Efficient stochastic thermostatting of path integral molecular dynamics.
Ceriotti, Michele; Parrinello, Michele; Markland, Thomas E; Manolopoulos, David E
2010-09-28
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.
Zhang, Zhijun; Liu, Xinzijian; Chen, Zifei; Zheng, Haifeng; Yan, Kangyu; Liu, Jian
2017-07-01
We show a unified second-order scheme for constructing simple, robust, and accurate algorithms for typical thermostats for configurational sampling for the canonical ensemble. When Langevin dynamics is used, the scheme leads to the BAOAB algorithm that has been recently investigated. We show that the scheme is also useful for other types of thermostats, such as the Andersen thermostat and Nosé-Hoover chain, regardless of whether the thermostat is deterministic or stochastic. In addition to analytical analysis, two 1-dimensional models and three typical real molecular systems that range from the gas phase, clusters, to the condensed phase are used in numerical examples for demonstration. Accuracy may be increased by an order of magnitude for estimating coordinate-dependent properties in molecular dynamics (when the same time interval is used), irrespective of which type of thermostat is applied. The scheme is especially useful for path integral molecular dynamics because it consistently improves the efficiency for evaluating all thermodynamic properties for any type of thermostat.
International Nuclear Information System (INIS)
Voter, A. F.; Sindhikara, Daniel J.; Kim, Seonah; Roitberg, Adrian E.
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
Sindhikara, Daniel J; Kim, Seonah; Voter, Arthur F; Roitberg, Adrian E
2009-06-09
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.
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.
Geometric integrators for stochastic rigid body dynamics
Tretyakov, Mikhail
2016-01-01
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.
A thermostatted kinetic theory model for event-driven pedestrian dynamics
Bianca, Carlo; Mogno, Caterina
2018-06-01
This paper is devoted to the modeling of the pedestrian dynamics by means of the thermostatted kinetic theory. Specifically the microscopic interactions among pedestrians and an external force field are modeled for simulating the evacuation of pedestrians from a metro station. The fundamentals of the stochastic game theory and the thermostatted kinetic theory are coupled for the derivation of a specific mathematical model which depicts the time evolution of the distribution of pedestrians at different exits of a metro station. The perturbation theory is employed in order to establish the stability analysis of the nonequilibrium stationary states in the case of a metro station consisting of two exits. A general sensitivity analysis on the initial conditions, the magnitude of the external force field and the number of exits is presented by means of numerical simulations which, in particular, show how the asymptotic distribution and the convergence time are affected by the presence of an external force field. The results show how, in evacuation conditions, the interaction dynamics among pedestrians can be negligible with respect to the external force. The important role of the thermostat term in allowing the reaching of the nonequilibrium stationary state is stressed out. Research perspectives are underlined at the end of paper, in particular for what concerns the derivation of frameworks that take into account the definition of local external actions and the introduction of the space and velocity dynamics.
Modeling Populations of Thermostatic Loads with Switching Rate Actuation
DEFF Research Database (Denmark)
Totu, Luminita Cristiana; Wisniewski, Rafal; Leth, John-Josef
2015-01-01
We model thermostatic devices using a stochastic hybrid description, and introduce an external actuation mechanism that creates random switch events in the discrete dynamics. We then conjecture the form of the Fokker-Planck equation and successfully verify it numerically using Monte Carlo...... simulations. The actuation mechanism and subsequent modeling result are relevant for power system operation....
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...
Deterministic time-reversible thermostats: chaos, ergodicity, and the zeroth law of thermodynamics
Patra, Puneet Kumar; Sprott, Julien Clinton; Hoover, William Graham; Griswold Hoover, Carol
2015-09-01
The relative stability and ergodicity of deterministic time-reversible thermostats, both singly and in coupled pairs, are assessed through their Lyapunov spectra. Five types of thermostat are coupled to one another through a single Hooke's-law harmonic spring. The resulting dynamics shows that three specific thermostat types, Hoover-Holian, Ju-Bulgac, and Martyna-Klein-Tuckerman, have very similar Lyapunov spectra in their equilibrium four-dimensional phase spaces and when coupled in equilibrium or nonequilibrium pairs. All three of these oscillator-based thermostats are shown to be ergodic, with smooth analytic Gaussian distributions in their extended phase spaces (coordinate, momentum, and two control variables). Evidently these three ergodic and time-reversible thermostat types are particularly useful as statistical-mechanical thermometers and thermostats. Each of them generates Gibbs' universal canonical distribution internally as well as for systems to which they are coupled. Thus they obey the zeroth law of thermodynamics, as a good heat bath should. They also provide dissipative heat flow with relatively small nonlinearity when two or more such temperature baths interact and provide useful deterministic replacements for the stochastic Langevin equation.
Evaluating functions of positive-definite matrices using colored-noise thermostats
Nava, Marco; Ceriotti, Michele; Dryzun, Chaim; Parrinello, Michele
2014-02-01
Many applications in computational science require computing the elements of a function of a large matrix. A commonly used approach is based on the the evaluation of the eigenvalue decomposition, a task that, in general, involves a computing time that scales with the cube of the size of the matrix. We present here a method that can be used to evaluate the elements of a function of a positive-definite matrix with a scaling that is linear for sparse matrices and quadratic in the general case. This methodology is based on the properties of the dynamics of a multidimensional harmonic potential coupled with colored-noise, generalized Langevin equation thermostats. This "f-thermostat" approach allows us to calculate directly elements of functions of a positive-definite matrix by carefully tailoring the properties of the stochastic dynamics. We demonstrate the scaling and the accuracy of this approach for both dense and sparse problems and compare the results with other established methodologies.
