Efficient stochastic thermostatting of path integral molecular dynamics
Ceriotti, Michele; Parrinello, Michele; Markland, Thomas E.; Manolopoulos, David E.
2010-09-01
The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently developed colored noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nosé-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.
Sindhikara, Daniel J; Kim, Seonah; Voter, Arthur F; Roitberg, Adrian E
2009-06-01
Molecular dynamics simulations starting from different initial conditions are commonly used to mimic the behavior of an experimental ensemble. We show in this article that when a Langevin thermostat is used to maintain constant temperature during such simulations, extreme care must be taken when choosing the random number seeds to prevent statistical correlation among the MD trajectories. While recent studies have shown that stochastically thermostatted trajectories evolving within a single potential basin with identical random number seeds tend to synchronize, we show that there is a synchronization effect even for complex, biologically relevant systems. We demonstrate this effect in simulations of alanine trimer and pentamer and in a simulation of a temperature-jump experiment for peptide folding of a 14-residue peptide. Even in replica-exchange simulations, in which the trajectories are at different temperatures, we find partial synchronization occurring when the same random number seed is employed. We explain this by extending the recent derivation of the synchronization effect for two trajectories in a harmonic well to the case in which the trajectories are at two different temperatures. Our results suggest several ways in which mishandling selection of a pseudorandom number generator initial seed can lead to corruption of simulation data. Simulators can fall into this trap in simple situations such as neglecting to specifically indicate different random seeds in either parallel or sequential restart simulations, utilizing a simulation package with a weak pseudorandom number generator, or using an advanced simulation algorithm that has not been programmed to distribute initial seeds.
Passler, Peter P; Hofer, Thomas S
2017-02-15
Stochastic dynamics is a widely employed strategy to achieve local thermostatization in molecular dynamics simulation studies; however, it suffers from an inherent violation of momentum conservation. Although this short-coming has little impact on structural and short-time dynamic properties, it can be shown that dynamics in the long-time limit such as diffusion is strongly dependent on the respective thermostat setting. Application of the methodically similar dissipative particle dynamics (DPD) provides a simple, effective strategy to ensure the advantages of local, stochastic thermostatization while at the same time the linear momentum of the system remains conserved. In this work, the key parameters to employ the DPD thermostats in the framework of periodic boundary conditions are investigated, in particular the dependence of the system properties on the size of the DPD-region as well as the treatment of forces near the cutoff. Structural and dynamical data for light and heavy water as well as a Lennard-Jones fluid have been compared to simulations executed via stochastic dynamics as well as via use of the widely employed Nose-Hoover chain and Berendsen thermostats. It is demonstrated that a small size of the DPD region is sufficient to achieve local thermalization, while at the same time artifacts in the self-diffusion characteristic for stochastic dynamics are eliminated. © 2016 Wiley Periodicals, Inc.
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Voter, A F [Los Alamos National Laboratory; Sindhikara, Daniel J [UNIV OF FLORIDA; Kim, Seonah [UNIV OF CALIFORNIA; Roitberg, Adrian E [UNIV OF FLORIDA
2009-01-01
Molecular dynamics simulations starting from different initial conditions are commonly used to mimic the behavior of an experimental ensemble. We show in this article that when a Langevin thermostat is used to maintain constant temperature during such simulations, extreme care must be taken when choosing the random number seeds used in order to prevent statistical correlation among the MD trajectories. While recent studies have shown that stochastically thermostatted trajectories evolving within a single potential basin with identical random number seeds tend to synchronize, we show that there is a synchronization effect even for complex, biologically relevant systems. We demonstrate this effect in simulations of Alanine trimer and pentamer and in a simulation of a temperature-jump experiment for peptide folding of a 14-residue peptide. Even in replica-exchange simulations, in which the trajectories are at different temperatures, we find partial synchronization occurring when the same random number seed is employed. We explain this by extending the recent derivation of the synchronization effect for two trajectories in a harmonic well to the case in which the trajectories are at two different temperatures. Our results suggest several ways in which mishandling selection of a pseudo random number generator initial seed can lead to corruption of simulation data. Simulators can fall into this trap in simple situations such as neglecting to specifically indicate different random seeds in either parallel or sequential restart simulations, utilizing a simulation package with a weak pseudorandom number generator, or using an advanced simulation algorithm that hasn't been programmed to distribute initial seeds.
Geometric integrators for stochastic rigid body dynamics
Tretyakov, Mikhail
2016-01-05
Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.
Observation-based correction of dynamical models using thermostats
Frank, Jason; Leimkuhler, Benedict
2017-01-01
Models used in simulation may give accurate short-term trajectories but distort long-term (statistical) properties. In this work, we augment a given approximate model with a control law (a ‘thermostat’) that gently perturbs the dynamical system to target a thermodynamic state consistent with a set of prescribed (possibly evolving) observations. As proof of concept, we provide an example involving a point vortex fluid model on the sphere, for which we show convergence of equilibrium quantities (in the stationary case) and the ability of the thermostat to dynamically track a transient state. PMID:28265197
Pastorino, C; Kreer, T; Müller, M; Binder, K
2007-08-01
In this work we compare and characterize the behavior of Langevin and dissipative particle dynamics (DPD) thermostats in a broad range of nonequilibrium simulations of polymeric systems. Polymer brushes in relative sliding motion, polymeric liquids in Poiseuille and Couette flows, and brush-melt interfaces are used as model systems to analyze the efficiency and limitations of different Langevin and DPD thermostat implementations. Widely used coarse-grained bead-spring models under good and poor solvent conditions are employed to assess the effects of the thermostats. We considered equilibrium, transient, and steady state examples for testing the ability of the thermostats to maintain constant temperature and to reproduce the underlying physical phenomena in nonequilibrium situations. The common practice of switching off the Langevin thermostat in the flow direction is also critically revisited. The efficiency of different weight functions for the DPD thermostat is quantitatively analyzed as a function of the solvent quality and the nonequilibrium situation.
A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat
Liu, Jian; Li, Dezhang; Liu, Xinzijian
2016-07-01
We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used.
A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat.
Liu, Jian; Li, Dezhang; Liu, Xinzijian
2016-07-14
We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used.
Discrete Particle Dynamics Simulations of Adhesive Systems with Thermostatting
Pierce, Flint; Lechman, Jeremy; Hewson, John
2012-02-01
Aggregation/coagulation/flocculation processes are ubiquitous in modern industry from fields as diverse as waste water treatment, the food industry, algae biofuel production, and materials processing where control of the size and morphology of aggregates is paramount to the application of interest. Population balance models have historically been used with success in predicting aggregation kinetics and size distributions for these processes. However, even the most robust population balance schemes can lack an exact description of the underlying physical processes governing attractive or adhesive particulate matter suspended in a background medium, including finite aggregate strength and yield stress, restructuring length and time scales, and response to hydrodynamic forces. In order to elucidate these phenomena, We develop and use a JKR type model for simulating adhesive particulate matter in a background medium varying from dilute gas to liquid. We evaluate the time and length scales for restructuring/fragmentation that result from this model as a function of aggregate size and fractal dimension. We additionally introduce a method for pairwise thermostatting of the adhesive potential and discuss the applicability of this model to various adhesive systems.
Pairwise adaptive thermostats for improved accuracy and stability in dissipative particle dynamics
Leimkuhler, Benedict
2016-01-01
We examine the formulation and numerical treatment of dissipative particle dynamics (DPD) and momentum-conserving molecular dynamics. We show that it is possible to improve both the accuracy and the stability of DPD by employing a pairwise adaptive Langevin thermostat that precisely matches the dynamical characteristics of DPD simulations (e.g., autocorrelation functions) while automatically correcting thermodynamic averages using a negative feedback loop. In the low friction regime, it is possible to replace DPD by a simpler momentum-conserving variant of the Nos\\'{e}--Hoover--Langevin method based on thermostatting only pairwise interactions; we show that this method has an extra order of accuracy for an important class of observables (a superconvergence result), while also allowing larger timesteps than alternatives. All the methods mentioned in the article are easily implemented. Numerical experiments are performed in both equilibrium and nonequilibrium settings; using Lees--Edwards boundary conditions to...
Pairwise adaptive thermostats for improved accuracy and stability in dissipative particle dynamics
Leimkuhler, Benedict; Shang, Xiaocheng
2016-11-01
We examine the formulation and numerical treatment of dissipative particle dynamics (DPD) and momentum-conserving molecular dynamics. We show that it is possible to improve both the accuracy and the stability of DPD by employing a pairwise adaptive Langevin thermostat that precisely matches the dynamical characteristics of DPD simulations (e.g., autocorrelation functions) while automatically correcting thermodynamic averages using a negative feedback loop. In the low friction regime, it is possible to replace DPD by a simpler momentum-conserving variant of the Nosé-Hoover-Langevin method based on thermostatting only pairwise interactions; we show that this method has an extra order of accuracy for an important class of observables (a superconvergence result), while also allowing larger timesteps than alternatives. All the methods mentioned in the article are easily implemented. Numerical experiments are performed in both equilibrium and nonequilibrium settings; using Lees-Edwards boundary conditions to induce shear flow.
Stochastic longshore current dynamics
Restrepo, Juan M.; Venkataramani, Shankar
2016-12-01
We develop a stochastic parametrization, based on a 'simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the "missing physics" to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation. We introduce a novel measure of the utility of stochastic models of complex processes, that we call consistency of sensitivity. A model with poor consistency of sensitivity requires a great deal of tuning of parameters and has a very narrow range of realistic parameters leading to outcomes consistent with a reasonable spectrum of physical outcomes. We apply this metric to our stochastic parametrization and show that, the loss of certainty inherent in model due to its stochastic nature is offset by the model's resulting consistency of sensitivity. In particular, the stochastic model still retains the forward sensitivity of the deterministic model and hence respects important structural/physical constraints, yet has a broader range of parameters capable of producing outcomes consistent with the field data used in evaluating the model. This leads to an expanded range of model applicability. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation that were not used in tuning the model.
Chen, Wen-Hwa; Wu, Chun-Hung; Cheng, Hsien-Chie
2011-07-01
Nosé-Hoover (NH) thermostat methods incorporated with molecular dynamics (MD) simulation have been widely used to simulate the instantaneous system temperature and feedback energy in a canonical ensemble. The method simply relates the kinetic energy to the system temperature via the particles' momenta based on the ideal gas law. However, when used in a tightly bound system such as solids, the method may suffer from deriving a lower system temperature and potentially inducing early breaking of atomic bonds at relatively high temperature due to the neglect of the effect of the potential energy of atoms based on solid state physics. In this paper, a modified NH thermostat method is proposed for solid system. The method takes into account the contribution of phonons by virtue of the vibrational energy of lattice and the zero-point energy, derived based on the Debye theory. Proof of the equivalence of the method and the canonical ensemble is first made. The modified NH thermostat is tested on different gold nanocrystals to characterize their melting point and constant volume specific heat, and also their size and temperature dependence. Results show that the modified NH method can give much more comparable results to both the literature experimental and theoretical data than the standard NH. Most importantly, the present model is the only one, among the six thermostat algorithms under comparison, that can accurately reproduce the experimental data and also the T 3-law at temperature below the Debye temperature, where the specific heat of a solid at constant volume is proportional to the cube of temperature.
Stochastic dynamics and irreversibility
Tomé, Tânia
2015-01-01
This textbook presents an exposition of stochastic dynamics and irreversibility. It comprises the principles of probability theory and the stochastic dynamics in continuous spaces, described by Langevin and Fokker-Planck equations, and in discrete spaces, described by Markov chains and master equations. Special concern is given to the study of irreversibility, both in systems that evolve to equilibrium and in nonequilibrium stationary states. Attention is also given to the study of models displaying phase transitions and critical phenomema both in thermodynamic equilibrium and out of equilibrium. These models include the linear Glauber model, the Glauber-Ising model, lattice models with absorbing states such as the contact process and those used in population dynamic and spreading of epidemic, probabilistic cellular automata, reaction-diffusion processes, random sequential adsorption and dynamic percolation. A stochastic approach to chemical reaction is also presented.The textbook is intended for students of ...
Combining Berendsen Thermostat with Dissipative Particle Dynamics (DPD) for Polymer Simulation
Moga, Sunita Andreea; Goga, Nicolae; Hadar, Anton
2013-01-01
In this article we present a new thermostat - theory and simulation results - obtained by combining two thermostats Berendsen and DPD types. The new thermostat provides a predictable behavior with temperatures that do not deviate from the reference and with thermal rate constant agreement between si
Institute of Scientific and Technical Information of China (English)
Li Rui; Hu Yuan-Zhong; Wang Hui; Zhang Yu-Jun
2008-01-01
In this paper,single-walled carbon nanotubes (SWCNTs) are studied through molecular dynamics (MD) simulation.The simulations are performed at temperatures of 1 and 300 K separately,with atomic interactions characterized by the second Reactive Empirical Bond Order (REBO) potential,and temperature controlled by a certain thermostat,i.e.by separately using the velocity scaling,the Berendsen scheme,the Nose-Hoover scheme,and the generalized Langevin scheme.Results for a (5,5) SWCNT with a length of 24.5 nm show apparent distortions in nanotube configuration,which can further enter into periodic vibrations,except in simulations using the generalized Langevin thermostat,which is ascribed to periodic boundary conditions used in simulation.The periodic boundary conditions may implicitly be applied in the form of an inconsistent constraint along the axis of the nanotube.The combination of the inconsistent constraint with the cumulative errors in calculation causes the distortions of nanotubes.When the generalized Langevin thermostat is applied,inconsistently distributed errors are dispersed by the random forces,and so the distortions and vibrations disappear.This speculation is confirmed by simulation in the case without periodic boundary conditions,where no apparent distortion and vibration occur.It is also revealed that numerically induced distortions and vibrations occur only in simulation of nanotubes with a small diameter and a large length-to-diameter ratio.When MD simulation is applied to a system with a particular geometry,attention should be paid to avoiding the numerical distortion and the result infidelity.
Molecular shear heating and vortex dynamics in thermostatted two-dimensional Yukawa liquids
Gupta, Akanksha; Joy, Ashwin
2016-01-01
It is well known that two-dimensional macroscale shear flows are susceptible to instabilities leading to macroscale vortical structures. The linear and nonlinear fate of such a macroscale flow in a strongly coupled medium is a fundamental problem. A popular example of a strongly coupled medium is a dusty plasma, often modelled as a Yukawa liquid. Recently, laboratory experiments and MD studies of shear flows in strongly coupled Yukawa liquids, indicated occurrence of strong molecular shear heating, which is found to reduce the coupling strength exponentially leading to destruction of macroscale vorticity. To understand the vortex dynamics of strongly coupled molecular fluids undergoing macroscale shear flows and molecular shear heating, MD simulation has been performed, which allows the macroscopic vortex dynamics to evolve while at the same time, "removes" the microscopically generated heat without using the velocity degrees of freedom. We demonstrate that by using a configurational thermostat in a novel way...
Dynamics of stochastic systems
Klyatskin, Valery I
2005-01-01
Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''''oil slicks''''), wave propagation and scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere.Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields.The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of ...
Molecular dynamics with deterministic and stochastic numerical methods
Leimkuhler, Ben
2015-01-01
This book describes the mathematical underpinnings of algorithms used for molecular dynamics simulation, including both deterministic and stochastic numerical methods. Molecular dynamics is one of the most versatile and powerful methods of modern computational science and engineering and is used widely in chemistry, physics, materials science and biology. Understanding the foundations of numerical methods means knowing how to select the best one for a given problem (from the wide range of techniques on offer) and how to create new, efficient methods to address particular challenges as they arise in complex applications. Aimed at a broad audience, this book presents the basic theory of Hamiltonian mechanics and stochastic differential equations, as well as topics including symplectic numerical methods, the handling of constraints and rigid bodies, the efficient treatment of Langevin dynamics, thermostats to control the molecular ensemble, multiple time-stepping, and the dissipative particle dynamics method...
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
Hele, Timothy J H
2015-01-01
We obtain thermostatted ring polymer molecular dynamics (TRPMD) from exact quantum dynamics via Matsubara dynamics, a recently-derived form of linearization which conserves the quantum Boltzmann distribution. Performing a contour integral in the complex quantum Boltzmann distribution of Matsubara dynamics, replacement of the imaginary Liouvillian which results with a Fokker-Planck term gives TRPMD. We thereby provide error terms between TRPMD and quantum dynamics and predict the systems in which they are likely to be small. Using a harmonic analysis we show that careful addition of friction causes the correct oscillation frequency of the higher ring-polymer normal modes in a harmonic well, which we illustrate with calculation of the position-squared autocorrelation function. However, no physical friction parameter will produce the correct fluctuation dynamics for a parabolic barrier. The results in this paper are consistent with previous numerical studies and advise the use of TRPMD for the computation of spe...
Colored-noise thermostats \\`a la carte
Ceriotti, Michele; Parrinello, Michele; 10.1021/ct900563s
2012-01-01
Recently, we have shown how a colored-noise Langevin equation can be used in the context of molecular dynamics as a tool to obtain dynamical trajectories whose properties are tailored to display desired sampling features. In the present paper, after having reviewed some analytical results for the stochastic differential equations forming the basis of our approach, we describe in detail the implementation of the generalized Langevin equation thermostat and the fitting procedure used to obtain optimal parameters. We discuss in detail the simulation of nuclear quantum effects, and demonstrate that, by carefully choosing parameters, one can successfully model strongly anharmonic solids such as neon. For the reader's convenience, a library of thermostat parameters and some demonstrative code can be downloaded from an on-line repository.
Should Thermostatted Ring Polymer Molecular Dynamics be used to calculate reaction rates?
Hele, Timothy J H
2015-01-01
We apply Thermostatted Ring Polymer Molecular Dynamics (TRPMD), a recently-proposed approximate quantum dynamics method, to the computation of thermal reaction rates. Its short-time Transition-State Theory (TST) limit is identical to rigorous Quantum Transition-State Theory, and we find that its long-time limit is independent of the location of the dividing surface. TRPMD rate theory is then applied to one-dimensional model systems, the atom-diatom bimolecular reactions H+H$_2$, D+MuH and F+H$_2$, and the prototypical polyatomic reaction H+CH$_4$. Above the crossover temperature, the TRPMD rate is virtually invariant to the strength of the friction applied to the internal ring-polymer normal modes, and beneath the crossover temperature the TRPMD rate generally decreases with increasing friction, in agreement with the predictions of Kramers theory. We therefore find that TRPMD is less accurate than Ring Polymer Molecular Dynamics (RPMD) for symmetric reactions, and in certain asymmetric systems closer to the q...
Should thermostatted ring polymer molecular dynamics be used to calculate thermal reaction rates?
Energy Technology Data Exchange (ETDEWEB)
Hele, Timothy J. H., E-mail: tjhh2@cam.ac.uk [Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW (United Kingdom); Suleimanov, Yury V. [Computation-based Science and Technology Research Center, Cyprus Institute, 20 Kavafi St., Nicosia 2121 (Cyprus); Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139 (United States)
2015-08-21
We apply Thermostatted Ring Polymer Molecular Dynamics (TRPMD), a recently proposed approximate quantum dynamics method, to the computation of thermal reaction rates. Its short-time transition-state theory limit is identical to rigorous quantum transition-state theory, and we find that its long-time limit is independent of the location of the dividing surface. TRPMD rate theory is then applied to one-dimensional model systems, the atom-diatom bimolecular reactions H + H{sub 2}, D + MuH, and F + H{sub 2}, and the prototypical polyatomic reaction H + CH{sub 4}. Above the crossover temperature, the TRPMD rate is virtually invariant to the strength of the friction applied to the internal ring-polymer normal modes, and beneath the crossover temperature the TRPMD rate generally decreases with increasing friction, in agreement with the predictions of Kramers theory. We therefore find that TRPMD is approximately equal to, or less accurate than, ring polymer molecular dynamics for symmetric reactions, and for certain asymmetric systems and friction parameters closer to the quantum result, providing a basis for further assessment of the accuracy of this method.
Adaptive Thermostats for Noisy Gradient Systems
Leimkuhler, Benedict
2015-01-01
We study numerical methods for sampling probability measures in high dimensions where the underlying model is only approximately identified with a gradient system. Extended stochastic dynamical methods are discussed which have application to multiscale models, nonequilibrium molecular dynamics and Bayesian sampling techniques arising in emerging machine learning applications. In addition to providing a more comprehensive discussion of the foundations of these methods, we propose a new numerical method for the Adaptive Langevin/stochastic gradient Nos\\'e-Hoover thermostat that achieves a dramatic improvement in numerical efficiency over the most popular stochastic gradient methods reported in the literature. We also demonstrate that the newly-established method inherits a superconvergence property (fourth order convergence to the invariant measure for configurational quantities) recently demonstrated in the setting of Langevin dynamics. Our findings are verified by numerical experiments.
Hamiltonian for a restricted isoenergetic thermostat
Dettmann, C. P.
1999-01-01
Nonequilibrium molecular dynamics simulations often use mechanisms called thermostats to regulate the temperature. A Hamiltonian is presented for the case of the isoenergetic (constant internal energy) thermostat corresponding to a tunable isokinetic (constant kinetic energy) thermostat, for which a Hamiltonian has recently been given.
Introduction to stochastic dynamic programming
Ross, Sheldon M; Lukacs, E
1983-01-01
Introduction to Stochastic Dynamic Programming presents the basic theory and examines the scope of applications of stochastic dynamic programming. The book begins with a chapter on various finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Subsequent chapters study infinite-stage models: discounting future returns, minimizing nonnegative costs, maximizing nonnegative returns, and maximizing the long-run average return. Each of these chapters first considers whether an optimal policy need exist-providing counterexamples where appropriate-and the
Stochastic dynamics and control
Sun, Jian-Qiao; Zaslavsky, George
2006-01-01
This book is a result of many years of author's research and teaching on random vibration and control. It was used as lecture notes for a graduate course. It provides a systematic review of theory of probability, stochastic processes, and stochastic calculus. The feedback control is also reviewed in the book. Random vibration analyses of SDOF, MDOF and continuous structural systems are presented in a pedagogical order. The application of the random vibration theory to reliability and fatigue analysis is also discussed. Recent research results on fatigue analysis of non-Gaussian stress proc
Stochastic dynamic equations on general time scales
Directory of Open Access Journals (Sweden)
Martin Bohner
2013-02-01
Full Text Available In this article, we construct stochastic integral and stochastic differential equations on general time scales. We call these equations stochastic dynamic equations. We provide the existence and uniqueness theorem for solutions of stochastic dynamic equations. The crucial tool of our construction is a result about a connection between the time scales Lebesgue integral and the Lebesgue integral in the common sense.
Dynamic stochastic optimization
Ermoliev, Yuri; Pflug, Georg
2004-01-01
Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explic itly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objec tive or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard deterministic optimization and optimal control methods. In the stochastic optimization the accent is on problems with a large number of deci sion and random variables, and consequently the focus ofattention is directed to efficient solution procedures rather than to (analytical) closed-form solu tions. Objective an...
The dynamics of stochastic processes
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas
In the present thesis the dynamics of stochastic processes is studied with a special attention to the semimartingale property. This is mainly motivated by the fact that semimartingales provide the class of the processes for which it is possible to define a reasonable stochastic calculus due...... average processes, and when the driving process is a Lévy or a chaos process the semimartingale property is characterized in the filtration spanned by the driving process and in the natural filtration when the latter is a Brownian motion. To obtain some of the above results an integrability of seminorm...
Thermostat Interface and Usability: A Survey
Energy Technology Data Exchange (ETDEWEB)
Meier, Alan; Peffer, Therese; Pritoni, Marco; Aragon, Cecilia
2010-09-04
This report investigates the history of thermostats to better understand the context and legacy regarding the development of this important tool, as well as thermostats' relationships to heating, cooling, and other environmental controls. We analyze the architecture, interfaces, and modes of interaction used by different types of thermostats. For over sixty years, home thermostats have translated occupants' temperature preferences into heating and cooling system operations. In this position of an intermediary, the millions of residential thermostats control almost half of household energy use, which corresponds to about 10percent of the nation's total energy use. Thermostats are currently undergoing rapid development in response to emerging technologies, new consumer and utility demands, and declining manufacturing costs. Energy-efficient homes require more careful balancing of comfort, energy consumption, and health. At the same time, new capabilities will be added to thermostats, including scheduling, control of humidity and ventilation, responsiveness to dynamic electricity prices, and the ability to join communication networks inside homes. Recent studies have found that as many as 50percent of residential programmable thermostats are in permanent"hold" status. Other evaluations found that homes with programmable thermostats consumed more energy than those relying on manual thermostats. Occupants find thermostats cryptic and baffling to operate because manufacturers often rely on obscure, and sometimes even contradictory, terms, symbols, procedures, and icons. It appears that many people are unable to fully exploit even the basic features in today's programmable thermostats, such as setting heating and cooling schedules. It is important that people can easily, reliably, and confidently operate thermostats in their homes so as to remain comfortable while minimizing energy use.
Stochastic Model of Microtubule Dynamics
Hryniv, Ostap; Martínez Esteban, Antonio
2017-10-01
We introduce a continuous time stochastic process on strings made of two types of particle, whose dynamics mimics that of microtubules in a living cell. The long term behaviour of the system is described in terms of the velocity v of the string end. We show that v is an analytic function of its parameters and study its monotonicity properties. We give a complete characterisation of the phase diagram of the model and derive several criteria of the growth (v>0) and the shrinking (v<0) regimes of the dynamics.
Danfos: Thermostatic Radiator Valves
DEFF Research Database (Denmark)
Gregersen, Niels; Oliver, James; Hjorth, Poul G.
2000-01-01
This problem deals with modelling the flow through a typical Danfoss thermostatic radiator valve.Danfoss is able to employ Computational Fluid Dynamics (CFD) in calculations of the capacity of valves, but an experienced engineer can often by rules of thumb "guess" the capacity, with a precision...... similar to the one achieved by the expensive and time-consuming CFD calculations. So CFD is only used in case of entirely new designs or where a very detailed knowledge of the flow is required. Even though rules of thumb are useful for those, who have developed them, Danfoss needs an objective and general...... method that can be used to predict the performance of valves....
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.
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.
Variational principles for stochastic soliton dynamics.
Holm, Darryl D; Tyranowski, Tomasz M
2016-03-01
We develop a variational method of deriving stochastic partial differential equations whose solutions follow the flow of a stochastic vector field. As an example in one spatial dimension, we numerically simulate singular solutions (peakons) of the stochastically perturbed Camassa-Holm (CH) equation derived using this method. These numerical simulations show that peakon soliton solutions of the stochastically perturbed CH equation persist and provide an interesting laboratory for investigating the sensitivity and accuracy of adding stochasticity to finite dimensional solutions of stochastic partial differential equations. In particular, some choices of stochastic perturbations of the peakon dynamics by Wiener noise (canonical Hamiltonian stochastic deformations, CH-SD) allow peakons to interpenetrate and exchange order on the real line in overtaking collisions, although this behaviour does not occur for other choices of stochastic perturbations which preserve the Euler-Poincaré structure of the CH equation (parametric stochastic deformations, P-SD), and it also does not occur for peakon solutions of the unperturbed deterministic CH equation. The discussion raises issues about the science of stochastic deformations of finite-dimensional approximations of evolutionary partial differential equation and the sensitivity of the resulting solutions to the choices made in stochastic modelling.
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.
Variational principles for stochastic fluid dynamics.
Holm, Darryl D
2015-04-08
This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the corresponding deterministic fluid models. The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models. As with deterministic ideal flows, motion along the stochastic Stratonovich paths also preserves the helicity of the vortex field lines in incompressible stochastic flows. However, these Stratonovich properties are not apparent in the equivalent Itô representation, because they are disguised by the quadratic covariation drift term arising in the Stratonovich to Itô transformation. This term is a geometric generalization of the quadratic covariation drift term already found for scalar densities in Stratonovich's famous 1966 paper. The paper also derives motion equations for two examples of stochastic geophysical fluid dynamics; namely, the Euler-Boussinesq and quasi-geostropic approximations.
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
Field Evaluation of Programmable Thermostats
Energy Technology Data Exchange (ETDEWEB)
Sachs, O. [Fraunhofer Center for Sustainable Energy Systems (CSE), Cambridge, MA (United States); Tiefenbeck, V. [Fraunhofer Center for Sustainable Energy Systems (CSE), Cambridge, MA (United States); Duvier, C. [Fraunhofer Center for Sustainable Energy Systems (CSE), Cambridge, MA (United States); Qin, A. [Fraunhofer Center for Sustainable Energy Systems (CSE), Cambridge, MA (United States); Cheney, K. [Fraunhofer Center for Sustainable Energy Systems (CSE), Cambridge, MA (United States); Akers, C. [Fraunhofer Center for Sustainable Energy Systems (CSE), Cambridge, MA (United States); Roth, K. [Fraunhofer Center for Sustainable Energy Systems (CSE), Cambridge, MA (United States)
2012-12-01
Prior research suggests that poor programmable thermostats usability may prevent their effective use to save energy. The Fraunhofer team hypothesized that home occupants with high-usability thermostats would be more likely to use them to save energy than people with a basic thermostats. In this report, the team discusses results of a project in which the team monitored and compared programmable thermostats with basic thermostats in an affordable housing apartment complex.
Principal axes for stochastic dynamics.
Vasconcelos, V V; Raischel, F; Haase, M; Peinke, J; Wächter, M; Lind, P G; Kleinhans, D
2011-09-01
We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the computation of the eigenvalues and the corresponding eigenvectors of local diffusion matrices. We demonstrate our algorithm by applying it to two examples of systems showing Hopf bifurcation. We argue that computing the eigenvectors associated to the eigenvalues of the diffusion matrix at local mesh points in the phase space enables one to define vector fields of stochastic eigendirections. In particular, the eigenvector associated to the lowest eigenvalue defines the path of minimum stochastic forcing in phase space, and a transform to a new coordinate system aligned with the eigenvectors can increase the predictability of the system.
Principal axes for stochastic dynamics
Vasconcelos, V V; Haase, M; Peinke, J; Wächter, M; Lind, P G; Kleinhans, D
2011-01-01
We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the computation of the eigenvalues and the corresponding eigenvectors of local diffusion matrices. We demonstrate our algorithm by applying it to two examples of systems showing Hopf-bifurcation. We argue that computing the eigenvectors associated to the eigenvalues of the diffusion matrix at local mesh points in the phase space enables one to define vector fields of stochastic eigendirections. In particular, the eigenvector associated to the lowest eigenvalue defines the path of minimum stochastic forcing in phase space, and a transform to a new coordinate system aligned with the eigenvectors can increase the predictability of the system.
On the stochastic dynamics of molecular conformation
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
An important functioning mechanism of biological macromolecules is the transition between different conformed states due to thermal fluctuation. In the present paper, a biological macromolecule is modeled as two strands with side chains facing each other, and its stochastic dynamics including the statistics of stationary motion and the statistics of conformational transition is studied by using the stochastic averaging method for quasi Hamiltonian systems. The theoretical results are confirmed with the results from Monte Carlo simulation.
Dynamically orthogonal field equations for stochastic flows and particle dynamics
2011-02-01
turbulence. Cambridge University Press, 1959. [10] G.K. Batchelor . An Introduction to Fluid Dynamics . Cambridge University Press, 2000. [11] D. Bau III... Dynamically orthogonal field equations for stochastic fluid flows and particle dynamics by Themistoklis P. Sapsis Dipl., National Technical...unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 2 Dynamically orthogonal field equations for stochastic fluid flows and particle
Dynamic and stochastic multi-project planning
Melchiors, Philipp
2015-01-01
This book deals with dynamic and stochastic methods for multi-project planning. Based on the idea of using queueing networks for the analysis of dynamic-stochastic multi-project environments this book addresses two problems: detailed scheduling of project activities, and integrated order acceptance and capacity planning. In an extensive simulation study, the book thoroughly investigates existing scheduling policies. To obtain optimal and near optimal scheduling policies new models and algorithms are proposed based on the theory of Markov decision processes and Approximate Dynamic programming.
Automated Flight Routing Using Stochastic Dynamic Programming
Ng, Hok K.; Morando, Alex; Grabbe, Shon
2010-01-01
Airspace capacity reduction due to convective weather impedes air traffic flows and causes traffic congestion. This study presents an algorithm that reroutes flights in the presence of winds, enroute convective weather, and congested airspace based on stochastic dynamic programming. A stochastic disturbance model incorporates into the reroute design process the capacity uncertainty. A trajectory-based airspace demand model is employed for calculating current and future airspace demand. The optimal routes minimize the total expected traveling time, weather incursion, and induced congestion costs. They are compared to weather-avoidance routes calculated using deterministic dynamic programming. The stochastic reroutes have smaller deviation probability than the deterministic counterpart when both reroutes have similar total flight distance. The stochastic rerouting algorithm takes into account all convective weather fields with all severity levels while the deterministic algorithm only accounts for convective weather systems exceeding a specified level of severity. When the stochastic reroutes are compared to the actual flight routes, they have similar total flight time, and both have about 1% of travel time crossing congested enroute sectors on average. The actual flight routes induce slightly less traffic congestion than the stochastic reroutes but intercept more severe convective weather.
Dynamics of a Stochastic Intraguild Predation Model
Directory of Open Access Journals (Sweden)
Zejing Xing
2016-04-01
Full Text Available Intraguild predation (IGP is a widespread ecological phenomenon which occurs when one predator species attacks another predator species with which it competes for a shared prey species. The objective of this paper is to study the dynamical properties of a stochastic intraguild predation model. We analyze stochastic persistence and extinction of the stochastic IGP model containing five cases and establish the sufficient criteria for global asymptotic stability of the positive solutions. This study shows that it is possible for the coexistence of three species under the influence of environmental noise, and that the noise may have a positive effect for IGP species. A stationary distribution of the stochastic IGP model is established and it has the ergodic property, suggesting that the time average of population size with the development of time is equal to the stationary distribution in space. Finally, we show that our results may be extended to two well-known biological systems: food chains and exploitative competition.
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.
Field Evaluation of Programmable Thermostats
Energy Technology Data Exchange (ETDEWEB)
Sachs, O.; Tiefenbeck, V.; Duvier, C.; Qin, A.; Cheney, K.; Akers, C.; Roth, K.
2012-12-01
Prior research suggests that poor programmable thermostats usability may prevent their effective use to save energy. We hypothesized that home occupants with a high-usability thermostats would be more likely to use them to save energy than people with a basic thermostat. We randomly installed a high-usability thermostat in half the 77 apartments of an affordable housing complex, installing a basic thermostat in the other half. During the heating season, we collected space temperature and furnace on-off data to evaluate occupant interaction with the thermostats, foremost nighttime setbacks. We found that thermostat usability did not influence energy-saving behaviors, finding no significant difference in temperature maintained among apartments with high- and low-usability thermostats.
Thermostatic Radiator Valve Evaluation
Energy Technology Data Exchange (ETDEWEB)
Dentz, J.; Ansanelli, E.
2015-01-01
A large stock of multifamily buildings in the Northeast and Midwest are heated by steam distribution systems. Losses from these systems are typically high and a significant number of apartments are overheated much of the time. Thermostatically controlled radiator valves (TRVs) are one potential strategy to combat this problem, but have not been widely accepted by the residential retrofit market.
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.
ENSO dynamics: low-dimensional-chaotic or stochastic?
Zivkovic, Tatjana
2012-01-01
We apply a test for low-dimensional, deterministic dynamics to the Nino 3 time series for the El Nino Southern Oscillation (ENSO). The test is negative, indicating that the dynamics is high-dimensional/stochastic. However, application of stochastic forcing to a time-delay equation for equatorial-wave dynamics can reproduce this stochastic dynamics and other important aspects of ENSO. Without such stochastic forcing this model yields low-dimensional, deterministic dynamics, hence these results emphasize the importance of the stochastic nature of the atmosphere-ocean interaction in low-dimensional models of ENSO.
Stochastic Resonance in Protein Folding Dynamics.
Davtyan, Aram; Platkov, Max; Gruebele, Martin; Papoian, Garegin A
2016-05-04
Although protein folding reactions are usually studied under static external conditions, it is likely that proteins fold in a locally fluctuating cellular environment in vivo. To mimic such behavior in in vitro experiments, the local temperature of the solvent can be modulated either harmonically or using correlated noise. In this study, coarse-grained molecular simulations are used to investigate these possibilities, and it is found that both periodic and correlated random fluctuations of the environment can indeed accelerate folding kinetics if the characteristic frequencies of the applied fluctuations are commensurate with the internal timescale of the folding reaction; this is consistent with the phenomenon of stochastic resonance observed in many other condensed-matter processes. To test this theoretical prediction, the folding dynamics of phosphoglycerate kinase under harmonic temperature fluctuations are experimentally probed using Förster resonance energy transfer fluorescence measurements. To analyze these experiments, a combination of theoretical approaches is developed, including stochastic simulations of folding kinetics and an analytical mean-field kinetic theory. The experimental observations are consistent with the theoretical predictions of stochastic resonance in phosphoglycerate kinase folding. When combined with an alternative experiment on the protein VlsE using a power spectrum analysis, elaborated in Dave et al., ChemPhysChem 2016, 10.1002/cphc.201501041, the overall data overwhelmingly point to the experimental confirmation of stochastic resonance in protein folding dynamics.
Computational Methods in Stochastic Dynamics Volume 2
Stefanou, George; Papadopoulos, Vissarion
2013-01-01
The considerable influence of inherent uncertainties on structural behavior has led the engineering community to recognize the importance of a stochastic approach to structural problems. Issues related to uncertainty quantification and its influence on the reliability of the computational models are continuously gaining in significance. In particular, the problems of dynamic response analysis and reliability assessment of structures with uncertain system and excitation parameters have been the subject of continuous research over the last two decades as a result of the increasing availability of powerful computing resources and technology. This book is a follow up of a previous book with the same subject (ISBN 978-90-481-9986-0) and focuses on advanced computational methods and software tools which can highly assist in tackling complex problems in stochastic dynamic/seismic analysis and design of structures. The selected chapters are authored by some of the most active scholars in their respective areas and...
Dynamic range of hypercubic stochastic excitable media
de Assis, Vladimir R V
2007-01-01
We study the response properties of d-dimensional hypercubic excitable networks to a stochastic stimulus. Each site, modelled either by a three-state stochastic susceptible-infected-recovered-susceptible (SIRS) system or by the probabilistic Greenberg-Hastings cellular automaton (GHCA), is continuously and independently stimulated by an external Poisson rate h. The response function (mean density of active sites rho versus h) is obtained via simulations (for d=1, 2, 3, 4) and mean field approximations at the single-site and pair levels (for all d). In any dimension, the dynamic range of the response function is maximized precisely at the nonequilibrium phase transition to self-sustained activity, in agreement with a reasoning recently proposed. Moreover, the maximum dynamic range attained at a given dimension d is a decreasing function of d.
NONLINEAR STOCHASTIC DYNAMICS: A SURVEY OF RECENT DEVELOPMENTS
Institute of Scientific and Technical Information of China (English)
朱位秋; 蔡国强
2002-01-01
This paper provides an overview of significant advances in nonlinearstochastic dynamics during the past two decades, including random response, stochas-tic stability, stochastic bifurcation, first passage problem and nonlinear stochasticcontrol. Topics for future research are also suggested.
Effective "Gluon" Dynamics in a Stochastic Vacuum
Magpantay, J A
2002-01-01
Using the new scalar and vector degrees of freedom derived from the non-linear gauge condition (grad-dot-D)(grad-dot-A)=0, we show that the effective dynamics of the vector fields (identified as ``gluons'') in the stochastic vacuum defined by the scalars result in the vector fields acquiring a mass. We also find the vector fields losing their self-interactions.
Inverse problems in stochastic computational dynamics
Capiez-Lernout, Evangéline; Soize, Christian
2008-01-01
International audience; This paper deals with robust updating of dynamical systems using stochastic computational models for which model and parameter uncertainties are taken into account by the nonparametric probabilistic approach. Such a problem is formulated as an inverse problem consisting in identifying the parameters of the mean computational model and the parameters of the probabilistic model of uncertainties. This inverse problem leads us to solve an optimization problem for which the...
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.
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.
Effect of signal modulating noise in bistable stochastic dynamical systems
Institute of Scientific and Technical Information of China (English)
肖方红; 闫桂荣; 张新武
2003-01-01
The effect of signal modulating noise in bistable stochastic dynamical systems is studied.The concept of instan taneous steady state is proposed for bistable dynamical systems.By making a dynamical analysis of bistable stochastic systems,we find that global and local effect of signal modulating noise as well as stochastic resonance can occur in bistable dynamical systems on which both a weak sinusoidal signal and noise are forced.The effect is demonstrated by numerical simulation.
Global dynamics of a stochastic neuronal oscillator
Yamanobe, Takanobu
2013-11-01
Nonlinear oscillators have been used to model neurons that fire periodically in the absence of input. These oscillators, which are called neuronal oscillators, share some common response structures with other biological oscillations such as cardiac cells. In this study, we analyze the dependence of the global dynamics of an impulse-driven stochastic neuronal oscillator on the relaxation rate to the limit cycle, the strength of the intrinsic noise, and the impulsive input parameters. To do this, we use a Markov operator that both reflects the density evolution of the oscillator and is an extension of the phase transition curve, which describes the phase shift due to a single isolated impulse. Previously, we derived the Markov operator for the finite relaxation rate that describes the dynamics of the entire phase plane. Here, we construct a Markov operator for the infinite relaxation rate that describes the stochastic dynamics restricted to the limit cycle. In both cases, the response of the stochastic neuronal oscillator to time-varying impulses is described by a product of Markov operators. Furthermore, we calculate the number of spikes between two consecutive impulses to relate the dynamics of the oscillator to the number of spikes per unit time and the interspike interval density. Specifically, we analyze the dynamics of the number of spikes per unit time based on the properties of the Markov operators. Each Markov operator can be decomposed into stationary and transient components based on the properties of the eigenvalues and eigenfunctions. This allows us to evaluate the difference in the number of spikes per unit time between the stationary and transient responses of the oscillator, which we show to be based on the dependence of the oscillator on past activity. Our analysis shows how the duration of the past neuronal activity depends on the relaxation rate, the noise strength, and the impulsive input parameters.
Double inverse stochastic resonance with dynamic synapses
Uzuntarla, Muhammet; Torres, Joaquin J.; So, Paul; Ozer, Mahmut; Barreto, Ernest
2017-01-01
We investigate the behavior of a model neuron that receives a biophysically realistic noisy postsynaptic current based on uncorrelated spiking activity from a large number of afferents. We show that, with static synapses, such noise can give rise to inverse stochastic resonance (ISR) as a function of the presynaptic firing rate. We compare this to the case with dynamic synapses that feature short-term synaptic plasticity and show that the interval of presynaptic firing rate over which ISR exists can be extended or diminished. We consider both short-term depression and facilitation. Interestingly, we find that a double inverse stochastic resonance (DISR), with two distinct wells centered at different presynaptic firing rates, can appear.
Hybrid Differential Dynamic Programming with Stochastic Search
Aziz, Jonathan; Parker, Jeffrey; Englander, Jacob
2016-01-01
Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASAs Dawn mission. The Dawn trajectory was designed with the DDP-based Static Dynamic Optimal Control algorithm used in the Mystic software. Another recently developed method, Hybrid Differential Dynamic Programming (HDDP) is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.
Output Feedback for Stochastic Nonlinear Systems with Unmeasurable Inverse Dynamics
Institute of Scientific and Technical Information of China (English)
Xin Yu; Na Duan
2009-01-01
This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability (iISS) in deterministic systems and stochastic input-to-state stability (SISS) in stochastic systems, a concept of stochastic integral input-to-state stability (SiISS) using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.
Stochastic Dynamics through Hierarchically Embedded Markov Chains
Vasconcelos, Vítor V.; Santos, Fernando P.; Santos, Francisco C.; Pacheco, Jorge M.
2017-02-01
Studying dynamical phenomena in finite populations often involves Markov processes of significant mathematical and/or computational complexity, which rapidly becomes prohibitive with increasing population size or an increasing number of individual configuration states. Here, we develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects—such as mutations in evolutionary dynamics and a random exploration of choices in social systems—including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.
The Stochastic Search Dynamics of Interneuron Migration
Britto, Joanne M.; Johnston, Leigh A.; Tan, Seong-Seng
2009-01-01
Abstract Migration is a dynamic process in which a cell searches the environment and translates acquired information into somal advancement. In particular, interneuron migration during development is accomplished by two distinct processes: the extension of neurites tipped with growth cones; and nucleus translocation, termed nucleokinesis. The primary purpose of our study is to investigate neurite branching and nucleokinesis using high-resolution time-lapse confocal microscopy and computational modeling. We demonstrate that nucleokinesis is accurately modeled by a spring-dashpot system and that neurite branching is independent of the nucleokinesis event, and displays the dynamics of a stochastic birth-death process. This is in contrast to traditional biological descriptions, which suggest a closer relationship between the two migratory mechanisms. Our models are validated on independent data sets acquired using two different imaging protocols, and are shown to be robust to alterations in guidance cues and cellular migratory mechanisms, through treatment with brain-derived neurotrophic factor, neurotrophin-4, and blebbistatin. We postulate that the stochastic branch dynamics exhibited by interneurons undergoing guidance-directed migration permit efficient exploration of the environment. PMID:19651028
Quantum Dynamics as a Stochastic Process
Figueiredo, J M A
2002-01-01
We study the classical motion of a particle subject to a stochastic force. We then present a perturbative schema for the associated Fokker-Planck equation where, in the limit of a vanishingly small noise source, a consistent dynamical model is obtained. The resulting theory is similar to Quantum Mechanics, having the same field equations for probability measures, the same operator structure and symmetric ordering of operators. The model is valid for general electromagnetic interaction as well as many body systems with mutual interactions of general nature.
Stochastic dynamic model of SARS spreading
Institute of Scientific and Technical Information of China (English)
SHI Yaolin
2003-01-01
Based upon the simulation of the stochastic process of infection, onset and spreading of each SARS patient, a system dynamic model of SRAS spreading is constructed. Data from Vietnam is taken as an example for Monte Carlo test. The preliminary results indicate that the time-dependent infection rate is the most important control factor for SARS spreading. The model can be applied to prediction of the course with fluctuations of the epidemics, if the previous history of the epidemics and the future infection rate under control measures are known.
Selective recoupling and stochastic dynamical decoupling
Kern, O
2006-01-01
An embedded selective recoupling method is proposed which is based on the idea of embedding the recently proposed deterministic selective recoupling scheme of Yamaguchi et al. [quant-ph/0411099] into a stochastic dynamical decoupling method, such as the recently proposed Pauli-random-error-correction-(PAREC) scheme [Eur. Phys. J. D 32, 153, quant-ph/0407262]. The recoupling scheme enables the implementation of elementary quantum gates in a quantum information processor by partial suppression of the unwanted interactions. The random dynamical decoupling method cancels a significant part of the residual interactions. Thus the time scale of reliable quantum computation is increased significantly. Numerical simulations are presented for a conditional two-qubit swap gate and for a complex iterative quantum algorithm.
Thermostatic Radiator Valve Evaluation
Energy Technology Data Exchange (ETDEWEB)
Dentz, J. [Advanced Residential Integrated Energy Solutions Collaborative (ARIES), New York, NY (United States); Ansanelli, E. [Advanced Residential Integrated Energy Solutions Collaborative (ARIES), New York, NY (United States)
2015-01-01
A large stock of multifamily buildings in the Northeast and Midwest are heated by steam distribution systems. Losses from these systems are typically high and a significant number of apartments are overheated much of the time. Thermostatically controlled radiator valves (TRVs) are one potential strategy to combat this problem, but have not been widely accepted by the residential retrofit market. In this project, the ARIES team sought to better understand the current usage of TRVs by key market players in steam and hot water heating and to conduct limited experiments on the effectiveness of new and old TRVs as a means of controlling space temperatures and reducing heating fuel consumption. The project included a survey of industry professionals, a field experiment comparing old and new TRVs, and cost-benefit modeling analysis using BEopt™ (Building Energy Optimization software).
Stochastic evolutionary dynamics of direct reciprocity.
Imhof, Lorens A; Nowak, Martin A
2010-02-01
Evolutionary game theory is the study of frequency-dependent selection. The success of an individual depends on the frequencies of strategies that are used in the population. We propose a new model for studying evolutionary dynamics in games with a continuous strategy space. The population size is finite. All members of the population use the same strategy. A mutant strategy is chosen from some distribution over the strategy space. The fixation probability of the mutant strategy in the resident population is calculated. The new mutant takes over the population with this probability. In this case, the mutant becomes the new resident. Otherwise, the existing resident remains. Then, another mutant is generated. These dynamics lead to a stationary distribution over the entire strategy space. Our new approach generalizes classical adaptive dynamics in three ways: (i) the population size is finite; (ii) mutants can be drawn non-locally and (iii) the dynamics are stochastic. We explore reactive strategies in the repeated Prisoner's Dilemma. We perform 'knock-out experiments' to study how various strategies affect the evolution of cooperation. We find that 'tit-for-tat' is a weak catalyst for the emergence of cooperation, while 'always cooperate' is a strong catalyst for the emergence of defection. Our analysis leads to a new understanding of the optimal level of forgiveness that is needed for the evolution of cooperation under direct reciprocity.
Nonlinear and stochastic dynamics in the heart
Energy Technology Data Exchange (ETDEWEB)
Qu, Zhilin, E-mail: zqu@mednet.ucla.edu [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Hu, Gang [Department of Physics, Beijing Normal University, Beijing 100875 (China); Garfinkel, Alan [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Department of Integrative Biology and Physiology, University of California, Los Angeles, CA 90095 (United States); Weiss, James N. [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Department of Physiology, David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States)
2014-10-10
In a normal human life span, the heart beats about 2–3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.
Stochastic epidemic dynamics on extremely heterogeneous networks
Parra-Rojas, César; McKane, Alan J
2016-01-01
Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many contacts. We derive a two-dimensional diffusion model for the full temporal behavior of the stochastic susceptible-infectious-recovered (SIR) model on such a network, by making use of a time-scale separation in the deterministic limit of the dynamics. This low-dimensional process is an accurate approximation to the full model in the limit of large populations, even for cases when the time-scale separation is not too pronounced, provided the maximum degree is not of the order of the population size.
Stochastic epidemic dynamics on extremely heterogeneous networks
Parra-Rojas, César; House, Thomas; McKane, Alan J.
2016-12-01
Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many contacts. We derive a two-dimensional diffusion model for the full temporal behavior of the stochastic susceptible-infectious-recovered (SIR) model on such a network, by making use of a time-scale separation in the deterministic limit of the dynamics. This low-dimensional process is an accurate approximation to the full model in the limit of large populations, even for cases when the time-scale separation is not too pronounced, provided the maximum degree is not of the order of the population size.
Nambu mechanics for stochastic magnetization dynamics
Thibaudeau, Pascal; Nicolis, Stam
2016-01-01
The Landau-Lifshitz-Gilbert (LLG) equation describes the dynamics of a damped magnetization vector that can be understood as a generalization of Larmor spin precession. The LLG equation cannot be deduced from the Hamiltonian framework, by introducing a coupling to a usual bath, but requires the introduction of additional constraints. It is shown that these constraints can be formulated elegantly and consistently in the framework of dissipative Nambu mechanics. This has many consequences for both the variational principle and for topological aspects of hidden symmetries that control conserved quantities. We particularly study how the damping terms of dissipative Nambu mechanics affect the consistent interaction of magnetic systems with stochastic reservoirs and derive a master equation for the magnetization. The proposals are supported by numerical studies using symplectic integrators that preserve the topological structure of Nambu equations. These results are compared to computations performed by direct samp...
Wolbachia spread dynamics in stochastic environments.
Hu, Linchao; Huang, Mugen; Tang, Moxun; Yu, Jianshe; Zheng, Bo
2015-12-01
Dengue fever is a mosquito-borne viral disease with 100 million people infected annually. A novel strategy for dengue control uses the bacterium Wolbachia to invade dengue vector Aedes mosquitoes. As the impact of environmental heterogeneity on Wolbachia spread dynamics in natural areas has been rarely quantified, we develop a model of differential equations for which the environmental conditions switch randomly between two regimes. We find some striking phenomena that random regime transitions could drive Wolbachia to extinction from certain initial states confirmed Wolbachia fixation in homogeneous environments, and mosquito releasing facilitates Wolbachia invasion more effectively when the regimes transit frequently. By superimposing the phase spaces of the ODE systems defined in each regime, we identify the threshold curves below which Wolbachia invades the whole population, which extends the theory of threshold infection frequency to stochastic environments.
