Brownian limits, local limits, extreme value and variance asymptotics for convex hulls in the ball
Calka, Pierre; Yukich, J E
2009-01-01
The paper of Schreiber and Yukich [40] establishes an asymptotic representation for random convex polytope geometry in the unit ball $\\B_d, d \\geq 2,$ in terms of the general theory of stabilizing functionals of Poisson point processes as well as in terms of the so-called generalized paraboloid growth process. This paper further exploits this connection, introducing also a dual object termed the paraboloid hull process. Via these growth processes we establish local functional and measure-level limit theorems for the properly scaled radius-vector and support functions as well as for curvature measures and $k$-face empirical measures of convex polytopes generated by high density Poisson samples. We use general techniques of stabilization theory to establish Brownian sheet limits for the defect volume and mean width functionals, and we provide explicit variance asymptotics and central limit theorems for the $k$-face and intrinsic volume functionals. We establish extreme value theorems for radius-vector and suppo...
A limit theorem for moments in space of the increments of Brownian local time
Campese, Simon
2015-01-01
We proof a limit theorem for moments in space of the increments of Brownian local time. As special cases for the second and third moments, previous results by Chen et al. (Ann. Prob. 38, 2010, no. 1) and Rosen (Stoch. Dyn. 11, 2011, no. 1), which were later reproven by Hu and Nualart (Electron. Commun. Probab. 14, 2009; Electron. Commun. Probab. 15, 2010) and Rosen (S\\'eminaire de Probabilit\\'es XLIII, Springer, 2011) are included. Furthermore, a conjecture of Rosen for the fourth moment is s...
Continuum limits of random matrices and the Brownian carousel
Valko, Benedek; Virag, Balint
2007-01-01
We show that at any location away from the spectral edge, the eigenvalues of the Gaussian unitary ensemble and its general beta siblings converge to Sine_beta, a translation invariant point process. This process has a geometric description in term of the Brownian carousel, a deterministic function of Brownian motion in the hyperbolic plane. The Brownian carousel, a description of the a continuum limit of random matrices, provides a convenient way to analyze the limiting point processes. We sh...
Self-intersection local times and collision local times of bifractional Brownian motions
Institute of Scientific and Technical Information of China (English)
2009-01-01
In this paper, we consider the local time and the self-intersection local time for a bifractional Brownian motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the existence and smoothness of the self-intersection local time and the collision local time, through the strong local nondeterminism of bifractional Brownian motion, L2 convergence and Chaos expansion.
Self-intersection local times and collision local times of bifractional Brownian motions
Institute of Scientific and Technical Information of China (English)
JIANG YiMing; WANG YongJin
2009-01-01
In this paper, we consider the local time and the self-intersection local time for a bifrac-tional Brownish motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the existence and smoothness of the self-intersection local time and the collision local time, through the strong local nondeterminism of bifractional Brownian motion, L2 convergence and Chaos expansion.
SOME RESULTS ON LAG INCREMENTS OF PRINCIPAL VALUE OF BROWNIAN LOCAL TIME
Institute of Scientific and Technical Information of China (English)
WenJiwei
2002-01-01
Let W be a standard Brownian motion,and define Y(t) =∫ods/W(s) as Cauchy's principal value related to the local time of W. We study some limit results on lag increments of Y(t) and obtain various results all of which are related to earlier work by Hanson and Russo in 1983.
Some Results on Fractional Brownian Sheets and Their Local Times
Institute of Scientific and Technical Information of China (English)
Zong-mao Cheng; Zheng-yan Lin
2008-01-01
Let BHO={BHO(t),E RN+} be a real-valued fractional Brownian sheet. Define the (N,d)-Ganssian random field BH by where BH1,..., BHd are independent copies of BHO. The existence and joint continuity of local times of BH is proven in some given conditions in [22]. We then study further properties of the local times of BH, such as the moments of increments of local times, the large increments and the maximum moduli of continuity of local times and as a result, we answer the questions posed in [22].
Functionals of Brownian motion, localization and metric graphs
Energy Technology Data Exchange (ETDEWEB)
Comtet, Alain [Laboratoire de Physique Theorique et Modeles Statistiques, UMR 8626 du CNRS, Universite Paris-Sud, Bat. 100, F-91405 Orsay Cedex (France); Institut Henri Poincare, 11 rue Pierre et Marie Curie, F-75005 Paris (France); Desbois, Jean [Laboratoire de Physique Theorique et Modeles Statistiques, UMR 8626 du CNRS, Universite Paris-Sud, Bat. 100, F-91405 Orsay Cedex (France); Texier, Christophe [Laboratoire de Physique Theorique et Modeles Statistiques, UMR 8626 du CNRS, Universite Paris-Sud, Bat. 100, F-91405 Orsay Cedex (France); Laboratoire de Physique des Solides, UMR 8502 du CNRS, Universite Paris-Sud, Bat. 510, F-91405 Orsay Cedex (France)
2005-09-16
We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of Brownian motion arise in the study of electronic transport in weakly disordered metals (weak localization). Two aspects of the physics of the one-dimensional strong localization are reviewed: some properties of the scattering by a random potential (time delay distribution) and a study of the spectrum of a random potential on a bounded domain (the extreme value statistics of the eigenvalues). Then we mention several results concerning the diffusion on graphs, and more generally the spectral properties of the Schroedinger operator on graphs. The interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated. Finally, we consider a two-dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices. We recall the connection between spectral properties of this model and winding functionals of planar Brownian motion. (topical review)
Functionals of Brownian motion, localization and metric graphs
International Nuclear Information System (INIS)
We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of Brownian motion arise in the study of electronic transport in weakly disordered metals (weak localization). Two aspects of the physics of the one-dimensional strong localization are reviewed: some properties of the scattering by a random potential (time delay distribution) and a study of the spectrum of a random potential on a bounded domain (the extreme value statistics of the eigenvalues). Then we mention several results concerning the diffusion on graphs, and more generally the spectral properties of the Schroedinger operator on graphs. The interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated. Finally, we consider a two-dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices. We recall the connection between spectral properties of this model and winding functionals of planar Brownian motion. (topical review)
Non-Markovian weak coupling limit of quantum Brownian motion
Maniscalco, Sabrina; Piilo, Jyrki; Suominen, Kalle-Antti
2008-01-01
We derive and solve analytically the non-Markovian master equation for harmonic quantum Brownian motion proving that, for weak system-reservoir couplings and high temperatures, it can be recast in the form of the master equation for a harmonic oscillator interacting with a squeezed thermal bath. This equivalence guarantees preservation of positivity of the density operator during the time evolution and allows one to establish a connection between the dynamics of Schr\\"odinger cat states in sq...
Overdamped limit and inverse-friction expansion for Brownian motion in an inhomogeneous medium.
Durang, Xavier; Kwon, Chulan; Park, Hyunggyu
2015-06-01
We revisit the problem of the overdamped (large-friction) limit of the Brownian dynamics in an inhomogeneous medium characterized by a position-dependent friction coefficient and a multiplicative noise (local temperature) in one-dimensional space. Starting from the Kramers equation and analyzing it through the expansion in terms of eigenfunctions of a quantum harmonic oscillator, we derive analytically the corresponding Fokker-Planck equation in the overdamped limit. The result is fully consistent with the previous finding by Sancho, San Miguel, and Dürr [J. Stat. Phys. 28, 291 (1982)]. Our method allows us to generalize the Brinkman's hierarchy, and thus it would be straightforward to obtain higher-order corrections in a systematic inverse-friction expansion without any assumption. Our results are confirmed by numerical simulations for simple examples. PMID:26172672
Some scaled limit theorems for an immigration super-Brownian motion
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper,the small time limit behaviors for an immigration super-Brownian motion are studied,where the immigration is determined by Lebesgue measure.We first prove a functional central limit theorem,and then study the large and moderate deviations associated with this central tendency.
Single potassium niobate nano/microsized particles as local mechano-optical Brownian probes
Mor, Flavio M.; Sienkiewicz, Andrzej; Magrez, Arnaud; Forró, László; Jeney, Sylvia
2016-03-01
fluctuations and optical forces of singly-trapped KNbO3 particles within the optical trapping volume of a PFM microscope. We also show that, under near-infrared (NIR) excitation of the highly focused laser beam of the PFM microscope, a single optically-trapped KNbO3 particle reveals a strong SHG signal manifested by a narrow peak (λem = 532 nm) at half the excitation wavelength (λex = 1064 nm). Moreover, we demonstrate that the thus induced SHG emission can be used as a local light source that is capable of optically exciting molecules of an organic dye, Rose Bengal (RB), which adhere to the particle surface, through the mechanism of luminescence energy transfer (LET). Electronic supplementary information (ESI) available: Further details concerning the computation of the trap stiffness and estimation of the upper size limit for optically trappable `cubic-shaped' KNbO3 particles (Fig. S1), the experimental setup (Fig. S2), the evaluation of the size of KNbO3 nano/microsized particles, the quantification of Brownian motion spheres (Fig. S3), the one-photon excitation of RB molecules (Fig. S4), as well as regarding the laser-induced heating in PFM experiments. See DOI: 10.1039/C5NR08090H
Brownian Motion as a Limit to Physical Measuring Processes
DEFF Research Database (Denmark)
Niss, Martin
2016-01-01
and received widespread recognition, but his way of modeling the system was contested by his contemporaries. With the more embracing notion of noise that developed during and after World War II, Ising’s conclusion was reinterpreted as showing that noise puts a limit on physical measurement processes. Hence...
A weak limit theorem for numerical approximation of Brownian semi-stationary processes
DEFF Research Database (Denmark)
Podolskij, Mark; Thamrongrat, Nopporn
In this paper we present a weak limit theorem for a numerical approximation of Brownian semi-stationary processes studied in [14]. In the original work of [14] the authors propose to use Fourier transformation to embed a given one dimensional (Levy) Brownian semi-stationary process into a two......-parameter stochastic field. For the latter they use a simple iteration procedure and study the strong approximation error of the resulting numerical scheme given that the volatility process is fully observed. In this work we present the corresponding weak limit theorem for the setting, where the volatility....../drift process needs to be numerically simulated. In particular, weak approximation errors for smooth test functions can be obtained from our asymptotic theory....
Limitation of the Least Square Method in the Evaluation of Dimension of Fractal Brownian Motions
Qiao, Bingqiang; Zeng, Houdun; Li, Xiang; Dai, Benzhong
2015-01-01
With the standard deviation for the logarithm of the re-scaled range $\\langle |F(t+\\tau)-F(t)|\\rangle$ of simulated fractal Brownian motions $F(t)$ given in a previous paper \\cite{q14}, the method of least squares is adopted to determine the slope, $S$, and intercept, $I$, of the log$(\\langle |F(t+\\tau)-F(t)|\\rangle)$ vs $\\rm{log}(\\tau)$ plot to investigate the limitation of this procedure. It is found that the reduced $\\chi^2$ of the fitting decreases with the increase of the Hurst index, $H$ (the expectation value of $S$), which may be attributed to the correlation among the re-scaled ranges. Similarly, it is found that the errors of the fitting parameters $S$ and $I$ are usually smaller than their corresponding standard deviations. These results show the limitation of using the simple least square method to determine the dimension of a fractal time series. Nevertheless, they may be used to reinterpret the fitting results of the least square method to determine the dimension of fractal Brownian motions more...
International Nuclear Information System (INIS)
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
Single potassium niobate nano/microsized particles as local mechano-optical Brownian probes.
Mor, Flavio M; Sienkiewicz, Andrzej; Magrez, Arnaud; Forró, László; Jeney, Sylvia
2016-03-28
Perovskite alkaline niobates, due to their strong nonlinear optical properties, including birefringence and the capability to produce second-harmonic generation (SHG) signals, attract a lot of attention as potential candidates for applications as local nano/microsized mechano-optical probes. Here, we report on an implementation of photonic force microscopy (PFM) to explore the Brownian motion and optical trappability of monocrystalline potassium niobate (KNbO3) nano/microsized particles having sizes within the range of 50 to 750 nm. In particular, we exploit the anisotropic translational diffusive regime of the Brownian motion to quantify thermal fluctuations and optical forces of singly-trapped KNbO3 particles within the optical trapping volume of a PFM microscope. We also show that, under near-infrared (NIR) excitation of the highly focused laser beam of the PFM microscope, a single optically-trapped KNbO3 particle reveals a strong SHG signal manifested by a narrow peak (λ(em) = 532 nm) at half the excitation wavelength (λ(ex) = 1064 nm). Moreover, we demonstrate that the thus induced SHG emission can be used as a local light source that is capable of optically exciting molecules of an organic dye, Rose Bengal (RB), which adhere to the particle surface, through the mechanism of luminescence energy transfer (LET). PMID:26956197
Institute of Scientific and Technical Information of China (English)
PENG ShiGe
2009-01-01
This is a survey on normal distributions and the related central limit theorem under sublinear expectation. We also present Brownian motion under sublinear expectations and the related stochastic calculus of Ito's type. The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk, statistics and other industrial problems.
Institute of Scientific and Technical Information of China (English)
2009-01-01
This is a survey on normal distributions and the related central limit theorem under sublinear expectation.We also present Brownian motion under sublinear expectations and the related stochastic calculus of It?’s type.The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk,statistics and other industrial problems.
Rob Gilsing
2005-01-01
Original title: Bestuur aan banden. A great deal is expected of local authority youth policy: the idea is that the local authority is in a better position than central government to develop policy that is tailored to the local situation. Moreover, it is felt that it is easier for local authorities
Delorme, Mathieu; Le Doussal, Pierre; Wiese, Kay Jörg
2016-05-01
The Brownian force model is a mean-field model for local velocities during avalanches in elastic interfaces of internal space dimension d, driven in a random medium. It is exactly solvable via a nonlinear differential equation. We study avalanches following a kick, i.e., a step in the driving force. We first recall the calculation of the distributions of the global size (total swept area) and of the local jump size for an arbitrary kick amplitude. We extend this calculation to the joint density of local and global sizes within a single avalanche in the limit of an infinitesimal kick. When the interface is driven by a single point, we find new exponents τ_{0}=5/3 and τ=7/4, depending on whether the force or the displacement is imposed. We show that the extension of a "single avalanche" along one internal direction (i.e., the total length in d=1) is finite, and we calculate its distribution following either a local or a global kick. In all cases, it exhibits a divergence P(ℓ)∼ℓ^{-3} at small ℓ. Most of our results are tested in a numerical simulation in dimension d=1. PMID:27300864
布朗局部时主值滞后增量的几个结果%SOME RESULTS ON LAG INCREMENTS OF PRINCIPAL VALUE OF BROWNIAN LOCAL TIME
Institute of Scientific and Technical Information of China (English)
闻继威
2002-01-01
Let W be a standard Brownian motion,and define Y(t)=∫t0dsW(s) as Cauchy's principal value related to the local time of W.We study some limit results on lag increments of Y(t) and obtain various results all of which are related to earlier work by Hanson and Russo in 1983.
Institute of Scientific and Technical Information of China (English)
Liu Jian; Wang Hai-Yan; Bao Jing-Dong
2013-01-01
A minimal system-plus-reservoir model yielding a nonergodic Langevin equation is proposed,which originates from the cubic-spectral density of environmental oscillators and momentum-dependent coupling.This model allows ballistic diffusion and classical localization simultaneously,in which the fluctuation-dissipation relation is still satisfied but the Khinchin theorem is broken.The asymptotical equilibrium for a nonergodic system requires the initial thermal equilibrium,however,when the system starts from nonthermal conditions,it does not approach the equilibration even though a nonlinear potential is used to bound the particle,this can be confirmed by the zeroth law of thermodynamics.In the dynamics of Brownian localization,due to the memory damping function inducing a constant term,our results show that the stationary distribution of the system depends on its initial preparation of coordinate rather than momentum.The coupled oscillator chain with a fixed end boundary acts as a heat bath,which has long been used in studies of collinear atom/solid-surface scattering and lattice vibration,we investigate this problem from the viewpoint of nonergodicity.
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.
International Nuclear Information System (INIS)
Graphical abstract: By invoking physically motivated coordinate transformation into quantum Smoluchowski equation, we have presented a transparent treatment for the determination of the effective diffusion coefficient and current of a quantum Brownian particle. Substantial enhancement in the efficiency of the diffusive transport is envisaged due to the quantum correction effects. Highlights:: ► Transport of a quantum Brownian particle in a periodic potential has been addressed. ► Governing quantum Smoluchowski equation (QSE) includes state dependent diffusion. ► A coordinate transformation is used to recast QSE with constant diffusion. ► Transport properties increases in comparison to the corresponding classical result. ► This enhancement is purely a quantum effect. - Abstract: The transport property of a quantum Brownian particle that interacts strongly with a bath (in which a typical damping constant by far exceeds a characteristic frequency of the isolated system) under the influence of a tilted periodic potential has been studied by solving quantum Smoluchowski equation (QSE). By invoking physically motivated coordinate transformation into QSE, we have presented a transparent treatment for the determination of the effective diffusion coefficient of a quantum Brownian particle and the current (the average stationary velocity). Substantial enhancement in the efficiency of the diffusive transport is envisaged due to the quantum correction effects only if the bath temperature hovers around an appropriate range of intermediate values. Our findings also confirm the results obtained in the classical cases.
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.
Michalet, Xavier
2010-01-01
We examine the capability of mean square displacement analysis to extract reliable values of the diffusion coefficient D of single particle undergoing Brownian motion in an isotropic medium in the presence of localization uncertainty. The theoretical results, supported by simulations, show that a simple unweighted least square fit of the MSD curve can provide the best estimate of D provided an optimal number of MSD points is used for the fit. We discuss the practical implications of these res...
Chernov, N.; Dolgopyat, D.
2008-01-01
A classical model of Brownian motion consists of a heavy molecule submerged into a gas of light atoms in a closed container. In this work we study a 2D version of this model, where the molecule is a heavy disk of mass M and the gas is represented by just one point particle of mass m = 1, which interacts with the disk and the walls of the container via elastic collisions. Chaotic behavior of the particles is ensured by convex (scattering) walls of the container. We prove that the position and ...
Lejay, Antoine; Torres, Soledad
2011-01-01
We study the asymptotic behavior of the maximum likelihood estimator corresponding to the observation of a trajectory of a Skew Brownian motion, through a uniform time discretization. We characterize the speed of convergence and the limiting distribution when the step size goes to zero, which in this case are non-classical, under the null hypothesis of the Skew Brownian motion being an usual Brownian motion. This allows to design a test on the skewness parameter. We show that numerical simulations that can be easily performed to estimate the skewness parameter, and provide an application in Biology.
Some Brownian functionals and their laws
Donati-Martin, C.; Yor, M.
1997-01-01
We develop some topics about Brownian motion with a particular emphasis on the study of principal values of Brownian local times. We show some links between principal values and Doob’s $h$-transforms of Brownian motion, for nonpositive harmonic functions $h$. We also give a survey and complement some martingale approaches to Ray–Knight theorems for local times.
Horvath, Illes; Veto, Balint
2010-01-01
The problems considered in the present paper have their roots in two different cultures. The 'true' (or myopic) self-avoiding walk model (TSAW) was introduced in the physics literature by Amit, Parisi and Peliti. This is a nearest neighbor non-Markovian random walk in Z^d which prefers to jump to those neighbors which were less visited in the past. The self-repelling Brownian polymer model (SRBP), initiated in the probabilistic literature by Durrett and Rogers (independently of the physics community), is the continuous space-time counterpart: a diffusion in R^d pushed by the negative gradient of the (mollified) occupation time measure of the process. In both cases, similar long memory effects are caused by a pathwise self-repellency of the trajectories due to a push by the negative gradient of (softened) local time. We investigate the asymptotic behaviour of TSAW and SRBP in the non-recurrent dimensions. First, we identify a natural stationary (in time) and ergodic distribution of the environment (the local t...
Functional limit theorems for generalized variations of the fractional Brownian sheet
DEFF Research Database (Denmark)
Pakkanen, Mikko; Réveillac, Anthony
and on the smallest component of the Hurst parameter vector of the fBs. The limiting process in the former result is another fBs, independent of the original fBs, whereas the limit given by the latter result is an Hermite sheet, which is driven by the same white noise as the original fBs. As an application, we derive...
Functional limit theorems for generalized variations of the fractional Brownian sheet
DEFF Research Database (Denmark)
Pakkanen, Mikko; Réveillac, Anthony
2016-01-01
and on the smallest component of the Hurst parameter vector of the fBs. The limiting process in the former result is another fBs, independent of the original fBs, whereas the limit given by the latter result is an Hermite sheet, which is driven by the same white noise as the original fBs. As an application, we derive...
Reactive Boundary Conditions as Limits of Interaction Potentials for Brownian and Langevin Dynamics
Chapman, S Jonathan; Isaacson, Samuel A
2015-01-01
A popular approach to modeling bimolecular reactions between diffusing molecules is through the use of reactive boundary conditions. One common model is the Smoluchowski partial absorption condition, which uses a Robin boundary condition in the separation coordinate between two possible reactants. This boundary condition can be interpreted as an idealization of a reactive interaction potential model, in which a potential barrier must be surmounted before reactions can occur. In this work we show how the reactive boundary condition arises as the limit of an interaction potential encoding a steep barrier within a shrinking region in the particle separation, where molecules react instantly upon reaching the peak of the barrier. The limiting boundary condition is derived by the method of matched asymptotic expansions, and shown to depend critically on the relative rate of increase of the barrier height as the width of the potential is decreased. Limiting boundary conditions for the same interaction potential in b...
Burdzy, Krzysztof; Pal, Soumik
2010-01-01
We prove that the distance between two reflected Brownian motions outside a sphere in a 3-dimensional flat torus does not converge to 0, a.s., if the radius of the sphere is sufficiently small, relative to the size of the torus.
Hu, Yueyun; Wouts, Marcel
2010-01-01
We study a quenched charged-polymer model, introduced by Garel and Orland in 1988, that reproduces the folding/unfolding transition of biopolymers. We prove that, below the critical inverse temperature, the polymer is delocalized in the sense that: (1) The rescaled trajectory of the polymer converges to the Brownian path; and (2) The partition function remains bounded. At the critical inverse temperature, we show that the maximum time spent at points jumps discontinuously from 0 to a positive fraction of the number of monomers, in the limit as the number of monomers tends to infinity. Finally, when the critical inverse temperature is large, we prove that the polymer collapses in the sense that a large fraction of its monomers live on four adjacent positions, and its diameter grows only logarithmically with the number of the monomers. Our methods also provide some insight into the annealed phase transition and at the transition due to a pulling force; both phase transitions are shown to be discontinuous.
Applying Brownian motion to the study of birth-death chains
Markowsky, Greg
2011-01-01
Basic properties of Brownian motion are used to derive two results concerning birth-death chains. First, the probability of extinction is calculated. Second, sufficient conditions on the transition probabilities of a birth-death chain are given to ensure that the expected value of the chain converges to a limit. The theory of Brownian motion local time figures prominently in the proof of the second result.
Palyulin, Vladimir V.; Chechkin, Aleksei V.; Klages, Rainer; Metzler, Ralf
2016-09-01
A combined dynamics consisting of Brownian motion and Lévy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of doing so economically of such dynamics thus poses an important problem. Here we model this dynamics by a one-dimensional fractional Fokker–Planck equation combining unbiased Brownian motion and Lévy flights. By solving this equation both analytically and numerically we show that the superposition of recurrent Brownian motion and Lévy flights with stable exponent α \\lt 1, by itself implying zero probability of hitting a point on a line, leads to transient motion with finite probability of hitting any point on the line. We present results for the exact dependence of the values of both the search reliability and the search efficiency on the distance between the starting and target positions as well as the choice of the scaling exponent α of the Lévy flight component.
Palyulin, Vladimir V.; Chechkin, Aleksei V.; Klages, Rainer; Metzler, Ralf
2016-09-01
A combined dynamics consisting of Brownian motion and Lévy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of doing so economically of such dynamics thus poses an important problem. Here we model this dynamics by a one-dimensional fractional Fokker-Planck equation combining unbiased Brownian motion and Lévy flights. By solving this equation both analytically and numerically we show that the superposition of recurrent Brownian motion and Lévy flights with stable exponent α \\lt 1, by itself implying zero probability of hitting a point on a line, leads to transient motion with finite probability of hitting any point on the line. We present results for the exact dependence of the values of both the search reliability and the search efficiency on the distance between the starting and target positions as well as the choice of the scaling exponent α of the Lévy flight component.
Dimensional Properties of Fractional Brownian Motion
Institute of Scientific and Technical Information of China (English)
Dong Sheng WU; Yi Min XIAO
2007-01-01
Let Bα = {Bα(t),t ∈ RN} be an (N,d)-fractional Brownian motion with Hurst index α∈ (0, 1). By applying the strong local nondeterminism of Bα, we prove certain forms of uniform Hausdorff dimension results for the images of Bα when N > αd. Our results extend those of Kaufman for one-dimensional Brownian motion.
Metamaterial localized resonance sensors: prospects and limitations
DEFF Research Database (Denmark)
Jeppesen, Claus; Xiao, Sanshui; Mortensen, Asger;
2010-01-01
The prospects and limitations of metamaterial localized resonance sensors are investigated theoretically and experimentally. Gold split-ring resonators are employed as the model system where the light induced LC-resonance yields a figure-of-merit, sensitivity divided by linewidth, up to 54...
Trefan, Gyorgy
1993-01-01
The goal of this thesis is to contribute to the ambitious program of the foundation of developing statistical physics using chaos. We build a deterministic model of Brownian motion and provide a microscopic derivation of the Fokker-Planck equation. Since the Brownian motion of a particle is the result of the competing processes of diffusion and dissipation, we create a model where both diffusion and dissipation originate from the same deterministic mechanism--the deterministic interaction of that particle with its environment. We show that standard diffusion which is the basis of the Fokker-Planck equation rests on the Central Limit Theorem, and, consequently, on the possibility of deriving it from a deterministic process with a quickly decaying correlation function. The sensitive dependence on initial conditions, one of the defining properties of chaos insures this rapid decay. We carefully address the problem of deriving dissipation from the interaction of a particle with a fully deterministic nonlinear bath, that we term the booster. We show that the solution of this problem essentially rests on the linear response of a booster to an external perturbation. This raises a long-standing problem concerned with Kubo's Linear Response Theory and the strong criticism against it by van Kampen. Kubo's theory is based on a perturbation treatment of the Liouville equation, which, in turn, is expected to be totally equivalent to a first-order perturbation treatment of single trajectories. Since the boosters are chaotic, and chaos is essential to generate diffusion, the single trajectories are highly unstable and do not respond linearly to weak external perturbation. We adopt chaotic maps as boosters of a Brownian particle, and therefore address the problem of the response of a chaotic booster to an external perturbation. We notice that a fully chaotic map is characterized by an invariant measure which is a continuous function of the control parameters of the map
Restructuring local distribution services: Possibilities and limitations
Energy Technology Data Exchange (ETDEWEB)
Duann, D.J.
1994-08-01
The restructuring of local distribution services is now the focus of the natural gas industry. It is the last major step in the ``reconstitution`` of the natural gas industry and a critical clement in realizing the full benefits of regulatory and market reforms that already have taken place in the wellhead and interstate markets. It could also be the most important regulatory initiative for most end-use customers because they are affected directly by the costs and reliability of distribution services. Several factors contribute to the current emphasis on distribution service restructuring. They include the unbundling and restructuring of upstream markets, a realization of the limitations of supply-side options (such as gas procurement oversight), and the increased diversity and volatility of gas demand facing local distribution companies. Local distribution service is not one but a series of activities that start with commodity gas procurement and extend to transportation, load balancing, storage, and metering and billing of services provided. There are also considerable differences in the economies of scale and scope associated with these various activities. Thus, a mixture of supply arrangements (such as a competitive market or a monopoly) is required for the most efficient delivery of local distribution services. A distinction must be made between the supply of commodity gas and the provision of a bundled distribution service. This distinction and identification of the best supply arrangements for various distribution service components are the most critical factors in developing appropriate restructuring policies. For most state public utility commissions the criteria for service restructuring should include pursuing the economies of scale and scope in gas distribution, differentiating and matching gas service reliability and quality with customer requirements, and controlling costs associated with the search, negotiation, and contracting of gas services.
Perturbative theory for Brownian vortexes.
Moyses, Henrique W; Bauer, Ross O; Grosberg, Alexander Y; Grier, David G
2015-06-01
Brownian vortexes are stochastic machines that use static nonconservative force fields to bias random thermal fluctuations into steadily circulating currents. The archetype for this class of systems is a colloidal sphere in an optical tweezer. Trapped near the focus of a strongly converging beam of light, the particle is displaced by random thermal kicks into the nonconservative part of the optical force field arising from radiation pressure, which then biases its diffusion. Assuming the particle remains localized within the trap, its time-averaged trajectory traces out a toroidal vortex. Unlike trivial Brownian vortexes, such as the biased Brownian pendulum, which circulate preferentially in the direction of the bias, the general Brownian vortex can change direction and even topology in response to temperature changes. Here we introduce a theory based on a perturbative expansion of the Fokker-Planck equation for weak nonconservative driving. The first-order solution takes the form of a modified Boltzmann relation and accounts for the rich phenomenology observed in experiments on micrometer-scale colloidal spheres in optical tweezers. PMID:26172698
Canonical active Brownian motion
Gluck, Alexander; Huffel, Helmuth; Ilijic, Sasa
2008-01-01
Active Brownian motion is the complex motion of active Brownian particles. They are active in the sense that they can transform their internal energy into energy of motion and thus create complex motion patterns. Theories of active Brownian motion so far imposed couplings between the internal energy and the kinetic energy of the system. We investigate how this idea can be naturally taken further to include also couplings to the potential energy, which finally leads to a general theory of cano...
Quantum Brownian motion in a Landau level
Cobanera, E.; Kristel, P.; Morais Smith, C.
2016-06-01
Motivated by questions about the open-system dynamics of topological quantum matter, we investigated the quantum Brownian motion of an electron in a homogeneous magnetic field. When the Fermi length lF=ℏ /(vFmeff) becomes much longer than the magnetic length lB=(ℏc /e B ) 1 /2 , then the spatial coordinates X ,Y of the electron cease to commute, [X ,Y ] =i lB2 . As a consequence, localization of the electron becomes limited by Heisenberg uncertainty, and the linear bath-electron coupling becomes unconventional. Moreover, because the kinetic energy of the electron is quenched by the strong magnetic field, the electron has no energy to give to or take from the bath, and so the usual connection between frictional forces and dissipation no longer holds. These two features make quantum Brownian motion topological, in the regime lF≫lB , which is at the verge of current experimental capabilities. We model topological quantum Brownian motion in terms of an unconventional operator Langevin equation derived from first principles, and solve this equation with the aim of characterizing diffusion. While diffusion in the noncommutative plane turns out to be conventional, with the mean displacement squared being proportional to tα and α =1 , there is an exotic regime for the proportionality constant in which it is directly proportional to the friction coefficient and inversely proportional to the square of the magnetic field: in this regime, friction helps diffusion and the magnetic field suppresses all fluctuations. We also show that quantum tunneling can be completely suppressed in the noncommutative plane for suitably designed metastable potential wells, a feature that might be worth exploiting for storage and protection of quantum information.
Kingman's coalescent and Brownian motion
Berestycki, J.; Berestycki, N
2009-01-01
We describe a simple construction of Kingman's coalescent in terms of a Brownian excursion. This construction is closely related to, and sheds some new light on, earlier work by Aldous and Warren. Our approach also yields some new results: for instance, we obtain the full multifractal spectrum of Kingman's coalescent. This complements earlier work on Beta-coalescents by the authors and Schweinsberg. Surprisingly, the thick part of the spectrum is not obtained by taking the limit as $\\alpha \\t...
Dobric, Vladimir; Marano, Lisa
2014-01-01
The L\\'evy-Ciesielski Construction of Brownian motion is used to determine non-asymptotic estimates for the maximal deviation of increments of a Brownian motion process $(W_{t})_{t\\in \\left[ 0,T\\right] }$ normalized by the global modulus function, for all positive $\\varepsilon $ and $\\delta $. Additionally, uniform results over $\\delta $ are obtained. Using the same method, non-asymptotic estimates for the distribution function for the standard Brownian motion normalized by its local modulus ...
Efficiency of Brownian heat engines.
Derényi, I; Astumian, R D
1999-06-01
We study the efficiency of one-dimensional thermally driven Brownian ratchets or heat engines. We identify and compare the three basic setups characterized by the type of the connection between the Brownian particle and the two heat reservoirs: (i) simultaneous, (ii) alternating in time, and (iii) position dependent. We make a clear distinction between the heat flow via the kinetic and the potential energy of the particle, and show that the former is always irreversible and it is only the third setup where the latter is reversible when the engine works quasistatically. We also show that in the third setup the heat flow via the kinetic energy can be reduced arbitrarily, proving that even for microscopic heat engines there is no fundamental limit of the efficiency lower than that of a Carnot cycle.
Martínez, I. A.; Roldán, É.; Dinis, L.; Petrov, D.; Parrondo, J. M. R.; Rica, R. A.
2016-01-01
The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors and some artificial micro-engines operate. As described by stochastic thermodynamics, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit. Here we report an experimental realization of a Carnot engine with a single optically trapped Brownian particle as the working substance. We present an exhaustive study of the energetics of the engine and analyse the fluctuations of the finite-time efficiency, showing that the Carnot bound can be surpassed for a small number of non-equilibrium cycles. As its macroscopic counterpart, the energetics of our Carnot device exhibits basic properties that one would expect to observe in any microscopic energy transducer operating with baths at different temperatures. Our results characterize the sources of irreversibility in the engine and the statistical properties of the efficiency--an insight that could inspire new strategies in the design of efficient nano-motors.
How superdiffusion gets arrested: ecological encounters explain shift from Levy to Brownian movement
de Jager, M.; Bartumeus, F.; Kölzsch, A.; Weissing, F.J.; Hengeveld, G.M.; Nolet, B.A.; Herman, P.M.J.; de Koppel, J.
2014-01-01
Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when fora
Limits on the local dark matter density
Directory of Open Access Journals (Sweden)
Read J.I.
2012-02-01
Full Text Available We study the systematic problems in determining the local dark matter density ρdm(R☉ from kinematics of stars in the Solar Neighbourhood, using a simulated Milky Way-like galaxy. We introduce a new unbiased method for recovering ρdm(R☉ based on the moments of the Jeans equations, combined with a Monte Carlo Markov Chain (MCMC technique and apply it to real data [1].
Limits on the local dark matter density
Garbari, Silvia; Lake, George
2011-01-01
We revisit systematics in determining the local dark matter density (rho_dm) from the vertical motion of stars in the Solar Neighbourhood. Using a simulation of a Milky Way-like galaxy, we determine the data-quality required to detect the dark matter density at its expected local value. We introduce a new method for recovering rho_dm that uses moments of the Jeans equations, combined with a Monte Carlo Markov Chain technique to marginalise over the unknown parameters. Given sufficiently good data, we show that our method can recover the correct local dark matter density even in the face of disc inhomogeneities, non-isothermal tracers and a non-separable distribution function. We illustrate the power of our technique by applying it to Hipparcos data [Holmberg & Flynn 2000,2004]. We first make the assumption that the A and F star tracer populations are isothermal. This recovers rho_dm=0.003^{+0.009}_{-0.007}Msun/pc^3 (with 90 per cent confidence), consistent with previous determinations. However, the vertic...
Anomalous Brownian refrigerator
Rana, Shubhashis; Pal, P. S.; Saha, Arnab; Jayannavar, A. M.
2016-02-01
We present a detailed study of a Brownian particle driven by Carnot-type refrigerating protocol operating between two thermal baths. Both the underdamped as well as the overdamped limits are investigated. The particle is in a harmonic potential with time-periodic strength that drives the system cyclically between the baths. Each cycle consists of two isothermal steps at different temperatures and two adiabatic steps connecting them. Besides working as a stochastic refrigerator, it is shown analytically that in the quasistatic regime the system can also act as stochastic heater, depending on the bath temperatures. Interestingly, in non-quasistatic regime, our system can even work as a stochastic heat engine for certain range of cycle time and bath temperatures. We show that the operation of this engine is not reliable. The fluctuations of stochastic efficiency/coefficient of performance (COP) dominate their mean values. Their distributions show power law tails, however the exponents are not universal. Our study reveals that microscopic machines are not the microscopic equivalent of the macroscopic machines that we come across in our daily life. We find that there is no one to one correspondence between the performance of our system under engine protocol and its reverse.
Brownian motion of helical flagella.
Hoshikawa, H; Saito, N
1979-07-01
We develops a theory of the Brownian motion of a rigid helical object such as bacterial flagella. The statistical properties of the random forces acting on the helical object are discussed and the coefficients of the correlations of the random forces are determined. The averages , and are also calculated where z and theta are the position along and angle around the helix axis respectively. Although the theory is limited to short time interval, direct comparison with experiment is possible by using the recently developed cinematography technique. PMID:16997210
Maragó, Onofrio M; Bonaccorso, Francesco; Saija, Rosalba; Privitera, Giulia; Gucciardi, Pietro G; Iatì, Maria Antonia; Calogero, Giuseppe; Jones, Philip H; Borghese, Ferdinando; Denti, Paolo; Nicolosi, Valeria; Ferrari, Andrea C
2010-12-28
Brownian motion is a manifestation of the fluctuation-dissipation theorem of statistical mechanics. It regulates systems in physics, biology, chemistry, and finance. We use graphene as prototype material to unravel the consequences of the fluctuation-dissipation theorem in two dimensions, by studying the Brownian motion of optically trapped graphene flakes. These orient orthogonal to the light polarization, due to the optical constants anisotropy. We explain the flake dynamics in the optical trap and measure force and torque constants from the correlation functions of the tracking signals, as well as comparing experiments with a full electromagnetic theory of optical trapping. The understanding of optical trapping of two-dimensional nanostructures gained through our Brownian motion analysis paves the way to light-controlled manipulation and all-optical sorting of biological membranes and anisotropic macromolecules. PMID:21133432
Diffusion of torqued active Brownian particles
Sevilla, Francisco J.
An analytical approach is used to study the diffusion of active Brownian particles that move at constant speed in three-dimensional space, under the influence of passive (external) and active (internal) torques. The Smoluchowski equation for the position distribution of the particles is obtained from the Kramer-Fokker-Planck equation corresponding to Langevin equations for active Brownian particles subject to torques. In addition of giving explicit formulas for the mean square-displacement, the non-Gaussian behavior is analyzed through the kurtosis of the position distribution that exhibits an oscillatory behavior in the short-time limit. FJS acknowledges support from PAPIIT-UNAM through the grant IN113114
On Kramers' general theory of Brownian motion
Brinkman, H.C.
1957-01-01
Kramer's general theory of Brownian motion 1) based on a diffusion equation in phase space is discussed from the standpoint of statistical thermodynamics. It is concluded that for particles moving in a medium in equilibrium the restrictions imposed by the second law of thermodynamics limit Kramer's
Brownian motion on a smash line
Ellinas, D; Ellinas, Demosthenes; Tsohantjis, Ioannis
2000-01-01
Brownian motion on a smash line algebra (a smash or braided version of the algebra resulting by tensoring the real line and the generalized paragrassmann line algebras), is constructed by means of its Hopf algebraic structure. Further, statistical moments, non stationary generalizations and its diffusion limit are also studied. The ensuing diffusion equation posseses triangular matrix realizations.
Noncommutative Brownian motion
Santos, Willien O; Souza, Andre M C
2016-01-01
We investigate the Brownian motion of a particle in a two-dimensional noncommutative (NC) space. Using the standard NC algebra embodied by the sympletic Weyl-Moyal formalism we find that noncommutativity induces a non-vanishing correlation between both coordinates at different times. The effect itself stands as a signature of spatial noncommutativity and offers further alternatives to experimentally detect the phenomena.
Meurs, P.; Broeck, C. Van Den
2005-01-01
Recently, a thermal Brownian motor was introduced [Van den Broeck, Kawai and Meurs, Phys. Rev. Lett. (2004)], for which an exact microscopic analysis is possible. The purpose of this paper is to review some further properties of this construction, and to discuss in particular specific issues including the relation with macroscopic response and the efficiency at maximum power.
Tax Limitations and Revenue Shifting Strategies in Local Government
DEFF Research Database (Denmark)
Blom-Hansen, Jens; Bækgaard, Martin; Serritzlew, Søren
2014-01-01
The literature on tax and expenditure limitations (TELs) shows how limiting the freedom of local governments to levy taxes may have considerable unexpected effects. Entities subjected to such limitations may, as their proponents hope, react by cutting expenditures and revenue, but they may also...... strategically change their revenue structure and increase reliance on income sources not subjected to limitations. However, these findings are overwhelmingly based on studies of state and local governments in the USA. Their relevance outside this empirical setting remains unclear. A study of Denmark, where...... the central government imposed tax limitations on municipalities in 2009, makes two contributions. First, it probes the empirical domain of the US findings. Second, it constitutes an empirical testing ground where endogeneity is not a pressing concern. In the USA, TELs are often self-imposed either by local...
Fundamental Limits of Wideband Localization - Part II: Cooperative Networks
Shen, Yuan; Win, Moe Z
2010-01-01
The availability of positional information is of great importance in many commercial, governmental, and military applications. Localization is commonly accomplished through the use of radio communication between mobile devices (agents) and fixed infrastructure (anchors). However, precise determination of agent positions is a challenging task, especially in harsh environments due to radio blockage or limited anchor deployment. In these situations, cooperation among agents can significantly improve localization accuracy and reduce localization outage probabilities. A general framework of analyzing the fundamental limits of wideband localization has been developed in Part I of the paper. Here, we build on this framework and establish the fundamental limits of wideband cooperative location-aware networks. Our analysis is based on the waveforms received at the nodes, in conjunction with Fisher information inequality. We provide a geometrical interpretation of equivalent Fisher information for cooperative networks....
A Haar component for quantum limits on locally symmetric spaces
Anantharaman, Nalini; Silberman, Lior
2010-01-01
We prove lower bounds for the entropy of limit measures associated to non-degenerate sequences of eigenfunctions on locally symmetric spaces of non-positive curvature. In the case of certain compact quotients of the space of positive definite $n\\times n$ matrices (any quotient for $n=3$, quotients associated to inner forms in general), measure classification results then show that the limit measures must have a Lebesgue component. This is consistent with the conjecture that the limit measures...
Gomez-Marin, A.; Sancho, J. M.
2004-01-01
In this paper we present a model of a symmetric Brownian motor (SBM) which changes the sign of its velocity when the temperature gradient is inverted. The velocity, external work and efficiency are studied as a function of the temperatures of the baths and other relevant parameters. The motor shows a current reversal when another parameter (a phase shift) is varied. Analytical predictions and results from numerical simulations are performed and agree very well. Generic properties of this type...
Local government broadband policies for areas with limited Internet access
Directory of Open Access Journals (Sweden)
Yoshio Arai
2014-03-01
Full Text Available Despite their wide diffusion in developed countries, broadband services are still limited in areas where providing them is not profitable for private telecom carriers. To address this, many local governments in Japan have implemented broadband deployment projects subsidized by the national government. In this paper, we discuss local government broadband policies based on survey data collected from municipalities throughout the country. With the support of national promotion policies, broadband services were rapidly introduced to most local municipalities in Japan during the 2000s. Local government deployment policies helped to reduce the number of areas with no broadband access. A business model based on the Indefeasible Right of Use (IRU contract between a private telecom carrier and a local government has been developed in recent years. Even local governments without the technical capacity to operate a broadband business can introduce broadband services into their territory using the IRU business model.