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.
Paterakis, N.G.; Medeiros, M.F.; Catalao, J.P.S.; Siaraka, A.; Bakirtzis, A.G.; Erdinc, O.
2015-01-01
In this study, a home energy management system structure is developed in order to determine the optimal commitment of a smart-household. Two types of loads are explicitly modeled: non-thermostatically controllable (electric vehicle, shiftable appliances) and thermostatically controllable loads (air
Investigation of a chaotic thermostat
Morales, G. J.
2018-03-01
A numerical study is presented of a free particle interacting with a deterministic thermostat in which the usual friction force is supplemented with a fluctuating force that depends on the self-consistent damping coefficient associated with coupling to the heat bath. It is found that this addition results in a chaotic environment in which a particle self-heats from rest and moves in positive and negative directions, exhibiting a characteristic diffusive behavior. The frequency power spectrum of the dynamical quantities displays the exponential frequency dependence ubiquitous to chaotic dynamics. The velocity distribution function approximates a Maxwellian distribution, but it does show departures from perfect thermal equilibrium, while the distribution function for the damping coefficient shows a closer fit. The behavior for the classic Nosé-Hoover (NH) thermostat is compared to that of the enlarged Martyna-Klein-Tuckerman (MKT) model. Over a narrow amplitude range, the application of a constant external force results quantitatively in the Einstein relation for the NH thermostat, and for the MKT model it differs by a factor of 2.
Dynamic principle for ensemble control tools.
Samoletov, A; Vasiev, B
2017-11-28
Dynamical equations describing physical systems in contact with a thermal bath are commonly extended by mathematical tools called "thermostats." These tools are designed for sampling ensembles in statistical mechanics. Here we propose a dynamic principle underlying a range of thermostats which is derived using fundamental laws of statistical physics and ensures invariance of the canonical measure. The principle covers both stochastic and deterministic thermostat schemes. Our method has a clear advantage over a range of proposed and widely used thermostat schemes that are based on formal mathematical reasoning. Following the derivation of the proposed principle, we show its generality and illustrate its applications including design of temperature control tools that differ from the Nosé-Hoover-Langevin scheme.
International Nuclear Information System (INIS)
Krommes, J.A.
2000-01-01
The delta f simulation method is revisited. Statistical coarse-graining is used to rigorously derive the equation for the fluctuation delta f in the particle distribution. It is argued that completely collisionless simulation is incompatible with the achievement of true statistically steady states with nonzero turbulent fluxes because the variance of the particle weights w grows with time. To ensure such steady states, it is shown that for dynamically collisionless situations a generalized thermostat or W-stat may be used in lieu of a full collision operator to absorb the flow of entropy to unresolved fine scales in velocity space. The simplest W-stat can be implemented as a self-consistently determined, time-dependent damping applied to w. A precise kinematic analogy to thermostatted nonequilibrium molecular dynamics (NEMD) is pointed out, and the justification of W-stats for simulations of turbulence is discussed. An extrapolation procedure is proposed such that the long-time, steady-state, collisionless flux can be deduced from several short W-statted runs with large effective collisionality, and a numerical demonstration is given
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...
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.
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.
Fast-forward Langevin dynamics with momentum flips
Hijazi, Mahdi; Wilkins, David M.; Ceriotti, Michele
2018-05-01
Stochastic thermostats based on the Langevin equation, in which a system is coupled to an external heat bath, are popular methods for temperature control in molecular dynamics simulations due to their ergodicity and their ease of implementation. Traditionally, these thermostats suffer from sluggish behavior in the limit of high friction, unlike thermostats of the Nosé-Hoover family whose performance degrades more gently in the strong coupling regime. We propose a simple and easy-to-implement modification to the integration scheme of the Langevin algorithm that addresses the fundamental source of the overdamped behavior of high-friction Langevin dynamics: if the action of the thermostat causes the momentum of a particle to change direction, it is flipped back. This fast-forward Langevin equation preserves the momentum distribution and so guarantees the correct equilibrium sampling. It mimics the quadratic behavior of Nosé-Hoover thermostats and displays similarly good performance in the strong coupling limit. We test the efficiency of this scheme by applying it to a 1-dimensional harmonic oscillator, as well as to water and Lennard-Jones polymers. The sampling efficiency of the fast-forward Langevin equation thermostat, measured by the correlation time of relevant system variables, is at least as good as the traditional Langevin thermostat, and in the overdamped regime, the fast-forward thermostat performs much better, improving the efficiency by an order of magnitude at the highest frictions we considered.
International Nuclear Information System (INIS)
Jepps, Owen G; Rondoni, Lamberto
2010-01-01
Deterministic 'thermostats' are mathematical tools used to model nonequilibrium steady states of fluids. The resulting dynamical systems correctly represent the transport properties of these fluids and are easily simulated on modern computers. More recently, the connection between such thermostats and entropy production has been exploited in the development of nonequilibrium fluid theories. The purpose and limitations of deterministic thermostats are discussed in the context of irreversible thermodynamics and the development of theories of nonequilibrium phenomena. We draw parallels between the development of such nonequilibrium theories and the development of notions of ergodicity in equilibrium theories. (topical review)
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
DEFF Research Database (Denmark)
Simonsen, Maria
This thesis treats stochastic systems with switching dynamics. Models with these characteristics are studied from several perspectives. Initially in a simple framework given in the form of stochastic differential equations and, later, in an extended form which fits into the framework of sliding...... mode control. It is investigated how to understand and interpret solutions to models of switched systems, which are exposed to discontinuous dynamics and uncertainties (primarily) in the form of white noise. The goal is to gain knowledge about the performance of the system by interpreting the solution...