An ergodic configurational thermostat using selective control of higher order temperatures.
Patra, Puneet Kumar; Bhattacharya, Baidurya
2015-05-21
The conventional Nosé-Hoover type deterministic thermostat scheme for controlling temperature by configurational variables (Braga-Travis (BT) thermostat) is non-ergodic for systems with a few degrees of freedom. While for the original Nosé-Hoover kinetic thermostat ergodicity has been achieved by controlling the higher order moments of kinetic energy, the issues of nonergodicity of BT thermostat persists. In this paper, we introduce two new measures of configurational temperature (second and third order) based on the generalized temperature-curvature relationship and obtain a family of deterministic thermostatting schemes by selectively (and simultaneously) controlling the different orders of temperatures through pseudo-friction terms. The ergodic characteristics of the proposed thermostats are tested using a single harmonic oscillator through statistical (normality of joint distributions at different Poincare sections) as well as dynamical tests (difference of the minimum and maximum largest Lyapunov exponent). Our results indicate that simultaneously controlling the first and the second order configurational temperatures (C(1,2) thermostat) is sufficient to make the dynamics ergodic. A 2000 particle Lennard-Jones system is subjected to (i) equilibrium and (ii) sudden temperature change under BT and C(1,2) thermostatting schemes. The C(1,2) thermostat is found to be more robust than the BT thermostat without increasing computational costs.
Dynamic analysis of stochastic transcription cycles.
Directory of Open Access Journals (Sweden)
Claire V Harper
2011-04-01
Full Text Available In individual mammalian cells the expression of some genes such as prolactin is highly variable over time and has been suggested to occur in stochastic pulses. To investigate the origins of this behavior and to understand its functional relevance, we quantitatively analyzed this variability using new mathematical tools that allowed us to reconstruct dynamic transcription rates of different reporter genes controlled by identical promoters in the same living cell. Quantitative microscopic analysis of two reporter genes, firefly luciferase and destabilized EGFP, was used to analyze the dynamics of prolactin promoter-directed gene expression in living individual clonal and primary pituitary cells over periods of up to 25 h. We quantified the time-dependence and cyclicity of the transcription pulses and estimated the length and variation of active and inactive transcription phases. We showed an average cycle period of approximately 11 h and demonstrated that while the measured time distribution of active phases agreed with commonly accepted models of transcription, the inactive phases were differently distributed and showed strong memory, with a refractory period of transcriptional inactivation close to 3 h. Cycles in transcription occurred at two distinct prolactin-promoter controlled reporter genes in the same individual clonal or primary cells. However, the timing of the cycles was independent and out-of-phase. For the first time, we have analyzed transcription dynamics from two equivalent loci in real-time in single cells. In unstimulated conditions, cells showed independent transcription dynamics at each locus. A key result from these analyses was the evidence for a minimum refractory period in the inactive-phase of transcription. The response to acute signals and the result of manipulation of histone acetylation was consistent with the hypothesis that this refractory period corresponded to a phase of chromatin remodeling which significantly
Stochastic dynamics for reinfection by transmitted diseases
Barros, Alessandro S.; Pinho, Suani T. R.
2017-06-01
The use of stochastic models to study the dynamics of infectious diseases is an important tool to understand the epidemiological process. For several directly transmitted diseases, reinfection is a relevant process, which can be expressed by endogenous reactivation of the pathogen or by exogenous reinfection due to direct contact with an infected individual (with smaller reinfection rate σ β than infection rate β ). In this paper, we examine the stochastic susceptible, infected, recovered, infected (SIRI) model simulating the endogenous reactivation by a spontaneous reaction, while exogenous reinfection by a catalytic reaction. Analyzing the mean-field approximations of a site and pairs of sites, and Monte Carlo (MC) simulations for the particular case of exogenous reinfection, we obtained continuous phase transitions involving endemic, epidemic, and no transmission phases for the simple approach; the approach of pairs is better to describe the phase transition from endemic phase (susceptible, infected, susceptible (SIS)-like model) to epidemic phase (susceptible, infected, and removed or recovered (SIR)-like model) considering the comparison with MC results; the reinfection increases the peaks of outbreaks until the system reaches endemic phase. For the particular case of endogenous reactivation, the approach of pairs leads to a continuous phase transition from endemic phase (SIS-like model) to no transmission phase. Finally, there is no phase transition when both effects are taken into account. We hope the results of this study can be generalized for the susceptible, exposed, infected, and removed or recovered (SEIRIE) model, for which the state exposed (infected but not infectious), describing more realistically transmitted diseases such as tuberculosis. In future work, we also intend to investigate the effect of network topology on phase transitions when the SIRI model describes both transmitted diseases (σ 1 ).
Extended Plefka expansion for stochastic dynamics
Bravi, B.; Sollich, P.; Opper, M.
2016-05-01
We propose an extension of the Plefka expansion, which is well known for the dynamics of discrete spins, to stochastic differential equations with continuous degrees of freedom and exhibiting generic nonlinearities. The scenario is sufficiently general to allow application to e.g. biochemical networks involved in metabolism and regulation. The main feature of our approach is to constrain in the Plefka expansion not just first moments akin to magnetizations, but also second moments, specifically two-time correlations and responses for each degree of freedom. The end result is an effective equation of motion for each single degree of freedom, where couplings to other variables appear as a self-coupling to the past (i.e. memory term) and a coloured noise. This constitutes a new mean field approximation that should become exact in the thermodynamic limit of a large network, for suitably long-ranged couplings. For the analytically tractable case of linear dynamics we establish this exactness explicitly by appeal to spectral methods of random matrix theory, for Gaussian couplings with arbitrary degree of symmetry.
Reliability-based Dynamic Network Design with Stochastic Networks
Li, H.
2009-01-01
Transportation systems are stochastic and dynamic systems. The road capacities and the travel demand are fluctuating from time to time within a day and at the same time from day to day. For road users, the travel time and travel costs experienced over time and space are stochastic, thus desire relia
Identification and stochastic control of helicopter dynamic modes
Molusis, J. A.; Bar-Shalom, Y.
1983-01-01
A general treatment of parameter identification and stochastic control for use on helicopter dynamic systems is presented. Rotor dynamic models, including specific applications to rotor blade flapping and the helicopter ground resonance problem are emphasized. Dynamic systems which are governed by periodic coefficients as well as constant coefficient models are addressed. The dynamic systems are modeled by linear state variable equations which are used in the identification and stochastic control formulation. The pure identification problem as well as the stochastic control problem which includes combined identification and control for dynamic systems is addressed. The stochastic control problem includes the effect of parameter uncertainty on the solution and the concept of learning and how this is affected by the control's duel effect. The identification formulation requires algorithms suitable for on line use and thus recursive identification algorithms are considered. The applications presented use the recursive extended kalman filter for parameter identification which has excellent convergence for systems without process noise.
Safety Analysis of Stochastic Dynamical Systems
DEFF Research Database (Denmark)
Sloth, Christoffer; Wisniewski, Rafael
2015-01-01
This paper presents a method for verifying the safety of a stochastic system. In particular, we show how to compute the largest set of initial conditions such that a given stochastic system is safe with probability p. To compute the set of initial conditions we rely on the moment method that via...
Dynamic consistency for Stochastic Optimal Control problems
Carpentier, Pierre; Cohen, Guy; De Lara, Michel; Girardeau, Pierre
2010-01-01
For a sequence of dynamic optimization problems, we aim at discussing a notion of consistency over time. This notion can be informally introduced as follows. At the very first time step $t_0$, the decision maker formulates an optimization problem that yields optimal decision rules for all the forthcoming time step $t_0, t_1, ..., T$; at the next time step $t_1$, he is able to formulate a new optimization problem starting at time $t_1$ that yields a new sequence of optimal decision rules. This process can be continued until final time $T$ is reached. A family of optimization problems formulated in this way is said to be time consistent if the optimal strategies obtained when solving the original problem remain optimal for all subsequent problems. The notion of time consistency, well-known in the field of Economics, has been recently introduced in the context of risk measures, notably by Artzner et al. (2007) and studied in the Stochastic Programming framework by Shapiro (2009) and for Markov Decision Processes...
Extending Newtonian Dynamics to Include Stochastic Processes
Zak, Michail
2009-01-01
A paper presents further results of continuing research reported in several previous NASA Tech Briefs articles, the two most recent being Stochastic Representations of Chaos Using Terminal Attractors (NPO-41519), [Vol. 30, No. 5 (May 2006), page 57] and Physical Principle for Generation of Randomness (NPO-43822) [Vol. 33, No. 5 (May 2009), page 56]. This research focuses upon a mathematical formalism for describing post-instability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism involves fictitious control forces that couple the equations of motion of the system with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These stabilizing forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in configuration space (ordinary three-dimensional space as commonly perceived) is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. As a result, the post-instability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable.
Stochastic single-molecule dynamics of synaptic membrane protein domains
Kahraman, Osman; Haselwandter, Christoph A
2016-01-01
Motivated by single-molecule experiments on synaptic membrane protein domains, we use a stochastic lattice model to study protein reaction and diffusion processes in crowded membranes. We find that the stochastic reaction-diffusion dynamics of synaptic proteins provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the single-molecule trajectories observed for synaptic proteins, and spatially inhomogeneous protein lifetimes at the cell membrane. Our results suggest that central aspects of the single-molecule and collective dynamics observed for membrane protein domains can be understood in terms of stochastic reaction-diffusion processes at the cell membrane.
Stochastic system identification in structural dynamics
Safak, Erdal
1988-01-01
Recently, new identification methods have been developed by using the concept of optimal-recursive filtering and stochastic approximation. These methods, known as stochastic identification, are based on the statistical properties of the signal and noise, and do not require the assumptions of current methods. The criterion for stochastic system identification is that the difference between the recorded output and the output from the identified system (i.e., the residual of the identification) should be equal to white noise. In this paper, first a brief review of the theory is given. Then, an application of the method is presented by using ambient vibration data from a nine-story building.
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.
Spatial stochastic dynamics enable robust cell polarization.
Directory of Open Access Journals (Sweden)
Michael J Lawson
Full Text Available Although cell polarity is an essential feature of living cells, it is far from being well-understood. Using a combination of computational modeling and biological experiments we closely examine an important prototype of cell polarity: the pheromone-induced formation of the yeast polarisome. Focusing on the role of noise and spatial heterogeneity, we develop and investigate two mechanistic spatial models of polarisome formation, one deterministic and the other stochastic, and compare the contrasting predictions of these two models against experimental phenotypes of wild-type and mutant cells. We find that the stochastic model can more robustly reproduce two fundamental characteristics observed in wild-type cells: a highly polarized phenotype via a mechanism that we refer to as spatial stochastic amplification, and the ability of the polarisome to track a moving pheromone input. Moreover, we find that only the stochastic model can simultaneously reproduce these characteristics of the wild-type phenotype and the multi-polarisome phenotype of a deletion mutant of the scaffolding protein Spa2. Significantly, our analysis also demonstrates that higher levels of stochastic noise results in increased robustness of polarization to parameter variation. Furthermore, our work suggests a novel role for a polarisome protein in the stabilization of actin cables. These findings elucidate the intricate role of spatial stochastic effects in cell polarity, giving support to a cellular model where noise and spatial heterogeneity combine to achieve robust biological function.
From thermostatics -- to the thermokinetics
Etkin, V A
2014-01-01
Present-day thermodynamics has long outgrown the initial frames of the heat-engine theory and transmuted into a rather general macroscopic method for studying kinetics of various transfer processes in their inseparable connection with the thermal form of motion. However its primary notions and mathematical instrument as before based on concepts of thermostatics, to wich time, speed and productivity of processes are alien, and on the equations transitory in case of irreversible processes in inequalities. It is offered essentially other approach at wich the thermostatics equations follow from thermokinetics of spatially non-uniform systems.
The Theory of Dynamic Public Transit Priority with Dynamic Stochastic Park and Ride
Directory of Open Access Journals (Sweden)
Chengming Zhu
2014-01-01
Full Text Available Public transit priority is very important for relieving traffic congestion. The connotation of dynamic public transit priority and dynamic stochastic park and ride is presented. Based on the point that the travel cost of public transit is not higher than the travel cost of car, how to determine the level of dynamic public transit priority is discussed. The traffic organization method of dynamic public transit priority is introduced. For dynamic stochastic park and ride, layout principle, scale, and charging standard are discussed. Traveler acceptability is high through the analysis of questionnaire survey. Dynamic public transit priority with dynamic stochastic park and ride has application feasibility.
Stochastic Euler Equations of Fluid Dynamics with Lvy Noise
2016-08-10
Asymptotic Analysis 99 (2016) 67–103 67 DOI 10.3233/ASY-161376 IOS Press Stochastic Euler equations of fluid dynamics with Lévy noise Manil T. Mohan...References [1] D. Applebaum, Lévy Processes and Stochastic Calculus , Cambridge Studies in Advanced Mathematics, Vol. 93, Cam- bridge University Press...2004. [2] H. Bessaih and F. Flandoli, 2-D Euler equation perturbed by noise, Nonlinear Differential Equations and Applications 6 (1998), 35–54. doi
Time averages, recurrence and transience in the stochastic replicator dynamics
Hofbauer, Josef; 10.1214/08-AAP577
2009-01-01
We investigate the long-run behavior of a stochastic replicator process, which describes game dynamics for a symmetric two-player game under aggregate shocks. We establish an averaging principle that relates time averages of the process and Nash equilibria of a suitably modified game. Furthermore, a sufficient condition for transience is given in terms of mixed equilibria and definiteness of the payoff matrix. We also present necessary and sufficient conditions for stochastic stability of pure equilibria.
Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach
Energy Technology Data Exchange (ETDEWEB)
Chertkov, Michael [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Skolkovo Inst. of Science and Technology, Moscow (Russia); Chernyak, Vladimir [Wayne State Univ., Detroit, MI (United States). Dept. of Chemistry
2017-01-17
Thermostatically Controlled Loads (TCL), e.g. air-conditioners and heaters, are by far the most wide-spread consumers of electricity. Normally the devices are calibrated to provide the so-called bang-bang control of temperature - changing from on to off , and vice versa, depending on temperature. Aggregation of a large group of similar devices into a statistical ensemble is considered, where the devices operate following the same dynamics subject to stochastic perturbations and randomized, Poisson on/off switching policy. We analyze, using theoretical and computational tools of statistical physics, how the ensemble relaxes to a stationary distribution and establish relation between the re- laxation and statistics of the probability flux, associated with devices' cycling in the mixed (discrete, switch on/off , and continuous, temperature) phase space. This allowed us to derive and analyze spec- trum of the non-equilibrium (detailed balance broken) statistical system. and uncover how switching policy affects oscillatory trend and speed of the relaxation. Relaxation of the ensemble is of a practical interest because it describes how the ensemble recovers from significant perturbations, e.g. forceful temporary switching o aimed at utilizing flexibility of the ensemble in providing "demand response" services relieving consumption temporarily to balance larger power grid. We discuss how the statistical analysis can guide further development of the emerging demand response technology.
Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach.
Chertkov, Michael; Chernyak, Vladimir
2017-08-17
Thermostatically controlled loads, e.g., air conditioners and heaters, are by far the most widespread consumers of electricity. Normally the devices are calibrated to provide the so-called bang-bang control - changing from on to off, and vice versa, depending on temperature. We considered aggregation of a large group of similar devices into a statistical ensemble, where the devices operate following the same dynamics, subject to stochastic perturbations and randomized, Poisson on/off switching policy. Using theoretical and computational tools of statistical physics, we analyzed how the ensemble relaxes to a stationary distribution and established a relationship between the relaxation and the statistics of the probability flux associated with devices' cycling in the mixed (discrete, switch on/off, and continuous temperature) phase space. This allowed us to derive the spectrum of the non-equilibrium (detailed balance broken) statistical system and uncover how switching policy affects oscillatory trends and the speed of the relaxation. Relaxation of the ensemble is of practical interest because it describes how the ensemble recovers from significant perturbations, e.g., forced temporary switching off aimed at utilizing the flexibility of the ensemble to provide "demand response" services to change consumption temporarily to balance a larger power grid. We discuss how the statistical analysis can guide further development of the emerging demand response technology.
A LEAP-FROG ALGORITHM FOR STOCHASTIC DYNAMICS
Van Gunsteren, W. F.; Berendsen, H. J. C.
1988-01-01
A third-order algorithm for stochastic dynamics (SD) simulations is proposed, identical to the powerful molecular dynamics leapfrog algorithm in the limit of infinitely small friction coefficient gamma. It belongs to the class of SD algorithms, in which the integration time step Delta t is not
A LEAP-FROG ALGORITHM FOR STOCHASTIC DYNAMICS
Van Gunsteren, W. F.; Berendsen, H. J. C.
1988-01-01
A third-order algorithm for stochastic dynamics (SD) simulations is proposed, identical to the powerful molecular dynamics leapfrog algorithm in the limit of infinitely small friction coefficient gamma. It belongs to the class of SD algorithms, in which the integration time step Delta t is not limit
Long term dynamics of stochastic evolution equations
Bierkens, Gregorius Nicolaas Johannes Cornelis
2010-01-01
Stochastic differential equations with delay are the inspiration for this thesis. Examples of such equations arise in population models, control systems with delay and noise, lasers, economical models, neural networks, environmental pollution and in many other situations. In such models we are often
Long term dynamics of stochastic evolution equations
Bierkens, Gregorius Nicolaas Johannes Cornelis
2010-01-01
Stochastic differential equations with delay are the inspiration for this thesis. Examples of such equations arise in population models, control systems with delay and noise, lasers, economical models, neural networks, environmental pollution and in many other situations. In such models we are often
Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay
Directory of Open Access Journals (Sweden)
Wenli Zhu
2013-01-01
Full Text Available Based on Lyapunov stability theory, Itô formula, stochastic analysis, and matrix theory, we study the exponential stability of the stochastic nonlinear dynamical price system. Using Taylor's theorem, the stochastic nonlinear system with delay is reduced to an n-dimensional semilinear stochastic differential equation with delay. Some sufficient conditions of exponential stability and corollaries for such price system are established by virtue of Lyapunov function. The time delay upper limit is solved by using our theoretical results when the system is exponentially stable. Our theoretical results show that if the classical price Rayleigh equation is exponentially stable, so is its perturbed system with delay provided that both the time delay and the intensity of perturbations are small enough. Two examples are presented to illustrate our results.
Stochastic hard-sphere dynamics for hydrodynamics of nonideal fluids.
Donev, Aleksandar; Alder, Berni J; Garcia, Alejandro L
2008-08-15
A novel stochastic fluid model is proposed with a nonideal structure factor consistent with compressibility, and adjustable transport coefficients. This stochastic hard-sphere dynamics (SHSD) algorithm is a modification of the direct simulation Monte Carlo algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and a pair correlation function identical to that of a deterministic Hamiltonian system of penetrable spheres interacting with linear core pair potentials. The fluctuating hydrodynamic behavior of the SHSD fluid is verified for the Brownian motion of a nanoparticle suspended in a compressible solvent.
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.
Stochastic synchronization for time-varying complex dynamical networks
Institute of Scientific and Technical Information of China (English)
Guo Xiao-Yong; Li Jun-Min
2012-01-01
This paper studies the stochastic synchronization problem for time-varying complex dynamical networks. This model is totally different from some existing network models. Based on the Lyapunov stability theory, inequality techniques, and the properties of the Weiner process, some controllers and adaptive laws are designed to ensure achieving stochastic synchronization of a complex dynamical network model. A sufficient synchronization condition is given to ensure that the proposed network model is mean-square stable. Theoretical analysis and numerical simulation fully verify the main results.
Average quantum dynamics of closed systems over stochastic Hamiltonians
Yu, Li
2011-01-01
We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in closed system dynamics, in addition to the usual unitary evolution. We then show that, for an important class of problems in which the Hamiltonian is proportional to a Gaussian random process, the 2nd-order master equation yields exact dynamics. The general formalism is applied to study the examples of a two-level system, two atoms in a stochastic magnetic field and the heating of a trapped ion.
Directory of Open Access Journals (Sweden)
Shaolin Ji
2013-01-01
Full Text Available This paper is devoted to a stochastic differential game (SDG of decoupled functional forward-backward stochastic differential equation (FBSDE. For our SDG, the associated upper and lower value functions of the SDG are defined through the solution of controlled functional backward stochastic differential equations (BSDEs. Applying the Girsanov transformation method introduced by Buckdahn and Li (2008, the upper and the lower value functions are shown to be deterministic. We also generalize the Hamilton-Jacobi-Bellman-Isaacs (HJBI equations to the path-dependent ones. By establishing the dynamic programming principal (DPP, we derive that the upper and the lower value functions are the viscosity solutions of the corresponding upper and the lower path-dependent HJBI equations, respectively.
Simulation of stochastic network dynamics via entropic matching.
Ramalho, Tiago; Selig, Marco; Gerland, Ulrich; Ensslin, Torsten A
2013-02-01
The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a model's dynamics over a large parameter space renders full-fledged stochastic simulations impractical, motivating approximation schemes. Here we propose an approximation scheme which improves upon the standard linear noise approximation while retaining similar computational complexity. The underlying idea is to minimize, at each time step, the Kullback-Leibler divergence between the true time evolved probability distribution and a Gaussian approximation (entropic matching). This condition leads to ordinary differential equations for the mean and the covariance matrix of the Gaussian. For cases of weak nonlinearity, the method is more accurate than the linear method when both are compared to stochastic simulations.
A new and effective method for thermostatting confined fluids
Energy Technology Data Exchange (ETDEWEB)
De Luca, Sergio; Todd, B. D., E-mail: btodd@swin.edu.au [Department of Mathematics, Faculty of Science, Engineering and Technology, and Centre for Molecular Simulation, Swinburne University of Technology, Melbourne, Victoria 3122 (Australia); Hansen, J. S. [DNRF Center “Glass and Time,” IMFUFA, Department of Science, Systems and Models, Roskilde University, DK-4000 Roskilde (Denmark); Daivis, Peter J. [School of Applied Sciences, RMIT University, Melbourne, Victoria 3001 (Australia)
2014-02-07
We present a simple thermostatting method suitable for nanoconfined fluid systems. Two conventional strategies involve thermostatting the fluid directly or employing a thermal wall that couples only the wall atoms with the thermostat. When only a thermal wall is implemented, the temperature control of the fluid is true to the actual experiment and the heat is transferred from the fluid to the walls. However, for large or complex systems it can often be computationally prohibitive to employ thermal walls. To overcome this limitation many researchers choose to freeze wall atoms and instead apply a synthetic thermostat to the fluid directly through the equations of motion. This, however, can have serious consequences for the mechanical, thermodynamic, and dynamical properties of the fluid by introducing unphysical behaviour into the system [Bernardi et al., J. Chem. Phys. 132, 244706 (2010)]. In this paper, we propose a simple scheme which enables working with both frozen walls and naturally thermostatted liquids. This is done by superimposing the walls with oscillating particles, which vibrate on the edge of the fluid control volume. These particles exchange energy with the fluid molecules, but do not interact with wall atoms or each other, thus behaving as virtual particles. Their displacements violate the Lindemann criterion for melting, in such a way that the net effect would not amount to an additional confining surface. One advantage over standard techniques is the reduced computational cost, particularly for large walls, since they can be kept rigid. Another advantage over accepted strategies is the opportunity to freeze complex charged walls such as β-cristobalite. The method furthermore overcomes the problem with polar fluids such as water, as thermalized charged surfaces require higher spring constants to preserve structural stability, due to the effects of strong Coulomb interactions, thus inevitably degrading the thermostatting efficiency.
A new and effective method for thermostatting confined fluids
De Luca, Sergio; Todd, B. D.; Hansen, J. S.; Daivis, Peter J.
2014-02-01
We present a simple thermostatting method suitable for nanoconfined fluid systems. Two conventional strategies involve thermostatting the fluid directly or employing a thermal wall that couples only the wall atoms with the thermostat. When only a thermal wall is implemented, the temperature control of the fluid is true to the actual experiment and the heat is transferred from the fluid to the walls. However, for large or complex systems it can often be computationally prohibitive to employ thermal walls. To overcome this limitation many researchers choose to freeze wall atoms and instead apply a synthetic thermostat to the fluid directly through the equations of motion. This, however, can have serious consequences for the mechanical, thermodynamic, and dynamical properties of the fluid by introducing unphysical behaviour into the system [Bernardi et al., J. Chem. Phys. 132, 244706 (2010)]. In this paper, we propose a simple scheme which enables working with both frozen walls and naturally thermostatted liquids. This is done by superimposing the walls with oscillating particles, which vibrate on the edge of the fluid control volume. These particles exchange energy with the fluid molecules, but do not interact with wall atoms or each other, thus behaving as virtual particles. Their displacements violate the Lindemann criterion for melting, in such a way that the net effect would not amount to an additional confining surface. One advantage over standard techniques is the reduced computational cost, particularly for large walls, since they can be kept rigid. Another advantage over accepted strategies is the opportunity to freeze complex charged walls such as β-cristobalite. The method furthermore overcomes the problem with polar fluids such as water, as thermalized charged surfaces require higher spring constants to preserve structural stability, due to the effects of strong Coulomb interactions, thus inevitably degrading the thermostatting efficiency.
How People Actually Use Thermostats
Energy Technology Data Exchange (ETDEWEB)
Meier, Alan; Aragon, Cecilia; Hurwitz, Becky; Mujumdar, Dhawal; Peffer, Therese; Perry, Daniel; Pritoni, Marco
2010-08-15
Residential thermostats have been a key element in controlling heating and cooling systems for over sixty years. However, today's modern programmable thermostats (PTs) are complicated and difficult for users to understand, leading to errors in operation and wasted energy. Four separate tests of usability were conducted in preparation for a larger study. These tests included personal interviews, an on-line survey, photographing actual thermostat settings, and measurements of ability to accomplish four tasks related to effective use of a PT. The interviews revealed that many occupants used the PT as an on-off switch and most demonstrated little knowledge of how to operate it. The on-line survey found that 89% of the respondents rarely or never used the PT to set a weekday or weekend program. The photographic survey (in low income homes) found that only 30% of the PTs were actually programmed. In the usability test, we found that we could quantify the difference in usability of two PTs as measured in time to accomplish tasks. Users accomplished the tasks in consistently shorter times with the touchscreen unit than with buttons. None of these studies are representative of the entire population of users but, together, they illustrate the importance of improving user interfaces in PTs.
Electricity Market Stochastic Dynamic Model and Its Mean Stability Analysis
Directory of Open Access Journals (Sweden)
Zhanhui Lu
2014-01-01
Full Text Available Based on the deterministic dynamic model of electricity market proposed by Alvarado, a stochastic electricity market model, considering the random nature of demand sides, is presented in this paper on the assumption that generator cost function and consumer utility function are quadratic functions. The stochastic electricity market model is a generalization of the deterministic dynamic model. Using the theory of stochastic differential equations, stochastic process theory, and eigenvalue techniques, the determining conditions of the mean stability for this electricity market model under small Gauss type random excitation are provided and testified theoretically. That is, if the demand elasticity of suppliers is nonnegative and the demand elasticity of consumers is negative, then the stochastic electricity market model is mean stable. It implies that the stability can be judged directly by initial data without any computation. Taking deterministic electricity market data combined with small Gauss type random excitation as numerical samples to interpret random phenomena from a statistical perspective, the results indicate the conclusions above are correct, valid, and practical.
A toolkit for analyzing nonlinear dynamic stochastic models easily
Uhlig, H.F.H.V.S.
1995-01-01
Often, researchers wish to analyze nonlinear dynamic discrete-time stochastic models. This paper provides a toolkit for solving such models easily, building on log-linearizing the necessary equations characterizing the equilibrium and solving for the recursive equilibrium law of motion with the meth
A toolkit for analyzing nonlinear dynamic stochastic models easily
Uhlig, H.F.H.V.S.
1995-01-01
Often, researchers wish to analyze nonlinear dynamic discrete-time stochastic models. This paper provides a toolkit for solving such models easily, building on log-linearizing the necessary equations characterizing the equilibrium and solving for the recursive equilibrium law of motion with the meth
Pricing decisions in an experimental dynamic stochastic general equilibrium economy
Noussair, C.N.; Pfajfar, D.; Zsiros, J.
2015-01-01
We construct experimental economies, populated with human subjects, with a structure based on a nonlinear version of the New Keynesian dynamic stochastic general equilibrium (DSGE) model. We analyze the behavior of firms’ pricing decisions in four different experimental economies. We consider how we
Rural Poverty Dynamics in Kenya: Structural Declines and Stochastic Escapes
Radeny, M.A.O.; Berg, van den M.M.; Schipper, R.A.
2012-01-01
We use panel survey data and household event-histories to explore patterns of rural poverty dynamics in Kenya over the period 2000–2009. We find substantial mobility across poverty categories using economic transition matrices. Drawing on asset-based approaches, we distinguish stochastic from struct
Dynamical Epidemic Suppression Using Stochastic Prediction and Control
2004-10-28
reduce the rate of input of susceptibles. By using the PDF flux, we are able to distinguish regions used in other chaos control schemes that are...use this information in a control algo- stochastic chaos control methods that account specifically for rithm to prevent bursting dynamics (that is, to
Pricing decisions in an experimental dynamic stochastic general equilibrium economy
Noussair, C.N.; Pfajfar, D.; Zsiros, J.
We construct experimental economies, populated with human subjects, with a structure based on a nonlinear version of the New Keynesian dynamic stochastic general equilibrium (DSGE) model. We analyze the behavior of firms’ pricing decisions in four different experimental economies. We consider how
Modeling and control of thermostatically controlled loads
Energy Technology Data Exchange (ETDEWEB)
Backhaus, Scott N [Los Alamos National Laboratory; Sinitsyn, Nikolai [Los Alamos National Laboratory; Kundu, S. [UNIV OF MICHIGAN; Hiskens, I. [UNIV OF MICHIGAN
2011-01-04
As the penetration of intermittent energy sources grows substantially, loads will be required to play an increasingly important role in compensating the fast time-scale fluctuations in generated power. Recent numerical modeling of thermostatically controlled loads (TCLs) has demonstrated that such load following is feasible, but analytical models that satisfactorily quantify the aggregate power consumption of a group of TCLs are desired to enable controller design. We develop such a model for the aggregate power response of a homogeneous population of TCLs to uniform variation of all TCL setpoints. A linearized model of the response is derived, and a linear quadratic regulator (LQR) has been designed. Using the TCL setpoint as the control input, the LQR enables aggregate power to track reference signals that exhibit step, ramp and sinusoidal variations. Although much of the work assumes a homogeneous population of TCLs with deterministic dynamics, we also propose a method for probing the dynamics of systems where load characteristics are not well known.
Approximation of stochastic equilibria for dynamic systems with colored noise
Energy Technology Data Exchange (ETDEWEB)
Bashkirtseva, Irina [Ural Federal University, Lenina 51, Ekaterinburg, 620083 (Russian Federation)
2015-03-10
We consider nonlinear dynamic systems forced by colored noise. Using first approximation systems, we study dynamics of deviations of stochastic solutions from stable deterministic equilibria. Equations for the stationary second moments of deviations of random states are derived. An application of the elaborated theory to Van der Pol system driven by colored noise is given. A dependence of the dispersion on the time correlation of the colored noise is studied.
Barbu, Viorel; Bonaccorsi, Stefano; Tubaro, Luciano
2015-01-01
This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with variable structure, that is with jump nonlin- earity. The treatment covers the finite dimensional stochastic systems and the stochastic diffusion equation with multiplicative noise.
Dynamical Monte Carlo method for stochastic epidemic models
Aiello, O E
2002-01-01
A new approach to Dynamical Monte Carlo Methods is introduced to simulate markovian processes. We apply this approach to formulate and study an epidemic Generalized SIRS model. The results are in excellent agreement with the forth order Runge-Kutta method in a region of deterministic solution. Introducing local stochastic interactions, the Runge-Kutta method is not applicable, and we solve and check it self-consistently with a stochastic version of the Euler Method. The results are also analyzed under the herd-immunity concept.
Stochastic and coherent dynamics of single and coupled beta cells
DEFF Research Database (Denmark)
phenomenon, modeled by a slow-fast nonlinear system of ordinary differential equations (ODEs). The single cell oscillations are complex as the dynamical behavior is a result of traversing a series of saddle node and homoclinic bifurcations, controlled by the slow variable. We shall present results...... is the simplest reaction-diffusion partial differential equation....... on the burst period as function of an external applied stochastic term and use a technique for reducing the stochastic differential equations to ODEs for the average and higher order moments. The later method is approximate and we shall discuss the limits of validity. The individual beta cells are coupled...
Particle dynamics in a relativistic invariant stochastic medium
Cabo-Bizet, A; Cabo-Bizet, Alejandro; Oca, Alejandro Cabo Montes de
2005-01-01
The dynamics of particles moving in a medium defined by its relativistically invariant stochastic properties is investigated. For this aim, the force exerted on the particles by the medium is defined by a stationary random variable as a function of the proper time of the particles. The equations of motion for a single one-dimensional particle are obtained and numerically solved. A conservation law for the drift momentum of the particle during its random motion is shown. Moreover, the conservation of the mean value of the total linear momentum for two particles repelling each other according with the Coulomb interaction is also following. Therefore, the results indicate the realization of a kind of stochastic Noether theorem in the system under study. Possible applications to the stochastic representation of Quantum Mechanics are advanced.
Stochastic heart-rate model can reveal pathologic cardiac dynamics
Kuusela, Tom
2004-03-01
A simple one-dimensional Langevin-type stochastic difference equation can simulate the heart-rate fluctuations in a time scale from minutes to hours. The model consists of a deterministic nonlinear part and a stochastic part typical of Gaussian noise, and both parts can be directly determined from measured heart-rate data. Data from healthy subjects typically exhibit the deterministic part with two or more stable fixed points. Studies of 15 congestive heart-failure subjects reveal that the deterministic part of pathologic heart dynamics has no clear stable fixed points. Direct simulations of the stochastic model for normal and pathologic cases can produce statistical parameters similar to those of real subjects. Results directly indicate that pathologic situations simplify the heart-rate control system.
Stochastic Circumplanetary Dynamics of Rotating Non-Spherical Dust Particles
Makuch, Martin; Brilliantov, N. V.; Sremcevic, M.; Spahn, F.; Krivov, A. V.
2006-12-01
Influence of stochastically fluctuating radiation pressure on the dynamics of dust grains on circumplanetary orbits was studied. Stochasticity stems from the permanent change of the particle cross-section due to rotation of nonspherical grains, exposed to the solar radiation. We found that stochasticity depends on the characteristic angular velocity of particles which, according to our estimates, spins very fast on the time scale of the orbital motion. According to this we modelled the stochastic part of the radiation pressure by a Gaussian white noise. Gauss perturbation equations with the radiation pressure being a sum of the deterministic and stochastic component have been used. We observed monotonous increasing standard deviation of the orbital elements, that is, the diffusive-like behaviour of the ensemble, which results in a spatial spreading of initially confined set of particles. By linear approximation we obtained expression for the effective diffusion coefficients and estimate their dependence on the geometrical characteristics of particles and their spin. Teoretical results were compared with numerical simulations performed for the putative dust tori of Mars. Our theory agrees fairly well with simulations for the initial period of the system evolution. The agreement however deteriorates with increasing time where impact of the non-linear terms of the perturbation equations becomes important. Analysis shows that the theoretical results may estimate the low boundary of the time-dependent standard deviation of the orbital elements. In the case of dust ejected from Martian moon Deimos we observed a change of orbital elements up to 10% of their initial values during the first 1000 years of orbital evolution. Our results indicate that the stochastic modulation of the radiation pressure can play an important role in the circumplanetary dynamics of dust and may, together with further noise sources (shadow, planetary bowshock, charge fluctuations, etc
Emergence of stochastic dynamics in plane Couette flow
Gvalani, Rishabh
2016-01-01
Spatially localized states play an important role in transition to turbulence in shear flows (Kawahara, Uhlmann & van Veen, Annu. Rev. Fluid Mech. 44, 203 (2012)). Despite the fact that some of them are attractors on the separatrix between laminar and turbulent flows, little is known of their dynamics. We investigate here the temporal dynamics of such steady spatially localized solutions in the context of plane Couette flow. These solutions exist on oscillating branches in parameter space. We consider the saddle-nodes of these branches as initial conditions of simulations run with offset Reynolds numbers. We observe a relaminarization regime mostly characterized by deterministic dynamics and identify within this regime the existence of parameter intervals in which the results are stochastic and long-lived chaotic transients are observed. These results are obtained below the threshold for transition, shed light on the emergence of stochasticity in transitional plane Couette flow and will likely inform a ra...
The Langevin Limit of the Nosé-Hoover-Langevin Thermostat
Frank, J.E.; Gottwald, G.A.
2011-01-01
In this note we study the asymptotic limit of large variance in a stochastically perturbed thermostat model, the Nos\\'{e}-Hoover-Langevin device. We show that in this limit, the model reduces to a Langevin equation with one-dimensional Wiener process, and that the perturbation is in the direction of
The Langevin limit of the Nosé-Hoover-Langevin thermostat
Frank, J.; Gottwald, G.A.
2011-01-01
In this note we study the asymptotic limit of large variance in a stochastically perturbed thermostat model, the Nosé-Hoover-Langevin device. We show that in this limit, the model reduces to a Langevin equation with one-dimensional Wiener process, and that the perturbation is in the direction of the
Evolution of cooperation on stochastic dynamical networks.
Directory of Open Access Journals (Sweden)
Bin Wu
Full Text Available Cooperative behavior that increases the fitness of others at a cost to oneself can be promoted by natural selection only in the presence of an additional mechanism. One such mechanism is based on population structure, which can lead to clustering of cooperating agents. Recently, the focus has turned to complex dynamical population structures such as social networks, where the nodes represent individuals and links represent social relationships. We investigate how the dynamics of a social network can change the level of cooperation in the network. Individuals either update their strategies by imitating their partners or adjust their social ties. For the dynamics of the network structure, a random link is selected and breaks with a probability determined by the adjacent individuals. Once it is broken, a new one is established. This linking dynamics can be conveniently characterized by a Markov chain in the configuration space of an ever-changing network of interacting agents. Our model can be analytically solved provided the dynamics of links proceeds much faster than the dynamics of strategies. This leads to a simple rule for the evolution of cooperation: The more fragile links between cooperating players and non-cooperating players are (or the more robust links between cooperators are, the more likely cooperation prevails. Our approach may pave the way for analytically investigating coevolution of strategy and structure.
Heat conduction in one-dimensional oscillator lattices using Nose-Hoover chain thermostats
Energy Technology Data Exchange (ETDEWEB)
Romero-Bastida, M; Aguilar, J F [Centro de Investigacion en PolImeros, Marcos Achar Lobaton No. 2, Tepexpan, 55885 Acolman, Estado de Mexico (Mexico)
2006-09-08
In this work, we numerically study the dynamical evolution and heat transport properties of a system that consists of two time-reversible thermostats connected either by a one-dimensional Fermi-Pasta-Ulam or a Frenkel-Kontorova oscillator lattice, which are representative models of momentum-conserving and nonconserving systems, respectively. The thermostats were described by a chain of variables, Nose-Hoover chains, which enhances the ergodicity of the thermostats in comparison to the Nose-Hoover method. The time evolution of both lattices is not significantly altered by the dynamics of the thermostats. The temperature profile and heat flux of the Fermi-Pasta-Ulam model are more sensitive to the dynamics of the extended variables than those corresponding to the Frenkel-Kontorova model. Nevertheless we reproduce the scaling properties of the thermal conductivity with system size obtained by other authors.
Dynamic option pricing with endogenous stochastic arbitrage
Contreras, Mauricio; Montalva, Rodrigo; Pellicer, Rely; Villena, Marcelo
2010-09-01
Only few efforts have been made in order to relax one of the key assumptions of the Black-Scholes model: the no-arbitrage assumption. This is despite the fact that arbitrage processes usually exist in the real world, even though they tend to be short-lived. The purpose of this paper is to develop an option pricing model with endogenous stochastic arbitrage, capable of modelling in a general fashion any future and underlying asset that deviate itself from its market equilibrium. Thus, this investigation calibrates empirically the arbitrage on the futures on the S&P 500 index using transaction data from September 1997 to June 2009, from here a specific type of arbitrage called “arbitrage bubble”, based on a t-step function, is identified and hence used in our model. The theoretical results obtained for Binary and European call options, for this kind of arbitrage, show that an investment strategy that takes advantage of the identified arbitrage possibility can be defined, whenever it is possible to anticipate in relative terms the amplitude and timespan of the process. Finally, the new trajectory of the stock price is analytically estimated for a specific case of arbitrage and some numerical illustrations are developed. We find that the consequences of a finite and small endogenous arbitrage not only change the trajectory of the asset price during the period when it started, but also after the arbitrage bubble has already gone. In this context, our model will allow us to calibrate the B-S model to that new trajectory even when the arbitrage already started.
A data driven nonlinear stochastic model for blood glucose dynamics.
Zhang, Yan; Holt, Tim A; Khovanova, Natalia
2016-03-01
The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles.
An example of the stochastic dynamics of a causal set
Krugly, Alexey L
2011-01-01
An example of a discrete pregeometry on a microscopic scale is introduced. The model is a directed dyadic acyclic graph. This is the particular case of a causal set. The particles in this model must be self-organized repetitive structures. The dynamics of this model is a stochastic sequential growth dynamics. New vertexes are added one by one. The probability of this addition depends on the structure of existed graph. The particular case of the dynamics is considered. The numerical simulation provides some symptoms of self-organization.
Balibrea-Iniesta, Francisco; Lopesino, Carlos; Wiggins, Stephen; Mancho, Ana M.
2016-12-01
In this paper, we introduce a new technique for depicting the phase portrait of stochastic differential equations. Following previous work for deterministic systems, we represent the phase space by means of a generalization of the method of Lagrangian descriptors to stochastic differential equations. Analogously to the deterministic differential equations setting, the Lagrangian descriptors graphically provide the distinguished trajectories and hyperbolic structures arising within the stochastic dynamics, such as random fixed points and their stable and unstable manifolds. We analyze the sense in which structures form barriers to transport in stochastic systems. We apply the method to several benchmark examples where the deterministic phase space structures are well-understood. In particular, we apply our method to the noisy saddle, the stochastically forced Duffing equation, and the stochastic double gyre model that is a benchmark for analyzing fluid transport.
Stochastic population dynamic models as probability networks
M.E. and D.C. Lee. Borsuk
2009-01-01
The dynamics of a population and its response to environmental change depend on the balance of birth, death and age-at-maturity, and there have been many attempts to mathematically model populations based on these characteristics. Historically, most of these models were deterministic, meaning that the results were strictly determined by the equations of the model and...
Solution Methods for Stochastic Dynamic Linear Programs.
1980-12-01
Linear Programming, IIASA , Laxenburg, Austria, June 2-6, 1980. [2] Aghili, P., R.H., Cramer and H.W. Thompson, "On the applicability of two- stage...Laxenburg, Austria, May, 1978. [52] Propoi, A. and V. Krivonozhko, ’The simplex method for dynamic linear programs", RR-78-14, IIASA , Vienna, Austria
Dynamic two state stochastic models for ecological regime shifts
DEFF Research Database (Denmark)
Møller, Jan Kloppenborg; Carstensen, Niels Jacob; Madsen, Henrik
2009-01-01
A simple non-linear stochastic two state, discrete-time model is presented. The interaction between benthic and pelagic vegetation in aquatic ecosystems subject to changing external nutrient loading is described by the nonlinear functions. The dynamical behavior of the deterministic part...... of regimes, depending on how the noise propagates through the system. The dynamical properties of a system should therefore be described through propagation of the state distributions rather than the state means and consequently, stochastic models should be compared in a probabilistic framework....... of the model illustrates that hysteresis effect and regime shifts can be obtained for a limited range of parameter values only. The effect of multiplicative noise components entering at different levels of the model is presented and discussed. Including noise leads to very different results on the stability...
Stochastic dynamics of active swimmers in linear flows
Sandoval, Mario; Subramanian, Ganesh; Lauga, Eric
2014-01-01
Most classical work on the hydrodynamics of low-Reynolds-number swimming addresses deterministic locomotion in quiescent environments. Thermal fluctuations in fluids are known to lead to a Brownian loss of the swimming direction. As most cells or synthetic swimmers are immersed in external flows, we consider theoretically in this paper the stochastic dynamics of a model active particle (a self-propelled sphere) in a steady general linear flow. The stochasticity arises both from translational diffusion in physical space, and from a combination of rotary diffusion and run-and-tumble dynamics in orientation space. We begin by deriving a general formulation for all components of the long-time mean square displacement tensor for a swimmer with a time-dependent swimming velocity and whose orientation decorrelates due to rotary diffusion alone. This general framework is applied to obtain the convectively enhanced mean-squared displacements of a steadily-swimming particle in three canonical linear flows (extension, s...
RESIDENTIAL THERMOSTATS: COMFORT CONTROLS IN CALIFORNIA HOMES
Energy Technology Data Exchange (ETDEWEB)
Meier, Alan K.; Walker, Iain
2008-03-02
This report summarizes results of a literature review, a workshop, and many meetings with demand response and thermostat researchers and implementers. The information obtained from these resources was used to identify key issues of thermostat performance from both energy savings and peak demand perspectives. A research plan was developed to address these issues and activities have already begun to pursue the research agenda.
Stochastic effects on biodiversity in cyclic coevolutionary dynamics
Reichenbach, Tobias; Frey, Erwin
2008-01-01
Finite-size fluctuations arising in the dynamics of competing populations may have dramatic influence on their fate. As an example, in this article, we investigate a model of three species which dominate each other in a cyclic manner. Although the deterministic approach predicts (neutrally) stable coexistence of all species, for any finite population size, the intrinsic stochasticity unavoidably causes the eventual extinction of two of them.
Optimal control of stochastic magnetization dynamics by spin current
Wang, Yong; Zhang, Fu-Chun
2013-05-01
Fluctuation-induced stochastic magnetization dynamics plays an important role in spintronics devices. Here we propose that it can be optimally controlled by spin currents to minimize or maximize the Freidlin-Wentzell action functional of the system hence to increase or decrease the probability of the large fluctuations. We apply this method to study the thermally activated magnetization switching problem and to demonstrate the merits of the optimal control strategy.
AN INVARIANCE PRINCIPLE IN LARGE POPULATION STOCHASTIC DYNAMIC GAMES
Institute of Scientific and Technical Information of China (English)
Minyi HUANG; Peter E. CAINES; Roland P. MALHAM(E)
2007-01-01
We study large population stochastic dynamic games where the so-called Nash certainty equivalence based control laws are implemented by the individual players. We first show a martingale property for the limiting control problem of a single agent and then perform averaging across the population; this procedure leads to a constant value for the martingale which shows an invariance property of the population behavior induced by the Nash strategies.
Dynamical entropy for systems with stochastic perturbation
Ostruszka; Pakonski; Slomczynski; Zyczkowski
2000-08-01
Dynamics of deterministic systems perturbed by random additive noise is characterized quantitatively. Since for such systems the Kolmogorov-Sinai (KS) entropy diverges if the diameter of the partition tends to zero, we analyze the difference between the total entropy of a noisy system and the entropy of the noise itself. We show that this quantity is finite and non-negative and we call it the dynamical entropy of the noisy system. In the weak noise limit this quantity is conjectured to tend to the KS entropy of the deterministic system. In particular, we consider one-dimensional systems with noise described by a finite-dimensional kernel for which the Frobenius-Perron operator can be represented by a finite matrix.
Dynamical entropy for systems with stochastic perturbation
Ostruszka, A; Slomczynski, W; Zyczkowski, K; Ostruszka, Andrzej; Pakonski, Prot; Slomczynski, Wojciech; Zyczkowski, Karol
1999-01-01
Dynamics of deterministic systems perturbed by random additive noise is characterized quantitatively. Since for such systems the KS-entropy diverges we analyse the difference between the total entropy of a noisy system and the entropy of the noise itself. We show that this quantity is non negative and in the weak noise limit is conjectured to tend to the KS-entropy of the deterministic system. In particular, we consider one-dimensional systems with noise described by a finite-dimensional kernel, for which the Frobenius-Perron operator can be represented by a finite matrix.
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.
The stochastic network dynamics underlying perceptual discrimination
Directory of Open Access Journals (Sweden)
Genis Prat-Ortega
2015-04-01
Full Text Available The brain is able to interpret streams of high-dimensional ambiguous information and yield coherent percepts. The mechanisms governing sensory integration have been extensively characterized using time-varying visual stimuli (Britten et al. 1996; Roitman and Shadlen 2002, but some of the basic principles regarding the network dynamics underlying this process remain largely unknown. We captured the basic features of a neural integrator using three canonical one-dimensional models: (1 the Drift Diffusion Model (DDM, (2 the Perfect Integrator (PI which is a particular case of the DDM where the bounds are set to infinity and (3 the double-well potential (DW which captures the dynamics of the attractor networks (Wang 2002; Roxin and Ledberg 2008. Although these models has been widely studied (Bogacz et al. 2006; Roxin and Ledberg 2008; Gold and Shadlen 2002, it has been difficult to experimentally discriminate among them because most of the observables measured are only quantitatively different among these models (e.g. psychometric curves. Here we aim to find experimentally measurable quantities that can yield qualitatively different behaviors depending on the nature of the underlying network dynamics. We examined the categorization dynamics of these models in response to fluctuating stimuli of different duration (T. On each time step, stimuli are drawn from a Gaussian distribution N(μ, σ and the two stimulus categories are defined by μ > 0 and μ < 0. Psychometric curves can therefore be obtained by quantifying the probability of the integrator to yield one category versus μ . We find however that varying σ can reveal more clearly the differences among the different integrators. In the small σ regime, both the DW and the DDM perform transient integration and exhibit a decaying stimulus reverse correlation kernel revealing a primacy effect (Nienborg and Cumming 2009; Wimmer et al. 2015 . In the large σ regime, the integration in the DDM
Indirect Identification of Linear Stochastic Systems with Known Feedback Dynamics
Huang, Jen-Kuang; Hsiao, Min-Hung; Cox, David E.
1996-01-01
An algorithm is presented for identifying a state-space model of linear stochastic systems operating under known feedback controller. In this algorithm, only the reference input and output of closed-loop data are required. No feedback signal needs to be recorded. The overall closed-loop system dynamics is first identified. Then a recursive formulation is derived to compute the open-loop plant dynamics from the identified closed-loop system dynamics and known feedback controller dynamics. The controller can be a dynamic or constant-gain full-state feedback controller. Numerical simulations and test data of a highly unstable large-gap magnetic suspension system are presented to demonstrate the feasibility of this indirect identification method.
Quantum mechanics emerging from stochastic dynamics of virtual particles
Tsekov, R
2015-01-01
It is demonstrated how quantum mechanics emerges from the stochastic dynamics of force-carriers. It is shown that the quantum Moyal equation corresponds to some dynamic correlations between the momentum of a real particle and the position of a virtual particle, which are not present in classical mechanics. The new concept throws light on the physical meaning of quantum theory, showing that the Planck constant square is a second-second cross-cumulant. The novel approach to quantum systems is extended to the relativistic case and an expression is derived for the relativistic mass in the Wigner quantum phase-space.
Particle dynamics in a relativistic invariant stochastic medium
Energy Technology Data Exchange (ETDEWEB)
Cabo-Bizet, Alejandro [Facultad de Fisica, Universidad de La Habana, Colina Universitaria, Havana (Cuba); Cabo Montes de Oca, Alejandro [Grupo de Fisica Teorica, Instituto de Cibernetica, Matematica y Fisica, Havana (Cuba) and Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, Miramare, Trieste (Italy)]. E-mail: cabo@fis.puc.cl
2006-11-27
The dynamics of particles moving in a medium defined by its relativistically invariant stochastic properties is investigated. For this aim, the force exerted on the particles by the medium is defined by a stationary random variable as a function of the proper time of the particles. The equations of motion for a single one-dimensional particle are obtained and numerically solved. A conservation law for the drift momentum of the particle during its random motion is shown. Moreover, the conservation of the mean value of the total linear momentum for two particles repelling each other according to the Coulomb interaction also follows. Therefore, the results indicate the realization of a kind of stochastic Noether theorem in the system under study.