Brownian Motion, "Diverse and Undulating"
Duplantier, Bertrand
2016-01-01
We describe in detail the history of Brownian motion, as well as the contributions of Einstein, Sutherland, Smoluchowski, Bachelier, Perrin and Langevin to its theory. The always topical importance in physics of the theory of Brownian motion is illustrated by recent biophysical experiments, where it serves, for instance, for the measurement of the pulling force on a single DNA molecule. In a second part, we stress the mathematical importance of the theory of Brownian motion, illustrated by two chosen examples. The by-now classic representation of the Newtonian potential by Brownian motion is explained in an elementary way. We conclude with the description of recent progress seen in the geometry of the planar Brownian curve. At its heart lie the concepts of conformal invariance and multifractality, associated with the potential theory of the Brownian curve itself.
Brownian motion meets Riemann curvature
International Nuclear Information System (INIS)
The general covariance of the diffusion equation is exploited in order to explore the curvature effects appearing in Brownian motion over a d-dimensional curved manifold. We use the local frame defined by the so-called Riemann normal coordinates to derive a general formula for the mean-square geodesic distance (MSD) at the short-time regime. This formula is written in terms of O(d) invariants that depend on the Riemann curvature tensor. We study the n-dimensional sphere case to validate these results. We also show that the diffusion for positive constant curvature is slower than the diffusion in a plane space, while the diffusion for negative constant curvature turns out to be faster. Finally the two-dimensional case is emphasized, as it is relevant for single-particle diffusion on biomembranes
Fundamental Limits of Wideband Localization - Part I: A General Framework
Shen, Yuan
2010-01-01
The availability of positional information is of great importance in many commercial, public safety, and military applications. The coming years will see the emergence of location-aware networks with sub-meter accuracy, relying on accurate range measurements provided by wide bandwidth transmissions. In this two-part paper, we determine the fundamental limits of localization accuracy of wideband wireless networks in harsh multipath environments. We first develop a general framework to characterize the localization accuracy of a given node here and then extend our analysis to cooperative location-aware networks in Part II. In this paper, we characterize localization accuracy in terms of a performance measure called the squared position error bound (SPEB), and introduce the notion of equivalent Fisher information to derive the SPEB in a succinct expression. This methodology provides insights into the essence of the localization problem by unifying localization information from individual anchors and information ...
A Haar component for quantum limits on locally symmetric spaces
Anantharaman, Nalini
2010-01-01
We prove lower bounds for the entropy of limit measures associated to non-degenerate sequences of eigenfunctions on locally symmetric spaces of non-positive curvature. In the case of certain compact quotients of the space of positive definite $n\\times n$ matrices (any quotient for $n=3$, quotients associated to inner forms in general), measure classification results then show that the limit measures must have a Lebesgue component. This is consistent with the conjecture that the limit measures are absolutely continuous.
Brownian motion, martingales, and stochastic calculus
Le Gall, Jean-François
2016-01-01
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested i...
Brownian Motion Theory and Experiment
Basu, K; Basu, Kasturi; Baishya, Kopinjol
2003-01-01
Brownian motion is the perpetual irregular motion exhibited by small particles immersed in a fluid. Such random motion of the particles is produced by statistical fluctuations in the collisions they suffer with the molecules of the surrounding fluid. Brownian motion of particles in a fluid (like milk particles in water) can be observed under a microscope. Here we describe a simple experimental set-up to observe Brownian motion and a method of determining the diffusion coefficient of the Brownian particles, based on a theory due to Smoluchowski. While looking through the microscope we focus attention on a fixed small volume, and record the number of particles that are trapped in that volume, at regular intervals of time. This gives us a time-series data, which is enough to determine the diffusion coefficient of the particles to a good degree of accuracy.
Limits of Commutative Triangular Systems on Locally Compact Groups
Indian Academy of Sciences (India)
Riddhi Shah
2001-02-01
On a locally compact group , if $_{n}^{k_{n}} →$, ( →∞), for some probability measures and on , then a sufficient condition is obtained for the set = {$_n^m|$ ≤ } to be relatively compact; this in turn implies the embeddability of a shift of . The condition turns out to be also necessary when is totally disconnected. In particular, it is shown that if is a discrete linear group over $\\mathsf{R}$ then a shift of the limit is embeddable. It is also shown that any infinitesimally divisible measure on a connected nilpotent real algebraic group is embeddable.
Local versus basin-scale limitation of marine nitrogen fixation.
Weber, Thomas; Deutsch, Curtis
2014-06-17
Nitrogen (N) fixation by diazotrophic plankton is the primary source of this crucial nutrient to the ocean, but the factors limiting its rate and distribution are controversial. According to one view, the ecological niche of diazotrophs is primarily controlled by the ocean through internally generated N deficits that suppress the growth of their competitors. A second view posits an overriding limit from the atmosphere, which restricts diazotrophs to regions where dust deposition satisfies their high iron (Fe) requirement, thus separating N sources from sinks at a global scale. Here we use multiple geochemical signatures of N2 fixation to show that the Fe limitation of diazotrophs is strong enough to modulate the regional distribution of N2 fixation within ocean basins--particularly the Fe-poor Pacific--but not strong enough to influence its partition between basins, which is instead governed by rates of N loss. This scale-dependent limitation of N2 fixation reconciles local observations of Fe stress in diazotroph communities with an inferred spatial coupling of N sources and sinks. Within this regime of intermediate Fe control, the oceanic N reservoir would respond only weakly to enhanced dust fluxes during glacial climates, but strongly to the reduced fluxes hypothesized under anthropogenic climate warming.
Generalization of Brownian Motion with Autoregressive Increments
Fendick, Kerry
2011-01-01
This paper introduces a generalization of Brownian motion with continuous sample paths and stationary, autoregressive increments. This process, which we call a Brownian ray with drift, is characterized by three parameters quantifying distinct effects of drift, volatility, and autoregressiveness. A Brownian ray with drift, conditioned on its state at the beginning of an interval, is another Brownian ray with drift over the interval, and its expected path over the interval is a ray with a slope that depends on the conditioned state. This paper shows how Brownian rays can be applied in finance for the analysis of queues or inventories and the valuation of options. We model a queue's net input process as a superposition of Brownian rays with drift and derive the transient distribution of the queue length conditional on past queue lengths and on past states of the individual Brownian rays comprising the superposition. The transient distributions of Regulated Brownian Motion and of the Regulated Brownian Bridge are...
Harmonic functions on Walsh's Brownian motion
Jehring, Kristin Elizabeth
2009-01-01
In this dissertation we examine a variation of two- dimensional Brownian motion introduced in 1978 by Walsh. Walsh's Brownian motion can be described as a Brownian motion on the spokes of a (rimless) bicycle wheel. We will construct such a process by randomly assigning an angle to the excursions of a reflecting Brownian motion from 0. With this construction we see that Walsh's Brownian motion in R² behaves like one-dimensional Brownian motion away from the origin, but at the origin behaves di...
Quantum Limits to Optical Point-Source Localization
Tsang, Mankei
2014-01-01
Many superresolution microscopic techniques rely on the accurate localization of optical point sources from far field. To investigate the fundamental limits to their resolution, here I derive measurement-independent quantum lower bounds on the error of locating point sources in free space, taking full account of the quantum, nonparaxial, and vectoral nature of photons. To arrive at analytic results, I focus mainly on the cases of one and two classical monochromatic sources with an initial vacuum optical state. For one source, a lower bound on the root-mean-square position estimation error is on the order of $\\lambda_0/\\sqrt{N}$, where $\\lambda_0$ is the free-space wavelength and $N$ is the average number of radiated photons. For two sources, owing to a nuisance parameter effect, the error bound diverges when their radiated fields overlap significantly. The use of squeezed light to further enhance the accuracy of locating one point source is also discussed.
On the weak convergence of super-Brownian motion with immigration
Institute of Scientific and Technical Information of China (English)
2009-01-01
We prove fluctuation limit theorems for the occupation times of super-Brownian motion with immigration. The weak convergence of the processes is established, which improves the results in references. The limiting processes are Gaussian processes.
Arithmetic area for m planar Brownian paths
Desbois, Jean
2012-01-01
We pursue the analysis made in [1] on the arithmetic area enclosed by m closed Brownian paths. We pay a particular attention to the random variable S{n1,n2, ...,n} (m) which is the arithmetic area of the set of points, also called winding sectors, enclosed n1 times by path 1, n2 times by path 2, ...,nm times by path m. Various results are obtained in the asymptotic limit m->infinity. A key observation is that, since the paths are independent, one can use in the m paths case the SLE information, valid in the 1-path case, on the 0-winding sectors arithmetic area.
Arithmetic area for m planar Brownian paths
Desbois, Jean; Ouvry, Stephane
2012-01-01
We pursue the analysis made in [1] on the arithmetic area enclosed by m closed Brownian paths. We pay a particular attention to the random variable S{n1,n2, ...,n} (m) which is the arithmetic area of the set of points, also called winding sectors, enclosed n1 times by path 1, n2 times by path 2, ...,nm times by path m. Various results are obtained in the asymptotic limit m->infinity. A key observation is that, since the paths are independent, one can use in the m paths case the SLE informatio...
Effect of interfaces on the nearby Brownian motion
Huang, Kai
2016-01-01
Near-boundary Brownian motion is a classic hydrodynamic problem of great importance in a variety of fields, from biophysics to micro-/nanofluidics. However, due to challenges in experimental measurements of near-boundary dynamics, the effect of interfaces on Brownian motion has remained elusive. Here, we report a computational study of this effect using microsecond-long large-scale molecular dynamics simulations and our newly developed Green-Kubo relation for friction at the liquid-solid interface. Our computer experiment unambiguously reveals that the t^(-3/2) long-time decay of the velocity autocorrelation function of a Brownian particle in bulk liquid is replaced by a t^(-5/2) decay near a boundary. We discover a general breakdown of traditional no-slip boundary condition at short time scales and we show that this breakdown has a profound impact on the near-boundary Brownian motion. Our results demonstrate the potential of Brownian-particle based micro-/nano-sonar to probe the local wettability of liquid-s...
Entropic forces in Brownian motion
Roos, Nico
2013-01-01
The interest in the concept of entropic forces has risen considerably since E. Verlinde proposed to interpret the force in Newton s second law and Gravity as entropic forces. Brownian motion, the motion of a small particle (pollen) driven by random impulses from the surrounding molecules, may be the first example of a stochastic process in which such forces are expected to emerge. In this note it is shown that at least two types of entropic motion can be identified in the case of 3D Brownian motion (or random walk). This yields simple derivations of known results of Brownian motion, Hook s law and, applying an external (nonradial) force, Curie s law and the Langevin-Debye equation.
Brownian movement and molecular reality
Perrin, Jean
2005-01-01
How do we know that molecules really exist? An important clue came from Brownian movement, a concept developed in 1827 by botanist Robert Brown, who noticed that tiny objects like pollen grains shook and moved erratically when viewed under a microscope. Nearly 80 years later, in 1905, Albert Einstein explained this ""Brownian motion"" as the result of bombardment by molecules. Einstein offered a quantitative explanation by mathematically estimating the average distance covered by the particles over time as a result of molecular bombardment. Four years later, Jean Baptiste Perrin wrote Brownia
STOCHASTIC INTEGRATION FOR TEMPERED FRACTIONAL BROWNIAN MOTION.
Meerschaert, Mark M; Sabzikar, Farzad
2014-07-01
Tempered fractional Brownian motion is obtained when the power law kernel in the moving average representation of a fractional Brownian motion is multiplied by an exponential tempering factor. This paper develops the theory of stochastic integrals for tempered fractional Brownian motion. Along the way, we develop some basic results on tempered fractional calculus. PMID:24872598
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.
The maximum of Brownian motion with parabolic drift
Janson, Svante; Louchard, Guy; Martin-Löf, Anders
2010-01-01
We study the maximum of a Brownian motion with a parabolic drift; this is a random variable that often occurs as a limit of the maximum of discrete processes whose expectations have a maximum at an interior point. We give new series expansions and integral formulas for the distribution and the first two moments, together with numerical values to high precision.
Fuzzy Itand#244; Integral Driven by a Fuzzy Brownian Motion
Didier Kumwimba Seya; Rostin Mabela Makengo; Marcel Rémon; Walo Omana Rebecca
2015-01-01
In this paper we take into account the fuzzy stochastic integral driven by fuzzy Brownian motion. To define the metric between two fuzzy numbers and to take into account the limit of a sequence of fuzzy numbers, we invoke the Hausdorff metric. First this fuzzy stochastic integral is constructed for fuzzy simple stochastic functions, then the construction is done for fuzzy stochastic integrable functions.
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 ...
Pushing BitTorrent Locality to the Limit
Blond, Stevens Le; Dabbous, Walid; 10.1016/j.comnet.2010.09.014
2010-01-01
Peer-to-peer (P2P) locality has recently raised a lot of interest in the community. Indeed, whereas P2P content distribution enables financial savings for the content providers, it dramatically increases the traffic on inter-ISP links. To solve this issue, the idea to keep a fraction of the P2P traffic local to each ISP was introduced a few years ago. Since then, P2P solutions exploiting locality have been introduced. However, several fundamental issues on locality still need to be explored. In particular, how far can we push locality, and what is, at the scale of the Internet, the reduction of traffic that can be achieved with locality? In this paper, we perform extensive experiments on a controlled environment with up to 10,000 BitTorrent clients to evaluate the impact of high locality on inter-ISP links traffic and peers download completion time. We introduce two simple mechanisms that make high locality possible in challenging scenarios and we show that we save up to several orders of magnitude inter-ISP ...
Role of Brownian motion on the thermal conductivity enhancement of nanofluids
Gupta, Amit; Kumar, Ranganathan
2007-11-01
This study involves Brownian dynamics simulations of a real nanofluid system in which the interparticle potential is determined based on Debye length and surface interaction of the fluid and the solid. This paper shows that Brownian motion can increase the thermal conductivity of the nanofluid by 6% primarily due to "random walk" motion and not only through diffusion. This increase is limited by the maximum concentration for each particle size and is below that predicted by the effective medium theory. Beyond the maximum limit, particle aggregates begin to form. Brownian motion contribution stays as a constant beyond a certain particle diameter.
Pushing BitTorrent Locality to the Limit
Blond, Stevens Le; Dabbous, Walid
2008-01-01
Peer-to-peer locality has recently raised a lot of interest in the community. Indeed, whereas peer-to-peer content distribution enables financial saving for the content providers who do not have to maintain a dedicated infrastructure, it dramatically increases the traffic on inter-ISP links. To solve this issue, the idea to keep a fraction of the peer-to-peer traffic local to each ISP was introduced a few years ago. Since then, peer-to-peer solutions exploiting locality have been introduced. However, several fundamental issues on locality still need to be explored. For instance, how far can we push locality for a peer-to-peer distribution without impacting its robustness? In this paper, we perform extensive experiments on a controlled environment with up to 10 000 peers to evaluate the impact of locality on inter-ISP links traffic and peers download completion time. In particular, we show that high locality values enable up to two orders of magnitude saving on inter-ISP links without any significant impact on...
Moderate deviations for the quenched mean of the super-Brownian motion with random immigration
Institute of Scientific and Technical Information of China (English)
2008-01-01
Moderate deviations for the quenched mean of the super-Brownian motion with random immigration are proved for 3≤d≤6, which fills in the gap between central limit theorem(CLT)and large deviation principle(LDP).
Estimation of cavitation limits from local head loss coefficient
Sánchez Calvo, Raúl; Juana Sirgado, Luis; Laguna Peñuelas, Francisco; Rodríguez Sinobas, Leonor
2008-01-01
Cavitation effects in valves and other sudden transitions in water distribution systems are studied as their better understanding and quantification is needed for design and analysis purposes and for predicting and controlling their operation. Two dimensionless coefficients are used to characterize and verify local effects under cavitating flow conditions: the coefficient of local head losses and the minimum value of the cavitation number. In principle, both coefficients must be determined ex...
Stochastic description of quantum Brownian dynamics
Yan, Yun-An; Shao, Jiushu
2016-08-01
Classical Brownian motion has well been investigated since the pioneering work of Einstein, which inspired mathematicians to lay the theoretical foundation of stochastic processes. A stochastic formulation for quantum dynamics of dissipative systems described by the system-plus-bath model has been developed and found many applications in chemical dynamics, spectroscopy, quantum transport, and other fields. This article provides a tutorial review of the stochastic formulation for quantum dissipative dynamics. The key idea is to decouple the interaction between the system and the bath by virtue of the Hubbard-Stratonovich transformation or Itô calculus so that the system and the bath are not directly entangled during evolution, rather they are correlated due to the complex white noises introduced. The influence of the bath on the system is thereby defined by an induced stochastic field, which leads to the stochastic Liouville equation for the system. The exact reduced density matrix can be calculated as the stochastic average in the presence of bath-induced fields. In general, the plain implementation of the stochastic formulation is only useful for short-time dynamics, but not efficient for long-time dynamics as the statistical errors go very fast. For linear and other specific systems, the stochastic Liouville equation is a good starting point to derive the master equation. For general systems with decomposable bath-induced processes, the hierarchical approach in the form of a set of deterministic equations of motion is derived based on the stochastic formulation and provides an effective means for simulating the dissipative dynamics. A combination of the stochastic simulation and the hierarchical approach is suggested to solve the zero-temperature dynamics of the spin-boson model. This scheme correctly describes the coherent-incoherent transition (Toulouse limit) at moderate dissipation and predicts a rate dynamics in the overdamped regime. Challenging problems
Radiation Reaction on Brownian Motions
Seto, Keita
2016-01-01
Tracking the real trajectory of a quantum particle is one of the interpretation problem and it is expressed by the Brownian (stochastic) motion suggested by E. Nelson. Especially the dynamics of a radiating electron, namely, radiation reaction which requires us to track its trajectory becomes important in the high-intensity physics by PW-class lasers at present. It has been normally treated by the Furry picture in non-linear QED, but it is difficult to draw the real trajectory of a quantum particle. For the improvement of this, I propose the representation of a stochastic particle interacting with fields and show the way to describe radiation reaction on its Brownian motion.
Cooperative Transport of Brownian Particles
Derenyi, Imre; Vicsek, Tamas
1998-01-01
We consider the collective motion of finite-sized, overdamped Brownian particles (e.g., motor proteins) in a periodic potential. Simulations of our model have revealed a number of novel cooperative transport phenomena, including (i) the reversal of direction of the net current as the particle density is increased and (ii) a very strong and complex dependence of the average velocity on both the size and the average distance of the particles.
On two-dimensional fractional Brownian motion and fractional Brownian random field
Qian, Hong; Raymond, Gary M.; Bassingthwaighte, James B.
1998-01-01
As a generalization of one-dimensional fractional Brownian motion (1dfBm), we introduce a class of two-dimensional, self-similar, strongly correlated random walks whose variance scales with power law N2H (0 < H < 1). We report analytical results on the statistical size and shape, and segment distribution of its trajectory in the limit of large N. The relevance of these results to polymer theory is discussed. We also study the basic properties of a second generalization of 1dfBm, the two-dimen...
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.
Locality and the classical limit of quantum systems
Banks, T
2009-01-01
I argue that conventional estimates of the criterion for classical behavior of a macroscopic body are incorrect in most circumstances,because they do not take into account the locality of interactions, which characterizes the behavior of all systems described approximately by local quantum field theory. The deviations from classical behavior of a macroscopic body, except for those that can be described as classical uncertainties in the initial values of macroscopic variables,are {\\it exponentially} small as a function of the volume of the macro-system in microscopic units. Conventional estimates are correct only when the internal degrees of freedom of the macrosystem are in their ground state, and the classical motion of collective coordinates is adiabatic. Otherwise, the system acts as its own environment and washes out quantum phase correlations between different classical states of its collective coordinates. I suggest that it is likely that we can only achieve meso-scopic superpositions, for systems which...
POPULAR PARTICIPATION IN A LOCAL HEALTH COUNCIL: LIMITS AND POTENTIALS
Directory of Open Access Journals (Sweden)
Juliano de Amorim Busana
2015-01-01
Full Text Available Este estudio cualitativo tuvo como objetivo analizar el potencial y los límites de la participación popular en los Consejos Locales de Salud, a través del Itinerario de Investigación Paulo Freire. El estudio incluyó once miembros de un Consejo Local de Salud del municipio de Santa Catarina. Habían cinco Círculos de Cultura y de la investigación revelaron seis temas: Probabilidad de ciudadanía; Establecimiento de un espacio educativo; Toma de decisiones la intencionalidad que representa a la comunidad; Desconocimiento de las responsabilidades de lo Consejo; Exigüidad de participación de la comunitaria y Descrédito. Los resultados apuntan a la necesidad de comprender los roles de los concejales y Juntas Locales de Salud para fortalecer las acciones de promoción de la salud basadas en las ideas y el intercambio de experiencias entre los participantes del Consejo se dio cuenta de la creación de zonas de diálogo y la comprensión del ejercicio del poder mediante el fortalecimiento de los participantes al dialogicidad en estas áreas públicas.
G- Brownian motion and Its Applications
EBRAHIMBEYGI, Atena; DASTRANJ, Elham
2015-01-01
Abstract. The concept of G-Brownian motion and G-Ito integral has been introduced by Peng. Also Ito isometry lemma is proved for Ito integral and Brownian motion. In this paper we first investigate the Ito isometry lemma for G-Brownian motion and G-Ito Integral. Then after studying of MG2,0-class functions [4], we introduce Stratonovich integral for G-Brownian motion,say G- Stratonovich integral. Then we present a special construction for G- Stratonovich integral.
Pricing European option under the time-changed mixed Brownian-fractional Brownian model
Guo, Zhidong; Yuan, Hongjun
2014-07-01
This paper deals with the problem of discrete time option pricing by a mixed Brownian-fractional subdiffusive Black-Scholes model. Under the assumption that the price of the underlying stock follows a time-changed mixed Brownian-fractional Brownian motion, we derive a pricing formula for the European call option in a discrete time setting.
Objectivisation In Simplified Quantum Brownian Motion Models
Directory of Open Access Journals (Sweden)
Jan Tuziemski
2015-02-01
Full Text Available The birth of objective properties from the subjective quantum world has been one of the key questions in the quantum-to-classical transition. Based on recent results in the field, we study it in a quantum mechanical model of a boson-boson interaction—quantum Brownian motion. Using various simplifications, we prove a formation for thermal environments of, so called, spectrum broadcast structures, responsible for perceived objectivity. In the quantum measurement limit we prove that this structure is always formed, providing the characteristic timescales. Including self-Hamiltonians of the environment, we show the exponential scaling of the effect with the size of the environment. Finally, in the full model we numerically study the influence of squeezing in the initial state of the environment, showing broader regions of formation than for non-squeezed thermal states.
Arithmetic area for m planar Brownian paths
International Nuclear Information System (INIS)
We pursue the analysis made in Desbois and Ouvry (2011 J. Stat. Mech. P05024) on the arithmetic area enclosed by m closed Brownian paths. We pay particular attention to the random variable Sn1,n2,...,nm(m), which is the arithmetic area of the set of points, also called winding sectors, enclosed n1 times by path 1, n2 times by path 2,..., and nm times by path m. Various results are obtained in the asymptotic limit m→∞. A key observation is that, since the paths are independent, one can use in the m-path case the SLE information, valid in the one-path case, on the zero-winding sectors arithmetic area
Arithmetic area for m planar Brownian paths
Desbois, Jean; Ouvry, Stéphane
2012-05-01
We pursue the analysis made in Desbois and Ouvry (2011 J. Stat. Mech. P05024) on the arithmetic area enclosed by m closed Brownian paths. We pay particular attention to the random variable Sn1, n2,..., nm(m), which is the arithmetic area of the set of points, also called winding sectors, enclosed n1 times by path 1, n2 times by path 2,..., and nm times by path m. Various results are obtained in the asymptotic limit m\\to \\infty . A key observation is that, since the paths are independent, one can use in the m-path case the SLE information, valid in the one-path case, on the zero-winding sectors arithmetic area.
Random Brownian scaling identities and splicing of Bessel processes
Pitman, Jim; Yor, Marc
1998-01-01
An identity in distribution due to Knight for Brownian motion is extended in two different ways: first by replacing the supremum of a reflecting Brownian motion by the range of an unreflected Brownian motion and second by replacing the reflecting Brownian motion by a recurrent Bessel process. Both extensions are explained in terms of random Brownian scaling transformations and Brownian excursions. The first extension is related to two different constructions of Itô’s law of ...
Localization of acoustic emission sources. Possibilities and limits
International Nuclear Information System (INIS)
It is necessary to dispose of a system capable of data acquisition and processing in real time. The coordinates of emissive sources must be calculated either immediately after the detection of information or after a brief storage time. Emphasis is laid on the various parameters liable to affect the measurement precision: transducers (type, selectivity, form of signal), threshold device (dynamics, influence on the precision), screening device (influence on the number of data received). Four-transducer patterns are now in common use: square, centred equilateral triangle, lozenge mesh ... Each geometry possesses zones of indetermination. The accuracy on the coordinates of the source varies according to the position of this source with respect to the four-transducer mesh, which leads to a case-by-case study of the arrangement and dimensions of the meshes placed on the structure to be observed. Detection and localization equipment must be designed as a whole system flexible and easy to adapt to any structure
International Nuclear Information System (INIS)
Using the analogy between brownian motion and Quantum Mechanics, we study the winding angle θ of planar brownian curves around a given point, say the origin O. In particular, we compute the characteristic function for the probability distribution of θ and recover Spitzer's law in the limit of infinitely large times. Finally, we study the (large) change in the winding angle distribution when we add a repulsive potential at the origin
Nonlinear Brownian motion - mean square displacement
Directory of Open Access Journals (Sweden)
W.Ebeling
2004-01-01
Full Text Available The stochastic dynamics of self-propelled Brownian particles is studied by means of the Langevin and the Fokker-Planck approach. We model the driving by a nonlinear friction function which has a negative part at small velocities, leading to active Brownian motion of the particles. The mean square displacement is estimated analytically and compared with numerical simulations.
The maximum of Brownian motion with parabolic drift (Extended abstract)
Janson, Svante; Louchard, Guy; Martin-Löf, Anders
2010-01-01
We study the maximum of a Brownian motion with a parabolic drift; this is a random variable that often occurs as a limit of the maximum of discrete processes whose expectations have a maximum at an interior point. This has some applications in algorithmic and data structures analysis. We give series expansions and integral formulas for the distribution and the first two moments, together with numerical values to high precision.
Ideal bulk pressure of active Brownian particles
Speck, Thomas; Jack, Robert L.
2016-06-01
The extent to which active matter might be described by effective equilibrium concepts like temperature and pressure is currently being discussed intensely. Here, we study the simplest model, an ideal gas of noninteracting active Brownian particles. While the mechanical pressure exerted onto confining walls has been linked to correlations between particles' positions and their orientations, we show that these correlations are entirely controlled by boundary effects. We also consider a definition of local pressure, which describes interparticle forces in terms of momentum exchange between different regions of the system. We present three pieces of analytical evidence which indicate that such a local pressure exists, and we show that its bulk value differs from the mechanical pressure exerted on the walls of the system. We attribute this difference to the fact that the local pressure in the bulk does not depend on boundary effects, contrary to the mechanical pressure. We carefully examine these boundary effects using a channel geometry, and we show a virial formula for the pressure correctly predicts the mechanical pressure even in finite channels. However, this result no longer holds in more complex geometries, as exemplified for a channel that includes circular obstacles.
Figlio, David N.; O'Sullivan, Arthur
2001-01-01
This paper provides evidence that some cities subject to a statewide tax limit manipulate their mix of productive and administrative services in an attempt to get voters to override the statewide limit. When a statewide limit reduces a city's budget, one manipulative response is to cut "service" inputs (for example, teachers or uniformed police officers) by a relatively large amount, while cutting administrative inputs by a relatively small amount. This approach reveals a relatively large tra...
Combinatorial fractal Brownian motion model
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
To solve the problem of how to determine the non-scaled interval when processing radar clutter using fractal Brownian motion (FBM) model, a concept of combinatorial FBM model is presented. Since the earth (or sea) surface varies diversely with space, a radar clutter contains several fractal structures, which coexist on all scales. Taking the combination of two FBMs into account, via theoretical derivation we establish a combinatorial FBM model and present a method to estimate its fractal parameters. The correctness of the model and the method is proved by simulation experiments and computation of practial data. Furthermore, we obtain the relationship between fractal parameters when processing combinatorial model with a single FBM model. Meanwhile, by theoretical analysis it is concluded that when combinatorial model is observed on different scales, one of the fractal structures is more obvious.
Limit load analysis for local wall-thinning steam generator tubes
International Nuclear Information System (INIS)
Steam generator(SG) tubes form approximately 80% of pressure boundary of the reactor primary coolant[1]. During the past 40 years, a large number of operating PWPs have experienced degradation due to local wall-thinning of SG tubes, which was caused by corrosion or squeezing of tubes at support plate or tubesheet intersections or other reasons. This paper introduced the study of experiment and numerical analyses for plastic limit loads of local wall-thinning SG tubes. The effect of the dimension of local wall-thinning on plastic limit load was analyzed. The main contents in this paper were summarized as follows: 1 Experiment equipment which could test not only bursting pressure but also plastic limit load was built. Two kinds of local wall-thinning shapes were respectively made on SG tubes. One kind of local wall-thinning shape was rectangle-like flaw, which was used to simulate local wall-thinning caused by squeezing of tubes at support plate. The other kind of local wall-thinning shape was arc-like flaw, which was used to simulate local wall-thinning caused by corrosion. Different size local wall-thinning SG tubes of these two kinds of shape were test by using the equipment. 2 Regularization method for local wall-thinning defect was provided based on experimental and finite element method. 3 The effect order of local wall-thinning configuration on plastic limit load was studied. It was found that: Except defect thickness, the longitudinal length and circumferential length of SGT defect can also influence the plastic limit load; When the longitudinal length of SGT defect exceeded 6 mm, the effect of longitudinal length on plastic limit load can be ignored; When the circumferential angle of defect exceed 45 degree, the effect of circumferential angle on plastic limit load can be ignored. (authors)
Blending Brownian motion and heat equation
Cristiani, Emiliano
2015-01-01
In this short communication we present an original way to couple the Brownian motion and the heat equation. More in general, we suggest a way for coupling the Langevin equation for a particle, which describes a single realization of its trajectory, with the associated Fokker-Planck equation, which instead describes the evolution of the particle's probability density function. Numerical results show that it is indeed possible to obtain a regularized Brownian motion and a Brownianized heat equation still preserving the global statistical properties of the solutions. The results also suggest that the more macroscale leads the dynamics the more one can reduce the microscopic degrees of freedom.
Renewal Structure of the Brownian Taut String
Schertzer, Emmanuel
2015-01-01
In a recent paper, M. Lifshits and E. Setterqvist introduced the taut string of a Brownian motion $w$, defined as the function of minimal quadratic energy on $[0,T]$ staying in a tube of fixed width $h>0$ around $w$. The authors showed a Law of Large Number (L.L.N.) for the quadratic energy spent by the string for a large time $T$. In this note, we exhibit a natural renewal structure for the Brownian taut string, which is directly related to the time decomposition of the Brownian motion in te...
Amoeba-inspired nanoarchitectonic computing implemented using electrical Brownian ratchets.
Aono, M; Kasai, S; Kim, S-J; Wakabayashi, M; Miwa, H; Naruse, M
2015-06-12
In this study, we extracted the essential spatiotemporal dynamics that allow an amoeboid organism to solve a computationally demanding problem and adapt to its environment, thereby proposing a nature-inspired nanoarchitectonic computing system, which we implemented using a network of nanowire devices called 'electrical Brownian ratchets (EBRs)'. By utilizing the fluctuations generated from thermal energy in nanowire devices, we used our system to solve the satisfiability problem, which is a highly complex combinatorial problem related to a wide variety of practical applications. We evaluated the dependency of the solution search speed on its exploration parameter, which characterizes the fluctuation intensity of EBRs, using a simulation model of our system called 'AmoebaSAT-Brownian'. We found that AmoebaSAT-Brownian enhanced the solution searching speed dramatically when we imposed some constraints on the fluctuations in its time series and it outperformed a well-known stochastic local search method. These results suggest a new computing paradigm, which may allow high-speed problem solving to be implemented by interacting nanoscale devices with low power consumption.
Bradetich, Ryan; Dearien, Jason A; Grussling, Barry Jakob; Remaley, Gavin
2013-11-05
The present disclosure provides systems and methods for remote device management. According to various embodiments, a local intelligent electronic device (IED) may be in communication with a remote IED via a limited bandwidth communication link, such as a serial link. The limited bandwidth communication link may not support traditional remote management interfaces. According to one embodiment, a local IED may present an operator with a management interface for a remote IED by rendering locally stored templates. The local IED may render the locally stored templates using sparse data obtained from the remote IED. According to various embodiments, the management interface may be a web client interface and/or an HTML interface. The bandwidth required to present a remote management interface may be significantly reduced by rendering locally stored templates rather than requesting an entire management interface from the remote IED. According to various embodiments, an IED may comprise an encryption transceiver.
Brownian relaxation of an inelastic sphere in air
Bird, G. A.
2016-06-01
The procedures that are used to calculate the forces and moments on an aerodynamic body in the rarefied gas of the upper atmosphere are applied to a small sphere of the size of an aerosol particle at sea level. While the gas-surface interaction model that provides accurate results for macroscopic bodies may not be appropriate for bodies that are comprised of only about a thousand atoms, it provides a limiting case that is more realistic than the elastic model. The paper concentrates on the transfer of energy from the air to an initially stationary sphere as it acquires Brownian motion. Individual particle trajectories vary wildly, but a clear relaxation process emerges from an ensemble average over tens of thousands of trajectories. The translational and rotational energies in equilibrium Brownian motion are determined. Empirical relationships are obtained for the mean translational and rotational relaxation times, the mean initial power input to the particle, the mean rates of energy transfer between the particle and air, and the diffusivity. These relationships are functions of the ratio of the particle mass to an average air molecule mass and the Knudsen number, which is the ratio of the mean free path in the air to the particle diameter. The ratio of the molecular radius to the particle radius also enters as a correction factor. The implications of Brownian relaxation for the second law of thermodynamics are discussed.
Local Central Limit Theorem for diffusions in a degenerate and unbounded Random Medium
Chiarini, Alberto; Deuschel, Jean-Dominique
2015-01-01
We study a symmetric diffusion $X$ on $\\mathbb{R}^d$ in divergence form in a stationary and ergodic environment, with measurable unbounded and degenerate coefficients. We prove a quenched local central limit theorem for $X$, under some moment conditions on the environment; the key tool is a local parabolic Harnack inequality obtained with Moser iteration technique.
Local Environmental Dependence of Galaxy Properties in a Volume-Limited Sample of Main Galaxies
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Using a volume-limited sample of Main Galaxies from SDSS Data Release 5, we investigate the dependence of galaxy properties on local environment. For each galaxy, a local three-dimensional density is calculated. We find that the galaxy morphological type depends strongly on the local environment: galaxies in dense environments have predominantly early type morphologies. Galaxy colors have only a weak dependence on the environment. This puts an important constraint on the process of galaxy formation.
Brownian dipole rotator in alternating electric field
Rozenbaum, V. M.; Vovchenko, O. Ye.; Korochkova, T. Ye.
2008-06-01
The study addresses the azimuthal jumping motion of an adsorbed polar molecule in a periodic n -well potential under the action of an external alternating electric field. Starting from the perturbation theory of the Pauli equation with respect to the weak field intensity, explicit analytical expressions have been derived for the time dependence of the average dipole moment as well as the frequency dependences of polarizability and the average angular velocity, the three quantities exhibiting conspicuous stochastic resonance. As shown, unidirectional rotation can arise only provided simultaneous modulation of the minima and maxima of the potential by an external alternating field. For a symmetric potential of hindered rotation, the average angular velocity, if calculated by the second-order perturbation theory with respect to the field intensity, has a nonzero value only at n=2 , i.e., when two azimuthal wells specify a selected axis in the system. Particular consideration is given to the effect caused by the asymmetry of the two-well potential on the dielectric loss spectrum and other Brownian motion parameters. When the asymmetric potential in a system of dipole rotators arises from the average local fields induced by an orientational phase transition, the characteristics concerned show certain peculiarities which enable detection of the phase transition and determination of its parameters.
Brownian dipole rotator in alternating electric field.
Rozenbaum, V M; Vovchenko, O Ye; Korochkova, T Ye
2008-06-01
The study addresses the azimuthal jumping motion of an adsorbed polar molecule in a periodic n -well potential under the action of an external alternating electric field. Starting from the perturbation theory of the Pauli equation with respect to the weak field intensity, explicit analytical expressions have been derived for the time dependence of the average dipole moment as well as the frequency dependences of polarizability and the average angular velocity, the three quantities exhibiting conspicuous stochastic resonance. As shown, unidirectional rotation can arise only provided simultaneous modulation of the minima and maxima of the potential by an external alternating field. For a symmetric potential of hindered rotation, the average angular velocity, if calculated by the second-order perturbation theory with respect to the field intensity, has a nonzero value only at n=2 , i.e., when two azimuthal wells specify a selected axis in the system. Particular consideration is given to the effect caused by the asymmetry of the two-well potential on the dielectric loss spectrum and other Brownian motion parameters. When the asymmetric potential in a system of dipole rotators arises from the average local fields induced by an orientational phase transition, the characteristics concerned show certain peculiarities which enable detection of the phase transition and determination of its parameters. PMID:18643221
Plastic limit load analysis for steam generator tubes with local wall-thinning
International Nuclear Information System (INIS)
This paper introduces the study of experimental and numerical analysis for plastic limit loads of Inconel 690 steam generators (SG) tubes with local wall-thinning defects. Meanwhile, the effect of the three dimensions of a local wall-thinning defect on the plastic limit load of SG tubes is analyzed. A test facility which can test both burst pressure and plastic limit load of SG tubes was established and SG tubes with 3 typical types of defects were tested by using the facility. A regularization method for local wall-thinning defect is proposed and the finite element method was used to analyze the plastic limit load of SG tubes with defects. Compared with the experimental results of SG tubes with real defects, the calculated values of plastic limit load for SG tubes with regularized defects are conservative. Based on finite element method, the effect of the three dimensions of local wall-thinning defects on plastic limit loads of defected Inconel 690 SG tubes has been got. The studied results show that the defect depth of a local wall-thinning defect is the main factor influencing the plastic limit load of SG tubes, on the other hand, both the longitudinal length and the circumferential length of a defect have effect on the plastic limit load of SG tubes. It is found that in some cases, when the longitudinal length and the circumferential angle of a local wall-thinning defect exceed some extent, the effect of the longitudinal length and the circumferential angle on plastic limit load can be ignored.
Engineered swift equilibration of a Brownian particle
Martínez, Ignacio A.; Petrosyan, Artyom; Guéry-Odelin, David; Trizac, Emmanuel; Ciliberto, Sergio
2016-09-01
A fundamental and intrinsic property of any device or natural system is its relaxation time τrelax, which is the time it takes to return to equilibrium after the sudden change of a control parameter. Reducing τrelax is frequently necessary, and is often obtained by a complex feedback process. To overcome the limitations of such an approach, alternative methods based on suitable driving protocols have been recently demonstrated, for isolated quantum and classical systems. Their extension to open systems in contact with a thermostat is a stumbling block for applications. Here, we design a protocol, named Engineered Swift Equilibration (ESE), that shortcuts time-consuming relaxations, and we apply it to a Brownian particle trapped in an optical potential whose properties can be controlled in time. We implement the process experimentally, showing that it allows the system to reach equilibrium 100 times faster than the natural equilibration rate. We also estimate the increase of the dissipated energy needed to get such a time reduction. The method paves the way for applications in micro- and nano-devices, where the reduction of operation time represents as substantial a challenge as miniaturization.
Coulomb Friction Driving Brownian Motors
International Nuclear Information System (INIS)
We review a family of models recently introduced to describe Brownian motors under the influence of Coulomb friction, or more general non-linear friction laws. It is known that, if the heat bath is modeled as the usual Langevin equation (linear viscosity plus white noise), additional non-linear friction forces are not sufficient to break detailed balance, i.e. cannot produce a motor effect. We discuss two possibile mechanisms to elude this problem. A first possibility, exploited in several models inspired to recent experiments, is to replace the heat bath's white noise by a “collisional noise”, that is the effect of random collisions with an external equilibrium gas of particles. A second possibility is enlarging the phase space, e.g. by adding an external potential which couples velocity to position, as in a Klein—Kramers equation. In both cases, non-linear friction becomes sufficient to achieve a non-equilibrium steady state and, in the presence of an even small spatial asymmetry, a motor effect is produced. (general)
Random functions via Dyson Brownian Motion: progress and problems
Wang, Gaoyuan; Battefeld, Thorsten
2016-09-01
We develope a computationally efficient extension of the Dyson Brownian Motion (DBM) algorithm to generate random function in C2 locally. We further explain that random functions generated via DBM show an unstable growth as the traversed distance increases. This feature restricts the use of such functions considerably if they are to be used to model globally defined ones. The latter is the case if one uses random functions to model landscapes in string theory. We provide a concrete example, based on a simple axionic potential often used in cosmology, to highlight this problem and also offer an ad hoc modification of DBM that suppresses this growth to some degree.
Random Functions via Dyson Brownian Motion: Progress and Problems
Wang, Gaoyuan
2016-01-01
We develope a computationally efficient extension of the Dyson Brownian Motion (DBM) algorithm to generate random function in C2 locally. We further explain that random functions generated via DBM show an unstable growth as the traversed distance increases. This feature restricts the use of such functions considerably if they are to be used to model globally defined ones. The latter is the case if one used random functions to model landscapes in string theory. We provide a concrete example, based on a simple axionic potential often used in cosmology, to highlight this problem and also offer an ad hoc modification of DBM that suppresses this growth to some degree.
Plasmonic localized heating beyond the diffraction limit via magnetic polariton excitation
Alshehri, Hassan; Ying, Xiaoyan; Wang, Hao; Wang, Liping
2016-09-01
Optical localized heating in the nanoscale has recently attracted great attention due to its unique small hot spot size with high energy. However, the hot spot size is conventionally constrained by the diffraction limit. Plasmonic localized heating can provide solutions to this limitation in nanoscale patterning, cancer treatment, and data storage. Plasmonic approaches to overcome the diffraction limit in hot spot size have mainly utilized the excitation of surface plasmon or localized surface plasmon resonance. However, achieving plasmonic localized heating by the excitation of magnetic polariton has not been researched extensively yet. In this work, we numerically investigated the optical response of a nanoscale metamaterial composed of a gold nanowire array and a gold film separated by an ultrathin polymer spacer using ANSYS High Frequency Structural Simulator. A strong absorption peak at the wavelength of 760 nm was exhibited, and the underlying physical mechanism for the strong absorption was verified via the local electromagnetic field distribution to be magnetic resonance excitation. An inductor-capacitor circuit model was used to predict the magnetic resonance wavelength and compare with the numerical results for varied geometrical parameters. Volume loss density due to the strong local optical energy confinement was transferred as heat generation to an ANSYS thermal solver to obtain the local temperature profile. The steady state temperature profile shows an average temperature of 145 °C confined in a local area as small as 33 nm within the spacer, with a full-width at half-maximum of 50 nm along the x-direction. Moreover, the temperature rise from ambient drops to half its maximum value at a distance of 5 nm from the top of the spacer along the z-direction. This clearly demonstrates plasmonic localized heating beyond the diffraction limit via magnetic polariton excitation. Furthermore, the transient temperature profile shows that the system reached
Non-Linear Localized Modes Give Rise to a Reflective Optical Limiter
Makri, Eleana; Kottos, Tsampikos; Vitebskiy, Ilya
2013-01-01
Optical limiters are designed to transmit low intensity light, while blocking the light with excessively high intensity. A typical passive limiter absorbs excessive electromagnetic energy, which can cause its overheating and destruction. We propose the concept of a layered reflective limiter based on resonance transmission via a non-linear localized mode. Such a limiter does not absorb the high level radiation, but rather reflects it back to space. Importantly, the total reflection occurs within a broad frequency range and for an arbitrary direction of incidence. The same concept can be applied to infrared and microwave frequencies.
