Brownian motion from molecular dynamics
Shin, Hyun Kyung; Talkner, Peter; Lee, Eok Kyun
2010-01-01
Brownian motion of single particles with various masses M and diameters D is studied by molecular dynamics simulations. Besides the momentum auto-correlation function of the Brownian particle the memory function and the fluctuating force which enter the generalized Langevin equation of the Brownian particle are determined and their dependence on mass and diameter are investigated for two different fluid densities. Deviations of the fluctuating force distribution from a Gaussian form are observed for small particle diameters. For heavy particles the deviations of the fluctuating force from the total force acting on the Brownian particle decrease linearly with the mass ratio m/M where m denotes the mass of a fluid particle.
Generalized uncertainty relations and entanglement dynamics in quantum Brownian motion models
Anastopoulos, C; Mylonas, D
2010-01-01
We study entanglement dynamics in quantum Brownian motion (QBM) models. Our main tool is the Wigner function propagator. Time evolution in the Wigner picture is physically intuitive and it leads to a simple derivation of a master equation for any number of system harmonic oscillators and spectral density of the environment. It also provides generalized uncertainty relations, valid for any initial state that allow a characterization of the environment in terms of the modifications it causes to the system's dynamics. In particular, the uncertainty relations are very informative about the entanglement dynamics of Gaussian states, and to a lesser extent for other families of states. For concreteness, we apply these techniques to a bipartite QBM model, describing the processes of entanglement creation, disentanglement and decoherence at all temperatures and timescales.
Electrostatic channeling in P. falciparum DHFR-TS: Brownian dynamics and Smoluchowski modeling.
Metzger, Vincent T; Eun, Changsun; Kekenes-Huskey, Peter M; Huber, Gary; McCammon, J Andrew
2014-11-18
We perform Brownian dynamics simulations and Smoluchowski continuum modeling of the bifunctional Plasmodium falciparum dihydrofolate reductase-thymidylate synthase (P. falciparum DHFR-TS) with the objective of understanding the electrostatic channeling of dihydrofolate generated at the TS active site to the DHFR active site. The results of Brownian dynamics simulations and Smoluchowski continuum modeling suggest that compared to Leishmania major DHFR-TS, P. falciparum DHFR-TS has a lower but significant electrostatic-mediated channeling efficiency (?15-25%) at physiological pH (7.0) and ionic strength (150 mM). We also find that removing the electric charges from key basic residues located between the DHFR and TS active sites significantly reduces the channeling efficiency of P. falciparum DHFR-TS. Although several protozoan DHFR-TS enzymes are known to have similar tertiary and quaternary structure, subtle differences in structure, active-site geometry, and charge distribution appear to influence both electrostatic-mediated and proximity-based substrate channeling.
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.
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.
Rotational Brownian dynamics simulations of clathrin cage formation.
Ilie, Ioana M; den Otter, Wouter K; Briels, Wim J
2014-08-14
The self-assembly of nearly rigid proteins into ordered aggregates is well suited for modeling by the patchy particle approach. Patchy particles are traditionally simulated using Monte Carlo methods, to study the phase diagram, while Brownian Dynamics simulations would reveal insights into the assembly dynamics. However, Brownian Dynamics of rotating anisotropic particles gives rise to a number of complications not encountered in translational Brownian Dynamics. We thoroughly test the Rotational Brownian Dynamics scheme proposed by Naess and Elsgaeter [Macromol. Theory Simul. 13, 419 (2004); Naess and Elsgaeter Macromol. Theory Simul. 14, 300 (2005)], confirming its validity. We then apply the algorithm to simulate a patchy particle model of clathrin, a three-legged protein involved in vesicle production from lipid membranes during endocytosis. Using this algorithm we recover time scales for cage assembly comparable to those from experiments. We also briefly discuss the undulatory dynamics of the polyhedral cage.
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.
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.
Combinatorial fractal Brownian motion model
Institute of Scientific and Technical Information of China (English)
朱炬波; 梁甸农
2000-01-01
To solve the problem of how to determine the non-scaled interval when processing radar clutter using fractal Brownian motion (FBM) model, a concept of combinatorial FBM model is presented. Since the earth (or sea) surface varies diversely with space, a radar clutter contains several fractal structures, which coexist on all scales. Taking the combination of two FBMs into account, via theoretical derivation we establish a combinatorial FBM model and present a method to estimate its fractal parameters. The correctness of the model and the method is proved by simulation experiments and computation of practial data. Furthermore, we obtain the relationship between fractal parameters when processing combinatorial model with a single FBM model. Meanwhile, by theoretical analysis it is concluded that when combinatorial model is observed on different scales, one of the fractal structures is more obvious.
Brownian 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.
Brownian motion on random dynamical landscapes
Suñé Simon, Marc; Sancho, José María; Lindenberg, Katja
2016-03-01
We present a study of overdamped Brownian particles moving on a random landscape of dynamic and deformable obstacles (spatio-temporal disorder). The obstacles move randomly, assemble, and dissociate following their own dynamics. This landscape may account for a soft matter or liquid environment in which large obstacles, such as macromolecules and organelles in the cytoplasm of a living cell, or colloids or polymers in a liquid, move slowly leading to crowding effects. This representation also constitutes a novel approach to the macroscopic dynamics exhibited by active matter media. We present numerical results on the transport and diffusion properties of Brownian particles under this disorder biased by a constant external force. The landscape dynamics are characterized by a Gaussian spatio-temporal correlation, with fixed time and spatial scales, and controlled obstacle concentrations.
Models for twistable elastic polymers in Brownian dynamics, and their implementation for LAMMPS
Brackley, C A; Marenduzzo, D
2014-01-01
An elastic rod model for semi-flexible polymers is presented. Theory for a continuum rod is reviewed, and it is shown that a popular discretised model used in numerical simulations gives the correct continuum limit. Correlation functions relating to both bending and twisting of the rod are derived for both continuous and discrete cases, and results are compared with numerical simulations. Finally, two possible implementations of the discretised model in the multi-purpose molecular dynamics software package LAMMPS are described.
Rotational Brownian Dynamics simulations of clathrin cage formation
Ilie, I.M.; Otter, den W.K.; Briels, W.J.
2014-01-01
The self-assembly of nearly rigid proteins into ordered aggregates is well suited for modeling by the patchy particle approach. Patchy particles are traditionally simulated using Monte Carlo methods, to study the phase diagram, while Brownian Dynamics simulations would reveal insights into the assem
From generalized Langevin equations to Brownian dynamics and embedded Brownian dynamics
Ma, Lina; Li, Xiantao; Liu, Chun
2016-09-01
We present the reduction of generalized Langevin equations to a coordinate-only stochastic model, which in its exact form involves a forcing term with memory and a general Gaussian noise. It will be shown that a similar fluctuation-dissipation theorem still holds at this level. We study the approximation by the typical Brownian dynamics as a first approximation. Our numerical test indicates how the intrinsic frequency of the kernel function influences the accuracy of this approximation. In the case when such an approximate is inadequate, further approximations can be derived by embedding the nonlocal model into an extended dynamics without memory. By imposing noises in the auxiliary variables, we show how the second fluctuation-dissipation theorem is still exactly satisfied.
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 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
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.
Moghani, Mahdy Malekzadeh; Khomami, Bamin
2017-02-01
The computational efficiency of Brownian dynamics (BD) simulation of the constrained model of a polymeric chain (bead-rod) with n beads and in the presence of hydrodynamic interaction (HI) is reduced to the order of n2 via an efficient algorithm which utilizes the conjugate-gradient (CG) method within a Picard iteration scheme. Moreover, the utility of the Barnes and Hut (BH) multipole method in BD simulation of polymeric solutions in the presence of HI, with regard to computational cost, scaling, and accuracy, is discussed. Overall, it is determined that this approach leads to a scaling of O (n1.2) . Furthermore, a stress algorithm is developed which accurately captures the transient stress growth in the startup of flow for the bead-rod model with HI and excluded volume (EV) interaction. Rheological properties of the chains up to n =350 in the presence of EV and HI are computed via the former algorithm. The result depicts qualitative differences in shear thinning behavior of the polymeric solutions in the intermediate values of the Weissenburg number (10
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.
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.
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.
d'Auvergne, Edward J; Gooley, Paul R
2008-02-01
The key to obtaining the model-free description of the dynamics of a macromolecule is the optimisation of the model-free and Brownian rotational diffusion parameters using the collected R (1), R (2) and steady-state NOE relaxation data. The problem of optimising the chi-squared value is often assumed to be trivial, however, the long chain of dependencies required for its calculation complicates the model-free chi-squared space. Convolutions are induced by the Lorentzian form of the spectral density functions, the linear recombinations of certain spectral density values to obtain the relaxation rates, the calculation of the NOE using the ratio of two of these rates, and finally the quadratic form of the chi-squared equation itself. Two major topological features of the model-free space complicate optimisation. The first is a long, shallow valley which commences at infinite correlation times and gradually approaches the minimum. The most severe convolution occurs for motions on two timescales in which the minimum is often located at the end of a long, deep, curved tunnel or multidimensional valley through the space. A large number of optimisation algorithms will be investigated and their performance compared to determine which techniques are suitable for use in model-free analysis. Local optimisation algorithms will be shown to be sufficient for minimisation not only within the model-free space but also for the minimisation of the Brownian rotational diffusion tensor. In addition the performance of the programs Modelfree and Dasha are investigated. A number of model-free optimisation failures were identified: the inability to slide along the limits, the singular matrix failure of the Levenberg-Marquardt minimisation algorithm, the low precision of both programs, and a bug in Modelfree. Significantly, the singular matrix failure of the Levenberg-Marquardt algorithm occurs when internal correlation times are undefined and is greatly amplified in model-free analysis by
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.
Properties of Brownian Image Models in Scale-Space
DEFF Research Database (Denmark)
Pedersen, Kim Steenstrup
2003-01-01
In this paper it is argued that the Brownian image model is the least committed, scale invariant, statistical image model which describes the second order statistics of natural images. Various properties of three different types of Gaussian image models (white noise, Brownian and fractional...... Brownian images) will be discussed in relation to linear scale-space theory, and it will be shown empirically that the second order statistics of natural images mapped into jet space may, within some scale interval, be modeled by the Brownian image model. This is consistent with the 1/f 2 power spectrum...... law that apparently governs natural images. Furthermore, the distribution of Brownian images mapped into jet space is Gaussian and an analytical expression can be derived for the covariance matrix of Brownian images in jet space. This matrix is also a good approximation of the covariance matrix...
Diffusion in crowded biological environments: applications of Brownian dynamics
Directory of Open Access Journals (Sweden)
Długosz Maciej
2011-03-01
Full Text Available Abstract Biochemical reactions in living systems occur in complex, heterogeneous media with total concentrations of macromolecules in the range of 50 - 400 mgml. Molecular species occupy a significant fraction of the immersing medium, up to 40% of volume. Such complex and volume-occupied environments are generally termed 'crowded' and/or 'confined'. In crowded conditions non-specific interactions between macromolecules may hinder diffusion - a major process determining metabolism, transport, and signaling. Also, the crowded media can alter, both qualitatively and quantitatively, the reactions in vivo in comparison with their in vitro counterparts. This review focuses on recent developments in particle-based Brownian dynamics algorithms, their applications to model diffusive transport in crowded systems, and their abilities to reproduce and predict the behavior of macromolecules under in vivo conditions.
Brownian dynamics determine universality of charge transport in ionic liquids
Energy Technology Data Exchange (ETDEWEB)
Sangoro, Joshua R [ORNL; Iacob, Ciprian [University of Leipzig; Mierzwa, Michal [University of Silesia, Uniwersytecka, Katowice, Poland; Paluch, Marian [University of Silesia, Uniwersytecka, Katowice, Poland; Kremer, Friedrich [University of Leipzig
2012-01-01
Broadband dielectric spectroscopy is employed to investigate charge transport in a variety of glass-forming ionic liquids over wide frequency, temperature and pressure ranges. Using a combination of Einstein, Einstein-Smoluchowski, and Langevin relations, the observed universal scaling of charge transport in ionic liquids is traced back to the dominant role of Brownian dynamics.
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.
Molecular dynamics test of the Brownian description of Na(+) motion in water
Wilson, M. A.; Pohorille, A.; Pratt, L. R.
1985-01-01
The present paper provides the results of molecular dynamics calculations on a Na(+) ion in aqueous solution. Attention is given to the sodium-oxygen and sodium-hydrogen radial distribution functions, the velocity autocorrelation function for the Na(+) ion, the autocorrelation function of the force on the stationary ion, and the accuracy of Brownian motion assumptions which are basic to hydrodynamic models of ion dyanmics in solution. It is pointed out that the presented calculations provide accurate data for testing theories of ion dynamics in solution. The conducted tests show that it is feasible to calculate Brownian friction constants for ions in aqueous solutions. It is found that for Na(+) under the considered conditions the Brownian mobility is in error by only 60 percent.
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.
From Brownian Dynamics to Markov Chain: an Ion Channel Example
Chen, Wan; Chapman, S Jonathan
2012-01-01
A discrete rate theory for general multi-ion channels is presented, in which the continuous dynamics of ion diffusion is reduced to transitions between Markovian discrete states. In an open channel, the ion permeation process involves three types of events: an ion entering the channel, an ion escaping from the channel, or an ion hopping between different energy minima in the channel. The continuous dynamics leads to a hierarchy of Fokker-Planck equations, indexed by channel occupancy. From these the mean escape times and splitting probabilities (denoting from which side an ion has escaped) can be calculated. By equating these with the corresponding expressions from the Markov model the Markovian transition rates can be determined. The theory is illustrated with a two-ion one-well channel. The stationary probability of states is compared with that from both Brownian dynamics simulation and the hierarchical Fokker-Planck equations. The conductivity of the channel is also studied, and the optimal geometry maximi...
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...
Multiscale reaction-diffusion algorithms: PDE-assisted Brownian dynamics
Franz, Benjamin; Chapman, S Jonathan; Erban, Radek
2012-01-01
Two algorithms that combine Brownian dynamics (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use of a mean-field reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD simulations with PDEs by randomly creating new particles close to the interface which partitions the domain and by reincorporating particles into the continuum PDE-description when they cross the interface. The second PBD algorithm introduces an overlap region, where both descriptions exist in parallel. It is shown that to accurately compute variances using the PBD simulation requires the overlap region. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented.
Brownian dynamics without Green's functions
Energy Technology Data Exchange (ETDEWEB)
Delong, Steven; Donev, Aleksandar, E-mail: donev@courant.nyu.edu [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States); Usabiaga, Florencio Balboa; Delgado-Buscalioni, Rafael [Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Univeridad Autónoma de Madrid, Madrid 28049 (Spain); Griffith, Boyce E. [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States); Leon H. Charney Division of Cardiology, Department of Medicine, New York University School of Medicine, New York, New York 10016 (United States)
2014-04-07
We develop a Fluctuating Immersed Boundary (FIB) method for performing Brownian dynamics simulations of confined particle suspensions. Unlike traditional methods which employ analytical Green's functions for Stokes flow in the confined geometry, the FIB method uses a fluctuating finite-volume Stokes solver to generate the action of the response functions “on the fly.” Importantly, we demonstrate that both the deterministic terms necessary to capture the hydrodynamic interactions among the suspended particles, as well as the stochastic terms necessary to generate the hydrodynamically correlated Brownian motion, can be generated by solving the steady Stokes equations numerically only once per time step. This is accomplished by including a stochastic contribution to the stress tensor in the fluid equations consistent with fluctuating hydrodynamics. We develop novel temporal integrators that account for the multiplicative nature of the noise in the equations of Brownian dynamics and the strong dependence of the mobility on the configuration for confined systems. Notably, we propose a random finite difference approach to approximating the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. Through comparisons with analytical and existing computational results, we numerically demonstrate the ability of the FIB method to accurately capture both the static (equilibrium) and dynamic properties of interacting particles in flow.
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.
Ising model for a Brownian donkey
Cleuren, B.; Van den Broeck, C.
2001-04-01
We introduce a thermal engine consisting of N interacting Brownian particles moving in a periodic potential, featuring an alternation of hot and cold symmetric peaks. A discretized Ising-like version is solved analytically. In response to an external force, absolute negative mobility is observed for N >= 4. For N → ∞ a nonequilibrium phase transition takes place with a spontaneous symmetry breaking entailing the appearance of a current in the absence of an external force.
Vijaykumar, Adithya; Wolde, Pieter Rein ten; Bolhuis, Peter G
2016-01-01
The modeling of complex reaction-diffusion processes in, for instance, cellular biochemical networks or self-assembling soft matter can be tremendously sped up by employing a multiscale algorithm which combines the mesoscopic Green's Function Reaction Dynamics (GFRD) method with explicit stochastic Brownian, Langevin, or deterministic Molecular Dynamics to treat reactants at the microscopic scale [A. Vijaykumar, P.G. Bolhuis and P.R. ten Wolde, J. Chem. Phys. {\\bf 43}, 21: 214102 (2015)]. Here we extend this multiscale BD-GFRD approach to include the orientational dynamics that is crucial to describe the anisotropic interactions often prevalent in biomolecular systems. We illustrate the novel algorithm using a simple patchy particle model. After validation of the algorithm we discuss its performance. The rotational BD-GFRD multiscale method will open up the possibility for large scale simulations of e.g. protein signalling networks.
Coupling all-atom molecular dynamics simulations of ions in water with Brownian dynamics
Erban, Radek
2015-01-01
Molecular dynamics (MD) simulations of ions (K$^+$, Na$^+$, Ca$^{2+}$ and Cl$^-$) in aqueous solutions are investigated. Water is described using the SPC/E model. A stochastic coarse-grained description for ion behaviour is presented and parameterized using MD simulations. It is given as a system of coupled stochastic and ordinary differential equations, describing the ion position, velocity and acceleration. The stochastic coarse-grained model provides an intermediate description between all-atom MD simulations and Brownian dynamics (BD) models. It is used to develop a multiscale method which uses all-atom MD simulations in parts of the computational domain and (less detailed) BD simulations in the remainder of the domain.
Bellesia, Giovanni
2015-01-01
We investigate, via Brownian dynamics simulations, the reaction dynamics of a simple, non-linear chemical network (the Willamowski-Rossler network) under spatial confinement and crowding conditions. Our results show that the presence of inert crowders has a non-nontrivial effect on the dynamics of the network and, consequently, that effective modeling efforts aiming at a general understanding of the behavior of biochemical networks in vivo should be stochastic in nature and based on an explicit representation of both spatial confinement and macromolecular crowding.
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).
Effect of internal viscosity on Brownian dynamics of DNA molecules in shear flow.
Yang, Xiao-Dong; Melnik, Roderick V N
2007-04-01
The results of Brownian dynamics simulations of a single DNA molecule in shear flow are presented taking into account the effect of internal viscosity. The dissipative mechanism of internal viscosity is proved necessary in the research of DNA dynamics. A stochastic model is derived on the basis of the balance equation for forces acting on the chain. The Euler method is applied to the solution of the model. The extensions of DNA molecules for different Weissenberg numbers are analyzed. Comparison with the experimental results available in the literature is carried out to estimate the contribution of the effect of internal viscosity.
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.
Momentum conserving Brownian dynamics propagator for complex soft matter fluids
Energy Technology Data Exchange (ETDEWEB)
Padding, J. T. [Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven (Netherlands); Briels, W. J. [Computational Biophysics, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands)
2014-12-28
We present a Galilean invariant, momentum conserving first order Brownian dynamics scheme for coarse-grained simulations of highly frictional soft matter systems. Friction forces are taken to be with respect to moving background material. The motion of the background material is described by locally averaged velocities in the neighborhood of the dissolved coarse coordinates. The velocity variables are updated by a momentum conserving scheme. The properties of the stochastic updates are derived through the Chapman-Kolmogorov and Fokker-Planck equations for the evolution of the probability distribution of coarse-grained position and velocity variables, by requiring the equilibrium distribution to be a stationary solution. We test our new scheme on concentrated star polymer solutions and find that the transverse current and velocity time auto-correlation functions behave as expected from hydrodynamics. In particular, the velocity auto-correlation functions display a long time tail in complete agreement with hydrodynamics.
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.
Weighted-ensemble Brownian dynamics simulation: sampling of rare events in nonequilibrium systems.
Kromer, Justus A; Schimansky-Geier, Lutz; Toral, Raul
2013-06-01
We provide an algorithm based on weighted-ensemble (WE) methods, to accurately sample systems at steady state. Applying our method to different one- and two-dimensional models, we succeed in calculating steady-state probabilities of order 10(-300) and reproduce the Arrhenius law for rates of order 10(-280). Special attention is payed to the simulation of nonpotential systems where no detailed balance assumption exists. For this large class of stochastic systems, the stationary probability distribution density is often unknown and cannot be used as preknowledge during the simulation. We compare the algorithm's efficiency with standard Brownian dynamics simulations and the original WE method.
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.
A Brownian Model for Crystal Nucleation
Durán-Olivencia, Miguel A
2013-01-01
In this work a phenomenological Stochastic Differential Equation (SDE) is proposed for modelling the time-evolution of the radius of a pre-critical molecular cluster during nucleation (the classical order parameter). Such a SDE constitutes the basis for the calculation of the (nucleation) induction time under the Kramers' theory of thermally activated escape processes. Considering the nucleation stage as a Poisson's rare-event, analytical expressions for the induction time statistics are deduced for both steady and unsteady conditions, the latter assuming the semiadiabatic limit. These expressions can be used to identify the underlying mechanism of molecular cluster formation (distinguishing between homogeneous or heterogeneous nucleation from the nucleation statistics is possible) as well as to predict induction times and induction time distributions. The predictions of this model are in good agreement with experimentally measured induction times at constant temperature but agreement is not so good for induc...
Beyond multifractional Brownian motion: new stochastic models for geophysical modelling
Directory of Open Access Journals (Sweden)
J. Lévy Véhel
2013-09-01
Full Text Available Multifractional Brownian motion (mBm has proved to be a useful tool in various areas of geophysical modelling. Although a versatile model, mBm is of course not always an adequate one. We present in this work several other stochastic processes which could potentially be useful in geophysics. The first alternative type is that of self-regulating processes: these are models where the local regularity is a function of the amplitude, in contrast to mBm where it is tuned exogenously. We demonstrate the relevance of such models for digital elevation maps and for temperature records. We also briefly describe two other types of alternative processes, which are the counterparts of mBm and of self-regulating processes when the intensity of local jumps is considered in lieu of local regularity: multistable processes allow one to prescribe the local intensity of jumps in space/time, while this intensity is governed by the amplitude for self-stabilizing processes.
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.
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.
A Brownian Dynamics Approach to ESR Line Shape Calculations
Wright, Matthew P.
The work presented in this thesis uses a Monte Carlo technique to simulate spectra for 14N spin-labels and 15N spin labels. The algorithm presented here also has the capability to produce simulated spectra for any admixture of 14N and 15N. The algorithm makes use of `iterative loops' to model Brownian rotational diffusion and for the repeated evaluation of the spectral correlation function (relaxation function). The method described in this work starts with a derivation of an angular dependent "Spin Hamiltonian" that when diagonalized yields orientation dependent eigenvalues. The resulting eigenvalue equations are later used to calculate the energy trajectories of a nitroxide spin-label undergoing rotational diffusion. The energy trajectories are then used to evaluate the relaxation function. The absorption spectrum is obtained by applying a Fourier transform to the relaxation function. However, the application of the Fourier transform to the relaxation function produces "leakage" effects that manifest as spurious peaks in the first derivative spectrum. To counter "leakage" effects a data windowing function was applied to the relaxation function prior to the Fourier transform. In order to test the accuracy of this algorithm, simulated spectra for 14N, and 15N spin labels diffusing in a glycerol-water mixture as well as a 14N-15N admixture diffusing in the same solvent were produced and compared to experimental spectra. An attempt to quantify the level of agreement was made by calculating the mean square residual of the simulated and experimental spectra. The main spectral features were reproduced with reasonable fidelity by the simulated spectra.
Hopkins, Paul; Fortini, Andrea; Archer, Andrew J; Schmidt, Matthias
2010-12-14
We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the "self " component having only one particle, the "distinct" component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities.
A simple model for Brownian motion leading to the Langevin equation
Grooth, de Bart G.
1999-01-01
A simple one-dimensional model is presented for the motion of a Brownian particle. It is shown how the collisions between a Brownian particle and its surrounding molecules lead to the Langevin equation, the power spectrum of the stochastic force, and the equipartition of kinetic energy.
Dubina, Sean Hyun; Wedgewood, Lewis Edward
2016-07-01
Ferrofluids are often favored for their ability to be remotely positioned via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally simulated using the Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely, Maxwell's equations. An iterative constraint method was developed to satisfy Maxwell's equations when a uniform magnetic field is imposed on ferrofluids in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters in a mesoscale particle collection. This was accomplished by allowing a particulate system in a simple shear flow to advance by a time step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint method applied over sub-volume length scales until Maxwell's equations were satisfied. The resultant ferrofluid model with constraints demonstrates that the magnetoviscosity contribution is not as substantial when compared to homogeneous simulations that assume the material's magnetism is a direct response to the external magnetic field. This was detected across varying intensities of particle-particle interaction, Brownian motion, and shear flow. Ferroparticle aggregation was still extensively present but less so than typically observed.
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.
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.
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
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...
Energy Technology Data Exchange (ETDEWEB)
Reeves, Daniel B., E-mail: dbr@Dartmouth.edu; Weaver, John B. [Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755 (United States)
2015-06-21
Magnetic nanoparticles are promising tools for a host of therapeutic and diagnostic medical applications. The dynamics of rotating magnetic nanoparticles in applied magnetic fields depend strongly on the type and strength of the field applied. There are two possible rotation mechanisms and the decision for the dominant mechanism is often made by comparing the equilibrium relaxation times. This is a problem when particles are driven with high-amplitude fields because they are not necessarily at equilibrium at all. Instead, it is more appropriate to consider the “characteristic timescales” that arise in various applied fields. Approximate forms for the characteristic time of Brownian particle rotations do exist and we show agreement between several analytical and phenomenological-fit models to simulated data from a stochastic Langevin equation approach. We also compare several approximate models with solutions of the Fokker-Planck equation to determine their range of validity for general fields and relaxation times. The effective field model is an excellent approximation, while the linear response solution is only useful for very low fields and frequencies for realistic Brownian particle rotations.
Polymer deformation in Brownian ratchets: theory and molecular dynamics simulations.
Kenward, Martin; Slater, Gary W
2008-11-01
We examine polymers in the presence of an applied asymmetric sawtooth (ratchet) potential which is periodically switched on and off, using molecular dynamics (MD) simulations with an explicit Lennard-Jones solvent. We show that the distribution of the center of mass for a polymer in a ratchet is relatively wide for potential well depths U0 on the order of several kBT. The application of the ratchet potential also deforms the polymer chains. With increasing U0 the Flory exponent varies from that for a free three-dimensional (3D) chain, nu=35 (U0=0), to that corresponding to a 2D compressed (pancake-shaped) polymer with a value of nu=34 for moderate U0. This has the added effect of decreasing a polymer's diffusion coefficient from its 3D value D3D to that of a pancaked-shaped polymer moving parallel to its minor axis D2D. The result is that a polymer then has a time-dependent diffusion coefficient D(t) during the ratchet off time. We further show that this suggests a different method to operate a ratchet, where the off time of the ratchet, toff, is defined in terms of the relaxation time of the polymer, tauR. We also derive a modified version of the Bader ratchet model [Bader, Proc. Natl. Acad. Sci. U.S.A. 96, 13165 (1999)] which accounts for this deformation and we present a simple expression to describe the time dependent diffusion coefficient D(t). Using this model we then illustrate that polymer deformation can be used to modulate polymer migration in a ratchet potential.
Silva, Antonio
2005-03-01
It is well-known that the mathematical theory of Brownian motion was first developed in the Ph. D. thesis of Louis Bachelier for the French stock market before Einstein [1]. In Ref. [2] we studied the so-called Heston model, where the stock-price dynamics is governed by multiplicative Brownian motion with stochastic diffusion coefficient. We solved the corresponding Fokker-Planck equation exactly and found an analytic formula for the time-dependent probability distribution of stock price changes (returns). The formula interpolates between the exponential (tent-shaped) distribution for short time lags and the Gaussian (parabolic) distribution for long time lags. The theoretical formula agrees very well with the actual stock-market data ranging from the Dow-Jones index [2] to individual companies [3], such as Microsoft, Intel, etc. [] [1] Louis Bachelier, ``Th'eorie de la sp'eculation,'' Annales Scientifiques de l''Ecole Normale Sup'erieure, III-17:21-86 (1900).[] [2] A. A. Dragulescu and V. M. Yakovenko, ``Probability distribution of returns in the Heston model with stochastic volatility,'' Quantitative Finance 2, 443--453 (2002); Erratum 3, C15 (2003). [cond-mat/0203046] [] [3] A. C. Silva, R. E. Prange, and V. M. Yakovenko, ``Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact,'' Physica A 344, 227--235 (2004). [cond-mat/0401225
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.
Butler, Jason E.; Shaqfeh, Eric S. G.
2005-01-01
Using methods adapted from the simulation of suspension dynamics, we have developed a Brownian dynamics algorithm with multibody hydrodynamic interactions for simulating the dynamics of polymer molecules. The polymer molecule is modeled as a chain composed of a series of inextensible, rigid rods with constraints at each joint to ensure continuity of the chain. The linear and rotational velocities of each segment of the polymer chain are described by the slender-body theory of Batchelor [J. Fluid Mech. 44, 419 (1970)]. To include hydrodynamic interactions between the segments of the chain, the line distribution of forces on each segment is approximated by making a Legendre polynomial expansion of the disturbance velocity on the segment, where the first two terms of the expansion are retained in the calculation. Thus, the resulting linear force distribution is specified by a center of mass force, couple, and stresslet on each segment. This method for calculating the hydrodynamic interactions has been successfully used to simulate the dynamics of noncolloidal suspensions of rigid fibers [O. G. Harlen, R. R. Sundararajakumar, and D. L. Koch, J. Fluid Mech. 388, 355 (1999); J. E. Butler and E. S. G. Shaqfeh, J. Fluid Mech. 468, 204 (2002)]. The longest relaxation time and center of mass diffusivity are among the quantities calculated with the simulation technique. Comparisons are made for different levels of approximation of the hydrodynamic interactions, including multibody interactions, two-body interactions, and the "freely draining" case with no interactions. For the short polymer chains studied in this paper, the results indicate a difference in the apparent scaling of diffusivity with polymer length for the multibody versus two-body level of approximation for the hydrodynamic interactions.
Cosseddu, Salvatore M; Allen, Michael P; Rodger, P M; Luchinsky, Dmitry G; McClintock, Peter V E
2013-01-01
The statistical and dynamical properties of ions in the selectivity filter of the KcsA ion channel are considered on the basis of molecular dynamics (MD) simulations of the KcsA protein embedded in a lipid membrane surrounded by an ionic solution. A new approach to the derivation of a Brownian dynamics (BD) model of ion permeation through the filter is discussed, based on unbiased MD simulations. It is shown that depending on additional assumptions, ion's dynamics can be described either by under-damped Langevin equation with constant damping and white noise or by Langevin equation with a fractional memory kernel. A comparison of the potential of the mean force derived from unbiased MD simulations with the potential produced by the umbrella sampling method demonstrates significant differences in these potentials. The origin of these differences is an open question that requires further clarifications.
Haliloglu, Turkan; Bahar, Ivet; Erman, Burak
1996-08-01
The behavior of a single polyethylene chain grafted to an impenetrable surface, under shear flow, is investigated using Brownian dynamics simulations. Both short-range conformational energies and excluded volume effects are included in the model. Simulations are performed in good and poor solvent conditions in order to explore the effect of solvent quality. The shear flow is represented by the superposition of a force profile increasing linearly with the distance from the surface. Distribution of rotational angles, chain dimensions, components of the radius of gyration, segment density distribution, average layer thickness, and average orientation of bond vectors with respect to flow direction are determined and compared with other studies. Above a certain value of the shear rate, a significant increase in chain dimensions is observed for both good and poor solvents, the transition from coiled to stretched state being sharper in poor solvent. In good solvent, chain dimensions along the two perpendicular directions to the flow direction diminish with increasing shear rate. On the other hand, in poor solvent, there is an overall expansion in chain dimensions in all directions at low shear rates, which is subsequently followed by the orientation and alignment of the chain along the direction of flow. The experimentally observed increase in chain dimensions normal to the flow field at low shear rates is evidenced for the first time by simulations.
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
The double-temperature ratchet model and current reversal of coupled Brownian motors
Li, Chen-pu; Zheng, Zhi-gang
2016-01-01
Based on the transport features and experimental phenomena observed in studies of molecular motors, we proposed the double-temperature ratchet model of coupled motors to reveal the dynamical mechanism of cooperative transport of motors with two heads, where the interactions and the asynchronous between two motor heads are taken into account. We investigated the collective unidirectional transport of coupled system, and find that the direction of motion can be inversed under certain conditions. Inverse motion can be achieved by modulating the coupling strength, the coupling free length and the asymmetric efficient of the periodic potential, which is understood in terms of the effective-potential theory. The dependence of directed current on various parameters is studied systematically. Directed transport of coupled Brownian motors can be manipulated and optimized by adjusting pulsating period or the phase shift of the pulsating temperature.
Solano, Carlos J F; Pothula, Karunakar R; Prajapati, Jigneshkumar D; De Biase, Pablo M; Noskov, Sergei Yu; Kleinekathöfer, Ulrich
2016-05-10
All-atom molecular dynamics simulations have a long history of applications studying ion and substrate permeation across biological and artificial pores. While offering unprecedented insights into the underpinning transport processes, MD simulations are limited in time-scales and ability to simulate physiological membrane potentials or asymmetric salt solutions and require substantial computational power. While several approaches to circumvent all of these limitations were developed, Brownian dynamics simulations remain an attractive option to the field. The main limitation, however, is an apparent lack of protein flexibility important for the accurate description of permeation events. In the present contribution, we report an extension of the Brownian dynamics scheme which includes conformational dynamics. To achieve this goal, the dynamics of amino-acid residues was incorporated into the many-body potential of mean force and into the Langevin equations of motion. The developed software solution, called BROMOCEA, was applied to ion transport through OmpC as a test case. Compared to fully atomistic simulations, the results show a clear improvement in the ratio of permeating anions and cations. The present tests strongly indicate that pore flexibility can enhance permeation properties which will become even more important in future applications to substrate translocation.
Structure Analysis of Jungle-Gym-Type Gels by Brownian Dynamics Simulation
Ohta, Noriyoshi; Ono, Kohki; Takasu, Masako; Furukawa, Hidemitsu
2008-02-01
We investigated the structure and the formation process of two kinds of gels by Brownian dynamics simulation. The effect of flexibility of main chain oligomer was studied. From our results, hard gel with rigid main chain forms more homogeneous network structure than soft gel with flexible main chain. In soft gel, many small loops are formed, and clusters tend to shrink. This heterogeneous network structure may be caused by microgels. In the low density case, soft gel shows more heterogeneity than the high density case.
Institute of Scientific and Technical Information of China (English)
WEI Jin-Jia; KAWAGUCHI Yasuo; YU Bo; LI Feng-Chen
2008-01-01
@@ Brownian dynamics simulation is conducted for a dilute surfactant solution under a steady uniaxial elongational flow.A new inter-cluster potential is used for the interaction among surfactant micelles to determine the micellar network structures in the surfactant solution.The micellar network is successfully simulated.It is formed at low elongation rates and destroyed by high elongation rates.The computed elongational viscosities show elongation-thinning characteristics.The relationship between the elongational viscosities and the microstructure of the surfactant solution is revealed.
Brownian motion and parabolic Anderson model in a renormalized Poisson potential
Chen, Xia; Kulik, Alexey M.
2012-01-01
A method known as renormalization is proposed for constructing some more physically realistic random potentials in a Poisson cloud. The Brownian motion in the renormalized random potential and related parabolic Anderson models are modeled. With the renormalization, for example, the models consistent to Newton’s law of universal attraction can be rigorously constructed.
Malgaretti, Paolo; Pagonabarraga, Ignacio; Rubi, J Miguel
2013-05-21
We analyze the dynamics of Brownian ratchets in a confined environment. The motion of the particles is described by a Fick-Jakobs kinetic equation in which the presence of boundaries is modeled by means of an entropic potential. The cases of a flashing ratchet, a two-state model, and a ratchet under the influence of a temperature gradient are analyzed in detail. We show the emergence of a strong cooperativity between the inherent rectification of the ratchet mechanism and the entropic bias of the fluctuations caused by spatial confinement. Net particle transport may take place in situations where none of those mechanisms leads to rectification when acting individually. The combined rectification mechanisms may lead to bidirectional transport and to new routes to segregation phenomena. Confined Brownian ratchets could be used to control transport in mesostructures and to engineer new and more efficient devices for transport at the nanoscale.
Generalized Scaling and the Master Variable for Brownian Magnetic Nanoparticle Dynamics.
Directory of Open Access Journals (Sweden)
Daniel B Reeves
Full Text Available Understanding the dynamics of magnetic particles can help to advance several biomedical nanotechnologies. Previously, scaling relationships have been used in magnetic spectroscopy of nanoparticle Brownian motion (MSB to measure biologically relevant properties (e.g., temperature, viscosity, bound state surrounding nanoparticles in vivo. Those scaling relationships can be generalized with the introduction of a master variable found from non-dimensionalizing the dynamical Langevin equation. The variable encapsulates the dynamical variables of the surroundings and additionally includes the particles' size distribution and moment and the applied field's amplitude and frequency. From an applied perspective, the master variable allows tuning to an optimal MSB biosensing sensitivity range by manipulating both frequency and field amplitude. Calculation of magnetization harmonics in an oscillating applied field is also possible with an approximate closed-form solution in terms of the master variable and a single free parameter.
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...
Blood rheology using a Brownian dynamics simulation of bead spring ring with a constant area
Lopez, Rogelio
Coronary artery disease is epidemic in the western world. Occlusive vascular disease, when considered in terms of total incidence rather than separated to organ involvement, is the leading human's health hazard. A better understanding of occlusive vascular disease is so important that does not need to be justified. Blood theological properties are important factors in the occurrence and onset development of these diseases and may help in a rational approach to predictive and anticipatory therapies. Blood is a suspension of red blood cells (RBC) and therefore has a complex flow behavior. This research presents a Brownian dynamics (BD) model that captures the complex rheological behavior of blood; a three-bead-spring ring with a holonomic constant area constraint is being used to model the RBC in a dilute Newtonian solvent. The BD model has been used in simulations of RBCs to generate the RBC configuration. The stress tensor or momentum flux tensor is obtained as an ensemble average over molecular configurations by Giesekus expression of the stress calculator. This stress calculator makes it possible to obtain the RBC rheological properties of the model blood suspension under different flow conditions: homogeneous simple shear flow, elongational flow, inception of a steady shear flow, stress relaxation after cessation of steady shear flow and flow within narrow vessels by considering the blood microstructure scale process. The model's main results obtained for the specified flows are as follows: (a) Simulations in steady shear flow in an unbounded space the dilute blood suspension model expresses both shear thinning behavior for the viscosity and first normal stress coefficient. (b) In steady elongational flow, the elongational viscosity of the dilute blood suspension increases when the elongational rate increases. (c) Stress growth upon inception of steady shear flow; increasing shear rates does the shear stress approach its steady state monotonically. (d) Stress
From Levy to Brownian: a computational model based on biological fluctuation.
Directory of Open Access Journals (Sweden)
Surya G Nurzaman
Full Text Available BACKGROUND: Theoretical studies predict that Lévy walks maximizes the chance of encountering randomly distributed targets with a low density, but Brownian walks is favorable inside a patch of targets with high density. Recently, experimental data reports that some animals indeed show a Lévy and Brownian walk movement patterns when forage for foods in areas with low and high density. This paper presents a simple, Gaussian-noise utilizing computational model that can realize such behavior. METHODOLOGY/PRINCIPAL FINDINGS: We extend Lévy walks model of one of the simplest creature, Escherichia coli, based on biological fluctuation framework. We build a simulation of a simple, generic animal to observe whether Lévy or Brownian walks will be performed properly depends on the target density, and investigate the emergent behavior in a commonly faced patchy environment where the density alternates. CONCLUSIONS/SIGNIFICANCE: Based on the model, animal behavior of choosing Lévy or Brownian walk movement patterns based on the target density is able to be generated, without changing the essence of the stochastic property in Escherichia coli physiological mechanism as explained by related researches. The emergent behavior and its benefits in a patchy environment are also discussed. The model provides a framework for further investigation on the role of internal noise in realizing adaptive and efficient foraging behavior.
Brownian nanoimaging of interface dynamics and ligand-receptor binding at cell surfaces in 3-D.
