study the infinite-dimensional conditional laws of Brownian semistationary processes. Motivated by the fact that these processes are typically not semimartingales, we present sufficient conditions ensuring that a Brownian semistationary process has conditional full support, a property introduced by Guasoni, R\\'asonyi, and Schachermayer [Ann. Appl. Probab., 18 (2008) pp. 491--520]. By the results of Guasoni, R\\'asonyi, and Schachermayer, this property has two important implications. It ensures, firstly, that the process admits no free lunches under proportional transaction costs, and secondly, that it can be approximated pathwise (in the sup norm) by semimartingales that admit equivalent martingale measures.
Diffusion of torqued active Brownian particles
Sevilla, Francisco J.
An analytical approach is used to study the diffusion of active Brownian particles that move at constant speed in three-dimensional space, under the influence of passive (external) and active (internal) torques. The Smoluchowski equation for the position distribution of the particles is obtained from the Kramer-Fokker-Planck equation corresponding to Langevin equations for active Brownian particles subject to torques. In addition of giving explicit formulas for the mean square-displacement, the non-Gaussian behavior is analyzed through the kurtosis of the position distribution that exhibits an oscillatory behavior in the short-time limit. FJS acknowledges support from PAPIIT-UNAM through the grant IN113114
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 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 machinery in physics and biology
Hänggi, Peter
2001-01-01
Brownian machinery in physics and biology. - In: Noise in physical systems and 1/f fluctuations : proceedings of the 16th internat. conference, Gainesville, Fl., 22-25 Oct. 2001 / Ed.: Gijs Bosman. - New Jersey u.a. : World Scientific, 2001. - S. 397-399
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
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 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
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.
Feedback control in a coupled Brownian ratchet
Institute of Scientific and Technical Information of China (English)
Gao Tian-Fu; Liu Feng-Shan; Chen Jin-Can
2012-01-01
On the basis of the double-well ratchet potential which can be calculated theoretically and implemented experimentally,the influences of the time delay,the coupling constant,and the asymmetric parameter of the potential on the performance of a delayed feedback ratchet consisting of two Brownian particles coupled mutually with a linear elastic force are investigated.The centre-of-mass velocity of two coupled Brownian particles.the average effective diffusion coefficient,and the Pe number are calculated.It is found that the parameters are affected by not only the time delay and coupling constant but also the asymmetric parameter of the double-well ratchet potential.It is also found that the enhancement of the current may be obtained by varying the coupling constant of the system for the weak coupling case.It is expected that the results obtained here may be observed in some physical and biological systems.
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...
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.
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.
Ising model for a Brownian donkey
Cleuren, B.; Van den Broeck, C.
2001-04-01
We introduce a thermal engine consisting of N interacting Brownian particles moving in a periodic potential, featuring an alternation of hot and cold symmetric peaks. A discretized Ising-like version is solved analytically. In response to an external force, absolute negative mobility is observed for N >= 4. For N → ∞ a nonequilibrium phase transition takes place with a spontaneous symmetry breaking entailing the appearance of a current in the absence of an external force.
Dynamics of Brownian motors in deformable medium
Woulaché, Rosalie Laure; Kepnang Pebeu, Fabrice Maxime; Kofané, Timoléon C.
2016-10-01
The directed transport in a one-dimensional overdamped, Brownian motor subjected to a travelling wave potential with variable shape and exposed to an external bias is studied numerically. We focus our attention on the class of Remoissenet-Peyrard parametrized on-site potentials with slight modification, whose shape can be varied as a function of a parameter s, recovering the sine-Gordon shape as the special case. We demonstrate that in the presence of the travelling wave potential the observed dynamical properties of the Brownian motor which crucially depends on the travelling wave speed, the intensity of the noise and the external load is significantly influenced also by the geometry of the system. In particular, we notice that systems with sharp wells and broad barriers favour the transport under the influence of an applied load. The efficiency of transport of Brownian motors in deformable systems remains equal to 1 (in the absence of an applied load) up to a critical value of the travelling wave speed greater than that of the pure sine-Gordon shape.
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.
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.
Properties of Brownian Image Models in Scale-Space
DEFF Research Database (Denmark)
Pedersen, Kim Steenstrup
2003-01-01
In this paper it is argued that the Brownian image model is the least committed, scale invariant, statistical image model which describes the second order statistics of natural images. Various properties of three different types of Gaussian image models (white noise, Brownian and fractional...... Brownian images) will be discussed in relation to linear scale-space theory, and it will be shown empirically that the second order statistics of natural images mapped into jet space may, within some scale interval, be modeled by the Brownian image model. This is consistent with the 1/f 2 power spectrum...... law that apparently governs natural images. Furthermore, the distribution of Brownian images mapped into jet space is Gaussian and an analytical expression can be derived for the covariance matrix of Brownian images in jet space. This matrix is also a good approximation of the covariance matrix...
Phase transition in non-brownian fiber suspensions
Franceschini, Alexandre; Filippidi, Emmanouella; Guazzelli, Elizabeth; Pine, David
2012-11-01
The simple shear of a suspension of fibers tends to align them with the flow direction. We previously reported that the oscillatory shear of neutrally buoyant non-Brownian fibers align them with the vorticity (Franceschini A. et al. PRL, 2011). We interpreted this phenomenon as the minimization of a ``corrected volume fraction'' defined as a function of the strain amplitude, the average orientation and the volume fraction. Below a critical value of this parameter, the system becomes fully reversible after a few periods. Above it, fluctuations remain and the fibers align with the vorticity, subsequently reducing the value of this corrected volume fraction. We present here the collective behavior of fibers constrained at the liquid-air interface. By pinning the liquid on the wall of a Couette cell, we can have a flat interface. By modifying the surface of the fibers, we get rid of most of surface tension mediated fiber-fiber interactions. In this 2D configuration we can measure spatial correlations, as well as the position and orientation of every fiber at each shear cycle. We similarly define a ``corrected surface fraction'' and see how this parameter help us understand the difference between the surface behavior and the suspension behavior. This work was supported by the NSF through the NYU MRSEC, Award DMR:0820341. Additional support was provided by a Lavoisier Fellowship (AF) and from the Onassis Foundation (EF).
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.
Collective Transport of Coupled Brownian Motors with Low Randomness
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The transport properties of coupled Brownian motors in rocking ratchet are investigated via solving single particle have been found. In the regime of low-to-moderate D, the average velocity of elastically coupled Brownian with the increase of a single Brownian motor. The results exhibit an interesting cooperative behavior between coupled particles subjected to a rocking force, which can generate directed transport with low randomness or high transport coherence in symmetrical periodic potential.
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.
Application of Brownian model in the northwestern Beijing, China
Institute of Scientific and Technical Information of China (English)
冉洪流; 周本刚
2004-01-01
The mathematic theory of Brownian passage-time model and its difference from other recurrence models such asPoisson, lognormal, gamma and Weibull, were introduced. We assessed and analyzed the earthquake probabilitiesof the major faults with the elapsed time much greater than the recurrence interval in the northwest region of Beijing (China) in 100-year by using both Brownian passage-time model and Poisson model, and concluded that thecalculated results obtained from Brownian passage-time model is more reasonable.
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.
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
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.
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.
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 $d=1,2$.
Brownian transport in corrugated channels with inertia
Ghosh, P K; Marchesoni, F; Nori, F; Schmid, G; 10.1103/PhysRevE.86.021112
2012-01-01
The transport of suspended Brownian particles dc-driven along corrugated narrow channels is numerically investigated in the regime of finite damping. We show that inertial corrections cannot be neglected as long as the width of the channel bottlenecks is smaller than an appropriate particle diffusion length, which depends on the the channel corrugation and the drive intensity. Being such a diffusion length inversely proportional to the damping constant, transport through sufficiently narrow obstructions turns out to be always sensitive to the viscosity of the suspension fluid. The inertia corrections to the transport quantifiers, mobility and diffusivity, markedly differ for smoothly and sharply corrugated channels.
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.
Hybrid scheme for Brownian semistationary processes
DEFF Research Database (Denmark)
Bennedsen, Mikkel; Lunde, Asger; Pakkanen, Mikko S.
the asymptotics of the mean square error of the hybrid scheme and we observe that the scheme leads to a substantial improvement of accuracy compared to the ordinary forward Riemann-sum scheme, while having the same computational complexity. We exemplify the use of the hybrid scheme by two numerical experiments......, where we examine the finite-sample properties of an estimator of the roughness parameter of a Brownian semistationary process and study Monte Carlo option pricing in the rough Bergomi model of Bayer et al. (2015), respectively....
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
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'').
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...
Brownian rod scheme in microenvironment sensing
Directory of Open Access Journals (Sweden)
Ian Gralinski
2012-03-01
Full Text Available Fluctuations of freely translating spherical particles via Brownian motion should provide inexhaustible information about the micro-environment, but is beset by the problem of particles drifting away from the venue of measurement as well as colliding with other particles. We propose a scheme here to circumvent this in which a Brownian rod that lies in proximity to a cylindrical pillar is drawn in by a tuneable attractive force from the pillar. The force is assumed to act through the centre of each body and the motion exclusive to the x-y plane. Simulation studies show two distinct states, one in which the rod is moving freely (state I and the other in which the rod contacts the cylinder surface (state II. Information about the micro-environment could be obtained by tracking the rotational diffusion coefficient Dθ populating in either of these two states. However, the magnitude of the normalized charge product in excess of 6.3x104 was found necessary for a rod of 6.81 × 0.93 μm2 (length × diameter and 10μm diameter cylindrical pillar to minimize deviation errors. It was also found that the extent of spatial sensing coverage could be controlled by varying the charge level. The conditions needed to ascertain the rotational sampling for angle determination through the Hough transform were also discussed.
Molecular Motors: Power Strokes Outperform Brownian Ratchets.
Wagoner, Jason A; Dill, Ken A
2016-07-07
Molecular motors convert chemical energy (typically from ATP hydrolysis) to directed motion and mechanical work. Their actions are often described in terms of "Power Stroke" (PS) and "Brownian Ratchet" (BR) mechanisms. Here, we use a transition-state model and stochastic thermodynamics to describe a range of mechanisms ranging from PS to BR. We incorporate this model into Hill's diagrammatic method to develop a comprehensive model of motor processivity that is simple but sufficiently general to capture the full range of behavior observed for molecular motors. We demonstrate that, under all conditions, PS motors are faster, more powerful, and more efficient at constant velocity than BR motors. We show that these differences are very large for simple motors but become inconsequential for complex motors with additional kinetic barrier steps.
Cost and Precision of Brownian Clocks
Barato, Andre C
2016-01-01
Brownian clocks are biomolecular networks that can count time. A paradigmatic example are proteins that go through a cycle thus regulating some oscillatory behaviour in a living system. Typically, such a cycle requires free energy often provided by ATP hydrolysis. We investigate the relation between the precision of such a clock and its thermodynamic costs. For clocks driven by a constant thermodynamic force, a given precision requires a minimal cost that diverges as the uncertainty of the clock vanishes. In marked contrast, we show that a clock driven by a periodic variation of an external protocol can achieve arbitrary precision at arbitrarily low cost. This result constitutes a fundamental difference between processes driven by a fixed thermodynamic force and those driven periodically. As a main technical tool, we map a periodically driven system with a deterministic protocol to one subject to an external protocol that changes in stochastic time intervals, which simplifies calculations significantly. In th...
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.
Communication: Memory effects and active Brownian diffusion
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Pulak K. [Department of Chemistry, Presidency University, Kolkata 700073 (India); Li, Yunyun, E-mail: yunyunli@tongji.edu.cn [Center for Phononics and Thermal Energy Science, Tongji University, Shanghai 200092 (China); Marchegiani, Giampiero [Dipartimento di Fisica, Università di Camerino, I-62032 Camerino (Italy); Marchesoni, Fabio [Center for Phononics and Thermal Energy Science, Tongji University, Shanghai 200092 (China); Dipartimento di Fisica, Università di Camerino, I-62032 Camerino (Italy)
2015-12-07
A self-propelled artificial microswimmer is often modeled as a ballistic Brownian particle moving with constant speed aligned along one of its axis, but changing direction due to random collisions with the environment. Similarly to thermal noise, its angular randomization is described as a memoryless stochastic process. Here, we speculate that finite-time correlations in the orientational dynamics can affect the swimmer’s diffusivity. To this purpose, we propose and solve two alternative models. In the first one, we simply assume that the environmental fluctuations governing the swimmer’s propulsion are exponentially correlated in time, whereas in the second one, we account for possible damped fluctuations of the propulsion velocity around the swimmer’s axis. The corresponding swimmer’s diffusion constants are predicted to get, respectively, enhanced or suppressed upon increasing the model memory time. Possible consequences of this effect on the interpretation of the experimental data are discussed.
Brownian Ratchets: Transport Controlled by Thermal Noise
Kula, J.; Czernik, T.; Łuczka, J.
1998-02-01
We analyze directed transport of overdamped Brownian particles in a 1D spatially periodic potential that are subjected to both zero-mean thermal equilibrium Nyquist noise and zero-mean exponentially correlated dichotomous fluctuations. We show that particles can reverse the direction of average motion upon a variation of noise parameters if two fundamental symmetries, namely, the reflection symmetry of the spatial periodic structure, and the statistical symmetry of dichotomous fluctuations, are broken. There is a critical thermal noise intensity Dc, or equivalently a critical temperature Tc, at which the mean velocity of particles is zero. Below Tc and above Tc particles move in opposite directions. At fixed temperature, there is a region of noise parameters in which particles of different linear size are transported in opposite directions.
From Molecular Dynamics to Brownian Dynamics
Erban, Radek
2014-01-01
Three coarse-grained molecular dynamics (MD) models are investigated with the aim of developing and analyzing multiscale methods which use MD simulations in parts of the computational domain and (less detailed) Brownian dynamics (BD) simulations in the remainder of the domain. The first MD model is formulated in one spatial dimension. It is based on elastic collisions of heavy molecules (e.g. proteins) with light point particles (e.g. water molecules). Two three-dimensional MD models are then investigated. The obtained results are applied to a simplified model of protein binding to receptors on the cellular membrane. It is shown that modern BD simulators of intracellular processes can be used in the bulk and accurately coupled with a (more detailed) MD model of protein binding which is used close to the membrane.
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.
Thermal equilibrium of two quantum Brownian particles
Valente, D M
2009-01-01
The influence of the environment in the thermal equilibrium properties of a bipartite continuous variable quantum system is studied. The problem is treated within a system-plus-reservoir approach. The considered model reproduces the conventional Brownian motion when the two particles are far apart and induces an effective interaction between them, depending on the choice of the spectral function of the bath. The coupling between the system and the environment guarantees the translational invariance of the system in the absence of an external potential. The entanglement between the particles is measured by the logarithmic negativity, which is shown to monotonically decrease with the increase of the temperature. A range of finite temperatures is found in which entanglement is still induced by the reservoir.
The Brownian Cactus I. Scaling limits of discrete cactuses
Curien, Nicolas; Miermont, Grégory
2011-01-01
The cactus of a pointed graph is a discrete tree associated with this graph. Similarly, with every pointed geodesic metric space $E$, one can associate an $\\R$-tree called the continuous cactus of $E$. We prove under general assumptions that the cactus of random planar maps distributed according to Boltzmann weights and conditioned to have a fixed large number of vertices converges in distribution to a limiting space called the Brownian cactus, in the Gromov-Hausdorff sense. Moreover, the Brownian cactus can be interpreted as the continuous cactus of the so-called Brownian map.
Critical Brownian sheet does not have double points
Dalang, Robert C; Nualart, Eulalia; Wu, Dongsheng; Xiao, Yimin
2010-01-01
We derive a decoupling formula for the Brownian sheet which has the following ready consequence: An $N$-parameter Brownian sheet in $\\R^d$ has double points if and only if $2(d-2N)
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.
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.
Optimal tuning of a confined Brownian information engine
Park, Jong-Min; Lee, Jae Sung; Noh, Jae Dong
2016-03-01
A Brownian information engine is a device extracting mechanical work from a single heat bath by exploiting the information on the state of a Brownian particle immersed in the bath. As for engines, it is important to find the optimal operating condition that yields the maximum extracted work or power. The optimal condition for a Brownian information engine with a finite cycle time τ has been rarely studied because of the difficulty in finding the nonequilibrium steady state. In this study, we introduce a model for the Brownian information engine and develop an analytic formalism for its steady-state distribution for any τ . We find that the extracted work per engine cycle is maximum when τ approaches infinity, while the power is maximum when τ approaches zero.
Rotational Brownian Dynamics simulations of clathrin cage formation
Energy Technology Data Exchange (ETDEWEB)
Ilie, Ioana M.; Briels, Wim J. [Computational BioPhysics, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands); MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands); Otter, Wouter K. den, E-mail: w.k.denotter@utwente.nl [Computational BioPhysics, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands); MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands); Multi Scale Mechanics, Faculty of Engineering Technology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands)
2014-08-14
The self-assembly of nearly rigid proteins into ordered aggregates is well suited for modeling by the patchy particle approach. Patchy particles are traditionally simulated using Monte Carlo methods, to study the phase diagram, while Brownian Dynamics simulations would reveal insights into the assembly dynamics. However, Brownian Dynamics of rotating anisotropic particles gives rise to a number of complications not encountered in translational Brownian Dynamics. We thoroughly test the Rotational Brownian Dynamics scheme proposed by Naess and Elsgaeter [Macromol. Theory Simul. 13, 419 (2004); Naess and Elsgaeter Macromol. Theory Simul. 14, 300 (2005)], confirming its validity. We then apply the algorithm to simulate a patchy particle model of clathrin, a three-legged protein involved in vesicle production from lipid membranes during endocytosis. Using this algorithm we recover time scales for cage assembly comparable to those from experiments. We also briefly discuss the undulatory dynamics of the polyhedral cage.
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.
Rotational Brownian dynamics simulations of clathrin cage formation.
Ilie, Ioana M; den Otter, Wouter K; Briels, Wim J
2014-08-14
The self-assembly of nearly rigid proteins into ordered aggregates is well suited for modeling by the patchy particle approach. Patchy particles are traditionally simulated using Monte Carlo methods, to study the phase diagram, while Brownian Dynamics simulations would reveal insights into the assembly dynamics. However, Brownian Dynamics of rotating anisotropic particles gives rise to a number of complications not encountered in translational Brownian Dynamics. We thoroughly test the Rotational Brownian Dynamics scheme proposed by Naess and Elsgaeter [Macromol. Theory Simul. 13, 419 (2004); Naess and Elsgaeter Macromol. Theory Simul. 14, 300 (2005)], confirming its validity. We then apply the algorithm to simulate a patchy particle model of clathrin, a three-legged protein involved in vesicle production from lipid membranes during endocytosis. Using this algorithm we recover time scales for cage assembly comparable to those from experiments. We also briefly discuss the undulatory dynamics of the polyhedral cage.
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 ...
Directed transport of Brownian particles in a changing temperature field
Energy Technology Data Exchange (ETDEWEB)
Grillo, A [DMFCI, Facolta di Ingegneria, Universita di Catania. Viale Andrea Doria 6, 95125 Catania (Italy); Jinha, A [HPL-Faculty of Kinesiology, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4 (Canada); Federico, S [HPL-Faculty of Kinesiology, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4 (Canada); Ait-Haddou, R [HPL-Faculty of Kinesiology, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4 (Canada); Herzog, W [HPL-Faculty of Kinesiology, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4 (Canada); Giaquinta, G [DMFCI, Facolta di Ingegneria, Universita di Catania. Viale Andrea Doria 6, 95125 Catania (Italy)
2008-01-11
We study the interaction of Brownian particles with a changing temperature field in the presence of a one-dimensional periodic adiabatic potential. We show the existence of directed transport through the determination of the overall current of Brownian particles crossing the boundary of the system. With respect to the case of Brownian particles in a thermal bath, we determine a current which exhibits a contribution explicitly related to the presence of a thermal gradient. Beyond the self-consistent calculation of the temperature and probability density distribution of Brownian particles, we evaluate the energy consumption for directed transport to take place. Our description is based on Streater's model, and solutions are obtained by perturbing the system from its initial thermodynamic equilibrium state.
Near-Field, On-Chip Optical Brownian Ratchets.
Wu, Shao-Hua; Huang, Ningfeng; Jaquay, Eric; Povinelli, Michelle L
2016-08-10
Nanoparticles in aqueous solution are subject to collisions with solvent molecules, resulting in random, Brownian motion. By breaking the spatiotemporal symmetry of the system, the motion can be rectified. In nature, Brownian ratchets leverage thermal fluctuations to provide directional motion of proteins and enzymes. In man-made systems, Brownian ratchets have been used for nanoparticle sorting and manipulation. Implementations based on optical traps provide a high degree of tunability along with precise spatiotemporal control. Here, we demonstrate an optical Brownian ratchet based on the near-field traps of an asymmetrically patterned photonic crystal. The system yields over 25 times greater trap stiffness than conventional optical tweezers. Our technique opens up new possibilities for particle manipulation in a microfluidic, lab-on-chip environment.
Brownian 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.
A Brownian Bridge Movement Model to Track Mobile Targets
2016-09-01
BRIDGE MOVEMENT MODEL TO TRACK MOBILE TARGETS by Chun Chieh Cheng September 2016 Thesis Advisor: Dashi I. Singham Second Reader: Michael P...DATES COVERED Master’s thesis 4. TITLE AND SUBTITLE A BROWNIAN BRIDGE MOVEMENT MODEL TO TRACK MOBILE TARGETS 5. FUNDING NUMBERS 6. AUTHOR(S...Approved for public release. Distribution is unlimited. A BROWNIAN BRIDGE MOVEMENT MODEL TO TRACK MOBILE TARGETS Chun Chieh Cheng Major
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.
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.
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....
Response of Brownian Fluctuations to External Forces
Laub, Jeffrey William
Millikan's law of particle fall is an empirical result which shows the dependence of particle fall rate in a gas on particle radius and host gas density. The size of submicron particles in gases has long been determined by Millikan's law. The dominant factor is Stokes' law with a correction added to account for the physics of slip. However, it was recently shown by Kim and Fedele that Brownian fluctuations affect the fall rate while showing no anomalies in the density dependence of the rms displacement. The effect was an enhancement of the fall rate of small particles as the density of the host gas is increased. This enhancement showed a size dependence in the form of a smooth transition from the one of decreasing fall rate with increasing density for large particles (~0.4 μm radius) to another of increasing fall rate with increasing gas density for small particles ( ~0.15mum radius). The magnitude of the anomaly is determined by how the rms Brownian velocity compares with its fall rate. In an effort to understand the effect of Brownian fluctuations coupling with gravity, a new experiment has been carried out where an AC field was applied to force particles to fluctuate more in the vertical direction on one hand and where a constant DC field was applied to change the effective force of gravity on the other. These fields were applied to a charged oil drop in the 0.2 to 0.3 μm radius range falling in a nitrogen environment. Displacements over a 4 second time interval were repeatedly measured in both the vertical and horizontal directions. The original experimental apparatus was used with some modifications. The modifications included computer automation of particle control and data taking to allow for longer use of the same particle, up to 120 hours, and to facilitate application of the additional fields. The objective was to make large particles appear to be smaller via forced oscillations and make them fall faster or slower via the DC bias to effect the change in
Engineered swift equilibration of a Brownian particle
Martínez, Ignacio A.; Petrosyan, Artyom; Guéry-Odelin, David; Trizac, Emmanuel; Ciliberto, Sergio
2016-09-01
A fundamental and intrinsic property of any device or natural system is its relaxation time τrelax, which is the time it takes to return to equilibrium after the sudden change of a control parameter. Reducing τrelax is frequently necessary, and is often obtained by a complex feedback process. To overcome the limitations of such an approach, alternative methods based on suitable driving protocols have been recently demonstrated, for isolated quantum and classical systems. Their extension to open systems in contact with a thermostat is a stumbling block for applications. Here, we design a protocol, named Engineered Swift Equilibration (ESE), that shortcuts time-consuming relaxations, and we apply it to a Brownian particle trapped in an optical potential whose properties can be controlled in time. We implement the process experimentally, showing that it allows the system to reach equilibrium 100 times faster than the natural equilibration rate. We also estimate the increase of the dissipated energy needed to get such a time reduction. The method paves the way for applications in micro- and nano-devices, where the reduction of operation time represents as substantial a challenge as miniaturization.