Holographic Brownian Motion in Three-Dimensional Gödel Black Hole
International Nuclear Information System (INIS)
By using the AdS/CFT correspondence and Gödel black hole background, we study the dynamics of heavy quark under a rotating plasma. In that case we follow Atmaja (2013) about Brownian motion in BTZ black hole. In this paper we receive some new results for the case of α2l2≠1. In this case, we must redefine the angular velocity of string fluctuation. We obtain the time evolution of displacement square and angular velocity and show that it behaves as a Brownian particle in non relativistic limit. In this plasma, it seems that relating the Brownian motion to physical observables is rather a difficult work. But our results match with Atmaja work in the limit α2l2→1
Ribeiro, Nuno A; Jorge, Susana M.
2013-01-01
In order to keep local public finances balanced, in many countries, measures restraining and controlling debt have been implemented. In Portugal such concerns have been considered too. Accordingly, several legal diplomas have been passed, namely local finances laws, defining rules, mainly related to limits and restrictions to interest, repayments of borrowings, as well as net debt level. Therefore, it should be expected that these legal restrictions would contribute to reduce municipal deb...
Severino Romano; Francesco Marangon; Roberto Polidori
2011-01-01
The aim of this work is to analyse the role that typical products can play in the local development process. Territorial resources involved, limits and strategies for their enhancement are analysed; this analysis will permit both to define the results that have been achieved since nowadays in the local development process and to point out future themes for the research in the field of agricultural economics. The typicality of an agri-food product regards qualitative characteristics that deriv...
Kinetics of self-induced aggregation of Brownian particles: non-Markovian and non-Gaussian features
Ghosh, Pulak Kumar; Bag, Bidhan Chandra
2012-01-01
In this paper we have studied a model for self-induced aggregation in Brownian particle incorporating the non-Markovian and non-Gaussian character of the associated random noise process. In this model the time evolution of each individual is guided by an over-damped Langevin equation of motion with a non-local drift resulting from the local unbalance distributions of the other individuals. Our simulation result shows that colored nose can induce the cluster formation even at large noise strength. Another observation is that critical noise strength grows very rapidly with increase of noise correlation time for Gaussian noise than non Gaussian one. However, at long time limit the cluster number in aggregation process decreases with time following a power law. The exponent in the power law increases remarkable for switching from Markovian to non Markovian noise process.
Brownian motion and Harmonic functions on Sol(p,q)
Brofferio, Sara; Salvatori, Maura; Woess, Wolfgang
2012-01-01
The Lie group Sol(p,q) is the semidirect product induced by the action of the real numbers R on the plane R^2 which is given by (x,y) --> (exp{p z} x, exp{-q z} y), where z is in R. Viewing Sol(p,q) as a 3-dimensional manifold, it carries a natural Riemannian metric and Laplace-Beltrami operator. We add a linear drift term in the z-variable to the latter, and study the associated Brownian motion with drift. We derive a central limit theorem and compute the rate of escape. Also, we introduce t...
Brownian semistationary processes and volatility/intermittency
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Schmiegel, Jürgen
A new class of stochastic processes, termed Brownian semistationary processes (BSS), is introduced and discussed. This class has similarities to that of Brownian semimartingales (BSM), but is mainly directed towards the study of stationary processes, and BSS processes are not in general of the...... turbulent velocity fields and is the purely temporal version of the general tempo-spatial framework of ambit processes. The latter, which may have applications also to the finance of energy markets, is briefly considered at the end of the paper, again with reference to the question of inference on the...
Generalized Einstein Relation for Brownian Motion in Tilted Periodic Potential
Sakaguchi, Hidetsugu
2006-01-01
A generalized Einstein relation is studied for Brownian motion in a tilted potential. The exact form of the diffusion constant of the Brownian motion is compared with the generalized Einstein relation. The generalized Einstein relation is a good approximation in a parameter range where the Brownian motion exhibits stepwise motion.
Quantum power source: putting in order of a Brownian motion without Maxwell's demon
Aristov, Vitaly V.; Nikulov, A. V.
2003-07-01
The problem of possible violation of the second law of thermodynamics is discussed. It is noted that the task of the well known challenge to the second law called Maxwell's demon is put in order a chaotic perpetual motion and if any ordered Brownian motion exists then the second law can be broken without this hypothetical intelligent entity. The postulate of absolute randomness of any Brownian motion saved the second law in the beginning of the 20th century when it was realized as perpetual motion. This postulate can be proven in the limits of classical mechanics but is not correct according to quantum mechanics. Moreover some enough known quantum phenomena, such as the persistent current at non-zero resistance, are an experimental evidence of the non-chaotic Brownian motion with non-zero average velocity. An experimental observation of a dc quantum power soruce is interperted as evidence of violation of the second law.
Building local human resources to implement SLMTA with limited donor funding: The Ghana experience
Directory of Open Access Journals (Sweden)
Bernard Nkrumah
2014-09-01
Full Text Available Background: In 2009, Ghana adopted the Strengthening Laboratory Management Toward Accreditation (SLMTA programme in order to improve laboratory quality. The programme was implemented successfully with limited donor funding and local human resources.Objectives: To demonstrate how Ghana, which received very limited PEPFAR funding, was able to achieve marked quality improvement using local human resources.Method: Local partners led the SLMTA implementation and local mentors were embedded in each laboratory. An in-country training-of-trainers workshop was conducted in order to increase the pool of local SLMTA implementers. Three laboratory cohorts were enrolled in SLMTA in 2011, 2012 and 2013. Participants from each cohort attended in a series of three workshops interspersed with improvement projects and mentorship. Supplemental trainingon internal audit was provided. Baseline, exit and follow-up audits were conducted using the Stepwise Laboratory Quality Improvement Process Towards Accreditation (SLIPTA checklist. In November 2013, four laboratories underwent official SLIPTA audits by the African Society for Laboratory Medicine (ASLM.Results: The local SLMTA team successfully implemented three cohorts of SLMTA in 15 laboratories. Seven out of the nine laboratories that underwent follow-up audits have reached at least one star. Three out of the four laboratories that underwent official ASLM audits were awarded four stars. Patient satisfaction increased from 25% to 70% and sample rejection rates decreased from 32% to 10%. On average, $40 000 was spent per laboratory to cover mentors’salaries, SLMTA training and improvement project support.Conclusion: Building in-country capacity through local partners is a sustainable model for improving service quality in resource-constrained countries such as Ghana. Such modelspromote country ownership, capacity building and the use of local human resources for the expansion of SLMTA.
Brownian particles in supramolecular polymer solutions
Gucht, van der J.; Besseling, N.A.M.; Knoben, W.; Bouteiller, L.; Cohen Stuart, M.A.
2003-01-01
The Brownian motion of colloidal particles embedded in solutions of hydrogen-bonded supramolecular polymers has been studied using dynamic light scattering. At short times, the motion of the probe particles is diffusive with a diffusion coefficient equal to that in pure solvent. At intermediate time
Brownian shape motion: Fission fragment mass distributions
Directory of Open Access Journals (Sweden)
Sierk Arnold J.
2012-02-01
Full Text Available It was recently shown that remarkably accurate fission-fragment mass distributions can be obtained by treating the nuclear shape evolution as a Brownian walk on previously calculated five-dimensional potential-energy surfaces; the current status of this novel method is described here.
Brownian coagulation at high particle concentrations
Trzeciak, T. M.
2012-01-01
The process of Brownian coagulation, whereby particles are brought together by thermal motion and grow by collisions, is one of the most fundamental processes influencing the final properties of particulate matter in a variety of technically important systems. It is of importance in colloids, emulsi
Brownian 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 ...
Chaos, Dissipation and Quantal Brownian Motion
Cohen, Doron
1999-01-01
Energy absorption by driven chaotic systems, the theory of energy spreading and quantal Brownian motion are considered. In particular we discuss the theory of a classical particle that interacts with quantal chaotic degrees of freedom, and try to relate it to the problem of quantal particle that interacts with an effective harmonic bath.
Ergodic Properties of Fractional Brownian-Langevin Motion
Deng, Weihua
2008-01-01
We investigate the time average mean square displacement $\\overline{\\delta^2}(x(t))=\\int_0^{t-\\Delta}[x(t^\\prime+\\Delta)-x(t^\\prime)]^2 dt^\\prime/(t-\\Delta)$ for fractional Brownian and Langevin motion. Unlike the previously investigated continuous time random walk model $\\overline{\\delta^2}$ converges to the ensemble average $ \\sim t^{2 H}$ in the long measurement time limit. The convergence to ergodic behavior is however slow, and surprisingly the Hurst exponent $H=3/4$ marks the critical point of the speed of convergence. When $H^2\\sim k(H) \\cdot\\Delta\\cdot t^{-1}$, when $H=3/4$, ${EB} \\sim (9/16)(\\ln t) \\cdot\\Delta \\cdot t^{-1}$, and when $3/4
Probing local order in glasses from limited-volume electron and x-ray diffraction
Liu, A. C. Y.; Tabor, R. F.; Bourgeois, L.; de Jonge, M. D.; Mudie, S. T.; Petersen, T. C.
2016-05-01
It has long been recognised that spatial fluctuations in local order in disordered assemblies of particles can be probed using limited-volume diffraction measurements. These measurements have unique advantages over broad-beam diffraction experiments that isotropically average over many structural configurations and result in one-dimensional intensity curves, requiring modelling to interpret. Despite the advantages of limiting illumination to a low number of particle configurations, obtaining quantitative measurements of local order from such experiments remains a challenge. The effects on the diffraction pattern of changing the beam energy, lateral size, aberrations and coherence and the specimen thickness have only recently been clarified. We review theoretical and experimental efforts in this direction in the fields of both electron and x-ray diffraction and identify promising areas of future development.
Time integration for particle Brownian motion determined through fluctuating hydrodynamics
Delmotte, Blaise
2015-01-01
Fluctuating hydrodynamics has been successfully combined with several computational methods to rapidly compute the correlated random velocities of Brownian particles. In the overdamped limit where both particle and fluid inertia are ignored, one must also account for a Brownian drift term in order to successfully update the particle positions. In this paper, we introduce and study a midpoint time integration scheme we refer to as the drifter-corrector (DC) that resolves the drift term for fluctuating hydrodynamics-based methods even when constraints are imposed on the fluid flow to obtain higher-order corrections to the particle hydrodynamic interactions. We explore this scheme in the context of the fluctuating force-coupling method (FCM) where the constraint is imposed on the rate-of-strain averaged over the volume occupied by the particle. For the DC, the constraint need only be imposed once per time step, leading to a significant reduction in computational cost with respect to other schemes. In fact, for f...
Manipulating nutrient limitation using modified local soils: A case study at Lake Taihu (China).
Wang, Lijing; Pan, Gang; Shi, Wenqing; Wang, Zhibin; Zhang, Honggang
2016-09-15
The effect of geo-engineering materials of chitosan modified local soil (MLS) on nutrient limitation was studied in comparable whole ponds in Lake Taihu in October 2013. After 20 kg MLS were sprayed in the whole water pond (400 m(2)), the chlorophyll-a (Chl-a) concentration was decreased from 42 to 18 μg L(-1) within 2 h and remained below 20 μg L(-1) in the following 15 months, while the average Chl-a was 36 μg L(-1) in the control pond throughout the experiment. In situ nutrient addition bioassay experiments indicated that the nutrient limitation was shifted from nitrogen (N) and phosphorus (P) co-limitation to P limitation after MLS treatment from October 2013 to March 2014 compared to the control pond. In the cyanobacterial bloom season of June 2014, N and P co-limitation remained and N was the primary limiting nutrient and P was a secondary one in the control pond where phytoplankton biomass showed significant increase by N addition and further increase by N + P additions, while both N and P became the limiting nutrient for phytoplankton growth where only combined N and P additions showed significant Chl-a stimulation in the treatment pond. In the next summer (June 2014), a cyanobacteria-dominated state still remained in the control pond but chlorophytes, bacillariophytes and cyanophytes distributed equally and submerged vegetation was largely restored in the treatment pond. Meanwhile, the upper limiting concentration of DIN was enhanced from 0.8 to 1.5 mg L(-1) and SRP from 0.1 to 0.3 mg L(-1) compared to the control pond. This study indicates that nutrient limitation can be manipulated by using MLS technology. PMID:27244294
Directory of Open Access Journals (Sweden)
Severino Romano
2011-02-01
Full Text Available The aim of this work is to analyse the role that typical products can play in the local development process. Territorial resources involved, limits and strategies for their enhancement are analysed; this analysis will permit both to define the results that have been achieved since nowadays in the local development process and to point out future themes for the research in the field of agricultural economics. The typicality of an agri-food product regards qualitative characteristics that derive from its tie with the territory, this tie becomes a relevant element for the differentiation of the typical product from the others. In this context, the typical product maintains all the specificities associated to its origin, involving also aspects related to the traditions and the culture of the territories, to the collective dimension and to the local knowledge. Consumers tent to look for good which are differentiated and to connect authenticity and local specificity of food with healthiness. Due to the strong socio-economic ties that typical products have with the territory, they play a crucial role in the economy of the local systems and can promote development in lagging areas.
Speckle Patterns and 2-Dimensional Brownian Motion
International Nuclear Information System (INIS)
We present the results of a Monte Carlo simulation of Brownian Motion on a 2-dimensional lattice with nearest-neighbor interactions described by a linear model. These nearest-neighbor interactions lead to a spatial variance structure on the lattice. The resulting Brownian pattern fluctuates in value from point to point in a manner characteristic of a stationary stochastic process. The value at a lattice point is interpreted as an intensity level. The difference in values in neighboring cells produces a fluctuating intensity pattern on the lattice. Changing the size of the mesh changes the relative size of the speckles. Increasing the mesh size tends to average out the intensity in the direction of the mean of the stationary process. (Author)
Modeling an efficient Brownian heat engine
Asfaw, Mesfin
2008-09-01
We discuss the effect of subdividing the ratchet potential on the performance of a tiny Brownian heat engine that is modeled as a Brownian particle hopping in a viscous medium in a sawtooth potential (with or without load) assisted by alternately placed hot and cold heat baths along its path. We show that the velocity, the efficiency and the coefficient of performance of the refrigerator maximize when the sawtooth potential is subdivided into series of smaller connected barrier series. When the engine operates quasistatically, we analytically show that the efficiency of the engine can not approach the Carnot efficiency and, the coefficient of performance of the refrigerator is always less than the Carnot refrigerator due to the irreversible heat flow via the kinetic energy.
Brownian particles in supramolecular polymer solutions
Gucht, van der, J.; Besseling, N.A.M.; Knoben, W.; Bouteiller, L; Cohen Stuart, M. A.
2003-01-01
The Brownian motion of colloidal particles embedded in solutions of hydrogen-bonded supramolecular polymers has been studied using dynamic light scattering. At short times, the motion of the probe particles is diffusive with a diffusion coefficient equal to that in pure solvent. At intermediate time scales the particles are slowed down as a result of trapping in elastic cages formed by the polymer chains, while at longer times the motion is diffusive again, but with a much smaller diffusion c...
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, emulsions, flocculation, air pollution, soot formation, materials manufacture and growth of interstellar dust, to name a few of its applications. With continuous progress in particulate matter processing...
Frustrated Brownian Motion of Nonlocal Solitary Waves
International Nuclear Information System (INIS)
We investigate the evolution of solitary waves in a nonlocal medium in the presence of disorder. By using a perturbational approach, we show that an increasing degree of nonlocality may largely hamper the Brownian motion of self-trapped wave packets. The result is valid for any kind of nonlocality and in the presence of nonparaxial effects. Analytical predictions are compared with numerical simulations based on stochastic partial differential equations.
Radiation Reaction for a Charged Brownian Particle
Vlasov, A A
2002-01-01
As it is known a model of a charged particle with finite size is a good tool to consider the effects of self- action and backreaction, caused by electromagnetic radiation. In this work the "size" of a charged particle is induced by its stochastic Brownian vibration. Appropriate equation of particle's motion with radiation force is derived. It is shown that the solutions of this equation correctly describe the effects of radiation reaction.
Intrinsic and extrinsic measurement for Brownian motion
International Nuclear Information System (INIS)
Based upon the Smoluchowski equation on curved manifolds, three physical observables are considered for Brownian displacement, namely geodesic displacement s, Euclidean displacement δR, and projected displacement δR⊥. The Weingarten–Gauss equations are used to calculate the mean-square Euclidean displacements in the short-time regime. Our findings show that from an extrinsic point of view the geometry of the space affects the Brownian motion in such a way that the particle’s diffusion is decelerated, contrasting with the intrinsic point of view where dynamics is controlled by the sign of the Gaussian curvature (Castro-Villarreal, 2010 J. Stat. Mech. P08006). Furthermore, it is possible to give exact formulas for 〈δR〉 and 〈δR2〉 on spheres and minimal surfaces, which are valid for all values of time. In the latter case, surprisingly, Brownian motion corresponds to the usual diffusion in flat geometries, albeit minimal surfaces have non-zero Gaussian curvature. Finally, the two-dimensional case is emphasized due to its close relation to surface self-diffusion in fluid membranes. (paper)
Evaluation of Brownian warps for shape alignment
Nielsen, Mads
2007-03-01
Many methods are used for warping images to non-rigidly register shapes and objects in between medical images in inter- and intra-patient studies. In landmark-based registration linear methods like thin-plate- or b-splines are often used. These linear methods suffer from a number of theoretical deficiencies: they may break or tear apart the shapes, they are not source-destination symmetric, and may not be invertible. Theoretically more satisfactory models using diffeomorphic approaches like "Large Deformations" and "Brownian warps" have earlier proved (in theory and practice) to remove these deficiencies. In this paper we show that the maximum-likelihood Brownian Warps also generalize better in the case of matching fractured vertebrae to normal vertebrae. X-rays of 10 fractured and 1 normal vertebrae have been annotated by a trained radiologist by 6 so-called height points used for fracture scoring, and by the full boundary. The fractured vertebrae have been registered to the normal vertebra using only the 6 height points as landmarks. After registration the Hausdorff distance between the boundaries is measured. The registrations based on Brownian warps show a significantly lower distance to the original boundary.
Dynamics of Brownian motors in deformable medium
Woulaché, Rosalie Laure; Kepnang Pebeu, Fabrice Maxime; Kofané, Timoléon C.
2016-10-01
The directed transport in a one-dimensional overdamped, Brownian motor subjected to a travelling wave potential with variable shape and exposed to an external bias is studied numerically. We focus our attention on the class of Remoissenet-Peyrard parametrized on-site potentials with slight modification, whose shape can be varied as a function of a parameter s, recovering the sine-Gordon shape as the special case. We demonstrate that in the presence of the travelling wave potential the observed dynamical properties of the Brownian motor which crucially depends on the travelling wave speed, the intensity of the noise and the external load is significantly influenced also by the geometry of the system. In particular, we notice that systems with sharp wells and broad barriers favour the transport under the influence of an applied load. The efficiency of transport of Brownian motors in deformable systems remains equal to 1 (in the absence of an applied load) up to a critical value of the travelling wave speed greater than that of the pure sine-Gordon shape.
Energy Technology Data Exchange (ETDEWEB)
Rossi, Tuomas P., E-mail: tuomas.rossi@alumni.aalto.fi; Sakko, Arto; Puska, Martti J. [COMP Centre of Excellence, Department of Applied Physics, Aalto University School of Science, P.O. Box 11100, FI-00076 Aalto (Finland); Lehtola, Susi, E-mail: susi.lehtola@alumni.helsinki.fi [COMP Centre of Excellence, Department of Applied Physics, Aalto University School of Science, P.O. Box 11100, FI-00076 Aalto (Finland); Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States); Nieminen, Risto M. [COMP Centre of Excellence, Department of Applied Physics, Aalto University School of Science, P.O. Box 11100, FI-00076 Aalto (Finland); Dean’s Office, Aalto University School of Science, P.O. Box 11000, FI-00076 Aalto (Finland)
2015-03-07
We present an approach for generating local numerical basis sets of improving accuracy for first-principles nanoplasmonics simulations within time-dependent density functional theory. The method is demonstrated for copper, silver, and gold nanoparticles that are of experimental interest but computationally demanding due to the semi-core d-electrons that affect their plasmonic response. The basis sets are constructed by augmenting numerical atomic orbital basis sets by truncated Gaussian-type orbitals generated by the completeness-optimization scheme, which is applied to the photoabsorption spectra of homoatomic metal atom dimers. We obtain basis sets of improving accuracy up to the complete basis set limit and demonstrate that the performance of the basis sets transfers to simulations of larger nanoparticles and nanoalloys as well as to calculations with various exchange-correlation functionals. This work promotes the use of the local basis set approach of controllable accuracy in first-principles nanoplasmonics simulations and beyond.
Voids in the Local Volume: a limit on appearance of a galaxy in a DM halo
Tikhonov, Anton V.; Klypin, Anatoly A.
2007-01-01
Current explanation of the overabundance of dark matter subhalos in the Local Group (LG) indicates that there maybe a limit on mass of a halo, which can host a galaxy. This idea can be tested using voids in the distribution of galaxies: at some level small voids should not contain any (even dwarf) galaxies. We use observational samples complete to M_B = -12 with distances less than 8 Mpc to construct the void function (VF): the distribution of sizes of voids empty of any galaxies. There are ~...
Phase space localization for anti-de Sitter quantum mechanics and its zero curvature limit
Elgradechi, Amine M.
1993-01-01
Using techniques of geometric quantization and SO(sub 0)(3,2)-coherent states, a notion of optimal localization on phase space is defined for the quantum theory of a massive and spinning particle in anti-de Sitter space time. It is shown that this notion disappears in the zero curvature limit, providing one with a concrete example of the regularizing character of the constant (nonzero) curvature of the anti-de Sitter space time. As a byproduct a geometric characterization of masslessness is obtained.
Momentum conserving Brownian dynamics propagator for complex soft matter fluids.
Padding, J T; Briels, W J
2014-12-28
We present a Galilean invariant, momentum conserving first order Brownian dynamics scheme for coarse-grained simulations of highly frictional soft matter systems. Friction forces are taken to be with respect to moving background material. The motion of the background material is described by locally averaged velocities in the neighborhood of the dissolved coarse coordinates. The velocity variables are updated by a momentum conserving scheme. The properties of the stochastic updates are derived through the Chapman-Kolmogorov and Fokker-Planck equations for the evolution of the probability distribution of coarse-grained position and velocity variables, by requiring the equilibrium distribution to be a stationary solution. We test our new scheme on concentrated star polymer solutions and find that the transverse current and velocity time auto-correlation functions behave as expected from hydrodynamics. In particular, the velocity auto-correlation functions display a long time tail in complete agreement with hydrodynamics. PMID:25554134
Collective Transport of Coupled Brownian Motors with Low Randomness
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The transport properties of coupled Brownian motors in rocking ratchet are investigated via solving single particle have been found. In the regime of low-to-moderate D, the average velocity of elastically coupled Brownian with the increase of a single Brownian motor. The results exhibit an interesting cooperative behavior between coupled particles subjected to a rocking force, which can generate directed transport with low randomness or high transport coherence in symmetrical periodic potential.
Application of Brownian model in the northwestern Beijing, China
Institute of Scientific and Technical Information of China (English)
冉洪流; 周本刚
2004-01-01
The mathematic theory of Brownian passage-time model and its difference from other recurrence models such asPoisson, lognormal, gamma and Weibull, were introduced. We assessed and analyzed the earthquake probabilitiesof the major faults with the elapsed time much greater than the recurrence interval in the northwest region of Beijing (China) in 100-year by using both Brownian passage-time model and Poisson model, and concluded that thecalculated results obtained from Brownian passage-time model is more reasonable.
RESEARCH NOTES On the support of super-Brownian motion with super-Brownian immigration
Institute of Scientific and Technical Information of China (English)
洪文明; 钟惠芳
2001-01-01
The support properties of the super Brownian motion with random immigration Xρ1 are considered,where the immigration rate is governed by the trajectory of another super-Brownian motion ρ. When both the initial state Xρo of the process and the immigration rate process ρo are of finite measure and with compact supports, the probability of the support of the process Xρi dominated by a ball is given by the solutions of a singular elliptic boundary value problem.
Energy Technology Data Exchange (ETDEWEB)
Plyukhin, A.V., E-mail: aplyukhin@anselm.edu [Department of Mathematics, Saint Anselm College, Manchester, NH 03102 (United States)
2013-06-03
A model of an autonomous isothermal Brownian motor with an internal propulsion mechanism is considered. The motor is a Brownian particle which is semi-transparent for molecules of surrounding ideal gas. Molecular passage through the particle is controlled by a potential similar to that in the transition rate theory, i.e. characterized by two stationary states with a finite energy difference separated by a potential barrier. The internal potential drop maintains the diode-like asymmetry of molecular fluxes through the particle, which results in the particle's stationary drift.
EFFECTIVE DIFFUSION AND EFFECTIVE DRAG COEFFICIENT OF A BROWNIAN PARTICLE IN A PERIODIC POTENTIAL
Institute of Scientific and Technical Information of China (English)
Hongyun Wang
2011-01-01
We study the stochastic motion of a Brownian particle driven by a constant force over a static periodic potential.We show that both the effective diffusion and the effective drag coefficient are mathematically well-defined and we derive analytic expressions for these two quantities.We then investigate the asymptotic behaviors of the effective diffusion and the effective drag coefficient,respectively,for small driving force and for large driving force.In the case of small driving force,the effective diffusion is reduced from its Brownian value by a factor that increases exponentially with the amplitude of the potential.The effective drag coefficient is increased by approximately the same factor.As a result,the Einstein relation between the diffusion coefficient and the drag coefficient is approximately valid when the driving force is small.For moderately large driving force,both the effective diffusion and the effective drag coefficient are increased from their Brownian values,and the Einstein relation breaks down. In the limit of very large driving force,both the effective diffusion and the effective drag coefficient converge to their Brownian values and the Einstein relation is once again valid.
The branching Brownian motion seen from its tip
Aïdékon, E; Brunet, É; Shi, Z
2011-01-01
Very recently, Arguin et al. have proved the conjecture (which can be found in the work of Lalley and Sellke) that the branching Brownian motion seen from its tip (e.g. from its rightmost particle) converges to an invariant point process. The main goal of the present work is to give a complete description of the limit object and an alternative proof of the convergence. As conjectured by Brunet and Derrida and proved by Arguin et al., the structure of this extremal point process turns out to be a certain Poisson point process with exponential intensity in which each atom has been decorated by an independent copy of an auxiliary point process. Here, we give an explicit construction of this decoration point process.
Blowup and Conditionings of $\\psi$-super Brownian Exit Measures
Athreya, Siva R
2011-01-01
We extend earlier results on conditioning of super-Brownian motion to general branching rules. We obtain representations of the conditioned process, both as an $h$-transform, and as an unconditioned superprocess with immigration along a branching tree. Unlike the finite-variance branching setting, these trees are no longer binary, and strictly positive mass can be created at branch points. This construction is singular in the case of stable branching. We analyze this singularity first by approaching the stable branching function via analytic approximations. In this context the singularity of the stable case can be attributed to blow up of the mass created at the first branch of the tree. Other ways of approaching the stable case yield a branching tree that is different in law. To explain this anomaly we construct a family of martingales whose backbones have multiple limit laws.
Brownian Motion and its Conditional Descendants
Garbaczewski, Piotr
It happened before [1] that I have concluded my publication with a special dedication to John R. Klauder. Then, the reason was John's PhD thesis [2] and the questions (perhaps outdated in the eyes of the band-wagon jumpers, albeit still retaining their full vitality [3]): (i) What are the uses of the classical (c-number, non-Grassmann) spinor fields, especially nonlinear ones, what are they for at all ? (ii) What are, if any, the classical partners for Fermi models and fields in particular ? The present dedication, even if not as conspicuously motivated as the previous one by John's research, nevertheless pertains to investigations pursued by John through the years and devoted to the analysis of random noise. Sometimes, re-reading old papers and re-analysing old, frequently forgotten ideas might prove more rewarding than racing the fashions. Following this attitude, let us take as the departure point Schrödinger's original suggestion [4] of the existence of a special class of random processes, which have their origin in the Einstein-Smoluchowski theory of the Brownian motion and its Wiener's codification. The original analysis due to Schrodinger of the probabilistic significance of the heat equation and of its time adjoint in parallel, remained unnoticed by the physics community, and since then forgotten. It reappeared however in the mathematical literature as an inspiration to generalise the concept of Markovian diffusions to the case of Bernstein stochastic processes. But, it stayed without consequences for a deeper understanding of the possible physical phenomena which might underly the corresponding abstract formalism. Schrödinger's objective was to initiate investigations of possible links between quantum theory and the theory of Brownian motion, an attempt which culminated later in the so-called Nelson's stochastic mechanics [8] and its encompassing formalism [7] in which the issue of the Brownian implementation of quantum dynamics is placed in the
Polar Functions of Multiparameter Bifractional Brownian Sheets
Institute of Scientific and Technical Information of China (English)
Zhen-long Chen
2009-01-01
Let BH,K={BH,K(t), t ∈RN+} be an (N,d)-bifractional Brownian sheet with Hurst indices for BH,Kare investigated. The relationship between the class of continuous functions satisfying the Lipschitz condition and the class of polar-functions of BH,Kis presented. The Hausdorff dimension of the fixed points and an inequality concerning the Kolmogorov's entropy index for BH,Kare obtained. A question proposed by LeGall about the existence of no-polar, continuous functions statisfying the Holder condition is also solved.
Effective diffusion of confined active Brownian swimmers
Sandoval, Mario; Dagdug, Leonardo
2014-11-01
We find theoretically the effect of confinement and thermal fluctuations, on the diffusivity of a spherical active swimmer moving inside a two-dimensional narrow cavity of general shape. The explicit formulas for the effective diffusion coefficient of a swimmer moving inside two particular cavities are presented. We also compare our analytical results with Brownian Dynamics simulations and we obtain excellent agreement. L.D. thanks Consejo Nacional de Ciencia y Tecnologia (CONACyT) Mexico, for partial support by Grant No. 176452. M. S. thanks CONACyT and Programa de Mejoramiento de Profesorado (PROMEP) for partially funding this work under Grant No. 103.5/13/6732.
LINEAR SEARCH FOR A BROWNIAN TARGET MOTION
Institute of Scientific and Technical Information of China (English)
A. B. El-Rayes; Abd El-Moneim A. Mohamed; Hamdy M. Abou Gabal
2003-01-01
A target is assumed to move according to a Brownian motion on the real line.The searcher starts from the origin and moves in the two directions from the starting point.The object is to detect the target.The purpose of this paper is to find the conditions under which the expected value of the first meeting time of the searcher and the target is finite,and to show the existence of a search plan which made this expected value minimum.
A Brownian model for recurrent earthquakes
Matthews, M.V.; Ellsworth, W.L.; Reasenberg, P.A.
2002-01-01
We construct a probability model for rupture times on a recurrent earthquake source. Adding Brownian perturbations to steady tectonic loading produces a stochastic load-state process. Rupture is assumed to occur when this process reaches a critical-failure threshold. An earthquake relaxes the load state to a characteristic ground level and begins a new failure cycle. The load-state process is a Brownian relaxation oscillator. Intervals between events have a Brownian passage-time distribution that may serve as a temporal model for time-dependent, long-term seismic forecasting. This distribution has the following noteworthy properties: (1) the probability of immediate rerupture is zero; (2) the hazard rate increases steadily from zero at t = 0 to a finite maximum near the mean recurrence time and then decreases asymptotically to a quasi-stationary level, in which the conditional probability of an event becomes time independent; and (3) the quasi-stationary failure rate is greater than, equal to, or less than the mean failure rate because the coefficient of variation is less than, equal to, or greater than 1/???2 ??? 0.707. In addition, the model provides expressions for the hazard rate and probability of rupture on faults for which only a bound can be placed on the time of the last rupture. The Brownian relaxation oscillator provides a connection between observable event times and a formal state variable that reflects the macromechanics of stress and strain accumulation. Analysis of this process reveals that the quasi-stationary distance to failure has a gamma distribution, and residual life has a related exponential distribution. It also enables calculation of "interaction" effects due to external perturbations to the state, such as stress-transfer effects from earthquakes outside the target source. The influence of interaction effects on recurrence times is transient and strongly dependent on when in the loading cycle step pertubations occur. Transient effects may
Brownian motion of particles in nematic fluids
Yao, Xuxia; Nayani, Karthik; Park, Jung; Srinivasarao, Mohan
2011-03-01
We studied the brownian motion of both charged and neutral polystyrene particles in two nematic fluids, a thermotropic liquid crystal, E7, and a lyotropic chromonic liquid crystal, Sunset Yellow FCF (SSY). Homogeneous planar alignment of E7 was easliy achieved by using rubbed polyimide film coated on the glass. For SSY planar mondomain, we used the capillary method recently developed in our lab. By tracking a single particle, the direction dependent diffussion coefficients and Stokes drag were measured in the nematic phase and isotropic phase for both systems.
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.
Metastable states in Brownian energy landscape
Cheliotis, Dimitris
2015-01-01
Random walks and diffusions in symmetric random environment are known to exhibit metastable behavior: they tend to stay for long times in wells of the environment. For the case that the environment is a one-dimensional two-sided standard Brownian motion, we study the process of depths of the consecutive wells of increasing depth that the motion visits. When these depths are looked in logarithmic scale, they form a stationary renewal cluster process. We give a description of the structure of t...
Bewerunge, Jörg; Ladadwa, Imad; Platten, Florian; Zunke, Christoph; Heuer, Andreas; Egelhaaf, Stefan U
2016-07-28
Anomalous diffusion is a ubiquitous phenomenon in complex systems. It is often quantified using time- and ensemble-averages to improve statistics, although time averages represent a non-local measure in time and hence can be difficult to interpret. We present a detailed analysis of the influence of time- and ensemble-averages on dynamical quantities by investigating Brownian particles in a rough potential energy landscape (PEL). Initially, the particle ensemble is randomly distributed, but the occupancy of energy values evolves towards the equilibrium distribution. This relaxation manifests itself in the time evolution of time- and ensemble-averaged dynamical measures. We use Monte Carlo simulations to study particle dynamics in a potential with a Gaussian distribution of energy values, where the long-time limit of the diffusion coefficient is known from theory. In our experiments, individual colloidal particles are exposed to a laser speckle pattern inducing a non-Gaussian roughness and are followed by optical microscopy. The relaxation depends on the kind and degree of roughness of the PEL. It can be followed and quantified by the time- and ensemble-averaged mean squared displacement. Moreover, the heterogeneity of the dynamics is characterized using single-trajectory analysis. The results of this work are relevant for the correct interpretation of single-particle tracking experiments in general. PMID:27353405
Avoiding the local-minimum problem in multi-agent systems with limited sensing and communication
Okamoto, Makiko; Akella, Maruthi R.
2016-06-01
In this paper, we consider a control problem for nonholonomic multi-agent systems in which agents and obstacles operate within a circular-shaped work area. We assume that agents only have limited sensing and communication ranges. We propose a novel control scheme using potential functions that drives agents from the initial to the goal configuration while avoiding collision with other agents, obstacles, and the boundary of the work area. The control scheme employs an avoidance strategy that ensures that the agents are never trapped at local minima that are typically encountered with most potential function-based approaches. A numerical simulation is presented to demonstrate the validity and effectiveness of the proposed control scheme.
Theoretical Limits on Errors and Acquisition Rates in Localizing Switchable Fluorophores
Small, Alexander R
2008-01-01
A variety of recent imaging techniques are able to beat the diffraction limit in fluorescence microcopy by activating and localizing subsets of the fluorescent molecules in the specimen, and repeating this process until all of the molecules have been imaged. In these techniques there is a tradeoff between speed (activating more molecules per imaging cycle) and error rates (activating more molecules risks producing overlapping images that hide information on molecular positions), and so intelligent image-processing approaches are needed to identify and reject overlapping images. We introduce here a formalism for defining error rates, derive a general relationship between error rates, image acquisition rates, and the performance characteristics of the image processing algorithms, and show that there is a minimum acquisition time irrespective of algorithm performance. We also consider algorithms that can infer molecular positions from images of overlapping blurs, and derive the dependence of the minimimum acquis...
Non-local meta-conformal invariance in diffusion-limited erosion
Henkel, Malte
2016-01-01
The non-stationary relaxation and physical ageing in the diffusion-limited erosion process ({\\sc dle}) is studied through the exact solution of its Langevin equation, in $d$ spatial dimensions. The dynamical exponent $z=1$, the growth exponent $\\beta=\\max(0,(1-d)/2)$ and the ageing exponents $a=b=d-1$ and $\\lambda_C=\\lambda_R=d$ are found. In $d=1$ spatial dimension, a new representation of the meta-conformal Lie algebra, isomorphic to $\\mathfrak{sl}(2,\\mathbb{R})\\oplus\\mathfrak{sl}(2,\\mathbb{R})$, acts as a dynamical symmetry of the noise-averaged {\\sc dle} Langevin equation. Its infinitesimal generators are non-local in space. The exact form of the full time-space dependence of the two-time response function of {\\sc dle} is reproduced for $d=1$ from this symmetry. The relationship to the terrace-step-kink model of vicinal surfaces is discussed.
Ely, Gregory
2013-01-01
In this paper we present a novel technique for micro-seismic localization using a group sparse penalization that is robust to the focal mechanism of the source and requires only a velocity model of the stratigraphy rather than a full Green's function model of the earth's response. In this technique we construct a set of perfect delta detector responses, one for each detector in the array, to a seismic event at a given location and impose a group sparsity across the array. This scheme is independent of the moment tensor and exploits the time compactness of the incident seismic signal. Furthermore we present a method for improving the inversion of the moment tensor and Green's function when the geometry of seismic array is limited. In particular we demonstrate that both Tikhonov regularization and truncated SVD can improve the recovery of the moment tensor and be robust to noise. We evaluate our algorithm on synthetic data and present error bounds for both estimation of the moment tensor as well as localization...
Population policy of local self-government: Necessities possibilities and limitation
Directory of Open Access Journals (Sweden)
Gavrilović Ana
2006-01-01
Full Text Available Taking into consideration the roles it objectively has, the state is also responsible for the formulation and implementation of population policy. In the process of its articulation, population policy of our state, although not explicitly formulated, continual and consistent, went through various phases of development, but was mostly in the shadow of other policies. In order to be successful, population policy has to be local, too. The need for definition and implementation of local population policy is indicated by insufficiency and inefficiency of government measures, knowledge of determinants of reproductive behavior and social processes, especially society democratization and globalization. The possibilities available are not sufficiently used. The attention is focused on the measures of material assistance, which is understandable in present conditions, while the measures of non-material assistance are almost missing. The paper is pointing out the non-material potentials and the necessity of their activation. The paper also contains the results of an empiric research carried out by interviewing the presidents of the population policy committees within municipal assemblies in the Autonomous Province of Vojvodina, thus providing the picture of the present situation, and knowledge of their positions, opinions and suggestions for the better use of potentials and overcoming of limitations in population policy.
Voids in the Local Volume: a limit on appearance of a galaxy in a DM halo
Tikhonov, Anton V
2007-01-01
Current explanation of the overabundance of dark matter subhalos in the Local Group (LG) indicates that there maybe a limit on mass of a halo, which can host a galaxy. This idea can be tested using voids in the distribution of galaxies: at some level small voids should not contain any (even dwarf) galaxies. We use observational samples complete to M_B = -12 with distances less than 8 Mpc to construct the void function (VF): the distribution of sizes of voids empty of any galaxies. There are ~30 voids with sizes ranging from 1 to 5 Mpc. We then study the distribution of dark matter halos in very high resolution simulations of the LCDM model. The theoretical VF matches the observations remarkably well only if we use halos with circular velocities larger than 45 +/- 10 km/s. This agrees with the Local Group predictions. There are smaller halos in the voids, but they should not produce any luminous matter. Small voids look quite similar to their giant cousins: the density has a minimum at the center of a void and...
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)
Magnetic fields and Brownian motion on the 2-sphere
International Nuclear Information System (INIS)
Using constrained path integrals, we study some statistical properties of Brownian paths on the two dimensional sphere. A generalized Levy's law for the probability P(A) that a closed Brownian path encloses an algebraic area A is obtained. Distributions of scaled variables related to the winding of paths around some fixed point are recovered in the asymptotic regime t → ∞
Holographic Brownian motion and time scales in strongly coupled plasmas
A. Nata Atmaja; J. de Boer; M. Shigemori
2010-01-01
We study Brownian motion of a heavy quark in field theory plasma in the AdS/CFT setup and discuss the time scales characterizing the interaction between the Brownian particle and plasma constituents. In particular, the mean-free-path time is related to the connected 4-point function of the random fo
The Stepping Motion of Brownian Particle Derived by Nonequilibrium Fluctuation
Institute of Scientific and Technical Information of China (English)
ZHAN Yong; ZHAO Tong-Jun; YU Hui; SONG Yan-Li; AN Hai-Long
2003-01-01
The direct motion of Brownian particle is considered as a result of system derived by external nonequilibriumfluctuating. The cooperative effects caused by asymmetric ratchet potential, external rocking force and additive colorednoise drive a Brownian particle in the directed stepping motion. This provides this kind of motion of kinesin along amicrotubule observed in experiments with a reasonable explanation.
Multi Sensor Fusion Framework for Indoor-Outdoor Localization of Limited Resource Mobile Robots
Directory of Open Access Journals (Sweden)
Pedro Albertos
2013-10-01
Full Text Available This paper presents a sensor fusion framework that improves the localization of mobile robots with limited computational resources. It employs an event based Kalman Filter to combine the measurements of a global sensor and an inertial measurement unit (IMU on an event based schedule, using fewer resources (execution time and bandwidth but with similar performance when compared to the traditional methods. The event is defined to reflect the necessity of the global information, when the estimation error covariance exceeds a predefined limit. The proposed experimental platforms are based on the LEGO Mindstorm NXT, and consist of a differential wheel mobile robot navigating indoors with a zenithal camera as global sensor, and an Ackermann steering mobile robot navigating outdoors with a SBG Systems GPS accessed through an IGEP board that also serves as datalogger. The IMU in both robots is built using the NXT motor encoders along with one gyroscope, one compass and two accelerometers from Hitecnic, placed according to a particle based dynamic model of the robots. The tests performed reflect the correct performance and low execution time of the proposed framework. The robustness and stability is observed during a long walk test in both indoors and outdoors environments.
Cartin, Daniel
2015-10-01
At this point in time, there is very little empirical evidence on the likelihood of a space-faring species originating in the biosphere of a habitable world. However, there is a tension between the expectation that such a probability is relatively high (given our own origins on Earth), and the lack of any basis for believing the Solar System has ever been visited by an extraterrestrial colonization effort. From the latter observational fact, this paper seeks to place upper limits on the probability of an interstellar civilization arising on a habitable planet in its stellar system, using a percolation model to simulate the progress of such a hypothetical civilization's colonization efforts in the local Solar neighbourhood. To be as realistic as possible, the actual physical positions and characteristics of all stars within 40 parsecs of the Solar System are used as possible colony sites in the percolation process. If an interstellar civilization is very likely to have such colonization programmes, and they can travel over large distances, then the upper bound on the likelihood of such a species arising per habitable world is of the order of 10-3 on the other hand, if civilizations are not prone to colonize their neighbours, or do not travel very far, then the upper limiting probability is much larger, even of order one.
Multi sensor fusion framework for indoor-outdoor localization of limited resource mobile robots.
