Hybrid scheme for Brownian semistationary processes
DEFF Research Database (Denmark)
Bennedsen, Mikkel; Lunde, Asger; Pakkanen, Mikko S.
is to approximate the kernel function by a power function near zero and by a step function elsewhere. The resulting approximation of the process is a combination of Wiener integrals of the power function and a Riemann sum, which is why we call this method a hybrid scheme. Our main theoretical result describes...... 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......We introduce a simulation scheme for Brownian semistationary processes, which is based on discretizing the stochastic integral representation of the process in the time domain. We assume that the kernel function of the process is regularly varying at zero. The novel feature of the scheme...
Brownian semi-stationary processes, turbulence and smooth processes
DEFF Research Database (Denmark)
Urbina, José Ulises Márquez
This thesis analysis the use of Brownian semi-stationary (BSS) processes to model the main statistical features present in turbulent time series, and some asymptotic properties of certain classes of smooth processes. Turbulence is a complex phenomena governed by the Navier-Stokes equations....... We also studied the distributional properties of the increments of BSS processes with the intent to better understand why the BSS processes seem to accurately reproduce the temporal turbulent dynamics. BSS processes in general are not semimartingales. However, there are conditions which make a BSS...
Brownian semistationary processes and volatility/intermittency
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Schmiegel, Jürgen
of the semimartingale type. We focus on semimartingale - nonsemimartingale issues and on inference problems concerning the underlying volatility/intermittency process, in the nonsemimartingale case and based on normalised realised quadratic variation. The concept of BSS processes has arisen out of an ongoing study...... on the volatility/intermittency....
A weak limit theorem for numerical approximation of Brownian semi-stationary processes
DEFF Research Database (Denmark)
Podolskij, Mark; Thamrongrat, Nopporn
-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......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...
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
-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...
Discretization of Lévy semistationary processes with application to estimation
DEFF Research Database (Denmark)
Bennedsen, Mikkel; Lunde, Asger; Pakkanen, Mikko
Motivated by the construction of the Ito stochastic integral, we consider a step function method to discretize and simulate volatility modulated Lévy semistationary processes. Moreover, we assess the accuracy of the method with a particular focus on integrating kernels with a singularity...... at the origin. Using the simulation method, we study the finite sample properties of some recently developed estimators of realized volatility and associated parametric estimators for Brownian semistationary processes. Although the theoretical properties of these estimators have been established under high...
Assessing Gamma kernels and BSS/LSS processes
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole E.
This paper reviews the roles of gamma type kernels in the theory and modelling for Brownian and Lévy semistationary processes. Applications to financial econometrics and the physics of turbulence are pointed out.......This paper reviews the roles of gamma type kernels in the theory and modelling for Brownian and Lévy semistationary processes. Applications to financial econometrics and the physics of turbulence are pointed out....
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
The Diffusion Process in Small Particles and Brownian Motion
Khoshnevisan, M.
Albert Einstein in 1926 published his book entitled ''INVESTIGATIONS ON THE THEORY OF THE BROWNIAN MOVEMENT''. He investigated the process of diffusion in an undissociated dilute solution. The diffusion process is subject to Brownian motion. Furthermore, he elucidated the fact that the heat content of a substance will change the position of the single molecules in an irregular fashion. In this paper, I have shown that in order for the displacement of the single molecules to be proportional to the square root of the time, and for v/2 - v 1 Δ =dv/dx , (where v1 and v2 are the concentrations in two cross sections that are separated by a very small distance), ∫ - ∞ ∞ Φ (Δ) dΔ = I and I/τ ∫ - ∞ ∞Δ2/2 Φ (Δ) dΔ = D conditions to hold, then equation (7a) D =√{ 2 D }√{ τ} must be changed to Δ =√{ 2 D }√{ τ} . I have concluded that D =√{ 2 D }√{ τ} is an unintended error, and it has not been amended for almost 90 years in INVESTIGATIONS ON THE THEORY OF THE BROWNIAN MOVEMENT, 1926 publication.
Brownian Motion as a Limit to Physical Measuring Processes
DEFF Research Database (Denmark)
Niss, Martin
2016-01-01
formulated a general conclusion concerning the nature of physical measurements, namely that there is a definite limit to the ultimate sensitivity of measuring instruments beyond which we cannot advance, and that this limit is determined by Brownian motion. Ising’s conclusion agreed with experiments......In this paper, we examine the history of the idea that noise presents a fundamental limit to physical measuring processes. This idea had its origins in research aimed at improving the accuracy of instruments for electrical measurements. Out of these endeavors, the Swedish physicist Gustaf A. Ising...... and received widespread recognition, but his way of modeling the system was contested by his contemporaries. With the more embracing notion of noise that developed during and after World War II, Ising’s conclusion was reinterpreted as showing that noise puts a limit on physical measurement processes. Hence...
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.
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 discusse...
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...
Directory of Open Access Journals (Sweden)
Toufik Guendouzi
2013-11-01
Full Text Available We prove a global existence and uniqueness result for the solution of a mixed stochastic functional differential equation driven by a Wiener process and fractional Brownian motion with Hurst index H > 1/2. We also study the dependence of the solution on the initial condition.
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.
Smoldyn on graphics processing units: massively parallel Brownian dynamics simulations.
Dematté, Lorenzo
2012-01-01
Space is a very important aspect in the simulation of biochemical systems; recently, the need for simulation algorithms able to cope with space is becoming more and more compelling. Complex and detailed models of biochemical systems need to deal with the movement of single molecules and particles, taking into consideration localized fluctuations, transportation phenomena, and diffusion. A common drawback of spatial models lies in their complexity: models can become very large, and their simulation could be time consuming, especially if we want to capture the systems behavior in a reliable way using stochastic methods in conjunction with a high spatial resolution. In order to deliver the promise done by systems biology to be able to understand a system as whole, we need to scale up the size of models we are able to simulate, moving from sequential to parallel simulation algorithms. In this paper, we analyze Smoldyn, a widely diffused algorithm for stochastic simulation of chemical reactions with spatial resolution and single molecule detail, and we propose an alternative, innovative implementation that exploits the parallelism of Graphics Processing Units (GPUs). The implementation executes the most computational demanding steps (computation of diffusion, unimolecular, and bimolecular reaction, as well as the most common cases of molecule-surface interaction) on the GPU, computing them in parallel on each molecule of the system. The implementation offers good speed-ups and real time, high quality graphics output
Brownian motion in non-equilibrium systems and the Ornstein-Uhlenbeck stochastic process.
Donado, F; Moctezuma, R E; López-Flores, L; Medina-Noyola, M; Arauz-Lara, J L
2017-10-03
The Ornstein-Uhlenbeck stochastic process is an exact mathematical model providing accurate representations of many real dynamic processes in systems in a stationary state. When applied to the description of random motion of particles such as that of Brownian particles, it provides exact predictions coinciding with those of the Langevin equation but not restricted to systems in thermal equilibrium but only conditioned to be stationary. Here, we investigate experimentally single particle motion in a two-dimensional granular system in a stationary state, consisting of 1 mm stainless balls on a plane circular surface. The motion of the particles is produced by an alternating magnetic field applied perpendicular to the surface of the container. The mean square displacement of the particles is measured for a range of low concentrations and it is found that following an appropriate scaling of length and time, the short-time experimental curves conform a master curve covering the range of particle motion from ballistic to diffusive in accordance with the description of the Ornstein-Uhlenbeck model.
Godrèche, Claude
2017-05-01
The probability distribution of the longest interval between two zeros of a simple random walk starting and ending at the origin, and of its continuum limit, the Brownian bridge, was analysed in the past by Rosén and Wendel, then extended by the latter to stable processes. We recover and extend these results using simple concepts of renewal theory, which allows to revisit past and recent works of the physics literature.
Huang, Yongxiang; Wang, Lipo; Schmitt, F. G.; Zheng, Xiaobo; Jiang, Nan; Liu, Yulu
2017-07-01
In recent years several local extrema-based methodologies have been proposed to investigate either the nonlinear or the nonstationary time series for scaling analysis. In the present work, we study systematically the distribution of the local extrema for both synthesized scaling processes and turbulent velocity data from experiments. The results show that for the fractional Brownian motion (fBm) without intermittency correction the measured extremal-point-density (EPD) agrees well with a theoretical prediction. For a multifractal random walk (MRW) with the lognormal statistics, the measured EPD is independent of the intermittency parameter μ , suggesting that the intermittency correction does not change the distribution of extremal points but changes the amplitude. By introducing a coarse-grained operator, the power-law behavior of these scaling processes is then revealed via the measured EPD for different scales. For fBm the scaling exponent ξ (H ) is found to be ξ (H )=H , where H is Hurst number, while for MRW ξ (μ ) shows a linear relation with the intermittency parameter μ . Such EPD approach is further applied to the turbulent velocity data obtained from a wind tunnel flow experiment with the Taylor scale λ -based Reynolds number Reλ=720 , and a turbulent boundary layer with the momentum thickness θ based Reynolds number Reθ=810 . A scaling exponent ξ ≃0.37 is retrieved for the former case. For the latter one, the measured EPD shows clearly four regimes, which agrees well with the corresponding sublayer structures inside the turbulent boundary layer.
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.
Two-time correlation and occupation time for the Brownian bridge and tied-down renewal processes
Godrèche, Claude
2017-07-01
Tied-down renewal processes are generalisations of the Brownian bridge, where an event (or a zero crossing) occurs both at the origin of time and at the final observation time t. We give an analytical derivation of the two-time correlation function for such processes in the Laplace space of all temporal variables. This yields the exact asymptotic expression of the correlation in the Porod regime of short separations between the two times and in the persistence regime of large separations. We also investigate other quantities, such as the backward and forward recurrence times, as well as the occupation time of the process. The latter has a broad distribution which is determined exactly. Physical implications of these results for the Poland Scheraga and related models are given. These results also give exact answers to questions posed in the past in the context of stochastically evolving surfaces.
Energy Technology Data Exchange (ETDEWEB)
Tejedor, V; Benichou, O; Voituriez, R [Laboratoire de Physique Theorique de la Matiere Condensee (UMR 7600), Universite Pierre et Marie Curie, 4 Place Jussieu, 75255 Paris Cedex (France); Metzler, Ralf, E-mail: voiturie@lptmc.jussieu.fr [Physics Department, Technical University of Munich, James Franck Strasse, 85747 Garching (Germany)
2011-06-24
We derive a functional equation for the mean first-passage time (MFPT) of a generic self-similar Markovian continuous process to a target in a one-dimensional domain and obtain its exact solution. We show that the obtained expression of the MFPT for continuous processes is actually different from the large system size limit of the MFPT for discrete jump processes allowing leapovers. In the case considered here, the asymptotic MFPT admits non-vanishing corrections, which we call residual MFPT. The case of Levy flights with diverging variance of jump lengths is investigated in detail, in particular, with respect to the associated leapover behavior. We also show numerically that our results apply with good accuracy to fractional Brownian motion, despite its non-Markovian nature.
Man'ko, V I
1993-01-01
Brownian motion may be embedded in the Fock space of bosonic free field in one dimension.Extending this correspondence to a family of creation and annihilation operators satisfying a q-deformed algebra, the notion of q-deformation is carried from the algebra to the domain of stochastic processes.The properties of q-deformed Brownian motion, in particular its non-Gaussian nature and cumulant structure,are established.
Directory of Open Access Journals (Sweden)
Davide Mercadante
Full Text Available Pectin methylesterases (PMEs hydrolyze the methylester groups that are found on the homogalacturonan (HG chains of pectic polysaccharides in the plant cell wall. Plant and bacterial PMEs are especially interesting as the resulting de-methylesterified (carboxylated sugar residues are found to be arranged contiguously, indicating a so-called processive nature of these enzymes. Here we report the results of continuum electrostatics calculations performed along the molecular dynamics trajectory of a PME-HG-decasaccharide complex. In particular it was observed that, when the methylester groups of the decasaccharide were arranged in order to mimic the just-formed carboxylate product of de-methylesterification, a net unidirectional sliding of the model decasaccharide was subsequently observed along the enzyme's binding groove. The changes that occurred in the electrostatic binding energy and protein dynamics during this translocation provide insights into the mechanism by which the enzyme rectifies Brownian motions to achieve processivity. The free energy that drives these molecular motors is thus demonstrated to be incorporated endogenously in the methylesterified groups of the HG chains and is not supplied exogenously.
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...
Tail behaviour of Gaussian processes with applications to the Brownian pillow
A.J. Koning (Alex); V. Protassov (Vladimir)
2001-01-01
textabstractIn this paper we investigate the tail behaviour of a random variable S which may be viewed as a functional T of a zero mean Gaussian process X, taking special interest in the situation where X obeys the structure which is typical for limiting processes ocurring in nonparametric testing
Crisanti, A; Sarracino, A; Zannetti, M
2017-05-01
We study analytically the probability distribution of the heat released by an ensemble of harmonic oscillators to the thermal bath, in the nonequilibrium relaxation process following a temperature quench. We focus on the asymmetry properties of the heat distribution in the nonstationary dynamics, in order to study the forms taken by the fluctuation theorem as the number of degrees of freedom is varied. After analyzing in great detail the cases of one and two oscillators, we consider the limit of a large number of oscillators, where the behavior of fluctuations is enriched by a condensation transition with a nontrivial phase diagram, characterized by reentrant behavior. Numerical simulations confirm our analytical findings. We also discuss and highlight how concepts borrowed from the study of fluctuations in equilibrium under symmetry-breaking conditions [Gaspard, J. Stat. Mech. (2012) P0802110.1088/1742-5468/2012/08/P08021] turn out to be quite useful in understanding the deviations from the standard fluctuation theorem.
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...
From fractional Brownian motion to multifractional and multistable motion
Falconer, Kenneth
2015-03-01
Fractional Brownian motion, introduced by Benoit Mandelbrot and John Van Ness in 1968, has had a major impact on stochastic processes and their applications. We survey a few of the many developments that have stemmed from their ideas. In particular we discuss the local structure of fractional and multifractional Brownian, stable and multistable processes, emphasising the `diagonal' construction of such processes. In all this, the ubiquity and centrality of fractional Brownian motion is striking.
On 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.
van den Broek, Martijn; Van den Broeck, Christian
2008-01-01
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.
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.
Broek, M. van den; Broeck, C. Van Den
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.
Electrical autonomous Brownian gyrator
Chiang, K.-H.; Lee, C.-L.; Lai, P.-Y.; Chen, Y.-F.
2017-09-01
We study experimentally and theoretically the steady-state dynamics of a simple stochastic electronic system featuring two resistor-capacitor circuits coupled by a third capacitor. The resistors are subject to thermal noises at real temperatures. The voltage fluctuation across each resistor can be compared to a one-dimensional Brownian motion. However, the collective dynamical behavior, when the resistors are subject to distinct thermal baths, is identical to that of a Brownian gyrator, as first proposed by Filliger and Reimann [Phys. Rev. Lett. 99, 230602 (2007), 10.1103/PhysRevLett.99.230602]. The average gyrating dynamics is originated from the absence of detailed balance due to unequal thermal baths. We look into the details of this stochastic gyrating dynamics, its dependences on the temperature difference and coupling strength, and the mechanism of heat transfer through this simple electronic circuit. Our work affirms the general principle and the possibility of a Brownian ratchet working near room temperature scale.
Irreversible Brownian Heat Engine
Taye, Mesfin Asfaw
2017-10-01
We model a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a linearly decreasing background temperature. We show that the efficiency of such Brownian heat engine approaches the efficiency of endoreversible engine η =1-√{{Tc/Th}} [23]. On the other hand, the maximum power efficiency of the engine approaches η ^{MAX}=1-({Tc/Th})^{1\\over 4}. It is shown that the optimized efficiency always lies between the efficiency at quasistatic limit and the efficiency at maximum power while the efficiency at maximum power is always less than the optimized efficiency since the fast motion of the particle comes at the expense of the energy cost. If the heat exchange at the boundary of the heat baths is included, we show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature. The role of time on the performance of the motor is also explored via numerical simulations. Our numerical results depict that the time t and the external load dictate the direction of the particle velocity. Moreover, the performance of the heat engine improves with time. At large t (steady state), the velocity, the efficiency and the coefficient of performance of the refrigerator attain their maximum value. Furthermore, we study the effect of temperature by considering a viscous friction that decreases exponentially as the background temperature increases. Our result depicts that the Brownian particle exhibits a fast unidirectional motion when the viscous friction is temperature dependent than that of constant viscous friction. Moreover, the efficiency of this motor is considerably enhanced when the viscous friction is temperature dependent. On the hand, the motor exhibits a higher performance of the refrigerator when the viscous friction is taken to be constant.
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,
Dynamical 3-Space: Anisotropic Brownian Motion Experiment
Directory of Open Access Journals (Sweden)
Cahill R. T.
2015-07-01
Full Text Available In 2014 Jiapei Dai reported evidence of anisotropic Brownian motion of a toluidine blue colloid solution in water. In 2015 Felix Scholkmann analysed the Dai data and detected a sidereal time dependence, indicative of a process driving the preferred Brownian mo- tion diffusion direction to a star-based preferred direction. Here we further analyse the Dai data and extract the RA and Dec of that preferred direction, and relate the data to previous determinations from NASA Spacecraft Earth-flyby Doppler shift data, and other determinations.
From N-parameter fractional Brownian motions to N-parameter multifractional Brownian motions
Herbin, E.
2005-01-01
International audience; Multifractional Brownian motion is an extension of the well-known fractional Brownian motion where the H¨older regularity is allowed to vary along the paths. In this paper, two kinds of multi-parameter extensions of mBm are studied: one is isotropic while the other is not. For each of these processes, a moving average representation, a harmonizable representation, and the covariance structure are given. The H¨older regularity is then studied. In particular, the case of...
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...
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.
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…
Fractional Brownian motion and multifractional Brownian motion of Riemann-Liouville type
Lim, S. C.
2001-02-01
The relationship between standard fractional Brownian motion (FBM) and FBM based on the Riemann-Liouville fractional integral (or RL-FBM) is clarified. The absence of stationary property in the increment process of RL-FBM is compensated by a weaker property of local stationarity, and the stationary property for the increments of the large-time asymptotic RL-FBM. Generalization of RL-FBM to the RL-multifractional Brownian motion (RL-MBM) can be carried out by replacing the constant Hölder exponent by a time-dependent function. RL-MBM is shown to satisfy a weaker scaling property known as the local asymptotic self-similarity. This local scaling property can be translated into the small-scale behaviour of the associated scalogram by using the wavelet transform.
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.
White noise flashing Brownian pump
Gomez-Marin, A.; Sancho, J. M.
2007-01-01
A Brownian pump of particles powered by a stochastic flashing ratchet mechanism is studied. The pumping device is embedded in a finite region and bounded by particle reservoirs. In the steady state, we exactly calculate the spatial density profile, the concentration ratio between both reservoirs and the particle flux. A simple numerical scheme is presented allowing for the consistent evaluation of all such observable quantities.
Brownian movement and microscopic irreversibility
Gordon, L. G. M.
1981-02-01
An extension of the hypothetical experiment of Szilard, which involved the action of a one-molecule gas in an isolated isothermal system, is developed to illustrate how irreversibility may arise out of Brownian motion. As this development requires a consideration of nonmolecular components such as wheels and pistons, the thought-experiment is remodeled in molecular terms and appears to function as a perpetuum mobile.
Extremes of multifractional Brownian motion
Bai, Long
2017-01-01
Let $B_{H}(t), t\\geq [0,T], T\\in(0,\\infty)$ be the standard Multifractional Brownian Motion(mBm), in this contribution we are concerned with the exact asymptotics of \\begin{eqnarray*} \\mathbb{P}\\left\\{\\sup_{t\\in[0,T]}B_{H}(t)>u\\right\\} \\end{eqnarray*} as $u\\rightarrow\\infty$. Mainly depended on the structures of $H(t)$, the results under several important cases are investigated.
Brownian dynamics without Green's functions.
Delong, Steven; Usabiaga, Florencio Balboa; Delgado-Buscalioni, Rafael; Griffith, Boyce E; Donev, Aleksandar
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.
Trajectories of Brownian particles with space-correlated noise
Indian Academy of Sciences (India)
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 ...
A Brownian model for multiclass queueing networks with finite buffers
Dai, Wanyang
2002-07-01
This paper is concerned with the heavy traffic behavior of a type of multiclass queueing networks with finite buffers. The network consists of d single server stations and is populated by K classes of customers. Each station has a finite capacity waiting buffer and operates under first-in first-out (FIFO) service discipline. The network is assumed to have a feedforward routing structure under a blocking scheme. A server stops working when the downstream buffer is full. The focus of this paper is on the Brownian model formulation. More specifically, the approximating Brownian model for the networks is proposed via the method of showing a pseudo-heavy-traffic limit theorem which states that the limit process is a reflecting Brownian motion (RBM) if the properly normalized d-dimensional workload process converges in distribution to a continuous process. Numerical algorithm with finite element method has been designed to effectively compute the solution of the Brownian model (W. Dai, Ph.D. thesis (1996); X. Shen et al. The finite element method for computing the stationary distribution of an SRBM in a hypercube with applications to finite buffer queueing networks, under revision for Queueing Systems).
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.
Assessing Relative Volatility/Intermittency/Energy Dissipation
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole E.; Pakkanen, Mikko; Schmiegel, Jürgen
process in particular. While this estimation method is motivated by the assessment of relative energy dissipation in empirical data of turbulence, we apply it also to energy price data. Moreover, we develop a probabilistic asymptotic theory for relative power variations of Brownian semistationary......We introduce the notion of relative volatility/intermittency and demonstrate how relative volatility statistics can be used to estimate consistently the temporal variation of volatility/intermittency even when the data of interest are generated by a non-semimartingale, or a Brownian semistationary...... processes and Ito semimartingales and discuss how it can be used for inference on relative volatility/intermittency....
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.
Stochastic Current of Bifractional Brownian Motion
Directory of Open Access Journals (Sweden)
Jingjun Guo
2014-01-01
Full Text Available We study the regularity of stochastic current defined as Skorohod integral with respect to bifractional Brownian motion through Malliavin calculus. Moreover, we similarly derive some results in the case of multidimensional multiparameter. Finally, we consider stochastic current of bifractional Brownian motion as a distribution in Watanabe spaces.
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
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...
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.
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.
Integrated fractional white noise as an alternative to multifractional Brownian motion
Sly, Allan
2007-01-01
Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show h...
Brownian Functionals in Physics and Computer Science
Majumdar, Satya N.
This is a brief review on Brownian functionals in one dimension and their various applications. After a brief description of Einstein's original derivation of the diffusion equation, this article provides a pedagogical introduction to the path integral methods leading to the derivation of the celebrated Feynman-Kac formula. The usefulness of this technique in calculating the statistical properties of Brownian functionals is illustrated with several examples in physics and probability theory, with particular emphasis on applications in computer science. The statistical properties of "first-passage Brownian functionals" and their applications are also discussed.
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...
Brownian Motion, Fractal Structure and Verification of A. Einstein's Formula
Nikolić, Dragiša; Nešić, Ljubiša
2010-01-01
The work offers a simple experimental verification of A. Einstein and M. Smoluhovski's formula for Brownian motion. In this experiment we used latex solved in water, glycerin and alcohol while the observations and recording were done with a binocular optical microscope and a digital camera. Video material is recorded in separate files put on the Internet and can be downloaded and used for demonstration in class or further computer processing.
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.
Gibbs measures relative to Brownian motion and Nelson's model
Betz, Volker
2007-01-01
Nelson's model describes a quantum mechanical particle interacting with its own bosonic field. Usually the Fock space is used in order to describe the field, but it was noticed already in 1964 by E. Nelson that the field may be alternatively described by an infinite dimensional Ornstein-Uhlenbeck process. For the free field, this point of view was extremely successful. The case where a coupling is present is more involved and leads to the theory of Gibbs measures relative to Brownian motion. ...
On some possible generalizations of fractional Brownian motion
Lim, S. C.; Muniandy, S. V.
2000-02-01
Fractional Brownian motion (fBm) can be generalized to multifractional Brownian motion (mBm) if the Hurst exponent H is replaced by a deterministic function H( t). The two possible generalizations of mBm based on the moving average representation and the harmonizable representation are first shown to be equivalent up to a multiplicative deterministic function of time by Cohen [S. Cohen, in: M. Dekking et al. (Eds.), Fractals: Theory and Applications in Engineering, Springer, Berlin, 1999, p. 3.] using the Fourier transform method. In this Letter, we give an alternative verification of such an equivalence based on the direct computation of the covariances of these two Gaussian processes. There also exists another equivalent representation of mBm, which is a variant version of the harmonizable representation. Finally, we consider a generalization based on the Riemann-Liouville fractional integral, and study the large time asymptotic properties of this version of mBm.
Stochastically gated local and occupation times of a Brownian particle
Bressloff, Paul C.
2017-01-01
We generalize the Feynman-Kac formula to analyze the local and occupation times of a Brownian particle moving in a stochastically gated one-dimensional domain. (i) The gated local time is defined as the amount of time spent by the particle in the neighborhood of a point in space where there is some target that only receives resources from (or detects) the particle when the gate is open; the target does not interfere with the motion of the Brownian particle. (ii) The gated occupation time is defined as the amount of time spent by the particle in the positive half of the real line, given that it can only cross the origin when a gate placed at the origin is open; in the closed state the particle is reflected. In both scenarios, the gate randomly switches between the open and closed states according to a two-state Markov process. We derive a stochastic, backward Fokker-Planck equation (FPE) for the moment-generating function of the two types of gated Brownian functional, given a particular realization of the stochastic gate, and analyze the resulting stochastic FPE using a moments method recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment-generating function, averaged with respect to realizations of the stochastic gate.
Cost and Precision of Brownian Clocks
Directory of Open Access Journals (Sweden)
Andre C. Barato
2016-12-01
Full Text Available Brownian clocks are biomolecular networks that can count time. A paradigmatic example are proteins that go through a cycle, thus regulating some oscillatory behavior 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 the nonequilibrium steady state of the resulting bipartite Markov process, the uncertainty of the clock can be deduced from the calculable dispersion of a corresponding current.
Cost and Precision of Brownian Clocks
Barato, Andre C.; Seifert, Udo
2016-10-01
Brownian clocks are biomolecular networks that can count time. A paradigmatic example are proteins that go through a cycle, thus regulating some oscillatory behavior 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 the nonequilibrium steady state of the resulting bipartite Markov process, the uncertainty of the clock can be deduced from the calculable dispersion of a corresponding current.
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.
Static structure of active Brownian hard disks
de Macedo Biniossek, N.; Löwen, H.; Voigtmann, Th; Smallenburg, F.
2018-02-01
We explore the changes in static structure of a two-dimensional system of active Brownian particles (ABP) with hard-disk interactions, using event-driven Brownian dynamics simulations. In particular, the effect of the self-propulsion velocity and the rotational diffusivity on the orientationally-averaged fluid structure factor is discussed. Typically activity increases structural ordering and generates a structure factor peak at zero wave vector which is a precursor of motility-induced phase separation. Our results provide reference data to test future statistical theories for the fluid structure of active Brownian systems. This manuscript was submitted for the special issue of the Journal of Physics: Condensed Matter associated with the Liquid Matter Conference 2017.
Lectures from Markov processes to Brownian motion
Chung, Kai Lai
1982-01-01
This book evolved from several stacks of lecture notes written over a decade and given in classes at slightly varying levels. In transforming the over lapping material into a book, I aimed at presenting some of the best features of the subject with a minimum of prerequisities and technicalities. (Needless to say, one man's technicality is another's professionalism. ) But a text frozen in print does not allow for the latitude of the classroom; and the tendency to expand becomes harder to curb without the constraints of time and audience. The result is that this volume contains more topics and details than I had intended, but I hope the forest is still visible with the trees. The book begins at the beginning with the Markov property, followed quickly by the introduction of option al times and martingales. These three topics in the discrete parameter setting are fully discussed in my book A Course In Probability Theory (second edition, Academic Press, 1974). The latter will be referred to throughout this book ...
Variance change point detection for fractional Brownian motion based on the likelihood ratio test
Kucharczyk, Daniel; Wyłomańska, Agnieszka; Sikora, Grzegorz
2018-01-01
Fractional Brownian motion is one of the main stochastic processes used for describing the long-range dependence phenomenon for self-similar processes. It appears that for many real time series, characteristics of the data change significantly over time. Such behaviour one can observe in many applications, including physical and biological experiments. In this paper, we present a new technique for the critical change point detection for cases where the data under consideration are driven by fractional Brownian motion with a time-changed diffusion coefficient. The proposed methodology is based on the likelihood ratio approach and represents an extension of a similar methodology used for Brownian motion, the process with independent increments. Here, we also propose a statistical test for testing the significance of the estimated critical point. In addition to that, an extensive simulation study is provided to test the performance of the proposed method.
Lim, S. C.; Teo, L. P.
2009-08-01
Single-file diffusion behaves as normal diffusion at small time and as subdiffusion at large time. These properties can be described in terms of fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann-Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with a step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as a solution of the fractional Langevin equation with zero damping. Various kinds of fractional Langevin equations and their generalizations are then considered in order to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where the dissipative memory kernel is a Dirac delta function, a power-law function and a combination of these functions are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of a process that begins as ballistic motion.
A series expansion of fractional Brownian motion
K.O. Dzhaparidze (Kacha); J.H. van Zanten (Harry)
2002-01-01
textabstractLet $B$ be a fractional Brownian motion with Hurst index $H in (0,1)$. Denote by $x_1 < x_2 < cdots$ the positive, real zeros of the Bessel function $J_{-H$ of the first kind of order $-H$, and let $y_1 < y_2 < cdots$ be the positive zeros of $J_{1-H$. We prove the series
Brownian Motion Problem: Random Walk and Beyond
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 10; Issue 8. Brownian Motion Problem: Random Walk and Beyond. Shama Sharma Vishwamittar. General Article Volume 10 Issue 8 August 2005 pp 49-66. Fulltext. Click here to view fulltext PDF. Permanent link:
Brownian Warps for Non-Rigid Registration
DEFF Research Database (Denmark)
Nielsen, Mads; Johansen, Peter; Jackson, Andrew D.
2008-01-01
A Brownian motion model in the group of diffeomorphisms has been introduced as inducing a least committed prior on warps. This prior is source-destination symmetric, fulfills a natural semi-group property for warps, and with probability 1 creates invertible warps. Using this as a least committed...
Jeon, Jae-Hyung; Metzler, Ralf
2010-02-01
Motivated by subdiffusive motion of biomolecules observed in living cells, we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time-averaged mean-squared displacement and displacement correlation) are affected by spatial confinement and dimensionality. In particular, we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain. The general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality. We define the displacement correlation function and find that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single-particle trajectory data.
Brownian Motion in a Weyl Chamber, Non-Colliding Particles, and Random Matrices
Grabiner, David J.
1997-01-01
Let $n$ particles move in standard Brownian motion in one dimension, with the process terminating if two particles collide. This is a specific case of Brownian motion constrained to stay inside a Weyl chamber; the Weyl group for this chamber is $A_{n-1}$, the symmetric group. For any starting positions, we compute a determinant formula for the density function for the particles to be at specified positions at time $t$ without having collided by time $t$. We show that the probability that ther...
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.
Detrended Fluctuation Analysis of multifractional Brownian motion
Setty, Venkat; Sharma, Surjalal
2013-03-01
Multifractional Brownian Motion (mBm) is a generalization of Fractional Brownian motion (fBm) with a time varying Hurst exponent, H (t) . Detrended Fluctuation Analysis (DFA) is a technique used to study the scaling behavior representing long term correlations in various dynamical systems. In our work, we apply DFA to calculate a time averaged Hurst exponent, in mBm data. The accuracy of estimation of was shown to depend on the range and variability of H (t) . Furthermore, the effect of uniform random noise in H (t) on the nature of scaling observed in DFA is studied. Our research focusses on the robustness and applicability of the DFA technique for studying long term correlations in systems with time varying Hurst exponents akin to mBm .
Velocity Gradient Power Functional for Brownian Dynamics.
de Las Heras, Daniel; Schmidt, Matthias
2018-01-12
We present an explicit and simple approximation for the superadiabatic excess (over ideal gas) free power functional, admitting the study of the nonequilibrium dynamics of overdamped Brownian many-body systems. The functional depends on the local velocity gradient and is systematically obtained from treating the microscopic stress distribution as a conjugate field. The resulting superadiabatic forces are beyond dynamical density functional theory and are of a viscous nature. Their high accuracy is demonstrated by comparison to simulation results.
Active Brownian motion tunable by light.
Buttinoni, Ivo; Volpe, Giovanni; Kümmel, Felix; Volpe, Giorgio; Bechinger, Clemens
2012-07-18
Active Brownian particles are capable of taking up energy from their environment and converting it into directed motion; examples range from chemotactic cells and bacteria to artificial micro-swimmers. We have recently demonstrated that Janus particles, i.e. gold-capped colloidal spheres, suspended in a critical binary liquid mixture perform active Brownian motion when illuminated by light. In this paper, we investigate in more detail their swimming mechanism, leading to active Brownian motion. We show that the illumination-borne heating induces a local asymmetric demixing of the binary mixture, generating a spatial chemical concentration gradient which is responsible for the particle's self-diffusiophoretic motion. We study this effect as a function of the functionalization of the gold cap, the particle size and the illumination intensity: the functionalization determines what component of the binary mixture is preferentially adsorbed at the cap and the swimming direction (towards or away from the cap); the particle size determines the rotational diffusion and, therefore, the random reorientation of the particle; and the intensity tunes the strength of the heating and, therefore, of the motion. Finally, we harness this dependence of the swimming strength on the illumination intensity to investigate the behavior of a micro-swimmer in a spatial light gradient, where its swimming properties are space-dependent.
Quantum dynamical framework for Brownian heat engines.
Agarwal, G S; Chaturvedi, S
2013-07-01
We present a self-contained formalism modeled after the Brownian motion of a quantum harmonic oscillator for describing the performance of microscopic Brownian heat engines such as Carnot, Stirling, and Otto engines. Our theory, besides reproducing the standard thermodynamics results in the steady state, enables us to study the role dissipation plays in determining the efficiency of Brownian heat engines under actual laboratory conditions. In particular, we analyze in detail the dynamics associated with decoupling a system in equilibrium with one bath and recoupling it to another bath and obtain exact analytical results, which are shown to have significant ramifications on the efficiencies of engines involving such a step. We also develop a simple yet powerful technique for computing corrections to the steady state results arising from finite operation time and use it to arrive at the thermodynamic complementarity relations for various operating conditions and also to compute the efficiencies of the three engines cited above at maximum power. Some of the methods and exactly solvable models presented here are interesting in their own right and could find useful applications in other contexts as well.
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.
On the tail asymptotics of the area swept under the Brownian storage graph
Arendarczyk, M.; Dȩbicki, K.; Mandjes, M.
2014-01-01
In this paper, the area swept under the workload graph is analyzed: with {Q(t): t≥0} denoting the stationary workload process, the asymptotic behavior of πT(u)(u):=P(∫T(u)0Q(r)dr>u) is analyzed. Focusing on regulated Brownian motion, first the exact asymptotics of πT(u)(u) are given for the case
Chaotic expansion and smoothness of some functionals of the fractional Brownian motion
Eddahbi, M’hamed; Vives, Josep
2003-01-01
This paper deals with some additive functionals of the fractional Brownian motion that arise as limits in law of some occupation times of this process. In concrete, this functionals are obtained via the Cauchy principal value and the Hadamard finite part. We derive some regularity properties of theses functionals in Sobolev-Watanabe sense.
Large-deviation properties of Brownian motion with dry friction
Chen, Yaming; Just, Wolfram
2014-10-01
We investigate piecewise-linear stochastic models with regard to the probability distribution of functionals of the stochastic processes, a question that occurs frequently in large deviation theory. The functionals that we are looking into in detail are related to the time a stochastic process spends at a phase space point or in a phase space region, as well as to the motion with inertia. For a Langevin equation with discontinuous drift, we extend the so-called backward Fokker-Planck technique for non-negative support functionals to arbitrary support functionals, to derive explicit expressions for the moments of the functional. Explicit solutions for the moments and for the distribution of the so-called local time, the occupation time, and the displacement are derived for the Brownian motion with dry friction, including quantitative measures to characterize deviation from Gaussian behavior in the asymptotic long time limit.
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.
Craven, Galen T.; Nitzan, Abraham
2018-01-01
Statistical properties of Brownian motion that arise by analyzing, separately, trajectories over which the system energy increases (upside) or decreases (downside) with respect to a threshold energy level are derived. This selective analysis is applied to examine transport properties of a nonequilibrium Brownian process that is coupled to multiple thermal sources characterized by different temperatures. Distributions, moments, and correlation functions of a free particle that occur during upside and downside events are investigated for energy activation and energy relaxation processes and also for positive and negative energy fluctuations from the average energy. The presented results are sufficiently general and can be applied without modification to the standard Brownian motion. This article focuses on the mathematical basis of this selective analysis. In subsequent articles in this series, we apply this general formalism to processes in which heat transfer between thermal reservoirs is mediated by activated rate processes that take place in a system bridging them.
A modified Brownian force for ultrafine particle penetration through building crack modeling
Chen, Chen; Zhao, Bin
2017-12-01
Combustion processes related to industry, traffic, agriculture, and waste treatment and disposal increase the amount of outdoor ultrafine particles (UFPs), which have adverse effects on human health. Given that people spend the majority of their time indoors, it is critical to understand the penetration of outdoor UFPs through building cracks in order to estimate human exposure to outdoor-originated UFPs. Lagrangian tracking is an efficient approach for modeling particle penetration. However, the Brownian motion for Lagrangian tracking in ANSYS Fluent®, a widely used software for particle dispersion modeling, is not able to model UFP dispersion accurately. In this study, we modified the Brownian force by rewriting the Brownian diffusion coefficient and particle integration time step with a user-defined function in ANSYS Fluent® to model particle penetration through building cracks. The results obtained using the modified model agree much better with the experimental results, with the averaged relative error less than 14% for the smooth crack cases and 21% for the rough crack case. We expect the modified Brownian force model proposed herein to be applied for UFP dispersion modeling in more indoor air quality studies.
Mean-field theory of quantum Brownian motion
Allahverdyan, A.; Balian, R.
2001-01-01
We investigate a mean-field approach to a quantum Brownian particle interacting with a quantum thermal bath at temperature T, and subjected to a non-linear potential. An exact, partially classical description of quantum Brownian motion is proposed, which uses negative probabilities in its
Brownian motion of a particle with arbitrary shape.
Cichocki, Bogdan; Ekiel-Jeżewska, Maria L; Wajnryb, Eligiusz
2015-06-07
Brownian motion of a particle with an arbitrary shape is investigated theoretically. Analytical expressions for the time-dependent cross-correlations of the Brownian translational and rotational displacements are derived from the Smoluchowski equation. The role of the particle mobility center is determined and discussed.
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...
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...
Tested Demonstrations. Brownian Motion: A Classroom Demonstration and Student Experiment.
Kirksey, H. Graden; Jones, Richard F.
1988-01-01
Shows how video recordings of the Brownian motion of tiny particles may be made. Describes a classroom demonstration and cites a reported experiment designed to show the random nature of Brownian motion. Suggests a student experiment to discover the distance a tiny particle travels as a function of time. (MVL)
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.
Hybrid finite element and Brownian dynamics method for charged particles
Energy Technology Data Exchange (ETDEWEB)
Huber, Gary A., E-mail: ghuber@ucsd.edu; Miao, Yinglong [Howard Hughes Medical Institute, University of California San Diego, La Jolla, California 92093-0365 (United States); Zhou, Shenggao [Department of Mathematics and Mathematical Center for Interdiscipline Research, Soochow University, 1 Shizi Street, Suzhou, 215006 Jiangsu (China); Li, Bo [Department of Mathematics and Quantitative Biology Graduate Program, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112 (United States); McCammon, J. Andrew [Howard Hughes Medical Institute, University of California San Diego, La Jolla, California 92093 (United States); Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093-0365 (United States); Department of Pharmacology, University of California San Diego, La Jolla, California 92093-0636 (United States)
2016-04-28
Diffusion is often the rate-determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. A previous study introduced a new hybrid diffusion method that couples the strengths of each of these two methods, but was limited by the lack of interactions among the particles; the force on each particle had to be from an external field. This study further develops the method to allow charged particles. The method is derived for a general multidimensional system and is presented using a basic test case for a one-dimensional linear system with one charged species and a radially symmetric system with three charged species.