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.
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.
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
Brownian Dynamics of charged particles in a constant magnetic field
Hou, L J; Piel, A; Shukla, P K
2009-01-01
Numerical algorithms are proposed for simulating the Brownian dynamics of charged particles in an external magnetic field, taking into account the Brownian motion of charged particles, damping effect and the effect of magnetic field self-consistently. Performance of these algorithms is tested in terms of their accuracy and long-time stability by using a three-dimensional Brownian oscillator model with constant magnetic field. Step-by-step recipes for implementing these algorithms are given in detail. It is expected that these algorithms can be directly used to study particle dynamics in various dispersed systems in the presence of a magnetic field, including polymer solutions, colloidal suspensions and, particularly complex (dusty) plasmas. The proposed algorithms can also be used as thermostat in the usual molecular dynamics simulation in the presence of magnetic field.
Near-field optically driven Brownian motors (Conference Presentation)
Wu, Shao-Hua; Huang, Ningfeng; Jaquay, Eric; Povinelli, Michelle L.
2016-09-01
Brownian ratchets are of fundamental interest in fields from statistical physics to molecular motors. The realization of Brownian ratchets in engineered systems opens up the potential to harness thermal energy for directed motion, with applications in transport and sorting of nanoparticles. Implementations based on optical traps provide a high degree of tunability along with precise spatiotemporal control. Near-field optical methods provide particular flexibility and ease of on-chip integration with other microfluidic components. Here, we demonstrate the first all-optical, near-field Brownian ratchet. Our approach uses an asymmetrically patterned photonic crystal and yields an ultra-stable trap stiffness of 253.6 pN/nm-W, 100x greater than conventional optical tweezers. By modulating the laser power, optical ratcheting with transport speed of 1 micron/s can be achieved, allowing a variety of dynamical lab-on-a-chip applications. The resulting transport speed matches well with the theoretical prediction.
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.
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...
Brownian versus Newtonian devitrification of hard-sphere glasses
Montero de Hijes, Pablo; Rosales-Pelaez, Pablo; Valeriani, Chantal; Pusey, Peter N.; Sanz, Eduardo
2017-08-01
In a recent molecular dynamics simulation work it has been shown that glasses composed of hard spheres crystallize via cooperative, stochastic particle displacements called avalanches [E. Sanz et al., Proc. Natl. Acad. Sci. USA 111, 75 (2014), 10.1073/pnas.1308338110]. In this Rapid Communication we investigate if such a devitrification mechanism is also present when the dynamics is Brownian rather than Newtonian. The research is motivated in part by the fact that colloidal suspensions, an experimental realization of hard-sphere systems, undergo Brownian motion. We find that Brownian hard-sphere glasses do crystallize via avalanches with very similar characteristics to those found in the Newtonian case. We briefly discuss the implications of these findings for experiments on colloids.
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.
From generalized Langevin equations to Brownian dynamics and embedded Brownian dynamics
Ma, Lina; Li, Xiantao; Liu, Chun
2016-09-01
We present the reduction of generalized Langevin equations to a coordinate-only stochastic model, which in its exact form involves a forcing term with memory and a general Gaussian noise. It will be shown that a similar fluctuation-dissipation theorem still holds at this level. We study the approximation by the typical Brownian dynamics as a first approximation. Our numerical test indicates how the intrinsic frequency of the kernel function influences the accuracy of this approximation. In the case when such an approximate is inadequate, further approximations can be derived by embedding the nonlocal model into an extended dynamics without memory. By imposing noises in the auxiliary variables, we show how the second fluctuation-dissipation theorem is still exactly satisfied.
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
Stochastic description of quantum Brownian dynamics
Yan, Yun-An; Shao, Jiushu
2016-08-01
Classical Brownian motion has well been investigated since the pioneering work of Einstein, which inspired mathematicians to lay the theoretical foundation of stochastic processes. A stochastic formulation for quantum dynamics of dissipative systems described by the system-plus-bath model has been developed and found many applications in chemical dynamics, spectroscopy, quantum transport, and other fields. This article provides a tutorial review of the stochastic formulation for quantum dissipative dynamics. The key idea is to decouple the interaction between the system and the bath by virtue of the Hubbard-Stratonovich transformation or Itô calculus so that the system and the bath are not directly entangled during evolution, rather they are correlated due to the complex white noises introduced. The influence of the bath on the system is thereby defined by an induced stochastic field, which leads to the stochastic Liouville equation for the system. The exact reduced density matrix can be calculated as the stochastic average in the presence of bath-induced fields. In general, the plain implementation of the stochastic formulation is only useful for short-time dynamics, but not efficient for long-time dynamics as the statistical errors go very fast. For linear and other specific systems, the stochastic Liouville equation is a good starting point to derive the master equation. For general systems with decomposable bath-induced processes, the hierarchical approach in the form of a set of deterministic equations of motion is derived based on the stochastic formulation and provides an effective means for simulating the dissipative dynamics. A combination of the stochastic simulation and the hierarchical approach is suggested to solve the zero-temperature dynamics of the spin-boson model. This scheme correctly describes the coherent-incoherent transition (Toulouse limit) at moderate dissipation and predicts a rate dynamics in the overdamped regime. Challenging problems
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.
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.
Brownian dynamics determine universality of charge transport in ionic liquids
Energy Technology Data Exchange (ETDEWEB)
Sangoro, Joshua R [ORNL; Iacob, Ciprian [University of Leipzig; Mierzwa, Michal [University of Silesia, Uniwersytecka, Katowice, Poland; Paluch, Marian [University of Silesia, Uniwersytecka, Katowice, Poland; Kremer, Friedrich [University of Leipzig
2012-01-01
Broadband dielectric spectroscopy is employed to investigate charge transport in a variety of glass-forming ionic liquids over wide frequency, temperature and pressure ranges. Using a combination of Einstein, Einstein-Smoluchowski, and Langevin relations, the observed universal scaling of charge transport in ionic liquids is traced back to the dominant role of Brownian dynamics.
Asset pricing puzzles explained by incomplete Brownian equilibria
DEFF Research Database (Denmark)
Christensen, Peter Ove; Larsen, Kasper
We examine a class of Brownian based models which produce tractable incomplete equilibria. The models are based on finitely many investors with heterogeneous exponential utilities over intermediate consumption who receive partially unspanned income. The investors can trade continuously on a finit...... markets. Consequently, our model can simultaneously help explaining the risk-free rate and equity premium puzzles....
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
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.
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.
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.
Rotational Brownian Dynamics simulations of clathrin cage formation
Ilie, I.M.; Otter, den W.K.; Briels, W.J.
2014-01-01
The self-assembly of nearly rigid proteins into ordered aggregates is well suited for modeling by the patchy particle approach. Patchy particles are traditionally simulated using Monte Carlo methods, to study the phase diagram, while Brownian Dynamics simulations would reveal insights into the assem
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.
Rotational Brownian Dynamics simulations of clathrin cage formation
Ilie, Ioana Mariuca; den Otter, Wouter K.; Briels, Willem J.
2014-01-01
The self-assembly of nearly rigid proteins into ordered aggregates is well suited for modeling by the patchy particle approach. Patchy particles are traditionally simulated using Monte Carlo methods, to study the phase diagram, while Brownian Dynamics simulations would reveal insights into the
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.
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).
Pressure and phase equilibria in interacting active brownian spheres.
Solon, Alexandre P; Stenhammar, Joakim; Wittkowski, Raphael; Kardar, Mehran; Kafri, Yariv; Cates, Michael E; Tailleur, Julien
2015-05-15
We derive a microscopic expression for the mechanical pressure P in a system of spherical active Brownian particles at density ρ. Our exact result relates P, defined as the force per unit area on a bounding wall, to bulk correlation functions evaluated far away from the wall. It shows that (i) P(ρ) is a state function, independent of the particle-wall interaction; (ii) interactions contribute two terms to P, one encoding the slow-down that drives motility-induced phase separation, and the other a direct contribution well known for passive systems; and (iii) P is equal in coexisting phases. We discuss the consequences of these results for the motility-induced phase separation of active Brownian particles and show that the densities at coexistence do not satisfy a Maxwell construction on P.
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...
Fast simulation of Brownian dynamics in a crowded environment
Smith, Stephen
2016-01-01
Brownian dynamics simulations are an increasingly popular tool for understanding spatially-distributed biochemical reaction systems. Recent improvements in our understanding of the cellular environment show that volume exclusion effects are fundamental to reaction networks inside cells. These systems are frequently studied by incorporating inert hard spheres (crowders) into three-dimensional Brownian dynamics simulations, however these methods are extremely slow owing to the sheer number of possible collisions between particles. Here we propose a rigorous "crowder-free" method to dramatically increase simulation speed for crowded biochemical reaction systems by eliminating the need to explicitly simulate the crowders. We consider both the case where the reactive particles are point particles, and where they themselves occupy a volume. We use simulations of simple chemical reaction networks to confirm that our simplification is just as accurate as the original algorithm, and that it corresponds to a large spee...
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.
Brownian transport controlled by dichotomic and thermal fluctuations
Kula, J.; Kostur, M.; Łuczka, J.
1998-09-01
We study transport of Brownian particles in spatially periodic structures, driven by both thermal equilibrium fluctuations and dichotomic noise of zero mean values. Introducing specific scaling, we show that the dimensionless Newton-Langevin type equation governing the motion of Brownian particles is very well approximated by the overdamped dynamics; inertial effects can be neglected because for generic systems dimensionless mass is many orders less than a dimensionless friction coefficient. An exact probability current, proportional to the mean drift velocity of particles, is obtained for a piecewise linear spatially periodic potential. We analyze in detail properties of the macroscopic averaged motion of particles. In dependence on statistics of both sources of fluctuations, the directed transport of particles exhibits such distinctive non-monotonic behavior as: bell-shaped dependence (there exists optimal statistics of fluctuations maximizing velocity) and reversal in the direction of macroscopic motion (there exists critical statistics at which the drift velocity is zero).
CNT based thermal Brownian motor to pump water in nanodevices
DEFF Research Database (Denmark)
Oyarzua, Elton; Zambrano, Harvey; Walther, Jens Honore
2016-01-01
Brownian molecular motors are nanoscale machines that exploit thermal fluctuations for directional motion by employing mechanisms such as the Feynman-Smoluchowski ratchet. In this study, using Non Equilibrium Molecular Dynamics, we propose a novel thermal Brownian motor for pumping water through...... Carbon Nanotubes (CNTs). To achieve this we impose a thermal gradient along the axis of a CNT filled with water and impose, in addition, a spatial asymmetry by flxing specific zones on the CNT in order to modify the vibrational modes of the CNT. We find that the temperature gradient and imposed spatial...... asymmetry drive the water ow in a preferential direction. We systematically modified the magnitude of the applied thermal gradient and the axial position of the fixed points. The analysis involves measurement of the vibrational modes in the CNTs using a Fast Fourier Transform (FFT) algorithm. We observed...
Driven Brownian transport through arrays of symmetric obstacles.
Ghosh, P K; Hänggi, P; Marchesoni, F; Martens, S; Nori, F; Schimansky-Geier, L; Schmid, G
2012-01-01
We numerically investigate the transport of a suspended overdamped Brownian particle which is driven through a two-dimensional rectangular array of circular obstacles with finite radius. Two limiting cases are considered in detail, namely, when the constant drive is parallel to the principal or the diagonal array axes. This corresponds to studying the Brownian transport in periodic channels with reflecting walls of different topologies. The mobility and diffusivity of the transported particles in such channels are determined as functions of the drive and the array geometric parameters. Prominent transport features, like negative differential mobilities, excess diffusion peaks, and unconventional asymptotic behaviors, are explained in terms of two distinct lengths, the size of single obstacles (trapping length), and the lattice constant of the array (local correlation length). Local correlation effects are further analyzed by continuously rotating the drive between the two limiting orientations. © 2012 American Physical Society
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
Continuous state branching processes in random environment: The Brownian case
Palau, Sandra; Pardo, Juan Carlos
2015-01-01
We consider continuous state branching processes that are perturbed by a Brownian motion. These processes are constructed as the unique strong solution of a stochastic differential equation. The long-term extinction and explosion behaviours are studied. In the stable case, the extinction and explosion probabilities are given explicitly. We find three regimes for the asymptotic behaviour of the explosion probability and, as in the case of branching processes in random environment, we find five...
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.
The Brownian Cactus I. Scaling limits of discrete cactuses
Curien, Nicolas; Gall, Jean-François Le; Miermont, Grégory
2011-01-01
The cactus of a pointed graph is a discrete tree associated with this graph. Similarly, with every pointed geodesic metric space $E$, one can associate an $\\mathbb{R}$-tree called the continuous cactus of $E$. We prove under general assumptions that the cactus of random planar maps distributed according to Boltzmann weights and conditioned to have a fixed large number of vertices converges in distribution to a limiting space called the Brownian cactus, in the Gromov–Hausdorff sense. Moreover,...
Analysis of a Brownian heat engine with ecological criteria
Açıkkalp, Emin
2016-12-01
The purpose of this study is to investigate the Brownian heat engine with thermo-ecological function ( ECF) and ecological coefficient of performance ( ECOP). Potential and kinetic heat flows are taken into account. Different parameters are considered in the analyses. Beside the thermo-ecological function and ecological coefficient of performance, the basic thermodynamics parameters involving power output and efficiency are investigated. Results are presented numerically and the optimum points of the system are determined.
Energy Technology Data Exchange (ETDEWEB)
Radiom, Milad, E-mail: milad.radiom@unige.ch; Ducker, William, E-mail: wducker@vt.edu [Department of Chemical Engineering, Virginia Tech, Blacksburg, Virginia 24060 (United States); Robbins, Brian; Paul, Mark [Department of Mechanical Engineering, Virginia Tech, Blacksburg, Virginia 24060 (United States)
2015-02-15
The hydrodynamic interaction of two closely spaced micron-scale spheres undergoing Brownian motion was measured as a function of their separation. Each sphere was attached to the distal end of a different atomic force microscopy cantilever, placing each sphere in a stiff one-dimensional potential (0.08 Nm{sup −1}) with a high frequency of thermal oscillations (resonance at 4 kHz). As a result, the sphere’s inertial and restoring forces were significant when compared to the force due to viscous drag. We explored interparticle gap regions where there was overlap between the two Stokes layers surrounding each sphere. Our experimental measurements are the first of their kind in this parameter regime. The high frequency of oscillation of the spheres means that an analysis of the fluid dynamics would include the effects of fluid inertia, as described by the unsteady Stokes equation. However, we find that, for interparticle separations less than twice the thickness of the wake of the unsteady viscous boundary layer (the Stokes layer), the hydrodynamic interaction between the Brownian particles is well-approximated by analytical expressions that neglect the inertia of the fluid. This is because elevated frictional forces at narrow gaps dominate fluid inertial effects. The significance is that interparticle collisions and concentrated suspensions at this condition can be modeled without the need to incorporate fluid inertia. We suggest a way to predict when fluid inertial effects can be ignored by including the gap-width dependence into the frequency number. We also show that low frequency number analysis can be used to determine the microrheology of mixtures at interfaces.
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...
Amoeba-inspired nanoarchitectonic computing implemented using electrical Brownian ratchets.
Aono, M; Kasai, S; Kim, S-J; Wakabayashi, M; Miwa, H; Naruse, M
2015-06-12
In this study, we extracted the essential spatiotemporal dynamics that allow an amoeboid organism to solve a computationally demanding problem and adapt to its environment, thereby proposing a nature-inspired nanoarchitectonic computing system, which we implemented using a network of nanowire devices called 'electrical Brownian ratchets (EBRs)'. By utilizing the fluctuations generated from thermal energy in nanowire devices, we used our system to solve the satisfiability problem, which is a highly complex combinatorial problem related to a wide variety of practical applications. We evaluated the dependency of the solution search speed on its exploration parameter, which characterizes the fluctuation intensity of EBRs, using a simulation model of our system called 'AmoebaSAT-Brownian'. We found that AmoebaSAT-Brownian enhanced the solution searching speed dramatically when we imposed some constraints on the fluctuations in its time series and it outperformed a well-known stochastic local search method. These results suggest a new computing paradigm, which may allow high-speed problem solving to be implemented by interacting nanoscale devices with low power consumption.
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.
Brownian dynamics without Green's functions
Energy Technology Data Exchange (ETDEWEB)
Delong, Steven; Donev, Aleksandar, E-mail: donev@courant.nyu.edu [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States); Usabiaga, Florencio Balboa; Delgado-Buscalioni, Rafael [Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Univeridad Autónoma de Madrid, Madrid 28049 (Spain); Griffith, Boyce E. [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States); Leon H. Charney Division of Cardiology, Department of Medicine, New York University School of Medicine, New York, New York 10016 (United States)
2014-04-07
We develop a Fluctuating Immersed Boundary (FIB) method for performing Brownian dynamics simulations of confined particle suspensions. Unlike traditional methods which employ analytical Green's functions for Stokes flow in the confined geometry, the FIB method uses a fluctuating finite-volume Stokes solver to generate the action of the response functions “on the fly.” Importantly, we demonstrate that both the deterministic terms necessary to capture the hydrodynamic interactions among the suspended particles, as well as the stochastic terms necessary to generate the hydrodynamically correlated Brownian motion, can be generated by solving the steady Stokes equations numerically only once per time step. This is accomplished by including a stochastic contribution to the stress tensor in the fluid equations consistent with fluctuating hydrodynamics. We develop novel temporal integrators that account for the multiplicative nature of the noise in the equations of Brownian dynamics and the strong dependence of the mobility on the configuration for confined systems. Notably, we propose a random finite difference approach to approximating the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. Through comparisons with analytical and existing computational results, we numerically demonstrate the ability of the FIB method to accurately capture both the static (equilibrium) and dynamic properties of interacting particles in flow.
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.
Brownian relaxation of an inelastic sphere in air
Bird, G. A.
2016-06-01
The procedures that are used to calculate the forces and moments on an aerodynamic body in the rarefied gas of the upper atmosphere are applied to a small sphere of the size of an aerosol particle at sea level. While the gas-surface interaction model that provides accurate results for macroscopic bodies may not be appropriate for bodies that are comprised of only about a thousand atoms, it provides a limiting case that is more realistic than the elastic model. The paper concentrates on the transfer of energy from the air to an initially stationary sphere as it acquires Brownian motion. Individual particle trajectories vary wildly, but a clear relaxation process emerges from an ensemble average over tens of thousands of trajectories. The translational and rotational energies in equilibrium Brownian motion are determined. Empirical relationships are obtained for the mean translational and rotational relaxation times, the mean initial power input to the particle, the mean rates of energy transfer between the particle and air, and the diffusivity. These relationships are functions of the ratio of the particle mass to an average air molecule mass and the Knudsen number, which is the ratio of the mean free path in the air to the particle diameter. The ratio of the molecular radius to the particle radius also enters as a correction factor. The implications of Brownian relaxation for the second law of thermodynamics are discussed.
Non-conservative optical forces and Brownian vortexes
Sun, Bo
Optical manipulation using optical tweezers has been widely adopted in physics, chemical engineering and biology. While most applications and fundamental studies of optical trapping have focused on optical forces resulting from intensity gradients, we have also explored the role of radiation pressure, which is directed by phase gradients in beams of light. Interestingly, radiation pressure turns out to be a non-conservative force and drives trapped objects out of thermodynamic equilibrium with their surrounding media. We have demonstrated the resulting nonequilibrium effects experimentally by tracking the thermally driven motions of optically trapped colloidal spheres using holographic video microscopy. Rather than undergoing equilibrium thermal fluctuations, as has been assumed for more than a quarter century, a sphere in an optical tweezer enters into a stochastic steady-state characterized by closed loops in its probability current density. These toroidal vortexes constitute a bias in the particle's otherwise random thermal fluctuations arising at least indirectly from a solenoidal component in the optical force. This surprising effect is a particular manifestation of a more general class of noise-driven machines that we call Brownian vortexes. This previously unrecognized class of stochastic heat engines operates on qualitatively different principles from such extensively studied nonequilibrium systems as thermal ratchets and Brownian motors. Among its interesting properties, a Brownian vortex can reverse its direction with changes in temperature or equivalent control parameters.
Brownian relaxation of an inelastic sphere in air
Energy Technology Data Exchange (ETDEWEB)
Bird, G. A., E-mail: gab@gab.com.au [University of Sydney, Sydney, NSW 2006 (Australia)
2016-06-15
The procedures that are used to calculate the forces and moments on an aerodynamic body in the rarefied gas of the upper atmosphere are applied to a small sphere of the size of an aerosol particle at sea level. While the gas-surface interaction model that provides accurate results for macroscopic bodies may not be appropriate for bodies that are comprised of only about a thousand atoms, it provides a limiting case that is more realistic than the elastic model. The paper concentrates on the transfer of energy from the air to an initially stationary sphere as it acquires Brownian motion. Individual particle trajectories vary wildly, but a clear relaxation process emerges from an ensemble average over tens of thousands of trajectories. The translational and rotational energies in equilibrium Brownian motion are determined. Empirical relationships are obtained for the mean translational and rotational relaxation times, the mean initial power input to the particle, the mean rates of energy transfer between the particle and air, and the diffusivity. These relationships are functions of the ratio of the particle mass to an average air molecule mass and the Knudsen number, which is the ratio of the mean free path in the air to the particle diameter. The ratio of the molecular radius to the particle radius also enters as a correction factor. The implications of Brownian relaxation for the second law of thermodynamics are discussed.
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...
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...
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.
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.
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.
A Flashing Model for Transport of Brownian Motors
Institute of Scientific and Technical Information of China (English)
赵同军; 展永; 吴建海; 王永宏
2002-01-01
A flashing coloured noise model is proposed to describe the motion of a molecular motor. In this model,the overdamped Brownian particle moves in an asymmetric periodic potential with a tashing Ornstein-Ulenbeck coloured noise. The relationship between the current and the parameters-such as the intensity, the correlation time of coloured noise and the flip rate of the noise-is discussed using the Monte Carlo simulation method.Current reversal occurs with the change of the correlation time and the flip rate of coloured noise, which may be related to the directed motion and the current reversal of molecular motors.