Condition-dependent mate choice: A stochastic dynamic programming approach.
Frame, Alicia M; Mills, Alex F
2014-09-01
We study how changing female condition during the mating season and condition-dependent search costs impact female mate choice, and what strategies a female could employ in choosing mates to maximize her own fitness. We address this problem via a stochastic dynamic programming model of mate choice. In the model, a female encounters males sequentially and must choose whether to mate or continue searching. As the female searches, her own condition changes stochastically, and she incurs condition-dependent search costs. The female attempts to maximize the quality of the offspring, which is a function of the female's condition at mating and the quality of the male with whom she mates. The mating strategy that maximizes the female's net expected reward is a quality threshold. We compare the optimal policy with other well-known mate choice strategies, and we use simulations to examine how well the optimal policy fares under imperfect information.
Stochastic Dynamics of Infrared Fluctuations in Accelerating Universe
Cho, Gihyuk; Kitamoto, Hiroyuki
2015-01-01
We extend investigations of infrared dynamics in accelerating universes. In the presence of massless and minimally coupled scalar fields, physical quantities may acquire growing time dependences through quantum fluctuations at super-horizon scales. From a semiclassical viewpoint, it was proposed that such infrared effects are described by a Langevin equation. In de Sitter space, the stochastic approach has been proved to be equivalent to resummation of the growing time dependences at the leading power. In this paper, we make the resummation derivation of the Langevin equation in a general accelerating universe. We first consider an accelerating universe whose slow-roll parameter is constant, and then extend the background as the slow-roll parameter becomes time dependent. The resulting Langevin equation contains a white noise term and the coefficient of each term is modified by the slow-roll parameter. Furthermore we find that the semiclassical description of the scalar fields leads to the same stochastic equ...
The stochastic resonance mechanism in the Aerosol Index dynamics
De Martino, S; Mona, L
2002-01-01
We consider Aerosol Index (AI) time-series extracted from TOMS archive for an area covering Italy $(7-18^o E ; 36-47^o N)$. The missing of convergence in estimating the embedding dimension of the system and the inability of the Independent Component Analysis (ICA) in separating the fluctuations from deterministic component of the signals are evidences of an intrinsic link between the periodic behavior of AI and its fluctuations. We prove that these time series are well described by a stochastic dynamical model. Moreover, the principal peak in the power spectrum of these signals can be explained whereby a stochastic resonance, linking variable external factors, such as Sun-Earth radiation budget and local insolation, and fluctuations on smaller spatial and temporal scale due to internal weather and antrophic components.
Can Strange Nonchaotic Dynamics be induced through Stochastic Driving?
Prasad, A K; Prasad, Awadhesh; Ramaswamy, Ramakrishna
1999-01-01
Upon addition of noise, chaotic motion in low-dimensional dynamical systems can sometimes be transformed into nonchaotic dynamics: namely, the largest Lyapunov exponent can be made nonpositive. We study this phenomenon in model systems with a view to understanding the circumstances when such behaviour is possible. This technique for inducing ``order'' through stochastic driving works by modifying the invariant measure on the attractor: by appropriately increasing measure on those portions of the attractor where the dynamics is contracting, the overall dynamics can be made nonchaotic, however {\\it not} a strange nonchaotic attractor. Alternately, by decreasing measure on contracting regions, the largest Lyapunov exponent can be enhanced. A number of different chaos control and anticontrol techniques are known to function on this paradigm.
Large Scale Demand Response of Thermostatic Loads
DEFF Research Database (Denmark)
Totu, Luminita Cristiana
This study is concerned with large populations of residential thermostatic loads (e.g. refrigerators, air conditioning or heat pumps). The purpose is to gain control over the aggregate power consumption in order to provide balancing services for the electrical grid. Without affecting...... the temperature limits and other operational constraints, and by using only limited communication, it is possible to make use of the individual thermostat deadband flexibility to step-up or step-down the power consumption of the population as if it were a power plant. The individual thermostatic loads experience...
Dynamic Stochastic Superresolution of sparsely observed turbulent systems
Energy Technology Data Exchange (ETDEWEB)
Branicki, M., E-mail: branicki@cims.nyu.edu [Department of Mathematics and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University (United States); Majda, A.J. [Department of Mathematics and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University (United States)
2013-05-15
Real-time capture of the relevant features of the unresolved turbulent dynamics of complex natural systems from sparse noisy observations and imperfect models is a notoriously difficult problem. The resulting lack of observational resolution and statistical accuracy in estimating the important turbulent processes, which intermittently send significant energy to the large-scale fluctuations, hinders efficient parameterization and real-time prediction using discretized PDE models. This issue is particularly subtle and important when dealing with turbulent geophysical systems with an vast range of interacting spatio-temporal scales and rough energy spectra near the mesh scale of numerical models. Here, we introduce and study a suite of general Dynamic Stochastic Superresolution (DSS) algorithms and show that, by appropriately filtering sparse regular observations with the help of cheap stochastic exactly solvable models, one can derive stochastically ‘superresolved’ velocity fields and gain insight into the important characteristics of the unresolved dynamics, including the detection of the so-called black swans. The DSS algorithms operate in Fourier domain and exploit the fact that the coarse observation network aliases high-wavenumber information into the resolved waveband. It is shown that these cheap algorithms are robust and have significant skill on a test bed of turbulent solutions from realistic nonlinear turbulent spatially extended systems in the presence of a significant model error. In particular, the DSS algorithms are capable of successfully capturing time-localized extreme events in the unresolved modes, and they provide good and robust skill for recovery of the unresolved processes in terms of pattern correlation. Moreover, we show that DSS improves the skill for recovering the primary modes associated with the sparse observation mesh which is equally important in applications. The skill of the various DSS algorithms depends on the energy spectrum
Directory of Open Access Journals (Sweden)
Wenjie Bi
2014-01-01
Full Text Available Dynamic portfolio choice is an important problem in finance, but the optimal strategy analysis is difficult when considering multiple stochastic volatility variables such as the stock price, interest rate, and income. Besides, recent research in experimental economics indicates that the agent shows limited attention, considering only the variables with high fluctuations but ignoring those with small ones. By extending the sparse max method, we propose an approach to solve dynamic programming problem with small stochastic volatility and the agent’s bounded rationality. This approach considers the agent’s behavioral factors and avoids effectively the “Curse of Dimensionality” in a dynamic programming problem with more than a few state variables. We then apply it to Merton dynamic portfolio choice model with stochastic volatility and get a tractable solution. Finally, the numerical analysis shows that the bounded rational agent may pay no attention to the varying equity premium and interest rate with small variance.
Study of the nonlinear longitudinal dynamics of a stochastic system
Directory of Open Access Journals (Sweden)
Cunha Americo
2014-01-01
Full Text Available This paper deals with the theoretical study of how discrete elements attached to a continuous stochastic systems can affect their dynamical behavior. For this, it is studied the nonlinear longitudinal dynamics of an elastic bar, attached to springs and a lumped mass, with a random elastic modulus and subjected to a Gaussian white-noise distributed external force. Numerical simulations are conducted and their results are analyzed in function of the ratio between the masses of the discrete and the continuous parts of the system. This analysis reveals that the dynamic behavior of the bar is significantly altered when the lumped mass is varied, being more inﬂuenced by the randomness for small values of the lumped mass.
A stochastic evolutionary model for capturing human dynamics
Fenner, Trevor; Loizou, George
2015-01-01
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in various contexts. Here we propose a generative model to capture the dynamics of survival analysis, traditionally employed in clinical trials and reliability analysis in engineering. We derive a general solution for the model in the form of a product, and then a continuous approximation to the solution via the renewal equation describing age-structured population dynamics. This enables us to model a wide rage of survival distributions, according to the choice of the mortality distribution. We provide empirical evidence for the validity of the model from a longitudinal data set of popular search engine queries over 114 months, showing that the survival function of these queries is closely matched by the solution for our model with power-law mortality.
A stochastic boundary forcing for dissipative particle dynamics
Altenhoff, Adrian M.; Walther, Jens H.; Koumoutsakos, Petros
2007-07-01
The method of dissipative particle dynamics (DPD) is an effective, coarse grained model of the hydrodynamics of complex fluids. DPD simulations of wall-bounded flows are however often associated with spurious fluctuations of the fluid properties near the wall. We present a novel stochastic boundary forcing for DPD simulations of wall-bounded flows, based on the identification of fluctuations in simulations of the corresponding homogeneous system at equilibrium. The present method is shown to enforce accurately the no-slip boundary condition, while minimizing spurious fluctuations of material properties, in a number of benchmark problems.
Diffusive dynamics and stochastic models of turbulent axisymmetric wakes
Rigas, G; Brackston, R D; Morrison, J F
2015-01-01
A modelling methodology to reproduce the experimental measurements of a turbulent flow under the presence of symmetry is presented. The flow is a three-dimensional wake generated by an axisymmetric body. We show that the dynamics of the turbulent wake- flow can be assimilated by a nonlinear two-dimensional Langevin equation, the deterministic part of which accounts for the broken symmetries which occur at the laminar and transitional regimes at low Reynolds numbers and the stochastic part of which accounts for the turbulent fluctuations. Comparison between theoretical and experimental results allows the extraction of the model parameters.
Dynamical behavior of a stochastic SVIR epidemic model with vaccination
Zhang, Xinhong; Jiang, Daqing; Hayat, Tasawar; Ahmad, Bashir
2017-10-01
In this paper, we investigate the dynamical behavior of SVIR models in random environments. Firstly, we show that if R0s model will die out exponentially; if R˜0s > 1, the disease will be prevail. Moreover, this system admits a unique stationary distribution and it is ergodic when R˜0s > 1. Results show that environmental white noise is helpful for disease control. Secondly, we give sufficient conditions for the existence of nontrivial periodic solutions to stochastic SVIR model with periodic parameters. Finally, numerical simulations validate the analytical results.
Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics
Institute of Scientific and Technical Information of China (English)
ZHANG Yu-Feng; P.Ao
2008-01-01
The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology. The statistical mechanics and thermodynamics, while enormous successful in physics, have been in an awkward situation of wanting a consistent dynamical understanding. Here we present from a formal point of view an exploration of the connection between thermodynamics and Darwinian dynamics and a few related topics. We first show that the stochasticity in Darwinian dynamics implies the existence temperature, hence the canonical distribution of Boltzmann-Gibbs type. In term of relative entropy the Second Law of thermodynamics is dynamically demonstrated without detailed balance condition, and is valid regardless of size of the system. In particular, the dynamical component responsible for breaking detailed ba/ance condition does not contribute to the change of the relative entropy. Two types of stochastic dynamical equalities of current interest are explicitly discussed in the present approach: One is based on Feynman-Kac formula and another is a generalization of Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that Darwinian dynamics represents logically a simple and straightforward starting point for statistical mechanics and thermodynamics and is complementary to and consistent with conservative dynamics that dominates the physical sciences. Present exploration suggests the existence of a unified stochastic dynamical framework both near and far from equilibrium.
Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics.
Ao, P
2008-05-15
The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology. The statistical mechanics and thermodynamics, while enormous successful in physics, have been in an awkward situation of wanting a consistent dynamical understanding. Here we present from a formal point of view an exploration of the connection between thermodynamics and Darwinian dynamics and a few related topics. We first show that the stochasticity in Darwinian dynamics implies the existence temperature, hence the canonical distribution of Boltzmann-Gibbs type. In term of relative entropy the Second Law of thermodynamics is dynamically demonstrated without detailed balance condition, and is valid regardless of size of the system. In particular, the dynamical component responsible for breaking detailed balance condition does not contribute to the change of the relative entropy. Two types of stochastic dynamical equalities of current interest are explicitly discussed in the present approach: One is based on Feynman-Kac formula and another is a generalization of Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that Darwinian dynamics represents logically a simple and straightforward starting point for statistical mechanics and thermodynamics and is complementary to and consistent with conservative dynamics that dominates the physical sciences. Present exploration suggests the existence of a unified stochastic dynamical framework both near and far from equilibrium.
Dynamic stochastic optimization models for air traffic flow management
Mukherjee, Avijit
This dissertation presents dynamic stochastic optimization models for Air Traffic Flow Management (ATFM) that enables decisions to adapt to new information on evolving capacities of National Airspace System (NAS) resources. Uncertainty is represented by a set of capacity scenarios, each depicting a particular time-varying capacity profile of NAS resources. We use the concept of a scenario tree in which multiple scenarios are possible initially. Scenarios are eliminated as possibilities in a succession of branching points, until the specific scenario that will be realized on a particular day is known. Thus the scenario tree branching provides updated information on evolving scenarios, and allows ATFM decisions to be re-addressed and revised. First, we propose a dynamic stochastic model for a single airport ground holding problem (SAGHP) that can be used for planning Ground Delay Programs (GDPs) when there is uncertainty about future airport arrival capacities. Ground delays of non-departed flights can be revised based on updated information from scenario tree branching. The problem is formulated so that a wide range of objective functions, including non-linear delay cost functions and functions that reflect equity concerns can be optimized. Furthermore, the model improves on existing practice by ensuring efficient use of available capacity without necessarily exempting long-haul flights. Following this, we present a methodology and optimization models that can be used for decentralized decision making by individual airlines in the GDP planning process, using the solutions from the stochastic dynamic SAGHP. Airlines are allowed to perform cancellations, and re-allocate slots to remaining flights by substitutions. We also present an optimization model that can be used by the FAA, after the airlines perform cancellation and substitutions, to re-utilize vacant arrival slots that are created due to cancellations. Finally, we present three stochastic integer programming
Thermostatted kinetic equations as models for complex systems in physics and life sciences.
Bianca, Carlo
2012-12-01
Statistical mechanics is a powerful method for understanding equilibrium thermodynamics. An equivalent theoretical framework for nonequilibrium systems has remained elusive. The thermodynamic forces driving the system away from equilibrium introduce energy that must be dissipated if nonequilibrium steady states are to be obtained. Historically, further terms were introduced, collectively called a thermostat, whose original application was to generate constant-temperature equilibrium ensembles. This review surveys kinetic models coupled with time-reversible deterministic thermostats for the modeling of large systems composed both by inert matter particles and living entities. The introduction of deterministic thermostats allows to model the onset of nonequilibrium stationary states that are typical of most real-world complex systems. The first part of the paper is focused on a general presentation of the main physical and mathematical definitions and tools: nonequilibrium phenomena, Gauss least constraint principle and Gaussian thermostats. The second part provides a review of a variety of thermostatted mathematical models in physics and life sciences, including Kac, Boltzmann, Jager-Segel and the thermostatted (continuous and discrete) kinetic for active particles models. Applications refer to semiconductor devices, nanosciences, biological phenomena, vehicular traffic, social and economics systems, crowds and swarms dynamics.
Stochastic cellular automata model for stock market dynamics
Bartolozzi, M.; Thomas, A. W.
2004-04-01
In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two-dimensional grid. Active traders are characterized by the decision to buy, σi (t)=+1 , or sell, σi (t)=-1 , a stock at a certain discrete time step. The remaining cells are inactive, σi (t)=0 . The trading dynamics is then determined by the stochastic interaction between traders belonging to the same cluster. Extreme, intermittent events, such as crashes or bubbles, are triggered by a phase transition in the state of the bigger clusters present on the grid, where almost all the active traders come to share the same spin orientation. Most of the stylized aspects of the financial market time series, including multifractal proprieties, are reproduced by the model. A direct comparison is made with the daily closures of the S&P500 index.
A Stochastic-Dynamic Model for Real Time Flood Forecasting
Chow, K. C. A.; Watt, W. E.; Watts, D. G.
1983-06-01
A stochastic-dynamic model for real time flood forecasting was developed using Box-Jenkins modelling techniques. The purpose of the forecasting system is to forecast flood levels of the Saint John River at Fredericton, New Brunswick. The model consists of two submodels: an upstream model used to forecast the headpond level at the Mactaquac Dam and a downstream model to forecast the water level at Fredericton. Inputs to the system are recorded values of the water level at East Florenceville, the headpond level and gate position at Mactaquac, and the water level at Fredericton. The model was calibrated for the spring floods of 1973, 1974, 1977, and 1978, and its usefulness was verified for the 1979 flood. The forecasting results indicated that the stochastic-dynamic model produces reasonably accurate forecasts for lead times up to two days. These forecasts were then compared to those from the existing forecasting system and were found to be as reliable as those from the existing system.
Stochastic Simulation of Biomolecular Networks in Dynamic Environments.
Directory of Open Access Journals (Sweden)
Margaritis Voliotis
2016-06-01
Full Text Available Simulation of biomolecular networks is now indispensable for studying biological systems, from small reaction networks to large ensembles of cells. Here we present a novel approach for stochastic simulation of networks embedded in the dynamic environment of the cell and its surroundings. We thus sample trajectories of the stochastic process described by the chemical master equation with time-varying propensities. A comparative analysis shows that existing approaches can either fail dramatically, or else can impose impractical computational burdens due to numerical integration of reaction propensities, especially when cell ensembles are studied. Here we introduce the Extrande method which, given a simulated time course of dynamic network inputs, provides a conditionally exact and several orders-of-magnitude faster simulation solution. The new approach makes it feasible to demonstrate-using decision-making by a large population of quorum sensing bacteria-that robustness to fluctuations from upstream signaling places strong constraints on the design of networks determining cell fate. Our approach has the potential to significantly advance both understanding of molecular systems biology and design of synthetic circuits.
Evaluation of Electric Power Procurement Strategies by Stochastic Dynamic Programming
Saisho, Yuichi; Hayashi, Taketo; Fujii, Yasumasa; Yamaji, Kenji
In deregulated electricity markets, the role of a distribution company is to purchase electricity from the wholesale electricity market at randomly fluctuating prices and to provide it to its customers at a given fixed price. Therefore the company has to take risk stemming from the uncertainties of electricity prices and/or demand fluctuation instead of the customers. The way to avoid the risk is to make a bilateral contact with generating companies or install its own power generation facility. This entails the necessity to develop a certain method to make an optimal strategy for electric power procurement. In such a circumstance, this research has the purpose for proposing a mathematical method based on stochastic dynamic programming and additionally considering the characteristics of the start-up cost of electric power generation facility to evaluate strategies of combination of the bilateral contract and power auto-generation with its own facility for procuring electric power in deregulated electricity market. In the beginning we proposed two approaches to solve the stochastic dynamic programming, and they are a Monte Carlo simulation method and a finite difference method to derive the solution of a partial differential equation of the total procurement cost of electric power. Finally we discussed the influences of the price uncertainty on optimal strategies of power procurement.
Outbreak and Extinction Dynamics in a Stochastic Ebola Model
Nieddu, Garrett; Bianco, Simone; Billings, Lora; Forgoston, Eric; Kaufman, James
A zoonotic disease is a disease that can be passed between animals and humans. In many cases zoonotic diseases can persist in the animal population even if there are no infections in the human population. In this case we call the infected animal population the reservoir for the disease. Ebola virus disease (EVD) and SARS are both notable examples of such diseases. There is little work devoted to understanding stochastic disease extinction and reintroduction in the presence of a reservoir. Here we build a stochastic model for EVD and explicitly consider the presence of an animal reservoir. Using a master equation approach and a WKB ansatz, we determine the associated Hamiltonian of the system. Hamilton's equations are then used to numerically compute the 12-dimensional optimal path to extinction, which is then used to estimate mean extinction times. We also numerically investigate the behavior of the model for dynamic population size. Our results provide an improved understanding of outbreak and extinction dynamics in diseases like EVD.
Abramov, Rafail V.
2017-03-01
The classical fluctuation-dissipation theorem predicts the average response of a dynamical system to an external deterministic perturbation via time-lagged statistical correlation functions of the corresponding unperturbed system. In this work we develop a fluctuation-response theory and test a computational framework for the leading order response of statistical averages of a deterministic or stochastic dynamical system to an external stochastic perturbation. In the case of a stochastic unperturbed dynamical system, we compute the leading order fluctuation-response formulas for two different cases: when the existing stochastic term is perturbed, and when a new, statistically independent, stochastic perturbation is introduced. We numerically investigate the effectiveness of the new response formulas for an appropriately rescaled Lorenz 96 system, in both the deterministic and stochastic unperturbed dynamical regimes.
Assessing predictability of a hydrological stochastic-dynamical system
Gelfan, Alexander
2014-05-01
The water cycle includes the processes with different memory that creates potential for predictability of hydrological system based on separating its long and short memory components and conditioning long-term prediction on slower evolving components (similar to approaches in climate prediction). In the face of the Panta Rhei IAHS Decade questions, it is important to find a conceptual approach to classify hydrological system components with respect to their predictability, define predictable/unpredictable patterns, extend lead-time and improve reliability of hydrological predictions based on the predictable patterns. Representation of hydrological systems as the dynamical systems subjected to the effect of noise (stochastic-dynamical systems) provides possible tool for such conceptualization. A method has been proposed for assessing predictability of hydrological system caused by its sensitivity to both initial and boundary conditions. The predictability is defined through a procedure of convergence of pre-assigned probabilistic measure (e.g. variance) of the system state to stable value. The time interval of the convergence, that is the time interval during which the system losses memory about its initial state, defines limit of the system predictability. The proposed method was applied to assess predictability of soil moisture dynamics in the Nizhnedevitskaya experimental station (51.516N; 38.383E) located in the agricultural zone of the central European Russia. A stochastic-dynamical model combining a deterministic one-dimensional model of hydrothermal regime of soil with a stochastic model of meteorological inputs was developed. The deterministic model describes processes of coupled heat and moisture transfer through unfrozen/frozen soil and accounts for the influence of phase changes on water flow. The stochastic model produces time series of daily meteorological variables (precipitation, air temperature and humidity), whose statistical properties are similar
Thermodynamics and stochastic dynamics of transport in confined media
Energy Technology Data Exchange (ETDEWEB)
Rubi, J.M. [Departament de Fisica Fonamental, Universitat de Barcelona, C/Marti i Franques 1, 08028 Barcelona (Spain); Reguera, D., E-mail: dreguera@ub.edu [Departament de Fisica Fonamental, Universitat de Barcelona, C/Marti i Franques 1, 08028 Barcelona (Spain)
2010-10-05
We show how a probabilistic interpretation of non-equilibrium thermodynamics, based on the assumption of local equilibrium at the mesoscale, can be used to analyze the stochastic dynamics of entropy driven diffusion processes characterized by the presence of entropic barriers. This approach sets up a systematic method to study the effect of confinement on the transport properties, providing a derivation of a generalized Fick-Jacobs equation for the constrained dynamics of the mesoscopic degrees of freedom. It is shown that confinement originates an entropic bias which gives rise to a geometric rectification of non-equilibrium fluctuations and that entropic effects in transport can be controlled by means of the application of an external force.
Stochastic kinetic models: Dynamic independence, modularity and graphs
Bowsher, Clive G
2010-01-01
The dynamic properties and independence structure of stochastic kinetic models (SKMs) are analyzed. An SKM is a highly multivariate jump process used to model chemical reaction networks, particularly those in biochemical and cellular systems. We identify SKM subprocesses with the corresponding counting processes and propose a directed, cyclic graph (the kinetic independence graph or KIG) that encodes the local independence structure of their conditional intensities. Given a partition $[A,D,B]$ of the vertices, the graphical separation $A\\perp B|D$ in the undirected KIG has an intuitive chemical interpretation and implies that $A$ is locally independent of $B$ given $A\\cup D$. It is proved that this separation also results in global independence of the internal histories of $A$ and $B$ conditional on a history of the jumps in $D$ which, under conditions we derive, corresponds to the internal history of $D$. The results enable mathematical definition of a modularization of an SKM using its implied dynamics. Gra...
Dynamics of stochastic nonclassical diffusion equations on unbounded domains
Directory of Open Access Journals (Sweden)
Wenqiang Zhao
2015-11-01
Full Text Available This article concerns the dynamics of stochastic nonclassical diffusion equation on $\\mathbb{R}^N$ perturbed by a $\\epsilon$-random term, where $\\epsilon\\in(0,1]$ is the intension of noise. By using an energy approach, we prove the asymptotic compactness of the associated random dynamical system, and then the existence of random attractors in $H^1(\\mathbb{R}^N$. Finally, we show the upper semi-continuity of random attractors at $\\epsilon=0$ in the sense of Hausdorff semi-metric in $H^1(\\mathbb{R}^N$, which implies that the obtained family of random attractors indexed by $\\epsilon$ converge to a deterministic attractor as $\\epsilon$ vanishes.
Interactive macroeconomics stochastic aggregate dynamics with heterogeneous and interacting agents
Di Guilmi, Corrado
2017-01-01
One of the major problems of macroeconomic theory is the way in which the people exchange goods in decentralized market economies. There are major disagreements among macroeconomists regarding tools to influence required outcomes. Since the mainstream efficient market theory fails to provide an internal coherent framework, there is a need for an alternative theory. The book provides an innovative approach for the analysis of agent based models, populated by the heterogeneous and interacting agents in the field of financial fragility. The text is divided in two parts; the first presents analytical developments of stochastic aggregation and macro-dynamics inference methods. The second part introduces macroeconomic models of financial fragility for complex systems populated by heterogeneous and interacting agents. The concepts of financial fragility and macroeconomic dynamics are explained in detail in separate chapters. The statistical physics approach is applied to explain theories of macroeconomic modelling a...
Two-strain competition in quasineutral stochastic disease dynamics
Kogan, Oleg; Khasin, Michael; Meerson, Baruch; Schneider, David; Myers, Christopher R.
2014-10-01
We develop a perturbation method for studying quasineutral competition in a broad class of stochastic competition models and apply it to the analysis of fixation of competing strains in two epidemic models. The first model is a two-strain generalization of the stochastic susceptible-infected-susceptible (SIS) model. Here we extend previous results due to Parsons and Quince [Theor. Popul. Biol. 72, 468 (2007), 10.1016/j.tpb.2007.04.002], Parsons et al. [Theor. Popul. Biol. 74, 302 (2008), 10.1016/j.tpb.2008.09.001], and Lin, Kim, and Doering [J. Stat. Phys. 148, 646 (2012), 10.1007/s10955-012-0479-9]. The second model, a two-strain generalization of the stochastic susceptible-infected-recovered (SIR) model with population turnover, has not been studied previously. In each of the two models, when the basic reproduction numbers of the two strains are identical, a system with an infinite population size approaches a point on the deterministic coexistence line (CL): a straight line of fixed points in the phase space of subpopulation sizes. Shot noise drives one of the strain populations to fixation, and the other to extinction, on a time scale proportional to the total population size. Our perturbation method explicitly tracks the dynamics of the probability distribution of the subpopulations in the vicinity of the CL. We argue that, whereas the slow strain has a competitive advantage for mathematically "typical" initial conditions, it is the fast strain that is more likely to win in the important situation when a few infectives of both strains are introduced into a susceptible population.
Stochastic model for aerodynamic force dynamics on wind turbine blades in unsteady wind inflow
Luhur, Muhammad Ramzan; Kühn, Martin; Wächter, Matthias
2015-01-01
The paper presents a stochastic approach to estimate the aerodynamic forces with local dynamics on wind turbine blades in unsteady wind inflow. This is done by integrating a stochastic model of lift and drag dynamics for an airfoil into the aerodynamic simulation software AeroDyn. The model is added as an alternative to the static table lookup approach in blade element momentum (BEM) wake model used by AeroDyn. The stochastic forces are obtained for a rotor blade element using full field turbulence simulated wind data input and compared with the classical BEM and dynamic stall models for identical conditions. The comparison shows that the stochastic model generates additional extended dynamic response in terms of local force fluctuations. Further, the comparison of statistics between the classical BEM, dynamic stall and stochastic models' results in terms of their increment probability density functions gives consistent results.
Stochastic and dynamical downscaling of ensemble precipitation forecasts
Brussolo, E.; von Hardenberg, J.; Rebora, N.
2009-04-01
Forecasting hydrogeological risk in small basins requires quantitative forecasts and an estimate of the probability of occurrence of severe, localized precipitation events at spatial scales of the order of tens of kilometers or less, significantly smaller than those currently provided by large scale, global, ensemble forecasting systems (EPS). Dynamically based forecasts at these scales can be obtained extending EPS scenarios with high-resolution, non-hydrostatic, limited area ensemble prediction systems. An alternative is represented by the direct application of stochastic downscaling techniques to the large scale ensemble forecasts. This work compares the performances of these two very different ensemble forecast downscaling approaches. To this purpose we consider ensemble forecasts provided by the ECMWF EPS, downscaled in space using the RainFARM stochastic technique [1], and ensembles of forecasts obtained from the COSMO-LEPS limited area prediction system (which also uses ECMWF EPS ensemble members as boundary conditions), for three intense precipitation events over northern Italy in 2006. The statistical properties of the fields produced with these two techniques are compared and the skill of the resulting ensembles is verified against direct precipitation measurements from a dense network of rain gauges. Reference: 1. Rebora, N., L. Ferraris, J. von Hardenberg, and A. Provenzale, 2006: The RainFARM: Rainfall Downscaling by a Filtered AutoRegressive Model. J. Hydrometeorol., 7, 724-738.
Dynamical simulations of classical stochastic systems using matrix product states.
Johnson, T H; Clark, S R; Jaksch, D
2010-09-01
We adapt the time-evolving block decimation (TEBD) algorithm, originally devised to simulate the dynamics of one-dimensional quantum systems, to simulate the time evolution of nonequilibrium stochastic systems. We describe this method in detail; a system's probability distribution is represented by a matrix product state (MPS) of finite dimension and then its time evolution is efficiently simulated by repeatedly updating and approximately refactorizing this representation. We examine the use of MPS as an approximation method, looking at parallels between the interpretations of applying it to quantum state vectors and probability distributions. In the context of stochastic systems we consider two types of factorization for use in the TEBD algorithm: non-negative matrix factorization (NMF), which ensures that the approximate probability distribution is manifestly non-negative, and the singular value decomposition (SVD). Comparing these factorizations, we find the accuracy of the SVD to be substantially greater than current NMF algorithms. We then apply TEBD to simulate the totally asymmetric simple exclusion process (TASEP) for systems of up to hundreds of lattice sites in size. Using exact analytic results for the TASEP steady state, we find that TEBD reproduces this state such that the error in calculating expectation values can be made negligible even when severely compressing the description of the system by restricting the dimension of the MPS to be very small. Out of the steady state we show for specific observables that expectation values converge as the dimension of the MPS is increased to a moderate size.
The dynamical system of weathering: deterministic and stochastic analysis
Calabrese, S.; Parolari, A.; Porporato, A. M.
2016-12-01
The critical zone is fundamental to human society as it provides most of the ecosystem services such as food and fresh water. However, climate change and intense land use are threatening the critical zone, so that theoretical frameworks, to predict its future response, are needed. In this talk, a new modeling approach to evaluate the effect of hydrologic fluctuations on soil water chemistry and weathering reactions is analyzed by means of a dynamical system approach. In this model, equilibrium is assumed for the aqueous carbonate system while a kinetic law is adopted for the weathering reaction. Also, through an algebraic manipulation, we eliminate the equilibrium reactions and reduce the order of the system. We first analyze the deterministic temporal evolution, and study the stability of the nonlinear system and its trajectories, as a function of the hydro-climatic parameters. By introducing a stochastic rainfall forcing, we then analyze the system probabilistically, and through averaging techniques determine the inter-annual response of the nonlinear stochastic system to the climatic regime and hydrologic parameters (e.g., ET, soil texture). Some fundamental thermodynamic aspects of the chemical reactions are also discussed. By introducing the weathering reaction into the system, any mineral, such as calcium carbonate or a silicate mineral, can be considered.
Shi Yun-yu, [No Value; Wang Lu, [No Value; Van Gunsteren, W. F.
1988-01-01
The molecular simulation technique of stochastic dynamics (SD) is tested by application to the immunosuppressive drug cyclosporin A (CPA). Two stochastic dynamics simulations are performed, one (SDCCl4) with atomic friction coefficients proportional to the viscosity of the nonpolar solvent CCl4, and
Random Dynamics of the Stochastic Boussinesq Equations Driven by Lévy Noises
Directory of Open Access Journals (Sweden)
Jianhua Huang
2013-01-01
Full Text Available This paper is devoted to the investigation of random dynamics of the stochastic Boussinesq equations driven by Lévy noise. Some fundamental properties of a subordinator Lévy process and the stochastic integral with respect to a Lévy process are discussed, and then the existence, uniqueness, regularity, and the random dynamical system generated by the stochastic Boussinesq equations are established. Finally, some discussions on the global weak solution of the stochastic Boussinesq equations driven by general Lévy noise are also presented.
Adaptive and Optimal Control of Stochastic Dynamical Systems
2015-09-14
games that does not require finding solutions to nonlinear partial differential equations or solv- ing backward stochastic differential equations ...for stochastic partial differential equations with fractional Brownian motions having the Hurst parameter in the interval (1/2,1), which includes the...Linear exponential-quadratic control problems for stochastic partial differential equations are explicitly solved. Discrete time linear quadratic
Modelling the heat dynamics of buildings using stochastic
DEFF Research Database (Denmark)
Andersen, Klaus Kaae; Madsen, Henrik
2000-01-01
This paper describes the continuous time modelling of the heat dynamics of a building. The considered building is a residential like test house divided into two test rooms with a water based central heating. Each test room is divided into thermal zones in order to describe both short and long term...... variations. Besides modelling the heat transfer between thermal zones, attention is put on modelling the heat input from radiators and solar radiation. The applied modelling procedure is based on collected building performance data and statistical methods. The statistical methods are used in parameter...... estimation and model validation, while physical knowledge is used in forming the model structure. The suggested lumped parameter model is thus based on thermodynamics and formulated as a system of stochastic differential equations. Due to the continuous time formulation the parameters of the model...
Setting development goals using stochastic dynamical system models
Nicolis, Stamatios C.; Bali Swain, Ranjula; Sumpter, David J. T.
2017-01-01
The Millennium Development Goals (MDG) programme was an ambitious attempt to encourage a globalised solution to important but often-overlooked development problems. The programme led to wide-ranging development but it has also been criticised for unrealistic and arbitrary targets. In this paper, we show how country-specific development targets can be set using stochastic, dynamical system models built from historical data. In particular, we show that the MDG target of two-thirds reduction of child mortality from 1990 levels was infeasible for most countries, especially in sub-Saharan Africa. At the same time, the MDG targets were not ambitious enough for fast-developing countries such as Brazil and China. We suggest that model-based setting of country-specific targets is essential for the success of global development programmes such as the Sustainable Development Goals (SDG). This approach should provide clear, quantifiable targets for policymakers. PMID:28241057
Setting development goals using stochastic dynamical system models.
Ranganathan, Shyam; Nicolis, Stamatios C; Bali Swain, Ranjula; Sumpter, David J T
2017-01-01
The Millennium Development Goals (MDG) programme was an ambitious attempt to encourage a globalised solution to important but often-overlooked development problems. The programme led to wide-ranging development but it has also been criticised for unrealistic and arbitrary targets. In this paper, we show how country-specific development targets can be set using stochastic, dynamical system models built from historical data. In particular, we show that the MDG target of two-thirds reduction of child mortality from 1990 levels was infeasible for most countries, especially in sub-Saharan Africa. At the same time, the MDG targets were not ambitious enough for fast-developing countries such as Brazil and China. We suggest that model-based setting of country-specific targets is essential for the success of global development programmes such as the Sustainable Development Goals (SDG). This approach should provide clear, quantifiable targets for policymakers.
Non-equilibrium stochastic dynamics in continuum: The free case
Directory of Open Access Journals (Sweden)
Y.Kondratiev
2008-12-01
Full Text Available We study the problem of identification of a proper state-space for the stochastic dynamics of free particles in continuum, with their possible birth and death. In this dynamics, the motion of each separate particle is described by a fixed Markov process M on a Riemannian manifold X. The main problem arising here is a possible collapse of the system, in the sense that, though the initial configuration of particles is locally finite, there could exist a compact set in X such that, with probability one, infinitely many particles will arrive at this set at some time t>0. We assume that X has infinite volume and, for each α���1, we consider the set Θα of all infinite configurations in X for which the number of particles in a compact set is bounded by a constant times the α-th power of the volume of the set. We find quite general conditions on the process M which guarantee that the corresponding infinite particle process can start at each configuration from Θα, will never leave Θα, and has cadlag (or, even, continuous sample paths in the vague topology. We consider the following examples of applications of our results: Brownian motion on the configuration space, free Glauber dynamics on the configuration space (or a birth-and-death process in X, and free Kawasaki dynamics on the configuration space. We also show that if X=Rd, then for a wide class of starting distributions, the (non-equilibrium free Glauber dynamics is a scaling limit of (non-equilibrium free Kawasaki dynamics.
Design and Development of New Digital Thermostat
Institute of Scientific and Technical Information of China (English)
DAI Xun-jiang; CHAO Qin
2008-01-01
The designed thermostat is based on the microcontroller featuring intelligence, programmable, environmental protection and power saving. The thermostat design is mainly composed of hardware and software design, the hardware includes the power supply circuit, temperature measurement circuit, humidity measurement circuit and backlight circuit; while the software design includes temperature measurement and compensation algorithm, moreover software flowchart is given as well. Finally the power supply circuit is simulated by the software of Pspice and the creative power stealing mode is verified by the simulation results. A target board is stuffed by hand with Pb-free electronic components and used to test hardware and debug software. Since the Pb-free components were used, power stealing mode is designed in hardware and temperature compensation algorithm is accomplished in software, and the thermostat is outstanding with its features of "green" and "power saving".
The stochastic dynamics of tethered microcantilevers in a viscous fluid
Energy Technology Data Exchange (ETDEWEB)
Robbins, Brian A.; Paul, Mark R. [Department of Mechanical Engineering, Virginia Tech, Blacksburg, Virginia 24061 (United States); Radiom, Milad; Ducker, William A. [Department of Chemical Engineering, Virginia Tech, Blacksburg, Virginia 24061 (United States); Walz, John Y. [Department of Chemical Engineering, University of Kentucky, Lexington, Kentucky 40506 (United States)
2014-10-28
We explore and quantify the coupled dynamics of a pair of micron scale cantilevers immersed in a viscous fluid that are also directly tethered to one another at their tips by a spring force. The spring force, for example, could represent the molecular stiffness or elasticity of a biomolecule or material tethered between the cantilevers. We use deterministic numerical simulations with the fluctuation-dissipation theorem to compute the stochastic dynamics of the cantilever pair for the conditions of experiment when driven only by Brownian motion. We validate our approach by comparing directly with experimental measurements in the absence of the tether which shows excellent agreement. Using numerical simulations, we quantify the correlated dynamics of the cantilever pair over a range of tether stiffness. Our results quantify the sensitivity of the auto- and cross-correlations of equilibrium fluctuations in cantilever displacement to the stiffness of the tether. We show that the tether affects the magnitude of the correlations which can be used in a measurement to probe the properties of an attached tethering substance. For the configurations of current interest using micron scale cantilevers in water, we show that the magnitude of the fluid coupling between the cantilevers is sufficiently small such that the influence of the tether can be significant. Our results show that the cross-correlation is more sensitive to tether stiffness than the auto-correlation indicating that a two-cantilever measurement has improved sensitivity when compared with a measurement using a single cantilever.
Stochastic P systems and the simulation of biochemical processes with dynamic compartments.
Spicher, Antoine; Michel, Olivier; Cieslak, Mikolaj; Giavitto, Jean-Louis; Prusinkiewicz, Przemyslaw
2008-03-01
We introduce a sequential rewriting strategy for P systems based on Gillespie's stochastic simulation algorithm, and show that the resulting formalism of stochastic P systems makes it possible to simulate biochemical processes in dynamically changing, nested compartments. Stochastic P systems have been implemented using the spatially explicit programming language MGS. Implementation examples include models of the Lotka-Volterra auto-catalytic system, and the life cycle of the Semliki Forest virus.
Luo, Albert C J
2011-01-01
In memory of Dr. George Zaslavsky, "Long-range Interactions, Stochasticity and Fractional Dynamics" covers the recent developments of long-range interaction, fractional dynamics, brain dynamics and stochastic theory of turbulence, each chapter was written by established scientists in the field. The book is dedicated to Dr. George Zaslavsky, who was one of three founders of the theory of Hamiltonian chaos. The book discusses self-similarity and stochasticity and fractionality for discrete and continuous dynamical systems, as well as long-range interactions and diluted networks. A comprehensive theory for brain dynamics is also presented. In addition, the complexity and stochasticity for soliton chains and turbulence are addressed. The book is intended for researchers in the field of nonlinear dynamics in mathematics, physics and engineering. Dr. Albert C.J. Luo is a Professor at Southern Illinois University Edwardsville, USA. Dr. Valentin Afraimovich is a Professor at San Luis Potosi University, Mexico.
Energy Technology Data Exchange (ETDEWEB)
Kryvohuz, Maksym, E-mail: mkryvohu@uci.edu; Mukamel, Shaul [Chemistry Department, University of California, Irvine, California 92697-2025 (United States)
2015-06-07
Generalized nonlinear response theory is presented for stochastic dynamical systems. Experiments in which multiple measurements of dynamical quantities are used along with multiple perturbations of parameters of dynamical systems are described by generalized response functions (GRFs). These constitute a new type of multidimensional measures of stochastic dynamics either in the time or the frequency domains. Closed expressions for GRFs in stochastic dynamical systems are derived and compared with numerical non-equilibrium simulations. Several types of perturbations are considered: impulsive and periodic perturbations of temperature and impulsive perturbations of coordinates. The present approach can be used to study various types of stochastic processes ranging from single-molecule conformational dynamics to chemical kinetics of finite-size reactors such as biocells.
Nonlinear dynamic characteristics of SMA intravascular stent under radial stochastic loads.
Zhu, Zhiwen; Zhang, Qingxin; Xu, Jia
2014-01-01
Nonlinear dynamic characteristics of shape memory alloy (SMA) intravascular stent under radial stochastic loads were studied in this paper. Von de Pol item was improved to interpret the hysteretic phenomena of SMA, and the nonlinear dynamic model of SMA intravascular stent under radial stochastic loads was developed. The conditions of stochastic stability of the system were obtained in singular boundary theory. The steady-state probability density function of the dynamic response of the system was given, and the stochastic Hopf bifurcation characteristics of the system were analyzed. Theoretical analysis and numerical simulation show that the stability of the trivial solution varies with bifurcation parameters, and stochastic Hopf bifurcation appears in the process, which can cause stent fracture or loss. The results of this paper are helpful to application of SMA intravascular stent in biomedical engineering fields.
Stochastic dynamics of the prisoner's dilemma with cooperation facilitators.
Mobilia, Mauro
2012-07-01
In the framework of the paradigmatic prisoner's dilemma game, we investigate the evolutionary dynamics of social dilemmas in the presence of "cooperation facilitators." In our model, cooperators and defectors interact as in the classical prisoner's dilemma, where selection favors defection. However, here the presence of a small number of cooperation facilitators enhances the fitness (reproductive potential) of cooperators, while it does not alter that of defectors. In a finite population of size N, the dynamics of the prisoner's dilemma with facilitators is characterized by the probability that cooperation takes over (fixation probability) by the mean times to reach the absorbing states. These quantities are computed exactly using Fokker-Planck equations. Our findings, corroborated by stochastic simulations, demonstrate that the influence of facilitators crucially depends on the difference between their density z and the game's cost-to-benefit ratio r. When z > r, the fixation of cooperators is likely in a large population and, under weak selection pressure, invasion and replacement of defection by cooperation is favored by selection if b(z - r)(1 - z) > N(-1), where 0
STOCHASTIC KINETIC MODELS: DYNAMIC INDEPENDENCE, MODULARITY AND GRAPHS.
Bowsher, Clive G
2010-08-01
The dynamic properties and independence structure of stochastic kinetic models (SKMs) are analyzed. An SKM is a highly multivariate jump process used to model chemical reaction networks, particularly those in biochemical and cellular systems. We identify SKM subprocesses with the corresponding counting processes and propose a directed, cyclic graph (the kinetic independence graph or KIG) that encodes the local independence structure of their conditional intensities. Given a partition [A, D, B] of the vertices, the graphical separation A ⊥ B|D in the undirected KIG has an intuitive chemical interpretation and implies that A is locally independent of B given A ∪ D. It is proved that this separation also results in global independence of the internal histories of A and B conditional on a history of the jumps in D which, under conditions we derive, corresponds to the internal history of D. The results enable mathematical definition of a modularization of an SKM using its implied dynamics. Graphical decomposition methods are developed for the identification and efficient computation of nested modularizations. Application to an SKM of the red blood cell advances understanding of this biochemical system.
Stochastic dynamic programming applied to planning of robot grinding tasks
Energy Technology Data Exchange (ETDEWEB)
Brown, M.L. (Digital Equipment Corp., Shrewsbury, MA (United States)); Whitney, D.E. (Massachusetts Inst. of Technology, Cambridge, MA (United States))
1994-10-01
This paper proposes an intelligent manufacturing system that can make decisions about the process in light of the uncertain outcome of these decisions and attempts to minimize the expected economic penalty resulting from those decisions. It uses robot weld bead grinding as an example of a process with significant process variations. The need for multiple grinding passes, the poor predictability of those passes, the task requirements, and the process constraints conspire to make planning and controlling weld bead grinding a formidable probe. A three tier hierarchical control system is proposed to plan an optimal sequence of grinding passes, dynamically simulate each pass, execute the planned sequence of controlled grinding passes, and modify the pass sequence as grinding continues. The top tier, described in this paper, plans the grinding sequence for each weld bead, and is implemented using Stochastic Dynamic Programming, selecting the volumetric removal and feedspeed for each pass in order to optimize the satisfaction of the task requirements by the entire grinding sequence within the equipment, task, and process constraints. The resulting optimal policies have quite complex structures, showing foresight, anxiety, indifference, and aggressiveness, depending upon the situation.
Stochastic dynamics of Arctic sea ice Part I: Additive noise
Moon, Woosok
2015-01-01
We analyze the numerical solutions of a stochastic Arctic sea ice model with constant additive noise over a wide range of external heat-fluxes, $\\Delta F_0$, which correspond to greenhouse gas forcing. The variability that the stochasticity provides to the deterministic steady state solutions (perennial and seasonal ice states) is illustrated by examining both the stochastic paths and probability density functions (PDFs). The principal stochastic moments (standard deviation, mean and skewness) are calculated and compared with those determined from a stochastic perturbation theory described previously by Moon and Wettlaufer (2013). We examine in detail the competing roles of the destabilizing sea ice-albedo-feedback and the stabilizing long-wave radiative loss contributions to the variability of the ice cover under increased greenhouse-gas forcing. In particular, the variability of the stochastic paths at the end of summer shows a clear maximum, which is due to the combination of the increasing importance of t...
A remark on symmetry of stochastic dynamical systems and their conserved quantities
Albeverio, Sergio A; Albeverio, Sergio; Fei, Shao Ming
1995-01-01
Symmetry properties of stochastic dynamical systems described by stochastic differential equation of Stratonovich type and related conserved quantities are discussed, extending previous results by Misawa. New conserved quantities are given by applying symmetry operators to known conserved quantities. Some detailed examples are presented.
A Dynamic Berth Allocation Problem with Priority Considerations under Stochastic Nature
Ursavas, Evrim; Bulut, Onder; Tasgetiren, Fatih
2012-01-01
Stochastic nature of vessel arrivals and handling times adds to the complexity of the well-known NP-hard berth allocation problem. To aid real decision-making under customer differentiations, a dynamic stochastic model designed to reflect different levels of vessel priorities is put forward. For
A Dynamic Berth Allocation Problem with Priority Considerations under Stochastic Nature
Ursavas, Evrim; Bulut, Onder; Tasgetiren, Fatih
2012-01-01
Stochastic nature of vessel arrivals and handling times adds to the complexity of the well-known NP-hard berth allocation problem. To aid real decision-making under customer differentiations, a dynamic stochastic model designed to reflect different levels of vessel priorities is put forward. For exp
Dynamics of the stochastic Lorenz chaotic system with long memory effects
Energy Technology Data Exchange (ETDEWEB)
Zeng, Caibin, E-mail: zeng.cb@mail.scut.edu.cn; Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Mathematics, South China University of Technology, Guangzhou 510640 (China)
2015-12-15
Little seems to be known about the ergodic dynamics of stochastic systems with fractional noise. This paper is devoted to discern such long time dynamics through the stochastic Lorenz chaotic system (SLCS) with long memory effects. By a truncation technique, the SLCS is proved to generate a continuous stochastic dynamical system Λ. Based on the Krylov-Bogoliubov criterion, the required Lyapunov function is further established to ensure the existence of the invariant measure of Λ. Meanwhile, the uniqueness of the invariant measure of Λ is proved by examining the strong Feller property, together with an irreducibility argument. Therefore, the SLCS has exactly one adapted stationary solution.
Optically levitated nanoparticle as a model system for stochastic bistable dynamics
Ricci, F.; Rica, R. A.; Spasenović, M.; Gieseler, J.; Rondin, L.; Novotny, L.; Quidant, R.
2017-05-01
Nano-mechanical resonators have gained an increasing importance in nanotechnology owing to their contributions to both fundamental and applied science. Yet, their small dimensions and mass raises some challenges as their dynamics gets dominated by nonlinearities that degrade their performance, for instance in sensing applications. Here, we report on the precise control of the nonlinear and stochastic bistable dynamics of a levitated nanoparticle in high vacuum. We demonstrate how it can lead to efficient signal amplification schemes, including stochastic resonance. This work contributes to showing the use of levitated nanoparticles as a model system for stochastic bistable dynamics, with applications to a wide variety of fields.
Dynamics of the stochastic Lorenz chaotic system with long memory effects
Zeng, Caibin; Yang, Qigui
2015-12-01
Little seems to be known about the ergodic dynamics of stochastic systems with fractional noise. This paper is devoted to discern such long time dynamics through the stochastic Lorenz chaotic system (SLCS) with long memory effects. By a truncation technique, the SLCS is proved to generate a continuous stochastic dynamical system Λ. Based on the Krylov-Bogoliubov criterion, the required Lyapunov function is further established to ensure the existence of the invariant measure of Λ. Meanwhile, the uniqueness of the invariant measure of Λ is proved by examining the strong Feller property, together with an irreducibility argument. Therefore, the SLCS has exactly one adapted stationary solution.
Stochastic dynamics of interacting haematopoietic stem cell niche lineages.
Directory of Open Access Journals (Sweden)
Tamás Székely
2014-09-01
Full Text Available Since we still know very little about stem cells in their natural environment, it is useful to explore their dynamics through modelling and simulation, as well as experimentally. Most models of stem cell systems are based on deterministic differential equations that ignore the natural heterogeneity of stem cell populations. This is not appropriate at the level of individual cells and niches, when randomness is more likely to affect dynamics. In this paper, we introduce a fast stochastic method for simulating a metapopulation of stem cell niche lineages, that is, many sub-populations that together form a heterogeneous metapopulation, over time. By selecting the common limiting timestep, our method ensures that the entire metapopulation is simulated synchronously. This is important, as it allows us to introduce interactions between separate niche lineages, which would otherwise be impossible. We expand our method to enable the coupling of many lineages into niche groups, where differentiated cells are pooled within each niche group. Using this method, we explore the dynamics of the haematopoietic system from a demand control system perspective. We find that coupling together niche lineages allows the organism to regulate blood cell numbers as closely as possible to the homeostatic optimum. Furthermore, coupled lineages respond better than uncoupled ones to random perturbations, here the loss of some myeloid cells. This could imply that it is advantageous for an organism to connect together its niche lineages into groups. Our results suggest that a potential fruitful empirical direction will be to understand how stem cell descendants communicate with the niche and how cancer may arise as a result of a failure of such communication.
Filtering nonlinear dynamical systems with linear stochastic models
Harlim, J.; Majda, A. J.