Kuznetsov, Igor R; Evans, Evan A
2013-04-01
We describe a method for nanoimaging interfacial dynamics and ligand-receptor binding at surfaces of live cells in 3-D. The imaging probe is a 1-μm diameter glass bead confined by a soft laser trap to create a "cloud" of fluctuating states. Using a facile on-line method of video image analysis, the probe displacements are reported at ~10 ms intervals with bare precisions (±SD) of 4-6 nm along the optical axis (elevation) and 2 nm in the transverse directions. We demonstrate how the Brownian distributions are analyzed to characterize the free energy potential of each small probe in 3-D taking into account the blur effect of its motions during CCD image capture. Then, using the approach to image interactions of a labeled probe with lamellae of leukocytic cells spreading on cover-glass substrates, we show that deformations of the soft distribution in probe elevations provide both a sensitive long-range sensor for defining the steric topography of a cell lamella and a fast telemetry for reporting rare events of probe binding with its surface receptors. Invoking established principles of Brownian physics and statistical thermodynamics, we describe an off-line method of super resolution that improves precision of probe separations from a non-reactive steric boundary to ~1 nm.
Brownian Motion and General Relativity
O'Hara, Paul
2013-01-01
We construct a model of Brownian Motion on a pseudo-Riemannian manifold associated with general relativity. There are two aspects of the problem: The first is to define a sequence of stopping times associated with the Brownian "kicks" or impulses. The second is to define the dynamics of the particle along geodesics in between the Brownian kicks. When these two aspects are taken together, we can associate various distributions with the motion. We will find that the statistics of space-time events will obey a temperature dependent four dimensional Gaussian distribution defined over the quaternions which locally can be identified with Minkowski space. Analogously, the statistics of the 4-velocities will obey a kind of Maxwell-Juttner distribution. In contrast to previous work, our processes are characterized by two independent proper time variables defined with respect to the laboratory frame: a discrete one corresponding to the stopping times when the impulses take place and a continuous one corresponding to th...
Roberts, Christopher C; Chang, Chia-En A
2016-08-25
We present the second-generation GeomBD Brownian dynamics software for determining interenzyme intermediate transfer rates and substrate association rates in biomolecular complexes. Substrate and intermediate association rates for a series of enzymes or biomolecules can be compared between the freely diffusing disorganized configuration and various colocalized or complexed arrangements for kinetic investigation of enhanced intermediate transfer. In addition, enzyme engineering techniques, such as synthetic protein conjugation, can be computationally modeled and analyzed to better understand changes in substrate association relative to native enzymes. Tools are provided to determine nonspecific ligand-receptor association residence times, and to visualize common sites of nonspecific association of substrates on receptor surfaces. To demonstrate features of the software, interenzyme intermediate substrate transfer rate constants are calculated and compared for all-atom models of DNA origami scaffold-bound bienzyme systems of glucose oxidase and horseradish peroxidase. Also, a DNA conjugated horseradish peroxidase enzyme was analyzed for its propensity to increase substrate association rates and substrate local residence times relative to the unmodified enzyme. We also demonstrate the rapid determination and visualization of common sites of nonspecific ligand-receptor association by using HIV-1 protease and an inhibitor, XK263. GeomBD2 accelerates simulations by precomputing van der Waals potential energy grids and electrostatic potential grid maps, and has a flexible and extensible support for all-atom and coarse-grained force fields. Simulation software is written in C++ and utilizes modern parallelization techniques for potential grid preparation and Brownian dynamics simulation processes. Analysis scripts, written in the Python scripting language, are provided for quantitative simulation analysis. GeomBD2 is applicable to the fields of biophysics, bioengineering
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.
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...
Energy Technology Data Exchange (ETDEWEB)
Mereghetti, Paolo; Wade, Rebecca C.
2012-07-26
High macromolecular concentrations are a distinguishing feature of living organisms. Understanding how the high concentration of solutes affects the dynamic properties of biological macromolecules is fundamental for the comprehension of biological processes in living systems. In this paper, we describe the implementation of mean field models of translational and rotational hydrodynamic interactions into an atomically detailed many-protein brownian dynamics simulation method. Concentrated solutions (30-40% volume fraction) of myoglobin, hemoglobin A, and sickle cell hemoglobin S were simulated, and static structure factors, oligomer formation, and translational and rotational self-diffusion coefficients were computed. Good agreement of computed properties with available experimental data was obtained. The results show the importance of both solvent mediated interactions and weak protein-protein interactions for accurately describing the dynamics and the association properties of concentrated protein solutions. Specifically, they show a qualitative difference in the translational and rotational dynamics of the systems studied. Although the translational diffusion coefficient is controlled by macromolecular shape and hydrodynamic interactions, the rotational diffusion coefficient is affected by macromolecular shape, direct intermolecular interactions, and both translational and rotational hydrodynamic interactions.
Relativistic Brownian motion: from a microscopic binary collision model to the Langevin equation.
Dunkel, Jörn; Hänggi, Peter
2006-11-01
The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy pointlike Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, nonrelativistic LE is deduced from this model, by taking into account the nonrelativistic conservation laws for momentum and kinetic energy. Subsequently, this procedure is generalized to the relativistic case. There, it is found that the relativistic stochastic force is still delta correlated (white noise) but no longer corresponds to a Gaussian white noise process. Explicit results for the friction and momentum-space diffusion coefficients are presented and discussed.
Barenbrug, Theo M. A. O. M.; Peters, E. A. J. F. (Frank); Schieber, Jay D.
2002-11-01
In Brownian Dynamics simulations, the diffusive motion of the particles is simulated by adding random displacements, proportional to the square root of the chosen time step. When computing average quantities, these Brownian contributions usually average out, and the overall simulation error becomes proportional to the time step. A special situation arises if the particles undergo hard-body interactions that instantaneously change their properties, as in absorption or association processes, chemical reactions, etc. The common "naı̈ve simulation method" accounts for these interactions by checking for hard-body overlaps after every time step. Due to the simplification of the diffusive motion, a substantial part of the actual hard-body interactions is not detected by this method, resulting in an overall simulation error proportional to the square root of the time step. In this paper we take the hard-body interactions during the time step interval into account, using the relative positions of the particles at the beginning and at the end of the time step, as provided by the naı̈ve method, and the analytical solution for the diffusion of a point particle around an absorbing sphere. Öttinger used a similar approach for the one-dimensional case [Stochastic Processes in Polymeric Fluids (Springer, Berlin, 1996), p. 270]. We applied the "corrected simulation method" to the case of a simple, second-order chemical reaction. The results agree with recent theoretical predictions [K. Hyojoon and Joe S. Kook, Phys. Rev. E 61, 3426 (2000)]. The obtained simulation error is proportional to the time step, instead of its square root. The new method needs substantially less simulation time to obtain the same accuracy. Finally, we briefly discuss a straightforward way to extend the method for simulations of systems with additional (deterministic) forces.
GPU accelerated Monte Carlo simulation of Brownian motors dynamics with CUDA
Spiechowicz, J.; Kostur, M.; Machura, L.
2015-06-01
This work presents an updated and extended guide on methods of a proper acceleration of the Monte Carlo integration of stochastic differential equations with the commonly available NVIDIA Graphics Processing Units using the CUDA programming environment. We outline the general aspects of the scientific computing on graphics cards and demonstrate them with two models of a well known phenomenon of the noise induced transport of Brownian motors in periodic structures. As a source of fluctuations in the considered systems we selected the three most commonly occurring noises: the Gaussian white noise, the white Poissonian noise and the dichotomous process also known as a random telegraph signal. The detailed discussion on various aspects of the applied numerical schemes is also presented. The measured speedup can be of the astonishing order of about 3000 when compared to a typical CPU. This number significantly expands the range of problems solvable by use of stochastic simulations, allowing even an interactive research in some cases.
GPU accelerated Monte Carlo simulation of Brownian motors dynamics with CUDA
Spiechowicz, J; Machura, L
2014-01-01
This work presents an updated and extended guide on methods of a proper acceleration of the Monte Carlo integration of stochastic differential equations with the commonly available NVIDIA Graphics Processing Units using the CUDA programming environment. We outline the general aspects of the scientific computing on graphics cards and demonstrate them with two models of a well known phenomenon of the noise induced transport of Brownian motors in periodic structures. As a source of fluctuations in the considered systems we selected the three most commonly occurring noises: the Gaussian white noise, the white Poissonian noise and the dichotomous process also known as a random telegraph signal. The detailed discussion on various aspects of the applied numerical schemes is also presented. The measured speedup can be of the astonishing order of 2000 when compared to a typical CPU. This number significantly expands the range of problems solvable by use of stochastic simulations, allowing even an interactive research ...
Brownian regime of finite-N corrections to particle motion in the XY hamiltonian mean field model
Ribeiro, Bruno V; Elskens, Yves
2016-01-01
We study the dynamics of the N-particle system evolving in the XY hamiltonian mean field (HMF) model for a repulsive potential, when no phase transition occurs. Starting from a homogeneous distribution, particles evolve in a mean field created by the interaction with all others. This interaction does not change the homogeneous state of the system, and particle motion is approximately ballistic with small corrections. For initial particle data approaching a waterbag, it is explicitly proved that corrections to the ballistic velocities are in the form of independent brownian noises over a time scale diverging not slower than $N^{2/5}$ as $N \\to \\infty$, which proves the propagation of molecular chaos. Molecular dynamics simulations of the XY-HMF model confirm our analytical findings.
Brownian regime of finite-N corrections to particle motion in the XY Hamiltonian mean field model
Ribeiro, Bruno V.; Amato, Marco A.; Elskens, Yves
2016-08-01
We study the dynamics of the N-particle system evolving in the XY Hamiltonian mean field (HMF) model for a repulsive potential, when no phase transition occurs. Starting from a homogeneous distribution, particles evolve in a mean field created by the interaction with all others. This interaction does not change the homogeneous state of the system, and particle motion is approximately ballistic with small corrections. For initial particle data approaching a waterbag, it is explicitly proved that corrections to the ballistic velocities are in the form of independent Brownian noises over a time scale diverging not slower than {N}2/5 as N\\to ∞ , which proves the propagation of molecular chaos. Molecular dynamics simulations of the XY-HMF model confirm our analytical findings.
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...
Fractional brownian functions as mathematical models of natural rhythm in architecture.
Cirovic, Ivana M
2014-10-01
Carl Bovill suggested and described a method of generating rhythm in architecture with the help of fractional Brownian functions, as they are mathematical models of natural rhythm. A relationship established in the stated procedure between fractional Brownian functions as models of rhythm, and the observed group of architectural elements, is recognized as an analogical relationship, and the procedure of generating rhythm as a process of analogical transfer from the natural domain to the architectural domain. Since analogical transfer implies relational similarity of two domains, and the establishment of one-to-one correspondence, this paper is trying to determine under which conditions such correspondence could be established. For example, if the values of the observed visual feature of architectural elements are not similar to each other in a way in which they can form a monotonically increasing, or a monotonically decreasing bounded sequence, then the structural alignment and the one-to-one correspondence with a single fractional Brownian function cannot be established, hence, this function is deemed inappropriate as a model for the architectural rhythm. In this case we propose overlapping of two or more functions, so that each of them is an analog for one subset of mutually similar values of the visual feature of architectural elements.
A Simple Discrete Model of Brownian Motors: Time-periodic Markov Chains
Ge, Hao; Jiang, Da-Quan; Qian, Min
2006-05-01
In this paper, we consider periodically inhomogeneous Markov chains, which can be regarded as a simple version of physical model—Brownian motors. We introduce for them the concepts of periodical reversibility, detailed balance, entropy production rate and circulation distribution. We prove the equivalence of the following statements: The time-periodic Markov chain is periodically reversible; It is in detailed balance; Kolmogorov's cycle condition is satisfied; Its entropy production rate vanishes; Every circuit and its reversed circuit have the same circulation weight. Hence, in our model of Markov chains, the directed transport phenomenon of Brownian motors, i.e. the existence of net circulation, can occur only in nonequilibrium and irreversible systems. Moreover, we verify the large deviation property and the Gallavotti-Cohen fluctuation theorem of sample entropy production rates of the Markov chain.
Directory of Open Access Journals (Sweden)
Linshuang Liu
2012-01-01
Full Text Available To investigate sludge drying process, a numerical simulation based on Brownian dynamic for the floc with uncharged and charged particles was conducted. The Langevin equation is used as dynamical equation for tracking each particle in a floc. An initial condition and periodic boundary condition which well conformed to reality is used for calculating the floc growth process. Each cell consists of 1000 primary particles with diameter 0.1 ∼ 4 μm. Floc growth is related to the thermal force and the electrostatic force. The electrostatic force on a particle in the simulation cell is considered as the sum of electrostatic forces from other particles in the original cell and its replicate cells. It is assumed that flocs are charged with precharged primary particles in dispersion system by ionization. By the analysis of the simulation figures, on one hand, the effects of initial particle size and sludge density on floc smashing time, floc radius of gyration, and fractal dimension were discussed. On the other hand, the effects of ionization on floc smashing time and floc structure were presented. This study has important practical value in the high-turbidity water treatment, especially for sludge drying.
Mücke, Norbert; Klenin, Konstantin; Kirmse, Robert; Bussiek, Malte; Herrmann, Harald; Hafner, Mathias; Langowski, Jörg
2009-01-01
Nanomechanical properties of filamentous biopolymers, such as the persistence length, may be determined from two-dimensional images of molecules immobilized on surfaces. For a single filament in solution, two principal adsorption scenarios are possible. Both scenarios depend primarly on the interaction strength between the filament and the support: i) For interactions in the range of the thermal energy, the filament can freely equilibrate on the surface during adsorption; ii) For interactions much stronger than the thermal energy, the filament will be captured by the surface without having equilibrated. Such a ‘trapping’ mechanism leads to more condensed filament images and hence to a smaller value for the apparent persistence length. To understand the capture mechanism in more detail we have performed Brownian dynamics simulations of relatively short filaments by taking the two extreme scenarios into account. We then compared these ‘ideal’ adsorption scenarios with observed images of immobilized vimentin intermediate filaments on different surfaces. We found a good agreement between the contours of the deposited vimentin filaments on mica (‘ideal’ trapping) and on glass (‘ideal’ equilibrated) with our simulations. Based on these data, we have developed a strategy to reliably extract the persistence length of short worm-like chain fragments or network forming filaments with unknown polymer-surface interactions. PMID:19888472
Directory of Open Access Journals (Sweden)
Norbert Mücke
Full Text Available Nanomechanical properties of filamentous biopolymers, such as the persistence length, may be determined from two-dimensional images of molecules immobilized on surfaces. For a single filament in solution, two principal adsorption scenarios are possible. Both scenarios depend primarily on the interaction strength between the filament and the support: i For interactions in the range of the thermal energy, the filament can freely equilibrate on the surface during adsorption; ii For interactions much stronger than the thermal energy, the filament will be captured by the surface without having equilibrated. Such a 'trapping' mechanism leads to more condensed filament images and hence to a smaller value for the apparent persistence length. To understand the capture mechanism in more detail we have performed Brownian dynamics simulations of relatively short filaments by taking the two extreme scenarios into account. We then compared these 'ideal' adsorption scenarios with observed images of immobilized vimentin intermediate filaments on different surfaces. We found a good agreement between the contours of the deposited vimentin filaments on mica ('ideal' trapping and on glass ('ideal' equilibrated with our simulations. Based on these data, we have developed a strategy to reliably extract the persistence length of short worm-like chain fragments or network forming filaments with unknown polymer-surface interactions.
Hilder, Tamsyn A; Chung, Shin-Ho
2013-02-01
Using the recently unveiled crystal structure, and molecular and Brownian dynamics simulations, we elucidate several conductance properties of the inwardly rectifying potassium channel, Kir3.2, which is implicated in cardiac and neurological disorders. We show that the pore is closed by a hydrophobic gating mechanism similar to that observed in Kv1.2. Once open, potassium ions move into, but not out of, the cell. The asymmetrical current-voltage relationship arises from the lack of negatively charged residues at the narrow intracellular mouth of the channel. When four phenylalanine residues guarding the intracellular gate are mutated to glutamate residues, the channel no longer shows inward rectification. Inward rectification is restored in the mutant Kir3.2 when it becomes blocked by intracellular Mg(2+). Tertiapin, a polypeptide toxin isolated from the honey bee, is known to block several subtypes of the inwardly rectifying channels with differing affinities. We identify critical residues in the toxin and Kir3.2 for the formation of the stable complex. A lysine residue of tertiapin protrudes into the selectivity filter of Kir3.2, while two other basic residues of the toxin form hydrogen bonds with acidic residues located just outside the channel entrance. The depth of the potential of mean force encountered by tertiapin is -16.1kT, thus indicating that the channel will be half-blocked by 0.4μM of the toxin.
Urbina-Villalba, German; García-Sucre, Máximo; Toro-Mendoza, Jhoan
2003-12-01
In order to account for the hydrodynamic interaction (HI) between suspended particles in an average way, Honig et al. [J. Colloid Interface Sci. 36, 97 (1971)] and more recently Heyes [Mol. Phys. 87, 287 (1996)] proposed different analytical forms for the diffusion constant. While the formalism of Honig et al. strictly applies to a binary collision, the one from Heyes accounts for the dependence of the diffusion constant on the local concentration of particles. However, the analytical expression of the latter approach is more complex and depends on the particular characteristics of each system. Here we report a combined methodology, which incorporates the formula of Honig et al. at very short distances and a simple local volume-fraction correction at longer separations. As will be shown, the flocculation behavior calculated from Brownian dynamics simulations employing the present technique, is found to be similar to that of Batchelor’s tensor [J. Fluid. Mech. 74, 1 (1976); 119, 379 (1982)]. However, it corrects the anomalous coalescence found in concentrated systems as a result of the overestimation of many-body HI.
Magnetization direction in the Heisenberg model exhibiting fractional Brownian motion
DEFF Research Database (Denmark)
Zhang, Zhengping; Mouritsen, Ole G.; Zuckermann, Martin J.
1993-01-01
The temporal magnetization-direction fluctuations in the three-dimensional classical ferromagnetic Heisenberg model have been generated by Monte Carlo simulation and analyzed by the rescaled-range method to yield the Hurst exponent H. A value of H congruent-to 1 has been found to apply...
Hoda, Nazish; Kumar, Satish
2007-12-21
The adsorption of single polyelectrolyte molecules in shear flow is studied using Brownian dynamics simulations with hydrodynamic interaction (HI). Simulations are performed with bead-rod and bead-spring chains, and electrostatic interactions are incorporated through a screened Coulombic potential with excluded volume accounted for by the repulsive part of a Lennard-Jones potential. A correction to the Rotne-Prager-Yamakawa tensor is derived that accounts for the presence of a planar wall. The simulations show that migration away from an uncharged wall, which is due to bead-wall HI, is enhanced by increases in the strength of flow and intrachain electrostatic repulsion, consistent with kinetic theory predictions. When the wall and polyelectrolyte are oppositely charged, chain behavior depends on the strength of electrostatic screening. For strong screening, chains get depleted from a region close to the wall and the thickness of this depletion layer scales as N(1/3)Wi(2/3) at high Wi, where N is the chain length and Wi is the Weissenberg number. At intermediate screening, bead-wall electrostatic attraction competes with bead-wall HI, and it is found that there is a critical Weissenberg number for desorption which scales as N(-1/2)kappa(-3)(l(B)|sigmaq|)(3/2), where kappa is the inverse screening length, l(B) is the Bjerrum length, sigma is the surface charge density, and q is the bead charge. When the screening is weak, adsorbed chains are observed to align in the vorticity direction at low shear rates due to the effects of repulsive intramolecular interactions. At higher shear rates, the chains align in the flow direction. The simulation method and results of this work are expected to be useful for a number of applications in biophysics and materials science in which polyelectrolyte adsorption plays a key role.
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.
Ratcheted electrophoresis of Brownian particles
Kowalik, Mikołaj; Bishop, Kyle J. M.
2016-05-01
The realization of nanoscale machines requires efficient methods by which to rectify unbiased perturbations to perform useful functions in the presence of significant thermal noise. The performance of such Brownian motors often depends sensitively on their operating conditions—in particular, on the relative rates of diffusive and deterministic motions. In this letter, we present a type of Brownian motor that uses contact charge electrophoresis of a colloidal particle within a ratcheted channel to achieve directed transport or perform useful work against an applied load. We analyze the stochastic dynamics of this model ratchet to show that it functions under any operating condition—even in the limit of strong thermal noise and in contrast to existing ratchets. The theoretical results presented here suggest that ratcheted electrophoresis could provide a basis for electrochemically powered, nanoscale machines capable of transport and actuation of nanoscale components.
Directory of Open Access Journals (Sweden)
Lorenzo Marcucci
Full Text Available Muscular force generation in response to external stimuli is the result of thermally fluctuating, cyclical interactions between myosin and actin, which together form the actomyosin complex. Normally, these fluctuations are modelled using transition rate functions that are based on muscle fiber behaviour, in a phenomenological fashion. However, such a basis reduces the predictive power of these models. As an alternative, we propose a model which uses direct single molecule observations of actomyosin fluctuations reported in the literature. We precisely estimate the actomyosin potential bias and use diffusion theory to obtain a brownian ratchet model that reproduces the complete cross-bridge cycle. The model is validated by simulating several macroscopic experimental conditions, while its interpretation is compatible with two different force-generating scenarios.
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...
Directory of Open Access Journals (Sweden)
Gayo Willy
2016-01-01
Full Text Available Philippine Stock Exchange Composite Index (PSEi is the main stock index of the Philippine Stock Exchange (PSE. PSEi is computed using a weighted mean of the top 30 publicly traded companies in the Philippines, called component stocks. It provides a single value by which the performance of the Philippine stock market is measured. Unfortunately, these weights, which may vary for every trading day, are not disclosed by the PSE. In this paper, we propose a model of forecasting the PSEi by estimating the weights based on historical data and forecasting each component stock using Monte Carlo simulation based on a Geometric Brownian Motion (GBM assumption. The model performance is evaluated and its forecast compared is with the results using a direct GBM forecast of PSEi over different forecast periods. Results showed that the forecasts using WGBM will yield smaller error compared to direct GBM forecast of PSEi.
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.
Acharya, R.C.; Dijke, van M.I.J.; Sorbie, K.S.; Zee, van der S.E.A.T.M.; Leijnse, A.
2007-01-01
We present a 3D network model with particle tracking to upscale 3D Brownian motion of non-reactive tracer particles subjected to a velocity field in the network bonds, representing both local diffusion and convection. At the intersections of the bonds (nodes) various jump conditions are implemented.
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.
The generalization of a class of impulse stochastic control models of a geometric Brownian motion
Institute of Scientific and Technical Information of China (English)
LIU XiaoPeng; LIU KunHui
2009-01-01
Recently, international academic circles advanced a class of new stochastic control models of a geometric Brownian motion which is an important kind of impulse control models whose cost structure is different from the others before, and it has a broad applying background and important theoretical significance in financial control and management of investment. This paper generalizes substantially the above stochastic control models under quite extensive conditions and describes the models more exactly under more normal theoretical system of stochastic process. By establishing a set of proper variational equations and proving the existence of its solution, and applying the means of stochastic analysis, this paper proves that the generalized stochastic control models have optimal controls.Meanwhile, we also analyze the structure of optimal controls carefully. Besides, we study the solution function of variational equations in a relatively deep-going way, which constitutes the value function of control models to some extent. Because the analysis methods of this paper are greatly different from those of original reference, this paper possesses considerable originality to some extent. In addition,this paper gives the strict proof to the part of original reference which is not fairly well-knit in analyses,and makes analyses and discussions of the model have the exactitude of mathematical sense.
Tsekov, Roumen
2016-06-01
A Brownian harmonic oscillator, which dissipates energy either by friction or via emission of electromagnetic radiation, is considered. This Brownian emitter is driven by the surrounding thermo-quantum fluctuations, which are theoretically described by the fluctuation-dissipation theorem. It is shown how the Abraham-Lorentz force leads to dependence of the half-width on the peak frequency of the oscillator amplitude spectral density. It is found that for the case of a charged particle moving in vacuum at zero temperature, its root-mean-square velocity fluctuation is a universal constant, equal to roughly 1/18 of the speed of light. The relevant Fokker-Planck and Smoluchowski equations are also derived.
Numerically pricing American options under the generalized mixed fractional Brownian motion model
Chen, Wenting; Yan, Bowen; Lian, Guanghua; Zhang, Ying
2016-06-01
In this paper, we introduce a robust numerical method, based on the upwind scheme, for the pricing of American puts under the generalized mixed fractional Brownian motion (GMFBM) model. By using portfolio analysis and applying the Wick-Itô formula, a partial differential equation (PDE) governing the prices of vanilla options under the GMFBM is successfully derived for the first time. Based on this, we formulate the pricing of American puts under the current model as a linear complementarity problem (LCP). Unlike the classical Black-Scholes (B-S) model or the generalized B-S model discussed in Cen and Le (2011), the newly obtained LCP under the GMFBM model is difficult to be solved accurately because of the numerical instability which results from the degeneration of the governing PDE as time approaches zero. To overcome this difficulty, a numerical approach based on the upwind scheme is adopted. It is shown that the coefficient matrix of the current method is an M-matrix, which ensures its stability in the maximum-norm sense. Remarkably, we have managed to provide a sharp theoretic error estimate for the current method, which is further verified numerically. The results of various numerical experiments also suggest that this new approach is quite accurate, and can be easily extended to price other types of financial derivatives with an American-style exercise feature under the GMFBM model.
Li, Minghai; Bansil, Rama
2010-01-01
The kinetics of the transformation from the hexagonal packed cylinder (HEX) phase to the face-centered-cubic (FCC) phase was simulated using Brownian Dynamics for an ABA triblock copolymer in a selective solvent for the A block. The kinetics was obtained by instantaneously changing either the temperature of the system or the well-depth of the Lennard-Jones potential. Detailed analysis showed that the transformation occurred via a rippling mechanism. The simulation results indicated that the order-order transformation (OOT) was a nucleation and growth process when the temperature of the system instantly jumped from 0.8 to 0.5. The time evolution of the structure factor obtained by Fourier Transformation showed that the peak intensities of the HEX and FCC phases could be fit well by an Avrami equation.
Ness, Christopher; Sun, Jin
2015-01-01
Shear flow of dense non-Brownian suspensions is simulated using the discrete element method taking particle contact and hydrodynamic lubrication into account. The resulting flow regimes are mapped in the parametric space of the solid volume fraction, shear rate, fluid viscosity, and particle stiffness. Below a critical volume fraction ϕc, the rheology is governed by the Stokes number, which distinguishes between viscous and inertial flow regimes. Above ϕc, a quasistatic regime exists for low and moderate shear rates. At very high shear rates, the ϕ dependence is lost, and soft-particle rheology is explored. The transitions between rheological regimes are associated with the evolving contribution of lubrication to the suspension stress. Transitions in microscopic phenomena, such as interparticle force distribution, fabric, and correlation length are found to correspond to those in the macroscopic flow. Motivated by the bulk rheology, a constitutive model is proposed combining a viscous pressure term with a dry granular model presented by Chialvo et al. [Phys. Rev. E 85, 021305 (2012), 10.1103/PhysRevE.85.021305]. The model is shown to successfully capture the flow regime transitions.
Isotropic Brownian motions over complex fields as a solvable model for May-Wigner stability analysis
Ipsen, J. R.; Schomerus, H.
2016-09-01
We consider matrix-valued stochastic processes known as isotropic Brownian motions, and show that these can be solved exactly over complex fields. While these processes appear in a variety of questions in mathematical physics, our main motivation is their relation to a May-Wigner-like stability analysis, for which we obtain a stability phase diagram. The exact results establish the full joint probability distribution of the finite-time Lyapunov exponents, and may be used as a starting point for a more detailed analysis of the stability-instability phase transition. Our derivations rest on an explicit formulation of a Fokker-Planck equation for the Lyapunov exponents. This formulation happens to coincide with an exactly solvable class of models of the Calgero-Sutherland type, originally encountered for a model of phase-coherent transport. The exact solution over complex fields describes a determinantal point process of biorthogonal type similar to recent results for products of random matrices, and is also closely related to Hermitian matrix models with an external source.
Brownian dynamics simulations of lipid bilayer membrane with hydrodynamic interactions in LAMMPS
Fu, Szu-Pei; Young, Yuan-Nan; Peng, Zhangli; Yuan, Hongyan
2016-11-01
Lipid bilayer membranes have been extensively studied by coarse-grained molecular dynamics simulations. Numerical efficiencies have been reported in the cases of aggressive coarse-graining, where several lipids are coarse-grained into a particle of size 4 6 nm so that there is only one particle in the thickness direction. Yuan et al. proposed a pair-potential between these one-particle-thick coarse-grained lipid particles to capture the mechanical properties of a lipid bilayer membrane (such as gel-fluid-gas phase transitions of lipids, diffusion, and bending rigidity). In this work we implement such interaction potential in LAMMPS to simulate large-scale lipid systems such as vesicles and red blood cells (RBCs). We also consider the effect of cytoskeleton on the lipid membrane dynamics as a model for red blood cell (RBC) dynamics, and incorporate coarse-grained water molecules to account for hydrodynamic interactions. The interaction between the coarse-grained water molecules (explicit solvent molecules) is modeled as a Lennard-Jones (L-J) potential. We focus on two sets of LAMMPS simulations: 1. Vesicle shape transitions with varying enclosed volume; 2. RBC shape transitions with different enclosed volume. This work is funded by NSF under Grant DMS-1222550.
Simulations of magnetic nanoparticle Brownian motion.
Reeves, Daniel B; Weaver, John B
2012-12-15
Magnetic nanoparticles are useful in many medical applications because they interact with biology on a cellular level thus allowing microenvironmental investigation. An enhanced understanding of the dynamics of magnetic particles may lead to advances in imaging directly in magnetic particle imaging or through enhanced MRI contrast and is essential for nanoparticle sensing as in magnetic spectroscopy of Brownian motion. Moreover, therapeutic techniques like hyperthermia require information about particle dynamics for effective, safe, and reliable use in the clinic. To that end, we have developed and validated a stochastic dynamical model of rotating Brownian nanoparticles from a Langevin equation approach. With no field, the relaxation time toward equilibrium matches Einstein's model of Brownian motion. In a static field, the equilibrium magnetization agrees with the Langevin function. For high frequency or low amplitude driving fields, behavior characteristic of the linearized Debye approximation is reproduced. In a higher field regime where magnetic saturation occurs, the magnetization and its harmonics compare well with the effective field model. On another level, the model has been benchmarked against experimental results, successfully demonstrating that harmonics of the magnetization carry enough information to infer environmental parameters like viscosity and temperature.
Sun, Bo; Lin, Jiayi; Darby, Ellis; Grosberg, Alexander Y.; Grier, David G.
2009-07-01
Mechanical equilibrium at zero temperature does not necessarily imply thermodynamic equilibrium at finite temperature for a particle confined by a static but nonconservative force field. Instead, the diffusing particle can enter into a steady state characterized by toroidal circulation in the probability flux, which we call a Brownian vortex. The circulatory bias in the particle’s thermally driven trajectory is not simply a deterministic response to the solenoidal component of the force but rather reflects interplay between advection and diffusion in which thermal fluctuations extract work from the nonconservative force field. As an example of this previously unrecognized class of stochastic heat engines, we consider a colloidal sphere diffusing in a conventional optical tweezer. We demonstrate both theoretically and experimentally that nonconservative optical forces bias the particle’s fluctuations into toroidal vortexes whose circulation can reverse direction with temperature or laser power.
Archimedes' principle for Brownian liquid
Burdzy, Krzysztof; Chen, Zhen-Qing; Pal, Soumik
2009-01-01
We consider a family of hard core objects moving as independent Brownian motions confined to a vessel by reflection. These are subject to gravitational forces modeled by drifts. The stationary distribution for the process has many interesting implications, including an illustration of the Archimedes’ principle. The analysis rests on constructing reflecting Brownian motion with drift in a general open connected domain and studying its stationary distribution. In dimension two we utilize known ...
Archimedes' principle for Brownian liquid
Burdzy, Krzysztof; Pal, Soumik
2009-01-01
We consider a family of hard core objects moving as independent Brownian motions confined to a vessel by reflection. These are subject to gravitational forces modeled by drifts. The stationary distribution for the process has many interesting implications, including an illustration of the Archimedes' principle. The analysis rests on constructing reflecting Brownian motion with drift in a general open connected domain and studying its stationary distribution. In dimension two we utilize known results about sphere packing.
Alicki's model of scattering-induced decoherence derived from Hamiltonian dynamics
Energy Technology Data Exchange (ETDEWEB)
Hellmich, Mario [Faculty of Physics, University of Bielefeld, 33615 Bielefeld (Germany)
2004-09-10
We study a semiphenomenological model introduced by Alicki (2002 Phys. Rev. A 65 034104), describing environmental decoherence by scattering of a Brownian particle in a gas environment. For a slightly wider class of models, we prove that the semigroup describing the dynamics of the Brownian particle can be approximated by the reduced dynamics arising from a Hamiltonian interaction between the particle and an infinite fermionic thermal gas reservoir, provided the scattering process is isotropic.
DEFF Research Database (Denmark)
Zhu, Jie
There exist dual-listed stocks which are issued by the same company in some stock markets. Although these stocks bare the same firm-specific risk and enjoy identical dividends and voting policies, they are priced differently. Some previous studies show this seeming deviation from the law of one...... price can be solved due to different ex- pected return and market price of risk for investors holding heterogeneous beliefs. This paper provides empirical evidence for that argument by testing the expected return and market price of risk between Chinese A and B shares listed in Shanghai and Shenzhen...... stock markets. Models with dynamic of Geometric Brownian Motion are adopted, multivariate GARCH models are also introduced to capture the feature of time-varying volatility in stock returns. The results suggest that the different pric- ing can be explained by the difference in expected returns between...
Feller processes: the next generation in modeling. Brownian motion, Levy processes and beyond.
Directory of Open Access Journals (Sweden)
Björn Böttcher
Full Text Available We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space dependent mixing of Lévy processes. Brownian Motion is one of the most frequently used continuous time Markov processes in applications. In recent years also Lévy processes, of which Brownian Motion is a special case, have become increasingly popular. Lévy processes are spatially homogeneous, but empirical data often suggest the use of spatially inhomogeneous processes. Thus it seems necessary to go to the next level of generalization: Feller processes. These include Lévy processes and in particular brownian motion as special cases but allow spatial inhomogeneities. Many properties of Feller processes are known, but proving the very existence is, in general, very technical. Moreover, an applicable framework for the generation of sample paths of a Feller process was missing. We explain, with practitioners in mind, how to overcome both of these obstacles. In particular our simulation technique allows to apply Monte Carlo methods to Feller processes.
Feller processes: the next generation in modeling. Brownian motion, Lévy processes and beyond.
Böttcher, Björn
2010-12-03
We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space dependent mixing of Lévy processes. Brownian Motion is one of the most frequently used continuous time Markov processes in applications. In recent years also Lévy processes, of which Brownian Motion is a special case, have become increasingly popular. Lévy processes are spatially homogeneous, but empirical data often suggest the use of spatially inhomogeneous processes. Thus it seems necessary to go to the next level of generalization: Feller processes. These include Lévy processes and in particular brownian motion as special cases but allow spatial inhomogeneities. Many properties of Feller processes are known, but proving the very existence is, in general, very technical. Moreover, an applicable framework for the generation of sample paths of a Feller process was missing. We explain, with practitioners in mind, how to overcome both of these obstacles. In particular our simulation technique allows to apply Monte Carlo methods to Feller processes.
Institute of Scientific and Technical Information of China (English)
顾凌云; 徐升华; 孙祉伟
2011-01-01
在对胶体晶体的研究中,带电粒子胶体晶体的形成机理比硬球胶体晶体更加复杂,对其形成条件目前还缺少有效的判断依据.有效硬球模型判据提出以有效直径作为判断参数.为了验证该判据的有效性,利用布朗动力学模拟研究了不同有效直径下带电粒子胶体晶体的特性.为了更加定量地研究单因素对带电胶体晶体形成的影响,取有效直径为2.8至0.8,并对一定的有效直径,研究了粒子几何直径和排斥力不同情况下的结晶行为.在布朗动力学模拟过程中,采用径向分布函数和键序参数方法检测体系的结构变化,并分析所形成的晶体结构.结果表明,在判断带电粒子胶体体系能否形成有序结构方面,有效硬球模型判据有一定的合理性.但是,并不能将有效直径作为唯一的判别参数,而是需要综合其他参数的影响,这显示出该判据的片面性.%The mechanism for the formation of colloidal crystals in charge-stabilized colloids is more complicated than that of hard-sphere colloidal crystals.And there is still lack of available criterion for the formation of charged colloidal crystals.The effective hard-sphere model suggests a criterion in which the effective diameter is used as a crucial parameter.In order to test the validity of this criterion,the characteristics of charged colloidal crystals with different effective diameters are investigated using Brownian dynamics simulations in this study.The crystallization behaviors with different geometric particle diameters and repulsive forces are also studied with some fixed effective diameters.In the simulation,the time evolution of crystallization process and the crystal structure during the simulation are characterized by means of the radial distribution functions and bond-order parameters.The results show that the effective hard-sphere model criterion has its reasonableness to some extent.However,the effective diameter cannot be
On Drift Parameter Estimation in Models with Fractional Brownian Motion by Discrete Observations
Directory of Open Access Journals (Sweden)
Yuliya Mishura
2014-06-01
Full Text Available We study a problem of an unknown drift parameter estimation in a stochastic differen- tial equation driven by fractional Brownian motion. We represent the likelihood ratio as a function of the observable process. The form of this representation is in general rather complicated. However, in the simplest case it can be simplified and we can discretize it to establish the a. s. convergence of the discretized version of maximum likelihood estimator to the true value of parameter. We also investigate a non-standard estimator of the drift parameter showing further its strong consistency.
Optimal Policy for Brownian Inventory Models with General Convex Inventory Cost
Institute of Scientific and Technical Information of China (English)
Da-cheng YAO
2013-01-01
We study an inventory system in which products are ordered from outside to meet demands,and the cumulative demand is governed by a Brownian motion.Excessive demand is backlogged.We suppose that the shortage and holding costs associated with the inventory are given by a general convex function.The product ordering from outside incurs a linear ordering cost and a setup fee.There is a constant leadtime when placing an order.The optimal policy is established so as to minimize the discounted cost including the inventory cost and ordering cost.
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...
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.
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.
Ikeda, Tatsushi; Tanimura, Yoshitaka
2015-01-01
We explore and describe the roles of inter-molecular vibrations in terms of a Brownian oscillator (BO) model with linear-linear (LL) and square-linear (SL) system-bath interactions, which we use to analyze two-dimensional (2D) THz-Raman spectra obtained by means of molecular dynamics (MD) simulations. In addition to linear absorption (1D IR), we calculate 2D Raman-THz-THz, THz-Raman-THz, and THz-THz-Raman signals for liquid formamide, water, and methanol using an equilibrium non-equilibrium hybrid MD simulation. The calculated 1D IR and 2D THz-Raman signals are then accounted by the LL+SL BO model with the use of the hierarchal Fokker-Planck equations for a non-perturbative and non-Markovian noise. All of the characteristic 2D profiles of the simulated signals are reproduced using the LL+SL BO model, indicating that the present model captures the essential features of the inter-molecular motion. We analyze the fitted the 2D profiles in terms of anharmonicity, nonlinear polarizability, and dephasing time. The ...
Zhao, Xujun; Hernandez-Ortiz, Juan; Karpeyev, Dmitry; de Pablo, Juan; Smith, Barry
In this work, we present an efficient parallel particle-in-mesh method for Brownian Dynamics simulations of many-particle systems confined in micro- and nano-fluidic devices. A general geometry Ewald-like method (GGEM) combined with finite element method is used to account for the hydrodynamic interaction. A fast parallel Krylov-type iterative solver with hybrid preconditioning techniques is developed for solving the large sparse systems of equations arising from finite element discretization of the Stokes equations. In addition, the current computer code is developed based on PETSc, a scalable library of numerical algorithms developed at Argonne, SLEPc - Scalable Library for Eigenvalue Problem Computations, and libMesh, a finite element library for numerical solution of PDEs built on top of PETSc, which allows for direct simulation of large scale systems with arbitrary confined geometries. This scheme is applied to Brownian dynamics simulations of flowing confined polymer solutions and colloidal dispersions in micro-fluid channels. The effects of hydrodynamics interactions and geometric confinement on the migration phenomena are illustrated.
Detection of two-sided alternatives in a Brownian motion model
Hadjiliadis, Olympia
2007-01-01
This work examines the problem of sequential detection of a change in the drift of a Brownian motion in the case of two-sided alternatives. Applications to real life situations in which two-sided changes can occur are discussed. Traditionally, 2-CUSUM stopping rules have been used for this problem due to their asymptotically optimal character as the mean time between false alarms tends to $\\infty$. In particular, attention has focused on 2-CUSUM harmonic mean rules due to the simplicity in calculating their first moments. In this paper, we derive closed-form expressions for the first moment of a general 2-CUSUM stopping rule. We use these expressions to obtain explicit upper and lower bounds for it. Moreover, we derive an expression for the rate of change of this first moment as one of the threshold parameters changes. Based on these expressions we obtain explicit upper and lower bounds to this rate of change. Using these expressions we are able to find the best 2-CUSUM stopping rule with respect to the exten...