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 ...
Texas traffic thermostat software tool.
2013-04-01
The traffic thermostat decision tool is built to help guide the user through a logical, step-wise, process of examining potential changes to their Manage Lane/toll facility. : **NOTE: Project Title: Application of the Traffic Thermostat Framework. Ap...
Texas traffic thermostat marketing package.
2013-04-01
The traffic thermostat decision tool is built to help guide the user through a logical, step-wise, process of examining potential changes to their Manage Lane/toll facility. : **NOTE: Project Title: Application of the Traffic Thermostat Framework. Ap...
Introducing the ecobee smart thermostat
Energy Technology Data Exchange (ETDEWEB)
NONE
2009-07-01
This pamphlet described a thermostat system designed to help households conserve energy and reduce the environmental impacts related to home heating. Features of the ecobee smart thermostat include a weather button that provides the latest forecast for the specific region and a quick save button designed to automatically set the thermostat into an energy conservation mode. A details button provides customer access to all customized heating and cooling settings interfaced in list format. A programming feature assists customers in basic and advanced programming. A vacation setting is also provided to allow customers to save energy while on vacation. The ecobee system uses advanced furnace fan control, ventilator control, and automatic setback calculations. The thermostat system includes a full colour display and integrated web portal designed to allow remote access and provide tools for easily adapting to changing rate structures. Optional broadband connectivity allows real time delivery to customers. The pamphlet also included technical specifications. 1 tab., 9 figs.
Path to Stochastic Stability: Comparative Analysis of Stochastic Learning Dynamics in Games
Jaleel, Hassan
2018-04-08
Stochastic stability is a popular solution concept for stochastic learning dynamics in games. However, a critical limitation of this solution concept is its inability to distinguish between different learning rules that lead to the same steady-state behavior. We address this limitation for the first time and develop a framework for the comparative analysis of stochastic learning dynamics with different update rules but same steady-state behavior. We present the framework in the context of two learning dynamics: Log-Linear Learning (LLL) and Metropolis Learning (ML). Although both of these dynamics have the same stochastically stable states, LLL and ML correspond to different behavioral models for decision making. Moreover, we demonstrate through an example setup of sensor coverage game that for each of these dynamics, the paths to stochastically stable states exhibit distinctive behaviors. Therefore, we propose multiple criteria to analyze and quantify the differences in the short and medium run behavior of stochastic learning dynamics. We derive and compare upper bounds on the expected hitting time to the set of Nash equilibria for both LLL and ML. For the medium to long-run behavior, we identify a set of tools from the theory of perturbed Markov chains that result in a hierarchical decomposition of the state space into collections of states called cycles. We compare LLL and ML based on the proposed criteria and develop invaluable insights into the comparative behavior of the two dynamics.
Room Thermostat with Servo Controlled by PIC Microcontroller
Directory of Open Access Journals (Sweden)
Jan Skapa
2013-01-01
Full Text Available This paper describes the design of room thermostat with Microchip PIC microcontroller. Thermostat is designated for two-pipe heating system. The microprocessor controls thermostatic valve via electric actuator with mechanical gear unit. The room thermostat uses for its activity measurements of air temperature in the room and calorimetric measurement of heat, which is served to the radiator. These features predestinate it mainly for underfloor heating regulation. The thermostat is designed to work in a network. Communication with heating system's central control unit is proceeded via RS485 bus with proprietary communication protocol. If the communication failure occurs the thermostat is able to work separately. The system uses its own real time clock circuit and memory with heating programs. These programs are able to cover the whole heating season. The method of position discontinuous PSD control is used in this equipment.
Dynamical and hamiltonian dilations of stochastic processes
International Nuclear Information System (INIS)
Baumgartner, B.; Gruemm, H.-R.
1982-01-01
This is a study of the problem, which stochastic processes could arise from dynamical systems by loss of information. The notions of ''dilation'' and ''approximate dilation'' of a stochastic process are introduced to give exact definitions of this particular relationship. It is shown that every generalized stochastic process is approximately dilatable by a sequence of dynamical systems, but for stochastic processes in full generality one needs nets. (Author)
Stochastic runaway of dynamical systems
International Nuclear Information System (INIS)
Pfirsch, D.; Graeff, P.
1984-10-01
One-dimensional, stochastic, dynamical systems are well studied with respect to their stability properties. Less is known for the higher dimensional case. This paper derives sufficient and necessary criteria for the asymptotic divergence of the entropy (runaway) and sufficient ones for the moments of n-dimensional, stochastic, dynamical systems. The crucial implication is the incompressibility of their flow defined by the equations of motion in configuration space. Two possible extensions to compressible flow systems are outlined. (orig.)
Stochastic Thermodynamics: A Dynamical Systems Approach
Directory of Open Access Journals (Sweden)
Tanmay Rajpurohit
2017-12-01
Full Text Available In this paper, we develop an energy-based, large-scale dynamical system model driven by Markov diffusion processes to present a unified framework for statistical thermodynamics predicated on a stochastic dynamical systems formalism. Specifically, using a stochastic state space formulation, we develop a nonlinear stochastic compartmental dynamical system model characterized by energy conservation laws that is consistent with statistical thermodynamic principles. In particular, we show that the difference between the average supplied system energy and the average stored system energy for our stochastic thermodynamic model is a martingale with respect to the system filtration. In addition, we show that the average stored system energy is equal to the mean energy that can be extracted from the system and the mean energy that can be delivered to the system in order to transfer it from a zero energy level to an arbitrary nonempty subset in the state space over a finite stopping time.