Properties of the Collision Efficiency of Nanoparticles in Brownian Coagulation
Institute of Scientific and Technical Information of China (English)
WANG Yu-Ming; LIN Jian-Zhong; CHEN Zhong-Li
2011-01-01
The collision efficiency of nanoparticles with diameters from 100 nm to 750nm in the Brownian coagulation is studied by building and solving numerically the equations of particle collision in the presence of the van der Waals force, the elastic deformation force, the Stokes resistance, the lubrication force and the electrostatic force. The results show that the collision efficiency decreases overall with the increasing particle diameter. It is found that there exists an abrupt increase in the collision efficiency when the particle diameter is equals to 550 nm. Finally a new expression for the collision efficiency is presented.
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.
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.
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.
Trajectories of Brownian particles with space-correlated noise
Indian Academy of Sciences (India)
EDOARDO MILOTTI
2017-07-01
The Langevin equation used to model Brownian motion includes a stochastic process that is routinely assumed to be a Gaussian white noise. Spatial correlations of the noise are usually ruled out, and the paths traced by the random walkers are statistically independent. In this study, I consider instead noise which is white in time and has a Gaussian correlation in space, and by means of numerical simulation, I show how the spatial correlation determines the time evolution of the spatial separation of random walkers.
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.
Entropic Ratchet transport of interacting active Brownian particles
Energy Technology Data Exchange (ETDEWEB)
Ai, Bao-Quan, E-mail: aibq@hotmail.com [Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, 510006 Guangzhou (China); He, Ya-Feng [College of Physics Science and Technology, Hebei University, 071002 Baoding (China); Zhong, Wei-Rong, E-mail: wrzhong@jnu.edu.cn [Department of Physics and Siyuan Laboratory, College of Science and Engineering, Jinan University, 510632 Guangzhou (China)
2014-11-21
Directed transport of interacting active (self-propelled) Brownian particles is numerically investigated in confined geometries (entropic barriers). The self-propelled velocity can break thermodynamical equilibrium and induce the directed transport. It is found that the interaction between active particles can greatly affect the ratchet transport. For attractive particles, on increasing the interaction strength, the average velocity first decreases to its minima, then increases, and finally decreases to zero. For repulsive particles, when the interaction is very weak, there exists a critical interaction at which the average velocity is minimal, nearly tends to zero, however, for the strong interaction, the average velocity is independent of the interaction.
Minimal Cost of a Brownian Risk without Ruin
Luo, Shangzhen
2011-01-01
In this paper, we study a risk process modeled by a Brownian motion with drift (the diffusion approximation model). The insurance entity can purchase reinsurance to lower its risk and receive cash injections at discrete times to avoid ruin. Proportional reinsurance and excess-of-loss reinsurance are considered. The objective is to find the optimal reinsurance and cash injection strategy that minimizes the total cost to keep the company's surplus process non-negative, i.e. without ruin, where the cost function is defined as the total discounted value of the injections. The optimal solution is found explicitly by solving the according quasi-variational inequalities (QVIs).
A parity breaking Ising chain Hamiltonian as a Brownian motor
Cornu, F.; Hilhorst, H. J.
2014-10-01
We consider the translationally invariant but parity (left-right symmetry) breaking Ising chain Hamiltonian {\\cal H} =-{U_2}\\sumk sksk+1 - {U_3}\\sumk sksk+1sk+3 and let this system evolve by Kawasaki spin exchange dynamics. Monte Carlo simulations show that perturbations forcing this system off equilibrium make it act as a Brownian molecular motor which, in the lattice gas interpretation, transports particles along the chain. We determine the particle current under various different circumstances, in particular as a function of the ratio {U_3}/{U_2} and of the conserved magnetization M=\\sum_ksk . The symmetry of the U3 term in the Hamiltonian is discussed.
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.
Analysis of Brownian Dynamics Simulations of Reversible Bimolecular Reactions
Lipková, Jana
2011-01-01
A class of Brownian dynamics algorithms for stochastic reaction-diffusion models which include reversible bimolecular reactions is presented and analyzed. The method is a generalization of the λ-bcȳ model for irreversible bimolecular reactions which was introduced in [R. Erban and S. J. Chapman, Phys. Biol., 6(2009), 046001]. The formulae relating the experimentally measurable quantities (reaction rate constants and diffusion constants) with the algorithm parameters are derived. The probability of geminate recombination is also investigated. © 2011 Society for Industrial and Applied Mathematics.
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.
Some Results on Fractional Brownian Sheets and Their Local Times
Institute of Scientific and Technical Information of China (English)
Zong-mao Cheng; Zheng-yan Lin
2008-01-01
Let BHO={BHO(t),E RN+} be a real-valued fractional Brownian sheet. Define the (N,d)-Ganssian random field BH by where BH1,..., BHd are independent copies of BHO. The existence and joint continuity of local times of BH is proven in some given conditions in [22]. We then study further properties of the local times of BH, such as the moments of increments of local times, the large increments and the maximum moduli of continuity of local times and as a result, we answer the questions posed in [22].
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.
A Fractional Characteristic Study of Liquid and Vapor Interface in Lennard—Jones Fluids
Institute of Scientific and Technical Information of China (English)
LIUChao; ZENGDanling
2002-01-01
The molecular dynamic simulation results for the liquid-vapor interface of the pure Lennard-Jones fluid are presented.The thermodynamic properties,the surface tension and the effective thickness of interfacial layer are determined.The rough characteristic of the liquid-vapor interface is discussed with fractional Brownian motion theory.Thereupon the fractal dimension d of the liqud-vapor interface is obtained.
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…
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.
Thermodynamic characteristics of a Brownian heat pump in a spatially periodic temperature field
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper has studied the thermodynamic performance of a thermal Brownian heat pump,which consists of Brownian particles moving at a periodic sawtooth potential with external forces and contacting with the alternating hot and cold reservoirs along the space coordinate.The heat flows driven by both potential and kinetic energies are taken into account.The analytical expressions for the heating load,coefficient of performance(COP) and power input of the Brownian heat pump are derived and the performance characteristics are obtained by numerical calculations.It is shown that due to the heat flow via the change of kinetic energy of the particles,the Brownian heat pump is always irreversible and the COP can never attain the Carnot COP.The study has also investigated the influences of the operating parameters,i.e.the external force,barrier height of the potential,asymmetry of the sawtooth potential and temperature ratio of the heat reservoirs,on the performance of the Brownian heat pump.The effective regions of external force and barrier height of the potential in which the Brownian motor can operates as a heat pump are determined.The results show that the performance of the Brownian heat pump greatly depends on the parameters;if the parameters are properly chosen,the Brownian heat pump may be controlled to operate in the optimal regimes.
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)
CNT based thermal Brownian motor to pump water in nanodevices
Oyarzua, Elton; Zambrano, Harvey; Walther, J. H.
2016-11-01
Brownian molecular motors are nanoscale machines that exploit thermal fluctuations for directional motion by employing mechanisms such as the Feynman-Smoluchowski ratchet. In this study, using Non Equilibrium Molecular Dynamics, we propose a novel thermal Brownian motor for pumping water through Carbon Nanotubes (CNTs). To achieve this we impose a thermal gradient along the axis of a CNT filled with water and impose, in addition, a spatial asymmetry by fixing specific zones on the CNT in order to modify the vibrational modes of the CNT. We find that the temperature gradient and imposed spatial asymmetry drive the water flow in a preferential direction. We systematically modified the magnitude of the applied thermal gradient and the axial position of the fixed points. The analysis involves measurement of the vibrational modes in the CNTs using a Fast Fourier Transform (FFT) algorithm. We observed water flow in CNTs of 0.94, 1.4 and 2.0 nm in diameter, reaching a maximum velocity of 5 m/s for a thermal gradient of 3.3 K/nm. The proposed thermal motor is capable of delivering a continuous flow throughout a CNT, providing a useful tool for driving liquids in nanofluidic devices by exploiting thermal gradients. We aknowledge partial support from Fondecyt project 11130559.
Mechanical radiation detection via sub-Brownian lever deflections
Hammig, Mark David
2005-07-01
A micromechanical lever that deflects in response to the impacts of charged particles is proposed as a means of improving upon the capabilities of existing radiation detection technology. When a particle strikes an object, momentum is transferred to the impacted body. The resulting body motion can be correlated to the energy of the incident particle. The momentum detector offers promise as a highly discriminating, high-resolution tool for ion sensing. Advances required to successfully realize a spectroscopic capability have been completed; specifically, techniques for reproducibly fabricating micromechanical structures have been optimized, and an instrument that measures miniscule deflections has been developed. Even absent substantial refinement efforts, the novel coupled-cavity optical detector can resolve lever motions on the order of 1--10 picometers. A method by which the Brownian motion of the lever can be stilled has been proven which elicits reductions sufficient to measure heavy-ion impact, the deflections from which may be several orders of magnitude below the thermal vibration amplitude. Using active forcing techniques, the Brownian vibration of the microlevers has been reduced from room temperature (288 K) to sub-Kelvin temperatures, for levers vibrating in air. The mechanical factors that limit the noise reduction magnitude are discussed and methods of surmounting those limitations are identified.
Intermittency and multifractional Brownian character of geomagnetic time series
Directory of Open Access Journals (Sweden)
G. Consolini
2013-07-01
Full Text Available The Earth's magnetosphere exhibits a complex behavior in response to the solar wind conditions. This behavior, which is described in terms of mutifractional Brownian motions, could be the consequence of the occurrence of dynamical phase transitions. On the other hand, it has been shown that the dynamics of the geomagnetic signals is also characterized by intermittency at the smallest temporal scales. Here, we focus on the existence of a possible relationship in the geomagnetic time series between the multifractional Brownian motion character and the occurrence of intermittency. In detail, we investigate the multifractional nature of two long time series of the horizontal intensity of the Earth's magnetic field as measured at L'Aquila Geomagnetic Observatory during two years (2001 and 2008, which correspond to different conditions of solar activity. We propose a possible double origin of the intermittent character of the small-scale magnetic field fluctuations, which is related to both the multifractional nature of the geomagnetic field and the intermittent character of the disturbance level. Our results suggest a more complex nature of the geomagnetic response to solar wind changes than previously thought.
Amoeba-inspired nanoarchitectonic computing implemented using electrical Brownian ratchets
Aono, M.; Kasai, S.; Kim, S.-J.; Wakabayashi, M.; Miwa, H.; Naruse, M.
2015-06-01
In this study, we extracted the essential spatiotemporal dynamics that allow an amoeboid organism to solve a computationally demanding problem and adapt to its environment, thereby proposing a nature-inspired nanoarchitectonic computing system, which we implemented using a network of nanowire devices called ‘electrical Brownian ratchets (EBRs)’. By utilizing the fluctuations generated from thermal energy in nanowire devices, we used our system to solve the satisfiability problem, which is a highly complex combinatorial problem related to a wide variety of practical applications. We evaluated the dependency of the solution search speed on its exploration parameter, which characterizes the fluctuation intensity of EBRs, using a simulation model of our system called ‘AmoebaSAT-Brownian’. We found that AmoebaSAT-Brownian enhanced the solution searching speed dramatically when we imposed some constraints on the fluctuations in its time series and it outperformed a well-known stochastic local search method. These results suggest a new computing paradigm, which may allow high-speed problem solving to be implemented by interacting nanoscale devices with low power consumption.
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.
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...
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.
Urbina-Villalba, German; García-Sucre, Máximo; Toro-Mendoza, Jhoan
2003-12-01
In order to account for the hydrodynamic interaction (HI) between suspended particles in an average way, Honig et al. [J. Colloid Interface Sci. 36, 97 (1971)] and more recently Heyes [Mol. Phys. 87, 287 (1996)] proposed different analytical forms for the diffusion constant. While the formalism of Honig et al. strictly applies to a binary collision, the one from Heyes accounts for the dependence of the diffusion constant on the local concentration of particles. However, the analytical expression of the latter approach is more complex and depends on the particular characteristics of each system. Here we report a combined methodology, which incorporates the formula of Honig et al. at very short distances and a simple local volume-fraction correction at longer separations. As will be shown, the flocculation behavior calculated from Brownian dynamics simulations employing the present technique, is found to be similar to that of Batchelor’s tensor [J. Fluid. Mech. 74, 1 (1976); 119, 379 (1982)]. However, it corrects the anomalous coalescence found in concentrated systems as a result of the overestimation of many-body HI.
DEFF Research Database (Denmark)
2009-01-01
A kinetic interface for orientation detection in a video training system is disclosed. The interface includes a balance platform instrumented with inertial motion sensors. The interface engages a participant's sense of balance in training exercises.......A kinetic interface for orientation detection in a video training system is disclosed. The interface includes a balance platform instrumented with inertial motion sensors. The interface engages a participant's sense of balance in training exercises....
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.
Momentum conserving Brownian dynamics propagator for complex soft matter fluids
Energy Technology Data Exchange (ETDEWEB)
Padding, J. T. [Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven (Netherlands); Briels, W. J. [Computational Biophysics, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands)
2014-12-28
We present a Galilean invariant, momentum conserving first order Brownian dynamics scheme for coarse-grained simulations of highly frictional soft matter systems. Friction forces are taken to be with respect to moving background material. The motion of the background material is described by locally averaged velocities in the neighborhood of the dissolved coarse coordinates. The velocity variables are updated by a momentum conserving scheme. The properties of the stochastic updates are derived through the Chapman-Kolmogorov and Fokker-Planck equations for the evolution of the probability distribution of coarse-grained position and velocity variables, by requiring the equilibrium distribution to be a stationary solution. We test our new scheme on concentrated star polymer solutions and find that the transverse current and velocity time auto-correlation functions behave as expected from hydrodynamics. In particular, the velocity auto-correlation functions display a long time tail in complete agreement with hydrodynamics.
Temporal Correlations of the Running Maximum of a Brownian Trajectory
Bénichou, Olivier; Krapivsky, P. L.; Mejía-Monasterio, Carlos; Oshanin, Gleb
2016-08-01
We study the correlations between the maxima m and M of a Brownian motion (BM) on the time intervals [0 ,t1] and [0 ,t2], with t2>t1. We determine the exact forms of the distribution functions P (m ,M ) and P (G =M -m ), and calculate the moments E {(M-m ) k} and the cross-moments E {mlMk} with arbitrary integers l and k . We show that correlations between m and M decay as √{t1/t2 } when t2/t1→∞ , revealing strong memory effects in the statistics of the BM maxima. We also compute the Pearson correlation coefficient ρ (m ,M ) and the power spectrum of Mt, and we discuss a possibility of extracting the ensemble-averaged diffusion coefficient in single-trajectory experiments using a single realization of the maximum process.
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 (
Diffusion in crowded biological environments: applications of Brownian dynamics
Directory of Open Access Journals (Sweden)
Długosz Maciej
2011-03-01
Full Text Available Abstract Biochemical reactions in living systems occur in complex, heterogeneous media with total concentrations of macromolecules in the range of 50 - 400 mgml. Molecular species occupy a significant fraction of the immersing medium, up to 40% of volume. Such complex and volume-occupied environments are generally termed 'crowded' and/or 'confined'. In crowded conditions non-specific interactions between macromolecules may hinder diffusion - a major process determining metabolism, transport, and signaling. Also, the crowded media can alter, both qualitatively and quantitatively, the reactions in vivo in comparison with their in vitro counterparts. This review focuses on recent developments in particle-based Brownian dynamics algorithms, their applications to model diffusive transport in crowded systems, and their abilities to reproduce and predict the behavior of macromolecules under in vivo conditions.
Blowup and Conditionings of $\\psi$-super Brownian Exit Measures
Athreya, Siva R
2011-01-01
We extend earlier results on conditioning of super-Brownian motion to general branching rules. We obtain representations of the conditioned process, both as an $h$-transform, and as an unconditioned superprocess with immigration along a branching tree. Unlike the finite-variance branching setting, these trees are no longer binary, and strictly positive mass can be created at branch points. This construction is singular in the case of stable branching. We analyze this singularity first by approaching the stable branching function via analytic approximations. In this context the singularity of the stable case can be attributed to blow up of the mass created at the first branch of the tree. Other ways of approaching the stable case yield a branching tree that is different in law. To explain this anomaly we construct a family of martingales whose backbones have multiple limit laws.
Momentum conserving Brownian dynamics propagator for complex soft matter fluids.
Padding, J T; Briels, W J
2014-12-28
We present a Galilean invariant, momentum conserving first order Brownian dynamics scheme for coarse-grained simulations of highly frictional soft matter systems. Friction forces are taken to be with respect to moving background material. The motion of the background material is described by locally averaged velocities in the neighborhood of the dissolved coarse coordinates. The velocity variables are updated by a momentum conserving scheme. The properties of the stochastic updates are derived through the Chapman-Kolmogorov and Fokker-Planck equations for the evolution of the probability distribution of coarse-grained position and velocity variables, by requiring the equilibrium distribution to be a stationary solution. We test our new scheme on concentrated star polymer solutions and find that the transverse current and velocity time auto-correlation functions behave as expected from hydrodynamics. In particular, the velocity auto-correlation functions display a long time tail in complete agreement with hydrodynamics.
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.
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.
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.
On the first-passage time of integrated Brownian motion
Directory of Open Access Journals (Sweden)
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.
BROWNIAN HEAT TRANSFER ENHANCEMENT IN THE TURBULENT REGIME
Directory of Open Access Journals (Sweden)
Suresh Chandrasekhar
2016-08-01
Full Text Available The paper presents convection heat transfer of a turbulent flow Al2O3/water nanofluid in a circular duct. The duct is a under constant and uniform heat flux. The paper computationally investigates the system’s thermal behavior in a wide range of Reynolds number and also volume concentration up to 6%. To obtain the nanofluid thermophysical properties, the Hamilton-Crosser model along with the Brownian motion effect are utilized. Then the thermal performance of the system with the nanofluid is compared to the conventional systems which use water as the working fluid. The results indicate that the use of nanofluid of 6% improves the heat transfer rate up to 36.8% with respect to pure water. Therefore, using the Al2O3/water nanofluid instead of water can be a great choice when better heat transfer is needed.
A Stability Result for Stochastic Differential Equations Driven by Fractional Brownian Motions
Directory of Open Access Journals (Sweden)
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.
Effect of Brownian Coagulation on the Liquid-liquid Decomposition in Gas-atomized Alloy Drops
Institute of Scientific and Technical Information of China (English)
Jiuzhou ZHAO; Lingling GAO; Jie HE; L.Ratke
2006-01-01
Modeling and simulation have been carried out for Al-Pb alloys to investigate the Brownian coagulation effect on the microstructure development in a gas-atomized drop during the liquid-liquid decomposition.The results indicate that Brownian coagulation has a weak effect on the nucleation and a relatively strong effect on coarsening the minority phase droplets. The influence of Brownian coagulation on the liquid-liquid decomposition decreases with the increase in the diameter (or the decrease in the cooling rate) of the atomized drop.
Kekre, Rahul; Butler, Jason E; Ladd, Anthony J C
2010-07-01
This paper compares results from lattice-Boltzmann and brownian-dynamics simulations of polymer migration in confined flows bounded by planar walls. We have considered both a uniform shear rate and a constant pressure gradient. Lattice-Boltzmann simulations of the center-of-mass distribution agree quantitatively with brownian-dynamics results, contradicting previously published results. The mean end-to-end distance of the extended polymer is more sensitive to grid resolution Δx and time-step Δt. Nevertheless, for sufficiently small Δx and Δt, convergent results for the polymer stretch are obtained which agree with brownian dynamics within statistical uncertainties. The brownian-dynamics simulations incorporate a mobility matrix for a confined polymer that is both symmetric and positive definite for all physically accessible configurations.
Mean Mobility and Rotation Number in Time-inhomogenous Brownian Ratchets
Institute of Scientific and Technical Information of China (English)
张雪娟
2004-01-01
@@ Recently, Brownian ratchets have attracted considerable attention due to their abitlity to realize a unidirectional transport only throught the use of a proper asymmetry and thermal noise fluctuation, for recent review, see[1,2].
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
Directory of Open Access Journals (Sweden)
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.
Communication: Green-Kubo approach to the average swim speed in active Brownian systems
Sharma, A.; Brader, J. M.
2016-10-01
We develop an exact Green-Kubo formula relating nonequilibrium averages in systems of interacting active Brownian particles to equilibrium time-correlation functions. The method is applied to calculate the density-dependent average swim speed, which is a key quantity entering coarse grained theories of active matter. The average swim speed is determined by integrating the equilibrium autocorrelation function of the interaction force acting on a tagged particle. Analytical results are validated using Brownian dynamics simulations.
The Pricing of Vulnerable Options in a Fractional Brownian Motion Environment
Directory of Open Access Journals (Sweden)
Chao Wang
2015-01-01
Full Text Available Under the assumption of the stock price, interest rate, and default intensity obeying the stochastic differential equation driven by fractional Brownian motion, the jump-diffusion model is established for the financial market in fractional Brownian motion setting. With the changes of measures, the traditional pricing method is simplified and the general pricing formula is obtained for the European vulnerable option with stochastic interest rate. At the same time, the explicit expression for it comes into being.
Asian Option Pricing with Monotonous Transaction Costs under Fractional Brownian Motion
Directory of Open Access Journals (Sweden)
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.
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.
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.
Modelling Collective Opinion Formation by Means of Active Brownian Particles
Schweitzer, F; Schweitzer, Frank; Holyst, Janusz
1999-01-01
The concept of active Brownian particles is used to model a collective opinion formation process. It is assumed that individuals in community create a two-component communication field that influences the change of opinions of other persons and/or can induce their migration. The communication field is described by a reaction-diffusion equation, meaning that it has a certain lifetime, which models memory effects, further it can spread out in the community. Within our stochastic approach, the opinion change of the individuals is described by a master equation, while the migration is described by a set of Langevin equations, coupled by the communication field. In the mean-field limit which holds for fast communication, we derive a critical population size, above which the community separates into a majority and a minority with opposite opinions. The existence of external support (e.g. from mass media) can change the ratio between minority and majority, until above a critical external support the supported subpop...
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.
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.
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.
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
From Brownian Dynamics to Markov Chain: An Ion Channel Example
Chen, Wan
2014-02-27
A discrete rate theory for multi-ion channels is presented, in which the continuous dynamics of ion diffusion is reduced to transitions between Markovian discrete states. In an open channel, the ion permeation process involves three types of events: an ion entering the channel, an ion escaping from the channel, or an ion hopping between different energy minima in the channel. The continuous dynamics leads to a hierarchy of Fokker-Planck equations, indexed by channel occupancy. From these the mean escape times and splitting probabilities (denoting from which side an ion has escaped) can be calculated. By equating these with the corresponding expressions from the Markov model, one can determine the Markovian transition rates. The theory is illustrated with a two-ion one-well channel. The stationary probability of states is compared with that from both Brownian dynamics simulation and the hierarchical Fokker-Planck equations. The conductivity of the channel is also studied, and the optimal geometry maximizing ion flux is computed. © 2014 Society for Industrial and Applied Mathematics.