A Brownian Energy Depot Model of the Basilar Membrane Oscillation with a Braking Mechanism
Zhang, Yong; Lee, Kong-Ju-Bock; Park, Youngah
2008-01-01
High auditory sensitivity, sharp frequency selectivity, and otoacoustic emissions are signatures of active amplification of the cochlea. The human ear can also detect very large amplitude sound without being damaged as long as the exposed time is not too long. The outer hair cells are believed as the best candidate for the active force generator of the mammalian cochlea. In this paper, we propose a new model for the basilar membrane oscillation which successfully describes both the active and the protective mechanisms by employing an energy depot concept and a critical velocity of the basilar membrane. One of the main results is that thermal noise in the absence of external stimulation can be amplified leading to the spontaneous basilar membrane oscillation. The compressive response of the basilar membrane at the characteristic frequency and the dynamic response to the stimulation are consistent with the experimental results as expected. Our model also shows the nonlinear distortion of the response of the bas...
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.
Optimization and universality of Brownian search in a basic model of quenched heterogeneous media
Godec, Aljaž; Metzler, Ralf
2015-05-01
The kinetics of a variety of transport-controlled processes can be reduced to the problem of determining the mean time needed to arrive at a given location for the first time, the so-called mean first-passage time (MFPT) problem. The occurrence of occasional large jumps or intermittent patterns combining various types of motion are known to outperform the standard random walk with respect to the MFPT, by reducing oversampling of space. Here we show that a regular but spatially heterogeneous random walk can significantly and universally enhance the search in any spatial dimension. In a generic minimal model we consider a spherically symmetric system comprising two concentric regions with piecewise constant diffusivity. The MFPT is analyzed under the constraint of conserved average dynamics, that is, the spatially averaged diffusivity is kept constant. Our analytical calculations and extensive numerical simulations demonstrate the existence of an optimal heterogeneity minimizing the MFPT to the target. We prove that the MFPT for a random walk is completely dominated by what we term direct trajectories towards the target and reveal a remarkable universality of the spatially heterogeneous search with respect to target size and system dimensionality. In contrast to intermittent strategies, which are most profitable in low spatial dimensions, the spatially inhomogeneous search performs best in higher dimensions. Discussing our results alongside recent experiments on single-particle tracking in living cells, we argue that the observed spatial heterogeneity may be beneficial for cellular signaling processes.
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.
Delorme, Mathieu; Le Doussal, Pierre; Wiese, Kay Jörg
2016-05-01
The Brownian force model is a mean-field model for local velocities during avalanches in elastic interfaces of internal space dimension d , driven in a random medium. It is exactly solvable via a nonlinear differential equation. We study avalanches following a kick, i.e., a step in the driving force. We first recall the calculation of the distributions of the global size (total swept area) and of the local jump size for an arbitrary kick amplitude. We extend this calculation to the joint density of local and global sizes within a single avalanche in the limit of an infinitesimal kick. When the interface is driven by a single point, we find new exponents τ0=5 /3 and τ =7 /4 , depending on whether the force or the displacement is imposed. We show that the extension of a "single avalanche" along one internal direction (i.e., the total length in d =1 ) is finite, and we calculate its distribution following either a local or a global kick. In all cases, it exhibits a divergence P (ℓ ) ˜ℓ-3 at small ℓ . Most of our results are tested in a numerical simulation in dimension d =1 .
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
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.
Van Den Broek, Martijn; Van Den Broeck, Christian
2007-01-01
We present the exact analysis of a chiral Brownian motor and heat pump. Optimization of the construction predicts, for a nanoscale device, frequencies of the order of kHz and cooling rates of the order of femtojoule per second.
van den Broek, M; Van den Broeck, C
2008-04-04
We present the exact analysis of a chiral Brownian motor and heat pump. Optimization of the construction predicts, for a nanoscale device, frequencies of the order of kHz and cooling rates of the order of femtojoule per second.
On-chip measurements of Brownian relaxation vs. concentration of 40nm magnetic beads
DEFF Research Database (Denmark)
Østerberg, Frederik Westergaard; Rizzi, Giovanni; Hansen, Mikkel Fougt
2012-01-01
are needed as the beads are magnetized by the field generated by the applied sensor bias current. We show that the Brownian relaxation frequency can be extracted from fitting the Cole-Cole model to measurements for bead concentrations of 64 mu g/ml or higher and that the measured dynamic magnetic response......We present on-chip Brownian relaxation measurements on a logarithmic dilution series of 40 nm beads dispersed in water with bead concentrations between 16 mu g/ml and 4000 mu g/ml. The measurements are performed using a planar Hall effect bridge sensor at frequencies up to 1 MHz. No external fields...
An exactly solvable model for Brownian motion : IV. Susceptibility and Nyquist's theorem
Ullersma, P.
1966-01-01
By means of an exactly solvable model, treated in a previous paper1), the relation between the microscopic and macroscopic susceptibility is discussed. Furthermore, the limits of the validity of Nyquist's theorem are given.
Minimal model for dynamic bonding in colloidal transient networks
Krinninger, Philip; Fortini, Andrea; Schmidt, Matthias
2016-04-01
We investigate a model for colloidal network formation using Brownian dynamics computer simulations. Hysteretic springs establish transient bonds between particles with repulsive cores. If a bonded pair of particles is separated by a cutoff distance, the spring vanishes and reappears only if the two particles contact each other. We present results for the bond lifetime distribution and investigate the properties of the van Hove dynamical two-body correlation function. The model displays crossover from fluidlike dynamics, via transient network formation, to arrested quasistatic network behavior.
Brownian Ratchets in Biophysics: from Diffusing Phospholipids to Polymerizing Actin Filaments
van Oudenaarden, Alexander
2000-03-01
In the 'Feynman Lectures on Physics' Feynman introduces a mechanical ratchet and pawl subjected to thermal fluctuations to demonstrate the impossibility to violate the second law of thermodynamics. Since this introduction the Brownian ratchet has evolved from Gedanken experiments to real experiments in the interdisciplinary sciences such as biophysics and biochemistry. In this symposium I will present two experiments in which the concept Brownian ratchet is of key importance. The first experiment addresses a so-called geometrical Brownian ratchet [1]. This ratchet consists of a two-dimensional microfabricated periodic array of asymmetric diffusion barriers. As an experimental realization of a two-dimensional fluid of Brownian particles, a bilayer of phospholipid molecules is used. I will demonstrate that the geometrical Brownian ratchet can be used as a molecular sieve to separate mixtures of membrane molecules without the need to extract them from the membrane. In the second experiment I explore the spontaneous symmetry breaking of polymerizing actin networks [2]. Small submicron size beads coated uniformly with a protein that catalyzes actin polymerization, are initially surrounded by a symmetrical cloud of actin filaments. This symmetry can be broken spontaneously after which the beads undergo directional motion with constant velocity. I will present a simple stochastic theory, in which each filament is modeled as an elastic Brownian ratchet that qualitatively reproduces the experimental results. The presence of the bead couples the dynamics of different filaments which results in a complex collective system of interacting Brownian ratchets that exhibits an emergent symmetry breaking behavior. [1] A. van Oudenaarden and S. G. Boxer, Science 285, 1046 (1999). [2] A. van Oudenaarden and J. A. Theriot, Nature Cell Biology 1, 493 (1999).
Dynamic stochastic accumulation model with application to pension savings management
Directory of Open Access Journals (Sweden)
Melicherčik Igor
2010-01-01
Full Text Available We propose a dynamic stochastic accumulation model for determining optimal decision between stock and bond investments during accumulation of pension savings. Stock prices are assumed to be driven by the geometric Brownian motion. Interest rates are modeled by means of the Cox-Ingersoll-Ross model. The optimal decision as a solution to the corresponding dynamic stochastic program is a function of the duration of saving, the level of savings and the short rate. Qualitative and quantitative properties of the optimal solution are analyzed. The model is tested on the funded pillar of the Slovak pension system. The results are calculated for various risk preferences of a saver.
Littelmann path model for geometric crystals, Whittaker functions on Lie groups and Brownian motion
Chhaibi, Reda
2013-02-01
Generally speaking, this thesis focuses on the interplay between the representations of Lie groups and probability theory. It subdivides into essentially three parts. In a first rather algebraic part, we construct a path model for geometric crystals in the sense of Berenstein and Kazhdan, for complex semi-simple Lie groups. We will mainly describe the algebraic structure, its natural morphisms and parameterizations. The theory of total positivity will play a particularly important role. Then, we anticipate on the probabilistic part by exhibiting a canonical measure on geometric crystals. It uses as ingredients the superpotential for the flag manifold and a measure invariant under the crystal actions. The image measure under the weight map plays the role of Duistermaat-Heckman measure. Its Laplace transform defines Whittaker functions, providing an interesting formula for all Lie groups. Then it appears clearly that Whittaker functions are to geometric crystals, what characters are to combinatorial crystals. The Littlewood-Richardson rule is also exposed. Finally we present the probabilistic approach that allows to find the canonical measure. It is based on the fundamental idea that the Wiener measure will induce the adequate measure on the algebraic structures through the path model. In the last chapter, we show how our geometric model degenerates to the continuous classical Littelmann path model and thus recover known results. For example, the canonical measure on a geometric crystal of highest weight degenerates into a uniform measure on a polytope, and recovers the parameterizations of continuous crystals.
Roynette, Bernard
2009-01-01
Penalising a process is to modify its distribution with a limiting procedure, thus defining a new process whose properties differ somewhat from those of the original one. We are presenting a number of examples of such penalisations in the Brownian and Bessel processes framework. The Martingale theory plays a crucial role. A general principle for penalisation emerges from these examples. In particular, it is shown in the Brownian framework that a positive sigma-finite measure takes a large class of penalisations into account.
Efficiency at maximum power and efficiency fluctuations in a linear Brownian heat-engine model
Park, Jong-Min; Chun, Hyun-Myung; Noh, Jae Dong
2016-07-01
We investigate the stochastic thermodynamics of a two-particle Langevin system. Each particle is in contact with a heat bath at different temperatures T1 and T2 (autonomous heat engine performing work against the external driving force. Linearity of the system enables us to examine thermodynamic properties of the engine analytically. We find that the efficiency of the engine at maximum power ηM P is given by ηM P=1 -√{T2/T1 } . This universal form has been known as a characteristic of endoreversible heat engines. Our result extends the universal behavior of ηM P to nonendoreversible engines. We also obtain the large deviation function of the probability distribution for the stochastic efficiency in the overdamped limit. The large deviation function takes the minimum value at macroscopic efficiency η =η ¯ and increases monotonically until it reaches plateaus when η ≤ηL and η ≥ηR with model-dependent parameters ηR and ηL.
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
Particle-scale modelling of financial price dynamics
Liu, David
2017-02-01
This paper proposes a particle-based computational framework for modeling of financial price dynamics, which is an extension of the recent empirical work of Financial Brownian Particle (FBP), and discretizes and solves the Langevin equation that is the continuum representation of a financial market. The framework enables us to simulate the limit order book of the USD/JPY exchange rates. The research yields results that are in good agreement with the published empirical results. Our framework of modelling financial prices is of multidisciplinary nature, and can bridge the fields of empirical studies of financial order books, particle dynamics simulation, and modelling of financial market.
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.
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.
Directory of Open Access Journals (Sweden)
Yamin Wang
2014-01-01
Full Text Available This paper is concerned with the random attractors for a class of second-order stochastic lattice dynamical systems. We first prove the uniqueness and existence of the solutions of second-order stochastic lattice dynamical systems in the space F=lλ2×l2. Then, by proving the asymptotic compactness of the random dynamical systems, we establish the existence of the global random attractor. The system under consideration is quite general, and many existing results can be regarded as the special case of our results.
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.
Kamleitner, Ingo
2010-01-01
We employ the theoretical framework of positive operator valued measures, to study Markovian open quantum systems. In particular, we discuss how a quantum system influences its environment. Using the theory of indirect measurements, we then draw conclusions about the information we could hypothetically obtain about the system by observing the environment. Although the environment is not actually observed, we can use these results to describe the change of the quantum system due to its interaction with the environment. We apply this technique to two different problems. In the first part, we study the coherently driven dynamics of a particle on a rail of quantum dots. This tunnelling between adjacent quantum dots can be controlled externally. We employ an adiabatic scheme similar to stimulated Raman adiabatic passage, to transfer the particle between different quantum dots. We compare two fundamentally different sources of decoherence. In the second part, we study the dynamics of a free quantum particle, which ...
Anomalous Brownian Refrigerator
Rana, Shubhashis; Pal, P. S.; Saha, Arnab; Jayannavar, A. M.
2015-01-01
We present a detailed study of a Brownian particle driven by Carnot-type refrigerating protocol operating between two thermal baths. Both the underdamped as well as the overdamped limits are investigated. The particle is in a harmonic potential with time-periodic strength that drives the particle cyclically between the baths. Each cycle consists of two isothermal steps at different temperatures and two adiabatic steps connecting them. Besides working as a stochastic refrigerator, it is shown ...
Dynamical Properties of Potassium Ion Channels with a Hierarchical Model
Institute of Scientific and Technical Information of China (English)
ZHAN Yong; AN Hai-Long; YU Hui; ZHANG Su-Hua; HAN Ying-Rong
2006-01-01
@@ It is well known that potassium ion channels have higher permeability than K ions, and the permeable rate of a single K ion channel is about 108 ions per second. We develop a hierarchical model of potassium ion channel permeation involving ab initio quantum calculations and Brownian dynamics simulations, which can consistently explain a range of channel dynamics. The results show that the average velocity of K ions, the mean permeable time of K ions and the permeable rate of single channel are about 0.92nm/ns, 4.35ns and 2.30×108 ions/s,respectively.
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.
Kamleitner, Ingo
2010-09-01
We employ the theoretical framework of positive operator valued measures, to study Markovian open quantum systems. In particular, we discuss how a quantum system influences its environment. Using the theory of indirect measurements, we then draw conclusions about the information we could hypothetically obtain about the system by observing the environment. Although the environment is not actually observed, we can use these results to describe the change of the quantum system due to its interaction with the environment. We apply this technique to two different problems. In the first part, we study the coherently driven dynamics of a particle on a rail of quantum dots. This tunnelling between adjacent quantum dots can be controlled externally. We employ an adiabatic scheme similar to stimulated Raman adiabatic passage, to transfer the particle between different quantum dots. We compare two fundamentally different sources of decoherence. In the second part, we study the dynamics of a free quantum particle, which experiences random collisions with gas particles. Previous studies on this topic applied scattering theory to momentum eigenstates. We present a supplementary approach, where we develop a rigorous measurement interpretation of the collision process to derive a master equation. Finally, we study the collisional decoherence process in terms of the Wigner function. We restrict ourselves to one spatial dimension. Nevertheless, we find some interesting new insight, including that the previously celebrated quantum contribution to position diffusion is not real, but a consequence of the Markovian approximation. Further, we discover that the leading decoherence process is due to phase averaging, rather than induced by the information transfer between the colliding particles.
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.
QUANTUM STOCHASTIC PROCESSES: BOSON AND FERMION BROWNIAN MOTION
Directory of Open Access Journals (Sweden)
A.E.Kobryn
2003-01-01
Full Text Available Dynamics of quantum systems which are stochastically perturbed by linear coupling to the reservoir can be studied in terms of quantum stochastic differential equations (for example, quantum stochastic Liouville equation and quantum Langevin equation. In order to work it out one needs to define the quantum Brownian motion. As far as only its boson version has been known until recently, in the present paper we present the definition which makes it possible to consider the fermion Brownian motion as well.
Ballestra, Luca Vincenzo; Pacelli, Graziella; Radi, Davide
2016-12-01
We propose a numerical method to compute the first-passage probability density function in a time-changed Brownian model. In particular, we derive an integral representation of such a density function in which the integrand functions must be obtained solving a system of Volterra equations of the first kind. In addition, we develop an ad-hoc numerical procedure to regularize and solve this system of integral equations. The proposed method is tested on three application problems of interest in mathematical finance, namely the calculation of the survival probability of an indebted firm, the pricing of a single-knock-out put option and the pricing of a double-knock-out put option. The results obtained reveal that the novel approach is extremely accurate and fast, and performs significantly better than the finite difference method.
Energy Technology Data Exchange (ETDEWEB)
Sorensen, C.M.
1976-01-01
An effort to expand light-scattering autocorrelation techniques to Brownian diffusional and critical fluid systems in which multiple scattering effects are important, and to understand the observed similarity of the Rayleigh linewidth of light scattered from these two seemingly different systems is discussed. A formalism was developed to find the light field multiply scattered from a suspension of Brownian diffusing particles. For the field doubly scattered from a system of noninteracting Brownian particles, the intensity and correlation time were much less dependent on the scattering angle than for the singly scattered component. The polarized and depolarized correlation times of light scattered from Brownian particle systems were measured. The double-scattering formalism was extended to light scattered from critical fluid systems. In the region k xi greater than 5 the doubly and singly scattered correlation times were nearly equal. The dynamic droplet model of critical phenomena was developed which gives the proper, experimentally verified, forms for the intensity and linewidth of light scattered from a critical fluid. To test the dynamic droplet model and the mode theories Rayleigh linewidth predictions, light-scattering measurements were performed on the critical fluid system methanol and cyclohexane. The data agreed with both the dynamic droplet and decoupled mode theory predictions. The depolarized scattered spectra from a critical fluid were measured, and qualitative agreement with the double-scattering theory was found. 57 figures, 5 tables.
Dynamic Latent Classification Model
DEFF Research Database (Denmark)
Zhong, Shengtong; Martínez, Ana M.; Nielsen, Thomas Dyhre
as possible. Motivated by this problem setting, we propose a generative model for dynamic classification in continuous domains. At each time point the model can be seen as combining a naive Bayes model with a mixture of factor analyzers (FA). The latent variables of the FA are used to capture the dynamics...... in the process as well as modeling dependences between attributes....
Ota, Satoshi; Kitaguchi, Ryoichi; Takeda, Ryoji; Yamada, Tsutomu; Takemura, Yasushi
2016-09-10
The dependence of magnetic relaxation on particle parameters, such as the size and anisotropy, has been conventionally discussed. In addition, the influences of external conditions, such as the intensity and frequency of the applied field, the surrounding viscosity, and the temperature on the magnetic relaxation have been researched. According to one of the basic theories regarding magnetic relaxation, the faster type of relaxation dominates the process. However, in this study, we reveal that Brownian and Néel relaxations coexist and that Brownian relaxation can occur after Néel relaxation despite having a longer relaxation time. To understand the mechanisms of Brownian rotation, alternating current (AC) hysteresis loops were measured in magnetic fluids of different viscosities. These loops conveyed the amplitude and phase delay of the magnetization. In addition, the intrinsic loss power (ILP) was calculated using the area of the AC hysteresis loops. The ILP also showed the magnetization response regarding the magnetic relaxation over a wide frequency range. To develop biomedical applications of magnetic nanoparticles, such as hyperthermia and magnetic particle imaging, it is necessary to understand the mechanisms of magnetic relaxation.
Directory of Open Access Journals (Sweden)
Satoshi Ota
2016-09-01
Full Text Available The dependence of magnetic relaxation on particle parameters, such as the size and anisotropy, has been conventionally discussed. In addition, the influences of external conditions, such as the intensity and frequency of the applied field, the surrounding viscosity, and the temperature on the magnetic relaxation have been researched. According to one of the basic theories regarding magnetic relaxation, the faster type of relaxation dominates the process. However, in this study, we reveal that Brownian and Néel relaxations coexist and that Brownian relaxation can occur after Néel relaxation despite having a longer relaxation time. To understand the mechanisms of Brownian rotation, alternating current (AC hysteresis loops were measured in magnetic fluids of different viscosities. These loops conveyed the amplitude and phase delay of the magnetization. In addition, the intrinsic loss power (ILP was calculated using the area of the AC hysteresis loops. The ILP also showed the magnetization response regarding the magnetic relaxation over a wide frequency range. To develop biomedical applications of magnetic nanoparticles, such as hyperthermia and magnetic particle imaging, it is necessary to understand the mechanisms of magnetic relaxation.
Multifractal heart rate dynamics in human cardiovascular model
Kotani, Kiyoshi; Takamasu, Kiyoshi; Safonov, Leonid; Yamamoto, Yoshiharu
2003-05-01
Human cardiovascular and/or cardio-respiratory systems are shown to exhibit both multifractal and synchronous dynamics, and we recently developed a nonlinear, physiologically plausible model for the synchronization between heartbeat and respiration (Kotani, et al. Phys. Rev. E 65: 051923, 2002). By using the same model, we now show the multifractality in the heart rate dynamics. We find that beat-to-beat monofractal noise (fractional Brownian motion) added to the brain stem cardiovascular areas results in significantly broader singularity spectra for heart rate through interactions between sympathetic and parasympathetic nervous systems. We conclude that the model proposed here would be useful in studying the complex cardiovascular and/or cardio- respiratory dynamics in humans.
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.
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.
Optimal tuning of a confined Brownian information engine
Park, Jong-Min; Lee, Jae Sung; Noh, Jae Dong
2016-03-01
A Brownian information engine is a device extracting mechanical work from a single heat bath by exploiting the information on the state of a Brownian particle immersed in the bath. As for engines, it is important to find the optimal operating condition that yields the maximum extracted work or power. The optimal condition for a Brownian information engine with a finite cycle time τ has been rarely studied because of the difficulty in finding the nonequilibrium steady state. In this study, we introduce a model for the Brownian information engine and develop an analytic formalism for its steady-state distribution for any τ . We find that the extracted work per engine cycle is maximum when τ approaches infinity, while the power is maximum when τ approaches zero.
Amoeba-inspired nanoarchitectonic computing implemented using electrical Brownian ratchets
Aono, M.; Kasai, S.; Kim, S.-J.; Wakabayashi, M.; Miwa, H.; Naruse, M.
2015-06-01
In this study, we extracted the essential spatiotemporal dynamics that allow an amoeboid organism to solve a computationally demanding problem and adapt to its environment, thereby proposing a nature-inspired nanoarchitectonic computing system, which we implemented using a network of nanowire devices called ‘electrical Brownian ratchets (EBRs)’. By utilizing the fluctuations generated from thermal energy in nanowire devices, we used our system to solve the satisfiability problem, which is a highly complex combinatorial problem related to a wide variety of practical applications. We evaluated the dependency of the solution search speed on its exploration parameter, which characterizes the fluctuation intensity of EBRs, using a simulation model of our system called ‘AmoebaSAT-Brownian’. We found that AmoebaSAT-Brownian enhanced the solution searching speed dramatically when we imposed some constraints on the fluctuations in its time series and it outperformed a well-known stochastic local search method. These results suggest a new computing paradigm, which may allow high-speed problem solving to be implemented by interacting nanoscale devices with low power consumption.
考虑电离作用的淤泥异向絮凝三维数值模拟%Brownian Dynamic Simulation of Sludge Perikinetic Flocculation with Ionization
Institute of Scientific and Technical Information of China (English)
刘林双; 杨国录; 余明辉
2012-01-01
A Brownian dynamic simulation of perikinetic flocculation of fine sediment with ionization is presented. Langevin equation is used as dynamical equation in tracking particles in a floc. Monte Carlo method is used in simulating random variation in particle movement. Sludge particles are supposed in uncharged and charged state in dispersion system. Electrostatic force on a particle in a simulation cell is considered as a sum of electrostatic force from other particles in the original cell. Particle initial place is decided by particle diameter and sludge density. Particle initial velocity is determined by Gauss random distribution. Effects of particle diameter and sludge density on flocculation and floc structure are discussed. On the other hand, effects of electrostatic force on flocculatinn are presented. The model proposed coincide well with practical situations.%鉴于试验观察淤泥絮凝结构的技术难度,本文尝试以布朗动力学为基础,采用蒙特卡洛方法动态模拟电离作用下颗粒成长为絮团的过程.为结合实际情况,泥沙颗粒初始位置由颗粒粒径和淤泥密度决定,颗粒初始速度按照相应条件下高斯随机分布给定.边界条件用和实际符合较好的循环边界.在模拟数据分析的基础上,讨论并比较了颗粒粒径和淤泥密度对絮凝时间以及絮团开放程度的影响.另一方面,讨论了电离作用后颗粒电荷量对絮团生长的影响.解释了泥沙颗粒表面电荷密度变化对絮凝过程和絮团结构的影响,模拟结果和实际情况较为一致.
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.
Martínez, I A; Roldán, É; Dinis, L; Petrov, D; Parrondo, J M R; Rica, R A
2016-01-01
The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths1. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors2 and some artificial micro-engines3-5 operate. As described by stochastic thermodynamics6,7, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit8. Here we report an experimental realization of a Carnot engine with a single optically trapped Brownian particle as the working substance. We present an exhaustive study of the energetics of the engine and analyse the fluctuations of the finite-time efficiency, showing that the Carnot bound can be surpassed for a small number of non-equilibrium cycles. As its macroscopic counterpart, the energetics of our Carnot device exhibits basic properties that one would expect to observe in any microscopic energy transducer operating with baths at different temperatures9-11. Our results characterize the sources of irreversibility in the engine and the statistical properties of the efficiency-an insight that could inspire new strategies in the design of efficient nano-motors.
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.
One-bead coarse-grained model for RNA dynamics
Villada-Balbuena, Mario; Carbajal-Tinoco, Mauricio D.
2017-01-01
We present a revised version of a coarse-grained model for RNA dynamics. In such approach, the description of nucleotides is reduced to single points that interact between them through a series of effective pair potentials that were obtained from an improved analysis of RNA structures from the Protein Data Bank. These interaction potentials are the main constituents of a Brownian dynamics simulation algorithm that allows to perform a variety of tasks by taking advantage of the reduced number of variables. Such tasks include the prediction of the three-dimensional configuration of a series of test molecules. Moreover, the model permits the inclusion of effective magnesium ions and the ends of the RNA chains can be pulled with an external force to study the process of unfolding. In spite of the simplicity of the model, we obtain a good agreement with the experimental results.
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...
Shah, Saqlain A.; Reeves, Daniel B.; Ferguson, R. Matthew; Weaver, John B.
2015-01-01
Superparamagnetic iron oxide nanoparticles with highly nonlinear magnetic behavior are attractive for biomedical applications like magnetic particle imaging and magnetic fluid hyperthermia. Such particles display interesting magnetic properties in alternating magnetic fields and here we document experiments that show differences between the magnetization dynamics of certain particles in frozen and melted states. This effect goes beyond the small temperature difference (ΔT ~ 20 °C) and we show the dynamics to be a mixture of Brownian alignment of the particles and Néel rotation of their moments occurring in liquid particle suspensions. These phenomena can be modeled in a stochastic differential equation approach by postulating log-normal distributions and partial Brownian alignment of an effective anisotropy axis. We emphasize that precise particle-specific characterization through experiments and nonlinear simulations is necessary to predict dynamics in solution and optimize their behavior for emerging biomedical applications including magnetic particle imaging. PMID:26504371
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.
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...
DEFF Research Database (Denmark)
Andreasen, Martin Møller; Meldrum, Andrew
This paper studies whether dynamic term structure models for US nominal bond yields should enforce the zero lower bound by a quadratic policy rate or a shadow rate specification. We address the question by estimating quadratic term structure models (QTSMs) and shadow rate models with at most four...
A stochastic phase-field model determined from molecular dynamics
von Schwerin, Erik
2010-03-17
The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and by capillary forces acting on the nanometer scale of the solid-liquid interface width. Its modelling is useful for instance in processing techniques based on casting. The phase-field method is widely used to study evolution of such microstructural phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen-Cahn/Ginzburg-Landau equation modelling the dynamics of an order parameter determining the solid and liquid phases, including also stochastic fluctuations to obtain the qualitatively correct result of dendritic side branching. This work presents a method to determine stochastic phase-field models from atomistic formulations by coarse-graining molecular dynamics. It has three steps: (1) a precise quantitative atomistic definition of the phase-field variable, based on the local potential energy; (2) derivation of its coarse-grained dynamics model, from microscopic Smoluchowski molecular dynamics (that is Brownian or over damped Langevin dynamics); and (3) numerical computation of the coarse-grained model functions. The coarse-grained model approximates Gibbs ensemble averages of the atomistic phase-field, by choosing coarse-grained drift and diffusion functions that minimize the approximation error of observables in this ensemble average. © EDP Sciences, SMAI, 2010.
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
Near-field optically driven Brownian motors (Conference Presentation)
Wu, Shao-Hua; Huang, Ningfeng; Jaquay, Eric; Povinelli, Michelle L.
2016-09-01
Brownian ratchets are of fundamental interest in fields from statistical physics to molecular motors. The realization of Brownian ratchets in engineered systems opens up the potential to harness thermal energy for directed motion, with applications in transport and sorting of nanoparticles. Implementations based on optical traps provide a high degree of tunability along with precise spatiotemporal control. Near-field optical methods provide particular flexibility and ease of on-chip integration with other microfluidic components. Here, we demonstrate the first all-optical, near-field Brownian ratchet. Our approach uses an asymmetrically patterned photonic crystal and yields an ultra-stable trap stiffness of 253.6 pN/nm-W, 100x greater than conventional optical tweezers. By modulating the laser power, optical ratcheting with transport speed of 1 micron/s can be achieved, allowing a variety of dynamical lab-on-a-chip applications. The resulting transport speed matches well with the theoretical prediction.
Models for Dynamic Applications
DEFF Research Database (Denmark)
Sales-Cruz, Mauricio; Morales Rodriguez, Ricardo; Heitzig, Martina;
2011-01-01
This chapter covers aspects of the dynamic modelling and simulation of several complex operations that include a controlled blending tank, a direct methanol fuel cell that incorporates a multiscale model, a fluidised bed reactor, a standard chemical reactor and finally a polymerisation reactor...
Salinelli, Ernesto
2014-01-01
This book provides an introduction to the analysis of discrete dynamical systems. The content is presented by an unitary approach that blends the perspective of mathematical modeling together with the ones of several discipline as Mathematical Analysis, Linear Algebra, Numerical Analysis, Systems Theory and Probability. After a preliminary discussion of several models, the main tools for the study of linear and non-linear scalar dynamical systems are presented, paying particular attention to the stability analysis. Linear difference equations are studied in detail and an elementary introduction of Z and Discrete Fourier Transform is presented. A whole chapter is devoted to the study of bifurcations and chaotic dynamics. One-step vector-valued dynamical systems are the subject of three chapters, where the reader can find the applications to positive systems, Markov chains, networks and search engines. The book is addressed mainly to students in Mathematics, Engineering, Physics, Chemistry, Biology and Economic...
Ghanem, Bernard
2013-01-01
This paper proposes the problem of modeling video sequences of dynamic swarms (DSs). We define a DS as a large layout of stochastically repetitive spatial configurations of dynamic objects (swarm elements) whose motions exhibit local spatiotemporal interdependency and stationarity, i.e., the motions are similar in any small spatiotemporal neighborhood. Examples of DS abound in nature, e.g., herds of animals and flocks of birds. To capture the local spatiotemporal properties of the DS, we present a probabilistic model that learns both the spatial layout of swarm elements (based on low-level image segmentation) and their joint dynamics that are modeled as linear transformations. To this end, a spatiotemporal neighborhood is associated with each swarm element, in which local stationarity is enforced both spatially and temporally. We assume that the prior on the swarm dynamics is distributed according to an MRF in both space and time. Embedding this model in a MAP framework, we iterate between learning the spatial layout of the swarm and its dynamics. We learn the swarm transformations using ICM, which iterates between estimating these transformations and updating their distribution in the spatiotemporal neighborhoods. We demonstrate the validity of our method by conducting experiments on real and synthetic video sequences. Real sequences of birds, geese, robot swarms, and pedestrians evaluate the applicability of our model to real world data. © 2012 Elsevier Inc. All rights reserved.
Kanatsu, Youhei; Sato, Masahide
2015-01-01
Large grains of a close-packed colloidal crystal have been experimentally shown to form in an inverted pyramidal pit by sedimentation [S. Matsuo et al., Appl. Phys. Lett. 82, 4285 (2003)]. Keeping this experiment in mind, we study the crystallization of Brownian particles. We carry out Brownian dynamics simulations in an inverted pyramidal-shaped container. The Brownian particles settle out toward the apex of the container by a uniform external force. If the apex angle is suitable, large grai...
Energy Technology Data Exchange (ETDEWEB)
Davtyan, Aram; Dama, James F.; Voth, Gregory A. [Department of Chemistry, The James Franck Institute, Institute for Biophysical Dynamics, and Computation Institute, The University of Chicago, Chicago, Illinois 60637 (United States); Andersen, Hans C., E-mail: hca@stanford.edu [Department of Chemistry, Stanford University, Stanford, California 94305 (United States)
2015-04-21
Coarse-grained (CG) models of molecular systems, with fewer mechanical degrees of freedom than an all-atom model, are used extensively in chemical physics. It is generally accepted that a coarse-grained model that accurately describes equilibrium structural properties (as a result of having a well constructed CG potential energy function) does not necessarily exhibit appropriate dynamical behavior when simulated using conservative Hamiltonian dynamics for the CG degrees of freedom on the CG potential energy surface. Attempts to develop accurate CG dynamic models usually focus on replacing Hamiltonian motion by stochastic but Markovian dynamics on that surface, such as Langevin or Brownian dynamics. However, depending on the nature of the system and the extent of the coarse-graining, a Markovian dynamics for the CG degrees of freedom may not be appropriate. In this paper, we consider the problem of constructing dynamic CG models within the context of the Multi-Scale Coarse-graining (MS-CG) method of Voth and coworkers. We propose a method of converting a MS-CG model into a dynamic CG model by adding degrees of freedom to it in the form of a small number of fictitious particles that interact with the CG degrees of freedom in simple ways and that are subject to Langevin forces. The dynamic models are members of a class of nonlinear systems interacting with special heat baths that were studied by Zwanzig [J. Stat. Phys. 9, 215 (1973)]. The properties of the fictitious particles can be inferred from analysis of the dynamics of all-atom simulations of the system of interest. This is analogous to the fact that the MS-CG method generates the CG potential from analysis of equilibrium structures observed in all-atom simulation data. The dynamic models generate a non-Markovian dynamics for the CG degrees of freedom, but they can be easily simulated using standard molecular dynamics programs. We present tests of this method on a series of simple examples that demonstrate that
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
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…
Dynamic modelling of windmills
DEFF Research Database (Denmark)
Akhmatov, Vladislav; Knudsen, Hans
1999-01-01
An empirical dynamic model of windmills is set up based on analysis of measured Fourier spectra of the active electric power from a wind farm. The model is based on the assumption that eigenswings of the mechanical construction of the windmills excited by the phenomenon of vortex tower interaction...... will be transferred through the shaft to the electrical generator and result in disturbances of the active electric power supplied by the windmills. The results of the model are found to be in agreement with measurements in the frequency range of the model that is from 0.1 to 10 Hz....
DEFF Research Database (Denmark)
Borregaard, Michael K.; Matthews, Thomas J.; Whittaker, Robert James
2016-01-01
Aim: Island biogeography focuses on understanding the processes that underlie a set of well-described patterns on islands, but it lacks a unified theoretical framework for integrating these processes. The recently proposed general dynamic model (GDM) of oceanic island biogeography offers a step t...
Directory of Open Access Journals (Sweden)
Sorin Dan ŞANDOR
2003-01-01
Full Text Available System Dynamics was introduced by Jay W. Forrester in the 1960s. Since then the methodology was adopted in many areas of natural or social sciences. This article tries to present briefly how this methodology works, both as Systems Thinking and as Modelling with Vensim computer software.
Armbruster, Benjamin
2011-01-01
We analyze random networks that change over time. First we analyze a dynamic Erdos-Renyi model, whose edges change over time. We describe its stationary distribution, its convergence thereto, and the SI contact process on the network, which has relevance for connectivity and the spread of infections. Second, we analyze the effect of node turnover, when nodes enter and leave the network, which has relevance for network models incorporating births, deaths, aging, and other demographic factors.
Dissipative particle dynamics model for colloid transport in porous media
Energy Technology Data Exchange (ETDEWEB)
Pan, W.; Tartakovsky, A. M.
2013-08-01
We present that the transport of colloidal particles in porous media can be effectively modeled with a new formulation of dissipative particle dynamics, which augments standard DPD with non-central dissipative shear forces between particles while preserving angular momentum. Our previous studies have demonstrated that the new formulation is able to capture accurately the drag forces as well as the drag torques on colloidal particles that result from the hydrodynamic retardation effect. In the present work, we use the new formulation to study the contact efficiency in colloid filtration in saturated porous media. Note that the present model include all transport mechanisms simultaneously, including gravitational sedimentation, interception and Brownian diffusion. Our results of contact efficiency show a good agreement with the predictions of the correlation equation proposed by Tufenkji and EliMelech, which also incorporate all transport mechanisms simultaneously without the additivity assumption.
Modal aerosol dynamics modeling
Energy Technology Data Exchange (ETDEWEB)
Whitby, E.R.; McMurry, P.H.; Shankar, U.; Binkowski, F.S.
1991-02-01
The report presents the governing equations for representing aerosol dynamics, based on several different representations of the aerosol size distribution. Analytical and numerical solution techniques for these governing equations are also reviewed. Described in detail is a computationally efficient numerical technique for simulating aerosol behavior in systems undergoing simultaneous heat transfer, fluid flow, and mass transfer in and between the gas and condensed phases. The technique belongs to a general class of models known as modal aerosol dynamics (MAD) models. These models solve for the temporal and spatial evolution of the particle size distribution function. Computational efficiency is achieved by representing the complete aerosol population as a sum of additive overlapping populations (modes), and solving for the time rate of change of integral moments of each mode. Applications of MAD models for simulating aerosol dynamics in continuous stirred tank aerosol reactors and flow aerosol reactors are provided. For the application to flow aerosol reactors, the discussion is developed in terms of considerations for merging a MAD model with the SIMPLER routine described by Patankar (1980). Considerations for incorporating a MAD model into the U.S. Environmental Protection Agency's Regional Particulate Model are also described. Numerical and analytical techniques for evaluating the size-space integrals of the modal dynamics equations (MDEs) are described. For multimodal logonormal distributions, an analytical expression for the coagulation integrals of the MDEs, applicable for all size regimes, is derived, and is within 20% of accurate numerical evaluation of the same moment coagulation integrals. A computationally efficient integration technique, based on Gauss-Hermite numerical integration, is also derived.
Dynamic equivalences in the hard-sphere dynamic universality class.
López-Flores, Leticia; Ruíz-Estrada, Honorina; Chávez-Páez, Martín; Medina-Noyola, Magdaleno
2013-10-01
We perform systematic simulation experiments on model systems with soft-sphere repulsive interactions to test the predicted dynamic equivalence between soft-sphere liquids with similar static structure. For this we compare the simulated dynamics (mean squared displacement, intermediate scattering function, α-relaxation time, etc.) of different soft-sphere systems, between them and with the hard-sphere liquid. We then show that the referred dynamic equivalence does not depend on the (Newtonian or Brownian) nature of the microscopic laws of motion of the constituent particles, and hence, applies independently to colloidal and to atomic simple liquids. Finally, we verify another more recently proposed dynamic equivalence, this time between the long-time dynamics of an atomic liquid and its corresponding Brownian fluid (i.e., the Brownian system with the same interaction potential).
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.
Quantum harmonic Brownian motion in a general environment: A modified phase-space approach
Energy Technology Data Exchange (ETDEWEB)
Yeh, L. [Univ. of California, Berkeley, CA (United States). Dept. of Physics]|[Lawrence Berkeley Lab., CA (United States)
1993-06-23
After extensive investigations over three decades, the linear-coupling model and its equivalents have become the standard microscopic models for quantum harmonic Brownian motion, in which a harmonically bound Brownian particle is coupled to a quantum dissipative heat bath of general type modeled by infinitely many harmonic oscillators. The dynamics of these models have been studied by many authors using the quantum Langevin equation, the path-integral approach, quasi-probability distribution functions (e.g., the Wigner function), etc. However, the quantum Langevin equation is only applicable to some special problems, while other approaches all involve complicated calculations due to the inevitable reduction (i.e., contraction) operation for ignoring/eliminating the degrees of freedom of the heat bath. In this dissertation, the author proposes an improved methodology via a modified phase-space approach which employs the characteristic function (the symplectic Fourier transform of the Wigner function) as the representative of the density operator. This representative is claimed to be the most natural one for performing the reduction, not only because of its simplicity but also because of its manifestation of geometric meaning. Accordingly, it is particularly convenient for studying the time evolution of the Brownian particle with an arbitrary initial state. The power of this characteristic function is illuminated through a detailed study of several physically interesting problems, including the environment-induced damping of quantum interference, the exact quantum Fokker-Planck equations, and the relaxation of non-factorizable initial states. All derivations and calculations axe shown to be much simplified in comparison with other approaches. In addition to dynamical problems, a novel derivation of the fluctuation-dissipation theorem which is valid for all quantum linear systems is presented.