Large scale Brownian dynamics of confined suspensions of rigid particles.
Sprinkle, Brennan; Balboa Usabiaga, Florencio; Patankar, Neelesh A; Donev, Aleksandar
2017-12-28
We introduce methods for large-scale Brownian Dynamics (BD) simulation of many rigid particles of arbitrary shape suspended in a fluctuating fluid. Our method adds Brownian motion to the rigid multiblob method [F. Balboa Usabiaga et al., Commun. Appl. Math. Comput. Sci. 11(2), 217-296 (2016)] at a cost comparable to the cost of deterministic simulations. We demonstrate that we can efficiently generate deterministic and random displacements for many particles using preconditioned Krylov iterative methods, if kernel methods to efficiently compute the action of the Rotne-Prager-Yamakawa (RPY) mobility matrix and its "square" root are available for the given boundary conditions. These kernel operations can be computed with near linear scaling for periodic domains using the positively split Ewald method. Here we study particles partially confined by gravity above a no-slip bottom wall using a graphical processing unit implementation of the mobility matrix-vector product, combined with a preconditioned Lanczos iteration for generating Brownian displacements. We address a major challenge in large-scale BD simulations, capturing the stochastic drift term that arises because of the configuration-dependent mobility. Unlike the widely used Fixman midpoint scheme, our methods utilize random finite differences and do not require the solution of resistance problems or the computation of the action of the inverse square root of the RPY mobility matrix. We construct two temporal schemes which are viable for large-scale simulations, an Euler-Maruyama traction scheme and a trapezoidal slip scheme, which minimize the number of mobility problems to be solved per time step while capturing the required stochastic drift terms. We validate and compare these schemes numerically by modeling suspensions of boomerang-shaped particles sedimented near a bottom wall. Using the trapezoidal scheme, we investigate the steady-state active motion in dense suspensions of confined microrollers, whose
Large scale Brownian dynamics of confined suspensions of rigid particles
Sprinkle, Brennan; Balboa Usabiaga, Florencio; Patankar, Neelesh A.; Donev, Aleksandar
2017-12-01
We introduce methods for large-scale Brownian Dynamics (BD) simulation of many rigid particles of arbitrary shape suspended in a fluctuating fluid. Our method adds Brownian motion to the rigid multiblob method [F. Balboa Usabiaga et al., Commun. Appl. Math. Comput. Sci. 11(2), 217-296 (2016)] at a cost comparable to the cost of deterministic simulations. We demonstrate that we can efficiently generate deterministic and random displacements for many particles using preconditioned Krylov iterative methods, if kernel methods to efficiently compute the action of the Rotne-Prager-Yamakawa (RPY) mobility matrix and its "square" root are available for the given boundary conditions. These kernel operations can be computed with near linear scaling for periodic domains using the positively split Ewald method. Here we study particles partially confined by gravity above a no-slip bottom wall using a graphical processing unit implementation of the mobility matrix-vector product, combined with a preconditioned Lanczos iteration for generating Brownian displacements. We address a major challenge in large-scale BD simulations, capturing the stochastic drift term that arises because of the configuration-dependent mobility. Unlike the widely used Fixman midpoint scheme, our methods utilize random finite differences and do not require the solution of resistance problems or the computation of the action of the inverse square root of the RPY mobility matrix. We construct two temporal schemes which are viable for large-scale simulations, an Euler-Maruyama traction scheme and a trapezoidal slip scheme, which minimize the number of mobility problems to be solved per time step while capturing the required stochastic drift terms. We validate and compare these schemes numerically by modeling suspensions of boomerang-shaped particles sedimented near a bottom wall. Using the trapezoidal scheme, we investigate the steady-state active motion in dense suspensions of confined microrollers, whose
Rectified brownian transport in corrugated channels: Fractional brownian motion and Lévy flights.
Ai, Bao-quan; Shao, Zhi-gang; Zhong, Wei-rong
2012-11-07
We study fractional brownian motion and Lévy flights in periodic corrugated channels without any external driving forces. From numerical simulations, we find that both fractional gaussian noise and Lévy-stable noise in asymmetric corrugated channels can break thermodynamical equilibrium and induce directed transport. The rectified mechanisms for fractional brownian motion and Lévy flights are different. The former is caused by non-uniform spectral distribution (low or high frequencies) of fractional gaussian noise, while the latter is due to the nonthermal character (occasional long jumps) of the Lévy-stable noise. For fractional brownian motion, average velocity increases with the Hurst exponent for the persistent case, while for the antipersistent case there exists an optimal value of Hurst exponent at which average velocity takes its maximal value. For Lévy flights, the group velocity decreases monotonically as the Lévy index increases. In addition, for both cases, the optimized periodicity and radius at the bottleneck can facilitate the directed transport. Our results could be implemented in constrained structures with narrow channels and pores where the particles undergo anomalous diffusion.
Predicting Protein Interactions by Brownian Dynamics Simulations
Directory of Open Access Journals (Sweden)
Xuan-Yu Meng
2012-01-01
Full Text Available We present a newly adapted Brownian-Dynamics (BD-based protein docking method for predicting native protein complexes. The approach includes global BD conformational sampling, compact complex selection, and local energy minimization. In order to reduce the computational costs for energy evaluations, a shell-based grid force field was developed to represent the receptor protein and solvation effects. The performance of this BD protein docking approach has been evaluated on a test set of 24 crystal protein complexes. Reproduction of experimental structures in the test set indicates the adequate conformational sampling and accurate scoring of this BD protein docking approach. Furthermore, we have developed an approach to account for the flexibility of proteins, which has been successfully applied to reproduce the experimental complex structure from the structure of two unbounded proteins. These results indicate that this adapted BD protein docking approach can be useful for the prediction of protein-protein interactions.
Brownian motion in dynamically disordered media.
Witkoskie, James B; Yang, Shilong; Cao, Jianshu
2002-11-01
The motion of Brownian test particles in a model random potential with time dependent correlations is investigated using four methods: renormalized perturbation, perturbation using Martin, Siggia, and Rose functional formalism (MSR), the Edwards variational method on the MSR functional, and renormalization group with the MSR function. The disorder averaged one-particle propagators determined by the renormalized perturbation expansion and MSR perturbation expansion are identical to the second and possibly higher order, and the two-particle propagators determined by these perturbation methods are identical at the first and possibly higher order. The one-particle propagator determined by the Edwards method is identical to the perturbation expansions at the first order, but the second-order analogue of the Edwards method has a more complex expression, which reduces to the second-order perturbation expression with additional higher-order terms. The diffusion constant and two-particle correlations are calculated from these propagators and are used to determine the effects of the random potential on the Brownian particles. Generally, the diffusion rate decreases with the disorder strength and increases with the temporal decay rate. The two competing mechanisms result in an enhancement of the diffusion constant for weak potentials with fast temporal fluctuations. The system exhibits two-particle correlations that are inherently non-Gaussian and indicate clustering behavior. The diffusion constant is also determined from a simple one-loop renormalization group calculation. In the static limit, the diffusion constant calculated by the renormalization group recovers the results of Deem and Chandler [M.W. Deem and D. Chandler, J. Stat. Phys. 76, 911 (1994)].
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.
Beyond multifractional Brownian motion: new stochastic models for geophysical modelling
Lévy Véhel, J.
2013-09-01
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.
Assessing relative volatility/intermittency/energy dissipation
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole E.; Pakkanen, Mikko S.; Schmiegel, Jürgen
2014-01-01
process in particular. This estimation method is motivated by the assessment of relative energy dissipation in empirical data of turbulence, but it is also applicable in other areas. We develop a probabilistic asymptotic theory for realised relative power variations of Brownian semistationary processes......, and introduce inference methods based on the theory. We also discuss how to extend the asymptotic theory to other classes of processes exhibiting stochastic volatility/intermittency. As an empirical application, we study relative energy dissipation in data of atmospheric turbulence.......We introduce the notion of relative volatility/intermittency and demonstrate how relative volatility statistics can be used to estimate consistently the temporal variation of volatility/intermittency when the data of interest are generated by a non-semimartingale, or a Brownian semistationary...
Weak convergence of the past and future of Brownian motion given ...
Indian Academy of Sciences (India)
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 σ 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 ...
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.
Random times and enlargements of filtrations in a Brownian setting
Mansuy, Roger
2006-01-01
In November 2004, M. Yor and R. Mansuy jointly gave six lectures at Columbia University, New York. These notes follow the contents of that course, covering expansion of filtration formulae; BDG inequalities up to any random time; martingales that vanish on the zero set of Brownian motion; the Azéma-Emery martingales and chaos representation; the filtration of truncated Brownian motion; attempts to characterize the Brownian filtration. The book accordingly sets out to acquaint its readers with the theory and main examples of enlargements of filtrations, of either the initial or the progressive kind. It is accessible to researchers and graduate students working in stochastic calculus and excursion theory, and more broadly to mathematicians acquainted with the basics of Brownian motion.
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.
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.
Estimation of the global regularity of a multifractional Brownian motion
Lebovits, Joachim; Podolskij, Mark
2016-01-01
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 th...
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.
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.
Shear thinning in non-Brownian suspensions.
Chatté, Guillaume; Comtet, Jean; Niguès, Antoine; Bocquet, Lydéric; Siria, Alessandro; Ducouret, Guylaine; Lequeux, François; Lenoir, Nicolas; Ovarlez, Guillaume; Colin, Annie
2018-02-14
We study the flow of suspensions of non-Brownian particles dispersed into a Newtonian solvent. Combining capillary rheometry and conventional rheometry, we evidence a succession of two shear thinning regimes separated by a shear thickening one. Through X-ray radiography measurements, we show that during each of those regimes, the flow remains homogeneous and does not involve particle migration. Using a quartz-tuning fork based atomic force microscope, we measure the repulsive force profile and the microscopic friction coefficient μ between two particles immersed into the solvent, as a function of normal load. Coupling measurements from those three techniques, we propose that (1) the first shear-thinning regime at low shear rates occurs for a lubricated rheology and can be interpreted as a decrease of the effective volume fraction under increasing particle pressures, due to short-ranged repulsive forces and (2) the second shear thinning regime after the shear-thickening transition occurs for a frictional rheology and can be interpreted as stemming from a decrease of the microscopic friction coefficient at large normal load.
Single particle Brownian motion with solid friction.
Das, Prasenjit; Puri, Sanjay; Schwartz, Moshe
2017-06-01
We study the Brownian dynamics of a solid particle on a vibrating solid surface. Phenomenologically, the interaction between the two solid surfaces is modeled by solid friction, and the Gaussian white noise models the vibration of the solid surface. The solid friction force is proportional to the sign of relative velocity. We derive the Fokker-Planck (FP) equation for the time-dependent probability distribution to find the particle at a given location. We calculate analytically the steady state velocity distribution function, mean-square velocity and diffusion coefficient in d-dimensions. We present a generic method of calculating the autocorrelations in d-dimensions. This results in one dimension in an exact evaluation of the steady state velocity autocorrelation. In higher dimensions our exact general expression enables the analytic evaluation of the autocorrelation to any required approximation. We present approximate analytic expressions in two and three dimensions. Next, we numerically calculate the mean-square velocity and steady state velocity autocorrelation function up to d = 3 . Our numerical results are in good agreement with the analytically obtained results.
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole E.
The density function of the gamma distribution is used as shift kernel in Brownian semistationary processes modelling the timewise behaviour of the velocity in turbulent regimes. This report presents exact and asymptotic properties of the second order structure function under such a model......, and relates these to results of von Karmann and Horwath. But first it is shown that the gamma kernel is interpretable as a Green’s function....
Brownian motion with adaptive drift for remaining useful life prediction: Revisited
Wang, Dong; Tsui, Kwok-Leung
2018-01-01
Linear Brownian motion with constant drift is widely used in remaining useful life predictions because its first hitting time follows the inverse Gaussian distribution. State space modelling of linear Brownian motion was proposed to make the drift coefficient adaptive and incorporate on-line measurements into the first hitting time distribution. Here, the drift coefficient followed the Gaussian distribution, and it was iteratively estimated by using Kalman filtering once a new measurement was available. Then, to model nonlinear degradation, linear Brownian motion with adaptive drift was extended to nonlinear Brownian motion with adaptive drift. However, in previous studies, an underlying assumption used in the state space modelling was that in the update phase of Kalman filtering, the predicted drift coefficient at the current time exactly equalled the posterior drift coefficient estimated at the previous time, which caused a contradiction with the predicted drift coefficient evolution driven by an additive Gaussian process noise. In this paper, to alleviate such an underlying assumption, a new state space model is constructed. As a result, in the update phase of Kalman filtering, the predicted drift coefficient at the current time evolves from the posterior drift coefficient at the previous time. Moreover, the optimal Kalman filtering gain for iteratively estimating the posterior drift coefficient at any time is mathematically derived. A discussion that theoretically explains the main reasons why the constructed state space model can result in high remaining useful life prediction accuracies is provided. Finally, the proposed state space model and its associated Kalman filtering gain are applied to battery prognostics.
Liu, Fan; Jiang, Li; Tan, Huei Ming; Yadav, Ashutosh; Biswas, Preetika; van der Maarel, Johan R. C.; Nijhuis, Christian A.; van Kan, Jeroen A.
2016-01-01
Brownian ratchet based particle separation systems for application in lab on chip devices have drawn interest and are subject to ongoing theoretical and experimental investigations. We demonstrate a compact microfluidic particle separation chip, which implements an extended on-off Brownian ratchet scheme that actively separates and sorts particles using periodically switching magnetic fields, asymmetric sawtooth channel sidewalls, and Brownian motion. The microfluidic chip was made with Polydimethylsiloxane (PDMS) soft lithography of SU-8 molds, which in turn was fabricated using Proton Beam Writing. After bonding of the PDMS chip to a glass substrate through surface activation by oxygen plasma treatment, embedded electromagnets were cofabricated by the injection of InSn metal into electrode channels. This fabrication process enables rapid production of high resolution and high aspect ratio features, which results in parallel electrodes accurately aligned with respect to the separation channel. The PDMS devices were tested with mixtures of 1.51 μm, 2.47 μm, and 2.60 μm superparamagnetic particles suspended in water. Experimental results show that the current device design has potential for separating particles with a size difference around 130 nm. Based on the promising results, we will be working towards extending this design for the separation of cells or biomolecules. PMID:27917252
Marquez-Lago, T T; Leier, A; Burrage, K
2012-08-01
There have been many recent studies from both experimental and simulation perspectives in order to understand the effects of spatial crowding in molecular biology. These effects manifest themselves in protein organisation on the plasma membrane, on chemical signalling within the cell and in gene regulation. Simulations are usually done with lattice- or meshless-based random walks but insights can also be gained through the computation of the underlying probability density functions of these stochastic processes. Until recently much of the focus had been on continuous time random walks, but some very recent work has suggested that fractional Brownian motion may be a good descriptor of spatial crowding effects in some cases. The study compares both fractional Brownian motion and continuous time random walks and highlights how well they can represent different types of spatial crowding and physical obstacles. Simulated spatial data, mimicking experimental data, was first generated by using the package Smoldyn. We then attempted to characterise this data through continuous time anomalously diffusing random walks and multifractional Brownian motion (MFBM) by obtaining MFBM paths that match the statistical properties of our sample data. Although diffusion around immovable obstacles can be reasonably characterised by a single Hurst exponent, we find that diffusion in a crowded environment seems to exhibit multifractional properties in the form of a different short- and long-time behaviour.
Arbitrage with fractional Gaussian processes
Zhang, Xili; Xiao, Weilin
2017-04-01
While the arbitrage opportunity in the Black-Scholes model driven by fractional Brownian motion has a long history, the arbitrage strategy in the Black-Scholes model driven by general fractional Gaussian processes is in its infancy. The development of stochastic calculus with respect to fractional Gaussian processes allowed us to study such models. In this paper, following the idea of Shiryaev (1998), an arbitrage strategy is constructed for the Black-Scholes model driven by fractional Gaussian processes, when the stochastic integral is interpreted in the Riemann-Stieltjes sense. Arbitrage opportunities in some fractional Gaussian processes, including fractional Brownian motion, sub-fractional Brownian motion, bi-fractional Brownian motion, weighted-fractional Brownian motion and tempered fractional Brownian motion, are also investigated.
A Mechanical Model of Brownian Motion for One Massive Particle Including Slow Light Particles
Liang, Song
2018-01-01
We provide a connection between Brownian motion and a classical mechanical system. Precisely, we consider a system of one massive particle interacting with an ideal gas, evolved according to non-random mechanical principles, via interaction potentials, without any assumption requiring that the initial velocities of the environmental particles should be restricted to be "fast enough". We prove the convergence of the (position, velocity)-process of the massive particle under a certain scaling limit, such that the mass of the environmental particles converges to 0 while the density and the velocities of them go to infinity, and give the precise expression of the limiting process, a diffusion process.
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.
Studying protein assembly with reversible Brownian dynamics of patchy particles
Energy Technology Data Exchange (ETDEWEB)
Klein, Heinrich C. R. [Institute for Theoretical Physics, Heidelberg University, 69120 Heidelberg (Germany); Schwarz, Ulrich S., E-mail: ulrich.schwarz@bioquant.uni-heidelberg.de [Institute for Theoretical Physics, Heidelberg University, 69120 Heidelberg (Germany); BioQuant, Heidelberg University, 69120 Heidelberg (Germany)
2014-05-14
Assembly of protein complexes like virus shells, the centriole, the nuclear pore complex, or the actin cytoskeleton is strongly determined by their spatial structure. Moreover, it is becoming increasingly clear that the reversible nature of protein assembly is also an essential element for their biological function. Here we introduce a computational approach for the Brownian dynamics of patchy particles with anisotropic assemblies and fully reversible reactions. Different particles stochastically associate and dissociate with microscopic reaction rates depending on their relative spatial positions. The translational and rotational diffusive properties of all protein complexes are evaluated on-the-fly. Because we focus on reversible assembly, we introduce a scheme which ensures detailed balance for patchy particles. We then show how the macroscopic rates follow from the microscopic ones. As an instructive example, we study the assembly of a pentameric ring structure, for which we find excellent agreement between simulation results and a macroscopic kinetic description without any adjustable parameters. This demonstrates that our approach correctly accounts for both the diffusive and reactive processes involved in protein assembly.
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...
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.
Quantum Brownian motion and its conflict with the second law
Nieuwenhuizen, Theo M.; Allahverdyan, Armen E.
2002-11-01
The Brownian motion of a harmonically bound quantum particle and coupled to a harmonic quantum bath is exactly solvable. At low enough temperatures the stationary state is non-Gibbsian due to an entanglement with the bath. This happens when a cloud of bath modes around the particle is formed. Equilibrium thermodynamics for particle plus bath together, does not imply standard thermodynamics for the particle itself at low T. Various formulations of the second law are then invalid. First, the Clausius inequality can be violated. Second, when the width of the confining potential is suddenly changed, there occurs a relaxation to equilibrium during which the rate of entropy production is partly negative. Third, for non-adiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Conditions are put forward under which perpetuum mobile of the second kind, having several work extraction cycles, enter the realm of condensed matter physics.
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.
Brownian dynamics of emulsion film formation and droplet coalescence.
Toro-Mendoza, Jhoan; Petsev, Dimiter N
2010-05-01
We analyze the evolution in thickness and radius of the film formed during the collision of two deformable emulsion Brownian droplets. These variables exhibit random fluctuations due to thermal disturbances from the continuous liquid phase. As a result, the system probes a random trajectory in the configurational space until it reaches a critical film thickness, at which point the droplets coalesce. Therefore, the film is modeled as a disk with thicknesses and radi that can fluctuate. Our analysis is based on a Langevin-Brownian dynamics approach, which accounts for the thermodynamic and hydrodynamic interactions in the lubrication approximation. We examine the effect of parameters such as droplet size, interfacial mobility, and electrolyte concentration on the coalescence of small Brownian droplets. The results suggest that the coalescence times depend on a complex interplay between the thermodynamic and hydrodynamic interactions.
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.
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.
Brownian motion of solitons in a Bose-Einstein condensate.
Aycock, Lauren M; Hurst, Hilary M; Efimkin, Dmitry K; Genkina, Dina; Lu, Hsin-I; Galitski, Victor M; Spielman, I B
2017-03-07
We observed and controlled the Brownian motion of solitons. We launched solitonic excitations in highly elongated [Formula: see text] Bose-Einstein condensates (BECs) and showed that a dilute background of impurity atoms in a different internal state dramatically affects the soliton. With no impurities and in one dimension (1D), these solitons would have an infinite lifetime, a consequence of integrability. In our experiment, the added impurities scatter off the much larger soliton, contributing to its Brownian motion and decreasing its lifetime. We describe the soliton's diffusive behavior using a quasi-1D scattering theory of impurity atoms interacting with a soliton, giving diffusion coefficients consistent with experiment.
Brownian motion with adhesion: harmonic oscillator with fluctuating mass.
Gitterman, M; Klyatskin, V I
2010-05-01
In contrast to the cases usually studied of a harmonic oscillator subject to a random force (Brownian motion) or having random frequency or random damping, we consider a random mass which corresponds to an oscillator for which the particles of the surrounding medium adhere to it for some (random) time after the collision, thereby changing the oscillator mass. This model, which describes Brownian motion with adhesion, can be useful for the analysis of chemical and biological solutions as well as nanotechnological devices. We consider dichotomous noise and its limiting case, white noise.
The Intersection Probability of Brownian Motion and SLEκ
Directory of Open Access Journals (Sweden)
Shizhong Zhou
2015-01-01
Full Text Available By using excursion measure Poisson kernel method, we obtain a second-order differential equation of the intersection probability of Brownian motion and SLEκ. Moreover, we find a transformation such that the second-order differential equation transforms into a hypergeometric differential equation. Then, by solving the hypergeometric differential equation, we obtain the explicit formula of the intersection probability for the trace of the chordal SLEκ and planar Brownian motion started from distinct points in an upper half-plane H-.
Generalized Multifractional Brownian Motion: Definition and Preliminary Results
Ayache, Antoine; Lévy Véhel, Jacques
1999-01-01
The Multifractional Brownian Motion (MBM) is a generalization of the well known Fractional Brownian Motion. One of the main reasons that makes the MBM interesting for modelization, is that one can prescribe its regularity: given any Hölder function H(t), with values in ]0,1[, one can construct an MBM admitting at any t0, a Hölder exponent equal to H(t0). However, the continuity of the function H(t) is sometimes undesirable, since it restricts the field of application. In this work we define a...
The valuation of currency options by fractional Brownian motion.
Shokrollahi, Foad; Kılıçman, Adem
2016-01-01
This research aims to investigate a model for pricing of currency options in which value governed by the fractional Brownian motion model (FBM). The fractional partial differential equation and some Greeks are also obtained. In addition, some properties of our pricing formula and simulation studies are presented, which demonstrate that the FBM model is easy to use.
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.
Brownian Motion: Theory and Experiment A Simple Classroom ...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 8; Issue 3. Brownian Motion: Theory and Experiment A Simple Classroom Measurement of the Diffusion Coefficient. Kasturi Basu Kopijol Baishya. Classroom Volume 8 Issue 3 March 2003 pp 71-80 ...
100 years of Einstein's Theory of Brownian Motion: From Pollen ...
Indian Academy of Sciences (India)
of the gambler corresponds to the directed movement of the Brownian particle in Figure 2. The ratcheting via time-dependent potential discussed above is not merely a theoretical possibility but nature exploits this for driving a class of molecular motors in- side cells of living organisms; this includes KIFIA, a family of kinesin ...
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 pump powered by a white-noise flashing ratchet.
Gomez-Marin, A; Sancho, J M
2008-03-01
A Brownian pump of particles powered by a stochastic flashing ratchet mechanism is studied. The pumping device is embedded in a finite region and bounded by particle reservoirs. In the steady state, we exactly calculate the spatial density profile, the concentration ratio between both reservoirs and the particle flux. We propose a simulation framework for the consistent evaluation of such observable quantities.
Response to "Rotational velocity autocorrelation function of interacting Brownian particles"
Lowe, C.P.; Hagen, M. H. J.; Frenkel, D.
2001-01-01
Comment on "Response to ‘Rotational velocity autocorrelation function of interacting Brownian particles’", Referred to by: Physica A: Statistical Mechanics and its Applications, Volume 297, Issues 1-2, 1 August 2001, Pages 115-116. B. Cichocki, and B. U. Felderhof
Suspended particle transport through constriction channel with Brownian motion
DEFF Research Database (Denmark)
Hanasaki, Itsuo; Walther, Jens Honore
2017-01-01
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 devia...
100 years of Einstein's Theory of Brownian Motion: From Pollen ...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 10; Issue 11. 100 years of Einstein's Theory of Brownian Motion: From Pollen Grains to Protein Trains – 2. Debashish Chowdhury. General Article Volume 10 Issue 11 November 2005 pp 42-54 ...
100 years of Einstein's Theory of Brownian Motion: from Pollen ...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 10; Issue 9. 100 Years of Einstein's Theory of Brownian Motion: from Pollen Grains to Protein Trains – 1. Debashish Chowdhury. General Article Volume 10 Issue 9 September 2005 pp 63-78 ...
Modeling of rheological behavior for polymer nanocomposites via Brownian dynamic simulation
Seong, Dong Gi; Youn, Jae Ryoun; Song, Young Seok
2016-11-01
Reptation dynamics of the coarse-grained polymer molecular chain is investigated to predict rheological behavior of polymeric nanocomposites by applying Brownian dynamics simulation to the proposed full chain reptation model. Extensibility of polymer chain and constraint release from chain stretch or retraction are of main concern in describing the nanocomposite systems. Rheological results are well predicted by applying the improved simulation algorithm using stepwise Wiener processes. Strong shear thinning and elongational strain hardening are predicted and compared with the experimental results of polyamide 6/organoclay nanocomposites. The full chain reptation model enables us to predict dynamic motion of the polymer chain segments and understand mechanisms for characteristic rheological behaviors.
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. PMID:27433525
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.
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.
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.
Self-assembly of actin monomers into long filaments: Brownian Dynamics simulations
DEFF Research Database (Denmark)
Shillcock, Julian C.
2009-01-01
Brownian dynamics simulations are used to study the dynamical process of self-assembly of actin monomers into long filaments containing up to 1000 actin protomers. In order to overcome the large separation of time scales between the diffusive motion of the freemonomers and the relatively slow....../detachment events. When a single filament is allowed to grow in a bath of constant concentration of free ADP-actin monomers, its growth rate increases linearly with the free monomer concentration in quantitative agreement with in vitro experiments. Theresults also show that the waiting time is governed by...
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.
The Local Fractional Bootstrap
DEFF Research Database (Denmark)
Bennedsen, Mikkel; Hounyo, Ulrich; Lunde, Asger
new resampling method, the local fractional bootstrap, relies on simulating an auxiliary fractional Brownian motion that mimics the fine properties of high frequency differences of the Brownian semistationary process under the null hypothesis. We prove the first order validity of the bootstrap method...... and in simulations we observe that the bootstrap-based hypothesis test provides considerable finite-sample improvements over an existing test that is based on a central limit theorem. This is important when studying the roughness properties of time series data; we illustrate this by applying the bootstrap method...
Diffusion mechanism of non-interacting Brownian particles through a deformed substrate
Arfa, Lahcen; Ouahmane, Mehdi; El Arroum, Lahcen
2018-02-01
We study the diffusion mechanism of non-interacting Brownian particles through a deformed substrate. The study is done at low temperature for different values of the friction. The deformed substrate is represented by a periodic Remoissenet-Peyrard potential with deformability parameter s. In this potential, the particles (impurity, adatoms…) can diffuse. We ignore the interactions between these mobile particles consider them merely as non-interacting Brownian particles and this system is described by a Fokker-Planck equation. We solve this equation numerically using the matrix continued fraction method to calculate the dynamic structure factor S(q , ω) . From S(q , ω) some relevant correlation functions are also calculated. In particular, we determine the half-width line λ(q) of the peak of the quasi-elastic dynamic structure factor S(q , ω) and the diffusion coefficient D. Our numerical results show that the diffusion mechanism is described, depending on the structure of the potential, either by a simple jump diffusion process with jump length close to the lattice constant a or by a combination of a jump diffusion model with jump length close to lattice constant a and a liquid-like motion inside the unit cell. It shows also that, for different friction regimes and various potential shapes, the friction attenuates the diffusion mechanism. It is found that, in the high friction regime, the diffusion process is more important through a deformed substrate than through a non-deformed one.
Processive motor protein as an overdamped brownian stepper.
Bier, Martin
2003-10-03
The two headed motor protein kinesin appears to "walk" along the biopolymer microtubule in 8 nm steps. There is ample justification for a model where the motion of the detached head to the next docking site on the biopolymer is described as ratcheted diffusion. The forward reorientation of an attached head can be conceived of as a power stroke. A model that is based on these premises can accurately predict parameters of motor protein motion.
Some new results on Brownian Directed Polymers in Random Environment
Comets, F
2004-01-01
We prove some new results on Brownian directed polymers in random environment recently introduced by the authors. The directed polymer in this model is a $d$-dimensional Brownian motion (up to finite time $t$) viewed under a Gibbs measure which is built up with a Poisson random measure on $\\R_+ \\times \\R^d$ (=time $\\times$ space). Here, the Poisson random measure plays the role of the random environment which is independent both in time and in space. We prove that (i) For $d \\ge 3$ and the inverse temperature $\\beta$ smaller than a certain positive value $\\beta_0$, the central limit theorem for the directed polymer holds almost surely with respect to the environment. (ii) If $d=1$ and $\\beta \
Driven Brownian transport through arrays of symmetric obstacles
Martens, Steffen; Ghosh, Pulak K.; Hänggi, Peter; Marchesoni, Fabio; Nori, Franco; Schimansky-Geier, Lutz; Schmid, Gerhard
2012-02-01
The transport of a suspended overdamped Brownian particle driven through a two-dimensional rectangular array of circular obstacles with finite radius is numerically investigated [P. K. Ghosh et. al., Phys. Rev. E, submitted (2011)]. 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 particle 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.
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.
Resonance of Brownian vortices in viscoelastic shear flows
Laas, K.; Mankin, R.
2015-10-01
The dynamics of a Brownian particle in an oscillatory viscoelastic shear flow is considered using the generalized Langevin equation. The interaction with fluctuations of environmental parameters is modeled by an additive external white noise and by an internal Mittag-Leffer noise with a finite memory time. Focusing on the mean angular momentum of particles it is shown that the presence of memory has a profound effect on the behavior of the Brownian vortices. Particularly, if an external noise dominates over the internal noise, a resonance-like dependence of the mean angular momentum of "free" particles, trapped due to the cage effect, on the characteristic memory time is observed. Moreover, it is established that memory effects can induce two kinds of resonance peaks: one resonance peak is related to the presence of external noise and the other is related to the initial positional distribution of particles. The bona fide resonance versus the shear frequency is also discussed.
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.
Human behavioral regularity, fractional Brownian motion, and exotic phase transition
Li, Xiaohui; Yang, Guang; An, Kenan; Huang, Jiping
2016-08-01
The mix of competition and cooperation (C&C) is ubiquitous in human society, which, however, remains poorly explored due to the lack of a fundamental method. Here, by developing a Janus game for treating C&C between two sides (suppliers and consumers), we show, for the first time, experimental and simulation evidences for human behavioral regularity. This property is proved to be characterized by fractional Brownian motion associated with an exotic transition between periodic and nonperiodic phases. Furthermore, the periodic phase echoes with business cycles, which are well-known in reality but still far from being well understood. Our results imply that the Janus game could be a fundamental method for studying C&C among humans in society, and it provides guidance for predicting human behavioral activity from the perspective of fractional Brownian motion.
Fractional Brownian Motion:. Theory and Application to DNA Walk
Lim, S. C.; Muniandy, S. V.
2001-09-01
This paper briefly reviews the theory of fractional Brownian motion (FBM) and its generalization to multifractional Brownian motion (MBM). FBM and MBM are applied to a biological system namely the DNA sequence. By considering a DNA sequence as a fractal random walk, it is possible to model the noncoding sequence of human retinoblastoma DNA as a discrete version of FBM. The average scaling exponent or Hurst exponent of the DNA walk is estimated to be H = 0.60 ± 0.05 using the monofractal R/S analysis. This implies that the mean square fluctuation of DNA walk belongs to anomalous superdiffusion type. We also show that the DNA landscape is not monofractal, instead one has multifractal DNA landscape. The empirical estimates of the Hurst exponent falls approximately within the range H ~ 0.62 - 0.72. We propose two multifractal models, namely the MBM and multiscale FBM to describe the existence of different Hurst exponents in DNA walk.
Fast simulation of Brownian dynamics in a crowded environment.
Smith, Stephen; Grima, Ramon
2017-01-14
Brownian dynamics simulations are an increasingly popular tool for understanding spatially extended 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 (BD) 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 the simulation speed for crowded biochemical reaction systems by eliminating the need to explicitly simulate the crowders. We consider both the cases where the reactive particles are point particles, and where they themselves occupy a volume. Using simulations of simple chemical reaction networks, we show that the "crowder-free" method is up to three orders of magnitude faster than conventional BD and yet leads to nearly indistinguishable results from the latter.
Improved diffusion Monte Carlo and the Brownian fan
Weare, J.; Hairer, M.
2012-12-01
Diffusion Monte Carlo (DMC) is a workhorse of stochastic computing. It was invented forty years ago as the central component in a Monte Carlo technique for estimating various characteristics of quantum mechanical systems. Since then it has been used in applied in a huge number of fields, often as a central component in sequential Monte Carlo techniques (e.g. the particle filter). DMC computes averages of some underlying stochastic dynamics weighted by a functional of the path of the process. The weight functional could represent the potential term in a Feynman-Kac representation of a partial differential equation (as in quantum Monte Carlo) or it could represent the likelihood of a sequence of noisy observations of the underlying system (as in particle filtering). DMC alternates between an evolution step in which a collection of samples of the underlying system are evolved for some short time interval, and a branching step in which, according to the weight functional, some samples are copied and some samples are eliminated. Unfortunately for certain choices of the weight functional DMC fails to have a meaningful limit as one decreases the evolution time interval between branching steps. We propose a modification of the standard DMC algorithm. The new algorithm has a lower variance per workload, regardless of the regime considered. In particular, it makes it feasible to use DMC in situations where the ``naive'' generalization of the standard algorithm would be impractical, due to an exponential explosion of its variance. We numerically demonstrate the effectiveness of the new algorithm on a standard rare event simulation problem (probability of an unlikely transition in a Lennard-Jones cluster), as well as a high-frequency data assimilation problem. We then provide a detailed heuristic explanation of why, in the case of rare event simulation, the new algorithm is expected to converge to a limiting process as the underlying stepsize goes to 0. This is shown
The underdamped Brownian duet and stochastic linear irreversible thermodynamics
Proesmans, Karel; Van den Broeck, Christian
2017-10-01
Building on our earlier work [Proesmans et al., Phys. Rev. X 6, 041010 (2016)], we introduce the underdamped Brownian duet as a prototype model of a dissipative system or of a work-to-work engine. Several recent advances from the theory of stochastic thermodynamics are illustrated with explicit analytic calculations and corresponding Langevin simulations. In particular, we discuss the Onsager-Casimir symmetry, the trade-off relations between power, efficiency and dissipation, and stochastic efficiency.
Brownian Duet: A Novel Tale of Thermodynamic Efficiency
Directory of Open Access Journals (Sweden)
Karel Proesmans
2016-10-01
Full Text Available We calculate analytically the stochastic thermodynamic properties of an isothermal Brownian engine driven by a duo of time-periodic forces, including its Onsager coefficients, the stochastic work of each force, and the corresponding stochastic entropy production. We verify the relations between different operational regimes, maximum power, maximum efficiency, and minimum dissipation, and reproduce the signature features of the stochastic efficiency. All of these results are experimentally tested without adjustable parameters on a colloidal system.
Quantum Dissipation versus Classical Dissipation for Generalized Brownian Motion
Cohen, D
1997-01-01
We try to clarify what are the genuine quantal effects that are associated with generalized Brownian Motion (BM). All the quantal effects that are associated with the Zwanzig-Feynman-Vernon-Caldeira-Leggett model are (formally) a solution of the classical Langevin equation. Non-stochastic, genuine quantum mechanical effects, are found for a model that takes into account either the disordered or the chaotic nature of some environment.
On the Generalized Brownian Motion and its Applications in Finance
DEFF Research Database (Denmark)
Høg, Esben; Frederiksen, Per; Schiemert, Daniel
This paper deals with dynamic term structure models (DTSMs) and proposes a new way to handle the limitation of the classical affine models. In particular, the paper expands the exibility of the DTSMs by applying generalized Brownian motions with dependent increments as the governing force of the ...... 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....
Synchronization and collective motion of globally coupled Brownian particles
Sevilla, Francisco J.; Dossetti, Victor; Heiblum-Robles, Alexandro
2014-01-01
In this work, we study a system of passive Brownian (non-self-propelled) particles in two dimensions, interacting only through a social-like force (velocity alignment in this case) that resembles Kuramoto's coupling among phase oscillators. We show that the kinematical stationary states of the system go from a phase in thermal equilibrium with no net flux of particles, to far-from-equilibrium phases exhibiting collective motion by increasing the coupling among particles. The mechanism that le...
Brownian Motion of Arbitrarily Shaped Particles in Two-Dimensions
Chakrabarty, Ayan; Konya, Andrew; Wang, Feng; Selinger, Jonathan V.; Sun, Kai; Wei, Qi-Huo
2014-01-01
Here we implement microfabricated boomerang particles with unequal arm lengths as a model for non-symmetry particles and study their Brownian motion in a quasi-two dimensional geometry by using high precision single particle motion tracking. We show that due to the coupling between translation and rotation, the mean squared displacements of a single asymmetric boomerang particle exhibit a non-linear crossover from short time faster to long time slower diffusion, and the mean displacements for...
Brownian dynamics of confined suspensions of active microrollers
Balboa Usabiaga, Florencio; Delmotte, Blaise; Donev, Aleksandar
2017-04-01
We develop efficient numerical methods for performing many-body Brownian dynamics simulations of a recently observed fingering instability in an active suspension of colloidal rollers sedimented above a wall [M. Driscoll, B. Delmotte, M. Youssef, S. Sacanna, A. Donev, and P. Chaikin, Nat. Phys. (2016), preprint arXiv:1609.08673. We present a stochastic Adams-Bashforth integrator for the equations of Brownian dynamics, which has the same cost but is more accurate than the widely used Euler-Maruyama scheme, and use a random finite difference to capture the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. We generate the Brownian increments using a Krylov method and show that for particles confined to remain in the vicinity of a no-slip wall by gravity or active flows, the number of iterations is independent of the number of particles. Our numerical experiments with active rollers show that the thermal fluctuations set the characteristic height of the colloids above the wall, both in the initial condition and the subsequent evolution dominated by active flows. The characteristic height in turn controls the time scale and wavelength for the development of the fingering instability.
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 motion of arbitrarily shaped particles in two dimensions.
Chakrabarty, Ayan; Konya, Andrew; Wang, Feng; Selinger, Jonathan V; Sun, Kai; Wei, Qi-Huo
2014-11-25
We implement microfabricated boomerang particles with unequal arm lengths as a model for nonsymmetric particles and study their Brownian motion in a quasi-two-dimensional geometry by using high-precision single-particle motion tracking. We show that because of the coupling between translation and rotation, the mean squared displacements of a single asymmetric boomerang particle exhibit a nonlinear crossover from short-time faster to long-time slower diffusion, and the mean displacements for fixed initial orientation are nonzero and saturate out at long times. The measured anisotropic diffusion coefficients versus the tracking point position indicate that there exists one unique point, i.e., the center of hydrodynamic stress (CoH), at which all coupled diffusion coefficients vanish. This implies that in contrast to motion in three dimensions where the CoH exists only for high-symmetry particles, the CoH always exists for Brownian motion in two dimensions. We develop an analytical model based on Langevin theory to explain the experimental results and show that among the six anisotropic diffusion coefficients only five are independent because the translation-translation coupling originates from the translation-rotation coupling. Finally, we classify the behavior of two-dimensional Brownian motion of arbitrarily shaped particles into four groups based on the particle shape symmetry group and discussed potential applications of the CoH in simplifying understanding of the circular motions of microswimmers.
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.
Correlational approach to study interactions between dust Brownian particles in a plasma
Lisin, E. A.; Vaulina, O. S.; Petrov, O. F.