Brownian aggregation rate of colloid particles with several active sites
Energy Technology Data Exchange (ETDEWEB)
Nekrasov, Vyacheslav M.; Yurkin, Maxim A.; Chernyshev, Andrei V., E-mail: chern@ns.kinetics.nsc.ru [Institute of Chemical Kinetics and Combustion, Institutskaya 3, 630090 Novosibirsk (Russian Federation); Physics Department, Novosibirsk State University, Pirogova 2, 630090 Novosibirsk (Russian Federation); Polshchitsin, Alexey A. [Institute of Chemical Kinetics and Combustion, Institutskaya 3, 630090 Novosibirsk (Russian Federation); JSC “VECTOR-BEST”, PO BOX 492, Novosibirsk 630117 (Russian Federation); Yakovleva, Galina E. [JSC “VECTOR-BEST”, PO BOX 492, Novosibirsk 630117 (Russian Federation); Maltsev, Valeri P. [Institute of Chemical Kinetics and Combustion, Institutskaya 3, 630090 Novosibirsk (Russian Federation); Physics Department, Novosibirsk State University, Pirogova 2, 630090 Novosibirsk (Russian Federation); Department of Preventive Medicine, Novosibirsk State Medical University, Krasny Prospect 52, 630091 Novosibirsk (Russian Federation)
2014-08-14
We theoretically analyze the aggregation kinetics of colloid particles with several active sites. Such particles (so-called “patchy particles”) are well known as chemically anisotropic reactants, but the corresponding rate constant of their aggregation has not yet been established in a convenient analytical form. Using kinematic approximation for the diffusion problem, we derived an analytical formula for the diffusion-controlled reaction rate constant between two colloid particles (or clusters) with several small active sites under the following assumptions: the relative translational motion is Brownian diffusion, and the isotropic stochastic reorientation of each particle is Markovian and arbitrarily correlated. This formula was shown to produce accurate results in comparison with more sophisticated approaches. Also, to account for the case of a low number of active sites per particle we used Monte Carlo stochastic algorithm based on Gillespie method. Simulations showed that such discrete model is required when this number is less than 10. Finally, we applied the developed approach to the simulation of immunoagglutination, assuming that the formed clusters have fractal structure.
Brownian dynamics simulations of nanosheet solutions under shear.
Xu, Yueyi; Green, Micah J
2014-07-14
The flow-induced conformation dynamics of nanosheets are simulated using a Brownian Dynamics (BD) formulation applied to a bead-rod sheetlike molecular model. This is the first-ever use of BD to simulate flow-induced dynamics of two-dimensional structures. Using this framework, we simulate dilute suspensions of coarse-grained nanosheets and compute conformation dynamics for simple shear flow. The data show power law scaling relationships between nanosheet parameters (such as bending moduli and molecular weight) and the resulting intrinsic viscosity and conformation. For nonzero bending moduli, an effective dimension of 2.77 at equilibrium is calculated from the scaling relationship between radius of gyration and molecular weight. We also find that intrinsic viscosity varies with molecular weight with an exponent of 2.12 ± 0.23; this dependence is significantly larger than those found for linear polymers. Weak shear thinning is observed at high Weissenberg number (Wi). This simulation method provides a computational basis for developing manufacturing processes for nanosheet-derived materials by relating flow forces and nanosheet parameters to the resulting material morphology.
From Brownian Dynamics to Markov Chain: an Ion Channel Example
Chen, Wan; Chapman, S Jonathan
2012-01-01
A discrete rate theory for general multi-ion channels is presented, in which the continuous dynamics of ion diffusion is reduced to transitions between Markovian discrete states. In an open channel, the ion permeation process involves three types of events: an ion entering the channel, an ion escaping from the channel, or an ion hopping between different energy minima in the channel. The continuous dynamics leads to a hierarchy of Fokker-Planck equations, indexed by channel occupancy. From these the mean escape times and splitting probabilities (denoting from which side an ion has escaped) can be calculated. By equating these with the corresponding expressions from the Markov model the Markovian transition rates can be determined. The theory is illustrated with a two-ion one-well channel. The stationary probability of states is compared with that from both Brownian dynamics simulation and the hierarchical Fokker-Planck equations. The conductivity of the channel is also studied, and the optimal geometry maximi...
Intermediate scattering function of an anisotropic active Brownian particle
Kurzthaler, Christina; Leitmann, Sebastian; Franosch, Thomas
2016-10-01
Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations.
Virial pressure in systems of spherical active Brownian particles.
Winkler, Roland G; Wysocki, Adam; Gompper, Gerhard
2015-09-01
The pressure of suspensions of self-propelled objects is studied theoretically and by simulation of spherical active Brownian particles (ABPs). We show that for certain geometries, the mechanical pressure as force/area of confined systems can be equally expressed by bulk properties, which implies the existence of a nonequilibrium equation of state. Exploiting the virial theorem, we derive expressions for the pressure of ABPs confined by solid walls or exposed to periodic boundary conditions. In both cases, the pressure comprises three contributions: the ideal-gas pressure due to white-noise random forces, an activity-induced pressure ("swim pressure"), which can be expressed in terms of a product of the bare and a mean effective particle velocity, and the contribution by interparticle forces. We find that the pressure of spherical ABPs in confined systems explicitly depends on the presence of the confining walls and the particle-wall interactions, which has no correspondence in systems with periodic boundary conditions. Our simulations of three-dimensional ABPs in systems with periodic boundary conditions reveal a pressure-concentration dependence that becomes increasingly nonmonotonic with increasing activity. Above a critical activity and ABP concentration, a phase transition occurs, which is reflected in a rapid and steep change of the pressure. We present and discuss the pressure for various activities and analyse the contributions of the individual pressure components.
Current control in inertial Brownian motors by noise recycling
Jia, Zheng-Lin; Li, Kai-Yi; Li, Chun; Yang, Chun-Yan; Mei, Dong-Cheng
2015-03-01
The transport properties of an inertial Brownian motor were numerically studied in the presence of recycled noise, which is obtained by re-injecting a fraction of the primary white noise after a processing time, being introduced into the system in a multiplicative way. The simulation results indicate that various parameters such as the external driving force, the friction coefficient, the mass of the particle, the recycling strength, and the delay time can induce the current reversal phenomenon when the sign of the recycling strength is in agreement with the sign of the external bias force, otherwise the current reversal cannot be observed. Additionally, the asymptotic mean velocity as a function of the delay time of the recycled noise always shows a resonance-like behavior with the presence of a maximum current. These results demonstrate that the delay time and the recycling strength of the recycled noise can be used as the feasible and flexible control parameters for the amplitude and direction of the current.
Beyond multifractional Brownian motion: new stochastic models for geophysical modelling
Directory of Open Access Journals (Sweden)
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.
DEFF Research Database (Denmark)
Staunstrup, Jørgen
1998-01-01
This paper proposes that Interface Consistency is an important issue for the development of modular designs. Byproviding a precise specification of component interfaces it becomes possible to check that separately developedcomponents use a common interface in a coherent matter thus avoiding a very...... significant source of design errors. Awide range of interface specifications are possible, the simplest form is a syntactical check of parameter types.However, today it is possible to do more sophisticated forms involving semantic checks....
DEFF Research Database (Denmark)
Ravn, Anders P.; Staunstrup, Jørgen
1994-01-01
This paper proposes a model for specifying interfaces between concurrently executing modules of a computing system. The model does not prescribe a particular type of communication protocol and is aimed at describing interfaces between both software and hardware modules or a combination of the two....... The model describes both functional and timing properties of an interface...
Delorme, Mathieu; Le Doussal, Pierre; Wiese, Kay Jörg
2016-05-01
The Brownian force model is a mean-field model for local velocities during avalanches in elastic interfaces of internal space dimension d , driven in a random medium. It is exactly solvable via a nonlinear differential equation. We study avalanches following a kick, i.e., a step in the driving force. We first recall the calculation of the distributions of the global size (total swept area) and of the local jump size for an arbitrary kick amplitude. We extend this calculation to the joint density of local and global sizes within a single avalanche in the limit of an infinitesimal kick. When the interface is driven by a single point, we find new exponents τ0=5 /3 and τ =7 /4 , depending on whether the force or the displacement is imposed. We show that the extension of a "single avalanche" along one internal direction (i.e., the total length in d =1 ) is finite, and we calculate its distribution following either a local or a global kick. In all cases, it exhibits a divergence P (ℓ ) ˜ℓ-3 at small ℓ . Most of our results are tested in a numerical simulation in dimension d =1 .
Delorme, Mathieu; Le Doussal, Pierre; Wiese, Kay Jörg
2016-05-01
The Brownian force model is a mean-field model for local velocities during avalanches in elastic interfaces of internal space dimension d, driven in a random medium. It is exactly solvable via a nonlinear differential equation. We study avalanches following a kick, i.e., a step in the driving force. We first recall the calculation of the distributions of the global size (total swept area) and of the local jump size for an arbitrary kick amplitude. We extend this calculation to the joint density of local and global sizes within a single avalanche in the limit of an infinitesimal kick. When the interface is driven by a single point, we find new exponents τ_{0}=5/3 and τ=7/4, depending on whether the force or the displacement is imposed. We show that the extension of a "single avalanche" along one internal direction (i.e., the total length in d=1) is finite, and we calculate its distribution following either a local or a global kick. In all cases, it exhibits a divergence P(ℓ)∼ℓ^{-3} at small ℓ. Most of our results are tested in a numerical simulation in dimension d=1.
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.
Kanatsu, Youhei; Sato, Masahide
2015-01-01
Large grains of a close-packed colloidal crystal have been experimentally shown to form in an inverted pyramidal pit by sedimentation [S. Matsuo et al., Appl. Phys. Lett. 82, 4285 (2003)]. Keeping this experiment in mind, we study the crystallization of Brownian particles. We carry out Brownian dynamics simulations in an inverted pyramidal-shaped container. The Brownian particles settle out toward the apex of the container by a uniform external force. If the apex angle is suitable, large grai...
Extremes of N vicious walkers for large N: application to the directed polymer and KPZ interfaces
Schehr, Gregory
2012-01-01
We compute the joint probability distribution function (jpdf) P_N(M, \\tau_M) of the maximum M and its position \\tau_M for N non-intersecting Brownian excursions, on the unit time interval, in the large N limit. For N \\to \\infty, this jpdf is peaked around M = \\sqrt{2N} and \\tau_M = 1/2, while the typical fluctuations behave for large N like M - \\sqrt{2N} \\propto s N^{-1/6} and \\tau_M - 1/2 \\propto w N^{-1/3} where s and w are correlated random variables. One obtains an explicit expression of the limiting jpdf P(s,w) in terms of the Tracy-Widom distribution for the Gaussian Orthogonal Ensemble (GOE) of Random Matrix Theory and the psi-function for the Hastings-McLeod solution to the Painlev\\'e II equation. Our result yields, up to a rescaling of the random variables s and w, an expression for the jpdf of the maximum and its position for the Airy_2 process minus a parabola. This latter describes the fluctuations in many different physical systems belonging to the Kardar-Parisi-Zhang (KPZ) universality class in ...
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).
Microstructure from simulated Brownian suspension flows at large shear rate
Morris, Jeffrey F.; Katyal, Bhavana
2002-06-01
Pair microstructure of concentrated Brownian suspensions in simple-shear flow is studied by sampling of configurations from dynamic simulations by the Stokesian Dynamics technique. Simulated motions are three dimensional with periodic boundary conditions to mimic an infinitely extended suspension. Hydrodynamic interactions through Newtonian fluid and Brownian motion are the only physical influences upon the motion of the monodisperse hard-sphere particles. The dimensionless parameters characterizing the suspension are the particle volume fraction and Péclet number, defined, respectively, as φ=(4π/3)na3 with n the number density and a the sphere radius, and Pe=6πηγ˙a3/kT with η the fluid viscosity, γ˙ the shear rate, and kT the thermal energy. The majority of the results reported are from simulations at Pe=1000; results of simulations at Pe=1, 25, and 100 are also reported for φ=0.3 and φ=0.45. The pair structure is characterized by the pair distribution function, g(r)=P1|1(r)/n, where P1|1(r) is the conditional probability of finding a pair at a separation vector r. The structure under strong shearing exhibits an accumulation of pair probability at contact, and angular distortion (from spherical symmetry at Pe=0), with both effects increasing with Pe. Flow simulations were performed at Pe=1000 for eight volume fractions in the range 0.2⩽φ⩽0.585. For φ=0.2-0.3, the pair structure at contact, g(|r|=2)≡g(2), is found to exhibit a single region of strong correlation, g(2)≫1, at points around the axis of compression, with a particle-deficient wake in the extensional zones. A qualitative change in microstructure is observed between φ=0.3 and φ=0.37. For φ⩾0.37, the maximum g(2) lies at points in the shear plane nearly on the x axis of the bulk simple shear flow Ux=γ˙y, while at smaller φ, the maximum g(2) lies near the compressional axis; long-range string ordering is not observed. For φ=0.3 and φ=0.45, g(2)˜Pe0.7 for 1⩽Pe⩽1000, a
A Brownian Dynamics Approach to ESR Line Shape Calculations
Wright, Matthew P.
The work presented in this thesis uses a Monte Carlo technique to simulate spectra for 14N spin-labels and 15N spin labels. The algorithm presented here also has the capability to produce simulated spectra for any admixture of 14N and 15N. The algorithm makes use of `iterative loops' to model Brownian rotational diffusion and for the repeated evaluation of the spectral correlation function (relaxation function). The method described in this work starts with a derivation of an angular dependent "Spin Hamiltonian" that when diagonalized yields orientation dependent eigenvalues. The resulting eigenvalue equations are later used to calculate the energy trajectories of a nitroxide spin-label undergoing rotational diffusion. The energy trajectories are then used to evaluate the relaxation function. The absorption spectrum is obtained by applying a Fourier transform to the relaxation function. However, the application of the Fourier transform to the relaxation function produces "leakage" effects that manifest as spurious peaks in the first derivative spectrum. To counter "leakage" effects a data windowing function was applied to the relaxation function prior to the Fourier transform. In order to test the accuracy of this algorithm, simulated spectra for 14N, and 15N spin labels diffusing in a glycerol-water mixture as well as a 14N-15N admixture diffusing in the same solvent were produced and compared to experimental spectra. An attempt to quantify the level of agreement was made by calculating the mean square residual of the simulated and experimental spectra. The main spectral features were reproduced with reasonable fidelity by the simulated spectra.
Two-component Brownian coagulation: Monte Carlo simulation and process characterization
Institute of Scientific and Technical Information of China (English)
Haibo Zhao; Chu guang Zheng
2011-01-01
The compositional distribution within aggregates of a given size is essential to the functionality of composite aggregates that are usually enlarged by rapid Brownian coagulation.There is no analytical solution for the process of such two-component systems.Monte Carlo method is an effective numerical approach for two-component coagulation.In this paper,the differentially weighted Monte Carlo method is used to investigate two-component Brownian coagulation,respectively,in the continuum regime,the freemolecular regime and the transition regime.It is found that ( 1 ) for Brownian coagulation in the continuum regime and in the free-molecular regime,the mono-variate compositional distribution,i.e.,the number density distribution function of one component amount (in the form of volume of the component in aggregates) satisfies self-preserving form the same as particle size distribution in mono-component Brownian coagulation; (2) however,for Brownian coagulation in the transition regime the mono-variate compositional distribution cannot reach self-similarity; and (3) the bivariate compositional distribution,i.e.,the combined number density distribution function of two component amounts in the three regimes satisfies a semi self-preserving form.Moreover,other new features inherent to aggregative mixing are also demonstrated; e.g.,the degree of mixing between components,which is largely controlled by the initial compositional mass fraction,improves as aggregate size increases.
Directory of Open Access Journals (Sweden)
Rajiv Joshi
2013-01-01
Full Text Available Interface dermatitis includes diseases in which the primary pathology involves the dermo-epidermal junction. The salient histological findings include basal cell vacuolization, apoptotic keratinocytes (colloid or Civatte bodies, and obscuring of the dermo-epidermal junction by inflammatory cells. Secondary changes of the epidermis and papillary dermis along with type, distribution and density of inflammatory cells are used for the differential diagnoses of the various diseases that exhibit interface changes. Lupus erythematosus, dermatomyositis, lichen planus, graft versus host disease, erythema multiforme, fixed drug eruptions, lichen striatus, and pityriasis lichenoides are considered major interface diseases. Several other diseases (inflammatory, infective, and neoplastic may show interface changes.
Holographic Brownian Motion in Three-Dimensional Gödel Black Hole
Directory of Open Access Journals (Sweden)
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.
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.
Financial Brownian Particle in the Layered Order-Book Fluid and Fluctuation-Dissipation Relations
Yura, Yoshihiro; Takayasu, Hideki; Sornette, Didier; Takayasu, Misako
2014-03-01
We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of comprehensive market data enables us to identify all motions of the fluid particles. Correlations between the motions of the Brownian particle and its surrounding fluid particles reflect specific layering interactions; in the inner layer the correlation is strong and with short memory, while in the outer layer it is weaker and with long memory. By interpreting and estimating the contribution from the outer layer as a drag resistance, we demonstrate the validity of the fluctuation-dissipation relation in this nonmaterial Brownian motion process.
Statistical Properties of Thermal Noise Driving the Brownian Particles in Fluids
Directory of Open Access Journals (Sweden)
Tóthová Jana
2016-01-01
Full Text Available In several recent works high-resolution interferometric detection allowed to study the Brownian motion of optically trapped microparticles in air and fluids. The observed positional fluctuations of the particles are well described by the generalized Langevin equation with the Boussinesq-Basset “history force” instead of the Stokes friction, which is valid only for the steady motion. Recently, also the time correlation function of the thermal random force Fth driving the Brownian particles through collisions with the surrounding molecules has been measured. In the present contribution we propose a method to describe the statistical properties of Fth in incompressible fluids. Our calculations show that the time decay of the correlator 〈Fth(tFth(0〉 is significantly slower than that found in the literature. It is also shown how the “color” of the thermal noise can be determined from the measured positions of the Brownian particles.
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.
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.
Steady nanofluid flow between parallel plates considering thermophoresis and Brownian effects
Directory of Open Access Journals (Sweden)
M. Sheikholeslami
2016-10-01
Full Text Available In this article, heat and mass transfer behavior of steady nanofluid flow between parallel plates in the presence of uniform magnetic field is studied. The important effect of Brownian motion and thermophoresis has been included in the model of nanofluid. The governing equations are solved via the Differential Transformation Method. The validity of this method was verified by comparison of previous work which is done for viscous fluid. The analysis is carried out for different parameters namely: viscosity parameter, Magnetic parameter, thermophoretic parameter and Brownian parameter. Results reveal that skin friction coefficient enhances with rise of viscosity and Magnetic parameters. Also it can be found that Nusselt number augments with an increase of viscosity parameters but it decreases with augment of Magnetic parameter, thermophoretic parameter and Brownian parameter.
Probing Brownian relaxation in water-glycerol mixtures using magnetic hyperthermia
Nemala, Humeshkar; Milgie, Michael; Wadehra, Anshu; Thakur, Jagdish; Naik, Vaman; Naik, Ratna
2013-03-01
Generation of heat by magnetic nanoparticles in the presence of an external oscillating magnetic field is known as magnetic hyperthermia (MHT). This heat is generated by two mechanisms: the Neel relaxation and Brownian relaxation. While the internal spin relaxation of the nanoparticles known as Neel relaxation is largely dependent on the magnetic properties of the nanoparticles, the physical motion of the particle or the Brownian relaxation is largely dependent on the viscous properties of the carrier liquid. The MHT properties of dextran coated iron oxide nanoparticles have been investigated at a frequency of 400KHz. To understand the influence of Brownian relaxation on heating, we probe the MHT properties of these ferrofluids in water-glycerol mixtures of varying viscosities. The heat generation is quantified using the specific absorption rate (SAR) and its maximum at a particular temperature is discussed with reference to the viscosity.
Brownian ratchets from statistical physics to bio and nano-motors
Cubero, David
2016-01-01
Illustrating the development of Brownian ratchets, from their foundations, to their role in the description of life at the molecular scale and in the design of artificial nano-machinery, this text will appeal to both advanced graduates and researchers entering the field. Providing a self-contained introduction to Brownian ratchets, devices which rectify microscopic fluctuations, Part I avoids technicalities and sets out the broad range of physical systems where the concept of ratchets is relevant. Part II supplies a single source for a complete and modern theoretical analysis of ratchets in regimes such as classical vs quantum and stochastic vs deterministic, and in Part III readers are guided through experimental developments in different physical systems, each highlighting a specific unique feature of ratchets. The thorough and systematic approach to the topic ensures that this book provides a complete guide to Brownian ratchets for newcomers and established researchers in physics, biology and biochemistry.
Brownian motion of a charged test particle in vacuum between two conducting plates
Yu, Hongwei; Chen, Jun
2004-12-01
The Brownian motion of a charged test particle caused by quantum electromagnetic vacuum fluctuations between two perfectly conducting plates is examined and the mean squared fluctuations in the velocity and position of the test particle are calculated. Our results show that the Brownian motion in the direction normal to the plates is reinforced in comparison to that in the single plate case. The effective temperature associated with this normal Brownian motion could be three times as large as that in the single plate case. However, the negative dispersions for the velocity and position in the longitudinal directions, which could be interpreted as reducing the quantum uncertainties of the particle, acquire positive corrections due to the presence of the second plate, and are thus weakened.
Brownian motion of a charged test particle in vacuum between two conducting plates
Yu, H; Yu, Hongwei; Chen, Jun
2004-01-01
The Brownian motion of a charged test particle caused by quantum electromagnetic vacuum fluctuations between two perfectly conducting plates is examined and the mean squared fluctuations in the velocity and position of the test particle are calculated. Our results show that the Brownian motion in the direction normal to the plates is reinforced in comparison to that in the single-plate case. The effective temperature associated with this normal Brownian motion could be three times as large as that in the single-plate case. However, the negative dispersions for the velocity and position in the longitudinal directions, which could be interpreted as reducing the quantum uncertainties of the particle, acquire positive corrections due to the presence of the second plate, and are thus weakened.
(Quantum) Fractional Brownian Motion and Multifractal Processes under the Loop of a Tensor Networks
Descamps, Benoît
2016-01-01
We derive fractional Brownian motion and stochastic processes with multifractal properties using a framework of network of Gaussian conditional probabilities. This leads to the derivation of new representations of fractional Brownian motion. These constructions are inspired from renormalization. The main result of this paper consists of constructing each increment of the process from two-dimensional gaussian noise inside the light-cone of each seperate increment. Not only does this allows us to derive fractional Brownian motion, we can introduce extensions with multifractal flavour. In another part of this paper, we discuss the use of the multi-scale entanglement renormalization ansatz (MERA), introduced in the study critical systems in quantum spin lattices, as a method for sampling integrals with respect to such multifractal processes. After proper calibration, a MERA promises the generation of a sample of size $N$ of a multifractal process in the order of $O(N\\log(N))$, an improvement over the known method...
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.
On-chip Brownian relaxation measurements of magnetic nanobeads in the time domain
DEFF Research Database (Denmark)
Østerberg, Frederik Westergaard; Rizzi, Giovanni; Hansen, Mikkel Fougt
2013-01-01
magnetic fields are needed. First, the method is demonstrated on Brownian relaxation measurements of beads with nominal sizes of 40, 80, 130, and 250 nm. The results are found to compare well to those obtained by an already established measurement technique in the frequency domain. Next, we demonstrate......We present and demonstrate a new method for on-chip Brownian relaxation measurements on magnetic nanobeads in the time domain using magnetoresistive sensors. The beads are being magnetized by the sensor self-field arising from the bias current passed through the sensors and thus no external...... the time and frequency domain methods on Brownian relaxation detection of clustering of streptavidin coated magnetic beads in the presence of different concentrations of biotin-conjugated bovine serum albumin and obtain comparable results. In the time domain, a measurement is carried out in less than 30 s...