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.
Brownian motion and stochastic calculus
Karatzas, Ioannis
1998-01-01
This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large num...
Inducing Tropical Cyclones to Undergo Brownian Motion
Hodyss, D.; McLay, J.; Moskaitis, J.; Serra, E.
2014-12-01
Stochastic parameterization has become commonplace in numerical weather prediction (NWP) models used for probabilistic prediction. Here, a specific stochastic parameterization will be related to the theory of stochastic differential equations and shown to be affected strongly by the choice of stochastic calculus. From an NWP perspective our focus will be on ameliorating a common trait of the ensemble distributions of tropical cyclone (TC) tracks (or position), namely that they generally contain a bias and an underestimate of the variance. With this trait in mind we present a stochastic track variance inflation parameterization. This parameterization makes use of a properly constructed stochastic advection term that follows a TC and induces its position to undergo Brownian motion. A central characteristic of Brownian motion is that its variance increases with time, which allows for an effective inflation of an ensemble's TC track variance. Using this stochastic parameterization we present a comparison of the behavior of TCs from the perspective of the stochastic calculi of Itô and Stratonovich within an operational NWP model. The central difference between these two perspectives as pertains to TCs is shown to be properly predicted by the stochastic calculus and the Itô correction. In the cases presented here these differences will manifest as overly intense TCs, which, depending on the strength of the forcing, could lead to problems with numerical stability and physical realism.
Dynamic wake meandering modeling
DEFF Research Database (Denmark)
Larsen, Gunner Chr.; Madsen Aagaard, Helge; Bingöl, Ferhat;
, are an integrated part the model complex. For design applications, the computational efficiency of wake deficit prediction is a key issue. Two computationally low cost models are developed for this purpose. The character of the added wake turbulence, generated by the up-stream turbine in the form of shed......We present a consistent, physically based theory for the wake meandering phenomenon, which we consider of crucial importance for the overall description of wind turbine loadings in wind farms. In its present version the model is confined to single wake situations. The model philosophy does, however......, have the potential to include also mutual wake interaction phenomenons. The basic conjecture behind the dynamic wake meandering model is that wake transportation in the atmospheric boundary layer is driven by the large scale lateral- and vertical turbulence components. Based on this conjecture...
Charpentier, Arthur; Durand, Marilou
2015-07-01
In this paper, we investigate questions arising in Parsons and Geist (Bull Seismol Soc Am 102:1-11, 2012). Pseudo causal models connecting magnitudes and waiting times are considered, through generalized regression. We do use conditional model (magnitude given previous waiting time, and conversely) as an extension to joint distribution model described in Nikoloulopoulos and Karlis (Environmetrics 19: 251-269, 2008). On the one hand, we fit a Pareto distribution for earthquake magnitudes, where the tail index is a function of waiting time following previous earthquake; on the other hand, waiting times are modeled using a Gamma or a Weibull distribution, where parameters are functions of the magnitude of the previous earthquake. We use those two models, alternatively, to generate the dynamics of earthquake occurrence, and to estimate the probability of occurrence of several earthquakes within a year or a decade.
Institute of Scientific and Technical Information of China (English)
秦天奇; 王飞; 杨博; 罗懋康
2015-01-01
Based on the theory of fractional integration, direct transport behaviors of coupled Brownian motors with feedback control in viscoelastic media are investigated. The mathematical model of fractional overdamped coupled Brownian motors is established by adopting the power function as damping kernel function of general Langevin equation due to the power-law memory characteristics of cytosol in biological cells. Numerical solution is observed by fractional difference method and the influence of model parameters on cooperative direct transport of the coupled Brownian motors is discussed in detail by numerical simulation. The research shows that the memory of the fractional dynamical system can affect the direct transport phenomenon of the coupled Brownian motors through changing the on-off switching frequency of the ratchet potential with feedback control. To be more specific, in a proper range of the fractional order, the memory of the dynamical system can increase the on-off switching frequency of the ratchet potential, which can lead to the velocity increase of the direct transport. Furthermore, in the case of small fractional order, since the coupled Brownian motors move under the competition between the damping force with memory and the potential force with feedback control, the resultant force exerted on the coupled particles is always positive when the ratchet potential with feedback control is on although the fractional damping force is large, which leads to the result that the coupled Brownian motors move in the positive direction in the mass. On the contrary, in the case of large fractional order, the on-off switching frequency of potential with feedback control becomes small, as a result of which the main influential factor of the direct transport becomes the potential depth. Therefore the coupled Brownian motors are more likely to stay in the potential wells for a long time because the probability that describes the possibility that the coupled Brownian
Østerberg, Frederik W.; Dalslet, Bjarke T.; Snakenborg, Detlef; Johansson, Christer; Hansen, Mikkel F.
2010-12-01
We present a simple `click-on' fluidic system with integrated electrical contacts, which is suited for electrical measurements on chips in microfluidic systems. We show that microscopic magnetic field sensors based on the planar Hall effect can be used for detecting the complex magnetic response using only the self-field arising from the bias current applied to the sensors as excitation field. We present measurements on a suspension of magnetic beads with a nominal diameter of 250 nm vs. temperature and find that the observations are consistent with the Cole-Cole model for Brownian relaxation with a constant hydrodynamic bead diameter when the temperature dependence of the viscosity of water is taken into account. These measurements demonstrate the feasibility of performing measurements of the Brownian relaxation response in a lab-on-a-chip system and constitute the first step towards an integrated biosensor based on the detection of the dynamic response of magnetic beads.
Structural dynamic modifications via models
Indian Academy of Sciences (India)
T K Kundra
2000-06-01
Structural dynamic modification techniques attempt to reduce dynamic design time and can be implemented beginning with spatial models of structures, dynamic test data or updated models. The models assumed in this discussion are mathematical models, namely mass, stiffness, and damping matrices of the equations of motion of a structure. These models are identified/extracted from dynamic test data viz. frequency response functions (FRFs). Alternatively these models could have been obtained by adjusting or updating the finite element model of the structure in the light of the test data. The methods of structural modification for getting desired dynamic characteristics by using modifiers namely mass, beams and tuned absorbers are discussed.
The Fractional Langevin Equation: Brownian Motion Revisited
Mainardi, Francesco
2008-01-01
We have revisited the Brownian motion on the basis of the fractional Langevin equation which turns out to be a particular case of the generalized Langevin equation introduced by Kubo on 1966. The importance of our approach is to model the Brownian motion more realistically than the usual one based on the classical Langevin equation, in that it takes into account also the retarding effects due to hydrodynamic backflow, i.e. the added mass and the Basset memory drag. On the basis of the two fluctuation-dissipation theorems and of the techniques of the Fractional Calculus we have provided the analytical expressions of the correlation functions (both for the random force and the particle velocity) and of the mean squared particle displacement. The random force has been shown to be represented by a superposition of the usual white noise with a "fractional" noise. The velocity correlation function is no longer expressed by a simple exponential but exhibits a slower decay, proportional to $t^{-3/2}$ as $t \\to \\infty...
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.
Molecular Motors: Power Strokes Outperform Brownian Ratchets.
Wagoner, Jason A; Dill, Ken A
2016-07-07
Molecular motors convert chemical energy (typically from ATP hydrolysis) to directed motion and mechanical work. Their actions are often described in terms of "Power Stroke" (PS) and "Brownian Ratchet" (BR) mechanisms. Here, we use a transition-state model and stochastic thermodynamics to describe a range of mechanisms ranging from PS to BR. We incorporate this model into Hill's diagrammatic method to develop a comprehensive model of motor processivity that is simple but sufficiently general to capture the full range of behavior observed for molecular motors. We demonstrate that, under all conditions, PS motors are faster, more powerful, and more efficient at constant velocity than BR motors. We show that these differences are very large for simple motors but become inconsequential for complex motors with additional kinetic barrier steps.
Communication: Green-Kubo approach to the average swim speed in active Brownian systems
Sharma, A.; Brader, J. M.
2016-10-01
We develop an exact Green-Kubo formula relating nonequilibrium averages in systems of interacting active Brownian particles to equilibrium time-correlation functions. The method is applied to calculate the density-dependent average swim speed, which is a key quantity entering coarse grained theories of active matter. The average swim speed is determined by integrating the equilibrium autocorrelation function of the interaction force acting on a tagged particle. Analytical results are validated using Brownian dynamics simulations.
Microtubules: dynamically unstable stochastic phase-switching polymers
Zakharov, P. N.; Arzhanik, V. K.; Ulyanov, E. V.; Gudimchuk, N. B.; Ataullakhanov, F. I.
2016-08-01
One of the simplest molecular motors, a biological microtubule, is reviewed as an example of a highly nonequilibrium molecular machine capable of stochastic transitions between slow growth and rapid disassembly phases. Basic properties of microtubules are described, and various approaches to simulating their dynamics, from statistical chemical kinetics models to molecular dynamics models using the Metropolis Monte Carlo and Brownian dynamics methods, are outlined.
A Langevin model for low density pedestrian dynamics
Corbetta, Alessandro; Lee, Chung-Min; Benzi, Roberto; Muntean, Adrian; Toschi, Federico
The dynamics of pedestrian crowds shares deep connections with statistical physics and fluid dynamics. Reaching a quantitative understanding, not only of the average behaviours but also of the statistics of (rare) fluctuations would have major impact, for instance, on the design and safety of civil infrastructures. A key feature of pedestrian dynamics is its strong intrinsic variability, that we can already observe at the single individual level. In this work we aim at a quantitative characterisation of this statistical variability by studying individual fluctuations. We consider experimental observations of low-density pedestrian flows in a corridor within a building at Eindhoven University of Technology. Few hundreds of thousands of pedestrian trajectories with high space and time resolutions have been collected via a Microsoft Kinect 3D-range sensor and automatic head tracking techniques. From these observations we model pedestrians as active Brownian particles by means of a generalised Langevin equation. With this model we can quantitatively reproduce the observed dynamics including the statistics of ordinary pedestrian fluctuations and of rarer U-turn events. Low density, pair-wise interactions between pedestrians are also discussed.
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.
Campagnoli, Patrizia; Petris, Giovanni
2009-01-01
State space models have gained tremendous popularity in as disparate fields as engineering, economics, genetics and ecology. Introducing general state space models, this book focuses on dynamic linear models, emphasizing their Bayesian analysis. It illustrates the fundamental steps needed to use dynamic linear models in practice, using R package.
de Boer, J.; Hubeny, V.E.; Rangamani, M.; Shigemori, M.
2009-01-01
We study Brownian motion and the associated Langevin equation in AdS/CFT. The Brownian particle is realized in the bulk spacetime as a probe fundamental string in an asymptotically AdS black hole background, stretching between the AdS boundary and the horizon. The modes on the string are excited by
Generalized functionals of Brownian motion
Directory of Open Access Journals (Sweden)
N. U. Ahmed
1994-01-01
Full Text Available In this paper we discuss some recent developments in the theory of generalized functionals of Brownian motion. First we give a brief summary of the Wiener-Ito multiple Integrals. We discuss some of their basic properties, and related functional analysis on Wiener measure space. then we discuss the generalized functionals constructed by Hida. The generalized functionals of Hida are based on L2-Sobolev spaces, thereby, admitting only Hs, s∈R valued kernels in the multiple stochastic integrals. These functionals are much more general than the classical Wiener-Ito class. The more recent development, due to the author, introduces a much more broad class of generalized functionals which are based on Lp-Sobolev spaces admitting kernels from the spaces p,s, s∈R. This allows analysis of a very broad class of nonlinear functionals of Brownian motion, which can not be handled by either the Wiener-Ito class or the Hida class. For s≤0, they represent generalized functionals on the Wiener measure space like Schwarz distributions on finite dimensional spaces. In this paper we also introduce some further generalizations, and construct a locally convex topological vector space of generalized functionals. We also present some discussion on the applications of these results.
Institute of Scientific and Technical Information of China (English)
张晨; 彭婷; 刘宇佳
2015-01-01
文章将广义自回归条件异方差（generalized autoregressive conditional heteroskedasticity ，GARCH ）模型和分形布朗运动结合引入碳金融期权定价研究中。通过对欧洲碳排放配额（European Union Allowance ， EUA）期货收盘价的样本数据检验，发现其存在尖峰厚尾、条件异方差性和分形特征；采用GARCH模型拟合并预测碳价收益率波动率；将预测的波动率作为输入值代入分形布朗运动期权定价方法，运用蒙特卡罗模拟对EUA期货期权进行定价，并与B‐S期权定价法（Black‐Scholes Option Pricing Model）比较。结果表明，基于GARCH分形布朗运动模型的碳期权定价法预测精度有显著提高。%This paper introduces the idea of combining generalized autoregressive conditional heteroskedasticity (GARCH) model and fractional Brownian motion into carbon option pricing .Firstly ,the test results from closing price of European Union Allowance (EUA) Futures show that obvious peak and fat tails ,heterosce‐dasticity and fractal feature reside in the data .Secondly ,the GARCH model is used to fit the volatility of EUA Futures price ,which can reasonably describe and forecast the time‐varying volatility .With the forecas‐ted volatility being the input in fractional Brownian motion carbon option pricing ,the Monte Carlo simulation is used to simulate the pricing of EUA Futures options ,and then the pricing result is compared with that of Black‐Scholes option pricing model .The result shows that carbon option pricing based on fractional Brownian motion combined with GARCH model can improve the pricing accuracy .
Thermal equilibrium of two quantum Brownian particles
Valente, D M
2009-01-01
The influence of the environment in the thermal equilibrium properties of a bipartite continuous variable quantum system is studied. The problem is treated within a system-plus-reservoir approach. The considered model reproduces the conventional Brownian motion when the two particles are far apart and induces an effective interaction between them, depending on the choice of the spectral function of the bath. The coupling between the system and the environment guarantees the translational invariance of the system in the absence of an external potential. The entanglement between the particles is measured by the logarithmic negativity, which is shown to monotonically decrease with the increase of the temperature. A range of finite temperatures is found in which entanglement is still induced by the reservoir.
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.
Asian Option Pricing with Monotonous Transaction Costs under Fractional Brownian Motion
Directory of Open Access Journals (Sweden)
Di Pan
2013-01-01
Full Text Available Geometric-average Asian option pricing model with monotonous transaction cost rate under fractional Brownian motion was established. The method of partial differential equations was used to solve this model and the analytical expressions of the Asian option value were obtained. The numerical experiments show that Hurst exponent of the fractional Brownian motion and transaction cost rate have a significant impact on the option value.
Friston, K J; Harrison, L; Penny, W
2003-08-01
In this paper we present an approach to the identification of nonlinear input-state-output systems. By using a bilinear approximation to the dynamics of interactions among states, the parameters of the implicit causal model reduce to three sets. These comprise (1) parameters that mediate the influence of extrinsic inputs on the states, (2) parameters that mediate intrinsic coupling among the states, and (3) [bilinear] parameters that allow the inputs to modulate that coupling. Identification proceeds in a Bayesian framework given known, deterministic inputs and the observed responses of the system. We developed this approach for the analysis of effective connectivity using experimentally designed inputs and fMRI responses. In this context, the coupling parameters correspond to effective connectivity and the bilinear parameters reflect the changes in connectivity induced by inputs. The ensuing framework allows one to characterise fMRI experiments, conceptually, as an experimental manipulation of integration among brain regions (by contextual or trial-free inputs, like time or attentional set) that is revealed using evoked responses (to perturbations or trial-bound inputs, like stimuli). As with previous analyses of effective connectivity, the focus is on experimentally induced changes in coupling (cf., psychophysiologic interactions). However, unlike previous approaches in neuroimaging, the causal model ascribes responses to designed deterministic inputs, as opposed to treating inputs as unknown and stochastic.
Li, Jin
2011-01-01
In this paper we consider the Stochastic isothermal, nonlinear, incompressible bipolar viscous fluids driven by a genuine cylindrical fractional Bronwnian motion with Hurst parameter $H \\in (1/4,1/2)$ under Dirichlet boundary condition on 2D square domain. First we prove the existence and regularity of the stochastic convolution corresponding to the stochastic non-Newtonian fluids. Then we obtain the existence and uniqueness results for the stochastic non-Newtonian fluids. Under certain condition, the random dynamical system generated by non-Newtonian fluids has a random attractor.
Brownian transport controlled by dichotomic and thermal fluctuations
Kula, J.; Kostur, M.; Łuczka, J.
1998-09-01
We study transport of Brownian particles in spatially periodic structures, driven by both thermal equilibrium fluctuations and dichotomic noise of zero mean values. Introducing specific scaling, we show that the dimensionless Newton-Langevin type equation governing the motion of Brownian particles is very well approximated by the overdamped dynamics; inertial effects can be neglected because for generic systems dimensionless mass is many orders less than a dimensionless friction coefficient. An exact probability current, proportional to the mean drift velocity of particles, is obtained for a piecewise linear spatially periodic potential. We analyze in detail properties of the macroscopic averaged motion of particles. In dependence on statistics of both sources of fluctuations, the directed transport of particles exhibits such distinctive non-monotonic behavior as: bell-shaped dependence (there exists optimal statistics of fluctuations maximizing velocity) and reversal in the direction of macroscopic motion (there exists critical statistics at which the drift velocity is zero).
CNT based thermal Brownian motor to pump water in nanodevices
DEFF Research Database (Denmark)
Oyarzua, Elton; Zambrano, Harvey; Walther, Jens Honore
2016-01-01
Brownian molecular motors are nanoscale machines that exploit thermal fluctuations for directional motion by employing mechanisms such as the Feynman-Smoluchowski ratchet. In this study, using Non Equilibrium Molecular Dynamics, we propose a novel thermal Brownian motor for pumping water through...... Carbon Nanotubes (CNTs). To achieve this we impose a thermal gradient along the axis of a CNT filled with water and impose, in addition, a spatial asymmetry by flxing specific zones on the CNT in order to modify the vibrational modes of the CNT. We find that the temperature gradient and imposed spatial...... asymmetry drive the water ow in a preferential direction. We systematically modified the magnitude of the applied thermal gradient and the axial position of the fixed points. The analysis involves measurement of the vibrational modes in the CNTs using a Fast Fourier Transform (FFT) algorithm. We observed...
Quantum and classical correlations in quantum Brownian motion
Eisert, J; Plenio, M. B.
2001-01-01
We investigate the entanglement properties of the joint state of a distinguished quantum system and its environment in the quantum Brownian motion model. This model is a frequent starting point for investigations of environment-induced superselection. Using recent methods from quantum information theory, we show that there exists a large class of initial states for which no entanglement will be created at all times between the system of salient interest and the environment. If the distinguish...
Florian Ion Tiberiu Petrescu; Relly Victoria Virgil Petrescu
2016-01-01
Otto engine dynamics are similar in almost all common internal combustion engines. We can speak so about dynamics of engines: Lenoir, Otto, and Diesel. The dynamic presented model is simple and original. The first thing necessary in the calculation of Otto engine dynamics, is to determine the inertial mass reduced at the piston. One uses then the Lagrange equation. Kinetic energy conservation shows angular speed variation (from the shaft) with inertial masses. One uses and elastic constant of...
Biased Brownian motion in narrow channels with asymmetry and anisotropy
To, Kiwing; Peng, Zheng
2016-11-01
We study Brownian motion of a single millimeter size bead confined in a quasi-two-dimensional horizontal channel with built-in anisotropy and asymmetry. Channel asymmetry is implemented by ratchet walls while anisotropy is introduced using a channel base that is grooved along the channel axis so that a bead can acquire a horizontal impulse perpendicular to the longitudinal direction when it collides with the base. When energy is injected to the channel by vertical vibration, the combination of asymmetric walls and anisotropic base induces an effective force which drives the bead into biased diffusive motion along the channel axis with diffusivity and drift velocity increase with vibration strength. The magnitude of this driving force, which can be measured in experiments of tilted channel, is found to be consistent to those obtained from dynamic mobility and position probability distribution measurements. These results are explained by a simple collision model that suggests the random kinetic energies transfer between different translational degrees of freedom may be turned into useful work in the presence of asymmetry and anisotropy.
Magnetic dynamics of ferrofluids: mathematical models and experimental investigations
Wu, Kai; Tu, Liang; Su, Diqing; Wang, Jian-Ping
2017-03-01
Magnetite ferrofluids with unique magnetic behaviors are attractive for biomedical applications such as magnetic fluid hyperthermia and magnetic particle imaging. A precise nanoparticle-specific characterization by theoretical models and experiments to predict dynamics of ferrofluids and optimize their behaviors for emerging biomedical applications is necessary. In this paper, combining experiments and modeling, we have uncovered interesting magnetic dynamics of nanoparticles that are dependent on magnetic field strength, polymer coating of nanoparticles, viscosity of ferrofluid, and dipolar interactions. It is concluded that either by changing the magnitude of magnetic field or the concentrations of nanoparticles, we are able to convert the dominating relaxation process of magnetic nanoparticles from Néel to Brownian, and vice versa. Polymer coatings on nanoparticles and viscosity of ferrofluids are demonstrated to have varying degrees of influence on effective relaxation times of nanoparticles with different sizes and under different field strengths. Our theoretical models are used to predict the magnetic response of ferrofluid consisting of 35 nm magnetite nanoparticles under alternating magnetic fields, and it turns out that our theoretical data fits well with the experimental data.
Brownian ratchets in physics and biology
Bier, Martin
1997-06-01
Thirty years ago Feynman et al. presented a paradox in the Lectures on Physics: an imagined device could let Brownian motion do work by allowing it in one direction and blocking it in the opposite direction. In the chapter Feynman et al. eventually show that such ratcheting can only be achieved if there is, in compliance with the basic conservation laws, some energy input from an external source. Now that technology is going into ever smaller dimensions, ratcheting Brownian motion seems to be a real possibility in nanotechnological applications. Furthermore, Brownian motion plays an essential role in the action of motor proteins (individual molecules that convert chemical energy into motion).
Intrinsic dynamics of heart regulatory systems on short time-scales: from experiment to modelling
Khovanov, I A; McClintock, P V E; Stefanovska, A
2009-01-01
We discuss open problems related to the stochastic modeling of cardiac function. The work is based on an experimental investigation of the dynamics of heart rate variability (HRV) in the absence of respiratory perturbations. We consider first the cardiac control system on short time scales via an analysis of HRV within the framework of a random walk approach. Our experiments show that HRV on timescales of less than a minute takes the form of free diffusion, close to Brownian motion, which can be described as a non-stationary process with stationary increments. Secondly, we consider the inverse problem of modeling the state of the control system so as to reproduce the experimentally observed HRV statistics of. We discuss some simple toy models and identify open problems for the modelling of heart dynamics.
The Pricing of Vulnerable Options in a Fractional Brownian Motion Environment
Directory of Open Access Journals (Sweden)
Chao Wang
2015-01-01
Full Text Available Under the assumption of the stock price, interest rate, and default intensity obeying the stochastic differential equation driven by fractional Brownian motion, the jump-diffusion model is established for the financial market in fractional Brownian motion setting. With the changes of measures, the traditional pricing method is simplified and the general pricing formula is obtained for the European vulnerable option with stochastic interest rate. At the same time, the explicit expression for it comes into being.
Zhao, Yu; Wang, Fang; Zhao, Jianing
2015-10-20
Size-resolved deposition rates and Brownian coagulation of particles between 20 and 900 nm (mobility diameter) were estimated in a well-mixed environmental chamber from a gasoline vehicle exhaust with a total peak particle concentration of 10(5)-10(6) particles/cm(3) at 12.24-25.22 °C. A deposition theory with modified friction velocity and coagulation model was also employed to predict particle concentration decay. Initially during particle decay, approximately 85% or more of the particles had diameters of vehicle exhaust particle dynamics and assess human exposure to vehicle particle pollutants in urban areas, tunnels, and underground parking lots.
Institute of Scientific and Technical Information of China (English)
曹玉松
2013-01-01
针对标的资产服从几何布朗运动的期权价格风险问题，通过购买看跌风险降低股票风险，将市场分为风险市场和无风险市场，建立服从几何布朗运动的资本运营过程，使其更加贴近实际情况。讨论了风险市场和无风险市场资本运营的情况，利用随机过程相关知识给出了购买过看跌期权后的期末最终资本的市场价格期望、最终资本的市场价格超过给定值的概率及期末最终损失的期望。所得结论对预防股票风险具有一定的指导意义。% On account of the problem that option price risk of which the underline asset follows the geometric Brownian, the problem of stock hedging through buying a put option is concerned, this paper divided the market into risky market and the risk free market, and built the process of capital operation which follows the geometric Brownian. The model reflects the realities. The problem about capital operation in risky market and the risk free market is studied. Using stochastic process knowledge, the paper obtained the expectation of the final market price of the portfolio, the probability of the final market price of the portfolio which exceeds a give threshold and the expectation of the final risk. This study is useful to prevent the risk of stock.
Analytical studies of Spectrum Broadcast Structures in Quantum Brownian Motion
2016-01-01
Spectrum Broadcast Structures are a new and fresh concept in the quantum-to-classical transition, introduced recently in the context of decoherence and the appearance of objective features in quantum mechanics. These are specific quantum state structures, responsible for an apparent objectivity of a decohered state of a system. Recently they have been shown to appear in the well known Quantum Brownian Motion model, however the final analysis relied on numerics. Here, after a presentation of t...
Fluctuation relations for a driven Brownian particle
Imparato, A.; Peliti, L.
2006-08-01
We consider a driven Brownian particle, subject to both conservative and nonconservative applied forces, whose probability evolves according to the Kramers equation. We derive a general fluctuation relation, expressing the ratio of the probability of a given Brownian path in phase space with that of the time-reversed path, in terms of the entropy flux to the heat reservoir. This fluctuation relation implies those of Seifert, Jarzynski, and Gallavotti-Cohen in different special cases.
Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion
Bodrova, Anna S.; Chechkin, Aleksei V.; Cherstvy, Andrey G.; Safdari, Hadiseh; Sokolov, Igor M.; Metzler, Ralf
2016-07-01
It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.
Computer Modelling of Dynamic Processes
Directory of Open Access Journals (Sweden)
B. Rybakin
2000-10-01
Full Text Available Results of numerical modeling of dynamic problems are summed in the article up. These problems are characteristic for various areas of human activity, in particular for problem solving in ecology. The following problems are considered in the present work: computer modeling of dynamic effects on elastic-plastic bodies, calculation and determination of performances of gas streams in gas cleaning equipment, modeling of biogas formation processes.
On a nonstandard Brownian motion and its maximal function
Andrade, Bernardo B. de
2015-07-01
This article uses Radically Elementary Probability Theory (REPT) to prove results about the Wiener walk (the radically elementary Brownian motion) without the technical apparatus required by stochastic integration. The techniques used replace measure-theoretic tools by discrete probability and the rigorous use of infinitesimals. Specifically, REPT is applied to the results in Palacios (The American Statistician, 2008) to calculate certain expectations related to the Wiener walk and its maximal function. Because Palacios uses mostly combinatorics and no measure theory his results carry over through REPT with minimal changes. The paper also presents a construction of the Wiener walk which is intended to mimic the construction of Brownian motion from "continuous" white noise. A brief review of the nonstandard model on which REPT is based is given in the Appendix in order to minimize the need for previous exposure to the subject.
Reflected Brownian motions in the KPZ universality class
Weiss, Thomas; Spohn, Herbert
2017-01-01
This book presents a detailed study of a system of interacting Brownian motions in one dimension. The interaction is point-like such that the n-th Brownian motion is reflected from the Brownian motion with label n-1. This model belongs to the Kardar-Parisi-Zhang (KPZ) universality class. In fact, because of the singular interaction, many universal properties can be established with rigor. They depend on the choice of initial conditions. Discussion addresses packed and periodic initial conditions (Chapter 5), stationary initial conditions (Chapter 6), and mixtures thereof (Chapter 7). The suitably scaled spatial process will be proven to converge to an Airy process in the long time limit. A chapter on determinantal random fields and another one on Airy processes are added to have the notes self-contained. These notes serve as an introduction to the KPZ universality class, illustrating the main concepts by means of a single model only. The notes will be of interest to readers from interacting diffusion processe...
Brownian 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.
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.
Launch Vehicle Dynamics Demonstrator Model
1963-01-01
Launch Vehicle Dynamics Demonstrator Model. The effect of vibration on launch vehicle dynamics was studied. Conditions included three modes of instability. The film includes close up views of the simulator fuel tank with and without stability control. [Entire movie available on DVD from CASI as Doc ID 20070030984. Contact help@sti.nasa.gov
Fractal Models of Earthquake Dynamics
Bhattacharya, Pathikrit; Kamal,; Samanta, Debashis
2009-01-01
Our understanding of earthquakes is based on the theory of plate tectonics. Earthquake dynamics is the study of the interactions of plates (solid disjoint parts of the lithosphere) which produce seismic activity. Over the last about fifty years many models have come up which try to simulate seismic activity by mimicking plate plate interactions. The validity of a given model is subject to the compliance of the synthetic seismic activity it produces to the well known empirical laws which describe the statistical features of observed seismic activity. Here we present a review of two such models of earthquake dynamics with main focus on a relatively new model namely The Two Fractal Overlap Model.
Brownian dynamics of confined rigid bodies
Energy Technology Data Exchange (ETDEWEB)
Delong, Steven; Balboa Usabiaga, Florencio; Donev, Aleksandar, E-mail: donev@courant.nyu.edu [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
2015-10-14
We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust, space efficient, and easy to accumulate. We construct a system of overdamped Langevin equations in the quaternion representation that accounts for hydrodynamic effects, preserves the unit-norm constraint on the quaternion, and is time reversible with respect to the Gibbs-Boltzmann distribution at equilibrium. We introduce two schemes for temporal integration of the overdamped Langevin equations of motion, one based on the Fixman midpoint method and the other based on a random finite difference approach, both of which ensure that the correct stochastic drift term is captured in a computationally efficient way. We study several examples of rigid colloidal particles diffusing near a no-slip boundary and demonstrate the importance of the choice of tracking point on the measured translational mean square displacement (MSD). We examine the average short-time as well as the long-time quasi-two-dimensional diffusion coefficient of a rigid particle sedimented near a bottom wall due to gravity. For several particle shapes, we find a choice of tracking point that makes the MSD essentially linear with time, allowing us to estimate the long-time diffusion coefficient efficiently using a Monte Carlo method. However, in general, such a special choice of tracking point does not exist, and numerical techniques for simulating long trajectories, such as the ones we introduce here, are necessary to study diffusion on long time scales.
Dynamic programming models and applications
Denardo, Eric V
2003-01-01
Introduction to sequential decision processes covers use of dynamic programming in studying models of resource allocation, methods for approximating solutions of control problems in continuous time, production control, more. 1982 edition.
Building dynamic spatial environmental models
Karssenberg, D.J.
2003-01-01
An environmental model is a representation or imitation of complex natural phenomena that can be discerned by human cognitive processes. This thesis deals with the type of environmental models referred to as dynamic spatial environmental models. The word spatial refers to the geographic domain whi
Dynamical models of the Galaxy
Directory of Open Access Journals (Sweden)
McMillan P.J.
2012-02-01
Full Text Available I discuss the importance of dynamical models for exploiting survey data, focusing on the advantages of “torus” models. I summarize a number of applications of these models to the study of the Milky Way, including the determination of the peculiar Solar velocity and investigation of the Hyades moving group.
DEFF Research Database (Denmark)
Knudsen, Torben
2011-01-01
The purpose with this deliverable 2.5 is to use fresh experimental data for validation and selection of a flow model to be used for control design in WP3-4. Initially the idea was to investigate the models developed in WP2. However, in the project it was agreed to include and focus on a additive...... model turns out not to be useful for prediction of the flow. Moreover, standard Box Jenkins model structures and multiple output auto regressive models proves to be superior as they can give useful predictions of the flow....
Adams, Neil S.; Bollenbacher, Gary
1992-01-01
This report discusses the development and underlying mathematics of a rigid-body computer model of a proposed cryogenic on-orbit liquid depot storage, acquisition, and transfer spacecraft (COLD-SAT). This model, referred to in this report as the COLD-SAT dynamic model, consists of both a trajectory model and an attitudinal model. All disturbance forces and torques expected to be significant for the actual COLD-SAT spacecraft are modeled to the required degree of accuracy. Control and experimental thrusters are modeled, as well as fluid slosh. The model also computes microgravity disturbance accelerations at any specified point in the spacecraft. The model was developed by using the Boeing EASY5 dynamic analysis package and will run on Apollo, Cray, and other computing platforms.
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...
A parity breaking Ising chain Hamiltonian as a Brownian motor
Cornu, F.; Hilhorst, H. J.
2014-10-01
We consider the translationally invariant but parity (left-right symmetry) breaking Ising chain Hamiltonian {\\cal H} =-{U_2}\\sumk sksk+1 - {U_3}\\sumk sksk+1sk+3 and let this system evolve by Kawasaki spin exchange dynamics. Monte Carlo simulations show that perturbations forcing this system off equilibrium make it act as a Brownian molecular motor which, in the lattice gas interpretation, transports particles along the chain. We determine the particle current under various different circumstances, in particular as a function of the ratio {U_3}/{U_2} and of the conserved magnetization M=\\sum_ksk . The symmetry of the U3 term in the Hamiltonian is discussed.
Energy Technology Data Exchange (ETDEWEB)
Jumarie, Guy E-mail: jumarie.guy@uqam.ca
2004-11-01
There are presently two different models of fractional Brownian motions available in the literature: the Riemann-Liouville fractional derivative of white noise on the one hand, and the complex-valued Brownian motion of order n defined by using a random walk in the complex plane, on the other hand. The paper provides a comparison between these two approaches, and in addition, takes this opportunity to contribute some complements. These two models are more or less equivalent on the theoretical standpoint for fractional order between 0 and 1/2, but their practical significances are quite different. Otherwise, for order larger than 1/2, the fractional derivative model has no counterpart in the complex plane. These differences are illustrated by an example drawn from mathematical finance. Taylor expansion of fractional order provides the expression of fractional difference in terms of finite difference, and this allows us to improve the derivation of Fokker-Planck equation and Kramers-Moyal expansion, and to get more insight in their relation with stochastic differential equations of fractional order. In the case of multi-fractal systems, the Fokker-Planck equation can be solved by using path integrals, and the fractional dynamic equations of the state moments of the stochastic system can be easily obtained. By combining fractional derivative and complex white noise of order n, one obtains a family of complex-valued fractional Brownian motions which exhibits long-range dependence. The conclusion outlines suggestions for further research, mainly regarding Lorentz transformation of fractional noises.
A CONTINUUM HARD-SPHERE MODEL OF PROTEIN ADSORPTION.
Finch, Craig; Clarke, Thomas; Hickman, James J
2013-07-01
Protein adsorption plays a significant role in biological phenomena such as cell-surface interactions and the coagulation of blood. Two-dimensional random sequential adsorption (RSA) models are widely used to model the adsorption of proteins on solid surfaces. Continuum equations have been developed so that the results of RSA simulations can be used to predict the kinetics of adsorption. Recently, Brownian dynamics simulations have become popular for modeling protein adsorption. In this work a continuum model was developed to allow the results from a Brownian dynamics simulation to be used as the boundary condition in a computational fluid dynamics (CFD) simulation. Brownian dynamics simulations were used to model the diffusive transport of hard-sphere particles in a liquid and the adsorption of the particles onto a solid surface. The configuration of the adsorbed particles was analyzed to quantify the chemical potential near the surface, which was found to be a function of the distance from the surface and the fractional surface coverage. The near-surface chemical potential was used to derive a continuum model of adsorption that incorporates the results from the Brownian dynamics simulations. The equations of the continuum model were discretized and coupled to a CFD simulation of diffusive transport to the surface. The kinetics of adsorption predicted by the continuum model closely matched the results from the Brownian dynamics simulation. This new model allows the results from mesoscale simulations to be incorporated into micro- or macro-scale CFD transport simulations of protein adsorption in practical devices.
Berg, van den, Aad; Meester, R.; White, Damien
1997-01-01
Consider an ordinary Boolean model, that is, a homogeneous Poisson point process in Rd, where the points are all centres of random balls with i.i.d. radii. Now let these points move around according to i.i.d. stochastic processes. It is not hard to show that at each xed time t we again have a Boolean model with the original distribution. Hence if the original model is supercritical then, for any t, the probability of having an unbounded occupied component at time t equals 1. We show that unde...
Free energy and entropy production rate for a Brownian particle that walks on overdamped medium
Taye, Mesfin Asfaw
2016-09-01
We derive general expressions for the free energy, entropy production, and entropy extraction rates for a Brownian particle that walks in a viscous medium where the dynamics of its motion is governed by the Langevin equation. It is shown that, when the system is out of equilibrium, it constantly produces entropy and at the same time extracts entropy out of the system. Its entropy production and extraction rates decrease in time and saturate to a constant value. In the long-time limit, the rate of entropy production balances the rate of entropy extraction and, at equilibrium, both entropy production and extraction rates become zero. Moreover, considering different model systems, not only do we investigate how various thermodynamic quantities behave in time but also we discuss the fluctuation theorem in detail.
Chechkin, A V; Metzler, R; Sokolov, I M
2016-01-01
A growing number of biological, soft, and active matter systems are observed to exhibit normal diffusive dynamics with a linear growth of the mean squared displacement, yet with a non-Gaussian distribution of increments. Based on the Chubinsky-Slater idea of a diffusing diffusivity we here establish and analyse a complete minimal model framework of diffusion processes with fluctuating diffusivity. In particular, we demonstrate the equivalence of the diffusing diffusivity process in the short time limit with a superstatistical approach based on a distribution of diffusivities. Moreover, we establish a subordination picture of Brownian but non-Gaussian diffusion processes, that can be used for a wide class of diffusivity fluctuation statistics. Our results are shown to be in excellent agreement with simulations and numerical evaluations.
Gabora, Liane
2008-01-01
EVOC (for EVOlution of Culture) is a computer model of culture that enables us to investigate how various factors such as barriers to cultural diffusion, the presence and choice of leaders, or changes in the ratio of innovation to imitation affect the diversity and effectiveness of ideas. It consists of neural network based agents that invent ideas for actions, and imitate neighbors' actions. The model is based on a theory of culture according to which what evolves through culture is not memes or artifacts, but the internal models of the world that give rise to them, and they evolve not through a Darwinian process of competitive exclusion but a Lamarckian process involving exchange of innovation protocols. EVOC shows an increase in mean fitness of actions over time, and an increase and then decrease in the diversity of actions. Diversity of actions is positively correlated with population size and density, and with barriers between populations. Slowly eroding borders increase fitness without sacrificing diver...
Institute of Scientific and Technical Information of China (English)
杨朝强
2013-01-01
利用混合分数布朗运动的Itó公式和复合泊松过程驱动的随机微分方程,建立了一类混合跳-扩散分数布朗运动环境下的价格模型,在Merton假设条件下对其随机微分方程的Cauchy初值问题采用迭代法作了估计,得到了混合跳-扩散模型下的欧式看跌期权定价的Merton公式,从而给出了混合跳-扩散分数布朗运动欧式浮动履约价的看涨回望期权和看跌回望期权定价公式.%The mixed jump-diffusion fractional Brownian motion model under the Itó formula and fractional diffusion process with non-homogeneous Poisson process was proposed.By using the iterative method,the Cauchy initial problem of stochastic differential equations were estimated under the conditions of Merton assumptions.Then the pricing Merton-formula of European option that meets the pricing model for the European floating strike price of the lookback option was obtained.Finally the pricing formulas of floating strike lookback call option and lookback put option were proofed.
Model of THz Magnetization Dynamics
Bocklage, Lars
2016-01-01
Magnetization dynamics can be coherently controlled by THz laser excitation, which can be applied in ultrafast magnetization control and switching. Here, transient magnetization dynamics are calculated for excitation with THz magnetic field pulses. We use the ansatz of Smit and Beljers, to formulate dynamic properties of the magnetization via partial derivatives of the samples free energy density, and extend it to solve the Landau-Lifshitz-equation to obtain the THz transients of the magnetization. The model is used to determine the magnetization response to ultrafast multi- and single-cycle THz pulses. Control of the magnetization trajectory by utilizing the THz pulse shape and polarization is demonstrated. PMID:26956997
Modeling Internet Topology Dynamics
Haddadi, H.; Uhlig, S.; Moore, A.; Mortier, R.; Rio, M.
Despite the large number of papers on network topology modeling and inference, there still exists ambiguity about the real nature of the Internet AS and router level topology. While recent findings have illustrated the inaccuracies in maps inferred from BGP peering and traceroute measurements, exist
Dynamic analysis of polymeric fluid in shear flow for dumbbell model with internal viscosity
Institute of Scientific and Technical Information of China (English)
杨晓东; R.V.N.MELNIK
2008-01-01
The dynamic analysis of semi-flexible polymers,such as DNA molecules,is an important multiscale problem with a wide range of applications in science and bioengineering.In this contribution,a dumbbell model with internal viscosity was studied in steady shear flows of polymeric fluid.The tensors with moments other than second moment were approximated in the terms of second moment tensor.Then,the nonlinear algebraic equation of the second moment conformation tensor was calculated in closed form.Finally,substituting the resulting conformation tensor into the Kramers equation of Hookean spring force,the constitutive equations were obtained.The shear material properties were discussed for different internal viscosities and compared with the results of Brownian dynamics simulation.