2018-01-01
A general approach to the correlational analysis of Brownian motion of strongly coupled particles in open dissipative systems is described. This approach can be applied to the theoretical description of various non-ideal statistically equilibrium systems (including non-Hamiltonian systems), as well as for the analysis of experimental data. In this paper, we consider an application of the correlational approach to the problem of experimental exploring the wake-mediated nonreciprocal interactions in complex plasmas. We derive simple analytic equations, which allows one to calculate the gradients of forces acting on a microparticle due to each of other particles as well as the gradients of external field, knowing only the information on time-averaged correlations of particles displacements and velocities. We show the importance of taking dissipative and random processes into account, without which consideration of a system with a nonreciprocal interparticle interaction as linearly coupled oscillators leads to significant errors in determining the characteristic frequencies in a system. In the examples of numerical simulations, we demonstrate that the proposed original approach could be an effective instrument in exploring the longitudinal wake structure of a microparticle in a plasma. Unlike the previous attempts to study the wake-mediated interactions in complex plasmas, our method does not require any external perturbations and is based on Brownian motion analysis only.
Directory of Open Access Journals (Sweden)
Aleksei V. Chechkin
2017-04-01
Full Text Available 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 analyze a minimal model framework of diffusion processes with fluctuating diffusivity. In particular, we demonstrate the equivalence of the diffusing diffusivity process with a superstatistical approach with a distribution of diffusivities, at times shorter than the diffusivity correlation time. At longer times, a crossover to a Gaussian distribution with an effective diffusivity emerges. Specifically, we establish a subordination picture of Brownian but non-Gaussian diffusion processes, which 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.
Fatalov, V. R.
2017-07-01
For the Brownian motion X_μ(t) on the half-axis \\lbrack 0,∞) with linear drift μ, reflected at zero and for fixed numbers p>0, δ>0, d>0, a ≥ 0, we calculate the exact asymptotics as T\\to∞ of the mathematical expectations and probabilities \\displaystyle \\mathsf E\\biggl \\lbrack \\exp\\biggl\\{-δ\\int_0T X_μ......l\\{\\frac1 T\\int_0T X_μ^p(t) dt as well as of their conditional versions. For p=1 we give explicit formulae for the emerging constants via the Airy function. We consider an application of the results obtained to the problem of studying the behaviour of a Brownian particle in a gravitational field in a container bounded below by an impenetrable wall when μ=-mg/(2kT K), where m is the mass of the Brownian particle, g is the gravitational acceleration, k is the Boltzmann constant, T K is the temperature in the Kelvin scale. The analysis is conducted by the Laplace method for the sojourn time of homogeneous Markov processes. Bibliography: 31 titles.
Sulochana, C.; Ashwinkumar, G. P.; Sandeep, N.
2017-09-01
In the current study, we investigated the impact of thermophoresis and Brownian moment on the boundary layer 2D forced convection flow of a magnetohydrodynamic nanofluid along a persistently moving horizontal needle with frictional heating effect. The various pertinent parameters are taken into account in the present analysis, namely, the thermophoresis and Brownian moment, uneven heat source/sink, Joule heating and frictional heating effects. To check the variation in the boundary layer behavior, we considered two distinct nanoparticles namely Al50Cu50 (alloy with 50% alumina and 50% copper) and Cu with water as base liquid. Numerical solutions are derived for the reduced system of governing PDEs by employing the shooting process. Computational results of the flow, energy and mass transport are interpreted with the support of tables and graphical illustrations. The obtained results indicate that the increase in the needle size significantly reduces the flow and thermal fields. In particular, the velocity field of the Cu-water nanofluid is highly affected when compared with the Al50Cu50 -water nanofluid. Also, we showed that the thermophoresis and Brownian moment parameters are capable of enhancing the thermal conductivity to a great extent.
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.
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...
Continuum Theory of Phase Separation Kinetics for Active Brownian Particles
Stenhammar, Joakim; Tiribocchi, Adriano; Allen, Rosalind J.; Marenduzzo, Davide; Cates, Michael E.
2013-10-01
Active Brownian particles (ABPs), when subject to purely repulsive interactions, are known to undergo activity-induced phase separation broadly resembling an equilibrium (attraction-induced) gas-liquid coexistence. Here we present an accurate continuum theory for the dynamics of phase-separating ABPs, derived by direct coarse graining, capturing leading-order density gradient terms alongside an effective bulk free energy. Such gradient terms do not obey detailed balance; yet we find coarsening dynamics closely resembling that of equilibrium phase separation. Our continuum theory is numerically compared to large-scale direct simulations of ABPs and accurately accounts for domain growth kinetics, domain topologies, and coexistence densities.
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.
Some fractional and multifractional Gaussian processes: A brief introduction
Lim, S. C.; Eab, C. H.
2015-01-01
This paper gives a brief introduction to some important fractional and multifractional Gaussian processes commonly used in modelling natural phenomena and man-made systems. The processes include fractional Brownian motion (both standard and the Riemann-Liouville type), multifractional Brownian motion, fractional and multifractional Ornstein-Uhlenbeck processes, fractional and mutifractional Reisz-Bessel motion. Possible applications of these processes are briefly mentioned.
On the calculation of the self-diffusion coefficient of interacting Brownian particles
Lekkerkerker, H.N.W.; Dhont, J.K.G.
1984-01-01
We consider two ways to calculate the self-diffusion coefficient of interacting Brownian particles. The first approach is based on the calculation of the mean square displacement of a Brownian particle starting from the Smoluchowski equation. In the second approach the self-diffusion coefficient is
Energy Technology Data Exchange (ETDEWEB)
Kang Yanmei [Department of Applied Mathematics, Xi' an Jiaotong University, Xi' an 710049 (China); Jiang Jun; Xie Yong, E-mail: kangyanmei2002@yahoo.com.cn [School of Aerospace, Xi' an Jiaotong University, Xi' an 710049 (China)
2011-01-21
The aim of this paper is to develop a simple and efficient method for observing the fluctuating spectral density of subdiffusive Brownian motion in an overdamped periodic potential for exploring the subdiffusive property in frequency domain. Based on the general frame of linear response theory for subdiffusive fractional Fokker-Planck equation systems, an explicit relation between fluctuating spectral density and linear dynamical susceptibility is deduced, and then a method of moments based on the expansion of trigonometric functions is proposed for calculating the linear dynamic susceptibility. With the linear dynamic susceptibility available, the fluctuating spectral density is finally obtained. The numerical results demonstrate that subdiffusion weakens coherent oscillations in the periodic system, but enhances aperiodic components. Our observation embodies the fact of the Mittag-Leffler residence time distribution with an infinite mean in the subdiffusive process from the frequency domain.
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.
Ergodic properties of fractional Brownian-Langevin motion.
Deng, Weihua; Barkai, Eli
2009-01-01
We investigate the time average mean-square displacement delta;{2}[over ](x(t))=integral_{0};{t-Delta}[x(t;{'}+Delta)-x(t;{'})];{2}dt;{'}(t-Delta) for fractional Brownian-Langevin motion where x(t) is the stochastic trajectory and Delta is the lag time. Unlike the previously investigated continuous-time random-walk model, delta;{2}[over ] converges to the ensemble average x;{2} approximately t;{2H} in the long measurement time limit. The convergence to ergodic behavior is slow, however, and surprisingly the Hurst exponent H=3/4 marks the critical point of the speed of convergence. When Hballistic limit H-->1 ergodicity is broken and E_{B} approximately 2 . The critical point H=3/4 is marked by the divergence of the coefficient k(H) . Fractional Brownian motion as a model for recent experiments of subdiffusion of mRNA in the cell is briefly discussed, and a comparison with the continuous-time random-walk model is made.
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.
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.
Intermittency and multifractional Brownian character of geomagnetic time series
Consolini, G.; De Marco, R.; De Michelis, P.
2013-07-01
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.
Mathematical interpretation of Brownian motor model: Limit cycles and directed transport phenomena
Yang, Jianqiang; Ma, Hong; Zhong, Suchuang
2018-03-01
In this article, we first suggest that the attractor of Brownian motor model is one of the reasons for the directed transport phenomenon of Brownian particle. We take the classical Smoluchowski-Feynman (SF) ratchet model as an example to investigate the relationship between limit cycles and directed transport phenomenon of the Brownian particle. We study the existence and variation rule of limit cycles of SF ratchet model at changing parameters through mathematical methods. The influences of these parameters on the directed transport phenomenon of a Brownian particle are then analyzed through numerical simulations. Reasonable mathematical explanations for the directed transport phenomenon of Brownian particle in SF ratchet model are also formulated on the basis of the existence and variation rule of the limit cycles and numerical simulations. These mathematical explanations provide a theoretical basis for applying these theories in physics, biology, chemistry, and engineering.
Zemánek, Pavel; Šiler, Martin; Brzobohatý, Oto; Jákl, Petr; Filip, Radim
2016-06-01
The noise-to-signal transitions belong to an exciting group of processes in physics. In Filip and Zemánek (2016, J. Opt. 18 065401) we theoretically analyse the stochastic noise-to-signal transition of overdamped Brownian motion of a particle in the cubic potential. In this part, we propose a feasible experimental setup for a proof-of-principle experiment that uses methods of optical trapping in shaped laser beams which provide cubic and quadratic potentials. Theoretical estimates and results from the numerical simulations indicate that the noise-to-signal transition can be observed under realistic experimental conditions.
Generalized Fokker-Planck equation, Brownian motion, and ergodicity.
Plyukhin, A V
2008-06-01
Microscopic theory of Brownian motion of a particle of mass M in a bath of molecules of mass mforce, and the generalized Fokker-Planck equation involves derivatives of order higher than 2. These equations are derived from first principles with coefficients expressed in terms of correlation functions of microscopic force on the particle. The coefficients are evaluated explicitly for a generalized Rayleigh model with a finite time of molecule-particle collisions. In the limit of a low-density bath, we recover the results obtained previously for a model with instantaneous binary collisions. In the general case, the equations contain additional corrections, quadratic in bath density, originating from a finite collision time. These corrections survive to order (m/M)2 and are found to make the stationary distribution non-Maxwellian. Some relevant numerical simulations are also presented.
Exact analytical thermodynamic expressions for a Brownian heat engine.
Taye, Mesfin Asfaw
2015-09-01
The nonequilibrium thermodynamics feature of a Brownian motor operating between two different heat baths is explored as a function of time t. Using the Gibbs entropy and Schnakenberg microscopic stochastic approach, we find exact closed form expressions for the free energy, the rate of entropy production, and the rate of entropy flow from the system to the outside. We show 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. Furthermore, via the present model, many thermodynamic theories can be checked.
First-passage time of Brownian motion with dry friction.
Chen, Yaming; Just, Wolfram
2014-02-01
We provide an analytic solution to the first-passage time (FPT) problem of a piecewise-smooth stochastic model, namely Brownian motion with dry friction, using two different but closely related approaches which are based on eigenfunction decompositions on the one hand and on the backward Kolmogorov equation on the other. For the simple case containing only dry friction, a phase-transition phenomenon in the spectrum is found which relates to the position of the exit point, and which affects the tail of the FPT distribution. For the model containing as well a driving force and viscous friction the impact of the corresponding stick-slip transition and of the transition to ballistic exit is evaluated quantitatively. The proposed model is one of the very few cases where FPT properties are accessible by analytical means.
Brownian rotational relaxation and power absorption in magnetite nanoparticles
Energy Technology Data Exchange (ETDEWEB)
Goya, G.F. [Institute of Nanoscience of Aragon (INA), University of Zaragoza, 50009 Zaragoza (Spain)]. E-mail: goya@unizar.es; Fernandez-Pacheco, R. [Institute of Nanoscience of Aragon (INA), University of Zaragoza, 50009 Zaragoza (Spain); Arruebo, M. [Institute of Nanoscience of Aragon (INA), University of Zaragoza, 50009 Zaragoza (Spain); Cassinelli, N. [Electronics Division, Bauer and Associates, Buenos Aires (Argentina); Facultad de Ingenieria, UNLP (Argentina); Ibarra, M.R. [Institute of Nanoscience of Aragon (INA), University of Zaragoza, 50009 Zaragoza (Spain)
2007-09-15
We present a study of the power absorption efficiency in several magnetite-based colloids, to asses their potential as magnetic inductive hyperthermia (MIH) agents. Relaxation times {tau} were measured through the imaginary susceptibility component {chi}{sup '}'(T), and analyzed within Debye's theory of dipolar fluid. The results indicated Brownian rotational relaxation and allowed to calculate the hydrodynamic radius close to the values obtained from photon correlation. The study of the colloid performances as power absorbers showed no detectable increase of temperature for dextran-coated Fe{sub 3}O{sub 4} nanoparticles, whereas a second Fe{sub 3}O{sub 4}-based dispersion of similar concentration could be heated up to 12K after 30min under similar experimental conditions. The different power absorption efficiencies are discussed in terms of the magnetic structure of the nanoparticles.
BROWNIAN 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.
Confined mobility in biomembranes modeled by early stage Brownian motion.
Gmachowski, Lech
2014-08-01
An equation of motion, derived from the fractal analysis of the Brownian particle trajectory, makes it possible to calculate the time dependence of the mean square displacement for early times, before the Einstein formula becomes valid. The diffusion coefficient increases with the distance travelled which can be restricted by the geometrical conditions. The corresponding diffusion coefficient cannot increase further to achieve a value characteristic for unrestricted environment. Explicit formula is derived for confined diffusivity related to the unrestricted one as dependent on the maximum particle mean square displacement possible normalized by the square of its mean free path. The model describes the lipid and protein diffusion in tubular membranes with different radii, originally fitted by the modified Saffman-Delbrück equation, and the lateral mobility of synthetic model peptides for which the diffusion coefficient is inversely proportional to the radius of the diffusing object and to the thickness of the membrane. Copyright © 2014 Elsevier Inc. All rights reserved.
Micro rectennas: Brownian ratchets for thermal-energy harvesting
Energy Technology Data Exchange (ETDEWEB)
Pan, Y.; Powell, C. V.; Balocco, C., E-mail: claudio.balocco@durham.ac.uk [School of Engineering and Computing Sciences, Durham University, Durham DH1 3LE (United Kingdom); Song, A. M. [School of Electrical and Electronic Engineering, University of Manchester, Manchester M13 9PL (United Kingdom)
2014-12-22
We experimentally demonstrated the operation of a rectenna for harvesting thermal (blackbody) radiation and converting it into dc electric power. The device integrates an ultrafast rectifier, the self-switching nanodiode, with a wideband log-periodic spiral microantenna. The radiation from the thermal source drives the rectenna out of thermal equilibrium, permitting the rectification of the excess thermal fluctuations from the antenna. The power conversion efficiency increases with the source temperatures up to 0.02% at 973 K. The low efficiency is attributed mainly to the impedance mismatch between antenna and rectifier, and partially to the large field of view of the antenna. Our device not only opens a potential solution for harvesting thermal energy but also provides a platform for experimenting with Brownian ratchets.
Micro rectennas: Brownian ratchets for thermal-energy harvesting
Pan, Y.; Powell, C. V.; Song, A. M.; Balocco, C.
2014-12-01
We experimentally demonstrated the operation of a rectenna for harvesting thermal (blackbody) radiation and converting it into dc electric power. The device integrates an ultrafast rectifier, the self-switching nanodiode, with a wideband log-periodic spiral microantenna. The radiation from the thermal source drives the rectenna out of thermal equilibrium, permitting the rectification of the excess thermal fluctuations from the antenna. The power conversion efficiency increases with the source temperatures up to 0.02% at 973 K. The low efficiency is attributed mainly to the impedance mismatch between antenna and rectifier, and partially to the large field of view of the antenna. Our device not only opens a potential solution for harvesting thermal energy but also provides a platform for experimenting with Brownian ratchets.
Crystallization and melting of bacteria colonies and Brownian bugs.
Ramos, Francisco; López, Cristóbal; Hernández-García, Emilio; Muñoz, Miguel A
2008-02-01
Motivated by the existence of remarkably ordered cluster arrays of bacteria colonies growing in Petri dishes and related problems, we study the spontaneous emergence of clustering and patterns in a simple nonequilibrium system: the individual-based interacting Brownian bug model. We map this discrete model into a continuous Langevin equation which is the starting point for our extensive numerical analyses. For the two-dimensional case we report on the spontaneous generation of localized clusters of activity as well as a melting-freezing transition from a disordered or isotropic phase to an ordered one characterized by hexagonal patterns. We study in detail the analogies and differences with the well-established Kosterlitz-Thouless-Halperin-Nelson-Young theory of equilibrium melting, as well as with another competing theory. For that, we study translational and orientational correlations and perform a careful defect analysis. We find a nonstandard one-stage, defect-mediated transition whose nature is only partially elucidated.
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.
Semicircular canals circumvent Brownian Motion overload of mechanoreceptor hair cells
DEFF Research Database (Denmark)
Muller, Mees; Heeck, Kier; Elemans, Coen P H
2016-01-01
Vertebrate semicircular canals (SCC) first appeared in the vertebrates (i.e. ancestral fish) over 600 million years ago. In SCC the principal mechanoreceptors are hair cells, which as compared to cochlear hair cells are distinctly longer (70 vs. 7 μm), 10 times more compliant to bending (44 vs. 500...... nN/m), and have a 100-fold higher tip displacement threshold (hair cells where the bundle is approximated as a stiff, cylindrical elastic rod subject to friction and thermal agitation. Our models suggest that the above...... differences aid SCC hair cells in circumventing the masking effects of Brownian motion noise of about 70 nm, and thereby permit transduction of very low frequency (
A 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.
The rate of collisions due to Brownian or gravitational motion of small drops
Zhang, Xiaoguang; Davis, Robert H.
1991-01-01
Quantitative predictions of the collision rate of two spherical drops undergoing Brownian diffusion or gravitational sedimentation are presented. The diffusion equation for relative Brownian motion of two drops is derived, and the relative motion of pairs of drops in gravitational sedimentation is traced via a trajectory analysis in order to develop theoretical models to determine the collision efficiencies, both with and without interparticle forces applied between the drops. It is concluded that finite collision rates between nondeforming fluid drops are possible for Brownian diffusion or gravitational sedimentation in the absence of attractive forces, in stark contrast to the prediction that lubrication forces prevent rigid spheres from contacting each other unless an attractive force that becomes infinite as the separation approaches zero is applied. Collision rates are shown to increase as the viscosity of the drop-phase decreases. In general, hydrodynamic interactions reduce the collision rates more for gravitational collisions than for Brownian collisions.
National Research Council Canada - National Science Library
Shokrollahi, Foad; Kılıçman, Adem
2015-01-01
This research aims to investigate the strategy of fair insurance premium actuarial approach for pricing currency option, when the value of foreign currency option follows the mixed fractional Brownian...
100 years of Einstein's Theory of Brownian Motion:from Pollen ...
Indian Academy of Sciences (India)
... random 'kicks' to the. Brownian particle are also responsible for its energy dis- sipation because of viscous drag. The incessant ran- dom motion of the Brownian particle is maintained for ever by the delicate balance of the random kicks it gets. -76-----------------------------~~--------RE-S-O-N-A-N-C-E-I--se-p-te-m-b-e-r--zo-o-s ...
Electromagnetic scattering on fractional Brownian surfaces and estimation of the Hurst exponent
Guérin, Charles-Antoine; Saillard, Marc
2001-01-01
International audience; Fractional Brownian motion is known to be a realistic model for many natural rough surfaces. It is defined by means of a single parameter, the Hurst exponent, which determines the fractal characteristics of the surface. We propose a method to estimate the Hurst exponent of a fractional Brownian profile from the electromagnetic scattering data. The method is developed in the framework of three usual approximations, with different domains of validity: the Kirchhoff appro...
Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation
Dunkel, Jörn; Hänggi, Peter (Prof. Dr. Dr. h.c. mult.)
2006-01-01
The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy point-like Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, non-relativistic LE is deduced from this model, by taking into account the non-relativistic conservation laws for momentum and kinetic energy. Subsequently, this procedure is generalized to the relativi...
The law of a stochastic integral with two independent fractional Brownian motions
Bardina, Xavier; Tudor, Ciprian
2007-01-01
Using the tools of the stochastic integration with respect to the fractional Brownian motion, we obtain the expression of the characteristic function of the random variable $\\int_{0}^{1}B^{\\alpha }_{s}dB^{H}_{s}$ where $B^{\\alpha }$ and $B^{H}$ are two independent fractional Brownian motions with Hurst parameters $\\alpha\\in(0,1) $ and $H>\\frac12$ respectively. The two-parameter case is also considered.
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.
Decoupling the short- and long-term behavior of stochastic volatility
DEFF Research Database (Denmark)
Bennedsen, Mikkel; Lunde, Asger; Pakkanen, Mikko
measures of close to two thousand individual US equities, we find that both roughness and persistence appear to be universal properties of volatility. Inspired by the empirical findings, we introduce a new class of continuous-time stochastic volatility models, capable of decoupling roughness (short-term...... behavior) from long memory and persistence (long-term behavior) in a simple and parsimonious way, which allows us to successfully model volatility at all intraday time scales. Our prime model is based on the so-called Brownian semistationary process and we derive a number of theoretical properties...
Frazier, Zachary
2012-01-01
Abstract Particle-based Brownian dynamics simulations offer the opportunity to not only simulate diffusion of particles but also the reactions between them. They therefore provide an opportunity to integrate varied biological data into spatially explicit models of biological processes, such as signal transduction or mitosis. However, particle based reaction-diffusion methods often are hampered by the relatively small time step needed for accurate description of the reaction-diffusion framework. Such small time steps often prevent simulation times that are relevant for biological processes. It is therefore of great importance to develop reaction-diffusion methods that tolerate larger time steps while maintaining relatively high accuracy. Here, we provide an algorithm, which detects potential particle collisions prior to a BD-based particle displacement and at the same time rigorously obeys the detailed balance rule of equilibrium reactions. We can show that for reaction-diffusion processes of particles mimicking proteins, the method can increase the typical BD time step by an order of magnitude while maintaining similar accuracy in the reaction diffusion modelling. PMID:22697237
Zhao, Mingfei; Yong, Xin
2017-11-01
Nanoparticle deposition coupled to hydrodynamics plays important roles in materials printing and thin-film processing. Investigations of nanoparticle dynamics in evaporating colloidal dispersions could elicit a greater understanding of the processing-structure relationship for evaporation-induced self-assembly and deposition. A 3D free-energy lattice Boltzmann method combined with Brownian dynamics is developed to simulate evaporating colloidal droplets and rivulets. In this work, we explore the deposition on solid substrates with different wetting properties, namely static contact angle and contact line motion. We highlight the influence of convective flows on the assembly kinetics and deposit patterns using the developed model. We introduce a novel approach to impose a pinned contact line for most of droplet lifetime. The time evolutions of contact angle and droplet volume are examined to characterize the pinning scheme. We observe the process of nanoparticle self-assembly during the evaporation of droplets and rivulets and quantitatively analyze the deposit structure. This work was supported by the National Science Foundation under Grant No. CMMI-1538090.
Bose polaron as an instance of quantum Brownian motion
Directory of Open Access Journals (Sweden)
Aniello Lampo
2017-09-01
Full Text Available We study the dynamics of a quantum impurity immersed in a Bose-Einstein condensate as an open quantum system in the framework of the quantum Brownian motion model. We derive a generalized Langevin equation for the position of the impurity. The Langevin equation is an integrodifferential equation that contains a memory kernel and is driven by a colored noise. These result from considering the environment as given by the degrees of freedom of the quantum gas, and thus depend on its parameters, e.g. interaction strength between the bosons, temperature, etc. We study the role of the memory on the dynamics of the impurity. When the impurity is untrapped, we find that it exhibits a super-diffusive behavior at long times. We find that back-flow in energy between the environment and the impurity occurs during evolution. When the particle is trapped, we calculate the variance of the position and momentum to determine how they compare with the Heisenberg limit. One important result of this paper is that we find position squeezing for the trapped impurity at long times. We determine the regime of validity of our model and the parameters in which these effects can be observed in realistic experiments.
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.
Unsteady sedimentation of flocculating non-Brownian suspensions
Zinchenko, Alexander
2017-11-01
Microstructural evolution and temporal dynamics of the sedimentation rate U(t) are studied for a monodisperse suspension of non-Brownian spherical particles subject to van der Waals attraction and electrostatic repulsion in the realistic range of colloidal parameters (Hamaker constant, surface potential, double layer thickness etc.). A novel economical high-order multipole algorithm is used to fully resolve hydrodynamical interactions in the dynamical simulations with up to 500 spheres in a periodic box and O(106) time steps, combined with geometry perturbation to incorporate lubrication and extend the solution to arbitrarily small particle separations. The total colloidal force near the secondary minimum often greatly exceeds the effective gravity/buoyancy force, resulting in the formation of strong but flexible bonds and large clusters as the suspension evolves from an initial well-mixed state of non-aggregated spheres. Ensemble averaging over many initial configurations is used to predict U(t) for particle volume fractions between 0.1 and 0.25. The results are fully convergent, system-size independent and cover a 2-2.5 fold growth of U(t) after a latency time.
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.
Relation between cooperative molecular motors and active Brownian particles.
Touya, Clément; Schwalger, Tilo; Lindner, Benjamin
2011-05-01
Active Brownian particles (ABPs), obeying a nonlinear Langevin equation with speed-dependent drift and noise amplitude, are well-known models used to describe self-propelled motion in biology. In this paper we study a model describing the stochastic dynamics of a group of coupled molecular motors (CMMs). Using two independent numerical methods, one based on the stationary velocity distribution of the motors and the other one on the local increments (also known as the Kramers-Moyal coefficients) of the velocity, we establish a connection between the CMM and the ABP models. The parameters extracted for the ABP via the two methods show good agreement for both symmetric and asymmetric cases and are independent of N, the number of motors, provided that N is not too small. This indicates that one can indeed describe the CMM problem with a simpler ABP model. However, the power spectrum of velocity fluctuations in the CMM model reveals a peak at a finite frequency, a peak which is absent in the velocity spectrum of the ABP model. This implies richer dynamic features of the CMM model which cannot be captured by an ABP model.
Directory of Open Access Journals (Sweden)
Linshuang Liu
2012-01-01
Full Text Available To investigate sludge drying process, a numerical simulation based on Brownian dynamic for the floc with uncharged and charged particles was conducted. The Langevin equation is used as dynamical equation for tracking each particle in a floc. An initial condition and periodic boundary condition which well conformed to reality is used for calculating the floc growth process. Each cell consists of 1000 primary particles with diameter 0.1 ∼ 4 μm. Floc growth is related to the thermal force and the electrostatic force. The electrostatic force on a particle in the simulation cell is considered as the sum of electrostatic forces from other particles in the original cell and its replicate cells. It is assumed that flocs are charged with precharged primary particles in dispersion system by ionization. By the analysis of the simulation figures, on one hand, the effects of initial particle size and sludge density on floc smashing time, floc radius of gyration, and fractal dimension were discussed. On the other hand, the effects of ionization on floc smashing time and floc structure were presented. This study has important practical value in the high-turbidity water treatment, especially for sludge drying.
Correlation Properties of (Discrete Fractional Gaussian Noise and Fractional Brownian Motion
Directory of Open Access Journals (Sweden)
Didier Delignières
2015-01-01
Full Text Available The fractional Gaussian noise/fractional Brownian motion framework (fGn/fBm has been widely used for modeling and interpreting physiological and behavioral data. The concept of 1/f noise, reflecting a kind of optimal complexity in the underlying systems, is of central interest in this approach. It is generally considered that fGn and fBm represent a continuum, punctuated by the boundary of “ideal” 1/f noise. In the present paper, we focus on the correlation properties of discrete-time versions of these processes (dfGn and dfBm. We especially derive a new analytical expression of the autocorrelation function (ACF of dfBm. We analyze the limit behavior of dfGn and dfBm when they approach their upper and lower limits, respectively. We show that, as H approaches 1, the ACF of dfGn tends towards 1 at all lags, suggesting that dfGn series tend towards straight line. Conversely, as H approaches 0, the ACF of dfBm tends towards 0 at all lags, suggesting that dfBm series tend towards white noise. These results reveal a severe breakdown of correlation properties around the 1/f boundary and challenge the idea of a smooth transition between dfGn and dfBm processes. We discuss the implications of these findings for the application of the dfGn/dfBm model to experimental series, in terms of theoretical interpretation and modeling.
Directory of Open Access Journals (Sweden)
Satoshi Ota
2016-09-01
Full Text Available The dependence of magnetic relaxation on particle parameters, such as the size and anisotropy, has been conventionally discussed. In addition, the influences of external conditions, such as the intensity and frequency of the applied field, the surrounding viscosity, and the temperature on the magnetic relaxation have been researched. According to one of the basic theories regarding magnetic relaxation, the faster type of relaxation dominates the process. However, in this study, we reveal that Brownian and Néel relaxations coexist and that Brownian relaxation can occur after Néel relaxation despite having a longer relaxation time. To understand the mechanisms of Brownian rotation, alternating current (AC hysteresis loops were measured in magnetic fluids of different viscosities. These loops conveyed the amplitude and phase delay of the magnetization. In addition, the intrinsic loss power (ILP was calculated using the area of the AC hysteresis loops. The ILP also showed the magnetization response regarding the magnetic relaxation over a wide frequency range. To develop biomedical applications of magnetic nanoparticles, such as hyperthermia and magnetic particle imaging, it is necessary to understand the mechanisms of magnetic relaxation.
Saccadic Tracking with Random Walk (brownian Motion) Stimuli.
Horner, Douglas Gordon
This study was designed to evaluate the saccadic system's response to continuously presented random walk (Brownian motion) stimuli. Our goals were: (1) to examine how closely timed consecutive saccades interact; and (2) to estimate the response modification time for the new position of the stimulus to give an estimate of integration and decision delays. Horizontal eye movements resulting from rapid continuous random target movements were recorded. Step amplitudes of 1.5 and 3.0 degrees were alternated between single- and rapid double-step movements every 200 to 400 msec. From these random multiple stimulus step sequences, saccadic responses to single 3.0 degree step stimuli were collected for subjects to evaluate interactions of consecutive saccades. The results showed that: (1) subjects are capable of making independent goal directed saccades with intersaccadic intervals as short as 50 msec, and (2) subjects had individual biases in the direction of the successive saccades. The main interaction between saccades was related to the spatial error of the preceding saccade combining with the new stimulus step to yield the new error signal for the next saccade. The magnitude of the new retinal error signal was reflected in the latency of the following saccade. To evaluate the decision period of the saccadic system, the single-step responses were used as templates to assess the modification times for staircase, pulse under -return and pulse over-return double-step stimuli. The responses were organized by whether consecutive saccades continued in the same direction or in the opposite direction. The results on the modification times indicate saccadic responses are directed to the new stimulus 85 to 90 msec after the new position of the stimulus. This modification time was independent of stimuli and preferred direction of responses. The 85-90 msec modification delay is used to estimate the time interval needed to program the next saccade.
Coarse-grained Brownian dynamics simulations of protein translocation through nanopores
Lee, Po-Hsien; Helms, Volkhard; Geyer, Tihamér
2012-10-01
A crucial process in biological cells is the translocation of newly synthesized proteins across cell membranes via integral membrane protein pores termed translocons. Recent improved techniques now allow producing artificial membranes with pores of similar dimensions of a few nm as the translocon system. For the translocon system, the protein has to be unfolded, whereas the artificial pores are wide enough so that small proteins can pass through even when folded. To study how proteins permeate through such membrane pores, we used coarse-grained Brownian dynamics simulations where the proteins were modeled as single beads or bead-spring polymers for both folded and unfolded states. The pores were modeled as cylindrical holes through the membrane with various radii and lengths. Diffusion was driven by a concentration gradient created across the porous membrane. Our results for both folded and unfolded configurations show the expected reciprocal relation between the flow rate and the pore length in agreement with an analytical solution derived by Brunn et al. [Q. J. Mech. Appl. Math. 37, 311 (1984)], 10.1093/qjmam/37.2.311. Furthermore, we find that the geometric constriction by the narrow pore leads to an accumulation of proteins at the pore entrance, which in turn compensates for the reduced diffusivity of the proteins inside the pore.
Luna-Singh, Jennifer; Barrera, Enrique; Varshney, Vikas; Kelley, John; Vaia, Richard
2014-03-01
Self-limiting assembly of nanoparticle (NP) and biomacromolecular arrays promises to revolutionize compliant device fabrication by enabling print-on-demand. Presently, quantitative understanding of the relationship between the array order, nanoparticle size, surface characteristics, and process conditions remain elusive. Previous simulations have shown that tuning particle and surface potentials, screening lengths, and particle concentrations can lead to ordering. However, identifying the experimental conditions to observe these in-plane order-disorder and order-order transitions for NPs remains a challenge. Here in, the absorption of electrostatically stabilized NPs with increasing ratio of particle-particle repulsion to particle-surface attraction via Brownian dynamics simulations is discussed. The orientation correlation function follows the KTHNY theory of phase transition as particle and surface potentials are tuned. Detailed Voronoi analysis reveals movement and defect annihilation during the final stages of adsorption. Identifying the transition between liquid, hexatic, and crystalline NP arrays will provide experimental conditions necessary to create high resolution patterns and smaller devices.
Height distribution tails in the Kardar–Parisi–Zhang equation with Brownian initial conditions
Meerson, Baruch; Schmidt, Johannes
2017-10-01
For stationary interface growth, governed by the Kardar–Parisi–Zhang (KPZ) equation in 1 + 1 dimensions, typical fluctuations of the interface height at long times are described by the Baik–Rains distribution. Recently Chhita et al (2016 arXiv:1611.06690) used the totally asymmetric simple exclusion process (TASEP) to study the height fluctuations in systems of the KPZ universality class for Brownian interfaces with arbitrary diffusion constant. They showed that there is a one-parameter family of long-time distributions, parameterized by the diffusion constant of the initial random height profile. They also computed these distributions numerically by using Monte Carlo (MC) simulations. Here we address this problem analytically and focus on the distribution tails at short times. We determine the (stretched exponential) tails of the height distribution by applying the optimal fluctuation method (OFM) to the KPZ equation. We argue that, by analogy with other initial conditions, the ‘slow’ tail holds at arbitrary times and therefore provides a proper asymptotic to the family of long-time distributions studied in Chhita et al (2016 arXiv:1611.06690). We verify this hypothesis by performing large-scale MC simulations of a TASEP with a parallel-update rule. The ‘fast’ tail, predicted by the OFM, is also expected to hold at arbitrary times, at sufficiently large heights.
Self-similar Gaussian processes for modeling anomalous diffusion
Lim, S. C.; Muniandy, S. V.
2002-08-01
We study some Gaussian models for anomalous diffusion, which include the time-rescaled Brownian motion, two types of fractional Brownian motion, and models associated with fractional Brownian motion based on the generalized Langevin equation. Gaussian processes associated with these models satisfy the anomalous diffusion relation which requires the mean-square displacement to vary with tα, 0Brownian motion and time-rescaled Brownian motion all have the same probability distribution function, the Slepian theorem can be used to compare their first passage time distributions, which are different. Finally, in order to model anomalous diffusion with a variable exponent α(t) it is necessary to consider the multifractional extensions of these Gaussian processes.
Process of random distributions : classification and prediction ...
African Journals Online (AJOL)
Dirichlet random distribution. The parameter of this process can be the distribution of any usual such as the (multifractional) Brownian motion. We also extend Kraft random distribution to the continuous time case. We give an application in ...
Analytical Solutions of a Model for Brownian Motion in the Double Well Potential
Liu, Ai-Jie; Zheng, Lian-Cun; Ma, Lian-Xi; Zhang, Xin-Xin
2015-01-01
In this paper, the analytical solutions of Schrödinger equation for Brownian motion in a double well potential are acquired by the homotopy analysis method and the Adomian decomposition method. Double well potential for Brownian motion is always used to obtain the solutions of Fokker—Planck equation known as the Klein—Kramers equation, which is suitable for separation and additive Hamiltonians. In essence, we could study the random motion of Brownian particles by solving Schrödinger equation. The analytical results obtained from the two different methods agree with each other well. The double well potential is affected by two parameters, which are analyzed and discussed in details with the aid of graphical illustrations. According to the final results, the shapes of the double well potential have significant influence on the probability density function.
Bhattacharyay, A.
2018-03-01
An alternative equilibrium stochastic dynamics for a Brownian particle in inhomogeneous space is derived. Such a dynamics can model the motion of a complex molecule in its conformation space when in equilibrium with a uniform heat bath. The derivation is done by a simple generalization of the formulation due to Zwanzig for a Brownian particle in homogeneous heat bath. We show that, if the system couples to different number of bath degrees of freedom at different conformations then the alternative model gets derived. We discuss results of an experiment by Faucheux and Libchaber which probably has indicated possible limitation of the Boltzmann distribution as equilibrium distribution of a Brownian particle in inhomogeneous space and propose experimental verification of the present theory using similar methods.
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.
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 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...
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.
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
Bai, Zhan-Wu; Zhang, Wei
2018-01-01
The diffusion behaviors of Brownian particles in a tilted periodic potential under the influence of an internal white noise and an external Ornstein-Uhlenbeck noise are investigated through numerical simulation. In contrast to the case when the bias force is smaller or absent, the diffusion coefficient exhibits a nonmonotonic dependence on the correlation time of the external noise when bias force is large. A mechanism different from locked-to-running transition theory is presented for the diffusion enhancement by a bias force in intermediate to large damping. In the underdamped regime and the presence of external noise, the diffusion coefficient is a monotonically decreasing function of low temperature rather than a nonmonotonic function when external noise is absent. The diffusive process undergoes four regimes when bias force approaches but is less than its critical value and noises intensities are small. These behaviors can be attributed to the locked-to-running transition of particles.
Sims, David W; Humphries, Nicolas E; Bradford, Russell W; Bruce, Barry D
2012-03-01
1. Search processes play an important role in physical, chemical and biological systems. In animal foraging, the search strategy predators should use to search optimally for prey is an enduring question. Some models demonstrate that when prey is sparsely distributed, an optimal search pattern is a specialised random walk known as a Lévy flight, whereas when prey is abundant, simple Brownian motion is sufficiently efficient. These predictions form part of what has been termed the Lévy flight foraging hypothesis (LFF) which states that as Lévy flights optimise random searches, movements approximated by optimal Lévy flights may have naturally evolved in organisms to enhance encounters with targets (e.g. prey) when knowledge of their locations is incomplete. 2. Whether free-ranging predators exhibit the movement patterns predicted in the LFF hypothesis in response to known prey types and distributions, however, has not been determined. We tested this using vertical and horizontal movement data from electronic tagging of an apex predator, the great white shark Carcharodon carcharias, across widely differing habitats reflecting different prey types. 3. Individual white sharks exhibited movement patterns that predicted well the prey types expected under the LFF hypothesis. Shark movements were best approximated by Brownian motion when hunting near abundant, predictable sources of prey (e.g. seal colonies, fish aggregations), whereas movements approximating truncated Lévy flights were present when searching for sparsely distributed or potentially difficult-to-detect prey in oceanic or shelf environments, respectively. 4. That movement patterns approximated by truncated Lévy flights and Brownian behaviour were present in the predicted prey fields indicates search strategies adopted by white sharks appear to be the most efficient ones for encountering prey in the habitats where such patterns are observed. This suggests that C. carcharias appears capable of exhibiting
Safdari, Hadiseh; Cherstvy, Andrey G.; Chechkin, Aleksei V.; Bodrova, Anna; Metzler, Ralf
2017-01-01
We investigate both analytically and by computer simulations the ensemble- and time-averaged, nonergodic, and aging properties of massive particles diffusing in a medium with a time dependent diffusivity. We call this stochastic diffusion process the (aging) underdamped scaled Brownian motion (UDSBM). We demonstrate how the mean squared displacement (MSD) and the time-averaged MSD of UDSBM are affected by the inertial term in the Langevin equation, both at short, intermediate, and even long diffusion times. In particular, we quantify the ballistic regime for the MSD and the time-averaged MSD as well as the spread of individual time-averaged MSD trajectories. One of the main effects we observe is that, both for the MSD and the time-averaged MSD, for superdiffusive UDSBM the ballistic regime is much shorter than for ordinary Brownian motion. In contrast, for subdiffusive UDSBM, the ballistic region extends to much longer diffusion times. Therefore, particular care needs to be taken under what conditions the overdamped limit indeed provides a correct description, even in the long time limit. We also analyze to what extent ergodicity in the Boltzmann-Khinchin sense in this nonstationary system is broken, both for subdiffusive and superdiffusive UDSBM. Finally, the limiting case of ultraslow UDSBM is considered, with a mixed logarithmic and power-law dependence of the ensemble- and time-averaged MSDs of the particles. In the limit of strong aging, remarkably, the ordinary UDSBM and the ultraslow UDSBM behave similarly in the short time ballistic limit. The approaches developed here open ways for considering other stochastic processes under physically important conditions when a finite particle mass and aging in the system cannot be neglected.