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.
Stochastic ice stream dynamics.
Mantelli, Elisa; Bertagni, Matteo Bernard; Ridolfi, Luca
2016-08-09
Ice streams are narrow corridors of fast-flowing ice that constitute the arterial drainage network of ice sheets. Therefore, changes in ice stream flow are key to understanding paleoclimate, sea level changes, and rapid disintegration of ice sheets during deglaciation. The dynamics of ice flow are tightly coupled to the climate system through atmospheric temperature and snow recharge, which are known exhibit stochastic variability. Here we focus on the interplay between stochastic climate forcing and ice stream temporal dynamics. Our work demonstrates that realistic climate fluctuations are able to (i) induce the coexistence of dynamic behaviors that would be incompatible in a purely deterministic system and (ii) drive ice stream flow away from the regime expected in a steady climate. We conclude that environmental noise appears to be crucial to interpreting the past behavior of ice sheets, as well as to predicting their future evolution.
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 dynamics of new inflation
International Nuclear Information System (INIS)
Nakao, Ken-ichi; Nambu, Yasusada; Sasaki, Misao.
1988-07-01
We investigate thoroughly the dynamics of an inflation-driving scalar field in terms of an extended version of the stochastic approach proposed by Starobinsky and discuss the spacetime structure of the inflationary universe. To avoid any complications which might arise due to quantum gravity, we concentrate our discussions on the new inflationary universe scenario in which all the energy scales involved are well below the planck mass. The investigation is done both analytically and numerically. In particular, we present a full numerical analysis of the stochastic scalar field dynamics on the phase space. Then implications of the results are discussed. (author)
Research on nonlinear stochastic dynamical price model
International Nuclear Information System (INIS)
Li Jiaorui; Xu Wei; Xie Wenxian; Ren Zhengzheng
2008-01-01
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
Hybrid Semantics of Stochastic Programs with Dynamic Reconfiguration
Directory of Open Access Journals (Sweden)
Alberto Policriti
2009-10-01
Full Text Available We begin by reviewing a technique to approximate the dynamics of stochastic programs --written in a stochastic process algebra-- by a hybrid system, suitable to capture a mixed discrete/continuous evolution. In a nutshell, the discrete dynamics is kept stochastic while the continuous evolution is given in terms of ODEs, and the overall technique, therefore, naturally associates a Piecewise Deterministic Markov Process with a stochastic program. The speciﬁc contribution in this work consists in an increase of the ﬂexibility of the translation scheme, obtained by allowing a dynamic reconﬁguration of the degree of discreteness/continuity of the semantics. We also discuss the relationships of this approach with other hybrid simulation strategies for biochemical systems.
Stochastic dynamic modeling of regular and slow earthquakes
Aso, N.; Ando, R.; Ide, S.
2017-12-01
Both regular and slow earthquakes are slip phenomena on plate boundaries and are simulated by a (quasi-)dynamic modeling [Liu and Rice, 2005]. In these numerical simulations, spatial heterogeneity is usually considered not only for explaining real physical properties but also for evaluating the stability of the calculations or the sensitivity of the results on the condition. However, even though we discretize the model space with small grids, heterogeneity at smaller scales than the grid size is not considered in the models with deterministic governing equations. To evaluate the effect of heterogeneity at the smaller scales we need to consider stochastic interactions between slip and stress in a dynamic modeling. Tidal stress is known to trigger or affect both regular and slow earthquakes [Yabe et al., 2015; Ide et al., 2016], and such an external force with fluctuation can also be considered as a stochastic external force. A healing process of faults may also be stochastic, so we introduce stochastic friction law. In the present study, we propose a stochastic dynamic model to explain both regular and slow earthquakes. We solve mode III problem, which corresponds to the rupture propagation along the strike direction. We use BIEM (boundary integral equation method) scheme to simulate slip evolution, but we add stochastic perturbations in the governing equations, which is usually written in a deterministic manner. As the simplest type of perturbations, we adopt Gaussian deviations in the formulation of the slip-stress kernel, external force, and friction. By increasing the amplitude of perturbations of the slip-stress kernel, we reproduce complicated rupture process of regular earthquakes including unilateral and bilateral ruptures. By perturbing external force, we reproduce slow rupture propagation at a scale of km/day. The slow propagation generated by a combination of fast interaction at S-wave velocity is analogous to the kinetic theory of gasses: thermal
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.
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.
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.
The Theory of Dynamic Public Transit Priority with Dynamic Stochastic Park and Ride
Zhu, Chengming; Chen, Yanyan; Ma, Changxi
2014-01-01
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, scal...
Phillips, Carolyn L.; Anderson, Joshua A.; Glotzer, Sharon C.
2011-08-01
Brownian Dynamics (BD), also known as Langevin Dynamics, and Dissipative Particle Dynamics (DPD) are implicit solvent methods commonly used in models of soft matter and biomolecular systems. The interaction of the numerous solvent particles with larger particles is coarse-grained as a Langevin thermostat is applied to individual particles or to particle pairs. The Langevin thermostat requires a pseudo-random number generator (PRNG) to generate the stochastic force applied to each particle or pair of neighboring particles during each time step in the integration of Newton's equations of motion. In a Single-Instruction-Multiple-Thread (SIMT) GPU parallel computing environment, small batches of random numbers must be generated over thousands of threads and millions of kernel calls. In this communication we introduce a one-PRNG-per-kernel-call-per-thread scheme, in which a micro-stream of pseudorandom numbers is generated in each thread and kernel call. These high quality, statistically robust micro-streams require no global memory for state storage, are more computationally efficient than other PRNG schemes in memory-bound kernels, and uniquely enable the DPD simulation method without requiring communication between threads.