Vehicle dynamics modeling and simulation
Schramm, Dieter; Bardini, Roberto
2014-01-01
The authors examine in detail the fundamentals and mathematical descriptions of the dynamics of automobiles. In this context different levels of complexity will be presented, starting with basic single-track models up to complex three-dimensional multi-body models. A particular focus is on the process of establishing mathematical models on the basis of real cars and the validation of simulation results. The methods presented are explained in detail by means of selected application scenarios.
Brownian semistationary processes and conditional full support
Pakkanen, Mikko S
2010-01-01
In this note, we study the infinite-dimensional conditional laws of Brownian semistationary processes. Motivated by the fact that these processes are typically not semimartingales, we present sufficient conditions ensuring that a Brownian semistationary process has conditional full support, a property introduced by Guasoni, R\\'asonyi, and Schachermayer [Ann. Appl. Probab., 18 (2008) pp. 491--520]. By the results of Guasoni, R\\'asonyi, and Schachermayer, this property has two important implications. It ensures, firstly, that the process admits no free lunches under proportional transaction costs, and secondly, that it can be approximated pathwise (in the sup norm) by semimartingales that admit equivalent martingale measures.
Diffusion of torqued active Brownian particles
Sevilla, Francisco J.
An analytical approach is used to study the diffusion of active Brownian particles that move at constant speed in three-dimensional space, under the influence of passive (external) and active (internal) torques. The Smoluchowski equation for the position distribution of the particles is obtained from the Kramer-Fokker-Planck equation corresponding to Langevin equations for active Brownian particles subject to torques. In addition of giving explicit formulas for the mean square-displacement, the non-Gaussian behavior is analyzed through the kurtosis of the position distribution that exhibits an oscillatory behavior in the short-time limit. FJS acknowledges support from PAPIIT-UNAM through the grant IN113114
Holographic Brownian Motion in Three-Dimensional Gödel Black Hole
Directory of Open Access Journals (Sweden)
J. Sadeghi
2014-01-01
Full Text Available By using the AdS/CFT correspondence and Gödel black hole background, we study the dynamics of heavy quark under a rotating plasma. In that case we follow Atmaja (2013 about Brownian motion in BTZ black hole. In this paper we receive some new results for the case of α2l2≠1. In this case, we must redefine the angular velocity of string fluctuation. We obtain the time evolution of displacement square and angular velocity and show that it behaves as a Brownian particle in non relativistic limit. In this plasma, it seems that relating the Brownian motion to physical observables is rather a difficult work. But our results match with Atmaja work in the limit α2l2→1.
Financial Brownian Particle in the Layered Order-Book Fluid and Fluctuation-Dissipation Relations
Yura, Yoshihiro; Takayasu, Hideki; Sornette, Didier; Takayasu, Misako
2014-03-01
We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of comprehensive market data enables us to identify all motions of the fluid particles. Correlations between the motions of the Brownian particle and its surrounding fluid particles reflect specific layering interactions; in the inner layer the correlation is strong and with short memory, while in the outer layer it is weaker and with long memory. By interpreting and estimating the contribution from the outer layer as a drag resistance, we demonstrate the validity of the fluctuation-dissipation relation in this nonmaterial Brownian motion process.
Random functions via Dyson Brownian Motion: progress and problems
Energy Technology Data Exchange (ETDEWEB)
Wang, Gaoyuan; Battefeld, Thorsten [Institute for Astrophysics, University of Goettingen,Friedrich Hund Platz 1, D-37077 Goettingen (Germany)
2016-09-05
We develope a computationally efficient extension of the Dyson Brownian Motion (DBM) algorithm to generate random function in C{sup 2} locally. We further explain that random functions generated via DBM show an unstable growth as the traversed distance increases. This feature restricts the use of such functions considerably if they are to be used to model globally defined ones. The latter is the case if one uses random functions to model landscapes in string theory. We provide a concrete example, based on a simple axionic potential often used in cosmology, to highlight this problem and also offer an ad hoc modification of DBM that suppresses this growth to some degree.
Non-Markovian quantum Brownian motion of a harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Tang, J.
1994-02-01
We apply the density-matrix method to the study of quantum Brownian motion of a harmonic oscillator coupled to a heat bath, a system investigated previously by Caldeira and Leggett using a different method. Unlike the earlier work, in our derivation of the master equation the non-Markovian terms are maintained. Although the same model of interaction is used, discrepancy is found between their results and our equation in the Markovian limit. We also point out that the particular interaction model used by both works cannot lead to the phenomenological generalized Langevin theory of Kubo.
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.
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).
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.
Energy Technology Data Exchange (ETDEWEB)
Pfeffer, A; Das, S; Lawless, D; Ng, B
2006-10-10
Many dynamic systems involve a number of entities that are largely independent of each other but interact with each other via a subset of state variables. We present global/local dynamic models (GLDMs) to capture these kinds of systems. In a GLDM, the state of an entity is decomposed into a globally influenced state that depends on other entities, and a locally influenced state that depends only on the entity itself. We present an inference algorithm for GLDMs called global/local particle filtering, that introduces the principle of reasoning globally about global dynamics and locally about local dynamics. We have applied GLDMs to an asymmetric urban warfare environment, in which enemy units form teams to attack important targets, and the task is to detect such teams as they form. Experimental results for this application show that global/local particle filtering outperforms ordinary particle filtering and factored particle filtering.
A dynamical model of terrorism
Directory of Open Access Journals (Sweden)
Firdaus Udwadia
2006-01-01
Full Text Available This paper develops a dynamical model of terrorism. We consider the population in a given region as being made up of three primary components: terrorists, those susceptible to both terrorist and pacifist propaganda, and nonsusceptibles, or pacifists. The dynamical behavior of these three populations is studied using a model that incorporates the effects of both direct military/police intervention to reduce the terrorist population, and nonviolent, persuasive intervention to influence the susceptibles to become pacifists. The paper proposes a new paradigm for studying terrorism, and looks at the long-term dynamical evolution in time of these three population components when such interventions are carried out. Many important features—some intuitive, others not nearly so—of the nature of terrorism emerge from the dynamical model proposed, and they lead to several important policy implications for the management of terrorism. The different circumstances in which nonviolent intervention and/or military/police intervention may be beneficial, and the specific conditions under which each mode of intervention, or a combination of both, may be useful, are obtained. The novelty of the model presented herein is that it deals with the time evolution of terrorist activity. It appears to be one of the few models that can be tested, evaluated, and improved upon, through the use of actual field data.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Agusdinata, Datu Buyung, E-mail: bagusdinata@niu.edu; Amouie, Mahbod [Northern Illinois University, Department of Industrial & Systems Engineering and Environment, Sustainability, & Energy Institute (United States); Xu, Tao [Northern Illinois University, Department of Chemistry and Biochemistry (United States)
2015-01-15
Due to their favorable electrical and optical properties, quantum dots (QDs) nanostructures have found numerous applications including nanomedicine and photovoltaic cells. However, increased future production, use, and disposal of engineered QD products also raise concerns about their potential environmental impacts. The objective of this work is to establish a modeling framework for predicting the diffusion dynamics and concentration of toxic materials released from Trioctylphosphine oxide-capped CdSe. To this end, an agent-based model simulation with reaction kinetics and Brownian motion dynamics was developed. Reaction kinetics is used to model the stability of surface capping agent particularly due to oxidation process. The diffusion of toxic Cd{sup 2+} ions in aquatic environment was simulated using an adapted Brownian motion algorithm. A calibrated parameter to reflect sensitivity to reaction rate is proposed. The model output demonstrates the stochastic spatial distribution of toxic Cd{sup 2+} ions under different values of proxy environmental factor parameters. With the only chemistry considered was oxidation, the simulation was able to replicate Cd{sup 2+} ion release from Thiol-capped QDs in aerated water. The agent-based method is the first to be developed in the QDs application domain. It adds both simplicity of the solubility and rate of release of Cd{sup 2+} ions and complexity of tracking of individual atoms of Cd at the same time.
Brownian coagulation at high particle concentrations
Trzeciak, T. M.
2012-01-01
The process of Brownian coagulation, whereby particles are brought together by thermal motion and grow by collisions, is one of the most fundamental processes influencing the final properties of particulate matter in a variety of technically important systems. It is of importance in colloids, emulsi
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 ap...
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.
Directory of Open Access Journals (Sweden)
Florian Ion Tiberiu Petrescu
2016-03-01
Full Text Available Otto engine dynamics are similar in almost all common internal combustion engines. We can speak so about dynamics of engines: Lenoir, Otto, and Diesel. The dynamic presented model is simple and original. The first thing necessary in the calculation of Otto engine dynamics, is to determine the inertial mass reduced at the piston. One uses then the Lagrange equation. Kinetic energy conservation shows angular speed variation (from the shaft with inertial masses. One uses and elastic constant of the crank shaft, k. Calculations should be made for an engine with a single cylinder. Finally it makes a dynamic analysis of the mechanism with discussion and conclusions. The ratio between the crank length r and the length of the connecting-rod l is noted with landa. When landa increases the mechanism dynamics is deteriorating. For a proper operation is necessary the reduction of the ratio landa, especially if we want to increase the engine speed. We can reduce the acceleration values by reducing the dimensions r and l.
DYNAMIC TEACHING RATIO PEDAGOGIC MODEL
Directory of Open Access Journals (Sweden)
Chen Jiaying
2010-11-01
Full Text Available This paper outlines an innovative pedagogic model, Dynamic Teaching Ratio (DTR Pedagogic Model, for learning design and teaching strategy aimed at the postsecondary technical education. The model draws on the theory of differential learning, which is widely recognized as an important tool for engaging students and addressing the individual needs of all students. The DTR model caters to the different abilities, interest or learning needs of students and provides different learning approaches based on a student’s learning ability. The model aims to improve students’ academic performance through increasing the lecturer-to-student ratio in the classroom setting. An experimental case study on the model was conducted and the outcome was favourable. Hence, a large-scale implementation was carried out upon the successful trial run. The paper discusses the methodology of the model and its application through the case study and the large-scale implementation.
Business model dynamics and innovation
DEFF Research Database (Denmark)
Cavalcante, Sergio Andre; Kesting, Peter; Ulhøi, John Parm
2011-01-01
and routine research into the concept of business model. The main focus of the paper is on strategic and terminological issues. Findings – The paper offers a new, process-based conceptualization of business model, which recognizes and integrates the role of individual agency. Based on this, it distinguishes......Purpose – This paper aims to discuss the need to dynamize the existing conceptualization of business model, and proposes a new typology to distinguish different types of business model change. Design/methodology/approach – The paper integrates basic insights of innovation, business process...... and specifies four different types of business model change: business model creation, extension, revision, and termination. Each type of business model change is associated with specific challenges. Practical implications – The proposed typology can serve as a basis for developing a management tool to evaluate...
DYNAMIC MODELING OF METAMORPHIC MECHANISM
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The concept of metamorphic mechanism is put forward according to the change of configurations from one state to another. Different configurations of metamorphic mechanism are described through the method of Huston lower body arrays. Kinematics analyses for metamorphic mechanism with generalized topological structure, including the velocity, angular velocity, acceleration and angular acceleration, are given. Dynamic equations for an arbitrary configuration, including close-loop constraints, are formed by using Kane's equations. For an arbitrary metamorphic mechanism, the transformation matrix of generalized speeds between configuration (*)and(*)+1 is obtained for the first time. Furthermore, configuration-complete dynamic modeling of metamorphic mechanism including all configurations is completely established.
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
Survival probability of mutually killing Brownian motions and the O'Connell process
Katori, Makoto
2011-01-01
Recently O'Connell introduced an interacting diffusive particle system in order to study a directed polymer model in 1+1 dimensions. The infinitesimal generator of the process is a harmonic transform of the quantum Toda-lattice Hamiltonian by the Whittaker function. As a physical interpretation of this construction, we show that the O'Connell process without drift is realized as a system of mutually killing Brownian motions conditioned that all particles survive forever. When the characteristic length of interaction killing other particles goes to zero, the process is reduced to the noncolliding Brownian motion (the Dyson model).
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.
Modelling group dynamic animal movement
DEFF Research Database (Denmark)
Langrock, Roland; Hopcraft, J. Grant C.; Blackwell, Paul G.;
2014-01-01
Group dynamic movement is a fundamental aspect of many species' movements. The need to adequately model individuals' interactions with other group members has been recognised, particularly in order to differentiate the role of social forces in individual movement from environmental factors. However...... makes its movement decisions relative to the group centroid. The basic idea is framed within the flexible class of hidden Markov models, extending previous work on modelling animal movement by means of multi-state random walks. While in simulation experiments parameter estimators exhibit some bias...
Dynamic Model of Mesoscale Eddies
Dubovikov, Mikhail S.
2003-04-01
Oceanic mesoscale eddies which are analogs of well known synoptic eddies (cyclones and anticyclones), are studied on the basis of the turbulence model originated by Dubovikov (Dubovikov, M.S., "Dynamical model of turbulent eddies", Int. J. Mod. Phys.B7, 4631-4645 (1993).) and further developed by Canuto and Dubovikov (Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: I. General formalism", Phys. Fluids8, 571-586 (1996a) (CD96a); Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: II. Sheardriven flows", Phys. Fluids8, 587-598 (1996b) (CD96b); Canuto, V.M., Dubovikov, M.S., Cheng, Y. and Dienstfrey, A., "A dynamical model for turbulence: III. Numerical results", Phys. Fluids8, 599-613 (1996c)(CD96c); Canuto, V.M., Dubovikov, M.S. and Dienstfrey, A., "A dynamical model for turbulence: IV. Buoyancy-driven flows", Phys. Fluids9, 2118-2131 (1997a) (CD97a); Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: V. The effect of rotation", Phys. Fluids9, 2132-2140 (1997b) (CD97b); Canuto, V.M., Dubovikov, M.S. and Wielaard, D.J., "A dynamical model for turbulence: VI. Two dimensional turbulence", Phys. Fluids9, 2141-2147 (1997c) (CD97c); Canuto, V.M. and Dubovikov, M.S., "Physical regimes and dimensional structure of rotating turbulence", Phys. Rev. Lett. 78, 666-669 (1997d) (CD97d); Canuto, V.M., Dubovikov, M.S. and Dienstfrey, A., "Turbulent convection in a spectral model", Phys. Rev. Lett. 78, 662-665 (1997e) (CD97e); Canuto, V.M. and Dubovikov, M.S., "A new approach to turbulence", Int. J. Mod. Phys.12, 3121-3152 (1997f) (CD97f); Canuto, V.M. and Dubovikov, M.S., "Two scaling regimes for rotating Raleigh-Benard convection", Phys. Rev. Letters78, 281-284, (1998) (CD98); Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: VII. The five invariants for shear driven flows", Phys. Fluids11, 659-664 (1999a) (CD99a); Canuto, V.M., Dubovikov, M.S. and Yu, G., "A dynamical model for turbulence: VIII. IR and UV
CNT based thermal Brownian motor to pump water in nanodevices
Oyarzua, Elton; Zambrano, Harvey; Walther, J. H.
2016-11-01
Brownian molecular motors are nanoscale machines that exploit thermal fluctuations for directional motion by employing mechanisms such as the Feynman-Smoluchowski ratchet. In this study, using Non Equilibrium Molecular Dynamics, we propose a novel thermal Brownian motor for pumping water through Carbon Nanotubes (CNTs). To achieve this we impose a thermal gradient along the axis of a CNT filled with water and impose, in addition, a spatial asymmetry by fixing specific zones on the CNT in order to modify the vibrational modes of the CNT. We find that the temperature gradient and imposed spatial asymmetry drive the water flow in a preferential direction. We systematically modified the magnitude of the applied thermal gradient and the axial position of the fixed points. The analysis involves measurement of the vibrational modes in the CNTs using a Fast Fourier Transform (FFT) algorithm. We observed water flow in CNTs of 0.94, 1.4 and 2.0 nm in diameter, reaching a maximum velocity of 5 m/s for a thermal gradient of 3.3 K/nm. The proposed thermal motor is capable of delivering a continuous flow throughout a CNT, providing a useful tool for driving liquids in nanofluidic devices by exploiting thermal gradients. We aknowledge partial support from Fondecyt project 11130559.
Berardi, Marco; Andrisani, Andrea; Lopez, Luciano; Vurro, Michele
2016-11-01
In this paper a new data assimilation technique is proposed which is based on the ensemble Kalman filter (EnKF). Such a technique will be effective if few observations of a dynamical system are available and a large model error occurs. The idea is to acquire a fine grid of synthetic observations in two steps: (1) first we interpolate the real observations with suitable polynomial curves; (2) then we estimate the relative measurement errors by means of Brownian bridges. This technique has been tested on the Richards' equation, which governs the water flow in unsaturated soils, where a large model error has been introduced by solving the Richards' equation by means of an explicit numerical scheme. The application of this technique to some synthetic experiments has shown improvements with respect to the classical ensemble Kalman filter, in particular for problems with a large model error.
Dynamics Modeling of Heavy Special Driving Simulator
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Based on the dynamical characteristic parameters of the real vehicle, the modeling approach and procedure of dynamics of vehicles are expatiated. The layout of vehicle dynamics is proposed, and the sub-models of the diesel engine, drivetrain system and vehicle multi-body dynamics are introduced. Finally, the running characteristic data of the virtual and real vehicles are compared, which shows that the dynamics model is similar closely to the real vehicle system.
Energy Technology Data Exchange (ETDEWEB)
Radiom, Milad, E-mail: milad.radiom@unige.ch; Ducker, William, E-mail: wducker@vt.edu [Department of Chemical Engineering, Virginia Tech, Blacksburg, Virginia 24060 (United States); Robbins, Brian; Paul, Mark [Department of Mechanical Engineering, Virginia Tech, Blacksburg, Virginia 24060 (United States)
2015-02-15
The hydrodynamic interaction of two closely spaced micron-scale spheres undergoing Brownian motion was measured as a function of their separation. Each sphere was attached to the distal end of a different atomic force microscopy cantilever, placing each sphere in a stiff one-dimensional potential (0.08 Nm{sup −1}) with a high frequency of thermal oscillations (resonance at 4 kHz). As a result, the sphere’s inertial and restoring forces were significant when compared to the force due to viscous drag. We explored interparticle gap regions where there was overlap between the two Stokes layers surrounding each sphere. Our experimental measurements are the first of their kind in this parameter regime. The high frequency of oscillation of the spheres means that an analysis of the fluid dynamics would include the effects of fluid inertia, as described by the unsteady Stokes equation. However, we find that, for interparticle separations less than twice the thickness of the wake of the unsteady viscous boundary layer (the Stokes layer), the hydrodynamic interaction between the Brownian particles is well-approximated by analytical expressions that neglect the inertia of the fluid. This is because elevated frictional forces at narrow gaps dominate fluid inertial effects. The significance is that interparticle collisions and concentrated suspensions at this condition can be modeled without the need to incorporate fluid inertia. We suggest a way to predict when fluid inertial effects can be ignored by including the gap-width dependence into the frequency number. We also show that low frequency number analysis can be used to determine the microrheology of mixtures at interfaces.
Models of ungulate population dynamics
Directory of Open Access Journals (Sweden)
L. L. Eberhardt
1991-10-01
Full Text Available A useful theory for analyzing ungulate population dynamics is available in the form of equations based on the work of A. J. Lotka. Because the Leslie matrix model yields identical results and is widely known, it is convenient to label the resulting equations as the "Lotka-Leslie" model. The approach is useful for assessing population trends and attempting to predict the outcomes of various management actions. A broad list of applications to large mammals, and two examples specific to caribou are presented with a simple spreadsheet approach to calculations.
Dynamical model of brushite precipitation
Oliveira, Cristina; Georgieva, Petia; Rocha, Fernando; Ferreira, António; Feyo de Azevedo, Sebastião
2007-07-01
The objectives of this work are twofold. From academic point of view the aim is to build a dynamical macro model to fit the material balance and explain the main kinetic mechanisms that govern the transformation of the hydroxyapatite (HAP) into brushite and the growth of brushite, based on laboratory experiments and collected database. From practical point of view, the aim is to design a reliable process simulator that can be easily imbedded in industrial software for model driven monitoring, optimization and control purposes. Based upon a databank of laboratory measurements of the calcium concentration in solution (on-line) and the particle size distribution (off-line) a reliable dynamical model of the dual nature of brushite particle formation for a range of initial concentrations of the reagents was derived as a system of ordinary differential equations of time. The performance of the model is tested with respect to the predicted evolution of mass of calcium in solution and the average (in mass) particle size along time. Results obtained demonstrate a good agreement between the model time trajectories and the available experimental data for a number of different initial concentrations of reagents.
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, 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...
Feedback control in a coupled Brownian ratchet
Institute of Scientific and Technical Information of China (English)
Gao Tian-Fu; Liu Feng-Shan; Chen Jin-Can
2012-01-01
On the basis of the double-well ratchet potential which can be calculated theoretically and implemented experimentally,the influences of the time delay,the coupling constant,and the asymmetric parameter of the potential on the performance of a delayed feedback ratchet consisting of two Brownian particles coupled mutually with a linear elastic force are investigated.The centre-of-mass velocity of two coupled Brownian particles.the average effective diffusion coefficient,and the Pe number are calculated.It is found that the parameters are affected by not only the time delay and coupling constant but also the asymmetric parameter of the double-well ratchet potential.It is also found that the enhancement of the current may be obtained by varying the coupling constant of the system for the weak coupling case.It is expected that the results obtained here may be observed in some physical and biological systems.
Dynamic pricing models for electronic business
Indian Academy of Sciences (India)
Y Narahari; C V L Raju; K Ravikumar; Sourabh Shah
2005-04-01
Dynamic pricing is the dynamic adjustment of prices to consumers depending upon the value these customers attribute to a product or service. Today’s digital economy is ready for dynamic pricing; however recent research has shown that the prices will have to be adjusted in fairly sophisticated ways, based on sound mathematical models, to derive the beneﬁts of dynamic pricing. This article attempts to survey different models that have been used in dynamic pricing. We ﬁrst motivate dynamic pricing and present underlying concepts, with several examples, and explain conditions under which dynamic pricing is likely to succeed. We then bring out the role of models in computing dynamic prices. The models surveyed include inventory-based models, data-driven models, auctions, and machine learning. We present a detailed example of an e-business market to show the use of reinforcement learning in dynamic pricing.
Modelling of the Manifold Filling Dynamics
DEFF Research Database (Denmark)
Hendricks, Elbert; Chevalier, Alain Marie Roger; Jensen, Michael
1996-01-01
Mean Value Engine Models (MVEMs) are dynamic models which describe dynamic engine variable (or state) responses on time scales slightly longer than an engine event. This paper describes a new model of the intake manifold filling dynamics which is simple and easy to calibrate for use in engine con...
Multiscale modeling of pedestrian dynamics
Cristiani, Emiliano; Tosin, Andrea
2014-01-01
This book presents mathematical models and numerical simulations of crowd dynamics. The core topic is the development of a new multiscale paradigm, which bridges the microscopic and macroscopic scales taking the most from each of them for capturing the relevant clues of complexity of crowds. The background idea is indeed that most of the complex trends exhibited by crowds are due to an intrinsic interplay between individual and collective behaviors. The modeling approach promoted in this book pursues actively this intuition and profits from it for designing general mathematical structures susceptible of application also in fields different from the inspiring original one. The book considers also the two most traditional points of view: the microscopic one, in which pedestrians are tracked individually, and the macroscopic one, in which pedestrians are assimilated to a continuum. Selected existing models are critically analyzed. The work is addressed to researchers and graduate students.
DYNAMICAL MODEL OF ELECTROMAGNETIC DRIVE
Directory of Open Access Journals (Sweden)
Trunev A. P.
2016-02-01
Full Text Available The article discusses the dynamic model of the rocket motor electromagnetic type, consisting of a source of electromagnetic waves of radio frequency band and a conical cavity in which electromagnetic waves are excited. The processes of excitation of electromagnetic oscillations in a cavity with conducting walls, as well as the waves of the YangMills field have been investigated. Multi-dimensional transient numerical model describing the processes of establishment of electromagnetic oscillations in a cavity with the conducting wall was created Separately, the case of standing waves in the cavity with conducting walls been tested. It is shown that the oscillation mode in the conducting resonator different from that in an ideal resonator, both in the steady and unsteady processes. The mechanism of formation of traction for the changes in the space-time metric, the contribution of particle currents, the Yang-Mills and electromagnetic field proposed. It is shown that the effect of the Yang-Mills field calls change the dielectric properties of vacuum, which leads to a change in capacitance of the resonator. Developed a dynamic model, which enables optimal traction on a significant number of parameters. It was found that the thrust increases in the Yang-Mills field parameters near the main resonance frequency. In the presence of thermal fluctuations and the Yang-Mills field as well the traction force changes sign, indicating the presence of various oscillation modes
Brenner, Howard
2005-12-01
A quiescent single-component gravity-free gas subject to a small steady uniform temperature gradient T, despite being at rest, is shown to experience a drift velocity UD=-D* gradient ln T, where D* is the gas's nonisothermal self-diffusion coefficient. D* is identified as being the gas's thermometric diffusivity alpha. The latter differs from the gas's isothermal isotopic self-diffusion coefficient D, albeit only slightly. Two independent derivations are given of this drift velocity formula, one kinematical and the other dynamical, both derivations being strictly macroscopic in nature. Within modest experimental and theoretical uncertainties, this virtual drift velocity UD=-alpha gradient ln T is shown to be constitutively and phenomenologically indistinguishable from the well-known experimental and theoretical formulas for the thermophoretic velocity U of a macroscopic (i.e., non-Brownian) non-heat-conducting particle moving under the influence of a uniform temperature gradient through an otherwise quiescent single-component rarefied gas continuum at small Knudsen numbers. Coupled with the size independence of the particle's thermophoretic velocity, the empirically observed equality, U=UD, leads naturally to the hypothesis that these two velocities, the former real and the latter virtual, are, in fact, simply manifestations of the same underlying molecular phenomenon, namely the gas's Brownian movement, albeit biased by the temperature gradient. This purely hydrodynamic continuum-mechanical equality is confirmed by theoretical calculations effected at the kinetic-molecular level on the basis of an existing solution of the Boltzmann equation for a quasi-Lorentzian gas, modulo small uncertainties pertaining to the choice of collision model. Explicitly, this asymptotically valid molecular model allows the virtual drift velocity UD of the light gas and the thermophoretic velocity U of the massive, effectively non-Brownian, particle, now regarded as the tracer particle
Eigenvalue Dynamics for Multimatrix Models
Koch, Robert de Mello; Nkumane, Lwazi; Tribelhorn, Laila
2016-01-01
By performing explicit computations of correlation functions, we find evidence that there is a sector of the two matrix model defined by the $SU(2)$ sector of ${\\cal N}=4$ super Yang-Mills theory, that can be reduced to eigenvalue dynamics. There is an interesting generalization of the usual Van der Monde determinant that plays a role. The observables we study are the BPS operators of the $SU(2)$ sector and include traces of products of both matrices, which are genuine multi matrix observables. These operators are associated to supergravity solutions of string theory.
Non-Markovian expansion in quantum Brownian motion
Fraga, Eduardo S.; Krein, Gastão; Palhares, Letícia F.
2014-01-01
We consider the non-Markovian Langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism. After discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the most common choices, we derive an analytic expansion for the exact non-Markovian dissipation kernel and the corresponding colored noise in the general case that is consistent with the fluctuation-dissipation theorem and incorporates systematically non-local corrections. We illustrate the modifications to results obtained using the traditional (Markovian) Langevin approach in the case of the exponential kernel and analyze the case of the non-Markovian Brownian motion. We present detailed results for the free and the quadratic cases, which can be compared to exact solutions to test the convergence of the method, and discuss potentials of a general nonlinear form.
Brownian motion on Lie groups and open quantum systems
Energy Technology Data Exchange (ETDEWEB)
Aniello, P; Marmo, G; Ventriglia, F [Dipartimento di Scienze Fisiche dell' Universita di Napoli ' Federico II' and Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, I-80126 Napoli (Italy); Kossakowski, A, E-mail: paolo.aniello@na.infn.i, E-mail: kossak@fyzika.umk.p, E-mail: marmo@na.infn.i, E-mail: ventriglia@na.infn.i [MECENAS, Universita di Napoli ' Federico II' , via Mezzocannone 8, I-80134 Napoli (Italy)
2010-07-02
We study the twirling semigroups of (super) operators, namely certain quantum dynamical semigroups that are associated, in a natural way, with the pairs formed by a projective representation of a locally compact group and a convolution semigroup of probability measures on this group. The link connecting this class of semigroups of operators with (classical) Brownian motion is clarified. It turns out that every twirling semigroup associated with a finite-dimensional representation is a random unitary semigroup, and, conversely, every random unitary semigroup arises as a twirling semigroup. Using standard tools of the theory of convolution semigroups of measures and of convex analysis, we provide a complete characterization of the infinitesimal generator of a twirling semigroup associated with a finite-dimensional unitary representation of a Lie group.
Brownian motion on Lie groups and open quantum systems
Aniello, P.; Kossakowski, A.; Marmo, G.; Ventriglia, F.
2010-07-01
We study the twirling semigroups of (super) operators, namely certain quantum dynamical semigroups that are associated, in a natural way, with the pairs formed by a projective representation of a locally compact group and a convolution semigroup of probability measures on this group. The link connecting this class of semigroups of operators with (classical) Brownian motion is clarified. It turns out that every twirling semigroup associated with a finite-dimensional representation is a random unitary semigroup, and, conversely, every random unitary semigroup arises as a twirling semigroup. Using standard tools of the theory of convolution semigroups of measures and of convex analysis, we provide a complete characterization of the infinitesimal generator of a twirling semigroup associated with a finite-dimensional unitary representation of a Lie group.
Brownian motion on Lie groups and open quantum systems
Aniello, P; Marmo, G; Ventriglia, F
2010-01-01
We study the twirling semigroups of (super)operators, namely, certain quantum dynamical semigroups that are associated, in a natural way, with the pairs formed by a projective representation of a locally compact group and a convolution semigroup of probability measures on this group. The link connecting this class of semigroups of operators with (classical) Brownian motion is clarified. It turns out that every twirling semigroup associated with a finite-dimensional representation is a random unitary semigroup, and, conversely, every random unitary semigroup arises as a twirling semigroup. Using standard tools of the theory of convolution semigroups of measures and of convex analysis, we provide a complete characterization of the infinitesimal generator of a twirling semigroup associated with a finite-dimensional unitary representation of a Lie group.
Emsellem, E; Bacon, R; Emsellem, Eric; Dejonghe, Herwig; Bacon, Roland
1998-01-01
We present new dynamical models of the S0 galaxy N3115, making use of the available published photometry and kinematics as well as of two-dimensional TIGER spectrography. We first examined the kinematics in the central 40 arcsec in the light of two integral f(E,J) models. Jeans equations were used to constrain the mass to light ratio, and the central dark mass whose existence was suggested by previous studies. The even part of the distribution function was then retrieved via the Hunter & Qian formalism. We thus confirmed that the velocity and dispersion profiles in the central region could be well fit with a two-integral model, given the presence of a central dark mass of ~10^9 Msun. However, no two integral model could fit the h_3 profile around a radius of 25 arcsec where the outer disc dominates the surface brightness distribution. Three integral analytical models were therefore built using a Quadratic Programming technique. These models showed that three integral components do indeed provide a reasona...
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.
Confinement-Induced Glassy Dynamics in a Model for Chromosome Organization
Kang, Hongsuk; Yoon, Young-Gui; Thirumalai, D.; Hyeon, Changbong
2015-11-01
Recent experiments showing scaling of the intrachromosomal contact probability, P (s )˜s-1 with the genomic distance s , are interpreted to mean a self-similar fractal-like chromosome organization. However, scaling of P (s ) varies across organisms, requiring an explanation. We illustrate dynamical arrest in a highly confined space as a discriminating marker for genome organization, by modeling chromosomes inside a nucleus as a homopolymer confined to a sphere of varying sizes. Brownian dynamics simulations show that the chain dynamics slows down as the polymer volume fraction (ϕ ) inside the confinement approaches a critical value ϕc. The universal value of ϕc∞≈0.44 for a sufficiently long polymer (N ≫1 ) allows us to discuss genome dynamics using ϕ as the sole parameter. Our study shows that the onset of glassy dynamics is the reason for the segregated chromosome organization in humans (N ≈3 ×109, ϕ ≳ϕc∞), whereas chromosomes of budding yeast (N ≈108, ϕ <ϕc∞) are equilibrated with no clear signature of such organization.
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.
Performance of Brownian-motion-generated universal portfolios
Tan, Choon Peng; Pang, Sook Theng
2014-06-01
Investment in a market of m stocks is considered. Generating a universal portfolio using m independent Brownian motions is demonstrated. The asymptotic behaviour of a Brownian-motion-generated universal portfolio is described. The empirical performance of such portfolios on some selected three-stock data sets is analysed. Investment wealth can be increased by varying the drift coefficients or parameters of the Brownian motions.
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
Brownian heat engine have been explored intensively by considering different-model systems.
Energy Technology Data Exchange (ETDEWEB)
Cipiti, Benjamin B. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-03-01
The Co-Decontamination (CoDCon) Demonstration project is designed to test the separation of a mixed U and Pu product from dissolved spent nuclear fuel. The primary purpose of the project is to quantify the accuracy and precision to which a U/Pu mass ratio can be achieved without removing a pure Pu product. The system includes an on-line monitoring system using spectroscopy to monitor the ratios throughout the process. A dynamic model of the CoDCon flowsheet and on-line monitoring system was developed in order to expand the range of scenarios that can be examined for process control and determine overall measurement uncertainty. The model development and initial results are presented here.
Characterizing and modeling citation dynamics
Eom, Young-Ho; 10.1371/journal.pone.0024926
2011-01-01
Citation distributions are crucial for the analysis and modeling of the activity of scientists. We investigated bibliometric data of papers published in journals of the American Physical Society, searching for the type of function which best describes the observed citation distributions. We used the goodness of fit with Kolmogorov-Smirnov statistics for three classes of functions: log-normal, simple power law and shifted power law. The shifted power law turns out to be the most reliable hypothesis for all citation networks we derived, which correspond to different time spans. We find that citation dynamics is characterized by bursts, usually occurring within a few years since publication of a paper, and the burst size spans several orders of magnitude. We also investigated the microscopic mechanisms for the evolution of citation networks, by proposing a linear preferential attachment with time dependent initial attractiveness. The model successfully reproduces the empirical citation distributions and accounts...
Random Matrix Theory in molecular dynamics analysis.
Palese, Luigi Leonardo
2015-01-01
It is well known that, in some situations, principal component analysis (PCA) carried out on molecular dynamics data results in the appearance of cosine-shaped low index projections. Because this is reminiscent of the results obtained by performing PCA on a multidimensional Brownian dynamics, it has been suggested that short-time protein dynamics is essentially nothing more than a noisy signal. Here we use Random Matrix Theory to analyze a series of short-time molecular dynamics experiments which are specifically designed to be simulations with high cosine content. We use as a model system the protein apoCox17, a mitochondrial copper chaperone. Spectral analysis on correlation matrices allows to easily differentiate random correlations, simply deriving from the finite length of the process, from non-random signals reflecting the intrinsic system properties. Our results clearly show that protein dynamics is not really Brownian also in presence of the cosine-shaped low index projections on principal axes.
Qubit Decoherence and Non-Markovian Dynamics at Low Temperatures via an Effective Spin-Boson Model
Shiokawa, K
2004-01-01
Quantum Brownian oscillator model (QBM), in the Fock-space representation, can be viewed as a multi-level spin-boson model. At sufficiently low temperature, the oscillator degrees of freedom are dynamically reduced to the lowest two levels and the system behaves effectively as a two-level (E2L) spin-boson model (SBM) in this limit. We discuss the physical mechanism of level reduction and analyze the behavior of E2L-SBM from the QBM solutions. The availability of close solutions for the QBM enables us to study the non-Markovian features of decoherence and leakage in a SBM in the non-perturbative regime (e.g. without invoking the Born approximation) in better details than before. Our result captures very well the characteristic non-Markovian short time low temperature behavior common in many models.
Dynamical Modeling of Mars' Paleoclimate
Richardson, Mark I.
2004-01-01
This report summarizes work undertaken under a one-year grant from the NASA Mars Fundamental Research Program. The goal of the project was to initiate studies of the response of the Martian climate to changes in planetary obliquity and orbital elements. This work was undertaken with a three-dimensional numerical climate model based on the Geophysical Fluid Dynamics Laboratory (GFDL) Skyhi General Circulation Model (GCM). The Mars GCM code was adapted to simulate various obliquity and orbital parameter states. Using a version of the model with a basic water cycle (ice caps, vapor, and clouds), we examined changes in atmospheric water abundances and in the distribution of water ice sheets on the surface. This work resulted in a paper published in the Journal of Geophysical Research - Planets. In addition, the project saw the initial incorporation of a regolith water transport and storage scheme into the model. This scheme allows for interaction between water in the pores of the near subsurface (<3m) and the atmosphere. This work was not complete by the end of the one-year grant, but is now continuing within the auspices of a three-year grant of the same title awarded by the Mars Fundamental Research Program in late 2003.
Brownian motion of interacting particles
Energy Technology Data Exchange (ETDEWEB)
Ackerson, B.J.
1976-01-01
Guided by the descriptions which are used to describe noninteracting particles, it is argued that the generalized Smoluchowski equation, including the hydrodynamic interaction and corrections for ion cloud effects may be used to describe interacting particles for the temporal and spatial regimes probed by light beating spectroscopy. This equation is then used to find cumulants of decay of the intermediate scattering function. The generalized Smoluchowski equation is reduced to a simple diffusion equation. The resulting diffusion constant depends upon the interparticle forces and is reminiscent of some early descriptions for interacting systems. The generalized Smoluchowski equation is solved for the model system of a linear chain of colloidal particles interacting via nearest neighbor harmonic couplings. The results for the intermediate scattering function and the static structure factor are very reminiscent of corresponding measurements made for interacting colloidal systems. (GHT)
Randrup, Jorgen
2011-01-01
Although nuclear fission can be understood qualitatively as an evolution of the nuclear shape, a quantitative description has proven to be very elusive. In particular, until now, there exists no model with demonstrated predictive power for the fission fragment mass yields. Exploiting the expected strongly damped character of nuclear dynamics, we treat the nuclear shape evolution in analogy with Brownian motion and perform random walks on five-dimensional fission potential-energy surfaces which were calculated previously and are the most comprehensive available. Test applications give good reproduction of highly variable experimental mass yields. This novel general approach requires only a single new global parameter, namely the critical neck size at which the mass split is frozen in, and the results are remarkably insensitive to its specific value.
Randrup, Jørgen; Möller, Peter
2011-04-01
Although nuclear fission can be understood qualitatively as an evolution of the nuclear shape, a quantitative description has proven to be very elusive. In particular, until now, there existed no model with demonstrated predictive power for the fission-fragment mass yields. Exploiting the expected strongly damped character of nuclear dynamics, we treat the nuclear shape evolution in analogy with Brownian motion and perform random walks on five-dimensional fission potential-energy surfaces which were calculated previously and are the most comprehensive available. Test applications give good reproduction of highly variable experimental mass yields. This novel general approach requires only a single new global parameter, namely, the critical neck size at which the mass split is frozen in, and the results are remarkably insensitive to its specific value.
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.
Analytical studies of spectrum broadcast structures in quantum Brownian motion
Tuziemski, J.; Korbicz, J. K.
2016-11-01
Spectrum broadcast structures are a new and fresh concept in the quantum-to-classical transition, introduced recently in the context of decoherence and the appearance of objective features in quantum mechanics. These are specific quantum state structures, responsible for the objectivization of the decohered state of a system. Recently, they have been demonstrated by means of the well-known quantum Brownian motion model of the recoilless limit (infinitely massive central system), as the principal interest lies in information transfer from the system to the environment. However, a final analysis relied on numerics. Here, after a presentation of the main concepts, we perform analytical studies of the model, showing the timescales and the efficiency of the spectrum broadcast structure formation. We consider a somewhat simplified environment, being random with a uniform distribution of frequencies.
Brownian transport in corrugated channels with inertia
Ghosh, P K; Marchesoni, F; Nori, F; Schmid, G; 10.1103/PhysRevE.86.021112
2012-01-01
The transport of suspended Brownian particles dc-driven along corrugated narrow channels is numerically investigated in the regime of finite damping. We show that inertial corrections cannot be neglected as long as the width of the channel bottlenecks is smaller than an appropriate particle diffusion length, which depends on the the channel corrugation and the drive intensity. Being such a diffusion length inversely proportional to the damping constant, transport through sufficiently narrow obstructions turns out to be always sensitive to the viscosity of the suspension fluid. The inertia corrections to the transport quantifiers, mobility and diffusivity, markedly differ for smoothly and sharply corrugated channels.