2008-06-01
An important emerging scientific issue is the real time filtering through observations of noisy signals for nonlinear dynamical systems as well as the statistical accuracy of spatio-temporal discretizations for filtering such systems. From the practical standpoint, the demand for operationally practical filtering methods escalates as the model resolution is significantly increased. For example, in numerical weather forecasting the current generation of global circulation models with resolution of 35 km has a total of billions of state variables. Numerous ensemble based Kalman filters (Evensen 2003 Ocean Dyn. 53 343-67 Bishop et al 2001 Mon. Weather Rev. 129 420-36 Anderson 2001 Mon. Weather Rev. 129 2884-903 Szunyogh et al 2005 Tellus A 57 528-45 Hunt et al 2007 Physica D 230 112-26) show promising results in addressing this issue; however, all these methods are very sensitive to model resolution, observation frequency, and the nature of the turbulent signals when a practical limited ensemble size (typically less than 100) is used. In this paper, we implement a radical filtering approach to a relatively low (40) dimensional toy model, the L-96 model (Lorenz 1996 Proc. on Predictability (ECMWF, 4-8 September 1995) pp 1-18) in various chaotic regimes in order to address the 'curse of ensemble size' for complex nonlinear systems. Practically, our approach has several desirable features such as extremely high computational efficiency, filter robustness towards variations of ensemble size (we found that the filter is reasonably stable even with a single realization) which makes it feasible for high dimensional problems, and it is independent of any tunable parameters such as the variance inflation coefficient in an ensemble Kalman filter. This radical filtering strategy decouples the problem of filtering a spatially extended nonlinear deterministic system to filtering a Fourier diagonal system of parametrized linear stochastic differential equations (Majda and Grote
Dynamics of a rotating flat ellipsoid with a stochastic oblateness
Behar, Etienne; Pierret, Frédéric
2014-01-01
We derive a model for the motion of a rotating flat ellispoid with a stochastic flattening based on an invariance theorem for stochastic differential equations. A numerical study of a toy-model is performed leading to an intriguing coincidence with observational data.
Advanced Dynamically Adaptive Algorithms for Stochastic Simulations on Extreme Scales
Energy Technology Data Exchange (ETDEWEB)
Xiu, Dongbin [Univ. of Utah, Salt Lake City, UT (United States)
2017-03-03
The focus of the project is the development of mathematical methods and high-performance computational tools for stochastic simulations, with a particular emphasis on computations on extreme scales. The core of the project revolves around the design of highly efficient and scalable numerical algorithms that can adaptively and accurately, in high dimensional spaces, resolve stochastic problems with limited smoothness, even containing discontinuities.
The G-JF Thermostat for Accurate Configurational Sampling in Soft-Matter Simulations
Arad, Evyatar; Grønbech-Jensen, Niels
2016-01-01
We implement the statistically sound G-JF thermostat for Langevin Dynamics simulations into the ESPREesSo molecular package for large-scale simulations of soft matter systems. The implemented integration method is tested against the integrator currently used by the molecular package in simulations of a fluid bilayer membrane. While the latter exhibits deviations in the sampling statistics that increase with the integration time step dt, the former reproduces near-correct configurational statistics for all dt within the stability range of the simulations. We conclude that, with very modest revisions to existing codes, one can significantly improve the performance of statistical sampling using Langevin thermostats.
One Form of Lyapunov Operator for Stochastic Dynamic System with Markov Parameters
Directory of Open Access Journals (Sweden)
Taras Lukashiv
2016-01-01
Full Text Available The form of weak infinitesimal operator of Lyapunov type on solutions of stochastic dynamic systems of random structure with constant delay which exist under the action of Markov perturbations is obtained.
Order and stochastic dynamics in Drosophila planar cell polarity.
Directory of Open Access Journals (Sweden)
Yoram Burak
2009-12-01
Full Text Available Cells in the wing blade of Drosophila melanogaster exhibit an in-plane polarization causing distal orientation of hairs. Establishment of the Planar Cell Polarity (PCP involves intercellular interactions as well as a global orienting signal. Many of the genetic and molecular components underlying this process have been experimentally identified and a recently advanced system-level model has suggested that the observed mutant phenotypes can be understood in terms of intercellular interactions involving asymmetric localization of membrane bound proteins. Among key open questions in understanding the emergence of ordered polarization is the effect of stochasticity and the role of the global orienting signal. These issues relate closely to our understanding of ferromagnetism in physical systems. Here we pursue this analogy to understand the emergence of PCP order. To this end we develop a semi-phenomenological representation of the underlying molecular processes and define a "phase diagram" of the model which provides a global view of the dependence of the phenotype on parameters. We show that the dynamics of PCP has two regimes: rapid growth in the amplitude of local polarization followed by a slower process of alignment which progresses from small to large scales. We discuss the response of the tissue to various types of orienting signals and show that global PCP order can be achieved with a weak orienting signal provided that it acts during the early phase of the process. Finally we define and discuss some of the experimental predictions of the model.
A stochastic dynamic programming model for stream water quality management
Indian Academy of Sciences (India)
P P Mujumdar; Pavan Saxena
2004-10-01
This paper deals with development of a seasonal fraction-removal policy model for waste load allocation in streams addressing uncertainties due to randomness and fuzziness. A stochastic dynamic programming (SDP) model is developed to arrive at the steady-state seasonal fraction-removal policy. A fuzzy decision model (FDM) developed by us in an earlier study is used to compute the system performance measure required in the SDP model. The state of the system in a season is deﬁned by streamﬂows at the headwaters during the season and the initial DO deﬁcit at some pre-speciﬁed checkpoints. The random variation of streamﬂows is included in the SDP model through seasonal transitional probabilities. The decision vector consists of seasonal fraction-removal levels for the efﬂuent dischargers. Uncertainty due to imprecision (fuzziness) associated with water quality goals is addressed using the concept of fuzzy decision. Responses of pollution control agencies to the resulting end-of-season DO deﬁcit vector and that of dischargers to the fraction-removal levels are treated as fuzzy, and modelled with appropriate membership functions. Application of the model is illustrated with a case study of the Tungabhadra river in India.
Stochastic Rotation Dynamics simulations of wetting multi-phase flows
Hiller, Thomas; Sanchez de La Lama, Marta; Brinkmann, Martin
2016-06-01
Multi-color Stochastic Rotation Dynamics (SRDmc) has been introduced by Inoue et al. [1,2] as a particle based simulation method to study the flow of emulsion droplets in non-wetting microchannels. In this work, we extend the multi-color method to also account for different wetting conditions. This is achieved by assigning the color information not only to fluid particles but also to virtual wall particles that are required to enforce proper no-slip boundary conditions. To extend the scope of the original SRDmc algorithm to e.g. immiscible two-phase flow with viscosity contrast we implement an angular momentum conserving scheme (SRD+mc). We perform extensive benchmark simulations to show that a mono-phase SRDmc fluid exhibits bulk properties identical to a standard SRD fluid and that SRDmc fluids are applicable to a wide range of immiscible two-phase flows. To quantify the adhesion of a SRD+mc fluid in contact to the walls we measure the apparent contact angle from sessile droplets in mechanical equilibrium. For a further verification of our wettability implementation we compare the dewetting of a liquid film from a wetting stripe to experimental and numerical studies of interfacial morphologies on chemically structured surfaces.
Systemic risk in dynamical networks with stochastic failure criterion
Podobnik, B.; Horvatic, D.; Bertella, M. A.; Feng, L.; Huang, X.; Li, B.
2014-06-01
Complex non-linear interactions between banks and assets we model by two time-dependent Erdős-Renyi network models where each node, representing a bank, can invest either to a single asset (model I) or multiple assets (model II). We use a dynamical network approach to evaluate the collective financial failure —systemic risk— quantified by the fraction of active nodes. The systemic risk can be calculated over any future time period, divided into sub-periods, where within each sub-period banks may contiguously fail due to links to either i) assets or ii) other banks, controlled by two parameters, probability of internal failure p and threshold Th (“solvency” parameter). The systemic risk decreases with the average network degree faster when all assets are equally distributed across banks than if assets are randomly distributed. The more inactive banks each bank can sustain (smaller Th), the smaller the systemic risk —for some Th values in I we report a discontinuity in systemic risk. When contiguous spreading becomes stochastic ii) controlled by probability p2 —a condition for the bank to be solvent (active) is stochastic— the systemic risk decreases with decreasing p2. We analyse the asset allocation for the U.S. banks.
Motion in a stochastic layer described by symbolic dynamics
Energy Technology Data Exchange (ETDEWEB)
Misguich, J.H.; Reuss, J.D. [Association Euratom-CEA, Centre d`Etudes Nucleaires de Cadarache, 13 - Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee; Elskens, Y. [Universite de Provence, 13 - Marseille (France); Balescu, R. [Association Euratom, Brussels (Belgium)
1997-07-01
The motion in the stochastic layer surrounding an island can be studied by using the standard map: this problem is of direct relevance to the diffusion of magnetic field lines in a tokamak. In a previous work it was shown that this process can be adequately modelled by a continuous time random walk (CTRW) describing transitions of the running point between three basins representing, respectively, trapped motion around the island, and passing motion above or below the island. The sticking property of the island deeply modifies the nature of the transport process, leading to sub-diffusive behavior. In the present work it is shown that the motion can be analyzed in terms of a symbolic dynamics which leads to the possibility of an automatic measurement of the data necessary for the construction of the CTRW. The logical features of the procedure are described, and the method is applied to an analysis of long time series, thus completing the results of the previous work. (author) 10 refs.
Katori, Yuichi; Otsubo, Yosuke; Okada, Masato; Aihara, Kazuyuki
2013-01-01
We investigate the dynamical properties of an associative memory network consisting of stochastic neurons and dynamic synapses that show short-term depression and facilitation. In the stochastic neuron model used in this study, the efficacy of the synaptic transmission changes according to the short-term depression or facilitation mechanism. We derive a macroscopic mean field model that captures the overall dynamical properties of the stochastic model. We analyze the stability and bifurcation structure of the mean field model, and show the dependence of the memory retrieval performance on the noise intensity and parameters that determine the properties of the dynamic synapses, i.e., time constants for depressing and facilitating processes. The associative memory network exhibits a variety of dynamical states, including the memory and pseudo-memory states, as well as oscillatory states among memory patterns. This study provides comprehensive insight into the dynamical properties of the associative memory network with dynamic synapses.
Institute of Scientific and Technical Information of China (English)
陈志平
2003-01-01
A new deterministic formulation,called the conditional expectation formulation,is proposed for dynamic stochastic programming problems in order to overcome some disadvantages of existing deterministic formulations.We then check the impact of the new deterministic formulation and other two deterministic formulations on the corresponding problem size,nonzero elements and solution time by solving some typical dynamic stochastic programming problems with different interior point algorithms.Numerical results show the advantage and application of the new deterministic formulation.
Stochastic Hard-Sphere Dynamics for Hydrodynamics of Non-Ideal Fluids
Donev, Aleksandar; Alder, Berni J.; Garcia, Alejandro L.
2008-01-01
A novel stochastic fluid model is proposed with non-ideal structure factor consistent with compressibility, and adjustable transport coefficients. This Stochastic Hard Sphere Dynamics (SHSD) algorithm is a modification of the Direct Simulation Monte Carlo (DSMC) algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and pair correlation function identical to that of a deterministic Hamiltonian sys...
Summing over trajectories of stochastic dynamics with multiplicative noise
Energy Technology Data Exchange (ETDEWEB)
Tang, Ying, E-mail: jamestang23@gmail.com; Ao, Ping, E-mail: aoping@sjtu.edu.cn [Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240 (China); Key Laboratory of Systems Biomedicine Ministry of Education, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai 200240 (China); Yuan, Ruoshi [School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200240 (China)
2014-07-28
We demonstrate that previous path integral formulations for the general stochastic interpretation generate incomplete results exemplified by the geometric Brownian motion. We thus develop a novel path integral formulation for the overdamped Langevin equation with multiplicative noise. The present path integral leads to the corresponding Fokker-Planck equation, and naturally generates a normalized transition probability in examples. Our result solves the inconsistency of the previous path integral formulations for the general stochastic interpretation, and can have wide applications in chemical and physical stochastic processes.
Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics
Arampatzis, Georgios; Katsoulakis, Markos A.; Rey-Bellet, Luc
2016-03-01
We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in long-time and steady-state regimes. These estimators rely on a new covariance formulation of the likelihood ratio that includes as a submatrix a Fisher information matrix for stochastic dynamics and can also be used for fast screening of insensitive parameters and parameter combinations. The proposed methods are applicable to broad classes of stochastic dynamics such as chemical reaction networks, Langevin-type equations and stochastic models in finance, including systems with a high dimensional parameter space and/or disparate decorrelation times between different observables. Furthermore, they are simple to implement as a standard observable in any existing simulation algorithm without additional modifications.
Exact and Approximate Stochastic Simulation of Intracellular Calcium Dynamics
Directory of Open Access Journals (Sweden)
Nicolas Wieder
2011-01-01
pathways. The purpose of the present paper is to provide an overview of the aforementioned simulation approaches and their mutual relationships in the spectrum ranging from stochastic to deterministic algorithms.
Advanced Dynamically Adaptive Algorithms for Stochastic Simulations on Extreme Scales
Energy Technology Data Exchange (ETDEWEB)
Xiu, Dongbin [Purdue Univ., West Lafayette, IN (United States)
2016-06-21
The focus of the project is the development of mathematical methods and high-performance com- putational tools for stochastic simulations, with a particular emphasis on computations on extreme scales. The core of the project revolves around the design of highly e cient and scalable numer- ical algorithms that can adaptively and accurately, in high dimensional spaces, resolve stochastic problems with limited smoothness, even containing discontinuities.
Modeling and control of thermostatically controlled loads
2011-01-01
As the penetration of intermittent energy sources grows substantially, loads will be required to play an increasingly important role in compensating the fast time-scale fluctuations in generated power. Recent numerical modeling of thermostatically controlled loads (TCLs) has demonstrated that such load following is feasible, but analytical models that satisfactorily quantify the aggregate power consumption of a group of TCLs are desired to enable controller design. We develop such a model for...
Stochastic rotation dynamics simulation of electro-osmosis
Ceratti, Davide R.; Obliger, Amaël; Jardat, Marie; Rotenberg, Benjamin; Dahirel, Vincent
2015-09-01
Stochastic Rotation Dynamics (SRD) is a mesoscale simulation technique that captures hydrodynamic couplings in simple and complex fluids. It can be used in various hydrodynamic regimes and it is not restricted to specific geometries. We show here that SRD using the collisional coupling approach to capture momentum transfer between the semi-implicit solvent and the explicit counterions, is able to describe electro-kinetic effects, i.e. coupled electrostatic and hydrodynamic phenomena occurring at charged solid-liquid interfaces. The method is first validated for electro-osmosis in the simple case of a slit pore without added salt, for which an analytical solution of the Helmholtz-Smoluchowski theory is known, in a physical regime where this mean-field theory is valid. We then discuss the predictions of SRD for electro-osmosis beyond the range of validity of the Helmholtz-Smoluchowski (or Poisson-Nernst-Planck) theory, in particular due to ion-ion correlations at the surface, to charge localisation on discrete sites at the solid surface and to surface charge heterogeneity, that all contribute to a reduction of the electro-osmotic flow. In order to disentangle these last two aspects, we also investigate at the mean-field level a simple system with alternate charged and neutral stripes, using lattice-Boltzmann electro-kinetics simulations. Overall, this work opens new perspectives for the use of SRD as a generic mesoscopic simulation method for soft matter problems, in particular under confinement, since in practice many interfaces between fluids and solids are charged.
Stochastic optimal control in infinite dimension dynamic programming and HJB equations
Fabbri, Giorgio; Święch, Andrzej
2017-01-01
Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite ...
Advanced models of neural networks nonlinear dynamics and stochasticity in biological neurons
Rigatos, Gerasimos G
2015-01-01
This book provides a complete study on neural structures exhibiting nonlinear and stochastic dynamics, elaborating on neural dynamics by introducing advanced models of neural networks. It overviews the main findings in the modelling of neural dynamics in terms of electrical circuits and examines their stability properties with the use of dynamical systems theory. It is suitable for researchers and postgraduate students engaged with neural networks and dynamical systems theory.
Integral characteristics: a key to understanding structure formation in stochastic dynamic systems
Energy Technology Data Exchange (ETDEWEB)
Klyatskin, Valery I, E-mail: klyatskin@yandex.ru
2011-05-31
Some general problems concerning the stochastic approach are discussed in relation to parametrically excited stochastic dynamic systems described by partial differential equations. Such problems arise in hydrodynamics, magnetohydrodynamics, and astro, plasma, and radio physics and share the feature that the statistical characteristics of their solutions (moments, correlation and spectral functions, and so on) increasing exponentially with time, whereas some solution implementations lead to the formation of random structures with probability one as a result of clustering. The goal of this paper is to use the ideas of stochastic topography to find conditions under which such structures arise. (reviews of topical problems)
Non-Markovian Fermionic Stochastic Schr\\"{o}dinger Equation for Open System Dynamics
Shi, Wufu; Yu, Ting
2012-01-01
In this paper we present an exact Grassmann stochastic Schr\\"{o}dinger equation for the dynamics of an open fermionic quantum system coupled to a reservoir consisting of a finite or infinite number of fermions. We use this stochastic approach to derive the exact master equation for a fermionic system strongly coupled to electronic reservoirs. The generality and applicability of this Grassmann stochastic approach is justified and exemplified by several quantum open system problems concerning quantum decoherence and quantum transport for both vacuum and finite-temperature fermionic reservoirs. We show that the quantum coherence property of the quantum dot system can be profoundly modified by the environment memory.
Threshold Dynamics in Stochastic SIRS Epidemic Models with Nonlinear Incidence and Vaccination.
Wang, Lei; Teng, Zhidong; Tang, Tingting; Li, Zhiming
2017-01-01
In this paper, the dynamical behaviors for a stochastic SIRS epidemic model with nonlinear incidence and vaccination are investigated. In the models, the disease transmission coefficient and the removal rates are all affected by noise. Some new basic properties of the models are found. Applying these properties, we establish a series of new threshold conditions on the stochastically exponential extinction, stochastic persistence, and permanence in the mean of the disease with probability one for the models. Furthermore, we obtain a sufficient condition on the existence of unique stationary distribution for the model. Finally, a series of numerical examples are introduced to illustrate our main theoretical results and some conjectures are further proposed.
Sun, Yongzheng; Li, Wang; Zhao, Donghua
2012-06-01
In this paper, the finite-time stochastic outer synchronization between two different complex dynamical networks with noise perturbation is investigated. By using suitable controllers, sufficient conditions for finite-time stochastic outer synchronization are derived based on the finite-time stability theory of stochastic differential equations. It is noticed that the coupling configuration matrix is not necessary to be symmetric or irreducible, and the inner coupling matrix need not be symmetric. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results. The effect of control parameters on the settling time is also numerically demonstrated.
Model identification in computational stochastic dynamics using experimental modal data
Batou, A.; Soize, C.; Audebert, S.
2015-01-01
This paper deals with the identification of a stochastic computational model using experimental eigenfrequencies and mode shapes. In the presence of randomness, it is difficult to construct a one-to-one correspondence between the results provided by the stochastic computational model and the experimental data because of the random modes crossing and veering phenomena that may occur from one realization to another one. In this paper, this correspondence is constructed by introducing an adapted transformation for the computed modal quantities. Then the transformed computed modal quantities can be compared with the experimental data in order to identify the parameters of the stochastic computational model. The methodology is applied to a booster pump of thermal units for which experimental modal data have been measured on several sites.
Karachanskaya, Elena
2012-01-01
Investigate the stochastic dynamic non-linear system with the Wiener and the Poisson perturbations. For such systems we construct the program control with probability one, which allows this system to move on the given trajectory. In this case the control program is solution of the algebraic system of linear equations. Considered algorithm is based on the first integral theory for stochastic differential equations system.
Refining Dynamics of Gene Regulatory Networks in a Stochastic π-Calculus Framework
Paulevé, Loïc; Magnin, Morgan; Roux, Olivier
2011-01-01
International audience; In this paper, we introduce a framework allowing to model and analyse efficiently Gene Regulatory Networks in their temporal and stochastic aspects. The analysis of stable states and inference of René Thomas' discrete parameters derives from this logical formalism. We offer a compositional approach which comes with a natural translation to the Stochastic π-Calculus. The method we propose consists in successive refinements of generalized dynamics of Gene Regulatory Netw...
Stochastic linear dynamical programming in order to apply it in energy modelling
Energy Technology Data Exchange (ETDEWEB)
El Hachem, S.
1995-11-01
This thesis contributes to the development of new algorithms for the computation of stochastic dynamic problem and its mini-maxi variant for the case of imperfect knowledge on random data. The proposed algorithms are scenarios aggregation type. It also contributes to integrate these algorithms in a decision support approach and to discuss the stochastic modeling of two energy problems: the refining and the portfolio gas contracts. (author). 112 refs., 5 tabs.
Zhang, Yue; Zheng, Yan; Liu, Xi; Zhang, Qingling; Li, Aihua
2016-11-01
This study considers a class of differential algebraic stage-structured bio-economic models with stochastic fluctuations. The stochastic bio-economic model is simplified to an Itô equation using the stochastic averaging method. The stochastic stability, Hopf bifurcation, and P-bifurcation are discussed based on the singular boundary theory of the diffusion process for the system and the invariant measure theory of dynamic systems. Numerical simulations are presented to illustrate our main results.
Directory of Open Access Journals (Sweden)
Na Duan
2012-01-01
Full Text Available The adaptive stabilization scheme based on tuning function for stochastic nonlinear systems with stochastic integral input-to-state stability (SiISS inverse dynamics is investigated. By combining the stochastic LaSalle theorem and small-gain type conditions on SiISS, an adaptive output feedback controller is constructively designed. It is shown that all the closed-loop signals are bounded almost surely and the stochastic closed-loop system is globally stable in probability.
Stochastic evolutions of dynamic traffic flow modeling and applications
Chen, Xiqun (Michael); Shi, Qixin
2015-01-01
This book reveals the underlying mechanisms of complexity and stochastic evolutions of traffic flows. Using Eulerian and Lagrangian measurements, the authors propose lognormal headway/spacing/velocity distributions and subsequently develop a Markov car-following model to describe drivers’ random choices concerning headways/spacings, putting forward a stochastic fundamental diagram model for wide scattering flow-density points. In the context of highway onramp bottlenecks, the authors present a traffic flow breakdown probability model and spatial-temporal queuing model to improve the stability and reliability of road traffic flows. This book is intended for researchers and graduate students in the fields of transportation engineering and civil engineering.
Wang, Qing; Yao, Jing-Zheng
2010-12-01
Several algorithms were proposed relating to the development of a framework of the perturbation-based stochastic finite element method (PSFEM) for large variation nonlinear dynamic problems. For this purpose, algorithms and a framework related to SFEM based on the stochastic virtual work principle were studied. To prove the validity and practicality of the algorithms and framework, numerical examples for nonlinear dynamic problems with large variations were calculated and compared with the Monte-Carlo Simulation method. This comparison shows that the proposed approaches are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.
National Research Council Canada - National Science Library
Muhammad Murtadha Othman; Nur Ashida Salim; Ismail Musirin
2017-01-01
.... This paper presents the proposed stochastic event tree technique used to assess the sustainability against the occurrence of dynamic power system blackout emanating from implication of critical...
Modeling of stochastic dynamics of time-dependent flows under high-dimensional random forcing
Babaee, Hessam; Karniadakis, George
2016-11-01
In this numerical study the effect of high-dimensional stochastic forcing in time-dependent flows is investigated. To efficiently quantify the evolution of stochasticity in such a system, the dynamically orthogonal method is used. In this methodology, the solution is approximated by a generalized Karhunen-Loeve (KL) expansion in the form of u (x , t ω) = u ̲ (x , t) + ∑ i = 1 N yi (t ω)ui (x , t) , in which u ̲ (x , t) is the stochastic mean, the set of ui (x , t) 's is a deterministic orthogonal basis and yi (t ω) 's are the stochastic coefficients. Explicit evolution equations for u ̲ , ui and yi are formulated. The elements of the basis ui (x , t) 's remain orthogonal for all times and they evolve according to the system dynamics to capture the energetically dominant stochastic subspace. We consider two classical fluid dynamics problems: (1) flow over a cylinder, and (2) flow over an airfoil under up to one-hundred dimensional random forcing. We explore the interaction of intrinsic with extrinsic stochasticity in these flows. DARPA N66001-15-2-4055, Office of Naval Research N00014-14-1-0166.
Path integral methods for the dynamics of stochastic and disordered systems
DEFF Research Database (Denmark)
Hertz, John A.; Roudi, Yasser; Sollich, Peter
2017-01-01
We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin–Siggia–Rose/Janssen–De Dominicis–Peliti path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey...... in studying the disorder-averaged dynamics. Finally, we discuss the path integral approach for the case of hard Ising spins and review some recent developments in the dynamics of such kinetic Ising models....
Directory of Open Access Journals (Sweden)
Angelica María Atehortúa Labrador
2012-09-01
Full Text Available This article describes DSamala toolbox, a computational tool for simulating and analysing discrete, continuous, stochastic dynamic systems; It is presented as a MATLAB toolbox. DSamala toolbox makes a significant contribution to studying dynamic systems through the use of information and communication technology (ICT, especially when equations modelling these systems are difficult or impossible to solve analytically.
Lukasevich, V. I.; Kramarov, S. O.; Sokolov, Sergey V.
2015-01-01
It is solved a problem of a posteriori estimation of dynamically modified parameters of angular movement of the object by satellite measurements. There are shown advantages of application of the methods of stochastic non-linear dynamic filtration before single-stage measurements. It is represented an example, showing efficiency of proposed approach.
A Hierarchical Latent Stochastic Differential Equation Model for Affective Dynamics
Oravecz, Zita; Tuerlinckx, Francis; Vandekerckhove, Joachim
2011-01-01
In this article a continuous-time stochastic model (the Ornstein-Uhlenbeck process) is presented to model the perpetually altering states of the core affect, which is a 2-dimensional concept underlying all our affective experiences. The process model that we propose can account for the temporal changes in core affect on the latent level. The key…
Stochastic Online Learning in Dynamic Networks under Unknown Models
2016-08-02
setting where multiple distributed players share the arms without information exchange. Under both an exogenous restless model and an endogenous ...decision making under unknown models and incomplete observations. The technical approach rests on a stochastic online learning framework based on...general, potentially heavy-tailed distribution. In [1], we developed a general approach based on a Deterministic Sequencing of Exploration and
Time Evolution of the Dynamical Variables of a Stochastic System.
de la Pena, L.
1980-01-01
By using the method of moments, it is shown that several important and apparently unrelated theorems describing average properties of stochastic systems are in fact particular cases of a general law; this method is applied to generalize the virial theorem and the fluctuation-dissipation theorem to the time-dependent case. (Author/SK)
Attractors for stochastic lattice dynamical systems with a multiplicative noise
Institute of Scientific and Technical Information of China (English)
Tomás CARABALLO; Kening LU
2008-01-01
In this paper,we consider a stochastic lattice differential equation with diffusive nearest neighbor interaction,a dissipative nonlinear reaction term,and multiplicative white noise at each node.We prove the existence of a compact global random attractor which,pulled back,attracts tempered random bounded sets.
Demand Response on domestic thermostatically controlled loads
DEFF Research Database (Denmark)
Lakshmanan, Venkatachalam
. In general, the electricity consumers are classified as industrial, commercial and domestic. In this dissertation, only the thermostatically controlled loads (TCLs) in the domestic segment are considered for the demand response study. The study is funded by Danish Council for Strategic Research (DCSR......, with respect to different power reduction levels, are analysed. Finally, the impact of demand response activation on the TCLs aggregated power is studied in terms of error in power limit, ramping rates and peak overshoot in different control scenarios. Lastly, the advantage and disadvantage of the different...
Directory of Open Access Journals (Sweden)
Weikang Wang
Full Text Available Tumors are often heterogeneous in which tumor cells of different phenotypes have distinct properties. For scientific and clinical interests, it is of fundamental importance to understand their properties and the dynamic variations among different phenotypes, specifically under radio- and/or chemo-therapy. Currently there are two controversial models describing tumor heterogeneity, the cancer stem cell (CSC model and the stochastic model. To clarify the controversy, we measured probabilities of different division types and transitions of cells via in situ immunofluorescence. Based on the experiment data, we constructed a model that combines the CSC with the stochastic concepts, showing the existence of both distinctive CSC subpopulations and the stochastic transitions from NSCCs to CSCs. The results showed that the dynamic variations between CSCs and non-stem cancer cells (NSCCs can be simulated with the model. Further studies also showed that the model can be used to describe the dynamics of the two subpopulations after radiation treatment. More importantly, analysis demonstrated that the experimental detectable equilibrium CSC proportion can be achieved only when the stochastic transitions from NSCCs to CSCs occur, indicating that tumor heterogeneity may exist in a model coordinating with both the CSC and the stochastic concepts. The mathematic model based on experimental parameters may contribute to a better understanding of the tumor heterogeneity, and provide references on the dynamics of CSC subpopulation during radiotherapy.
Rosenbaum, Robert; Rubin, Jonathan E; Doiron, Brent
2013-01-01
Correlated neuronal activity is an important feature in many neural codes, a neural correlate of a variety of cognitive states, as well as a signature of several disease states in the nervous system. The cellular and circuit mechanics of neural correlations is a vibrant area of research. Synapses throughout the cortex exhibit a form of short-term depression where increased presynaptic firing rates deplete neurotransmitter vesicles, which transiently reduces synaptic efficacy. The release and recovery of these vesicles are inherently stochastic, and this stochasticity introduces variability into the conductance elicited by depressing synapses. The impact of spiking and subthreshold membrane dynamics on the transfer of neuronal correlations has been studied intensively, but an investigation of the impact of short-term synaptic depression and stochastic vesicle dynamics on correlation transfer is lacking. We find that short-term synaptic depression and stochastic vesicle dynamics can substantially reduce correlations, shape the timescale over which these correlations occur, and alter the dependence of spiking correlations on firing rate. Our results show that short-term depression and stochastic vesicle dynamics need to be taken into account when modeling correlations in neuronal populations.
Directory of Open Access Journals (Sweden)
Dongping Wei
2015-01-01
Full Text Available Management of ecological tourism in protected areas faces many challenges, with visitation-related resource degradations and cultural impacts being two of them. To address those issues, several strategies including regulations, site managements, and visitor education programs have been commonly used in China and other countries. This paper presents a multiparameter stochastic differential equation model of an Ecological Tourism System to study how the populations of stakeholders vary in a finite time. The solution of Ordinary Differential Equation of Ecological Tourism System reveals that the system collapses when there is a lack of visitor educational intervention. Hence, the Stochastic Dynamic of Ecological Tourism System is introduced to suppress the explosion of the system. But the simulation results of the Stochastic Dynamic of Ecological Tourism System show that the system is still unstable and chaos in some small time interval. The Multiparameters Stochastic Dynamics of Ecological Tourism System is proposed to improve the performance in this paper. The Multiparameters Stochastic Dynamics of Ecological Tourism System not only suppresses the explosion of the system in a finite time, but also keeps the populations of stakeholders in an acceptable level. In conclusion, the Ecological Tourism System develops steadily and sustainably when land managers employ effective visitor education intervention programs to deal with recreation impacts.
Huang, Yandong; Rüdiger, Sten; Shuai, Jianwei
2013-12-01
The random opening and closing of ion channels establishes channel noise, which can be approximated and included into stochastic differential equations (Langevin approach). The Langevin approach is often incorporated to model stochastic ion channel dynamics for systems with a large number of channels. Here, we introduce a discretization procedure of a channel-based Langevin approach to simulate the stochastic channel dynamics with small and intermediate numbers of channels. We show that our Langevin approach with discrete channel open fractions can give a good approximation of the original Markov dynamics even for only 10 K channels. We suggest that the better approximation by the discretized Langevin approach originates from the improved representation of events that trigger action potentials.
Energy Technology Data Exchange (ETDEWEB)
Huang, Yandong [Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005 (China); Rüdiger, Sten [Institute of Physics, Humboldt-Universität zu Berlin (Germany); Shuai, Jianwei, E-mail: jianweishuai@xmu.edu.cn [Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005 (China)
2013-12-13
The random opening and closing of ion channels establishes channel noise, which can be approximated and included into stochastic differential equations (Langevin approach). The Langevin approach is often incorporated to model stochastic ion channel dynamics for systems with a large number of channels. Here, we introduce a discretization procedure of a channel-based Langevin approach to simulate the stochastic channel dynamics with small and intermediate numbers of channels. We show that our Langevin approach with discrete channel open fractions can give a good approximation of the original Markov dynamics even for only 10 K{sup +} channels. We suggest that the better approximation by the discretized Langevin approach originates from the improved representation of events that trigger action potentials.
Energy Technology Data Exchange (ETDEWEB)
Rizzoni, G. (Michigan Univ., Ann Arbor, MI (USA). Dept. of Electrical Engineering and Computer Science)
1989-08-01
In-cylinder gas pressure has long been recognized as a fundamental measure of performance in the internal combustion engine. Among the issues that have been the subject of research in recent years is the study of the effects cyclic combustion variability has on the cycle-to-cycle and cylinder-to-cylinder fluctuations in combustion pressures. Some of the research problems pertaining to cyclic combustion variability are to reformulate from a perspective markedly different from the fluid dynamic and thermodynamic models which traditionally characterize this research: a system viewpoint is embraced to construct a stochastic model for the indicated pressure process and the dynamics of the internal combustion engine. First a deterministic model for the dynamics of the engine is described; then a stochastic model is proposed for the cylinder pressure process. The deterministic model and the stochastic representation are then tied together in a Kalman filter model. Experimental results are discussed to validate the models.
Kulasiri, Don
2002-01-01
Most of the natural and biological phenomena such as solute transport in porous media exhibit variability which can not be modeled by using deterministic approaches. There is evidence in natural phenomena to suggest that some of the observations can not be explained by using the models which give deterministic solutions. Stochastic processes have a rich repository of objects which can be used to express the randomness inherent in the system and the evolution of the system over time. The attractiveness of the stochastic differential equations (SDE) and stochastic partial differential equations (SPDE) come from the fact that we can integrate the variability of the system along with the scientific knowledge pertaining to the system. One of the aims of this book is to explaim some useufl concepts in stochastic dynamics so that the scientists and engineers with a background in undergraduate differential calculus could appreciate the applicability and appropriateness of these developments in mathematics. The ideas ...
Mechanisms of Avalanche Dynamics in a Stochastic Four-State Sandpile Model
Institute of Scientific and Technical Information of China (English)
张端明; 潘贵军; 雷雅洁
2003-01-01
We study the stochastic four-state sandpile model on the square lattice. The static and dynamical properties of the model are investigated and compared with the deterministic sandpile model of Bak, Tang, and Wiesenfeld [Phys. Rev. Lett. 59 (1987) 381]. The numerical results show that the stochastic model defines a new universality class with respect to the deterministic sandpile. We also find that the waves in an avalanche are uncorrelated in the stochastic model (in the BTW model, the waves in an avalanche are correlated). The physical origin of the critical behaviour of the stochastic model being different from that of the BTW model is ascribed to the ordering and deterministic property of the toppling law in the BTW model.
Directory of Open Access Journals (Sweden)
Zhi-Wen Zhu
2015-01-01
Full Text Available A kind of high-aspect-ratio shape memory alloy (SMA composite wing is proposed to reduce the wing’s fluttering. The nonlinear dynamic characteristics and optimal control of the SMA composite wings subjected to in-plane stochastic excitation are investigated where the great bending under the flight loads is considered. The stochastic stability of the system is analyzed, and the system’s response is obtained. The conditions of stochastic Hopf bifurcation are determined, and the probability density of the first-passage time is obtained. Finally, the optimal control strategy is proposed. Numerical simulation shows that the stability of the system varies with bifurcation parameters, and stochastic Hopf bifurcation appears in the process; the reliability of the system is improved through optimal control, and the first-passage time is delayed. Finally, the effects of the control strategy are proved by experiments. The results of this paper are helpful for engineering applications of SMA.
Dynamic data integration and stochastic inversion of a confined aquifer
Wang, D.; Zhang, Y.; Irsa, J.; Huang, H.; Wang, L.
2013-12-01
Much work has been done in developing and applying inverse methods to aquifer modeling. The scope of this paper is to investigate the applicability of a new direct method for large inversion problems and to incorporate uncertainty measures in the inversion outcomes (Wang et al., 2013). The problem considered is a two-dimensional inverse model (50×50 grid) of steady-state flow for a heterogeneous ground truth model (500×500 grid) with two hydrofacies. From the ground truth model, decreasing number of wells (12, 6, 3) were sampled for facies types, based on which experimental indicator histograms and directional variograms were computed. These parameters and models were used by Sequential Indicator Simulation to generate 100 realizations of hydrofacies patterns in a 100×100 (geostatistical) grid, which were conditioned to the facies measurements at wells. These realizations were smoothed with Simulated Annealing, coarsened to the 50×50 inverse grid, before they were conditioned with the direct method to the dynamic data, i.e., observed heads and groundwater fluxes at the same sampled wells. A set of realizations of estimated hydraulic conductivities (Ks), flow fields, and boundary conditions were created, which centered on the 'true' solutions from solving the ground truth model. Both hydrofacies conductivities were computed with an estimation accuracy of ×10% (12 wells), ×20% (6 wells), ×35% (3 wells) of the true values. For boundary condition estimation, the accuracy was within × 15% (12 wells), 30% (6 wells), and 50% (3 wells) of the true values. The inversion system of equations was solved with LSQR (Paige et al, 1982), for which coordinate transform and matrix scaling preprocessor were used to improve the condition number (CN) of the coefficient matrix. However, when the inverse grid was refined to 100×100, Gaussian Noise Perturbation was used to limit the growth of the CN before the matrix solve. To scale the inverse problem up (i.e., without smoothing
Sampling-Based RBDO Using Stochastic Sensitivity and Dynamic Kriging for Broader Army Applications
2011-08-09
AND DYNAMIC KRIGING FOR BROADER ARMY APPLICATIONS K.K. Choi, Ikjin Lee, Liang Zhao, and Yoojeong Noh Department of Mechanical and Industrial...Thus, for broader Army applications, a sampling-based RBDO method using surrogate model has been developed recently. The Dynamic Kriging (DKG) method...Uuing Stochastic Sensitivity and Dynamic Kriging for Broader Army Applications 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6
Energy Technology Data Exchange (ETDEWEB)
Benderskii, V. A., E-mail: bender@icp.ac.ru [Russian Academy of Sciences, Institute of Problems of Chemical Physics (Russian Federation); Kats, E. I., E-mail: efim.i.kats@gmail.com [Russian Academy of Sciences, Landau Institute for Theoretical Physics (Russian Federation)
2013-01-15
The quantum dynamics problem for a 1D chain consisting of 2N + 1 sites (N Much-Greater-Than 1) with the interaction of nearest neighbors and an impurity site at the middle differing in energy and in coupling constant from the sites of the remaining chain is solved analytically. The initial excitation of the impurity is accompanied by the propagation of excitation over the chain sites and with the emergence of Loschmidt echo (partial restoration of the impurity site population) in the recurrence cycles with a period proportional to N. The echo consists of the main (most intense) component modulated by damped oscillations. The intensity of oscillations increases with increasing cycle number and matrix element C of the interaction of the impurity site n = 0 with sites n = {+-}1 (0 < C {<=} 1; for the remaining neighboring sites, the matrix element is equal to unity). Mixing of the components of echo from neighboring cycles induces a transition from the regular to stochastic evolution. In the regular evolution region, the wave packet propagates over the chain at a nearly constant group velocity, embracing a number of sites varying periodically with time. In the stochastic regime, the excitation is distributed over a number of sites close to 2N, with the populations varying irregularly with time. The model explains qualitatively the experimental data on ballistic propagation of the vibrational energy in linear chains of CH{sub 2} fragments and predicts the possibility of a nondissipative energy transfer between reaction centers associated with such chains.
Stochastic dynamics of penetrable rods in one dimension: Entangled dynamics and transport properties
Energy Technology Data Exchange (ETDEWEB)
Craven, Galen T.; Popov, Alexander V.; Hernandez, Rigoberto, E-mail: hernandez@chemistry.gatech.edu [Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400 (United States)
2015-04-21
The dynamical properties of a system of soft rods governed by stochastic hard collisions (SHCs) have been determined over a varying range of softness using molecular dynamics simulations in one dimension and analytic theory. The SHC model allows for interpenetration of the system’s constituent particles in the simulations, generating overlapping clustering behavior analogous to the spatial structures observed in systems governed by deterministic bounded potentials. Through variation of an assigned softness parameter δ, the limiting ranges of intermolecular softness are bridged, connecting the limiting ensemble behavior from hard to ideal (completely soft). Various dynamical and structural observables are measured from simulation and compared to developed theoretical values. The spatial properties are found to be well predicted by theories developed for the deterministic penetrable-sphere model with a transformation from energetic to probabilistic arguments. While the overlapping spatial structures are complex, the dynamical properties can be adequately approximated through a theory built on impulsive interactions with Enskog corrections. Our theory suggests that as the softness of interaction is varied toward the ideal limit, correlated collision processes are less important to the energy transfer mechanism, and Markovian processes dominate the evolution of the configuration space ensemble. For interaction softness close to hard limit, collision processes are highly correlated and overlapping spatial configurations give rise to entanglement of single-particle trajectories.
Estimation of Dynamic Panel Data Models with Stochastic Volatility Using Particle Filters
Directory of Open Access Journals (Sweden)
Wen Xu
2016-10-01
Full Text Available Time-varying volatility is common in macroeconomic data and has been incorporated into macroeconomic models in recent work. Dynamic panel data models have become increasingly popular in macroeconomics to study common relationships across countries or regions. This paper estimates dynamic panel data models with stochastic volatility by maximizing an approximate likelihood obtained via Rao-Blackwellized particle filters. Monte Carlo studies reveal the good and stable performance of our particle filter-based estimator. When the volatility of volatility is high, or when regressors are absent but stochastic volatility exists, our approach can be better than the maximum likelihood estimator which neglects stochastic volatility and generalized method of moments (GMM estimators.
De Martino, S; Illuminati, F; Martino, Salvatore De; Siena, Silvio De; Illuminati, Fabrizio
1999-01-01
A recent proposal (see quant-ph/9803068) to simulate semiclassical corrections to classical dynamics by suitable classical stochastic fluctuations is applied to the specific instance of charged beam dynamics in particle accelerators. The resulting picture is that the collective beam dynamics, at the leading semiclassical order in Planck constant can be described by a particular diffusion process, the Nelson process, which is time-reversal invariant. Its diffusion coefficient $\\sqrt{N}\\lambda_{c}$ represents a semiclassical unit of emittance (here $N$ is the number of particles in the beam, and $\\lambda_{c}$ is the Compton wavelength). The stochastic dynamics of the Nelson type can be easily recast in the form of a Schroedinger equation, with the semiclassical unit of emittance replacing Planck constant. Therefore we provide a physical foundation to the several quantum-like models of beam dynamics proposed in recent years. We also briefly touch upon applications of the Nelson and Schroedinger formalisms to inc...
Stochastic modeling of uncertain mass characteristics in rigid body dynamics
Richter, Lanae A.; Mignolet, Marc P.
2017-03-01
This paper focuses on the formulation, assessment, and application of a modeling strategy of uncertainty on the mass characteristics of rigid bodies, i.e. mass, position of center of mass, and inertia tensor. These characteristics are regrouped into a 4×4 matrix the elements of which are represented as random variables with joint probability density function derived following the maximum entropy framework. This stochastic model is first shown to satisfy all properties expected of the mass and tensor of inertia of rigid bodies. Its usefulness and computational efficiency are next demonstrated on the behavior of a rigid body in pure rotation exhibiting significant uncertainty in mass distribution.
Research on Nonlinear and Stochastic Dynamics with Defense Applications
2009-03-30
sensitivity of phase-synchronization time in stochastic resonance: Theory and experiment," Physical Review E 75, 046205(1-5) (2007). • K. Park, Y...34 Physical Review E 77, 026210(1-6) (2008). • Q.-F. Chen, L. Huang, and Y.-C. Lai, "Chaos-induced intrinsic localized modes in coupled mir...localized modes in micro-oscillator ar- rays," submitted to Physical Review E. Small-sized systems such as MEM resonators have become common in many
Dynamic Asset Allocation with Stochastic Income and Interest Rates
DEFF Research Database (Denmark)
Munk, Claus; Sørensen, Carsten
2010-01-01
We solve for optimal portfolios when interest rates and labor income are stochastic with the expected income growth being affine in the short-term interest rate in order to encompass business cycle variations in wages. Our calibration based on the Panel Study of Income Dynamics (PSID) data supports...
Inter-species competition-facilitation in stochastic riparian vegetation dynamics.
Tealdi, Stefano; Camporeale, Carlo; Ridolfi, Luca
2013-02-07
Riparian vegetation is a highly dynamic community that lives on river banks and which depends to a great extent on the fluvial hydrology. The stochasticity of the discharge and erosion/deposition processes in fact play a key role in determining the distribution of vegetation along a riparian transect. These abiotic processes interact with biotic competition/facilitation mechanisms, such as plant competition for light, water, and nutrients. In this work, we focus on the dynamics of plants characterized by three components: (1) stochastic forcing due to river discharges, (2) competition for resources, and (3) inter-species facilitation due to the interplay between vegetation and fluid dynamics processes. A minimalist stochastic bio-hydrological model is proposed for the dynamics of the biomass of two vegetation species: one species is assumed dominant and slow-growing, the other is subdominant, but fast-growing. The stochastic model is solved analytically and the probability density function of the plant biomasses is obtained as a function of both the hydrologic and biologic parameters. The impact of the competition/facilitation processes on the distribution of vegetation species along the riparian transect is investigated and remarkable effects are observed. Finally, a good qualitative agreement is found between the model results and field data.
A stochastic differential equation framework for the timewise dynamics of turbulent velocities
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Schmiegel, Jürgen
2008-01-01
We discuss a stochastic differential equation as a modeling framework for the timewise dynamics of turbulent velocities. The equation is capable of capturing basic stylized facts of the statistics of temporal velocity increments. In particular, we focus on the evolution of the probability density...
Directory of Open Access Journals (Sweden)
Anders Gjelsvik
1982-07-01
Full Text Available A first-order differential dynamic programming (DDP algorithm is used for computing optimal control for a five-reservoir system, where the stochastic inflow process has been approximated by a few discrete disturbance values in each time step. The method is found to be faster than linear programming, previously tried on the same system model.
Noussair, C.N.; Pfajfar, D.; Zsiros, J.
2011-01-01
New Keynesian dynamic stochastic general equilibrium models are the principal paradigm currently employed for central bank policymaking. In this paper, we construct experimental economies, populated with human subjects, with the structure of a New Keynesian DSGE model. We give individuals monetary
Directory of Open Access Journals (Sweden)
Jingtao Shi
2013-01-01
Full Text Available This paper is concerned with the relationship between maximum principle and dynamic programming for stochastic recursive optimal control problems. Under certain differentiability conditions, relations among the adjoint processes, the generalized Hamiltonian function, and the value function are given. A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result.
Who Is Afraid of Liquidity Risk? : Dynamic Portfolio Choice with Stochastic Illiquidity
J.J.A.G. Driessen (Joost); R. Xing (Rang)
2016-01-01
textabstractRecent empirical work documents large liquidity risk premiums in stock markets. We calculate the liquidity risk premiums demanded by large investors by solving a dynamic portfolio choice problem with stochastic price impact of trading, CRRA utility and a time-varying investment
Who Is Afraid of Liquidity Risk? : Dynamic Portfolio Choice with Stochastic Illiquidity
J.J.A.G. Driessen (Joost); R. Xing (Rang)
2016-01-01
textabstractRecent empirical work documents large liquidity risk premiums in stock markets. We calculate the liquidity risk premiums demanded by large investors by solving a dynamic portfolio choice problem with stochastic price impact of trading, CRRA utility and a time-varying investment opportuni
Noussair, C.N.; Pfajfar, D.; Zsiros, J.
2011-01-01
New Keynesian dynamic stochastic general equilibrium models are the principal paradigm currently employed for central bank policymaking. In this paper, we construct experimental economies, populated with human subjects, with the structure of a New Keynesian DSGE model. We give individuals monetary i
Is There Really a Global Business Cycle? : A Dynamic Factor Model with Stochastic Factor Selection
T. Berger (Tino); L.C.G. Pozzi (Lorenzo)
2016-01-01
textabstractWe investigate the presence of international business cycles in macroeconomic aggregates (output, consumption, investment) using a panel of 60 countries over the period 1961-2014. The paper presents a Bayesian stochastic factor selection approach for dynamic factor models with
Stability analysis of associative memory network composed of stochastic neurons and dynamic synapses
Directory of Open Access Journals (Sweden)
Yuichi eKatori
2013-02-01
Full Text Available We investigate the dynamical properties of an associative memory network consisting of stochastic neurons and dynamic synapses that show short-term depression and facilitation. In the stochastic neuron model used in this study, the eﬃcacy of the synaptic transmission changes according to the short-term depression or facilitation mechanism. We derive a macroscopic mean ﬁeld model that captures the overall dynamical properties of the stochastic model. We analyze the stability and bifurcation structure of the mean ﬁeld model, and show the dependence of the memory retrieval performance on the noise intensity and parameters that determine the properties of the dynamic synapses, i.e., time constants for depressing and facilitating processes. The associative memory network exhibits a variety of dynamical states, including the memory and pseudo-memory states, as well as oscillatory states among memory patterns. This study provides comprehensive insight into the dynamical properties of the associative memory network with dynamic synapses.
Kuehn, Christian
2011-01-01
Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms "critical transition" or "tipping point" have been used to describe this situation. Critical transitions have been observed in an astonishingly diverse set of applications from ecosystems and climate change to medicine and finance. The goal of this paper is to bring together a variety of techniques from dynamical systems theory to analyze critical transitions. In particular, we shall focus on identifying indicators for catastrophic shifts in the dynamics. Starting from classical bifurcation theory and incorporating multiple time scale dynamics we are able to give a detailed analysis of local bifurcations that induce critical transitions. We characterize several early warning signs for a transition such as slowing down and bifurcation delay. Then we take into account stochastic effects and proceed to model critical transitions by fast-slow stochastic differential equations. The interplay betw...
Jiang, Shixiao W.; Lu, Haihao; Zhou, Douglas; Cai, David
2016-08-01
Characterizing dispersive wave turbulence in the long time dynamics is central to understanding of many natural phenomena, e.g., in atmosphere ocean dynamics, nonlinear optics, and plasma physics. Using the β-Fermi-Pasta-Ulam nonlinear system as a prototypical example, we show that in thermal equilibrium and non-equilibrium steady state the turbulent state even in the strongly nonlinear regime possesses an effective linear stochastic structure in renormalized normal variables. In this framework, we can well characterize the spatiotemporal dynamics, which are dominated by long-wavelength renormalized waves. We further demonstrate that the energy flux is nearly saturated by the long-wavelength renormalized waves in non-equilibrium steady state. The scenario of such effective linear stochastic dynamics can be extended to study turbulent states in other nonlinear wave systems.
The Kac Model Coupled to a Thermostat
Bonetto, Federico; Loss, Michael; Vaidyanathan, Ranjini
2014-08-01
In this paper we study a model of randomly colliding particles interacting with a thermal bath. Collisions between particles are modeled via the Kac master equation while the thermostat is seen as an infinite gas at thermal equilibrium at inverse temperature . The system admits the canonical distribution at inverse temperature as the unique equilibrium state. We prove that any initial distribution approaches the equilibrium distribution exponentially fast both by computing the gap of the generator of the evolution, in a proper function space, as well as by proving exponential decay in relative entropy. We also show that the evolution propagates chaos and that the one particle marginal, in the large system limit, satisfies an effective Boltzmann-type equation.