Non-Brownian diffusion in lipid membranes: Experiments and simulations.
Metzler, R; Jeon, J-H; Cherstvy, A G
2016-10-01
The dynamics of constituents and the surface response of cellular membranes-also in connection to the binding of various particles and macromolecules to the membrane-are still a matter of controversy in the membrane biophysics community, particularly with respect to crowded membranes of living biological cells. We here put into perspective recent single particle tracking experiments in the plasma membranes of living cells and supercomputing studies of lipid bilayer model membranes with and without protein crowding. Special emphasis is put on the observation of anomalous, non-Brownian diffusion of both lipid molecules and proteins embedded in the lipid bilayer. While single component, pure lipid bilayers in simulations exhibit only transient anomalous diffusion of lipid molecules on nanosecond time scales, the persistence of anomalous diffusion becomes significantly longer ranged on the addition of disorder-through the addition of cholesterol or proteins-and on passing of the membrane lipids to the gel phase. Concurrently, experiments demonstrate the anomalous diffusion of membrane embedded proteins up to macroscopic time scales in the minute time range. Particular emphasis will be put on the physical character of the anomalous diffusion, in particular, the occurrence of ageing observed in the experiments-the effective diffusivity of the measured particles is a decreasing function of time. Moreover, we present results for the time dependent local scaling exponent of the mean squared displacement of the monitored particles. Recent results finding deviations from the commonly assumed Gaussian diffusion patterns in protein crowded membranes are reported. The properties of the displacement autocorrelation function of the lipid molecules are discussed in the light of their appropriate physical anomalous diffusion models, both for non-crowded and crowded membranes. In the last part of this review we address the upcoming field of membrane distortion by elongated membrane
DEFF Research Database (Denmark)
Thomsen, Bodil Marie Stavning
2015-01-01
and memories. From a transvisual perspective, the question is whether or not these (by now realized) diagrammatic modes involving the body in ubiquitous global media can be analysed in terms of the affects and events created in concrete interfaces. The examples used are filmic as felt sensations...... of an interface are invisible and not easy to describe....
DEFF Research Database (Denmark)
Hansen, Klaus Marius
2001-01-01
Fluid interaction, interaction by the user with the system that causes few breakdowns, is essential to many user interfaces. We present two concrete software systems that try to support fluid interaction for different work practices. Furthermore, we present specificity, generality, and minimality...... as design goals for fluid interfaces....
DEFF Research Database (Denmark)
Pold, Søren
2005-01-01
This article argues for seeing the interface as an important representational and aesthetic form with implications for postmodern culture and digital aesthetics. The interface emphasizes realism due in part to the desire for transparency in Human-Computer Interaction (HCI) and partly to the devel...
An Approach to Enhance the Efficiency of a Brownian Heat Engine
Institute of Scientific and Technical Information of China (English)
ZHANG Yan-Ping; HE Ji-Zhou; XIAO Yu-Ling
2011-01-01
A Brownian microscopic heat engine, driven by temperature difference and consisting of a Brownian particle moving in a sawtooth potential with an external load, is investigated. The heat Hows, driven by both potential and kinetic energies, are taken into account. Based on the master equation, the expressions for efficiency and power output are derived analytically, and performance characteristic curves are plotted. It is shown that the heat How via the kinetic energy of the particle decreases. The efficiency of the engine is enhanced, but the power output reduces as the a shape parameter of the sawtooth potential increases. The influence of the a shape parameter on efficiency and power output is then analyzed in detail.%A Brownian microscopic heat engine,driven by temperature difference and consisting of a Brownian particle moving in a sawtooth potential with an external load,is investigated.The heat flows,driven by both potential and kinetic energies,are taken into account.Based on the master equation,the expressions for efficiency and power output are derived analytically,and performance characteristic curves are plotted.It is shown that the heat flow via the kinetic energy of the particle decreases.The efficiency of the engine is enhanced,but the power output reduces as the α shape parameter of the sawtooth potential increases.The influence of the α shape parameter on efficiency and power output is then analyzed in detail.Like the Carnot cycle,the Brownian heat engine can extract work from the temperature difference between heat reservoirs,where the Brownian working material operates as a transducer of thermal energy into mechanical work.In the last few decades,the study of Brownian heat engines has received considerable attention,not only for the construction of the miniaturized engine that helps us utilize energy resources at microscopic scales,but also for a better understanding of nonequilibrium statistical physics.[1-3] The thermodynamic properties of the
Feedback control of two-headed Brownian motors in flashing ratchet potential
Institute of Scientific and Technical Information of China (English)
Zhao A-Ke; Zhang Hong-Wei; Li Yu-Xiao
2010-01-01
We presented a detailed investigation on the movement of two-headed Brownian motors in an asymmetric potential under a feedback control. By numerical simulations the direct current is obtained. The current is periodic in the initial length of spring. There is an optimal value of the spring constant. And the dependence of the current on the opposing force is reversed. Then we found that when the change of the temperature and the opposing force have optimal values, the Brownian motors can also obtain the optimal efficiency.
Brownian agents and active particles collective dynamics in the natural and social sciences
Schweitzer, Frank
2007-01-01
""This book lays out a vision for a coherent framework for understanding complex systems"" (from the foreword by J. Doyne Farmer). By developing the genuine idea of Brownian agents, the author combines concepts from informatics, such as multiagent systems, with approaches of statistical many-particle physics. This way, an efficient method for computer simulations of complex systems is developed which is also accessible to analytical investigations and quantitative predictions. The book demonstrates that Brownian agent models can be successfully applied in many different contexts, ranging from
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.
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...
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.
An elementary singularity-free Rotational Brownian Dynamics algorithm for anisotropic particles
Energy Technology Data Exchange (ETDEWEB)
Ilie, Ioana M.; Briels, Wim J. [Computational Biophysics, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands); MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands); Otter, Wouter K. den, E-mail: w.k.denotter@utwente.nl [Computational Biophysics, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands); MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands); Multi Scale Mechanics, Faculty of Engineering Technology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands)
2015-03-21
Brownian Dynamics is the designated technique to simulate the collective dynamics of colloidal particles suspended in a solution, e.g., the self-assembly of patchy particles. Simulating the rotational dynamics of anisotropic particles by a first-order Langevin equation, however, gives rise to a number of complications, ranging from singularities when using a set of three rotational coordinates to subtle metric and drift corrections. Here, we derive and numerically validate a quaternion-based Rotational Brownian Dynamics algorithm that handles these complications in a simple and elegant way. The extension to hydrodynamic interactions is also discussed.
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).
On-chip measurements of Brownian relaxation vs. concentration of 40nm magnetic beads
DEFF Research Database (Denmark)
Østerberg, Frederik Westergaard; Rizzi, Giovanni; Hansen, Mikkel Fougt
2012-01-01
are needed as the beads are magnetized by the field generated by the applied sensor bias current. We show that the Brownian relaxation frequency can be extracted from fitting the Cole-Cole model to measurements for bead concentrations of 64 mu g/ml or higher and that the measured dynamic magnetic response......We present on-chip Brownian relaxation measurements on a logarithmic dilution series of 40 nm beads dispersed in water with bead concentrations between 16 mu g/ml and 4000 mu g/ml. The measurements are performed using a planar Hall effect bridge sensor at frequencies up to 1 MHz. No external fields...
DEFF Research Database (Denmark)
Holbøll, Joachim T.; Henriksen, Mogens; Nilson, Jesper K.;
1999-01-01
The wide use of solid insulating materials combinations in combinations has introduced problems in the interfaces between components. The most common insulating materials are cross-linked polyethylene (XLPE), silicone rubber (SIR) and ethylene-propylene rubbers (EPR). Assemblies of these materials...... have caused major failures. In the Netherlands, a major black out was caused by interface problems in 150kV cable terminations, causing a cascade of breakdowns. There is a need to investigate the reasons for this and other similar breakdowns.The major problem is expected to lie in the interface between...... two different materials. Environmental influence, surface treatment, defects in materials and interface, design, pressure and rubbing are believed to have an effect on interface degradation. These factors are believed to increase the possibility of partial discharges (PD). PD will, with time, destroy...
Improved liquid-solid-gas interface deposition of nanoparticle thin films
Institute of Scientific and Technical Information of China (English)
Diao Jia-Jie; Chen Guang-De; Qiu Fu-Sheng; Yan Guo-Jun
2004-01-01
A liquid-solid-gas interface deposition method to prepare nanoparticle thin films is presented in this paper. The nanoparticles in the part of suspension located close to the solid-liquid-gas interface grow on the substrate under the influence of interface force when the partially immersed substrate moves relatively to the suspension. By using statistical theory of the Brownian motion, growth equations for mono-component and multi-component nanoparticle thin films are obtained and some parameters for deposition process are discussed.
Vears, R E
2014-01-01
Microprocessor Interfacing provides the coverage of the Business and Technician Education Council level NIII unit in Microprocessor Interfacing (syllabus U86/335). Composed of seven chapters, the book explains the foundation in microprocessor interfacing techniques in hardware and software that can be used for problem identification and solving. The book focuses on the 6502, Z80, and 6800/02 microprocessor families. The technique starts with signal conditioning, filtering, and cleaning before the signal can be processed. The signal conversion, from analog to digital or vice versa, is expl
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.
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.
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
From Levy to Brownian: a computational model based on biological fluctuation.
Directory of Open Access Journals (Sweden)
Surya G Nurzaman
Full Text Available BACKGROUND: Theoretical studies predict that Lévy walks maximizes the chance of encountering randomly distributed targets with a low density, but Brownian walks is favorable inside a patch of targets with high density. Recently, experimental data reports that some animals indeed show a Lévy and Brownian walk movement patterns when forage for foods in areas with low and high density. This paper presents a simple, Gaussian-noise utilizing computational model that can realize such behavior. METHODOLOGY/PRINCIPAL FINDINGS: We extend Lévy walks model of one of the simplest creature, Escherichia coli, based on biological fluctuation framework. We build a simulation of a simple, generic animal to observe whether Lévy or Brownian walks will be performed properly depends on the target density, and investigate the emergent behavior in a commonly faced patchy environment where the density alternates. CONCLUSIONS/SIGNIFICANCE: Based on the model, animal behavior of choosing Lévy or Brownian walk movement patterns based on the target density is able to be generated, without changing the essence of the stochastic property in Escherichia coli physiological mechanism as explained by related researches. The emergent behavior and its benefits in a patchy environment are also discussed. The model provides a framework for further investigation on the role of internal noise in realizing adaptive and efficient foraging behavior.
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.
DEFF Research Database (Denmark)
Donolato, M.; Sogne, E.; Dalslet, Bjarke Thomas
2011-01-01
We demonstrate the detection of the Brownian relaxation frequency of 250 nm diameter magnetic beads using a lab-on-chip platform based on current lines for exciting the beads with alternating magnetic fields and highly sensitive magnetic tunnel junction (MTJ) sensors with a superparamagnetic free...
EFFECTIVE DIFFUSION AND EFFECTIVE DRAG COEFFICIENT OF A BROWNIAN PARTICLE IN A PERIODIC POTENTIAL
Institute of Scientific and Technical Information of China (English)
Hongyun Wang
2011-01-01
We study the stochastic motion of a Brownian particle driven by a constant force over a static periodic potential.We show that both the effective diffusion and the effective drag coefficient are mathematically well-defined and we derive analytic expressions for these two quantities.We then investigate the asymptotic behaviors of the effective diffusion and the effective drag coefficient,respectively,for small driving force and for large driving force.In the case of small driving force,the effective diffusion is reduced from its Brownian value by a factor that increases exponentially with the amplitude of the potential.The effective drag coefficient is increased by approximately the same factor.As a result,the Einstein relation between the diffusion coefficient and the drag coefficient is approximately valid when the driving force is small.For moderately large driving force,both the effective diffusion and the effective drag coefficient are increased from their Brownian values,and the Einstein relation breaks down. In the limit of very large driving force,both the effective diffusion and the effective drag coefficient converge to their Brownian values and the Einstein relation is once again valid.
On the cumulants of increments for two classes of Brownian semi-stationary processes
DEFF Research Database (Denmark)
Urbina, José Ulises Márquez
2015-01-01
In this article we obtain formulae for the cumulants of the increments of two classes of Brownian semi-stationary (BSS) processes. The first class corresponds to BSS processes where the volatility is a Lévy semi-stationary process and the second class consists in BSS processes where the volatilit...
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
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.
Influence of Brownian Diffusion on Levitation of Bodies in Magnetic Fluid
Directory of Open Access Journals (Sweden)
V. Bashtovoi
2013-12-01
Full Text Available The present work deals with experimental investigation of the levitation of magnetic and non-magnetic bodies in a magnetic fluid when essentially influenced by Brownian diffusion of magnetic particles in it. It is established that the point of levitation of bodies in a magnetic fluid varies with time.
DEFF Research Database (Denmark)
E. Barndorff-Nielsen, Ole; Benth, Fred Espen; Szozda, Benedykt
This paper generalizes the integration theory for volatility modulated Brownian-driven Volterra processes onto the space G* of Potthoff-Timpel distributions. Sufficient conditions for integrability of generalized processes are given, regularity results and properties of the integral are discussed...
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole E.; Benth, Fred Espen; Szozda, Benedykt
This paper generalizes the integration theory for volatility modulated Brownian-driven Volterra processes onto the space G∗ of Potthoff--Timpel distributions. Sufficient conditions for integrability of generalized processes are given, regularity results and properties of the integral are discussed...
Energy Technology Data Exchange (ETDEWEB)
Maldonado-Camargo, L. [Department of Chemical Engineering, University of Florida, Gainesville, FL 32611 (United States); Torres-Díaz, I. [J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, FL 32611 (United States); Chiu-Lam, A. [Department of Chemical Engineering, University of Florida, Gainesville, FL 32611 (United States); Hernández, M. [J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, FL 32611 (United States); Rinaldi, C., E-mail: carlos.rinaldi@bme.ufl.edu [Department of Chemical Engineering, University of Florida, Gainesville, FL 32611 (United States); J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, FL 32611 (United States)
2016-08-15
We demonstrate how dynamic magnetic susceptibility measurements (DMS) can be used to estimate the relative contributions of Brownian and Néel relaxation to the dynamic magnetic response of a magnetic fluid, a suspension of magnetic nanoparticles. The method applies to suspensions with particles that respond through Brownian or Néel relaxation and for which the characteristic Brownian and Néel relaxation times are widely separated. First, we illustrate this using magnetic fluids consisting of mixtures of particles that relax solely by the Brownian or Néel mechanisms. Then, it is shown how the same approach can be applied to estimate the relative contributions of Brownian and Néel relaxation in a suspension consisting of particles obtained from a single synthesis and whose size distribution straddles the transition from Néel to Brownian relaxation. - Highlights: • Method to estimate the contributions of the relaxation mechanism to the magnetic response. • Method applies to cases where the Brownian and Néel peaks do not overlap. • The method applies for ferrofluids prepared with as–synthesized particles.
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.
Nanoparticles at liquid interfaces: Rotational dynamics and angular locking
Energy Technology Data Exchange (ETDEWEB)
Razavi, Sepideh; Kretzschmar, Ilona [Department of Chemical Engineering, City College of City University of New York, New York, New York 10031 (United States); Koplik, Joel [Department of Physics and The Benjamin Levich Institute for Physico-chemical Hydrodynamics, City College of City University of New York, New York, New York 10031 (United States); Colosqui, Carlos E., E-mail: carlos.colosqui@stonybrook.edu [Department of Mechanical Engineering, Stony Brook University, Stony Brook, New York 11794 (United States)
2014-01-07
Nanoparticles with different surface morphologies that straddle the interface between two immiscible liquids are studied via molecular dynamics simulations. The methodology employed allows us to compute the interfacial free energy at different angular orientations of the nanoparticle. Due to their atomistic nature, the studied nanoparticles present both microscale and macroscale geometrical features and cannot be accurately modeled as a perfectly smooth body (e.g., spheres and cylinders). Under certain physical conditions, microscale features can produce free energy barriers that are much larger than the thermal energy of the surrounding media. The presence of these energy barriers can effectively “lock” the particle at specific angular orientations with respect to the liquid-liquid interface. This work provides new insights on the rotational dynamics of Brownian particles at liquid interfaces and suggests possible strategies to exploit the effects of microscale features with given geometric characteristics.
Nanoparticles at liquid interfaces: rotational dynamics and angular locking.
Razavi, Sepideh; Kretzschmar, Ilona; Koplik, Joel; Colosqui, Carlos E
2014-01-07
Nanoparticles with different surface morphologies that straddle the interface between two immiscible liquids are studied via molecular dynamics simulations. The methodology employed allows us to compute the interfacial free energy at different angular orientations of the nanoparticle. Due to their atomistic nature, the studied nanoparticles present both microscale and macroscale geometrical features and cannot be accurately modeled as a perfectly smooth body (e.g., spheres and cylinders). Under certain physical conditions, microscale features can produce free energy barriers that are much larger than the thermal energy of the surrounding media. The presence of these energy barriers can effectively "lock" the particle at specific angular orientations with respect to the liquid-liquid interface. This work provides new insights on the rotational dynamics of Brownian particles at liquid interfaces and suggests possible strategies to exploit the effects of microscale features with given geometric characteristics.
Tidwell, Jenifer
2010-01-01
Despite all of the UI toolkits available today, it's still not easy to design good application interfaces. This bestselling book is one of the few reliable sources to help you navigate through the maze of design options. By capturing UI best practices and reusable ideas as design patterns, Designing Interfaces provides solutions to common design problems that you can tailor to the situation at hand. This updated edition includes patterns for mobile apps and social media, as well as web applications and desktop software. Each pattern contains full-color examples and practical design advice th
Fikkert, F.W.
2007-01-01
Take away mouse and keyboard. Now, how do you interact with a computer? Especially one that has a display that is the size of an entire wall. One possibility is through gesture interfaces. Remember Minority Report? Cool stuff, but that was already five years ago.. So, what is already possible now an
Houten, van F.J.A.M.
1992-01-01
The paper identifies the changing needs and requirements with respect to the interfacing of manufacturing functions. It considers the manufacturing system, its components and their relationships from the technological and logistic point of view, against the background of concurrent engineering. Desi
DEFF Research Database (Denmark)
Holbøll, Joachim T.; Henriksen, Mogens; Nilson, Jesper K.;
1999-01-01
The wide use of solid insulating materials combinations in combinations has introduced problems in the interfaces between components. The most common insulating materials are cross-linked polyethylene (XLPE), silicone rubber (SIR) and ethylene-propylene rubbers (EPR). Assemblies of these materials...
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.
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}).
Long-lived and unstable modes of Brownian suspensions in microchannels
Khoshnood, Atefeh
2012-01-01
We investigate the stability of the pressure-driven, low-Reynolds flow of Brownian suspensions with spherical particles in microchannels. We find two general families of stable/unstable modes: (i) degenerate modes with symmetric and anti-symmetric patterns; (ii) single modes that are either symmetric or anti-symmetric. The concentration profiles of degenerate modes have strong peaks near the channel walls, while single modes diminish there. Once excited, both families would be detectable through high-speed imaging. We find that unstable modes occur in concentrated suspensions whose velocity profiles are sufficiently flattened near the channel centreline. The patterns of growing unstable modes suggest that they are triggered due to Brownian migration of particles between the central bulk that moves with an almost constant velocity, and highly-sheared low-velocity region near the wall. Modes are amplified because shear-induced diffusion cannot efficiently disperse particles from the cavities of the perturbed ve...
A weak limit theorem for numerical approximation of Brownian semi-stationary processes
DEFF Research Database (Denmark)
Podolskij, Mark; Thamrongrat, Nopporn
In this paper we present a weak limit theorem for a numerical approximation of Brownian semi-stationary processes studied in [14]. In the original work of [14] the authors propose to use Fourier transformation to embed a given one dimensional (Levy) Brownian semi-stationary process into a two......-parameter stochastic field. For the latter they use a simple iteration procedure and study the strong approximation error of the resulting numerical scheme given that the volatility process is fully observed. In this work we present the corresponding weak limit theorem for the setting, where the volatility....../drift process needs to be numerically simulated. In particular, weak approximation errors for smooth test functions can be obtained from our asymptotic theory....
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.
A surface-bound molecule that undergoes optically biased Brownian rotation
Hutchison, James A.; Uji-I, Hiroshi; Deres, Ania; Vosch, Tom; Rocha, Susana; Müller, Sibylle; Bastian, Andreas A.; Enderlein, Jörg; Nourouzi, Hassan; Li, Chen; Herrmann, Andreas; Müllen, Klaus; de Schryver, Frans; Hofkens, Johan
2014-02-01
Developing molecular systems with functions analogous to those of macroscopic machine components, such as rotors, gyroscopes and valves, is a long-standing goal of nanotechnology. However, macroscopic analogies go only so far in predicting function in nanoscale environments, where friction dominates over inertia. In some instances, ratchet mechanisms have been used to bias the ever-present random, thermally driven (Brownian) motion and drive molecular diffusion in desired directions. Here, we visualize the motions of surface-bound molecular rotors using defocused fluorescence imaging, and observe the transition from hindered to free Brownian rotation by tuning medium viscosity. We show that the otherwise random rotations can be biased by the polarization of the excitation light field, even though the associated optical torque is insufficient to overcome thermal fluctuations. The biased rotation is attributed instead to a fluctuating-friction mechanism in which photoexcitation of the rotor strongly inhibits its diffusion rate.
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.
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.
Institute of Scientific and Technical Information of China (English)
Feng Yu; Lin Jian-Zhong
2008-01-01
The collision efficiency in the Brownian coagulation is investigated. A new mechanical model of collision between two identical spherical particles is proposed, and a set of corresponding collision equations is established. The equations are solved numerically, thereby obtaining the collision efficiency for the monodisperse dioctyl phthalate spherical aerosols with diameters ranging from 100 to 760 nm in the presence of van der Waals force and the elastic deformation force.The calculated collision efficiency, in agreement with the experimental data qualitatively, decreases with the increase of particle diameter except a small peak appearing in the particles with a diameter of 510 nm. The results show that the interparticle elastic deformation force cannot be neglected in the computation of particle Brownian coagulation.Finally, a set of new expressions relating collision efficiency to particle diameter is established.
Dwell time of a Brownian interacting molecule in a cellular microdomain
Taflia, A; Taflia, Adi; Holcman, David
2006-01-01
The time spent by an interacting Brownian molecule inside a bounded microdomain has many applications in cellular biology, because the number of bounds is a quantitative signal, which can initiate a cascade of chemical reactions and thus has physiological consequences. In the present article, we propose to estimate the mean time spent by a Brownian molecule inside a microdomain $\\Omega$ which contains small holes on the boundary and agonist molecules located inside. We found that the mean time depends on several parameters such as the backward binding rate (with the agonist molecules), the mean escape time from the microdomain and the mean time a molecule reaches the binding sites (forward binding rate). In addition, we estimate the mean and the variance of the number of bounds made by a molecule before it exits $\\Omega$. These estimates rely on a boundary layer analysis of a conditional mean first passage time, solution of a singular partial differential equation. In particular, we apply the present results ...