A Stochastic Model for Malaria Transmission Dynamics
Directory of Open Access Journals (Sweden)
Rachel Waema Mbogo
2018-01-01
Full Text Available Malaria is one of the three most dangerous infectious diseases worldwide (along with HIV/AIDS and tuberculosis. In this paper we compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in malaria transmission dynamics. Relationships between the basic reproduction number for malaria transmission dynamics between humans and mosquitoes and the extinction thresholds of corresponding continuous-time Markov chain models are derived under certain assumptions. The stochastic model is formulated using the continuous-time discrete state Galton-Watson branching process (CTDSGWbp. The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction from stochastic models contribute crucial knowledge on disease control and elimination and mitigation of infectious diseases. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that malaria outbreak is more likely if the disease is introduced by infected mosquitoes as opposed to infected humans. These insights demonstrate the importance of a policy or intervention focusing on controlling the infected mosquito population if the control of malaria is to be realized.
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.
Collisionally induced stochastic dynamics of fast ions in solids
International Nuclear Information System (INIS)
Burgdoerfer, J.
1989-01-01
Recent developments in the theory of excited state formation in collisions of fast highly charged ions with solids are reviewed. We discuss a classical transport theory employing Monte-Carlo sampling of solutions of a microscopic Langevin equation. Dynamical screening by the dielectric medium as well as multiple collisions are incorporated through the drift and stochastic forces in the Langevin equation. The close relationship between the extrinsically stochastic dynamics described by the Langevin and the intrinsic stochasticity in chaotic nonlinear dynamical systems is stressed. Comparison with experimental data and possible modification by quantum corrections are discussed. 49 refs., 11 figs
Path to Stochastic Stability: Comparative Analysis of Stochastic Learning Dynamics in Games
Jaleel, Hassan; Shamma, Jeff S.
2018-01-01
dynamics: Log-Linear Learning (LLL) and Metropolis Learning (ML). Although both of these dynamics have the same stochastically stable states, LLL and ML correspond to different behavioral models for decision making. Moreover, we demonstrate through
Sparse learning of stochastic dynamical equations
Boninsegna, Lorenzo; Nüske, Feliks; Clementi, Cecilia
2018-06-01
With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics (SINDy) has been introduced to identify the governing equations of dynamical systems from simulation data. In this study, we extend SINDy to stochastic dynamical systems which are frequently used to model biophysical processes. We prove the asymptotic correctness of stochastic SINDy in the infinite data limit, both in the original and projected variables. We discuss algorithms to solve the sparse regression problem arising from the practical implementation of SINDy and show that cross validation is an essential tool to determine the right level of sparsity. We demonstrate the proposed methodology on two test systems, namely, the diffusion in a one-dimensional potential and the projected dynamics of a two-dimensional diffusion process.
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.
ENERGY STAR Certified Smart Thermostats
U.S. Environmental Protection Agency — Certified models meet all ENERGY STAR requirements as listed in the Version 1.0 ENERGY STAR Program Requirements for Connected Thermostats that are effective as of...
Energy Technology Data Exchange (ETDEWEB)
Wu, F.; Song, D.; Sheng, K.; Wu, J. [Changcheng Institute of Metrology and Measurement, 100095, Beijing (China); Yi, X. [China National South Aviation industry CO., LTD., 412002, Hunan (China); Yu, Z. [Dalian Jinzhou Institute of Measurement and Testing, 116100, Liaoning (China)
2013-09-11
In this paper the authors report a newly developed Cesium Heat-Pipe Thermostat (Cs HPT) with the operation range of 400 °C to 800 °C. The working medium is cesium (Cs) of 99.98% purity and contains no radioisotope. A Cs filing device is developed which can prevent Cs being in contact with air. The structural material is stainless steel. A 5000 h test has been made to confirm the compatibility between cesium and stainless steel. The Cs HPT has several thermometer wells of 220mm depth with different diameters for different sizes of thermometers. The temperature uniformity of the Cs HPT is 0.06 °C to 0.20 °C. A precise temperature controller is used to ensure the temperature fluctuation within ±0.03 °C. The size of Cs HPT is 380mm×320mm×280mm with foot wheels for easy moving. The thermostat has been successfully used for the calibration of industrial platinum resistance thermometers and thermocouples.
Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics
International Nuclear Information System (INIS)
Ao, P.
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 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
Stochastic properties of the Friedman dynamical system
International Nuclear Information System (INIS)
Szydlowski, M.; Heller, M.; Golda, Z.
1985-01-01
Some mathematical aspects of the stochastic cosmology are discussed in the corresponding ordinary Friedman world models. In particulare, it is shown that if the strong and Lorentz energy conditions are known, or the potential function is given, or a stochastic measure is suitably defined then the structure of the phase plane of the Friedman dynamical system is determined. 11 refs., 2 figs. (author)
Stochastic control theory dynamic programming principle
Nisio, Makiko
2015-01-01
This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems. First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory. When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise. This problem is treated in the same frameworks, via the nonlinear semigroup. Its results are applicable to the American option price problem. Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-ma...
Dynamics of non-holonomic systems with stochastic transport
Holm, D. D.; Putkaradze, V.