Some Fractional and Multifractional Gaussian Processes: A Brief Introduction
Lim, S. C.; Eab, C. H.
2014-01-01
This paper gives a brief introduction to some important fractional and multifractional Gaussian processes commonly used in modelling natural phenomena and man-made systems. The processes include fractional Brownian motion (both standard and the Riemann-Liouville type), multifractional Brownian motion, fractional and multifrac- tional Ornstein-Uhlenbeck processes, fractional and mutifractional Reisz-Bessel motion. Possible applications of these processes are briefly mentioned.
Large shear deformation of particle gels studied by Brownian Dynamics simulations
Rzepiela, A.A.; Opheusden, van J.H.J.; Vliet, van T.
2004-01-01
Brownian Dynamics (BD) simulations have been performed to study structure and rheology of particle gels under large shear deformation. The model incorporates soft spherical particles, and reversible flexible bond formation. Two different methods of shear deformation are discussed, namely affine and
Energy Technology Data Exchange (ETDEWEB)
Shit, Anindita [Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103 (India); Chattopadhyay, Sudip, E-mail: sudip_chattopadhyay@rediffmail.com [Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103 (India); Chaudhuri, Jyotipratim Ray, E-mail: jprc_8@yahoo.com [Department of Physics, Katwa College, Katwa, Burdwan 713130 (India)
2012-03-13
Graphical abstract: By invoking physically motivated coordinate transformation into quantum Smoluchowski equation, we have presented a transparent treatment for the determination of the effective diffusion coefficient and current of a quantum Brownian particle. Substantial enhancement in the efficiency of the diffusive transport is envisaged due to the quantum correction effects. Highlights:: Black-Right-Pointing-Pointer Transport of a quantum Brownian particle in a periodic potential has been addressed. Black-Right-Pointing-Pointer Governing quantum Smoluchowski equation (QSE) includes state dependent diffusion. Black-Right-Pointing-Pointer A coordinate transformation is used to recast QSE with constant diffusion. Black-Right-Pointing-Pointer Transport properties increases in comparison to the corresponding classical result. Black-Right-Pointing-Pointer This enhancement is purely a quantum effect. - Abstract: The transport property of a quantum Brownian particle that interacts strongly with a bath (in which a typical damping constant by far exceeds a characteristic frequency of the isolated system) under the influence of a tilted periodic potential has been studied by solving quantum Smoluchowski equation (QSE). By invoking physically motivated coordinate transformation into QSE, we have presented a transparent treatment for the determination of the effective diffusion coefficient of a quantum Brownian particle and the current (the average stationary velocity). Substantial enhancement in the efficiency of the diffusive transport is envisaged due to the quantum correction effects only if the bath temperature hovers around an appropriate range of intermediate values. Our findings also confirm the results obtained in the classical cases.
An elementary singularity-free Rotational Brownian Dynamics algorithm for anisotropic particles
Ilie, Ioana Mariuca; Briels, Willem J.; den Otter, Wouter K.
2015-01-01
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
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
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 fiel...
Functional limit theorems for generalized variations of the fractional Brownian sheet
DEFF Research Database (Denmark)
Pakkanen, Mikko; Réveillac, Anthony
2016-01-01
We prove functional central and non-central limit theorems for generalized variations of the anisotropic d-parameter fractional Brownian sheet (fBs) for any natural number d. Whether the central or the non-central limit theorem applies depends on the Hermite rank of the variation functional...
Functional limit theorems for generalized variations of the fractional Brownian sheet
DEFF Research Database (Denmark)
Pakkanen, Mikko; Réveillac, Anthony
We prove functional central and non-central limit theorems for generalized variations of the anisotropic d-parameter fractional Brownian sheet (fBs) for any natural number d. Whether the central or the non-central limit theorem applies depends on the Hermite rank of the variation functional...
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...
A series expansion of fractional Brownian motion with Hurst index exceeding 1/2
K.O. Dzhaparidze (Kacha); J.H. van Zanten (Harry)
2002-01-01
textabstractLet $B$ be a fractional Brownian motion with Hurst index $H ge 1/2$. Denote by $x_1 < x_2 < cdots$ the positive, real zeros of the Bessel function $J_{-H$ of the first kind of order $-H$, and by $y_1 < y_2 < cdots$ the positive zeros of $J_{1-H$. We prove the series representation
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...
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
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...
Numerically modeling Brownian thermal noise in amorphous and crystalline thin coatings
Lovelace, Geoffrey; Demos, Nicholas; Khan, Haroon
2018-01-01
Thermal noise is expected to be one of the noise sources limiting the astrophysical reach of Advanced LIGO (once commissioning is complete) and third-generation detectors. Adopting crystalline materials for thin, reflecting mirror coatings, rather than the amorphous coatings used in current-generation detectors, could potentially reduce thermal noise. Understanding and reducing thermal noise requires accurate theoretical models, but modeling thermal noise analytically is especially challenging with crystalline materials. Thermal noise models typically rely on the fluctuation-dissipation theorem, which relates the power spectral density of the thermal noise to an auxiliary elastic problem. In this paper, we present results from a new, open-source tool that numerically solves the auxiliary elastic problem to compute the Brownian thermal noise for both amorphous and crystalline coatings. We employ the open-source deal.ii and PETSc frameworks to solve the auxiliary elastic problem using a finite-element method, adaptive mesh refinement, and parallel processing that enables us to use high resolutions capable of resolving the thin reflective coating. We verify numerical convergence, and by running on up to hundreds of compute cores, we resolve the coating elastic energy in the auxiliary problem to approximately 0.1%. We compare with approximate analytic solutions for amorphous materials, and we verify that our solutions scale as expected with changing beam size, mirror dimensions, and coating thickness. Finally, we model the crystalline coating thermal noise in an experiment reported by Cole et al (2013 Nat. Photon. 7 644–50), comparing our results to a simpler numerical calculation that treats the coating as an ‘effectively amorphous’ material. We find that treating the coating as a cubic crystal instead of as an effectively amorphous material increases the thermal noise by about 3%. Our results are a step toward better understanding and reducing thermal noise to
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.
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.
Directory of Open Access Journals (Sweden)
Kaili Xiang
2014-01-01
Full Text Available Option pricing is always one of the critical issues in financial mathematics and economics. Brownian motion is the basic hypothesis of option pricing model, which questions the fractional property of stock price. In this paper, under the assumption that the exchange rate follows the extended Vasicek model, we obtain the closed form of the pricing formulas for two kinds of power options under fractional Brownian Motion (FBM jump-diffusion models.
Work distribution function for a Brownian particle driven by a nonconservative force
Saha, Bappa; Mukherji, Sutapa
2015-06-01
We derive the distribution function of work performed by a harmonic force acting on a uniformly dragged Brownian particle subjected to a rotational torque. Following the Onsager and Machlup's functional integral approach, we obtain the transition probability of finding the Brownian particle at a particular position at time t given that it started the journey from a specific location at an earlier time. The difference between the forward and the time-reversed form of the generalized Onsager-Machlup's Lagrangian is identified as the rate of medium entropy production which further helps us develop the stochastic thermodynamics formalism for our model. The probability distribution for the work done by the harmonic trap is evaluated for an equilibrium initial condition. Although this distribution has a Gaussian form, it is found that the distribution does not satisfy the conventional work fluctuation theorem.
Neuronal shot noise and Brownian 1/f2 behavior in the local field potential.
Directory of Open Access Journals (Sweden)
Joshua Milstein
Full Text Available We demonstrate that human electrophysiological recordings of the local field potential (LFP from intracranial electrodes, acquired from a variety of cerebral regions, show a ubiquitous 1/f(2 scaling within the power spectrum. We develop a quantitative model that treats the generation of these fields in an analogous way to that of electronic shot noise, and use this model to specifically address the cause of this 1/f(2 Brownian noise. The model gives way to two analytically tractable solutions, both displaying Brownian noise: 1 uncorrelated cells that display sharp initial activity, whose extracellular fields slowly decay in time and 2 rapidly firing, temporally correlated cells that generate UP-DOWN states.
A note on 'Langevin theory of anomalous Brownian motion made simple'
Energy Technology Data Exchange (ETDEWEB)
Tothova, Jana; Vasziova, Gabriela; Lisy, Vladimir [Department of Physics, Faculty of Electrical Engineering and Informatics, Technical University of Kosice, Park Komenskeho 2, 042 00 Kosice (Slovakia); Glod, Lukas, E-mail: vladimir.lisy@tuke.sk [Department of Mathematics and Physics, The University of Security Management, Kukucinova 17, 04001 Kosice (Slovakia)
2011-11-15
In our recent paper (Tothova et al 2011 Eur. J. Phys. 32 645), we extensively used a rule allowing us to convert linear stochastic equations of motion for the position of a Brownian particle to deterministic equations for its mean square displacement. This rule was established in a little known and hardly accessible work (Vladimirsky 1942 Z. Eksp. Teor. Phys. 12 199, in Russian), and so far it has not been used in solving the generalized Langevin equations with memory. To make our paper more self-contained and readable for students, we present a very simple substantiation of our approach, which is suitable for the description of both normal and anomalous Brownian motion. (letters and comments)
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.
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.
Nieuwenhuizen, Th. M.; Allahverdyan, A. E.
2002-09-01
The Brownian motion of a quantum particle in a harmonic confining potential and coupled to harmonic quantum thermal bath is exactly solvable. Though this system presents at high temperatures a pedagogic example to explain the laws of thermodynamics, it is shown that at low enough temperatures the stationary state is non-Gibbsian due to an entanglement with the bath. In physical terms, this happens when the cloud of bath modes around the particle starts to play a nontrivial role, namely, when the bath temperature T is smaller than the coupling energy. Indeed, equilibrium thermodynamics of the total system, particle plus bath, does not imply standard equilibrium thermodynamics for the particle itself at low T. Various formulations of the second law are found to be invalid at low T. First, the Clausius inequality can be violated, because heat can be extracted from the zero point energy of the cloud of bath modes. Second, when the width of the confining potential is suddenly changed, there occurs a relaxation to equilibrium during which the entropy production is partly negative. In this process the energy put on the particle does not relax monotonically, but oscillates between particle and bath, even in the limit of strong damping. Third, for nonadiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Conditions are put forward under which perpetuum mobility of the second kind, having one or several work extraction cycles, enter the realm of condensed matter physics. Fourth, it follows that the equivalence between different formulations of the second law (e.g., those by Clausius and Thomson) can be violated at low temperatures. These effects are the consequence of quantum entanglement in the presence of the slightly off-equilibrium nature of the thermal bath, and become important when the characteristic quantum time scale ħ/kBT is larger than or
Longmire, K.; Frojmovic, M.
1990-01-01
The Smoluchowski theory describing aggregation in suspensions of spherical colloidal particles due to Brownian diffusion-controlled two-body collisions, was used to obtain collision efficiencies, alpha B, for adenosine diphosphate (ADP)-induced platelet aggregation in citrated platelet-rich plasma (PRP) from humans, dogs, and rabbits. For these diffusion studies, PRP was stirred with 10 microM ADP for 0.5 s, then kept nonstirred at 37 degrees C for varying times before fixation; the percent a...
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...
First passage time statistics of Brownian motion with purely time dependent drift and diffusion
Molini, Annalisa; Talkner, Peter; Katul, Gabriel G.; Porporato, Amilcare
2010-01-01
Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by time-dependent drift and diffusion coefficients. Modeling such systems requires solving the associated Fokker-Planck equation subject to an absorbing barrier. Transitional probabilities are derived via the method of images, whose applicability to time dependent pr...
Study of Submicron Particle Size Distributions by Laser Doppler Measurement of Brownian Motion.
1984-10-29
acquisition and recording apparatus; and c) Development of appropriate software for analysis of signals obtained from the Brownian motion instrument...time scales (e.g., the transit time of the A-17 .- -. . , " 2.0 19 _j 1.2 08 0.6 0.4 0.2 0.0 0 500 1000 1500 2000 TIPOE STEP (10 ns/step) 2.0 1.8
GaAs-Based Nanowire Devices with Multiple Asymmetric Gates for Electrical Brownian Ratchets
Tanaka, Takayuki; Nakano, Yuki; Kasai, Seiya
2013-01-01
GaAs-based nanowire devices having multiple asymmetric gates for electrical Brownian ratchets were fabricated and characterized. From three-dimensional potential simulation results and current–voltage characteristics, we confirmed the formation of the asymmetric potential in our device design. Direct current was generated at room temperature by repeatedly switching the potential in a multiple-asymmetric-gate device on and off. Such current was not observed in either a single-asymmetric-gate d...
Local times for multifractional Brownian motion in higher dimensions: A white noise approach
Bock, Wolfgang; da Silva, José Luís; Suryawan, Herry P.
2016-11-01
We present the expansion of the multifractional Brownian motion (mBm) local time in higher dimensions, in terms of Wick powers of white noises (or multiple Wiener integrals). If a suitable number of kernels is subtracted, they exist in the sense of generalized white noise functionals. Moreover, we show the convergence of the regularized truncated local times for mBm in the sense of Hida distributions.
Dynamics of a magnetic active Brownian particle under a uniform magnetic field
Vidal-Urquiza, Glenn C.; Córdova-Figueroa, Ubaldo M.
2017-11-01
The dynamics of a magnetic active Brownian particle undergoing three-dimensional Brownian motion, both translation and rotation, under the influence of a uniform magnetic field is investigated. The particle self-propels at a constant speed along its magnetic dipole moment, which reorients due to the interplay between Brownian and magnetic torques, quantified by the Langevin parameter α . In this work, the time-dependent active diffusivity and the crossover time (τcross)—from ballistic to diffusive regimes—are calculated through the time-dependent correlation function of the fluctuations of the propulsion direction. The results reveal that, for any value of α , the particle undergoes a directional (or ballistic) propulsive motion at very short times (t ≪τcross ). In this regime, the correlation function decreases linearly with time, and the active diffusivity increases with it. It the opposite time limit (t ≫τcross ), the particle moves in a purely diffusive regime with a correlation function that decays asymptotically to zero and an active diffusivity that reaches a constant value equal to the long-time active diffusivity of the particle. As expected in the absence of a magnetic field (α =0 ), the crossover time is equal to the characteristic time scale for rotational diffusion, τrot. In the presence of a magnetic field (α >0 ), the correlation function, the active diffusivity, and the crossover time decrease with increasing α . The magnetic field regulates the regimes of propulsion of the particle. Here, the field reduces the period of time at which the active particle undergoes a directional motion. Consequently, the active particle rapidly reaches a diffusive regime at τcross≪τrot . In the limit of weak fields (α ≪1 ), the crossover time decreases quadratically with α , while in the limit of strong fields (α ≫1 ) it decays asymptotically as α-1. The results are in excellent agreement with those obtained by Brownian dynamics
Page 1 Brownian approximation for scheduling 917 To develop the ...
Indian Academy of Sciences (India)
, using the central limit theorem for renewal processes(see Wolff 1989), the random time change theorem and the continuous mapping theorem discussed in §(2.1), we can show that the nominal inventory level process Wh(t) converges weakly ...
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.
Parameter inference from hitting times for perturbed Brownian motion
DEFF Research Database (Denmark)
Tamborrino, Massimiliano; Ditlevsen, Susanne; Lansky, Peter
2015-01-01
? To answer this question we describe the effect of the intervention through parameter changes of the law governing the internal process. Then, the time interval between the start of the process and the final event is divided into two subintervals: the time from the start to the instant of intervention....... Also covariates and handling of censored observations are incorporated into the statistical model, and the method is illustrated on lung cancer data....
Brownian motion of a nano-colloidal particle: the role of the solvent.
Torres-Carbajal, Alexis; Herrera-Velarde, Salvador; Castañeda-Priego, Ramón
2015-07-15
Brownian motion is a feature of colloidal particles immersed in a liquid-like environment. Usually, it can be described by means of the generalised Langevin equation (GLE) within the framework of the Mori theory. In principle, all quantities that appear in the GLE can be calculated from the molecular information of the whole system, i.e., colloids and solvent molecules. In this work, by means of extensive Molecular Dynamics simulations, we study the effects of the microscopic details and the thermodynamic state of the solvent on the movement of a single nano-colloid. In particular, we consider a two-dimensional model system in which the mass and size of the colloid are two and one orders of magnitude, respectively, larger than the ones associated with the solvent molecules. The latter ones interact via a Lennard-Jones-type potential to tune the nature of the solvent, i.e., it can be either repulsive or attractive. We choose the linear momentum of the Brownian particle as the observable of interest in order to fully describe the Brownian motion within the Mori framework. We particularly focus on the colloid diffusion at different solvent densities and two temperature regimes: high and low (near the critical point) temperatures. To reach our goal, we have rewritten the GLE as a second kind Volterra integral in order to compute the memory kernel in real space. With this kernel, we evaluate the momentum-fluctuating force correlation function, which is of particular relevance since it allows us to establish when the stationarity condition has been reached. Our findings show that even at high temperatures, the details of the attractive interaction potential among solvent molecules induce important changes in the colloid dynamics. Additionally, near the critical point, the dynamical scenario becomes more complex; all the correlation functions decay slowly in an extended time window, however, the memory kernel seems to be only a function of the solvent density. Thus, the
Dependence of Brownian and Néel relaxation times on magnetic field strength.
Deissler, Robert J; Wu, Yong; Martens, Michael A
2014-01-01
In magnetic particle imaging (MPI) and magnetic particle spectroscopy (MPS) the relaxation time of the magnetization in response to externally applied magnetic fields is determined by the Brownian and Néel relaxation mechanisms. Here the authors investigate the dependence of the relaxation times on the magnetic field strength and the implications for MPI and MPS. The Fokker-Planck equation with Brownian relaxation and the Fokker-Planck equation with Néel relaxation are solved numerically for a time-varying externally applied magnetic field, including a step-function, a sinusoidally varying, and a linearly ramped magnetic field. For magnetic fields that are applied as a step function, an eigenvalue approach is used to directly calculate both the Brownian and Néel relaxation times for a range of magnetic field strengths. For Néel relaxation, the eigenvalue calculations are compared to Brown's high-barrier approximation formula. The relaxation times due to the Brownian or Néel mechanisms depend on the magnitude of the applied magnetic field. In particular, the Néel relaxation time is sensitive to the magnetic field strength, and varies by many orders of magnitude for nanoparticle properties and magnetic field strengths relevant for MPI and MPS. Therefore, the well-known zero-field relaxation times underestimate the actual relaxation times and, in particular, can underestimate the Néel relaxation time by many orders of magnitude. When only Néel relaxation is present--if the particles are embedded in a solid for instance--the authors found that there can be a strong magnetization response to a sinusoidal driving field, even if the period is much less than the zero-field relaxation time. For a ferrofluid in which both Brownian and Néel relaxation are present, only one relaxation mechanism may dominate depending on the magnetic field strength, the driving frequency (or ramp time), and the phase of the magnetization relative to the applied magnetic field. A simple
Trajectories of Brownian particles with space-correlated noise
Indian Academy of Sciences (India)
EDOARDO MILOTTI
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. Keywords. Stochastic processes; fluctuations; random walks. 1. Introduction. There are physical systems that display ...
Page 1 § > * r | *, Brownian approximation for scheduling {}39 ...
Indian Academy of Sciences (India)
Van Laarhoven P J M, Aarts E H L, Lenstra J K 1992 Job shop scheduling by simulated annealing. Oper. Res. 40: 1156–1179. Veatch M H, Wein L. M. 1992 ... Slochastic processes and queueing theory (Englewood Cliffs, NJ: Prentice Hall). Yao D D, Shantikumar J C 1990 Optimal scheduling control of a flexible machine.
Conserved linear dynamics of single-molecule Brownian motion
Serag, Maged F.
2017-06-06
Macromolecular diffusion in homogeneous fluid at length scales greater than the size of the molecule is regarded as a random process. The mean-squared displacement (MSD) of molecules in this regime increases linearly with time. Here we show that non-random motion of DNA molecules in this regime that is undetectable by the MSD analysis can be quantified by characterizing the molecular motion relative to a latticed frame of reference. Our lattice occupancy analysis reveals unexpected sub-modes of motion of DNA that deviate from expected random motion in the linear, diffusive regime. We demonstrate that a subtle interplay between these sub-modes causes the overall diffusive motion of DNA to appear to conform to the linear regime. Our results show that apparently random motion of macromolecules could be governed by non-random dynamics that are detectable only by their relative motion. Our analytical approach should advance broad understanding of diffusion processes of fundamental relevance.
Directory of Open Access Journals (Sweden)
Zoran Gligoric
2014-01-01
Full Text Available Underground mine projects are often associated with diverse sources of uncertainties. Having the ability to plan for these uncertainties plays a key role in the process of project evaluation and is increasingly recognized as critical to mining project success. To make the best decision, based on the information available, it is necessary to develop an adequate model incorporating the uncertainty of the input parameters. The model is developed on the basis of full discounted cash flow analysis of an underground zinc mine project. The relationships between input variables and economic outcomes are complex and often nonlinear. Fuzzy-interval grey system theory is used to forecast zinc metal prices while geometric Brownian motion is used to forecast operating costs over the time frame of the project. To quantify the uncertainty in the parameters within a project, such as capital investment, ore grade, mill recovery, metal content of concentrate, and discount rate, we have applied the concept of interval numbers. The final decision related to project acceptance is based on the net present value of the cash flows generated by the simulation over the time project horizon.
Energy Technology Data Exchange (ETDEWEB)
Meade, Nigel [Imperial College, Business School London (United Kingdom)
2010-11-15
For oil related investment appraisal, an accurate description of the evolving uncertainty in the oil price is essential. For example, when using real option theory to value an investment, a density function for the future price of oil is central to the option valuation. The literature on oil pricing offers two views. The arbitrage pricing theory literature for oil suggests geometric Brownian motion and mean reversion models. Empirically driven literature suggests ARMA-GARCH models. In addition to reflecting the volatility of the market, the density function of future prices should also incorporate the uncertainty due to price jumps, a common occurrence in the oil market. In this study, the accuracy of density forecasts for up to a year ahead is the major criterion for a comparison of a range of models of oil price behaviour, both those proposed in the literature and following from data analysis. The Kullbach Leibler information criterion is used to measure the accuracy of density forecasts. Using two crude oil price series, Brent and West Texas Intermediate (WTI) representing the US market, we demonstrate that accurate density forecasts are achievable for up to nearly two years ahead using a mixture of two Gaussians innovation processes with GARCH and no mean reversion. (author)
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Mereghetti, Paolo; Wade, Rebecca C.
2012-07-26
High macromolecular concentrations are a distinguishing feature of living organisms. Understanding how the high concentration of solutes affects the dynamic properties of biological macromolecules is fundamental for the comprehension of biological processes in living systems. In this paper, we describe the implementation of mean field models of translational and rotational hydrodynamic interactions into an atomically detailed many-protein brownian dynamics simulation method. Concentrated solutions (30-40% volume fraction) of myoglobin, hemoglobin A, and sickle cell hemoglobin S were simulated, and static structure factors, oligomer formation, and translational and rotational self-diffusion coefficients were computed. Good agreement of computed properties with available experimental data was obtained. The results show the importance of both solvent mediated interactions and weak protein-protein interactions for accurately describing the dynamics and the association properties of concentrated protein solutions. Specifically, they show a qualitative difference in the translational and rotational dynamics of the systems studied. Although the translational diffusion coefficient is controlled by macromolecular shape and hydrodynamic interactions, the rotational diffusion coefficient is affected by macromolecular shape, direct intermolecular interactions, and both translational and rotational hydrodynamic interactions.
Fractional rotational Brownian motion in a uniform dc external field.
Kalmykov, Yuri P
2004-11-01
The longitudinal and transverse components of the complex dielectric susceptibility tensor of an assembly of dipolar particles subjected to a dc bias field are evaluated in the context of a fractional noninertial rotational diffusion model. Exact and approximate solutions for the dielectric dispersion and absorption spectra are obtained. It is shown that a knowledge of the effective relaxation times for normal rotational diffusion is sufficient to predict accurately the anomalous dielectric relaxation behavior of the system for all time scales of interest. Simple equations for the characteristic frequencies of the dielectric loss spectra are obtained in terms of the physical model parameters (dimensionless field and fractional exponent). The model explains the anomalous (Cole-Cole like) relaxation of complex dipolar systems, where the anomalous exponent differs from unity (corresponding to the normal dielectric relaxation), i.e., the relaxation process is characterized by a broad distribution of relaxation times.
Urdapilleta, Eugenio
2015-12-01
In one-dimensional systems, the dynamics of a Brownian particle are governed by the force derived from a potential as well as by diffusion properties. In this work, we obtain the first-passage-time statistics of a Brownian particle driven by an arbitrary potential with an exponential temporally decaying superimposed field up to a prescribed threshold. The general system analyzed here describes the sub-threshold signal integration of integrate-and-fire neuron models, of any kind, supplemented by an adaptation-like current, whereas the first-passage-time corresponds to the declaration of a spike. Following our previous studies, we base our analysis on the backward Fokker-Planck equation and study the survival probability and the first-passage-time density function in the space of the initial condition. By proposing a series solution we obtain a system of recurrence equations, which given the specific structure of the exponential time-dependent drift, easily admit a simpler Laplace representation. Naturally, the present general derivation agrees with the explicit solution we found previously for the Wiener process in (2012 J. Phys. A: Math. Theor. 45 185001). However, to demonstrate the generality of the approach, we further explicitly evaluate the first-passage-time statistics of the underlying Ornstein-Uhlenbeck process. To test the validity of the series solution, we extensively compare theoretical expressions with the data obtained from numerical simulations in different regimes. As shown, agreement is precise whenever the series is truncated at an appropriate order. Beyond the fact that both the Wiener and Ornstein-Uhlenbeck processes have a direct interpretation in the context of neuronal models, given their ubiquity in different fields, our present results will be of interest in other settings where an additive state-independent temporal relaxation process is being developed as the particle diffuses.
Quantum harmonic Brownian motion in a general environment: A modified phase-space approach
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Yeh, Leehwa [Univ. of California, Berkeley, CA (United States). Dept. of Physics
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.
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.
Ordering transition of non-Brownian suspensions in confined steady shear flow.
Yeo, Kyongmin; Maxey, Martin R
2010-05-01
We report on ordering transitions of concentrated non-Brownian suspensions confined by two parallel walls under steady shear. At a volume fraction as low as ϕ=0.48, particles near the wall assemble into strings which are organized as a simple hexagonal array by hydrodynamic interactions. The suspension exhibits a complex phase behavior depending on the ratio of the channel height to the particle radius, Hy/a. In a strongly confined system Hy/aplane changes between hexagonal and rectangular structures depending on Hy/a. It is shown that the relative viscosity is a function of both the volume fraction and the ordered state.
GaAs-Based Nanowire Devices with Multiple Asymmetric Gates for Electrical Brownian Ratchets
Tanaka, Takayuki; Nakano, Yuki; Kasai, Seiya
2013-06-01
GaAs-based nanowire devices having multiple asymmetric gates for electrical Brownian ratchets were fabricated and characterized. From three-dimensional potential simulation results and current-voltage characteristics, we confirmed the formation of the asymmetric potential in our device design. Direct current was generated at room temperature by repeatedly switching the potential in a multiple-asymmetric-gate device on and off. Such current was not observed in either a single-asymmetric-gate device or a multiple-symmetric-gate device. The current direction and input frequency dependences of the net current indicated that the observed current was generated by the flashing-ratchet mechanism.
Phase diagrams for quantum Brownian motion on two-dimensional Bravais lattices
Zhang, Grace H.
2017-11-01
We study quantum Brownian motion (QBM) models for a particle in a dissipative environment coupled to a periodic potential. We review QBM for a particle in a one-dimensional periodic potential and extend the study to that for a particle in two-dimensional (2D) periodic potentials of four Bravais lattice types: square, rectangular, triangular (hexagonal), and centered rectangular. We perform perturbative renormalization group analyses to derive the zero temperature flow diagrams and phase boundaries for a particle in these potentials, and observe localization behavior dependent on the anisotropy of the lattice parameters.
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Gianni Pagnini
2012-01-01
inhomogeneity and nonstationarity properties of the medium. For instance, when this superposition is applied to the time-fractional diffusion process, the resulting Master Equation emerges to be the governing equation of the Erdélyi-Kober fractional diffusion, that describes the evolution of the marginal distribution of the so-called generalized grey Brownian motion. This motion is a parametric class of stochastic processes that provides models for both fast and slow anomalous diffusion: it is made up of self-similar processes with stationary increments and depends on two real parameters. The class includes the fractional Brownian motion, the time-fractional diffusion stochastic processes, and the standard Brownian motion. In this framework, the M-Wright function (known also as Mainardi function emerges as a natural generalization of the Gaussian distribution, recovering the same key role of the Gaussian density for the standard and the fractional Brownian motion.
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.
De Biase, Pablo M; Markosyan, Suren; Noskov, Sergei
2015-02-05
The transport of ions and solutes by biological pores is central for cellular processes and has a variety of applications in modern biotechnology. The time scale involved in the polymer transport across a nanopore is beyond the accessibility of conventional MD simulations. Moreover, experimental studies lack sufficient resolution to provide details on the molecular underpinning of the transport mechanisms. BROMOC, the code presented herein, performs Brownian dynamics simulations, both serial and parallel, up to several milliseconds long. BROMOC can be used to model large biological systems. IMC-MACRO software allows for the development of effective potentials for solute-ion interactions based on radial distribution function from all-atom MD. BROMOC Suite also provides a versatile set of tools to do a wide variety of preprocessing and postsimulation analysis. We illustrate a potential application with ion and ssDNA transport in MspA nanopore. © 2014 Wiley Periodicals, Inc.
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Dettmer, Simon L.; Keyser, Ulrich F.; Pagliara, Stefano [Cavendish Laboratory, University of Cambridge, 19 J J Thomson Avenue, Cambridge CB3 0HE (United Kingdom)
2014-02-15
In this article we present methods for measuring hindered Brownian motion in the confinement of complex 3D geometries using digital video microscopy. Here we discuss essential features of automated 3D particle tracking as well as diffusion data analysis. By introducing local mean squared displacement-vs-time curves, we are able to simultaneously measure the spatial dependence of diffusion coefficients, tracking accuracies and drift velocities. Such local measurements allow a more detailed and appropriate description of strongly heterogeneous systems as opposed to global measurements. Finite size effects of the tracking region on measuring mean squared displacements are also discussed. The use of these methods was crucial for the measurement of the diffusive behavior of spherical polystyrene particles (505 nm diameter) in a microfluidic chip. The particles explored an array of parallel channels with different cross sections as well as the bulk reservoirs. For this experiment we present the measurement of local tracking accuracies in all three axial directions as well as the diffusivity parallel to the channel axis while we observed no significant flow but purely Brownian motion. Finally, the presented algorithm is suitable also for tracking of fluorescently labeled particles and particles driven by an external force, e.g., electrokinetic or dielectrophoretic forces.
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.
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
2014-01-01
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. PMID:25418308
Reeves, Daniel B.; Weaver, John B.
2015-01-01
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. PMID:26130846
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.
Stochastic processes from physics to finance
Paul, Wolfgang
2013-01-01
This book introduces the theory of stochastic processes with applications taken from physics and finance. Fundamental concepts like the random walk or Brownian motion but also Levy-stable distributions are discussed. Applications are selected to show the interdisciplinary character of the concepts and methods. In the second edition of the book a discussion of extreme events ranging from their mathematical definition to their importance for financial crashes was included. The exposition of basic notions of probability theory and the Brownian motion problem as well as the relation between conservative diffusion processes and quantum mechanics is expanded. The second edition also enlarges the treatment of financial markets. Beyond a presentation of geometric Brownian motion and the Black-Scholes approach to option pricing as well as the econophysics analysis of the stylized facts of financial markets, an introduction to agent based modeling approaches is given.
Weyl and Riemann Liouville multifractional Ornstein Uhlenbeck processes
Lim, S. C.; Teo, L. P.
2007-06-01
This paper considers two new multifractional stochastic processes, namely the Weyl multifractional Ornstein-Uhlenbeck process and the Riemann-Liouville multifractional Ornstein-Uhlenbeck process. Basic properties of these processes such as locally self-similar property and Hausdorff dimension are studied. The relationship between the multifractional Ornstein-Uhlenbeck processes and the corresponding multifractional Brownian motions is established.
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.
Solution of the Master Equation for Quantum Brownian Motion Given by the Schrödinger Equation
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R. Sinuvasan
2016-12-01
Full Text Available We consider the master equation of quantum Brownian motion, and with the application of the group invariant transformation, we show that there exists a surface on which the solution of the master equation is given by an autonomous one-dimensional Schrödinger Equation.
Longmire, K.; Frojmovic, M.
1990-01-01
The Smoluchowski theory describing aggregation in suspensions of spherical colloidal particles due to Brownian diffusion-controlled two-body collisions, was used to obtain collision efficiencies, alpha B, for adenosine diphosphate (ADP)-induced platelet aggregation in citrated platelet-rich plasma (PRP) from humans, dogs, and rabbits. For these diffusion studies, PRP was stirred with 10 microM ADP for 0.5 s, then kept nonstirred at 37 degrees C for varying times before fixation; the percent aggregation was computed from the decrease in particle concentration with time measured with a resistive particle counter. Up to 20% of rabbit platelets formed microaggregates within 60 s of ADP addition to such nonstirred suspensions, corresponding to mean alpha B values of approximately 0.9. However, human and dog platelets aggregated approximately 10 times and 2-3 times faster than rabbit platelets within the first 60 s of ADP addition, corresponding to alpha B approximately 8 and 2, respectively. These high alpha B (much greater than 1) for human platelets were independent of initial platelet count and were equally observed with the calcium ionophore A23187 as activator. In about one-third of human, dog, or rabbit PRP, comparable and lower values of alpha B (less than 0.5) were obtained for a slower second phase of aggregation seen for the nonstirred PRP over 60-300 s post ADP-addition. Platelet aggregability in continually stirred PRP was distinct from that observed in Brownian diffusion (nonstirred) because comparable aggregation was observed for all three species' stirred PRP, whereas greater than 3-8 times more ADP is required to yield 50% of maximal rates of aggregation for nonstirred than for stirred PRP. The above results point to the existence of long-range interactions mediating platelet aggregation in Brownian diffusion-controlled platelet collisions which varies according to human > dog > rabbit platelets. The roles for platelet pseudopods and adhesive sites in
Mapping migratory flyways in Asia using dynamic Brownian bridge movement models.
Palm, Eric C; Newman, Scott H; Prosser, Diann J; Xiao, Xiangming; Ze, Luo; Batbayar, Nyambayar; Balachandran, Sivananinthaperumal; Takekawa, John Y
2015-01-01
Identifying movement routes and stopover sites is necessary for developing effective management and conservation strategies for migratory animals. In the case of migratory birds, a collection of migration routes, known as a flyway, is often hundreds to thousands of kilometers long and can extend across political boundaries. Flyways encompass the entire geographic range between the breeding and non-breeding areas of a population, species, or a group of species, and they provide spatial frameworks for management and conservation across international borders. Existing flyway maps are largely qualitative accounts based on band returns and survey data rather than observed movement routes. In this study, we use satellite and GPS telemetry data and dynamic Brownian bridge movement models to build upon existing maps and describe waterfowl space use probabilistically in the Central Asian and East Asian-Australasian Flyways. Our approach provided new information on migratory routes that was not easily attainable with existing methods to describe flyways. Utilization distributions from dynamic Brownian bridge movement models identified key staging and stopover sites, migration corridors and general flyway outlines in the Central Asian and East Asian-Australasian Flyways. A map of space use from ruddy shelducks depicted two separate movement corridors within the Central Asian Flyway, likely representing two distinct populations that show relatively strong connectivity between breeding and wintering areas. Bar-headed geese marked at seven locations in the Central Asian Flyway showed heaviest use at several stopover sites in the same general region of high-elevation lakes along the eastern Qinghai-Tibetan Plateau. Our analysis of data from multiple Anatidae species marked at sites throughout Asia highlighted major movement corridors across species and confirmed that the Central Asian and East Asian-Australasian Flyways were spatially distinct. The dynamic Brownian bridge
Transport and diffusion properties of Brownian particles powered by a rotating wheel.
Ai, Bao-Quan
2017-07-01
Diffusion and rectification of Brownian particles powered by a rotating wheel are numerically investigated in a two-dimensional channel. The nonequilibrium driving comes from the rotating wheel, which can break thermodynamical equilibrium and induce the directed transport in an asymmetric potential. It is found that the direction of the transport along the potential is determined by the asymmetry of the potential and the position of the wheel. The average velocity is a peaked function of the angular speed (or the diffusion coefficient) and the position of the peak shifts to large angular speed (or diffusion coefficient) when the diffusion coefficient (or the angular speed) increases. There exists an optimal angular speed (or diffusion coefficient) at which the effective diffusion coefficient takes its maximal value. Remarkably, the giant acceleration of diffusion is observed by suitably adjusting the system parameters. The parameters corresponding to the maximum effective diffusion coefficient are not the same as the parameters at which average velocity is maximum.
Double-temperature ratchet model and current reversal of coupled Brownian motors
Li, Chen-Pu; Chen, Hong-Bin; Zheng, Zhi-Gang
2017-12-01
On the basis of the transport features and experimental phenomena observed in studies of molecular motors, we propose a double-temperature ratchet model of coupled motors to reveal the dynamical mechanism of cooperative transport of motors with two heads, where the interactions and asynchrony between two motor heads are taken into account. We investigate the collective unidirectional transport of coupled system and find that the direction of motion can be reversed under certain conditions. Reverse motion can be achieved by modulating the coupling strength, coupling free length, and asymmetric coefficient of the periodic potential, which is understood in terms of the effective potential theory. The dependence of the directed current on various parameters is studied systematically. Directed transport of coupled Brownian motors can be manipulated and optimized by adjusting the pulsation period or the phase shift of the pulsation temperature.
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.
Duan, Zhao-Wen; Li, Wei; Xie, Ping; Dou, Shuo-Xing; Wang, Peng-Ye
2010-04-01
Using Brownian dynamics simulation, we studied the effect of histone modifications on conformations of an array of nucleosomes in a segment of chromatin. The simulation demonstrated that the segment of chromatin shows the dynamic behaviour that its conformation can switch between a state with nearly all of the histones being wrapped by DNA and a state with nearly all of the histones being unwrapped by DNA, thus involving the “cross-talking" interactions among the histones. Each state can stay for a sufficiently long time. These conformational states are essential for gene expression or gene silence. The simulation also shows that these conformational states can be inherited by the daughter DNAs during DNA replication, giving a theoretical explanation of the epigenetic phenomenon.
Directory of Open Access Journals (Sweden)
T. Turiv
2015-06-01
Full Text Available As recently reported [Turiv T. et al., Science, 2013, Vol. 342, 1351], fluctuations in the orientation of the liquid crystal (LC director can transfer momentum from the LC to a colloid, such that the diffusion of the colloid becomes anomalous on a short time scale. Using video microscopy and single particle tracking, we investigate random thermal motion of colloidal particles in a nematic liquid crystal for the time scales shorter than the expected time of director fluctuations. At long times, compared to the characteristic time of the nematic director relaxation we observe typical anisotropic Brownian motion with the mean square displacement (MSD linear in time τ and inversly proportional to the effective viscosity of the nematic medium. At shorter times, however, the dynamics is markedly nonlinear with MSD growing more slowly (subdiffusion or faster (superdiffusion than τ. These results are discussed in the context of coupling of colloidal particle's dynamics to the director fluctuation dynamics.
Prediction of Brownian particle deposition in porous media using the constricted tube model.
Chang, You-Im; Chen, Shan-Chih; Lee, Eric
2003-10-01
The deposition of colloidal particles onto the collector surfaces of porous media is investigated using the Brownian dynamics simulation method. The pore structure in a filter bed was characterized by the constricted tube model. The effects of various shapes of the total interaction energy curves of DLVO theory and the effects of different particle diameters on the collection efficiencies of particles are examined. The simulation results show that the particle collection efficiency is strongly dependent on the geometry of the tube and on the shape of the total interaction energy curve. In a comparison with the available experimental measurements of the filter coefficient, it is found that the present model can give a smaller discrepancy than that of the convective diffusion model in the unfavorable deposition region.