Methodology Aspects of Quantifying Stochastic Climate Variability with Dynamic Models
Nuterman, Roman; Jochum, Markus; Solgaard, Anna
2015-04-01
The paleoclimatic records show that climate has changed dramatically through time. For the past few millions of years it has been oscillating between ice ages, with large parts of the continents covered with ice, and warm interglacial periods like the present one. It is commonly assumed that these glacial cycles are related to changes in insolation due to periodic changes in Earth's orbit around Sun (Milankovitch theory). However, this relationship is far from understood. The insolation changes are so small that enhancing feedbacks must be at play. It might even be that the external perturbation only plays a minor role in comparison to internal stochastic variations or internal oscillations. This claim is based on several shortcomings in the Milankovitch theory: Prior to one million years ago, the duration of the glacial cycles was indeed 41,000 years, in line with the obliquity cycle of Earth's orbit. This duration changed at the so-called Mid-Pleistocene transition to approximately 100,000 years. Moreover, according to Milankovitch's theory the interglacial of 400,000 years ago should not have happened. Thus, while prior to one million years ago the pacing of these glacial cycles may be tied to changes in Earth's orbit, we do not understand the current magnitude and phasing of the glacial cycles. In principle it is possible that the glacial/interglacial cycles are not due to variations in Earth's orbit, but due to stochastic forcing or internal modes of variability. We present a new method and preliminary results for a unified framework using a fully coupled Earth System Model (ESM), in which the leading three ice age hypotheses will be investigated together. Was the waxing and waning of ice sheets due to an internal mode of variability, due to variations in Earth's orbit, or simply due to a low-order auto-regressive process (i.e., noise integrated by system with memory)? The central idea is to use the Generalized Linear Models (GLM), which can handle both
Facilitating Energy Savings through Enhanced Usability of Thermostats
Energy Technology Data Exchange (ETDEWEB)
Meier, Alan; Aragon, Cecilia; Peffer, Therese; Perry, Daniel; Pritoni, Marco
2011-05-23
Residential thermostats play a key role in controlling heating and cooling systems. Occupants often find the controls of programmable thermostats confusing, sometimes leading to higher heating consumption than when the buildings are controlled manually. A high degree of usability is vital to a programmable thermostat's effectiveness because, unlike a more efficient heating system, occupants must engage in specific actions after installation to obtain energy savings. We developed a procedure for measuring the usability of thermostats and tested this methodology with 31 subjects on five thermostats. The procedure requires first identifying representative tasks associated with the device and then testing the subjects ability to accomplish those tasks. The procedure was able to demonstrate the subjects wide ability to accomplish tasks and the influence of a device's usability on success rates. A metric based on the time to accomplish the tasks and the fraction of subjects actually completing the tasks captured the key aspects of each thermostat's usability. The procedure was recently adopted by the Energy Star Program for its thermostat specification. The approach appears suitable for quantifying usability of controls in other products, such as heat pump water heaters and commercial lighting.
Simulation of quantum dynamics based on the quantum stochastic differential equation.
Li, Ming
2013-01-01
The quantum stochastic differential equation derived from the Lindblad form quantum master equation is investigated. The general formulation in terms of environment operators representing the quantum state diffusion is given. The numerical simulation algorithm of stochastic process of direct photodetection of a driven two-level system for the predictions of the dynamical behavior is proposed. The effectiveness and superiority of the algorithm are verified by the performance analysis of the accuracy and the computational cost in comparison with the classical Runge-Kutta algorithm.
Stochastic description of the dynamics of a random-exchange Heisenberg chain
Energy Technology Data Exchange (ETDEWEB)
Vainstein, M.H. [Instituto de Fisica and Nucleo de Supercomputacao e Sistemas Complexos, ICCMP, Universidade de Brasilia, CP 04513, 70919-970 Brasilia, DF (Brazil); Morgado, R. [Instituto de Fisica and Nucleo de Supercomputacao e Sistemas Complexos, ICCMP, Universidade de Brasilia, CP 04513, 70919-970 Brasilia, DF (Brazil); Oliveira, F.A. [Instituto de Fisica and Nucleo de Supercomputacao e Sistemas Complexos, ICCMP, Universidade de Brasilia, CP 04513, 70919-970 Brasilia, DF (Brazil); Moura, F.A.B.F. de [Laboratorio de Fisica Teorica e Computacional, Departamento de Fisica, Universidade Federal de Pernambuco, 50670-901 Recife, PE (Brazil) and Departamento de Fisica, Universidade Federal de Alagoas, 57072-970 Maceio, AL (Brazil)]. E-mail: fidelis@df.ufal.br; Coutinho-Filho, M.D. [Laboratorio de Fisica Teorica e Computacional, Departamento de Fisica, Universidade Federal de Pernambuco, 50670-901 Recife, PE (Brazil)
2005-05-16
We study the diffusion process in a Heisenberg chain with correlated spatial disorder, with a power spectrum in the momentum space behaving as k{sup -{beta}}, using a stochastic description. It establishes a direct connection between the fluctuation in the spin-wave density of states and the noise density of states. For continuous ranges of the exponent {beta}, we find superdiffusive and ballistic spin-wave motions. Both diffusion exponents predicted by the stochastic procedure agree with the ones calculated using the Hamiltonian dynamics.
Stochastic Properties of Neurotransmitter Release Expand the Dynamic Range of Synapses
Yang, Hua
2013-01-01
Release of neurotransmitter is an inherently random process, which could degrade the reliability of postsynaptic spiking, even at relatively large synapses. This is particularly important at auditory synapses, where the rate and precise timing of spikes carry information about sounds. However, the functional consequences of the stochastic properties of release are unknown. We addressed this issue at the mouse endbulb of Held synapse, which is formed by auditory nerve fibers onto bushy cells (BCs) in the anteroventral cochlear nucleus. We used voltage clamp to characterize synaptic variability. Dynamic clamp was used to compare BC spiking with stochastic or deterministic synaptic input. The stochastic component increased the responsiveness of the BC to conductances that were on average subthreshold, thereby increasing the dynamic range of the synapse. This had the benefit that BCs relayed auditory nerve activity even when synapses showed significant depression during rapid activity. However, the precision of spike timing decreased with stochastic conductances, suggesting a trade-off between encoding information in spike timing versus probability. These effects were confirmed in fiber stimulation experiments, indicating that they are physiologically relevant, and that synaptic randomness, dynamic range, and jitter are causally related. PMID:24005293
The Stochastic Multi-strain Dengue Model: Analysis of the Dynamics
Aguiar, Maíra; Stollenwerk, Nico; Kooi, Bob W.
2011-09-01
Dengue dynamics is well known to be particularly complex with large fluctuations of disease incidences. An epidemic multi-strain model motivated by dengue fever epidemiology shows deterministic chaos in wide parameter regions. The addition of seasonal forcing, mimicking the vectorial dynamics, and a low import of infected individuals, which is realistic in the dynamics of infectious diseases epidemics show complex dynamics and qualitatively a good agreement between empirical DHF monitoring data and the obtained model simulation. The addition of noise can explain the fluctuations observed in the empirical data and for large enough population size, the stochastic system can be well described by the deterministic skeleton.
A new and effective method for thermostatting confined fluids
DEFF Research Database (Denmark)
De Luca, Sergio; Billy, Todd; Hansen, Jesper Schmidt;
2014-01-01
We present a simple thermostatting method suitable for nanoconfined fluid systems. Two conventional strategies involve thermostatting the fluid directly or employing a thermal wall that couples only the wall atoms with the thermostat. When only a thermal wall is implemented, the temperature control......, particularly for large walls, since they can be kept rigid. Another advantage over accepted strategies is the opportunity to freeze complex charged walls such as β-cristobalite. The method furthermore overcomes the problem with polar fluids such as water, as thermalized charged surfaces require higher spring...
Threshold Dynamics in Stochastic SIRS Epidemic Models with Nonlinear Incidence and Vaccination
Wang, Lei; Tang, Tingting
2017-01-01
In this paper, the dynamical behaviors for a stochastic SIRS epidemic model with nonlinear incidence and vaccination are investigated. In the models, the disease transmission coefficient and the removal rates are all affected by noise. Some new basic properties of the models are found. Applying these properties, we establish a series of new threshold conditions on the stochastically exponential extinction, stochastic persistence, and permanence in the mean of the disease with probability one for the models. Furthermore, we obtain a sufficient condition on the existence of unique stationary distribution for the model. Finally, a series of numerical examples are introduced to illustrate our main theoretical results and some conjectures are further proposed. PMID:28194223
Metaheuristics for the dynamic stochastic dial-a-ride problem with expected return transports.
Schilde, M; Doerner, K F; Hartl, R F
2011-12-01
The problem of transporting patients or elderly people has been widely studied in literature and is usually modeled as a dial-a-ride problem (DARP). In this paper we analyze the corresponding problem arising in the daily operation of the Austrian Red Cross. This nongovernmental organization is the largest organization performing patient transportation in Austria. The aim is to design vehicle routes to serve partially dynamic transportation requests using a fixed vehicle fleet. Each request requires transportation from a patient's home location to a hospital (outbound request) or back home from the hospital (inbound request). Some of these requests are known in advance. Some requests are dynamic in the sense that they appear during the day without any prior information. Finally, some inbound requests are stochastic. More precisely, with a certain probability each outbound request causes a corresponding inbound request on the same day. Some stochastic information about these return transports is available from historical data. The purpose of this study is to investigate, whether using this information in designing the routes has a significant positive effect on the solution quality. The problem is modeled as a dynamic stochastic dial-a-ride problem with expected return transports. We propose four different modifications of metaheuristic solution approaches for this problem. In detail, we test dynamic versions of variable neighborhood search (VNS) and stochastic VNS (S-VNS) as well as modified versions of the multiple plan approach (MPA) and the multiple scenario approach (MSA). Tests are performed using 12 sets of test instances based on a real road network. Various demand scenarios are generated based on the available real data. Results show that using the stochastic information on return transports leads to average improvements of around 15%. Moreover, improvements of up to 41% can be achieved for some test instances.
Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems.
Venturi, D; Karniadakis, G E
2014-06-08
Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima-Zwanzig-Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection-reaction problems.
General formalism for singly thermostated Hamiltonian dynamics.
Ramshaw, John D
2015-11-01
A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems are ergodic, canonical ensemble averages can be computed as dynamical time averages over a single trajectory. Systems of this type were unknown until their recent discovery by Hoover and colleagues. The present formalism should facilitate the discovery, construction, and classification of other such systems by encompassing a wide class of them within a single unified framework. This formalism includes both canonical and generalized Hamiltonian systems in a state space of arbitrary dimensionality (either even or odd) and therefore encompasses both few- and many-particle systems. Particular attention is devoted to the physical motivation and interpretation of the formalism, which largely determine its structure. An analogy to stochastic thermostats and fluctuation-dissipation theorems is briefly discussed.
Emergence of Dynamic Cooperativity in the Stochastic Kinetics of Fluctuating Enzymes
Kumar, Ashutosh; Nandi, Mintu; Dua, Arti
2016-01-01
Dynamic cooperativity in monomeric enzymes is characterized in terms of a non-Michaelis-Menten kinetic behaviour. The latter is believed to be associated with mechanisms that include multiple reaction pathways due to enzymatic conformational fluctuations. Recent advances in single-molecule fluorescence spectroscopy have provided new fundamental insights on the possible mechanisms underlying reactions catalyzed by fluctuating enzymes. Here, we present a bottom-up approach to understand enzyme turnover kinetics at physiologically relevant mesoscopic concentrations informed by mechanisms extracted from single-molecule stochastic trajectories. The stochastic approach, presented here, shows the emergence of dynamic cooperativity in terms of a slowing down of the Michaelis-Menten (MM) kinetics resulting in negative cooperativity. For fewer enzymes, dynamic cooperativity emerges due to the combined effects of enzymatic conformational fluctuations and molecular discreteness. The increase in the number of enzymes, how...
Langevin approach with rescaled noise for stochastic channel dynamics in Hodgkin-Huxley neurons
Huang, Yan-Dong; Xiang, Li; Shuai, Jian-Wei
2015-12-01
The Langevin approach has been applied to model the random open and closing dynamics of ion channels. It has long been known that the gate-based Langevin approach is not sufficiently accurate to reproduce the statistics of stochastic channel dynamics in Hodgkin-Huxley neurons. Here, we introduce a modified gate-based Langevin approach with rescaled noise strength to simulate stochastic channel dynamics. The rescaled independent gate and identical gate Langevin approaches improve the statistical results for the mean membrane voltage, inter-spike interval, and spike amplitude. Project supported by the National Natural Science Foundation for Distinguished Young Scholars of China (Grant No. 11125419), the National Natural Science Foundation of China (Grant No. 10925525), and the Funds for the Leading Talents of Fujian Province, China.
Fuzzy-stochastic functor machine for general humanoid-robot dynamics.
Ivancevic, V G; Snoswell, M
2001-01-01
In this paper the fuzzy-stochastic-Hamiltonian functor-machine is proposed as a general model for the humanoid-robot dynamics, including all necessary degrees of freedom to match the "realistic" human-like motion. Starting with the continual-sequential generalization of the standard state equation for the linear MIMO-systems, the "meta-cybernetic" model of the "functor-machine" is developed as a three-stage nonlinear description of humanoid dynamics: (1) dissipative, muscle-driven Hamiltonian dynamics, (2) stochastic fluctuations and discrete jumps, and (3) fuzzy inputs, parameters and initial conditions. An example of symmetrical three-dimensional (3-D) load-lifting is used to illustrate all the phases in developing the functor-machine model.
Energy Technology Data Exchange (ETDEWEB)
Guo, Kong-Ming, E-mail: kmguo@xidian.edu.cn [School of Electromechanical Engineering, Xidian University, P.O. Box 187, Xi' an 710071 (China); Jiang, Jun, E-mail: jun.jiang@mail.xjtu.edu.cn [State Key Laboratory for Strength and Vibration, Xi' an Jiaotong University, Xi' an 710049 (China)
2014-07-04
To apply stochastic sensitivity function method, which can estimate the probabilistic distribution of stochastic attractors, to non-autonomous dynamical systems, a 1/N-period stroboscopic map for a periodic motion is constructed in order to discretize the continuous cycle into a discrete one. In this way, the sensitivity analysis of a cycle for discrete map can be utilized and a numerical algorithm for the stochastic sensitivity analysis of periodic solutions of non-autonomous nonlinear dynamical systems under stochastic disturbances is devised. An external excited Duffing oscillator and a parametric excited laser system are studied as examples to show the validity of the proposed method. - Highlights: • A method to analyze sensitivity of stochastic periodic attractors in non-autonomous dynamical systems is proposed. • Probabilistic distribution around periodic attractors in an external excited Φ{sup 6} Duffing system is obtained. • Probabilistic distribution around a periodic attractor in a parametric excited laser system is determined.
Stochastic collective dynamics of charged-particle beams in the stability regime.
Petroni, N C; De Martino, S; De Siena, S; Illuminati, F
2001-01-01
We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations. In this scheme, the collective beam dynamics is described by time-reversal invariant diffusion processes deduced by stochastic variational principles (Nelson processes). By general arguments, we show that the diffusion coefficient, expressed in units of length, is given by lambda(c)sqrt[N], where N is the number of particles in the beam and lambda(c) the Compton wavelength of a single constituent. This diffusion coefficient represents an effective unit of beam emittance. The hydrodynamic equations of the stochastic dynamics can be easily recast in the form of a Schrödinger equation, with the unit of emittance replacing the Planck action constant. This fact provides a natural connection to the so-called "quantum-like approaches" to beam dynamics. The transition probabilities associated to Nelson processes can be exploited to model evolutions suitable to control the transverse beam dynamics. In particular we show how to control, in the quadrupole approximation to the beam-field interaction, both the focusing and the transverse oscillations of the beam, either together or independently.
An explicit algorithm for fully flexible unit cell simulation with recursive thermostat chains.
Jung, Kwangsub; Cho, Maenghyo
2008-10-28
Through the combination of the recursive multiple thermostat (RMT) Nose-Poincare and Parrinello-Rahman methods, the recursive multiple thermostat chained fully flexible unit cell (RMT-NsigmaT) molecular dynamics method is proposed for isothermal-isobaric simulation. The RMT method is known to have the advantage of achieving the ergodicity that is required for canonical sampling of the harmonic oscillator. Thus, an explicit time integration algorithm is developed for RMT-NsigmaT. We examine the ergodicity for various parameters of RMT-NsigmaT using bulk and thin film structures with different numbers of copper atoms and thicknesses in various environments. Through the numerical simulations, we conclude that the RMT-NsigmaT method is advantageous in the cases of lower temperatures.
Computing the optimal path in stochastic dynamical systems.
Bauver, Martha; Forgoston, Eric; Billings, Lora
2016-08-01
In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensional system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly simple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higher-dimensional spaces.
Computing the optimal path in stochastic dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Bauver, Martha; Forgoston, Eric, E-mail: eric.forgoston@montclair.edu; Billings, Lora [Department of Mathematical Sciences, Montclair State University, 1 Normal Avenue, Montclair, New Jersey 07043 (United States)
2016-08-15
In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensional system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly simple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higher-dimensional spaces.
Stochastic dynamics of Arctic sea ice Part II: Multiplicative noise
Moon, Woosok
2015-01-01
We analyze the numerical solutions of a stochastic Arctic sea ice model with multiplicative noise over a wide range of external heat-fluxes, $\\Delta F_0$, which correspond to greenhouse gas forcing. When the noise is multiplicative, the noise-magnitude depends on the state-variable, and this will influence the statistical moments in a manner that differs from the additive case, which we analyzed in Part I of this study. The state variable describing the deterministic backbone of our model is the energy, $E(t)$, contained in the ice or the ocean and for a thorough comparison and contrast we choose the simplest form of multiplicative noise $\\sigma E(t) \\xi(t)$, where $\\sigma$ is the noise amplitude and $\\xi(t)$ is the noise process. The case of constant additive noise (CA) we write as $\\sigma\\overline{E_S}\\xi(t)$, in which $\\overline{E_S}$ is the seasonally averaged value of the periodic deterministic steady-state solution $E_S(t)$, or the deterministic seasonal cycle. We then treat the case of seasonally-varyi...
2015-11-30
Scientific Publishing Company DOI : 10.1142/S0219024915500521 OPTION PRICING WITH A LEVY-TYPE STOCHASTIC DYNAMIC MODEL FOR STOCK PRICE PROCESS UNDER SEMI...Applebaum (2009) Levy Processes and Stochastic Calculus . Cambridge University Press. K. Back & S. R. Pliska (1991) On the fundamental theorem of asset
Efficient Algorithms for Langevin and DPD Dynamics.
Goga, N; Rzepiela, A J; de Vries, A H; Marrink, S J; Berendsen, H J C
2012-10-09
In this article, we present several algorithms for stochastic dynamics, including Langevin dynamics and different variants of Dissipative Particle Dynamics (DPD), applicable to systems with or without constraints. The algorithms are based on the impulsive application of friction and noise, thus avoiding the computational complexity of algorithms that apply continuous friction and noise. Simulation results on thermostat strength and diffusion properties for ideal gas, coarse-grained (MARTINI) water, and constrained atomic (SPC/E) water systems are discussed. We show that the measured thermal relaxation rates agree well with theoretical predictions. The influence of various parameters on the diffusion coefficient is discussed.
Stochastic lattice gas model describing the dynamics of the SIRS epidemic process
de Souza, David R.; Tomé, Tânia
2010-03-01
We study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed of individuals of three classes: susceptible (S), infected (I), and recovered (R). The stochastic process is defined by local rules and involves the following cyclic process: S → I → R → S (SIRS). The open process S → I → R (SIR) is studied as a particular case of the SIRS process. The epidemic process is analyzed at different levels of description: by a stochastic lattice gas model and by a birth and death process. By means of Monte Carlo simulations and dynamical mean-field approximations we show that the SIRS stochastic lattice gas model exhibit a line of critical points separating the two phases: an absorbing phase where the lattice is completely full of S individuals and an active phase where S, I and R individuals coexist, which may or may not present population cycles. The critical line, that corresponds to the onset of epidemic spreading, is shown to belong in the directed percolation universality class. By considering the birth and death process we analyze the role of noise in stabilizing the oscillations.
Institute of Scientific and Technical Information of China (English)
Shao Yuan-Zhi; Zhong Wei-Rong; Lin Guang-Ming; Li Jian-Can
2005-01-01
The dynamic response and stochastic resonance of a kinetic Ising spin system (ISS) subject to the joint action of an external field of weak sinusoidal modulation and stochastic white-noise are studied by solving the mean-field equation of motion based on Glauber dynamics. The periodically driven stochastic ISS shows that the characteristic stochastic resonance as well as nonequilibrium dynamic phase transition (NDPT) occurs when the frequency ω and amplitude h0 of driving field, the temperature t of the system and noise intensity D are all specifically in accordance with each other in quantity. There exist in the system two typical dynamic phases, referred to as dynamic disordered paramagnetic and ordered ferromagnetic phases respectively, corresponding to a zero- and a unit-dynamic order parameter. The NDPT boundary surface of the system which separates the dynamic paramagnetic phase from the dynamic ferromagnetic phase in the 3D parameter space of h0-t-D is also investigated. An interesting dynamical ferromagnetic phase with an intermediate order parameter of 0.66 is revealed for the first time in the ISS subject to the perturbation of a joint determinant and stochastic field. The intermediate order dynamical ferromagnetic phase is dynamically metastable in nature and owns a peculiar characteristic in its stability as well as the response to external driving field as compared with a fully order dynamic ferromagnetic phase.
Role of energy distribution in contacts on thermal transport in Si: A molecular dynamics study
Dunn, Jonathan; Antillon, Edwin; Maassen, Jesse; Lundstrom, Mark; Strachan, Alejandro
2016-12-01
We use molecular dynamics simulations to investigate how the energy input and distribution in contacts affect the thermal transport in silicon as described by the Stillinger-Webber potential. We create a temperature difference across a Si specimen by maintaining the temperature of two contacts (also made of Si) using widely used thermostats: the deterministic Nosé-Hoover approach and a stochastic Langevin bath. Quite surprisingly, the phonon thermal conductivity of the channel obtained using the two thermostats but under otherwise identical conditions can differ by a factor of up to three. The discrepancy between the two methods vanishes as the coupling strength between the thermostat and material is reduced and for long channels. A spectral analysis of the contacts and channel shows that increasing the coupling of the stochastic Langevin thermostat affects the spectral energy distribution in the contacts away from that based on the vibrational density of states, broadening peaks and smoothening the distribution. This results in contacts injecting phonons preferentially in low frequency modes and in transport through the channel away from local equilibrium. A comparison of the MD results with Boltzmann transport equation simulations provides an additional insight into the role of contacts on thermal transport in nanoscale specimens. These results stress the importance of contacts in nanoscale thermal transport in simulations and in the interpretation of experimental data.
Stochastic modelling of soil moisture dynamics in a grassland of Qilian Mountain at point scale
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Stochastic modeling of soil moisture dynamics is crucial to the quantitative understanding of plant responses to water stresses, hydrological control of nutrient cycling processes, water competition among plants, and some other ecological dynamics, and thus has become a hotspot in ecohydrology at present. In this paper, we based on the continuously monitored data of soil moisture during 2002-2005 and daily precipitation date of 1992-2006, and tried to make a probabilistic analysis of soil moisture dynamics at point scale in a grassland of Qilian Mountain by integrating the stochastic model improved by Laio and the Monte Carlo method. The results show that the inter-annual variations for the soil moisture patterns at different depths are very significant, and that the coefficient of variance (CV) of surface soil moisture (20 cm) is almost continually kept at about 0.23 whether in the rich or poor rainy years. Interestingly, it has been found that the maximal CV of soil moisture has not always appeared at the surface layer. Comparison of the analytically derived soil moisture probability density function (PDF) with the statistical distribution of the observed soil moisture data suggests that the stochastic model can reasonably describe and predict the soil moisture dynamics of the grassland in Qilian Mountain at point scale. By extracting the statistical information of the historical precipitation data in 1994-2006, and inputting them into the stochastic model, we analytically derived the long-term soil moisture PDF without considering the inter-annual climate fluctuations, and then numerically derived the one when considering the inter-annual fluctuation effects in combination with a Monte-Carlo procedure. It was found that, though the peak position of the probability density distribution significantly moved towards drought when considering the disturbance forces, and its width was narrowed, accordingly its peak value was increased, no significant bimodality was
Fixation, transient landscape, and diffusion dilemma in stochastic evolutionary game dynamics.
Zhou, Da; Qian, Hong
2011-09-01
Agent-based stochastic models for finite populations have recently received much attention in the game theory of evolutionary dynamics. Both the ultimate fixation and the pre-fixation transient behavior are important to a full understanding of the dynamics. In this paper, we study the transient dynamics of the well-mixed Moran process through constructing a landscape function. It is shown that the landscape playing a central theoretical "device" that integrates several lines of inquiries: the stable behavior of the replicator dynamics, the long-time fixation, and continuous diffusion approximation associated with asymptotically large population. Several issues relating to the transient dynamics are discussed: (i) multiple time scales phenomenon associated with intra- and inter-attractoral dynamics; (ii) discontinuous transition in stochastically stationary process akin to Maxwell construction in equilibrium statistical physics; and (iii) the dilemma diffusion approximation facing as a continuous approximation of the discrete evolutionary dynamics. It is found that rare events with exponentially small probabilities, corresponding to the uphill movements and barrier crossing in the landscape with multiple wells that are made possible by strong nonlinear dynamics, plays an important role in understanding the origin of the complexity in evolutionary, nonlinear biological systems.
Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes.
Kumar, Ashutosh; Chatterjee, Sambarta; Nandi, Mintu; Dua, Arti
2016-08-28
Dynamic co-operativity in monomeric enzymes is characterized in terms of a non-Michaelis-Menten kinetic behaviour. The latter is believed to be associated with mechanisms that include multiple reaction pathways due to enzymatic conformational fluctuations. Recent advances in single-molecule fluorescence spectroscopy have provided new fundamental insights on the possible mechanisms underlying reactions catalyzed by fluctuating enzymes. Here, we present a bottom-up approach to understand enzyme turnover kinetics at physiologically relevant mesoscopic concentrations informed by mechanisms extracted from single-molecule stochastic trajectories. The stochastic approach, presented here, shows the emergence of dynamic co-operativity in terms of a slowing down of the Michaelis-Menten (MM) kinetics resulting in negative co-operativity. For fewer enzymes, dynamic co-operativity emerges due to the combined effects of enzymatic conformational fluctuations and molecular discreteness. The increase in the number of enzymes, however, suppresses the effect of enzymatic conformational fluctuations such that dynamic co-operativity emerges solely due to the discrete changes in the number of reacting species. These results confirm that the turnover kinetics of fluctuating enzyme based on the parallel-pathway MM mechanism switches over to the single-pathway MM mechanism with the increase in the number of enzymes. For large enzyme numbers, convergence to the exact MM equation occurs in the limit of very high substrate concentration as the stochastic kinetics approaches the deterministic behaviour.
A bi-level approximation tool for the computation of FRFs in stochastic dynamic systems
Chatterjee, Tanmoy; Chakraborty, Souvik; Chowdhury, Rajib
2016-03-01
Frequency response functions (FRFs) are considered to be a significant aspect in the evaluation of structural response subjected to dynamic loading. A new approach, referred to as the hybrid polynomial correlated function expansion (H-PCFE) has been developed for predicting the natural frequencies and the FRF of stochastic dynamical systems. H-PCFE has been developed by incorporating the advantages of two available techniques namely, PCFE and Gaussian process (GP) modeling. These two methods are coupled in such a way that PCFE handles the global behavior of the model using a set of component functions and GP interpolates local variations as a function of the sample points, performing as a two level approximation. Implementation of the proposed approach for stochastic dynamic problems has been demonstrated with four problems. The main focus of this study lies in the prediction of FRFs. The efficiency and accuracy of H-PCFE to compute FRFs of stochastic dynamic systems is assessed by a comparison with direct Monte Carlo simulation (MCS). Excellent results in terms of accuracy and computational effort obtained makes the proposed methodology potential for application in large scale structural applications.
Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes
Kumar, Ashutosh; Chatterjee, Sambarta; Nandi, Mintu; Dua, Arti
2016-08-01
Dynamic co-operativity in monomeric enzymes is characterized in terms of a non-Michaelis-Menten kinetic behaviour. The latter is believed to be associated with mechanisms that include multiple reaction pathways due to enzymatic conformational fluctuations. Recent advances in single-molecule fluorescence spectroscopy have provided new fundamental insights on the possible mechanisms underlying reactions catalyzed by fluctuating enzymes. Here, we present a bottom-up approach to understand enzyme turnover kinetics at physiologically relevant mesoscopic concentrations informed by mechanisms extracted from single-molecule stochastic trajectories. The stochastic approach, presented here, shows the emergence of dynamic co-operativity in terms of a slowing down of the Michaelis-Menten (MM) kinetics resulting in negative co-operativity. For fewer enzymes, dynamic co-operativity emerges due to the combined effects of enzymatic conformational fluctuations and molecular discreteness. The increase in the number of enzymes, however, suppresses the effect of enzymatic conformational fluctuations such that dynamic co-operativity emerges solely due to the discrete changes in the number of reacting species. These results confirm that the turnover kinetics of fluctuating enzyme based on the parallel-pathway MM mechanism switches over to the single-pathway MM mechanism with the increase in the number of enzymes. For large enzyme numbers, convergence to the exact MM equation occurs in the limit of very high substrate concentration as the stochastic kinetics approaches the deterministic behaviour.
Stochastic dynamics of model proteins on a directed graph.
Bongini, Lorenzo; Casetti, Lapo; Livi, Roberto; Politi, Antonio; Torcini, Alessandro
2009-06-01
A method for reconstructing the potential energy landscape of simple polypeptidic chains is described. We show how to obtain a faithful representation of the energy landscape in terms of a suitable directed graph. Topological and dynamical indicators of the graph are shown to yield an effective estimate of the time scales associated with both folding and equilibration processes. This conclusion is drawn by comparing molecular dynamics simulations at constant temperature with the dynamics on the graph, defined as a temperature-dependent Markov process. The main advantage of the graph representation is that its dynamics can be naturally renormalized by collecting nodes into "hubs" while redefining their connectivity. We show that the dynamical properties at large time scales are preserved by the renormalization procedure. Moreover, we obtain clear indications that the heteropolymers exhibit common topological properties, at variance with the homopolymer, whose peculiar graph structure stems from its spatial homogeneity. In order to distinguish between "fast" and "slow" folders, one has to look at the kinetic properties of the corresponding directed graphs. In particular, we find that the average time needed to the fast folder for reaching its native configuration is two orders of magnitude smaller than its equilibration time while for the bad folder these time scales are comparable.
Energy, Carbon-emission and Financial Savings from Thermostat Control
Energy Technology Data Exchange (ETDEWEB)
Blasing, T J [ORNL; Schroeder, Dana [University of Georgia, Athens, GA
2013-08-01
Among the easiest approaches to energy, and cost, savings for most people is the adjustment of thermostats to save energy. Here we estimate savings of energy, carbon, and money in the United States of America (USA) that would result from adjusting thermostats in residential and commercial buildings by about half a degree Celsius downward during the heating season and upward during the cooling season. To obtain as small a unit as possible, and therefore the least likely to be noticeable by most people, we selected an adjustment of one degree Fahrenheit (0.56 degree Celsius) which is the gradation used almost exclusively on thermostats in the USA and is the smallest unit of temperature that has been used historically. Heating and/or cooling of interior building space for personal comfort is sometimes referred to as space conditioning, a term we will use for convenience throughout this work without consideration of humidity. Thermostat adjustment, as we use the term here, applies to thermostats that control the indoor temperature, and not to other thermostats such as those on water heaters. We track emissions of carbon only, rather than of carbon dioxide, because carbon atoms change atomic partners as they move through the carbon cycle, from atmosphere to biosphere or ocean and, on longer time scales, through the rock cycle. To convert a mass of carbon to an equivalent mass of carbon dioxide (thereby including the mass of the 2 oxygen atoms in each molecule) simply multiply by 3.67.
Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows
Ueckermann, M. P.; Lermusiaux, P. F. J.; Sapsis, T. P.
2013-01-01
The quantification of uncertainties is critical when systems are nonlinear and have uncertain terms in their governing equations or are constrained by limited knowledge of initial and boundary conditions. Such situations are common in multiscale, intermittent and non-homogeneous fluid and ocean flows. The dynamically orthogonal (DO) field equations provide an adaptive methodology to predict the probability density functions of such flows. The present work derives efficient computational schemes for the DO methodology applied to unsteady stochastic Navier-Stokes and Boussinesq equations, and illustrates and studies the numerical aspects of these schemes. Semi-implicit projection methods are developed for the mean and for the DO modes, and time-marching schemes of first to fourth order are used for the stochastic coefficients. Conservative second-order finite-volumes are employed in physical space with new advection schemes based on total variation diminishing methods. Other results include: (i) the definition of pseudo-stochastic pressures to obtain a number of pressure equations that is linear in the subspace size instead of quadratic; (ii) symmetric advection schemes for the stochastic velocities; (iii) the use of generalized inversion to deal with singular subspace covariances or deterministic modes; and (iv) schemes to maintain orthonormal modes at the numerical level. To verify our implementation and study the properties of our schemes and their variations, a set of stochastic flow benchmarks are defined including asymmetric Dirac and symmetric lock-exchange flows, lid-driven cavity flows, and flows past objects in a confined channel. Different Reynolds number and Grashof number regimes are employed to illustrate robustness. Optimal convergence under both time and space refinements is shown as well as the convergence of the probability density functions with the number of stochastic realizations.
Equilibrium solutions for microscopic stochastic systems in population dynamics.
Lachowicz, Mirosław; Ryabukha, Tatiana
2013-06-01
The present paper deals with the problem of existence of equilibrium solutions of equations describing the general population dynamics at the microscopic level of modified Liouville equation (individually--based model) corresponding to a Markov jump process. We show the existence of factorized equilibrium solutions and discuss uniqueness. The conditions guaranteeing uniqueness or non-uniqueness are proposed under the assumption of periodic structures.
Stochastic dynamics of a trapped Bose-Einstein condensate
Duine, R.A.; Stoof, H.T.C.
2001-01-01
We present a variational solution of the Langevin field equation describing the nonequilibrium dynamics of a harmonically trapped Bose-Einstein condensate. If the thermal cloud remains in equilibrium at all times, we find that the equations of motion for the parameters in our variational ansatz are
Stochastic dynamics of a trapped Bose-Einstein condensate
Duine, R.A.; Stoof, H.T.C.
2001-01-01
We present a varional solution of the Langevin field equation describing the nonequilibrium dynamics of a harmonically trapped Bese-Einsten condensate. If the thermal cloud remains in equilibrium at all times, we find that the equation of motions for the parameters in our variational ansatz are equi
Stochastic simulation of HIV population dynamics through complex network modelling
Sloot, P.M.A.; Ivanov, S.V.; Boukhanovsky, A.V.; van de Vijver, D.A.M.C.; Boucher, C.A.B.
2008-01-01
We propose a new way to model HIV infection spreading through the use of dynamic complex networks. The heterogeneous population of HIV exposure groups is described through a unique network degree probability distribution. The time evolution of the network nodes is modelled by a Markov process and
Stochastic simulation of HIV population dynamics through complex network modelling
Sloot, P. M. A.; Ivanov, S. V.; Boukhanovsky, A. V.; van de Vijver, D. A. M. C.; Boucher, C. A. B.
We propose a new way to model HIV infection spreading through the use of dynamic complex networks. The heterogeneous population of HIV exposure groups is described through a unique network degree probability distribution. The time evolution of the network nodes is modelled by a Markov process and
Pareto Optimal Solutions for Stochastic Dynamic Programming Problems via Monte Carlo Simulation
Directory of Open Access Journals (Sweden)
R. T. N. Cardoso
2013-01-01
Full Text Available A heuristic algorithm is proposed for a class of stochastic discrete-time continuous-variable dynamic programming problems submitted to non-Gaussian disturbances. Instead of using the expected values of the objective function, the randomness nature of the decision variables is kept along the process, while Pareto fronts weighted by all quantiles of the objective function are determined. Thus, decision makers are able to choose any quantile they wish. This new idea is carried out by using Monte Carlo simulations embedded in an approximate algorithm proposed to deterministic dynamic programming problems. The new method is tested in instances of the classical inventory control problem. The results obtained attest for the efficiency and efficacy of the algorithm in solving these important stochastic optimization problems.
Plyasunov, S
2005-01-01
This paper is concerned with classes of models of stochastic reaction dynamics with time-scales separation. We demonstrate that the existence of the time-scale separation naturally leads to the application of the averaging principle and elimination of degrees of freedom via the renormalization of transition rates of slow reactions. The method suggested in this work is more general than other approaches presented previously: it is not limited to a particular type of stochastic processes and can be applied to different types of processes describing fast dynamics, and also provides crossover to the case when separation of time scales is not well pronounced. We derive a family of exact fluctuation-dissipation relations which establish the connection between effective rates and the statistics of the reaction events in fast reaction channels. An illustration of the technique is provided. Examples show that renormalized transition rates exhibit in general non-exponential relaxation behavior with a broad range of pos...
Chorošajev, Vladimir; Gelzinis, Andrius; Valkunas, Leonas; Abramavicius, Darius
2016-12-01
Time dependent variational approach is a convenient method to characterize the excitation dynamics in molecular aggregates for different strengths of system-bath interaction a, which does not require any additional perturbative schemes. Until recently, however, this method was only applicable in zero temperature case. It has become possible to extend this method for finite temperatures with the introduction of stochastic time dependent variational approach. Here we present a comparison between this approach and the exact hierarchical equations of motion approach for describing excitation dynamics in a broad range of temperatures. We calculate electronic population evolution, absorption and auxiliary time resolved fluorescence spectra in different regimes and find that the stochastic approach shows excellent agreement with the exact approach when the system-bath coupling is sufficiently large and temperatures are high. The differences between the two methods are larger, when temperatures are lower or the system-bath coupling is small.
A microtube viscometer with a thermostat
Energy Technology Data Exchange (ETDEWEB)
Silber-Li, Z.H. [LNM, Institute of Mechanics, Chinese Academy of Sciences, 15, Bei Si Huan Xi Lu, 100080, Beijing (China); Tan, Y.P. [LNM, Institute of Mechanics, Chinese Academy of Sciences, 15, Bei Si Huan Xi Lu, 100080, Beijing (China); Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 200072, Shanghai (China); Weng, P.F. [Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 200072, Shanghai (China)
2004-04-01
The viscometer presented in this paper is suitable for measuring the viscosity of liquids in micro-litre quantities. It consists of a micro-flow experimental system with a thermostat. Using the measurements of the flow rates and pressure drops of a liquid passing through a microtube, the liquid's viscosity can be calculated from on Hagen-Poiseuille theory. After calibration, the viscometer was used to measure viscosities of deionized water and ethyl alcohol at temperatures ranging from 0 to 40 C. For both test liquids, the relative deviation of the measured values from those quoted in the literature (obtained using other viscometers) was less than 2.6%. The relative uncertainty of the experimental system was reduced to {+-}1.8% using the relative measuring method. Due to the micro-scale of the test section, only a micro-litre quantity of liquid is needed for a test; this is a potential advantage for measurement of bio-liquid viscosities. (orig.)
Institute of Scientific and Technical Information of China (English)
ZHANG Ning; ZHANG Hui-Min; LIU Zhi-Qiang; DING Xue-Li; YANG Ming-Hao; GU Hua-Guang; REN Wei
2009-01-01
Dissolved cardiac myocytes can couple together and generate synchronous beatings in culture. We observed a synchronized early after-depolarization(EAD)-like rhythm in cultured cardiac myocytes and reproduced the experimental observation in a network mathematical model whose dynamics are close to a Hopf bifurcation. The mechanism for this EAD-like rhythm is attributed to noised-induced stochastic alternatings between the focus and the limit cycle. These results provide novel understandings for pathological heart rhythms like the early immature beatings.
Modeling the dynamic optimal advertising in stochastic condition
Institute of Scientific and Technical Information of China (English)
Rong DU; Qiying HU; Zhiqing MENG
2004-01-01
An effort to model the dynamic optimal advertising was made with the uncertainty of sales responses in consideration. The problem of dynamic advertising was depicted as a Markov decision process with two state variables. When a firm launches an advertising campaign, it may predict the probability that the campaign will obtain the sales reponse. This probability was chosen as one state variable. Cumulative sales volume was chosen as another state variable which varies randomly with advertising. The only decision variable was advertising expenditure. With these variables, a multi-stage Markov decision process model was formulated. On the basis of some propositions the model was analyzed. Some analytical results about the optimal strategy have been derived, and their practical implications have been explained.
Stochastic models of cover class dynamics. [remote sensing of vegetation
Barringer, T. H.; Robinson, V. B.
1981-01-01
Investigations related to satellite remote sensing of vegetation have been concerned with questions of signature identification and extension, cover inventory accuracy, and change detection and monitoring. Attention is given to models of ecological succession, present directions in successional modeling and analysis, nondynamic spatial models, issues in the analysis of spatial data, and aspects of spatial modeling. Issues in time-series analysis are considered along with dynamic spatial models, and problems of model specification and identification.
Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models
Daunizeau, J.; Friston, K. J.; Kiebel, S. J.
2009-11-01
In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.
Sutrisno; Widowati; Solikhin
2016-06-01
In this paper, we propose a mathematical model in stochastic dynamic optimization form to determine the optimal strategy for an integrated single product inventory control problem and supplier selection problem where the demand and purchasing cost parameters are random. For each time period, by using the proposed model, we decide the optimal supplier and calculate the optimal product volume purchased from the optimal supplier so that the inventory level will be located at some point as close as possible to the reference point with minimal cost. We use stochastic dynamic programming to solve this problem and give several numerical experiments to evaluate the model. From the results, for each time period, the proposed model was generated the optimal supplier and the inventory level was tracked the reference point well.
Alexandrov, D. V.; Bashkirtseva, I. A.; Ryashko, L. B.
2016-08-01
In this work, a non-linear dynamics of a simple three-dimensional climate model in the presence of stochastic forcing is studied. We demonstrate that a dynamic scenario of mixed-mode stochastic oscillations of the climate system near its equilibrium can be formed. As this takes place, a growth of noise intensity increases the frequency of interspike intervals responsible for the abrupt climate changes. In addition, a certain enhancement of stochastic forcing abruptly increases the atmospheric carbon dioxide and decreases the Earth's ice mass. A transition from order to chaos occurring at a critical noise is shown.
Stochastic calculus application to dynamic bifurcations and threshold crossings
Jansons, K M; Jansons, Kalvis M.
1997-01-01
For the dynamic pitchfork bifurcation in the presence of white noise, the statistics of the last time at zero are calculated as a function of the noise level and the rate of change of the parameter. The threshold crossing problem used, for example, to model the firing of a single cortical neuron is considered, concentrating on quantities that may be experimentally measurable but have so far received little attention. Expressions for the statistics of pre-threshold excursions, occupation density and last crossing time of zero are compared with results from numerical generation of paths.
Stochastic dynamics of a warmer Great Barrier Reef.
Cooper, Jennifer K; Spencer, Matthew; Bruno, John F
2015-07-01
Pressure on natural communities from human activities continues to increase. Even unique ecosystems like the Great Barrier Reef (GBR), that until recently were considered near-pristine and well-protected, are showing signs of rapid degradation. We collated recent (1996-2006) spatiotemporal relationships between benthic community composition on the GBR and environmental variables (ocean temperature and local threats resulting from human activity). We built multivariate models of the effects of these variables on short-term dynamics, and developed an analytical approach to study their long-term consequences. We used this approach to study the effects of ocean warming under different levels of local threat. Observed short-term changes in benthic community structure (e.g., declining coral cover) were associated with ocean temperature (warming) and local threats. Our model projected that, in the long-term, coral cover of less than 10% was not implausible. With increasing temperature and/or local threats, corals were initially replaced by sponges, gorgonians, and other taxa, with an eventual moderately high probability of domination (> 50%) by macroalgae when temperature increase was greatest (e.g., 3.5 degrees C of warming). Our approach to modeling community dynamics, based on multivariate statistical models, enabled us to project how environmental change (and thus local and international policy decisions) will influence the future state of coral reefs. The same approach could be applied to other systems for which time series of ecological and environmental variables are available.
Modeling dynamics of HIV infected cells using stochastic cellular automaton
Precharattana, Monamorn; Triampo, Wannapong
2014-08-01
Ever since HIV was first diagnosed in human, a great number of scientific works have been undertaken to explore the biological mechanisms involved in the infection and progression of the disease. Several cellular automata (CA) models have been introduced to gain insights into the dynamics of the disease progression but none of them has taken into account effects of certain immune cells such as the dendritic cells (DCs) and the CD8+ T lymphocytes (CD8+ T cells). In this work, we present a CA model, which incorporates effects of the HIV specific immune response focusing on the cell-mediated immunities, and investigate the interaction between the host immune response and the HIV infected cells in the lymph nodes. The aim of our work is to propose a model more realistic than the one in Precharattana et al. (2010) [10], by incorporating roles of the DCs, the CD4+ T cells, and the CD8+ T cells into the model so that it would reproduce the HIV infection dynamics during the primary phase of HIV infection.
Population dynamics of wild rodents induce stochastic fadeouts of a zoonotic pathogen.
Guzzetta, Giorgio; Tagliapietra, Valentina; Perkins, Sarah E; Hauffe, Heidi C; Poletti, Piero; Merler, Stefano; Rizzoli, Annapaola
2017-02-19
Stochastic processes play an important role in the infectious disease dynamics of wildlife, especially in species subject to large population oscillations. Here we study the case of a free ranging population of yellow-necked mice (Apodemus flavicollis) in northern Italy, where circulation of Dobrava-Belgrade hantavirus (DOBV) has been detected intermittently since 2001, until an outbreak emerged in 2010. We analyzed the transmission dynamics of the recent outbreak using a computational model that accounts for seasonal changes of the host population and territorial behavior. Model parameters were informed by capture-mark-recapture data collected over 14 years and longitudinal seroprevalence data from 2010 to 2013. The intermittent observation of DOBV before 2010 can be interpreted as repeated stochastic fadeouts after multiple introductions of infectious rodents migrating from neighboring areas. We estimated that only 20% of introductions in a naïve host population results in sustained transmission after two years, despite an effective reproduction number well above the epidemic threshold (mean 4.5, 95% credible intervals, CI: 0.65-15.8). Following the 2010 outbreak, DOBV has become endemic in the study area, but we predict a constant probability of about 4.7% per year that infection dies out, following large population drops in winter. In the absence of stochastic fadeout, viral prevalence is predicted to continue its growth to an oscillating equilibrium around a value of 24% (95% CI: 3-57%). We presented an example of invasion dynamics of a zoonotic virus where stochastic fadeout have played a major role and may induce future extinction of the endemic infection. This article is protected by copyright. All rights reserved.
An Approach for Dynamic Optimization of Prevention Program Implementation in Stochastic Environments
Kang, Yuncheol; Prabhu, Vittal
The science of preventing youth problems has significantly advanced in developing evidence-based prevention program (EBP) by using randomized clinical trials. Effective EBP can reduce delinquency, aggression, violence, bullying and substance abuse among youth. Unfortunately the outcomes of EBP implemented in natural settings usually tend to be lower than in clinical trials, which has motivated the need to study EBP implementations. In this paper we propose to model EBP implementations in natural settings as stochastic dynamic processes. Specifically, we propose Markov Decision Process (MDP) for modeling and dynamic optimization of such EBP implementations. We illustrate these concepts using simple numerical examples and discuss potential challenges in using such approaches in practice.
Directory of Open Access Journals (Sweden)
Huimei Jia
2013-01-01
Full Text Available This paper is concerned with the issues of passivity analysis and dynamic output feedback (DOF passive control for uncertain switched stochastic systems with time-varying delay via multiple storage functions (MSFs method. Firstly, based on the MSFs method, a sufficient condition for the existence of the passivity of the underlying system is established in terms of linear matrix inequalities (LMIs. Furthermore, the problem of dynamic output feedback passive control is investigated. Based on the obtained passivity condition, a sufficient condition for the existence of the desired switched passive controller is derived. Finally, a numerical example is presented to show the effectiveness of the proposed method.
STOCHASTIC DYNAMICS OF PRICES IN A MODEL OF FINANCIAL MARKET WITH DIFFERENT TYPES OF NOISE TRADERS
Directory of Open Access Journals (Sweden)
Lebedeva T. S.
2015-12-01
Full Text Available In the present study, the calculations of price dynamics are made in the model of a financial market consisting of fundamentalist and noise traders. Numerical calculations are carried out in accordance with the full Walrasian dynamic price adjustment rule. To describe fluctuations in the number of optimistic and pessimistic noise traders, a seminal stochastic Kirman’s ant model (reducible to a Markov chain is used, as well as its modification with different scaling properties of the parameter controlling the strength of herding behavior of noise agents
Cross-correlation markers in stochastic dynamics of complex systems
Panischev, O Yu; Bhattacharya, J; 10.1016/j.physa.2010.06.026
2010-01-01
The neuromagnetic activity (magnetoencephalogram, MEG) from healthy human brain and from an epileptic patient against chromatic flickering stimuli has been earlier analyzed on the basis of a memory functions formalism (MFF). Information measures of memory as well as relaxation parameters revealed high individuality and unique features in the neuromagnetic brain responses of each subject. The current paper demonstrates new capabilities of MFF by studying cross-correlations between MEG signals obtained from multiple and distant brain regions. It is shown that the MEG signals of healthy subjects are characterized by well-defined effects of frequency synchronization and at the same time by the domination of low-frequency processes. On the contrary, the MEG of a patient is characterized by a sharp abnormality of frequency synchronization, and also by prevalence of high-frequency quasi-periodic processes. Modification of synchronization effects and dynamics of cross-correlations offer a promising method of detectin...
Dynamics of popstar record sales on phonographic market -- stochastic model
Jarynowski, Amdrzej
2013-01-01
We investigate weekly record sales of the world's most popular 30 artists (2003-2013). Time series of sales have non-trivial kind of memory (anticorrelations, strong seasonality and constant autocorrelation decay within 120 weeks). Amount of artists record sales are usually the highest in the first week after premiere of their brand new records and then decrease to fluctuate around zero till next album release. We model such a behavior by discrete mean-reverting geometric jump diffusion (MRGJD) and Markov regime switching mechanism (MRS) between the base and the promotion regimes. We can built up the evidence through such a toy model that quantifies linear and nonlinear dynamical components (with stationary and nonstationary parameters set), and measure local divergence of the system with collective behavior phenomena. We find special kind of disagreement between model and data for Christmas time due to unusual shopping behavior. Analogies to earthquakes, product life-cycles, and energy markets will also be d...
Non-autonomous and stochastic dynamics of oceanic gravity currents
Bongolan-Walsh, Vena Pearl
The incompressible Navier-Stokes equations (the momentum, continuity and scalar transport equations) are the fundamental equations of fluid mechanics. Of great importance to weather and climate studies is the thermohaline circulation, which is affected by gravity currents, hence we chose it as our application. First, we studied the Navier-Stokes equations (without scalar transport) using non-autonomous dynamical systems techniques, and showed the existence of recurrent or Poisson stable motions under recurrent or Poisson stable forcing, respectively. This was motivated by observed periodic and recurrent motions in nature. Next, we investigated the coupled Navier-Stokes and scalar transport equations (we may take the scalar to be salinity, say), with spatially correlated white noise on the boundary. We employed random dynamical system ideas, and showed that this system is ergodic under suitable conditions for mean salinity input flux on the boundary, Prandtl number and covariance of the noise. This addition of a random term to the boundary conditions was motivated by observed seasonal variations in the salinity flux in gravity currents. The final part of this thesis are numerical simulations studying the effects of different boundary conditions on the entrainment behavior, salinity distribution and salinity transport properties of gravity currents. The finding is that gravity currents developing under Neumann and Dirichlet boundary conditions differ most in the way they transport salinity from the middle salinity parts (roughly the middle of the current) towards the fresher part (roughly the top of the current). This study contributes to understanding the behavior of the Navier-Stokes Equations under time-periodic forcings, uncertain boundary conditions, and how gravity currents are affected by different boundary conditions.
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Zhu, Z. W., E-mail: zhuzhiwen@tju.edu.cn [Department of Mechanics, Tianjin University, 300072, Tianjin (China); Tianjin Key Laboratory of Non-linear Dynamics and Chaos Control, 300072, Tianjin (China); Zhang, W. D., E-mail: zhangwenditju@126.com; Xu, J., E-mail: xujia-ld@163.com [Department of Mechanics, Tianjin University, 300072, Tianjin (China)
2014-03-15
The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.