2018-01-01
This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under non-holonomic constraints. For this purpose, we derive, analyse and numerically study the example of an unbalanced spherical ball rolling under gravity along a stochastic path. Our approach uses the Hamilton-Pontryagin variational principle, constrained by a stochastic rolling condition, which we show is equivalent to the corresponding stochastic Lagrange-d'Alembert principle. In the example of the rolling ball, the stochasticity represents uncertainty in the observation and/or error in the computational simulation of the angular velocity of rolling. The influence of the stochasticity on the deterministically conserved quantities is investigated both analytically and numerically. Our approach applies to a wide variety of stochastic, non-holonomically constrained systems, because it preserves the mathematical properties inherited from the variational principle.
Testing the effect of defaults on the thermostat settings of OECD employees
International Nuclear Information System (INIS)
Brown, Zachary; Johnstone, Nick; Haščič, Ivan; Vong, Laura; Barascud, Francis
2013-01-01
We describe a randomized controlled experiment in which the default settings on office thermostats in an OECD office building were manipulated during the winter heating season, and employees' chosen thermostat setting observed over a 6-week period. Using difference-in-differences, panel, and censored regression models (to control for maximum allowable thermostat settings), we find that a 1 °C decrease in the default caused a reduction in the chosen setting by 0.38 °C, on average. Sixty-five percent of this effect could be attributed to office occupant behavior (p-value = 0.044). The difference-in-differences models show that small decreases in the default (1°) led to a greater reduction in chosen settings than large decreases (2°). We also find that office occupants who were more apt to adjust their thermostats prior to the intervention were less susceptible to the default. We conclude that this kind of intervention can increase building-level energy efficiency, and discuss potential explanations and broader policy implications of our findings. - Highlights: • We conduct a randomized controlled trial to test if thermostat defaults affect agent behavior. • Two treatments (schedules of default settings) were tested against a control for 6 weeks at OECD. • Small changes in defaults had a greater effect on chosen settings than larger changes in defaults. • Occupants who frequently changed their thermostats in baseline were less affected by defaults. • Thermostat defaults in office environments can be manipulated to increase energy efficiency
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
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. Copyright © 2012 Elsevier Ltd. All rights reserved.
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 ...
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...
Thermostatic Radiator Valve Evaluation
Energy Technology Data Exchange (ETDEWEB)
Dentz, Jordan [Advanced Residential Integrated Energy Solutions Collaborative, New York, NY (United States); Ansanelli, Eric [Advanced Residential Integrated Energy Solutions Collaborative, 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.
Stochastic dynamics of melt ponds and sea ice-albedo climate feedback
Sudakov, Ivan
Evolution of melt ponds on the Arctic sea surface is a complicated stochastic process. We suggest a low-order model with ice-albedo feedback which describes stochastic dynamics of melt ponds geometrical characteristics. The model is a stochastic dynamical system model of energy balance in the climate system. We describe the equilibria in this model. We conclude the transition in fractal dimension of melt ponds affects the shape of the sea ice albedo curve.
Stochastic beam dynamics in storage rings
International Nuclear Information System (INIS)
Pauluhn, A.
1993-12-01
In this thesis several approaches to stochastic dynamics in storage rings are investigated. In the first part the theory of stochastic differential equations and Fokker-Planck equations is used to describe the processes which have been assumed to be Markov processes. The mathematical theory of Markov processes is well known. Nevertheless, analytical solutions can be found only in special cases and numerical algorithms are required. Several numerical integration schemes for stochastic differential equations will therefore be tested in analytical solvable examples and then applied to examples from accelerator physics. In particular the stochastically perturbed synchrotron motion is treated. For the special case of a double rf system several perturbation theoretical methods for deriving the Fokker-Planck equation in the action variable are used and compared with numerical results. The second part is concerned with the dynamics of electron storage rings. Due to the synchrotron radiation the electron motion is influenced by damping and exciting forces. An algorithm for the computation of the density function in the phase space of such a dissipative stochastically excited system is introduced. The density function contains all information of a process, e.g. it determines the beam dimensions and the lifetime of a stored electron beam. The new algorithm consists in calculating a time propagator for the density function. By means of this propagator the time evolution of the density is modelled very computing time efficient. The method is applied to simple models of the beam-beam interaction (one-dimensional, round beams) and the results of the density calculations are compared with results obtained from multiparticle tracking. Furthermore some modifications of the algorithm are introduced to improve its efficiency concerning computing time and storage requirements. Finally, extensions to two-dimensional beam-beam models are described. (orig.)
Reformulation of a stochastic action principle for irregular dynamics
International Nuclear Information System (INIS)
Wang, Q.A.; Bangoup, S.; Dzangue, F.; Jeatsa, A.; Tsobnang, F.; Le Mehaute, A.
2009-01-01
A stochastic action principle for random dynamics is revisited. Numerical diffusion experiments are carried out to show that the diffusion path probability depends exponentially on the Lagrangian action A=∫ a b Ldt. This result is then used to derive the Shannon measure for path uncertainty. It is shown that the maximum entropy principle and the least action principle of classical mechanics can be unified into δA-bar=0 where the average is calculated over all possible paths of the stochastic motion between two configuration points a and b. It is argued that this action principle and the maximum entropy principle are a consequence of the mechanical equilibrium condition extended to the case of stochastic dynamics.
Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics
Energy Technology Data Exchange (ETDEWEB)
Arampatzis, Georgios; Katsoulakis, Markos A.; Rey-Bellet, Luc [Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003 (United States)
2016-03-14
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.
Forecasting financial asset processes: stochastic dynamics via learning neural networks.