Saraogi, Vishal; Padmapriya, P.; Paul, Apurba; Tatu, Utpal S.; Natarajan, Vasant
2010-05-01
We study the properties of single red blood cells (RBCs) held in an optical-tweezers trap. We observe a change in the spectrum of Brownian fluctuations between RBCs from normal and malaria-infected samples. The change, caused by infection-induced structural changes in the cell, appears as a statistical increase in the mean (by 25%) and standard deviation (by 200%) of the corner frequency measured over ~100 cells. The increase is observed even though the ensemble of cells being measured consists mostly of cells that do not actually host the parasite, but are from an infected pool. This bystander effect appears to vindicate other observations that infected cells can affect the biomechanical properties of uninfected cells. The change is also observed to be independent of the stage of infection and its duration, highlighting its potential for disease detection.
Brownian dynamics simulation of insulin microsphere formation from break-up of a fractal network.
Li, Wei; Gunton, J D; Khan, Siddique J; Schoelz, J K; Chakrabarti, A
2011-01-14
Motivated by a recent experiment on insulin microsphere formation where polyethylene glycol (PEG) is used as the precipitating agent, we have developed a simple theoretical model that can predict the formation of a fractal network of insulin monomers and the subsequent break-up of the fractal network into microsphere aggregates. In our approach the effect of PEG on insulin is modeled via a standard depletion attraction mechanism via the Asakura-Oosawa model. We show that even in the context of this simple model, it is possible to mimic important aspects of the insulin experiment in a brownian dynamics simulation. We simulate the effect of changing temperature in our model by changing the well depth of the Asakura-Oosawa potential. A fractal network is observed in a "deep quench" of the system, followed by a "heating" that results in a break-up of the network and subsequent formation of microspheres.
Volume fraction instability in an oscillating non-Brownian iso-dense suspension.
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Roht Y.L.
2017-01-01
Full Text Available 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.
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.
Density profiles of granular gases studied by molecular dynamics and Brownian bridges
Peñuñuri, F.; Montoya, J. A.; Carvente, O.
2018-02-01
Despite the inherent frictional forces and dissipative collisions, confined granular matter can be regarded as a system in a stationary state if we inject energy continuously. Under these conditions, both the density and the granular temperature are, in general, non-monotonic variables along the height of the container. In consequence, an analytical description of a granular system is hard to conceive. Here, by using molecular dynamics simulations, we measure the packing fraction profiles for a vertically vibrating three-dimensional granular system in several gaseous-like stationary states. We show that by using the Brownian bridge concept, the determined packing fraction profiles can be reproduced accurately and give a complete description of the distribution of the particles inside the simulation box.
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.
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.
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.
Invariance principle, multifractional Gaussian processes and long-range dependence
Cohen, Serge; Marty, Renaud
2008-01-01
This paper is devoted to establish an invariance principle where the limit process is a multifractional Gaussian process with a multifractional function which takes its values in $(1/2,1)$. Some properties, such as regularity and local self-similarity of this process are studied. Moreover the limit process is compared to the multifractional Brownian motion.
Selected papers on noise and stochastic processes
1954-01-01
Six classic papers on stochastic process, selected to meet the needs of physicists, applied mathematicians, and engineers. Contents: 1.Chandrasekhar, S.: Stochastic Problems in Physics and Astronomy. 2. Uhlenbeck, G. E. and Ornstein, L. S.: On the Theory of the Browninan Motion. 3. Ming Chen Wang and Uhlenbeck, G. E.: On the Theory of the Browninan Motion II. 4. Rice, S. O.: Mathematical Analysis of Random Noise. 5. Kac, Mark: Random Walk and the Theory of Brownian Motion. 6. Doob, J. L.: The Brownian Movement and Stochastic Equations. Unabridged republication of the Dover reprint (1954). Pre
Energy Technology Data Exchange (ETDEWEB)
Cleary, Liam; Coffey, William T; Dowling, William J [Department of Electronic and Electrical Engineering, Trinity College, Dublin 2 (Ireland); Kalmykov, Yuri P [Laboratoire de Mathematiques et Physique, Universite de Perpignan Via Domitia, 52, Avenue de Paul Alduy, 66860 Perpignan Cedex (France); Titov, Serguey V, E-mail: kalmykov@univ-perp.fr [Institute of Radio Engineering and Electronics of the Russian Academy of Sciences, Vvedenskii Square 1, Fryazino, 141190 (Russian Federation)
2011-11-25
The dynamics of quantum Brownian particles in a cosine periodic potential are studied using the phase space formalism associated with the Wigner representation of quantum mechanics. Various kinetic phase space master equation models describing quantum Brownian motion in a potential are compared by evaluating the dynamic structure factor and escape rate from the differential recurrence relations generated by the models. The numerical solution is accomplished via matrix continued fractions in the manner customarily used for the classical Fokker-Planck equation. The results of numerical calculations of the escape rate from a well of the cosine potential are compared with those given analytically by the quantum-mechanical reaction rate theory solution of the Kramers turnover problem for a periodic potential, given by Georgievskii and Pollak (1994 Phys. Rev. E 49 5098), enabling one to appraise each model. (paper)
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.
Jung, Jiyun; Lee, Jumin; Kim, Jun Soo
2015-03-01
We present a simulation study on the mechanisms of a phase separation in dilute fluids of Lennard-Jones (LJ) particles as a model of self-interacting molecules. Molecular dynamics (MD) and Brownian dynamics (BD) simulations of the LJ fluids are employed to model the condensation of a liquid droplet in the vapor phase and the mesoscopic aggregation in the solution phase, respectively. With emphasis on the cluster growth at late times well beyond the nucleation stage, we find that the growth mechanisms can be qualitatively different: cluster diffusion and coalescence in the MD simulations and Ostwald ripening in the BD simulations. We also show that the rates of the cluster growth have distinct scaling behaviors during cluster growth. This work suggests that in the solution phase the random Brownian nature of the solute dynamics may lead to the Ostwald ripening that is qualitatively different from the cluster coalescence in the vapor phase.
The integrated periodogram for stable processes
Kluppelberg, C; Mikosch, T
1996-01-01
We study the asymptotic behavior of the integrated periodogram for alpha-stable linear processes. For alpha is an element of (1, 2) we prove a functional limit theorem for the integrated periodogram. The limit is an alpha-stable analogue to the Brownian bridge. We apply our results to investigate
Sun, Mingmei; Xu, Meng
2017-12-01
A class of stochastic singular hybrid systems driven by both Brownian motion and Poisson jumps are studied. This paper is devoted to discussing the exponential stability and interval stability of such stochastic singular hybrid systems. The concept of interval admissibility is proposed. Sufficient conditions are given for exponential mean square admissibility and interval admissibility by using Itô's formula, H-representation and spectrum technique. Finally, two simulation cases are presented to demonstrate the theoretical results.
Abe, Yushi; Kuroda, Ryota; Ying, Xiang; Sato, Masaki; Tanaka, Takayuki; Kasai, Seiya
2015-01-01
We investigated the structural parameter dependence of the directed current in GaAs-nanowire-based Brownian ratchet devices. The directed current was generated by flashing a ratchet potential array repeatedly using multiple asymmetric gates with a periodic signal. The amount of current in the fabricated device increased as the nanowire width W decreased, which contradicted the theoretical model. The current also depended on the number of the gates N, when N was smaller than 6. We discussed th...
Hiotelis, Nicos; Del Popolo, Antonino
2017-03-01
We construct an integral equation for the first crossing distributions for fractional Brownian motion in the case of a constant barrier and we present an exact analytical solution. Additionally we present first crossing distributions derived by simulating paths from fractional Brownian motion. We compare the results of the analytical solutions with both those of simulations and those of some approximated solutions which have been used in the literature. Finally, we present multiplicity functions for dark matter structures resulting from our analytical approach and we compare with those resulting from N-body simulations. We show that the results of analytical solutions are in good agreement with those of path simulations but differ significantly from those derived from approximated solutions. Additionally, multiplicity functions derived from fractional Brownian motion are poor fits of the those which result from N-body simulations. We also present comparisons with other models which are exist in the literature and we discuss different ways of improving the agreement between analytical results and N-body simulations.
Mezzasalma, Stefano A
2007-03-15
The theoretical basis of a recent theory of Brownian relativity for polymer solutions is deepened and reexamined. After the problem of relative diffusion in polymer solutions is addressed, its two postulates are formulated in all generality. The former builds a statistical equivalence between (uncorrelated) timelike and shapelike reference frames, that is, among dynamical trajectories of liquid molecules and static configurations of polymer chains. The latter defines the "diffusive horizon" as the invariant quantity to work with in the special version of the theory. Particularly, the concept of universality in polymer physics corresponds in Brownian relativity to that of covariance in the Einstein formulation. Here, a "universal" law consists of a privileged observation, performed from the laboratory rest frame and agreeing with any diffusive reference system. From the joint lack of covariance and simultaneity implied by the Brownian Lorentz-Poincaré transforms, a relative uncertainty arises, in a certain analogy with quantum mechanics. It is driven by the difference between local diffusion coefficients in the liquid solution. The same transformation class can be used to infer Fick's second law of diffusion, playing here the role of a gauge invariance preserving covariance of the spacetime increments. An overall, noteworthy conclusion emerging from this view concerns the statistics of (i) static macromolecular configurations and (ii) the motion of liquid molecules, which would be much more related than expected.
Energy Technology Data Exchange (ETDEWEB)
Dubina, Sean Hyun, E-mail: sdubin2@uic.edu; Wedgewood, Lewis Edward, E-mail: wedge@uic.edu [Department of Chemical Engineering, University of Illinois at Chicago, 810 S. Clinton St. (MC 110), Chicago, Illinois 60607-4408 (United States)
2016-07-15
Ferrofluids are often favored for their ability to be remotely positioned via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally simulated using the Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely, Maxwell’s equations. An iterative constraint method was developed to satisfy Maxwell’s equations when a uniform magnetic field is imposed on ferrofluids in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters in a mesoscale particle collection. This was accomplished by allowing a particulate system in a simple shear flow to advance by a time step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint method applied over sub-volume length scales until Maxwell’s equations were satisfied. The resultant ferrofluid model with constraints demonstrates that the magnetoviscosity contribution is not as substantial when compared to homogeneous simulations that assume the material’s magnetism is a direct response to the external magnetic field. This was detected across varying intensities of particle-particle interaction, Brownian motion, and shear flow. Ferroparticle aggregation was still extensively present but less so than typically observed.
Phase structure of XX0 spin chain and nonintersecting Brownian motion
Saeedian, M.; Zahabi, A.
2018-01-01
We study finite size and temperature XX0 Heisenberg spin chain in weak and strong coupling regimes. By using an elegant connection of the model to integrable combinatorics and probability, we explore and interpret a possible phase structure of the model in asymptotic limit: the limit of large inverse temperature and size. First, the partition function and free energy of the model are derived by using techniques and results from random matrix models and nonintersecting Brownian motion. We show that, in the asymptotic limit, partition function of the model, written in terms of matrix integral, is governed by the Tracy–Widom distribution. Second, the exact analytic results for the free energy, which is obtained by the asymptotic analysis of the Tracy–Widom distribution, indicate a completely new and sophisticated phase structure of the model. This phase structure consists of second- and third-order phase transitions. Finally, to shed light on our new results, we provide a possible new interpretation of the phase structure in terms of dynamical behaviour of magnons in the spin chain. We demonstrate distinct features of the phases with schematic spin configurations which have definite features in each region of the phase diagram.
Active Brownian particles and run-and-tumble particles separate inside a maze
Khatami, Maryam; Wolff, Katrin; Pohl, Oliver; Ejtehadi, Mohammad Reza; Stark, Holger
2016-11-01
A diverse range of natural and artificial self-propelled particles are known and are used nowadays. Among them, active Brownian particles (ABPs) and run-and-tumble particles (RTPs) are two important classes. We numerically study non-interacting ABPs and RTPs strongly confined to different maze geometries in two dimensions. We demonstrate that by means of geometrical confinement alone, ABPs are separable from RTPs. By investigating Matryoshka-like mazes with nested shells, we show that a circular maze has the best filtration efficiency. Results on the mean first-passage time reveal that ABPs escape faster from the center of the maze, while RTPs reach the center from the rim more easily. According to our simulations and a rate theory, which we developed, ABPs in steady state accumulate in the outermost region of the Matryoshka-like mazes, while RTPs occupy all locations within the maze with nearly equal probability. These results suggest a novel technique for separating different types of self-propelled particles by designing appropriate confining geometries without using chemical or biological agents.
Directory of Open Access Journals (Sweden)
O. V. Shavykin
2016-09-01
Full Text Available The Brownian dynamics method has been used to study the effect of the branching asymmetry on the local orientational mobility of segments and bonds in dendrimers in good solvent. “Coarse-grained” models of flexible dendrimers with different branching symmetry but with the same average segment length were considered. The frequency dependences of the rate of the spin-lattice relaxation nuclear magnetic resonance (NMR [1/T1H(H] for segments or bonds located at different distances from terminal monomers were calculated. After the exclusion of the contribution of the overall dendrimer rotation the position of the maxima of the frequency dependences [1/T1H(ωH] for different segments with the same length doesn’t depend on their location inside a dendrimer both for phantom models and for models with excluded volume interactions. This effect doesn’t depend also on the branching symmetry, but the position of the maximum [1/T1H(ωH] is determined by the segment length. For bonds inside segments the positions of the maximum [1/T1H(ωH] coincide for all models considered. Therefore, the obtained earlier conclusion about the weak influence of the excluded volume interactions on the local dynamics in the flexible symmetric dendrimers can be generalized for dendrimers with an asymmetric branching.
Thermodynamic feature of a Brownian heat engine operating between two heat baths.
Asfaw, Mesfin
2014-01-01
A generalized theory of nonequilibrium thermodynamics for a Brownian motor operating between two different heat baths is presented. Via a simple paradigmatic model, we not only explore the thermodynamic feature of the engine in the regime of the nonequilibrium steady state but also study the short time behavior of the system for either the isothermal case with load or, in general, the nonisothermal case with or without load. Many elegant thermodynamic theories can be checked via the present model. Furthermore the dependence of the velocity, the efficiency, and the performance of the refrigerator on time t is examined. Our study reveals a current reversal due to time t. In the early system relaxation period, the model works neither as a heat engine nor as a refrigerator and only after a certain period of time does the model start functioning as a heat engine or as a refrigerator. The performance of the engine also improves with time and at steady state the engine manifests a higher efficiency or performance as a refrigerator. Furthermore the effect of energy exchange via the kinetic energy on the performance of the heat engine is explored.
Brownian dynamic study of an enzyme metabolon in the TCA cycle: Substrate kinetics and channeling.
Huang, Yu-Ming M; Huber, Gary A; Wang, Nuo; Minteer, Shelley D; McCammon, J Andrew
2018-02-01
Malate dehydrogenase (MDH) and citrate synthase (CS) are two pacemaking enzymes involved in the tricarboxylic acid (TCA) cycle. Oxaloacetate (OAA) molecules are the intermediate substrates that are transferred from the MDH to CS to carry out sequential catalysis. It is known that, to achieve a high flux of intermediate transport and reduce the probability of substrate leaking, a MDH-CS metabolon forms to enhance the OAA substrate channeling. In this study, we aim to understand the OAA channeling within possible MDH-CS metabolons that have different structural orientations in their complexes. Three MDH-CS metabolons from native bovine, wild-type porcine, and recombinant sources, published in recent work, were selected to calculate OAA transfer efficiency by Brownian dynamics (BD) simulations and to study, through electrostatic potential calculations, a possible role of charges that drive the substrate channeling. Our results show that an electrostatic channel is formed in the metabolons of native bovine and recombinant porcine enzymes, which guides the oppositely charged OAA molecules passing through the channel and enhances the transfer efficiency. However, the channeling probability in a suggested wild-type porcine metabolon conformation is reduced due to an extended diffusion length between the MDH and CS active sites, implying that the corresponding arrangements of MDH and CS result in the decrease of electrostatic steering between substrates and protein surface and then reduce the substrate transfer efficiency from one active site to another. © 2017 The Protein Society.
Robust unidirectional rotation in three-tooth Brownian rotary ratchet systems
Tutu, Hiroki; Nagata, Soichiro
2013-02-01
We apply a simple Brownian ratchet model to an artificial molecular rotary system mounted in a biological membrane, in which the rotor always maintains unidirectional rotation in response to a linearly polarized weak ac field. Because the rotor and stator compose a ratchet system, we describe the motion of the rotor tip with the Langevin equation for a particle in a two-dimensional three-tooth ratchet potential of threefold symmetry. Unidirectional rotation can be induced under the field and optimized by stochastic resonance, wherein the mean angular momentum (MAM) of the rotor exhibits a bell-shaped curve for the noise strength. We obtain analytical expressions for the MAM and power loss from the corresponding Fokker-Planck equation, via a Markov transition model for coarse-grained states (six-state model). The MAM expression reveals a significant effect depending on the chirality of the ratchet potential: in achiral cases, the MAM approximately vanishes with respect to the polarization angle ϕ of the field; in chiral cases, the MAM does not crucially depend on ϕ, but depends on the direction of the ratchet; i.e., the parity of the unidirectional rotation is inherent in the ratchet structure. This feature is useful for artificial rotary systems to maintain robust unidirectional rotation independent of the mounting condition.
Blanchet, Adrien
2009-01-01
A periodic perturbation of a Gaussian measure modifies the sharp constants in Poincarae and logarithmic Sobolev inequalities in the homogeniz ation limit, that is, when the period of a periodic perturbation converges to zero. We use variational techniques to determine the homogenized constants and get optimal convergence rates toward s equilibrium of the solutions of the perturbed diffusion equations. The study of these sharp constants is motivated by the study of the stochastic Stokes\\' drift. It also applies to Brownian ratchets and molecular motors in biology. We first establish a transport phenomenon. Asymptotically, the center of mass of the solution moves with a constant velocity, which is determined by a doubly periodic problem. In the reference frame attached to the center of mass, the behavior of the solution is governed at large scale by a diffusion with a modified diffusion coefficient. Using the homogenized logarithmic Sobolev inequality, we prove that the solution converges in self-similar variables attached to t he center of mass to a stationary solution of a Fokker-Planck equation modulated by a periodic perturbation with fast oscillations, with an explicit rate. We also give an asymptotic expansion of the traveling diffusion front corresponding to the stochastic Stokes\\' drift with given potential flow. © 2009 Society for Industrial and Applied Mathematics.
Zou, Weizhong; Larson, Ronald
2015-03-01
We describe the rheology of polymeric glasses by combining a simple constitutive equation for the fast segmental modes, borrowed from Fielding, et al., with Brownian dynamics (BD) simulations of the slow polymer modes. The BD simulations determine the polymeric stress from ensembles of finitely extensible bead-spring chains, where the bead drag coefficient is governed by solutions to the equation for segmental relaxation. Thus the model treats the short glassy segmental mode as ``solvent'' for the polymer modes. With rubbery modulus for the slow-relaxing polymer modes as one of our model parameters, stress-dependent relaxation, physical aging, flow rejuvenation as well as strain-hardening and recovery can be successfully accounted for in uniaxial extension and steady shear, without the use of an artificial ``crinkle factor'' used to account for recoil dynamics in previous work. Our simulation results remarkably agree with the experimental data from Lee et al. A comparison between our model and the barrier-hopping theory is also made. The authors acknowledge discussions with M. E. Cates and S. M. Fielding.
First passage time statistics of Brownian motion with purely time dependent drift and diffusion
Molini, A.; Talkner, P.; Katul, G. G.; Porporato, A.
2011-06-01
Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by time-dependent drift and diffusion coefficients. Modeling such systems requires solving the associated Fokker-Planck equation subject to an absorbing barrier. Transitional probabilities are derived via the method of images, whose applicability to time dependent problems is shown to be limited to state-independent drift and diffusion coefficients that only depend on time and are proportional to each other. First passage time statistics, such as the survival probabilities and first passage time densities are obtained analytically. The analysis includes the study of different functional forms of the time dependent drift and diffusion, including power-law time dependence and different periodic drivers. As a case study of these theoretical results, a stochastic model of water resources availability in snowmelt dominated regions is presented, where both temperature effects and snow-precipitation input are incorporated.
Brownian dynamics of a protein-polymer chain complex in a solid-state nanopore
Wells, Craig C.; Melnikov, Dmitriy V.; Gracheva, Maria E.
2017-08-01
We study the movement of a polymer attached to a large protein inside a nanopore in a thin silicon dioxide membrane submerged in an electrolyte solution. We use Brownian dynamics to describe the motion of a negatively charged polymer chain of varying lengths attached to a neutral protein modeled as a spherical bead with a radius larger than that of the nanopore, allowing the chain to thread the nanopore but preventing it from translocating. The motion of the protein-polymer complex within the pore is also compared to that of a freely translocating polymer. Our results show that the free polymer's standard deviations in the direction normal to the pore axis is greater than that of the protein-polymer complex. We find that restrictions imposed by the protein, bias, and neighboring chain segments aid in controlling the position of the chain in the pore. Understanding the behavior of the protein-polymer chain complex may lead to methods that improve molecule identification by increasing the resolution of ionic current measurements.
Directory of Open Access Journals (Sweden)
Norbert Mücke
Full Text Available Nanomechanical properties of filamentous biopolymers, such as the persistence length, may be determined from two-dimensional images of molecules immobilized on surfaces. For a single filament in solution, two principal adsorption scenarios are possible. Both scenarios depend primarily on the interaction strength between the filament and the support: i For interactions in the range of the thermal energy, the filament can freely equilibrate on the surface during adsorption; ii For interactions much stronger than the thermal energy, the filament will be captured by the surface without having equilibrated. Such a 'trapping' mechanism leads to more condensed filament images and hence to a smaller value for the apparent persistence length. To understand the capture mechanism in more detail we have performed Brownian dynamics simulations of relatively short filaments by taking the two extreme scenarios into account. We then compared these 'ideal' adsorption scenarios with observed images of immobilized vimentin intermediate filaments on different surfaces. We found a good agreement between the contours of the deposited vimentin filaments on mica ('ideal' trapping and on glass ('ideal' equilibrated with our simulations. Based on these data, we have developed a strategy to reliably extract the persistence length of short worm-like chain fragments or network forming filaments with unknown polymer-surface interactions.
Cuetos, Alejandro; Patti, Alessandro
2015-08-01
We propose a simple but powerful theoretical framework to quantitatively compare Brownian dynamics (BD) and dynamic Monte Carlo (DMC) simulations of multicomponent colloidal suspensions. By extending our previous study focusing on monodisperse systems of rodlike colloids, here we generalize the formalism described there to multicomponent colloidal mixtures and validate it by investigating the dynamics in isotropic and liquid crystalline phases containing spherical and rodlike particles. In order to investigate the dynamics of multicomponent colloidal systems by DMC simulations, it is key to determine the elementary time step of each species and establish a unique timescale. This is crucial to consistently study the dynamics of colloidal particles with different geometry. By analyzing the mean-square displacement, the orientation autocorrelation functions, and the self part of the van Hove correlation functions, we show that DMC simulation is a very convenient and reliable technique to describe the stochastic dynamics of any multicomponent colloidal system. Our theoretical formalism can be easily extended to any colloidal system containing size and/or shape polydisperse particles.
Siksik, May; Krishnamurthy, Vikram
2017-09-01
This paper proposes a multi-dielectric Brownian dynamics simulation framework for design-space-exploration (DSE) studies of ion-channel permeation. The goal of such DSE studies is to estimate the channel modeling-parameters that minimize the mean-squared error between the simulated and expected "permeation characteristics." To address this computational challenge, we use a methodology based on statistical inference that utilizes the knowledge of channel structure to prune the design space. We demonstrate the proposed framework and DSE methodology using a case study based on the KcsA ion channel, in which the design space is successfully reduced from a 6-D space to a 2-D space. Our results show that the channel dielectric map computed using the framework matches with that computed directly using molecular dynamics with an error of 7%. Finally, the scalability and resolution of the model used are explored, and it is shown that the memory requirements needed for DSE remain constant as the number of parameters (degree of heterogeneity) increases.
Brownian and advective dynamics in microflow studied by coherent X-ray scattering experiments.
Urbani, Raphael; Westermeier, Fabian; Banusch, Benjamin; Sprung, Michael; Pfohl, Thomas
2016-11-01
Combining microfluidics with coherent X-ray illumination offers the possibility to not only measure the structure but also the dynamics of flowing samples in a single-scattering experiment. Here, the power of this combination is demonstrated by studying the advective and Brownian dynamics of colloidal suspensions in microflow of different geometries. Using an experimental setup with a fast two-dimensional detector and performing X-ray correlation spectroscopy by calculating two-dimensional maps of the intensity auto-correlation functions, it was possible to evaluate the sample structure and furthermore to characterize the detailed flow behavior, including flow geometry, main flow directions, advective flow velocities and diffusive dynamics. By scanning a microfocused X-ray beam over a microfluidic device, the anisotropic auto-correlation functions of driven colloidal suspensions in straight, curved and constricted microchannels were mapped with the spatial resolution of the X-ray beam. This method has not only a huge potential for studying flow patterns in complex fluids but also to generally characterize anisotropic dynamics in materials.
Borodin, Andrei N
2017-01-01
This book provides a rigorous yet accessible introduction to the theory of stochastic processes. A significant part of the book is devoted to the classic theory of stochastic processes. In turn, it also presents proofs of well-known results, sometimes together with new approaches. Moreover, the book explores topics not previously covered elsewhere, such as distributions of functionals of diffusions stopped at different random times, the Brownian local time, diffusions with jumps, and an invariance principle for random walks and local times. Supported by carefully selected material, the book showcases a wealth of examples that demonstrate how to solve concrete problems by applying theoretical results. It addresses a broad range of applications, focusing on concrete computational techniques rather than on abstract theory. The content presented here is largely self-contained, making it suitable for researchers and graduate students alike.
Representation and properties of a class of conditionally Gaussian processes
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Pedersen, Jan
2009-01-01
It is shown that the class of conditionally Gaussian processes with independent increments is stable under marginalisation and conditioning. Moreover, in general such processes can be represented as integrals of a time changed Brownian motion where the time change and the integrand are jointly...
Zou, Weizhong; Larson, Ronald G
2016-08-10
We present a hybrid model for polymeric glasses under deformation that combines a minimal model of segmental dynamics with a beads-and-springs model of a polymer, solved by Brownian dynamics (BD) simulations, whose relaxation is coupled to the segmental dynamics through the drag coefficient of the beads. This coarse-grained model allows simulations that are much faster than molecular dynamics and successfully capture the entire range of mechanical response including yielding, plastic flow, strain-hardening, and incomplete strain recovery. The beads-and-springs model improves upon the dumbbell model for glassy polymers proposed by Fielding et al. (Phys. Rev. Lett., 2012, 108, 048301) by capturing the small elastic recoil seen experimentally without the use of ad hoc adjustments of parameters required in the model of Fielding et al. With appropriate choice of parameters, predictions of creep, recovery, and segmental relaxation are found to be in good agreement with poly(methylmethacrylate) (PMMA) data of Lee et al. (Science, 2009, 323, 231-234). Our model shows dramatic differences in behavior of the segmental relaxation time between extensional creep and steady extension, and between extension and shear. The non-monotonic response of the segmental relaxation time to extensional creep and the small elastic recovery after removal of stress are shown to arise from sub-chains that are trapped between folds, and that become highly oriented and stretched at strains of order unity, connecting the behavior of glassy polymers under creep to that of dilute polymer solutions under fast extensional flows. We are also able to predict the effects of polymer pre-orientation in the parallel or orthogonal direction on the subsequent response to extensional deformation.
Brownian Dynamics of a Suspension of Particles with Constrained Voronoi Cell Volumes
Singh, John P.
2015-06-23
© 2015 American Chemical Society. Solvent-free polymer-grafted nanoparticle fluids consist of inorganic core particles fluidized by polymers tethered to their surfaces. The attachment of the suspending fluid to the particle surface creates a strong penalty for local variations in the fluid volume surrounding the particles. As a model of such a suspension we perform Brownian dynamics of an equilibrium system consisting of hard spheres which experience a many-particle potential proportional to the variance of the Voronoi volumes surrounding each particle (E = α(Vi-V0)^{2}). The coefficient of proportionality α can be varied such that pure hard sphere dynamics is recovered as α → 0, while an incompressible array of hairy particles is obtained as α →. As α is increased the distribution of Voronoi volumes becomes narrower, the mean coordination number of the particle increases and the variance in the number of nearest neighbors decreases. The nearest neighbor peaks in the pair distribution function are suppressed and shifted to larger radial separations as the constraint acts to maintain relatively uniform interstitial regions. The structure factor of the model suspension satisfies S(k=0) → 0 as α → in accordance with expectation for a single component (particle plus tethered fluid) incompressible system. The tracer diffusivity of the particles is reduced by the volume constraint and goes to zero at φ 0.52, indicating an earlier glass transition than has been observed in hard sphere suspensions. The total pressure of the suspension grows in proportion to (αkBT)^{1/2} as the strength of the volume-constraint potential grows. This stress arises primarily from the interparticle potential forces, while the hard-sphere collisional contribution to the stress is suppressed by the volume constraint.
Energy Technology Data Exchange (ETDEWEB)
Roura, Albert [Los Alamos National Laboratory; Fleming, C H [UNIV OF MARYLAND; Hu, B L [UNIV OF MARYLAND
2008-01-01
We revisit the model of a system made up of a Brownian quantum oscillator linearly coupled to an environment made up of many quantum oscillators at finite temperature. We show that the HPZ master equation for the reduced density matrix derived earlier [B.L. Hu, J.P. Paz, Y. Zhang, Phys. Rev. D 45, 2843 (1992)] has incorrectly specified coefficients for the case of nonlocal dissipation. We rederive the QBM master equation, correctly specifying all coefficients, and determine the position uncertainty to be free of excessive cutoff sensitivity. Our coefficients and solutions are reduced entirely to contour integration for analytic spectra at arbitrary temperature, coupling strength, and cut-off. As an illustration we calculate the master equation coefficients and solve the master equation for ohmic coupling (with finite cutoff) and example supra-ohmic and sub-ohmic spectral densities. We determine the effect of an external force on the quantum oscillator and also show that our representation of the master equation and solutions naturally extends to a system of multiple oscillators bilinearly coupled to themselves and the bath in arbitrary fashion. This produces a formula for investigating the standard quantum limit which is central to addressing many theoretical issues in macroscopic quantum phenomena and experimental concerns related to low temperature precision measurements. We find that in a dissipative environment, all initial states settle down to a Gaussian density matrix whose covariance is determined by the thermal reservoir and whose mean is determined by the external force. We specify the thermal covariance for the spectral densities we explore.
Dynamics in crowded environments: is non-Gaussian Brownian diffusion normal?
Kwon, Gyemin; Sung, Bong June; Yethiraj, Arun
2014-07-17
The dynamics of colloids and proteins in dense suspensions is of fundamental importance, from a standpoint of understanding the biophysics of proteins in the cytoplasm and for the many interesting physical phenomena in colloidal dispersions. Recent experiments and simulations have raised questions about our understanding of the dynamics of these systems. Experiments on vesicles in nematic fluids and colloids in an actin network have shown that the dynamics of particles can be "non-Gaussian"; that is, the self-part of the van Hove correlation function, Gs(r,t), is an exponential rather than Gaussian function of r, in regimes where the mean-square displacement is linear in t. It is usually assumed that a linear mean-square displacement implies a Gaussian Gs(r,t). In a different result, simulations of a mixture of proteins, aimed at mimicking the cytoplasm of Escherichia coli, have shown that hydrodynamic interactions (HI) play a key role in slowing down the dynamics of proteins in concentrated (relative to dilute) solutions. In this work, we study a simple system, a dilute tracer colloidal particle immersed in a concentrated solution of larger spheres, using simulations with and without HI. The simulations reproduce the non-Gaussian Brownian diffusion of the tracer, implying that this behavior is a general feature of colloidal dynamics and is a consequence of local heterogeneities on intermediate time scales. Although HI results in a lower diffusion constant, Gs(r,t) is very similar to and without HI, provided they are compared at the same value of the mean-square displacement.
Brownian Dynamics of a Suspension of Particles with Constrained Voronoi Cell Volumes.
Singh, John P; Walsh, Stuart D C; Koch, Donald L
2015-06-23
Solvent-free polymer-grafted nanoparticle fluids consist of inorganic core particles fluidized by polymers tethered to their surfaces. The attachment of the suspending fluid to the particle surface creates a strong penalty for local variations in the fluid volume surrounding the particles. As a model of such a suspension we perform Brownian dynamics of an equilibrium system consisting of hard spheres which experience a many-particle potential proportional to the variance of the Voronoi volumes surrounding each particle (E = α(Vi-V0)(2)). The coefficient of proportionality α can be varied such that pure hard sphere dynamics is recovered as α → 0, while an incompressible array of hairy particles is obtained as α → ∞. As α is increased the distribution of Voronoi volumes becomes narrower, the mean coordination number of the particle increases and the variance in the number of nearest neighbors decreases. The nearest neighbor peaks in the pair distribution function are suppressed and shifted to larger radial separations as the constraint acts to maintain relatively uniform interstitial regions. The structure factor of the model suspension satisfies S(k=0) → 0 as α → ∞ in accordance with expectation for a single component (particle plus tethered fluid) incompressible system. The tracer diffusivity of the particles is reduced by the volume constraint and goes to zero at ϕ ∼ 0.52, indicating an earlier glass transition than has been observed in hard sphere suspensions. The total pressure of the suspension grows in proportion to (αkBT)(1/2) as the strength of the volume-constraint potential grows. This stress arises primarily from the interparticle potential forces, while the hard-sphere collisional contribution to the stress is suppressed by the volume constraint.
Zhang, Wei-Guo; Li, Zhe; Liu, Yong-Jun
2018-01-01
In this paper, we study the pricing problem of the continuously monitored fixed and floating strike geometric Asian power options in a mixed fractional Brownian motion environment. First, we derive both closed-form solutions and mixed fractional partial differential equations for fixed and floating strike geometric Asian power options based on delta-hedging strategy and partial differential equation method. Second, we present the lower and upper bounds of the prices of fixed and floating strike geometric Asian power options under the assumption that both risk-free interest rate and volatility are interval numbers. Finally, numerical studies are performed to illustrate the performance of our proposed pricing model.
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...... 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...... biosensor based on the detection of the dynamic response of magnetic beads....
Abe, Yushi; Kuroda, Ryota; Ying, Xiang; Sato, Masaki; Tanaka, Takayuki; Kasai, Seiya
2015-06-01
We investigated the structural parameter dependence of the directed current in GaAs-nanowire-based Brownian ratchet devices. The directed current was generated by flashing a ratchet potential array repeatedly using multiple asymmetric gates with a periodic signal. The amount of current in the fabricated device increased as the nanowire width W decreased, which contradicted the theoretical model. The current also depended on the number of the gates N, when N was smaller than 6. We discussed the obtained results in terms of the structural parameter dependence of carrier transfer efficiency and the effect of electron reservoirs on current generation in flashing ratchet operation.
Records in fractal stochastic processes.
Aliakbari, A; Manshour, P; Salehi, M J
2017-03-01
The record statistics in stationary and non-stationary fractal time series is studied extensively. By calculating various concepts in record dynamics, we find some interesting results. In stationary fractional Gaussian noises, we observe a universal behavior for the whole range of Hurst exponents. However, for non-stationary fractional Brownian motions, the record dynamics is crucially dependent on the memory, which plays the role of a non-stationarity index, here. Indeed, the deviation from the results of the stationary case increases by increasing the Hurst exponent in fractional Brownian motions. We demonstrate that the memory governs the dynamics of the records as long as it causes non-stationarity in fractal stochastic processes; otherwise, it has no impact on the record statistics.
Asymmetric skew Bessel processes and their applications to finance
Decamps, M.; Goovaerts, M.J.; Schoutens, W.
2006-01-01
In this paper, we extend the Harrison and Shepp's construction of the skew Brownian motion (1981) and we obtain a diffusion similar to the two-dimensional Bessel process with speed and scale densities discontinuous at one point. Natural generalizations to multi-dimensional and fractional order
DEFF Research Database (Denmark)
Zhu, Jie
stock markets. Models with dynamic of Geometric Brownian Motion are adopted, multivariate GARCH models are also introduced to capture the feature of time-varying volatility in stock returns. The results suggest that the different pric- ing can be explained by the difference in expected returns between...
Hahn, Melinda W; O'Meliae, Charles R
2004-01-01
The deposition and reentrainment of particles in porous media have been examined theoretically and experimentally. A Brownian Dynamics/Monte Carlo (MC/BD) model has been developed that simulates the movement of Brownian particles near a collector under "unfavorable" chemical conditions and allows deposition in primary and secondary minima. A simple Maxwell approach has been used to estimate particle attachment efficiency by assuming deposition in the secondary minimum and calculating the probability of reentrainment. The MC/BD simulations and the Maxwell calculations support an alternative view of the deposition and reentrainment of Brownian particles under unfavorable chemical conditions. These calculations indicate that deposition into and subsequent release from secondary minima can explain reported discrepancies between classic model predictions that assume irreversible deposition in a primary well and experimentally determined deposition efficiencies that are orders of magnitude larger than Interaction Force Boundary Layer (IFBL) predictions. The commonly used IFBL model, for example, is based on the notion of transport over an energy barrier into the primary well and does not address contributions of secondary minimum deposition. A simple Maxwell model based on deposition into and reentrainment from secondary minima is much more accurate in predicting deposition rates for column experiments at low ionic strengths. It also greatly reduces the substantial particle size effects inherent in IFBL models, wherein particle attachment rates are predicted to decrease significantly with increasing particle size. This view is consistent with recent work by others addressing the composition and structure of the first few nanometers at solid-water interfaces including research on modeling water at solid-liquid interfaces, surface speciation, interfacial force measurements, and the rheological properties of concentrated suspensions. It follows that deposition under these
1999-01-01
multifractal point of view, and with ∗This property is also known as the Lv́ey modulus of continuity in the case of Brownian motion . For fBm see [5...where V is fBm. Then, we use the term FB(MF) to abbreviate fractional Brownian motion in multifractal time: B(t) = BH(M(t)). First, to obtain an...conclude: Corollary 1.2 (Fractional Brownian Motion in Multifractal Time). Let BH denote fBm of Hurst parameter H. Let M(t) be of almost surely
Directory of Open Access Journals (Sweden)
Kwang-Il Ahn
2013-01-01
Full Text Available The Hurst exponent and variance are two quantities that often characterize real-life, high-frequency observations. Such real-life signals are generally measured under noise environments. We develop a multiscale statistical method for simultaneous estimation of a time-changing Hurst exponent H(t and a variance parameter C in a multifractional Brownian motion model in the presence of white noise. The method is based on the asymptotic behavior of the local variation of its sample paths which applies to coarse scales of the sample paths. This work provides stable and simultaneous estimators of both parameters when independent white noise is present. We also discuss the accuracy of the simultaneous estimators compared with a few selected methods and the stability of computations with regard to adapted wavelet filters.
Directory of Open Access Journals (Sweden)
Ryo Kanada
Full Text Available Kinesin is a family of molecular motors that move unidirectionally along microtubules (MT using ATP hydrolysis free energy. In the family, the conventional two-headed kinesin was experimentally characterized to move unidirectionally through "walking" in a hand-over-hand fashion by coordinated motions of the two heads. Interestingly a single-headed kinesin, a truncated KIF1A, still can generate a biased Brownian movement along MT, as observed by in vitro single molecule experiments. Thus, KIF1A must use a different mechanism from the conventional kinesin to achieve the unidirectional motions. Based on the energy landscape view of proteins, for the first time, we conducted a set of molecular simulations of the truncated KIF1A movements over an ATP hydrolysis cycle and found a mechanism exhibiting and enhancing stochastic forward-biased movements in a similar way to those in experiments. First, simulating stand-alone KIF1A, we did not find any biased movements, while we found that KIF1A with a large friction cargo-analog attached to the C-terminus can generate clearly biased Brownian movements upon an ATP hydrolysis cycle. The linked cargo-analog enhanced the detachment of the KIF1A from MT. Once detached, diffusion of the KIF1A head was restricted around the large cargo which was located in front of the head at the time of detachment, thus generating a forward bias of the diffusion. The cargo plays the role of a diffusional anchor, or cane, in KIF1A "walking."