Marín, Leonardo; Vallés, Marina; Soriano, Ángel; Valera, Ángel; Albertos, Pedro
2013-10-21
This paper presents a sensor fusion framework that improves the localization of mobile robots with limited computational resources. It employs an event based Kalman Filter to combine the measurements of a global sensor and an inertial measurement unit (IMU) on an event based schedule, using fewer resources (execution time and bandwidth) but with similar performance when compared to the traditional methods. The event is defined to reflect the necessity of the global information, when the estimation error covariance exceeds a predefined limit. The proposed experimental platforms are based on the LEGO Mindstorm NXT, and consist of a differential wheel mobile robot navigating indoors with a zenithal camera as global sensor, and an Ackermann steering mobile robot navigating outdoors with a SBG Systems GPS accessed through an IGEP board that also serves as datalogger. The IMU in both robots is built using the NXT motor encoders along with one gyroscope, one compass and two accelerometers from Hitecnic, placed according to a particle based dynamic model of the robots. The tests performed reflect the correct performance and low execution time of the proposed framework. The robustness and stability is observed during a long walk test in both indoors and outdoors environments.
Properties of Brownian Image Models in Scale-Space
DEFF Research Database (Denmark)
Pedersen, Kim Steenstrup
2003-01-01
law that apparently governs natural images. Furthermore, the distribution of Brownian images mapped into jet space is Gaussian and an analytical expression can be derived for the covariance matrix of Brownian images in jet space. This matrix is also a good approximation of the covariance matrix...... Brownian images) will be discussed in relation to linear scale-space theory, and it will be shown empirically that the second order statistics of natural images mapped into jet space may, within some scale interval, be modeled by the Brownian image model. This is consistent with the 1/f 2 power spectrum...... of natural images in jet space. The consequence of these results is that the Brownian image model can be used as a least committed model of the covariance structure of the distribution of natural images....
Dynamics and Efficiency of Brownian Rotors
Bauer, Wolfgang R
2008-01-01
Brownian rotors play an important role in biological systems and in future nano-technological applications. However the mechanisms determining their dynamics, efficiency and performance remain to be characterized. Here the F0 portion of the F-ATP synthase is considered as a paradigm of a Brownian rotor. In a generic analytical model we analyze the stochastic rotation of F0-like motors as a function of the driving free energy difference and of the free energy profile the rotor is subjected to. The latter is composed of the rotor interaction with its surroundings, of the free energy of chemical transitions, and of the workload. The dynamics and mechanical efficiency of the rotor depends on the magnitude of its stochastic motion driven by the free energy energy difference and its rectification on the reaction-diffusion path. We analyze which free energy profiles provide maximum flow and how their arrangement on the underlying reaction-diffusion path affects rectification and -- by this -- the efficiency.
Tau leaping of stiff stochastic chemical systems via local central limit approximation
International Nuclear Information System (INIS)
Stiffness manifests in stochastic dynamic systems in a more complex manner than in deterministic systems; it is not only important for a time-stepping method to remain stable but it is also important for the method to capture the asymptotic variances accurately. In the context of stochastic chemical systems, time stepping methods are known as tau leaping. Well known existing tau leaping methods have shortcomings in this regard. The implicit tau method is far more stable than the trapezoidal tau method but underestimates the asymptotic variance. On the other hand, the trapezoidal tau method which estimates the asymptotic variance exactly for linear systems suffers from the fact that the transients of the method do not decay fast enough in the context of very stiff systems. We propose a tau leaping method that possesses the same stability properties as the implicit method while it also captures the asymptotic variance with reasonable accuracy at least for the test system S1↔S2. The proposed method uses a central limit approximation (CLA) locally over the tau leaping interval and is referred to as the LCLA-τ. The CLA predicts the mean and covariance as solutions of certain differential equations (ODEs) and for efficiency we solve these using a single time step of a suitable low order method. We perform a mean/covariance stability analysis of various possible low order schemes to determine the best scheme. Numerical experiments presented show that LCLA-τ performs favorably for stiff systems and that the LCLA-τ is also able to capture bimodal distributions unlike the CLA itself. The proposed LCLA-τ method uses a split implicit step to compute the mean update. We also prove that any tau leaping method employing a split implicit step converges in the fluid limit to the implicit Euler method as applied to the fluid limit differential equation
Yariv, Ehud; Schnitzer, Ory
2014-09-01
We consider the motion of self-propelling Brownian particles in two-dimensional periodically corrugated channels. The point-size swimmers propel themselves in a direction which fluctuates by Brownian rotation; in addition, they undergo Brownian motion. The impermeability of the channel boundaries in conjunction with an asymmetry of the unit-cell geometry enables ratcheting, where a nonzero particle current is animated along the channel. This effect is studied here in the continuum limit using a diffusion-advection description of the probability density in a four-dimensional position-orientation space. Specifically, the mean particle velocity is calculated using macrotransport (generalized Taylor-dispersion) theory. This description reveals that the ratcheting mechanism is indirect: swimming gives rise to a biased spatial particle distribution which in turn results in a purely diffusive net current. For a slowly varying channel geometry, the dependence of this current upon the channel geometry and fluid-particle parameters is studied via a long-wave approximation over a reduced two-dimensional space. This allows for a straightforward seminumerical solution. In the limit where both rotational diffusion and swimming are strong, we find an asymptotic approximation to the particle current, scaling inversely with the square of the swimming Péclet number. For a given swimmer-fluid system, this limit is physically realized with increasing unit-cell size.
Impurity driven Brownian motion of solitons in elongated Bose-Einstein Condensates
Aycock, L M; Genkina, D; Lu, H -I; Galitski, V; Spielman, I B
2016-01-01
Solitons, spatially-localized, mobile excitations resulting from an interplay between nonlinearity and dispersion, are ubiquitous in physical systems from water channels and oceans to optical fibers and Bose-Einstein condensates (BECs). For the first time, we observed and controlled the Brownian motion of solitons. We launched long-lived dark solitons in highly elongated $^{87}\\rm{Rb}$ BECs and showed that a dilute background of impurity atoms in a different internal state dramatically affects the soliton. With no impurities and in one-dimension (1-D), these solitons would have an infinite lifetime, a consequence of integrability. In our experiment, the added impurities scatter off the much larger soliton, contributing to its Brownian motion and decreasing its lifetime. We describe the soliton's diffusive behavior using a quasi-1-D scattering theory of impurity atoms interacting with a soliton, giving diffusion coefficients consistent with experiment.
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.
Cartin, Daniel
2015-01-01
At this point in time, there is very little empirical evidence on the likelihood of a space-faring species originating in the biosphere of a habitable world. However, there is a tension between the expectation that such a probability is relatively high (given our own origins on Earth), and the lack of any basis for believing the Solar System has ever been visited by an extraterrestrial colonization effort. This paper seeks to place upper limits on the probability of an interstellar civilization arising on a habitable planet in its stellar system, using a percolation model to simulate the progress of such a hypothetical civilization's colonization efforts in the local Solar neighborhood. To be as realistic as possible, the actual physical positions and characteristics of all stars within 40 parsecs of the Solar System are used as possible colony sites in the percolation process. If an interstellar civilization is very likely to have such colonization programs, and they can travel over large distances, then the...
Exploiting the color of Brownian motion for high-frequency microrheology of Newtonian fluids
Domínguez-García, Pablo; Mor, Flavio M.; Forró, László; Jeney, Sylvia
2013-09-01
Einstein's stochastic description of the random movement of small objects in a fluid, i.e. Brownian motion, reveals to be quite different, when observed on short timescales. The limitations of Einstein's theory with respect to particle inertia and hydrodynamic memory yield to the apparition of a colored frequency-dependent component in the spectrum of the thermal forces, which is called "the color of Brownian motion". The knowledge of the characteristic timescales of the motion of a trapped microsphere motion in a Newtonian fluid allowed to develop a high-resolution calibration method for optical interferometry. Well-calibrated correlation quantities, such as the mean square displacement or the velocity autocorrelation function, permit to study the mechanical properties of fluids at high frequencies. These properties are estimated by microrheological calculations based on the theoretical relations between the complex mobility of the beads and the rheological properties of a complex fluid.
From Molecular Dynamics to Brownian Dynamics
Erban, Radek
2014-01-01
Three coarse-grained molecular dynamics (MD) models are investigated with the aim of developing and analyzing multiscale methods which use MD simulations in parts of the computational domain and (less detailed) Brownian dynamics (BD) simulations in the remainder of the domain. The first MD model is formulated in one spatial dimension. It is based on elastic collisions of heavy molecules (e.g. proteins) with light point particles (e.g. water molecules). Two three-dimensional MD models are then investigated. The obtained results are applied to a simplified model of protein binding to receptors on the cellular membrane. It is shown that modern BD simulators of intracellular processes can be used in the bulk and accurately coupled with a (more detailed) MD model of protein binding which is used close to the membrane.
Hybrid scheme for Brownian semistationary processes
DEFF Research Database (Denmark)
Bennedsen, Mikkel; Lunde, Asger; Pakkanen, Mikko S.
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 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...
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
International Nuclear Information System (INIS)
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
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.
On the quantiles of Brownian motion and their hitting times
Dassios, Angelos
2005-01-01
The distribution of the α-quantile of a Brownian motion on an interval [0,t] has been obtained motivated by a problem in financial mathematics. In this paper we generalize these results by calculating an explicit expression for the joint density of the α-quantile of a standard Brownian motion, its first and last hitting times and the value of the process at time t. Our results can easily be generalized to a Brownian motion with drift. It is shown that the first and last hitting times follow a...
Langevin model for a Brownian system with directed motion
Ambía, Francisco; Híjar, Humberto
2016-08-01
We propose a model for an active Brownian system that exhibits one-dimensional directed motion. This system consists of two Brownian spherical particles that interact through an elastic potential and have time-dependent radii. We suggest an algorithm by which the sizes of the particles can be varied, such that the center of mass of the system is able to move at an average constant speed in one direction. The dynamics of the system is studied theoretically using a Langevin model, as well as from Brownian Dynamics simulations.
The exit distribution for iterated Brownian motion in cones
Banuelos, Rodrigo; DeBlassie, Dante
2004-01-01
We study the distribution of the exit place of iterated Brownian motion in a cone, obtaining information about the chance of the exit place having large magnitude. Along the way, we determine the joint distribution of the exit time and exit place of Brownian motion in a cone. This yields information on large values of the exit place (harmonic measure) for Brownian motion. The harmonic measure for cones has been studied by many authors for many years. Our results are sharper than any previousl...
40 CFR 1400.11 - Limitation on dissemination to State and local government officials.
2010-07-01
... and local government officials. 1400.11 Section 1400.11 Protection of Environment ENVIRONMENTAL... dissemination to State and local government officials. Except as authorized by this part and by 42 U.S.C. 7412(r)(7)(H)(v)(III), Federal, State, and local government officials, and qualified researchers...
Parameter Estimation for Generalized Brownian Motion with Autoregressive Increments
Fendick, Kerry
2011-01-01
This paper develops methods for estimating parameters for a generalization of Brownian motion with autoregressive increments called a Brownian ray with drift. We show that a superposition of Brownian rays with drift depends on three types of parameters - a drift coefficient, autoregressive coefficients, and volatility matrix elements, and we introduce methods for estimating each of these types of parameters using multidimensional times series data. We also cover parameter estimation in the contexts of two applications of Brownian rays in the financial sphere: queuing analysis and option valuation. For queuing analysis, we show how samples of queue lengths can be used to estimate the conditional expectation functions for the length of the queue and for increments in its net input and lost potential output. For option valuation, we show how the Black-Scholes-Merton formula depends on the price of the security on which the option is written through estimates not only of its volatility, but also of a coefficient ...
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.
Convergence rates of posterior distributions for Brownian semimartingale models
F.H. van der Meulen; A.W. van der Vaart; J.H. van Zanten
2006-01-01
Key words and Phrases: Bayesian estimation, Continuous semimartingale, Dirichlet process, Hellinger distance, Infinite dimensional model, Rate of convergence, Wavelets. We consider the asymptotic behavior of posterior distributions based on continuous observations from a Brownian semimartingale mode
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.
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.
Brownian Motion on a Sphere: Distribution of Solid Angles
Krishna, M. M. G.; Samuel, Joseph; Sinha, Supurna
2000-01-01
We study the diffusion of Brownian particles on the surface of a sphere and compute the distribution of solid angles enclosed by the diffusing particles. This function describes the distribution of geometric phases in two state quantum systems (or polarised light) undergoing random evolution. Our results are also relevant to recent experiments which observe the Brownian motion of molecules on curved surfaces like micelles and biological membranes. Our theoretical analysis agrees well with the...
Brownian motion and gambling: from ratchets to paradoxical games
Parrondo, J M R
2014-01-01
Two losing gambling games, when alternated in a periodic or random fashion, can produce a winning game. This paradox has been inspired by certain physical systems capable of rectifying fluctuations: the so-called Brownian ratchets. In this paper we review this paradox, from Brownian ratchets to the most recent studies on collective games, providing some intuitive explanations of the unexpected phenomena that we will find along the way.
Symmetry Relations for Trajectories of a Brownian Motor
Astumian, R. Dean
2007-01-01
A Brownian Motor is a nanoscale or molecular device that combines the effects of thermal noise, spatial or temporal asymmetry, and directionless input energy to drive directed motion. Because of the input energy, Brownian motors function away from thermodynamic equilibrium and concepts such as linear response theory, fluctuation dissipation relations, and detailed balance do not apply. The {\\em generalized} fluctuation-dissipation relation, however, states that even under strongly thermodynam...
Energy Technology Data Exchange (ETDEWEB)
McGarry, Conor K., E-mail: conor.mcgarry@belfasttrust.hscni.net [Radiotherapy Physics, Northern Ireland Cancer Centre, Belfast Health and Social Care Trust, Belfast, Northern Ireland (United Kingdom); Bokrantz, Rasmus [Optimization and Systems Theory, KTH Royal Institute of Technology, Stockholm (Sweden); RaySearch Laboratories, Stockholm (Sweden); O’Sullivan, Joe M. [Centre for Cancer Research and Cell Biology, Queen’s University Belfast, Belfast, Northern Ireland (United Kingdom); Clinical Oncology, Northern Ireland Cancer Centre, Belfast Health and Social Care Trust, Belfast, Northern Ireland (United Kingdom); Hounsell, Alan R. [Radiotherapy Physics, Northern Ireland Cancer Centre, Belfast Health and Social Care Trust, Belfast, Northern Ireland (United Kingdom); Centre for Cancer Research and Cell Biology, Queen’s University Belfast, Belfast, Northern Ireland (United Kingdom)
2014-10-01
Efficacy of inverse planning is becoming increasingly important for advanced radiotherapy techniques. This study’s aims were to validate multicriteria optimization (MCO) in RayStation (v2.4, RaySearch Laboratories, Sweden) against standard intensity-modulated radiation therapy (IMRT) optimization in Oncentra (v4.1, Nucletron BV, the Netherlands) and characterize dose differences due to conversion of navigated MCO plans into deliverable multileaf collimator apertures. Step-and-shoot IMRT plans were created for 10 patients with localized prostate cancer using both standard optimization and MCO. Acceptable standard IMRT plans with minimal average rectal dose were chosen for comparison with deliverable MCO plans. The trade-off was, for the MCO plans, managed through a user interface that permits continuous navigation between fluence-based plans. Navigated MCO plans were made deliverable at incremental steps along a trajectory between maximal target homogeneity and maximal rectal sparing. Dosimetric differences between navigated and deliverable MCO plans were also quantified. MCO plans, chosen as acceptable under navigated and deliverable conditions resulted in similar rectal sparing compared with standard optimization (33.7 ± 1.8 Gy vs 35.5 ± 4.2 Gy, p = 0.117). The dose differences between navigated and deliverable MCO plans increased as higher priority was placed on rectal avoidance. If the best possible deliverable MCO was chosen, a significant reduction in rectal dose was observed in comparison with standard optimization (30.6 ± 1.4 Gy vs 35.5 ± 4.2 Gy, p = 0.047). Improvements were, however, to some extent, at the expense of less conformal dose distributions, which resulted in significantly higher doses to the bladder for 2 of the 3 tolerance levels. In conclusion, similar IMRT plans can be created for patients with prostate cancer using MCO compared with standard optimization. Limitations exist within MCO regarding conversion of navigated plans to
Escape rate of an active Brownian particle over a potential barrier.
Burada, P S; Lindner, B
2012-03-01
We study the dynamics of an active Brownian particle with a nonlinear friction function located in a spatial cubic potential. For strong but finite damping, the escape rate of the particle over the spatial potential barrier shows a nonmonotonic dependence on the noise intensity. We relate this behavior to the fact that the active particle escapes from a limit cycle rather than from a fixed point and that a certain amount of noise can stabilize the sojourn of the particle on this limit cycle. PMID:22587135
Asymptotic theory for Brownian semi-stationary processes with application to turbulence
DEFF Research Database (Denmark)
Corcuera, José Manuel; Hedevang, Emil; Pakkanen, Mikko S.;
2013-01-01
This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of the BSS model. We review the limit theory discussed......-stationary processes. In "Prokhorov and Contemporary Probability Theory", Springer.] and present some new connections to fractional diffusion models. We apply our probabilistic results to construct a family of estimators for the smoothness parameter of the BSS process. In this context we develop estimates with gaps......, which allow to obtain a valid central limit theorem for the critical region. Finally, we apply our statistical theory to turbulence data....
Miles, J. A.; Das, Diptaranjan; Simmons, Z. J.; Yavuz, D. D.
2015-09-01
We experimentally demonstrate the localization of excitation between hyperfine ground states of 87Rb atoms to as small as λ /13 -wide spatial regions. We use ultracold atoms trapped in a dipole trap and utilize electromagnetically induced transparency (EIT) for the atomic excitation. The localization is achieved by combining a spatially varying coupling laser (standing wave) with the intensity dependence of EIT. The excitation is fast (150 ns laser pulses) and the dark-state fidelity can be made higher than 94% throughout the standing wave. Because the width of the localized regions is much smaller than the wavelength of the driving light, traditional optical imaging techniques cannot resolve the localized features. Therefore, to measure the excitation profile, we use an autocorrelation-like method where we perform two EIT sequences separated by a time delay, during which we move the standing wave.
Institute of Scientific and Technical Information of China (English)
蒋义文; 刘禄勤
2003-01-01
The representation of additive functionals and local times for jump Markovprocesses are obtained. The results of uniformly functional moderate deviation and theirapplications to birth-death processes are also presented.
Subotnik, Joseph E; Sodt, Alex; Head-Gordon, Martin
2008-01-21
Local coupled-cluster theory provides an algorithm for measuring electronic correlation quickly, using only the spatial locality of localized electronic orbitals. Previously, we showed [J. Subotnik et al., J. Chem. Phys. 125, 074116 (2006)] that one may construct a local coupled-cluster singles-doubles theory which (i) yields smooth potential energy surfaces and (ii) achieves near linear scaling. That theory selected which orbitals to correlate based only on the distances between the centers of different, localized orbitals, and the approximate potential energy surfaces were characterized as smooth using only visual identification. This paper now extends our previous algorithm in three important ways. First, locality is now based on both the distances between the centers of orbitals as well as the spatial extent of the orbitals. We find that, by accounting for the spatial extent of a delocalized orbital, one can account for electronic correlation in systems with some electronic delocalization using fast correlation methods designed around orbital locality. Second, we now enforce locality on not just the amplitudes (which measure the exact electron-electron correlation), but also on the two-electron integrals themselves (which measure the bare electron-electron interaction). Our conclusion is that we can bump integrals as well as amplitudes, thereby gaining a tremendous increase in speed and paradoxically increasing the accuracy of our LCCSD approach. Third and finally, we now make a rigorous definition of chemical smoothness as requiring that potential energy surfaces not support artificial maxima, minima, or inflection points. By looking at first and second derivatives from finite difference techniques, we demonstrate complete chemical smoothness of our potential energy surfaces (bumping both amplitudes and integrals). These results are significant both from a theoretical and from a computationally practical point of view. PMID:18205484
Brownian dynamics simulations of ellipsoidal magnetizable particle suspensions
Torres-Díaz, I.; Rinaldi, C.
2014-06-01
The rotational motion of soft magnetic tri-axial ellipsoidal particles suspended in a Newtonian fluid has been studied using rotational Brownian dynamics simulations by solving numerically the stochastic angular momentum equation in an orientational space described by the quaternion parameters. The model is applicable to particles where the effect of shape anisotropy is dominant. The algorithm quantifies the magnetization of a monodisperse suspension of tri-axial ellipsoids in dilute limit conditions under applied constant and time-varying magnetic fields. The variation of the relative permeability with the applied magnetic field of the particle's bulk material was included in the simulations. The results show that the equilibrium magnetization of a suspension of magnetizable tri-axial ellipsoids saturates at high magnetic field amplitudes. Additionally, the dynamic susceptibility at low magnetic field intensity presents a peak in the out-of-phase component, which is significantly smaller than the in-phase component and depends on the Langevin parameter. The dynamic magnetization of the particle suspension is in phase with the magnetic field at low and high frequencies far from the peak of the out-of-phase component.
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...
Local Joint-Limits using Distance Field Cones in Euler Angle Space
DEFF Research Database (Denmark)
Engell-Nørregård, Morten Pol; Niebe, Sarah Maria; Erleben, Kenny
2010-01-01
Joint–limits are often modeled too simple, causing redundancy and allowing unnatural poses. We model the boundary of the feasible region, using a geometric approach. We show how to generate fast, general joint–limit cones for kinematic figures using signed distance fields. The distance–cone joint...
A generalized Brownian motion model for turbulent relative particle dispersion
Shivamoggi, B. K.
2016-08-01
There is speculation that the difficulty in obtaining an extended range with Richardson-Obukhov scaling in both laboratory experiments and numerical simulations is due to the finiteness of the flow Reynolds number Re in these situations. In this paper, a generalized Brownian motion model has been applied to describe the relative particle dispersion problem in more realistic turbulent flows and to shed some light on this issue. The fluctuating pressure forces acting on a fluid particle are taken to be a colored noise and follow a stationary process and are described by the Uhlenbeck-Ornstein model while it appears plausible to take their correlation time to have a power-law dependence on Re, thus introducing a bridge between the Lagrangian quantities and the Eulerian parameters for this problem. This ansatz is in qualitative agreement with the possibility of a connection speculated earlier by Corrsin [26] between the white-noise representation for the fluctuating pressure forces and the large-Re assumption in the Kolmogorov [4] theory for the 3D fully developed turbulence (FDT) as well as a similar argument of Monin and Yaglom [23] and a similar result of Sawford [13] and Borgas and Sawford [24]. It also provides an insight into the result that the Richardson-Obukhov scaling holds only in the infinite-Re limit and disappears otherwise. This ansatz further provides a determination of the Richardson-Obukhov constant g as a function of Re, with an asymptotic constant value in the infinite-Re limit. It is shown to lead to full agreement, in the small-Re limit as well, with the Batchelor-Townsend [27] scaling for the rate of change of the mean square interparticle separation in 3D FDT, hence validating its soundness further.
Incremental bus service design: combining limited-stop and local bus services
Chiraphadhanakul, Virot; Barnhart, Cynthia
2013-01-01
Long in-vehicle travel times resulting from frequent stops make bus service an unattractive choice for many commuters. Limited-stop bus services however have the advantage of shorter in-vehicle times experienced by passengers. In this work, we seek to modify a given bus service by optimally reassigning some number of bus trips, as opposed to providing additional trips, to operate a limited-stop service. We propose an optimization model to determine a limited-stop service route to be operated ...
Numerous strategies but limited implementation guidance in US local adaptation plans
Woodruff, Sierra C.; Stults, Missy
2016-08-01
Adaptation planning offers a promising approach for identifying and devising solutions to address local climate change impacts. Yet there is little empirical understanding of the content and quality of these plans. We use content analysis to evaluate 44 local adaptation plans in the United States and multivariate regression to examine how plan quality varies across communities. We find that plans draw on multiple data sources to analyse future climate impacts and include a breadth of strategies. Most plans, however, fail to prioritize impacts and strategies or provide detailed implementation processes, raising concerns about whether adaptation plans will translate into on-the-ground reductions in vulnerability. Our analysis also finds that plans authored by the planning department and those that engaged elected officials in the planning process were of higher quality. The results provide important insights for practitioners, policymakers and scientists wanting to improve local climate adaptation planning and action.
Limit of the local approach application of the brittle fracture on hydrogen charged steels
International Nuclear Information System (INIS)
The local approach of the brittle fracture by cleavage developed by BEREMIN relies the macroscopic mechanical properties to local criteria. It allows to predict the probability of failure of the structure by performing detailed calculation of the stress and deformation fields in the different element volumes within this structure. It also takes into account the distribution of the defects initiating the fracture in a specific zone. The local approach allows then the determination of a statistical criterion to be applied on cleavage fracture. The cumulative distribution function PR, over a small volume V0 ahead of a crack tip or defect can be expressed as: PR 1 - exp[-σw/σu)m] where σw WEIBULL stress and σu mean cleavage stress defined as the stress / volume leading to PR = 0.63 and m is an empirically determined parameter presenting the degree of scatter in measured strength values. The paper deals with the application of this approach on three steels in absence and in presence of hydrogen: railway steel FM80, with pearlitic structure, 35CD4 steel employed in tool's joints in a tempered martensitic state and a bainitic A508.3 used in nuclear power plants. The goal of this work is to show that in the case hydrogenated steel, the local approach is improved if the defects promoted by high stress triaxiality and local critical hydrogen concentration do not exceed the element volume V0 in which the material is considered to be statistically homogeneous. The results show that in the two first steel the local approach is improved even in presence of hydrogen. In the hydrogenated bainitic steel (A508.3), the application of this method is not possible due to development in the material of fish eyes which the size is very large with respect to V0. (author). 7 refs., 4 figs., 1 tab
Hijacked organic, limited local, faulty fair trade: what's a radical to eat?
Engler, Mark
2012-01-01
Organic farming has been hijacked by big business. Local food can have a larger carbon footprint than products shipped in from overseas. Fair trade doesn't address the real concerns of farmers in the global South. As the food movement has moved from the countercultural fringe to become a mainstream phenomenon, organic, local, and fair trade advocates have been beset by criticism from overt foes and erstwhile allies alike. Now that Starbucks advertises fair trade coffee and Kraft owns Boca soy burgers, it's fair to ask, "What's a radical to eat?" PMID:22834045
Hijacked organic, limited local, faulty fair trade: what's a radical to eat?
Engler, Mark
2012-01-01
Organic farming has been hijacked by big business. Local food can have a larger carbon footprint than products shipped in from overseas. Fair trade doesn't address the real concerns of farmers in the global South. As the food movement has moved from the countercultural fringe to become a mainstream phenomenon, organic, local, and fair trade advocates have been beset by criticism from overt foes and erstwhile allies alike. Now that Starbucks advertises fair trade coffee and Kraft owns Boca soy burgers, it's fair to ask, "What's a radical to eat?"
The Second Painlev\\'e Equation in the Large-Parameter Limit I: Local Asymptotic Analysis
Joshi, Nalini
1997-01-01
In this paper, we find all possible asymptotic behaviours of the solutions of the second Painlev\\'e equation $y''=2y^3+xy +\\alpha$ as the parameter $\\alpha\\to\\infty$ in the local region $x\\ll\\alpha^{2/3}$. We prove that these are asymptotic behaviours by finding explicit error bounds. Moreover, we show that they are connected and complete in the sense that they correspond to all possible values of initial data given at a point in the local region.
Decoupling Limits of sGoldstino Modes in Global and Local Supersymmetry
Farakos, Fotis
2013-01-01
We study the decoupling limit of a superheavy sgoldstino field in spontaneously broken ${\\cal{N}}=1$ supergravity. After discussing sgoldstino decoupling in spontaneously broken globally supersymmetric theories in superspace, we analyze the same limit in supergravity. Our approach is based on K\\"ahler superspace, which, among others, allows direct formulation of ${\\cal N}=1$ supergravity in the Einstein frame and correct identifications of mass parameters. Allowing for a non-renormalizable K\\"ahler potential in the hidden sector, the decoupling limit of a superheavy sgoldstino is identified with an infinite negative K\\"ahler curvature. Constraints that lead to non-linear realizations of supersymmetry emerge as consequence of the equations of motion of the goldstino superfield when considering the decoupling limit. We also analyze supersymmetry breaking and sgoldstino decoupling in the case of many chiral multiplets. Finally, by employing superspace Bianchi identities, we identify the real chiral superfield, w...
Harnack Inequality and Regularity for a Product of Symmetric Stable Process and Brownian Motion
Karli, Deniz
2010-01-01
In this paper, we consider a product of a symmetric stable process in $\\mathbb{R}^d$ and a one-dimensional Brownian motion in $\\mathbb{R}^+$. Then we define a class of harmonic functions with respect to this product process. We show that bounded non-negative harmonic functions in the upper-half space satisfy Harnack inequality and prove that they are locally H\\"older continuous. We also argue a result on Littlewood-Paley functions which are obtained by the $\\alpha$-harmonic extension of an $L...
Implementation of a workplace smoking ban in bars: The limits of local discretion
Directory of Open Access Journals (Sweden)
Bero Lisa A
2008-12-01
Full Text Available Abstract Background In January 1998, the California state legislature extended a workplace smoking ban to bars. The purpose of this study was to explore the conditions that facilitate or hinder compliance with a smoking ban in bars. Methods We studied the implementation of the smoking ban in bars by interviewing three sets of policy participants: bar employers responsible for complying with the law; local government officials responsible for enforcing the law; and tobacco control activists who facilitated implementation. We transcribed the interviews and did a qualitative analysis of the text. Results The conditions that facilitated bar owners' compliance with a smoking ban in bars included: if the cost to comply was minimal; if the bars with which they were in competition were in compliance with the smoking ban; and if there was authoritative, consistent, coordinated, and uniform enforcement. Conversely, the conditions that hindered compliance included: if the law had minimal sanctions; if competing bars in the area allowed smoking; and if enforcement was delayed or inadequate. Conclusion Many local enforcers wished to forfeit their local discretion and believed the workplace smoking ban in bars would be best implemented by a state agency. The potential implication of this study is that, given the complex nature of local politics, smoking bans in bars are best implemented at a broader provincial or national level.
Localization of type I interferon receptor limits interferon-induced TLR-3 in epithelial cells
This study aimed to expand on the role of type I IFNs in the influenza-induced upregulation of TLR3 and determine whether and how the localization of the IFN-alpha/beta receptor (IFNAR) in respiratory epithelial cells could modify IFN-induced responses. Using differentiated prima...
DEFF Research Database (Denmark)
Hargreaves, Anna; Bailey, Susan; Laird, Robert
2015-01-01
Dispersal ability will largely determine whether species track their climatic niches during climate change, a process especially important for populations at contracting (low-latitude/low-elevation) range limits that otherwise risk extinction. We investigate whether dispersal evolution...... at contracting range limits is facilitated by two processes that potentially enable edge populations to experience and adjust to the effects of climate deterioration before they cause extinction: (i) climate-induced fitness declines towards range limits and (ii) local adaptation to a shifting climate gradient....... We simulate a species distributed continuously along a temperature gradient using a spatially explicit, individual-based model. We compare range-wide dispersal evolution during climate stability vs. directional climate change, with uniform fitness vs. fitness that declines towards range limits (RLs...
Maximum precision closed-form solution for localizing diffraction-limited spots in noisy images.
Larkin, Joshua D; Cook, Peter R
2012-07-30
Super-resolution techniques like PALM and STORM require accurate localization of single fluorophores detected using a CCD. Popular localization algorithms inefficiently assume each photon registered by a pixel can only come from an area in the specimen corresponding to that pixel (not from neighboring areas), before iteratively (slowly) fitting a Gaussian to pixel intensity; they fail with noisy images. We present an alternative; a probability distribution extending over many pixels is assigned to each photon, and independent distributions are joined to describe emitter location. We compare algorithms, and recommend which serves best under different conditions. At low signal-to-noise ratios, ours is 2-fold more precise than others, and 2 orders of magnitude faster; at high ratios, it closely approximates the maximum likelihood estimate.
Neutrophil recruitment to lymph nodes limits local humoral response to Staphylococcus aureus.
Kamenyeva, Olena; Boularan, Cedric; Kabat, Juraj; Cheung, Gordon Y C; Cicala, Claudia; Yeh, Anthony J; Chan, June L; Periasamy, Saravanan; Otto, Michael; Kehrl, John H
2015-04-01
Neutrophils form the first line of host defense against bacterial pathogens. They are rapidly mobilized to sites of infection where they help marshal host defenses and remove bacteria by phagocytosis. While splenic neutrophils promote marginal zone B cell antibody production in response to administered T cell independent antigens, whether neutrophils shape humoral immunity in other lymphoid organs is controversial. Here we investigate the neutrophil influx following the local injection of Staphylococcus aureus adjacent to the inguinal lymph node and determine neutrophil impact on the lymph node humoral response. Using intravital microscopy we show that local immunization or infection recruits neutrophils from the blood to lymph nodes in waves. The second wave occurs temporally with neutrophils mobilized from the bone marrow. Within lymph nodes neutrophils infiltrate the medulla and interfollicular areas, but avoid crossing follicle borders. In vivo neutrophils form transient and long-lived interactions with B cells and plasma cells, and their depletion augments production of antigen-specific IgG and IgM in the lymph node. In vitro activated neutrophils establish synapse- and nanotube-like interactions with B cells and reduce B cell IgM production in a TGF-β1 dependent manner. Our data reveal that neutrophils mobilized from the bone marrow in response to a local bacterial challenge dampen the early humoral response in the lymph node. PMID:25884622
Neutrophil recruitment to lymph nodes limits local humoral response to Staphylococcus aureus.
Directory of Open Access Journals (Sweden)
Olena Kamenyeva
2015-04-01
Full Text Available Neutrophils form the first line of host defense against bacterial pathogens. They are rapidly mobilized to sites of infection where they help marshal host defenses and remove bacteria by phagocytosis. While splenic neutrophils promote marginal zone B cell antibody production in response to administered T cell independent antigens, whether neutrophils shape humoral immunity in other lymphoid organs is controversial. Here we investigate the neutrophil influx following the local injection of Staphylococcus aureus adjacent to the inguinal lymph node and determine neutrophil impact on the lymph node humoral response. Using intravital microscopy we show that local immunization or infection recruits neutrophils from the blood to lymph nodes in waves. The second wave occurs temporally with neutrophils mobilized from the bone marrow. Within lymph nodes neutrophils infiltrate the medulla and interfollicular areas, but avoid crossing follicle borders. In vivo neutrophils form transient and long-lived interactions with B cells and plasma cells, and their depletion augments production of antigen-specific IgG and IgM in the lymph node. In vitro activated neutrophils establish synapse- and nanotube-like interactions with B cells and reduce B cell IgM production in a TGF-β1 dependent manner. Our data reveal that neutrophils mobilized from the bone marrow in response to a local bacterial challenge dampen the early humoral response in the lymph node.
Energy Technology Data Exchange (ETDEWEB)
Mueller, A.C.; Gani, C.; Weinmann, M.; Bamberg, M.; Eckert, F. [Tuebingen Univ. (Germany). Dept. of Radiooncology; Mayer, F. [Tuebingen Univ. (Germany). Dept. of Medical Oncology; Sipos, B. [Tuebingen Univ. (Germany). Dept. of Pathology
2012-03-15
As extra-pulmonary small cell carcinoma (EPSCC) is a rare entity of tumors, the available treatment recommendations are mainly based on retrospective analyses and deduction from treatment of small cell lung cancer. The aim of this study was to provide a detailed analysis concerning prognostic factors and treatment modalities. A total of 20 patients with limited disease (LD) of EPSCC treated at our institution from 1999-2009 were retrospectively analyzed. Data were gathered from chart review. Localization, lymph node involvement, as well as local and systemic treatment were documented and their impact on pattern of failure and survival times statistically evaluated. With a median follow-up of 21 months, the estimated median overall- and disease-free survival were 59 and 25 months, respectively. Local control was excellent with 100% at 2 years. Nodal involvement was observed in 74% (n = 14/19) of evaluable patients. However, outcome was not altered by this parameter. Local treatment consisted of surgery in 10 cases, radiotherapy in 7 cases, and a combination of both in 3 cases. Only 3 patients (15%) developed hematogenous central nervous system metastases, while none of the patients received prophylactic cranial irradiation. Nodal involvement did not worsen prognosis. Local control was excellent irrespective of local treatment modality and the leading cause of failure was distant metastasis. Therefore, systemic treatment should not be omitted. Prophylactic cranial irradiation might be dispensable but discussed for head and neck malignancies.
Brownian dynamics simulations with hard-body interactions: Spherical particles
Behringer, Hans; 10.1063/1.4761827
2012-01-01
A novel approach to account for hard-body interactions in (overdamped) Brownian dynamics simulations is proposed for systems with non-vanishing force fields. The scheme exploits the analytically known transition probability for a Brownian particle on a one-dimensional half-line. The motion of a Brownian particle is decomposed into a component that is affected by hard-body interactions and into components that are unaffected. The hard-body interactions are incorporated by replacing the affected component of motion by the evolution on a half-line. It is discussed under which circumstances this approach is justified. In particular, the algorithm is developed and formulated for systems with space-fixed obstacles and for systems comprising spherical particles. The validity and justification of the algorithm is investigated numerically by looking at exemplary model systems of soft matter, namely at colloids in flow fields and at protein interactions. Furthermore, a thorough discussion of properties of other heurist...
Stochastic calculus for fractional Brownian motion and related processes
Mishura, Yuliya S
2008-01-01
The theory of fractional Brownian motion and other long-memory processes are addressed in this volume. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. Among these are results about Levy characterization of fractional Brownian motion, maximal moment inequalities for Wiener integrals including the values 0
Brownian Dynamics of charged particles in a constant magnetic field
Hou, L J; Piel, A; Shukla, P K
2009-01-01
Numerical algorithms are proposed for simulating the Brownian dynamics of charged particles in an external magnetic field, taking into account the Brownian motion of charged particles, damping effect and the effect of magnetic field self-consistently. Performance of these algorithms is tested in terms of their accuracy and long-time stability by using a three-dimensional Brownian oscillator model with constant magnetic field. Step-by-step recipes for implementing these algorithms are given in detail. It is expected that these algorithms can be directly used to study particle dynamics in various dispersed systems in the presence of a magnetic field, including polymer solutions, colloidal suspensions and, particularly complex (dusty) plasmas. The proposed algorithms can also be used as thermostat in the usual molecular dynamics simulation in the presence of magnetic field.
Local times for solutions of the complex Ginzburg-Landau equation and the inviscid limit
Shirikyan, Armen
2010-01-01
We consider the behaviour of the distribution for stationary solutions of the complex Ginzburg-Landau equation perturbed by a random force. It was proved earlier that if the random force is proportional to the square root of the viscosity, then the family of stationary measures possesses an accumulation point as the viscosity goes to zero. We show that if $\\mu$ is such point, then the distributions of the L^2 norm and of the energy possess a density with respect to the Lebesgue measure. The proofs are based on It\\^o's formula and some properties of local time for semimartingales.
Cartin, Daniel
2015-01-01
At this point in time, there is very little empirical evidence on the likelihood of a space-faring species originating in the biosphere of a habitable world. However, there is a tension between the expectation that such a probability is relatively high (given our own origins on Earth), and the lack of any basis for believing the Solar System has ever been visited by an extraterrestrial colonization effort. This paper seeks to place upper limits on the probability of an interstellar civilizati...
Direct observation of ballistic Brownian motion on a single particle
Huang, Rongxin; Lukic, Branimir; Jeney, Sylvia; Florin, Ernst-Ludwig
2010-01-01
At fast timescales, the self-similarity of random Brownian motion is expected to break down and be replaced by ballistic motion. So far, an experimental verification of this prediction has been out of reach due to a lack of instrumentation fast and precise enough to capture this motion. With a newly developed detector, we have been able to observe the Brownian motion of a single particle in an optical trap with 75 MHz bandwidth and sub-{AA}ngstrom spatial precision. We report the first measur...
DNA transport by a micromachined Brownian ratchet device
Bader, J S; Henck, S A; Deem, M W; McDermott, G A; Bustillo, J M; Simpson, J W; Mulhern, G T; Rothberg, J M; Bader, Joel S; Hammond, Richard W.; Henck, Steven A.; Deem, Michael W.; Dermott, Gregory A. Mc; Bustillo, James M.; Simpson, John W.; Mulhern, Gregory T.; Rothberg, Jonathan M.
1999-01-01
We have micromachined a silicon-chip device that transports DNA with aBrownian ratchet that rectifies the Brownian motion of microscopic particles.Transport properties for a DNA 50mer agree with theoretical predictions, andthe DNA diffusion constant agrees with previous experiments. This type ofmicromachine could provide a generic pump or separation component for DNA orother charged species as part of a microscale lab-on-a-chip. A device withreduced feature size could produce a size-based separation of DNA molecules,with applications including the detection of single nucleotide polymorphisms.
Energy and efficiency optimization of a Brownian heat engine
Bekele, Mulugeta; Yalew, Yeneneh
2007-03-01
A simple Brownian heat engine is modeled as a Brownian particle moving in an external sawtooth potential (with or without) load assisted by the thermal kick it gets from alternately placed hot and cold heat reservoirs along its path. We get closed form expression for its current in terms of the parameters characterizing the model. After analyzing the way it consumes energy to do useful work, we also get closed form expressions for its efficiency as well as for its coefficient of performance when the engine performs as a refrigerator. Recently suggested optimization criteria enables us to exhaustively explore and compare the different operating conditions of the engine.
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...... 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...
The dimension of the Brownian frontier is greater than 1
Bishop, Christopher J.; Jones, Peter; Pemantle, Robin; Peres, Yuval
1995-01-01
Consider a planar Brownian motion run for finite time. The frontier or ``outer boundary'' of the path is the boundary of the unbounded component of the complement. Burdzy (1989) showed that the frontier has infinite length. We improve this by showing that the Hausdorff dimension of the frontier is strictly greater than 1. (It has been conjectured that the Brownian frontier has dimension $4/3$, but this is still open.) The proof uses Jones's Traveling Salesman Theorem and a self-similar tiling...
Winding statistics of a Brownian particle on a ring
International Nuclear Information System (INIS)
We consider a Brownian particle moving on a ring. We study the probability distributions of the total number of turns and the net number of counter-clockwise turns the particle makes until time t. Using a method based on the renewal properties of a Brownian walker, we find exact analytical expressions of these distributions. This method serves as an alternative to the standard path integral techniques which are not always easily adaptable for certain observables. For large t, we show that these distributions have Gaussian scaling forms. We also compute large deviation functions associated to these distributions characterizing atypically large fluctuations. We provide numerical simulations in support of our analytical results. (paper)
Fractional Brownian Motion and Sheet as White Noise Functionals
Institute of Scientific and Technical Information of China (English)
Zhi Yuan HUANG; Chu Jin LI; Jian Ping WAN; Ying WU
2006-01-01
In this short note, we show that it is more natural to look the fractional Brownian motion as functionals of the standard white noises, and the fractional white noise calculus developed by Hu and (φ)ksendal follows directly from the classical white noise functional calculus. As examples we prove that the fractional Girsanov formula, the Ito type integrals and the fractional Black-Scholes formula are easy consequences of their classical counterparts. An extension to the fractional Brownian sheet is also briefly discussed.
Energy Technology Data Exchange (ETDEWEB)
F. Cui; F.J. Presuel-Moreno; R.G. Kelly
2005-10-13
The ability of a SS316L surface wetted with a thin electrolyte layer to serve as an effective cathode for an active localized corrosion site was studied computationally. The dependence of the total net cathodic current, I{sub net}, supplied at the repassivation potential E{sub rp} (of the anodic crevice) on relevant physical parameters including water layer thickness (WL), chloride concentration ([Cl{sup -}]) and length of cathode (Lc) were investigated using a three-level, full factorial design. The effects of kinetic parameters including the exchange current density (i{sub o,c}) and Tafel slope ({beta}{sub c}) of oxygen reduction, the anodic passive current density (i{sub p}) (on the cathodic surface), and E{sub rp} were studied as well using three-level full factorial designs of [Cl{sup -}] and Lc with a fixed WL of 25 {micro}m. The study found that all the three parameters WL, [Cl{sup -}] and Lc as well as the interactions of Lc x WL and Lc x [Cl{sup -}] had significant impact on I{sub net}. A five-factor regression equation was obtained which fits the computation results reasonably well, but demonstrated that interactions are more complicated than can be explained with a simple linear model. Significant effects on I{sub net} were found upon varying either i{sub o,c}, {beta}{sub c}, or E{sub rp}, whereas i{sub p} in the studied range was found to have little impact. It was observed that I{sub net} asymptotically approached maximum values (I{sub max}) when Lc increased to critical minimum values. I{sub max} can be used to determine the stability of coupled localized corrosion and the critical Lc provides important information for experimental design and corrosion protection.