Giebel, S; Rainer, M
2010-01-01
Models for financial asset dynamics usually take into account their inherent unpredictable nature by including a suitable stochastic component into their process. Unknown (forward) values of financial assets (at a given time in the future) are usually estimated as expectations of the stochastic asset under a suitable risk-neutral measure. This estimation requires the stochastic model to be calibrated to some history of sufficient length in the past. Apart from inherent limitations, due to the stochastic nature of the process, the predictive power is also limited by the simplifying assumptions of the common calibration methods, such as maximum likelihood estimation and regression methods, performed often without weights on the historic time series, or with static weights only. Here we propose a novel method of "intelligent" calibration, using learning neural networks in order to dynamically adapt the parameters of the stochastic model. Hence we have a stochastic process with time dependent parameters, the dynamics of the parameters being themselves learned continuously by a neural network. The back propagation in training the previous weights is limited to a certain memory length (in the examples we consider 10 previous business days), which is similar to the maximal time lag of autoregressive processes. We demonstrate the learning efficiency of the new algorithm by tracking the next-day forecasts for the EURTRY and EUR-HUF exchange rates each.
Nambu mechanics for stochastic magnetization dynamics
Energy Technology Data Exchange (ETDEWEB)
Thibaudeau, Pascal, E-mail: pascal.thibaudeau@cea.fr [CEA DAM/Le Ripault, BP 16, F-37260 Monts (France); Nussle, Thomas, E-mail: thomas.nussle@cea.fr [CEA DAM/Le Ripault, BP 16, F-37260 Monts (France); CNRS-Laboratoire de Mathématiques et Physique Théorique (UMR 7350), Fédération de Recherche “Denis Poisson” (FR2964), Département de Physique, Université de Tours, Parc de Grandmont, F-37200 Tours (France); Nicolis, Stam, E-mail: stam.nicolis@lmpt.univ-tours.fr [CNRS-Laboratoire de Mathématiques et Physique Théorique (UMR 7350), Fédération de Recherche “Denis Poisson” (FR2964), Département de Physique, Université de Tours, Parc de Grandmont, F-37200 Tours (France)
2017-06-15
Highlights: • The LLG equation can be formulated in the framework of dissipative Nambu mechanics. • A master equation is derived for the spin dynamics for additive/multiplicative noises. • The derived stochastic equations are compared to moment equations obtained by closures. - Abstract: 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 sampling of the stochastic equations and by using closure assumptions for the moment equations, deduced from the master equation.
International Nuclear Information System (INIS)
Phillips, Carolyn L.; Anderson, Joshua A.; Glotzer, Sharon C.
2011-01-01
Highlights: → Molecular Dynamics codes implemented on GPUs have achieved two-order of magnitude computational accelerations. → Brownian Dynamics and Dissipative Particle Dynamics simulations require a large number of random numbers per time step. → We introduce a method for generating small batches of pseudorandom numbers distributed over many threads of calculations. → With this method, Dissipative Particle Dynamics is implemented on a GPU device without requiring thread-to-thread communication. - Abstract: Brownian Dynamics (BD), also known as Langevin Dynamics, and Dissipative Particle Dynamics (DPD) are implicit solvent methods commonly used in models of soft matter and biomolecular systems. The interaction of the numerous solvent particles with larger particles is coarse-grained as a Langevin thermostat is applied to individual particles or to particle pairs. The Langevin thermostat requires a pseudo-random number generator (PRNG) to generate the stochastic force applied to each particle or pair of neighboring particles during each time step in the integration of Newton's equations of motion. In a Single-Instruction-Multiple-Thread (SIMT) GPU parallel computing environment, small batches of random numbers must be generated over thousands of threads and millions of kernel calls. In this communication we introduce a one-PRNG-per-kernel-call-per-thread scheme, in which a micro-stream of pseudorandom numbers is generated in each thread and kernel call. These high quality, statistically robust micro-streams require no global memory for state storage, are more computationally efficient than other PRNG schemes in memory-bound kernels, and uniquely enable the DPD simulation method without requiring communication between threads.
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
2017-05-09
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
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.
Deviation from equilibrium conditions in molecular dynamic simulations of homogeneous nucleation.
Halonen, Roope; Zapadinsky, Evgeni; Vehkamäki, Hanna
2018-04-28
We present a comparison between Monte Carlo (MC) results for homogeneous vapour-liquid nucleation of Lennard-Jones clusters and previously published values from molecular dynamics (MD) simulations. Both the MC and MD methods sample real cluster configuration distributions. In the MD simulations, the extent of the temperature fluctuation is usually controlled with an artificial thermostat rather than with more realistic carrier gas. In this study, not only a primarily velocity scaling thermostat is considered, but also Nosé-Hoover, Berendsen, and stochastic Langevin thermostat methods are covered. The nucleation rates based on a kinetic scheme and the canonical MC calculation serve as a point of reference since they by definition describe an equilibrated system. The studied temperature range is from T = 0.3 to 0.65 ϵ/k. The kinetic scheme reproduces well the isothermal nucleation rates obtained by Wedekind et al. [J. Chem. Phys. 127, 064501 (2007)] using MD simulations with carrier gas. The nucleation rates obtained by artificially thermostatted MD simulations are consistently lower than the reference nucleation rates based on MC calculations. The discrepancy increases up to several orders of magnitude when the density of the nucleating vapour decreases. At low temperatures, the difference to the MC-based reference nucleation rates in some cases exceeds the maximal nonisothermal effect predicted by classical theory of Feder et al. [Adv. Phys. 15, 111 (1966)].