Cooperative rectification in confined Brownian ratchets.
Malgaretti, Paolo; Pagonabarraga, Ignacio; Rubí, J Miguel
2012-01-01
We analyze the rectified motion of a Brownian particle in a confined environment. We show the emergence of strong cooperativity between the inherent rectification of the ratchet mechanism and the entropic bias of the fluctuations caused by spatial confinement. Net particle transport may develop even in situations where separately the ratchet and the geometric restrictions do not give rise to particle motion. The combined rectification effects can lead to bidirectional transport depending on particle size, resulting in a different route for segregation. The reported mechanism can be used to control transport in mesostructures and nanodevices in which particles move in a reduced space.
The Isolation Time of Poisson Brownian motions
Peres, Yuval; Stauffer, Alexandre
2011-01-01
Let the nodes of a Poisson point process move independently in $\\R^d$ according to Brownian motions. We study the isolation time for a target particle that is placed at the origin, namely how long it takes until there is no node of the Poisson point process within distance $r$ of it. We obtain asymptotics for the tail probability which are tight up to constants in the exponent in dimension $d\\geq 3$ and tight up to logarithmic factors in the exponent for dimensions $d=1,2$.
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.
Optimal Control of Stochastic Systems Driven by Fractional Brownian Motions
2014-10-09
motions and other stochastic processes. For the control of both continuous time and discrete time finite dimensional linear systems with quadratic...problems for stochastic partial differential equations driven by fractional Brownian motions are explicitly solved. For the control of a continuous time...2010 30-Jun-2014 Approved for Public Release; Distribution Unlimited Final Report: Optimal Control of Stochastic Systems Driven by Fractional Brownian
Wind Farm Decentralized Dynamic Modeling With Parameters
DEFF Research Database (Denmark)
Soltani, Mohsen; Shakeri, Sayyed Mojtaba; Grunnet, Jacob Deleuran;
2010-01-01
Development of dynamic wind flow models for wind farms is part of the research in European research FP7 project AEOLUS. The objective of this report is to provide decentralized dynamic wind flow models with parameters. The report presents a structure for decentralized flow models with inputs from...
Dynamical model for virus spread
Camelo-Neto, G
1995-01-01
The steady state properties of the mean density population of infected cells in a viral spread is simulated by a general forest fire like cellular automaton model with two distinct populations of cells ( permissive and resistant ones) and studied in the framework of the mean field approximation. Stochastic dynamical ingredients are introduced in this model to mimic cells regeneration (with probability {\\it p}) and to consider infection processes by other means than contiguity (with probability {\\it f}). Simulations are carried on a L \\times L square lattice considering the eight first neighbors. The mean density population of infected cells (D_i) is measured as function of the regeneration probability {\\it p}, and analyzed for small values of the ratio {\\it f/p } and for distinct degrees of the cell resistance. The results obtained by a mean field like approach recovers the simulations results. The role of the resistant parameter R (R \\geq 2) on the steady state properties is investigated and discussed in com...
Characterizing and modeling citation dynamics.
Directory of Open Access Journals (Sweden)
Young-Ho Eom
Full Text Available Citation distributions are crucial for the analysis and modeling of the activity of scientists. We investigated bibliometric data of papers published in journals of the American Physical Society, searching for the type of function which best describes the observed citation distributions. We used the goodness of fit with Kolmogorov-Smirnov statistics for three classes of functions: log-normal, simple power law and shifted power law. The shifted power law turns out to be the most reliable hypothesis for all citation networks we derived, which correspond to different time spans. We find that citation dynamics is characterized by bursts, usually occurring within a few years since publication of a paper, and the burst size spans several orders of magnitude. We also investigated the microscopic mechanisms for the evolution of citation networks, by proposing a linear preferential attachment with time dependent initial attractiveness. The model successfully reproduces the empirical citation distributions and accounts for the presence of citation bursts as well.
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 (
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.
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.
Mean-squared-displacement statistical test for fractional Brownian motion
Sikora, Grzegorz; Burnecki, Krzysztof; Wyłomańska, Agnieszka
2017-03-01
Anomalous diffusion in crowded fluids, e.g., in cytoplasm of living cells, is a frequent phenomenon. A common tool by which the anomalous diffusion of a single particle can be classified is the time-averaged mean square displacement (TAMSD). A classical mechanism leading to the anomalous diffusion is the fractional Brownian motion (FBM). A validation of such process for single-particle tracking data is of great interest for experimentalists. In this paper we propose a rigorous statistical test for FBM based on TAMSD. To this end we analyze the distribution of the TAMSD statistic, which is given by the generalized chi-squared distribution. Next, we study the power of the test by means of Monte Carlo simulations. We show that the test is very sensitive for changes of the Hurst parameter. Moreover, it can easily distinguish between two models of subdiffusion: FBM and continuous-time random walk.
BROWNIAN 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.
Modelling the dynamics of youth subcultures
Holme, P; Holme, Petter; Gronlund, Andreas
2005-01-01
What are the dynamics behind youth subcultures such as punk, hippie, or hip-hop cultures? How does the global dynamics of these subcultures relate to the individual's search for a personal identity? We propose a simple dynamical model to address these questions and find that only a few assumptions of the individual's behaviour are necessary to regenerate known features of youth culture.
Relating structure and dynamics in organisation models
Jonkers, C.M.; Treur, J.
2008-01-01
To understand how an organisational structure relates to dynamics is an interesting fundamental challenge in the area of social modelling. Specifications of organisational structure usually have a diagrammatic form that abstracts from more detailed dynamics. Dynamic properties of agent systems, on t
Stochastic Physicochemical Dynamics
Tsekov, R.
2001-02-01
Thermodynamic Relaxation in Quantum Systems: A new approach to quantum Markov processes is developed and the corresponding Fokker-Planck equation is derived. The latter is examined to reproduce known results from classical and quantum physics. It was also applied to the phase-space description of a mechanical system thus leading to a new treatment of this problem different from the Wigner presentation. The equilibrium probability density obtained in the mixed coordinate-momentum space is a reasonable extension of the Gibbs canonical distribution. The validity of the Einstein fluctuation-dissipation relation is discussed in respect to the type of relaxation in an isothermal system. The first model, presuming isothermic fluctuations, leads to the Einstein formula. The second model supposes adiabatic fluctuations and yields another relation between the diffusion coefficient and mobility of a Brownian particle. A new approach to relaxations in quantum systems is also proposed that demonstrates applicability only of the adiabatic model for description of the quantum Brownian dynamics. Stochastic Dynamics of Gas Molecules: A stochastic Langevin equation is derived, describing the thermal motion of a molecule immersed in a rested fluid of identical molecules. The fluctuation-dissipation theorem is proved and a number of correlation characteristics of the molecular Brownian motion are obtained. A short review of the classical theory of Brownian motion is presented. A new method is proposed for derivation of the Fokker-Planck equations, describing the probability density evolution, from stochastic differential equations. It is also proven via the central limit theorem that the white noise is only Gaussian. The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Ito and Stratonovich forms, is introduced. It is shown that the new presentation is more appropriate for the description of thermodynamic
Dynamic stall model for wind turbine airfoils
DEFF Research Database (Denmark)
Larsen, J.W.; Nielsen, S.R.K.; Krenk, Steen
2007-01-01
A model is presented for aerodynamic lift of wind turbine profiles under dynamic stall. The model combines memory delay effects under attached flow with reduced lift due to flow separation under dynamic stall conditions. The model is based on a backbone curve in the form of the static lift...... conditions, nonstationary effects are included by three mechanisms: a delay of the lift coefficient of fully attached flow via a second-order filter, a delay of the development of separation represented via a first-order filter, and a lift contribution due to leading edge separation also represented via...... during dynamic stall conditions. The proposed model is compared with five other dynamic stall models including, among others, the Beddoes-Leishman model and the ONERA model. It is demonstrated that the proposed model performs equally well or even better than more complicated models and that the included...
An immune based dynamic intrusion detection model
Institute of Scientific and Technical Information of China (English)
LI Tao
2005-01-01
With the dynamic description method for self and antigen, and the concept of dynamic immune tolerance for lymphocytes in network-security domain presented in this paper, a new immune based dynamic intrusion detection model (Idid) is proposed. In Idid, the dynamic models and the corresponding recursive equations of the lifecycle of mature lymphocytes, and the immune memory are built. Therefore, the problem of the dynamic description of self and nonself in computer immune systems is solved, and the defect of the low efficiency of mature lymphocyte generating in traditional computer immune systems is overcome. Simulations of this model are performed, and the comparison experiment results show that the proposed dynamic intrusion detection model has a better adaptability than the traditional methods.
Workflow-Based Dynamic Enterprise Modeling
Institute of Scientific and Technical Information of China (English)
黄双喜; 范玉顺; 罗海滨; 林慧萍
2002-01-01
Traditional systems for enterprise modeling and business process control are often static and cannot adapt to the changing environment. This paper presents a workflow-based method to dynamically execute the enterprise model. This method gives an explicit representation of the business process logic and the relationships between the elements involved in the process. An execution-oriented integrated enterprise modeling system is proposed in combination with other enterprise views. The enterprise model can be established and executed dynamically in the actual environment due to the dynamic properties of the workflow model.
Dynamical model of the kinesin protein motor
Nesterov, Alexander I; Ramírez, Mónica F
2016-01-01
We model and simulate the stepping dynamics of the kinesin motor including electric and mechanical forces, environmental noise, and the complicated potentials produced by tracking and neighboring protofilaments. Our dynamical model supports the hand-over-hand mechanism of the kinesin stepping. Our theoretical predictions and numerical simulations include the off-axis displacements of the kinesin heads while the steps are performed. The results obtained are in a good agreement with recent experiments on the kinesin dynamics.
Comparative dynamics in a health investment model.
Eisenring, C
1999-10-01
The method of comparative dynamics fully exploits the inter-temporal structure of optimal control models. I derive comparative dynamic results in a simplified demand for health model. The effect of a change in the depreciation rate on the optimal paths for health capital and investment in health is studied by use of a phase diagram.
Dynamic Heat Transfer Model of Refrigerated Foodstuff
DEFF Research Database (Denmark)
Cai, Junping; Risum, Jørgen; Thybo, Claus
2006-01-01
their temperature relation. This paper discusses the dynamic heat transfer model of foodstuff inside the display cabinet, one-dimensional dynamic model is developed, and the Explicit Finite Difference Method is applied, to handle the unsteady heat transfer problem with phase change, as well as time varying boundary...
The Challenges to Coupling Dynamic Geospatial Models
Energy Technology Data Exchange (ETDEWEB)
Goldstein, N
2006-06-23
Many applications of modeling spatial dynamic systems focus on a single system and a single process, ignoring the geographic and systemic context of the processes being modeled. A solution to this problem is the coupled modeling of spatial dynamic systems. Coupled modeling is challenging for both technical reasons, as well as conceptual reasons. This paper explores the benefits and challenges to coupling or linking spatial dynamic models, from loose coupling, where information transfer between models is done by hand, to tight coupling, where two (or more) models are merged as one. To illustrate the challenges, a coupled model of Urbanization and Wildfire Risk is presented. This model, called Vesta, was applied to the Santa Barbara, California region (using real geospatial data), where Urbanization and Wildfires occur and recur, respectively. The preliminary results of the model coupling illustrate that coupled modeling can lead to insight into the consequences of processes acting on their own.
Conditional Density Models for Asset Pricing
Filipovic, Damir; Hughston, Lane P.; Macrina, Andrea
2010-01-01
We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the asset is driven by Brownian motion, an associated "master equation" for the dynamics of the conditional probability density is derived and expressed in integral form. By a "model" for the conditional density process we mean a solution to the master equation along wi...
Hydration dynamics near a model protein surface
Energy Technology Data Exchange (ETDEWEB)
Russo, Daniela; Hura, Greg; Head-Gordon, Teresa
2003-09-01
The evolution of water dynamics from dilute to very high concentration solutions of a prototypical hydrophobic amino acid with its polar backbone, N-acetyl-leucine-methylamide (NALMA), is studied by quasi-elastic neutron scattering and molecular dynamics simulation for both the completely deuterated and completely hydrogenated leucine monomer. We observe several unexpected features in the dynamics of these biological solutions under ambient conditions. The NALMA dynamics shows evidence of de Gennes narrowing, an indication of coherent long timescale structural relaxation dynamics. The translational water dynamics are analyzed in a first approximation with a jump diffusion model. At the highest solute concentrations, the hydration water dynamics is significantly suppressed and characterized by a long residential time and a slow diffusion coefficient. The analysis of the more dilute concentration solutions takes into account the results of the 2.0M solution as a model of the first hydration shell. Subtracting the first hydration layer based on the 2.0M spectra, the translational diffusion dynamics is still suppressed, although the rotational relaxation time and residential time are converged to bulk-water values. Molecular dynamics analysis shows spatially heterogeneous dynamics at high concentration that becomes homogeneous at more dilute concentrations. We discuss the hydration dynamics results of this model protein system in the context of glassy systems, protein function, and protein-protein interfaces.
Kröger, M; Hess, S
2003-01-01
We review, apply and compare diverse approaches to the theoretical understanding of the dynamical and rheological behaviour of ferrofluids and magnetorheological (MR) fluids subject to external magnetic and flow fields. Simple models are introduced which are directly solvable by nonequilibrium Brownian or molecular dynamics computer simulation. In particular, the numerical results for ferrofluids quantify the domain of validity of uniaxial alignment of magnetic moments (in and) out of equilibrium. A Fokker-Planck equation for the dynamics of the magnetic moments - corresponding to the Brownian dynamics approach - and its implications are analysed under this approximation. The basic approach considers the effect of external fields on the dynamics of ellipsoid shaped permanent ferromagnetic domains (aggregates), whose size should depend on the strength of flow and magnetic field, the magnetic interaction parameter and concentration (or packing fraction). Results from analytic calculations and from simulation ar...
Brownian Ratchets: Transport Controlled by Thermal Noise
Kula, J.; Czernik, T.; Łuczka, J.
1998-02-01
We analyze directed transport of overdamped Brownian particles in a 1D spatially periodic potential that are subjected to both zero-mean thermal equilibrium Nyquist noise and zero-mean exponentially correlated dichotomous fluctuations. We show that particles can reverse the direction of average motion upon a variation of noise parameters if two fundamental symmetries, namely, the reflection symmetry of the spatial periodic structure, and the statistical symmetry of dichotomous fluctuations, are broken. There is a critical thermal noise intensity Dc, or equivalently a critical temperature Tc, at which the mean velocity of particles is zero. Below Tc and above Tc particles move in opposite directions. At fixed temperature, there is a region of noise parameters in which particles of different linear size are transported in opposite directions.
Parallel Molecular Distributed Detection with Brownian Motion.
Rogers, Uri; Koh, Min-Sung
2016-12-05
This paper explores the in vivo distributed detection of an undesired biological agent's (BAs) biomarkers by a group of biological sized nanomachines in an aqueous medium under drift. The term distributed, indicates that the system information relative to the BAs presence is dispersed across the collection of nanomachines, where each nanomachine possesses limited communication, computation, and movement capabilities. Using Brownian motion with drift, a probabilistic detection and optimal data fusion framework, coined molecular distributed detection, will be introduced that combines theory from both molecular communication and distributed detection. Using the optimal data fusion framework as a guide, simulation indicates that a suboptimal fusion method exists, allowing for a significant reduction in implementation complexity while retaining BA detection accuracy.
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...
Lecture Notes on Quantum Brownian Motion
Erdos, Laszlo
2010-01-01
Einstein's kinetic theory of the Brownian motion, based upon light water molecules continuously bombarding a heavy pollen, provided an explanation of diffusion from the Newtonian mechanics. Since the discovery of quantum mechanics it has been a challenge to verify the emergence of diffusion from the Schr\\"odinger equation. The first step in this program is to verify the linear Boltzmann equation as a certain scaling limit of a Schr\\"odinger equation with random potential. In the second step, one considers a longer time scale that corresponds to infinitely many Boltzmann collisions. The intuition is that the Boltzmann equation then converges to a diffusive equation similarly to the central limit theorem for Markov processes with sufficient mixing. In these lecture notes (prepared for the Les Houches summer school in 2010 August) we present the mathematical tools to rigorously justify this intuition. The new material relies on joint papers with H.-T. Yau and M. Salmhofer.
Dynamic Factor Models for the Volatility Surface
DEFF Research Database (Denmark)
van der Wel, Michel; Ozturk, Sait R.; Dijk, Dick van
The implied volatility surface is the collection of volatilities implied by option contracts for different strike prices and time-to-maturity. We study factor models to capture the dynamics of this three-dimensional implied volatility surface. Three model types are considered to examine desirable...... features for representing the surface and its dynamics: a general dynamic factor model, restricted factor models designed to capture the key features of the surface along the moneyness and maturity dimensions, and in-between spline-based methods. Key findings are that: (i) the restricted and spline......-based models are both rejected against the general dynamic factor model, (ii) the factors driving the surface are highly persistent, (iii) for the restricted models option Delta is preferred over the more often used strike relative to spot price as measure for moneyness....
Comprehensive Survey on Dynamic Graph Models
Directory of Open Access Journals (Sweden)
Aya Zaki
2016-02-01
Full Text Available Most of the critical real-world networks are con-tinuously changing and evolving with time. Motivated by the growing importance and widespread impact of this type of networks, the dynamic nature of these networks have gained a lot of attention. Because of their intrinsic and special characteristics, these networks are best represented by dynamic graph models. To cope with their evolving nature, the representation model must keep the historical information of the network along with its temporal time. Storing such amount of data, poses many problems from the perspective of dynamic graph data management. This survey provides an in-depth overview on dynamic graph related problems. Novel categorization and classification of the state of the art dynamic graph models are also presented in a systematic and comprehensive way. Finally, we discuss dynamic graph processing including the output representation of its algorithms.
Effective reduced diffusion-models: a data driven approach to the analysis of neuronal dynamics.
Directory of Open Access Journals (Sweden)
Gustavo Deco
2009-12-01
Full Text Available We introduce in this paper a new method for reducing neurodynamical data to an effective diffusion equation, either experimentally or using simulations of biophysically detailed models. The dimensionality of the data is first reduced to the first principal component, and then fitted by the stationary solution of a mean-field-like one-dimensional Langevin equation, which describes the motion of a Brownian particle in a potential. The advantage of such description is that the stationary probability density of the dynamical variable can be easily derived. We applied this method to the analysis of cortical network dynamics during up and down states in an anesthetized animal. During deep anesthesia, intracellularly recorded up and down states transitions occurred with high regularity and could not be adequately described by a one-dimensional diffusion equation. Under lighter anesthesia, however, the distributions of the times spent in the up and down states were better fitted by such a model, suggesting a role for noise in determining the time spent in a particular state.
Clustering and heterogeneous dynamics in a kinetic Monte Carlo model of self-propelled hard disks.
Levis, Demian; Berthier, Ludovic
2014-06-01
We introduce a kinetic Monte Carlo model for self-propelled hard disks to capture with minimal ingredients the interplay between thermal fluctuations, excluded volume, and self-propulsion in large assemblies of active particles. We analyze in detail the resulting (density, self-propulsion) nonequilibrium phase diagram over a broad range of parameters. We find that purely repulsive hard disks spontaneously aggregate into fractal clusters as self-propulsion is increased and rationalize the evolution of the average cluster size by developing a kinetic model of reversible aggregation. As density is increased, the nonequilibrium clusters percolate to form a ramified structure reminiscent of a physical gel. We show that the addition of a finite amount of noise is needed to trigger a nonequilibrium phase separation, showing that demixing in active Brownian particles results from a delicate balance between noise, interparticle interactions, and self-propulsion. We show that self-propulsion has a profound influence on the dynamics of the active fluid. We find that the diffusion constant has a nonmonotonic behavior as self-propulsion is increased at finite density and that activity produces strong deviations from Fickian diffusion that persist over large time scales and length scales, suggesting that systems of active particles generically behave as dynamically heterogeneous systems.
Modelling the dynamics of turbulent floods
Mei, Z; Li, Z; Li, Zhenquan
1999-01-01
Consider the dynamics of turbulent flow in rivers, estuaries and floods. Based on the widely used k-epsilon model for turbulence, we use the techniques of centre manifold theory to derive dynamical models for the evolution of the water depth and of vertically averaged flow velocity and turbulent parameters. This new model for the shallow water dynamics of turbulent flow: resolves the vertical structure of the flow and the turbulence; includes interaction between turbulence and long waves; and gives a rational alternative to classical models for turbulent environmental flows.
Hanasaki, Itsuo; Nagura, Ryo; Kawano, Satoyuki
2015-03-14
The Brownian motion of a particle in a fluid is often described by the linear Langevin equation, in which it is assumed that the mass of the particle is sufficiently large compared to the surrounding fluid molecules. This assumption leads to a diffusion coefficient that is independent of the particle mass. The Stokes-Einstein equation indicates that the diffusion coefficient depends solely on the particle size, but the concept of size can be ambiguous when close to the molecular scale. We first examine the Brownian motion of simple model particles based on short-range interactions in water by the molecular dynamics method and show that the diffusion coefficient can vary with mass when this mass is comparable to that of the solvent molecules, and that this effect is evident when the solute particle size is sufficiently small. We then examine the properties of a water molecule considered as a solute in the bulk solvent consisting of the remainder of the water. A comparison with simple solute models is used to clarify the role of force fields. The long-range Coulomb interaction between water molecules is found to lead to a Gaussian force distribution in spite of a mass ratio and nominal size ratio of unity, such that solutes with short-range interactions exhibit non-Gaussian force distribution. Thus, the range of the interaction distance determines the effective size even if it does not represent the volume excluded by the repulsive force field.
Flapping Wing Flight Dynamic Modeling
2011-08-22
von Karman, T. and Burgers, J. M., Gerneral Aerodynamic Theory - Perfect Fluids , Vol. II, Julius Springer , Berlin, 1935. [24] Pesavento, U. and Wang...L., Methods of Analytical Dynamics , McGraw-Hill Book Company, New York, 1970. [34] Deng, X., Schenato, L., Wu, W. C., and Sastry, S. S., Flapping...Micro air vehicle- motivated computational biomechanics in bio ights: aerodynamics, ight dynamics and maneuvering stability, Acta Mechanica
The Brownian Cactus I. Scaling limits of discrete cactuses
Curien, Nicolas; Miermont, Grégory
2011-01-01
The cactus of a pointed graph is a discrete tree associated with this graph. Similarly, with every pointed geodesic metric space $E$, one can associate an $\\R$-tree called the continuous cactus of $E$. We prove under general assumptions that the cactus of random planar maps distributed according to Boltzmann weights and conditioned to have a fixed large number of vertices converges in distribution to a limiting space called the Brownian cactus, in the Gromov-Hausdorff sense. Moreover, the Brownian cactus can be interpreted as the continuous cactus of the so-called Brownian map.
Critical Brownian sheet does not have double points
Dalang, Robert C; Nualart, Eulalia; Wu, Dongsheng; Xiao, Yimin
2010-01-01
We derive a decoupling formula for the Brownian sheet which has the following ready consequence: An $N$-parameter Brownian sheet in $\\R^d$ has double points if and only if $2(d-2N)
Modeling Mitochondrial Bioenergetics with Integrated Volume Dynamics
Bazil, Jason N.; Buzzard, Gregery T.; Ann E Rundell
2010-01-01
Author Summary Mathematically modeling biological systems challenges our current understanding of the physical and biochemical events contributing to the observed dynamics. It requires careful consideration of hypothesized mechanisms, model development assumptions and details regarding the experimental conditions. We have adopted a modeling approach to translate these factors that explicitly considers the thermodynamic constraints, biochemical states and reaction mechanisms during model devel...
Dynamical CP violation in composite Higgs models
Hashimoto, S.; Inagaki, Tomohiro; Muta, Taizo
1993-01-01
The dynamical origin of the CP violation in electroweak theory is investigated in composite Higgs models. The mechanism of the spontaneous CP violation proposed in other context by Dashen is adopted to construct simple models of the dynamical CP violation. Within the models the size of the neutron electric dipole moment is estimated and the constraint on the $\\varepsilon$-parameter in K-meson decays is discussed.
Avalanche-like fluidization of a non-Brownian particle gel.
Kurokawa, Aika; Vidal, Valérie; Kurita, Kei; Divoux, Thibaut; Manneville, Sébastien
2015-12-14
We report on the fluidization dynamics of an attractive gel composed of non-Brownian particles made of fused silica colloids. Extensive rheology coupled to ultrasonic velocimetry allows us to characterize the global stress response together with the local dynamics of the gel during shear startup experiments. In practice, after being rejuvenated by a preshear, the gel is left to age for a time tw before being subjected to a constant shear rate [small gamma, Greek, dot above]. We investigate in detail the effects of both tw and [small gamma, Greek, dot above] on the fluidization dynamics and build a detailed state diagram of the gel response to shear startup flows. The gel may display either transient shear banding towards complete fluidization or steady-state shear banding. In the former case, we unravel that the progressive fluidization occurs by successive steps that appear as peaks on the global stress relaxation signal. Flow imaging reveals that the shear band grows until complete fluidization of the material by sudden avalanche-like events which are distributed heterogeneously along the vorticity direction and correlated to large peaks in the slip velocity at the moving wall. These features are robust over a wide range of tw and [small gamma, Greek, dot above] values, although the very details of the fluidization scenario vary with [small gamma, Greek, dot above]. Finally, the critical shear rate [small gamma, Greek, dot above]* that separates steady-state shear-banding from steady-state homogeneous flow depends on the width of the shear cell and exhibits a nonlinear dependence with tw. Our work brings about valuable experimental data on transient flows of attractive dispersions, highlighting the subtle interplay between shear, wall slip and aging whose modeling constitutes a major challenge that has not been met yet.
Very Large System Dynamics Models - Lessons Learned
Energy Technology Data Exchange (ETDEWEB)
Jacob J. Jacobson; Leonard Malczynski
2008-10-01
This paper provides lessons learned from developing several large system dynamics (SD) models. System dynamics modeling practice emphasize the need to keep models small so that they are manageable and understandable. This practice is generally reasonable and prudent; however, there are times that large SD models are necessary. This paper outlines two large SD projects that were done at two Department of Energy National Laboratories, the Idaho National Laboratory and Sandia National Laboratories. This paper summarizes the models and then discusses some of the valuable lessons learned during these two modeling efforts.
Comparing models of Red Knot population dynamics
McGowan, Conor
2015-01-01
Predictive population modeling contributes to our basic scientific understanding of population dynamics, but can also inform management decisions by evaluating alternative actions in virtual environments. Quantitative models mathematically reflect scientific hypotheses about how a system functions. In Delaware Bay, mid-Atlantic Coast, USA, to more effectively manage horseshoe crab (Limulus polyphemus) harvests and protect Red Knot (Calidris canutus rufa) populations, models are used to compare harvest actions and predict the impacts on crab and knot populations. Management has been chiefly driven by the core hypothesis that horseshoe crab egg abundance governs the survival and reproduction of migrating Red Knots that stopover in the Bay during spring migration. However, recently, hypotheses proposing that knot dynamics are governed by cyclical lemming dynamics garnered some support in data analyses. In this paper, I present alternative models of Red Knot population dynamics to reflect alternative hypotheses. Using 2 models with different lemming population cycle lengths and 2 models with different horseshoe crab effects, I project the knot population into the future under environmental stochasticity and parametric uncertainty with each model. I then compare each model's predictions to 10 yr of population monitoring from Delaware Bay. Using Bayes' theorem and model weight updating, models can accrue weight or support for one or another hypothesis of population dynamics. With 4 models of Red Knot population dynamics and only 10 yr of data, no hypothesis clearly predicted population count data better than another. The collapsed lemming cycle model performed best, accruing ~35% of the model weight, followed closely by the horseshoe crab egg abundance model, which accrued ~30% of the weight. The models that predicted no decline or stable populations (i.e. the 4-yr lemming cycle model and the weak horseshoe crab effect model) were the most weakly supported.
A Stochastic Cobweb Dynamical Model
Directory of Open Access Journals (Sweden)
Serena Brianzoni
2008-01-01
_,__0__1, and the forward predictor with probability (1−, so that the expected price at time is a random variable and consequently the dynamics describing the price evolution in time is governed by a stochastic dynamical system. The dynamical system becomes a Markov process when the memory rate vanishes. In particular, we study the Markov chain in the cases of discrete and continuous time. Using a mixture of analytical tools and numerical methods, we show that, when prices take discrete values, the corresponding Markov chain is asymptotically stable. In the case with continuous prices and nonnecessarily zero memory rate, numerical evidence of bounded price oscillations is shown. The role of the memory rate is studied through numerical experiments, this study confirms the stabilizing effects of the presence of resistant memory.
Modeling microbial growth and dynamics.
Esser, Daniel S; Leveau, Johan H J; Meyer, Katrin M
2015-11-01
Modeling has become an important tool for widening our understanding of microbial growth in the context of applied microbiology and related to such processes as safe food production, wastewater treatment, bioremediation, or microbe-mediated mining. Various modeling techniques, such as primary, secondary and tertiary mathematical models, phenomenological models, mechanistic or kinetic models, reactive transport models, Bayesian network models, artificial neural networks, as well as agent-, individual-, and particle-based models have been applied to model microbial growth and activity in many applied fields. In this mini-review, we summarize the basic concepts of these models using examples and applications from food safety and wastewater treatment systems. We further review recent developments in other applied fields focusing on models that explicitly include spatial relationships. Using these examples, we point out the conceptual similarities across fields of application and encourage the combined use of different modeling techniques in hybrid models as well as their cross-disciplinary exchange. For instance, pattern-oriented modeling has its origin in ecology but may be employed to parameterize microbial growth models when experimental data are scarce. Models could also be used as virtual laboratories to optimize experimental design analogous to the virtual ecologist approach. Future microbial growth models will likely become more complex to benefit from the rich toolbox that is now available to microbial growth modelers.
Equivalent dynamic model of DEMES rotary joint
Zhao, Jianwen; Wang, Shu; Xing, Zhiguang; McCoul, David; Niu, Junyang; Huang, Bo; Liu, Liwu; Leng, Jinsong
2016-07-01
The dielectric elastomer minimum energy structure (DEMES) can realize large angular deformations by a small voltage-induced strain of the dielectric elastomer (DE), so it is a suitable candidate to make a rotary joint for a soft robot. Dynamic analysis is necessary for some applications, but the dynamic response of DEMESs is difficult to model because of the complicated morphology and viscoelasticity of the DE film. In this paper, a method composed of theoretical analysis and experimental measurement is presented to model the dynamic response of a DEMES rotary joint under an alternating voltage. Based on measurements of equivalent driving force and damping of the DEMES, the model can be derived. Some experiments were carried out to validate the equivalent dynamic model. The maximum angle error between model and experiment is greater than ten degrees, but it is acceptable to predict angular velocity of the DEMES, therefore, it can be applied in feedforward-feedback compound control.
Structural Dynamics Model of a Cartesian Robot
1985-10-01
34 D FILE COPY AD-A198 053 *.CC Technical Report 1009 Structural Dynamics Model of a Cartesian Robot "DTIC SELEC T E 0 Alfonso Garcia Reynoso MIT...COVERED Structural Dynamics Model of a Cartesian Robot technical report G. PERFORMING ORG. REPORT NUM9ER 7. AUTHO0R(@) S. CONTRACT On GRANT NUMSER...8217 %S S Structural Dynamics Model of a Cartesian Robot by Alfonso Garcia Reynoso BSME Instituto Tecnol6gico de Veracruz (1967) MSME Instituto Tecnol6gico
Modeling the Dynamics of an Information System
Directory of Open Access Journals (Sweden)
Jacek Unold
2003-11-01
Full Text Available The article concentrates on the nature of a social subsystem of an information system. It analyzes the nature of information processes of collectivity within an IS and introduces a model of IS dynamics. The model is based on the assumption that a social subsystem of an information system works as a nonlinear dynamic system. The model of IS dynamics is verified on the indexes of the stock market. It arises from the basic assumption of the technical analysis of the markets, that is, the index chart reflects the play of demand and supply, which in turn represents the crowd sentiment on the market.
Schmidt, Christian; Piel, Alexander
2015-10-01
The Brownian motion of a single particle in the plasma sheath is studied to separate the effect of stochastic heating by charge fluctuations from heating by collective effects. By measuring the particle velocities in the ballistic regime and by carefully determining the particle mass from the Epstein drag it is shown that for a pressure of 10 Pa, which is typical of many experiments, the proper kinetic temperature of the Brownian particle remains close to the gas temperature and rises only slightly with particle size. This weak effect is confirmed by a detailed model for charging and charge fluctuations in the sheath. A substantial temperature rise is found for decreasing pressure, which approximately shows the expected scaling with p(-2). The system under study is an example for non-equilibrium Brownian motion under the influence of white noise without corresponding dissipation.
Suppression of a Brownian noise in a hole-type sensor due to induced-charge electro-osmosis
Sugioka, Hideyuki
2016-03-01
Noise reduction is essential for a single molecular sensor. Thus, we propose a novel noise reduction mechanism using a hydrodynamic force due to induced-charge electro-osmosis (ICEO) in a hole-type sensor and numerically examine the performance. By the boundary element method that considers both a Brownian motion and an ICEO flow of a polarizable particle, we find that the Brownian noise in a current signal is suppressed significantly in a converging channel because of the ICEO flow around the particle in the presence of an electric field. Further, we propose a simple model that explains a numerically obtained threshold voltage of the suppression of the Brownian noise due to ICEO. We believe that our findings contribute greatly to developments of a single molecular sensor.
Forecasting house prices in the 50 states using Dynamic Model Averaging and Dynamic Model Selection
DEFF Research Database (Denmark)
Bork, Lasse; Møller, Stig Vinther
2015-01-01
We examine house price forecastability across the 50 states using Dynamic Model Averaging and Dynamic Model Selection, which allow for model change and parameter shifts. By allowing the entire forecasting model to change over time and across locations, the forecasting accuracy improves...
Shotorban, Babak
2010-04-01
The dynamic least-squares kernel density (LSQKD) model [C. Pantano and B. Shotorban, Phys. Rev. E 76, 066705 (2007)] is used to solve the Fokker-Planck equations. In this model the probability density function (PDF) is approximated by a linear combination of basis functions with unknown parameters whose governing equations are determined by a global least-squares approximation of the PDF in the phase space. In this work basis functions are set to be Gaussian for which the mean, variance, and covariances are governed by a set of partial differential equations (PDEs) or ordinary differential equations (ODEs) depending on what phase-space variables are approximated by Gaussian functions. Three sample problems of univariate double-well potential, bivariate bistable neurodynamical system [G. Deco and D. Martí, Phys. Rev. E 75, 031913 (2007)], and bivariate Brownian particles in a nonuniform gas are studied. The LSQKD is verified for these problems as its results are compared against the results of the method of characteristics in nondiffusive cases and the stochastic particle method in diffusive cases. For the double-well potential problem it is observed that for low to moderate diffusivity the dynamic LSQKD well predicts the stationary PDF for which there is an exact solution. A similar observation is made for the bistable neurodynamical system. In both these problems least-squares approximation is made on all phase-space variables resulting in a set of ODEs with time as the independent variable for the Gaussian function parameters. In the problem of Brownian particles in a nonuniform gas, this approximation is made only for the particle velocity variable leading to a set of PDEs with time and particle position as independent variables. Solving these PDEs, a very good performance by LSQKD is observed for a wide range of diffusivities.
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.
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.
Holographic Brownian motion and time scales in strongly coupled plasmas
Energy Technology Data Exchange (ETDEWEB)
Atmaja, Ardian Nata [Research Center for Physics, Indonesian Institute of Sciences (LIPI), Kompleks PUSPITEK Serpong, Tangerang 15310 (Indonesia); Indonesia Center for Theoretical and Mathematical Physics (ICTMP), Bandung 40132 (Indonesia); Boer, Jan de [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands); Shigemori, Masaki [Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502 (Japan); Hakubi Center, Kyoto University, Yoshida-Ushinomiyacho, Sakyo-ku, Kyoto 606-8501 (Japan)
2014-03-15
We study Brownian motion of a heavy quark in field theory plasma in the AdS/CFT setup and discuss the time scales characterizing the interaction between the Brownian particle and plasma constituents. Based on a simple kinetic theory, we first argue that the mean-free-path time is related to the connected 4-point function of the random force felt by the Brownian particle. Then, by holographically computing the 4-point function and regularizing the IR divergence appearing in the computation, we write down a general formula for the mean-free-path time, and apply it to the STU black hole which corresponds to plasma charged under three U(1)R-charges. The result indicates that the Brownian particle collides with many plasma constituents simultaneously.
Parameter Estimation for Generalized Brownian Motion with Autoregressive Increments
Fendick, Kerry
2011-01-01
This paper develops methods for estimating parameters for a generalization of Brownian motion with autoregressive increments called a Brownian ray with drift. We show that a superposition of Brownian rays with drift depends on three types of parameters - a drift coefficient, autoregressive coefficients, and volatility matrix elements, and we introduce methods for estimating each of these types of parameters using multidimensional times series data. We also cover parameter estimation in the contexts of two applications of Brownian rays in the financial sphere: queuing analysis and option valuation. For queuing analysis, we show how samples of queue lengths can be used to estimate the conditional expectation functions for the length of the queue and for increments in its net input and lost potential output. For option valuation, we show how the Black-Scholes-Merton formula depends on the price of the security on which the option is written through estimates not only of its volatility, but also of a coefficient ...
Nonlinear dynamic phenomena in the beer model
DEFF Research Database (Denmark)
Mosekilde, Erik; Laugesen, Jakob Lund
2007-01-01
The production-distribution system or "beer game" is one of the most well-known system dynamics models. Notorious for the complex dynamics it produces, the beer game has been used for nearly five decades to illustrate how structure generates behavior and to explore human decision making. Here we...
System Dynamics Modelling for a Balanced Scorecard
DEFF Research Database (Denmark)
Nielsen, Steen; Nielsen, Erland Hejn
2008-01-01
Purpose - To construct a dynamic model/framework inspired by a case study based on an international company. As described by the theory, one of the main difficulties of BSC is to foresee the time lag dimension of different types of indicators and their combined dynamic effects. Design/methodology...
Phone Routing using the Dynamic Memory Model
DEFF Research Database (Denmark)
Bendtsen, Claus Nicolaj; Krink, Thiemo
2002-01-01
In earlier studies a genetic algorithm (GA) extended with the dynamic memory model has shown remarkable performance on real-world-like problems. In this paper we experiment with routing in communication networks and show that the dynamic memory GA performs remarkable well compared to ant colony o...
A new dynamics model for traffic flow
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
As a study method of traffic flow, dynamics models were developedand applied in the last few decades. However, there exist some flaws in most existing models. In this note, a new dynamics model is proposed by using car-following theory and the usual connection method of micro-macro variables, which can overcome some ubiquitous problems in the existing models. Numerical results show that the new model can very well simulate traffic flow conditions, such as congestion, evacuation of congestion, stop-and-go phenomena and phantom jam.
Response of Brownian Fluctuations to External Forces
Laub, Jeffrey William
Millikan's law of particle fall is an empirical result which shows the dependence of particle fall rate in a gas on particle radius and host gas density. The size of submicron particles in gases has long been determined by Millikan's law. The dominant factor is Stokes' law with a correction added to account for the physics of slip. However, it was recently shown by Kim and Fedele that Brownian fluctuations affect the fall rate while showing no anomalies in the density dependence of the rms displacement. The effect was an enhancement of the fall rate of small particles as the density of the host gas is increased. This enhancement showed a size dependence in the form of a smooth transition from the one of decreasing fall rate with increasing density for large particles (~0.4 μm radius) to another of increasing fall rate with increasing gas density for small particles ( ~0.15mum radius). The magnitude of the anomaly is determined by how the rms Brownian velocity compares with its fall rate. In an effort to understand the effect of Brownian fluctuations coupling with gravity, a new experiment has been carried out where an AC field was applied to force particles to fluctuate more in the vertical direction on one hand and where a constant DC field was applied to change the effective force of gravity on the other. These fields were applied to a charged oil drop in the 0.2 to 0.3 μm radius range falling in a nitrogen environment. Displacements over a 4 second time interval were repeatedly measured in both the vertical and horizontal directions. The original experimental apparatus was used with some modifications. The modifications included computer automation of particle control and data taking to allow for longer use of the same particle, up to 120 hours, and to facilitate application of the additional fields. The objective was to make large particles appear to be smaller via forced oscillations and make them fall faster or slower via the DC bias to effect the change in
Directory of Open Access Journals (Sweden)
Carlos Borau
Full Text Available Cells modulate themselves in response to the surrounding environment like substrate elasticity, exhibiting structural reorganization driven by the contractility of cytoskeleton. The cytoskeleton is the scaffolding structure of eukaryotic cells, playing a central role in many mechanical and biological functions. It is composed of a network of actins, actin cross-linking proteins (ACPs, and molecular motors. The motors generate contractile forces by sliding couples of actin filaments in a polar fashion, and the contractile response of the cytoskeleton network is known to be modulated also by external stimuli, such as substrate stiffness. This implies an important role of actomyosin contractility in the cell mechano-sensing. However, how cells sense matrix stiffness via the contractility remains an open question. Here, we present a 3-D Brownian dynamics computational model of a cross-linked actin network including the dynamics of molecular motors and ACPs. The mechano-sensing properties of this active network are investigated by evaluating contraction and stress in response to different substrate stiffness. Results demonstrate two mechanisms that act to limit internal stress: (i In stiff substrates, motors walk until they exert their maximum force, leading to a plateau stress that is independent of substrate stiffness, whereas (ii in soft substrates, motors walk until they become blocked by other motors or ACPs, leading to submaximal stress levels. Therefore, this study provides new insights into the role of molecular motors in the contraction and rigidity sensing of cells.