Yaroshchuk, Andriy
2012-11-15
The problem is considered theoretically of dynamics of current-induced concentration polarization of interfaces between ideally perm-selective and non-ideally perm-selective ("leaky") ion-exchange media in binary electrolyte solutions under galvanostatic conditions and at negligible volume flow. In contrast to the previous studies, the analysis is systematically carried out in terms of local thermodynamic equilibrium in the approximation of local electric neutrality in virtual solution. For macroscopically homogeneous media, this enables one to obtain model-independent results in quadratures for the stationary state as well as an approximate scaling-form solution for the transient response to the step-wise increase in electric-current density. These results are formulated in terms of such phenomenological properties of the "leaky" medium as ion transport numbers, diffusion permeability to salt and specific chemical capacity. An easy-to-solve numerically 1D PDE is also formulated in the same terms. A systematic parametric study is carried out within the scope of fine-pore model of "leaky" medium in terms of such properties as volumetric concentration of fixed electric charges and diffusivities of ions of symmetrical electrolyte. While previous studies paid principal attention to the shape and propagation rate of the so-called deionization "shocks", we also consider in detail the time evolution of voltage drop and interface salt concentration. Our analysis confirms the previously predicted pattern of propagating deionization "shocks" within the "leaky" medium but also reveals several novel features. In particular, we demonstrate that the deionization-shock pattern is really pronounced only at intermediate ratios of fixed-charge concentration to the initial salt concentration and at quite high steady-state voltages where the model used in this and previous studies is applicable only at relatively early stages of concentration-polarization process. PMID:22947188
Stability theorems for stochastic differential equations driven by G-Brownian motion
Zhang, Defei
2011-01-01
In this paper, stability theorems for stochastic differential equations and backward stochastic differential equations driven by G-Brownian motion are obtained. We show the existence and uniqueness of solutions to forward-backward stochastic differential equations driven by G-Brownian motion. Stability theorem for forward-backward stochastic differential equations driven by G-Brownian motion is also presented.
[Decentralization of the health sector in Mexico. Scope and limitations of local health systems].
González-Block, M A
1992-01-01
This paper is a product of the reflection on the decentralization and sectorization experiences in Mexico since 1917 with particular emphasis on the 1980s. The historical analysis included the creation of an analytical model designed to identify the relationship between the distinct sanitary policies implemented in Mexico and the tendencies towards decentralization and integration. This analysis is combined with a critical review of the recent decentralization experiences undertaken in the states of Guerrero, Oaxaca and Nuevo León. While comparing Guerrero and Oaxaca, restitution and deconcentration under similar socio-economic conditions were discussed. The comparison between Guerrero and Nuevo Leon allowed the discussion of the benefits and limits of restitution under different socio-economic conditions. In addition, with this model the author discusses a few generalizations regarding the possible future of decentralization.
Localized breaking of flux surfaces and the equilibrium beta limit in the W7AS stellarator
International Nuclear Information System (INIS)
We report on PIES three-dimensional equilibrium calculations for W7AS plasmas which exhibit degraded confinement at high beta with no indication that the confinement degradation is being caused by instabilities. The equilibrium calculations exhibit stochastic field lines in the outer region of the plasma, with the flux surfaces appearing to break only locally in the neighborhood of the outer midplane and to remain intact elsewhere. This conclusion follows from plots of field line trajectories, which show smooth, confined curves punctuated by rapid, erratic radial excursions appearing each time the trajectories cross the outer midplane. This result conforms with intuition and with conventional wisdom, which suggest that the flux surfaces should break near the outer midplane due to the strong compression of the three-dimensional flux surfaces there by the Shafranov shift. The results also conform with a WKB calculation (which is justified by the large mode numbers of the magnetic islands involved). This emerging picture, and the associated long connection lengths of the magnetic field lines, may explain why the impact of the predicted stochastic region on the pressure profile in the experiments may be modest. Although the pressure profile is modified in that region, a substantial pressure profile may be supported there. (author)
International Nuclear Information System (INIS)
The aim of this study was to update data of radiation therapy regimens for improvement in local control in patients with limited-stage small cell lung cancer, a retrospective study was conducted. Results of early concurrent chemoradiotherapy with accelerated hyperfractionation in 30 patients between 1998 and 2005 were retrospectively reviewed. The prescribed dose was 45 Gy in 30 fractions in all patients. All patients received a full dose of radiation therapy; however, interruptions for ≥5 days, mainly due to hematologic toxicity, were required in 18 patients (60%). The 5-year Kaplan-Meier survival rate and the median survival time were 26% and 26 months, respectively. The 4-year in-field control rate was 56%. Sites of relapse were local relapse in 9 patients (6 for in-field relapse, 3 for marginal relapse) and distant metastases in 16 patients (11 for distant metastases only, 5 for distant metastases with local relapse). The sites of marginal relapse were the upper margin in two patients and the peripheral margin in one patient. Grade 3 radiation esophagitis was observed in only three patients. Because in-field control was insufficient, a more effective approach should be sought to provide better local control. (author)
International Nuclear Information System (INIS)
The aim of this study was to assess the accuracy of technetium 99m-labeled red cell scintigraphy in localizing the site of lower gastrointestinal bleeding. The outcome of 203 patients undergoing technetium 99m-labeled red cell scintigraphy was reviewed, and the scan result was compared with the true site of bleeding. The true site of bleeding was determined by other methods including angiography and surgical pathology. Fifty-two scans (26%) were positive and indicated a specific site of bleeding. A definitive bleeding site was identified in 22 patients by other means and correlated with the technetium scan in only 9 cases. The nuclear scan was incorrect in the remaining 13 cases, implying a localization error of 25% (13 of 52). A subgroup of 19 patients with a positive scan underwent a surgical procedure directed by the nuclear scan. Eight of these 12 patients had incorrect surgical procedures based upon findings of more definitive tests, indicating a surgical error of 42% (8 of 19). We conclude that the technetium 99m-labeled red cell scan's ability to accurately localize the site of lower gastrointestinal bleeding is limited. Furthermore, performing a surgical procedure that relies exclusively on localization by red cell scintigraphy will produce an undesirable result in at least 42% of patients
Energy Technology Data Exchange (ETDEWEB)
Hunter, J.M.; Pezim, M.E. (Univ. of British Columbia, Vancouver (Canada))
1990-05-01
The aim of this study was to assess the accuracy of technetium 99m-labeled red cell scintigraphy in localizing the site of lower gastrointestinal bleeding. The outcome of 203 patients undergoing technetium 99m-labeled red cell scintigraphy was reviewed, and the scan result was compared with the true site of bleeding. The true site of bleeding was determined by other methods including angiography and surgical pathology. Fifty-two scans (26%) were positive and indicated a specific site of bleeding. A definitive bleeding site was identified in 22 patients by other means and correlated with the technetium scan in only 9 cases. The nuclear scan was incorrect in the remaining 13 cases, implying a localization error of 25% (13 of 52). A subgroup of 19 patients with a positive scan underwent a surgical procedure directed by the nuclear scan. Eight of these 12 patients had incorrect surgical procedures based upon findings of more definitive tests, indicating a surgical error of 42% (8 of 19). We conclude that the technetium 99m-labeled red cell scan's ability to accurately localize the site of lower gastrointestinal bleeding is limited. Furthermore, performing a surgical procedure that relies exclusively on localization by red cell scintigraphy will produce an undesirable result in at least 42% of patients.
Option Pricing in a Fractional Brownian Motion Environment
Cipian Necula
2008-01-01
The purpose of this paper is to obtain a fractional Black-Scholes formula for the price of an option for every t in [0,T], a fractional Black-Scholes equation and a risk-neutral valuation theorem if the underlying is driven by a fractional Brownian motion BH (t), 1/2
Occupation times distribution for Brownian motion on graphs
Desbois, J
2002-01-01
Considering a Brownian motion on a general graph, we study the joint law for the occupation times on all the bonds. In particular, we show that the Laplace transform of this distribution can be expressed as the ratio of two determinants. We give two formulations, with arc or vertex matrices, for this result and discuss a simple example. (letter to the editor)
Occupation times distribution for Brownian motion on graphs
International Nuclear Information System (INIS)
Considering a Brownian motion on a general graph, we study the joint law for the occupation times on all the bonds. In particular, we show that the Laplace transform of this distribution can be expressed as the ratio of two determinants. We give two formulations, with arc or vertex matrices, for this result and discuss a simple example. (letter to the editor)
Occupation times distribution for Brownian motion on graphs
Energy Technology Data Exchange (ETDEWEB)
Desbois, Jean [Laboratoire de Physique Theorique et Modeles Statistiques, Universite Paris-Sud, Bat. 100, F-91405 Orsay (France)
2002-11-22
Considering a Brownian motion on a general graph, we study the joint law for the occupation times on all the bonds. In particular, we show that the Laplace transform of this distribution can be expressed as the ratio of two determinants. We give two formulations, with arc or vertex matrices, for this result and discuss a simple example. (letter to the editor)
Diffusion of Particle in Hyaluronan Solution, a Brownian Dynamics Simulation
Takasu, Masako; Tomita, Jungo
2004-04-01
Diffusion of a particle in hyaluronan solution is investigated using Brownian dynamics simulation. The slowing down of diffusion is observed, in accordance with the experimental results. The temperature dependence of the diffusion is calculated, and a turnover is obtained when the temperature is increased.
Rotational Brownian Motion on Sphere Surface and Rotational Relaxation
Institute of Scientific and Technical Information of China (English)
Ekrem Aydner
2006-01-01
The spatial components of the autocorrelation function of noninteracting dipoles are analytically obtained in terms of rotational Brownian motion on the surface of a unit sphere using multi-level jumping formalism based on Debye's rotational relaxation model, and the rotational relaxation functions are evaluated.
SOME GEOMETRIC PROPERTIES OF BROWNIAN MOTION ON SIERPINSKI GASKET
Institute of Scientific and Technical Information of China (English)
WUJUN; XIAOYIMIN
1995-01-01
Let {X(t),t≥0} be Brownian motion on Sierpinski gasket,The Hausdorff and packing dimensions of the image of a ompact set are studied,The uniform Hausdorff and packing dimensions of the inverse image are also discussed.
Brownian motion, geometry, and generalizations of Picard's little theorem
Goldberg, S. I.; Mueller, C.
1982-01-01
Brownian motion is introduced as a tool in Riemannian geometry to show how useful it is in the function theory of manifolds, as well as the study of maps between manifolds. As applications, a generalization of Picard's little theorem, and a version of it for Riemann surfaces of large genus are given.
Brownian molecular rotors: Theoretical design principles and predicted realizations
Schönborn, Jan Boyke; Herges, Rainer; Hartke, Bernd
2009-01-01
We propose simple design concepts for molecular rotors driven by Brownian motion and external photochemical switching. Unidirectionality and efﬁciency of the motion is measured by explicit simulations. Two different molecular scaffolds are shown to yield viable molecular rotors when decorated with suitable substituents.
ABSOLUTE CONTINUITY FOR INTERACTING MEASURE-VALUED BRANCHING BROWNIAN MOTIONS
Institute of Scientific and Technical Information of China (English)
ZHAOXUELEI
1997-01-01
The moments and absohite continuity of measure-valued branching Brownian motions with bounded interacting intensity are hivestigated. An estimate of higher order moments is obtained. The ahsolute continuity is verified in the one dimension case. This therehy verifies the conjecture of Méléard and Roelly in [5].
Wrapping Brownian motion and heat kernels II: symmetric spaces
Maher, David G
2010-01-01
In this paper we extend our previous results on wrapping Brownian motion and heat kernels onto compact Lie groups to various symmetric spaces, where a global generalisation of Rouvi\\`ere's formula and the $e$-function are considered. Additionally, we extend some of our results to complex Lie groups, and certain non-compact symmetric spaces.
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. PMID:27504243
Brownian motion and the parabolicity of minimal graphs
Neel, Robert W.
2008-01-01
We prove that minimal graphs (other than planes) are parabolic in the sense that any bounded harmonic function is determined by its boundary values. The proof relies on using the coupling introduced in the author's earlier paper "A martingale approach to minimal surfaces" to show that Brownian motion on such a minimal graph almost surely strikes the boundary in finite time.
Brownian motion of massive black hole binaries and the final parsec problem
Bortolas, E.; Gualandris, A.; Dotti, M.; Spera, M.; Mapelli, M.
2016-09-01
Massive black hole binaries (BHBs) are expected to be one of the most powerful sources of gravitational waves in the frequency range of the pulsar timing array and of forthcoming space-borne detectors. They are believed to form in the final stages of galaxy mergers, and then harden by slingshot ejections of passing stars. However, evolution via the slingshot mechanism may be ineffective if the reservoir of interacting stars is not readily replenished, and the binary shrinking may come to a halt at roughly a parsec separation. Recent simulations suggest that the departure from spherical symmetry, naturally produced in merger remnants, leads to efficient loss cone refilling, preventing the binary from stalling. However, current N-body simulations able to accurately follow the evolution of BHBs are limited to very modest particle numbers. Brownian motion may artificially enhance the loss cone refilling rate in low-N simulations, where the binary encounters a larger population of stars due its random motion. Here we study the significance of Brownian motion of BHBs in merger remnants in the context of the final parsec problem. We simulate mergers with various particle numbers (from 8k to 1M) and with several density profiles. Moreover, we compare simulations where the BHB is fixed at the centre of the merger remnant with simulations where the BHB is free to random walk. We find that Brownian motion does not significantly affect the evolution of BHBs in simulations with particle numbers in excess of one million, and that the hardening measured in merger simulations is due to collisionless loss cone refilling.
High-resolution detection of Brownian motion for quantitative optical tweezers experiments.
Grimm, Matthias; Franosch, Thomas; Jeney, Sylvia
2012-08-01
We have developed an in situ method to calibrate optical tweezers experiments and simultaneously measure the size of the trapped particle or the viscosity of the surrounding fluid. The positional fluctuations of the trapped particle are recorded with a high-bandwidth photodetector. We compute the mean-square displacement, as well as the velocity autocorrelation function of the sphere, and compare it to the theory of Brownian motion including hydrodynamic memory effects. A careful measurement and analysis of the time scales characterizing the dynamics of the harmonically bound sphere fluctuating in a viscous medium directly yields all relevant parameters. Finally, we test the method for different optical trap strengths, with different bead sizes and in different fluids, and we find excellent agreement with the values provided by the manufacturers. The proposed approach overcomes the most commonly encountered limitations in precision when analyzing the power spectrum of position fluctuations in the region around the corner frequency. These low frequencies are usually prone to errors due to drift, limitations in the detection, and trap linearity as well as short acquisition times resulting in poor statistics. Furthermore, the strategy can be generalized to Brownian motion in more complex environments, provided the adequate theories are available. PMID:23005790
Chavanis, Pierre-Henri; Sire, Clément
2006-06-01
We propose a general kinetic and hydrodynamic description of self-gravitating Brownian particles in d dimensions. We go beyond the usual approximations by considering inertial effects and finite-N effects while previous works use a mean-field approximation valid in a proper thermodynamic limit (N --> +infinity) and consider an overdamped regime (xi --> +infinity). We recover known models in some particular cases of our general description. We derive the expression of the virial theorem for self-gravitating Brownian particles and study the linear dynamical stability of isolated clusters of particles and uniform systems by using techniques introduced in astrophysics. We investigate the influence of the equation of state, of the dimension of space, and of the friction coefficient on the dynamical stability of the system. We obtain the exact expression of the critical temperature Tc for a multicomponents self-gravitating Brownian gas in d = 2. We also consider the limit of weak frictions, xi --> 0, and derive the orbit-averaged Kramers equation. PMID:16906911
Chavanis, Pierre-Henri; Sire, Clément
2006-06-01
We propose a general kinetic and hydrodynamic description of self-gravitating Brownian particles in d dimensions. We go beyond the usual approximations by considering inertial effects and finite-N effects while previous works use a mean-field approximation valid in a proper thermodynamic limit (N --> +infinity) and consider an overdamped regime (xi --> +infinity). We recover known models in some particular cases of our general description. We derive the expression of the virial theorem for self-gravitating Brownian particles and study the linear dynamical stability of isolated clusters of particles and uniform systems by using techniques introduced in astrophysics. We investigate the influence of the equation of state, of the dimension of space, and of the friction coefficient on the dynamical stability of the system. We obtain the exact expression of the critical temperature Tc for a multicomponents self-gravitating Brownian gas in d = 2. We also consider the limit of weak frictions, xi --> 0, and derive the orbit-averaged Kramers equation.
Institute of Scientific and Technical Information of China (English)
Xu Sheng-Hua; Sun Zhi-Wei; Li Xu; Jin Tong Wang
2012-01-01
Simultaneous orthokinetic and perikinetic coagulations(SOPCs)are studied for small and large Peclet numbers(Pe)using Brownian dynamics simulation.The results demonstrate that the contributions of the Brownian motion and the shear flow to the overall coagulation rate are basically not additive.At the early stages of coagulation with small Peclet numbers,the ratio of overall coagulation rate to the rate of pure perikinetic coagulation is proportional to Pe1/2,while with high Peclet numbers,the ratio of overall coagulation rate to the rate of pure orthokinetic coagulation is proportional to pe-1/2.Moreover,our results show that the aggregation rate generally changes with time for the SOPC,which is different from that for pure preikinetic and pure orthokinetic coagulations.By comparing the SOPC with pure preikinetic and pure orthokinetic coagulations,we show that the redistribution of particles due to Brownian motion can play a very important role in the SOPC.In addition,the effects of redistribution in the directions perpendicular and parallel to the shear flow direction are different.This perspective explains the behavior of coagulation due to the joint effects of the Brownian motion(perikinetic)and the fluid motion(orthokinetic).
Energy Technology Data Exchange (ETDEWEB)
Sano, Nobuyuki, E-mail: sano@esys.tsukuba.ac.jp [Institute of Applied Physics, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573 (Japan)
2015-12-28
The impurity-limited resistance and the effect of the phase interference among localized multiple impurities in the quasi-one dimensional (quasi-1D) nanowire structures are systematically investigated under the framework of the scattering theory. We derive theoretical expressions of the impurity-limited resistance in the nanowire under the linear response regime from the Landauer formula and from the Boltzmann transport equation (BTE) with the relaxation time approximation. We show that the formula from the BTE exactly coincides with that from the Landauer approach with the weak-scattering limit when the energy spectrum of the in-coming electrons from the reservoirs is narrow and, thus, point out a possibility that the distinction of the impurity-limited resistances derived from the Landauer formula and that of the BTE could be made clear. The derived formulas are applied to the quasi-1D nanowires doped with multiple localized impurities with short-range scattering potential and the validity of various approximations on the resistance are discussed. It is shown that impurity scattering becomes so strong under the nanowire structures that the weak-scattering limit breaks down in most cases. Thus, both phase interference and phase randomization simultaneously play a crucial role in determining the impurity-limited resistance even under the fully coherent framework. When the impurity separation along the wire axis direction is small, the constructive phase interference dominates and the resistance is much greater than the average resistance. As the separation becomes larger, however, it approaches the series resistance of the single-impurity resistance due to the phase randomization. Furthermore, under the uniform configuration of impurities, the space-average resistance of multiple impurities at room temperature is very close to the series resistance of the single-impurity resistance, and thus, each impurity could be regarded as an independent scattering center. The
Sano, Nobuyuki
2015-12-01
The impurity-limited resistance and the effect of the phase interference among localized multiple impurities in the quasi-one dimensional (quasi-1D) nanowire structures are systematically investigated under the framework of the scattering theory. We derive theoretical expressions of the impurity-limited resistance in the nanowire under the linear response regime from the Landauer formula and from the Boltzmann transport equation (BTE) with the relaxation time approximation. We show that the formula from the BTE exactly coincides with that from the Landauer approach with the weak-scattering limit when the energy spectrum of the in-coming electrons from the reservoirs is narrow and, thus, point out a possibility that the distinction of the impurity-limited resistances derived from the Landauer formula and that of the BTE could be made clear. The derived formulas are applied to the quasi-1D nanowires doped with multiple localized impurities with short-range scattering potential and the validity of various approximations on the resistance are discussed. It is shown that impurity scattering becomes so strong under the nanowire structures that the weak-scattering limit breaks down in most cases. Thus, both phase interference and phase randomization simultaneously play a crucial role in determining the impurity-limited resistance even under the fully coherent framework. When the impurity separation along the wire axis direction is small, the constructive phase interference dominates and the resistance is much greater than the average resistance. As the separation becomes larger, however, it approaches the series resistance of the single-impurity resistance due to the phase randomization. Furthermore, under the uniform configuration of impurities, the space-average resistance of multiple impurities at room temperature is very close to the series resistance of the single-impurity resistance, and thus, each impurity could be regarded as an independent scattering center. The
Self-Propelling Nanomotors in the Presence of Strong Brownian Forces
2014-01-01
Motility in living systems is due to an array of complex molecular nanomotors that are essential for the function and survival of cells. These protein nanomotors operate not only despite of but also because of stochastic forces. Artificial means of realizing motility rely on local concentration or temperature gradients that are established across a particle, resulting in slip velocities at the particle surface and thus motion of the particle relative to the fluid. However, it remains unclear if these artificial motors can function at the smallest of scales, where Brownian motion dominates and no actively propelled living organisms can be found. Recently, the first reports have appeared suggesting that the swimming mechanisms of artificial structures may also apply to enzymes that are catalytically active. Here we report a scheme to realize artificial Janus nanoparticles (JNPs) with an overall size that is comparable to that of some enzymes ∼30 nm. Our JNPs can catalyze the decomposition of hydrogen peroxide to water and oxygen and thus actively move by self-electrophoresis. Geometric anisotropy of the Pt–Au Janus nanoparticles permits the simultaneous observation of their translational and rotational motion by dynamic light scattering. While their dynamics is strongly influenced by Brownian rotation, the artificial Janus nanomotors show bursts of linear ballistic motion resulting in enhanced diffusion. PMID:24707952
Coster, Stephanie S; Babbitt, Kimberly J; Cooper, Andrew; Kovach, Adrienne I
2015-02-01
Dispersal and gene flow within animal populations are influenced by the composition and configuration of the landscape. In this study, we evaluated hypotheses about the impact of natural and anthropogenic factors on genetic differentiation in two amphibian species, the spotted salamander (Ambystoma maculatum) and the wood frog (Lithobates sylvaticus) in a commercial forest in central Maine. We conducted this analysis at two scales: a local level, focused on factors measured at each breeding pond, and a landscape level, focused on factors measured between ponds. We investigated the effects of a number of environmental factors in six categories including Productivity, Physical, Land Composition, Land Configuration, Isolation and Location. Embryos were sampled from 56 spotted salamander breeding ponds and 39 wood frog breeding ponds. We used a hierarchical Bayesian approach in the program GESTE at each breeding pond and a random forest algorithm in conjunction with a network analysis between the ponds. We found overall high genetic connectivity across distances up to 17 km for both species and a limited effect of natural and anthropogenic factors on gene flow. We found the null models best explained patterns of genetic differentiation at a local level and found several factors at the landscape level that weakly influenced gene flow. This research indicates multiscale investigations that incorporate local and landscape factors are valuable for understanding patterns of gene flow. Our findings suggest that dispersal rates in this system are high enough to minimize genetic structuring and that current forestry practices do not significantly impede dispersal. PMID:25580642
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. PMID:17223124
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.
Directory of Open Access Journals (Sweden)
Nicholas John Deacon
Full Text Available Quercus oleoides Cham. and Schlect., tropical live oak, is a species of conservation importance in its southern range limit of northwestern Costa Rica. It occurs in high-density stands across a fragmented landscape spanning a contrasting elevation and precipitation gradient. We examined genetic diversity and spatial genetic structure in this geographically isolated and genetically distinct population. We characterized population genetic diversity at 11 nuclear microsatellite loci in 260 individuals from 13 sites. We monitored flowering time at 10 sites, and characterized the local environment in order to compare observed spatial genetic structure to hypotheses of isolation-by-distance and isolation-by-environment. Finally, we quantified pollen dispersal distances and tested for local adaptation through a reciprocal transplant experiment in order to experimentally address these hypotheses.High genetic diversity is maintained in the population and the genetic variation is significantly structured among sampled sites. We identified 5 distinct genetic clusters and average pollen dispersal predominately occurred over short distances. Differences among sites in flowering phenology and environmental factors, however, were not strictly associated with genetic differentiation. Growth and survival of upland and lowland progeny in their native and foreign environments was expected to exhibit evidence of local adaptation due to the more extreme dry season in the lowlands. Seedlings planted in the lowland garden experienced much higher mortality than seedlings in the upland garden, but we did not identify evidence for local adaptation.Overall, this study indicates that the Costa Rican Q. oleoides population has a rich population genetic history. Despite environmental heterogeneity and habitat fragmentation, isolation-by-distance and isolation-by-environment alone do not explain spatial genetic structure. These results add to studies of genetic structure by
The effect of temperature dependence of viscosity on a Brownian heat engine
Taye, Mesfin Asfaw; Duki, Solomon Fekade
2015-12-01
We modeled a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a spatially varying temperature. The strength for the viscous friction γ( x) is considered to decrease exponentially when the temperature T( x) of the medium increases ( γ( x) = B e - AT( x)) as proposed originally by Reynolds [O. Reynolds, Phil. Trans. R. Soc. London 177, 157 (1886)]. Our result depicts that the velocity of the motor is considerably higher when the viscous friction is temperature dependent than that of the case where the viscous friction is temperature independent. The dependence of the efficiency η as well as the coefficient of performance of the refrigerator P ref on model parameters is also explored. If the motor designed to achieve a high velocity against a frictional drag, in the absence of external load f, we show that Carnot efficiency or Carnot refrigerator is unattainable even at quasistatic limit as long as the viscous friction is temperature dependent A ≠ 0. On the contrary, in the limit A → 0 or in general in the presence of an external load (for any A) f ≠ 0, at quasistatic limit, Carnot efficiency or Carnot refrigerator is attainable as long as the heat exchange via kinetic energy is omitted. For all cases, far from quasistatic limit, the efficiency and the coefficient of performance of the refrigerator are higher for constant γ case than the case where γ is temperature dependent. On the other hand, if one includes the heat exchange at the boundary of the heat baths, Carnot efficiency or Carnot refrigerator is unattainable even at quasistatic limit. Moreover, the dependence for the optimized and maximum power efficiencies on the determinant model parameters is explored.
Non-Brownian diffusion in lipid membranes: Experiments and simulations.
Metzler, R; Jeon, J-H; Cherstvy, A G
2016-10-01
The dynamics of constituents and the surface response of cellular membranes-also in connection to the binding of various particles and macromolecules to the membrane-are still a matter of controversy in the membrane biophysics community, particularly with respect to crowded membranes of living biological cells. We here put into perspective recent single particle tracking experiments in the plasma membranes of living cells and supercomputing studies of lipid bilayer model membranes with and without protein crowding. Special emphasis is put on the observation of anomalous, non-Brownian diffusion of both lipid molecules and proteins embedded in the lipid bilayer. While single component, pure lipid bilayers in simulations exhibit only transient anomalous diffusion of lipid molecules on nanosecond time scales, the persistence of anomalous diffusion becomes significantly longer ranged on the addition of disorder-through the addition of cholesterol or proteins-and on passing of the membrane lipids to the gel phase. Concurrently, experiments demonstrate the anomalous diffusion of membrane embedded proteins up to macroscopic time scales in the minute time range. Particular emphasis will be put on the physical character of the anomalous diffusion, in particular, the occurrence of ageing observed in the experiments-the effective diffusivity of the measured particles is a decreasing function of time. Moreover, we present results for the time dependent local scaling exponent of the mean squared displacement of the monitored particles. Recent results finding deviations from the commonly assumed Gaussian diffusion patterns in protein crowded membranes are reported. The properties of the displacement autocorrelation function of the lipid molecules are discussed in the light of their appropriate physical anomalous diffusion models, both for non-crowded and crowded membranes. In the last part of this review we address the upcoming field of membrane distortion by elongated membrane
Non-Brownian diffusion in lipid membranes: Experiments and simulations.
Metzler, R; Jeon, J-H; Cherstvy, A G
2016-10-01
The dynamics of constituents and the surface response of cellular membranes-also in connection to the binding of various particles and macromolecules to the membrane-are still a matter of controversy in the membrane biophysics community, particularly with respect to crowded membranes of living biological cells. We here put into perspective recent single particle tracking experiments in the plasma membranes of living cells and supercomputing studies of lipid bilayer model membranes with and without protein crowding. Special emphasis is put on the observation of anomalous, non-Brownian diffusion of both lipid molecules and proteins embedded in the lipid bilayer. While single component, pure lipid bilayers in simulations exhibit only transient anomalous diffusion of lipid molecules on nanosecond time scales, the persistence of anomalous diffusion becomes significantly longer ranged on the addition of disorder-through the addition of cholesterol or proteins-and on passing of the membrane lipids to the gel phase. Concurrently, experiments demonstrate the anomalous diffusion of membrane embedded proteins up to macroscopic time scales in the minute time range. Particular emphasis will be put on the physical character of the anomalous diffusion, in particular, the occurrence of ageing observed in the experiments-the effective diffusivity of the measured particles is a decreasing function of time. Moreover, we present results for the time dependent local scaling exponent of the mean squared displacement of the monitored particles. Recent results finding deviations from the commonly assumed Gaussian diffusion patterns in protein crowded membranes are reported. The properties of the displacement autocorrelation function of the lipid molecules are discussed in the light of their appropriate physical anomalous diffusion models, both for non-crowded and crowded membranes. In the last part of this review we address the upcoming field of membrane distortion by elongated membrane
Derrida, Bernard; Meerson, Baruch; Sasorov, Pavel V
2016-04-01
Consider a one-dimensional branching Brownian motion and rescale the coordinate and time so that the rates of branching and diffusion are both equal to 1. If X_{1}(t) is the position of the rightmost particle of the branching Brownian motion at time t, the empirical velocity c of this rightmost particle is defined as c=X_{1}(t)/t. Using the Fisher-Kolmogorov-Petrovsky-Piscounov equation, we evaluate the probability distribution P(c,t) of this empirical velocity c in the long-time t limit for c>2. It is already known that, for a single seed particle, P(c,t)∼exp[-(c^{2}/4-1)t] up to a prefactor that can depend on c and t. Here we show how to determine this prefactor. The result can be easily generalized to the case of multiple seed particles and to branching random walks associated with other traveling-wave equations. PMID:27176286
Realization of a Brownian engine to study transport phenomena: a semiclassical approach.
Ghosh, Pradipta; Shit, Anindita; Chattopadhyay, Sudip; Chaudhuri, Jyotipratim Ray
2010-06-01
Brownian particles moving in a periodic potential with or without external load are often used as good theoretical models for the phenomenological studies of microscopic heat engines. The model that we propose here, assumes the particle to be moving in a nonequilibrium medium and we have obtained the exact expression for the stationary current density. We have restricted our consideration to the overdamped motion of the Brownian particle. We present here a self-consistent theory based on the system-reservoir coupling model, within a microscopic approach, of fluctuation induced transport in the semiclassical limit for a general system coupled with two heat baths kept at different temperatures. This essentially puts forth an approach to semiclassical state-dependent diffusion. We also explore the possibility of observing a current when the temperature of the two baths are different, and also envisage that our system may act as a Carnot engine even when the bath temperatures are the same. The condition for such a construction has been elucidated. PMID:20866383
Híjar, Humberto
2015-02-01
We study the Brownian motion of a particle bound by a harmonic potential and immersed in a fluid with a uniform shear flow. We describe this problem first in terms of a linear Fokker-Planck equation which is solved to obtain the probability distribution function for finding the particle in a volume element of its associated phase space. We find the explicit form of this distribution in the stationary limit and use this result to show that both the equipartition law and the equation of state of the trapped particle are modified from their equilibrium form by terms increasing as the square of the imposed shear rate. Subsequently, we propose an alternative description of this problem in terms of a generalized Langevin equation that takes into account the effects of hydrodynamic correlations and sound propagation on the dynamics of the trapped particle. We show that these effects produce significant changes, manifested as long-time tails and resonant peaks, in the equilibrium and nonequilibrium correlation functions for the velocity of the Brownian particle. We implement numerical simulations based on molecular dynamics and multiparticle collision dynamics, and observe a very good quantitative agreement between the predictions of the model and the numerical results, thus suggesting that this kind of numerical simulations could be used as complement of current experimental techniques. PMID:25768490
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...
Two-dimensional motion of Brownian swimmers in linear flows.
Sandoval, Mario; Jimenez, Alonso
2016-03-01
The motion of viruses and bacteria and even synthetic microswimmers can be affected by thermal fluctuations and by external flows. In this work, we study the effect of linear external flows and thermal fluctuations on the diffusion of those swimmers modeled as spherical active (self-propelled) particles moving in two dimensions. General formulae for their mean-square displacement under a general linear flow are presented. We also provide, at short and long times, explicit expressions for the mean-square displacement of a swimmer immersed in three canonical flows, namely, solid-body rotation, shear and extensional flows. These expressions can now be used to estimate the effect of external flows on the displacement of Brownian microswimmers. Finally, our theoretical results are validated by using Brownian dynamics simulations. PMID:26428909
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.
Fast simulation of Brownian dynamics in a crowded environment
Smith, Stephen
2016-01-01
Brownian dynamics simulations are an increasingly popular tool for understanding spatially-distributed biochemical reaction systems. Recent improvements in our understanding of the cellular environment show that volume exclusion effects are fundamental to reaction networks inside cells. These systems are frequently studied by incorporating inert hard spheres (crowders) into three-dimensional Brownian dynamics simulations, however these methods are extremely slow owing to the sheer number of possible collisions between particles. Here we propose a rigorous "crowder-free" method to dramatically increase simulation speed for crowded biochemical reaction systems by eliminating the need to explicitly simulate the crowders. We consider both the case where the reactive particles are point particles, and where they themselves occupy a volume. We use simulations of simple chemical reaction networks to confirm that our simplification is just as accurate as the original algorithm, and that it corresponds to a large spee...
Grachev, Andrey A; Fairall, Christopher W; Guest, Peter S; Persson, P Ola G
2012-01-01
Measurements of atmospheric turbulence made over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are used to determine the limits of applicability of Monin-Obukhov similarity theory (in the local scaling formulation) in the stable atmospheric boundary layer. Based on spectral analysis of wind velocity and air temperature fluctuations, it is shown that when both gradient Richardson number, Ri, and flux Richardson number, Rf, exceed a 'critical value' about 0.20-0.25, the inertial subrange associated with the Kolmogorov cascade dies out and vertical turbulent fluxes become small. Some small-scale turbulence survives even in the supercritical regime, but this is non-Kolmogorov turbulence and it decays rapidly with further increasing stability. Similarity theory is based on the turbulent fluxes in the high-frequency part of the spectra that are associated with energy-containing/flux-carrying eddies. Spectral densities in this high-frequency band diminish as the Kolmogorov...
The frustrated Brownian motion of nonlocal solitary waves
Folli, Viola
2010-01-01
We investigate the evolution of solitary waves in a nonlocal medium in the presence of disorder. By using a perturbational approach, we show that an increasing degree of nonlocality may largely hamper the Brownian motion of self-trapped wave-packets. The result is valid for any kind of nonlocality and in the presence of non-paraxial effects. Analytical predictions are compared with numerical simulations based on stochastic partial differential equation
GENERALIZED BROWNIAN SHEET IMAGES AND BESSEL-RIESZ CAPACITY
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Let (W) be a two-parameter Rd-valued generalized Brownian sheet. The author obtains an explicit Bessel-Riesz capacity estimate for the images of a two-dimensional set under (W). He also presents the connections between the Lebesgue measure of the image of (W) and Bessel-Riesz capacity. His conclusions also solve a problem proposed by J.P.Kahane.
Anyonic partition functions and windings of planar Brownian motion
International Nuclear Information System (INIS)
The computation of the N-cycle Brownian paths contribution FN(α) to the N-anyon partition function is addressed. A detailed numerical analysis based on a random walk on a lattice indicates that FN0(α)=product k=1N-1[1-(N/k)α]. In the paramount three-anyon case, one can show that F3(α) is built by linear states belonging to the bosonic, fermionic, and mixed representations of S3
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.
Rapid morphological characterization of isolated mitochondria using Brownian motion†
Palanisami, Akilan; Fang, Jie; Lowder, Thomas W.; Kunz, Hawley; John H Miller
2012-01-01
Mitochondrial morphology has been associated with numerous pathologies including cancer, diabetes, obesity and heart disease. However, the connection is poorly understood—in part due to the difficulty of characterizing the morphology. This impedes the use of morphology as a tool for disease detection/monitoring. Here, we use the Brownian motion of isolated mitochondria to characterize their size and shape in a high throughput fashion. By using treadmill exercise training, mitochondria from he...
Hidden symmetries, instabilities, and current suppression in Brownian ratchets
Cubero, David; Renzoni, Ferruccio
2015-01-01
The operation of Brownian motors is usually described in terms of out-of-equilibrium and symmetrybreaking settings, with the relevant spatiotemporal symmetries identified from the analysis of the equations of motion for the system at hand. When the appropriate conditions are satisfied,symmetry related trajectories with opposite current are thought to balance each other, yielding suppression of transport. The direction of the current can be precisely controlled around these symmetry points by...
Brownian motion vs. pure-jump processes for individual stocks
Benoît Sévi; César Baena
2011-01-01
Using recent activity signature function methodology developed in Todorov and Tauchen (2010), we provide empirical evidence that individual stocks from the New York Stock Exchange are adequately represented by a Brownian motion plus medium to large (rare) jumps thus invalidating the pure-jump process hypothesis proposed in numerous contributions. This result improves our understanding of the fine structure of asset prices and has implications for derivatives pricing.
Directory of Open Access Journals (Sweden)
Bogdan Suditu
2014-02-01
Full Text Available In the context of the changes that have occurred in the Romanian society, the public authorities are required to play a coordinating role in providing the framework for a sustainable and balanced development of the national territory, and to ensure the quality of life of the citizens. In order to achieve these goals of social responsibility, the public administration authorities must build and adapt the tools of public territorial action based on their specificity and within the existing legal framework and resources,. Thus, the study shows the national and European context that frames the actions of public administration for what concerns the sustainable territorial development. It analyzes the characteristics of administrative-territorial structures of Romania, highlighting their socio-demographic diversity and the territorial forms of institutional cooperation. The approach of these issues is based in the first instance on an analysis of the European strategic documents in the field, as well as on the national regulations concerning the organization and functioning of public administration and territorial planning. The implementation of decentralization and local public autonomy has led to the capitalization of the local potential of some administrative divisions and caused a competition and a difficult cooperation between them. By analogy with the provisions of the quality standards regarding the responsibilities of the organizations towards customers, the study illustrates and analyzes the responsibilities and limits of public administration authorities in promoting sustainable development, territorial equity and the quality of life for the users of public services, i.e. the community members.
Directory of Open Access Journals (Sweden)
Gordon Wang
Full Text Available Photon diffraction limits the resolution of conventional light microscopy at the lateral focal plane to 0.61λ/NA (λ = wavelength of light, NA = numerical aperture of the objective and at the axial plane to 1.4nλ/NA(2 (n = refractive index of the imaging medium, 1.51 for oil immersion, which with visible wavelengths and a 1.4NA oil immersion objective is -220 nm and -600 nm in the lateral plane and axial plane respectively. This volumetric resolution is too large for the proper localization of protein clustering in subcellular structures. Here we combine the newly developed proteomic imaging technique, Array Tomography (AT, with its native 50-100 nm axial resolution achieved by physical sectioning of resin embedded tissue, and a 2D maximum likelihood deconvolution method, based on Bayes' rule, which significantly improves the resolution of protein puncta in the lateral plane to allow accurate and fast computational segmentation and analysis of labeled proteins. The physical sectioning of AT allows tissue specimens to be imaged at the physical optimum of modern high NA plan-apochormatic objectives. This translates to images that have little out of focus light, minimal aberrations and wave-front distortions. Thus, AT is able to provide images with truly invariant point spread functions (PSF, a property critical for accurate deconvolution. We show that AT with deconvolution increases the volumetric analytical fidelity of protein localization by significantly improving the modulation of high spatial frequencies up to and potentially beyond the spatial frequency cut-off of the objective. Moreover, we are able to achieve this improvement with no noticeable introduction of noise or artifacts and arrive at object segmentation and localization accuracies on par with image volumes captured using commercial implementations of super-resolution microscopes.
A discrete impulsive model for random heating and Brownian motion
Ramshaw, John D.
2010-01-01
The energy of a mechanical system subjected to a random force with zero mean increases irreversibly and diverges with time in the absence of friction or dissipation. This random heating effect is usually encountered in phenomenological theories formulated in terms of stochastic differential equations, the epitome of which is the Langevin equation of Brownian motion. We discuss a simple discrete impulsive model that captures the essence of random heating and Brownian motion. The model may be regarded as a discrete analog of the Langevin equation, although it is developed ab initio. Its analysis requires only simple algebraic manipulations and elementary averaging concepts, but no stochastic differential equations (or even calculus). The irreversibility in the model is shown to be a consequence of a natural causal stochastic condition that is closely analogous to Boltzmann's molecular chaos hypothesis in the kinetic theory of gases. The model provides a simple introduction to several ostensibly more advanced topics, including random heating, molecular chaos, irreversibility, Brownian motion, the Langevin equation, and fluctuation-dissipation theorems.
Stochastic Calculus with respect to multifractional Brownian motion
Lebovits, Joachim
2011-01-01
Stochastic calculus with respect to fractional Brownian motion (fBm) has attracted a lot of interest in recent years, motivated in particular by applications in finance and Internet traffic modeling. Multifractional Brownian motion (mBm) is a Gaussian extension of fBm that allows to control the pointwise regularity of the paths of the process and to decouple it from its long range dependence properties. This generalization is obtained by replacing the constant Hurst parameter H of fBm by a function h(t). Multifractional Brownian motion has proved useful in many applications, including the ones just mentioned. In this work we extend to mBm the construction of a stochastic integral with respect to fBm. This stochastic integral is based on white noise theory, as originally proposed in [15], [6], [4] and in [5]. In that view, a multifractional white noise is defined, which allows to integrate with respect to mBm a large class of stochastic processes using Wick products. It\\^o formulas (both for tempered distribut...
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.
Semicircular Canals Circumvent Brownian Motion Overload of Mechanoreceptor Hair Cells.
Muller, Mees; Heeck, Kier; Elemans, Coen P H
2016-01-01
Vertebrate semicircular canals (SCC) first appeared in the vertebrates (i.e. ancestral fish) over 600 million years ago. In SCC the principal mechanoreceptors are hair cells, which as compared to cochlear hair cells are distinctly longer (70 vs. 7 μm), 10 times more compliant to bending (44 vs. 500 nN/m), and have a 100-fold higher tip displacement threshold (< 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. PMID:27448330
Transport coefficients for a confined Brownian ratchet operating between two heat reservoirs
Ryabov, A.; Holubec, V.; Yaghoubi, M. H.; Varga, M.; Foulaadvand, M. E.; Chvosta, P.