A Simple Discrete Model of Brownian Motors: Time-periodic Markov Chains
Ge, Hao; Jiang, Da-Quan; Qian, Min
2006-05-01
In this paper, we consider periodically inhomogeneous Markov chains, which can be regarded as a simple version of physical model—Brownian motors. We introduce for them the concepts of periodical reversibility, detailed balance, entropy production rate and circulation distribution. We prove the equivalence of the following statements: The time-periodic Markov chain is periodically reversible; It is in detailed balance; Kolmogorov's cycle condition is satisfied; Its entropy production rate vanishes; Every circuit and its reversed circuit have the same circulation weight. Hence, in our model of Markov chains, the directed transport phenomenon of Brownian motors, i.e. the existence of net circulation, can occur only in nonequilibrium and irreversible systems. Moreover, we verify the large deviation property and the Gallavotti-Cohen fluctuation theorem of sample entropy production rates of the Markov chain.
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.
Environmental context explains Lévy and Brownian movement patterns of marine predators
Nicolas E Humphries; Queiroz, Nuno; Dyer, Jennifer R.M.; Pade, Nicolas G.; Musyl, Michael K.; Schaefer, Kurt M.; Fuller, Daniel W.; Brunnschweiler, Juerg M.; Thomas K. Doyle; Jonathan D.R. Houghton; Hays, Graeme C.; Jones, Catherine S.; Noble, Leslie R.; Wearmouth, Victoria J.; Southall, Emily J.
2010-01-01
An optimal search theory, the so-called Lévy-flight foraging hypothesis, predicts that predators should adopt search strategies known as Lévy flights where prey is sparse and distributed unpredictably, but that Brownian movement is sufficiently efficient for locating abundant prey. Empirical studies have generated controversy because the accuracy of statistical methods that have been used to identify Lévy behaviour has recently been questioned. Consequently, whether foragers exhibit Lévy flig...
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.
Shukla, Pragya
2004-01-01
We find that the statistics of levels undergoing metal-insulator transition in systems with multi-parametric Gaussian disorders and non-interacting electrons behaves in a way similar to that of the single parametric Brownian ensembles \\cite{dy}. The latter appear during a Poisson $\\to$ Wigner-Dyson transition, driven by a random perturbation. The analogy provides the analytical evidence for the single parameter scaling of the level-correlations in disordered systems as well as a tool to obtai...
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.
Shukla, Pragya
2004-01-01
We find that the statistics of levels undergoing metal-insulator transition in systems with multi-parametric Gaussian disorders and non-interacting electrons behaves in a way similar to that of the single parametric Brownian ensembles \\cite{dy}. The latter appear during a Poisson $\\to$ Wigner-Dyson transition, driven by a random perturbation. The analogy provides the analytical evidence for the single parameter scaling of the level-correlations in disordered systems as well as a tool to obtai...
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...
Vertices of the least concave majorant of Brownian motion with parabolic drift
Groeneboom, Piet
2010-01-01
It was shown in Groeneboom (1983) that the least concave majorant of one-sided Brownian motion without drift can be characterized by a jump process with independent increments, which is the inverse of the process of slopes of the least concave majorant. This result can be used to prove the result of Sparre Andersen (1954) that the number of vertices of the smallest concave majorant of the empirical distribution function of a sample of size n from the uniform distribution on [0,1] is asymptotically normal, with an asymptotic expectation and variance which are both of order log n. A similar (Markovian) inverse jump process was introduced in Groeneboom (1989), in an analysis of the least concave majorant of two-sided Brownian motion with a parabolic drift. This process is quite different from the process for one-sided Brownian motion without drift: the number of vertices in a (corresponding slopes) interval has an expectation proportional to the length of the interval and the variance of the number of vertices i...
Fractional Brownian motion, the Matérn process, and stochastic modeling of turbulent dispersion
Lilly, Jonathan M.; Sykulski, Adam M.; Early, Jeffrey J.; Olhede, Sofia C.
2017-08-01
Stochastic processes exhibiting power-law slopes in the frequency domain are frequently well modeled by fractional Brownian motion (fBm), with the spectral slope at high frequencies being associated with the degree of small-scale roughness or fractal dimension. However, a broad class of real-world signals have a high-frequency slope, like fBm, but a plateau in the vicinity of zero frequency. This low-frequency plateau, it is shown, implies that the temporal integral of the process exhibits diffusive behavior, dispersing from its initial location at a constant rate. Such processes are not well modeled by fBm, which has a singularity at zero frequency corresponding to an unbounded rate of dispersion. A more appropriate stochastic model is a much lesser-known random process called the Matérn process, which is shown herein to be a damped version of fractional Brownian motion. This article first provides a thorough introduction to fractional Brownian motion, then examines the details of the Matérn process and its relationship to fBm. An algorithm for the simulation of the Matérn process in O(NlogN) operations is given. Unlike fBm, the Matérn process is found to provide an excellent match to modeling velocities from particle trajectories in an application to two-dimensional fluid turbulence.
Fractional brownian functions as mathematical models of natural rhythm in architecture.
Cirovic, Ivana M
2014-10-01
Carl Bovill suggested and described a method of generating rhythm in architecture with the help of fractional Brownian functions, as they are mathematical models of natural rhythm. A relationship established in the stated procedure between fractional Brownian functions as models of rhythm, and the observed group of architectural elements, is recognized as an analogical relationship, and the procedure of generating rhythm as a process of analogical transfer from the natural domain to the architectural domain. Since analogical transfer implies relational similarity of two domains, and the establishment of one-to-one correspondence, this paper is trying to determine under which conditions such correspondence could be established. For example, if the values of the observed visual feature of architectural elements are not similar to each other in a way in which they can form a monotonically increasing, or a monotonically decreasing bounded sequence, then the structural alignment and the one-to-one correspondence with a single fractional Brownian function cannot be established, hence, this function is deemed inappropriate as a model for the architectural rhythm. In this case we propose overlapping of two or more functions, so that each of them is an analog for one subset of mutually similar values of the visual feature of architectural elements.
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...
Stochastic interactions of two Brownian hard spheres in the presence of depletants
Energy Technology Data Exchange (ETDEWEB)
Karzar-Jeddi, Mehdi; Fan, Tai-Hsi, E-mail: thfan@engr.uconn.edu [Department of Mechanical Engineering, University of Connecticut, Storrs, Connecticut 06269-3139 (United States); Tuinier, Remco [Van' t Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute, Department of Chemistry, Utrecht University, Padualaan 8, 3584 CH, Utrecht (Netherlands); DSM ChemTech R and D, P.O. Box 18, 6160 MD Geleen (Netherlands); Taniguchi, Takashi [Graduate School of Engineering, Kyoto University Katsura Campus, Nishikyo-ku, Kyoto 615-8510 (Japan)
2014-06-07
A quantitative analysis is presented for the stochastic interactions of a pair of Brownian hard spheres in non-adsorbing polymer solutions. The hard spheres are hypothetically trapped by optical tweezers and allowed for random motion near the trapped positions. The investigation focuses on the long-time correlated Brownian motion. The mobility tensor altered by the polymer depletion effect is computed by the boundary integral method, and the corresponding random displacement is determined by the fluctuation-dissipation theorem. From our computations it follows that the presence of depletion layers around the hard spheres has a significant effect on the hydrodynamic interactions and particle dynamics as compared to pure solvent and uniform polymer solution cases. The probability distribution functions of random walks of the two interacting hard spheres that are trapped clearly shift due to the polymer depletion effect. The results show that the reduction of the viscosity in the depletion layers around the spheres and the entropic force due to the overlapping of depletion zones have a significant influence on the correlated Brownian interactions.
Dual-frequency magnetic particle imaging of the Brownian particle contribution
Viereck, Thilo; Kuhlmann, Christian; Draack, Sebastian; Schilling, Meinhard; Ludwig, Frank
2017-04-01
Magnetic particle imaging (MPI) is an emerging medical imaging modality based on the non-linear response of magnetic nanoparticles to an exciting magnetic field. MPI has been recognized as a fast imaging technique with high spatial resolution in the mm range. For some applications of MPI, especially in the field of functional imaging, the determination of the particle mobility (Brownian rotation) is of great interest, as it enables binding detection in MPI. It also enables quantitative imaging in the presence of Brownian-dominated particles, which is otherwise implausible. Discrimination of different particle responses in MPI is possible via the joint reconstruction approach. In this contribution, we propose a dual-frequency acquisition scheme to enhance sensitivity and contrast in the detection of different particle mobilities compared to a standard single-frequency MPI protocol. The method takes advantage of the fact, that the magnetization response of the tracer is strongly frequency-dependent, i.e. for low excitation frequencies a stronger Brownian contribution is observed.
DEFF Research Database (Denmark)
Thorhauge, Sally
2014-01-01
"Interface learning - New goals for museum and upper secondary school collaboration" investigates and analyzes the learning that takes place when museums and upper secondary schools in Denmark work together in local partnerships to develop and carry out school-related, museum-based coursework...... for students. The research focuses on the learning that the students experience in the interface of the two learning environments: The formal learning environment of the upper secondary school and the informal learning environment of the museum. Focus is also on the learning that the teachers and museum...... professionals experience as a result of their collaboration. The dissertation demonstrates how a given partnership’s collaboration affects the students’ learning experiences when they are doing the coursework. The dissertation presents findings that museum-school partnerships can use in order to develop...
DEFF Research Database (Denmark)
Pold, Søren
2007-01-01
Søren Pold gør sig overvejelser med udgangspunkt i museumsprojekterne Kongedragter.dk og Stigombord.dk. Han argumenterer for, at udviklingen af internettets interfaces skaber nye måder at se, forstå og interagere med kulturen på. Brugerne får nye medievaner og perceptionsmønstre, der må medtænkes i...
DEFF Research Database (Denmark)
Pold, Søren
2007-01-01
Søren Pold gør sig overvejelser med udgangspunkt i museumsprojekterne Kongedragter.dk og Stigombord.dk. Han argumenterer for, at udviklingen af internettets interfaces skaber nye måder at se, forstå og interagere med kulturen på. Brugerne får nye medievaner og perceptionsmønstre, der må medtænkes i...
Wei, Lin; Ye, Zhongju; Luo, Wenjuan; Chen, Bo; Xiao, Lehui
2016-08-01
Many intriguing physical and chemical processes commonly take place at the solid/liquid interface. Total internal reflection illumination, together with single molecule spectroscopy, provides a robust platform for the selective exploration of kinetic processes close the interface. With these techniques, it was observed that the distribution of Rhodamine B molecules close to a solid/liquid interface could be regulated in a photo-induced route. The laser-induced repulsion force at this interface is enough to compromise the Brownian diffusion of single molecules in a range of several hundred nanometers normal to the solid/liquid interface. This observation is fundamentally and practically interesting because moderate laser intensity is enough to initiate this repulsion effect. Therefore, it might display extensive applications in the development of photo-modulation technique with high throughput capability.
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.
Non-equilibrium surface tension of the vapour-liquid interface of active Lennard-Jones particles
Paliwal, Siddharth; Prymidis, Vasileios; Filion, Laura; Dijkstra, Marjolein
2017-08-01
We study a three-dimensional system of self-propelled Brownian particles interacting via the Lennard-Jones potential. Using Brownian dynamics simulations in an elongated simulation box, we investigate the steady states of vapour-liquid phase coexistence of active Lennard-Jones particles with planar interfaces. We measure the normal and tangential components of the pressure tensor along the direction perpendicular to the interface and verify mechanical equilibrium of the two coexisting phases. In addition, we determine the non-equilibrium interfacial tension by integrating the difference of the normal and tangential components of the pressure tensor and show that the surface tension as a function of strength of particle attractions is well fitted by simple power laws. Finally, we measure the interfacial stiffness using capillary wave theory and the equipartition theorem and find a simple linear relation between surface tension and interfacial stiffness with a proportionality constant characterized by an effective temperature.
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.
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.
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.
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.
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.
Bellesia, Giovanni
2015-01-01
We investigate, via Brownian dynamics simulations, the reaction dynamics of a simple, non-linear chemical network (the Willamowski-Rossler network) under spatial confinement and crowding conditions. Our results show that the presence of inert crowders has a non-nontrivial effect on the dynamics of the network and, consequently, that effective modeling efforts aiming at a general understanding of the behavior of biochemical networks in vivo should be stochastic in nature and based on an explicit representation of both spatial confinement and macromolecular crowding.
Thermal equilibrium of a Brownian particle in a fluctuating fluid: a numerical study
Liu, Yi; Nie, Deming
2017-07-01
In this work the fluctuating lattice Boltzmann method was adopted to simulate the motion of a Brownian particle in a fluid in two dimensions. The temperatures characterizing the translation motion and rotational motion of the particle were calculated to evaluate the thermal equilibrium between the particle and the fluid. Furthermore, the effects of the fluid temperature and viscosity on the fluid pressure fluctuation were investigated. The linear relationships were observed in a log-log coordinate. Besides, the slopes of the linear relation were obtained, which keeps constant for all cases studied.
Structure Analysis of Jungle-Gym-Type Gels by Brownian Dynamics Simulation
Ohta, Noriyoshi; Ono, Kohki; Takasu, Masako; Furukawa, Hidemitsu
2008-02-01
We investigated the structure and the formation process of two kinds of gels by Brownian dynamics simulation. The effect of flexibility of main chain oligomer was studied. From our results, hard gel with rigid main chain forms more homogeneous network structure than soft gel with flexible main chain. In soft gel, many small loops are formed, and clusters tend to shrink. This heterogeneous network structure may be caused by microgels. In the low density case, soft gel shows more heterogeneity than the high density case.
Joint distributions of partial and global maxima of a Brownian bridge
Bénichou, Olivier; Krapivsky, P. L.; Mejía-Monasterio, Carlos; Oshanin, Gleb
2016-08-01
We analyze the joint distributions and temporal correlations between the partial maximum m and the global maximum M achieved by a Brownian bridge on the subinterval [0,{t}1] and on the entire interval [0,t], respectively. We determine three probability distribution functions: the joint distribution P(m,M) of both maxima; the distribution P(m) of the partial maximum; and the distribution {{\\Pi }}(G) of the gap between the maxima, G=M-m. We present exact results for the moments of these distributions and quantify the temporal correlations between m and M by calculating the Pearson correlation coefficient.
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.
Analytical estimates of free brownian diffusion times in corrugated narrow channels.
Bosi, Leone; Ghosh, Pulak K; Marchesoni, Fabio
2012-11-07
The diffusion of a suspended brownian particle along a sinusoidally corrugated narrow channel is investigated to assess the validity of two competing analytical schemes, both based on effective one-dimensional kinetic equations, one continuous (entropic channel scheme) and the other discrete (random walker scheme). For narrow pores, the characteristic diffusion time scale is represented by the mean first exit time out of a channel compartment. Such a diffusion time has been analytically calculated in both approximate schemes; the two analytical results coincide in leading order and are in excellent agreement with the simulation data.
Tamburini, F; Bianchini, A
1999-01-01
A time-correlated EPR pairs protocol is analized, based on detection of fractal correlated signals into a statistical mixture of EPR correlated pairs: an approximated alpha-Fractional Brownian Motion (FBM) is induced on the group of EPR pairs (e.g. by sender-third party eavesdropper-like interactions as in Ekert quantum cryptography), to be detected by the receiver using a non - orthogonal wavelet filter, able to characterize the FBM from a noisy enviroment by formalizing a nonlinear optimization problem for the FBM alpha-characteristic parameter extimation.
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.
Measurements of Brownian relaxation of magnetic nanobeads using planar Hall effect bridge sensors
DEFF Research Database (Denmark)
Østerberg, Frederik Westergaard; Rizzi, Giovanni; Zardán Gómez de la Torre, T.
2013-01-01
We compare measurements of the Brownian relaxation response of magnetic nanobeads in suspension using planar Hall effect sensors of cross geometry and a newly proposed bridge geometry. We find that the bridge sensor yields six times as large signals as the cross sensor, which results in a more ac...... performed in a commercial AC susceptometer. The presented bridge sensor is, thus, a promising component in future lab-on-a-chip biosensors for detection of clinically relevant analytes, including bacterial genomic DNA and proteins....
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.
Effect of internal viscosity on Brownian dynamics of DNA molecules in shear flow.
Yang, Xiao-Dong; Melnik, Roderick V N
2007-04-01
The results of Brownian dynamics simulations of a single DNA molecule in shear flow are presented taking into account the effect of internal viscosity. The dissipative mechanism of internal viscosity is proved necessary in the research of DNA dynamics. A stochastic model is derived on the basis of the balance equation for forces acting on the chain. The Euler method is applied to the solution of the model. The extensions of DNA molecules for different Weissenberg numbers are analyzed. Comparison with the experimental results available in the literature is carried out to estimate the contribution of the effect of internal viscosity.
Brownian dynamics simulations on CPU and GPU with BD_BOX.
Długosz, Maciej; Zieliński, Paweł; Trylska, Joanna
2011-09-01
There has been growing interest in simulating biological processes under in vivo conditions due to recent advances in experimental techniques dedicated to study single particle behavior in crowded environments. We have developed a software package, BD_BOX, for multiscale Brownian dynamics simulations. BD_BOX can simulate either single molecules or multicomponent systems of diverse, interacting molecular species using flexible, coarse-grained bead models. BD_BOX is written in C and employs modern computer architectures and technologies; these include MPI for distributed-memory architectures, OpenMP for shared-memory platforms, NVIDIA CUDA framework for GPGPU, and SSE vectorization for CPU. Copyright © 2011 Wiley Periodicals, Inc.
Asymptotic theory for Brownian semi-stationary processes with application to turbulence
DEFF Research Database (Denmark)
Corcuera, José Manuel; Hedevang, Emil; Pakkanen, Mikko S.;
2013-01-01
This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of the BSS model. We review the limit theory discussed......-stationary processes. In "Prokhorov and Contemporary Probability Theory", Springer.] and present some new connections to fractional diffusion models. We apply our probabilistic results to construct a family of estimators for the smoothness parameter of the BSS process. In this context we develop estimates with gaps......, which allow to obtain a valid central limit theorem for the critical region. Finally, we apply our statistical theory to turbulence data....
Triampo, W; Newman, T J
1999-08-01
This work is a continuation of our previous investigation of binary data corruption due to a Brownian agent [Phys. Rev. E 59, 5172 (1999)]. We extend our study in three main directions which allow us to make closer contact with real bistable systems. These are (i) a detailed analysis of two dimensions, (ii) the case of competing agents, and (iii) the cases of asymmetric and quenched random couplings. Most of our results are obtained by extending our original phenomenological model, and are supported by extensive numerical simulations.
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.
Weighted-ensemble Brownian dynamics simulation: sampling of rare events in nonequilibrium systems.
Kromer, Justus A; Schimansky-Geier, Lutz; Toral, Raul
2013-06-01
We provide an algorithm based on weighted-ensemble (WE) methods, to accurately sample systems at steady state. Applying our method to different one- and two-dimensional models, we succeed in calculating steady-state probabilities of order 10(-300) and reproduce the Arrhenius law for rates of order 10(-280). Special attention is payed to the simulation of nonpotential systems where no detailed balance assumption exists. For this large class of stochastic systems, the stationary probability distribution density is often unknown and cannot be used as preknowledge during the simulation. We compare the algorithm's efficiency with standard Brownian dynamics simulations and the original WE method.
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.
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.
Institute of Scientific and Technical Information of China (English)
WEI Jin-Jia; KAWAGUCHI Yasuo; YU Bo; LI Feng-Chen
2008-01-01
@@ Brownian dynamics simulation is conducted for a dilute surfactant solution under a steady uniaxial elongational flow.A new inter-cluster potential is used for the interaction among surfactant micelles to determine the micellar network structures in the surfactant solution.The micellar network is successfully simulated.It is formed at low elongation rates and destroyed by high elongation rates.The computed elongational viscosities show elongation-thinning characteristics.The relationship between the elongational viscosities and the microstructure of the surfactant solution is revealed.
Optimal Policy for Brownian Inventory Models with General Convex Inventory Cost
Institute of Scientific and Technical Information of China (English)
Da-cheng YAO
2013-01-01
We study an inventory system in which products are ordered from outside to meet demands,and the cumulative demand is governed by a Brownian motion.Excessive demand is backlogged.We suppose that the shortage and holding costs associated with the inventory are given by a general convex function.The product ordering from outside incurs a linear ordering cost and a setup fee.There is a constant leadtime when placing an order.The optimal policy is established so as to minimize the discounted cost including the inventory cost and ordering cost.
Institute of Scientific and Technical Information of China (English)
BAI Zhan-Wu
2008-01-01
@@ We study in phase space a zero-dimensional system of Brownian particles which move in a periodic potential and subject to an internal time derivative Ornstein-Uhlenbeck noise. To resolve the Fokker-Planck equation in such a case, we propose an approximate analytical method. The theoretical predictions exhibit a second order noise-induced nonequilibrium phase transition, which is confirmed by numerical simulation results. The phase transition brings the system from an ergodicity to a nonergodicity phase as the potential barrier height decreases.
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.
Accumulation of swimming bacteria near an interface
Tang, Jay; Li, Guanglai
2012-11-01
Microbes inhabit planet earth over billions of years and have adapted to diverse physical environment of water, soil, and particularly at or near interfaces. We focused our attention on the locomotion of Caulobacter crescentus, a singly flagellated bacterium, at the interface of water/solid or water/air. We measured the distribution of a forward swimming strain of C. crescentus near a surface using a three-dimensional tracking technique based on dark field microscopy and found that the swimming bacteria accumulate heavily within a micrometer from the surface. We attribute this accumulation to frequent collisions of the swimming cells with the surface, causing them to align parallel to the surface as they continually move forward. The extent of accumulation at the steady state is accounted for by balancing alignment caused by these collisions with rotational Brownian motion of the micrometer-sized bacteria. We performed a simulation based on this model, which reproduced the measured results. Additional simulations demonstrate the dependence of accumulation on swimming speed and cell size, showing that longer and faster cells accumulate more near a surface than shorter and slower ones do. The overarching goal of our study is to describe interfacial microbial behavior through detailed analysis of their motion. We acknowledge support by NSF PHY 1058375.
Suppression of a Brownian noise in a hole-type sensor due to induced-charge electro-osmosis
Sugioka, Hideyuki
2016-03-01
Noise reduction is essential for a single molecular sensor. Thus, we propose a novel noise reduction mechanism using a hydrodynamic force due to induced-charge electro-osmosis (ICEO) in a hole-type sensor and numerically examine the performance. By the boundary element method that considers both a Brownian motion and an ICEO flow of a polarizable particle, we find that the Brownian noise in a current signal is suppressed significantly in a converging channel because of the ICEO flow around the particle in the presence of an electric field. Further, we propose a simple model that explains a numerically obtained threshold voltage of the suppression of the Brownian noise due to ICEO. We believe that our findings contribute greatly to developments of a single molecular sensor.
Schmidt, Christian; Piel, Alexander
2015-10-01
The Brownian motion of a single particle in the plasma sheath is studied to separate the effect of stochastic heating by charge fluctuations from heating by collective effects. By measuring the particle velocities in the ballistic regime and by carefully determining the particle mass from the Epstein drag it is shown that for a pressure of 10 Pa, which is typical of many experiments, the proper kinetic temperature of the Brownian particle remains close to the gas temperature and rises only slightly with particle size. This weak effect is confirmed by a detailed model for charging and charge fluctuations in the sheath. A substantial temperature rise is found for decreasing pressure, which approximately shows the expected scaling with p(-2). The system under study is an example for non-equilibrium Brownian motion under the influence of white noise without corresponding dissipation.