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.
Brownian Motion of a Classical Particle in Quantum Environment
Tsekov, R.
2017-01-01
The Klein-Kramers equation, governing the Brownian motion of a classical particle in quantum environment under the action of an arbitrary external potential, is derived. Quantum temperature and friction operators are introduced and at large friction the corresponding Smoluchowski equation is obtained. Introducing the Bohm quantum potential, this Smoluchowski equation is extended to describe the Brownian motion of a quantum particle in quantum environment.
Airship dynamics modeling: A literature review
Li, Yuwen; Nahon, Meyer; Sharf, Inna
2011-04-01
The resurgence of airships has created a need for dynamics models and simulation capabilities adapted to these lighter-than-air vehicles. However, the modeling techniques for airship dynamics have lagged behind and are less systematic than those for fixed-wing aircraft. A state-of-the-art literature review is presented on airship dynamics modeling, aiming to provide a comprehensive description of the main problems in this area and a useful source of references for researchers and engineers interested in modern airship applications. The references are categorized according to the major topics in this area: aerodynamics, flight dynamics, incorporation of structural flexibility, incorporation of atmospheric turbulence, and effects of ballonets. Relevant analytical, numerical, and semi-empirical techniques are discussed, with a particular focus on how the main differences between lighter-than-air and heavier-than-air aircraft have been addressed in the modeling. Directions are suggested for future research on each of these topics.
Molecular dynamics model of dimethyl ether
Energy Technology Data Exchange (ETDEWEB)
Lin, B.; Halley, W.J. [Univ. of Minnesota, Minneapolis, MN (United States)
1995-11-02
We report a molecular dynamics model of the monomeric liquid dimethyl ether. The united atom approach is used to treat CH{sub 3} groups as point source centers. Partial charges are derived from the experimental dipole moment. Harmonic force constants are used for intramolecular interactions, and their values are so chosen that the model`s fundamental frequencies agree with experimental results. Because we are interested in solvation properties, the model contains flexible molecules, allowing molecular distortion and internal dynamical quantities. We report radial distribution functions and the static structure factors as well as some dynamical quantities such as the dynamical structure factor, infrared absorption, and Raman scattering spectra. Calculated results agree reasonably well with experimental and other simulation results. 25 refs., 8 figs., 1 tab.
MODELING MICROBUBBLE DYNAMICS IN BIOMEDICAL APPLICATIONS
Institute of Scientific and Technical Information of China (English)
CHAHINE Georges L.; HSIAO Chao-Tsung
2012-01-01
Controlling mierobubble dynamics to produce desirable biomedical outcomes when and where necessary and avoid deleterious effects requires advanced knowledge,which can be achieved only through a combination of experimental and numerical/analytical techniques.The present communication presents a multi-physics approach to study the dynamics combining viscousinviseid effects,liquid and structure dynamics,and multi bubble interaction.While complex numerical tools are developed and used,the study aims at identifying the key parameters influencing the dynamics,which need to be included in simpler models.
Bayesian semiparametric dynamic Nelson-Siegel model
C. Cakmakli
2011-01-01
This paper proposes the Bayesian semiparametric dynamic Nelson-Siegel model where the density of the yield curve factors and thereby the density of the yields are estimated along with other model parameters. This is accomplished by modeling the error distributions of the factors according to a Diric
System Identification by Dynamic Factor Models
C. Heij (Christiaan); W. Scherrer; M. Destler
1996-01-01
textabstractThis paper concerns the modelling of stochastic processes by means of dynamic factor models. In such models the observed process is decomposed into a structured part called the latent process, and a remainder that is called noise. The observed variables are treated in a symmetric way, so
Damping mechanisms and models in structural dynamics
DEFF Research Database (Denmark)
Krenk, Steen
2002-01-01
Several aspects of damping models for dynamic analysis of structures are investigated. First the causality condition for structural response is used to identify rules for the use of complex-valued frequency dependent material models, illustrated by the shortcomings of the elastic hysteretic model...
Dynamic Models of Insurgent Activity
2014-05-19
is a natural Eulerian limit involving nonlocal interactions and in the other case particle paths can cross and one may consider only a kinetic model ...SECURITY CLASSIFICATION OF: The purpose of this project was to develop the modeling and analysis of both PDE-based and statistical point process models ...to the point where models developed in research papers several years ago are now in place in the field in over 30 cities worldwide. This project
Probabilistic Modeling in Dynamic Information Retrieval
Sloan, M. C.
2016-01-01
Dynamic modeling is used to design systems that are adaptive to their changing environment and is currently poorly understood in information retrieval systems. Common elements in the information retrieval methodology, such as documents, relevance, users and tasks, are dynamic entities that may evolve over the course of several interactions, which is increasingly captured in search log datasets. Conventional frameworks and models in information retrieval treat these elements as static, or only...
Identification and Modelling of Linear Dynamic Systems
Directory of Open Access Journals (Sweden)
Stanislav Kocur
2006-01-01
Full Text Available System identification and modelling are very important parts of system control theory. System control is only as good as good is created model of system. So this article deals with identification and modelling problems. There are simple classification and evolution of identification methods, and then the modelling problem is described. Rest of paper is devoted to two most known and used models of linear dynamic systems.
Fedosov, Dmitry A; Karniadakis, George Em; Caswell, Bruce
2010-04-14
Polymer fluids are modeled with dissipative particle dynamics (DPD) as undiluted bead-spring chains and their solutions. The models are assessed by investigating their steady shear-rate properties. Non-Newtonian viscosity and normal stress coefficients, for shear rates from the lower to the upper Newtonian regimes, are calculated from both plane Couette and plane Poiseuille flows. The latter is realized as reverse Poiseuille flow (RPF) generated from two Poiseuille flows driven by uniform body forces in opposite directions along two-halves of a computational domain. Periodic boundary conditions ensure the RPF wall velocity to be zero without density fluctuations. In overlapping shear-rate regimes the RPF properties are confirmed to be in good agreement with those calculated from plane Couette flow with Lees-Edwards periodic boundary conditions (LECs), the standard virtual rheometer for steady shear-rate properties. The concentration and the temperature dependence of the properties of the model fluids are shown to satisfy the principles of concentration and temperature superposition commonly employed in the empirical correlation of real polymer-fluid properties. The thermodynamic validity of the equation of state is found to be a crucial factor for the achievement of time-temperature superposition. With these models, RPF is demonstrated to be an accurate and convenient virtual rheometer for the acquisition of steady shear-rate rheological properties. It complements, confirms, and extends the results obtained with the standard LEC configuration, and it can be used with the output from other particle-based methods, including molecular dynamics, Brownian dynamics, smooth particle hydrodynamics, and the lattice Boltzmann method.
Institute of Scientific and Technical Information of China (English)
Feng Yu; Lin Jian-Zhong
2008-01-01
The collision efficiency in the Brownian coagulation is investigated. A new mechanical model of collision between two identical spherical particles is proposed, and a set of corresponding collision equations is established. The equations are solved numerically, thereby obtaining the collision efficiency for the monodisperse dioctyl phthalate spherical aerosols with diameters ranging from 100 to 760 nm in the presence of van der Waals force and the elastic deformation force.The calculated collision efficiency, in agreement with the experimental data qualitatively, decreases with the increase of particle diameter except a small peak appearing in the particles with a diameter of 510 nm. The results show that the interparticle elastic deformation force cannot be neglected in the computation of particle Brownian coagulation.Finally, a set of new expressions relating collision efficiency to particle diameter is established.
Directory of Open Access Journals (Sweden)
K. C. Lee
2013-02-01
Full Text Available Multifractional Brownian motions have become popular as flexible models in describing real-life signals of high-frequency features in geoscience, microeconomics, and turbulence, to name a few. The time-changing Hurst exponent, which describes regularity levels depending on time measurements, and variance, which relates to an energy level, are two parameters that characterize multifractional Brownian motions. This research suggests a combined method of estimating the time-changing Hurst exponent and variance using the local variation of sampled paths of signals. The method consists of two phases: initially estimating global variance and then accurately estimating the time-changing Hurst exponent. A simulation study shows its performance in estimation of the parameters. The proposed method is applied to characterization of atmospheric stability in which descriptive statistics from the estimated time-changing Hurst exponent and variance classify stable atmosphere flows from unstable ones.
Lee, K. C.
2013-02-01
Multifractional Brownian motions have become popular as flexible models in describing real-life signals of high-frequency features in geoscience, microeconomics, and turbulence, to name a few. The time-changing Hurst exponent, which describes regularity levels depending on time measurements, and variance, which relates to an energy level, are two parameters that characterize multifractional Brownian motions. This research suggests a combined method of estimating the time-changing Hurst exponent and variance using the local variation of sampled paths of signals. The method consists of two phases: initially estimating global variance and then accurately estimating the time-changing Hurst exponent. A simulation study shows its performance in estimation of the parameters. The proposed method is applied to characterization of atmospheric stability in which descriptive statistics from the estimated time-changing Hurst exponent and variance classify stable atmosphere flows from unstable ones.
A stochastic model of human gait dynamics
Ashkenazy, Yosef; M. Hausdorff, Jeffrey; Ch. Ivanov, Plamen; Eugene Stanley, H.
2002-12-01
We present a stochastic model of gait rhythm dynamics, based on transitions between different “neural centers”, that reproduces distinctive statistical properties of normal human walking. By tuning one model parameter, the transition (hopping) range, the model can describe alterations in gait dynamics from childhood to adulthood-including a decrease in the correlation and volatility exponents with maturation. The model also generates time series with multifractal spectra whose broadness depends only on this parameter. Moreover, we find that the volatility exponent increases monotonically as a function of the width of the multifractal spectrum, suggesting the possibility of a change in multifractality with maturation.
Integration of Dynamic Models in Range Operations
Bardina, Jorge; Thirumalainambi, Rajkumar
2004-01-01
This work addresses the various model interactions in real-time to make an efficient internet based decision making tool for Shuttle launch. The decision making tool depends on the launch commit criteria coupled with physical models. Dynamic interaction between a wide variety of simulation applications and techniques, embedded algorithms, and data visualizations are needed to exploit the full potential of modeling and simulation. This paper also discusses in depth details of web based 3-D graphics and applications to range safety. The advantages of this dynamic model integration are secure accessibility and distribution of real time information to other NASA centers.
Engineered swift equilibration of a Brownian particle
Martínez, Ignacio A.; Petrosyan, Artyom; Guéry-Odelin, David; Trizac, Emmanuel; Ciliberto, Sergio
2016-09-01
A fundamental and intrinsic property of any device or natural system is its relaxation time τrelax, which is the time it takes to return to equilibrium after the sudden change of a control parameter. Reducing τrelax is frequently necessary, and is often obtained by a complex feedback process. To overcome the limitations of such an approach, alternative methods based on suitable driving protocols have been recently demonstrated, for isolated quantum and classical systems. Their extension to open systems in contact with a thermostat is a stumbling block for applications. Here, we design a protocol, named Engineered Swift Equilibration (ESE), that shortcuts time-consuming relaxations, and we apply it to a Brownian particle trapped in an optical potential whose properties can be controlled in time. We implement the process experimentally, showing that it allows the system to reach equilibrium 100 times faster than the natural equilibration rate. We also estimate the increase of the dissipated energy needed to get such a time reduction. The method paves the way for applications in micro- and nano-devices, where the reduction of operation time represents as substantial a challenge as miniaturization.
From Brownian motion to power of fluctuations
Directory of Open Access Journals (Sweden)
B. Berche
2012-12-01
Full Text Available The year 2012 marks the 140th birth anniversary of Marian Smoluchowski (28.05.1872-5.09.1917, a man who "made ground-breaking contribution to the theory of Brownian motion, the theory of sedimentation, the statistical nature of the Second Law, the theory and practice of density fluctuations (critical opalescence. During his final years of scientific creativity his pioneering theory of coagulation and diffusion-limited reaction rate appeared. These outstanding achievements present true gems which dominate the description of soft matter physics and chemical physics as well as the related areas up till now!" This quotation was taken from the lecture by Peter Hanggi given at international conference Statistical Physics: Modern Trends and Applications that took place in Lviv, Ukraine on July 3-6, 2012 (see conference web-page for more details and was dedicated to the commemoration of Smoluchowski's work. This and forthcoming issues of the Condensed Matter Physics contain papers presented at this conference.
The future dynamic world model
Karr, Thomas J.
2014-10-01
Defense and security forces exploit sensor data by means of a model of the world. They use a world model to geolocate sensor data, fuse it with other data, navigate platforms, recognize features and feature changes, etc. However, their need for situational awareness today exceeds the capabilities of their current world model for defense operations, despite the great advances of sensing technology in recent decades. I review emerging technologies that may enable a great improvement in the spatial and spectral coverage, the timeliness, and the functional insight of their world model.
ReaDDy--a software for particle-based reaction-diffusion dynamics in crowded cellular environments.
Directory of Open Access Journals (Sweden)
Johannes Schöneberg
Full Text Available We introduce the software package ReaDDy for simulation of detailed spatiotemporal mechanisms of dynamical processes in the cell, based on reaction-diffusion dynamics with particle resolution. In contrast to other particle-based reaction kinetics programs, ReaDDy supports particle interaction potentials. This permits effects such as space exclusion, molecular crowding and aggregation to be modeled. The biomolecules simulated can be represented as a sphere, or as a more complex geometry such as a domain structure or polymer chain. ReaDDy bridges the gap between small-scale but highly detailed molecular dynamics or Brownian dynamics simulations and large-scale but little-detailed reaction kinetics simulations. ReaDDy has a modular design that enables the exchange of the computing core by efficient platform-specific implementations or dynamical models that are different from Brownian dynamics.
Uncertainty and Sensitivity in Surface Dynamics Modeling
Kettner, Albert J.; Syvitski, James P. M.
2016-05-01
Papers for this special issue on 'Uncertainty and Sensitivity in Surface Dynamics Modeling' heralds from papers submitted after the 2014 annual meeting of the Community Surface Dynamics Modeling System or CSDMS. CSDMS facilitates a diverse community of experts (now in 68 countries) that collectively investigate the Earth's surface-the dynamic interface between lithosphere, hydrosphere, cryosphere, and atmosphere, by promoting, developing, supporting and disseminating integrated open source software modules. By organizing more than 1500 researchers, CSDMS has the privilege of identifying community strengths and weaknesses in the practice of software development. We recognize, for example, that progress has been slow on identifying and quantifying uncertainty and sensitivity in numerical modeling of earth's surface dynamics. This special issue is meant to raise awareness for these important subjects and highlight state-of-the-art progress.
Dynamic stiffness model of spherical parallel robots
Cammarata, Alessandro; Caliò, Ivo; D`Urso, Domenico; Greco, Annalisa; Lacagnina, Michele; Fichera, Gabriele
2016-12-01
A novel approach to study the elastodynamics of Spherical Parallel Robots is described through an exact dynamic model. Timoshenko arches are used to simulate flexible curved links while the base and mobile platforms are modelled as rigid bodies. Spatial joints are inherently included into the model without Lagrangian multipliers. At first, the equivalent dynamic stiffness matrix of each leg, made up of curved links joined by spatial joints, is derived; then these matrices are assembled to obtain the Global Dynamic Stiffness Matrix of the robot at a given pose. Actuator stiffness is also included into the model to verify its influence on vibrations and modes. The latter are found by applying the Wittrick-Williams algorithm. Finally, numerical simulations and direct comparison to commercial FE results are used to validate the proposed model.
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.
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.
Model Reduction of Nonlinear Fire Dynamics Models
Lattimer, Alan Martin
2016-01-01
Due to the complexity, multi-scale, and multi-physics nature of the mathematical models for fires, current numerical models require too much computational effort to be useful in design and real-time decision making, especially when dealing with fires over large domains. To reduce the computational time while retaining the complexity of the domain and physics, our research has focused on several reduced-order modeling techniques. Our contributions are improving wildland fire reduced-order mod...
Energy Technology Data Exchange (ETDEWEB)
Haddad, Zoubida [Department of Mechanical Engineering, Technology Faculty, Firat University, TR-23119, Elazig (Turkey); Department of Fluid Mechanics, Faculty of Physics, University of Sciences and Technology-Houari Boumediene, Algiers (Algeria); Abu-Nada, Eiyad [Department of Mechanical Engineering, King Faisal University, Al-Ahsa 31982 (Saudi Arabia); Oztop, Hakan F. [Department of Mechanical Engineering, Technology Faculty, Firat University, TR-23119, Elazig (Turkey); Mataoui, Amina [Department of Fluid Mechanics, Faculty of Physics, University of Sciences and Technology-Houari Boumediene, Algiers (Algeria)
2012-07-15
Natural convection heat transfer and fluid flow of CuO-Water nano-fluids is studied using the Rayleigh-Benard problem. A two component non-homogenous equilibrium model is used for the nano-fluid that incorporates the effects of Brownian motion and thermophoresis. Variable thermal conductivity and variable viscosity are taken into account in this work. Finite volume method is used to solve governing equations. Results are presented by streamlines, isotherms, nano-particle distribution, local and mean Nusselt numbers and nano-particle profiles at top and bottom side. Comparison of two cases as absence of Brownian and thermophoresis effects and presence of Brownian and thermophoresis effects showed that higher heat transfer is formed with the presence of Brownian and thermophoresis effect. In general, by considering the role of thermophoresis and Brownian motion, an enhancement in heat transfer is observed at any volume fraction of nano-particles. However, the enhancement is more pronounced at low volume fraction of nano-particles and the heat transfer decreases by increasing nano-particle volume fraction. On the other hand, by neglecting the role of thermophoresis and Brownian motion, deterioration in heat transfer is observed and this deterioration elevates by increasing the volume fraction of nano-particles. (authors)
Forecasting with Dynamic Regression Models
Pankratz, Alan
2012-01-01
One of the most widely used tools in statistical forecasting, single equation regression models is examined here. A companion to the author's earlier work, Forecasting with Univariate Box-Jenkins Models: Concepts and Cases, the present text pulls together recent time series ideas and gives special attention to possible intertemporal patterns, distributed lag responses of output to input series and the auto correlation patterns of regression disturbance. It also includes six case studies.
Intermediate scattering function of an anisotropic active Brownian particle
Kurzthaler, Christina; Leitmann, Sebastian; Franosch, Thomas
2016-10-01
Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations.
Towards Disaggregate Dynamic Travel Forecasting Models
Institute of Scientific and Technical Information of China (English)
Moshe Ben-Akiva; Jon Bottom; Song Gao; Haris N. Koutsopoulos; Yang Wen
2007-01-01
The authors argue that travel forecasting models should be dynamic and disaggregate in their representation of demand, supply, and supply-demand interactions, and propose a framework for such models.The proposed framework consists of disaggregate activity-based representation of travel choices of individual motorists on the demand side integrated with disaggregate dynamic modeling of network performance,through vehicle-based traffic simulation models on the supply side. The demand model generates individual members of the population and assigns to them socioeconomic characteristics. The generated motorists maintain these characteristics when they are loaded on the network by the supply model. In an equilibrium setting, the framework lends itself to a fixed-point formulation to represent and resolve demand-supply interactions. The paper discusses some of the remaining development challenges and presents an example of an existing travel forecasting model system that incorporates many of the proposed elements.
A stochastic evolutionary model for survival dynamics
Fenner, Trevor; Loizou, George
2014-01-01
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis, traditionally employed in clinical trials and reliability analysis in engineering. In our model, the only implicit assumption made is that the longer an actor has been in the system, the more likely it is to have failed. We derive a power-law distribution for the process and provide preliminary empirical evidence for the validity of the model from two well-known survival analysis data sets.
Dynamical modelling of coordinated multiple robot systems
Hayati, Samad
1987-01-01
The state of the art in the modeling of the dynamics of coordinated multiple robot manipulators is summarized and various problems related to this subject are discussed. It is recognized that dynamics modeling is a component used in the design of controllers for multiple cooperating robots. As such, the discussion addresses some problems related to the control of multiple robots. The techniques used to date in the modeling of closed kinematic chains are summarized. Various efforts made to date for the control of coordinated multiple manipulators is summarized.
Cellular automata modeling of pedestrian's crossing dynamics
Institute of Scientific and Technical Information of China (English)
张晋; 王慧; 李平
2004-01-01
Cellular automata modeling techniques and the characteristics of mixed traffic flow were used to derive the 2-dimensional model presented here for simulation of pedestrian's crossing dynamics.A conception of "stop point" is introduced to deal with traffic obstacles and resolve conflicts among pedestrians or between pedestrians and the other vehicles on the crosswalk.The model can be easily extended,is very efficient for simulation of pedestrian's crossing dynamics,can be integrated into traffic simulation software,and has been proved feasible by simulation experiments.
Stochastic transition model for pedestrian dynamics
Schultz, Michael
2012-01-01
The proposed stochastic model for pedestrian dynamics is based on existing approaches using cellular automata, combined with substantial extensions, to compensate the deficiencies resulting of the discrete grid structure. This agent motion model is extended by both a grid-based path planning and mid-range agent interaction component. The stochastic model proves its capabilities for a quantitative reproduction of the characteristic shape of the common fundamental diagram of pedestrian dynamics. Moreover, effects of self-organizing behavior are successfully reproduced. The stochastic cellular automata approach is found to be adequate with respect to uncertainties in human motion patterns, a feature previously held by artificial noise terms alone.
Concept-Oriented Modeling of Dynamic Behavior
Breedveld, P.C.; Borutzky, Wolfgang
2011-01-01
This chapter introduces the reader to the concept-oriented approach to modeling that clearly separates ideal concepts from the physical components of a system when modeling its dynamic behavior for a specific problem context. This is done from a port-based point of view for which the domain-independ
A system dynamics model for communications networks
Awcock, A. J.; King, T. E. G.
1985-09-01
An abstract model of a communications network in system dynamics terminology is developed as implementation of this model by a FORTRAN program package developed at RSRE is discussed. The result of this work is a high-level simulation package in which the performance of adaptive routing algorithms and other network controls may be assessed for a network of arbitrary topology.
Dynamic modeling of the INAPRO aquaponic system
Karimanzira, Divas; Keesman, Karel J.; Kloas, Werner; Baganz, Daniela; Rauschenbach, Thomas
2016-01-01
The use of modeling techniques to analyze aquaponics systems is demonstrated with an example of dynamic modeling for the production of Nile tilapia (Oreochromis niloticus) and tomatoes (Solanum lycopersicon) using the innovative double recirculating aquaponic system ASTAF-PRO. For the management and
A Discrete Dynamical Model of Signed Partitions
Directory of Open Access Journals (Sweden)
G. Chiaselotti
2013-01-01
Full Text Available We use a discrete dynamical model with three evolution rules in order to analyze the structure of a partially ordered set of signed integer partitions whose main properties are actually not known. This model is related to the study of some extremal combinatorial sum problems.
Dynamical effects of overparametrization in nonlinear models
Aguirre, Luis Antonio; Billings, S. A.
1995-01-01
This paper is concemed with dynamical reconstruction for nonlinear systems. The effects of the driving function and of the complexity of a given representation on the bifurcation patter are investigated. It is shown that the use of different driving functions to excite the system may yield models with different bifurcation patterns. The complexity of the reconstructions considered is quantified by the embedding dimension and the number of estimated parameters. In this respect it appears that models which reproduce the original bifurcation behaviour are of limited complexity and that excessively complex models tend to induce ghost bifurcations and spurious dynamical regimes. Moreover, some results suggest that the effects of overparametrization on the global dynamical behaviour of a nonlinear model may be more deleterious than the presence of moderate noise levels. In order to precisely quantify the complexity of the reconstructions, global polynomials are used although the results are believed to apply to a much wider class of representations including neural networks.
Dynamic optimization deterministic and stochastic models
Hinderer, Karl; Stieglitz, Michael
2016-01-01
This book explores discrete-time dynamic optimization and provides a detailed introduction to both deterministic and stochastic models. Covering problems with finite and infinite horizon, as well as Markov renewal programs, Bayesian control models and partially observable processes, the book focuses on the precise modelling of applications in a variety of areas, including operations research, computer science, mathematics, statistics, engineering, economics and finance. Dynamic Optimization is a carefully presented textbook which starts with discrete-time deterministic dynamic optimization problems, providing readers with the tools for sequential decision-making, before proceeding to the more complicated stochastic models. The authors present complete and simple proofs and illustrate the main results with numerous examples and exercises (without solutions). With relevant material covered in four appendices, this book is completely self-contained.
Replicator-dynamics models of sexual conflict.
Kimura, Mariko; Ihara, Yasuo
2009-09-07
Evolutionary conflict between the sexes has been studied in various taxa and in various contexts. When the sexes are in conflict over mating rates, natural selection favors both males that induce higher mating rates and females that are more successful at resisting mating attempts. Such sexual conflict may result in an escalating coevolutionary arms race between males and females. In this article, we develop simple replicator-dynamics models of sexual conflict in order to investigate its evolutionary dynamics. Two specific models of the dependence of a female's fitness on her number of matings are considered: in model 1, female fitness decreases linearly with increasing number of matings and in model 2, there is an optimal number of matings that maximizes female fitness. For each of these models, we obtain the conditions for a coevolutionary process to establish costly male and female traits and examine under what circumstances polymorphism is maintained at equilibrium. Then we discuss how assumptions in previous models of sexual conflict are translated to fit to our model framework and compare our results with those of the previous studies. The simplicity of our models allows us to consider sexual conflict in various contexts within a single framework. In addition, we find that our model 2 shows more complicated evolutionary dynamics than model 1. In particular, the population exhibits bistability, where the evolutionary outcome depends on the initial state, only in model 2.
Cosmological model with dynamical curvature
Stichel, Peter C
2016-01-01
We generalize the recently introduced relativistic Lagrangian darkon fluid model (EPJ C (2015) 75:9) by starting with a self-gravitating geodesic fluid whose energy-momentum tensor is dust-like with a nontrivial energy flow. The corresponding covariant propagation and constraint equations are considered in a shear-free nonrelativistic limit whose analytic solutions determine the 1st-order relativistic correction to the spatial curvature. This leads to a cosmological model where the accelerated expansion of the Universe is driven by a time-dependent spatial curvature without the need for introducing any kind of dark energy. We derive the differential equation to be satisfied by the area distance for this model.
Adaptation dynamics of the quasispecies model
Jain, Kavita
2009-02-01
We study the adaptation dynamics of an initially maladapted population evolving via the elementary processes of mutation and selection. The evolution occurs on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and have many local peaks separated by low fitness valleys. We mainly focus on the Eigen's model that describes the deterministic dynamics of an infinite number of self-replicating molecules. In the stationary state, for small mutation rates such a population forms a {\\it quasispecies} which consists of the fittest genotype and its closely related mutants. The quasispecies dynamics on rugged fitness landscape follow a punctuated (or step-like) pattern in which a population jumps from a low fitness peak to a higher one, stays there for a considerable time before shifting the peak again and eventually reaches the global maximum of the fitness landscape. We calculate exactly several properties of this dynamical process within a simplified version of the quasispecies model.
A dynamical model for the Utricularia trap
Llorens, Coraline; Argentina, Médéric; Bouret, Yann; Marmottant, Philippe; Vincent, Olivier
2012-01-01
We propose a model that captures the dynamics of a carnivorous plant, Utricularia inflata. This plant possesses tiny traps for capturing small aquatic animals. Glands pump water out of the trap, yielding a negative pressure difference between the plant and its surroundings. The trap door is set into a meta-stable state and opens quickly as an extra pressure is generated by the displacement of a potential prey. As the door opens, the pressure difference sucks the animal into the trap. We write an ODE model that captures all the physics at play. We show that the dynamics of the plant is quite similar to neuronal dynamics and we analyse the effect of a white noise on the dynamics of the trap. PMID:22859569
Adaptation dynamics of the quasispecies model
Indian Academy of Sciences (India)
Kavita Jain
2008-08-01
We study the adaptation dynamics of an initially maladapted population evolving via the elementary processes of mutation and selection. The evolution occurs on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and have many local peaks separated by low fitness valleys. We mainly focus on the Eigen’s model that describes the deterministic dynamics of an infinite number of self-replicating molecules. In the stationary state, for small mutation rates such a population forms a quasispecies which consists of the fittest genotype and its closely related mutants. The quasispecies dynamics on rugged fitness landscape follow a punctuated (or step-like) pattern in which a population jumps from a low fitness peak to a higher one, stays there for a considerable time before shifting the peak again and eventually reaches the global maximum of the fitness landscape. We calculate exactly several properties of this dynamical process within a simplified version of the quasispecies model.
OpenCL/OpenGL aproach for studying active Brownian motion
Żabicki, Michał A
2011-01-01
This work presents a methodology for studying active Brownian dynamics on ratchet potentials using interoperating OpenCL and OpenGL frameworks. Programing details along with optimization issues are discussed, followed by a comparison of performance on different devices. Time of visualization using OpenGL sharing buffer with OpenCL has been tested against another technique which, while using OpenGL, does not share memory buffer with OpenCL. Both methods has been compared with visualizing data to external software - gnuplot. OpenCL/OpenGL interoperating method has been found the most appropriate to visualize large set of data for which calculation itself is not very long.
Modeling hybrid perovskites by molecular dynamics.
Mattoni, Alessandro; Filippetti, Alessio; Caddeo, Claudia
2017-02-01
The topical review describes the recent progress in the modeling of hybrid perovskites by molecular dynamics simulations. Hybrid perovskites and in particular methylammonium lead halide (MAPI) have a tremendous technological relevance representing the fastest-advancing solar material to date. They also represent the paradigm of an organic-inorganic crystalline material with some conceptual peculiarities: an inorganic semiconductor for what concerns the electronic and absorption properties with a hybrid and solution processable organic-inorganic body. After briefly explaining the basic concepts of ab initio and classical molecular dynamics, the model potential recently developed for hybrid perovskites is described together with its physical motivation as a simple ionic model able to reproduce the main dynamical properties of the material. Advantages and limits of the two strategies (either ab initio or classical) are discussed in comparison with the time and length scales (from pico to microsecond scale) necessary to comprehensively study the relevant properties of hybrid perovskites from molecular reorientations to electrocaloric effects. The state-of-the-art of the molecular dynamics modeling of hybrid perovskites is reviewed by focusing on a selection of showcase applications of methylammonium lead halide: molecular cations disorder; temperature evolution of vibrations; thermally activated defects diffusion; thermal transport. We finally discuss the perspectives in the modeling of hybrid perovskites by molecular dynamics.
Modeling hybrid perovskites by molecular dynamics
Mattoni, Alessandro; Filippetti, Alessio; Caddeo, Claudia
2017-02-01
The topical review describes the recent progress in the modeling of hybrid perovskites by molecular dynamics simulations. Hybrid perovskites and in particular methylammonium lead halide (MAPI) have a tremendous technological relevance representing the fastest-advancing solar material to date. They also represent the paradigm of an organic-inorganic crystalline material with some conceptual peculiarities: an inorganic semiconductor for what concerns the electronic and absorption properties with a hybrid and solution processable organic-inorganic body. After briefly explaining the basic concepts of ab initio and classical molecular dynamics, the model potential recently developed for hybrid perovskites is described together with its physical motivation as a simple ionic model able to reproduce the main dynamical properties of the material. Advantages and limits of the two strategies (either ab initio or classical) are discussed in comparison with the time and length scales (from pico to microsecond scale) necessary to comprehensively study the relevant properties of hybrid perovskites from molecular reorientations to electrocaloric effects. The state-of-the-art of the molecular dynamics modeling of hybrid perovskites is reviewed by focusing on a selection of showcase applications of methylammonium lead halide: molecular cations disorder; temperature evolution of vibrations; thermally activated defects diffusion; thermal transport. We finally discuss the perspectives in the modeling of hybrid perovskites by molecular dynamics.
Dispersive models describing mosquitoes’ population dynamics
Yamashita, W. M. S.; Takahashi, L. T.; Chapiro, G.
2016-08-01
The global incidences of dengue and, more recently, zica virus have increased the interest in studying and understanding the mosquito population dynamics. Understanding this dynamics is important for public health in countries where climatic and environmental conditions are favorable for the propagation of these diseases. This work is based on the study of nonlinear mathematical models dealing with the life cycle of the dengue mosquito using partial differential equations. We investigate the existence of traveling wave solutions using semi-analytical method combining dynamical systems techniques and numerical integration. Obtained solutions are validated through numerical simulations using finite difference schemes.
Induction generator models in dynamic simulation tools
DEFF Research Database (Denmark)
Knudsen, Hans; Akhmatov, Vladislav
1999-01-01
. It is found to be possible to include a transient model in dynamic stability tools and, then, obtain correct results also in dynamic tools. The representation of the rotating system influences on the voltage recovery shape which is an important observation in case of windmills, where a heavy mill is connected......For AC network with large amount of induction generators (windmills) the paper demonstrates a significant discrepancy in the simulated voltage recovery after fault in weak networks when comparing dynamic and transient stability descriptions and the reasons of discrepancies are explained...
Dynamics of the supermarket model
MacPhee, I M; Vachkovskaia, M
2010-01-01
We consider the long term behaviour of a Markov chain \\xi(t) on \\Z^N based on the N station supermarket model. Different routing policies for the supermarket model give different Markov chains. We show that for a general class of local routing policies, "join the least weighted queue" (JLW), the N one-dimensional components \\xi_i(t) can be partitioned into disjoint clusters C_k. Within each cluster C_k the "speed" of each component \\xi_j converges to a constant V_k and under certain conditions \\xi is recurrent in shape on each cluster. To establish these results we have assembled methods from two distinct areas of mathematics, semi-martingale techniques used for showing stability of Markov chains together with the theory of optimal flows in networks. As corollaries to our main result we obtain the stability classification of the supermarket model under any JLW policy and can explicitly compute the C_k and V_k for any instance of the model and specific JLW policy.
Intermittent rainfall in dynamic multimedia fate modeling.
Hertwich, E G
2001-03-01
It has been shown that steady-state multimedia models (level III fugacity models) lead to a substantial underestimate of air concentrations for chemicals with a low Henry's law constant (H multimedia models are used to estimate the spatial range or inhalation exposure. A dynamic model of pollutant fate is developed for conditions of intermittent rainfall to calculate the time profile of pollutant concentrations in different environmental compartments. The model utilizes a new, mathematically efficient approach to dynamic multimedia fate modeling that is based on the convolution of solutions to the initial conditions problem. For the first time, this approach is applied to intermittent conditions. The investigation indicates that the time-averaged pollutant concentrations under intermittent rainfall can be approximated by the appropriately weighted average of steady-state concentrations under conditions with and without rainfall.
Experimental Modeling of Dynamic Systems
DEFF Research Database (Denmark)
Knudsen, Morten Haack
2006-01-01
insight. It is based on a sensitivity approach that is useful for choice of model structure, for experiment design, and for accuracy verification. The method is implemented in the Matlab toolkit Senstools. The method and the presentation have been developed with generally preferred learning styles in mind....... In a comprehensive evaluation of the course, student responses to a course questionnaire and to an Index Of Learning Styles Questionnaire are analyzed and correlated....
Feature Extraction for Structural Dynamics Model Validation
Energy Technology Data Exchange (ETDEWEB)
Farrar, Charles [Los Alamos National Laboratory; Nishio, Mayuko [Yokohama University; Hemez, Francois [Los Alamos National Laboratory; Stull, Chris [Los Alamos National Laboratory; Park, Gyuhae [Chonnam Univesity; Cornwell, Phil [Rose-Hulman Institute of Technology; Figueiredo, Eloi [Universidade Lusófona; Luscher, D. J. [Los Alamos National Laboratory; Worden, Keith [University of Sheffield
2016-01-13
As structural dynamics becomes increasingly non-modal, stochastic and nonlinear, finite element model-updating technology must adopt the broader notions of model validation and uncertainty quantification. For example, particular re-sampling procedures must be implemented to propagate uncertainty through a forward calculation, and non-modal features must be defined to analyze nonlinear data sets. The latter topic is the focus of this report, but first, some more general comments regarding the concept of model validation will be discussed.
Dynamic exponents for potts model cluster algorithms
Coddington, Paul D.; Baillie, Clive F.
We have studied the Swendsen-Wang and Wolff cluster update algorithms for the Ising model in 2, 3 and 4 dimensions. The data indicate simple relations between the specific heat and the Wolff autocorrelations, and between the magnetization and the Swendsen-Wang autocorrelations. This implies that the dynamic critical exponents are related to the static exponents of the Ising model. We also investigate the possibility of similar relationships for the Q-state Potts model.
The dynamic model of enterprise revenue management
Mitsel, A. A.; Kataev, M. Yu; Kozlov, S. V.; Korepanov, K. V.
2017-01-01
The article presents the dynamic model of enterprise revenue management. This model is based on the quadratic criterion and linear control law. The model is founded on multiple regression that links revenues with the financial performance of the enterprise. As a result, optimal management is obtained so as to provide the given enterprise revenue, namely, the values of financial indicators that ensure the planned profit of the organization are acquired.
Dynamic queuing transmission model for dynamic network loading
DEFF Research Database (Denmark)
Raovic, Nevena; Nielsen, Otto Anker; Prato, Carlo Giacomo
2016-01-01
and allowing for the representation of multiple vehicle classes, queue spillbacks and shock waves. The model assumes that a link is split into a moving part plus a queuing part, and p that traffic dynamics are given by a triangular fundamental diagram. A case-study is investigated and the DQTM is compared...... with single-class LTM, single-class DQM and multi-class DQM. Under the model assumptions, single-class models indicate that the LTM and the DQTM give similar results and that the shock wave property is properly included in the DQTM, while the multi-class models show substantially different travel times...... for two vehicle classes. Moreover, the results show that the travel time will be underestimated without considering the shock wave property...
Dynamic Model for Life History of Scyphozoa.
Directory of Open Access Journals (Sweden)
Congbo Xie
Full Text Available A two-state life history model governed by ODEs is formulated to elucidate the population dynamics of jellyfish and to illuminate the triggering mechanism of its blooms. The polyp-medusa model admits trichotomous global dynamic scenarios: extinction, polyps survival only, and both survival. The population dynamics sensitively depend on several biotic and abiotic limiting factors such as substrate, temperature, and predation. The combination of temperature increase, substrate expansion, and predator diminishment acts synergistically to create a habitat that is more favorable for jellyfishes. Reducing artificial marine constructions, aiding predator populations, and directly controlling the jellyfish population would help to manage the jellyfish blooms. The theoretical analyses and numerical experiments yield several insights into the nature underlying the model and shed some new light on the general control strategy for jellyfish.
Dynamic Model Identification for Industrial Robots
Directory of Open Access Journals (Sweden)
Ngoc Dung Vuong
2009-12-01
Full Text Available In this paper, a systematic procedure for identifying the dynamics of industrialrobots is presented. Since joint friction can be highly nonlinearwith time varyingcharacteristics in the low speed region,a simple and yet effective scheme has been used toidentify the boundary velocity that separates this “dynamic” friction region from its staticregion. The robot’s dynamic model is then identified in this static region, where thenonlinnear friction model is reduced to the linear-in-parameter form. To overcome thedrawbacks of the least squares estimator, which does not take in any constraints, anonlinear optimization problem is formulated to guarantee the physical feasibility of theidentified parameters. The proposed procedure has been demonstrated on the first fourlinks of the Mitsubishi PA10 manipulator, an improved dynamic model was obtained andthe the effectiveness of the proposed identification procedure is demonstrated.
A Dynamic Model for Energy Structure Analysis
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Energy structure is a complicated system concerning economic development, natural resources, technological innovation, ecological balance, social progress and many other elements. It is not easy to explain clearly the developmental mechanism of an energy system and the mutual relations between the energy system and its related environments by the traditional methods. It is necessary to develop a suitable dynamic model, which can reflect the dynamic characteristics and the mutual relations of the energy system and its related environments. In this paper, the historical development of China's energy structure was analyzed. A new quantitative analysis model was developed based on system dynamics principles through analysis of energy resources, and the production and consumption of energy in China and comparison with the world. Finally, this model was used to predict China's future energy structures under different conditions.