Energy Technology Data Exchange (ETDEWEB)
McMullan, G., E-mail: gm2@mrc-lmb.cam.ac.uk; Vinothkumar, K.R.; Henderson, R.
2015-11-15
We have recorded dose-fractionated electron cryo-microscope images of thin films of pure flash-frozen amorphous ice and pre-irradiated amorphous carbon on a Falcon II direct electron detector using 300 keV electrons. We observe Thon rings [1] in both the power spectrum of the summed frames and the sum of power spectra from the individual frames. The Thon rings from amorphous carbon images are always more visible in the power spectrum of the summed frames whereas those of amorphous ice are more visible in the sum of power spectra from the individual frames. This difference indicates that while pre-irradiated carbon behaves like a solid during the exposure, amorphous ice behaves like a fluid with the individual water molecules undergoing beam-induced motion. Using the measured variation in the power spectra amplitude with number of electrons per image we deduce that water molecules are randomly displaced by a mean squared distance of ∼1.1 Å{sup 2} for every incident 300 keV e{sup −}/Å{sup 2}. The induced motion leads to an optimal exposure with 300 keV electrons of 4.0 e{sup −}/Å{sup 2} per image with which to observe Thon rings centred around the strong 3.7 Å scattering peak from amorphous ice. The beam-induced movement of the water molecules generates pseudo-Brownian motion of embedded macromolecules. The resulting blurring of single particle images contributes an additional term, on top of that from radiation damage, to the minimum achievable B-factor for macromolecular structure determination. - Highlights: • Thon rings can be seen from amorphous ice. • Radiation damage to amorphous ice randomly displaces water molecules. • Each incident 300 keV e{sup −}/Å{sup 2} displaces water molecules on average by ∼1 Å. • Macromolecules embedded in amorphous ice undergo beam induced Brownian motion.
Potential analysis of stable processes and its extensions
Stos, Andrzej
2009-01-01
Stable Lévy processes and related stochastic processes play an important role in stochastic modelling in applied sciences, in particular in financial mathematics. This book is about the potential theory of stable stochastic processes. It also deals with related topics, such as the subordinate Brownian motions (including the relativistic process) and Feynman–Kac semigroups generated by certain Schroedinger operators. The authors focus on classes of stable and related processes that contain the Brownian motion as a special case. This is the first book devoted to the probabilistic potential theory of stable stochastic processes, and, from the analytical point of view, of the fractional Laplacian. The introduction is accessible to non-specialists and provides a general presentation of the fundamental objects of the theory. Besides recent and deep scientific results the book also provides a didactic approach to its topic, as all chapters have been tested on a wide audience, including young mathematicians at a C...
Invariance principles for linear processes with application to isotonic regression
Dedecker, Jérôme; Merlevède, Florence; Peligrad, Magda
2009-01-01
In this paper, we prove maximal inequalities and study the functional central limit theorem for the partial sums of linear processes generated by dependent innovations. Due to the general weights, these processes can exhibit long-range dependence and the limiting distribution is a fractional Brownian motion. The proofs are based on new approximations by a linear process with martingale difference innovations. The results are then applied to study an estimator of the isotonic regression when t...
Maximal inequalities for bessel processes
Directory of Open Access Journals (Sweden)
Graversen SE
1998-01-01
Full Text Available It is proved that the uniform law of large numbers (over a random parameter set for the -dimensional ( Bessel process started at 0 is valid: for all stopping times for . The rate obtained (on the right-hand side is shown to be the best possible. The following inequality is gained as a consequence: for all stopping times for , where the constant satisfies as . This answers a question raised in [4]. The method of proof relies upon representing the Bessel process as a time changed geometric Brownian motion. The main emphasis of the paper is on the method of proof and on the simplicity of solution.
Karim, M. Enamul; Samad, M. Abdus; Ferdows, M.
2017-06-01
The present note investigates the magneto hall effect on unsteady flow of elastico-viscous nanofluid in a channel with slip boundary considering the presence of thermal radiation and heat generation with Brownian motion. Numerical results are achieved by solving the governing equations by the implicit Finite Difference Method (FDM) obtaining primary and secondary velocities, temperature, nanoparticles volume fraction and concentration distributions within the boundary layer entering into the problem. The influences of several interesting parameters such as elastico-viscous parameter, magnetic field, hall parameter, heat generation, thermal radiation and Brownian motion parameters on velocity, heat and mass transfer characteristics of the fluid flow are discussed with the help of graphs. Also the effects of the pertinent parameters, which are of physical and engineering interest, such as Skin friction parameter, Nusselt number and Sherwood number are sorted out. It is found that the flow field and other quantities of physical concern are significantly influenced by these parameters.
Attard, Phil; Gray-Weale, Angus
2008-03-21
A Brownian particle subject to a time- and space-varying force is studied with the second entropy theory for nonequilibrium statistical mechanics. A fluctuation expression is obtained for the second entropy of the path, and this is maximized to obtain the most likely path of the particle. Two approaches are used, one based on the velocity correlation function and one based on the position correlation function. The approaches are a perturbation about the free particle result and are exact for weak external forces. They provide a particularly simple way of including memory effects in time-varying driven diffusion. The theories are tested against computer simulation data for a Brownian particle trapped in an oscillating parabolic well. They accurately predict the phase lag and amplitude as a function of drive frequency, and they account quantitatively for the memory effects that are important at high frequencies and that are missing in the simplest Langevin equation.
Energy Technology Data Exchange (ETDEWEB)
Jumarie, Guy [Department of Mathematics, University of Quebec at Montreal, P.O. Box 8888, Downtown Station, Montreal, QC, H3C 3P8 (Canada)]. E-mail: jumarie.guy@uqam.ca
2006-06-15
The (complex-valued) Brownian motion of order n is defined as the limit of a random walk on the complex roots of the unity. Real-valued fractional noises are obtained as fractional derivatives of the Gaussian white noise (or order two). Here one combines these two approaches and one considers the new class of fractional noises obtained as fractional derivative of the complex-valued Brownian motion of order n. The key of the approach is the relation between differential and fractional differential provided by the fractional Taylor's series of analytic function f(z+h)=E{sub {alpha}}(h{sup {alpha}}D{sub z}{sup {alpha}}).f(z), where E{sub {alpha}} is the Mittag-Leffler function on the one hand, and the generalized Maruyama's notation, on the other hand. Some questions are revisited such as the definition of fractional Brownian motion as integral w.r.t. (dt){sup {alpha}}, and the exponential growth equation driven by fractional Brownian motion, to which a new solution is proposed. As a first illustrative example of application, in mathematical finance, one proposes a new approach to the optimal management of a stochastic portfolio of fractional order via the Lagrange variational technique applied to the state moment dynamical equations. In the second example, one deals with non-random Lagrangian mechanics of fractional order. The last example proposes a new approach to fractional stochastic mechanics, and the solution so obtained gives rise to the question as to whether physical systems would not have their own internal random times.
Probability distribution of the time-averaged mean-square displacement of a Gaussian process.
Grebenkov, Denis S
2011-09-01
We study the probability distribution of the time-averaged mean-square displacement of a discrete Gaussian process. An empirical approximation for the probability density is suggested and numerically validated for fractional Brownian motion. The optimality of quadratic forms for inferring dynamical and microrheological quantities from individual random trajectories is discussed, with emphasis on a reliable interpretation of single-particle tracking experiments.
Energy Technology Data Exchange (ETDEWEB)
Geenen, P.V.; Bennis, J.
1989-04-04
A process is described for minimizing the cracking tendency and uncontrolled dimensional change, and improving the strength of a rammed plastic refractory reactor liner comprising phosphate-bonded silicon carbide or phosphate-bonded alumina. It consists of heating the reactor liner placed or mounted in a reactor, prior to its first use, from ambient temperature up to a temperature of from about 490/sup 0/C to about 510/sup 0/C, the heating being carried out by heating the liner at a rate to produce a temperature increase of the liner not greater than about 6/sup 0/C per hour.
Directory of Open Access Journals (Sweden)
F. Mabood
Full Text Available This article addresses the combined effects of chemical reaction and viscous dissipation on MHD radiative heat and mass transfer of nanofluid flow over a rotating stretching surface. The model used for the nanofluid incorporates the effects of the Brownian motion and thermophoresis in the presence of heat source. Similarity transformation variables have been used to model the governing equations of momentum, energy, and nanoparticles concentration. Runge-Kutta-Fehlberg method with shooting technique is applied to solve the resulting coupled ordinary differential equations. Physical features for all pertinent parameters on the dimensionless velocity, temperature, skin friction coefficient, and heat and mass transfer rates are analyzed graphically. The numerical comparison has also presented for skin friction coefficient and local Nusselt number as a special case for our study. It is noted that fluid velocity enhances when rotational parameter is increased. Surface heat transfer rate enhances for larger values of Prandtl number and heat source parameter while mass transfer rate increases for larger values of chemical reaction parameter. Keywords: Nanofluid, MHD, Chemical reaction, Rotating stretching sheet, Radiation
Yeo, Kyongmin; Maxey, Martin R
2010-06-01
We investigate the effect of an external torque, applied in the vorticity direction, to particles in a sheared non-Brownian suspension confined by rigid walls. At volume fractions of ϕ=0.48-0.52 such suspension flows undergo an ordering transition, developing a hexagonal structure of particle strings in the velocity gradient-vorticity plane. The hexagonal structure is disturbed by negative torques, leading to an increase in the shear viscosity. Positive torque has a favorable effect on the ordered state. However, if the magnitude of the positive torque exceeds a certain threshold, the hexagonal order begins to be weakened. Due to the significant changes in suspension microstructures, rheological parameters such as the shear and vortex viscosities exhibit nonlinear responses to the external torques. On the other hand, at lower volume fractions ϕ≤0.40, where ordered structures are not developed, suspension microstructure is not sensitive to an external torque and the apparent viscosity is a linear function of the torque.
Eka Putri, Irana; Gita Redhyka, Grace
2017-07-01
Micro-air-bubble has a high potential contribution in waste water, farming, and fishery treatment. In this research, submicron scale of micro-air-bubble was observed to determine its stability in H2O solvent. By increasing its stability, it can be used for several applications, such as bio-preservative for medical and food transport. The micro-air-bubble was assumed in spherical shape that in incompressible gas boundary condition. So, the random motion of particle (Brownian motion) can be solved by using Stokes-Einstein approximation. But, Hadamard and Rybczynski equation is promoted to solve for larger bubble (micro scale). While, the effect of physical properties (e.g. diffusion coefficient, density, and flow rate) have taken important role in its characteristics in water. According to the theoretical investigation that have been done, decreasing of bubble velocity indicates that the bubble dissolves away or shrinking to the surface. To obtain longevity bubble in pure water medium, it is recomended to apply some surfactant molecules (e.g. NaCl) in micro-air-bubble medium.
Dietrich, Kilian; Renggli, Damian; Zanini, Michele; Volpe, Giovanni; Buttinoni, Ivo; Isa, Lucio
2017-06-01
Colloidal particles equipped with platinum patches can establish chemical gradients in H2O2-enriched solutions and undergo self-propulsion due to local diffusiophoretic migration. In bulk (3D), this class of active particles swim in the direction of the surface heterogeneities introduced by the patches and consequently reorient with the characteristic rotational diffusion time of the colloids. In this article, we present experimental and numerical evidence that planar 2D confinements defy this simple picture. Instead, the motion of active particles both on solid substrates and at flat liquid-liquid interfaces is captured by a 2D active Brownian motion model, in which rotational and translational motion are constrained in the xy-plane. This leads to an active motion that does not follow the direction of the surface heterogeneities and to timescales of reorientation that do not match the free rotational diffusion times. Furthermore, 2D-confinement at fluid-fluid interfaces gives rise to a unique distribution of swimming velocities: the patchy colloids uptake two main orientations leading to two particle populations with velocities that differ up to one order of magnitude. Our results shed new light on the behavior of active colloids in 2D, which is of interest for modeling and applications where confinements are present.
Energy Technology Data Exchange (ETDEWEB)
Torres-Diaz, I.; Cortes, A.; Rinaldi, C., E-mail: carlos.rinaldi@bme.ufl.edu [Department of Chemical Engineering, University of Puerto Rico, Mayagüez, Puerto Rico 00681-9000 (United States); Cedeño-Mattei, Y. [Department of Chemistry, University of Puerto Rico, Mayagüez, Puerto Rico 00681-9019 (United States); Perales-Perez, O. [Department of Engineering Science and Materials, University of Puerto Rico, Mayagüez, Puerto Rico 00681-9044 (United States)
2014-01-15
Ferrofluid flow in cylindrical and annular geometries under the influence of a uniform rotating magnetic field was studied experimentally using aqueous ferrofluids consisting of low concentrations (<0.01 v/v) of cobalt ferrite nanoparticles with Brownian relaxation to test the ferrohydrodynamic equations, elucidate the existence of couple stresses, and determine the value of the spin viscosity in these fluids. An ultrasound technique was used to measure bulk velocity profiles in the spin-up (cylindrical) and annular geometries, varying the intensity and frequency of the rotating magnetic field generated by a two pole stator winding. Additionally, torque measurements in the cylindrical geometry were made. Results show rigid-body like velocity profiles in the bulk, and no dependence on the axial direction. Experimental velocity profiles were in quantitative agreement with the predictions of the spin diffusion theory, with a value of the spin viscosity of ∼10{sup −8} kg m/s, two orders of magnitude larger than the value estimated earlier for iron oxide based ferrofluids, and 12 orders of magnitude larger than estimated using dimensional arguments valid in the infinite dilution limit. These results provide further evidence of the existence of couple stresses in ferrofluids and their role in driving the spin-up flow phenomenon.
Eloi, J-C; Okuda, M; Jones, S E Ward; Schwarzacher, W
2013-06-18
For applications from food science to the freeze-thawing of proteins it is important to understand the often complex freezing behavior of solutions of biomolecules. Here we use a magnetic method to monitor the Brownian rotation of a quasi-spherical cage-shaped protein, apoferritin, approaching the glass transition Tg in a freeze-concentrated buffer (Tris-HCl). The protein incorporates a synthetic magnetic nanoparticle (Co-doped Fe3O4 (magnetite)). We use the magnetic signal from the nanoparticles to monitor the protein orientation. As T decreases toward Tg of the buffer solution the protein's rotational relaxation time increases exponentially, taking values in the range from a few seconds up to thousands of seconds, i.e., orders of magnitude greater than usually accessed, e.g., by NMR. The longest relaxation times measured correspond to estimated viscosities >2 MPa s. As well as being a means to study low-temperature, high-viscosity environments, our method provides evidence that, for the cooling protocol used, the following applies: 1), the concentration of the freeze-concentrated buffer at Tg is independent of its initial concentration; 2), little protein adsorption takes place at the interface between ice and buffer; and 3), the protein is free to rotate even at temperatures as low as 207 K. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Prabhu, A.; Babu, S. B.; Dolado, J. S.; Gimel, J.-C.
2014-07-01
We present a novel simulation technique derived from Brownian cluster dynamics used so far to study the isotropic colloidal aggregation. It now implements the classical Kern-Frenkel potential to describe patchy interactions between particles. This technique gives access to static properties, dynamics and kinetics of the system, even far from the equilibrium. Particle thermal motions are modeled using billions of independent small random translations and rotations, constrained by the excluded volume and the connectivity. This algorithm, applied to a single polymer chain leads to correct static and dynamic properties, in the framework where hydrodynamic interactions are ignored. By varying patch angles, various local chain flexibilities can be obtained. We have used this new algorithm to model step-growth polymerization under various solvent qualities. The polymerization reaction is modeled by an irreversible aggregation between patches while an isotropic finite square-well potential is superimposed to mimic the solvent quality. In bad solvent conditions, a competition between a phase separation (due to the isotropic interaction) and polymerization (due to patches) occurs. Surprisingly, an arrested network with a very peculiar structure appears. It is made of strands and nodes. Strands gather few stretched chains that dip into entangled globular nodes. These nodes act as reticulation points between the strands. The system is kinetically driven and we observe a trapped arrested structure. That demonstrates one of the strengths of this new simulation technique. It can give valuable insights about mechanisms that could be involved in the formation of stranded gels.
Kwaadgras, B.W.; Dijkstra, M.|info:eu-repo/dai/nl/123538807; van Roij, R.H.H.G.|info:eu-repo/dai/nl/152978984
2012-01-01
Self-assembly and alignment of anisotropic colloidal particles are important processes that can be influenced by external electric fields. However, dielectric nanoparticles are generally hard to align this way because of their small size and low polarizability. In this work, we employ the coupled
The dynamics of stochastic processes
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas
In the present thesis the dynamics of stochastic processes is studied with a special attention to the semimartingale property. This is mainly motivated by the fact that semimartingales provide the class of the processes for which it is possible to define a reasonable stochastic calculus due...... to the Bichteler-Dellacherie Theorem. The semimartingale property of Gaussian processes is characterized in terms of their covariance function, spectral measure and spectral representation. In addition, representation and expansion of filtration results are provided as well. Special attention is given to moving...... average processes, and when the driving process is a Lévy or a chaos process the semimartingale property is characterized in the filtration spanned by the driving process and in the natural filtration when the latter is a Brownian motion. To obtain some of the above results an integrability of seminorm...
Wavelet analysis and covariance structure of some classes of non-stationary processes
Guérin, Charles-Antoine
2000-01-01
Processes with stationary n-increments are known to be characterized by the stationarity of their continuous wavelet coefficients. We extend this result to the case of processes with stationary fractional increments and locally stationary processes. Then we give two applications of these properties. First, we derive the explicit covariance structure of processes with stationary n-increments. Second, for fractional Brownian motion, the stationarity of the fractional increments of order greater...
McMullan, G; Vinothkumar, K R; Henderson, R
2015-11-01
We have recorded dose-fractionated electron cryo-microscope images of thin films of pure flash-frozen amorphous ice and pre-irradiated amorphous carbon on a Falcon II direct electron detector using 300 keV electrons. We observe Thon rings [1] in both the power spectrum of the summed frames and the sum of power spectra from the individual frames. The Thon rings from amorphous carbon images are always more visible in the power spectrum of the summed frames whereas those of amorphous ice are more visible in the sum of power spectra from the individual frames. This difference indicates that while pre-irradiated carbon behaves like a solid during the exposure, amorphous ice behaves like a fluid with the individual water molecules undergoing beam-induced motion. Using the measured variation in the power spectra amplitude with number of electrons per image we deduce that water molecules are randomly displaced by a mean squared distance of ∼1.1 Å(2) for every incident 300 keV e(-)/Å(2). The induced motion leads to an optimal exposure with 300 keV electrons of 4.0 e(-)/Å(2) per image with which to observe Thon rings centred around the strong 3.7 Å scattering peak from amorphous ice. The beam-induced movement of the water molecules generates pseudo-Brownian motion of embedded macromolecules. The resulting blurring of single particle images contributes an additional term, on top of that from radiation damage, to the minimum achievable B-factor for macromolecular structure determination. Copyright © 2015 The Authors. Published by Elsevier B.V. All rights reserved.
Kumar, Suveen; Ashish; Kumar, Saurabh; Augustine, Shine; Yadav, Santosh; Yadav, Birendra Kumar; Chauhan, Rishi Pal; Dewan, Ajay Kumar; Malhotra, Bansi Dhar
2018-04-15
We report results of the studies relating to fabrication of nanostructured metal oxide (NMO) based cancer biosensor. With the help of 2D electroactive reduced graphene oxide (RGO), we successfully inhibited the Brownian motion of NMO that led to reduced agglomeration of NMO. The nanostructured hafnium oxide (nHfO2) was used as a model NMO. The reduced agglomeration of nHfO2 was achieved through controlled hydrothermal synthesis and investigated via nanoparticles tracking analysis (NTA). X-ray diffraction (XRD), scanning electron microscopy (SEM) and transmission electron microscope (TEM) techniques were used for phase identification as well as morphological analysis of the synthesized nanohybrid (nHfO2@RGO) material. The 3-aminopropyl triethoxysilane (APTES) was used for the functionalization of nHfO2@RGO and electrophoretic deposition (EPD) technique was used for its deposition onto ITO coated glass electrode. Further, antibodies of cancer biomarker (anti-CYFRA-21-1) were immobilized via EDC-NHS chemistry and Bovine serum albumin (BSA) was used for blocking of the non-specific binding sites. The electrochemical response studies of fabricated immunoelectrode (BSA/anti-CYFRA-21-1/APTES/nHfO2@RGO/ITO) revealed higher sensitivity (18.24µAmLng-1), wide linear detection range (0 to 30ngmL-1), with remarkable lower detection limit (0.16ngmL-1). The obtained results showed good agreement with the concentration of CYFRA-21-1 obtained through enzyme linked immunosorbent assay (ELISA) in saliva samples of oral cancer patients. Copyright © 2017 Elsevier B.V. All rights reserved.
2007-08-01
Stochastic Processes O 6:00PM Marc Yor, Universite de Paris 6, France S Wine and Cheese Reception at the Illini Union 9:25-10:10 AM - o Invasion Percolation... analogues of the one-dimensional fractional condition changed over the period in time with multi- Brownian motion. We establish integral representations
Directory of Open Access Journals (Sweden)
Aimé Lachal
2014-01-01
Full Text Available Let N be a positive integer, c a positive constant and (ξnn≥1 be a sequence of independent identically distributed pseudorandom variables. We assume that the ξn’s take their values in the discrete set {-N,-N+1,…,N-1,N} and that their common pseudodistribution is characterized by the (positive or negative real numbers ℙ{ξn=k}=δk0+(-1k-1c(2Nk+N for any k∈{-N,-N+1,…,N-1,N}. Let us finally introduce (Snn≥0 the associated pseudorandom walk defined on ℤ by S0=0 and Sn=∑j=1nξj for n≥1. In this paper, we exhibit some properties of (Snn≥0. In particular, we explicitly determine the pseudodistribution of the first overshooting time of a given threshold for (Snn≥0 as well as that of the first exit time from a bounded interval. Next, with an appropriate normalization, we pass from the pseudorandom walk to the pseudo-Brownian motion driven by the high-order heat-type equation ∂/∂t=(-1N-1c∂2N/∂x2N. We retrieve the corresponding pseudodistribution of the first overshooting time of a threshold for the pseudo-Brownian motion (Lachal, 2007. In the same way, we get the pseudodistribution of the first exit time from a bounded interval for the pseudo-Brownian motion which is a new result for this pseudoprocess.
Ozboyaci, M; Kokh, D B; Wade, R C
2016-04-21
The addition of three N-terminal histidines to β-lactamase inhibitor protein was shown experimentally to increase its binding potency to an Au(111) surface substantially but the binding mechanism was not resolved. Here, we propose a complete adsorption mechanism for this fusion protein by means of a multi-scale simulation approach and free energy calculations. We find that adsorption is a three-step process: (i) recognition of the surface predominantly by the histidine fusion peptide and formation of an encounter complex facilitated by a reduced dielectric screening of water in the interfacial region, (ii) adsorption of the protein on the surface and adoption of a specific binding orientation, and (iii) adaptation of the protein structure on the metal surface accompanied by induced fit. We anticipate that the mechanistic features of protein adsorption to an Au(111) surface revealed here can be extended to other inorganic surfaces and proteins and will therefore aid the design of specific protein-surface interactions.
Applied probability and stochastic processes
Sumita, Ushio
1999-01-01
Applied Probability and Stochastic Processes is an edited work written in honor of Julien Keilson. This volume has attracted a host of scholars in applied probability, who have made major contributions to the field, and have written survey and state-of-the-art papers on a variety of applied probability topics, including, but not limited to: perturbation method, time reversible Markov chains, Poisson processes, Brownian techniques, Bayesian probability, optimal quality control, Markov decision processes, random matrices, queueing theory and a variety of applications of stochastic processes. The book has a mixture of theoretical, algorithmic, and application chapters providing examples of the cutting-edge work that Professor Keilson has done or influenced over the course of his highly-productive and energetic career in applied probability and stochastic processes. The book will be of interest to academic researchers, students, and industrial practitioners who seek to use the mathematics of applied probability i...
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Liaqat Ali
2017-04-01
Full Text Available This paper explores Liquid Film Flow of Williamson Fluid over an Unstable Stretching Surface in a Porous Space . The Brownian motion and Thermophoresis effect of the liquid film flow on a stretching sheet have been observed. This research include, to focus on the variation in the thickness of the liquid film in a porous space. The self-similarity variables have been applied to convert the modelled equations into a set of non-linear coupled differential equations. These non-linear differential equations have been treated through an analytical technique known as Homotopy Analysis Method (HAM. The effect of physical non-dimensional parameters like, Eckert Number, Prandtl Number, Porosity Parameter, Brownian Motion Parameter, Unsteadiness Parameter, Schmidt Number, Thermophoresis Parameter, Dimensionless Film Thickness, and Williamson Fluid Constant on the liquid film size are investigated and conferred in this endeavor. The obtained results through HAM are authenticated, from its comparison with numerical (ND-Solve Method. The graphical comparison of these two methods is elaborated. The numerical comparison with absolute errors are also been shown in the tables. The physical and numerical results using h curves for the residuals of the velocity, temperature and concentration profiles are obtained
Energy Technology Data Exchange (ETDEWEB)
Sanchez, Jorge H. [Department of Chemical Engineering, University of Puerto Rico, Mayaguez campus, P.O. Box 9046, Mayaguez, PR 00681 (Puerto Rico); Facultad de Ingenieria Quimica, Universidad Pontificia Bolivariana, Medellin (Colombia); Rinaldi, Carlos [Department of Chemical Engineering, University of Puerto Rico, Mayaguez campus, P.O. Box 9046, Mayaguez, PR 00681 (Puerto Rico)], E-mail: crinaldi@uprm.edu
2009-10-15
The rotational Brownian motion of magnetized tri-axial ellipsoidal particles (orthotropic particles) suspended in a Newtonian fluid, in the dilute suspension limit, under applied d.c. and a.c. magnetic fields was studied using rotational Brownian dynamics simulations. The algorithm describing the change in the suspension magnetization was obtained from the stochastic angular momentum equation using the fluctuation-dissipation theorem and a quaternion formulation of orientation space. Simulation results are in agreement with the Langevin function for equilibrium magnetization and with single-exponential relaxation from equilibrium at small fields using Perrin's effective relaxation time. Dynamic susceptibilities for ellipsoidal particles of different aspect ratios were obtained from the response to oscillating magnetic fields of different frequencies and described by Debye's model for the complex susceptibility using Perrin's effective relaxation time. Simulations at high equilibrium and probe fields indicate that Perrin's effective relaxation time continues to describe relaxation from equilibrium and response to oscillating fields even beyond the small field limit.
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Habib-Olah Sayehvand
Full Text Available Numerical investigation the problem of nanofluid heat and mass transfer in a channel partially filled with a porous medium in the presence of uniform magnetic field is carried out by a new computational iterative approach known as the spectral local linearization method (SLLM. The similarity solution is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations which are then solved by SLLM and validity of our solutions is verified by the numerical results (fourth-order Runge-Kutta scheme with the shooting method. In modeling the flow in the channel, the effects of flow inertia, Brinkman friction, nanoparticles concentration and thickness of the porous region are taken into account. The results are obtained for velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number. Also, effects of active parameters such as viscosity parameter, Hartmann number, Darcy number, Prandtl number, Schmidt number, Eckert number, Brownian motion parameter, thermophoresis parameter and the thickness of porous region on the hydrodynamics, heat and mass transfer behaviors are investigated. Keywords: Brownian, Nanofluid, Porous medium, Spectral local linearization method, Thermophoresis
Brownian parametric oscillators
Zerbe, Christine; Jung, Peter; Hänggi, Peter
1994-05-01
We discuss the stochastic dynamics of dissipative, white-noise-driven Floquet oscillators, characterized by a time-periodic stiffness. Thus far, little attention has been paid to these exactly solvable nonstationary systems, although they carry a rich potential for several experimental applications. Here, we calculate and discuss the mean values and variances, as well as the correlation functions and the Floquet spectrum. As one main result, we find for certain parameter values that the fluctuations of the position coordinate are suppressed as compared to the equilibrium value of a harmonic oscillator (parametric squeezing).
Li, Guohui; Cui, Qiang
2004-01-01
The structural flexibilities of two molecular machines, myosin and Ca2+-ATPase, have been analyzed with normal mode analysis and discussed in the context of their energy conversion functions. The normal mode analysis with physical intermolecular interactions was made possible by an improved implementation of the block normal mode (BNM) approach. The BNM results clearly illustrated that the large-scale conformational transitions implicated in the functional cycles of the two motor systems can be largely captured with a small number of low-frequency normal modes. Therefore, the results support the idea that structural flexibility is an essential part of the construction principle of molecular motors through evolution. Such a feature is expected to be more prevalent in motor proteins than in simpler systems (e.g., signal transduction proteins) because in the former, large-scale conformational transitions often have to occur before the chemical events (e.g., ATP hydrolysis in myosin and ATP binding/phosphorylation in Ca2+-ATPase). This highlights the importance of Brownian motions associated with the protein domains that are involved in the functional transitions; in this sense, Brownian molecular machines is an appropriate description of molecular motors, although the normal mode results do not address the origin of the ratchet effect. The results also suggest that it might be more appropriate to describe functional transitions in some molecular motors as intrinsic elastic motions modulating local structural changes in the active site, which in turn gets stabilized by the subsequent chemical events, in contrast with the conventional idea of local changes somehow getting amplified into larger-scale motions. In the case of myosin, for example, we favor the idea that Brownian motions associated with the flexible converter propagates to the Switch I/II region, where the salt-bridge formation gets stabilized by ATP hydrolysis, in contrast with the textbook notion that ATP
Ballestra, Luca Vincenzo; Pacelli, Graziella; Radi, Davide
2016-12-01
We propose a numerical method to compute the first-passage probability density function in a time-changed Brownian model. In particular, we derive an integral representation of such a density function in which the integrand functions must be obtained solving a system of Volterra equations of the first kind. In addition, we develop an ad-hoc numerical procedure to regularize and solve this system of integral equations. The proposed method is tested on three application problems of interest in mathematical finance, namely the calculation of the survival probability of an indebted firm, the pricing of a single-knock-out put option and the pricing of a double-knock-out put option. The results obtained reveal that the novel approach is extremely accurate and fast, and performs significantly better than the finite difference method.
Long, Wei; Hilpert, Markus
2009-06-15
In this paper, we develop a new correlation for the clean-bed filter coefficient (lambda0) for Brownian particles, for which diffusion is the main deposition mechanism. The correlation is based on numerical Lattice-Boltzmann (LB) simulations in random packings of spheres of uniform diameter. We use LB methods to solve the Navier-Stokes equation for flow and then the advection-diffusion equation for particle transport. We determine a correlation for an "equivalent" single-collector diffusion efficiency, etaD, so that we can compare our predictions to "true" single-collector correlations stemming from unit-cell modeling approaches. We compared our new correlation to experiments on the filtration of latex particles. For small particle diameters, 50 nm etaG and nI terms from unit-cell correlations to our etaD model. The resulting correlation predicts experiments with latex particles of dp > 300 nm well.
Pond, Mark J; Errington, Jeffrey R; Truskett, Thomas M
2011-02-28
Computer simulations are used to test whether a recently introduced generalization of Rosenfeld's excess-entropy scaling method for estimating transport coefficients in systems obeying molecular dynamics can be extended to predict long-time diffusivities in fluids of particles undergoing Brownian dynamics in the absence of interparticle hydrodynamic forces. Model fluids with inverse-power-law, Gaussian-core, and Hertzian pair interactions are considered. Within the generalized Rosenfeld scaling method, long-time diffusivities of ultrasoft Gaussian-core and Hertzian particle fluids, which display anomalous trends with increasing density, are predicted (to within 20%) based on knowledge of interparticle interactions, excess entropy, and scaling behavior of simpler inverse-power-law fluids.
Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco
2013-05-13
Two-particle dispersion is investigated in the context of anomalous diffusion. Two different modelling approaches related to time subordination are considered and unified in the framework of self-similar stochastic processes. By assuming a single-particle fractional Brownian motion and that the two-particle correlation function decreases in time with a power law, the particle relative separation density is computed for the cases with time sub-ordination directed by a unilateral M-Wright density and by an extremal Lévy stable density. Looking for advisable mathematical properties (for instance, the stationarity of the increments), the corresponding self-similar stochastic processes are represented in terms of fractional Brownian motions with stochastic variance, whose profile is modelled by using the M-Wright density or the Lévy stable density.
d'Auvergne, Edward J; Gooley, Paul R
2008-02-01
The key to obtaining the model-free description of the dynamics of a macromolecule is the optimisation of the model-free and Brownian rotational diffusion parameters using the collected R (1), R (2) and steady-state NOE relaxation data. The problem of optimising the chi-squared value is often assumed to be trivial, however, the long chain of dependencies required for its calculation complicates the model-free chi-squared space. Convolutions are induced by the Lorentzian form of the spectral density functions, the linear recombinations of certain spectral density values to obtain the relaxation rates, the calculation of the NOE using the ratio of two of these rates, and finally the quadratic form of the chi-squared equation itself. Two major topological features of the model-free space complicate optimisation. The first is a long, shallow valley which commences at infinite correlation times and gradually approaches the minimum. The most severe convolution occurs for motions on two timescales in which the minimum is often located at the end of a long, deep, curved tunnel or multidimensional valley through the space. A large number of optimisation algorithms will be investigated and their performance compared to determine which techniques are suitable for use in model-free analysis. Local optimisation algorithms will be shown to be sufficient for minimisation not only within the model-free space but also for the minimisation of the Brownian rotational diffusion tensor. In addition the performance of the programs Modelfree and Dasha are investigated. A number of model-free optimisation failures were identified: the inability to slide along the limits, the singular matrix failure of the Levenberg-Marquardt minimisation algorithm, the low precision of both programs, and a bug in Modelfree. Significantly, the singular matrix failure of the Levenberg-Marquardt algorithm occurs when internal correlation times are undefined and is greatly amplified in model-free analysis by
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Okada, Kazuya [School of Akita Prefectural University, Yurihonjo (Japan); Satoh, Akira, E-mail: asatoh@akita-pu.ac.jp [Department of Machine Intelligence and System Engineering, Akita Prefectural University, Yurihonjo (Japan)
2017-09-01
Highlights: • Monte Carlo simulations have been employed for the aggregate structures. • Brownian dynamics simulations have been employed for the magneto-rheology. • Even a weak shear flow induces a significant regime change in the aggregates. • A strong external magnetic field drastically changes the aggregates. • The dependence of the viscosity on these factors is governed in a complex manner. - Abstract: In the present study, we address a suspension composed ferromagnetic rod-like particles to elucidate a regime change in the aggregate structures and the magneto-rheological characteristics. Monte Carlo simulations have been employed for investigating the aggregate structures in thermodynamic equilibrium, and Brownian dynamics simulations for magneto-rheological features in a simple shear flow. The main results obtained here are summarized as follows. For the case of thermodynamic equilibrium, the rod-like particles aggregate to form thick chain-like clusters and the neighboring clusters incline in opposite directions. If the external magnetic field is increased, the thick chain-like clusters in the magnetic field direction grow thicker by adsorbing the neighboring clusters that incline in the opposite direction. Hence, a significant phase change in the particle aggregates is not induced by an increase in the magnetic field strength. For the case of a simple shear flow, even a weak shear flow induces a significant regime change from the thick chain-like clusters of thermodynamic equilibrium into wall-like aggregates composed of short raft-like clusters. A strong external magnetic field drastically changes these aggregates into wall-like aggregates composed of thick chain-like clusters rather than the short raft-like clusters. The internal structure of these aggregates is not strongly influenced by a shear flow, and the formation of the short raft-like clusters is maintained inside the aggregates. The main contribution to the net viscosity is the
Dubina, Sean Hyun; Wedgewood, Lewis Edward
2017-09-01
Ferrofluids are steadily rising in applications across many fields, preferred for their ability to be remotely positioned and controlled via external magnetic fields. In magnetic separation operations, nonuniform magnetic fields elicit a phenomenon known as magnetophoresis so that the ferroparticles will undergo migration toward areas of higher magnetism. To comprehend this behavior, the authors developed a Brownian dynamics simulation of particles in ferromagnetic clusters under the influences of a simple shear flow and an applied magnetic field gradient. An iterative constraint mechanism was implemented to satisfy Maxwell's equations throughout the dense colloidal suspension, ensuring that essential laws of magnetostatics are rigorously fulfilled at all times over small, finite sub-volumes of the system. Because of the presence of nonuniform magnetic fields, magnetophoresis and magnetic separation behavior were analyzed to assess the effectiveness of the model. Results showed that, when compared to "unconstrained" models, separation caused by magnetic field gradients occurred at a decreased rate under the constraint scheme due to relatively weaker non-Newtonian aggregation property trends. Through application of a dimensionless number analysis to observe varied levels of particle-particle interactions, thermal fluctuations, and viscous shearing, it was confirmed that the aggregation and magnetic separation modeling of ferrofluid colloidal suspensions without acceptable adherence to Maxwell's equations produces an unreliable representation of current ferrofluids.
Suriyanto; Ng, E Y K; Kumar, S D
2017-03-23
Current clinically accepted technologies for cancer treatment still have limitations which lead to the exploration of new therapeutic methods. Since the past few decades, the hyperthermia treatment has attracted the attention of investigators owing to its strong biological rationales in applying hyperthermia as a cancer treatment modality. Advancement of nanotechnology offers a potential new heating method for hyperthermia by using nanoparticles which is termed as magnetic fluid hyperthermia (MFH). In MFH, superparamagnetic nanoparticles dissipate heat through Néelian and Brownian relaxation in the presence of an alternating magnetic field. The heating power of these particles is dependent on particle properties and treatment settings. A number of pre-clinical and clinical trials were performed to test the feasibility of this novel treatment modality. There are still issues yet to be solved for the successful transition of this technology from bench to bedside. These issues include the planning, execution, monitoring and optimization of treatment. The modeling and simulation play crucial roles in solving some of these issues. Thus, this review paper provides a basic understanding of the fundamental and rationales of hyperthermia and recent development in the modeling and simulation applied to depict the heat generation and transfer phenomena in the MFH.
Dienerowitz, Maria; Ilchenko, Mykhailo; Su, Bertram; Deckers-Hebestreit, Gabriele; Mayer, Günter; Henkel, Thomas; Heitkamp, Thomas; Börsch, Michael
2016-02-01
Observation times of freely diffusing single molecules in solution are limited by the photophysics of the attached fluorescence markers and by a small observation volume in the femtolitre range that is required for a sufficient signal-to-background ratio. To extend diffusion-limited observation times through a confocal detection volume, A. E. Cohen and W. E. Moerner have invented and built the ABELtrap -- a microfluidic device to actively counteract Brownian motion of single nanoparticles with an electrokinetic trap. Here we present a version of an ABELtrap with a laser focus pattern generated by electro-optical beam deflectors and controlled by a programmable FPGA chip. This ABELtrap holds single fluorescent nanoparticles for more than 100 seconds, increasing the observation time of fluorescent nanoparticles compared to free diffusion by a factor of 10000. To monitor conformational changes of individual membrane proteins in real time, we record sequential distance changes between two specifically attached dyes using Förster resonance energy transfer (smFRET). Fusing the a-subunit of the FoF1-ATP synthase with mNeonGreen results in an improved signal-to-background ratio at lower laser excitation powers. This increases our measured trap duration of proteoliposomes beyond 2 s. Additionally, we observe different smFRET levels attributed to varying distances between the FRET donor (mNeonGreen) and acceptor (Alexa568) fluorophore attached at the a- and c-subunit of the FoF1-ATP synthase respectively.