McKetterick, Thomas John; Giuggioli, Luca
2014-10-01
Delayed dynamics result from finite transmission speeds of a signal in the form of energy, mass, or information. In stochastic systems the resulting lagged dynamics challenge our understanding due to the rich behavioral repertoire encompassing monotonic, oscillatory, and unstable evolution. Despite the vast literature, quantifying this rich behavior is limited by a lack of explicit analytic studies of high-dimensional stochastic delay systems. Here we fill this gap for systems governed by a linear Langevin equation of any number of delays and spatial dimensions with additive Gaussian noise. By exploiting Laplace transforms we are able to derive an exact time-dependent analytic solution of the Langevin equation. By using characteristic functionals we are able to construct the full time dependence of the multivariate probability distribution of the stochastic process as a function of the delayed and nondelayed random variables. As an application we consider interactions in animal collective movement that go beyond the traditional assumption of instantaneous alignment. We propose models for coordinated maneuvers of comoving agents applicable to recent empirical findings in pigeons and bats whereby individuals copy the heading of their neighbors with some delay. We highlight possible strategies that individual pairs may adopt to reduce the variance in their velocity difference and/or in their spatial separation. We also show that a minimum in the variance of the spatial separation at long times can be achieved with certain ratios of measurement to reaction delay.
Sahoo, Avimanyu; Jagannathan, Sarangapani
2017-02-01
In this paper, an event-driven stochastic adaptive dynamic programming (ADP)-based technique is introduced for nonlinear systems with a communication network within its feedback loop. A near optimal control policy is designed using an actor-critic framework and ADP with event sampled state vector. First, the system dynamics are approximated by using a novel neural network (NN) identifier with event sampled state vector. The optimal control policy is generated via an actor NN by using the NN identifier and value function approximated by a critic NN through ADP. The stochastic NN identifier, actor, and critic NN weights are tuned at the event sampled instants leading to aperiodic weight tuning laws. Above all, an adaptive event sampling condition based on estimated NN weights is designed by using the Lyapunov technique to ensure ultimate boundedness of all the closed-loop signals along with the approximation accuracy. The net result is event-driven stochastic ADP technique that can significantly reduce the computation and network transmissions. Finally, the analytical design is substantiated with simulation results.
Dynamic modeling of tourism by stochastic method: a case of the Beijing-Tianjin-Hebei region
Dai, Juan; Zhang, Shihui; Xue, Chongsheng
2009-10-01
As an efficient way to stimulate the growth of economy, tourism is promoted by most counties allover the world, and has become one of the world's largest and fastest-growing industries. Essentially, tourism is a spatiotemporal system, with tourist attractions located in different geographic areas and tourist flows exchanging between different geographic regions. In this paper, we present a dynamic model for the simulation of tourism and tourist's activities in the context of GIS and stochastic method, using a case of the Beijing-Tianjin-Hebei region. The model is developed on stochastic method and multiple geospatial data sources. In the model, the spatiotemporal behavior of tourist on the Earth's Surface is governed by the evolution rules, which are extracted from the researches on tourist's activities and executed via stochastic method and multiple geospatial data. By means of the model, we simulate the tourism in the Beijing-Tianjin- Hebei region, and find that there is good correspondence between the tourist arrivals calculated with the model and those obtained from the tourism statistics. This shows that the animated dynamic modeling of tourism based on geospatial data can be used as an indicator of the tourism in the realistic world, and is also can be embedded in the GIS applications.
Stochastic dynamics of time correlation in complex systems with discrete time
Yulmetyev; Hanggi; Gafarov
2000-11-01
In this paper we present the concept of description of random processes in complex systems with discrete time. It involves the description of kinetics of discrete processes by means of the chain of finite-difference non-Markov equations for time correlation functions (TCFs). We have introduced the dynamic (time dependent) information Shannon entropy S(i)(t) where i=0,1,2,3,ellipsis, as an information measure of stochastic dynamics of time correlation (i=0) and time memory (i=1,2,3,ellipsis). The set of functions S(i)(t) constitute the quantitative measure of time correlation disorder (i=0) and time memory disorder (i=1,2,3,ellipsis) in complex system. The theory developed started from the careful analysis of time correlation involving dynamics of vectors set of various chaotic states. We examine two stochastic processes involving the creation and annihilation of time correlation (or time memory) in details. We carry out the analysis of vectors' dynamics employing finite-difference equations for random variables and the evolution operator describing their natural motion. The existence of TCF results in the construction of the set of projection operators by the usage of scalar product operation. Harnessing the infinite set of orthogonal dynamic random variables on a basis of Gram-Shmidt orthogonalization procedure tends to creation of infinite chain of finite-difference non-Markov kinetic equations for discrete TCFs and memory functions (MFs). The solution of the equations above thereof brings to the recurrence relations between the TCF and MF of senior and junior orders. This offers new opportunities for detecting the frequency spectra of power of entropy function S(i)(t) for time correlation (i=0) and time memory (i=1,2,3,ellipsis). The results obtained offer considerable scope for attack on stochastic dynamics of discrete random processes in a complex systems. Application of this technique on the analysis of stochastic dynamics of RR intervals from human ECG
Teodorescu, Razvan
2009-10-01
Systems of oscillators coupled non-linearly (stochastically or not) are ubiquitous in nature and can explain many complex phenomena: coupled Josephson junction arrays, cardiac pacemaker cells, swarms or flocks of insects and birds, etc. They are know to have a non-trivial phase diagram, which includes chaotic, partially synchronized, and fully synchronized phases. A traditional model for this class of problems is the Kuramoto system of oscillators, which has been studied extensively for the last three decades. The model is a canonical example for non-equilibrium, dynamical phase transitions, so little understood in physics. From a stochastic analysis point of view, the transition is described by the large deviations principle, which offers little information on the scaling behavior near the critical point. I will discuss a special case of the model, which allows a rigorous analysis of the critical properties of the model, and reveals a new, anomalous scaling behavior in the vicinity of the critical point.
Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost
Energy Technology Data Exchange (ETDEWEB)
Bokanowski, Olivier, E-mail: boka@math.jussieu.fr [Laboratoire Jacques-Louis Lions, Université Paris-Diderot (Paris 7) UFR de Mathématiques - Bât. Sophie Germain (France); Picarelli, Athena, E-mail: athena.picarelli@inria.fr [Projet Commands, INRIA Saclay & ENSTA ParisTech (France); Zidani, Hasnaa, E-mail: hasnaa.zidani@ensta.fr [Unité de Mathématiques appliquées (UMA), ENSTA ParisTech (France)
2015-02-15
This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system of controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach.
Price-Dynamics of Shares and Bohmian Mechanics: Deterministic or Stochastic Model?
Choustova, Olga
2007-02-01
We apply the mathematical formalism of Bohmian mechanics to describe dynamics of shares. The main distinguishing feature of the financial Bohmian model is the possibility to take into account market psychology by describing expectations of traders by the pilot wave. We also discuss some objections (coming from conventional financial mathematics of stochastic processes) against the deterministic Bohmian model. In particular, the objection that such a model contradicts to the efficient market hypothesis which is the cornerstone of the modern market ideology. Another objection is of pure mathematical nature: it is related to the quadratic variation of price trajectories. One possibility to reply to this critique is to consider the stochastic Bohm-Vigier model, instead of the deterministic one. We do this in the present note.
Institute of Scientific and Technical Information of China (English)
潘子刚; 刘允刚; 施颂椒
2001-01-01
In this paper, we study the problem of output feedback stabilization for stochastic nonlinear systems. We consider a class of stochastic nonlinear systems in observer canonical form with stable zero-dynamics. We introduce a sequence of state transformations that transform the system into a lower triangular structure that is amenable for integrator backstepping design. Then we design the output-feedback controller and prove that the closed-loop system is bounded in probability. Furthermore, when the disturbance vector field vanishes at the origin, the closed-loop system is asymptotically stable in the large. With special care, the controller preserves the equilibrium of the nonlinear system. An example is included to illustrate the theoretical findings.
Dynamics of stochastic predator-prey models with Holling II functional response
Liu, Qun; Zu, Li; Jiang, Daqing
2016-08-01
In this paper, we consider the dynamics of stochastic predator-prey models with Holling II functional response. For the stochastic systems, we firstly establish sufficient conditions for the existence of the globally positive solutions. Then we investigate the asymptotic moment estimations of the positive solutions and study the ultimately bounded in the mean of them. Thirdly, by constructing some suitable Lyapunov functions, we verify that there are unique stationary distributions and they are ergodic. The obtained results show that the systems still retain some stability in the sense of weak stability provided that the intensity of the white noise is relatively small. Finally, some numerical simulations are introduced to illustrate our main results.
Qian, Hong
2016-01-01
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity, but population wise with statistical rate laws in their syntheses, degradations, spatial diffusion, individual state transitions, and interactions. Such a formal kinetic system in a small volume $V$, like a single cell, can be rigorously treated in terms of a Markov process describing its nonlinear kinetics as well as nonequilibrium thermodynamics at a mesoscopic scale. We introduce notions such as open, driven chemical systems, entropy production, free energy dissipation, etc. Then in the macroscopic limit, we illustrate how two new "laws", in terms of a generalized free energy of the mesoscopic stochastic dynamics, emerge. Detailed balance and complex balance are two special classes of "simple" nonlinear kinetics. Phase transition is intrinsically related to multi-stability...
Dynamics of an electric dipole moment in a stochastic electric field.
Band, Y B
2013-08-01
The mean-field dynamics of an electric dipole moment in a deterministic and a fluctuating electric field is solved to obtain the average over fluctuations of the dipole moment and the angular momentum as a function of time for a Gaussian white-noise stochastic electric field. The components of the average electric dipole moment and the average angular momentum along the deterministic electric-field direction do not decay to zero, despite fluctuations in all three components of the electric field. This is in contrast to the decay of the average over fluctuations of a magnetic moment in a stochastic magnetic field with Gaussian white noise in all three components. The components of the average electric dipole moment and the average angular momentum perpendicular to the deterministic electric-field direction oscillate with time but decay to zero, and their variance grows with time.
On the dynamics of mean-field equations for stochastic neural fields with delays
Touboul, Jonathan
2011-01-01
The cortex is composed of large-scale cell assemblies sharing the same individual properties and receiving the same input, in charge of certain functions, and subject to noise. Such assemblies are characterized by specific space locations and space-dependent delayed interactions. The mean-field equations for such systems were rigorously derived in a recent paper for general models, under mild assumptions on the network, using probabilistic methods. We summarize and investigate general implications of this result. We then address the dynamics of these stochastic neural field equations in the case of firing-rate neurons. This is a unique case where the very complex stochastic mean-field equations exactly reduce to a set of delayed differential or integro-differential equations on the two first moments of the solutions, this reduction being possible due to the Gaussian nature of the solutions. The obtained equations differ from more customary approaches in that it incorporates intrinsic noise levels nonlinearly ...
Microstructure and velocity of field-driven Ising interfaces moving under a soft stochastic dynamic.
Rikvold, Per Arne; Kolesik, M
2003-06-01
We present theoretical and dynamic Monte Carlo simulation results for the mobility and microscopic structure of (1+1)-dimensional Ising interfaces moving far from equilibrium in an applied field under a single-spin-flip "soft" stochastic dynamic. The soft dynamic is characterized by the property that the effects of changes in field energy and interaction energy factorize in the transition rate, in contrast to the nonfactorizing nature of the traditional Glauber and Metropolis rates "hard" dynamics). This work extends our previous studies of the Ising model with a hard dynamic and the unrestricted solid-on-solid (SOS) model with soft and hard dynamics. [P. A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 (2000); J. Phys. A 35, L117 (2002); Phys. Rev. E 66, 066116 (2002).] The Ising model with soft dynamics is found to have closely similar properties to the SOS model with the same dynamic. In particular, the local interface width does not diverge with increasing field as it does for hard dynamics. The skewness of the interface at nonzero field is very weak and has the opposite sign of that obtained with hard dynamics.
Miller, David A; Clark, William R; Arnold, Stevan J; Bronikowski, Anne M
2011-08-01
Comparative evaluations of population dynamics in species with temporal and spatial variation in life-history traits are rare because they require long-term demographic time series from multiple populations. We present such an analysis using demographic data collected during the interval 1978-1996 for six populations of western terrestrial garter snakes (Thamnophis elegans) from two evolutionarily divergent ecotypes. Three replicate populations from a slow-living ecotype, found in mountain meadows of northeastern California, were characterized by individuals that develop slowly, mature late, reproduce infrequently with small reproductive effort, and live longer than individuals of three populations of a fast-living ecotype found at lakeshore locales. We constructed matrix population models for each of the populations based on 8-13 years of data per population and analyzed both deterministic dynamics based on mean annual vital rates and stochastic dynamics incorporating annual variation in vital rates. (1) Contributions of highly variable vital rates to fitness (lambda(s)) were buffered against the negative effects of stochastic variation, and this relationship was consistent with differences between the meadow (M-slow) and lakeshore (L-fast) ecotypes. (2) Annual variation in the proportion of gravid females had the greatest negative effect among all vital rates on lambda(s). The magnitude of variation in the proportion of gravid females and its effect on lambda(s) was greater in M-slow than L-fast populations. (3) Variation in the proportion of gravid females, in turn, depended on annual variation in prey availability, and its effect on lambda(s) was 4 23 times greater in M-slow than L-fast populations. In addition to differences in stochastic dynamics between ecotypes, we also found higher mean mortality rates across all age classes in the L-fast populations. Our results suggest that both deterministic and stochastic selective forces have affected the evolution of
Miller, David A.; Clark, W.R.; Arnold, S.J.; Bronikowski, A.M.
2011-01-01
Comparative evaluations of population dynamics in species with temporal and spatial variation in life-history traits are rare because they require long-term demographic time series from multiple populations. We present such an analysis using demographic data collected during the interval 1978-1996 for six populations of western terrestrial garter snakes (Thamnophis elegans) from two evolutionarily divergent ecotypes. Three replicate populations from a slow-living ecotype, found in mountain meadows of northeastern California, were characterized by individuals that develop slowly, mature late, reproduce infrequently with small reproductive effort, and live longer than individuals of three populations of a fast-living ecotype found at lakeshore locales. We constructed matrix population models for each of the populations based on 8-13 years of data per population and analyzed both deterministic dynamics based on mean annual vital rates and stochastic dynamics incorporating annual variation in vital rates. (1) Contributions of highly variable vital rates to fitness (??s) were buffered against the negative effects of stochastic variation, and this relationship was consistent with differences between the meadow (M-slow) and lakeshore (L-fast) ecotypes. (2) Annual variation in the proportion of gravid females had the greatest negative effect among all vital rates on ?? s. The magnitude of variation in the proportion of gravid females and its effect on ??s was greater in M-slow than L-fast populations. (3) Variation in the proportion of gravid females, in turn, depended on annual variation in prey availability, and its effect on ??s was 4- 23 times greater in M-slow than L-fast populations. In addition to differences in stochastic dynamics between ecotypes, we also found higher mean mortality rates across all age classes in the L-fast populations. Our results suggest that both deterministic and stochastic selective forces have affected the evolution of divergent life
Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics
Bressloff, Paul C.
2010-11-03
We analyze a stochastic model of neuronal population dynamics with intrinsic noise. In the thermodynamic limit N→∞, where N determines the size of each population, the dynamics is described by deterministic Wilson-Cowan equations. On the other hand, for finite N the dynamics is described by a master equation that determines the probability of spiking activity within each population. We first consider a single excitatory population that exhibits bistability in the deterministic limit. The steady-state probability distribution of the stochastic network has maxima at points corresponding to the stable fixed points of the deterministic network; the relative weighting of the two maxima depends on the system size. For large but finite N, we calculate the exponentially small rate of noise-induced transitions between the resulting metastable states using a Wentzel-Kramers- Brillouin (WKB) approximation and matched asymptotic expansions. We then consider a two-population excitatory or inhibitory network that supports limit cycle oscillations. Using a diffusion approximation, we reduce the dynamics to a neural Langevin equation, and show how the intrinsic noise amplifies subthreshold oscillations (quasicycles). © 2010 The American Physical Society.
Patterns of Stochastic Behavior in Dynamically Unstable High-Dimensional Biochemical Networks
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Simon Rosenfeld
2009-01-01
Full Text Available The question of dynamical stability and stochastic behavior of large biochemical networks is discussed. It is argued that stringent conditions of asymptotic stability have very little chance to materialize in a multidimensional system described by the differential equations of chemical kinetics. The reason is that the criteria of asymptotic stability (Routh- Hurwitz, Lyapunov criteria, Feinberg’s Deficiency Zero theorem would impose the limitations of very high algebraic order on the kinetic rates and stoichiometric coefficients, and there are no natural laws that would guarantee their unconditional validity. Highly nonlinear, dynamically unstable systems, however, are not necessarily doomed to collapse, as a simple Jacobian analysis would suggest. It is possible that their dynamics may assume the form of pseudo-random fluctuations quite similar to a shot noise, and, therefore, their behavior may be described in terms of Langevin and Fokker-Plank equations. We have shown by simulation that the resulting pseudo-stochastic processes obey the heavy-tailed Generalized Pareto Distribution with temporal sequence of pulses forming the set of constituent-specific Poisson processes. Being applied to intracellular dynamics, these properties are naturally associated with burstiness, a well documented phenomenon in the biology of gene expression.
Patterns of stochastic behavior in dynamically unstable high-dimensional biochemical networks.
Rosenfeld, Simon
2009-01-29
The question of dynamical stability and stochastic behavior of large biochemical networks is discussed. It is argued that stringent conditions of asymptotic stability have very little chance to materialize in a multidimensional system described by the differential equations of chemical kinetics. The reason is that the criteria of asymptotic stability (Routh-Hurwitz, Lyapunov criteria, Feinberg's Deficiency Zero theorem) would impose the limitations of very high algebraic order on the kinetic rates and stoichiometric coefficients, and there are no natural laws that would guarantee their unconditional validity. Highly nonlinear, dynamically unstable systems, however, are not necessarily doomed to collapse, as a simple Jacobian analysis would suggest. It is possible that their dynamics may assume the form of pseudo-random fluctuations quite similar to a shot noise, and, therefore, their behavior may be described in terms of Langevin and Fokker-Plank equations. We have shown by simulation that the resulting pseudo-stochastic processes obey the heavy-tailed Generalized Pareto Distribution with temporal sequence of pulses forming the set of constituent-specific Poisson processes. Being applied to intracellular dynamics, these properties are naturally associated with burstiness, a well documented phenomenon in the biology of gene expression.
Granik, V
2002-01-01
Proceeding from the concept of rational expectations, a new dynamic model of supply and demand in a single market with one supplier, one buyer, and one kind of commodity is developed. Unlike the cob-web dynamic theories with adaptive expectations that are made up of deterministic difference equations, the new model is cast in the form of stochastic differential equations. The stochasticity is due to random disturbances ("input") to endogenous variables. The disturbances are assumed to be stationary to the second order with zero means and given covariance functions. Two particular versions of the model with different endogenous variables are considered. The first version involves supply, demand, and price. In the second version the stock of commodity is added. Covariance functions and variances of the endogenous variables ("output") are obtained in terms of the spectral theory of stochastic stationary processes. The impact of both deterministic parameters of the model and the random input on the stochastic out...
Dynamic response of mechanical systems to impulse process stochastic excitations: Markov approach
Iwankiewicz, R.
2016-05-01
Methods for determination of the response of mechanical dynamic systems to Poisson and non-Poisson impulse process stochastic excitations are presented. Stochastic differential and integro-differential equations of motion are introduced. For systems driven by Poisson impulse process the tools of the theory of non-diffusive Markov processes are used. These are: the generalized Itô’s differential rule which allows to derive the differential equations for response moments and the forward integro-differential Chapman-Kolmogorov equation from which the equation governing the probability density of the response is obtained. The relation of Poisson impulse process problems to the theory of diffusive Markov processes is given. For systems driven by a class of non-Poisson (Erlang renewal) impulse processes an exact conversion of the original non-Markov problem into a Markov one is based on the appended Markov chain corresponding to the introduced auxiliary pure jump stochastic process. The derivation of the set of integro-differential equations for response probability density and also a moment equations technique are based on the forward integro-differential Chapman-Kolmogorov equation. An illustrating numerical example is also included.
Model predictive control for a thermostatic controlled system
DEFF Research Database (Denmark)
Shafiei, Seyed Ehsan; Rasmussen, Henrik; Stoustrup, Jakob
2013-01-01
This paper proposes a model predictive control scheme to provide temperature set-points to thermostatic controlled cooling units in refrigeration systems. The control problem is formulated as a convex programming problem to minimize the overall operating cost of the system. The foodstuff temperat......This paper proposes a model predictive control scheme to provide temperature set-points to thermostatic controlled cooling units in refrigeration systems. The control problem is formulated as a convex programming problem to minimize the overall operating cost of the system. The foodstuff...
DEFF Research Database (Denmark)
Sørensen, J.T.; Enevoldsen, Carsten
1994-01-01
Infectious diseases, such as bovine virus diarrhoea (BVD) virus infections in cattle, are often studied by Markov chain models. However, it is difficult to simulate dynamic interactions between production of a reproductive herd and the disease by this type of model. As an alternative, a dynamic...... stochastic model simulating the herd production was suggested. A dynamic stochastic model simulating the effect of BVD virus infection in a dairy cattle herd was used to exemplify how this type of model could be applied in research. The simulation example demonstrated that the effect of a BVD virus infection...
Wang, Xin-Fan; Wang, Jian-Qiang; Deng, Sheng-Yue
2013-01-01
We investigate the dynamic stochastic multicriteria decision making (SMCDM) problems, in which the criterion values take the form of log-normally distributed random variables, and the argument information is collected from different periods. We propose two new geometric aggregation operators, such as the log-normal distribution weighted geometric (LNDWG) operator and the dynamic log-normal distribution weighted geometric (DLNDWG) operator, and develop a method for dynamic SMCDM with log-normally distributed random variables. This method uses the DLNDWG operator and the LNDWG operator to aggregate the log-normally distributed criterion values, utilizes the entropy model of Shannon to generate the time weight vector, and utilizes the expectation values and variances of log-normal distributions to rank the alternatives and select the best one. Finally, an example is given to illustrate the feasibility and effectiveness of this developed method.
Beyond the quasi-particle: stochastic domain wall dynamics in soft ferromagnetic nanowires
Hayward, T. J.; Omari, K. A.
2017-03-01
We study the physical origins of stochastic domain wall pinning in soft ferromagnetic nanowires using focused magneto-optic Kerr effect measurements and dynamic micromagnetic simulations. Our results illustrate the ubiquitous nature of these effects in Ni80Fe20 nanowires, and show that they are not only a result of the magnetisation history of the system (i.e. the magnetisation structure of the injected domain walls), and the onset of non-linear propagation dynamics above the Walker breakdown field, but also a complex interplay between the two. We show that this means that, while micromagnetics can be used to make qualitative predictions of the behaviour of domain walls at defect sites, making quantitative predictions is much more challenging. Together, our results reinforce the view that even in these simple pseudo-one dimensional nanomagnets, domain walls must be considered as complex, dynamically evolving objects rather than simple quasi-particles.
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Xin-Fan Wang
2013-01-01
Full Text Available We investigate the dynamic stochastic multicriteria decision making (SMCDM problems, in which the criterion values take the form of log-normally distributed random variables, and the argument information is collected from different periods. We propose two new geometric aggregation operators, such as the log-normal distribution weighted geometric (LNDWG operator and the dynamic log-normal distribution weighted geometric (DLNDWG operator, and develop a method for dynamic SMCDM with log-normally distributed random variables. This method uses the DLNDWG operator and the LNDWG operator to aggregate the log-normally distributed criterion values, utilizes the entropy model of Shannon to generate the time weight vector, and utilizes the expectation values and variances of log-normal distributions to rank the alternatives and select the best one. Finally, an example is given to illustrate the feasibility and effectiveness of this developed method.
A stochastic agent-based model of pathogen propagation in dynamic multi-relational social networks
Khan, Bilal; Dombrowski, Kirk; Saad, Mohamed
2015-01-01
We describe a general framework for modeling and stochastic simulation of epidemics in realistic dynamic social networks, which incorporates heterogeneity in the types of individuals, types of interconnecting risk-bearing relationships, and types of pathogens transmitted across them. Dynamism is supported through arrival and departure processes, continuous restructuring of risk relationships, and changes to pathogen infectiousness, as mandated by natural history; dynamism is regulated through constraints on the local agency of individual nodes and their risk behaviors, while simulation trajectories are validated using system-wide metrics. To illustrate its utility, we present a case study that applies the proposed framework towards a simulation of HIV in artificial networks of intravenous drug users (IDUs) modeled using data collected in the Social Factors for HIV Risk survey. PMID:25859056
Abdullaev, Sadrilla
2014-01-01
This is the first book to systematically consider the modern aspects of chaotic dynamics of magnetic field lines and charged particles in magnetically confined fusion plasmas. The analytical models describing the generic features of equilibrium magnetic fields and magnetic perturbations in modern fusion devices are presented. It describes mathematical and physical aspects of onset of chaos, generic properties of the structure of stochastic magnetic fields, transport of charged particles in tokamaks induced by magnetic perturbations, new aspects of particle turbulent transport, etc. The presentation is based on the classical and new unique mathematical tools of Hamiltonian dynamics, like the action--angle formalism, classical perturbation theory, canonical transformations of variables, symplectic mappings, the Poincaré-Melnikov integrals. They are extensively used for analytical studies as well as for numerical simulations of magnetic field lines, particle dynamics, their spatial structures and statisti...
Zhang, Wei; Wang, Jun
2017-09-01
In attempt to reproduce price dynamics of financial markets, a stochastic agent-based financial price model is proposed and investigated by stochastic exclusion process. The exclusion process, one of interacting particle systems, is usually thought of as modeling particle motion (with the conserved number of particles) in a continuous time Markov process. In this work, the process is utilized to imitate the trading interactions among the investing agents, in order to explain some stylized facts found in financial time series dynamics. To better understand the correlation behaviors of the proposed model, a new time-dependent intrinsic detrended cross-correlation (TDI-DCC) is introduced and performed, also, the autocorrelation analyses are applied in the empirical research. Furthermore, to verify the rationality of the financial price model, the actual return series are also considered to be comparatively studied with the simulation ones. The comparison results of return behaviors reveal that this financial price dynamics model can reproduce some correlation features of actual stock markets.
A principle of fractal-stochastic dualism and Gompertzian dynamics of growth and self-organization.
Waliszewski, Przemyslaw
2005-10-01
The emergence of Gompertzian dynamics at the macroscopic, tissue level during growth and self-organization is determined by the existence of fractal-stochastic dualism at the microscopic level of supramolecular, cellular system. On one hand, Gompertzian dynamics results from the complex coupling of at least two antagonistic, stochastic processes at the molecular cellular level. It is shown that the Gompertz function is a probability function, its derivative is a probability density function, and the Gompertzian distribution of probability is of non-Gaussian type. On the other hand, the Gompertz function is a contraction mapping and defines fractal dynamics in time-space; a prerequisite condition for the coupling of processes. Furthermore, the Gompertz function is a solution of the operator differential equation with the Morse-like anharmonic potential. This relationship indicates that distribution of intrasystemic forces is both non-linear and asymmetric. The anharmonic potential is a measure of the intrasystemic interactions. It attains a point of the minimum (U(0), t(0)) along with a change of both complexity and connectivity during growth and self-organization. It can also be modified by certain factors, such as retinoids.
Directory of Open Access Journals (Sweden)
Arild Helseth
2015-12-01
Full Text Available Stochastic dual dynamic programming (SDDP has become a popular algorithm used in practical long-term scheduling of hydropower systems. The SDDP algorithm is computationally demanding, but can be designed to take advantage of parallel processing. This paper presents a novel parallel scheme for the SDDP algorithm, where the stage-wise synchronization point traditionally used in the backward iteration of the SDDP algorithm is partially relaxed. The proposed scheme was tested on a realistic model of a Norwegian water course, proving that the synchronization point relaxation significantly improves parallel efficiency.
The ‘hit’ phenomenon: a mathematical model of human dynamics interactions as a stochastic process
Ishii, Akira; Arakaki, Hisashi; Matsuda, Naoya; Umemura, Sanae; Urushidani, Tamiko; Yamagata, Naoya; Yoshida, Narihiko
2012-06-01
A mathematical model for the ‘hit’ phenomenon in entertainment within a society is presented as a stochastic process of human dynamics interactions. The model uses only the advertisement budget time distribution as an input, and word-of-mouth (WOM), represented by posts on social network systems, is used as data to make a comparison with the calculated results. The unit of time is days. The WOM distribution in time is found to be very close to the revenue distribution in time. Calculations for the Japanese motion picture market based on the mathematical model agree well with the actual revenue distribution in time.
Cooperative Effects of Noise and Coupling on Stochastic Dynamics of a Membrane-Bulk Coupling Model
Institute of Scientific and Technical Information of China (English)
TANG Jun; JIA Ya; YI Ming
2009-01-01
Based on a membrane-bulk coupling cell model proposed by Gomez-Marin et al. [ Phys. Rev. Lett. 98 (2007) 168303], the cooperative effects of noise and coupling on the stochastic dynamical behavior are investigated, For parameters in a certain region, the oscillation can be induced by the cooperative effect of noise and coupling. Whether considering the coupling or not, corresponding coherence resonance phenomena are observed. Furthermore, the effects of two coupling parameters, cell size L and coupling intensity k, on the noise-induced oscillation of membranes are studied. Contrary effects of noise are found in and out of the deterministic oscillatory regions.
Wang, Tingting; Dai, Weidi; Jiao, Pengfei; Wang, Wenjun
2016-05-01
Many real-world data can be represented as dynamic networks which are the evolutionary networks with timestamps. Analyzing dynamic attributes is important to understanding the structures and functions of these complex networks. Especially, studying the influential nodes is significant to exploring and analyzing networks. In this paper, we propose a method to identify influential nodes in dynamic social networks based on identifying such nodes in the temporal communities which make up the dynamic networks. Firstly, we detect the community structures of all the snapshot networks based on the degree-corrected stochastic block model (DCBM). After getting the community structures, we capture the evolution of every community in the dynamic network by the extended Jaccard’s coefficient which is defined to map communities among all the snapshot networks. Then we obtain the initial influential nodes of the dynamic network and aggregate them based on three widely used centrality metrics. Experiments on real-world and synthetic datasets demonstrate that our method can identify influential nodes in dynamic networks accurately, at the same time, we also find some interesting phenomena and conclusions for those that have been validated in complex network or social science.
Irving, J. D.; Singha, K.
2010-12-01
Traditionally, hydrological measurements have been used to estimate subsurface properties controlling groundwater flow and contaminant transport. However, such measurements are limited by their support volume and expense. A considerable benefit of geophysical measurements is that they provide a degree of spatial coverage and resolution that are unattainable with other methods, and the data can be acquired in a cost-effective manner. In particular, dynamic geophysical data allow us to indirectly observe changes in hydrological state variables as flow and transport processes occur, and can thus provide a link to hydrological properties when coupled with a process-based model. Stochastic fusion of these two data types offers the potential to provide not only estimates of subsurface hydrological properties, but also a quantification of their uncertainty. This information is critical when considering the end use of the data, which may be for groundwater remediation and management decision making. Here, we examine a number of key issues in the stochastic fusion of dynamic hydrogeophysical data. We focus our attention on the specific problem of integrating time-lapse crosshole electrical resistivity measurements and saline tracer-test concentration data in order to estimate the spatial distribution of hydraulic conductivity (K). To assimilate the geophysical and hydrological measurements in a stochastic manner, we use a Bayesian Markov-chain-Monte-Carlo (McMC) methodology. This provides multiple realizations of the subsurface K field that are consistent with the measured data and assumptions regarding model structure and data errors. To account for incomplete petrophysical knowledge, the geophysical and hydrological forward models are linked through an uncertain relationship between electrical resistivity and concentration following the general form of Archie’s law. To make the spatially distributed, fully stochastic inverse problem computationally tractable, we take
Design and Implementation of Frequency-responsive Thermostat Control
DEFF Research Database (Denmark)
Nyeng, Preben; Østergaard, Jacob; Togeby, Mikael
2010-01-01
properties and needs of each application, and on the other hand the requirements of the system operator. The control algorithms are implemented on a microcontroller unit that is interfaced with existing thermostats for each application. To validate the control algorithms and overall system design, a series...
Schilde, M; Doerner, K F; Hartl, R F
2014-10-01
In urban areas, logistic transportation operations often run into problems because travel speeds change, depending on the current traffic situation. If not accounted for, time-dependent and stochastic travel speeds frequently lead to missed time windows and thus poorer service. Especially in the case of passenger transportation, it often leads to excessive passenger ride times as well. Therefore, time-dependent and stochastic influences on travel speeds are relevant for finding feasible and reliable solutions. This study considers the effect of exploiting statistical information available about historical accidents, using stochastic solution approaches for the dynamic dial-a-ride problem (dynamic DARP). The authors propose two pairs of metaheuristic solution approaches, each consisting of a deterministic method (average time-dependent travel speeds for planning) and its corresponding stochastic version (exploiting stochastic information while planning). The results, using test instances with up to 762 requests based on a real-world road network, show that in certain conditions, exploiting stochastic information about travel speeds leads to significant improvements over deterministic approaches.
The Stochastic Dynamics for Ecological Tourism System with Visitor Educational Intervention
Directory of Open Access Journals (Sweden)
Dongping Wei
2013-01-01
Full Text Available The ever-increasing visitation in parks and protected areas continues to present a considerable challenge for worldwide land managers with allowing recreational use while preserving natural conditions. In China, the fast expanding visitation in protected areas is quickly damaging the natural resources and precious culture without effective visitor education, while regulation and site management are also gaining very limited efficacy. We propose a differential equation to describe the ecological tourism system. Shown by the theoretical proof and numerical simulation, the ecological tourism system is unstable without any perturbed factors, especially visitor educational intervention, because the solution of the dynamic system explodes in a finite time given any initial value. Supposing that the intrinsic increasing rate of stakeholders in the systems stochastically perturbed by the visitor educational intervention, we discover that the stochastic dynamic model can effectively suppress the explosion of the solution. As such, we demonstrate that the tourism system can develop steadily and safely even under a large amount of visitors in public vacation, when employing continuous visitor education intervention programmes.
The role of phase dynamics in a stochastic model of a passively advected scalar
Moradi, Sara
2016-01-01
Collective synchronous motion of the phases is introduced in a model for the stochastic passive advection-diffusion of a scalar with external forcing. The model for the phase coupling dynamics follows the well known Kuramoto model paradigm of limit-cycle oscillators. The natural frequencies in the Kuramoto model are assumed to obey a given scale dependence through a dispersion relation of the drift-wave form $-\\beta\\frac{k}{1+k^2}$, where $\\beta$ is a constant representing the typical strength of the gradient. The present aim is to study the importance of collective phase dynamics on the characteristic time evolution of the fluctuation energy and the formation of coherent structures. Our results show that the assumption of a fully stochastic phase state of turbulence is more relevant for high values of $\\beta$, where we find that the energy spectrum follows a $k^{-7/2}$ scaling. Whereas for lower $\\beta$ there is a significant difference between a-synchronised and synchronised phase states, and one could expe...
Melanson, Alexandre; Mejias, Jorge F; Jun, James J; Maler, Leonard; Longtin, André
2017-01-01
The neural basis of spontaneous movement generation is a fascinating open question. Long-term monitoring of fish, swimming freely in a constant sensory environment, has revealed a sequence of behavioral states that alternate randomly and spontaneously between periods of activity and inactivity. We show that key dynamical features of this sequence are captured by a 1-D diffusion process evolving in a nonlinear double well energy landscape, in which a slow variable modulates the relative depth of the wells. This combination of stochasticity, nonlinearity, and nonstationary forcing correctly captures the vastly different timescales of fluctuations observed in the data (∼1 to ∼1000 s), and yields long-tailed residence time distributions (RTDs) also consistent with the data. In fact, our model provides a simple mechanism for the emergence of long-tailed distributions in spontaneous animal behavior. We interpret the stochastic variable of this dynamical model as a decision-like variable that, upon reaching a threshold, triggers the transition between states. Our main finding is thus the identification of a threshold crossing process as the mechanism governing spontaneous movement initiation and termination, and to infer the presence of underlying nonstationary agents. Another important outcome of our work is a dimensionality reduction scheme that allows similar segments of data to be grouped together. This is done by first extracting geometrical features in the dataset and then applying principal component analysis over the feature space. Our study is novel in its ability to model nonstationary behavioral data over a wide range of timescales.
A Stochastic Phase-Field Model Computed From Coarse-Grained Molecular Dynamics
von Schwerin, Erik
2007-01-01
Results are presented from numerical experiments aiming at the computation of stochastic phase-field models for phase transformations by coarse-graining molecular dynamics. The studied phase transformations occur between a solid crystal and a liquid. Nucleation and growth, sometimes dendritic, of crystal grains in a sub-cooled liquid is determined by diffusion and convection of heat, on the macroscopic level, and by interface effects, where the width of the solid-liquid interface is on an atomic length-scale. Phase-field methods are widely used in the study of the continuum level time evolution of the phase transformations; they introduce an order parameter to distinguish between the phases. The dynamics of the order parameter is modelled by an Allen--Cahn equation and coupled to an energy equation, where the latent heat at the phase transition enters as a source term. Stochastic fluctuations are sometimes added in the coupled system of partial differential equations to introduce nucleation and to get qualita...
Keith, David A; Akçakaya, H Resit; Thuiller, Wilfried; Midgley, Guy F; Pearson, Richard G; Phillips, Steven J; Regan, Helen M; Araújo, Miguel B; Rebelo, Tony G
2008-10-23
Species responses to climate change may be influenced by changes in available habitat, as well as population processes, species interactions and interactions between demographic and landscape dynamics. Current methods for assessing these responses fail to provide an integrated view of these influences because they deal with habitat change or population dynamics, but rarely both. In this study, we linked a time series of habitat suitability models with spatially explicit stochastic population models to explore factors that influence the viability of plant species populations under stable and changing climate scenarios in South African fynbos, a global biodiversity hot spot. Results indicate that complex interactions between life history, disturbance regime and distribution pattern mediate species extinction risks under climate change. Our novel mechanistic approach allows more complete and direct appraisal of future biotic responses than do static bioclimatic habitat modelling approaches, and will ultimately support development of more effective conservation strategies to mitigate biodiversity losses due to climate change.
Dynamic corner frequency in source spectral model for stochastic synthesis of ground motion
Institute of Scientific and Technical Information of China (English)
Xiaodan Sun; Xiaxin Tao; Guoxin Wang; Taojun Liu
2009-01-01
The static corner frequency and dynamic corner frequency in stochastic synthesis of ground motion from finite-fault modeling are introduced, and conceptual disadvantages of the two are discussed in this paper. Furthermore, the non-uniform radiation of seismic wave on the fault plane, as well as the trend of the larger rupture area, the lower corner frequency, can be described by the source spectral model developed by the authors. A new dynamic corner frequency can be developed directly from the model. The dependence of ground motion on the size of subfault can be eliminated if this source spectral model is adopted in the synthesis. Finally, the approach presented is validated from the comparison between the synthesized and observed ground motions at six rock stations during the Northridge earthquake in 1994.
Directory of Open Access Journals (Sweden)
Bruno H. Dias
2010-01-01
Full Text Available This paper presents a new approach for the expected cost-to-go functions modeling used in the stochastic dynamic programming (SDP algorithm. The SDP technique is applied to the long-term operation planning of electrical power systems. Using state space discretization, the Convex Hull algorithm is used for constructing a series of hyperplanes that composes a convex set. These planes represent a piecewise linear approximation for the expected cost-to-go functions. The mean operational costs for using the proposed methodology were compared with those from the deterministic dual dynamic problem in a case study, considering a single inflow scenario. This sensitivity analysis shows the convergence of both methods and is used to determine the minimum discretization level. Additionally, the applicability of the proposed methodology for two hydroplants in a cascade is demonstrated. With proper adaptations, this work can be extended to a complete hydrothermal system.
DEFF Research Database (Denmark)
Iversen, Jan Emil Banning; Morales González, Juan Miguel; Møller, Jan Kloppenborg
2017-01-01
a dynamic power curve. The model thus decomposes the dynamics of wind power prediction errors into wind speed forecast errors and errors related to the conversion from wind speed to wind power. We test the proposed model on an out-of-sample period of 1 year for a wind farm with a rated capacity of 21 MW...... of the uncertainty over time or the inter-temporal correlation of forecast errors for different horizons. This information is very important for forecast end-users optimizing time-dependent variables or dealing with multi-period decision-making problems, such as the management and operation of power systems...... with a high penetration of renewable generation. This paper provides input to these problems by proposing a model based on stochastic differential equations that allows generating predictive densities as well as scenarios for wind power. We build upon a probabilistic model for wind speed and introduce...
Stochastic Dynamics of Electrical Membrane with Voltage-Dependent Ion Channel Fluctuations
Qian, Hong; Qian, Min
2014-01-01
Brownian ratchet like stochastic theory for the electrochemical membrane system of Hodgkin-Huxley (HH) is developed. The system is characterized by a continuous variable $Q_m(t)$, representing mobile membrane charge density, and a discrete variable $K_t$ representing ion channel conformational dynamics. A Nernst-Planck-Nyquist-Johnson type equilibrium is obtained when multiple conducting ions have a common reversal potential. Detailed balance yields a previously unknown relation between the channel switching rates and membrane capacitance, bypassing Eyring-type explicit treatment of gating charge kinetics. From a molecular structural standpoint, membrane charge $Q_m$ is a more natural dynamic variable than potential $V_m$; our formalism treats $Q_m$-dependent conformational transition rates $\\lambda_{ij}$ as intrinsic parameters. Therefore in principle, $\\lambda_{ij}$ vs. $V_m$ is experimental protocol dependent,e.g., different from voltage or charge clamping measurements. For constant membrane capacitance pe...
Analytical vs. Simulation Solution Techniques for Pulse Problems in Non-linear Stochastic Dynamics
DEFF Research Database (Denmark)
Iwankiewicz, R.; Nielsen, Søren R. K.
-numerical techniques suitable for Markov response problems such as moments equation, Petrov-Galerkin and cell-to-cell mapping techniques are briefly discussed. Usefulness of these techniques is limited by the fact that effectiveness of each of them depends on the mean rate of impulses. Another limitation is the size...... of the problem, i.e. the number of state variables of the dynamical systems. In contrast, the application of the simulation techniques is not limited to Markov problems, nor is it dependent on the mean rate of impulses. Moreover their use is straightforward for a large class of point processes, at least......Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically...
A stochastic, local mode study of neon-liquid surface collision dynamics.
Packwood, Daniel M; Phillips, Leon F
2011-01-14
Equations of motion for a fast, light rare gas atom passing over a liquid surface are derived and used to infer the dynamics of neon collisions with squalane and perfluorinated polyether surfaces from experimental data. The equations incorporate the local mode model of a liquid surface via a stochastic process and explicitly account for impulsive collisional energy loss to the surface. The equations predict angular distributions for scattering of neon that are in good quantitative agreement with experimental data. Our key dynamical conclusions are that experimental angular distributions derive mainly from local mode surface topography rather than from structural features of individual surface molecules, and that the available data for these systems can be accounted for almost exclusively by single collisions between neon atoms and the liquid surface.
DEFF Research Database (Denmark)
Davidsen, Claus; Liu, Suxia; Mo, Xinguo
2014-01-01
costs. As in traditional SDP approaches, one step-ahead sub-problems are solved to find the optimal management at any time knowing the inflow scenario and reservoir/aquifer storage levels. These non-linear sub-problems are solved using a genetic algorithm (GA) that minimizes the sum of the immediate......, reservoir states, and inflow scenarios are used as future costs to drive a forward moving simulation under uncertain water availability. The use of a GA to solve the sub-problems is computationally more costly than a traditional SDP approach with linearly interpolated future costs. However, in a two....... A stochastic dynamic programming (SDP) approach is used to minimize the basin-wide total costs arising from water allocations and water curtailments. Dynamic allocation problems with inclusion of groundwater resources proved to be more complex to solve with SDP than pure surface water allocation problems due...
An Algorithm for the Stochastic Simulation of Gene Expression and Heterogeneous Population Dynamics
Charlebois, Daniel A; Fraser, Dawn; Kaern, Mads
2011-01-01
We present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics. The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte Carlo method to simulate time-dependent statistical characteristics of growing cell populations. To benchmark performance, we compare simulation results with steadystate and time-dependent analytical solutions for several scenarios, including steadystate and time-dependent gene expression, and the effects on population heterogeneity of cell growth, division, and DNA replication. This comparison demonstrates that the algorithm provides an efficient and accurate approach to simulate how complex biological features influence gene expression. We also use the algorithm to model gene expression dynamics within "bet-hedging" cell populations during their adaption to environmental stress. These simulations indicate that the algorithm provides a framework suitable for simulating and ana...
de Mendonça, J. Ricardo G.
2012-01-01
We investigate the interface dynamics of the two-dimensional stochastic Ising model in an external field under helicoidal boundary conditions. At sufficiently low temperatures and fields, the dynamics of the interface is described by an exactly solvable high-spin asymmetric quantum Hamiltonian that is the infinitesimal generator of the zero range process. Generally, the critical dynamics of the interface fluctuations is in the Kardar-Parisi-Zhang universality class of critical behavior. We re...
Miyamoto, Hitoshi; Kimura, Ryo
2016-09-01
This paper proposes a stochastic evaluation method for examining tree population states in a river cross section using an integrated model with Monte Carlo simulation. The integrated model consists of four processes as submodels, i.e., tree population dynamics, flow discharge stochasticity, stream hydraulics, and channel geomorphology. A floodplain of the Kako River in Japan was examined as a test site, which is currently well vegetated and features many willows that have been growing in both individual size and overall population over the last several decades. The model was used to stochastically evaluate the effects of hydrologic and geomorphologic changes on tree population dynamics through the Monte Carlo simulation. The effects including the magnitude of flood impacts and the relative change in the floodplain level are examined using very simple scenarios for flow regulation, climate change, and channel form changes. The stochastic evaluation method revealed a tradeoff point in floodplain levels, at which the tendency of a fully vegetated state switches to that of a bare floodplain under small impacts of flood. It is concluded from these results that the states of tree population in a floodplain can be determined by the mutual interactions among flood impacts, seedling recruitment, tree growth, and channel geomorphology. These interactions make it difficult to obtain a basic understanding of tree population dynamics from a field study of a specific floodplain. The stochastic approach used in this paper could constitute an effective method for evaluating fundamental channel characteristics for a vegetated floodplain.
Sensitivity of train stochastic dynamics to long-term evolution of track irregularities
Lestoille, N.; Soize, C.; Funfschilling, C.
2016-05-01
The influence of the track geometry on the dynamic response of the train is of great concern for the railway companies, because they have to guarantee the safety of the train passengers in ensuring the stability of the train. In this paper, the long-term evolution of the dynamic response of the train on a stretch of the railway track is studied with respect to the long-term evolution of the track geometry. The characterisation of the long-term evolution of the train response allows the railway companies to start off maintenance operations of the track at the best moment. The study is performed using measurements of the track geometry, which are carried out very regularly by a measuring train. A stochastic model of the studied stretch of track is created in order to take into account the measurement uncertainties in the track geometry. The dynamic response of the train is simulated with a multibody software. A noise is added in output of the simulation to consider the uncertainties in the computational model of the train dynamics. Indicators on the dynamic response of the train are defined, allowing to visualize the long-term evolution of the stability and the comfort of the train, when the track geometry deteriorates.
Wang, Xiu-Ling; Gao, Xin-Qi; Wang, Xue-Chen
2011-08-01
Actin filaments and chloroplasts in guard cells play roles in stomatal function. However, detailed actin dynamics vary, and the roles that they play in chloroplast localization during stomatal movement remain to be determined. We examined the dynamics of actin filaments and chloroplast localization in transgenic tobacco expressing green fluorescent protein (GFP)-mouse talin in guard cells by time-lapse imaging. Actin filaments showed sliding, bundling and branching dynamics in moving guard cells. During stomatal movement, long filaments can be severed into small fragments, which can form longer filaments by end-joining activities. With chloroplast movement, actin filaments near chloroplasts showed severing and elongation activity in guard cells during stomatal movement. Cytochalasin B treatment abolished elongation, bundling and branching activities of actin filaments in guard cells, and these changes of actin filaments, and as a result, more chloroplasts were localized at the centre of guard cells. However, chloroplast turning to avoid high light, and sliding of actin fragments near the chloroplast, was unaffected following cytochalasin B treatment in guard cells. We suggest that the sliding dynamics of actin may play roles in chloroplast turning in guard cells. Our results indicate that the stochastic dynamics of actin filaments in guard cells regulate chloroplast localization during stomatal movement.
Wilson, James D; Woodall, William H
2016-01-01
In many applications it is of interest to identify anomalous behavior within a dynamic interacting system. Such anomalous interactions are reflected by structural changes in the network representation of the system. We propose and investigate the use of a dynamic version of the degree corrected stochastic block model (DCSBM) as a means to model and monitor dynamic networks that undergo a significant structural change. Our model provides a means to simulate a variety of local and global changes in a time-varying network. Furthermore, one can efficiently detect such changes using the maximum likelihood estimates of the parameters that characterize the DCSBM. We assess the utility of the dynamic DCSBM on both simulated and real networks. Using a simple monitoring strategy on the DCSBM, we are able to detect significant changes in the U.S. Senate co-voting network that reflects both times of cohesion and times of polarization among Republican and Democratic members. Our analysis suggests that the dynamic DCSBM pr...
Yang, Hong-Liu; Radons, Günter
2008-01-01
Crossover from weak to strong chaos in high-dimensional Hamiltonian systems at the strong stochasticity threshold (SST) was anticipated to indicate a global transition in the geometric structure of phase space. Our recent study of Fermi-Pasta-Ulam models showed that corresponding to this transition the energy density dependence of all Lyapunov exponents is identical apart from a scaling factor. The current investigation of the dynamic XY model discovers an alternative scenario for the energy dependence of the system dynamics at SSTs. Though similar in tendency, the Lyapunov exponents now show individually different energy dependencies except in the near-harmonic regime. Such a finding restricts the use of indices such as the largest Lyapunov exponent and the Ricci curvatures to characterize the global transition in the dynamics of high-dimensional Hamiltonian systems. These observations are consistent with our conjecture that the quasi-isotropy assumption works well only when parametric resonances are the dominant sources of dynamical instabilities. Moreover, numerical simulations demonstrate the existence of hydrodynamical Lyapunov modes (HLMs) in the dynamic XY model and show that corresponding to the crossover in the Lyapunov exponents there is also a smooth transition in the energy density dependence of significance measures of HLMs. In particular, our numerical results confirm that strong chaos is essential for the appearance of HLMs.
Stochastic processes - quantum physics
Energy Technology Data Exchange (ETDEWEB)
Streit, L. (Bielefeld Univ. (Germany, F.R.))
1984-01-01
The author presents an elementary introduction to stochastic processes. He starts from simple quantum mechanics and considers problems in probability, finally presenting quantum dynamics in terms of stochastic processes.
Dynamic UAV-based traffic monitoring under uncertainty as a stochastic arc-inventory routing policy
Directory of Open Access Journals (Sweden)
Joseph Y.J. Chow
2016-10-01
Full Text Available Given the rapid advances in unmanned aerial vehicles, or drones, and increasing need to monitor at a city level, one of the current research gaps is how to systematically deploy drones over multiple periods. We propose a real-time data-driven approach: we formulate the first deterministic arc-inventory routing problem and derive its stochastic dynamic policy. The policy is expected to be of greatest value in scenarios where uncertainty is highest and costliest, such as city monitoring during major events. The Bellman equation for an approximation of the proposed inventory routing policy is formulated as a selective vehicle routing problem. We propose an approximate dynamic programming algorithm based on Least Squares Monte Carlo simulation to find that policy. The algorithm has been modified so that the least squares dependent variable is defined to be the “expected stock out cost upon the next replenishment”. The new algorithm is tested on 30 simulated instances of real time trajectories over 5 time periods of the selective vehicle routing problem to evaluate the proposed policy and algorithm. Computational results on the selected instances show that the algorithm on average outperforms the myopic policy by 23–28%, depending on the parametric design. Further tests are conducted on classic benchmark arc routing problem instances. The 11-link instance gdb19 (Golden et al., 1983 is expanded into a sequential 15-period stochastic dynamic example and used to demonstrate why a naïve static multi-period deployment plan would not be effective in real networks.