Directory of Open Access Journals (Sweden)
María Teresa Soto Sanfiel
2012-04-01
Full Text Available Este artículo describe y piensa al fenómeno de las Interfaces habladas (IH desde variados puntos de vista y niveles de análisis. El texto se ha concebido con los objetivos específicos de: 1.- procurar una visión panorámica de aspectos de la producción y consumo comunicativo de las IH; 2.- ofrecer recomendaciones para su creación y uso eficaz, y 3.- llamar la atención sobre su proliferación e inspirar su estudio desde la comunicación. A pesar de la creciente presencia de las IF en nues-tras vidas cotidianas, hay ausencia de textos que las caractericen y analicen por sus aspectos comunicativos. El trabajo es pertinente porque el fenómeno significa un cambio respecto a estadios comunica-tivos precedentes con consecuencias en las concepciones intelectuales y emocionales de los usuarios. La proliferación de IH nos abre a nue-vas realidades comunicativas: hablamos con máquinas.
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.
Brites, Carlos D. S.; Xie, Xiaoji; Debasu, Mengistie L.; Qin, Xian; Chen, Runfeng; Huang, Wei; Rocha, João; Liu, Xiaogang; Carlos, Luís D.
2016-10-01
Brownian motion is one of the most fascinating phenomena in nature. Its conceptual implications have a profound impact in almost every field of science and even economics, from dissipative processes in thermodynamic systems, gene therapy in biomedical research, artificial motors and galaxy formation to the behaviour of stock prices. However, despite extensive experimental investigations, the basic microscopic knowledge of prototypical systems such as colloidal particles in a fluid is still far from being complete. This is particularly the case for the measurement of the particles' instantaneous velocities, elusive due to the rapid random movements on extremely short timescales. Here, we report the measurement of the instantaneous ballistic velocity of Brownian nanocrystals suspended in both aqueous and organic solvents. To achieve this, we develop a technique based on upconversion nanothermometry. We find that the population of excited electronic states in NaYF4:Yb/Er nanocrystals at thermal equilibrium can be used for temperature mapping of the nanofluid with great thermal sensitivity (1.15% K-1 at 296 K) and a high spatial resolution (<1 μm). A distinct correlation between the heat flux in the nanofluid and the temporal evolution of Er3+ emission allows us to measure the instantaneous velocity of nanocrystals with different sizes and shapes.
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.
Solano, Carlos J F; Pothula, Karunakar R; Prajapati, Jigneshkumar D; De Biase, Pablo M; Noskov, Sergei Yu; Kleinekathöfer, Ulrich
2016-05-10
All-atom molecular dynamics simulations have a long history of applications studying ion and substrate permeation across biological and artificial pores. While offering unprecedented insights into the underpinning transport processes, MD simulations are limited in time-scales and ability to simulate physiological membrane potentials or asymmetric salt solutions and require substantial computational power. While several approaches to circumvent all of these limitations were developed, Brownian dynamics simulations remain an attractive option to the field. The main limitation, however, is an apparent lack of protein flexibility important for the accurate description of permeation events. In the present contribution, we report an extension of the Brownian dynamics scheme which includes conformational dynamics. To achieve this goal, the dynamics of amino-acid residues was incorporated into the many-body potential of mean force and into the Langevin equations of motion. The developed software solution, called BROMOCEA, was applied to ion transport through OmpC as a test case. Compared to fully atomistic simulations, the results show a clear improvement in the ratio of permeating anions and cations. The present tests strongly indicate that pore flexibility can enhance permeation properties which will become even more important in future applications to substrate translocation.
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.
Electrostatic channeling in P. falciparum DHFR-TS: Brownian dynamics and Smoluchowski modeling.
Metzger, Vincent T; Eun, Changsun; Kekenes-Huskey, Peter M; Huber, Gary; McCammon, J Andrew
2014-11-18
We perform Brownian dynamics simulations and Smoluchowski continuum modeling of the bifunctional Plasmodium falciparum dihydrofolate reductase-thymidylate synthase (P. falciparum DHFR-TS) with the objective of understanding the electrostatic channeling of dihydrofolate generated at the TS active site to the DHFR active site. The results of Brownian dynamics simulations and Smoluchowski continuum modeling suggest that compared to Leishmania major DHFR-TS, P. falciparum DHFR-TS has a lower but significant electrostatic-mediated channeling efficiency (?15-25%) at physiological pH (7.0) and ionic strength (150 mM). We also find that removing the electric charges from key basic residues located between the DHFR and TS active sites significantly reduces the channeling efficiency of P. falciparum DHFR-TS. Although several protozoan DHFR-TS enzymes are known to have similar tertiary and quaternary structure, subtle differences in structure, active-site geometry, and charge distribution appear to influence both electrostatic-mediated and proximity-based substrate channeling.
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.
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
Energy Technology Data Exchange (ETDEWEB)
Reeves, Daniel B., E-mail: dbr@Dartmouth.edu; Weaver, John B. [Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755 (United States)
2015-06-21
Magnetic nanoparticles are promising tools for a host of therapeutic and diagnostic medical applications. The dynamics of rotating magnetic nanoparticles in applied magnetic fields depend strongly on the type and strength of the field applied. There are two possible rotation mechanisms and the decision for the dominant mechanism is often made by comparing the equilibrium relaxation times. This is a problem when particles are driven with high-amplitude fields because they are not necessarily at equilibrium at all. Instead, it is more appropriate to consider the “characteristic timescales” that arise in various applied fields. Approximate forms for the characteristic time of Brownian particle rotations do exist and we show agreement between several analytical and phenomenological-fit models to simulated data from a stochastic Langevin equation approach. We also compare several approximate models with solutions of the Fokker-Planck equation to determine their range of validity for general fields and relaxation times. The effective field model is an excellent approximation, while the linear response solution is only useful for very low fields and frequencies for realistic Brownian particle rotations.
Lock-and-key dimerization in dense Brownian systems of hard annular sector particles
Hodson, Wade D.; Mason, Thomas G.
2016-08-01
We develop a translational-rotational cage model that describes the behavior of dense two-dimensional (2D) Brownian systems of hard annular sector particles (ASPs), resembling C shapes. At high particle densities, pairs of ASPs can form mutually interdigitating lock-and-key dimers. This cage model considers either one or two mobile central ASPs which can translate and rotate within a static cage of surrounding ASPs that mimics the system's average local structure and density. By comparing with recent measurements made on dispersions of microscale lithographic ASPs [P. Y. Wang and T. G. Mason, J. Am. Chem. Soc. 137, 15308 (2015), 10.1021/jacs.5b10549], we show that mobile two-particle predictions of the probability of dimerization Pdimer, equilibrium constant K , and 2D osmotic pressure Π2 D as a function of the particle area fraction ϕA correspond closely to these experiments. By contrast, predictions based on only a single mobile particle do not agree well with either the two-particle predictions or the experimental data. Thus, we show that collective entropy can play an essential role in the behavior of dense Brownian systems composed of nontrivial hard shapes, such as ASPs.
Lock-and-key dimerization in dense Brownian systems of hard annular sector particles.
Hodson, Wade D; Mason, Thomas G
2016-08-01
We develop a translational-rotational cage model that describes the behavior of dense two-dimensional (2D) Brownian systems of hard annular sector particles (ASPs), resembling C shapes. At high particle densities, pairs of ASPs can form mutually interdigitating lock-and-key dimers. This cage model considers either one or two mobile central ASPs which can translate and rotate within a static cage of surrounding ASPs that mimics the system's average local structure and density. By comparing with recent measurements made on dispersions of microscale lithographic ASPs [P. Y. Wang and T. G. Mason, J. Am. Chem. Soc. 137, 15308 (2015)JACSAT0002-786310.1021/jacs.5b10549], we show that mobile two-particle predictions of the probability of dimerization P_{dimer}, equilibrium constant K, and 2D osmotic pressure Π_{2D} as a function of the particle area fraction ϕ_{A} correspond closely to these experiments. By contrast, predictions based on only a single mobile particle do not agree well with either the two-particle predictions or the experimental data. Thus, we show that collective entropy can play an essential role in the behavior of dense Brownian systems composed of nontrivial hard shapes, such as ASPs.
Single potassium niobate nano/microsized particles as local mechano-optical Brownian probes
Mor, Flavio M.; Sienkiewicz, Andrzej; Magrez, Arnaud; Forró, László; Jeney, Sylvia
2016-03-01
Perovskite alkaline niobates, due to their strong nonlinear optical properties, including birefringence and the capability to produce second-harmonic generation (SHG) signals, attract a lot of attention as potential candidates for applications as local nano/microsized mechano-optical probes. Here, we report on an implementation of photonic force microscopy (PFM) to explore the Brownian motion and optical trappability of monocrystalline potassium niobate (KNbO3) nano/microsized particles having sizes within the range of 50 to 750 nm. In particular, we exploit the anisotropic translational diffusive regime of the Brownian motion to quantify thermal fluctuations and optical forces of singly-trapped KNbO3 particles within the optical trapping volume of a PFM microscope. We also show that, under near-infrared (NIR) excitation of the highly focused laser beam of the PFM microscope, a single optically-trapped KNbO3 particle reveals a strong SHG signal manifested by a narrow peak (λem = 532 nm) at half the excitation wavelength (λex = 1064 nm). Moreover, we demonstrate that the thus induced SHG emission can be used as a local light source that is capable of optically exciting molecules of an organic dye, Rose Bengal (RB), which adhere to the particle surface, through the mechanism of luminescence energy transfer (LET).Perovskite alkaline niobates, due to their strong nonlinear optical properties, including birefringence and the capability to produce second-harmonic generation (SHG) signals, attract a lot of attention as potential candidates for applications as local nano/microsized mechano-optical probes. Here, we report on an implementation of photonic force microscopy (PFM) to explore the Brownian motion and optical trappability of monocrystalline potassium niobate (KNbO3) nano/microsized particles having sizes within the range of 50 to 750 nm. In particular, we exploit the anisotropic translational diffusive regime of the Brownian motion to quantify thermal
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.
Energy Technology Data Exchange (ETDEWEB)
Sorensen, C.M.
1976-01-01
An effort to expand light-scattering autocorrelation techniques to Brownian diffusional and critical fluid systems in which multiple scattering effects are important, and to understand the observed similarity of the Rayleigh linewidth of light scattered from these two seemingly different systems is discussed. A formalism was developed to find the light field multiply scattered from a suspension of Brownian diffusing particles. For the field doubly scattered from a system of noninteracting Brownian particles, the intensity and correlation time were much less dependent on the scattering angle than for the singly scattered component. The polarized and depolarized correlation times of light scattered from Brownian particle systems were measured. The double-scattering formalism was extended to light scattered from critical fluid systems. In the region k xi greater than 5 the doubly and singly scattered correlation times were nearly equal. The dynamic droplet model of critical phenomena was developed which gives the proper, experimentally verified, forms for the intensity and linewidth of light scattered from a critical fluid. To test the dynamic droplet model and the mode theories Rayleigh linewidth predictions, light-scattering measurements were performed on the critical fluid system methanol and cyclohexane. The data agreed with both the dynamic droplet and decoupled mode theory predictions. The depolarized scattered spectra from a critical fluid were measured, and qualitative agreement with the double-scattering theory was found. 57 figures, 5 tables.
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.
The Measurement and Analysis of Brownian Particle Fall Rates in a New Regime of Dense Gases.
Fedele, Paul David
Millikan's law of fall is an empirical relationship describing the dependence of the fall rate of submicron particles in gases in terms of the particle radius and the gas density. It had been long thought that the physics of slip, embodied in the law, gave a complete description of the phenomenon. During measurements of the velocity autocorrelation function for a single Brownian particle at different gas densities, we have discovered that for sufficiently small particles the fall rate increases with increasing density, in contrast to the prediction of Millikan's law. Vertical displacements during a 10 sec interval of a single oil drop have been measured as a function of nitrogen gas density in the range of one to 22 atm at room temperature by retaining the particle for up to 15 hours. Altogether 24 particles in the radius range of 0.1 to 0.4 (mu)m have been analyzed. The density dependence of the average fall rate undergoes a smooth transition from the Millikan behavior in the large size limit to the newly observed behavior in the small size limit. No anomalies are seen, however, in the density dependence of the rms displacement. In attempts to explain the observations we have examined a model based on the fact that Brownian fluctuation increases with decreasing particle size at a given gas density that the contributions of the vorticity field about such a Brownian particle on the fluctuation increases with density and that gravity sustains the entire system of the host gas and the test particle in a steady non-equilibrium state. The modified Langevin equation with gravity has been numerically solved under varying conditions. The fluctuating force is modeled by means of a series of randomly applied impulsive velocities of the test particle. The results are that while there is no sufficient physics in the model to generate any asymmetry in the fluctuation, the model has a mechanism to preserve any asymmetry given to the system for a long time and to produce
Combination of fractional Brownian random field and lacunarity for iris recognition
Liu, Kai; Zhou, Weidong; Wang, Yu
2011-10-01
Feature extraction plays a vital role in iris recognition, affecting the performance of iris recognition algorithm strongly. In this paper, we present an individual recognition algorithm using fractal dimension based on fractional Brownian random field and lacunarity in feature extraction. Making use of the fractal feature of iris, such as self-similarity and random patterns, fractal dimension can extract texture information effectively. Lacunarity overcomes the limitation of fractal dimension that fractal sets with different textures may share the same fractal dimension value. The combination of fractal dimension and lacunarity makes the feature extraction more comprehensive and distinguishable. The experimental results show that this recognition algorithm can obtain great performance on CASIA 1.0 iris database
Zaccone, Alessio; Gentili, Daniele; Wu, Hua; Morbidelli, Massimo
2010-04-07
The aggregation of interacting brownian particles in sheared concentrated suspensions is an important issue in colloid and soft matter science per se. Also, it serves as a model to understand biochemical reactions occurring in vivo where both crowding and shear play an important role. We present an effective medium approach within the Smoluchowski equation with shear which allows one to calculate the encounter kinetics through a potential barrier under shear at arbitrary colloid concentrations. Experiments on a model colloidal system in simple shear flow support the validity of the model in the concentration range considered. By generalizing Kramers' rate theory to the presence of shear and collective hydrodynamics, our model explains the significant increase in the shear-induced reaction-limited aggregation kinetics upon increasing the colloid concentration.
The double-temperature ratchet model and current reversal of coupled Brownian motors
Li, Chen-pu; Zheng, Zhi-gang
2016-01-01
Based on the transport features and experimental phenomena observed in studies of molecular motors, we proposed the double-temperature ratchet model of coupled motors to reveal the dynamical mechanism of cooperative transport of motors with two heads, where the interactions and the asynchronous between two motor heads are taken into account. We investigated the collective unidirectional transport of coupled system, and find that the direction of motion can be inversed under certain conditions. Inverse motion can be achieved by modulating the coupling strength, the coupling free length and the asymmetric efficient of the periodic potential, which is understood in terms of the effective-potential theory. The dependence of directed current on various parameters is studied systematically. Directed transport of coupled Brownian motors can be manipulated and optimized by adjusting pulsating period or the phase shift of the pulsating temperature.
Optimal estimates of the diffusion coefficient of a single Brownian trajectory.
Boyer, Denis; Dean, David S; Mejía-Monasterio, Carlos; Oshanin, Gleb
2012-03-01
Modern developments in microscopy and image processing are revolutionizing areas of physics, chemistry, and biology as nanoscale objects can be tracked with unprecedented accuracy. The goal of single-particle tracking is to determine the interaction between the particle and its environment. The price paid for having a direct visualization of a single particle is a consequent lack of statistics. Here we address the optimal way to extract diffusion constants from single trajectories for pure Brownian motion. It is shown that the maximum likelihood estimator is much more efficient than the commonly used least-squares estimate. Furthermore, we investigate the effect of disorder on the distribution of estimated diffusion constants and show that it increases the probability of observing estimates much smaller than the true (average) value.
Transport coefficients for a confined Brownian ratchet operating between two heat reservoirs
Ryabov, A.; Holubec, V.; Yaghoubi, M. H.; Varga, M.; Foulaadvand, M. E.; Chvosta, P.
2016-09-01
We discuss two-dimensional diffusion of a Brownian particle confined to a periodic asymmetric channel with soft walls modeled by a parabolic potential. In the channel, the particle experiences different thermal noise intensities, or temperatures, in the transversal and longitudinal directions. The model is inspired by the famous Feynman’s ratchet and pawl. Although the standard Fick-Jacobs approximation predicts correctly the effective diffusion coefficient, it fails to capture the ratchet effect. Deriving a correction, which breaks the local detailed balance with the transversal noise source, we obtain a correct mean velocity of the particle and a stationary probability density in the potential unit cell. The derived results are exact for small channel width. Yet, we check by exact numerical calculation that they qualitatively describe the ratchet effect observed for an arbitrary width of the channel.
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.
On the description of Brownian particles in confinement on a non-Cartesian coordinates basis
Dagdug, Leonardo; García-Chung, Angel A.; Chacón-Acosta, Guillermo
2016-08-01
We developed a theoretical framework to study the diffusion of Brownian point-like particles in bounded geometries in two and three dimensions. We use the Frenet-Serret moving frame as the coordinate system. For narrow tubes and channels, we use an effective one-dimensional description reducing the diffusion equation to a Fick-Jacobs-like equation. From this last equation, we can calculate the effective diffusion coefficient applying Neumann boundary conditions. On one hand, for channels with a straight axis our theoretical approximation for the effective coefficient does coincide with the reported in the literature [D. Reguera and J. M. Rubí, Phys. Rev. E 64, 061106 (2001) and P. Kalinay and J. K. Percus, ibid. 74, 041203 (2006)]. On the other hand, for tubes with a straight axis and circular cross-section our analytical expression does not coincide with the reported by Rubí and Reguera and by Kalinay and Percus, although it is practically identical.
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...
Energy Technology Data Exchange (ETDEWEB)
Park, Kyoungchul; Sonkusale, Sameer [Department of Electrical and Computer Engineering, Tufts University, Medford, MA 02155 (United States); Harrah, Tim; Goldberg, Edward B [Department of Molecular Biology and Microbiology, Tufts University, Boston, MA 02111 (United States); Guertin, Robert P, E-mail: sameer@ece.tufts.edu [Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)
2011-02-25
A novel multiplexed sensing scheme based on the measurement of the magnetic susceptibility of the affinity captured target molecules on magnetic nanoparticles in liquid suspension is proposed. The AC magnetic susceptibility provides a measurement of Brownian relaxation behavior of biomolecules bound to magnetic nanoparticles (MNPs) that is related to its hydrodynamic size. A room temperature, compact AC susceptometer is designed and developed to measure complex AC magnetic susceptibility of such magnetic nanoparticles. The AC susceptometer exhibits high sensitivity in magnetic fields as low as 10 {mu}T for 1 mg ml{sup -1} concentration and 5 {mu}l volume, and is fully software programmable. The capability of biological sensing using the proposed scheme has been demonstrated in proof of principle using the binding of biotinylated horseradish peroxidase (HRP) to streptavidin-coated MNPs. The proposed technique and instrument are readily compatible with lab-on-chip applications for point-of-care medical applications.
Vijaykumar, Adithya; Wolde, Pieter Rein ten; Bolhuis, Peter G
2016-01-01
The modeling of complex reaction-diffusion processes in, for instance, cellular biochemical networks or self-assembling soft matter can be tremendously sped up by employing a multiscale algorithm which combines the mesoscopic Green's Function Reaction Dynamics (GFRD) method with explicit stochastic Brownian, Langevin, or deterministic Molecular Dynamics to treat reactants at the microscopic scale [A. Vijaykumar, P.G. Bolhuis and P.R. ten Wolde, J. Chem. Phys. {\\bf 43}, 21: 214102 (2015)]. Here we extend this multiscale BD-GFRD approach to include the orientational dynamics that is crucial to describe the anisotropic interactions often prevalent in biomolecular systems. We illustrate the novel algorithm using a simple patchy particle model. After validation of the algorithm we discuss its performance. The rotational BD-GFRD multiscale method will open up the possibility for large scale simulations of e.g. protein signalling networks.
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
The cut-tree of large Galton-Watson trees and the Brownian CRT
Bertoin, Jean
2012-01-01
Consider the edge-deletion process in which the edges of some finite tree $T$ are removed one after the other in the uniform random order. Roughly speaking, the cut-tree then describes the genealogy of connected components appearing in this edge-deletion process. Our main result shows that after a proper rescaling, the cut-tree of a critical Galton-Watson tree with finite variance and conditioned to have size $n$, converges as $n\\to \\infty$ to a Brownian CRT in the weak sense induced by the Gromov-Prokhorov topology. This yields a multi-dimensional extension of a limit theorem due to Janson \\cite{Janson} for the number of random cuts needed to isolate the root in Galton-Watson trees conditioned by their sizes, and generalizes also a recent result \\cite{Be} obtained in the special case of Cayley trees.
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).
Brownian dynamics simulation of the effect of histone modification on nucleosome structure
Li, Wei; Dou, Shuo-Xing; Xie, Ping; Wang, Peng-Ye
2007-05-01
Using Brownian dynamics we simulate the effect of histone modification, such as phosphorylation, acetylation, and methylation, on nucleosome structure by varying the interaction force between DNA and the histone octamer. The simulation shows that the structural stability of nucleosome is very sensitive to the interaction force, and the DNA unwrapping from the modified histone octamer usually occurs turn by turn. Furthermore, the effects of temperature and DNA break as well as the competition between modified and normal histone octamers are investigated, with the simulation results being in agreement with the experimental observation that phosphorylated nucleosomes near DNA breaks are more easily depleted. Though the simulation study may only give a coarse grained view of the DNA unwrapping process for the modified histone octamer, it may provide insight into the mechanism of DNA repair.
Volume fraction instability in an oscillating non-Brownian iso-dense suspension.
Roht, Y. L.; Gauthier, G.; Hulin, J. P.; Salin, D.; Chertcoff, R.; Auradou, H.; Ippolito, I.
2017-06-01
The instability of an iso-dense non-Brownian suspension of polystyrene beads of diameter 40 μm dispersed in a water-glycerol mixture submitted to a periodic square wave oscillating flow in a Hele-Shaw cell is studied experimentally. The instability gives rise to stationary bead concentration waves transverse to the flow. It has been observed for average particle volume fractions between 0.25 and 0.4, for periods of the square wave flow variation between 0.4 and 10 s and in finite intervals of the amplitude of the fluid displacement. The study shows that the wavelength λ increases roughly linearly with the amplitude of the oscillatory flow; on the other hand, λ is independent of the particle concentration and of the period of oscillation of the flow although the minimum threshold amplitude for observing the instability increases with the period.
Surface diffusion of a Brownian particle subjected to an external harmonic noise
Bai, Zhan-Wu; Ding, Li-Ping
2017-05-01
Langevin simulation is performed to investigate the diffusion coefficient of a Brownian particle subjected to an external harmonic noise in a two-dimensional coupled periodic potential. Resonant diffusion phenomenon is observed as a result of the coupling between the central frequency of the spectral density of the harmonic noise and the frequency of the potential well bottom. The diffusion coefficient presents approximately linear functions of the strengths of the internal and external noises for low values of the strengths, these functions can be understood by the local linearization approximation of the potential force. The damping coefficient dependence of the diffusion coefficient in lower damping is well fitted by a negative power function, as an internal Gaussian white noise case does, but with a power whose absolute value is larger than 1.