Energy Technology Data Exchange (ETDEWEB)
D' Auvergne, Edward J. [Max Planck Institute for Biophysical Chemistry, Department of NMR-based Structural Biology (Germany)], E-mail: edward@nmr-relax.com; Gooley, Paul R. [University of Melbourne, Department of Biochemistry and Molecular Biology, Bio21 Institute of Biotechnology and Molecular Science (Australia)
2008-02-15
Finding the dynamics of an entire macromolecule is a complex problem as the model-free parameter values are intricately linked to the Brownian rotational diffusion of the molecule, mathematically through the autocorrelation function of the motion and statistically through model selection. The solution to this problem was formulated using set theory as an element of the universal set U-the union of all model-free spaces (d'Auvergne EJ and Gooley PR (2007) Mol BioSyst 3(7), 483-494). The current procedure commonly used to find the universal solution is to initially estimate the diffusion tensor parameters, to optimise the model-free parameters of numerous models, and then to choose the best model via model selection. The global model is then optimised and the procedure repeated until convergence. In this paper a new methodology is presented which takes a different approach to this diffusion seeded model-free paradigm. Rather than starting with the diffusion tensor this iterative protocol begins by optimising the model-free parameters in the absence of any global model parameters, selecting between all the model-free models, and finally optimising the diffusion tensor. The new model-free optimisation protocol will be validated using synthetic data from Schurr JM et al. (1994) J Magn Reson B 105(3), 211-224 and the relaxation data of the bacteriorhodopsin (1-36)BR fragment from Orekhov VY (1999) J Biomol NMR 14(4), 345-356. To demonstrate the importance of this new procedure the NMR relaxation data of the Olfactory Marker Protein (OMP) of Gitti R et al. (2005) Biochem 44(28), 9673-9679 is reanalysed. The result is that the dynamics for certain secondary structural elements is very different from those originally reported.
Three phase model of the processive motor protein kinesin.
Zhang, Yunxin
2008-07-01
Kinesin is a stepping motor that successively produces forward and backward 8-nm steps along microtubules. Under physiological conditions, the steps powering kinesin's motility are biased in one direction and drive various biological motile processes. So far, the physical mechanism underlying the unidirectional bias of the kinesin is not fully understood. Recently, Martin Bier have provided a stepper model [Martin Bier, 2003, Processive motor protein as an overdamped Brownian stepper, Phys. Rev. Lett. 91, 148104], in which the stepping cycle of kinesin includes two distinguished phases: (i) a power stroke phase and (ii) a ratcheted diffusion phase which is characterized as a "random diffusional search". At saturating ATP level, this model can fit the experimental results accurately. In this paper, we'll provide a modified Brownian stepper model, in which the dependence of ATP concentration is considered. In our model, the stepping cycle of kinesin is distinguished into three phases: an ATP-binding phase, a power stroke phase and a ratcheted diffusion phase. This modified model can reconstruct most of the experimental results accurately.
Directory of Open Access Journals (Sweden)
Guozhong Yang
2014-05-01
Full Text Available Based on real option theory, the article analyses the decision-making of enterprises during the process of technological innovation diffusion under an uncertain circumstance. Under the assumption that the returns of enterprises follow geometric Brownian motion, the article firstly estimates the transition value of imitating technology innovators and the average latency of imitation, then it analyses the influence of every parameter on the diffusion process. It can be concluded that both the market demand and the rate have significant effects on the diffusion rate of innovative technology.
On time-dependent diffusion coefficients arising from stochastic processes with memory
Carpio-Bernido, M. Victoria; Barredo, Wilson I.; Bernido, Christopher C.
2017-08-01
Time-dependent diffusion coefficients arise from anomalous diffusion encountered in many physical systems such as protein transport in cells. We compare these coefficients with those arising from analysis of stochastic processes with memory that go beyond fractional Brownian motion. Facilitated by the Hida white noise functional integral approach, diffusion propagators or probability density functions (pdf) are obtained and shown to be solutions of modified diffusion equations with time-dependent diffusion coefficients. This should be useful in the study of complex transport processes.
Okada, Kazuya; Satoh, Akira
2017-09-01
In the present study, we address a suspension composed ferromagnetic rod-like particles to elucidate a regime change in the aggregate structures and the magneto-rheological characteristics. Monte Carlo simulations have been employed for investigating the aggregate structures in thermodynamic equilibrium, and Brownian dynamics simulations for magneto-rheological features in a simple shear flow. The main results obtained here are summarized as follows. For the case of thermodynamic equilibrium, the rod-like particles aggregate to form thick chain-like clusters and the neighboring clusters incline in opposite directions. If the external magnetic field is increased, the thick chain-like clusters in the magnetic field direction grow thicker by adsorbing the neighboring clusters that incline in the opposite direction. Hence, a significant phase change in the particle aggregates is not induced by an increase in the magnetic field strength. For the case of a simple shear flow, even a weak shear flow induces a significant regime change from the thick chain-like clusters of thermodynamic equilibrium into wall-like aggregates composed of short raft-like clusters. A strong external magnetic field drastically changes these aggregates into wall-like aggregates composed of thick chain-like clusters rather than the short raft-like clusters. The internal structure of these aggregates is not strongly influenced by a shear flow, and the formation of the short raft-like clusters is maintained inside the aggregates. The main contribution to the net viscosity is the viscosity component due to magnetic particle-particle interaction forces in relation to the present volumetric fraction. Hence, a larger magnetic interaction strength and also a stronger external magnetic field give rise to a larger magneto-rheological effect. However, the dependence of the viscosity on these factors is governed in a complex manner by whether or not the wall-like aggregates are composed mainly of short raft
Some probabilistic properties of fractional point processes
Garra, Roberto
2017-05-16
In this article, the first hitting times of generalized Poisson processes N-f (t), related to Bernstein functions f are studied. For the spacefractional Poisson processes, N alpha (t), t > 0 ( corresponding to f = x alpha), the hitting probabilities P{T-k(alpha) < infinity} are explicitly obtained and analyzed. The processes N-f (t) are time-changed Poisson processes N( H-f (t)) with subordinators H-f (t) and here we study N(Sigma H-n(j= 1)f j (t)) and obtain probabilistic features of these extended counting processes. A section of the paper is devoted to processes of the form N( G(H,v) (t)) where G(H,v) (t) are generalized grey Brownian motions. This involves the theory of time-dependent fractional operators of the McBride form. While the time-fractional Poisson process is a renewal process, we prove that the space-time Poisson process is no longer a renewal process.
Self-similar processes in collective risk theory
Directory of Open Access Journals (Sweden)
Zbigniew Michna
1998-01-01
Full Text Available Collective risk theory is concerned with random fluctuations of the total assets and the risk reserve of an insurance company. In this paper we consider self-similar, continuous processes with stationary increments for the renewal model in risk theory. We construct a risk model which shows a mechanism of long range dependence of claims. We approximate the risk process by a self similar process with drift. The ruin probability within finite time is estimated for fractional Brownian motion with drift. A similar model is applicable in queueing systems, describing long range dependence in on/off processes and associated fluid models. The obtained results are useful in communication network models, as well as storage and inventory models.
Brownian Motion, "Diverse and Undulating"
Duplantier, Bertrand
Truly man is a marvelously vain, diverse, and undulating object. It is hard to found any constant and uniform judgment on him. Michel de Montaigne, Les Essais, Book I, Chapter 1: "By diverse means we arrive at the same end"; in The Complete Essays of Montaigne, Donald M. Frame transl., Stanford University Press (1958).
A renewal jump-diffusion process with threshold dividend strategy
Li, Bo; Wu, Rong; Song, Min
2009-06-01
In this paper, we consider a jump-diffusion risk process with the threshold dividend strategy. Both the distributions of the inter-arrival times and the claims are assumed to be in the class of phase-type distributions. The expected discounted dividend function and the Laplace transform of the ruin time are discussed. Motivated by Asmussen [S. Asmussen, Stationary distributions for fluid flow models with or without Brownian noise, Stochastic Models 11 (1) (1995) 21-49], instead of studying the original process, we study the constructed fluid flow process and their closed-form formulas are obtained in terms of matrix expression. Finally, numerical results are provided to illustrate the computation.
On the Lower Classes of Some Mixed Fractional Gaussian Processes with Two Logarithmic Factors
Directory of Open Access Journals (Sweden)
Charles El-Nouty
2008-01-01
Full Text Available We introduce the fractional mixed fractional Brownian sheet and investigate the small ball behavior of its sup-norm statistic by establishing a general result on the small ball probability of the sum of two not necessarily independent joint Gaussian random vectors. Then, we state general conditions and characterize the sufficiency part of the lower classes of some statistics of the above process by an integral test. Finally, when we consider the sup-norm statistic, the necessity part is given by a second integral test.
Nechaev, S
2003-01-01
We investigate the statistical properties of random walks on the simplest nontrivial braid group B sub 3 , and on related hyperbolic groups. We provide a method using Cayley graphs of groups allowing us to compute explicitly the probability distribution of the basic statistical characteristics of random trajectories - the drift and the return probability. The action of the groups under consideration in the hyperbolic plane is investigated, and the distribution of a geometric invariant - the hyperbolic distance - is analysed. It is shown that a random walk on B sub 3 can be viewed as a 'magnetic random walk' on the group PSL(2, Z).
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Nechaev, Sergei [Laboratoire de Physique Theorique et Modeles Statistiques, Universite Paris Sud, 91405 Orsay Cedex (France); Voituriez, Raphael [Laboratoire de Physique Theorique et Modeles Statistiques, Universite Paris Sud, 91405 Orsay Cedex (France)
2003-01-10
We investigate the statistical properties of random walks on the simplest nontrivial braid group B{sub 3}, and on related hyperbolic groups. We provide a method using Cayley graphs of groups allowing us to compute explicitly the probability distribution of the basic statistical characteristics of random trajectories - the drift and the return probability. The action of the groups under consideration in the hyperbolic plane is investigated, and the distribution of a geometric invariant - the hyperbolic distance - is analysed. It is shown that a random walk on B{sub 3} can be viewed as a 'magnetic random walk' on the group PSL(2, Z)
Energy Technology Data Exchange (ETDEWEB)
Jones, R. [Department of Physics and Astronomy, University of Sheffield (United Kingdom)]. E-mail: r.a.l.jones@sheffield.ac.uk
2007-02-15
The glamour of physics is often associated with the very big or the very small. Popular-science books stress the mysteries of the large-scale structure of the universe or of the tiniest of subatomic particles. Of course, this fails to reflect the emphasis of practicing physicists, most of whom deal with matters intermediate in scale. Thus one must salute Mark Haw's brave attempt to write an account of the less flashy physics of the 'middle world', centring on the discovery and explanation of Brownian motion. Richard Feynman once opined that, in the event of some cataclysmic disaster that wiped out all knowledge of modern science, the single fact that one would want to salvage to allow future generations to rebuild the lost edifice would be that matter is made of atoms and molecules. This is, of course, well known to everyone today, but it may surprise many that certainty and consensus about the atomic hypothesis came less than 100 years ago. The story's hero is French Nobel laureate Jean Baptiste Perrin (1870-1942), whose beautiful and painstaking experiments quantitatively confirmed the theories of Albert Einstein and Marian Smoluchowski that Brownian motion could be explained by the random collisions of molecules. Perrin also decisively connected physics and chemistry by determining the value of Avogradro's constant, and convinced the last doubters of the reality of molecules and the validity of statistical mechanics. In the February issue of Physics World, Richard Jones rates the rest of Haw's story about physics at the molecular scale. (U.K.)
Hybrid colored noise process with space-dependent switching rates
Bressloff, Paul C.; Lawley, Sean D.
2017-07-01
A fundamental issue in the theory of continuous stochastic process is the interpretation of multiplicative white noise, which is often referred to as the Itô-Stratonovich dilemma. From a physical perspective, this reflects the need to introduce additional constraints in order to specify the nature of the noise, whereas from a mathematical perspective it reflects an ambiguity in the formulation of stochastic differential equations (SDEs). Recently, we have identified a mechanism for obtaining an Itô SDE based on a form of temporal disorder. Motivated by switching processes in molecular biology, we considered a Brownian particle that randomly switches between two distinct conformational states with different diffusivities. In each state, the particle undergoes normal diffusion (additive noise) so there is no ambiguity in the interpretation of the noise. However, if the switching rates depend on position, then in the fast switching limit one obtains Brownian motion with a space-dependent diffusivity of the Itô form. In this paper, we extend our theory to include colored additive noise. We show that the nature of the effective multiplicative noise process obtained by taking both the white-noise limit (κ →0 ) and fast switching limit (ɛ →0 ) depends on the order the two limits are taken. If the white-noise limit is taken first, then we obtain Itô, and if the fast switching limit is taken first, then we obtain Stratonovich. Moreover, the form of the effective diffusion coefficient differs in the two cases. The latter result holds even in the case of space-independent transition rates, where one obtains additive noise processes with different diffusion coefficients. Finally, we show that yet another form of multiplicative noise is obtained in the simultaneous limit ɛ ,κ →0 with ɛ /κ2 fixed.
Emergence of patterns in random processes. II. Stochastic structure in random events.
Newman, William I
2014-06-01
Random events can present what appears to be a pattern in the length of peak-to-peak sequences in time series and other point processes. Previously, we showed that this was the case in both individual and independently distributed processes as well as for Brownian walks. In addition, we introduced the use of the discrete form of the Langevin equation of statistical mechanics as a device for connecting the two limiting sets of behaviors, which we then compared with a variety of observations from the physical and social sciences. Here, we establish a probabilistic framework via the Smoluchowski equation for exploring the Langevin equation and its expected peak-to-peak sequence lengths, and we introduce a concept we call "stochastic structure in random events," or SSRE. We extend the Brownian model to include antipersistent processes via autoregressive (AR) models. We relate the latter to describe the behavior of Old Faithful Geyser in Yellowstone National Park, and we devise a further test for the validity of the Langevin and AR models. Given our analytic results, we show how the Langevin equation can be adapted to describe population cycles of three to four years observed among many mammalian species in biology.
Thygesen, Uffe Høgsbro
2016-03-01
We consider organisms which use a renewal strategy such as run-tumble when moving in space, for example to perform chemotaxis in chemical gradients. We derive a diffusion approximation for the motion, applying a central limit theorem due to Anscombe for renewal-reward processes; this theorem has not previously been applied in this context. Our results extend previous work, which has established the mean drift but not the diffusivity. For a classical model of tumble rates applied to chemotaxis, we find that the resulting chemotactic drift saturates to the swimming velocity of the organism when the chemical gradients grow increasingly steep. The dispersal becomes anisotropic in steep gradients, with larger dispersal across the gradient than along the gradient. In contrast to one-dimensional settings, strong bias increases dispersal. We next include Brownian rotation in the model and find that, in limit of high chemotactic sensitivity, the chemotactic drift is 64% of the swimming velocity, independent of the magnitude of the Brownian rotation. We finally derive characteristic timescales of the motion that can be used to assess whether the diffusion limit is justified in a given situation. The proposed technique for obtaining diffusion approximations is conceptually and computationally simple, and applicable also when statistics of the motion is obtained empirically or through Monte Carlo simulation of the motion.
Directory of Open Access Journals (Sweden)
Amin Jafarimoghaddam
Full Text Available The present study aims to experimentally investigate heat transfer performance of rectangular and semicircular tubes in the presence of Ag / water nanofluids. The nanoparticles of Ag (silver were used in seven different volume concentrations of 0.03%, 0.07%, 0.1%, 0.2%, 0.4%, 1% and 2%. The experiment was conducted in relatively low Reynolds numbers of 301 to 740. A heater with the power of 200 W was used to keep the outer surface of the tubes under a constant heat flux condition. In addition, the rectangular tube has been designed within the same length as the semicircular one and also within the same hydraulic diameter. Moreover, the average nanoparticles size was 20 nm. The outcome results of the present empirical work indicate that, for all the examined Reynolds numbers, the semicircular tube has higher convective heat transfer coefficient for all the utilized volume concentrations of Ag nanoparticles. The possible reasons behind this advantage are discussed through the present work mainly by taking the boundary effect on Brownian motions into account. Coming to this point that the conventional design for cooling system of photovoltaic cells is a heat sink with the rectangular graves, it is discussed that using a semicircular design may have the advantage over the rectangular one in convective heat transfer coefficient enhancement and hence a better cooling performance for these solar cells.
Jafarimoghaddam, Amin; Aberoumand, Sadegh
2017-01-01
The present study aims to experimentally investigate heat transfer performance of rectangular and semicircular tubes in the presence of Ag / water nanofluids. The nanoparticles of Ag (silver) were used in seven different volume concentrations of 0.03%, 0.07%, 0.1%, 0.2%, 0.4%, 1% and 2%. The experiment was conducted in relatively low Reynolds numbers of 301 to 740. A heater with the power of 200 W was used to keep the outer surface of the tubes under a constant heat flux condition. In addition, the rectangular tube has been designed within the same length as the semicircular one and also within the same hydraulic diameter. Moreover, the average nanoparticles size was 20 nm. The outcome results of the present empirical work indicate that, for all the examined Reynolds numbers, the semicircular tube has higher convective heat transfer coefficient for all the utilized volume concentrations of Ag nanoparticles. The possible reasons behind this advantage are discussed through the present work mainly by taking the boundary effect on Brownian motions into account. Coming to this point that the conventional design for cooling system of photovoltaic cells is a heat sink with the rectangular graves, it is discussed that using a semicircular design may have the advantage over the rectangular one in convective heat transfer coefficient enhancement and hence a better cooling performance for these solar cells.
Capasso, Vincenzo
2015-01-01
This textbook, now in its third edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Key topics include: * Markov processes * Stochastic differential equations * Arbitrage-free markets and financial derivatives * Insurance risk * Population dynamics, and epidemics * Agent-based models New to the Third Edition: * Infinitely divisible distributions * Random measures * Levy processes * Fractional Brownian motion * Ergodic theory * Karhunen-Loeve expansion * Additional applications * Additional exercises * Smoluchowski approximation of Langevin systems An Introduction to Continuous-Time Stochastic Processes, Third Editio...
Liang, Xiao; Wang, Linshan; Wang, Yangfan; Wang, Ruili
2016-09-01
In this paper, we focus on the long time behavior of the mild solution to delayed reaction-diffusion Hopfield neural networks (DRDHNNs) driven by infinite dimensional Wiener processes. We analyze the existence, uniqueness, and stability of this system under the local Lipschitz function by constructing an appropriate Lyapunov-Krasovskii function and utilizing the semigroup theory. Some easy-to-test criteria affecting the well-posedness and stability of the networks, such as infinite dimensional noise and diffusion effect, are obtained. The criteria can be used as theoretic guidance to stabilize DRDHNNs in practical applications when infinite dimensional noise is taken into consideration. Meanwhile, considering the fact that the standard Brownian motion is a special case of infinite dimensional Wiener process, we undertake an analysis of the local Lipschitz condition, which has a wider range than the global Lipschitz condition. Two samples are given to examine the availability of the results in this paper. Simulations are also given using the MATLAB.
A comparative study of processing simulated and experimental data in elastic laser light scattering.
Popovici, M A; Mincu, N; Popovici, A
1999-03-15
The intensity of the laser light scattered by a suspension of biological particles undergoing Brownian motion contains information about their size distribution function and optical properties. We used several methods (implemented in MathCAD programs), including a new one, to invert the Fredholm integral equation of the first kind, which represents the angular dependence of the elastic scattering of light. The algorithms were first tested on different sets of simulated data. Experimental data were obtained using biological samples and an experimental arrangement which are briefly described. We study the stability of the inversion procedures relative to the noise levels, and compute the first two moments of the retrieved size distribution function. A comparison of the results corresponding to simulated and experimental data is done, to select the best processing algorithm.
Optimal protocol for maximum work extraction in a feedback process with a time-varying potential
Kwon, Chulan
2017-12-01
The nonequilibrium nature of information thermodynamics is characterized by the inequality or non-negativity of the total entropy change of the system, memory, and reservoir. Mutual information change plays a crucial role in the inequality, in particular if work is extracted and the paradox of Maxwell's demon is raised. We consider the Brownian information engine where the protocol set of the harmonic potential is initially chosen by the measurement and varies in time. We confirm the inequality of the total entropy change by calculating, in detail, the entropic terms including the mutual information change. We rigorously find the optimal values of the time-dependent protocol for maximum extraction of work both for the finite-time and the quasi-static process.
The distribution of particles in the plane dispersed by a simple 3-dimensional diffusion process
DEFF Research Database (Denmark)
Stockmarr, Anders
2002-01-01
Populations of particles dispersed in the 2-dimensional plane from a single pointsource may be grouped as focus expansion patterns, with an exponentially decreasing density, and more diffuse patterns with thicker tails. Exponentially decreasing distributions are often modelled as the result of 2......-dimensional diffusion processes acting to disperse the particles, while thick-tailed distributions tend to be modelled by purely descriptive distributions. Models based on the Cauchy distribution have been suggested, but these have not been related to diffusion modelling. However, the distribution...... of particles dispersed from a point source by a 3-dimensional Brownian motion that incorporates a constant drift, under the condition that the particle starts at a given height and is stopped when it reaches the xy plane (zero height) may be shown to result in both slim-tailed exponentially decreasing...
Basarab, M A; Basarab, D A; Konnova, N S; Matsievskiy, D D; Matveev, V A
2016-01-01
The aim of this work was to develop a novel technique for digital processing of Doppler ultrasound blood flow sensor data from noisy blood flow velocity waveforms. To evaluate the fluctuating blood flow parameters, various nonlinear dynamics methods and algorithms are often being used. Here, for identification of chaotic and noise components in a fluctuating coronary blood flow, for the first time the Allan variance technique was used. Analysis of different types of noises (White, Brownian, Flicker) was carried out and their strong correlation with fractality of time series (the Hurst exponent) was revealed. Based on a specialized software realizing the developed technique, numerical experiments with real clinical data were carried out. Recommendations for identification of noisy patterns of coronary blood flow in normal and pathological states were developed. The methodology gives us the possibility for the more detailed quantitative and qualitative analysis of a noisy fluctuating blood flow data.
Active Brownian motion in a narrow channel
Ao, X.; Ghosh, P. K.; Li, Y.; Schmid, G.; Hänggi, P.; Marchesoni, F.
2014-12-01
We review recent advances in rectification control of artificial microswimmers, also known as Janus particles, diffusing along narrow, periodically corrugated channels. The swimmer self-propulsion mechanism is modeled so as to incorporate a nonzero torque (propulsion chirality). We first summarize the effects of chirality on the autonomous current of microswimmers freely diffusing in channels of different geometries. In particular, left-right and upside-down asymmetric channels are shown to exhibit different transport properties. We then report new results on the dependence of the diffusivity of chiral microswimmers on the channel geometry and their own self-propulsion mechanism. The self-propulsion torque turns out to play a key role as a transport control parameter.
Rheology of Confined Non-Brownian Suspensions.
Fornari, Walter; Brandt, Luca; Chaudhuri, Pinaki; Lopez, Cyan Umbert; Mitra, Dhrubaditya; Picano, Francesco
2016-01-08
We study the rheology of confined suspensions of neutrally buoyant rigid monodisperse spheres in plane-Couette flow using direct numerical simulations. We find that if the width of the channel is a (small) integer multiple of the sphere diameter, the spheres self-organize into two-dimensional layers that slide on each other and the effective viscosity of the suspension is significantly reduced. Each two-dimensional layer is found to be structurally liquidlike but its dynamics is frozen in time.
Brownian dynamics of confined rigid bodies
Energy Technology Data Exchange (ETDEWEB)
Delong, Steven; Balboa Usabiaga, Florencio; Donev, Aleksandar, E-mail: donev@courant.nyu.edu [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
2015-10-14
We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust, space efficient, and easy to accumulate. We construct a system of overdamped Langevin equations in the quaternion representation that accounts for hydrodynamic effects, preserves the unit-norm constraint on the quaternion, and is time reversible with respect to the Gibbs-Boltzmann distribution at equilibrium. We introduce two schemes for temporal integration of the overdamped Langevin equations of motion, one based on the Fixman midpoint method and the other based on a random finite difference approach, both of which ensure that the correct stochastic drift term is captured in a computationally efficient way. We study several examples of rigid colloidal particles diffusing near a no-slip boundary and demonstrate the importance of the choice of tracking point on the measured translational mean square displacement (MSD). We examine the average short-time as well as the long-time quasi-two-dimensional diffusion coefficient of a rigid particle sedimented near a bottom wall due to gravity. For several particle shapes, we find a choice of tracking point that makes the MSD essentially linear with time, allowing us to estimate the long-time diffusion coefficient efficiently using a Monte Carlo method. However, in general, such a special choice of tracking point does not exist, and numerical techniques for simulating long trajectories, such as the ones we introduce here, are necessary to study diffusion on long time scales.
Power output for a nonlinear Brownian machine
Defaveri, Lucianno A. C. A.; Morgado, Welles A. M.; Queirós, Sílvio M. Duarte
2017-11-01
We propose a method that makes use of the nonlinear properties of some hypothetical microscopic solid material as the working substance for a microscopic machine. The protocols used are simple (step and elliptic) and allow us to obtain the work and heat exchanged between machine and reservoirs. We calculate the work for a nonlinear single-particle machine that can be treated perturbingly. We obtain the instantaneous work and heat for the machine undergoing cycles that mimic the Carnot and multireservoir protocols. The work calculations are then extended to high values of the nonlinear parameter yielding the quasistatic limit, which is verified numerically. The model we propose is fluctuation driven and we can study in detail its thermostatistics, namely, the work distribution both per cycle and instantaneous and the corresponding fluctuation relations.
Tail Behaviour for Suprema of Empirical Processes.
1984-09-01
Departmento de Matematicas y Ciencia de la Computacion, Univ. Simon Bolivar, Venezuela. [4] CABANA, E.M. and WSCHEBOR, M. (1982). The two parameter...determinazione empirica di una legge di distribuzione. Inst. Ital. Atti. Giorn. 4 83-91. [25] KUELBS, J. (1975) Sample path behaviour for Brownian motion in
The Fractional Ornstein-Uhlenbeck Process
DEFF Research Database (Denmark)
Høg, Esben; Frederiksen, Per H.
The paper revisits dynamic term structure models (DTSMs) and proposes a new way in dealing with the limitation of the classical affine models. In particular, this paper expands the flexibility of the DTSMs by applying a fractional Brownian motion as the governing force of the state variable instead...
Least Squares Estimators for Unit Root Processes with Locally Stationary Disturbance
Directory of Open Access Journals (Sweden)
Junichi Hirukawa
2012-01-01
Full Text Available The random walk is used as a model expressing equitableness and the effectiveness of various finance phenomena. Random walk is included in unit root process which is a class of nonstationary processes. Due to its nonstationarity, the least squares estimator (LSE of random walk does not satisfy asymptotic normality. However, it is well known that the sequence of partial sum processes of random walk weakly converges to standard Brownian motion. This result is so-called functional central limit theorem (FCLT. We can derive the limiting distribution of LSE of unit root process from the FCLT result. The FCLT result has been extended to unit root process with locally stationary process (LSP innovation. This model includes different two types of nonstationarity. Since the LSP innovation has time-varying spectral structure, it is suitable for describing the empirical financial time series data. Here we will derive the limiting distributions of LSE of unit root, near unit root and general integrated processes with LSP innovation. Testing problem between unit root and near unit root will be also discussed. Furthermore, we will suggest two kind of extensions for LSE, which include various famous estimators as special cases.
Zou, Yong; Donner, Reik V; Kurths, Jürgen
2015-02-01
Long-range correlated processes are ubiquitous, ranging from climate variables to financial time series. One paradigmatic example for such processes is fractional Brownian motion (fBm). In this work, we highlight the potentials and conceptual as well as practical limitations when applying the recently proposed recurrence network (RN) approach to fBm and related stochastic processes. In particular, we demonstrate that the results of a previous application of RN analysis to fBm [Liu et al. Phys. Rev. E 89, 032814 (2014)] are mainly due to an inappropriate treatment disregarding the intrinsic nonstationarity of such processes. Complementarily, we analyze some RN properties of the closely related stationary fractional Gaussian noise (fGn) processes and find that the resulting network properties are well-defined and behave as one would expect from basic conceptual considerations. Our results demonstrate that RN analysis can indeed provide meaningful results for stationary stochastic processes, given a proper selection of its intrinsic methodological parameters, whereas it is prone to fail to uniquely retrieve RN properties for nonstationary stochastic processes like fBm.
Mulder, W.J.; Harmsen, P.F.H.; Sanders, J.P.M.; Carre, P.; Kamm, B.; Schoenicke, P.
2012-01-01
Primary processing of oil-containing material involves pre-treatment processes, oil recovery processes and the extraction and valorisation of valuable compounds from waste streams. Pre-treatment processes, e.g. thermal, enzymatic, electrical and radio frequency, have an important effect on the oil
DEFF Research Database (Denmark)
Bech-Nielsen, Gregers
1997-01-01
Electrochemical processes in: Power sources, Electrosynthesis, Corrosion.Pourbaix-diagrams.Decontamination of industrial waste water for heavy metals.......Electrochemical processes in: Power sources, Electrosynthesis, Corrosion.Pourbaix-diagrams.Decontamination of industrial waste water for heavy metals....
Observation of drying process of multilayered paint using fOCT based on dynamic speckles
Fukai, T.; Kadono, H.
2015-08-01
Recently, a demand for the precise observation of a multilayered paint system have been increasing such as in car industry. However, conventional methods can observe only the surface condition of the paint. In this study, we propose a new method to observe a three dimensional drying process of the multilayered paint using functional Optical Coherence Tomography (fOCT). In this method, the dynamic speckles that appear in OCT signal were utilized. The temporal properties of the dynamic speckle is related to the Brownian motion of the scattering particles in the paint, and thus depends on the drying condition. Autocorrelation function of the speckle signal was calculated and its width, i.e., correlation length (CL), was used as a measure. In the experiment, two layer system consisting of different paints on the thin glass plate, and the drying process was observed for two hours. In the second layer exposed to the air, CL showed a monotonic increment indicating a steady progress of the drying process while in the first layer (deeper layer), CL decreased slightly for the first 50min. and then started to increase. This implies that drying process has been reversed due to the transport of the solvent from the second layer in the early stage. Such a complicated drying process of the multilayer system could also be confirmed from OCT signal image of the interface between the layers. This analysis was performed using the phase term obtained in the OCT interference signal with an accuracy of 0.1μm.
Fry, T F
2013-01-01
Data Processing discusses the principles, practices, and associated tools in data processing. The book is comprised of 17 chapters that are organized into three parts. The first part covers the characteristics, systems, and methods of data processing. Part 2 deals with the data processing practice; this part discusses the data input, output, and storage. The last part discusses topics related to systems and software in data processing, which include checks and controls, computer language and programs, and program elements and structures. The text will be useful to practitioners of computer-rel
DEFF Research Database (Denmark)
van der Aalst, W.M.P.; Rubin, V.; Verbeek, H.M.W.
2010-01-01
Process mining includes the automated discovery of processes from event logs. Based on observed events (e.g., activities being executed or messages being exchanged) a process model is constructed. One of the essential problems in process mining is that one cannot assume to have seen all possible...... behavior. At best, one has seen a representative subset. Therefore, classical synthesis techniques are not suitable as they aim at finding a model that is able to exactly reproduce the log. Existing process mining techniques try to avoid such “overfitting” by generalizing the model to allow for more...
Parzen, Emanuel
1962-01-01
Well-written and accessible, this classic introduction to stochastic processes and related mathematics is appropriate for advanced undergraduate students of mathematics with a knowledge of calculus and continuous probability theory. The treatment offers examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models, and it develops the methods of probability model-building.Chapter 1 presents precise definitions of the notions of a random variable and a stochastic process and introduces the Wiener and Poisson processes. Subsequent chapters examine
Federal Laboratory Consortium — The Magnetics Processing Lab equipped to perform testing of magnetometers, integrate them into aircraft systems, and perform data analysis, including noise reduction...
DEFF Research Database (Denmark)
Ovesen, Nis
2009-01-01
Inspiration for most research and optimisations on design processes still seem to focus within the narrow field of the traditional design practise. The focus in this study turns to associated businesses of the design professions in order to learn from their development processes. Through interviews...... advantages and challenges of agile processes in mobile software and web businesses are identified. The applicability of these agile processes is discussed in re- gards to design educations and product development in the domain of Industrial Design and is briefly seen in relation to the concept of dromology...
Jong, de Peter J.; Emmelkamp, Paul; Ehring, Thomas
2014-01-01
Cognitive models imply that emotional disorders critically depend on the existence of maladaptive cognitive structures in memory. These so-called schemas are assumed to automatically influence all stages of individuals' information processing. The basic assumption of the information-processing
Teodorowicz, Malgorzata; Neerven, Van Joost; Savelkoul, Huub
2017-01-01
The majority of foods that are consumed in our developed society have been processed. Processing promotes a non-enzymatic reaction between proteins and sugars, the Maillard reaction (MR). Maillard reaction products (MRPs) contribute to the taste, smell and color of many food products, and thus
DEFF Research Database (Denmark)
Kristensen, Niels Heine
2004-01-01
Kristensen_NH and_Beck A: Sustainable processing. In Otto Schmid, Alexander Beck and Ursula Kretzschmar (Editors) (2004): Underlying Principles in Organic and "Low-Input Food" Processing - Literature Survey. Research Institute of Organic Agriculture FiBL, CH-5070 Frick, Switzerland. ISBN 3-906081-58-3...
van der Heijden, Ferdinand; Spreeuwers, Lieuwe Jan; Blanken, Henk; Vries de, A.P.; Blok, H.E.; Feng, L; Feng, L.
2007-01-01
The field of image processing addresses handling and analysis of images for many purposes using a large number of techniques and methods. The applications of image processing range from enhancement of the visibility of cer- tain organs in medical images to object recognition for handling by
DEFF Research Database (Denmark)
Hull Kristensen, Peer; Bojesen, Anders
This paper invites to discuss the processes of individualization and organizing being carried out under what we might see as an emerging regime of change. The underlying argumentation is that in certain processes of change, competence becomes questionable at all times. The hazy characteristics...
Eberle, Hanna; Unger, Tobias; Leymann, Frank
The concepts presented in this paper are motivated by the assumption that process knowledge is distributed knowledge and not completely known just by one person. Driven by this assumption we deal in this paper with the following questions: How can partial process knowledge be represented? How can this partial knowledge be used to define something more complete? To use higher level artefacts as building blocks to new applications has a long tradition in software engineering to increase flexibility and reduce modeling costs. In this paper we take a first step in applying this concept to processes, by defining process building blocks and operations which compose process building blocks. The building blocks will be referred to as process fragments in the following. The process fragment composition may take place either at design or runtime of the process. The design time approach reduces design costs by reusing artefacts. However the runtime fragment composition approach realizes high flexibility due to the possibility in the dynamic selection of the fragments to be composed. The contribution of this work lies in a fragment definition that enables the fragment modeler to represent his 'local' and fragmentary knowledge in a formal way and which allows fragment models to be composed.
Staszak, Katarzyna
2017-11-01
The membrane processes have played important role in the industrial separation process. These technologies can be found in all industrial areas such as food, beverages, metallurgy, pulp and paper, textile, pharmaceutical, automotive, biotechnology and chemical industry, as well as in water treatment for domestic and industrial application. Although these processes are known since twentieth century, there are still many studies that focus on the testing of new membranes' materials and determining of conditions for optimal selectivity, i. e. the optimum transmembrane pressure (TMP) or permeate flux to minimize fouling. Moreover the researchers proposed some calculation methods to predict the membrane processes properties. In this article, the laboratory scale experiments of membrane separation techniques, as well their validation by calculation methods are presented. Because membrane is the "heart" of the process, experimental and computational methods for its characterization are also described.
Effects of Cloud-Processed CCN on Warm Clouds
Noble, S. R., Jr.; Hudson, J. G.
2014-12-01
Cloud condensation nuclei (CCN) distributions are transformed by in-cloud processing. This can be chemical: aqueous oxidation; or physical: Brownian scavenging, collision and coalescence. Droplet evaporation then leaves behind the cloud-processed CCN. Chemical processing increases CCN size (lower critical supersaturation; Sc) but does not change CCN concentration (NCCN) (Feingold and Kreidenweis, 2000). Physical processing leads to an increase in size (lower Sc) and decrease of NCCN. These processes are especially important in stratus clouds that cover large areas and persist for long periods. Modified CCN in turn modify cloud droplet spectra. Both chemical and physical processing were observed during the 2005 MArine Stratus/stratocumulus Experiment (MASE) field campaign. Higher concentrations of SO4 and NO3 anions with lower SO2 and O3 were associated with bimodal CCN spectra whereas monomodal spectra had lower SO4 and NO3 and higher SO2 and O3. These are consistent with chemical processing. Two nearby MASE CCN spectra, one bimodal and one monomodal were input to an adiabatic cloud droplet growth model. Model runs at various updrafts (W) show that the low Sc cloud processed mode of the bimodal CCN spectrum augmented droplet activation creating higher cloud droplet concentrations (Nc) for low W characteristic of stratus clouds (Fig. 1a, black). Higher NCCN at low Sc (black data) also increased condensation competition and thus reduced cloud effective S (Seff) (Fig.1b). This increases W importance for determining Nc (Hudson and Noble, 2014). These high NCCN at low Sc and lower Seff of the bimodal CCN spectrum reduce droplet mean diameter (MD; Fig. 1c) and broaden droplet distributions (sigma; Fig. 1d). Increased Nc and decreased MD of chemical processing seems to augment the indirect aerosol effect (IAE) whereas inherently decreased Nc and increased MD of coalescence processing reduces IAE. CCN cloud-processing alters cloud microphysics (Nc, Seff, MD, and sigma
Sequential Testing Problems for Bessel Processes
Johnson, Peter; Peskir, Goran
2018-01-01
Consider the motion of a Brownian particle that takes place either in a two-dimensional plane or in three-dimensional space. Given that only the distance of the particle to the origin is being observed, the problem is to detect the true dimension as soon as possible and with minimal probabilities of the wrong terminal decisions. We solve this problem in the Bayesian formulation under any prior probability of the true dimension when the passage of time is penalised linearly.
DEFF Research Database (Denmark)
Hvitved-Jacobsen, Thorkild; Vollertsen, Jes; Nielsen, Asbjørn Haaning
Since the first edition was published over a decade ago, advancements have been made in the design, operation, and maintenance of sewer systems, and new problems have emerged. For example, sewer processes are now integrated in computer models, and simultaneously, odor and corrosion problems caused...... by hydrogen sulfide and other volatile organic compounds, as well as other potential health issues, have caused environmental concerns to rise. Reflecting the most current developments, Sewer Processes: Microbial and Chemical Process Engineering of Sewer Networks, Second Edition, offers the reader updated...... and valuable information on the sewer as a chemical and biological reactor. It focuses on how to predict critical impacts and control adverse effects. It also provides an integrated description of sewer processes in modeling terms. This second edition is full of illustrative examples and figures, includes...
DEFF Research Database (Denmark)
Bech-Nielsen, Gregers
1997-01-01
The notes describe in detail primary and secondary galvanic cells, fuel cells, electrochemical synthesis and electroplating processes, corrosion: measurments, inhibitors, cathodic and anodic protection, details of metal dissolution reactions, Pourbaix diagrams and purification of waste water from...
DEFF Research Database (Denmark)
Ødum, Anders Sebastian Rosenkrans
Processing proteases are proteases which proteolytically activate proteins and peptides into their biologically active form. Processing proteases play an important role in biotechnology as tools in protein fusion technology. Fusion strategies where helper proteins or peptide tags are fused...... to the protein of interest are an elaborate method to optimize expression or purification systems. It is however critical that fusion proteins can be removed and processing proteases can facilitate this in a highly specific manner. The commonly used proteases all have substrate specificities to the N......-terminal of the scissile bond, leaving C-terminal fusions to have non-native C-termini after processing. A solution yielding native C-termini would allow novel expression and purification systems for therapeutic proteins and peptides.The peptidyl-Lys metallopeptidase (LysN) of the fungus Armillaria mellea (Am) is one...
1986-01-01
coupling two Gamma processes so that the marginal processes will have negative serial correlations. It is actually easier to implement this scheme...to analyze a long sequence of wind speeds. This sequence is very non-stationary, containing yearly cycles. The model actually used is v(n)G n , where P...1967). "Some Problems of Statistical Inference Relating to Double-Gamma Distribution," Trabajos de Estadistica , 18, 67-87. Hugus, D. K. (1982
Mitov, Kosto V
2014-01-01
This monograph serves as an introductory text to classical renewal theory and some of its applications for graduate students and researchers in mathematics and probability theory. Renewal processes play an important part in modeling many phenomena in insurance, finance, queuing systems, inventory control and other areas. In this book, an overview of univariate renewal theory is given and renewal processes in the non-lattice and lattice case are discussed. A pre-requisite is a basic knowledge of probability theory.