Institute of Scientific and Technical Information of China (English)
KANG Yan-Mei; JIANG Yao-Lin
2008-01-01
To explore the influence of anomalous diffusion on stochastic resonance (SR) more deeply and effectively, the method of moments is extended to subdiffusive overdamped bistable fractional Fokker-Planck systems for calculating the long-time linear dynamic response. It is found that the method of moments attains high accuracy with the truncation order N = 10, and in normal diffusion such obtained spectral amplification factor (SAF) of the first-order harmonic is also confirmed by stochastic simulation. Observing the SAF of the odd-order harmonics we find some interesting results, i.e. for smaller driving frequency the decrease of subdiffusion exponent inhibits the stochastic resonance (SR), while for larger driving frequency the decrease of subdiffusion exponent enhances the second SR peak, but the first one vanishes and a double SR is induced in the third-order harmonic at the same time. These observations suggest that the anomalous diffusion has important influence on the bistable dynamics.
Energy Technology Data Exchange (ETDEWEB)
Lu, Yunfan, E-mail: yunfanlu@yeah.net; Wang, Jun; Niu, Hongli
2015-06-12
An agent-based financial stock price model is developed and investigated by a stochastic interacting epidemic system, which is one of the statistical physics systems and has been used to model the spread of an epidemic or a forest fire. Numerical and statistical analysis are performed on the simulated returns of the proposed financial model. Complexity properties of the financial time series are explored by calculating the correlation dimension and using the modified multiscale entropy method. In order to verify the rationality of the financial model, the real stock market indexes, Shanghai Composite Index and Shenzhen Component Index, are studied in comparison with the simulation data of the proposed model for the different infectiousness parameters. The empirical research reveals that this financial model can reproduce some important features of the real stock markets. - Highlights: • A new agent-based financial price model is developed by stochastic interacting epidemic system. • The structure of the proposed model allows to simulate the financial dynamics. • Correlation dimension and MMSE are applied to complexity analysis of financial time series. • Empirical results show the rationality of the proposed financial model.
A Stochastic Fractional Dynamics Model of Space-time Variability of Rain
Kundu, Prasun K.; Travis, James E.
2013-01-01
Rainfall varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, that allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and times scales. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and in Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to the second moment statistics of radar data. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well without any further adjustment.
An effective field theory during inflation II: stochastic dynamics and power spectrum suppression
Boyanovsky, D
2015-01-01
We obtain the non-equilibrium effective action of an inflaton like scalar field --the system-- by tracing over sub Hubble degrees of freedom of ``environmental'' light scalar fields. The effective action is stochastic leading to effective Langevin equations of motion for the fluctuations of the inflaton-like field, with self-energy corrections and stochastic noise correlators that obey a de Sitter space-time analog of a fluctuation dissipation relation. We solve the Langevin equation implementing a dynamical renormalization group resummation of the leading secular terms and obtain the corrections to the power spectrum of super Hubble fluctuations of the inflaton field, $\\mathcal{P}(k;\\eta) = \\mathcal{P}_0(k)\\,e^{-\\gamma(k;\\eta)}$ where $\\mathcal{P}_0(k)$ is the nearly scale invariant power spectrum in absence of coupling. $\\gamma(k;\\eta)>0$ describes the suppression of the power spectrum, it features Sudakov-type double logarithms and entails violations of scale invariance. We also obtain the effective action...
On p-adic Stochastic Dynamics, Supersymmetry and the Riemann Conjecture
Castro, C
2001-01-01
We construct (assuming the quantum inverse scattering problem has a solution) the operator that yields the zeroes of the Riemman zeta function by defining explicitly the supersymmetric quantum mechanical model (SUSY QM) associated with the p-adic stochastic dynamics of a particle undergoing a Brownian random walk . The zig-zagging occurs after collisions with an infinite array of scattering centers that fluctuate ~randomly. Since the prime numbers are themselves randomly distributed, this physical system can be reformulated as the scattering of the particle about the infinite locations of the prime numbers positions. We are able then to reformulate such p-adic stochastic process, that has an underlying hidden Parisi-Sourlas supersymmetry, as the effective motion of a particle in a potential due to an infinite collection of p-adic harmonic oscillators with fundamental (Wick-rotated imaginary) frequencies $\\omega_p = i log~p$ (p is a prime) and whose harmonics are $\\omega_{p, n} = i log ~ p^n$. The p-adic harmo...
Stochastic Lagrangian dynamics for charged flows in the E-F regions of ionosphere
Tang, Wenbo; Mahalov, Alex
2013-03-01
We develop a three-dimensional numerical model for the E-F region ionosphere and study the Lagrangian dynamics for plasma flows in this region. Our interest rests on the charge-neutral interactions and the statistics associated with stochastic Lagrangian motion. In particular, we examine the organizing mixing patterns for plasma flows due to polarized gravity wave excitations in the neutral field, using Lagrangian coherent structures (LCS). LCS objectively depict the flow topology—the extracted attractors indicate generation of ionospheric density gradients, due to accumulation of plasma. Using Lagrangian measures such as the finite-time Lyapunov exponents, we locate the Lagrangian skeletons for mixing in plasma, hence where charged fronts are expected to appear. With polarized neutral wind, we find that the corresponding plasma velocity is also polarized. Moreover, the polarized velocity alone, coupled with stochastic Lagrangian motion, may give rise to polarized density fronts in plasma. Statistics of these trajectories indicate high level of non-Gaussianity. This includes clear signatures of variance, skewness, and kurtosis of displacements taking polarized structures aligned with the gravity waves, and being anisotropic.
Energy Technology Data Exchange (ETDEWEB)
Wu, Wei [Department of Physics and Astronomy and Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794 (United States); Wang, Jin, E-mail: jin.wang.1@stonybrook.edu [Department of Physics and Astronomy and Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794 (United States); State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, 130022 Changchun, China and College of Physics, Jilin University, 130021 Changchun (China)
2014-09-14
We have established a general non-equilibrium thermodynamic formalism consistently applicable to both spatially homogeneous and, more importantly, spatially inhomogeneous systems, governed by the Langevin and Fokker-Planck stochastic dynamics with multiple state transition mechanisms, using the potential-flux landscape framework as a bridge connecting stochastic dynamics with non-equilibrium thermodynamics. A set of non-equilibrium thermodynamic equations, quantifying the relations of the non-equilibrium entropy, entropy flow, entropy production, and other thermodynamic quantities, together with their specific expressions, is constructed from a set of dynamical decomposition equations associated with the potential-flux landscape framework. The flux velocity plays a pivotal role on both the dynamic and thermodynamic levels. On the dynamic level, it represents a dynamic force breaking detailed balance, entailing the dynamical decomposition equations. On the thermodynamic level, it represents a thermodynamic force generating entropy production, manifested in the non-equilibrium thermodynamic equations. The Ornstein-Uhlenbeck process and more specific examples, the spatial stochastic neuronal model, in particular, are studied to test and illustrate the general theory. This theoretical framework is particularly suitable to study the non-equilibrium (thermo)dynamics of spatially inhomogeneous systems abundant in nature. This paper is the second of a series.
On the numerical treatment of dissipative particle dynamics and related systems
Leimkuhler, Benedict
2014-01-01
We review and compare numerical methods that simultaneously control temperature while preserving the momentum, a family of particle simulation methods commonly used for mesoscale models for complex fluids and polymers. The class of methods considered includes dissipative particle dynamics (DPD) as well as extended stochastic-dynamics models incorporating a generalized pairwise thermostat scheme in which stochastic forces are eliminated and the coefficient of dissipation is treated as an additional auxiliary variable subject to a feedback (kinetic energy) control mechanism. In the latter case, we consider the addition of a coupling of the auxiliary variable, as in the Nos\\'{e}-Hoover-Langevin (NHL) method, with stochastic dynamics to ensure ergodicity, and find that the convergence of ensemble averages is substantially improved. The techniques discussed here are fully consistent with hydrodynamics (Galilean invariant) and straightforward to treat numerically. To this end, splitting methods are developed and st...
Energy Technology Data Exchange (ETDEWEB)
Cheng, Mulin, E-mail: mulinch@caltech.edu; Hou, Thomas Y., E-mail: hou@cms.caltech.edu; Zhang, Zhiwen, E-mail: zhangzw@caltech.edu
2013-06-01
We propose a dynamically bi-orthogonal method (DyBO) to solve time dependent stochastic partial differential equations (SPDEs). The objective of our method is to exploit some intrinsic sparse structure in the stochastic solution by constructing the sparsest representation of the stochastic solution via a bi-orthogonal basis. It is well-known that the Karhunen–Loeve expansion (KLE) minimizes the total mean squared error and gives the sparsest representation of stochastic solutions. However, the computation of the KL expansion could be quite expensive since we need to form a covariance matrix and solve a large-scale eigenvalue problem. The main contribution of this paper is that we derive an equivalent system that governs the evolution of the spatial and stochastic basis in the KL expansion. Unlike other reduced model methods, our method constructs the reduced basis on-the-fly without the need to form the covariance matrix or to compute its eigendecomposition. In the first part of our paper, we introduce the derivation of the dynamically bi-orthogonal formulation for SPDEs, discuss several theoretical issues, such as the dynamic bi-orthogonality preservation and some preliminary error analysis of the DyBO method. We also give some numerical implementation details of the DyBO methods, including the representation of stochastic basis and techniques to deal with eigenvalue crossing. In the second part of our paper [11], we will present an adaptive strategy to dynamically remove or add modes, perform a detailed complexity analysis, and discuss various generalizations of this approach. An extensive range of numerical experiments will be provided in both parts to demonstrate the effectiveness of the DyBO method.
Energy Technology Data Exchange (ETDEWEB)
Zhu, Zhi-Wen [Department of Mechanics, Tianjin University, 92 Weijin Road, Nankai District, Tianjin 300072 (China); Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control 92 Weijin Road, Nankai District, Tianjin 300072 (China); Zhang, Qing-Xin [Department of Mechanics, Tianjin University, 92 Weijin Road, Nankai District, Tianjin 300072 (China); Xu, Jia, E-mail: xujia_ld@163.com [Department of Mechanics, Tianjin University, 92 Weijin Road, Nankai District, Tianjin 300072 (China)
2014-11-03
A kind of shape memory alloy (SMA) hysteretic nonlinear model was developed, and the nonlinear dynamics and bifurcation characteristics of the SMA thin film subjected to in-plane stochastic excitation were investigated. Van der Pol difference item was introduced to describe the hysteretic phenomena of the SMA strain–stress curves, and the nonlinear dynamic model of the SMA thin film subjected to in-plane stochastic excitation was developed. The conditions of global stochastic stability of the system were determined in singular boundary theory, and the probability density function of the system response was obtained. Finally, the conditions of stochastic Hopf bifurcation were analyzed. The results of theoretical analysis and numerical simulation indicate that self-excited vibration is induced by the hysteretic nonlinear characteristics of SMA, and stochastic Hopf bifurcation appears when the bifurcation parameter was changed; there are two limit cycles in the stationary probability density of the dynamic response of the system in some cases, which means that there are two vibration amplitudes whose probabilities are both very high, and jumping phenomena between the two vibration amplitudes appear with the change in conditions. The results obtained in this current paper are helpful for the application of the SMA thin film in stochastic vibration fields. - Highlights: • Hysteretic nonlinear model of shape memory alloy was developed. • Van der Pol item was introduced to interpret hysteretic strain–stress curves. • Nonlinear dynamic characteristics of the shape memory alloy film were analyzed. • Jumping phenomena were observed in the change of the parameters.
Directory of Open Access Journals (Sweden)
Yijin Zhang
2013-01-01
Full Text Available This work is concerned with the random dynamics of two-dimensional stochastic Boussinesq system with dynamical boundary condition. The white noises affect the system through a dynamical boundary condition. Using a method based on the theory of omega-limit compactness of a random dynamical system, we prove that the L2-random attractor for the generated random dynamical system is exactly the H1-random attractor. This improves a recent conclusion derived by Brune et al. on the existence of the L2-random attractor for the same system.
Directory of Open Access Journals (Sweden)
Muhammad Ramzan Luhur
2014-01-01
Full Text Available This contribution provides the development of a stochastic lift and drag model for an airfoil FX 79-W-151A under unsteady wind inflow based on wind tunnel measurements. Here we present the integration of the stochastic model into a well-known standard BEM (Blade Element Momentum model to obtain the corresponding aerodynamic forces on a rotating blade element. The stochastic model is integrated as an alternative to static tabulated data used by classical BEM. The results show that in comparison to classical BEM, the BEM with stochastic approach additionally reflects the local force dynamics and therefore provides more information on aerodynamic forces that can be used by wind turbine simulation codes
Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed
2017-03-01
In this paper, we develop a mathematical model for a tuberculosis model with constant recruitment and varying total population size by incorporating stochastic perturbations. By constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of an ergodic stationary distribution as well as extinction of the disease to the stochastic system.
Application of dynamic stochastic general equilibrium models to the case of the Serbian economy
Directory of Open Access Journals (Sweden)
Urošević Branko
2014-01-01
Full Text Available This paper proposes a dynamic stochastic general equilibrium (DSGE model for the Serbian economy. It is a modification of the existing models of Goodhart, Osorio and Tsomocos (2009 and Martinez and Tsomocos (2012. The model introduces important features of the Serbian economy, financial dollarization and foreign ownership of the banking system, while retaining the most important element of the reference models, financial friction. To solve the model we use Dynare, a specialized Matlab program for solving DSGE models. The model is subject to three different shocks: monetary, productivity, and regulatory, and the results are presented in the form of impulse response functions. It is concluded that the proposed platform has good characteristics, but its complete application to the case of the Serbian economy requires further research. [Projekat Ministarstva nauke Republike Srbije, br. 179005
DEFF Research Database (Denmark)
Davidsen, Claus; Cardenal, Silvio Javier Pereira; Liu, Suxia;
2015-01-01
of stochastic dynamic programming, to optimize water resources management in the Ziya River basin. Natural runoff from the upper basin was estimated with a rainfall-runoff model autocalibrated using in situ measured discharge. The runoff serial correlation was described by a Markov chain and used as input...... for the optimization model. This model was used to assess the economic impacts of ecosystem minimum flow constraints, limited groundwater pumping, and the middle route of the South–North Water Transfer Project (SNWTP). A regional climate shift has exacerbated water scarcity and increased water values, resulting...... in stricter water management. The results show that the SNWTP reduces the impacts of water scarcity and impacts optimal water management in the basin. The presented modeling framework provides an objective basis for the development of tools to avoid overpumping groundwater resources at minimum costs....
Stochastic dynamics and the predictability of big hits in online videos
Miotto, Jose M; Altmann, Eduardo G
2016-01-01
The competition for the attention of users is a central element of the Internet. Crucial issues are the origin and predictability of big hits, the few items that capture a big portion of the total attention. We address these issues analyzing 10 million time series of videos' views from YouTube. We find that the average gain of views is linearly proportional to the number of views a video already has, in agreement with usual rich-get-richer mechanisms and Gibrat's law, but this fails to explain the prevalence of big hits. The reason is that the fluctuations around the average views are themselves heavy tailed. Based on these empirical observations, we propose a stochastic differential equation with Le\\'evy noise as a model of the dynamics of videos. We show how this model is substantially better in estimating the probability of an ordinary item becoming a big hit, which is considerably underestimated in the traditional proportional-growth models.
Using stochastic dynamic programming to support catchment-scale water resources management in China
DEFF Research Database (Denmark)
Davidsen, Claus; Cardenal, Silvio Javier Pereira; Liu, Suxia
2013-01-01
allocation costs for the different water sources (surface water, groundwater and external water) and fixed costs of water supply curtailment. The multiple reservoirs in the basin are aggregated into a single reservoir to reduce the dimensions of decisions. Water availability is estimated using a hydrological...... to low and extremely seasonal precipitation, and the intense agricultural production is highly dependent on irrigation. Large reservoirs provide water storage for dry months while groundwater and the external South-to-North Water Transfer Project are alternative sources of water. An optimization model...... based on stochastic dynamic programming has been developed. The objective function is to minimize the total cost of supplying water to the users, while satisfying minimum ecosystem flow constraints. Each user group (agriculture, domestic and industry) is characterized by fixed demands, fixed water...
Coarse-graining the calcium dynamics on a stochastic reaction-diffusion lattice model
Shen, Chuansheng
2013-01-01
We develop a coarse grained (CG) approach for efficiently simulating calcium dynamics in the endoplasmic reticulum membrane based on a fine stochastic lattice gas model. By grouping neighboring microscopic sites together into CG cells and deriving CG reaction rates using local mean field approximation, we perform CG kinetic Monte Carlo (kMC) simulations and find the results of CG-kMC simulations are in excellent agreement with that of the microscopic ones. Strikingly, there is an appropriate range of coarse proportion $m$, corresponding to the minimal deviation of the phase transition point compared to the microscopic one. For fixed $m$, the critical point increases monotonously as the system size increases, especially, there exists scaling law between the deviations of the phase transition point and the system size. Moreover, the CG approach provides significantly faster Monte Carlo simulations which are easy to implement and are directly related to the microscopics, so that one can study the system size eff...
Stochastic predator-prey dynamics of transposons in the human genome
Xue, Chi
2016-01-01
Transposable elements (TE) are DNA sequences that can jump from site to site in the genome during the life cycle of a cell, usually encoding the very enzymes which perform their excision. However, some TEs are parasitic, relying on the enzymes produced by the regular TEs. In this case, we show that a stochastic model, which takes into account the small copy numbers of the TEs in a cell, predicts noise-induced predator-prey oscillations with a characteristic time scale that is much longer than the cell replication time, indicating that the state of the predator-prey oscillator is stored in the genome and transmitted to successive generations. Our work demonstrates the important role of number fluctuations in the expression of mobile genetic elements, and shows explicitly how ecological concepts can be applied to the dynamics and fluctuations of living genomes.
Beam dynamics simulations in laser electron storage rings and optical stochastic cooling
Duru, Alper
Laser-electron storage rings are potential compact X-ray sources. Longitudinal dynamics in laser-electron storage rings is studied including the effects of both laser interaction and synchrotron radiation. It is shown that the steady state energy spread can reach as high as a few percent. The main reason is the wide spread in the energy loss by electrons to laser photons. Optical stochastic cooling has been studied numerically. The effects of the finite bandwidth of the amplifier are mixing and signal distortion. Both are included in the simulations and the results are compared to theoretical results. It is shown that the beam can be cooled both in transverse and longitudinal phase phase spaces simultaneously.
Stochastic Predator-Prey Dynamics of Transposons in the Human Genome
Xue, Chi; Goldenfeld, Nigel
2016-11-01
Transposable elements, or transposons, are DNA sequences that can jump from site to site in the genome during the life cycle of a cell, usually encoding the very enzymes which perform their excision. However, some transposons are parasitic, relying on the enzymes produced by the regular transposons. In this case, we show that a stochastic model, which takes into account the small copy numbers of the active transposons in a cell, predicts noise-induced predator-prey oscillations with a characteristic time scale that is much longer than the cell replication time, indicating that the state of the predator-prey oscillator is stored in the genome and transmitted to successive generations. Our work demonstrates the important role of the number fluctuations in the expression of mobile genetic elements, and shows explicitly how ecological concepts can be applied to the dynamics and fluctuations of living genomes.
Stochastic Dynamic Programming for Three-Echelon Inventory System of Limited Shelf Life Products
Directory of Open Access Journals (Sweden)
Galal Noha M.
2016-01-01
Full Text Available Coordination of inventory decisions within the supply chain is one of the major determinants of its competitiveness in the global market. Products with limited shelf life impose additional challenges in managing the inventory across the supply chain because of the additional wastage costs incurred in case of being stored beyond product’s useful life. This paper presents a stochastic dynamic programming model for inventory replenishment in a serial multi-echelon distribution supply chain. The model considers uncertain stationary discrete demand at the retailer and zero lead time. The objective is to minimize expected total costs across the supply chain echelons, while maintaining a preset service level. The results illustrate that a cost saving of around 17% is achievable due to coordinating inventory decisions across the supply chain.
Garrett, Bruce C.; Swaminathan, P. K.; Murthy, C. S.; Redmon, Michael J.
1987-01-01
A variable time step algorithm has been implemented for solving the stochastic equations of motion for gas-surface collisions. It has been tested for a simple model of electronically inelastic collisions with an insulator surface in which the phonon manifold acts as a heat bath and electronic states are localized. In addition to reproducing the accurate nuclear dynamics of the surface atoms, numerical calculations have shown the algorithm to yield accurate ensemble averages of physical observables such as electronic transition probabilities and total energy loss of the gas atom to the surface. This new algorithm offers a gain in efficieny of up to an order of magnitude compared to fixed time step integration.
Stochastic dynamical model of a growing network based on self-exciting point process
Golosovsky, Michael; 10.1103/PhysRevLett.109.098701
2012-01-01
We perform experimental verification of the preferential attachment model that is commonly accepted as a generating mechanism of the scale-free complex networks. To this end we chose citation network of Physics papers and traced citation history of 40,195 papers published in one year. Contrary to common belief, we found that citation dynamics of the individual papers follows the \\emph{superlinear} preferential attachment, with the exponent $\\alpha= 1.25-1.3$. Moreover, we showed that the citation process cannot be described as a memoryless Markov chain since there is substantial correlation between the present and recent citation rates of a paper. Basing on our findings we constructed a stochastic growth model of the citation network, performed numerical simulations based on this model and achieved an excellent agreement with the measured citation distributions.
A stochastic model of the dynamics of HIV under a combination therapeutic intervention
Directory of Open Access Journals (Sweden)
VSS Yadavalli
2009-06-01
Full Text Available Drug resistance to single therapeutic treatment in HIV infected individuals has promoted research into combined treatments. In this paper we propose a stochastic model under combined therapeutic treatment by extending the model of HIV pathogenesis under treatment by anti-viral drugs given in [Perelson AS, Neumann AU, Markowits M, Leonard JM & Ho DD, 1996, "HIV-1 dynamics in vivo virion clearance rate, infected cell life span, and viral generation time", Science New Series, 271, pp. 1582-1586]. Variance and co-variance structures of variables are obtainable via this approach in addition to the mean numbers of free HIV, infectious free HIV and non-infectious free HIV that were obtained by Perelson et al. Comparing simulated data for before and after treatment indicates the importance of combined treatment and its overall effect(s.
Almaraz, Pablo; Green, Andy J; Aguilera, Eduardo; Rendón, Miguel A; Bustamante, Javier
2012-09-01
1. Understanding the impact of environmental variability on migrating species requires the estimation of sequential abiotic effects in different geographic areas across the life cycle. For instance, waterfowl (ducks, geese and swans) usually breed widely dispersed throughout their breeding range and gather in large numbers in their wintering headquarters, but there is a lack of knowledge on the effects of the sequential environmental conditions experienced by migrating birds on the long-term community dynamics at their wintering sites. 2. Here, we analyse multidecadal time-series data of 10 waterfowl species wintering in the Guadalquivir Marshes (SW Spain), the single most important wintering site for waterfowl breeding in Europe. We use a multivariate state-space approach to estimate the effects of biotic interactions, local environmental forcing during winter and large-scale climate during breeding and migration on wintering multispecies abundance fluctuations, while accounting for partial observability (observation error and missing data) in both population and environmental data. 3. The joint effect of local weather and large-scale climate explained 31·6% of variance at the community level, while the variability explained by interspecific interactions was negligible (observations through data augmentation increased the estimated magnitude of environmental forcing by an average 30·1% and reduced the impact of stochasticity by 39·3% when accounting for observation error. Interestingly however, the impact of environmental forcing on community dynamics was underestimated by an average 15·3% and environmental stochasticity overestimated by 14·1% when ignoring both observation error and data augmentation. 5. These results provide a salient example of sequential multiscale environmental forcing in a major migratory bird community, which suggests a demographic link between the breeding and wintering grounds operating through nonlinear environmental effects
Xu, Hao; Jagannathan, Sarangapani
2013-03-01
The stochastic optimal controller design for the nonlinear networked control system (NNCS) with uncertain system dynamics is a challenging problem due to the presence of both system nonlinearities and communication network imperfections, such as random delays and packet losses, which are not unknown a priori. In the recent literature, neuro dynamic programming (NDP) techniques, based on value and policy iterations, have been widely reported to solve the optimal control of general affine nonlinear systems. However, for realtime control, value and policy iterations-based methodology are not suitable and time-based NDP techniques are preferred. In addition, output feedback-based controller designs are preferred for implementation. Therefore, in this paper, a novel NNCS representation incorporating the system uncertainties and network imperfections is introduced first by using input and output measurements for facilitating output feedback. Then, an online neural network (NN) identifier is introduced to estimate the control coefficient matrix, which is subsequently utilized for the controller design. Subsequently, the critic and action NNs are employed along with the NN identifier to determine the forward-in-time, time-based stochastic optimal control of NNCS without using value and policy iterations. Here, the value function and control inputs are updated once a sampling instant. By using novel NN weight update laws, Lyapunov theory is used to show that all the closed-loop signals and NN weights are uniformly ultimately bounded in the mean while the approximated control input converges close to its target value with time. Simulation results are included to show the effectiveness of the proposed scheme.
Jun, James J.; Longtin, André
2017-01-01
Abstract The neural basis of spontaneous movement generation is a fascinating open question. Long-term monitoring of fish, swimming freely in a constant sensory environment, has revealed a sequence of behavioral states that alternate randomly and spontaneously between periods of activity and inactivity. We show that key dynamical features of this sequence are captured by a 1-D diffusion process evolving in a nonlinear double well energy landscape, in which a slow variable modulates the relative depth of the wells. This combination of stochasticity, nonlinearity, and nonstationary forcing correctly captures the vastly different timescales of fluctuations observed in the data (∼1 to ∼1000 s), and yields long-tailed residence time distributions (RTDs) also consistent with the data. In fact, our model provides a simple mechanism for the emergence of long-tailed distributions in spontaneous animal behavior. We interpret the stochastic variable of this dynamical model as a decision-like variable that, upon reaching a threshold, triggers the transition between states. Our main finding is thus the identification of a threshold crossing process as the mechanism governing spontaneous movement initiation and termination, and to infer the presence of underlying nonstationary agents. Another important outcome of our work is a dimensionality reduction scheme that allows similar segments of data to be grouped together. This is done by first extracting geometrical features in the dataset and then applying principal component analysis over the feature space. Our study is novel in its ability to model nonstationary behavioral data over a wide range of timescales. PMID:28374017
Institute of Scientific and Technical Information of China (English)
MA Juan; CHEN Jian-jun; XU Ya-lan; JIANG Tao
2006-01-01
A new fuzzy stochastic finite element method based on the fuzzy factor method and random factor method is given and the analysis of structural dynamic characteristic for fuzzy stochastic truss structures is presented. Considering the fuzzy randomness of the structural physical parameters and geometric dimensions simultaneously, the structural stiffness and mass matrices are constructed based on the fuzzy factor method and random factor method; from the Rayleigh's quotient of structural vibration, the structural fuzzy random dynamic characteristic is obtained by means of the interval arithmetic;the fuzzy numeric characteristics of dynamic characteristic are then derived by using the random variable's moment function method and algebra synthesis method. Two examples are used to illustrate the validity and rationality of the method given. The advantage of this method is that the effect of the fuzzy randomness of one of the structural parameters on the fuzzy randomness of the dynamic characteristic can be reflected expediently and objectively.
Hierarchical Control of Thermostatically Controller Loads for Primary Frequency Control
DEFF Research Database (Denmark)
Zhao, Haoran; Wu, Qiuwei; Huang, Shaojun
2016-01-01
This paper proposes a hierarchical control of Thermostatically Controlled Loads (TCLs) to provide primary frequency control support. The control architecture is comprised of three levels. At the high level, an aggregator coordinates multiple distribution substations and dispatches the primary...... respond to the frequency event autonomously. Case studies show that the proposed controller can efficiently respond to frequency events and fulfill the requirement specified by the system operator. The users’ comforts are not compromised and the short cycling of TCLs is largely reduced. Due...
Armstrong, Cameron R; David, John A; Thompson, John R
2015-07-13
We present a simple numerical model that is used in conjunction with a systematic algorithm for parameter optimization to understand the three-dimensional stochastic intensity dynamics of stimulated Brillouin scattering in a two-mode optical fiber. The primary factors driving the complex dynamics appear to be thermal density fluctuations, transverse pump fluctuations, and asymmetric transverse mode fractions over the beam cross-section.
Charalambous, Charalambos D.; Ahmed, Nasir U.
2013-01-01
In this paper, we present two methods which generalize static team theory to dynamic team theory, in the context of continuous-time stochastic nonlinear differential decentralized decision systems, with relaxed strategies, which are measurable to different noisy information structures. For both methods we apply Girsanov's measure transformation to obtain an equivalent dynamic team problem under a reference probability measure, so that the observations and information structures available for ...
Ross, J V
2010-01-07
The dynamics of many diseases and populations possess distinct recurring phases. For example, many species breed only during a subset of the year and the infection dynamics of many pathogens have transmission rates that vary with season. Here I investigate computational methods for studying transient and long-term behaviour of stochastic models which have periodic phases-several different potential techniques for studying long-term behaviour will be contrasted. I illustrate the results with two studies: The first is of a spatially realistic metapopulation model of malleefowl (Leipoa ocellata), a species which disperses only during a quarter of the year; this model is used to highlight the advantages and disadvantages of the particular methods presented. The second study is of a model for disease dynamics which incorporates seasonality in both the rate of within-population transmission and also in the rate of transmission effected via aerosol importation. This model has applications to studying disease invasion and persistence in captive-breeding populations. We demonstrate, via comparison to appropriately matched models with constant transmission rates and also no aerosol transmission, that seasonality and aerosol importation may alter control choices, with possibly an increase in the threshold population size for local control surveillance, transfer of importance to limiting aerosol transmission, and the use of temporally targetted surveillance. The methodology presented is the gold-standard for dealing with many phased processes in ecology and epidemiology, but its application is limited to systems of small size.
Hu, Yan; Wen, Jing-Ya; Li, Xiao-Li; Wang, Da-Zhou; Li, Yu
2013-10-15
A dynamic multimedia fuzzy-stochastic integrated environmental risk assessment approach was developed for contaminated sites management. The contaminant concentrations were simulated by a validated interval dynamic multimedia fugacity model, and different guideline values for the same contaminant were represented as a fuzzy environmental guideline. Then, the probability of violating environmental guideline (Pv) can be determined by comparison between the modeled concentrations and the fuzzy environmental guideline, and the constructed relationship between the Pvs and environmental risk levels was used to assess the environmental risk level. The developed approach was applied to assess the integrated environmental risk at a case study site in China, simulated from 1985 to 2020. Four scenarios were analyzed, including "residential land" and "industrial land" environmental guidelines under "strict" and "loose" strictness. It was found that PAH concentrations will increase steadily over time, with soil found to be the dominant sink. Source emission in soil was the leading input and atmospheric sedimentation was the dominant transfer process. The integrated environmental risks primarily resulted from petroleum spills and coke ovens, while the soil environmental risks came from coal combustion. The developed approach offers an effective tool for quantifying variability and uncertainty in the dynamic multimedia integrated environmental risk assessment and the contaminated site management.
Kuehn, Christian
2011-06-01
Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms “critical transition” or “tipping point” have been used to describe this situation. Critical transitions have been observed in an astonishingly diverse set of applications from ecosystems and climate change to medicine and finance. The main goal of this paper is to give an overview which standard mathematical theories can be applied to critical transitions. We shall focus on early-warning signs that have been suggested to predict critical transitions and point out what mathematical theory can provide in this context. Starting from classical bifurcation theory and incorporating multiple time scale dynamics one can give a detailed analysis of local bifurcations that induce critical transitions. We suggest that the mathematical theory of fast-slow systems provides a natural definition of critical transitions. Since noise often plays a crucial role near critical transitions the next step is to consider stochastic fast-slow systems. The interplay between sample path techniques, partial differential equations and random dynamical systems is highlighted. Each viewpoint provides potential early-warning signs for critical transitions. Since increasing variance has been suggested as an early-warning sign we examine it in the context of normal forms analytically, numerically and geometrically; we also consider autocorrelation numerically. Hence we demonstrate the applicability of early-warning signs for generic models. We end with suggestions for future directions of the theory.
Interpreting the power spectrum of Dansgaard-Oeschger events via stochastic dynamical systems
Mitsui, Takahito; Lenoir, Guillaume; Crucifix, Michel
2017-04-01
Dansgaard-Oeschger (DO) events are abrupt climate shifts, which are particularly pronounced in the North Atlantic region during glacial periods [Dansgaard et al. 1993]. The signals are most clearly found in δ 18O or log [Ca2+] records of Greenland ice cores. The power spectrum S(f) of DO events has attracted attention over two decades with debates on the apparent 1.5-kyr periodicity [Grootes & Stuiver 1997; Schultz et al. 2002; Ditlevsen et al. 2007] and scaling property over several time scales [Schmitt, Lovejoy, & Schertzer 1995; Rypdal & Rypdal 2016]. The scaling property is written most simply as S(f)˜ f-β , β ≈ 1.4. However, physical as well as underlying dynamics of the periodicity and the scaling property are still not clear. Pioneering works for modelling the spectrum of DO events are done by Cessi (1994) and Ditlevsen (1999), but their model-data comparisons of the spectra are rather qualitative. Here, we show that simple stochastic dynamical systems can generate power spectra statistically consistent with the observed spectra over a wide range of frequency from orbital to the Nyquist frequency (=1/40 yr-1). We characterize the scaling property of the spectrum by defining a local scaling exponentβ _loc. For the NGRIP log [Ca2+] record, the local scaling exponent β _loc increases from ˜ 1 to ˜ 2 as the frequency increases from ˜ 1/5000 yr-1 to ˜ 1/500 yr-1, and β _loc decreases toward zero as the frequency increases from ˜ 1/500 yr-1 to the Nyquist frequency. For the δ 18O record, the local scaling exponent β _loc increases from ˜ 1 to ˜ 1.5 as the frequency increases from ˜ 1/5000 yr^{-1 to ˜ 1/1000 yr-1, and β _loc decreases toward zero as the frequency increases from ˜ 1/1000 yr-1 to the Nyquist frequency. This systematic breaking of a single scaling is reproduced by the simple stochastic models. Especially, the models suggest that the flattening of the spectra starting from multi-centennial scale and ending at the Nyquist frequency
ASCERTAINMENT OF DYNAMIC CHARACTERISTICS OF THE INDUSTRIAL FACILITIES BY MEANS OF STOCHASTIC ACTIONS
Directory of Open Access Journals (Sweden)
Ya. А. Gusentsova
2016-01-01
Full Text Available The paper presents comparison of different methods for identifying the dynamic characteristics of objects associated with thermal energy generation or the medium cooling in the cooling systems of internal-combustion engines. Reaction identification to the reference exposure is considered, videlicet – stepwise, impulse and harmonic. The study shows that on a number of occasions for the type of objects being involved their application is unacceptable. In those instances it is expediential to apply statistical characteristics of the input and output signals, i. a. to employ the data of so-called passive experiment. In which case the task is divisible into two stages – determination of statistical characteristics of the variates at the ins and outs of the object and calculation of the dynamic characteristics based on them. The statistical characteristics of the variates at the input and output are obtained through time averaging of values of the variates dependent on the ordinate of the processes. Inasmuch as stochastic processes occurring in the objects under examination possess ergodic property, their averaged values are constant. All the data required for calculating characteristics of the linear systems appears in their correlative functions. Heat generating objects as well as the cooling systems of internal-combustion engines are the objects fed back by the regulator. Therefore, in this instance cross-correlated functions are employed for determining their dynamic characteristics. The suggested random-input analytical method for dynamic characteristics constitutes a good match with the results of active experiments reported in a variety of sources. This allows recommending the random signals estimation method of dynamic characteristics for the involved type of objects.
Stochastic dynamics of superparamagnetic moments in polidisperse ferrofluids
Scherer, C.
2007-12-01
In previous works, we studied the dynamics of the magnetic moments in ferrofluids te{schererBJP,scherer-matuttis, scherer-ricci}, and other authors have also dealt with this problem te{shliomis}. In our previous works also computational simulations have been performed. The present work differs from those in two important aspects: (i) the magnetic particles are not of uniform size, but have a lognormal distribution of diameters; (ii) the parameters used in the simulations, like magnetization, anisotropy constant, liquid viscosity, applied field, temperature, etc., correspond to the values for realistic ferrofluids (in the previous works we used values, which were convenient for the simulations). For this reason, we will briefly re-derive the equations of motion, keeping all the relevant constants in them. To avoid big powers of 10 in the simulations, we introduce an appropriate system of units. The equations of motion for the particles' rotation and for the rotation of their magnetic moments are stochastic differential equations with multiplicative noise. Therefore, they have to be interpreted as Stratonovich-Langevin equations and the roles of stochastic calculus have to be used in the simulations. In our simulations, the response functions are "measured" and from them the complex susceptibilities are calculated. We performed several simulations, varying each parameter around a standard value, in order to see how the susceptibilities are correlated with the physical constants of the material. In the conclusions of special mention is the verification that the line broadening is very big. To be explicit, the ratio of the line-width of the polydisperse to that of the monodisperse with a diameter equal to the median diameter of the polydisperse, is much bigger than the ratio of the diameter's distribution width to the median diameter. It is interesting to note that for small dispersion width of diameters the resonance frequency does not change significantly with
Stochastic Dynamics of Proteins and the Action of Biological Molecular Machines
Directory of Open Access Journals (Sweden)
Michal Kurzynski
2014-04-01
Full Text Available It is now well established that most if not all enzymatic proteins display a slow stochastic dynamics of transitions between a variety of conformational substates composing their native state. A hypothesis is stated that the protein conformational transition networks, as just as higher-level biological networks, the protein interaction network, and the metabolic network, have evolved in the process of self-organized criticality. Here, the criticality means that all the three classes of networks are scale-free and, moreover, display a transition from the fractal organization on a small length-scale to the small-world organization on the large length-scale. Good mathematical models of such networks are stochastic critical branching trees extended by long-range shortcuts. Biological molecular machines are proteins that operate under isothermal conditions and hence are referred to as free energy transducers. They can be formally considered as enzymes that simultaneously catalyze two chemical reactions: the free energy-donating (input reaction and the free energy-accepting (output one. The far-from-equilibrium degree of coupling between the output and the input reaction fluxes have been studied both theoretically and by means of the Monte Carlo simulations on model networks. For single input and output gates the degree of coupling cannot exceed unity. Study simulations of random walks on model networks involving more extended gates indicate that the case of the degree of coupling value higher than one is realized on the mentioned above critical branching trees extended by long-range shortcuts.
Dynamic-stochastic modeling of snow cover formation on the European territory of Russia
Directory of Open Access Journals (Sweden)
A. N. Gelfan
2014-01-01
Full Text Available A dynamic-stochastic model, which combines a deterministic model of snow cover formation with a stochastic weather generator, has been developed. The deterministic snow model describes temporal change of the snow depth, content of ice and liquid water, snow density, snowmelt, sublimation, re-freezing of melt water, and snow metamorphism. The model has been calibrated and validated against the long-term data of snow measurements over the territory of the European Russia. The model showed good performance in simulating time series of the snow water equivalent and snow depth. The developed weather generator (NEsted Weather Generator, NewGen includes nested generators of annual, monthly and daily time series of weather variables (namely, precipitation, air temperature, and air humidity. The parameters of the NewGen have been adjusted through calibration against the long-term meteorological data in the European Russia. A disaggregation procedure has been proposed for transforming parameters of the annual weather generator into the parameters of the monthly one and, subsequently, into the parameters of the daily generator. Multi-year time series of the simulated daily weather variables have been used as an input to the snow model. Probability properties of the snow cover, such as snow water equivalent and snow depth for return periods of 25 and 100 years, have been estimated against the observed data, showing good correlation coefficients. The described model has been applied to different landscapes of European Russia, from steppe to taiga regions, to show the robustness of the proposed technique.
Erdmann, Thorsten; Albert, Philipp J; Schwarz, Ulrich S
2013-11-07
Non-processive molecular motors have to work together in ensembles in order to generate appreciable levels of force or movement. In skeletal muscle, for example, hundreds of myosin II molecules cooperate in thick filaments. In non-muscle cells, by contrast, small groups with few tens of non-muscle myosin II motors contribute to essential cellular processes such as transport, shape changes, or mechanosensing. Here we introduce a detailed and analytically tractable model for this important situation. Using a three-state crossbridge model for the myosin II motor cycle and exploiting the assumptions of fast power stroke kinetics and equal load sharing between motors in equivalent states, we reduce the stochastic reaction network to a one-step master equation for the binding and unbinding dynamics (parallel cluster model) and derive the rules for ensemble movement. We find that for constant external load, ensemble dynamics is strongly shaped by the catch bond character of myosin II, which leads to an increase of the fraction of bound motors under load and thus to firm attachment even for small ensembles. This adaptation to load results in a concave force-velocity relation described by a Hill relation. For external load provided by a linear spring, myosin II ensembles dynamically adjust themselves towards an isometric state with constant average position and load. The dynamics of the ensembles is now determined mainly by the distribution of motors over the different kinds of bound states. For increasing stiffness of the external spring, there is a sharp transition beyond which myosin II can no longer perform the power stroke. Slow unbinding from the pre-power-stroke state protects the ensembles against detachment.
Erdmann, Thorsten; Albert, Philipp J.; Schwarz, Ulrich S.
2013-11-01
Non-processive molecular motors have to work together in ensembles in order to generate appreciable levels of force or movement. In skeletal muscle, for example, hundreds of myosin II molecules cooperate in thick filaments. In non-muscle cells, by contrast, small groups with few tens of non-muscle myosin II motors contribute to essential cellular processes such as transport, shape changes, or mechanosensing. Here we introduce a detailed and analytically tractable model for this important situation. Using a three-state crossbridge model for the myosin II motor cycle and exploiting the assumptions of fast power stroke kinetics and equal load sharing between motors in equivalent states, we reduce the stochastic reaction network to a one-step master equation for the binding and unbinding dynamics (parallel cluster model) and derive the rules for ensemble movement. We find that for constant external load, ensemble dynamics is strongly shaped by the catch bond character of myosin II, which leads to an increase of the fraction of bound motors under load and thus to firm attachment even for small ensembles. This adaptation to load results in a concave force-velocity relation described by a Hill relation. For external load provided by a linear spring, myosin II ensembles dynamically adjust themselves towards an isometric state with constant average position and load. The dynamics of the ensembles is now determined mainly by the distribution of motors over the different kinds of bound states. For increasing stiffness of the external spring, there is a sharp transition beyond which myosin II can no longer perform the power stroke. Slow unbinding from the pre-power-stroke state protects the ensembles against detachment.
Analysing animal social network dynamics: the potential of stochastic actor-oriented models.
Fisher, David N; Ilany, Amiyaal; Silk, Matthew J; Tregenza, Tom
2017-03-01
Animals are embedded in dynamically changing networks of relationships with conspecifics. These dynamic networks are fundamental aspects of their environment, creating selection on behaviours and other traits. However, most social network-based approaches in ecology are constrained to considering networks as static, despite several calls for such analyses to become more dynamic. There are a number of statistical analyses developed in the social sciences that are increasingly being applied to animal networks, of which stochastic actor-oriented models (SAOMs) are a principal example. SAOMs are a class of individual-based models designed to model transitions in networks between discrete time points, as influenced by network structure and covariates. It is not clear, however, how useful such techniques are to ecologists, and whether they are suited to animal social networks. We review the recent applications of SAOMs to animal networks, outlining findings and assessing the strengths and weaknesses of SAOMs when applied to animal rather than human networks. We go on to highlight the types of ecological and evolutionary processes that SAOMs can be used to study. SAOMs can include effects and covariates for individuals, dyads and populations, which can be constant or variable. This allows for the examination of a wide range of questions of interest to ecologists. However, high-resolution data are required, meaning SAOMs will not be useable in all study systems. It remains unclear how robust SAOMs are to missing data and uncertainty around social relationships. Ultimately, we encourage the careful application of SAOMs in appropriate systems, with dynamic network analyses likely to prove highly informative. Researchers can then extend the basic method to tackle a range of existing questions in ecology and explore novel lines of questioning. © 2016 The Authors. Journal of Animal Ecology published by John Wiley & Sons Ltd on behalf of British Ecological Society.
Erdmann, Thorsten; Schwarz, Ulrich S
2013-01-01
Non-processive molecular motors have to work together in ensembles in order to generate appreciable levels of force or movement. In skeletal muscle, for example, hundreds of myosin II molecules cooperate in thick filaments. In non-muscle cells, by contrast, small groups with few tens of non-muscle myosin II motors contribute to essential cellular processes such as transport, shape changes or mechanosensing. Here we introduce a detailed and analytically tractable model for this important situation. Using a three-state crossbridge model for the myosin II motor cycle and exploiting the assumptions of fast power stroke kinetics and equal load sharing between motors in equivalent states, we reduce the stochastic reaction network to a one-step master equation for the binding and unbinding dynamics (parallel cluster model) and derive the rules for ensemble movement. We find that for constant external load, ensemble dynamics is strongly shaped by the catch bond character of myosin II, which leads to an increase of th...
Elenchezhiyan, M; Prakash, J
2015-09-01
In this work, state estimation schemes for non-linear hybrid dynamic systems subjected to stochastic state disturbances and random errors in measurements using interacting multiple-model (IMM) algorithms are formulated. In order to compute both discrete modes and continuous state estimates of a hybrid dynamic system either an IMM extended Kalman filter (IMM-EKF) or an IMM based derivative-free Kalman filters is proposed in this study. The efficacy of the proposed IMM based state estimation schemes is demonstrated by conducting Monte-Carlo simulation studies on the two-tank hybrid system and switched non-isothermal continuous stirred tank reactor system. Extensive simulation studies reveal that the proposed IMM based state estimation schemes are able to generate fairly accurate continuous state estimates and discrete modes. In the presence and absence of sensor bias, the simulation studies reveal that the proposed IMM unscented Kalman filter (IMM-UKF) based simultaneous state and parameter estimation scheme outperforms multiple-model UKF (MM-UKF) based simultaneous state and parameter estimation scheme.
Stochastic dynamics of phase singularities under ventricular fibrillation in 2D Beeler-Reuter model
Suzuki, Akio; Konno, Hidetoshi
2011-09-01
The dynamics of ventricular fibrillation (VF) has been studied extensively, and the initiation mechanism of VF has been elucidated to some extent. However, the stochastic dynamical nature of sustained VF remains unclear so far due to the complexity of high dimensional chaos in a heterogeneous system. In this paper, various statistical mechanical properties of sustained VF are studied numerically in 2D Beeler-Reuter-Drouhard-Roberge (BRDR) model with normal and modified ionic current conductance. The nature of sustained VF is analyzed by measuring various fluctuations of spatial phase singularity (PS) such as velocity, lifetime, the rates of birth and death. It is found that the probability density function (pdf) for lifetime of PSs is independent of system size. It is also found that the hyper-Gamma distribution serves as a universal pdf for the counting number of PSs for various system sizes and various parameters of our model tissue under VF. Further, it is demonstrated that the nonlinear Langevin equation associated with a hyper-Gamma process can mimic the pdf and temporal variation of the number of PSs in the 2D BRDR model.
Stochastic dynamics of phase singularities under ventricular fibrillation in 2D Beeler-Reuter model
Directory of Open Access Journals (Sweden)
Akio Suzuki
2011-09-01
Full Text Available The dynamics of ventricular fibrillation (VF has been studied extensively, and the initiation mechanism of VF has been elucidated to some extent. However, the stochastic dynamical nature of sustained VF remains unclear so far due to the complexity of high dimensional chaos in a heterogeneous system. In this paper, various statistical mechanical properties of sustained VF are studied numerically in 2D Beeler-Reuter-Drouhard-Roberge (BRDR model with normal and modified ionic current conductance. The nature of sustained VF is analyzed by measuring various fluctuations of spatial phase singularity (PS such as velocity, lifetime, the rates of birth and death. It is found that the probability density function (pdf for lifetime of PSs is independent of system size. It is also found that the hyper-Gamma distribution serves as a universal pdf for the counting number of PSs for various system sizes and various parameters of our model tissue under VF. Further, it is demonstrated that the nonlinear Langevin equation associated with a hyper-Gamma process can mimic the pdf and temporal variation of the number of PSs in the 2D BRDR model.
Stochastic dynamics of complex systems: from glasses to evolution (series on complexity science)
Sibani, Paolo
2013-01-01
Dynamical evolution over long time scales is a prominent feature of all the systems we intuitively think of as complex - for example, ecosystems, the brain or the economy. In physics, the term ageing is used for this type of slow change, occurring over time scales much longer than the patience, or indeed the lifetime, of the observer. The main focus of this book is on the stochastic processes which cause ageing, and the surprising fact that the ageing dynamics of systems which are very different at the microscopic level can be treated in similar ways. The first part of this book provides the necessary mathematical and computational tools and the second part describes the intuition needed to deal with these systems. Some of the first few chapters have been covered in several other books, but the emphasis and selection of the topics reflect both the authors' interests and the overall theme of the book. The second part contains an introduction to the scientific literature and deals in some detail with the desc...
Low-dimensional stochastic dynamics underly the emergence of spontaneous movement in electric fish
Melanson, Alexandre; Jun, James J.; Mejias, Jorge F.; Maler, Leonard; Longtin, Andre
2015-03-01
Observing unconstrained animals can lead to simple descriptions of complex behaviours. We apply this principle here to infer the neural basis of spontaneous movements in electric fish. Long-term monitoring of fish in freely swimming, stimuli-free conditions has revealed a sequence of behavioural states that alternate randomly between periods of activity (movement, high active sensing rate) and inactivity (no movement, low active sensing rate). We show that key features of this sequence are well captured by a 1-D diffusion process in a double well energy landscape, where we assume the existence of a slow variable that modulates the relative depth of the wells. Model validation is two-fold: i) state duration distributions are well fitted by exponential mixtures, indicating non-stationary transition rates in the switching process. ii) Monte Carlo simulations with progressive tilting of the double well is consistent with the observed transition-triggered average. We interpret the stochastic variable of this dynamical model as a decision-like variable that, upon reaching a threshold, triggers the transition between states. We thus identify threshold crossing as a possible mechanism for spontaneous movement initiation and offer a dynamical explanation for slower behavioural changes. Funded by NSERC
A matrix product algorithm for stochastic dynamics on locally tree-like graphs
Barthel, Thomas; de Bacco, Caterina; Franz, Silvio
In this talk, I describe a novel algorithm for the efficient simulation of generic stochastic dynamics of classical degrees of freedom defined on the vertices of locally tree-like graphs. Such models correspond for example to spin-glass systems, Boolean networks, neural networks, or other technological, biological, and social networks. Building upon the cavity method and ideas from quantum many-body theory, the algorithm is based on a matrix product approximation of the so-called edge messages - conditional probabilities of vertex variable trajectories. The matrix product edge messages (MPEM) are constructed recursively. Computation costs and accuracy can be tuned by controlling the matrix dimensions of the MPEM in truncations. In contrast to Monte Carlo simulations, the approach has a better error scaling and works for both, single instances as well as the thermodynamic limit. Due to the absence of cancellation effects, observables with small expectation values can be evaluated accurately, allowing for the study of decay processes and temporal correlations with unprecedented accuracy. The method is demonstrated for the prototypical non-equilibrium Glauber dynamics of an Ising spin system. Reference: arXiv:1508.03295.
The availability of filament ends modulates actin stochastic dynamics in live plant cells
Li, Jiejie; Staiger, Benjamin H.; Henty-Ridilla, Jessica L.; Abu-Abied, Mohamad; Sadot, Einat; Blanchoin, Laurent; Staiger, Christopher J.