Brownian aggregation rate of colloid particles with several active sites
Energy Technology Data Exchange (ETDEWEB)
Nekrasov, Vyacheslav M.; Yurkin, Maxim A.; Chernyshev, Andrei V., E-mail: chern@ns.kinetics.nsc.ru [Institute of Chemical Kinetics and Combustion, Institutskaya 3, 630090 Novosibirsk (Russian Federation); Physics Department, Novosibirsk State University, Pirogova 2, 630090 Novosibirsk (Russian Federation); Polshchitsin, Alexey A. [Institute of Chemical Kinetics and Combustion, Institutskaya 3, 630090 Novosibirsk (Russian Federation); JSC “VECTOR-BEST”, PO BOX 492, Novosibirsk 630117 (Russian Federation); Yakovleva, Galina E. [JSC “VECTOR-BEST”, PO BOX 492, Novosibirsk 630117 (Russian Federation); Maltsev, Valeri P. [Institute of Chemical Kinetics and Combustion, Institutskaya 3, 630090 Novosibirsk (Russian Federation); Physics Department, Novosibirsk State University, Pirogova 2, 630090 Novosibirsk (Russian Federation); Department of Preventive Medicine, Novosibirsk State Medical University, Krasny Prospect 52, 630091 Novosibirsk (Russian Federation)
2014-08-14
We theoretically analyze the aggregation kinetics of colloid particles with several active sites. Such particles (so-called “patchy particles”) are well known as chemically anisotropic reactants, but the corresponding rate constant of their aggregation has not yet been established in a convenient analytical form. Using kinematic approximation for the diffusion problem, we derived an analytical formula for the diffusion-controlled reaction rate constant between two colloid particles (or clusters) with several small active sites under the following assumptions: the relative translational motion is Brownian diffusion, and the isotropic stochastic reorientation of each particle is Markovian and arbitrarily correlated. This formula was shown to produce accurate results in comparison with more sophisticated approaches. Also, to account for the case of a low number of active sites per particle we used Monte Carlo stochastic algorithm based on Gillespie method. Simulations showed that such discrete model is required when this number is less than 10. Finally, we applied the developed approach to the simulation of immunoagglutination, assuming that the formed clusters have fractal structure.
Modeling Of Ballistic Missile Dynamics
Directory of Open Access Journals (Sweden)
Salih Mahmoud Attiya
2013-05-01
Full Text Available Aerodynamic modeling of ballistic missile in pitch plane is performed and the open-loop transfer function related to the jet deflector angle as input and pitch rate, normal acceleration as output has been derived with certain acceptable assumptions. For typical values of ballistic missile parameters such as mass, velocity, altitude, moment of inertia, thrust, moment and lift coefficient show that, the step time response and frequency response of the missile is unstable. The steady state gain, damping ratio and undraped natural frequency depend on the missile parameters. To stabilize the missile a lead compensator must be added to the forward loop.
Dynamic modeling of solar dynamic components and systems
Hochstein, John I.; Korakianitis, T.
1992-09-01
The purpose of this grant was to support NASA in modeling efforts to predict the transient dynamic and thermodynamic response of the space station solar dynamic power generation system. In order to meet the initial schedule requirement of providing results in time to support installation of the system as part of the initial phase of space station, early efforts were executed with alacrity and often in parallel. Initially, methods to predict the transient response of a Rankine as well as a Brayton cycle were developed. Review of preliminary design concepts led NASA to select a regenerative gas-turbine cycle using a helium-xenon mixture as the working fluid and, from that point forward, the modeling effort focused exclusively on that system. Although initial project planning called for a three year period of performance, revised NASA schedules moved system installation to later and later phases of station deployment. Eventually, NASA selected to halt development of the solar dynamic power generation system for space station and to reduce support for this project to two-thirds of the original level.
Directory of Open Access Journals (Sweden)
Davide Mercadante
Full Text Available Pectin methylesterases (PMEs hydrolyze the methylester groups that are found on the homogalacturonan (HG chains of pectic polysaccharides in the plant cell wall. Plant and bacterial PMEs are especially interesting as the resulting de-methylesterified (carboxylated sugar residues are found to be arranged contiguously, indicating a so-called processive nature of these enzymes. Here we report the results of continuum electrostatics calculations performed along the molecular dynamics trajectory of a PME-HG-decasaccharide complex. In particular it was observed that, when the methylester groups of the decasaccharide were arranged in order to mimic the just-formed carboxylate product of de-methylesterification, a net unidirectional sliding of the model decasaccharide was subsequently observed along the enzyme's binding groove. The changes that occurred in the electrostatic binding energy and protein dynamics during this translocation provide insights into the mechanism by which the enzyme rectifies Brownian motions to achieve processivity. The free energy that drives these molecular motors is thus demonstrated to be incorporated endogenously in the methylesterified groups of the HG chains and is not supplied exogenously.
Dynamical Model of Weak Pion Production Reactions
Sato, T; Lee, T S H
2003-01-01
The dynamical model of pion electroproduction has been extended to investigate the weak pion production reactions. The predicted cross sections of neutrino-induced pion production reactions are in good agreement with the existing data. We show that the renormalized(dressed) axial N-$\\Delta$ form factor contains large dynamical pion cloud effects and this renormalization effects are crucial in getting agreement with the data. We conclude that the N-$\\Delta$ transitions predicted by the constituent quark model are consistent with the existing neutrino induced pion production data in the $\\Delta$ region.
Dynamical properties of the Rabi model
Hu, Binglu; Zhou, Huili; Chen, Shujie; Xianlong, Gao; Wang, Kelin
2017-02-01
We study the dynamical properties of the quantum Rabi model using a systematic expansion method. Based on the observation that the parity symmetry of the Rabi model is kept during evolution of the states, we decompose the initial state and the time-dependent one into positive and negative parity parts expanded by superposition of the coherent states. The evolutions of the corresponding positive and the negative parities are obtained, in which the expansion coefficients in the dynamical equations are known from the derived recurrence relation.
Research on nonlinear stochastic dynamical price model
Energy Technology Data Exchange (ETDEWEB)
Li Jiaorui [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); School of Statistics, Xi' an University of Finance and Economics, Xi' an 710061 (China)], E-mail: jiaoruili@mail.nwpu.edu.cn; Xu Wei; Xie Wenxian; Ren Zhengzheng [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)
2008-09-15
In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies.
Modeling emotional dynamics : currency versus field.
Energy Technology Data Exchange (ETDEWEB)
Sallach, D .L.; Decision and Information Sciences; Univ. of Chicago
2008-08-01
Randall Collins has introduced a simplified model of emotional dynamics in which emotional energy, heightened and focused by interaction rituals, serves as a common denominator for social exchange: a generic form of currency, except that it is active in a far broader range of social transactions. While the scope of this theory is attractive, the specifics of the model remain unconvincing. After a critical assessment of the currency theory of emotion, a field model of emotion is introduced that adds expressiveness by locating emotional valence within its cognitive context, thereby creating an integrated orientation field. The result is a model which claims less in the way of motivational specificity, but is more satisfactory in modeling the dynamic interaction between cognitive and emotional orientations at both individual and social levels.
Dynamic model for the popularity of websites
Lee, Chang-Yong; Kim, Seungwhan
2002-03-01
In this paper, we have studied a dynamic model to explain the observed characteristics of websites in the World Wide Web. The dynamic model consists of the self-growth term for each website and the external force term acting on the website. With simulations of the model, we can explain most of the important characteristics of websites. These characteristics include a power-law distribution of the number of visitors to websites, fluctuation in the fractional growth of individual websites, and the relationship between the age and the popularity of the websites. We also investigated a few variants of the model and showed that the ingredients included in the model adequately explain the behavior of the websites.
Modelling environmental dynamics. Advances in goematic solutions
Energy Technology Data Exchange (ETDEWEB)
Paegelow, Martin [Toulouse-2 Univ., 31 (France). GEODE UMR 5602 CNRS; Camacho Olmedo, Maria Teresa (eds.) [Granada Univ (Spain). Dpto. de Analisis Geografico Regional y Geografia Fisica
2008-07-01
Modelling environmental dynamics is critical to understanding and predicting the evolution of the environment in response to the large number of influences including urbanisation, climate change and deforestation. Simulation and modelling provide support for decision making in environmental management. The first chapter introduces terminology and provides an overview of methodological modelling approaches which may be applied to environmental and complex dynamics. Based on this introduction this book illustrates various models applied to a large variety of themes: deforestation in tropical regions, fire risk, natural reforestation in European mountains, agriculture, biodiversity, urbanism, climate change and land management for decision support, etc. These case studies, provided by a large international spectrum of researchers and presented in a uniform structure, focus particularly on methods and model validation so that this book is not only aimed at researchers and graduates but also at professionals. (orig.)
Modeling the dynamics of dissent
Lee, Eun; Lee, Sang Hoon
2016-01-01
We investigate opinion formation against authority in an authoritarian society composed of agents with different levels of authority. We explore a (symbolically) "right" opinion, held by lower-ranking, obedient, less authoritative people, spreading in an environment of a "wrong" opinion held by authoritative leaders. The mental picture would be that of a corrupt society where the ruled people revolts against authority, but it could be argued to hold in more general situations. In our model, agents can change their opinion depending on the relative authority to their neighbors and their own confidence level. In addition, with a certain probability, agents can override the authority to take the right opinion of a neighbor. Based on analytic derivation and numerical simulations, we observe that both the network structure and heterogeneity in authority, and their correlation significantly affect the possibility of the right opinion to spread in the population. In particular, the right opinion is suppressed when t...
Microstructure from simulated Brownian suspension flows at large shear rate
Morris, Jeffrey F.; Katyal, Bhavana
2002-06-01
Pair microstructure of concentrated Brownian suspensions in simple-shear flow is studied by sampling of configurations from dynamic simulations by the Stokesian Dynamics technique. Simulated motions are three dimensional with periodic boundary conditions to mimic an infinitely extended suspension. Hydrodynamic interactions through Newtonian fluid and Brownian motion are the only physical influences upon the motion of the monodisperse hard-sphere particles. The dimensionless parameters characterizing the suspension are the particle volume fraction and Péclet number, defined, respectively, as φ=(4π/3)na3 with n the number density and a the sphere radius, and Pe=6πηγ˙a3/kT with η the fluid viscosity, γ˙ the shear rate, and kT the thermal energy. The majority of the results reported are from simulations at Pe=1000; results of simulations at Pe=1, 25, and 100 are also reported for φ=0.3 and φ=0.45. The pair structure is characterized by the pair distribution function, g(r)=P1|1(r)/n, where P1|1(r) is the conditional probability of finding a pair at a separation vector r. The structure under strong shearing exhibits an accumulation of pair probability at contact, and angular distortion (from spherical symmetry at Pe=0), with both effects increasing with Pe. Flow simulations were performed at Pe=1000 for eight volume fractions in the range 0.2⩽φ⩽0.585. For φ=0.2-0.3, the pair structure at contact, g(|r|=2)≡g(2), is found to exhibit a single region of strong correlation, g(2)≫1, at points around the axis of compression, with a particle-deficient wake in the extensional zones. A qualitative change in microstructure is observed between φ=0.3 and φ=0.37. For φ⩾0.37, the maximum g(2) lies at points in the shear plane nearly on the x axis of the bulk simple shear flow Ux=γ˙y, while at smaller φ, the maximum g(2) lies near the compressional axis; long-range string ordering is not observed. For φ=0.3 and φ=0.45, g(2)˜Pe0.7 for 1⩽Pe⩽1000, a
Dynamic Model Averaging in Large Model Spaces Using Dynamic Occam’s Window*
Onorante, Luca; Raftery, Adrian E.
2015-01-01
Bayesian model averaging has become a widely used approach to accounting for uncertainty about the structural form of the model generating the data. When data arrive sequentially and the generating model can change over time, Dynamic Model Averaging (DMA) extends model averaging to deal with this situation. Often in macroeconomics, however, many candidate explanatory variables are available and the number of possible models becomes too large for DMA to be applied in its original form. We propose a new method for this situation which allows us to perform DMA without considering the whole model space, but using a subset of models and dynamically optimizing the choice of models at each point in time. This yields a dynamic form of Occam’s window. We evaluate the method in the context of the problem of nowcasting GDP in the Euro area. We find that its forecasting performance compares well with that of other methods. PMID:26917859
Dynamics models of soil organic carbon
Institute of Scientific and Technical Information of China (English)
YANGLi-xia; PANJian-jun
2003-01-01
As the largest pool of terrestrial organic carbon, soils interact strongly with atmosphere composition, climate, and land change. Soil organic carbon dynamics in ecosystem plays a great role in global carbon cycle and global change. With development of mathematical models that simulate changes in soil organic carbon, there have been considerable advances in understanding soil organic carbon dynamics. This paper mainly reviewed the composition of soil organic matter and its influenced factors, and recommended some soil organic matter models worldwide. Based on the analyses of the developed results at home and abroad, it is suggested that future soil organic matter models should be developed toward based-process models, and not always empirical ones. The models are able to reveal their interaction between soil carbon systems, climate and land cover by technique and methods of GIS (Geographical Information System) and RS (Remote Sensing). These models should be developed at a global scale, in dynamically describing the spatial and temporal changes of soil organic matter cycle. Meanwhile, the further researches on models should be strengthen for providing theory basis and foundation in making policy of green house gas emission in China.
Hidden Symmetry of a Fluid Dynamical Model
Neves, C
2001-01-01
A connection between solutions of the relativistic d-brane system in (d+1) dimensions with the solutions of a Galileo invariant fluid in d-dimensions is by now well established. However, the physical nature of the light-cone gauge description of a relativistic membrane changes after the reduction to the fluid dynamical model since the gauge symmetry is lost. In this work we argue that the original gauge symmetry present in a relativistic d-brane system can be recovered after the reduction process to a d-dimensional fluid model. To this end we propose, without introducing Wess-Zumino fields, a gauge invariant theory of isentropic fluid dynamics and show that this symmetry corresponds to the invariance under local translation of the velocity potential in the fluid dynamics picture. We show that different but equivalent choices of the sympletic sector lead to distinct representations of the embedded gauge algebra.
Dynamic landscape models of coevolutionary games
Richter, Hendrik
2016-01-01
Players of coevolutionary games may update not only their strategies but also their networks of interaction. Based on interpreting the payoff of players as fitness, dynamic landscape models are proposed. The modeling procedure is carried out for Prisoner's Dilemma (PD) and Snowdrift (SD) games that both use either birth-death (BD) or death-birth (DB) strategy updating. With the main focus on using dynamic fitness landscapes as an alternative tool for analyzing coevolutionary games, landscape measures such as modality, ruggedness and information content are computed and analyzed. In addition, fixation properties of the games and quantifiers characterizing the network of interaction are calculated numerically. Relations are established between landscape properties expressed by landscape measures and quantifiers of coevolutionary game dynamics such as fixation probabilities, fixation times and network properties
Knowledge Map: Mathematical Model and Dynamic Behaviors
Institute of Scientific and Technical Information of China (English)
Hai Zhuge; Xiang-Feng Luo
2005-01-01
Knowledge representation and reasoning is a key issue of the Knowledge Grid. This paper proposes a Knowledge Map (KM) model for representing and reasoning causal knowledge as an overlay in the Knowledge Grid. It extends Fuzzy Cognitive Maps (FCMs) to represent and reason not only simple cause-effect relations, but also time-delay causal relations, conditional probabilistic causal relations and sequential relations. The mathematical model and dynamic behaviors of KM are presented. Experiments show that, under certain conditions, the dynamic behaviors of KM can translate between different states. Knowing this condition, experts can control or modify the constructed KM while its dynamic behaviors do not accord with their expectation. Simulations and applications show that KM is more powerful and natural than FCM in emulating real world.
Contact force models for multibody dynamics
Flores, Paulo
2016-01-01
This book analyzes several compliant contact force models within the context of multibody dynamics, while also revisiting the main issues associated with fundamental contact mechanics. In particular, it presents various contact force models, from linear to nonlinear, from purely elastic to dissipative, and describes their parameters. Addressing the different numerical methods and algorithms for contact problems in multibody systems, the book describes the gross motion of multibody systems by using a two-dimensional formulation based on the absolute coordinates and employs different contact models to represent contact-impact events. Results for selected planar multibody mechanical systems are presented and utilized to discuss the main assumptions and procedures adopted throughout this work. The material provided here indicates that the prediction of the dynamic behavior of mechanical systems involving contact-impact strongly depends on the choice of contact force model. In short, the book provides a comprehens...
System and mathematical modeling of quadrotor dynamics
Goodman, Jacob M.; Kim, Jinho; Gadsden, S. Andrew; Wilkerson, Stephen A.
2015-05-01
Unmanned aerial systems (UAS) are becoming increasingly visible in our daily lives; and range in operation from search and rescue, monitoring hazardous environments, and to the delivery of goods. One of the most popular UAS are based on a quad-rotor design. These are typically small devices that rely on four propellers for lift and movement. Quad-rotors are inherently unstable, and rely on advanced control methodologies to keep them operating safely and behaving in a predictable and desirable manner. The control of these devices can be enhanced and improved by making use of an accurate dynamic model. In this paper, we examine a simple quadrotor model, and note some of the additional dynamic considerations that were left out. We then compare simulation results of the simple model with that of another comprehensive model.
Human Muscle Fatigue Model in Dynamic Motions
Ma, Ruina; Bennis, Fouad; Ma, Liang
2012-01-01
Human muscle fatigue is considered to be one of the main reasons for Musculoskeletal Disorder (MSD). Recent models have been introduced to define muscle fatigue for static postures. However, the main drawbacks of these models are that the dynamic effect of the human and the external load are not taken into account. In this paper, each human joint is assumed to be controlled by two muscle groups to generate motions such as push/pull. The joint torques are computed using Lagrange's formulation to evaluate the dynamic factors of the muscle fatigue model. An experiment is defined to validate this assumption and the result for one person confirms its feasibility. The evaluation of this model can predict the fatigue and MSD risk in industry production quickly.
Wrapping Brownian motion and heat kernels I: compact Lie groups
Maher, David G
2010-01-01
An important object of study in harmonic analysis is the heat equation. On a Euclidean space, the fundamental solution of the associated semigroup is known as the heat kernel, which is also the law of Brownian motion. Similar statements also hold in the case of a Lie group. By using the wrapping map of Dooley and Wildberger, we show how to wrap a Brownian motion to a compact Lie group from its Lie algebra (viewed as a Euclidean space) and find the heat kernel. This is achieved by considering It\\^o type stochastic differential equations and applying the Feynman-Ka\\v{c} theorem.
Brownian motion of solitons in a Bose-Einstein condensate.
Aycock, Lauren M; Hurst, Hilary M; Efimkin, Dmitry K; Genkina, Dina; Lu, Hsin-I; Galitski, Victor M; Spielman, I B
2017-03-07
We observed and controlled the Brownian motion of solitons. We launched solitonic excitations in highly elongated [Formula: see text] Bose-Einstein condensates (BECs) and showed that a dilute background of impurity atoms in a different internal state dramatically affects the soliton. With no impurities and in one dimension (1D), these solitons would have an infinite lifetime, a consequence of integrability. In our experiment, the added impurities scatter off the much larger soliton, contributing to its Brownian motion and decreasing its lifetime. We describe the soliton's diffusive behavior using a quasi-1D scattering theory of impurity atoms interacting with a soliton, giving diffusion coefficients consistent with experiment.
The quantum Rabi model: solution and dynamics
Xie, Qiongtao; Batchelor, Murray T; Lee, Chaohong
2016-01-01
This article presents a review of recent developments on various aspects of the quantum Rabi model. Particular emphasis is given on the exact analytic solution obtained in terms of confluent Heun functions. The analytic solutions for various generalisations of the quantum Rabi model are also discussed. Results are also reviewed on the level statistics and the dynamics of the quantum Rabi model. The article concludes with an introductory overview of several experimental realisations of the quantum Rabi model. An outlook towards future developments is also given.
The quantum Rabi model: solution and dynamics
Xie, Qiongtao; Zhong, Honghua; Batchelor, Murray T.; Lee, Chaohong
2017-03-01
This article presents a review of recent developments on various aspects of the quantum Rabi model. Particular emphasis is given on the exact analytic solution obtained in terms of confluent Heun functions. The analytic solutions for various generalisations of the quantum Rabi model are also discussed. Results are also reviewed on the level statistics and the dynamics of the quantum Rabi model. The article concludes with an introductory overview of several experimental realisations of the quantum Rabi model. An outlook towards future developments is also given.
Modeling of Reactor Kinetics and Dynamics
Energy Technology Data Exchange (ETDEWEB)
Matthew Johnson; Scott Lucas; Pavel Tsvetkov
2010-09-01
In order to model a full fuel cycle in a nuclear reactor, it is necessary to simulate the short time-scale kinetic behavior of the reactor as well as the long time-scale dynamics that occur with fuel burnup. The former is modeled using the point kinetics equations, while the latter is modeled by coupling fuel burnup equations with the kinetics equations. When the equations are solved simultaneously with a nonlinear equation solver, the end result is a code with the unique capability of modeling transients at any time during a fuel cycle.
Modeling the Hydrogen Bond within Molecular Dynamics
Lykos, Peter
2004-01-01
The structure of a hydrogen bond is elucidated within the framework of molecular dynamics based on the model of Rahman and Stillinger (R-S) liquid water treatment. Thus, undergraduates are exposed to the powerful but simple use of classical mechanics to solid objects from a molecular viewpoint.
A Stochastic Dynamic Model of Computer Viruses
Directory of Open Access Journals (Sweden)
Chunming Zhang
2012-01-01
Full Text Available A stochastic computer virus spread model is proposed and its dynamic behavior is fully investigated. Specifically, we prove the existence and uniqueness of positive solutions, and the stability of the virus-free equilibrium and viral equilibrium by constructing Lyapunov functions and applying Ito's formula. Some numerical simulations are finally given to illustrate our main results.
Advances in Inventory Management: Dynamic Models
C. Pinçe (Çerağ)
2010-01-01
textabstractIn this study, we develop and analyze models incorporating some of the dynamic aspects of inventory systems. In particular, we focus on two major themes to be analyzed separately: nonstationarity in demand rate and unfixed purchasing prices. In the first part of the study, we consider a
A Dynamic Distribution Model for Combat Logistics
1999-11-23
develop a heuristic algorithm for a similar problem, only capacity expansion can occur in any amount (modeled with continuous variables) while in...and Rutenberg (1977) solve it with a heuristic algorithm . Our problem is also related to the dynamic facility location problem. This problem seeks to
Nearly Unbiased Estimationin Dynamic Panel Data Models
M.A. Carree (Martin)
2002-01-01
textabstractThis paper introduces two easy to calculate estimators with desirable properties for the autoregressive parameter in dynamic panel data models. The estimators are (nearly) unbiased and perform satisfactorily even for small samples in either the time-series or cross-section dimension.
Structural Equation Modeling of Travel Choice Dynamics
Golob, Thomas F.
1988-01-01
This research has two objectives. The first objective is to explore the use of the modeling tool called "latent structural equations" (structural equations with latent variables) in the general field of travel behavior analysis and the more specific field of dynamic analysis of travel behavior. The second objective is to apply a latent structural equation model in order to determine the causal relationships between income, car ownership, and mobility. Many transportation researchers ...
Population mixture model for nonlinear telomere dynamics
Itzkovitz, Shalev; Shlush, Liran I.; Gluck, Dan; Skorecki, Karl
2008-12-01
Telomeres are DNA repeats protecting chromosomal ends which shorten with each cell division, eventually leading to cessation of cell growth. We present a population mixture model that predicts an exponential decrease in telomere length with time. We analytically solve the dynamics of the telomere length distribution. The model provides an excellent fit to available telomere data and accounts for the previously unexplained observation of telomere elongation following stress and bone marrow transplantation, thereby providing insight into the nature of the telomere clock.
Feature extraction for structural dynamics model validation
Energy Technology Data Exchange (ETDEWEB)
Hemez, Francois [Los Alamos National Laboratory; Farrar, Charles [Los Alamos National Laboratory; Park, Gyuhae [Los Alamos National Laboratory; Nishio, Mayuko [UNIV OF TOKYO; Worden, Keith [UNIV OF SHEFFIELD; Takeda, Nobuo [UNIV OF TOKYO
2010-11-08
This study focuses on defining and comparing response features that can be used for structural dynamics model validation studies. Features extracted from dynamic responses obtained analytically or experimentally, such as basic signal statistics, frequency spectra, and estimated time-series models, can be used to compare characteristics of structural system dynamics. By comparing those response features extracted from experimental data and numerical outputs, validation and uncertainty quantification of numerical model containing uncertain parameters can be realized. In this study, the applicability of some response features to model validation is first discussed using measured data from a simple test-bed structure and the associated numerical simulations of these experiments. issues that must be considered were sensitivity, dimensionality, type of response, and presence or absence of measurement noise in the response. Furthermore, we illustrate a comparison method of multivariate feature vectors for statistical model validation. Results show that the outlier detection technique using the Mahalanobis distance metric can be used as an effective and quantifiable technique for selecting appropriate model parameters. However, in this process, one must not only consider the sensitivity of the features being used, but also correlation of the parameters being compared.
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....
Nonsmooth dynamics in spiking neuron models
Coombes, S.; Thul, R.; Wedgwood, K. C. A.
2012-11-01
Large scale studies of spiking neural networks are a key part of modern approaches to understanding the dynamics of biological neural tissue. One approach in computational neuroscience has been to consider the detailed electrophysiological properties of neurons and build vast computational compartmental models. An alternative has been to develop minimal models of spiking neurons with a reduction in the dimensionality of both parameter and variable space that facilitates more effective simulation studies. In this latter case the single neuron model of choice is often a variant of the classic integrate-and-fire model, which is described by a nonsmooth dynamical system. In this paper we review some of the more popular spiking models of this class and describe the types of spiking pattern that they can generate (ranging from tonic to burst firing). We show that a number of techniques originally developed for the study of impact oscillators are directly relevant to their analysis, particularly those for treating grazing bifurcations. Importantly we highlight one particular single neuron model, capable of generating realistic spike trains, that is both computationally cheap and analytically tractable. This is a planar nonlinear integrate-and-fire model with a piecewise linear vector field and a state dependent reset upon spiking. We call this the PWL-IF model and analyse it at both the single neuron and network level. The techniques and terminology of nonsmooth dynamical systems are used to flesh out the bifurcation structure of the single neuron model, as well as to develop the notion of Lyapunov exponents. We also show how to construct the phase response curve for this system, emphasising that techniques in mathematical neuroscience may also translate back to the field of nonsmooth dynamical systems. The stability of periodic spiking orbits is assessed using a linear stability analysis of spiking times. At the network level we consider linear coupling between voltage
Direct modeling for computational fluid dynamics
Xu, Kun
2015-06-01
All fluid dynamic equations are valid under their modeling scales, such as the particle mean free path and mean collision time scale of the Boltzmann equation and the hydrodynamic scale of the Navier-Stokes (NS) equations. The current computational fluid dynamics (CFD) focuses on the numerical solution of partial differential equations (PDEs), and its aim is to get the accurate solution of these governing equations. Under such a CFD practice, it is hard to develop a unified scheme that covers flow physics from kinetic to hydrodynamic scales continuously because there is no such governing equation which could make a smooth transition from the Boltzmann to the NS modeling. The study of fluid dynamics needs to go beyond the traditional numerical partial differential equations. The emerging engineering applications, such as air-vehicle design for near-space flight and flow and heat transfer in micro-devices, do require further expansion of the concept of gas dynamics to a larger domain of physical reality, rather than the traditional distinguishable governing equations. At the current stage, the non-equilibrium flow physics has not yet been well explored or clearly understood due to the lack of appropriate tools. Unfortunately, under the current numerical PDE approach, it is hard to develop such a meaningful tool due to the absence of valid PDEs. In order to construct multiscale and multiphysics simulation methods similar to the modeling process of constructing the Boltzmann or the NS governing equations, the development of a numerical algorithm should be based on the first principle of physical modeling. In this paper, instead of following the traditional numerical PDE path, we introduce direct modeling as a principle for CFD algorithm development. Since all computations are conducted in a discretized space with limited cell resolution, the flow physics to be modeled has to be done in the mesh size and time step scales. Here, the CFD is more or less a direct
Davtyan, Aram; Voth, Gregory A.; Andersen, Hans C.
2016-12-01
We recently developed a dynamic force matching technique for converting a coarse-grained (CG) model of a molecular system, with a CG potential energy function, into a dynamic CG model with realistic dynamics [A. Davtyan et al., J. Chem. Phys. 142, 154104 (2015)]. This is done by supplementing the model with additional degrees of freedom, called "fictitious particles." In that paper, we tested the method on CG models in which each molecule is coarse-grained into one CG point particle, with very satisfactory results. When the method was applied to a CG model of methanol that has two CG point particles per molecule, the results were encouraging but clearly required improvement. In this paper, we introduce a new type (called type-3) of fictitious particle that exerts forces on the center of mass of two CG sites. A CG model constructed using type-3 fictitious particles (as well as type-2 particles previously used) gives a much more satisfactory dynamic model for liquid methanol. In particular, we were able to construct a CG model that has the same self-diffusion coefficient and the same rotational relaxation time as an all-atom model of liquid methanol. Type-3 particles and generalizations of it are likely to be useful in converting more complicated CG models into dynamic CG models.
Analysing the temporal dynamics of model performance for hydrological models
Reusser, D.E.; Blume, T.; Schaefli, B.; Zehe, E.
2009-01-01
The temporal dynamics of hydrological model performance gives insights into errors that cannot be obtained from global performance measures assigning a single number to the fit of a simulated time series to an observed reference series. These errors can include errors in data, model parameters, or m
A dynamical model of non regulated markets
Schaale, A
1999-01-01
The main focus of this work is to understand the dynamics of non regulated markets. The present model can describe the dynamics of any market where the pricing is based on supply and demand. It will be applied here, as an example, for the German stock market presented by the Deutscher Aktienindex (DAX), which is a measure for the market status. The duality of the present model consists of the superposition of the two components - the long and the short term behaviour of the market. The long term behaviour is characterised by a stable development which is following a trend for time periods of years or even decades. This long term growth (or decline) is based on the development of fundamental market figures. The short term behaviour is described as a dynamical evaluation (trading) of the market by the participants. The trading process is described as an exchange between supply and demand. In the framework of this model there the trading is modelled by a system of nonlinear differential equations. The model also...
Traffic flow dynamics data, models and simulation
Treiber, Martin
2013-01-01
This textbook provides a comprehensive and instructive coverage of vehicular traffic flow dynamics and modeling. It makes this fascinating interdisciplinary topic, which to date was only documented in parts by specialized monographs, accessible to a broad readership. Numerous figures and problems with solutions help the reader to quickly understand and practice the presented concepts. This book is targeted at students of physics and traffic engineering and, more generally, also at students and professionals in computer science, mathematics, and interdisciplinary topics. It also offers material for project work in programming and simulation at college and university level. The main part, after presenting different categories of traffic data, is devoted to a mathematical description of the dynamics of traffic flow, covering macroscopic models which describe traffic in terms of density, as well as microscopic many-particle models in which each particle corresponds to a vehicle and its driver. Focus chapters on ...
Dynamic Circuit Model for Spintronic Devices
Alawein, Meshal
2017-01-09
In this work we propose a finite-difference scheme based circuit model of a general spintronic device and benchmark it with other models proposed for spintronic switching devices. Our model is based on the four-component spin circuit theory and utilizes the widely used coupled stochastic magnetization dynamics/spin transport framework. In addition to the steady-state analysis, this work offers a transient analysis of carrier transport. By discretizing the temporal and spatial derivatives to generate a linear system of equations, we derive new and simple finite-difference conductance matrices that can, to the first order, capture both static and dynamic behaviors of a spintronic device. We also discuss an extension of the spin modified nodal analysis (SMNA) for time-dependent situations based on the proposed scheme.
Dynamical Models of Dyadic Interactions with Delay
Bielczyk, Natalia; Płatkowski, Tadeusz
2012-01-01
When interpersonal interactions between individuals are described by the (discrete or continuous) dynamical systems, the interactions are usually assumed to be instantaneous: the rates of change of the actual states of the actors at given instant of time are assumed to depend on their states at the same time. In reality the natural time delay should be included in the corresponding models. We investigate a general class of linear models of dyadic interactions with a constant discrete time delay. We prove that in such models the changes of stability of the stationary points from instability to stability or vice versa occur for various intervals of the parameters which determine the intensity of interactions. The conditions guaranteeing arbitrary number (zero, one ore more) of switches are formulated and the relevant theorems are proved. A systematic analysis of all generic cases is carried out. It is obvious that the dynamics of interactions depend both on the strength of reactions of partners on their own sta...
Modeling epidemics dynamics on heterogenous networks.
Ben-Zion, Yossi; Cohen, Yahel; Shnerb, Nadav M
2010-05-21
The dynamics of the SIS process on heterogenous networks, where different local communities are connected by airlines, is studied. We suggest a new modeling technique for travelers movement, in which the movement does not affect the demographic parameters characterizing the metapopulation. A solution to the deterministic reaction-diffusion equations that emerges from this model on a general network is presented. A typical example of a heterogenous network, the star structure, is studied in detail both analytically and using agent-based simulations. The interplay between demographic stochasticity, spatial heterogeneity and the infection dynamics is shown to produce some counterintuitive effects. In particular it was found that, while movement always increases the chance of an outbreak, it may decrease the steady-state fraction of sick individuals. The importance of the modeling technique in estimating the outcomes of a vaccination campaign is demonstrated.
Dynamic Intellectual Capital Model in a Company
Directory of Open Access Journals (Sweden)
Vladimir Shatrevich
2015-06-01
Full Text Available The aim of this paper is to indicate the relations between company’s value added (VA and intangible assets. Authors declare that Intellectual capital (IC is one of the most relevant intangibles for a company, and the concept with measurement, and the relation with value creation is necessary for modern markets. Since relationship between IC elements and VA are complicated, this paper is aimed to create a usable dynamic model for building company’s value added through intellectual capital. The model is incorporating that outputs from IC elements are not homogeneously received and made some contributions to dynamic nature of IC relation and VA. Variables that will help companies to evaluate contribution of each element of IC are added to the model. This paper emphasizes the importance of a company’s IC and the positive interaction between them in generating profits for company.
Switched Dynamical Latent Force Models for Modelling Transcriptional Regulation
López-Lopera, Andrés F
2015-01-01
In order to develop statistical approaches for transcription networks, statistical community has proposed several methods to infer activity levels of proteins, from time-series measurements of targets' expression levels. A few number of approaches have been proposed in order to outperform the representation of fast switching time instants, but computational overheads are significant due to complex inference algorithms. Using the theory related to latent force models (LFM), the development of this project provide a switched dynamical hybrid model based on Gaussian processes (GPs). To deal with discontinuities in dynamical systems (or latent driving force), an extension of the single input motif approach is introduced, that switches between different protein concentrations, and different dynamical systems. This creates a versatile representation for transcription networks that can capture discrete changes and non-linearities in the dynamics. The proposed method is evaluated on both simulated data and real data,...
Global Langevin model of multidimensional biomolecular dynamics
Schaudinnus, Norbert; Lickert, Benjamin; Biswas, Mithun; Stock, Gerhard
2016-11-01
Molecular dynamics simulations of biomolecular processes are often discussed in terms of diffusive motion on a low-dimensional free energy landscape F ( 𝒙 ) . To provide a theoretical basis for this interpretation, one may invoke the system-bath ansatz á la Zwanzig. That is, by assuming a time scale separation between the slow motion along the system coordinate x and the fast fluctuations of the bath, a memory-free Langevin equation can be derived that describes the system's motion on the free energy landscape F ( 𝒙 ) , which is damped by a friction field and driven by a stochastic force that is related to the friction via the fluctuation-dissipation theorem. While the theoretical formulation of Zwanzig typically assumes a highly idealized form of the bath Hamiltonian and the system-bath coupling, one would like to extend the approach to realistic data-based biomolecular systems. Here a practical method is proposed to construct an analytically defined global model of structural dynamics. Given a molecular dynamics simulation and adequate collective coordinates, the approach employs an "empirical valence bond"-type model which is suitable to represent multidimensional free energy landscapes as well as an approximate description of the friction field. Adopting alanine dipeptide and a three-dimensional model of heptaalanine as simple examples, the resulting Langevin model is shown to reproduce the results of the underlying all-atom simulations. Because the Langevin equation can also be shown to satisfy the underlying assumptions of the theory (such as a delta-correlated Gaussian-distributed noise), the global model provides a correct, albeit empirical, realization of Zwanzig's formulation. As an application, the model can be used to investigate the dependence of the system on parameter changes and to predict the effect of site-selective mutations on the dynamics.
Critical behavior of a dynamical percolation model
Institute of Scientific and Technical Information of China (English)
YU Mei-Ling; XU Ming-Mei; LIU Zheng-You; LIU Lian-Shou
2009-01-01
The critical behavior of the dynamical percolation model, which realizes the molecular-aggregation conception and describes the crossover between the hadronic phase and the partonic phase, is studied in detail. The critical percolation distance for this model is obtained by using the probability P∞ of the appearance of an infinite cluster. Utilizing the finite-size scaling method the critical exponents γ/v and T are extracted from the distribution of the average cluster size and cluster number density. The influences of two model related factors, I.e. The maximum bond number and the definition of the infinite cluster, on the critical behavior are found to be small.
DYNAMICS IN A CLASS OF NEURON MODELS
Institute of Scientific and Technical Information of China (English)
Wang Junping; Ruan Jiong
2009-01-01
In this paper, we investigate the dynamics in a class of discrete-time neuron mo-dels. The neuron model we discussed, defined by such periodic input-output mapping as a sinusoidal function, has a remarkably larger memory capacity than the conven-tional association system with the monotonous function. Our results show that the orbit of the model takes a conventional bifurcation route, from stable equilibrium, to periodicity, even to chaotic region. And the theoretical analysis is verified by numerical simulations.
Polarizable water model for Dissipative Particle Dynamics
Pivkin, Igor; Peter, Emanuel
2015-11-01
Dissipative Particle Dynamics (DPD) is an efficient particle-based method for modeling mesoscopic behavior of fluid systems. DPD forces conserve the momentum resulting in a correct description of hydrodynamic interactions. Polarizability has been introduced into some coarse-grained particle-based simulation methods; however it has not been done with DPD before. We developed a new polarizable coarse-grained water model for DPD, which employs long-range electrostatics and Drude oscillators. In this talk, we will present the model and its applications in simulations of membrane systems, where polarization effects play an essential role.
Model for Dynamic Multiple of CPPI Strategy
Directory of Open Access Journals (Sweden)
Guangyuan Xing
2014-01-01
Full Text Available Focusing on the parameter “Multiple” of CPPI strategy, this study proposes a dynamic setting model of multiple for gap risk management purpose. First, CPPI gap risk is measured as the probability that the value loss of active asset exceeds its allowed maximum drop determined by a given multiple setting. Moreover, according to the statistical estimation using SV-EVT approach, a dynamic choice of multiple is detailed as a function of time-varying asset volatility, expected loss, and the possibility of occurrence of extreme events in the active asset returns illustrated empirically on Shanghai composite index data. This study not only enriches the literature of dynamic proportion portfolio insurance, but also provides a practical reference for CPPI investors to choose a moderate risky exposure achieving gap risk management, which promotes CPPI’s application in emerging capital market.
Five challenges in modelling interacting strain dynamics
DEFF Research Database (Denmark)
Wikramaratna, Paul S; Kurcharski, Adam; Gupta, Sunetra
2015-01-01
Population epidemiological models where hosts can be infected sequentially by different strains have the potential to help us understand many important diseases. Researchers have in recent years started to develop and use such models, but the extra layer of complexity from multiple strains brings...... with it many technical challenges. It is therefore hard to build models which have realistic assumptions yet are tractable. Here we outline some of the main challenges in this area. First we begin with the fundamental question of how to translate from complex small-scale dynamics within a host to useful...... population models. Next we consider the nature of so-called “strain space”. We describe two key types of host heterogeneities, and explain how models could help generate a better understanding of their effects. Finally, for diseases with many strains, we consider the challenge of modelling how immunity...
Structural system identification: Structural dynamics model validation
Energy Technology Data Exchange (ETDEWEB)
Red-Horse, J.R.
1997-04-01
Structural system identification is concerned with the development of systematic procedures and tools for developing predictive analytical models based on a physical structure`s dynamic response characteristics. It is a multidisciplinary process that involves the ability (1) to define high fidelity physics-based analysis models, (2) to acquire accurate test-derived information for physical specimens using diagnostic experiments, (3) to validate the numerical simulation model by reconciling differences that inevitably exist between the analysis model and the experimental data, and (4) to quantify uncertainties in the final system models and subsequent numerical simulations. The goal of this project was to develop structural system identification techniques and software suitable for both research and production applications in code and model validation.