Katiyar, Ajay; Das, Sarit K; Nandi, Tandra
2015-01-01
Magnetic nanocolloids with synthesized super paramagnetic Fe3O4 nanoparticles (SPION) (5 to 15 nm) dispersed in insitu developed Polyethylene Glycol (PEG 400) and nano silica complex have been synthesized. The PEG nano Silica complex physically encapsulates the SPIONs, ensuring no phase separation under high magnetic fields (1.2 T). Exhaustive magnetorheological investigations have been performed to comprehend the structural behavior and response of the ferrocolloids. Remarkable stability and reversibility have been observed under magnetic field for concentrated systems. The results exhibit the impact of particle concentration, size and encapsulation efficiency on parameters such as shear viscosity, yield stress, viscoelastic moduli, magnetoviscous hysteresis etc. Analytical models to reveal the system mechanism and mathematically predict the magnetoviscosity and magneto yield stress has been theorized. The mechanistic approach based on near field magnetostatics and Neel Brownian interactivities can predict t...
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.
A Langevin Approach to a Classical Brownian Oscillator in an Electromagnetic Field
Espinoza Ortiz, J. S.; Bauke, F. C.; Lagos, R. E.
2016-08-01
We consider a charged Brownian particle bounded by an harmonic potential, embedded in a Markovian heat bath and driven from equilibrium by external electric and magnetic fields. We develop a quaternionic-like (or Pauli spinor-like) representation, hitherto exploited in classical Lorentz related dynamics. Within this formalism, in a very straight forward and elegant fashion, we compute the exact solution for the resulting generalized Langevin equation, for the case of a constant magnetic field. For the case the source electromagnetic fields satisfy Maxwell's equations, yielding spinor-like Mathieu equations, we compute the solutions within the JWKB approximation. With the solutions at hand we further compute spatial, velocities and crossed time correlations. In particular we study the (kinetically defined) nonequilbrium temperature. Therefore, we can display the system's time evolution towards equilibrium or towards non equilibrium (steady or not) states.
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.
Free energy and entropy production rate for a Brownian particle that walks on overdamped medium
Taye, Mesfin Asfaw
2016-09-01
We derive general expressions for the free energy, entropy production, and entropy extraction rates for a Brownian particle that walks in a viscous medium where the dynamics of its motion is governed by the Langevin equation. It is shown that, when the system is out of equilibrium, it constantly produces entropy and at the same time extracts entropy out of the system. Its entropy production and extraction rates decrease in time and saturate to a constant value. In the long-time limit, the rate of entropy production balances the rate of entropy extraction and, at equilibrium, both entropy production and extraction rates become zero. Moreover, considering different model systems, not only do we investigate how various thermodynamic quantities behave in time but also we discuss the fluctuation theorem in detail.
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.
Generalized Scaling and the Master Variable for Brownian Magnetic Nanoparticle Dynamics.
Directory of Open Access Journals (Sweden)
Daniel B Reeves
Full Text Available Understanding the dynamics of magnetic particles can help to advance several biomedical nanotechnologies. Previously, scaling relationships have been used in magnetic spectroscopy of nanoparticle Brownian motion (MSB to measure biologically relevant properties (e.g., temperature, viscosity, bound state surrounding nanoparticles in vivo. Those scaling relationships can be generalized with the introduction of a master variable found from non-dimensionalizing the dynamical Langevin equation. The variable encapsulates the dynamical variables of the surroundings and additionally includes the particles' size distribution and moment and the applied field's amplitude and frequency. From an applied perspective, the master variable allows tuning to an optimal MSB biosensing sensitivity range by manipulating both frequency and field amplitude. Calculation of magnetization harmonics in an oscillating applied field is also possible with an approximate closed-form solution in terms of the master variable and a single free parameter.
Clustering determines the survivor for competing Brownian and L\\'evy walkers
Heinsalu, Els; López, Cristóbal
2013-01-01
The competition between two ecologically similar species that use the same resources and differ from each other only in the type of spatial motion they undergo is studied. The latter is assumed to be described either by Brownian motion or L\\'evy flights. Competition is taken into account by assuming that individuals reproduce in a density-dependent fashion. It is observed that no influence of the type of motion occurs when the two species are in a well-mixed unstructured state. However, as soon as the species develop spatial clustering, the one forming more concentrated clusters gets a competitive advantage and eliminates the other. Similar competitive advantage would occur between walkers of the same type but with different diffusivities if this leads also to different clustering. Coexistence of both species is also possible under certain conditions.
Directory of Open Access Journals (Sweden)
Lorenzo Marcucci
Full Text Available Muscular force generation in response to external stimuli is the result of thermally fluctuating, cyclical interactions between myosin and actin, which together form the actomyosin complex. Normally, these fluctuations are modelled using transition rate functions that are based on muscle fiber behaviour, in a phenomenological fashion. However, such a basis reduces the predictive power of these models. As an alternative, we propose a model which uses direct single molecule observations of actomyosin fluctuations reported in the literature. We precisely estimate the actomyosin potential bias and use diffusion theory to obtain a brownian ratchet model that reproduces the complete cross-bridge cycle. The model is validated by simulating several macroscopic experimental conditions, while its interpretation is compatible with two different force-generating scenarios.
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.
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.
GPU accelerated Monte Carlo simulation of Brownian motors dynamics with CUDA
Spiechowicz, J; Machura, L
2014-01-01
This work presents an updated and extended guide on methods of a proper acceleration of the Monte Carlo integration of stochastic differential equations with the commonly available NVIDIA Graphics Processing Units using the CUDA programming environment. We outline the general aspects of the scientific computing on graphics cards and demonstrate them with two models of a well known phenomenon of the noise induced transport of Brownian motors in periodic structures. As a source of fluctuations in the considered systems we selected the three most commonly occurring noises: the Gaussian white noise, the white Poissonian noise and the dichotomous process also known as a random telegraph signal. The detailed discussion on various aspects of the applied numerical schemes is also presented. The measured speedup can be of the astonishing order of 2000 when compared to a typical CPU. This number significantly expands the range of problems solvable by use of stochastic simulations, allowing even an interactive research ...
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.
GPU accelerated Monte Carlo simulation of Brownian motors dynamics with CUDA
Spiechowicz, J.; Kostur, M.; Machura, L.
2015-06-01
This work presents an updated and extended guide on methods of a proper acceleration of the Monte Carlo integration of stochastic differential equations with the commonly available NVIDIA Graphics Processing Units using the CUDA programming environment. We outline the general aspects of the scientific computing on graphics cards and demonstrate them with two models of a well known phenomenon of the noise induced transport of Brownian motors in periodic structures. As a source of fluctuations in the considered systems we selected the three most commonly occurring noises: the Gaussian white noise, the white Poissonian noise and the dichotomous process also known as a random telegraph signal. The detailed discussion on various aspects of the applied numerical schemes is also presented. The measured speedup can be of the astonishing order of about 3000 when compared to a typical CPU. This number significantly expands the range of problems solvable by use of stochastic simulations, allowing even an interactive research in some cases.
Measurements of Brownian relaxation of magnetic nanobeads using planar Hall effect bridge sensors.
Østerberg, F W; Rizzi, G; Zardán Gómez de la Torre, T; Strömberg, M; Strømme, M; Svedlindh, P; Hansen, M F
2013-02-15
We compare measurements of the Brownian relaxation response of magnetic nanobeads in suspension using planar Hall effect sensors of cross geometry and a newly proposed bridge geometry. We find that the bridge sensor yields six times as large signals as the cross sensor, which results in a more accurate determination of the hydrodynamic size of the magnetic nanobeads. Finally, the bridge sensor has successfully been used to measure the change in dynamic magnetic response when rolling circle amplified DNA molecules are bound to the magnetic nanobeads. The change is validated by measurements performed in a commercial AC susceptometer. The presented bridge sensor is, thus, a promising component in future lab-on-a-chip biosensors for detection of clinically relevant analytes, including bacterial genomic DNA and proteins.
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...
Coupling all-atom molecular dynamics simulations of ions in water with Brownian dynamics
Erban, Radek
2015-01-01
Molecular dynamics (MD) simulations of ions (K$^+$, Na$^+$, Ca$^{2+}$ and Cl$^-$) in aqueous solutions are investigated. Water is described using the SPC/E model. A stochastic coarse-grained description for ion behaviour is presented and parameterized using MD simulations. It is given as a system of coupled stochastic and ordinary differential equations, describing the ion position, velocity and acceleration. The stochastic coarse-grained model provides an intermediate description between all-atom MD simulations and Brownian dynamics (BD) models. It is used to develop a multiscale method which uses all-atom MD simulations in parts of the computational domain and (less detailed) BD simulations in the remainder of the domain.
Chechkin, A V; Metzler, R; Sokolov, I M
2016-01-01
A growing number of biological, soft, and active matter systems are observed to exhibit normal diffusive dynamics with a linear growth of the mean squared displacement, yet with a non-Gaussian distribution of increments. Based on the Chubinsky-Slater idea of a diffusing diffusivity we here establish and analyse a complete minimal model framework of diffusion processes with fluctuating diffusivity. In particular, we demonstrate the equivalence of the diffusing diffusivity process in the short time limit with a superstatistical approach based on a distribution of diffusivities. Moreover, we establish a subordination picture of Brownian but non-Gaussian diffusion processes, that can be used for a wide class of diffusivity fluctuation statistics. Our results are shown to be in excellent agreement with simulations and numerical evaluations.
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.
Barenbrug, Theo M. A. O. M.; Peters, E. A. J. F. (Frank); Schieber, Jay D.
2002-11-01
In Brownian Dynamics simulations, the diffusive motion of the particles is simulated by adding random displacements, proportional to the square root of the chosen time step. When computing average quantities, these Brownian contributions usually average out, and the overall simulation error becomes proportional to the time step. A special situation arises if the particles undergo hard-body interactions that instantaneously change their properties, as in absorption or association processes, chemical reactions, etc. The common "naı̈ve simulation method" accounts for these interactions by checking for hard-body overlaps after every time step. Due to the simplification of the diffusive motion, a substantial part of the actual hard-body interactions is not detected by this method, resulting in an overall simulation error proportional to the square root of the time step. In this paper we take the hard-body interactions during the time step interval into account, using the relative positions of the particles at the beginning and at the end of the time step, as provided by the naı̈ve method, and the analytical solution for the diffusion of a point particle around an absorbing sphere. Öttinger used a similar approach for the one-dimensional case [Stochastic Processes in Polymeric Fluids (Springer, Berlin, 1996), p. 270]. We applied the "corrected simulation method" to the case of a simple, second-order chemical reaction. The results agree with recent theoretical predictions [K. Hyojoon and Joe S. Kook, Phys. Rev. E 61, 3426 (2000)]. The obtained simulation error is proportional to the time step, instead of its square root. The new method needs substantially less simulation time to obtain the same accuracy. Finally, we briefly discuss a straightforward way to extend the method for simulations of systems with additional (deterministic) forces.
The effect of temperature dependence of viscosity on a Brownian heat engine
Taye, Mesfin Asfaw; Duki, Solomon Fekade
2015-12-01
We modeled a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a spatially varying temperature. The strength for the viscous friction γ( x) is considered to decrease exponentially when the temperature T( x) of the medium increases ( γ( x) = B e - AT( x)) as proposed originally by Reynolds [O. Reynolds, Phil. Trans. R. Soc. London 177, 157 (1886)]. Our result depicts that the velocity of the motor is considerably higher when the viscous friction is temperature dependent than that of the case where the viscous friction is temperature independent. The dependence of the efficiency η as well as the coefficient of performance of the refrigerator P ref on model parameters is also explored. If the motor designed to achieve a high velocity against a frictional drag, in the absence of external load f, we show that Carnot efficiency or Carnot refrigerator is unattainable even at quasistatic limit as long as the viscous friction is temperature dependent A ≠ 0. On the contrary, in the limit A → 0 or in general in the presence of an external load (for any A) f ≠ 0, at quasistatic limit, Carnot efficiency or Carnot refrigerator is attainable as long as the heat exchange via kinetic energy is omitted. For all cases, far from quasistatic limit, the efficiency and the coefficient of performance of the refrigerator are higher for constant γ case than the case where γ is temperature dependent. On the other hand, if one includes the heat exchange at the boundary of the heat baths, Carnot efficiency or Carnot refrigerator is unattainable even at quasistatic limit. Moreover, the dependence for the optimized and maximum power efficiencies on the determinant model parameters is explored.
Miao, Linling; Young, Charles D.; Sing, Charles E.
2017-07-01
Brownian Dynamics (BD) simulations are a standard tool for understanding the dynamics of polymers in and out of equilibrium. Quantitative comparison can be made to rheological measurements of dilute polymer solutions, as well as direct visual observations of fluorescently labeled DNA. The primary computational challenge with BD is the expensive calculation of hydrodynamic interactions (HI), which are necessary to capture physically realistic dynamics. The full HI calculation, performed via a Cholesky decomposition every time step, scales with the length of the polymer as O(N3). This limits the calculation to a few hundred simulated particles. A number of approximations in the literature can lower this scaling to O(N2 - N2.25), and explicit solvent methods scale as O(N); however both incur a significant constant per-time step computational cost. Despite this progress, there remains a need for new or alternative methods of calculating hydrodynamic interactions; large polymer chains or semidilute polymer solutions remain computationally expensive. In this paper, we introduce an alternative method for calculating approximate hydrodynamic interactions. Our method relies on an iterative scheme to establish self-consistency between a hydrodynamic matrix that is averaged over simulation and the hydrodynamic matrix used to run the simulation. Comparison to standard BD simulation and polymer theory results demonstrates that this method quantitatively captures both equilibrium and steady-state dynamics after only a few iterations. The use of an averaged hydrodynamic matrix allows the computationally expensive Brownian noise calculation to be performed infrequently, so that it is no longer the bottleneck of the simulation calculations. We also investigate limitations of this conformational averaging approach in ring polymers.
Interface Simulation Distances
Directory of Open Access Journals (Sweden)
Pavol Černý
2012-10-01
Full Text Available The classical (boolean notion of refinement for behavioral interfaces of system components is the alternating refinement preorder. In this paper, we define a distance for interfaces, called interface simulation distance. It makes the alternating refinement preorder quantitative by, intuitively, tolerating errors (while counting them in the alternating simulation game. We show that the interface simulation distance satisfies the triangle inequality, that the distance between two interfaces does not increase under parallel composition with a third interface, and that the distance between two interfaces can be bounded from above and below by distances between abstractions of the two interfaces. We illustrate the framework, and the properties of the distances under composition of interfaces, with two case studies.
DEFF Research Database (Denmark)
Troiano, Giovanni Maria
Deformable and shape-changing interfaces are rapidly emerging in the field of human-computer interaction (HCI). Deformable interfaces provide users with newer input possibilities such as bending, squeezing, or stretching, which were impossible to achieve with rigid interfaces. Shape-changing inte......Deformable and shape-changing interfaces are rapidly emerging in the field of human-computer interaction (HCI). Deformable interfaces provide users with newer input possibilities such as bending, squeezing, or stretching, which were impossible to achieve with rigid interfaces. Shape...
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...
Domínguez-García, P; Jeney, Sylvia
2016-01-01
We provide a detailed study of the interplay between the different interactions which appear in the Brownian motion of a micronsized sphere immersed in a viscoelastic fluid measured with optical trapping interferometry. To explore a wide range of viscous, elastic and optical forces, we analyze two different viscoelastic solutions at various concentrations, which provide a dynamic polymeric structure surrounding the Brownian sphere. Our experiments show that, depending of the fluid, optical forces, even if small, slightly modify the complex modulus at low frequencies. Based on our findings, we propose an alternative methodology to calibrate this kind of experimental set-up when non-Newtonian fluids are used. Understanding the influence of the optical potential is essential for a correct interpretation of the mechanical properties obtained by optically-trapped probe-based studies of biomaterials and living matter.
Østerberg, Frederik W.; Dalslet, Bjarke T.; Snakenborg, Detlef; Johansson, Christer; Hansen, Mikkel F.
2010-12-01
We present a simple `click-on' fluidic system with integrated electrical contacts, which is suited for electrical measurements on chips in microfluidic systems. We show that microscopic magnetic field sensors based on the planar Hall effect can be used for detecting the complex magnetic response using only the self-field arising from the bias current applied to the sensors as excitation field. We present measurements on a suspension of magnetic beads with a nominal diameter of 250 nm vs. temperature and find that the observations are consistent with the Cole-Cole model for Brownian relaxation with a constant hydrodynamic bead diameter when the temperature dependence of the viscosity of water is taken into account. These measurements demonstrate the feasibility of performing measurements of the Brownian relaxation response in a lab-on-a-chip system and constitute the first step towards an integrated biosensor based on the detection of the dynamic response of magnetic beads.
Shah, Saqlain A.; Reeves, Daniel B.; Ferguson, R. Matthew; Weaver, John B.
2015-01-01
Superparamagnetic iron oxide nanoparticles with highly nonlinear magnetic behavior are attractive for biomedical applications like magnetic particle imaging and magnetic fluid hyperthermia. Such particles display interesting magnetic properties in alternating magnetic fields and here we document experiments that show differences between the magnetization dynamics of certain particles in frozen and melted states. This effect goes beyond the small temperature difference (ΔT ~ 20 °C) and we show the dynamics to be a mixture of Brownian alignment of the particles and Néel rotation of their moments occurring in liquid particle suspensions. These phenomena can be modeled in a stochastic differential equation approach by postulating log-normal distributions and partial Brownian alignment of an effective anisotropy axis. We emphasize that precise particle-specific characterization through experiments and nonlinear simulations is necessary to predict dynamics in solution and optimize their behavior for emerging biomedical applications including magnetic particle imaging. PMID:26504371
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.
Domínguez-García, P.; Forró, László; Jeney, Sylvia
2016-10-01
We provide a detailed study of the interplay between the different interactions which appear in the Brownian motion of a micronsized sphere immersed in a viscoelastic fluid measured with optical trapping interferometry. To explore a wide range of viscous, elastic, and optical forces, we analyze two different viscoelastic solutions at various concentrations, which provide a dynamic polymeric structure surrounding the Brownian sphere. Our experiments show that, depending on the fluid, optical forces, even if small, slightly modify the complex modulus at low frequencies. Based on our findings, we propose an alternative methodology to calibrate this kind of experimental set-up when non-Newtonian fluids are used. Understanding the influence of the optical potential is essential for a correct interpretation of the mechanical properties obtained by optically-trapped probe-based studies of biomaterials and living matter.
DEFF Research Database (Denmark)
Østerberg, Frederik Westergaard; Dalslet, Bjarke Thomas; Snakenborg, Detlef
2010-01-01
We present a simple 'click-on' fluidic system with integrated electrical contacts, which is suited for electrical measurements on chips in microfluidic systems. We show that microscopic magnetic field sensors based on the planar Hall effect can be used for detecting the complex magnetic response...... with a constant hydrodynamic bead diameter when the temperature dependence of the viscosity of water is taken into account. These measurements demonstrate the feasibility of performing measurements of the Brownian relaxation response in a lab-on-a-chip system and constitute the first step towards an integrated...... using only the self-field arising from the bias current applied to the sensors as excitation field. We present measurements on a suspension of magnetic beads with a nominal diameter of 250 nm vs. temperature and find that the observations are consistent with the Cole-Cole model for Brownian relaxation...
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 .
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.
On-chip measurements of Brownian relaxation of magnetic beads with diameters from 10 nm to 250 nm
DEFF Research Database (Denmark)
Østerberg, Frederik Westergaard; Rizzi, Giovanni; Hansen, Mikkel Fougt
2013-01-01
We demonstrate the use of planar Hall effect magnetoresistive sensors for AC susceptibility measurements of magnetic beads with frequencies ranging from DC to 1 MHz. This wide frequency range allows for measuring Brownian relaxation of magnetic beads with diameters ranging from 10 nm to 250 nm...... to sedimentation, magnetic trapping, and signal per bead. Among the investigated beads, we conclude that the beads with a nominal diameter of 80 nm are best suited for future on-chip volume-based biosensing experiments using planar Hall effect sensors........ Brownian relaxation is measured for six different magnetic bead types and their hydrodynamic diameters are determined. The hydrodynamic diameters are found to be within 40% of the nominal bead diameters. We discuss the applicability of the different bead types for volume-based biosensing with respect...
DEFF Research Database (Denmark)
Troiano, Giovanni Maria
to convey particular information (e.g., big-isurgent, loud-is-up). The second work presents a large-scale analysis of 340 Sci-Fi movies that identifies instances of shape-changing interfaces. Results from the analysis reveals emergent behavioral patterns of shape change, namely Reconfiguration......Deformable and shape-changing interfaces are rapidly emerging in the field of human-computer interaction (HCI). Deformable interfaces provide users with newer input possibilities such as bending, squeezing, or stretching, which were impossible to achieve with rigid interfaces. Shape......-changing interfaces can reconfigure their shape dynamically, providing users with new affordances and output modalities. This thesis contributes to both the field of deformable interfaces and shape-changing interfaces through empirical research. In the area of deformable interfaces, this thesis presents two studies...
Interface localization near criticality
Delfino, Gesualdo
2016-01-01
The theory of interface localization in near-critical planar systems at phase coexistence is formulated from first principles. We show that mutual delocalization of two interfaces, amounting to interfacial wetting, occurs when the bulk correlation length critical exponent $\
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)
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.
Microcomputer interfacing and applications
Mustafa, M A
1990-01-01
This is the applications guide to interfacing microcomputers. It offers practical non-mathematical solutions to interfacing problems in many applications including data acquisition and control. Emphasis is given to the definition of the objectives of the interface, then comparing possible solutions and producing the best interface for every situation. Dr Mustafa A Mustafa is a senior designer of control equipment and has written many technical articles and papers on the subject of computers and their application to control engineering.
Complex Interfaces Under Change
DEFF Research Database (Denmark)
Rosbjerg, Dan
and mechanical processes that develop within this structure. Water-related processes at the interfaces between the compartments are complex, depending both on the interface itself, and on the characteristics of the interfaced compartments. Various aspects of global change directly or indirectly impact...
DEFF Research Database (Denmark)
Björneholm, Olle; Hansen, Martin Hangaard; Hodgson, Andrew
2016-01-01
The interfaces of neat water and aqueous solutions play a prominent role in many technological processes and in the environment. Examples of aqueous interfaces are ultrathin water films that cover most hydrophilic surfaces under ambient relative humidities, the liquid/solid interface which drives...
Dubina, Sean Hyun; Wedgewood, Lewis Edward
2016-07-01
Ferrofluids are often favored for their ability to be remotely positioned via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally simulated using the Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely, Maxwell's equations. An iterative constraint method was developed to satisfy Maxwell's equations when a uniform magnetic field is imposed on ferrofluids in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters in a mesoscale particle collection. This was accomplished by allowing a particulate system in a simple shear flow to advance by a time step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint method applied over sub-volume length scales until Maxwell's equations were satisfied. The resultant ferrofluid model with constraints demonstrates that the magnetoviscosity contribution is not as substantial when compared to homogeneous simulations that assume the material's magnetism is a direct response to the external magnetic field. This was detected across varying intensities of particle-particle interaction, Brownian motion, and shear flow. Ferroparticle aggregation was still extensively present but less so than typically observed.