Yu, Guihua; Kushwaha, Amit; Lee, Jungkyu K; Shaqfeh, Eric S G; Bao, Zhenan
2011-01-25
DNA has been recently explored as a powerful tool for developing molecular scaffolds for making reproducible and reliable metal contacts to single organic semiconducting molecules. A critical step in the process of exploiting DNA-organic molecule-DNA (DOD) array structures is the controlled tethering and stretching of DNA molecules. Here we report the development of reproducible surface chemistry for tethering DNA molecules at tunable density and demonstrate shear flow processing as a rationally controlled approach for stretching/aligning DNA molecules of various lengths. Through enzymatic cleavage of λ-phage DNA to yield a series of DNA chains of various lengths from 17.3 μm down to 4.2 μm, we have investigated the flow/extension behavior of these tethered DNA molecules under different flow strengths in the flow-gradient plane. We compared Brownian dynamic simulations for the flow dynamics of tethered λ-DNA in shear, and found our flow-gradient plane experimental results matched well with our bead-spring simulations. The shear flow processing demonstrated in our studies represents a controllable approach for tethering and stretching DNA molecules of various lengths. Together with further metallization of DNA chains within DOD structures, this bottom-up approach can potentially enable efficient and reliable fabrication of large-scale nanoelectronic devices based on single organic molecules, therefore opening opportunities in both fundamental understanding of charge transport at the single molecular level and many exciting applications for ever-shrinking molecular circuits.
Jump locations of jump-diffusion processes with state-dependent rates
Miles, Christopher E.; Keener, James P.
2017-10-01
We propose a general framework for studying statistics of jump-diffusion systems driven by both Brownian noise (diffusion) and a jump process with state-dependent intensity. Of particular natural interest in many physical systems are the jump locations: the system evaluated at the jump times. As an example, this could be the voltage at which a neuron fires, or the so-called ‘threshold voltage’. However, the state-dependence of the jump rate provides direct coupling between the diffusion and jump components, making it difficult to disentangle the two to study individually. In this work, we provide an iterative map formulation of the sequence of distributions of jump locations. The distributions computed by this map can be used to elucidate other interesting quantities about the process, including statistics of the interjump times. Ultimately, the limit of the map reveals that knowledge of the stationary distribution of the full process is sufficient to recover (but not necessarily equal to) the distribution of jump locations. We propose two biophysical examples to illustrate the use of this framework to provide insight about a system. We find that a sharp threshold voltage emerges robustly in a simple stochastic integrate-and-fire neuronal model. The interplay between the two sources of noise is also investigated in a stepping model of molecular motor in intracellular transport pulling a diffusive cargo.
Feynman-Kac equation for anomalous processes with space- and time-dependent forces
Cairoli, Andrea; Baule, Adrian
2017-04-01
Functionals of a stochastic process Y(t) model many physical time-extensive observables, for instance particle positions, local and occupation times or accumulated mechanical work. When Y(t) is a normal diffusive process, their statistics are obtained as the solution of the celebrated Feynman-Kac equation. This equation provides the crucial link between the expected values of diffusion processes and the solutions of deterministic second-order partial differential equations. When Y(t) is non-Brownian, e.g. an anomalous diffusive process, generalizations of the Feynman-Kac equation that incorporate power-law or more general waiting time distributions of the underlying random walk have recently been derived. A general representation of such waiting times is provided in terms of a Lévy process whose Laplace exponent is directly related to the memory kernel appearing in the generalized Feynman-Kac equation. The corresponding anomalous processes have been shown to capture nonlinear mean square displacements exhibiting crossovers between different scaling regimes, which have been observed in numerous experiments on biological systems like migrating cells or diffusing macromolecules in intracellular environments. However, the case where both space- and time-dependent forces drive the dynamics of the generalized anomalous process has not been solved yet. Here, we present the missing derivation of the Feynman-Kac equation in such general case by using the subordination technique. Furthermore, we discuss its extension to functionals explicitly depending on time, which are of particular relevance for the stochastic thermodynamics of anomalous diffusive systems. Exact results on the work fluctuations of a simple non-equilibrium model are obtained. An additional aim of this paper is to provide a pedagogical introduction to Lévy processes, semimartingales and their associated stochastic calculus, which underlie the mathematical formulation of anomalous diffusion as a
McMillan, T.S.
1957-10-29
A process for the fluorination of uranium metal is described. It is known that uranium will react with liquid chlorine trifluoride but the reaction proceeds at a slow rate. However, a mixture of a halogen trifluoride together with hydrogen fluoride reacts with uranium at a significantly faster rate than does a halogen trifluoride alone. Bromine trifluoride is suitable for use in the process, but chlorine trifluoride is preferred. Particularly suitable is a mixture of ClF/sub 3/ and HF having a mole ratio (moles
DEFF Research Database (Denmark)
Kolodovski, A.
2006-01-01
Purpose of this report: This report was prepared for RISO team involved in design of the innovation system Report provides innovation methodology to establish common understanding of the process concepts and related terminology The report does not includeRISO- or Denmark-specific cultural, economic...
O'Grady, William
2015-01-01
I propose that the course of development in first and second language acquisition is shaped by two types of processing pressures--internal efficiency-related factors relevant to easing the burden on working memory and external input-related factors such as frequency of occurrence. In an attempt to document the role of internal factors, I consider…
Directory of Open Access Journals (Sweden)
Anamarija Kutlić
2012-07-01
Full Text Available Bentonite has vide variety of uses. Special use of bentonite, where its absorbing properties are employed to provide water-tight sealing is for an underground repository in granites In this paper, bentonite processing and beneficiation are described.
Energy Technology Data Exchange (ETDEWEB)
Welz, H.
1943-10-22
The Arobin (Aromatenbenzin = aromatic gasoline) process was developed to operate on highly aromatic residues from various other processes (especially the HF process) for production of aviation gasoline and similar fuels. Those residues generally had boiling points from about 165/sup 0/ to 325/sup 0/C, so they were not included in the gasoline mde by the other processes. The Arobin process was able to split these residues into lower-boiling-point compounds which made up a high-performance gasoline containing 70% to 75% aromatics by volume. In order to accomplish this, it was necessary to choose the proper catalyst, one in which the splitting effect was much more pronounced than the hydrogenating effect. The catalyst which seemed to be most effective was an alkali-free aluminum silicate with small amounts (1%) molybdic acid (MoO/sub 3/) added. (An aluminum oxide catalyst used at about 500/sup 0/C produced even higher percentages of aromatics, but it seemed best suited for production of single pure compounds such as toluene.) The Arobin process was carried out at about 200 atm pressure and 400/sup 0/C, with a ratio of 1:1 for fresh starting material to recycled material and a throughput of 1 kg per liter of catalyst per hour. The overall yield of gasoline distilled up to 165/sup 0/C was 85% to 87%, and the time-yield was 0.43 kg per liter of catalyst per hour; the process used 360 m/sup 3/ hydrogen and 200 Calories of heat per (metric) ton of product gasoline. The Arobin gasoline could be blended with a lower-octane aviation gasoline to produce a blend with 50% aromatics; in this way, one (metric) ton of HF residue could give rise to 1.2 tons of such blended gasoline. The oxide catalyst could generally be regenerated by a heated steam of nitrogen diluted with air, unless damaged by certain nitrogen or oxygen compounds. 1 diagram, 3 tables.
DEFF Research Database (Denmark)
Schindler, Christoph; Tamke, Martin; Tabatabai, Ali
2014-01-01
Angled and forked wood – a desired material until 19th century, was swept away by industrialization and its standardization of processes and materials. Contemporary information technology has the potential for the capturing and recognition of individual geometries through laser scanning and compu......Angled and forked wood – a desired material until 19th century, was swept away by industrialization and its standardization of processes and materials. Contemporary information technology has the potential for the capturing and recognition of individual geometries through laser scanning...... and computation and subsequently design and bespoke CNC fabrication. The question whether this allows for a new approach to the uniqueness that is offered to us by nature is discussed in a series of workshops and projects, which explore the performative potential of naturally grown materials....
1986-06-01
and evaluation of technologies suitable for discrete optical computing is described, where particular emphasis has applied to ZnSe non- linea :, and...met. The processes are similar to that used in proving an algebraic theorem. Among the daunting practical difficulties encount- ered are:- (a) Formal...implementation of algorithms. Usually, such algorithms exhibit a highly regular S- structure as typified by linear algebra problems, and are generally
Energy Technology Data Exchange (ETDEWEB)
Gieg, W.; Rank, V.
1942-10-15
In the first stage of coal hydrogenation, the liquid phase, light and heavy oils were produced; the latter containing the nonliquefied parts of the coal, the coal ash, and the catalyst substances. It was the problem of residue processing to extract from these so-called let-down oils that which could be used as pasting oils for the coal. The object was to obtain a maximum oil extraction and a complete removal of the solids, because of the latter were returned to the process they would needlessly burden the reaction space. Separation of solids in residue processing could be accomplished by filtration, centrifugation, extraction, distillation, or low-temperature carbonization (L.T.C.). Filtration or centrifugation was most suitable since a maximum oil yield could be expected from it, since only a small portion of the let-down oil contained in the filtration or centrifugation residue had to be thermally treated. The most satisfactory centrifuge at this time was the Laval, which delivered liquid centrifuge residue and centrifuge oil continuously. By comparison, the semi-continuous centrifuges delivered plastic residues which were difficult to handle. Various apparatus such as the spiral screw kiln and the ball kiln were used for low-temperature carbonization of centrifuge residues. Both were based on the idea of carbonization in thin layers. Efforts were also being made to produce electrode carbon and briquette binder as by-products of the liquid coal phase.
Beauchamp, Patricia M.; Alkalai, Leon; Brown, Robert H.; Capps, Richard W.; Chen, Gun-Shing; Crisp, Michael P.; Cutts, James A.; Davidson, J. M.; Petrick, Stanley W.; Rodgers, David H.; Vane, Gregg; Soderblom, Laurance A.; Yelle, Roger V.
1996-10-01
In this paper, the authors propose a new process for the development and operation of unmanned vehicles for the exploration of space. We call the vehicle (and the process used to create it) sciencecraft. A Sciencecraft is an integrated unit that combines into a single system those elements (but no more) which are necessary to achieve the science objectives of the mission, including science instruments, electronics, telecommunications, power, and propulsion. the design of a sciencecraft begins with the definition of the mission science objectives. This is followed by the establishment of measurement goals and the definition of a critical data set. Next an observational sequence is developed, which will provide the data set. This step is followed by the design of the integrated sensor system that will make the observations. The final step in the development of a sciencecraft is the design of the hardware subsystems needed to deliver the sensor to its target and return the science data to the earth. This approach assures that the sciencecraft hardware design and overall architecture will be driven by the science objectives and the sensor requirements rather than the reverse, as has historically been the case. Throughout the design process, there is an emphasis on shared functionality, shared redundancy, and reduced cost. We illustrate the power of the sciencecraft approach by describing the Planetary Integrated Camera Spectrometer (PICS), an integrated sensor system in which the 'sciencecraft' process has been applied to the development of a single subsystem, which integrates multiple functionalities. PICS is a case-in-point where the sciencecraft process has been successfully demonstrated. We then describe a sciencecraft mission for exploration of the outer Solar System, including flybys of Uranus, Neptune, and an object in the Kuiper Belt. This mission, called the Kuiper Express, will use solar electric propulsion to shape its trajectory in the inner solar system
DEFF Research Database (Denmark)
Slepniov, Dmitrij; Sørensen, Brian Vejrum; Katayama, Hiroshi
2011-01-01
The purpose of this chapter is to contribute to the knowledge on how production offshoring and international operations management vary across cultural contexts. The chapter attempts to shed light on how companies approach the process of offshoring in different cultural contexts. In order...... to achieve this objective, the authors employ a qualitative methodology and compare three Danish and three Japanese manufacturing companies. On the basis of this comparative investigation, the authors find that the parent companies from both contexts employ offshoring as a remedy for the challenges...
Directory of Open Access Journals (Sweden)
María Auxiliadora Gálvez Pérez
2015-05-01
Full Text Available AbstractThe comparison between the creative processes in dance and architecture constitute a panorama, which is able to fi gure out reality with different and intense perceptive connotations. It is about a reality where the important thing is the immersion into the spatial-temporal phenomena, the contact of the space of our body and the spatial essence that is outside our skin limits. Under an architectonical point of view, dance would be a key discipline, a laboratory where it is possible to freely explore the concepts related to the body-space system, consequently it is also a good frame to seek the necessary tools to work with them. One of the most important examples of this laboratory consolidated in the intersection of choreographical, and architectonical processes is the collaboration betweenLawrence Halprin, landscape architect, and Anna Halprin, choreographer. Through the direct experience of the body in space, they will develop notations and creative cycles able to work with the material of this expanded perception of reality. The review of these creative cycles tested mainly in the sixties is nowadays specially appropriated, when diverse branches of philosophy rooted in phenomenology are interested precisely in dance and architecture as key territories. It seems that it is the opportune moment to expand the architectonical tools, which have been implemented till now, following phenomenological concerns.
Kirkwood, James R
2015-01-01
Review of ProbabilityShort HistoryReview of Basic Probability DefinitionsSome Common Probability DistributionsProperties of a Probability DistributionProperties of the Expected ValueExpected Value of a Random Variable with Common DistributionsGenerating FunctionsMoment Generating FunctionsExercisesDiscrete-Time, Finite-State Markov ChainsIntroductionNotationTransition MatricesDirected Graphs: Examples of Markov ChainsRandom Walk with Reflecting BoundariesGamblerâ€™s RuinEhrenfest ModelCentral Problem of Markov ChainsCondition to Ensure a Unique Equilibrium StateFinding the Equilibrium StateTransient and Recurrent StatesIndicator FunctionsPerron-Frobenius TheoremAbsorbing Markov ChainsMean First Passage TimeMean Recurrence Time and the Equilibrium StateFundamental Matrix for Regular Markov ChainsDividing a Markov Chain into Equivalence ClassesPeriodic Markov ChainsReducible Markov ChainsSummaryExercisesDiscrete-Time, Infinite-State Markov ChainsRenewal ProcessesDelayed Renewal ProcessesEquilibrium State f...
Adler, Robert J.; Brown, William R.; Auyang, Lun; Liu, Yin-Chang; Cook, W. Jeffrey
1986-01-01
An improved crystallization process is disclosed for separating a crystallizable material and an excluded material which is at least partially excluded from the solid phase of the crystallizable material obtained upon freezing a liquid phase of the materials. The solid phase is more dense than the liquid phase, and it is separated therefrom by relative movement with the formation of a packed bed of solid phase. The packed bed is continuously formed adjacent its lower end and passed from the liquid phase into a countercurrent flow of backwash liquid. The packed bed extends through the level of the backwash liquid to provide a drained bed of solid phase adjacent its upper end which is melted by a condensing vapor.
Energy Technology Data Exchange (ETDEWEB)
Baldridge, W. [and others
2000-12-01
The authors used geophysical, geochemical, and numerical modeling to study selected problems related to Earth's lithosphere. We interpreted seismic waves to better characterize the thickness and properties of the crust and lithosphere. In the southwestern US and Tien Shari, crust of high elevation is dynamically supported above buoyant mantle. In California, mineral fabric in the mantle correlate with regional strain history. Although plumes of buoyant mantle may explain surface deformation and magmatism, our geochemical work does not support this mechanism for Iberia. Generation and ascent of magmas remains puzzling. Our work in Hawaii constrains the residence of magma beneath Hualalai to be a few hundred to about 1000 years. In the crust, heat drives fluid and mass transport. Numerical modeling yielded robust and accurate predictions of these processes. This work is important fundamental science, and applies to mitigation of volcanic and earthquake hazards, Test Ban Treaties, nuclear waste storage, environmental remediation, and hydrothermal energy.
Zambrow, J.; Hausner, H.
1957-09-24
A method of joining metal parts for the preparation of relatively long, thin fuel element cores of uranium or alloys thereof for nuclear reactors is described. The process includes the steps of cleaning the surfaces to be jointed, placing the sunfaces together, and providing between and in contact with them, a layer of a compound in finely divided form that is decomposable to metal by heat. The fuel element members are then heated at the contact zone and maintained under pressure during the heating to decompose the compound to metal and sinter the members and reduced metal together producing a weld. The preferred class of decomposable compounds are the metal hydrides such as uranium hydride, which release hydrogen thus providing a reducing atmosphere in the vicinity of the welding operation.
Bailey, Kenneth W
2003-07-01
The United States dairy processing sector is dynamic and adaptive to new changes in the market place. Changes in consumer preferences and manufacturing technologies are resulting in new challenges to the processing sector. Consumers want a wider array of quality dairy products. Fluid processors are adapting to changing consumer demands for beverage products by introducing new flavors, providing ultrapasteurization, and using creative packaging. In addition, United States food manufacturers are requesting dairy processors to provide new dairy fractions such as MPC for new nutrition products. United States dairy policy is attempting to adapt to these changes. Federal order reform has resulted in new market-oriented signals for dairy farmers to produce what the market wants; namely, quality milk components. US dairy farmers, however, also wants to maintain programs such as the DPSP that have had the unfortunate consequence of spurring demand for protein imports (i.e., MPCs, casein, and caseinates) and also resulted in a disincentive to produce these new innovative protein products here in the United States. Surplus skim milk solids are now moving into US Government warehouses rather than into commercial markets. The future of the United States dairy industry will clearly be toward producing innovative products that the market wants. There is a strong market for dairy products not only here in the United States but also overseas, which will mean learning to compete on a global scale. The challenge is to modernize our United States milk pricing programs to provide dairy farmers and processors proper price signals while providing a minimum level of support to dairy farmers. The benefit of a greater orientation toward the market place will be stronger rates of growth for United States-produced dairy products.
A simplified model of aerosol removal by natural processes in reactor containments
Energy Technology Data Exchange (ETDEWEB)
Powers, D.A.; Washington, K.E.; Sprung, J.L. [Sandia National Labs., Albuquerque, NM (United States); Burson, S.B. [Nuclear Regulatory Commission, Washington, DC (United States)
1996-07-01
Simplified formulae are developed for estimating the aerosol decontamination that can be achieved by natural processes in the containments of pressurized water reactors and in the drywells of boiling water reactors under severe accident conditions. These simplified formulae were derived by correlation of results of Monte Carlo uncertainty analyses of detailed models of aerosol behavior under accident conditions. Monte Carlo uncertainty analyses of decontamination by natural aerosol processes are reported for 1,000, 2,000, 3,000, and 4,000 MW(th) pressurized water reactors and for 1,500, 2,500, and 3,500 MW(th) boiling water reactors. Uncertainty distributions for the decontamination factors and decontamination coefficients as functions of time were developed in the Monte Carlo analyses by considering uncertainties in aerosol processes, material properties, reactor geometry and severe accident progression. Phenomenological uncertainties examined in this work included uncertainties in aerosol coagulation by gravitational collision, Brownian diffusion, turbulent diffusion and turbulent inertia. Uncertainties in aerosol deposition by gravitational settling, thermophoresis, diffusiophoresis, and turbulent diffusion were examined. Electrostatic charging of aerosol particles in severe accidents is discussed. Such charging could affect both the coagulation and deposition of aerosol particles. Electrostatic effects are not considered in most available models of aerosol behavior during severe accidents and cause uncertainties in predicted natural decontamination processes that could not be taken in to account in this work. Median (50%), 90 and 10% values of the uncertainty distributions for effective decontamination coefficients were correlated with time and reactor thermal power. These correlations constitute a simplified model that can be used to estimate the decontamination by natural aerosol processes at 3 levels of conservatism. Applications of the model are described.
Information Processing - Administrative Data Processing
Bubenko, Janis
A three semester, 60-credit course package in the topic of Administrative Data Processing (ADP), offered in 1966 at Stockholm University (SU) and the Royal Institute of Technology (KTH) is described. The package had an information systems engineering orientation. The first semester focused on datalogical topics, while the second semester focused on the infological topics. The third semester aimed to deepen the students’ knowledge in different parts of ADP and at writing a bachelor thesis. The concluding section of this paper discusses various aspects of the department’s first course effort. The course package led to a concretisation of our discipline and gave our discipline an identity. Our education seemed modern, “just in time”, and well adapted to practical needs. The course package formed the first concrete activity of a group of young teachers and researchers. In a forty-year perspective, these people have further developed the department and the topic to an internationally well-reputed body of knowledge and research. The department has produced more than thirty professors and more than one hundred doctoral degrees.
Stochastic differential equations and diffusion processes
Ikeda, N
1989-01-01
Being a systematic treatment of the modern theory of stochastic integrals and stochastic differential equations, the theory is developed within the martingale framework, which was developed by J.L. Doob and which plays an indispensable role in the modern theory of stochastic analysis.A considerable number of corrections and improvements have been made for the second edition of this classic work. In particular, major and substantial changes are in Chapter III and Chapter V where the sections treating excursions of Brownian Motion and the Malliavin Calculus have been expanded and refined. Sectio
Directory of Open Access Journals (Sweden)
Svetlana Strbac Savic
2015-01-01
Full Text Available Forecasting the operational efficiency of an existing underground mine plays an important role in strategic planning of production. Degree of Operating Leverage (DOL is used to express the operational efficiency of production. The forecasting model should be able to involve common time horizon, taking the characteristics of the input variables that directly affect the value of DOL. Changes in the magnitude of any input variable change the value of DOL. To establish the relationship describing the way of changing we applied multivariable grey modeling. Established time sequence multivariable response formula is also used to forecast the future values of operating leverage. Operational efficiency of production is often associated with diverse sources of uncertainties. Incorporation of these uncertainties into multivariable forecasting model enables mining company to survive in today’s competitive environment. Simulation of mean reversion process and geometric Brownian motion is used to describe the stochastic diffusion nature of metal price, as a key element of revenues, and production costs, respectively. By simulating a forecasting model, we imitate its action in order to measure its response to different inputs. The final result of simulation process is the expected value of DOL for every year of defined time horizon.
Cherstvy, Andrey G; Chechkin, Aleksei V; Metzler, Ralf
2014-03-14
We study the thermal Markovian diffusion of tracer particles in a 2D medium with spatially varying diffusivity D(r), mimicking recently measured, heterogeneous maps of the apparent diffusion coefficient in biological cells. For this heterogeneous diffusion process (HDP) we analyse the mean squared displacement (MSD) of the tracer particles, the time averaged MSD, the spatial probability density function, and the first passage time dynamics from the cell boundary to the nucleus. Moreover we examine the non-ergodic properties of this process which are important for the correct physical interpretation of time averages of observables obtained from single particle tracking experiments. From extensive computer simulations of the 2D stochastic Langevin equation we present an in-depth study of this HDP. In particular, we find that the MSDs along the radial and azimuthal directions in a circular domain obey anomalous and Brownian scaling, respectively. We demonstrate that the time averaged MSD stays linear as a function of the lag time and the system thus reveals a weak ergodicity breaking. Our results will enable one to rationalise the diffusive motion of larger tracer particles such as viruses or submicron beads in biological cells.
AN ADVANCED OXIDATION PROCESS : FENTON PROCESS
Directory of Open Access Journals (Sweden)
Engin GÜRTEKİN
2008-03-01
Full Text Available Biological wastewater treatment is not effective treatment method if raw wastewater contains toxic and refractory organics. Advanced oxidation processes are applied before or after biological treatment for the detoxification and reclamation of this kind of wastewaters. The advanced oxidation processes are based on the formation of powerful hydroxyl radicals. Among advanced oxidation processes Fenton process is one of the most promising methods. Because application of Fenton process is simple and cost effective and also reaction occurs in a short time period. Fenton process is applied for many different proposes. In this study, Fenton process was evaluated as an advanced oxidation process in wastewater treatment.
Linear filtering with Ornstein–Ulhenbeck process as noise
Indian Academy of Sciences (India)
1980, also theorem 18.11 from Elliott 1982) which is used in the next section. Suppose that the observation model is given by. Z(t) = ∫ t. 0. H (u, X, Z)du +. ∫ t. 0 α(u)dW (u), where W is standard Brownian motion, the observation function H a non-anticipating func- tional of (X, Z) and α a deterministic function bounded away ...
Management of processes of electrochemical dimensional processing
Akhmetov, I. D.; Zakirova, A. R.; Sadykov, Z. B.
2017-09-01
In different industries a lot high-precision parts are produced from hard-processed scarce materials. Forming such details can only be acting during non-contact processing, or a minimum of effort, and doable by the use, for example, of electro-chemical processing. At the present stage of development of metal working processes are important management issues electrochemical machining and its automation. This article provides some indicators and factors of electrochemical machining process.
Studies on process synthesis and process integration
Fien, Gert-Jan A. F.
1994-01-01
This thesis discusses topics in the field of process engineering that have received much attention over the past twenty years: (1) conceptual process synthesis using heuristic shortcut methods and (2) process integration through heat-exchanger networks and energy-saving power and refrigeration systems. The shortcut methods for conceptual process synthesis presented in Chapter 2, utilize Residue Curve Maps in ternary diagrams and are illustrated with examples of processes...
Extensible packet processing architecture
Robertson, Perry J.; Hamlet, Jason R.; Pierson, Lyndon G.; Olsberg, Ronald R.; Chun, Guy D.
2013-08-20
A technique for distributed packet processing includes sequentially passing packets associated with packet flows between a plurality of processing engines along a flow through data bus linking the plurality of processing engines in series. At least one packet within a given packet flow is marked by a given processing engine to signify by the given processing engine to the other processing engines that the given processing engine has claimed the given packet flow for processing. A processing function is applied to each of the packet flows within the processing engines and the processed packets are output on a time-shared, arbitered data bus coupled to the plurality of processing engines.
A Note on the Distribution of Multivariate Brownian Extrema
Directory of Open Access Journals (Sweden)
Marcos Escobar
2014-01-01
reflections and the link to the method of images. This joint distribution can be used in financial mathematics to obtain prices of credit or market related products in high dimension. The solution could be generalized to account for stochastic volatility and other stylized features of the financial markets.
Asset pricing puzzles explained by incomplete Brownian equilibria
DEFF Research Database (Denmark)
Christensen, Peter Ove; Larsen, Kasper
time interval in a money market account as well as a risky security. Besides establishing the existence of an equilibrium, our main result shows that the resulting equilibrium can display a lower risk-free rate and a higher risk premium relative to the usual Pareto efficient equilibrium in complete...
Quantum electrodynamical torques in the presence of Brownian motion
Munday, J. N.; Iannuzzi, D.; Capasso, F.
2006-01-01
Quantum fluctuations of the electromagnetic field give rise to a zero-point energy that persists even in the absence of electromagnetic sources. One striking consequence of the zero-point energy is manifested in the Casimir force, which causes two electrically neutral metallic plates to attract in
Brownian motion of massive skyrmions in magnetic thin films
Energy Technology Data Exchange (ETDEWEB)
Troncoso, Roberto E., E-mail: r.troncoso.c@gmail.com [Centro para el Desarrollo de la Nanociencia y la Nanotecnología, CEDENNA, Avda. Ecuador 3493, Santiago 9170124 (Chile); Núñez, Álvaro S., E-mail: alnunez@dfi.uchile.cl [Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago (Chile)
2014-12-15
We report on the thermal effects on the motion of current-driven massive magnetic skyrmions. The reduced equation for the motion of skyrmion has the form of a stochastic generalized Thiele’s equation. We propose an ansatz for the magnetization texture of a non-rigid single skyrmion that depends linearly with the velocity. By using this ansatz it is found that the skyrmion mass tensor is closely related to intrinsic skyrmion parameters, such as Gilbert damping, skyrmion-charge and dissipative force. We have found an exact expression for the average drift velocity as well as the mean-square velocity of the skyrmion. The longitudinal and transverse mobility of skyrmions for small spin-velocity of electrons is also determined and found to be independent of the skyrmion mass.
Tumbling of a Brownian particle in an extensional flow
Plan, Emmanuel Lance Christopher VI Medillo
2016-01-01
The phenomenon of tumbling of microscopic objects is commonly associated with shear flows. We address the question of whether tumbling can also occur in stretching-dominated flows. To answer this, we study the dynamics of a semi-flexible trumbbell in a planar extensional velocity field. We show that the trumbbell undergoes a random tumbling-through-folding motion. The probability distribution of long tumbling times is exponential with a time scale exponentially increasing with the Weissenberg number.
A Brownian Bridge Movement Model to Track Mobile Targets
2016-09-01
Vietnam, the Philippines, Taiwan, Malaysia and Brunei have competing claims in the South China Sea, as depicted in Figure 1. China’s claim is the most...has been upset with the election of the Democratic Progressive Party 14 (DPP) into Taiwanese government, a party that has strongly advocated the
Dynamical Gibbs-non-Gibbs transitions and Brownian percolation
Martinez, Julian Facundo
2014-01-01
This thesis deals with two different models in two different contexts. The first part deals with dynamical Gibbs-non-Gibbs transitions. Gibbs measures describe the equilibrium states of a system consisting of a large number of components that interact with each other. Due to the large number of
Normal-metal-superconductor tunnel junction as a Brownian refrigerator.
Pekola, J P; Hekking, F W J
2007-05-25
Thermal noise generated by a hot resistor (resistance R) can, under proper conditions, catalyze heat removal from a cold normal metal (N) in contact with a superconductor (S) via a tunnel barrier (I). Such a NIS junction is reminiscent of Maxwell's demon, rectifying the heat flow. Upon reversal of the temperature gradient between the resistor and the junction, the heat fluxes are reversed: this presents a regime which is not accessible in an ordinary voltage-biased NIS structure. We obtain analytical results for the cooling performance in an idealized high impedance environment and perform numerical calculations for general R. We conclude by assessing the experimental feasibility of the proposed effect.
Testing the Maxwell-Boltzmann distribution using Brownian particles
National Research Council Canada - National Science Library
Mo, Jianyong; Simha, Akarsh; Kheifets, Simon; Raizen, Mark G
2015-01-01
.... We provide a direct verification of a modified Maxwell-Boltzmann velocity distribution and modified energy equipartition theorem that account for the kinetic energy of the liquid displaced by the particle...
Brownian Motion of Vacancy Islands on Ag(111)
Morgenstern, Karina; Rosenfeld, G.; Poelsema, Bene; Comsa, George
1995-01-01
The motion of monatomic deep vacancy islands on crystal surfaces is studied both theoretically and experimentally. We develop a new theoretical model which allows us to deduce the microscopic mechanism of mass transport from measuring the diffusion coefficients of the vacancy islands as a function
Rheology, microstructure and migration in brownian colloidal suspensions.
Pan, Wenxiao; Caswell, Bruce; Karniadakis, George Em
2010-01-05
We demonstrate that suspended spherical colloidal particles can be effectively modeled as single dissipative particle dynamics (DPD) particles provided that the conservative repulsive force is appropriately chosen. The suspension model is further improved with a new formulation, which augments standard DPD with noncentral dissipative shear forces between particles while preserving angular momentum. Using the new DPD formulation we investigate the rheology, microstructure and shear-induced migration of a monodisperse suspension of colloidal particles in plane shear flows (Couette and Poiseuille). Specifically, to achieve a well-dispersed suspension we employ exponential conservative forces for the colloid-colloid and colloid-solvent interactions but keep the conventional linear force for the solvent-solvent interactions. Our simulations yield relative viscosity versus volume fraction predictions in good agreement with both experimental data and empirical correlations. We also compute the shear-dependent viscosity and the first and second normal-stress differences and coefficients in both Couette and Poiseuille flow. Simulations near the close packingvolume-fraction (64%) at low shear rates demonstrate a transition to flow-induced string-like structures of colloidal particles simultaneously with a transition to a nonlinear Couette velocity profile in agreement with experimental observations. After a sufficient increase ofthe shear rate the ordered structure melts into disorder with restoration of the linear velocity profile. Migration effects simulated in Poiseuille flow compare well with experiments and model predictions. The important role of angular momentum and torque in nondilute suspensions is also demonstrated when compared with simulations by the standard DPD, which omits the angular degrees of freedom. Overall, the new method agrees very well with the Stokesian Dynamics method but it seems to have lower computational complexity and is applicable to general complex fluids systems.
Brownian motion of grains and negative friction in dusty plasmas
Directory of Open Access Journals (Sweden)
S.A.Trigger
2004-01-01
Full Text Available Within the approximation of dominant charging collisions the explicit microscopic calculations of the Fokker-Planck kinetic coefficients for highly-charged grains moving in plasma are performed. It is shown that due to ion absorption by grain the friction coefficient can be negative and thus the appropriate threshold value of the grain charge is found. The stationary solutions of the Fokker-Planck equation with the velocity dependent kinetic coefficient are obtained and a considerable deviation of such solutions from the Maxwellian distribution is established.
Fractional Feynman-Kac equation for non-brownian functionals.
Turgeman, Lior; Carmi, Shai; Barkai, Eli
2009-11-06
We derive backward and forward fractional Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing anomalous diffusion. Fractional substantial derivatives introduced by Friedrich and co-workers [Phys. Rev. Lett. 96, 230601 (2006)10.1103/PhysRevLett.96.230601] provide the correct fractional framework for the problem. For applications, we calculate the distribution of occupation times in half space and show how the statistics of anomalous functionals is related to weak ergodicity breaking.
Brownian Motion: Theory and Experiment A Simple Classroom ...
Indian Academy of Sciences (India)
project work he and Kasturi did at RRI .... where the integration over rl is extended over all points in the interior of v while that over r2 is extended over all points exterior to v. Alternatively, we can also write. 1 - P = 1. 1 exp [-lr2 - rll2] drldr2' (6). 41T DTV n ,r2Ev. 4Dr where now the integration over both rl and r2 are ex-.
Black hole Brownian motion in a rotating environment
Lingam, Manasvi
2018-01-01
A Langevin equation is set up to model the dynamics of a supermassive black hole (massive particle) in a rotating environment (of light particles), typically the inner region of the galaxy, under the influence of dynamical friction, gravity and stochastic forces. The formal solution is derived, and the displacement and velocity two-point correlation functions are computed. The correlators perpendicular to the axis of rotation are equal to one another and different from those parallel to the axis. By computing this difference, it is suggested that one can, perhaps, observationally determine the magnitude of the rotation. In the case with sufficiently fast rotation, it is suggested that this model can lead to an ejection. If either one of dynamical friction and Eddington accretion is included, it is shown that a near-identical Langevin equation follows, allowing us to treat the two cases in a unified manner. The limitations of the model are also presented and compared against previous results.
Modelling Migration and Economic Agglomeration with Active Brownian Particles
Schweitzer, F
1999-01-01
We propose a stochastic dynamic model of migration and economic aggregation in a system of employed (immobile) and unemployed (mobile) agents which respond to local wage gradients. Dependent on the local economic situation, described by a production function which includes cooperative effects, employed agents can become unemployed and vice versa. The spatio-temporal distribution of employed and unemployed agents is investigated both analytically and by means of stochastic computer simulations. We find the establishment of distinct economic centers out of a random initial distribution. The evolution of these centers occurs in two different stages: (i) small economic centers are formed based on the positive feedback of mutual stimulation/cooperation among the agents, (ii) some of the small centers grow at the expense of others, which finally leads to the concentration of the labor force in different extended economic regions. This crossover to large-scale production is accompanied by an increase in the unemploy...
Brownian Motion Problem: Random Walk and Beyond -RE ...
Indian Academy of Sciences (India)
University, Chandigarh and his present research activities are in non eqUilibrium statistical mechanics. He has written articles on teaching of physics, history and .... 2 Review article entitled 'Brown- ian Movement and Molecular. Reality' based on his work. has been translated into English by. F Soddy and published by Tay-.
Beyond Brownian Motion: A Levy Flight in Magic Boots -50 ...
Indian Academy of Sciences (India)
, Levy distribu- tion, fractals. Nalini Chakravarti. In recent times, it has become quite common in the scientific community to observe molecular aggregates which travel at times like Tom Thumb wearing his magic boots. This requires an under-.
Fractional Brownian motion of director fluctuations in nematic ordering
DEFF Research Database (Denmark)
Zhang, Z.; Mouritsen, Ole G.; Otnes, K.
1993-01-01
Temporal director fluctuations in nematic ordering were studied by computer simulation on the Lebwohl-Lasher model as well as by neutron-scattering experiments on the nematogen d-PAA. The time-series data have been analyzed by the rescaled-range method and in terms of the power spectrum in order ...
Thinning spatial point processes into Poisson processes
DEFF Research Database (Denmark)
Møller, Jesper; Schoenberg, Frederic Paik
, and where one simulates backwards and forwards in order to obtain the thinned process. In the case of a Cox process, a simple independent thinning technique is proposed. In both cases, the thinning results in a Poisson process if and only if the true Papangelou conditional intensity is used, and thus can...
Thinning spatial point processes into Poisson processes
DEFF Research Database (Denmark)
Møller, Jesper; Schoenberg, Frederic Paik
2010-01-01
are identified, and where we simulate backwards and forwards in order to obtain the thinned process. In the case of a Cox process, a simple independent thinning technique is proposed. In both cases, the thinning results in a Poisson process if and only if the true Papangelou conditional intensity is used, and...
Hermann, Philipp; Mrkvička, Tomáš; Mattfeldt, Torsten; Minárová, Mária; Helisová, Kateřina; Nicolis, Orietta; Wartner, Fabian; Stehlík, Milan
2015-08-15
Fractals are models of natural processes with many applications in medicine. The recent studies in medicine show that fractals can be applied for cancer detection and the description of pathological architecture of tumors. This fact is not surprising, as due to the irregular structure, cancerous cells can be interpreted as fractals. Inspired by Sierpinski carpet, we introduce a flexible parametric model of random carpets. Randomization is introduced by usage of binomial random variables. We provide an algorithm for estimation of parameters of the model and illustrate theoretical and practical issues in generation of Sierpinski gaskets and Hausdorff measure calculations. Stochastic geometry models can also serve as models for binary cancer images. Recently, a Boolean model was applied on the 200 images of mammary cancer tissue and 200 images of mastopathic tissue. Here, we describe the Quermass-interaction process, which can handle much more variations in the cancer data, and we apply it to the images. It was found out that mastopathic tissue deviates significantly stronger from Quermass-interaction process, which describes interactions among particles, than mammary cancer tissue does. The Quermass-interaction process serves as a model describing the tissue, which structure is broken to a certain level. However, random fractal model fits well for mastopathic tissue. We provide a novel discrimination method between mastopathic and mammary cancer tissue on the basis of complex wavelet-based self-similarity measure with classification rates more than 80%. Such similarity measure relates to Hurst exponent and fractional Brownian motions. The R package FractalParameterEstimation is developed and introduced in the paper. Copyright © 2015 John Wiley & Sons, Ltd.
DEFF Research Database (Denmark)
Møller, Jesper; McCullagh, Peter
We extend the boson process first to a large class of Cox processes and second an even larger class of infinitely divisible point processes. Density and moment results are studied in detail. These results are obtained in closed form as weighted permanents, so the extension is called a permanent...... process. Temporal extensions and a particularly tractable case of the permanent process are also studied. Extensions of the ferminon process along similar lines, leading to so-called determinant processes, are discussed at the end. While the permanent process is attractive, the determinant process...
Food processing and allergenicity
Verhoeckx, K.C.M.; Vissers, Y.M.; Baumert, J.L.; Faludi, R.; Feys, M.; Flanagan, S.; Herouet-Guicheney, C.; Holzhauser, T.; Shimojo, R.; Bolt, N. van der; Wichers, H.; Kimber, I.
2015-01-01
Food processing can have many beneficial effects. However, processing may also alter the allergenic properties of food proteins. A wide variety of processing methods is available and their use depends largely on the food to be processed. In this review the impact of processing (heat and non-heat
Food Processing and Allergenicity
Verhoeckx, K.; Vissers, Y.; Baumert, J.L.; Faludi, R.; Fleys, M.; Flanagan, S.; Herouet-Guicheney, C.; Holzhauser, T.; Shimojo, R.; Bolt, van der Nieke; Wichers, H.J.; Kimber, I.
2015-01-01
Food processing can have many beneficial effects. However, processing may also alter the allergenic properties of food proteins. A wide variety of processing methods is available and their use depends largely on the food to be processed.
In this review the impact of processing (heat and
Process Intensification: A Perspective on Process Synthesis
DEFF Research Database (Denmark)
Lutze, Philip; Gani, Rafiqul; Woodley, John
2010-01-01
In recent years, process intensification (PI) has attracted considerable academic interest as a potential means for process improvement, to meet the increasing demands for sustainable production. A variety of intensified operations developed in academia and industry creates a large number...... of options to potentially improve the process but to identify the set of feasible solutions for PI in which the optimal can be found takes considerable resources. Hence, a process synthesis tool to achieve PI would potentially assist in the generation and evaluation of PI options. Currently, several process...... design tools with a clear focus on specific PI tasks exist. Therefore, in this paper, the concept of a general systematic framework for synthesis and design of PI options in hierarchical steps through analyzing an existing process, generating PI options in a superstructure and evaluating intensified...