2014-01-01
A network of individual filaments that undergoes incessant remodeling through a process known as stochastic dynamics comprises the cortical actin cytoskeleton in plant epidermal cells. From images at high spatial and temporal resolution, it has been inferred that the regulation of filament barbed ends plays a central role in choreographing actin organization and turnover. How this occurs at a molecular level, whether different populations of ends exist in the array, and how individual filament behavior correlates with the overall architecture of the array are unknown. Here we develop an experimental system to modulate the levels of heterodimeric capping protein (CP) and examine the consequences for actin dynamics, architecture, and cell expansion. Significantly, we find that all phenotypes are the opposite for CP-overexpression (OX) cells compared with a previously characterized cp-knockdown line. Specifically, CP OX lines have fewer filament–filament annealing events, as well as reduced filament lengths and lifetimes. Further, cp-knockdown and OX lines demonstrate the existence of a subpopulation of filament ends sensitive to CP concentration. Finally, CP levels correlate with the biological process of axial cell expansion; for example, epidermal cells from hypocotyls with reduced CP are longer than wild-type cells, whereas CP OX lines have shorter cells. On the basis of these and other genetic studies in this model system, we hypothesize that filament length and lifetime positively correlate with the extent of axial cell expansion in dark-grown hypocotyls. PMID:24523291
Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach
2012-01-01
The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the...
D'Onofrio, Giuseppe; Pirozzi, Enrica
2017-05-01
We consider a stochastic differential equation in a strip, with coefficients suitably chosen to describe the acto-myosin interaction subject to time-varying forces. By simulating trajectories of the stochastic dynamics via an Euler discretization-based algorithm, we fit experimental data and determine the values of involved parameters. The steps of the myosin are represented by the exit events from the strip. Motivated by these results, we propose a specific stochastic model based on the corresponding time-inhomogeneous Gauss-Markov and diffusion process evolving between two absorbing boundaries. We specify the mean and covariance functions of the stochastic modeling process taking into account time-dependent forces including the effect of an external load. We accurately determine the probability density function (pdf) of the first exit time (FET) from the strip by solving a system of two non singular second-type Volterra integral equations via a numerical quadrature. We provide numerical estimations of the mean of FET as approximations of the dwell-time of the proteins dynamics. The percentage of backward steps is given in agreement to experimental data. Numerical and simulation results are compared and discussed.
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.
Joint effects of habitat configuration and temporal stochasticity on population dynamics
Jennifer M. Fraterrigo; Scott M. Pearson; Monica G. Turner
2009-01-01
Habitat configuration and temporal stochasticity in the environment are recognized as important drivers of population structure, yet few studies have examined the combined influence of these factors....
National Research Council Canada - National Science Library
Monzel, C; Schmidt, D; Kleusch, C; Kirchenbüchler, D; Seifert, U; Smith, A-S; Sengupta, K; Merkel, R
2015-01-01
Stochastic displacements or fluctuations of biological membranes are increasingly recognized as an important aspect of many physiological processes, but hitherto their precise quantification in living...
Energy Technology Data Exchange (ETDEWEB)
Herter, Karen; Wayland, Seth; Rasin, Josh
2009-09-25
This report documents a field study of 78 small commercial customers in the Sacramento Municipal Utility District service territory who volunteered for an integrated energy-efficiency/demand-response (EE-DR) program in the summer of 2008. The original objective for the pilot was to provide a better understanding of demand response issues in the small commercial sector. Early findings justified a focus on offering small businesses (1) help with the energy efficiency of their buildings in exchange for occasional load shed, and (2) a portfolio of options to meet the needs of a diverse customer sector. To meet these expressed needs, the research pilot provided on-site energy efficiency advice and offered participants several program options, including the choice of either a dynamic rate or monthly payment for air-conditioning setpoint control. An analysis of hourly load data indicates that the offices and retail stores in our sample provided significant demand response, while the restaurants did not. Thermostat data provides further evidence that restaurants attempted to precool and reduce AC service during event hours, but were unable to because their air-conditioning units were undersized. On a 100 F reference day, load impacts of all participants during events averaged 14%, while load impacts of office and retail buildings (excluding restaurants) reached 20%. Overall, pilot participants including restaurants had 2007-2008 summer energy savings of 20% and bill savings of 30%. About 80% of participants said that the program met or surpassed their expectations, and three-quarters said they would probably or definitely participate again without the $120 participation incentive. These results provide evidence that energy efficiency programs, dynamic rates and load control programs can be used concurrently and effectively in the small business sector, and that communicating thermostats are a reliable tool for providing air-conditioning load shed and enhancing the ability
Holistic irrigation water management approach based on stochastic soil water dynamics
Alizadeh, H.; Mousavi, S. J.
2012-04-01
Appreciating the essential gap between fundamental unsaturated zone transport processes and soil and water management due to low effectiveness of some of monitoring and modeling approaches, this study presents a mathematical programming model for irrigation management optimization based on stochastic soil water dynamics. The model is a nonlinear non-convex program with an economic objective function to address water productivity and profitability aspects in irrigation management through optimizing irrigation policy. Utilizing an optimization-simulation method, the model includes an eco-hydrological integrated simulation model consisting of an explicit stochastic module of soil moisture dynamics in the crop-root zone with shallow water table effects, a conceptual root-zone salt balance module, and the FAO crop yield module. Interdependent hydrology of soil unsaturated and saturated zones is treated in a semi-analytical approach in two steps. At first step analytical expressions are derived for the expected values of crop yield, total water requirement and soil water balance components assuming fixed level for shallow water table, while numerical Newton-Raphson procedure is employed at the second step to modify value of shallow water table level. Particle Swarm Optimization (PSO) algorithm, combined with the eco-hydrological simulation model, has been used to solve the non-convex program. Benefiting from semi-analytical framework of the simulation model, the optimization-simulation method with significantly better computational performance compared to a numerical Mote-Carlo simulation-based technique has led to an effective irrigation management tool that can contribute to bridging the gap between vadose zone theory and water management practice. In addition to precisely assessing the most influential processes at a growing season time scale, one can use the developed model in large scale systems such as irrigation districts and agricultural catchments. Accordingly
Institute of Scientific and Technical Information of China (English)
SHAO Yuanzhi; ZHONG Weirong; HE Zhenhui
2005-01-01
We report the nonequilibrium dynamical phase transition (NDPT) appearing in a kinetic Ising spin system (ISS) subject to the joint application of a deterministic external field and the stochastic mutually correlated noises simultaneously. A time-dependent Ginzburg-Landau stochastic differential equation, including an oscillating modulation and the correlated multiplicative and additive white noises, was addressed and the numerical solution to the relevant Fokker-Planck equation was presented on the basis of an average-period approach of driven field. The correlated white noises and the deterministic modulation induce a kind of dynamic symmetry-breaking order, analogous to the stochastic resonance in trend, in the kinetic ISS, and the reentrant transition has been observed between the dynamic disorder and order phases when the intensities of multiplicative and additive noises were changing. The dependencies of a dynamic order parameter Q upon the intensities of additive noise A and multiplicative noise M, the correlation λ between two noises, and the amplitude of applied external field h were investigated quantitatively and visualized vividly. Here a brief discussion is given to outline the underlying mechanism of the NDPT in a kinetic ISS driven by an external force and correlated noises.
On the numerical treatment of dissipative particle dynamics and related systems
Energy Technology Data Exchange (ETDEWEB)
Leimkuhler, Benedict, E-mail: b.leimkuhler@ed.ac.uk; Shang, Xiaocheng, E-mail: x.shang@ed.ac.uk
2015-01-01
We review and compare numerical methods that simultaneously control temperature while preserving the momentum, a family of particle simulation methods commonly used for the modelling of complex fluids and polymers. The class of methods considered includes dissipative particle dynamics (DPD) as well as extended stochastic-dynamics models incorporating a generalized pairwise thermostat scheme in which stochastic forces are eliminated and the coefficient of dissipation is treated as an additional auxiliary variable subject to a feedback (kinetic energy) control mechanism. In the latter case, we consider the addition of a coupling of the auxiliary variable, as in the Nosé–Hoover–Langevin (NHL) method, with stochastic dynamics to ensure ergodicity, and find that the convergence of ensemble averages is substantially improved. To this end, splitting methods are developed and studied in terms of their thermodynamic accuracy, two-point correlation functions, and convergence. In terms of computational efficiency as measured by the ratio of thermodynamic accuracy to CPU time, we report significant advantages in simulation for the pairwise NHL method compared to popular alternative schemes (up to an 80% improvement), without degradation of convergence rate. The momentum-conserving thermostat technique described here provides a consistent hydrodynamic model in the low-friction regime, but it will also be of use in both equilibrium and nonequilibrium molecular simulation applications owing to its efficiency and simple numerical implementation.
Emotion as a thermostat: representing emotion regulation using a damped oscillator model.
Chow, Sy-Miin; Ram, Nilam; Boker, Steven M; Fujita, Frank; Clore, Gerald
2005-06-01
The authors present in this study a damped oscillator model that provides a direct mathematical basis for testing the notion of emotion as a self-regulatory thermostat. Parameters from this model reflect individual differences in emotional lability and the ability to regulate emotion. The authors discuss concepts such as intensity, rate of change, and acceleration in the context of emotion, and they illustrate the strengths of this approach in comparison with spectral analysis and growth curve models. The utility of this modeling approach is illustrated using daily emotion ratings from 179 college students over 52 consecutive days. Overall, the damped oscillator model provides a meaningful way of representing emotion regulation as a dynamic process and helps identify the dominant periodicities in individuals' emotions.
Dynamics of a stochastic HIV-1 infection model with logistic growth
Jiang, Daqing; Liu, Qun; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed; Xia, Peiyan
2017-03-01
This paper is concerned with a stochastic HIV-1 infection model with logistic growth. Firstly, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HIV-1 infection model. Then we obtain sufficient conditions for extinction of the infection. The stationary distribution shows that the infection can become persistent in vivo.
Stochastic Phenomena in One-Dimensional Rulkov Model of Neuronal Dynamics
Directory of Open Access Journals (Sweden)
Irina Bashkirtseva
2015-01-01
transitions in a zone of bistability are considered. It is shown how such random transitions can generate a new neuronal regime of the stochastic bursting and transfer the system from order to chaos. A transient zone of values of noise intensity corresponding to the onset of noise-induced bursting and chaotization is localized by the stochastic sensitivity functions technique.
Control for large scale demand response of thermostatic loads
DEFF Research Database (Denmark)
Totu, Luminita Cristiana; Leth, John; Wisniewski, Rafal
2013-01-01
Demand response is an important Smart Grid concept that aims at facilitating the integration of volatile energy resources into the electricity grid. This paper considers a residential demand response scenario and specifically looks into the problem of managing a large number thermostatbased...... appliances with on/off operation. The objective is to reduce the consumption peak of a group of loads composed of both flexible and inflexible units. The power flexible units are the thermostat-based appliances. We discuss a centralized, model predictive approach and a distributed structure with a randomized...
Uniform Approximation of a Maxwellian Thermostat by Finite Reservoirs
Bonetto, F.; Loss, M.; Tossounian, H.; Vaidyanathan, R.
2017-04-01
We study a system of M particles in contact with a large but finite reservoir of {N ≫ M} particles within the framework of the Kac master equation modeling random collisions. The reservoir is initially in equilibrium at temperature {T=β^{-1}}. We show that for large N, this evolution can be approximated by an effective equation in which the reservoir is described by a Maxwellian thermostat at temperature T. This approximation is proven for a suitable {L^2} norm as well as for the Gabetta-Toscani-Wennberg (GTW) distance and is uniform in time.
Programmable Thermostat Module Upgrade for the Multipurpose Logistics Module
Clark, D. W.; Glasgow, S. d.; Reagan, S. E.; Presson, K. H.; Howard, D. E.; Smith, D. A.
2007-01-01
The STS-121/ULF 1.1 mission was the maiden flight of the programmable thermostat module (PTM) system used to control the 28 V shell heaters on the multi-purpose logistics module (MPLM). These PTMs, in conjunction with a data recorder module (DRM), provide continuous closed loop temperature control and data recording of MPLM on-orbit heater operations. This Technical Memorandum discusses the hardware design, development, test, and verification (DDT&V) activities performed at the Marshall Space Flight Center as well as the operational implementation and mission performance.
Extended-Range Prediction with Low-Dimensional, Stochastic-Dynamic Models: A Data-driven Approach
2013-09-30
Dmitri Kondrashov Dept. of Atmospheric & Oceanic Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA...chaotic and dissipative dynamical systems, Chekroun et al. (2013c) have shown that the recurrences observed in planetary flows can play a key role...are the most energetic and correlations decay slowly. Parameterizing manifolds for stochastic partial differential equations Chekroun et al. (2013a,b
Collaborative Research: Robust Climate Projections and Stochastic Stability of Dynamical Systems
Energy Technology Data Exchange (ETDEWEB)
Ghil, Michael; McWilliams, James; Neelin, J. David; Zaliapin, Ilya; Chekroun, Mickael; Kondrashov, Dmitri; Simonnet, Eric
2011-10-13
The project was completed along the lines of the original proposal, with additional elements arising as new results were obtained. The originally proposed three thrusts were expanded to include an additional, fourth one. (i) The e ffects of stochastic perturbations on climate models have been examined at the fundamental level by using the theory of deterministic and random dynamical systems, in both nite and in nite dimensions. (ii) The theoretical results have been implemented first on a delay-diff erential equation (DDE) model of the El-Nino/Southern-Oscillation (ENSO) phenomenon. (iii) More detailed, physical aspects of model robustness have been considered, as proposed, within the stripped-down ICTP-AGCM (formerly SPEEDY) climate model. This aspect of the research has been complemented by both observational and intermediate-model aspects of mid-latitude and tropical climate. (iv) An additional thrust of the research relied on new and unexpected results of (i) and involved reduced-modeling strategies and associated prediction aspects have been tested within the team's empirical model reduction (EMR) framework. Finally, more detailed, physical aspects have been considered within the stripped-down SPEEDY climate model. The results of each of these four complementary e fforts are presented in the next four sections, organized by topic and by the team members concentrating on the topic under discussion.
Coordinating two-period ordering and advertising policies in a dynamic market with stochastic demand
Wang, Junping; Wang, Shengdong; Min, Jie
2015-03-01
In this paper, we study the optimal two-stage advertising and ordering policies and the channel coordination issues in a supply chain composed of one manufacturer and one retailer. The manufacturer sells a short-life-cycle product through the retailer facing stochastic demand in dynamic markets characterised by price declines and product obsolescence. Following a two-period newsvendor framework, we develop two members' optimal ordering and advertising models under both the centralised and decentralised settings, and present the closed-form solutions to the developed models as well. Moreover, we design a two-period revenue-sharing contract, and develop sufficient conditions such that the channel coordination can be achieved and a win-win outcome can be guaranteed. Our analysis suggests that the centralised decision creates an incentive for the retailer to increase the advertising investments in two periods and put the purchase forward, but the decentralised decision mechanism forces the retailer to decrease the advertising investments in two periods and postpone/reduce its purchase in the first period. This phenomenon becomes more evident when demand variability is high.
Energy Technology Data Exchange (ETDEWEB)
Banerjee, Kinshuk, E-mail: kbpchem@gmail.com [Department of Chemistry, University of Calcutta, 92 A.P.C. Road, Kolkata 700 009 (India)
2015-05-14
In this work, we have studied the stochastic response of a single voltage-gated potassium ion channel to a periodic external voltage that keeps the system out-of-equilibrium. The system exhibits memory, resulting from time-dependent driving, that is reflected in terms of dynamic hysteresis in the current-voltage characteristics. The hysteresis loop area has a maximum at some intermediate voltage frequency and disappears in the limits of low and high frequencies. However, the (average) dissipation at long-time limit increases and finally goes to saturation with rising frequency. This raises the question: how diminishing hysteresis can be associated with growing dissipation? To answer this, we have studied the nonequilibrium thermodynamics of the system and analyzed different thermodynamic functions which also exhibit hysteresis. Interestingly, by applying a temporal symmetry analysis in the high-frequency limit, we have analytically shown that hysteresis in some of the periodic responses of the system does not vanish. On the contrary, the rates of free energy and internal energy change of the system as well as the rate of dissipative work done on the system show growing hysteresis with frequency. Hence, although the current-voltage hysteresis disappears in the high-frequency limit, the memory of the ion channel is manifested through its specific nonequilibrium thermodynamic responses.
Using stochastic dual dynamic programming in problems with multiple near-optimal solutions
Rougé, Charles; Tilmant, Amaury
2016-05-01
Stochastic dual dynamic programming (SDDP) is one of the few algorithmic solutions available to optimize large-scale water resources systems while explicitly considering uncertainty. This paper explores the consequences of, and proposes a solution to, the existence of multiple near-optimal solutions (MNOS) when using SDDP for mid or long-term river basin management. These issues arise when the optimization problem cannot be properly parametrized due to poorly defined and/or unavailable data sets. This work shows that when MNOS exists, (1) SDDP explores more than one solution trajectory in the same run, suggesting different decisions in distinct simulation years even for the same point in the state-space, and (2) SDDP is shown to be very sensitive to even minimal variations of the problem setting, e.g., initial conditions—we call this "algorithmic chaos." Results that exhibit such sensitivity are difficult to interpret. This work proposes a reoptimization method, which simulates system decisions by periodically applying cuts from one given year from the SDDP run. Simulation results obtained through this reoptimization approach are steady state solutions, meaning that their probability distributions are stable from year to year.
Effect of reaction-step-size noise on the switching dynamics of stochastic populations
Be'er, Shay; Heller-Algazi, Metar; Assaf, Michael
2016-05-01
In genetic circuits, when the messenger RNA lifetime is short compared to the cell cycle, proteins are produced in geometrically distributed bursts, which greatly affects the cellular switching dynamics between different metastable phenotypic states. Motivated by this scenario, we study a general problem of switching or escape in stochastic populations, where influx of particles occurs in groups or bursts, sampled from an arbitrary distribution. The fact that the step size of the influx reaction is a priori unknown and, in general, may fluctuate in time with a given correlation time and statistics, introduces an additional nondemographic reaction-step-size noise into the system. Employing the probability-generating function technique in conjunction with Hamiltonian formulation, we are able to map the problem in the leading order onto solving a stationary Hamilton-Jacobi equation. We show that compared to the "usual case" of single-step influx, bursty influx exponentially decreases the population's mean escape time from its long-lived metastable state. In particular, close to bifurcation we find a simple analytical expression for the mean escape time which solely depends on the mean and variance of the burst-size distribution. Our results are demonstrated on several realistic distributions and compare well with numerical Monte Carlo simulations.
Dynamics of bed use in accommodating emergency admissions: stochastic simulation model.
Bagust, A; Place, M; Posnett, J W
1999-07-17
To examine the daily bed requirements arising from the flow of emergency admissions to an acute hospital, to identify the implications of fluctuating and unpredictable demands for emergency admission for the management of hospital bed capacity, and to quantify the daily risk of insufficient capacity for patients requiring immediate admission. Modelling of the dynamics of the hospital system, using a discrete-event stochastic simulation model, which reflects the relation between demand and available bed capacity. Hypothetical acute hospital in England. Simulated emergency admissions of all types except mental disorder. The risk of having no bed available for any patient requiring immediate admission; the daily risk that there is no bed available for at least one patient requiring immediate admission; the mean bed occupancy rate. Risks are discernible when average bed occupancy rates exceed about 85%, and an acute hospital can expect regular bed shortages and periodic bed crises if average bed occupancy rises to 90% or more. There are limits to the occupancy rates that can be achieved safely without considerable risk to patients and to the efficient delivery of emergency care. Spare bed capacity is therefore essential for the effective management of emergency admissions, and its cost should be borne by purchasers as an essential element of an acute hospital service.
Feedback optimal control of dynamic stochastic two-machine flowshop with a finite buffer
Directory of Open Access Journals (Sweden)
Thang Diep
2010-06-01
Full Text Available This paper examines the optimization of production involving a tandem two-machine system producing a single part type, with each machine being subject to random breakdowns and repairs. An analytical model is formulated with a view to solving an optimal stochastic production problem of the system with machines having up-downtime non-exponential distributions. The model developed is obtained by using a dynamic programming approach and a semi-Markov process. The control problem aims to find the production rates needed by the machines to meet the demand rate, through a minimization of the inventory/shortage cost. Using the Bellman principle, the optimality conditions obtained satisfy the Hamilton-Jacobi-Bellman equation, which depends on time and system states, and ultimately, leads to a feedback control. Consequently, the new model enables us to improve the coefficient of variation (CVup/down to be less than one while it is equal to one in Markov model. Heuristics methods are used to involve the problem because of the difficulty of the analytical model using several states, and to show what control law should be used in each system state (i.e., including Kanban, feedback and CONWIP control. Numerical methods are used to solve the optimality conditions and to show how a machine should produce.
On the range of validity of the fluctuation theorem for stochastic Markovian dynamics
Rákos, A.; Harris, R. J.
2008-05-01
We consider the fluctuations of generalized currents in stochastic Markovian dynamics. The large deviations of current fluctuations are shown to obey a Gallavotti-Cohen (GC) type symmetry in systems with a finite state space. However, this symmetry is not guaranteed to hold in systems with an infinite state space. A simple example of such a case is the zero-range process (ZRP). Here we discuss in more detail the already reported (Harris et al 2006 Europhys. Lett. 75 227) breakdown of the GC symmetry in the context of the ZRP with open boundaries and we give a physical interpretation of the phases that appear. Furthermore, the earlier analytical results for the single-site case are extended to cover multiple-site systems. We also use our exact results to test an efficient numerical algorithm of Giardinà et al (2006 Phys. Rev. Lett. 96 120603), which was developed to measure the current large deviation function directly. We find that this method breaks down in some phases which we associate with the gapless spectrum of an effective Hamiltonian.
Stochastic optimal foraging: tuning intensive and extensive dynamics in random searches.
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Frederic Bartumeus
Full Text Available Recent theoretical developments had laid down the proper mathematical means to understand how the structural complexity of search patterns may improve foraging efficiency. Under information-deprived scenarios and specific landscape configurations, Lévy walks and flights are known to lead to high search efficiencies. Based on a one-dimensional comparative analysis we show a mechanism by which, at random, a searcher can optimize the encounter with close and distant targets. The mechanism consists of combining an optimal diffusivity (optimally enhanced diffusion with a minimal diffusion constant. In such a way the search dynamics adequately balances the tension between finding close and distant targets, while, at the same time, shifts the optimal balance towards relatively larger close-to-distant target encounter ratios. We find that introducing a multiscale set of reorientations ensures both a thorough local space exploration without oversampling and a fast spreading dynamics at the large scale. Lévy reorientation patterns account for these properties but other reorientation strategies providing similar statistical signatures can mimic or achieve comparable efficiencies. Hence, the present work unveils general mechanisms underlying efficient random search, beyond the Lévy model. Our results suggest that animals could tune key statistical movement properties (e.g. enhanced diffusivity, minimal diffusion constant to cope with the very general problem of balancing out intensive and extensive random searching. We believe that theoretical developments to mechanistically understand stochastic search strategies, such as the one here proposed, are crucial to develop an empirically verifiable and comprehensive animal foraging theory.
Dynamical Modelling, Stochastic Simulation and Optimization in the Context of Damage Tolerant Design
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Sergio Butkewitsch
2006-01-01
Full Text Available This paper addresses the situation in which some form of damage is induced by cyclic mechanical stresses yielded by the vibratory motion of a system whose dynamical behaviour is, in turn, affected by the evolution of the damage. It is assumed that both phenomena, vibration and damage propagation, can be modeled by means of time depended equations of motion whose coupled solution is sought. A brief discussion about the damage tolerant design philosophy for aircraft structures is presented at the introduction, emphasizing the importance of the accurate definition of inspection intervals and, for this sake, the need of a representative damage propagation model accounting for the actual loading environment in which a structure may operate. For the purpose of illustration, the finite element model of a cantilever beam is formulated, providing that the stiffness matrix can be updated as long as a crack of an assumed initial length spreads in a given location of the beam according to a proper propagation model. This way, it is possible to track how the mechanical vibration, through its varying amplitude stress field, activates and develops the fatigue failure mechanism. Conversely, it is also possible to address how the effect of the fatigue induced stiffness degradation influences the motion of the beam, closing the loop for the analysis of a coupled vibration-degradation dynamical phenomenon. In the possession of this working model, stochastic simulation of the beam behaviour is developed, aiming at the identification of the most influential parameters and at the characterization of the probability distributions of the relevant responses of interest. The knowledge of the parameters and responses allows for the formulation of optimization problems aiming at the improvement of the beam robustness with respect to the fatigue induced stiffness degradation. The overall results are presented and analyzed, conducting to the conclusions and outline of future
Uncovering the dynamics of cardiac systems using stochastic pacing and frequency domain analyses.
Lemay, Mathieu; de Lange, Enno; Kucera, Jan P
2012-01-01
Alternans of cardiac action potential duration (APD) is a well-known arrhythmogenic mechanism which results from dynamical instabilities. The propensity to alternans is classically investigated by examining APD restitution and by deriving APD restitution slopes as predictive markers. However, experiments have shown that such markers are not always accurate for the prediction of alternans. Using a mathematical ventricular cell model known to exhibit unstable dynamics of both membrane potential and Ca²⁺ cycling, we demonstrate that an accurate marker can be obtained by pacing at cycle lengths (CLs) varying randomly around a basic CL (BCL) and by evaluating the transfer function between the time series of CLs and APDs using an autoregressive-moving-average (ARMA) model. The first pole of this transfer function corresponds to the eigenvalue (λ(alt)) of the dominant eigenmode of the cardiac system, which predicts that alternans occurs when λ(alt) ≤ -1. For different BCLs, control values of λ(alt) were obtained using eigenmode analysis and compared to the first pole of the transfer function estimated using ARMA model fitting in simulations of random pacing protocols. In all versions of the cell model, this pole provided an accurate estimation of λ(alt). Furthermore, during slow ramp decreases of BCL or simulated drug application, this approach predicted the onset of alternans by extrapolating the time course of the estimated λ(alt). In conclusion, stochastic pacing and ARMA model identification represents a novel approach to predict alternans without making any assumptions about its ionic mechanisms. It should therefore be applicable experimentally for any type of myocardial cell.
Uncovering the dynamics of cardiac systems using stochastic pacing and frequency domain analyses.
Directory of Open Access Journals (Sweden)
Mathieu Lemay
Full Text Available Alternans of cardiac action potential duration (APD is a well-known arrhythmogenic mechanism which results from dynamical instabilities. The propensity to alternans is classically investigated by examining APD restitution and by deriving APD restitution slopes as predictive markers. However, experiments have shown that such markers are not always accurate for the prediction of alternans. Using a mathematical ventricular cell model known to exhibit unstable dynamics of both membrane potential and Ca²⁺ cycling, we demonstrate that an accurate marker can be obtained by pacing at cycle lengths (CLs varying randomly around a basic CL (BCL and by evaluating the transfer function between the time series of CLs and APDs using an autoregressive-moving-average (ARMA model. The first pole of this transfer function corresponds to the eigenvalue (λ(alt of the dominant eigenmode of the cardiac system, which predicts that alternans occurs when λ(alt ≤ -1. For different BCLs, control values of λ(alt were obtained using eigenmode analysis and compared to the first pole of the transfer function estimated using ARMA model fitting in simulations of random pacing protocols. In all versions of the cell model, this pole provided an accurate estimation of λ(alt. Furthermore, during slow ramp decreases of BCL or simulated drug application, this approach predicted the onset of alternans by extrapolating the time course of the estimated λ(alt. In conclusion, stochastic pacing and ARMA model identification represents a novel approach to predict alternans without making any assumptions about its ionic mechanisms. It should therefore be applicable experimentally for any type of myocardial cell.
Drummond, Jen; Davies-Colley, Rob; Stott, Rebecca; Sukias, James; Nagels, John; Sharp, Alice; Packman, Aaron
2014-05-01
Transport dynamics of microbial cells and organic fine particles are important to stream ecology and biogeochemistry. Cells and particles continuously deposit and resuspend during downstream transport owing to a variety of processes including gravitational settling, interactions with in-stream structures or biofilms at the sediment-water interface, and hyporheic exchange and filtration within underlying sediments. Deposited cells and particles are also resuspended following increases in streamflow. Fine particle retention influences biogeochemical processing of substrates and nutrients (C, N, P), while remobilization of pathogenic microbes during flood events presents a hazard to downstream uses such as water supplies and recreation. We are conducting studies to gain insights into the dynamics of fine particles and microbes in streams, with a campaign of experiments and modeling. The results improve understanding of fine sediment transport, carbon cycling, nutrient spiraling, and microbial hazards in streams. We developed a stochastic model to describe the transport and retention of fine particles and microbes in rivers that accounts for hyporheic exchange and transport through porewaters, reversible filtration within the streambed, and microbial inactivation in the water column and subsurface. This model framework is an advance over previous work in that it incorporates detailed transport and retention processes that are amenable to measurement. Solute, particle, and microbial transport were observed both locally within sediment and at the whole-stream scale. A multi-tracer whole-stream injection experiment compared the transport and retention of a conservative solute, fluorescent fine particles, and the fecal indicator bacterium Escherichia coli. Retention occurred within both the underlying sediment bed and stands of submerged macrophytes. The results demonstrate that the combination of local measurements, whole-stream tracer experiments, and advanced modeling
Vellela, Melissa; Qian, Hong
2009-10-06
Schlögl's model is the canonical example of a chemical reaction system that exhibits bistability. Because the biological examples of bistability and switching behaviour are increasingly numerous, this paper presents an integrated deterministic, stochastic and thermodynamic analysis of the model. After a brief review of the deterministic and stochastic modelling frameworks, the concepts of chemical and mathematical detailed balances are discussed and non-equilibrium conditions are shown to be necessary for bistability. Thermodynamic quantities such as the flux, chemical potential and entropy production rate are defined and compared across the two models. In the bistable region, the stochastic model exhibits an exchange of the global stability between the two stable states under changes in the pump parameters and volume size. The stochastic entropy production rate shows a sharp transition that mirrors this exchange. A new hybrid model that includes continuous diffusion and discrete jumps is suggested to deal with the multiscale dynamics of the bistable system. Accurate approximations of the exponentially small eigenvalue associated with the time scale of this switching and the full time-dependent solution are calculated using Matlab. A breakdown of previously known asymptotic approximations on small volume scales is observed through comparison with these and Monte Carlo results. Finally, in the appendix section is an illustration of how the diffusion approximation of the chemical master equation can fail to represent correctly the mesoscopically interesting steady-state behaviour of the system.
Stochastic dynamics of complexation reaction in the limit of small numbers.
Ghosh, Kingshuk
2011-05-21
We study stochastic dynamics of the non-linear bimolecular reaction A + B↔AB. These reactions are common in several bio-molecular systems such as binding, complexation, protein multimerization to name a few. We use master equation to compute the full distribution of several stochastic equilibrium properties such as number of complexes formed (N(c)), equilibrium constant (K). We provide exact analytical and simpler approximate expression for equilibrium fluctuation quantities to quickly estimate the amount of noise as a function of reactant molecules and rates. We construct the phase diagram for a fluctuational quantity f, defined as the ratio of standard deviation to average (f=√(ΔN(c))(2)/N(c)), as a function of different number of reactant molecules and reaction rates. One of the striking result is, it is possible to have f as high as 45% or higher in significant regions of the phase diagram even when number of reactants involved are around 20-40, typical in biology. Our finding indicates studying averages alone using mass action law needs careful scrutiny. We also outline possible application of our findings in gene expression. Furthermore, we compute average and fluctuation properties of time dependent quantities and derive equations of motion for different moments such as N(c)(t) and N(c)(t)(2). While mean-field mass action law fails to reproduce the exact time dependence, approximate solutions of coupled equations of motions for different moments, capturing fluctuation, is in good agreement with exact results. This may be a way to compute time development of averages and fluctuations in such non-linear systems where mass action law breaks down. Moreover, for this reaction, we outline connection to variational principle of maximum caliber and other more traditional approaches such as chemical Langevin equation. We derive noise statistics for the equivalent Langevin equation and show possible departure from Gaussian white noise. We believe quantitative
Set back thermostat and controller with independent multizone control
Energy Technology Data Exchange (ETDEWEB)
1985-11-01
A multi-zone setback thermostat and controller has been developed. It is based on a RCA1802 microprocessor and is designed to optimize a variable air volume air conditioning system for comfort and convenience of control, while achieving energy savings. The unit reads temperatures from up to 16 zones and controls temperatures by adjusting dampers. Each zone can be independently scheduled for four different setpoints for each day. Preset values are maintained in each zone that has no user setpoints entered, enabling the unit to control the air handling system immediately on power up. An alphanumeric display enables the user to view data in memory and as it is keyed in; unauthorized use can be prevented by entering appropriate codes. This report includes detailed descriptions of the thermostat and components, including circuit diagrams, a program listing, software description, and a user manual. A market survey was conducted in Calgary, Alberta to determine the target market and a suitable marketing strategy. Results indicate a place for this product in building retrofit situations; existing pricing that was obtained shows the unit could have an installed price advantage of about $500 per zone. 7 refs., 31 figs.
Stochastic dynamics and chaos in the 3D Hindmarsh-Rose model
Ryashko, Lev; Bashkirtseva, Irina; Slepukhina, Evdokia; Fedotov, Sergei
2016-12-01
We study the effect of random disturbances on the three-dimensional Hindmarsh-Rose model of neural activity. In a parametric zone, where the only attractor of the system is a stable equilibrium, a stochastic generation of bursting oscillations is observed. For a sufficiently small noise, random states concentrate near the equilibrium. With an increase of the noise intensity, along with small-amplitude oscillations around the equilibrium, bursts are observed. The relationship of the noise-induced generation of bursts with system transitions from order to chaos is discussed. For a quantitative analysis of these stochastic phenomena, an approach based on the stochastic sensitivity function technique is suggested.
Denteneer, Dee; Verbitskiy, Evgeny
2006-01-01
Contains 29 contributions by Mike's closest colleagues and friends, covering a broad range of topics in Dynamics and Stochastics. - To celebrate Mike's scientific achievements, a conference entitled "Dynamical Systems, Probability Theory and Statistical Mechanics" was organized in Eindhoven, The Netherlands, during the week of January 3-7, 2005. This conference was hosted jointly by EURANDOM and by Philips Research. It drew over 80 participants from 5 continents, which is a sign of the warm affection and high esteem for Mike felt by the international mathematics community.
Liu, Chao; Wang, Luping; Zhang, Qingling; Yan, Yun
2017-09-01
This paper presents a double delayed bioeconomic phytoplankton zooplankton system with commercial harvesting on zooplankton and environmental stochasticity. Maturation delay for toxin producing phytoplankton and gestation delay for zooplankton are considered. Environmental stochasticity is incorporated into the proposed system in form of Gaussian white noises. Some sufficient conditions are derived to show that the proposed system has a unique global positive solution. In absence of double time delays, stochastic stability and existence of stochastic Hopf bifurcation are studied based on invariant measure theory and singular boundary theory of diffusion process for the proposed system. In presence of double time delays, asymptotic behaviors of the interior equilibrium are discussed by constructing some appropriate Lyapunov functions.
Davidsen, Claus; Liu, Suxia; Mo, Xingguo; Rosbjerg, Dan; Bauer-Gottwein, Peter
2014-05-01
Optimal management of conjunctive use of surface water and groundwater has been attempted with different algorithms in the literature. In this study, a hydro-economic modelling approach to optimize conjunctive use of scarce surface water and groundwater resources under uncertainty is presented. A stochastic dynamic programming (SDP) approach is used to minimize the basin-wide total costs arising from water allocations and water curtailments. Dynamic allocation problems with inclusion of groundwater resources proved to be more complex to solve with SDP than pure surface water allocation problems due to head-dependent pumping costs. These dynamic pumping costs strongly affect the total costs and can lead to non-convexity of the future cost function. The water user groups (agriculture, industry, domestic) are characterized by inelastic demands and fixed water allocation and water supply curtailment costs. As in traditional SDP approaches, one step-ahead sub-problems are solved to find the optimal management at any time knowing the inflow scenario and reservoir/aquifer storage levels. These non-linear sub-problems are solved using a genetic algorithm (GA) that minimizes the sum of the immediate and future costs for given surface water reservoir and groundwater aquifer end storages. The immediate cost is found by solving a simple linear allocation sub-problem, and the future costs are assessed by interpolation in the total cost matrix from the following time step. Total costs for all stages, reservoir states, and inflow scenarios are used as future costs to drive a forward moving simulation under uncertain water availability. The use of a GA to solve the sub-problems is computationally more costly than a traditional SDP approach with linearly interpolated future costs. However, in a two-reservoir system the future cost function would have to be represented by a set of planes, and strict convexity in both the surface water and groundwater dimension cannot be maintained
Zhang, Yunxin; Qian, Hong
2010-01-01
Multistability of mesoscopic, driven biochemical reaction systems has implications to a wide range of cellular processes. Using several simple models, we show that one class of bistable chemical systems has a deterministic counterpart in the nonlinear dynamics based on the Law of Mass Action, while another class, widely known as noise-induced stochastic bistability, does not. Observing the system's volume ($V$) playing a similar role as the inverse temperature ($\\beta$) in classical rate theory, an van't Hoff-Arrhenius like analysis is introduced. In one-dimensional systems, a transition rate between two states, represented in terms of a barrier in the landscape for the dynamics $\\Phi(x,V)$, $k\\propto\\exp\\{-V\\Delta\\Phi^{\\ddag}(V)\\}$, can be understood from a decomposition $\\Delta\\Phi^{\\ddag}(V) \\approx\\Delta\\phi_0^{\\ddag} \\Delta\\phi_1^{\\ddag}/V$. Nonlinear bistability means $\\Delta\\phi_0^{\\ddag}>0$ while stochastic bistability has $\\Delta\\phi_0^{\\ddag}0$. Stochastic bistabilities can be viewed as remants (or ...
Dynamics of a stochastic multi-strain SIS epidemic model driven by Lévy noise
Chen, Can; Kang, Yanmei
2017-01-01
A stochastic multi-strain SIS epidemic model is formulated by introducing Lévy noise into the disease transmission rate of each strain. First, we prove that the stochastic model admits a unique global positive solution, and, by the comparison theorem, we show that the solution remains within a positively invariant set almost surely. Next we investigate stochastic stability of the disease-free equilibrium, including stability in probability and pth moment asymptotic stability. Then sufficient conditions for persistence in the mean of the disease are established. Finally, based on an Euler scheme for Lévy-driven stochastic differential equations, numerical simulations for a stochastic two-strain model are carried out to verify the theoretical results. Moreover, numerical comparison results of the stochastic two-strain model and the deterministic version are also given. Lévy noise can cause the two strains to become extinct almost surely, even though there is a dominant strain that persists in the deterministic model. It can be concluded that the introduction of Lévy noise reduces the disease extinction threshold, which indicates that Lévy noise may suppress the disease outbreak.
A dynamic stochastic model for DNA replication initiation in early embryos.
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Arach Goldar
Full Text Available BACKGROUND: Eukaryotic cells seem unable to monitor replication completion during normal S phase, yet must ensure a reliable replication completion time. This is an acute problem in early Xenopus embryos since DNA replication origins are located and activated stochastically, leading to the random completion problem. DNA combing, kinetic modelling and other studies using Xenopus egg extracts have suggested that potential origins are much more abundant than actual initiation events and that the time-dependent rate of initiation, I(t, markedly increases through S phase to ensure the rapid completion of unreplicated gaps and a narrow distribution of completion times. However, the molecular mechanism that underlies this increase has remained obscure. METHODOLOGY/PRINCIPAL FINDINGS: Using both previous and novel DNA combing data we have confirmed that I(t increases through S phase but have also established that it progressively decreases before the end of S phase. To explore plausible biochemical scenarios that might explain these features, we have performed comparisons between numerical simulations and DNA combing data. Several simple models were tested: i recycling of a limiting replication fork component from completed replicons; ii time-dependent increase in origin efficiency; iii time-dependent increase in availability of an initially limiting factor, e.g. by nuclear import. None of these potential mechanisms could on its own account for the data. We propose a model that combines time-dependent changes in availability of a replication factor and a fork-density dependent affinity of this factor for potential origins. This novel model quantitatively and robustly accounted for the observed changes in initiation rate and fork density. CONCLUSIONS/SIGNIFICANCE: This work provides a refined temporal profile of replication initiation rates and a robust, dynamic model that quantitatively explains replication origin usage during early embryonic S phase
A stochastic approach for the description of the water balance dynamics in a river basin
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S. Manfreda
2008-09-01
Full Text Available The present paper introduces an analytical approach for the description of the soil water balance dynamics over a schematic river basin. The model is based on a stochastic differential equation where the rainfall forcing is interpreted as an additive noise in the soil water balance. This equation can be solved assuming known the spatial distribution of the soil moisture over the basin transforming the two-dimensional problem in space in a one dimensional one. This assumption is particularly true in the case of humid and semihumid environments, where spatial redistribution becomes dominant producing a well defined soil moisture pattern. The model allowed to derive the probability density function of the saturated portion of a basin and of its relative saturation. This theory is based on the assumption that the soil water storage capacity varies across the basin following a parabolic distribution and the basin has homogeneous soil texture and vegetation cover. The methodology outlined the role played by the soil water storage capacity distribution of the basin on soil water balance. In particular, the resulting probability density functions of the relative basin saturation were found to be strongly controlled by the maximum water storage capacity of the basin, while the probability density functions of the relative saturated portion of the basin are strongly influenced by the spatial heterogeneity of the soil water storage capacity. Moreover, the saturated areas reach their maximum variability when the mean rainfall rate is almost equal to the soil water loss coefficient given by the sum of the maximum rate of evapotranspiration and leakage loss in the soil water balance. The model was tested using the results of a continuous numerical simulation performed with a semi-distributed model in order to validate the proposed theoretical distributions.
Directory of Open Access Journals (Sweden)
Muhammad Murtadha Othman
2017-06-01
Full Text Available With the advent of advanced technology in smart grid, the implementation of renewable energy in a stressed and complicated power system operation, aggravated by a competitive electricity market and critical system contingencies, this will inflict higher probabilities of the occurrence of a severe dynamic power system blackout. This paper presents the proposed stochastic event tree technique used to assess the sustainability against the occurrence of dynamic power system blackout emanating from implication of critical system contingencies such as the rapid increase in total loading condition and sensitive initial transmission line tripping. An extensive analysis of dynamic power system blackout has been carried out in a case study of the following power systems: IEEE RTS-79 and IEEE RTS-96. The findings have shown that the total loading conditions and sensitive transmission lines need to be given full attention by the utility to prevent the occurrence of dynamic power system blackout.
Moshfegh, Abouzar; Ahmadi, Goodarz; Jabbarzadeh, Ahmad
2015-12-01
Thermodynamic, hydrodynamic and rheological interactions between velocity-dependent thermostats of Lowe-Andersen (LA) and Nosé-Hoover-Lowe-Andersen (NHLA), and modified Lees-Edwards (M-LEC) boundary condition were studied in the context of Dissipative Particle Dynamics method. Comparisons were made with original Lees-Edwards method to characterise the improvements that M-LEC offers in conserving the induced shear momentum. Different imposed shear velocities, heat bath collision/exchange frequencies and thermostating probabilities were considered. The presented analyses addressed an unusual discontinuity in momentum transfer that appeared in form of nonphysical jumps in velocity and temperature profiles. The usefulness of M-LEC was then quantified by evaluating the enhancements in obtained effective shear velocity, effective shear rate, Péclet number, and dynamic viscosity. System exchange frequency (Γ) with Maxwellian heat bath was found to play an important role, in that its larger values facilitated achieving higher shear rates with proper temperature control at the cost of deviation from an ideal momentum transfer. Similar dynamic viscosities were obtained under both shearing modes between LA and NHLA thermostats up to Γ = 10, whilst about twice the range of viscosity (1 %). The main benefits of this modification were to facilitate momentum flow from shear boundaries to the system bulk. In addition, it was found that there exist upper thresholds for imposing shear on the system beyond which temperature cannot be controlled properly and nonphysical jumps reappear.
Economic MPC based on LPV model for thermostatically controlled loads
DEFF Research Database (Denmark)
Zemtsov, Nikita; Hlava, Jaroslav; Frantsuzova, Galina
2017-01-01
Rapid increase of the renewable energy share in electricity production requires optimization and flexibility of the power consumption side. Thermostatically controlled loads (TCLs) have a large potential for regulation service provision. Economic model predictive control (MPC) is an advanced...... control method which can be used to syncronize the power consumption with undispatchable renewable electricity production. Thermal behavior of TCLs can be described by linear models based on energy balance of the system. In some cases, parameters of the model may be time-varying. In this work, we present....... As a case study, we present control system that minimizes operational cost of swimming pool heating system, where parameters of the model depend on the weather forecast. Simulation results demonstrate that the proposed method is able to deal with this kind of systems....
Stochastic models, estimation, and control
Maybeck, Peter S
1982-01-01
This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.
Energy Technology Data Exchange (ETDEWEB)
Jang, Hong; Lee, Jay H. [Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of); Braatz, Richard D. [Massachusetts Institute of Technology (MIT), Cambridge (United States)
2016-01-15
This paper proposes a maximum likelihood estimation (MLE) method for estimating time varying local concentration of the target molecule proximate to the sensor from the time profile of monomolecular adsorption and desorption on the surface of the sensor at nanoscale. Recently, several carbon nanotube sensors have been developed that can selectively detect target molecules at a trace concentration level. These sensors use light intensity changes mediated by adsorption or desorption phenomena on their surfaces. The molecular events occurring at trace concentration levels are inherently stochastic, posing a challenge for optimal estimation. The stochastic behavior is modeled by the chemical master equation (CME), composed of a set of ordinary differential equations describing the time evolution of probabilities for the possible adsorption states. Given the significant stochastic nature of the underlying phenomena, rigorous stochastic estimation based on the CME should lead to an improved accuracy over than deterministic estimation formulated based on the continuum model. Motivated by this expectation, we formulate the MLE based on an analytical solution of the relevant CME, both for the constant and the time-varying local concentrations, with the objective of estimating the analyte concentration field in real time from the adsorption readings of the sensor array. The performances of the MLE and the deterministic least squares are compared using data generated by kinetic Monte Carlo (KMC) simulations of the stochastic process. Some future challenges are described for estimating and controlling the concentration field in a distributed domain using the sensor technology.
Stochastic dynamic study of optical transition properties of single GFP-like molecules.
Lin, Hanbing; Yuan, Jian-Min
2016-03-01
Due to high fluctuations and quantum uncertainty, the processes of single-molecules should be treated by stochastic methods. To study fluorescence time series and their statistical properties, we have applied two stochastic methods, one of which is an analytic method to study the off-time distributions of certain fluorescence transitions and the other is Gillespie's method of stochastic simulations. These methods have been applied to study the optical transition properties of two single-molecule systems, GFPmut2 and a Dronpa-like molecule, to yield results in approximate agreement with experimental observations on these systems. Rigorous oscillatory time series of GFPmut2 before it unfolds in the presence of denaturants have not been obtained based on the stochastic method used, but, on the other hand, the stochastic treatment puts constraints on the conditions under which such oscillatory behavior is possible. Furthermore, a sensitivity analysis is carried out on GFPmut2 to assess the effects of transition rates on the observables, such as fluorescence intensities.
Energy Technology Data Exchange (ETDEWEB)
Herter, Karen; Wayland, Seth
2008-10-31
Programmable Communicating Thermostats are thermostats that can be programmed by the user to respond to signals indicating a grid-level system emergency or pricing event. The California Energy Commission is considering standards that would include a requirement for Programmable Communicating Thermostats in residential and small commercial applications. The current specification for Programmable Communicating Thermostats requires Radio Data System communications to Programmable Communicating Thermostats. This study tested the signal strength and reliability of Radio Data System signals at 40 customer sites within the Sacramento Municipal Utility District, which is serviced by 17 radio stations that already transmit Radio Data System signals. The study also tested the functionality of a commercially available Programmable Communicating Thermostat for compliance with California Energy Commission design standards. Test results demonstrated that Radio Data System is capable of reliably sending price and emergency signals. This study also provides evidence that existing Programmable Communicating Thermostats, on receiving a Radio Data System pricing or event signal, are capable of automatically increasing set points to a customer-determined or utility-determined level, thus providing air-conditioning demand response within seconds or just a few (less than 5) minutes.
Deng, Chenhui; Plan, Elodie L; Karlsson, Mats O
2016-06-01
Parameter variation in pharmacometric analysis studies can be characterized as within subject parameter variability (WSV) in pharmacometric models. WSV has previously been successfully modeled using inter-occasion variability (IOV), but also stochastic differential equations (SDEs). In this study, two approaches, dynamic inter-occasion variability (dIOV) and adapted stochastic differential equations, were proposed to investigate WSV in pharmacometric count data analysis. These approaches were applied to published count models for seizure counts and Likert pain scores. Both approaches improved the model fits significantly. In addition, stochastic simulation and estimation were used to explore further the capability of the two approaches to diagnose and improve models where existing WSV is not recognized. The results of simulations confirmed the gain in introducing WSV as dIOV and SDEs when parameters vary randomly over time. Further, the approaches were also informative as diagnostics of model misspecification, when parameters changed systematically over time but this was not recognized in the structural model. The proposed approaches in this study offer strategies to characterize WSV and are not restricted to count data.
Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach
Directory of Open Access Journals (Sweden)
S. L. Han
2012-01-01
Full Text Available The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the information insufficiency in parameter of interests or errors in measurement. The probability space is estimated using Markov chain Monte Carlo (MCMC. The applicability of the proposed method is demonstrated through numerical experiment and particular application to a realistic problem related to ship roll motion.
Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis.
Szabó-Solticzky, András; Berthouze, Luc; Kiss, Istvan Z; Simon, Péter L
2016-04-01
An adaptive network model using SIS epidemic propagation with link-type-dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out, showing that three typical behaviours may occur; namely, oscillations can be observed besides disease-free or endemic steady states. The oscillatory behaviour in the stochastic simulations is studied using Fourier analysis, as well as through analysing the exact master equations of the stochastic model. By going beyond simply comparing simulation results to mean-field models, our approach yields deeper insights into the observed phenomena and help better understand and map out the limitations of mean-field models.
Exact many-body dynamics with stochastic one-body density matrix evolution
Energy Technology Data Exchange (ETDEWEB)
Lacroix, D
2004-05-01
In this article, we discuss some properties of the exact treatment of the many-body problem with stochastic Schroedinger equation (SSE). Starting from the SSE theory, an equivalent reformulation is proposed in terms of quantum jumps in the density matrix space. The technical details of the derivation a stochastic version of the Liouville von Neumann equation are given. It is shown that the exact Many-Body problem could be replaced by an ensemble of one-body density evolution, where each density matrix evolves according to its own mean-field augmented by a one-body noise. (author)
Babaee, Hessam; Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em
2017-09-01
We develop a new robust methodology for the stochastic Navier-Stokes equations based on the dynamically-orthogonal (DO) and bi-orthogonal (BO) methods [1-3]. Both approaches are variants of a generalized Karhunen-Loève (KL) expansion in which both the stochastic coefficients and the spatial basis evolve according to system dynamics, hence, capturing the low-dimensional structure of the solution. The DO and BO formulations are mathematically equivalent [3], but they exhibit computationally complimentary properties. Specifically, the BO formulation may fail due to crossing of the eigenvalues of the covariance matrix, while both BO and DO become unstable when there is a high condition number of the covariance matrix or zero eigenvalues. To this end, we combine the two methods into a robust hybrid framework and in addition we employ a pseudo-inverse technique to invert the covariance matrix. The robustness of the proposed method stems from addressing the following issues in the DO/BO formulation: (i) eigenvalue crossing: we resolve the issue of eigenvalue crossing in the BO formulation by switching to the DO near eigenvalue crossing using the equivalence theorem and switching back to BO when the distance between eigenvalues is larger than a threshold value; (ii) ill-conditioned covariance matrix: we utilize a pseudo-inverse strategy to invert the covariance matrix; (iii) adaptivity: we utilize an adaptive strategy to add/remove modes to resolve the covariance matrix up to a threshold value. In particular, we introduce a soft-threshold criterion to allow the system to adapt to the newly added/removed mode and therefore avoid repetitive and unnecessary mode addition/removal. When the total variance approaches zero, we show that the DO/BO formulation becomes equivalent to the evolution equation of the Optimally Time-Dependent modes [4]. We demonstrate the capability of the proposed methodology with several numerical examples, namely (i) stochastic Burgers equation: we