2016-09-01
We discuss two-dimensional diffusion of a Brownian particle confined to a periodic asymmetric channel with soft walls modeled by a parabolic potential. In the channel, the particle experiences different thermal noise intensities, or temperatures, in the transversal and longitudinal directions. The model is inspired by the famous Feynman’s ratchet and pawl. Although the standard Fick-Jacobs approximation predicts correctly the effective diffusion coefficient, it fails to capture the ratchet effect. Deriving a correction, which breaks the local detailed balance with the transversal noise source, we obtain a correct mean velocity of the particle and a stationary probability density in the potential unit cell. The derived results are exact for small channel width. Yet, we check by exact numerical calculation that they qualitatively describe the ratchet effect observed for an arbitrary width of the channel.
Brownian motion at fast time scales and thermal noise imaging
Huang, Rongxin
This dissertation presents experimental studies on Brownian motion at fast time scales, as well as our recent developments in Thermal Noise Imaging which uses thermal motions of microscopic particles for spatial imaging. As thermal motions become increasingly important in the studies of soft condensed matters, the study of Brownian motion is not only of fundamental scientific interest but also has practical applications. Optical tweezers with a fast position-sensitive detector provide high spatial and temporal resolution to study Brownian motion at fast time scales. A novel high bandwidth detector was developed with a temporal resolution of 30 ns and a spatial resolution of 1 A. With this high bandwidth detector, Brownian motion of a single particle confined in an optical trap was observed at the time scale of the ballistic regime. The hydrodynamic memory effect was fully studied with polystyrene particles of different sizes. We found that the mean square displacements of different sized polystyrene particles collapse into one master curve which is determined by the characteristic time scale of the fluid inertia effect. The particle's inertia effect was shown for particles of the same size but different densities. For the first time the velocity autocorrelation function for a single particle was shown. We found excellent agreement between our experiments and the hydrodynamic theories that take into account the fluid inertia effect. Brownian motion of a colloidal particle can be used to probe three-dimensional nano structures. This so-called thermal noise imaging (TNI) has been very successful in imaging polymer networks with a resolution of 10 nm. However, TNI is not efficient at micrometer scale scanning since a great portion of image acquisition time is wasted on large vacant volume within polymer networks. Therefore, we invented a method to improve the efficiency of large scale scanning by combining traditional point-to-point scanning to explore large vacant
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.
Convergence in Law to Operator Fractional Brownian Motion of Riemann-Liouville Type
Institute of Scientific and Technical Information of China (English)
Hong Shuai DAI
2013-01-01
In this paper,we extend the well-studied fractional Brownian motion of Riemann-Liouville type to the multivariate case,and the corresponding processes are called operator fractional Brownian motions of Riemann-Liouville type.We also provide two results on approximation to operator fractional Brownian motions of Riemann-Liouville type.The first approximation is based on a Poisson process,and the second one is based on a sequence of I.I.D.random variables.
The Local Fractional Bootstrap
DEFF Research Database (Denmark)
Bennedsen, Mikkel; Hounyo, Ulrich; Lunde, Asger;
We introduce a bootstrap procedure for high-frequency statistics of Brownian semistationary processes. More specifically, we focus on a hypothesis test on the roughness of sample paths of Brownian semistationary processes, which uses an estimator based on a ratio of realized power variations. Our...... to two empirical data sets: we assess the roughness of a time series of high-frequency asset prices and we test the validity of Kolmogorov's scaling law in atmospheric turbulence data.......We introduce a bootstrap procedure for high-frequency statistics of Brownian semistationary processes. More specifically, we focus on a hypothesis test on the roughness of sample paths of Brownian semistationary processes, which uses an estimator based on a ratio of realized power variations. Our...... 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...
Directory of Open Access Journals (Sweden)
L. Spruzeniece
2015-04-01
Full Text Available This study focuses on physiochemical processes occurring in a brittle-ductile shear zone at both fluid-present and fluid-limited conditions. In the studied shear zone (Wyangala, SE Australia, a coarse-grained two feldspar-quartz-biotite granite is transformed into a medium grained orthogneiss at the shear zone margins and a fine-grained quartz-muscovite phyllonite in the central parts. The orthogneiss displays cataclasis of feldspar and crystal-plastic deformation of quartz. Quartz accommodates most of the deformation and is extensively recrystallized showing distinct crystallographic preferred orientation (CPO. Feldspar-to-muscovite, biotite-to-muscovite and albitization reactions occur locally at porphyroclasts' fracture surfaces and margins. However, the bulk rock composition shows very little change in respect to the wall rock composition. In contrast, in the shear zone centre quartz occurs as large, weakly deformed porphyroclasts, in sizes similar to that in the wall rock, suggesting that it has undergone little deformation. Feldspars and biotite are almost completely reacted to muscovite, which is arranged in a fine-grained interconnected matrix. Muscovite-rich layers contain significant amounts of fine-grained intermixed quartz with random CPO. These domains are interpreted to have accommodated most of the strain. Bulk rock chemistry data shows a significant increase in SiO2 and depletion in NaO content compared to the wall rock composition. We suggest that the high and low strain fabrics represent markedly different scenarios and cannot be interpreted as a simple sequential development with respect to strain. We suggest that the fabrics and mineralogical changes in the shear zone centre have formed due to fluid influx probably along an initially brittle fracture. Here, hydration reactions dramatically changed the rheological properties of the rock. In the newly produced muscovite-quartz layers creep cavitation associated with grain
Anomalous velocity distributions in active Brownian suspensions.
Fiege, Andrea; Vollmayr-Lee, Benjamin; Zippelius, Annette
2013-08-01
Large-scale simulations and analytical theory have been combined to obtain the nonequilibrium velocity distribution, f(v), of randomly accelerated particles in suspension. The simulations are based on an event-driven algorithm, generalized to include friction. They reveal strongly anomalous but largely universal distributions, which are independent of volume fraction and collision processes, which suggests a one-particle model should capture all the essential features. We have formulated this one-particle model and solved it analytically in the limit of strong damping, where we find that f(v) decays as 1/v for multiple decades, eventually crossing over to a Gaussian decay for the largest velocities. Many particle simulations and numerical solution of the one-particle model agree for all values of the damping. PMID:24032806
Diffusion theory of Brownian particles moving at constant speed in D dimensions
Sevilla, Francisco J.
2015-03-01
The propagation of Brownian-active particles that move at constant speed in the limit of short times, differs from wave-like propagation in that active particles propagate without leaving a wake trailing characteristic of wave propagation in even dimensions. In the long time regime, normal diffusion is expected due to random fluctuations that disperse the particle direction of motion. A phenomenological equation that describe the transition from the behavior free of effects of wake, to the normal diffusion of the particles is proposed. A comparison of the results predicted by such equation with those obtained from models using Langevin equations is presented in the spherically symmetric case. FJS acknowledges support from PAPIIT-UNAM through the Grant IN113114.
Brownian motion of massive black hole binaries and the final parsec problem
Bortolas, E; Dotti, M; Spera, M; Mapelli, M
2016-01-01
Massive black hole binaries (BHBs) are expected to be one of the most powerful sources of gravitational waves (GWs) in the frequency range of the pulsar timing array and of forthcoming space-borne detectors. They are believed to form in the final stages of galaxy mergers, and then harden by slingshot ejections of passing stars. However, evolution via the slingshot mechanism may be ineffective if the reservoir of interacting stars is not readily replenished, and the binary shrinking may come to a halt at roughly a parsec separation. Recent simulations suggest that the departure from spherical symmetry, naturally produced in merger remnants, leads to efficient loss cone refilling, preventing the binary from stalling. However, current N-body simulations able to accurately follow the evolution of BHBs are limited to very modest particle numbers. Brownian motion may artificially enhance the loss cone refilling rate in low-N simulations, where the binary encounters a larger population of stars due its random motion...
Brownian motion properties of optoelectronic random bit generators based on laser chaos.
Li, Pu; Yi, Xiaogang; Liu, Xianglian; Wang, Yuncai; Wang, Yongge
2016-07-11
The nondeterministic property of the optoelectronic random bit generator (RBG) based on laser chaos are experimentally analyzed from two aspects of the central limit theorem and law of iterated logarithm. The random bits are extracted from an optical feedback chaotic laser diode using a multi-bit extraction technique in the electrical domain. Our experimental results demonstrate that the generated random bits have no statistical distance from the Brownian motion, besides that they can pass the state-of-the-art industry-benchmark statistical test suite (NIST SP800-22). All of them give a mathematically provable evidence that the ultrafast random bit generator based on laser chaos can be used as a nondeterministic random bit source. PMID:27410852
Stochastic shell models driven by a multiplicative fractional Brownian-motion
Bessaih, Hakima; Garrido-Atienza, María J.; Schmalfuss, Björn
2016-04-01
We prove existence and uniqueness of the solution of a stochastic shell-model. The equation is driven by an infinite dimensional fractional Brownian-motion with Hurst-parameter H ∈(1 / 2 , 1) , and contains a non-trivial coefficient in front of the noise which satisfies special regularity conditions. The appearing stochastic integrals are defined in a fractional sense. First, we prove the existence and uniqueness of variational solutions to approximating equations driven by piecewise linear continuous noise, for which we are able to derive important uniform estimates in some functional spaces. Then, thanks to a compactness argument and these estimates, we prove that these variational solutions converge to a limit solution, which turns out to be the unique pathwise mild solution associated to the shell-model with fractional noise as driving process.
New models and predictions for Brownian coagulation of non-interacting spheres.
Kelkar, Aniruddha V; Dong, Jiannan; Franses, Elias I; Corti, David S
2013-01-01
The classical steady-state Smoluchowski model for Brownian coagulation is evaluated using Brownian Dynamics Simulations (BDS) as a benchmark. The predictions of this approach compare favorably with the results of BDS only in the dilute limit, that is, for volume fractions of φ≤5×10(-4). From the solution of the more general unsteady-state diffusion equation, a new model for coagulation is developed. The resulting coagulation rate constant is time-dependent and approaches the steady-state limit only at large times. Moreover, in contrast to the Smoluchowski model, this rate constant depends on the particle size, with the transient effects becoming more significant at larger sizes. The predictions of the unsteady-state model agree well with the BDS results up to volume fractions of about φ=0.1, at which the aggregation half-time predicted by the Smoluchowski model is five times that of the BDS. A new procedure to extract the aggregation rate constant from simulation results based on this model is presented. The choice of the rate constant kernel used in the population balance equations for complete aggregation is also evaluated. Extension of the new model to a variable rate constant kernel leads to increased accuracy of the predictions, especially for φ≤5×10(-3). This size-dependence of the rate constant kernel affects particularly the predictions for initially polydisperse sphere systems. In addition, the model is extended to account in a novel way for both short-range viscous two-particle interactions and long-range many-particle Hydrodynamic Interactions (HI). Predictions including HI agree best with the BDS results. The new models presented here offer accurate and computationally less-intensive predictions of the coagulation dynamics while also accounting for hydrodynamic coupling. PMID:23036339
Jorgensen, Christopher F.; Powell, Larkin A.; Lusk, Jeffery J.; Bishop, Andrew A.; Fontaine, Joseph J.
2014-01-01
Landscapes in agricultural systems continue to undergo significant change, and the loss of biodiversity is an ever-increasing threat. Although habitat restoration is beneficial, management actions do not always result in the desired outcome. Managers must understand why management actions fail; yet, past studies have focused on assessing habitat attributes at a single spatial scale, and often fail to consider the importance of ecological mechanisms that act across spatial scales. We located survey sites across southern Nebraska, USA and conducted point counts to estimate Ring-necked Pheasant abundance, an economically important species to the region, while simultaneously quantifying landscape effects using a geographic information system. To identify suitable areas for allocating limited management resources, we assessed land cover relationships to our counts using a Bayesian binomial-Poisson hierarchical model to construct predictive Species Distribution Models of relative abundance. Our results indicated that landscape scale land cover variables severely constrained or, alternatively, facilitated the positive effects of local land management for Ring-necked Pheasants. PMID:24918779
Brownian dynamics in a confined geometry. Experiments and numerical simulations
Garnier, Nicolas; Ostrowsky, N.
1991-01-01
The Brownian dynamics of a colloidal suspension is measured in the immediate vicinity of a rigid surface by the Evanescent Quasielastic Light Scattering Technique. A net decrease of the measured diffusion coefficient is observed, due to the hydrodynamic slowing down of the particles very close to the wall. This effect is all the more important when the particles are allowed to get closer to the wall, i.e. when the range of the static wall/particle repulsive interaction decreases. It thus prov...
A Flashing Model for Transport of Brownian Motors
Institute of Scientific and Technical Information of China (English)
赵同军; 展永; 吴建海; 王永宏
2002-01-01
A flashing coloured noise model is proposed to describe the motion of a molecular motor. In this model,the overdamped Brownian particle moves in an asymmetric periodic potential with a tashing Ornstein-Ulenbeck coloured noise. The relationship between the current and the parameters-such as the intensity, the correlation time of coloured noise and the flip rate of the noise-is discussed using the Monte Carlo simulation method.Current reversal occurs with the change of the correlation time and the flip rate of coloured noise, which may be related to the directed motion and the current reversal of molecular motors.
Quantum correlations from Brownian diffusion of chaotic level-spacings
Evangelou, S N
2004-01-01
Quantum chaos is linked to Brownian diffusion of the underlying quantum energy level-spacing sequences. The level-spacings viewed as functions of their order execute random walks which imply uncorrelated random increments of the level-spacings while the integrability to chaos transition becomes a change from Poisson to Gauss statistics for the level-spacing increments. This universal nature of quantum chaotic spectral correlations is numerically demonstrated for eigenvalues from random tight binding lattices and for zeros of the Riemann zeta function.
Occupation times for planar and higher dimensional Brownian motion
International Nuclear Information System (INIS)
We consider a planar Brownian motion starting from O at time t = 0 and stopped at t. Denoting by T the time spent in a wedge of apex O and angle Θ, we develop a method to compute systematically the moments of T for general Θ values. We apply it to obtain analytically the second and third moments for a general wedge angle and, also, the fourth moment for the quadrant (Θ = π/2). We compare our results with numerical simulations. Finally, with standard perturbation theory, we establish a general formula for the second moment of an orthant occupation time
Moments of inertia and the shapes of Brownian paths
International Nuclear Information System (INIS)
The joint probability law of the principal moments of inertia of Brownian paths (open or closed) is computed, using constrained path integrals and Random Matrix Theory. The case of two-dimensional paths is discussed in detail. In particular, it is shown that the ratio of the average values of the largest and smallest moments is equal to 4.99 (open paths) and 3.07 (closed paths). Results of numerical simulations are also presented, which include investigation of the relationships between the moments of inertia and the arithmetic area enclosed by a path. (authors) 28 refs., 2 figs
Algebraic and arithmetic area for $m$ planar Brownian paths
Desbois, Jean; Ouvry, Stephane
2011-01-01
The leading and next to leading terms of the average arithmetic area $$ enclosed by $m\\to\\infty$ independent closed Brownian planar paths, with a given length $t$ and starting from and ending at the same point, is calculated. The leading term is found to be $ \\sim {\\pi t\\over 2}\\ln m$ and the $0$-winding sector arithmetic area inside the $m$ paths is subleading in the asymptotic regime. A closed form expression for the algebraic area distribution is also obtained and discussed.
Occupation times for planar and higher dimensional Brownian motion
Energy Technology Data Exchange (ETDEWEB)
Desbois, Jean [CNRS, University Paris Sud, UMR8626, LPTMS, ORSAY CEDEX, F-91405 (France)
2007-03-09
We consider a planar Brownian motion starting from O at time t = 0 and stopped at t. Denoting by T the time spent in a wedge of apex O and angle {theta}, we develop a method to compute systematically the moments of T for general {theta} values. We apply it to obtain analytically the second and third moments for a general wedge angle and, also, the fourth moment for the quadrant ({theta} = {pi}/2). We compare our results with numerical simulations. Finally, with standard perturbation theory, we establish a general formula for the second moment of an orthant occupation time.
Anyonic Partition Functions and Windings of Planar Brownian Motion
Desbois, Jean; Heinemann, Christine; Ouvry, Stéphane
1994-01-01
The computation of the $N$-cycle brownian paths contribution $F_N(\\alpha)$ to the $N$-anyon partition function is adressed. A detailed numerical analysis based on random walk on a lattice indicates that $F_N^{(0)}(\\alpha)= \\prod_{k=1}^{N-1}(1-{N\\over k}\\alpha)$. In the paramount $3$-anyon case, one can show that $F_3(\\alpha)$ is built by linear states belonging to the bosonic, fermionic, and mixed representations of $S_3$.
Moments of inertia and the shapes of Brownian paths
Energy Technology Data Exchange (ETDEWEB)
Fougere, F.; Desbois, J.
1993-12-31
The joint probability law of the principal moments of inertia of Brownian paths (open or closed) is computed, using constrained path integrals and Random Matrix Theory. The case of two-dimensional paths is discussed in detail. In particular, it is shown that the ratio of the average values of the largest and smallest moments is equal to 4.99 (open paths) and 3.07 (closed paths). Results of numerical simulations are also presented, which include investigation of the relationships between the moments of inertia and the arithmetic area enclosed by a path. (authors) 28 refs., 2 figs.
Algebraic and arithmetic area for m planar Brownian paths
International Nuclear Information System (INIS)
The leading and next to leading terms of the average arithmetic area (S(m)) enclosed by m→∞ independent closed Brownian planar paths, with a given length t and starting from and ending at the same point, are calculated. The leading term is found to be (S(m)) ∼ (πt/2)lnm and the 0-winding sector arithmetic area inside the m paths is subleading in the asymptotic regime. A closed form expression for the algebraic area distribution is also obtained and discussed
Entropic Ratchet transport of interacting active Brownian particles
Energy Technology Data Exchange (ETDEWEB)
Ai, Bao-Quan, E-mail: aibq@hotmail.com [Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, 510006 Guangzhou (China); He, Ya-Feng [College of Physics Science and Technology, Hebei University, 071002 Baoding (China); Zhong, Wei-Rong, E-mail: wrzhong@jnu.edu.cn [Department of Physics and Siyuan Laboratory, College of Science and Engineering, Jinan University, 510632 Guangzhou (China)
2014-11-21
Directed transport of interacting active (self-propelled) Brownian particles is numerically investigated in confined geometries (entropic barriers). The self-propelled velocity can break thermodynamical equilibrium and induce the directed transport. It is found that the interaction between active particles can greatly affect the ratchet transport. For attractive particles, on increasing the interaction strength, the average velocity first decreases to its minima, then increases, and finally decreases to zero. For repulsive particles, when the interaction is very weak, there exists a critical interaction at which the average velocity is minimal, nearly tends to zero, however, for the strong interaction, the average velocity is independent of the interaction.
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.
Phenomenon of Repeated Current Reversals in the Brownian Ratchet
Institute of Scientific and Technical Information of China (English)
杨明; 曹力; 吴大进; 李湘莲
2002-01-01
We study the probability current of the Brownian particles in a tilted periodic piecewise linear "saw-tooth"potential. It is found that the stationary probability current takes on a maximum value at a given additive noise if the intensity of the multiplicative noise is appropriate and at the same time both noises are correlated;and the direction of the stationary probability current is reversed more than once upon some certain correlation intensities between both noises. It is proven that the occurrence of current reversal is only dependent on the relative intensity of the multiplicative and additive noises, but has nothing to do with the absolute intensities of the two noises.
Cavity-enhanced optical detection of carbon nanotube Brownian motion
Stapfner, S; Hunger, D; Weig, E M; Reichel, J; Favero, I
2012-01-01
Optical cavities with small mode volume are well-suited to detect the vibration of sub-wavelength sized objects. Here we employ a fiber-based, high-finesse optical microcavity to detect the Brownian motion of a freely suspended carbon nanotube at room temperature under vacuum. The optical detection resolves deflections of the oscillating tube down to 50pm/Hz^1/2. A full vibrational spectrum of the carbon nanotube is obtained and confirmed by characterization of the same device in a scanning electron microscope. Our work successfully extends the principles of high-sensitivity optomechanical detection to molecular scale nanomechanical systems.
Role of Brownian Motion Hydrodynamics on Nanofluid Thermal Conductivity
Energy Technology Data Exchange (ETDEWEB)
W Evans, J Fish, P Keblinski
2005-11-14
We use a simple kinetic theory based analysis of heat flow in fluid suspensions of solid nanoparticles (nanofluids) to demonstrate that the hydrodynamics effects associated with Brownian motion have a minor effect on the thermal conductivity of the nanofluid. Our conjecture is supported by the results of molecular dynamics simulations of heat flow in a model nanofluid with well-dispersed particles. Our findings are consistent with the predictions of the effective medium theory as well as with recent experimental results on well dispersed metal nanoparticle suspensions.
Brownian dynamics simulation for modeling ion permeation across bionanotubes.
Krishnamurthy, Vikram; Chung, Shin-Ho
2005-03-01
The principles underlying Brownian dynamics (BD), its statistical consistency, and algorithms for practical implementation are outlined here. The ability to compute current flow across ion channels confers a distinct advantage to BD simulations compared to other simulation techniques. Thus, two obvious applications of BD ion channels are in calculation of the current-voltage and current-concentration curves, which can be directly compared to the physiological measurements to assess the reliability of the model and predictive power of the method. We illustrate how BD simulations are used to unravel the permeation dynamics in two biological ion channels-the KcsA K+ channel and CIC Cl- channel. PMID:15816176
Brownian Motion and Harmonic Functions on Rotationally Symmetric Manifolds
March, Peter
1986-01-01
We consider Brownian motion $X$ on a rotationally symmetric manifold $M_g = (\\mathbb{R}^n, ds^2), ds^2 = dr^2 + g(r)^2 d\\theta^2$. An integral test is presented which gives a necessary and sufficient condition for the nontriviality of the invariant $\\sigma$-field of $X$, hence for the existence of nonconstant bounded harmonic functions on $M_g$. Conditions on the sectional curvatures are given which imply the convergence or the divergence of the test integral.
Minimal Cost of a Brownian Risk without Ruin
Luo, Shangzhen
2011-01-01
In this paper, we study a risk process modeled by a Brownian motion with drift (the diffusion approximation model). The insurance entity can purchase reinsurance to lower its risk and receive cash injections at discrete times to avoid ruin. Proportional reinsurance and excess-of-loss reinsurance are considered. The objective is to find the optimal reinsurance and cash injection strategy that minimizes the total cost to keep the company's surplus process non-negative, i.e. without ruin, where the cost function is defined as the total discounted value of the injections. The optimal solution is found explicitly by solving the according quasi-variational inequalities (QVIs).
Consistent finite-element approach to Brownian polymer dynamics with anisotropic friction.
Cyron, Christian J; Wall, Wolfgang A
2010-12-01
In the last decades simulation tools for Brownian dynamics of polymers have attracted more and more interest. Here we present a mathematically consistent finite element approach to the simulation of Brownian polymer dynamics. The viscous damping forces are accounted for by an anisotropic friction model. By comparison with theoretical predictions and experimental data we demonstrate the reliability and efficiency of this method. PMID:21230752
On the expectation of normalized Brownian functionals up to first hitting times
Elie, Romuald; Rosenbaum, Mathieu; Yor, Marc
2013-01-01
Let B be a Brownian motion and T its first hitting time of the level 1. For U a uniform random variable independent of B, we study in depth the distribution of T^{-1/2}B_{UT}, that is the rescaled Brownian motion sampled at uniform time. In particular, we show that this variable is centered.
Thermodynamic characteristics of a Brownian heat pump in a spatially periodic temperature field
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper has studied the thermodynamic performance of a thermal Brownian heat pump,which consists of Brownian particles moving at a periodic sawtooth potential with external forces and contacting with the alternating hot and cold reservoirs along the space coordinate.The heat flows driven by both potential and kinetic energies are taken into account.The analytical expressions for the heating load,coefficient of performance(COP) and power input of the Brownian heat pump are derived and the performance characteristics are obtained by numerical calculations.It is shown that due to the heat flow via the change of kinetic energy of the particles,the Brownian heat pump is always irreversible and the COP can never attain the Carnot COP.The study has also investigated the influences of the operating parameters,i.e.the external force,barrier height of the potential,asymmetry of the sawtooth potential and temperature ratio of the heat reservoirs,on the performance of the Brownian heat pump.The effective regions of external force and barrier height of the potential in which the Brownian motor can operates as a heat pump are determined.The results show that the performance of the Brownian heat pump greatly depends on the parameters;if the parameters are properly chosen,the Brownian heat pump may be controlled to operate in the optimal regimes.
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…
Linear filtering with fractional Brownian motion in the signal and observation processes
Directory of Open Access Journals (Sweden)
M. L. Kleptsyna
1999-01-01
Full Text Available Integral equations for the mean-square estimate are obtained for the linear filtering problem, in which the noise generating the signal is a fractional Brownian motion with Hurst index h∈(3/4,1 and the noise in the observation process includes a fractional Brownian motion as well as a Wiener process.
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.
Novak, Wilhelm
2014-01-01
Local limit load solutions for plates containing semi-elliptical surface cracks subjected to pure membrane loading cases, pure bending loading cases and combinations of the two are determined using non-linear finite element analysis. Both loading cases that open the crack and loading cases that close the crack are considered. The study covers both shallow and deep cracks with different aspect ratios. Results from the finite element simulations are fitted to an analytical expression. The local...
Differential dynamic microscopy to characterize Brownian motion and bacteria motility
Germain, David; Leocmach, Mathieu; Gibaud, Thomas
2016-03-01
We have developed a lab module for undergraduate students, which involves the process of quantifying the dynamics of a suspension of microscopic particles using Differential Dynamic Microscopy (DDM). DDM is a relatively new technique that constitutes an alternative method to more classical techniques such as dynamic light scattering (DLS) or video particle tracking (VPT). The technique consists of imaging a particle dispersion with a standard light microscope and a camera and analyzing the images using a digital Fourier transform to obtain the intermediate scattering function, an autocorrelation function that characterizes the dynamics of the dispersion. We first illustrate DDM in the textbook case of colloids under Brownian motion, where we measure the diffusion coefficient. Then we show that DDM is a pertinent tool to characterize biological systems such as motile bacteria.
Brownian motion near a liquid-gas interface
Benavides-Parra, Juan Carlos; Jacinto-Méndez, Damián; Brotons, Guillaume; Carbajal-Tinoco, Mauricio D.
2016-09-01
By using digital video microscopy, we study the three-dimensional displacement of fluorescent colloidal particles that are located close to a water-air interface. Our technique takes advantage of the diffraction pattern generated by fluorescent spheres that are found below the focal plane of the microscope objective. By means of image analysis software, we are able to determine the spatial location of a few beads in a sequence of digital images, which allows us to reconstruct their trajectories. From their corresponding mean square displacements, we get the diffusion coefficients in the directions parallel and perpendicular to the interface. We find a qualitatively different kind of diffusion between the two directions, in agreement with theoretical predictions that are obtained from established models as well as our own proposals. Quite interesting, we observe the enhanced Brownian motion in the parallel direction.
The genealogy of branching Brownian motion with absorption
Berestycki, Julien; Schweinsberg, Jason
2010-01-01
We consider a system of particles which perform branching Brownian motion with negative drift and are killed upon reaching zero, in the near-critical regime where the total population stays roughly constant with approximately N particles. We show that the characteristic time scale for the evolution of this population is of order (log N)^3, in the sense that when time is measured in these units, the scaled number of particles converges to a variant of Neveu's continuous-state branching process. Furthermore, the genealogy of the particles is then governed by a coalescent process known as the Bolthausen-Sznitman coalescent. This validates the non-rigorous predictions by Brunet, Derrida, Muller, and Munier for a closely related model.
Active Brownian motion of an asymmetric rigid particle
Mammadov, Gulmammad
2012-01-01
Individual movements of a rod-like self-propelled particle on a flat substrate are quantified. Biological systems that fit into this description may be the Gram-negative delta-proteobacterium Myxococcus xanthus, Gram-negative bacterium Escherichia coli, and Mitochondria. There are also non-living analogues such as vibrated polar granulates and self-driven anisotropic colloidal particles. For that we study the Brownian motion of an asymmetric rod-like rigid particle self-propelled at a fixed speed along its long axis in two dimensions. The motion of such a particle in a uniform external potential field is also considered. The theoretical model presented here is anticipated to better describe individual cell motion as well as intracellular transport in 2D than previous models.
Normal and anomalous diffusion of Brownian particles on disordered potentials
Salgado-García, R.
2016-07-01
In this work we study the transition from normal to anomalous diffusion of Brownian particles on disordered potentials. The potential model consists of a series of "potential hills" (defined on a unit cell of constant length) whose heights are chosen randomly from a given distribution. We calculate the exact expression for the diffusion coefficient in the case of uncorrelated potentials for arbitrary distributions. We show that when the potential heights have a Gaussian distribution (with zero mean and a finite variance) the diffusion of the particles is always normal. In contrast, when the distribution of the potential heights is exponentially distributed the diffusion coefficient vanishes when the system is placed below a critical temperature. We calculate analytically the diffusion exponent for the anomalous (subdiffusive) phase by using the so-called "random trap model". Our predictions are tested by means of Langevin simulations obtaining good agreement within the accuracy of our numerical calculations.
Optimal dividends in the Brownian motion risk model with interest
Fang, Ying; Wu, Rong
2009-07-01
In this paper, we consider a Brownian motion risk model, and in addition, the surplus earns investment income at a constant force of interest. The objective is to find a dividend policy so as to maximize the expected discounted value of dividend payments. It is well known that optimality is achieved by using a barrier strategy for unrestricted dividend rate. However, ultimate ruin of the company is certain if a barrier strategy is applied. In many circumstances this is not desirable. This consideration leads us to impose a restriction on the dividend stream. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. Under this additional constraint, we show that the optimal dividend strategy is formed by a threshold strategy.
Modeling collective emotions: a stochastic approach based on Brownian agents
International Nuclear Information System (INIS)
We develop a agent-based framework to model the emergence of collective emotions, which is applied to online communities. Agents individual emotions are described by their valence and arousal. Using the concept of Brownian agents, these variables change according to a stochastic dynamics, which also considers the feedback from online communication. Agents generate emotional information, which is stored and distributed in a field modeling the online medium. This field affects the emotional states of agents in a non-linear manner. We derive conditions for the emergence of collective emotions, observable in a bimodal valence distribution. Dependent on a saturated or a super linear feedback between the information field and the agent's arousal, we further identify scenarios where collective emotions only appear once or in a repeated manner. The analytical results are illustrated by agent-based computer simulations. Our framework provides testable hypotheses about the emergence of collective emotions, which can be verified by data from online communities. (author)
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 (
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.
Temporal Correlations of the Running Maximum of a Brownian Trajectory
Bénichou, Olivier; Krapivsky, P. L.; Mejía-Monasterio, Carlos; Oshanin, Gleb
2016-08-01
We study the correlations between the maxima m and M of a Brownian motion (BM) on the time intervals [0 ,t1] and [0 ,t2], with t2>t1. We determine the exact forms of the distribution functions P (m ,M ) and P (G =M -m ), and calculate the moments E {(M-m ) k} and the cross-moments E {mlMk} with arbitrary integers l and k . We show that correlations between m and M decay as √{t1/t2 } when t2/t1→∞ , revealing strong memory effects in the statistics of the BM maxima. We also compute the Pearson correlation coefficient ρ (m ,M ) and the power spectrum of Mt, and we discuss a possibility of extracting the ensemble-averaged diffusion coefficient in single-trajectory experiments using a single realization of the maximum process.
On a non-linear transformation between Brownian martingales
Shkolnikov, Mykhaylo
2012-01-01
The paper studies a non-linear transformation between Brownian martingales, which is given by the inverse of the pricing operator in the mathematical finance terminology. Subsequently, the solvability of systems of equations corresponding to such transformations is investigated. The latter give rise to novel monotone pathwise couplings of an arbitrary number of certain diffusion processes with varying diffusion coefficients. In the case that there is an uncountable number of these diffusion processes and that the index set is an interval such couplings can be viewed as models for the growth of one-dimensional random surfaces. With this motivation in mind, we derive the appropriate stochastic partial differential equations for the growth of such surfaces.
An Efficient Method to Study Nondiffusive Motion of Brownian Particles
Directory of Open Access Journals (Sweden)
Lisý Vladimír
2016-01-01
Full Text Available The experimental access to short timescales has pointed to the inadequacy of the standard Langevin theory of the Brownian motion (BM in fluids. The hydrodynamic theory of the BM describes well the observed motion of the particles; however, the published approach should be improved in several points. In particular, it leads to incorrect correlation properties of the thermal noise driving the particles. In our contribution we present an efficient method, which is applicable to linear generalized Langevin equations describing the BM of particles with any kind of memory and apply it to interpret the experiments where nondiffusive BM of particles was observed. It is shown that the applicability of the method is much broader, allowing, among all, to obtain efficient solutions of various problems of anomalous BM.
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.
Brownian Dynamics of Colloidal Particles in Lyotropic Chromonic Liquid Crystals
Martinez, Angel; Collings, Peter J.; Yodh, Arjun G.
We employ video microscopy to study the Brownian dynamics of colloidal particles in the nematic phase of lyotropic chromonic liquid crystals (LCLCs). These LCLCs (in this case, DSCG) are water soluble, and their nematic phases are characterized by an unusually large elastic anisotropy. Our preliminary measurements of particle mean-square displacement for polystyrene colloidal particles (~5 micron-diameter) show diffusive and sub-diffusive behaviors moving parallel and perpendicular to the nematic director, respectively. In order to understand these motions, we are developing models that incorporate the relaxation of elastic distortions of the surrounding nematic field. Further experiments to confirm these preliminary results and to determine the origin of these deviations compared to simple diffusion theory are ongoing; our results will also be compared to previous diffusion experiments in nematic liquid crystals. We gratefully acknowledge financial support through NSF DMR12-05463, MRSEC DMR11-20901, and NASA NNX08AO0G.
On the first-passage time of integrated Brownian motion
Directory of Open Access Journals (Sweden)
Christian H. Hesse
2005-01-01
Full Text Available Let (Bt;t≥0 be a Brownian motion process starting from B0=ν and define Xν(t=∫0tBsds. For a≥0, set τa,ν:=inf{t:Xν(t=a} (with inf φ=∞. We study the conditional moments of τa,ν given τa,ν<∞. Using martingale methods, stopping-time arguments, as well as the method of dominant balance, we obtain, in particular, an asymptotic expansion for the conditional mean E(τa,ν|τa,ν<∞ as ν→∞. Through a series of simulations, it is shown that a truncation of this expansion after the first few terms provides an accurate approximation to the unknown true conditional mean even for small ν.
Transient cluster formation in sheared non-Brownian suspensions.
Thøgersen, Kjetil; Dabrowski, Marcin; Malthe-Sørenssen, Anders
2016-02-01
We perform numerical simulations of non-Brownian suspensions in the laminar flow regime to study the scaling behavior of particle clusters and collisions under shear. As the particle fraction approaches the maximum packing fraction, large transient clusters appear in the system. We use methods from percolation theory to discuss the cluster size distribution. We also give a scaling relation for the percolation threshold as well as system size effects through time-dependent fluctuations of this threshold and relate them to system size. System size effects are important close to the maximum packing fraction due to the divergence of the cluster length scale. We then investigate the transient nature of the clusters through characterization of particle collisions and show that collision times exhibit scale-invariant properties. Finally, we show that particle collision times can be modeled as first-passage processes. PMID:26986381
Effect of Brownian Coagulation on the Liquid-liquid Decomposition in Gas-atomized Alloy Drops
Institute of Scientific and Technical Information of China (English)
Jiuzhou ZHAO; Lingling GAO; Jie HE; L.Ratke
2006-01-01
Modeling and simulation have been carried out for Al-Pb alloys to investigate the Brownian coagulation effect on the microstructure development in a gas-atomized drop during the liquid-liquid decomposition.The results indicate that Brownian coagulation has a weak effect on the nucleation and a relatively strong effect on coarsening the minority phase droplets. The influence of Brownian coagulation on the liquid-liquid decomposition decreases with the increase in the diameter (or the decrease in the cooling rate) of the atomized drop.
Maximum of a Fractional Brownian Motion: Analytic Results from Perturbation Theory.
Delorme, Mathieu; Wiese, Kay Jörg
2015-11-20
Fractional Brownian motion is a non-Markovian Gaussian process X_{t}, indexed by the Hurst exponent H. It generalizes standard Brownian motion (corresponding to H=1/2). We study the probability distribution of the maximum m of the process and the time t_{max} at which the maximum is reached. They are encoded in a path integral, which we evaluate perturbatively around a Brownian, setting H=1/2+ϵ. This allows us to derive analytic results beyond the scaling exponents. Extensive numerical simulations for different values of H test these analytical predictions and show excellent agreement, even for large ϵ. PMID:26636835
Oscillation of harmonic functions for subordinate Brownian motion and its applications
Kim, Panki; Lee, Yunju
2012-01-01
In this paper, we establish an oscillation estimate of nonnegative harmonic functions for a pure-jump subordinate Brownian motion. The infinitesimal generator of such subordinate Brownian motion is an integro-differential operator. As an application, we give a probabilistic proof of the following form of relative Fatou theorem for such subordinate Brownian motion X in bounded kappa-fat open set; if u is a positive harmonic function with respect to X in a bounded kappa-fat open set D and h is ...
Moussavi-Baygi, R.; Mofrad, M. R. K.
2016-01-01
Conformational behavior of intrinsically disordered proteins, such as Phe-Gly repeat domains, alters drastically when they are confined in, and tethered to, nan channels. This has challenged our understanding of how they serve to selectively facilitate translocation of nuclear transport receptor (NTR)-bearing macromolecules. Heterogeneous FG-repeats, tethered to the NPC interior, nonuniformly fill the channel in a diameter-dependent manner and adopt a rapid Brownian motion, thereby forming a porous and highly dynamic polymeric meshwork that percolates in radial and axial directions and features two distinguishable zones: a dense hydrophobic rod-like zone located in the center, and a peripheral low-density shell-like zone. The FG-meshwork is locally disrupted upon interacting with NTR-bearing macromolecules, but immediately reconstructs itself between 0.44 μs and 7.0 μs, depending on cargo size and shape. This confers a perpetually-sealed state to the NPC, and is solely due to rapid Brownian motion of FG-repeats, not FG-repeat hydrophobic bonds. Elongated-shaped macromolecules, both in the presence and absence of NTRs, penetrate more readily into the FG-meshwork compared to their globular counterparts of identical volume and surface chemistry, highlighting the importance of the shape effects in nucleocytoplasmic transport. These results can help our understanding of geometrical effects in, and the design of, intelligent and responsive biopolymer-based materials in nanofiltration and artificial nanopores. PMID:27470900
Moussavi-Baygi, R; Mofrad, M R K
2016-01-01
Conformational behavior of intrinsically disordered proteins, such as Phe-Gly repeat domains, alters drastically when they are confined in, and tethered to, nan channels. This has challenged our understanding of how they serve to selectively facilitate translocation of nuclear transport receptor (NTR)-bearing macromolecules. Heterogeneous FG-repeats, tethered to the NPC interior, nonuniformly fill the channel in a diameter-dependent manner and adopt a rapid Brownian motion, thereby forming a porous and highly dynamic polymeric meshwork that percolates in radial and axial directions and features two distinguishable zones: a dense hydrophobic rod-like zone located in the center, and a peripheral low-density shell-like zone. The FG-meshwork is locally disrupted upon interacting with NTR-bearing macromolecules, but immediately reconstructs itself between 0.44 μs and 7.0 μs, depending on cargo size and shape. This confers a perpetually-sealed state to the NPC, and is solely due to rapid Brownian motion of FG-repeats, not FG-repeat hydrophobic bonds. Elongated-shaped macromolecules, both in the presence and absence of NTRs, penetrate more readily into the FG-meshwork compared to their globular counterparts of identical volume and surface chemistry, highlighting the importance of the shape effects in nucleocytoplasmic transport. These results can help our understanding of geometrical effects in, and the design of, intelligent and responsive biopolymer-based materials in nanofiltration and artificial nanopores. PMID:27470900
2011-07-28
... May 2008 (73 FR 29136) for public comment. The draft ICCVAM BRDs, draft ICCVAM test method.../immunotox/llna-ELISA/LLNA-pot/TMER.htm . ICCVAM. 2010. ICCVAM Test Method Evaluation Report on the Murine Local Lymph Node Assay: BrdU-ELISA, a Nonradioactive Alternative Test Method to Assess the...
International Nuclear Information System (INIS)
This paper explores how some UK Local Authorities (LAs) have opted to engage with the Energy Service Company (ESCo) model in a bid to enhance their influence over local energy system change and help them to deliver on their political ‘public good’ objectives. Three common approaches to LA ESCo model engagement are outlined including the: (1) LA owned ‘arm's-length’ model; (2) private sector owned concession agreement model; and (3) community owned and run model. The LA's decision to establish its own ESCo, or alternatively enter into a partnership with another, predominantly depends on: its willingness to expose itself to risk, the level of strategic control it desires and the resources it has at its disposal. However, the business case is contingent on the extent to which the national policy and regulatory framework facilitates and obligates LAs to play an active energy governance role. Stronger alignment of local and national energy agendas through communication and coordination between different governance actors could help to remove critical barriers to LA ESCo engagement and their wider energy governance activities. - Highlights: • Some UK Local Authorities (LAs) have engaged with Energy Service Company (ESCo). • Driven by a desire to shape local energy system to deliver on their objectives. • LA may establish an ‘arm's length’ ESCo or partner with a private or community ESCo. • Trade-off between strategic control over energy system change and exposure to risk. • LA can bolster ESCo business case but ultimately depends on central government
James, Peter; Ito, Kate; Banay, Rachel F; Buonocore, Jonathan J; Wood, Benjamin; Arcaya, Mariana C
2014-01-01
Decreasing traffic speeds increases the amount of time drivers have to react to road hazards, potentially averting collisions, and makes crashes that do happen less severe. Boston's regional planning agency, the Metropolitan Area Planning Council (MAPC), in partnership with the Massachusetts Department of Public Health (MDPH), conducted a Health Impact Assessment (HIA) that examined the potential health impacts of a proposed bill in the state legislature to lower the default speed limits on local roads from 30 miles per hour (mph) to 25 mph. The aim was to reduce vehicle speeds on local roads to a limit that is safer for pedestrians, cyclists, and children. The passage of this proposed legislation could have had far-reaching and potentially important public health impacts. Lower default speed limits may prevent around 18 fatalities and 1200 serious injuries to motorists, cyclists and pedestrians each year, as well as promote active transportation by making local roads feel more hospitable to cyclists and pedestrians. While a lower speed limit would increase congestion and slightly worsen air quality, the benefits outweigh the costs from both a health and economic perspective and would save the state approximately $62 million annually from prevented fatalities and injuries.
Chavanis, Pierre-Henri; Sire, Clément
2006-06-01
We derive the virial theorem appropriate to the generalized Smoluchowski-Poisson (GSP) system describing self-gravitating Brownian particles in an overdamped limit. We extend previous works by considering the case of an unbounded domain and an arbitrary equation of state. We use the virial theorem to study the diffusion (evaporation) of an isothermal Brownian gas above the critical temperature Tc in dimension d = 2 and show how the effective diffusion coefficient and the Einstein relation are modified by self-gravity. We also study the collapse at T = Tc and show that the central density increases logarithmically with time instead of exponentially in a bounded domain. Finally, for d > 2, we show that the evaporation of the system is essentially a pure diffusion slightly slowed down by self-gravity. We also study the linear dynamical stability of stationary solutions of the GSP system representing isolated clusters of particles and investigate the influence of the equation of state and of the dimension of space on the dynamical stability of the system. PMID:16906910
Chavanis, Pierre-Henri; Sire, Clément
2006-06-01
We derive the virial theorem appropriate to the generalized Smoluchowski-Poisson (GSP) system describing self-gravitating Brownian particles in an overdamped limit. We extend previous works by considering the case of an unbounded domain and an arbitrary equation of state. We use the virial theorem to study the diffusion (evaporation) of an isothermal Brownian gas above the critical temperature Tc in dimension d = 2 and show how the effective diffusion coefficient and the Einstein relation are modified by self-gravity. We also study the collapse at T = Tc and show that the central density increases logarithmically with time instead of exponentially in a bounded domain. Finally, for d > 2, we show that the evaporation of the system is essentially a pure diffusion slightly slowed down by self-gravity. We also study the linear dynamical stability of stationary solutions of the GSP system representing isolated clusters of particles and investigate the influence of the equation of state and of the dimension of space on the dynamical stability of the system.
Ilday, Serim; Akguc, Gursoy B.; Tokel, Onur; Makey, Ghaith; Yavuz, Ozgun; Yavuz, Koray; Pavlov, Ihor; Ilday, F. Omer; Gulseren, Oguz
We report a new dynamical self-assembly mechanism, where judicious use of convective and strong Brownian forces enables effective patterning of colloidal nanoparticles that are almost two orders of magnitude smaller than the laser beam. Optical trapping or tweezing effects are not involved, but the laser is used to create steep thermal gradients through multi-photon absorption, and thereby guide the colloids through convective forces. Convective forces can be thought as a positive feedback mechanism that helps to form and reinforce pattern, while Brownian motion act as a competing negative feedback mechanism to limit the growth of the pattern, as well as to increase the possibilities of bifurcation into different patterns, analogous to the competition observed in reaction-diffusion systems. By steering stochastic processes through these forces, we are able to gain control over the emergent pattern such as to form-deform-reform of a pattern, to change its shape and transport it spatially within seconds. This enables us to dynamically initiate and control large patterns comprised of hundreds of colloids. Further, by not relying on any specific chemical, optical or magnetic interaction, this new method is, in principle, completely independent of the material type being assembled.
Noguera, Pedro
2002-01-01
Drawing on research in Oakland, California over a twenty-year period, Noguera considers how poverty and racial isolation have contributed to the problems confronted by schools in that district and other inner-city communities around the state. He illuminates the factors that hinder the development of social capital in low-income communities, and, in doing so, demonstrates why local control does not make it easier for school systems to address the academic needs of poor students. The wide vari...
Mean Mobility and Rotation Number in Time-inhomogenous Brownian Ratchets
Institute of Scientific and Technical Information of China (English)
张雪娟
2004-01-01
@@ Recently, Brownian ratchets have attracted considerable attention due to their abitlity to realize a unidirectional transport only throught the use of a proper asymmetry and thermal noise fluctuation, for recent review, see[1,2].
On the time of the maximum of Brownian motion with drift
Directory of Open Access Journals (Sweden)
Emannuel Buffet
2003-01-01
Full Text Available The distribution of the time at which Brownian motion with drift attains its maximum on a given interval is obtained by elementary methods. The proof depends on a remarkable integral identity involving Gaussian distribution functions.
Song, Shiyu; Wang, Suxin; Wang, Yongjin
2016-08-01
Motivated by the close connection between the skew Brownian motion and the random particle motion in heterogeneous media, we investigate the reflected skew Brownian motion and try to find out its relationship with the corresponding dispersion problem when there exists a reflecting boundary. Through the use of the knowledge of stochastic analysis, we provide some basic properties of reflected skew Brownian motions, including the transition density, the Laplace transform of the first passage time, and some related results. A simple method to generate the sample path is also proposed. At the end of this paper, we reveal the strong relationship between the reflected skew Brownian motion and the solute dispersion in the presence of a sharp interface and a reflecting boundary.
Wu, Panyu
2011-01-01
The classical law of the iterated logarithm (LIL for short)as fundamental limit theorems in probability theory play an important role in the development of probability theory and its applications. Strassen (1964) extended LIL to large classes of functional random variables, it is well known as the invariance principle for LIL which provide an extremely powerful tool in probability and statistical inference. But recently many phenomena show that the linearity of probability is a limit for applications, for example in finance, statistics. As while a nonlinear expectation--- G-expectation has attracted extensive attentions of mathematicians and economists, more and more people began to study the nature of the G-expectation space. A natural question is: Can the classical invariance principle for LIL be generalized under G-expectation space? This paper gives a positive answer. We present the invariance principle of G-Brownian motion for the law of the iterated logarithm under G-expectation.
Volpe, Giorgio; Volpe, Giovanni; Gigan, Sylvain
2014-01-01
The motion of particles in random potentials occurs in several natural phenomena ranging from the mobility of organelles within a biological cell to the diffusion of stars within a galaxy. A Brownian particle moving in the random optical potential associated to a speckle, i.e., a complex interference pattern generated by the scattering of coherent light by a random medium, provides an ideal mesoscopic model system to study such phenomena. Here, we derive a theory for the motion of a Brownian ...
The probability of an encounter of two Brownian particles before escape
holcman, D
2009-01-01
We study the probability of two Brownian particles to meet before one of them exits a finite interval. We obtain an explicit expression for the probability as a function of the initial distance of the two particles using the Weierstrass elliptic function. We also find the law of the meeting location. Brownian simulations show the accuracy of our analysis. Finally, we discuss some applications to the probability that a double strand DNA break repairs in confined environments.
On exponential stability for stochastic differential equations disturbed by G-Brownian motion
Fei, Weiyin; Fei, Chen
2013-01-01
We first introduce the calculus of Peng's G-Brownian motion on a sublinear expectation space $(\\Omega, {\\cal H}, \\hat{\\mathbb{E}})$. Then we investigate the exponential stability of paths for a class of stochastic differential equations disturbed by a G-Brownian motion in the sense of quasi surely (q.s.). The analyses consist in G-Lyapunov function and some special inequalities. Various sufficient conditions are obtained to ensure the stability of strong solutions. In particular, by means of ...
Recurrence and transience for normally reflected Brownian motion in warped product manifolds
de Lima, Levi Lopes
2016-01-01
We establish an integral test describing the exact cut-off between recurrence and transience for normally reflected Brownian motion in certain unbounded domains in a class of warped product manifolds. Besides extending a previous result by Pinsky \\cite{P1}, who treated the case in which the ambient space is flat, our result recovers the classical test for the standard Brownian motion in model spaces. Moreover, it allows us to discuss the recurrence/transience dichotomy for certain generalized...
Estratégias colectivas de governação local no campo social: alcances e limites
Gonçalves, Hermínia Fernandes
2011-01-01
[ES]Esta investigación doctoral se organizó como un estudio comparativo entre España y Portugal. El método comparativo, mientras sea un instrumento fundamental a la explicación sociológica, sobre las estrategias legales de la gobernación local en el ámbito social, permitiría, en el sentido weberiano, comprender el conjunto de las posibles causas, los patrones fijos y las trayectorias específicas entre los casos observados. Por lo tanto, el razonamiento comparativo se apoyó en una estrategi...
International Nuclear Information System (INIS)
The Savannah River Site (SRS) is a Department of Energy (DOE) facility located near Aiken, South Carolina which is currently operated and managed by Westinghouse Savannah River Company (WSRC). The Sanitary Landfill (Sanitary Landfill) at the SRS is located approximately 2,000 feet Northwest of Upper Three Runs Creek (UTRC) on an approximately 70 acre site located south of Road C between the SRS B-Area and UTRC. The Sanitary Landfill has been receiving wastes since 1974 and operates as an unlined trench and fill operation. The original landfill site was 32 acres. This area reached its capacity around 1987 and a Northern Expansion of 16 acres and a Southern Expansion of 22 acres were added in 1987. The Northern Expansion has not been used for waste disposal to date and the Southern Expansion is expected to reach capacity in 1992 or 1993. The waste received at the Sanitary Landfill is predominantly paper, plastics, rubber, wood, metal, cardboard, rags saturated with degreasing solvents, pesticide bags, empty cans, and asbestos in bags. The landfill is not supposed to receive any radioactive wastes. However, tritium has been detected in the groundwater at the site. Gross alpha and gross beta are also evaluated at the landfill. The objectives of this modeling study are twofold: (1) to create a local scale Sanitary Landfill flow model to study hydraulic effects resulting from capping the Sanitary Landfill; and (2) to create a Sanitary Landfill local scale transport model to support ACL Demonstrations for a RCRA Part B Permit Renewal
Delayed plastic relaxation limit in SiGe islands grown by Ge diffusion from a local source
Vanacore, G. M.; Nicotra, G.; Zani, M.; Bollani, M.; Bonera, E.; Montalenti, F.; Capellini, G.; Isella, G.; Osmond, J.; Picco, A.; Boioli, F.; Tagliaferri, A.
2015-03-01
The hetero-epitaxial strain relaxation in nano-scale systems plays a fundamental role in shaping their properties. Here, the elastic and plastic relaxation of self-assembled SiGe islands grown by surface-thermal-diffusion from a local Ge solid source on Si(100) are studied by atomic force and transmission electron microscopies, enabling the simultaneous investigation of the strain relaxation in different dynamical regimes. Islands grown by this technique remain dislocation-free and preserve a structural coherence with the substrate for a base width as large as 350 nm. The results indicate that a delay of the plastic relaxation is promoted by an enhanced Si-Ge intermixing, induced by the surface-thermal-diffusion, which takes place already in the SiGe overlayer before the formation of a critical nucleus. The local entropy of mixing dominates, leading the system toward a thermodynamic equilibrium, where non-dislocated, shallow islands with a low residual stress are energetically stable. These findings elucidate the role of the interface dynamics in modulating the lattice distortion at the nano-scale, and highlight the potential use of our growth strategy to create composition and strain-controlled nano-structures for new-generation devices.
Energy Technology Data Exchange (ETDEWEB)
Kelly, V.A.; Beach, J.A.; Statham, W.H.; Pickens, J.F. [INTERA, Inc., Austin, TX (United States)
1993-02-19
The Savannah River Site (SRS) is a Department of Energy (DOE) facility located near Aiken, South Carolina which is currently operated and managed by Westinghouse Savannah River Company (WSRC). The Sanitary Landfill (Sanitary Landfill) at the SRS is located approximately 2,000 feet Northwest of Upper Three Runs Creek (UTRC) on an approximately 70 acre site located south of Road C between the SRS B-Area and UTRC. The Sanitary Landfill has been receiving wastes since 1974 and operates as an unlined trench and fill operation. The original landfill site was 32 acres. This area reached its capacity around 1987 and a Northern Expansion of 16 acres and a Southern Expansion of 22 acres were added in 1987. The Northern Expansion has not been used for waste disposal to date and the Southern Expansion is expected to reach capacity in 1992 or 1993. The waste received at the Sanitary Landfill is predominantly paper, plastics, rubber, wood, metal, cardboard, rags saturated with degreasing solvents, pesticide bags, empty cans, and asbestos in bags. The landfill is not supposed to receive any radioactive wastes. However, tritium has been detected in the groundwater at the site. Gross alpha and gross beta are also evaluated at the landfill. The objectives of this modeling study are twofold: (1) to create a local scale Sanitary Landfill flow model to study hydraulic effects resulting from capping the Sanitary Landfill; and (2) to create a Sanitary Landfill local scale transport model to support ACL Demonstrations for a RCRA Part B Permit Renewal.
Directory of Open Access Journals (Sweden)
Aida Maria Lovison
2015-01-01
Full Text Available To overcome the impasse that Brazilian society is facing requires that development policy will lead to an increasing homogenization of our society and create space to realizing the potential of our culture. The local endogenous development proposition emerges as an alternative to the current imperatives of globalization. The objective here is not to discuss the array of modern economic theories that support this proposal, but to discuss about the obstacles to building inclusive and compassionate alternatives as opposed to individualistic market logic and instrumental rationality. How to think of local endogenous development devoid of an ethical conception or a proposed update of emancipation where this process is actually experienced as a pedagogical process? How to establish the logic of solidarity in the dialogical subject, being-for-itself, and citizen action and collective? The simple inversion between the oppressed and oppressor does not serve the common good. The pedagogy of Paulo Freire, in all its texture, highlights this fundamental ontological condition that revives the hope into our critique: a response to the challenges of reality is problematic since the action of dialogical subject on it and to transform it.
Delayed plastic relaxation limit in SiGe islands grown by Ge diffusion from a local source
Energy Technology Data Exchange (ETDEWEB)
Vanacore, G. M.; Zani, M.; Tagliaferri, A., E-mail: alberto.tagliaferri@polimi.it [CNISM-Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano (Italy); Nicotra, G. [IMM-CNR, Stradale Primosole 50, I-95121 Catania (Italy); Bollani, M. [CNR-IFN, LNESS, Via Anzani 42, I-22100 Como (Italy); Bonera, E.; Montalenti, F.; Picco, A.; Boioli, F. [Dipartimento di Scienza dei Materiali and L-NESS, Università Milano-Bicocca, via Cozzi 53, I-20125 Milano (Italy); Capellini, G. [Department of Sciences at the Università Roma Tre, Via Vasca Navale 79, 00146 Roma (Italy); Isella, G. [CNISM, LNESS, Dipartimento di Fisica, Politecnico di Milano (Polo di Como), Via Anzani 42, I-22100 Como (Italy); Osmond, J. [ICFO–The Institute of Photonic Sciences, Av. Carl Friedrich Gauss, 3, E-08860 Castelldefels (Barcelona) (Spain)
2015-03-14
The hetero-epitaxial strain relaxation in nano-scale systems plays a fundamental role in shaping their properties. Here, the elastic and plastic relaxation of self-assembled SiGe islands grown by surface-thermal-diffusion from a local Ge solid source on Si(100) are studied by atomic force and transmission electron microscopies, enabling the simultaneous investigation of the strain relaxation in different dynamical regimes. Islands grown by this technique remain dislocation-free and preserve a structural coherence with the substrate for a base width as large as 350 nm. The results indicate that a delay of the plastic relaxation is promoted by an enhanced Si-Ge intermixing, induced by the surface-thermal-diffusion, which takes place already in the SiGe overlayer before the formation of a critical nucleus. The local entropy of mixing dominates, leading the system toward a thermodynamic equilibrium, where non-dislocated, shallow islands with a low residual stress are energetically stable. These findings elucidate the role of the interface dynamics in modulating the lattice distortion at the nano-scale, and highlight the potential use of our growth strategy to create composition and strain-controlled nano-structures for new-generation devices.
Delayed plastic relaxation limit in SiGe islands grown by Ge diffusion from a local source
International Nuclear Information System (INIS)
The hetero-epitaxial strain relaxation in nano-scale systems plays a fundamental role in shaping their properties. Here, the elastic and plastic relaxation of self-assembled SiGe islands grown by surface-thermal-diffusion from a local Ge solid source on Si(100) are studied by atomic force and transmission electron microscopies, enabling the simultaneous investigation of the strain relaxation in different dynamical regimes. Islands grown by this technique remain dislocation-free and preserve a structural coherence with the substrate for a base width as large as 350 nm. The results indicate that a delay of the plastic relaxation is promoted by an enhanced Si-Ge intermixing, induced by the surface-thermal-diffusion, which takes place already in the SiGe overlayer before the formation of a critical nucleus. The local entropy of mixing dominates, leading the system toward a thermodynamic equilibrium, where non-dislocated, shallow islands with a low residual stress are energetically stable. These findings elucidate the role of the interface dynamics in modulating the lattice distortion at the nano-scale, and highlight the potential use of our growth strategy to create composition and strain-controlled nano-structures for new-generation devices
Jeun, Minhong; Lee, Sanghoon; Kyeong Kang, Jae; Tomitaka, Asahi; Wook Kang, Keon; Il Kim, Young; Takemura, Yasushi; Chung, Kyung-Won; Kwak, Jiyeon; Bae, Seongtae
2012-02-01
Magnetic and AC magnetically induced heating characteristics of Fe3O4 nanoparticles (IONs) with different mean diameters, d, systematically controlled from 4.2 to 22.5 nm were investigated to explore the physical relationship between magnetic phase and specific loss power (SLP) for hyperthermia agent applications. It was experimentally confirmed that the IONs had three magnetic phases and correspondingly different SLP characteristics depending on the particle sizes. Furthermore, it was demonstrated that pure superparamagnetic phase IONs (d limiting for hyperthermia applications due to smaller AC hysteresis loss power (Néel relaxation loss power) originated from lower out-of-phase magnetic susceptibility.
Intrinsic irreversibility limits the efficiency of multidimensional molecular motors.
Jack, M W; Tumlin, C
2016-05-01
We consider the efficiency limits of Brownian motors able to extract work from the temperature difference between reservoirs or from external thermodynamic forces. These systems can operate in a variety of modes, including as isothermal engines, heat engines, refrigerators, and heat pumps. We derive analytical results showing that certain classes of multidimensional Brownian motor, including the Smoluchowski-Feynman ratchet, are unable to attain perfect efficiency (Carnot efficiency for heat engines). This demonstrates the presence of intrinsic irreversibilities in their operating mechanism. We present numerical simulations showing that in some cases the loss process that limits efficiency is associated with vortices in the probability current.
Intrinsic irreversibility limits the efficiency of multidimensional molecular motors
Jack, M. W.; Tumlin, C.
2016-05-01
We consider the efficiency limits of Brownian motors able to extract work from the temperature difference between reservoirs or from external thermodynamic forces. These systems can operate in a variety of modes, including as isothermal engines, heat engines, refrigerators, and heat pumps. We derive analytical results showing that certain classes of multidimensional Brownian motor, including the Smoluchowski-Feynman ratchet, are unable to attain perfect efficiency (Carnot efficiency for heat engines). This demonstrates the presence of intrinsic irreversibilities in their operating mechanism. We present numerical simulations showing that in some cases the loss process that limits efficiency is associated with vortices in the probability current.
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.
Iliafar, Sara; Vezenov, Dmitri; Jagota, Anand
2013-02-01
We used brownian dynamics to study the peeling of a polymer molecule, represented by a freely jointed chain, from a frictionless surface in an implicit solvent with parameters representative of single-stranded DNA adsorbed on graphite. For slow peeling rates, simulations match the predictions of an equilibrium statistical thermodynamic model. We show that deviations from equilibrium peeling forces are dominated by a combination of Stokes (viscous) drag forces acting on the desorbed section of the chain and a finite rate of hopping over a desorption barrier. Characteristic velocities separating equilibrium and nonequilibrium regimes are many orders of magnitude higher than values accessible in force spectroscopy experiments. Finite probe stiffness resulted in disappearance of force spikes due to desorption of individual links predicted by the statistical thermodynamic model under displacement control. Probe fluctuations also masked sharp transitions in peeling force between blocks of distinct sequences, indicating limitation in the ability of single-molecule force spectroscopy to distinguish small differences in homologous molecular structures.
Maldonado-Camargo, L.; Torres-Díaz, I.; Chiu-Lam, A.; Hernández, M.; Rinaldi, C.
2016-08-01
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.
Glassy dynamics of Brownian particles with velocity-dependent friction
Yazdi, Anoosheh; Sperl, Matthias
2016-09-01
We consider a two-dimensional model system of Brownian particles in which slow particles are accelerated while fast particles are damped. The motion of the individual particles is described by a Langevin equation with Rayleigh-Helmholtz velocity-dependent friction. In the case of noninteracting particles, the time evolution equations lead to a non-Gaussian velocity distribution. The velocity-dependent friction allows negative values of the friction or energy intakes by slow particles, which we consider active motion, and also causes breaking of the fluctuation dissipation relation. Defining the effective temperature proportional to the second moment of velocity, it is shown that for a constant effective temperature the higher the noise strength, the lower the number of active particles in the system. Using the Mori-Zwanzig formalism and the mode-coupling approximation, the equations of motion for the density autocorrelation function are derived. The equations are solved using the equilibrium structure factors. The integration-through-transients approach is used to derive a relation between the structure factor in the stationary state considering the interacting forces, and the conventional equilibrium static structure factor.
Survival of near-critical branching Brownian motion
Berestycki, Julien; Schweinsberg, Jason
2010-01-01
Consider a system of particles performing branching Brownian motion with negative drift $\\mu = \\sqrt{2 - \\epsilon}$ and killed upon hitting zero. Initially there is one particle at $x>0$. Kesten showed that the process survives with positive probability if and only if $\\epsilon>0$. Here we are interested in the asymptotics as $\\eps\\to 0$ of the survival probability $Q_\\mu(x)$. It is proved that if $L= \\pi/\\sqrt{\\epsilon}$ then for all $x \\in \\R$, $\\lim_{\\epsilon \\to 0} Q_\\mu(L+x) = \\theta(x) \\in (0,1)$ exists and is a travelling wave solution of the Fisher-KPP equation. Furthermore, we obtain sharp asymptotics of the survival probability when $x
Magnetoviscosity in dilute ferrofluids from rotational brownian dynamics simulations.
Soto-Aquino, D; Rinaldi, C
2010-10-01
Ferrofluids are suspensions of magnetic nanoparticles which respond to imposed magnetic fields by changing their viscosity without losing their fluidity. Prior work on modeling the behavior of ferrofluids has focused on using phenomenological suspension-scale continuum equations. A disadvantage of this approach is the controversy surrounding the equation describing the rate of change of the ferrofluid magnetization, the so-called magnetization relaxation equation. In this contribution the viscosity of dilute suspensions of spherical magnetic nanoparticles suspended in a Newtonian fluid and under applied shear and constant magnetic fields is studied through rotational brownian dynamics simulations. Simulation results are compared with the predictions of suspension-scale models based on three magnetization relaxation equations. Excellent agreement is observed between simulation results and the predictions of an equation due to Martsenyuk, Raikher, and Shliomis. Good qualitative agreement is observed with predictions of other equations, although these models fail to accurately predict the magnitude and shear rate dependence of the magnetic-field-dependent effective viscosity. Finally, simulation results over a wide range of conditions are collapsed into master curves using a Mason number defined based on the balance of hydrodynamic and magnetic torques. PMID:21230393
Nanofluidic Brownian Ratchet via atomically-stepped surfaces
Rahmani, Amir; Colosqui, Carlos
2015-11-01
Theoretical analysis and fully atomistic molecular dynamics simulations reveal a Brownian ratchet mechanism by which thermal motion can drive the directional displacement of liquids confined in micro- or nanoscale channels and pores. The particular systems discussed in this talk consist of two immiscible liquids confined in a slit-like nanochannel with atomically-stepped surfaces. Mean displacement rates reported in molecular dynamics simulations are in close agreement with theoretical predictions via analytical solution of a Smoluchowski equation for the probability density of the position of the liquid-liquid interface. The direction of the thermally-driven displacement of liquid is determined by the nanostructure surface geometry and thus imbibition or drainage can occur against the direction of action of capillary forces. The studied surface nanostructure with directional asymmetry can control the dynamics of wetting processes such as capillary filling, wicking, and imbibition in porous materials. The proposed physical mechanisms and derived analytical expressions can be applied to design nanofluidic and microfluidic devices for passive handling and separation.
Phase transition in non-brownian fiber suspensions
Franceschini, Alexandre; Filippidi, Emmanouella; Guazzelli, Elizabeth; Pine, David
2012-11-01
The simple shear of a suspension of fibers tends to align them with the flow direction. We previously reported that the oscillatory shear of neutrally buoyant non-Brownian fibers align them with the vorticity (Franceschini A. et al. PRL, 2011). We interpreted this phenomenon as the minimization of a ``corrected volume fraction'' defined as a function of the strain amplitude, the average orientation and the volume fraction. Below a critical value of this parameter, the system becomes fully reversible after a few periods. Above it, fluctuations remain and the fibers align with the vorticity, subsequently reducing the value of this corrected volume fraction. We present here the collective behavior of fibers constrained at the liquid-air interface. By pinning the liquid on the wall of a Couette cell, we can have a flat interface. By modifying the surface of the fibers, we get rid of most of surface tension mediated fiber-fiber interactions. In this 2D configuration we can measure spatial correlations, as well as the position and orientation of every fiber at each shear cycle. We similarly define a ``corrected surface fraction'' and see how this parameter help us understand the difference between the surface behavior and the suspension behavior. This work was supported by the NSF through the NYU MRSEC, Award DMR:0820341. Additional support was provided by a Lavoisier Fellowship (AF) and from the Onassis Foundation (EF).
Virial pressure in systems of spherical active Brownian particles.
Winkler, Roland G; Wysocki, Adam; Gompper, Gerhard
2015-09-01
The pressure of suspensions of self-propelled objects is studied theoretically and by simulation of spherical active Brownian particles (ABPs). We show that for certain geometries, the mechanical pressure as force/area of confined systems can be equally expressed by bulk properties, which implies the existence of a nonequilibrium equation of state. Exploiting the virial theorem, we derive expressions for the pressure of ABPs confined by solid walls or exposed to periodic boundary conditions. In both cases, the pressure comprises three contributions: the ideal-gas pressure due to white-noise random forces, an activity-induced pressure ("swim pressure"), which can be expressed in terms of a product of the bare and a mean effective particle velocity, and the contribution by interparticle forces. We find that the pressure of spherical ABPs in confined systems explicitly depends on the presence of the confining walls and the particle-wall interactions, which has no correspondence in systems with periodic boundary conditions. Our simulations of three-dimensional ABPs in systems with periodic boundary conditions reveal a pressure-concentration dependence that becomes increasingly nonmonotonic with increasing activity. Above a critical activity and ABP concentration, a phase transition occurs, which is reflected in a rapid and steep change of the pressure. We present and discuss the pressure for various activities and analyse the contributions of the individual pressure components. PMID:26221908
Virial pressure in systems of spherical active Brownian particles.
Winkler, Roland G; Wysocki, Adam; Gompper, Gerhard
2015-09-01
The pressure of suspensions of self-propelled objects is studied theoretically and by simulation of spherical active Brownian particles (ABPs). We show that for certain geometries, the mechanical pressure as force/area of confined systems can be equally expressed by bulk properties, which implies the existence of a nonequilibrium equation of state. Exploiting the virial theorem, we derive expressions for the pressure of ABPs confined by solid walls or exposed to periodic boundary conditions. In both cases, the pressure comprises three contributions: the ideal-gas pressure due to white-noise random forces, an activity-induced pressure ("swim pressure"), which can be expressed in terms of a product of the bare and a mean effective particle velocity, and the contribution by interparticle forces. We find that the pressure of spherical ABPs in confined systems explicitly depends on the presence of the confining walls and the particle-wall interactions, which has no correspondence in systems with periodic boundary conditions. Our simulations of three-dimensional ABPs in systems with periodic boundary conditions reveal a pressure-concentration dependence that becomes increasingly nonmonotonic with increasing activity. Above a critical activity and ABP concentration, a phase transition occurs, which is reflected in a rapid and steep change of the pressure. We present and discuss the pressure for various activities and analyse the contributions of the individual pressure components.
Brownian dynamics simulations of nanosheet solutions under shear.
Xu, Yueyi; Green, Micah J
2014-07-14
The flow-induced conformation dynamics of nanosheets are simulated using a Brownian Dynamics (BD) formulation applied to a bead-rod sheetlike molecular model. This is the first-ever use of BD to simulate flow-induced dynamics of two-dimensional structures. Using this framework, we simulate dilute suspensions of coarse-grained nanosheets and compute conformation dynamics for simple shear flow. The data show power law scaling relationships between nanosheet parameters (such as bending moduli and molecular weight) and the resulting intrinsic viscosity and conformation. For nonzero bending moduli, an effective dimension of 2.77 at equilibrium is calculated from the scaling relationship between radius of gyration and molecular weight. We also find that intrinsic viscosity varies with molecular weight with an exponent of 2.12 ± 0.23; this dependence is significantly larger than those found for linear polymers. Weak shear thinning is observed at high Weissenberg number (Wi). This simulation method provides a computational basis for developing manufacturing processes for nanosheet-derived materials by relating flow forces and nanosheet parameters to the resulting material morphology.
From Brownian Dynamics to Markov Chain: An Ion Channel Example
Chen, Wan
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.
Biased Brownian motion in narrow channels with asymmetry and anisotropy
Peng, Zheng; To, Kiwing
2016-08-01
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 on a tilted channel, is found to be consistent with those obtained from dynamic mobility and position probability distribution measurements. These results are explained by a simple collision model that suggests the random kinetic energy transfer between different translational degrees of freedom may be turned into useful work in the presence of asymmetry and anisotropy.
Weaver, Daniel M.; Coghlan Jr., Stephen M.; Zydlewski, Joseph
2016-01-01
Resource flows from adjacent ecosystems are critical in maintaining structure and function of freshwater food webs. Migrating sea lamprey (Petromyzon marinus) deliver a pulsed marine-derived nutrient subsidy to rivers in spring when the metabolic demand of producers and consumers are increasing. However, the spatial and temporal dynamics of these nutrient subsidies are not well characterized. We used sea lamprey carcass additions in a small stream to examine changes in nutrients, primary productivity, and nutrient assimilation among consumers. Algal biomass increased 57%–71% immediately adjacent to carcasses; however, broader spatial changes from multiple-site carcass addition may have been influenced by canopy cover. We detected assimilation of nutrients (via δ13C and δ15N) among several macroinvertebrate families including Heptageniidae, Hydropsychidae, and Perlidae. Our research suggests that subsidies may evoke localized patch-scale effects on food webs, and the pathways of assimilation in streams are likely coupled to adjacent terrestrial systems. This research underscores the importance of connectivity in streams, which may influence sea lamprey spawning and elicit varying food web responses from carcass subsidies due to fine-scale habitat variables.
Markey, Kathryn L; Abdo, Dave A; Evans, Scott N; Bosserelle, Cyprien
2016-01-01
In 2011 the first recorded bleaching event for the high latitude Houtman Abrolhos Islands (HAI) coral communities was documented. This bleaching event highlighted the question of whether a supply of 'heat tolerant' coral recruits from the tropical north would be sufficient to provide a level of resistance for these reefs to future warming events. Using Lagrangian modelling we showed that due to its regional isolation, large-scale larval input from potential tropical northern source populations to the HAI is unlikely, despite the southward flowing Leeuwin current. Successful recruitment to artificial substrates was recorded following the bleaching event. However, this was negligible (0.4 ± 0.1 recruits per tile) compared to 2013 post impact recruitment (128.8 ± 15.8 recruits per tile). Our data therefore provides preliminary evidence suggesting that the connectivity of the HAI with coral communities in the north is limited, and population maintenance and recovery is likely driven primarily by self-recruitment. Given the low thermal tolerance of the HAI coral communities, the dominance of Acropora, and the apparent reliance on self-recruitment, an increased frequency of thermally anomalous conditions at the HAI (such as experienced in 2011) has the potential to reduce the long-term stability of the HAI coral populations and species that depend upon them.
Directory of Open Access Journals (Sweden)
Kathryn L Markey
Full Text Available In 2011 the first recorded bleaching event for the high latitude Houtman Abrolhos Islands (HAI coral communities was documented. This bleaching event highlighted the question of whether a supply of 'heat tolerant' coral recruits from the tropical north would be sufficient to provide a level of resistance for these reefs to future warming events. Using Lagrangian modelling we showed that due to its regional isolation, large-scale larval input from potential tropical northern source populations to the HAI is unlikely, despite the southward flowing Leeuwin current. Successful recruitment to artificial substrates was recorded following the bleaching event. However, this was negligible (0.4 ± 0.1 recruits per tile compared to 2013 post impact recruitment (128.8 ± 15.8 recruits per tile. Our data therefore provides preliminary evidence suggesting that the connectivity of the HAI with coral communities in the north is limited, and population maintenance and recovery is likely driven primarily by self-recruitment. Given the low thermal tolerance of the HAI coral communities, the dominance of Acropora, and the apparent reliance on self-recruitment, an increased frequency of thermally anomalous conditions at the HAI (such as experienced in 2011 has the potential to reduce the long-term stability of the HAI coral populations and species that depend upon them.
Markey, Kathryn L; Abdo, Dave A; Evans, Scott N; Bosserelle, Cyprien
2016-01-01
In 2011 the first recorded bleaching event for the high latitude Houtman Abrolhos Islands (HAI) coral communities was documented. This bleaching event highlighted the question of whether a supply of 'heat tolerant' coral recruits from the tropical north would be sufficient to provide a level of resistance for these reefs to future warming events. Using Lagrangian modelling we showed that due to its regional isolation, large-scale larval input from potential tropical northern source populations to the HAI is unlikely, despite the southward flowing Leeuwin current. Successful recruitment to artificial substrates was recorded following the bleaching event. However, this was negligible (0.4 ± 0.1 recruits per tile) compared to 2013 post impact recruitment (128.8 ± 15.8 recruits per tile). Our data therefore provides preliminary evidence suggesting that the connectivity of the HAI with coral communities in the north is limited, and population maintenance and recovery is likely driven primarily by self-recruitment. Given the low thermal tolerance of the HAI coral communities, the dominance of Acropora, and the apparent reliance on self-recruitment, an increased frequency of thermally anomalous conditions at the HAI (such as experienced in 2011) has the potential to reduce the long-term stability of the HAI coral populations and species that depend upon them. PMID:26812259
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.
Risbud, Sumedh R
2014-01-01
We investigate the motion of a suspended non-Brownian sphere past a fixed cylindrical or spherical obstacle in the limit of zero Reynolds number for arbitrary particle-obstacle aspect ratios. We consider both a suspended sphere moving in a quiescent fluid under the action of a uniform force as well as a uniform ambient velocity field driving a freely suspended particle. We determine the distribution of particles around a single obstacle and solve for the individual particle trajectories to comment on the transport of dilute suspensions past an array of fixed obstacles. First, we obtain an expression for the probability density function governing the distribution of a dilute suspension of particles around an isolated obstacle, and we show that it is isotropic. We then present an analytical expression -- derived using both Eulerian and Lagrangian approaches -- for the minimum particle-obstacle separation attained during the motion, as a function of the incoming impact parameter, i.e. the initial offset between ...
Large-N limit of the two-dimensinal Non-Local Yang-Mills theory on arbitrary surfaces with boundary
Setare, M R
2006-01-01
The large-N limit of the two-dimensional non-local U$(N)$ Yang-Mills theory on an orientable and non-orientable surface with boundaries is studied. For the case which the holonomies of the gauge group on the boundaries are near the identity, $U\\simeq I$, it is shown that the phase structure of these theories is the same as that obtain for these theories on orientable and non-orientable surface without boundaries, with same genus but with a modified area $V+\\hat{A}$.
Two-component Brownian coagulation: Monte Carlo simulation and process characterization
Institute of Scientific and Technical Information of China (English)
Haibo Zhao; Chu guang Zheng
2011-01-01
The compositional distribution within aggregates of a given size is essential to the functionality of composite aggregates that are usually enlarged by rapid Brownian coagulation.There is no analytical solution for the process of such two-component systems.Monte Carlo method is an effective numerical approach for two-component coagulation.In this paper,the differentially weighted Monte Carlo method is used to investigate two-component Brownian coagulation,respectively,in the continuum regime,the freemolecular regime and the transition regime.It is found that ( 1 ) for Brownian coagulation in the continuum regime and in the free-molecular regime,the mono-variate compositional distribution,i.e.,the number density distribution function of one component amount (in the form of volume of the component in aggregates) satisfies self-preserving form the same as particle size distribution in mono-component Brownian coagulation; (2) however,for Brownian coagulation in the transition regime the mono-variate compositional distribution cannot reach self-similarity; and (3) the bivariate compositional distribution,i.e.,the combined number density distribution function of two component amounts in the three regimes satisfies a semi self-preserving form.Moreover,other new features inherent to aggregative mixing are also demonstrated; e.g.,the degree of mixing between components,which is largely controlled by the initial compositional mass fraction,improves as aggregate size increases.
Volpe, Giorgio; Volpe, Giovanni; Gigan, Sylvain
2014-01-01
The motion of particles in random potentials occurs in several natural phenomena ranging from the mobility of organelles within a biological cell to the diffusion of stars within a galaxy. A Brownian particle moving in the random optical potential associated to a speckle pattern, i.e., a complex interference pattern generated by the scattering of coherent light by a random medium, provides an ideal model system to study such phenomena. Here, we derive a theory for the motion of a Brownian particle in a speckle field and, in particular, we identify its universal characteristic timescale. Based on this theoretical insight, we show how speckle light fields can be used to control the anomalous diffusion of a Brownian particle and to perform some basic optical manipulation tasks such as guiding and sorting. Our results might broaden the perspectives of optical manipulation for real-life applications. PMID:24496461
Energy Technology Data Exchange (ETDEWEB)
Zhang Yunxin, E-mail: xyz@fudan.edu.c [School of Mathematical Sciences, Fudan University, Shanghai 200433 (China); Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai (China); Centre for Computational Systems Biology, Fudan University (China)
2009-07-20
In this research, diffusion of an overdamped Brownian particle in the tilted periodic potential is investigated. Using the one-dimensional hopping model, the formulations of the mean velocity V{sub N} and effective diffusion coefficient D{sub N} of the Brownian particle have been obtained [B. Derrida, J. Stat. Phys. 31 (1983) 433]. Based on the relation between the effective diffusion coefficient and the moments of the mean first passage time, the formulation of effective diffusion coefficient D{sub eff} of the Brownian particle also has been obtained [P. Reimann, et al., Phys. Rev. E 65 (2002) 031104]. In this research, we'll give another analytical expression of the effective diffusion coefficient D{sub eff} from the moments of the particle's coordinate.
Quantum Brownian motion in a bath of parametric oscillators a model for system-field interactions
Hu, B L; Andrew Matacz
1993-01-01
The quantum Brownian motion paradigm provides a unified framework where one can see the interconnection of some basic quantum statistical processes like decoherence, dissipation, particle creation, noise and fluctuation. We treat the case where the Brownian particle is coupled linearly to a bath of time dependent quadratic oscillators. While the bath mimics a scalar field, the motion of the Brownian particle modeled by a single oscillator could be used to depict the behavior of a particle detector, a quantum field mode or the scale factor of the universe. An important result of this paper is the derivation of the influence functional encompassing the noise and dissipation kernels in terms of the Bogolubov coefficients. This method enables one to trace the source of statistical processes like decoherence and dissipation to vacuum fluctuations and particle creation, and in turn impart a statistical mechanical interpretation of quantum field processes. With this result we discuss the statistical mechanical origi...
Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere
Millen, J.; Deesuwan, T.; Barker, P.; Anders, J.
2014-06-01
Einstein realized that the fluctuations of a Brownian particle can be used to ascertain the properties of its environment. A large number of experiments have since exploited the Brownian motion of colloidal particles for studies of dissipative processes, providing insight into soft matter physics and leading to applications from energy harvesting to medical imaging. Here, we use heated optically levitated nanospheres to investigate the non-equilibrium properties of the gas surrounding them. Analysing the sphere's Brownian motion allows us to determine the temperature of the centre-of-mass motion of the sphere, its surface temperature and the heated gas temperature in two spatial dimensions. We observe asymmetric heating of the sphere and gas, with temperatures reaching the melting point of the material. This method offers opportunities for accurate temperature measurements with spatial resolution on the nanoscale, and provides a means for testing non-equilibrium thermodynamics.
Brownian ratchets from statistical physics to bio and nano-motors
Cubero, David
2016-01-01
Illustrating the development of Brownian ratchets, from their foundations, to their role in the description of life at the molecular scale and in the design of artificial nano-machinery, this text will appeal to both advanced graduates and researchers entering the field. Providing a self-contained introduction to Brownian ratchets, devices which rectify microscopic fluctuations, Part I avoids technicalities and sets out the broad range of physical systems where the concept of ratchets is relevant. Part II supplies a single source for a complete and modern theoretical analysis of ratchets in regimes such as classical vs quantum and stochastic vs deterministic, and in Part III readers are guided through experimental developments in different physical systems, each highlighting a specific unique feature of ratchets. The thorough and systematic approach to the topic ensures that this book provides a complete guide to Brownian ratchets for newcomers and established researchers in physics, biology and biochemistry.
Brownian motion of a charged test particle in vacuum between two conducting plates
Yu, H; Yu, Hongwei; Chen, Jun
2004-01-01
The Brownian motion of a charged test particle caused by quantum electromagnetic vacuum fluctuations between two perfectly conducting plates is examined and the mean squared fluctuations in the velocity and position of the test particle are calculated. Our results show that the Brownian motion in the direction normal to the plates is reinforced in comparison to that in the single-plate case. The effective temperature associated with this normal Brownian motion could be three times as large as that in the single-plate case. However, the negative dispersions for the velocity and position in the longitudinal directions, which could be interpreted as reducing the quantum uncertainties of the particle, acquire positive corrections due to the presence of the second plate, and are thus weakened.
Millen, J; Deesuwan, T; Barker, P; Anders, J
2014-06-01
Einstein realized that the fluctuations of a Brownian particle can be used to ascertain the properties of its environment. A large number of experiments have since exploited the Brownian motion of colloidal particles for studies of dissipative processes, providing insight into soft matter physics and leading to applications from energy harvesting to medical imaging. Here, we use heated optically levitated nanospheres to investigate the non-equilibrium properties of the gas surrounding them. Analysing the sphere's Brownian motion allows us to determine the temperature of the centre-of-mass motion of the sphere, its surface temperature and the heated gas temperature in two spatial dimensions. We observe asymmetric heating of the sphere and gas, with temperatures reaching the melting point of the material. This method offers opportunities for accurate temperature measurements with spatial resolution on the nanoscale, and provides a means for testing non-equilibrium thermodynamics. PMID:24793558
(Quantum) Fractional Brownian Motion and Multifractal Processes under the Loop of a Tensor Networks
Descamps, Benoît
2016-01-01
We derive fractional Brownian motion and stochastic processes with multifractal properties using a framework of network of Gaussian conditional probabilities. This leads to the derivation of new representations of fractional Brownian motion. These constructions are inspired from renormalization. The main result of this paper consists of constructing each increment of the process from two-dimensional gaussian noise inside the light-cone of each seperate increment. Not only does this allows us to derive fractional Brownian motion, we can introduce extensions with multifractal flavour. In another part of this paper, we discuss the use of the multi-scale entanglement renormalization ansatz (MERA), introduced in the study critical systems in quantum spin lattices, as a method for sampling integrals with respect to such multifractal processes. After proper calibration, a MERA promises the generation of a sample of size $N$ of a multifractal process in the order of $O(N\\log(N))$, an improvement over the known method...
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
We present and demonstrate a new method for on-chip Brownian relaxation measurements on magnetic nanobeads in the time domain using magnetoresistive sensors. The beads are being magnetized by the sensor self-field arising from the bias current passed through the sensors and thus no external...... the time and frequency domain methods on Brownian relaxation detection of clustering of streptavidin coated magnetic beads in the presence of different concentrations of biotin-conjugated bovine serum albumin and obtain comparable results. In the time domain, a measurement is carried out in less than 30 s...... magnetic fields are needed. First, the method is demonstrated on Brownian relaxation measurements of beads with nominal sizes of 40, 80, 130, and 250 nm. The results are found to compare well to those obtained by an already established measurement technique in the frequency domain. Next, we demonstrate...
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.
A Brownian model for recurrent volcanic eruptions: an application to Miyakejima volcano (Japan)
Garcia-Aristizabal, Alexander; Marzocchi, Warner; Fujita, Eisuke
2012-03-01
The definition of probabilistic models as mathematical structures to describe the response of a volcanic system is a plausible approach to characterize the temporal behavior of volcanic eruptions and constitutes a tool for long-term eruption forecasting. This kind of approach is motivated by the fact that volcanoes are complex systems in which a completely deterministic description of the processes preceding eruptions is practically impossible. To describe recurrent eruptive activity, we apply a physically motivated probabilistic model based on the characteristics of the Brownian passage-time (BPT) distribution; the physical process defining this model can be described by the steady rise of a state variable from a ground state to a failure threshold; adding Brownian perturbations to the steady loading produces a stochastic load-state process (a Brownian relaxation oscillator) in which an eruption relaxes the load state to begin a new eruptive cycle. The Brownian relaxation oscillator and Brownian passage-time distribution connect together physical notions of unobservable loading and failure processes of a point process with observable response statistics. The Brownian passage-time model is parameterized by the mean rate of event occurrence, μ, and the aperiodicity about the mean, α. We apply this model to analyze the eruptive history of Miyakejima volcano, Japan, finding a value of 44.2 (±6.5 years) for the μ parameter and 0.51 (±0.01) for the (dimensionless) α parameter. The comparison with other models often used in volcanological literature shows that this physically motivated model may be a good descriptor of volcanic systems that produce eruptions with a characteristic size. BPT is clearly superior to the Exponential distribution, and the fit to the data is comparable to other two-parameters models. Nonetheless, being a physically motivated model, it provides an insight into the macro-mechanical processes driving the system.
An exactly solvable model for Brownian motion : III. Motion of a heavy mass in a linear chain
Ullersma, P.
1966-01-01
The theory on Brownian motion, developed in previous papers1) 2) is applied to a linear chain with harmonic coupling between nearest neighbours. All masses are equal except for one which is heavy compared to the others. This heavy particle behaves as a Brownian particle, which is not subject to an e
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(V
Accumulation of Microswimmers near a Surface Mediated by Collision and Rotational Brownian Motion
Li, Guanglai; Tang, Jay X.
2009-08-01
In this Letter we propose a kinematic model to explain how collisions with a surface and rotational Brownian motion give rise to accumulation of microswimmers near a surface. In this model, an elongated microswimmer invariably travels parallel to the surface after hitting it from an oblique angle. It then swims away from the surface, facilitated by rotational Brownian motion. Simulations based on this model reproduce the density distributions measured for the small bacteria E. coli and Caulobacter crescentus, as well as for the much larger bull spermatozoa swimming between two walls.
An Approach to Enhance the Efficiency of a Brownian Heat Engine
Institute of Scientific and Technical Information of China (English)
ZHANG Yan-Ping; HE Ji-Zhou; XIAO Yu-Ling
2011-01-01
A Brownian microscopic heat engine, driven by temperature difference and consisting of a Brownian particle moving in a sawtooth potential with an external load, is investigated. The heat Hows, driven by both potential and kinetic energies, are taken into account. Based on the master equation, the expressions for efficiency and power output are derived analytically, and performance characteristic curves are plotted. It is shown that the heat How via the kinetic energy of the particle decreases. The efficiency of the engine is enhanced, but the power output reduces as the a shape parameter of the sawtooth potential increases. The influence of the a shape parameter on efficiency and power output is then analyzed in detail.%A Brownian microscopic heat engine,driven by temperature difference and consisting of a Brownian particle moving in a sawtooth potential with an external load,is investigated.The heat flows,driven by both potential and kinetic energies,are taken into account.Based on the master equation,the expressions for efficiency and power output are derived analytically,and performance characteristic curves are plotted.It is shown that the heat flow via the kinetic energy of the particle decreases.The efficiency of the engine is enhanced,but the power output reduces as the α shape parameter of the sawtooth potential increases.The influence of the α shape parameter on efficiency and power output is then analyzed in detail.Like the Carnot cycle,the Brownian heat engine can extract work from the temperature difference between heat reservoirs,where the Brownian working material operates as a transducer of thermal energy into mechanical work.In the last few decades,the study of Brownian heat engines has received considerable attention,not only for the construction of the miniaturized engine that helps us utilize energy resources at microscopic scales,but also for a better understanding of nonequilibrium statistical physics.[1-3] The thermodynamic properties of the
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 Motion in wedges, last passage time and the second arc-sine law
Comtet, Alain; Desbois, Jean
2003-01-01
We consider a planar Brownian motion starting from $O$ at time $t=0$ and stopped at $t=1$ and a set $F= \\{OI_i ; i=1,2,..., n\\}$ of $n$ semi-infinite straight lines emanating from $O$. Denoting by $g$ the last time when $F$ is reached by the Brownian motion, we compute the probability law of $g$. In particular, we show that, for a symmetric $F$ and even $n$ values, this law can be expressed as a sum of $\\arcsin $ or $(\\arcsin)^2 $ functions. The original result of Levy is recovered as the spe...
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...
Brownian motion in a singular potential and a fractal renewal process
Ouyang, H. F.; Huang, Z. Q.; Ding, E. J.
1995-10-01
We have proposed a model for the one-dimensional Brownian motion of a single particle in a singular potential field in our previous paper [Phys. Rev. E 50, 2491 (1994)]. In this Brief Report, we further discuss this model and show that, in some special cases, the Brownian motion can be considered as a finite-valued alternating renewal process, which has been investigated by Lowen and Teich [Phys. Rev. E 47, 992 (1993)]. The numerical results here are in agreement with those drawn by Lowen and Teich.
Institute of Scientific and Technical Information of China (English)
ZHANG Jia-Lin; YU Hong-Wei
2005-01-01
@@ We show that the velocity and position dispersions of a test particle with a nonzero constant classical velocity undergoing Brownian motion caused by electromagnetic vacuum fluctuations in a space with plane boundaries can be obtained from those of the static case by Lorentz transformation. We explicitly derive the Lorentz transformations relating the dispersions of the two cases and then apply them to the case of the Brownian motion of a test particle with a constant classical velocity parallel to the boundary between two conducting planes. Our results show that the influence of a nonzero initial velocity is negligible for nonrelativistic test particles.
Brownian 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
Pitman, Jim
1999-01-01
For a random process $X$ consider the random vector defined by the values of $X$ at times $0 \\lt U_{n,1} \\lt ... \\lt U_{n,n} \\lt 1$ and the minimal values of $X$ on each of the intervals between consecutive pairs of these times, where the $U_{n,i}$ are the order statistics of $n$ independent uniform $(0,1)$ variables, independent of $X$. The joint law of this random vector is explicitly described when $X$ is a Brownian motion. Corresponding results for Brownian bridge, excursion, and meander ...
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 fields...... are needed as the beads are magnetized by the field generated by the applied sensor bias current. We show that the Brownian relaxation frequency can be extracted from fitting the Cole-Cole model to measurements for bead concentrations of 64 mu g/ml or higher and that the measured dynamic magnetic response...
Brownian Agents and Active Particles: Collective Dynamics in the Natural and Social Sciences
International Nuclear Information System (INIS)
This is a book about the modelling of complex systems and, unlike many books on this subject, concentrates on the discussion of specific systems and gives practical methods for modelling and simulating them. This is not to say that the author does not devote space to the general philosophy and definition of complex systems and agent-based modelling, but the emphasis is definitely on the development of concrete methods for analysing them. This is, in my view, to be welcomed and I thoroughly recommend the book, especially to those with a theoretical physics background who will be very much at home with the language and techniques which are used. The author has developed a formalism for understanding complex systems which is based on the Langevin approach to the study of Brownian motion. This is a mesoscopic description; details of the interactions between the Brownian particle and the molecules of the surrounding fluid are replaced by a randomly fluctuating force. Thus all microscopic detail is replaced by a coarse-grained description which encapsulates the essence of the interactions at the finer level of description. In a similar way, the influences on Brownian agents in a multi-agent system are replaced by stochastic influences which sum up the effects of these interactions on a finer scale. Unlike Brownian particles, Brownian agents are not structureless particles, but instead have some internal states so that, for instance, they may react to changes in the environment or to the presence of other agents. Most of the book is concerned with developing the idea of Brownian agents using the techniques of statistical physics. This development parallels that for Brownian particles in physics, but the author then goes on to apply the technique to problems in biology, economics and the social sciences. This is a clear and well-written book which is a useful addition to the literature on complex systems. It will be interesting to see if the use of Brownian agents becomes
Diffusion-limited aggregation with long range force
International Nuclear Information System (INIS)
The Diffusion-Limited aggregation model with long range force is investigated. Single particles are moved under the control of Brownian motion and drift motion produced by regular centrical long range force. The computer simulations under this condition have been studied in detail in two-dimension and the results are compared with properly electrolytic deposition experiments. (author)
First passage times for a tracer particle in single file diffusion and fractional Brownian motion.
Sanders, Lloyd P; Ambjörnsson, Tobias
2012-05-01
We investigate the full functional form of the first passage time density (FPTD) of a tracer particle in a single-file diffusion (SFD) system whose population is: (i) homogeneous, i.e., all particles having the same diffusion constant and (ii) heterogeneous, with diffusion constants drawn from a heavy-tailed power-law distribution. In parallel, the full FPTD for fractional Brownian motion [fBm-defined by the Hurst parameter, H ∈ (0, 1)] is studied, of interest here as fBm and SFD systems belong to the same universality class. Extensive stochastic (non-Markovian) SFD and fBm simulations are performed and compared to two analytical Markovian techniques: the method of images approximation (MIA) and the Willemski-Fixman approximation (WFA). We find that the MIA cannot approximate well any temporal scale of the SFD FPTD. Our exact inversion of the Willemski-Fixman integral equation captures the long-time power-law exponent, when H ≥ 1/3, as predicted by Molchan [Commun. Math. Phys. 205, 97 (1999)] for fBm. When H systems are compared to their fBm counter parts; and in the homogeneous system both scaled FPTDs agree on all temporal scales including also, the result by Molchan, thus affirming that SFD and fBm dynamics belong to the same universality class. In the heterogeneous case SFD and fBm results for heterogeneity-averaged FPTDs agree in the asymptotic time limit. The non-averaged heterogeneous SFD systems display a lack of self-averaging. An exponential with a power-law argument, multiplied by a power-law pre-factor is shown to describe well the FPTD for all times for homogeneous SFD and sub-diffusive fBm systems.
Soto-Aquino, D; Rosso, D; Rinaldi, C
2011-11-01
Ferrofluids are colloidal suspensions of magnetic nanoparticles that exhibit normal liquid behavior in the absence of magnetic fields but respond to imposed magnetic fields by changing their viscosity without loss of fluidity. The response of ferrofluids to constant shear and magnetic fields has received a lot of attention, but the response of ferrofluids to oscillatory shear remains largely unexplored. In the present work we used rotational Brownian dynamics to study the dynamic properties of ferrofluids with thermally blocked nanoparticles under oscillatory shear and constant magnetic fields. Comparisons between simulations and modeling using the ferrohydrodynamics equations were also made. Simulation results show that, for small rotational Péclet number, the in-phase and out-of-phase components of the complex viscosity depend on the magnitude of the magnetic field and frequency of the shear, following a Maxwell-like model with field-dependent viscosity and characteristic time equal to the field-dependent transverse magnetic relaxation time of the nanoparticles. Comparison between simulations and the numerical solution of the ferrohydrodynamic equations shows that the oscillatory rotational magnetoviscosity for an oscillating shear field obtained using the kinetic magnetization relaxation equation quantitatively agrees with simulations for a wide range of Péclet number and Langevin parameter but has quantitative deviations from the simulations at high values of the Langevin parameter. These predictions indicate an apparent elastic character to the rheology of these suspensions, even though we are considering the infinitely dilute limit in which there are negligible particle-particle interactions and, as such, chains do not form. Additionally, an asymptotic analytical solution of the ferrohydrodynamics equations, valid for Peferrofluids under conditions of small shear rates. At higher shear rates the Cox-Merz rule ceases to apply. PMID:22181497
Van Zanten, Agnès; Da Costa, Sylvie
2013-01-01
Cet article vise à mettre en évidence les enjeux, les dynamiques et les limites de la gouvernance éducative locale à propos de la gestion de la carte scolaire des collèges dans la seconde moitié des années 2000. Prenant appui sur l’analyse de diverses traces écrites ainsi que d’entretiens et d’observations réalisés dans le cadre d’une enquête de terrain dans la périphérie parisienne, il s’intéresse aux effets conjugués de deux choix politiques récents (l’attribution de la compétence en matièr...
Ziegler, Jörg; Schmidt, Stephan; Chutia, Ranju; Müller, Jens; Böttcher, Christoph; Strehmel, Nadine; Scheel, Dierk; Abel, Steffen
2016-03-01
Plants have evolved two major strategies to cope with phosphate (Pi) limitation. The systemic response, mainly comprising increased Pi uptake and metabolic adjustments for more efficient Pi use, and the local response, enabling plants to explore Pi-rich soil patches by reorganization of the root system architecture. Unlike previous reports, this study focused on root exudation controlled by the local response to Pi deficiency. To approach this, a hydroponic system separating the local and systemic responses was developed. Arabidopsis thaliana genotypes exhibiting distinct sensitivities to Pi deficiency could be clearly distinguished by their root exudate composition as determined by non-targeted reversed-phase ultraperformance liquid chromatography electrospray ionization quadrupole-time-of-flight mass spectrometry metabolite profiling. Compared with wild-type plants or insensitive low phosphate root 1 and 2 (lpr1 lpr2) double mutant plants, the hypersensitive phosphate deficiency response 2 (pdr2) mutant exhibited a reduced number of differential features in root exudates after Pi starvation, suggesting the involvement of PDR2-encoded P5-type ATPase in root exudation. Identification and analysis of coumarins revealed common and antagonistic regulatory pathways between Pi and Fe deficiency-induced coumarin secretion. The accumulation of oligolignols in root exudates after Pi deficiency was inversely correlated with Pi starvation-induced lignification at the root tips. The strongest oligolignol accumulation in root exudates was observed for the insensitive lpr1 lpr2 double mutant, which was accompanied by the absence of Pi deficiency-induced lignin deposition, suggesting a role of LPR ferroxidases in lignin polymerization during Pi starvation. PMID:26685189
Wang, Jun; Liang, Jin-Rong; Lv, Long-Jin; Qiu, Wei-Yuan; Ren, Fu-Yao
2012-02-01
In this paper, we study the problem of continuous time option pricing with transaction costs by using the homogeneous subdiffusive fractional Brownian motion (HFBM) Z(t)=X(Sα(t)), 0Black-Scholes equation and the Black-Scholes formula for the fair prices of European option, the turnover and transaction costs of replicating strategies. We also give the total transaction costs.
Time-changed geometric fractional Brownian motion and option pricing with transaction costs
Gu, Hui; Liang, Jin-Rong; Zhang, Yun-Xiu
2012-08-01
This paper deals with the problem of discrete time option pricing by a fractional subdiffusive Black-Scholes model. The price of the underlying stock follows a time-changed geometric fractional Brownian motion. By a mean self-financing delta-hedging argument, the pricing formula for the European call option in discrete time setting is obtained.
Accumulation of microswimmers near surface due to steric confinement and rotational Brownian motion
Li, Guanglai; Tang, Jay
2009-03-01
Microscopic swimmers display some intriguing features dictated by Brownian motion, low Reynolds number fluid mechanics, and boundary confinement. We re-examine the reported accumulation of swimming bacteria or bull spermatozoa near the boundaries of a fluid chamber, and propose a kinematic model to explain how collision with surface, confinement and rotational Brownian motion give rise to the accumulation of micro-swimmers near a surface. In this model, an elongated microswimmer invariably travels parallel to the surface after hitting it from any incident angle. It then takes off and swims away from the surface after some time due to rotational Brownian motion. Based on this analysis, we obtain through computer simulation steady state density distributions that reproduce the ones measured for the small bacteria E coli and Caulobacter crescentus, as well as for the much larger bull spermatozoa swimming near surfaces. These results suggest strongly that Brownian dynamics and surface confinement are the dominant factors for the accumulation of microswimmers near a surface.
Influence of Brownian Diffusion on Levitation of Bodies in Magnetic Fluid
Directory of Open Access Journals (Sweden)
V. Bashtovoi
2013-12-01
Full Text Available The present work deals with experimental investigation of the levitation of magnetic and non-magnetic bodies in a magnetic fluid when essentially influenced by Brownian diffusion of magnetic particles in it. It is established that the point of levitation of bodies in a magnetic fluid varies with time.
Brownian Motion on a Pseudo Sphere in Minkowski Space R^l_v
Jiang, Xiaomeng; Li, Yong
2016-10-01
For a Brownian motion moving on a pseudo sphere in Minkowski space R^l_v of radius r starting from point X, we obtain the distribution of hitting a fixed point on this pseudo sphere with l≥ 3 by solving Dirichlet problems. The proof is based on the method of separation of variables and the orthogonality of trigonometric functions and Gegenbauer polynomials.
Influence of Brownian Diffusion on Levitation of Bodies in Magnetic Fluid
V. Bashtovoi; A. Reks; S. Klimovich; А. Motsar; P. Ryapolov; A. Storozhenko; I. Shabanova
2013-01-01
The present work deals with experimental investigation of the levitation of magnetic and non-magnetic bodies in a magnetic fluid when essentially influenced by Brownian diffusion of magnetic particles in it. It is established that the point of levitation of bodies in a magnetic fluid varies with time.
Pricing Perpetual American Put Option in theMixed Fractional Brownian Motion
Institute of Scientific and Technical Information of China (English)
2015-01-01
Under the assumption of the underlying asset is driven by the mixed fractional Brownian motion, we obtain the mixed fractionalBlack-Scholes partial differential equation by fractional Ito formula, and the pricing formula of perpetual American put option bythis partial differential equation theory.
Directory of Open Access Journals (Sweden)
R. Maheswari
2015-03-01
Full Text Available In this paper we investigate the existence, uniqueness, asymptotic behavior of mild solutions to neutral stochastic differential equations with delays driven by a fractional Brownian motion in a Hilbert space. The cases of finite and infinite delays are analyzed.
DEFF Research Database (Denmark)
E. Barndorff-Nielsen, Ole; Benth, Fred Espen; Szozda, Benedykt
This paper generalizes the integration theory for volatility modulated Brownian-driven Volterra processes onto the space G* of Potthoff-Timpel distributions. Sufficient conditions for integrability of generalized processes are given, regularity results and properties of the integral are discussed...
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole E.; Benth, Fred Espen; Szozda, Benedykt
This paper generalizes the integration theory for volatility modulated Brownian-driven Volterra processes onto the space G∗ of Potthoff--Timpel distributions. Sufficient conditions for integrability of generalized processes are given, regularity results and properties of the integral are discussed...
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...
Brownian motion with variable drift: 0-1 laws, hitting probabilities and Hausdorff dimension
Peres, Yuval
2010-01-01
By the Cameron--Martin theorem, if a function $f$ is in the Dirichlet space $D$, then $B+f$ has the same a.s. properties as standard Brownian motion, $B$. In this paper we examine properties of $B+f$ when $f \
Stochastic optimal control problem with infinite horizon driven by G-Brownian motion
Hu, Mingshang; Wang, Falei
2016-01-01
The present paper considers a stochastic optimal control problem, in which the cost function is defined through a backward stochastic differential equation with infinite horizon driven by G-Brownian motion. Then we study the regularities of the value function and establish the dynamic programming principle. Moreover, we prove that the value function is the uniqueness viscosity solution of the related HJBI equation.
The oscillation of the occupation time process of super- Brownian motion on Sierpinski gasket
Institute of Scientific and Technical Information of China (English)
郭军义
2000-01-01
The occupation time process of super-Brownian motion on the Sierpinski gasket is studied. It is shown that this process does not possess stable property in the long run, but oscillates periodically in some sense. Other convergence properties are also studied.
The oscillation of the occupation time process of super-Brownian motion on Sierpinski gasket
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The occupation time process of super-Brownian motion on the Sierpinski gasket is studied. It is shown that this process does not possess stable property in the long run, but oscillates periodically in some sense. Other convergence properties are also studied.
Scaling Limits of Coalescent Processes Near Time Zero
Sengul, Bati
2013-01-01
In this paper we obtain scaling limits of $\\Lambda$-coalescents near time zero under a regularly varying assumption. In particular this covers the case of Kingman's coalescent and beta coalescents. The limiting processes are coalescents with infinite mass, obtained geometrically as tangent cones of Evans metric space associated with the coalescent. In the case of Kingman's coalescent we are able to obtain a simple construction of the limiting space using a two-sided Brownian motion.
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.
Local collective motion analysis for multi-probe dynamic imaging and microrheology.
Khan, Manas; Mason, Thomas G
2016-08-01
Dynamical artifacts, such as mechanical drift, advection, and hydrodynamic flow, can adversely affect multi-probe dynamic imaging and passive particle-tracking microrheology experiments. Alternatively, active driving by molecular motors can cause interesting non-Brownian motion of probes in local regions. Existing drift-correction techniques, which require large ensembles of probes or fast temporal sampling, are inadequate for handling complex spatio-temporal drifts and non-Brownian motion of localized domains containing relatively few probes. Here, we report an analytical method based on local collective motion (LCM) analysis of as few as two probes for detecting the presence of non-Brownian motion and for accurately eliminating it to reveal the underlying Brownian motion. By calculating an ensemble-average, time-dependent, LCM mean square displacement (MSD) of two or more localized probes and comparing this MSD to constituent single-probe MSDs, we can identify temporal regimes during which either thermal or athermal motion dominates. Single-probe motion, when referenced relative to the moving frame attached to the multi-probe LCM trajectory, provides a true Brownian MSD after scaling by an appropriate correction factor that depends on the number of probes used in LCM analysis. We show that LCM analysis can be used to correct many different dynamical artifacts, including spatially varying drifts, gradient flows, cell motion, time-dependent drift, and temporally varying oscillatory advection, thereby offering a significant improvement over existing approaches. PMID:27269299
Local collective motion analysis for multi-probe dynamic imaging and microrheology
Khan, Manas; Mason, Thomas G.
2016-08-01
Dynamical artifacts, such as mechanical drift, advection, and hydrodynamic flow, can adversely affect multi-probe dynamic imaging and passive particle-tracking microrheology experiments. Alternatively, active driving by molecular motors can cause interesting non-Brownian motion of probes in local regions. Existing drift-correction techniques, which require large ensembles of probes or fast temporal sampling, are inadequate for handling complex spatio-temporal drifts and non-Brownian motion of localized domains containing relatively few probes. Here, we report an analytical method based on local collective motion (LCM) analysis of as few as two probes for detecting the presence of non-Brownian motion and for accurately eliminating it to reveal the underlying Brownian motion. By calculating an ensemble-average, time-dependent, LCM mean square displacement (MSD) of two or more localized probes and comparing this MSD to constituent single-probe MSDs, we can identify temporal regimes during which either thermal or athermal motion dominates. Single-probe motion, when referenced relative to the moving frame attached to the multi-probe LCM trajectory, provides a true Brownian MSD after scaling by an appropriate correction factor that depends on the number of probes used in LCM analysis. We show that LCM analysis can be used to correct many different dynamical artifacts, including spatially varying drifts, gradient flows, cell motion, time-dependent drift, and temporally varying oscillatory advection, thereby offering a significant improvement over existing approaches.
Shit, Anindita; Ghosh, Pradipta; Chattopadhyay, Sudip; Chaudhuri, Jyotipratim Ray
2011-03-01
We explore the issue of a quantum-noise-induced directed transport of an overdamped Brownian particle that is allowed to move in a spatially periodic potential. The established system-reservoir model has been employed here to study the quantum-noise-induced transport of a Brownian particle in a periodic potential, where the reservoir is being modulated externally by a Gaussian-colored noise. The mobility of the Brownian particle in the linear response regime has been calculated. Then, using Einstein's relation, the analytical expression for the diffusion rate is evaluated for any arbitrary periodic potential for the high-temperature quantum regime. PMID:21517472
Fernández-Olmo, Ignacio; Andecochea, Carlos; Ruiz, Sara; Fernández-Ferreras, José Antonio; Irabien, Angel
2016-05-01
This study presents the analysis of the concentration levels, inter-site variation and source identification of trace metals at three urban/industrial mixed land-use sites of the Cantabria region (northern Spain), where local air quality plans were recently approved because the number of exceedances of the daily PM10 limit value according to the Directive 2008/50/EC had been relatively high in the last decade (more than 35 instances per year). PM10 samples were collected for over three years at the Torrelavega (TORR) and Los Corrales (CORR) sites and for over two years at the Camargo (GUAR) site and analysed for the presence of arsenic (As), cadmium (Cd), chromium (Cr), copper (Cu), lead (Pb), nickel (Ni), titanium (Ti), vanadium (V), molybdenum (Mo), manganese (Mn), iron (Fe), antimony (Sb) and zinc (Zn). Analysis of enrichment factors revealed an anthropogenic origin of most of the studied elements; Zn, Cd, Mo, Pb and Cu were the most enriched elements at the three sites, with Fe and V as the least enriched elements. Positive Matrix Factorisation (PMF) and pollutant roses (Cu at TORR, Zn at CORR and Mn at GUAR) were used to identify the local sources of the studied metals. Analysis of PMF results revealed the main sources of trace metals at each site as road traffic at the TORR site, iron foundry and casting industry at the CORR site and a ferro-manganese alloy industry at the GUAR site. Other sources were also identified at these sites, but with much lower contributions, such as minor industrial sources, combustion and traffic mixed with the previous sources.
Kim, Juntae; Helgeson, Matthew E.
2016-08-01
We investigate shear-induced clustering and its impact on fluid rheology in polymer-colloid mixtures at moderate colloid volume fraction. By employing a thermoresponsive system that forms associative polymer-colloid networks, we present experiments of rheology and flow-induced microstructure on colloid-polymer mixtures in which the relative magnitudes of the time scales associated with relaxation of viscoelasticity and suspension microstructure are widely and controllably varied. In doing so, we explore several limits of relative magnitude of the relevant dimensionless shear rates, the Weissenberg number Wi and the Péclet number Pe. In all of these limits, we find that the fluid exhibits two distinct regimes of shear thinning at relatively low and high shear rates, in which the rheology collapses by scaling with Wi and Pe, respectively. Using three-dimensionally-resolved flow small-angle neutron scattering measurements, we observe clustering of the suspension above a critical shear rate corresponding to Pe ˜0.1 over a wide range of fluid conditions, having anisotropy with projected orientation along both the vorticity and compressional axes of shear. The degree of anisotropy is shown to scale with Pe. From this we formulate an empirical model for the shear stress and viscosity, in which the viscoelastic network stress is augmented by an asymptotic shear thickening contribution due to hydrodynamic clustering. Overall, our results elucidate the significant role of hydrodynamic interactions in contributing to shear-induced clustering of Brownian suspensions in viscoelastic liquids.
Generalized Local Time of the Indefinite Wiener Integral:White Noise Approach
Institute of Scientific and Technical Information of China (English)
Jingjun GUO
2012-01-01
In this paper,the generalized local time of the indefinite Wiener integral Xt is discussed through white noise approach,which means to regard the local time as a Hida distribution.Moreover,similar result is also obtained in case of two independent Brownian motions by using the similar approach.
The weak coupling limit of disordered copolymer models
Caravenna, Francesco
2009-01-01
A copolymer is a chain of repetitive units (monomers) that are almost identical, but they differ in their degree of affinity for certain solvents. This difference leads to striking phenomena when the polymer fluctuates in a non-homogeneous medium, for example made up by two solvents separated by an interface. One may observe, for instance, the localization of the polymer at the interface between the two solvents. A discrete model of such system, based on the simple symmetric random walk on Z, has been investigated in [Bolthausen and den Hollander, Ann. Probab. 25 (1997), 1334-1366], notably in the weak polymer-solvent coupling limit, where the convergence of the discrete model toward a continuum model, based on Brownian motion, has been established. This result is remarkable because it strongly suggests a universal feature of copolymer models. In this work we prove that this is indeed the case. More precisely, we determine the weak coupling limit for a general class of discrete copolymer models, obtaining as ...
Madan, D.; Roynette, Bernard; Yor, Marc
2008-01-01
The celebrated Black-Scholes formula which gives the price of a European option, may be expressed as the cumulative function of a last passage time of Brownian motion. A related result involving first passage times is also obtained.
On the local time of random processes in random scenery
Castell, Fabienne; Pène, Françoise; Schapira, Bruno
2012-01-01
Random walks in random scenery are processes defined by $Z_n:=\\sum_{k=1}^n\\xi_{X_1+...+X_k}$, where basically $(X_k,k\\ge 1)$ and $(\\xi_y,y\\in\\mathbb Z)$ are two independent sequences of i.i.d. random variables. We assume here that $X_1$ is $\\ZZ$-valued, centered and with finite moments of all orders. We also assume that $\\xi_0$ is $\\ZZ$-valued, centered and square integrable. In this case H. Kesten and F. Spitzer proved that $(n^{-3/4}Z_{[nt]},t\\ge 0)$ converges in distribution as $n\\to \\infty$ toward some self-similar process $(\\Delta_t,t\\ge 0)$ called Brownian motion in random scenery. In a previous paper, we established that ${\\mathbb P}(Z_n=0)$ behaves asymptotically like a constant times $n^{-3/4}$, as $n\\to \\infty$. We extend here this local limit theorem: we give a precise asymptotic result for the probability for $Z$ to return to zero simultaneously at several times. As a byproduct of our computations, we show that $\\Delta$ admits a bi-continuous version of its local time process which is locally H\\"o...
Chavanis, Pierre-Henri; Sire, Clement
2005-01-01
We derive the Virial theorem appropriate to the generalized Smoluchowski-Poisson system describing self-gravitating Brownian particles and bacterial populations (chemotaxis). We extend previous works by considering the case of an unbounded domain and an arbitrary equation of state. We use the Virial theorem to study the diffusion (evaporation) of an isothermal Brownian gas above the critical temperature T_c in dimension d=2 and show how the effective diffusion coefficient and the Einstein rel...
Characterisation of a three-dimensional Brownian motor in optical lattices
Sjolund, P; Dion, C M; Hagman, H; Jonsell, S; Kastberg, A
2007-01-01
We present here a detailed study of the behaviour of a three dimensional Brownian motor based on cold atoms in a double optical lattice [P. Sjolund et al., Phys. Rev. Lett. 96, 190602 (2006)]. This includes both experiments and numerical simulations of a Brownian particle. The potentials used are spatially and temporally symmetric, but combined spatiotemporal symmetry is broken by phase shifts and asymmetric transfer rates between potentials. The diffusion of atoms in the optical lattices is rectified and controlled both in direction and speed along three dimensions. We explore a large range of experimental parameters, where irradiances and detunings of the optical lattice lights are varied within the dissipative regime. Induced drift velocities in the order of one atomic recoil velocity have been achieved.
Fleming, C H; Hu, B L
2010-01-01
We revisit the model of a quantum Brownian oscillator linearly coupled to an environment of quantum oscillators at finite temperature. By introducing a compact and particularly well-suited formulation, we give a rather quick and direct derivation of the master equation and its solutions for general spectral functions and arbitrary temperatures. The flexibility of our approach allows for an immediate generalization to cases with an external force and with an arbitrary number of Brownian oscillators. More importantly, we point out an important mathematical subtlety concerning boundary-value problems for integro-differential equations which led to incorrect master equation coefficients and impacts on the description of nonlocal dissipation effects in all earlier derivations. Furthermore, we provide explicit, exact analytical results for the master equation coefficients and its solutions in a wide variety of cases, including ohmic, sub-ohmic and supra-ohmic environments with a finite cut-off.
Quantal Brownian Motion from RPA dynamics: The master and Fokker-Planck equations
International Nuclear Information System (INIS)
From the purely quantal RPA description of the damped harmonic oscillator and of the corresponding Brownian Motion within the full space (phonon subspace plus reservoir), a master equation (as well as a Fokker-Planck equation) for the reduced density matrix (for the reduced Wigner function, respectively) within the phonon subspace is extracted. The RPA master equation agrees with the master equation derived by the time-dependent perturbative approaches which utilize Tamm-Dancoff Hilbert spaces and invoke the rotating wave approximation. Since the RPA yields a full, as well as a contracted description, it can account for both the kinetic and the unperturbed oscillator momenta. The RPA description of the quantal Brownian Motion contrasts with the descriptions provided by the time perturbative approaches whether they invoke or not the rotating wave approximation. The RPA description also contrasts with the phenomenological phase space quantization. (orig.)
Brownian motion in wedges, last passage time and the second arc-sine law
Energy Technology Data Exchange (ETDEWEB)
Comtet, Alain [Laboratoire de Physique Theorique et Modeles Statistiques. Universite Paris-Sud, Bat. 100, F-91405 Orsay Cedex (France); Desbois, Jean [Laboratoire de Physique Theorique et Modeles Statistiques. Universite Paris-Sud, Bat. 100, F-91405 Orsay Cedex (France)
2003-05-02
We consider a planar Brownian motion starting from O at time t = 0 and stopped at t = 1 and a set F = OI{sub i}; i = 1, 2, ..., n of n semi-infinite straight lines emanating from O. Denoting by g the last time when F is reached by the Brownian motion, we compute the probability law of g. In particular, we show that, for a symmetric F and even n values, this law can be expressed as a sum of arcsin or (arcsin){sup 2} functions. The original result of Levy is recovered as the special case n = 2. A relation with the problem of reaction-diffusion of a set of three particles in one dimension is discussed. (letter to the editor)
Brownian motion in wedges, last passage time and the second arc-sine law
International Nuclear Information System (INIS)
We consider a planar Brownian motion starting from O at time t = 0 and stopped at t = 1 and a set F = OIi; i = 1, 2, ..., n of n semi-infinite straight lines emanating from O. Denoting by g the last time when F is reached by the Brownian motion, we compute the probability law of g. In particular, we show that, for a symmetric F and even n values, this law can be expressed as a sum of arcsin or (arcsin)2 functions. The original result of Levy is recovered as the special case n = 2. A relation with the problem of reaction-diffusion of a set of three particles in one dimension is discussed. (letter to the editor)
On Nonlinear Quantum Mechanics, Brownian Motion, Weyl Geometry and Fisher Information
Directory of Open Access Journals (Sweden)
Castro C.
2006-01-01
Full Text Available A new nonlinear Schrödinger equation is obtained explicitly from the (fractal Brownian motion of a massive particle with a complex-valued diffusion constant. Real-valued energy plane-wave solutions and solitons exist in the free particle case. One remarkable feature of this nonlinear Schrödinger equation based on a (fractal Brownian motion model, over all the other nonlinear QM models, is that the quantummechanical energy functional coincides precisely with the field theory one. We finalize by showing why a complex momentum is essential to fully understand the physical implications of Weyl’s geometry in QM, along with the interplay between Bohm’s Quantum potential and Fisher Information which has been overlooked by several authors in the past.
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 inventory models with convex holding cost, Part 2: Discount-optimal controls
Jim Dai; Dacheng Yao
2013-01-01
We consider an inventory system in which inventory level fluctuates as a Brownian motion in the absence of control. The inventory continuously accumulates cost at a rate that is a general convex function of the inventory level, which can be negative when there is a backlog. At any time, the inventory level can be adjusted by a positive or negative amount, which incurs a fixed positive cost and a proportional cost. The challenge is to find an adjustment policy ...
Maximum likelihood drift estimation for the mixing of two fractional Brownian motions
Mishura, Yuliya
2015-01-01
We construct the maximum likelihood estimator (MLE) of the unknown drift parameter $\\theta\\in \\mathbb{R}$ in the linear model $X_t=\\theta t+\\sigma B^{H_1}(t)+B^{H_2}(t),\\;t\\in[0,T],$ where $B^{H_1}$ and $B^{H_2}$ are two independent fractional Brownian motions with Hurst indices $\\frac12
Stability of Linear Stochastic Differential Equations with Respect to Fractional Brownian Motion
Institute of Scientific and Technical Information of China (English)
SHU Hui-sheng; CHEN Chun-li; WEI Guo-liang
2009-01-01
This paper is concerned with the stochastically stability for the m -dimensional linear stochastic differential equations with respect to fractional Brownian motion (FBM) with Hurst parameter H∈ (1/2, 1). On the basis of the pioneering work of Duncan and Hu, a Ito's formula is given.An improved derivative operator to Lyapunov functions is constructed, and the sufficient conditions for the stochastically stability of linear stochastic differential equations driven by FBM are established. These extend the stochastic Lyapunov stability theories.
Random variables as pathwise integrals with respect to fractional Brownian motion
Mishura, Yuliya; Valkeila, Esko
2011-01-01
We show that a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand $g$ can have any prescribed distribution, moreover, we give both necessary and sufficient conditions when random variables can be represented in this form. We also prove that any random variable is a value of such integral in some improper sense. We discuss some applications of these results, in particular, to fractional Black--Scholes model of financial market.
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...
Fractional Brownian Motion Approximation Based on Fractional Integration of a White Noise
Chechkin, A. V.; Gonchar, V. Yu.
1999-01-01
We study simple approximations to fractional Gaussian noise and fractional Brownian motion. The approximations are based on spectral properties of the noise. They allow one to consider the noise as the result of fractional integration/differentiation of a white Gaussian noise. We study correlation properties of the approximation to fractional Gaussian noise and point to the peculiarities of persistent and anti-persistent behaviors. We also investigate self-similar properties of the approximat...
Hybrid finite element and Brownian dynamics method for diffusion-controlled reactions
Bauler, Patricia; Huber, Gary A.; McCammon, J. Andrew
2012-01-01
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. This paper proposes a new hybrid diffusion method that couples the strengths of each of these two methods. The method is derived for a general multidimensional system, and is presented using a basic test case for 1D linear and radially symmetri...
Optimal stochastic control and optimal consumption and portfolio with G-Brownian motion
Fei, Weiyin; Fei, Chen
2013-01-01
By the calculus of Peng's G-sublinear expectation and G-Brownian motion on a sublinear expectation space $(\\Omega, {\\cal H}, \\hat{\\mathbb{E}})$, we first set up an optimality principle of stochastic control problem. Then we investigate an optimal consumption and portfolio decision with a volatility ambiguity by the derived verification theorem. Next the two-fund separation theorem is explicitly obtained. And an illustrative example is provided.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The solutions of the following bilinearstochastic differential equation are stud-ied (X) where Atk, Bt are (deterministic)continuous matrix-valued functions of t and w1(t),..., wm(t) are m independent standard Brownian motions. Conditions are given such thatthe solution is positive if the initial condition is positive.The equation the most probable path must satisfy is also derived and applied to a mathematicalfinance problem.
Boundary behavior of a constrained Brownian motion between reflecting-repellent walls
Lépingle, Dominique
2009-01-01
International audience Stochastic variational inequalities provide a unified treatment for stochastic differential equations living in a closed domain with normal reflection and (or) singular repellent drift. When the domain is a polyhedron, we prove that the reflected-repelled Brownian motion does not hit the non-smooth part of the boundary. A sufficient condition for non-hitting a face of the polyhedron is derived from the one-dimensional case. A complete answer to the question of attain...
Generalized Scaling and the Master Variable for Brownian Magnetic Nanoparticle Dynamics
Reeves, Daniel B.; Yipeng Shi; Weaver, John B.
2016-01-01
Understanding the dynamics of magnetic particles can help to advance several biomedical nanotechnologies. Previously, scaling relationships have been used in magnetic spectroscopy of nanoparticle Brownian motion (MSB) to measure biologically relevant properties (e.g., temperature, viscosity, bound state) surrounding nanoparticles in vivo. Those scaling relationships can be generalized with the introduction of a master variable found from non-dimensionalizing the dynamical Langevin equation. T...
Fractional Brownian motion, the Matern process, and stochastic modeling of turbulent dispersion
Lilly, J M; Early, J J; Olhede, S C
2016-01-01
Stochastic process exhibiting power-law slopes in the frequency domain are frequently well modeled by fractional Brownian motion (fBm). In particular, the spectral slope at high frequencies is associated with the degree of small-scale roughness or fractal dimension. However, a broad class of real-world signals have a high-frequency slope, like fBm, but a plateau in the vicinity of zero frequency. This low-frequency plateau, it is shown, implies that the temporal integral of the process exhibits diffusive behavior, dispersing from its initial location at a constant rate. Such processes are not well modeled by fBm, which has a singularity at zero frequency corresponding to an unbounded rate of dispersion. A more appropriate stochastic model is a much lesser-known random process called the Matern process, which is shown herein to be a damped version of fractional Brownian motion. This article first provides a thorough introduction to fractional Brownian motion, then examines the details of the Matern process and...
Bessel processes and hyperbolic Brownian motions stopped at different random times
D'Ovidio, Mirko
2010-01-01
Iterated Bessel processes R^\\gamma(t), t>0, \\gamma>0 and their counterparts on hyperbolic spaces, i.e. hyperbolic Brownian motions B^{hp}(t), t>0 are examined and their probability laws derived. The higher-order partial differential equations governing the distributions of I_R(t)=_1R^\\gamma(_2R^\\gamma(t)), t>0 and J_R(t) =_1R^\\gamma(|_2R^\\gamma(t)|^2), t>0 are obtained and discussed. Processes of the form R^\\gamma(T_t), t>0, B^{hp}(T_t), t>0 where T_t=\\inf{s: B(s)=t} are examined and numerous probability laws derived, including the Student law, the arcsin laws (also their asymmetric versions), the Lamperti distribution of the ratio of independent positively skewed stable random variables and others. For the process R^{\\gamma}(T^\\mu_t), t>0 (where T^\\mu_t = \\inf{s: B^\\mu(s)=t} and B^\\mu is a Brownian motion with drift \\mu) the explicit probability law and the governing equation are obtained. For the hyperbolic Brownian motions on the Poincar\\'e half-spaces H^+_2, H^+_3 we study B^{hp}(T_t), t>0 and the corresp...
Vertices of the least concave majorant of Brownian motion with parabolic drift
Groeneboom, Piet
2010-01-01
It was shown in Groeneboom (1983) that the least concave majorant of one-sided Brownian motion without drift can be characterized by a jump process with independent increments, which is the inverse of the process of slopes of the least concave majorant. This result can be used to prove the result of Sparre Andersen (1954) that the number of vertices of the smallest concave majorant of the empirical distribution function of a sample of size n from the uniform distribution on [0,1] is asymptotically normal, with an asymptotic expectation and variance which are both of order log n. A similar (Markovian) inverse jump process was introduced in Groeneboom (1989), in an analysis of the least concave majorant of two-sided Brownian motion with a parabolic drift. This process is quite different from the process for one-sided Brownian motion without drift: the number of vertices in a (corresponding slopes) interval has an expectation proportional to the length of the interval and the variance of the number of vertices i...
Brownian motion of spins; generalized spin Langevin equation
International Nuclear Information System (INIS)
We derive the Langevin equations for a spin interacting with a heat bath, starting from a fully dynamical treatment. The obtained equations are non-Markovian with multiplicative fluctuations and concomitant dissipative terms obeying the fluctuation-dissipation theorem. In the Markovian limit our equations reduce to the phenomenological equations proposed by Kubo and Hashitsume. The perturbative treatment on our equations lead to Landau-Lifshitz equations and to other known results in the literature. (author). 16 refs
Gangopadhyay, Aparna; Nath, Partha; Biswas, Jaydip
2015-01-01
Background In our experience, induction docetaxel, platinum, and fluorouracil (TPF) chemotherapy and sequential chemoradiation in locally advanced head and neck cancer lowers compliance owing to their considerable toxicity. Most of our head and neck cancer patients have locally advanced disease at presentation. Physicians frequently prefer paclitaxel–cisplatin induction chemotherapy instead, because of better patient tolerance. Materials and methods A total of 207 locally advanced head and ne...
National Oceanic and Atmospheric Administration, Department of Commerce — SWFSC is developing tools for estimation of limit reference points for marine turtles. These tools are being applied initially to estimate a limit reference point...
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.
International Nuclear Information System (INIS)
Static/structural characteristics of non-covalent complexes, formed by terminally charged hyperbranched polymers and oppositely charged neutralizing linear polyelectrolytes, are examined by means of Brownian dynamics computer simulations. Excluded-volume, electrostatic and hydrodynamic interactions are taken into account in implicit solvent. Three pairs of complexes consisting of linear chains and hyperbranched molecules each bearing different molecular weight and distinctly diverse topologies are examined under conditions of varying electrostatic interactions. The findings from the present work demonstrate that through an appropriate modification of internal structure and external stimuli, key attributes of such complexes like size, shape and local density distribution, can be tuned at desired levels, rendering them promising candidates for a wide range of pertinent nanoscale applications