Smart Thermostats: An Experimental Facility to Test Their Capabilities and Savings Potential
Directory of Open Access Journals (Sweden)
Sergio Bustamante
2017-08-01
Full Text Available The European Commission has explained how heating and cooling in buildings and industry account for half of the energy consumption of the EU. Several studies explain how to achieve an energy saving at home, and the use of smart thermostats will help to reduce energy consumption while increasing the efficiency of households. In this article, a comparative evaluation was carried out between four smart thermostats that are now on the market, whose characteristics vary in terms of price, precision of measurements and set temperature, algorithms, etc. A thermal test chamber was designed and constructed from a refrigerator, a thermal blanket, a Raspberry Pi and the necessary electronic components for its control and data collection. From the tests carried out in the thermal chamber, data on the operation of the four thermostats such as the maintenance and the anticipation of the setpoint temperature, were obtained. It was necessary to run the system enough times for each thermostat to memorize the housing characteristics, such as its inertia and its thermal insulation. This would also allow for the generation of a better algorithm to regulate the temperature, which would create a lower oscillation with respect to the setpoint temperature. The learning of the thermostats was not demonstrated and for the anticipation mode it was seen that the thermostats failed to improve or learn in this aspect, as they did not improve the start-up times of the heating system, with the consequent increase in energy consumption.
Stochastic integer programming by dynamic programming
Lageweg, B.J.; Lenstra, J.K.; Rinnooy Kan, A.H.G.; Stougie, L.; Ermoliev, Yu.; Wets, R.J.B.
1988-01-01
Stochastic integer programming is a suitable tool for modeling hierarchical decision situations with combinatorial features. In continuation of our work on the design and analysis of heuristics for such problems, we now try to find optimal solutions. Dynamic programming techniques can be used to
Fast stochastic algorithm for simulating evolutionary population dynamics
Tsimring, Lev; Hasty, Jeff; Mather, William
2012-02-01
Evolution and co-evolution of ecological communities are stochastic processes often characterized by vastly different rates of reproduction and mutation and a coexistence of very large and very small sub-populations of co-evolving species. This creates serious difficulties for accurate statistical modeling of evolutionary dynamics. In this talk, we introduce a new exact algorithm for fast fully stochastic simulations of birth/death/mutation processes. It produces a significant speedup compared to the direct stochastic simulation algorithm in a typical case when the total population size is large and the mutation rates are much smaller than birth/death rates. We illustrate the performance of the algorithm on several representative examples: evolution on a smooth fitness landscape, NK model, and stochastic predator-prey system.
International Nuclear Information System (INIS)
Qian, Hong
2011-01-01
The nonlinear dynamics of biochemical reactions in a small-sized system on the order of a cell are stochastic. Assuming spatial homogeneity, the populations of n molecular species follow a multi-dimensional birth-and-death process on Z n . We introduce the Delbrück–Gillespie process, a continuous-time Markov jump process, whose Kolmogorov forward equation has been known as the chemical master equation, and whose stochastic trajectories can be computed via the Gillespie algorithm. Using simple models, we illustrate that a system of nonlinear ordinary differential equations on R n emerges in the infinite system size limit. For finite system size, transitions among multiple attractors of the nonlinear dynamical system are rare events with exponentially long transit times. There is a separation of time scales between the deterministic ODEs and the stochastic Markov jumps between attractors. No diffusion process can provide a global representation that is accurate on both short and long time scales for the nonlinear, stochastic population dynamics. On the short time scale and near deterministic stable fixed points, Ornstein–Uhlenbeck Gaussian processes give linear stochastic dynamics that exhibit time-irreversible circular motion for open, driven chemical systems. Extending this individual stochastic behaviour-based nonlinear population theory of molecular species to other biological systems is discussed. (invited article)
Dynamics of a Stochastic Intraguild Predation Model
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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.
Electricity Market Stochastic Dynamic Model and Its Mean Stability Analysis
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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.
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.
Constant pressure and temperature discrete-time Langevin molecular dynamics
Energy Technology Data Exchange (ETDEWEB)
Grønbech-Jensen, Niels [Department of Mechanical and Aerospace Engineering, University of California, Davis, California 95616 (United States); Department of Mathematics, University of California, Davis, California 95616 (United States); Farago, Oded [Department of Biomedical Engineering, Ben Gurion University of the Negev, Be' er Sheva 84105 (Israel); Ilse Katz Institute for Nanoscale Science and Technology, Ben Gurion University of the Negev, Be' er Sheva 84105 (Israel)
2014-11-21
We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems—a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation.
Discriminating chaotic and stochastic dynamics through the permutation spectrum test
Energy Technology Data Exchange (ETDEWEB)
Kulp, C. W., E-mail: Kulp@lycoming.edu [Department of Astronomy and Physics, Lycoming College, Williamsport, Pennsylvania 17701 (United States); Zunino, L., E-mail: lucianoz@ciop.unlp.edu.ar [Centro de Investigaciones Ópticas (CONICET La Plata—CIC), C.C. 3, 1897 Gonnet (Argentina); Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata (UNLP), 1900 La Plata (Argentina)
2014-09-01
In this paper, we propose a new heuristic symbolic tool for unveiling chaotic and stochastic dynamics: the permutation spectrum test. Several numerical examples allow us to confirm the usefulness of the introduced methodology. Indeed, we show that it is robust in situations in which other techniques fail (intermittent chaos, hyperchaotic dynamics, stochastic linear and nonlinear correlated dynamics, and deterministic non-chaotic noise-driven dynamics). We illustrate the applicability and reliability of this pragmatic method by examining real complex time series from diverse scientific fields. Taking into account that the proposed test has the advantages of being conceptually simple and computationally fast, we think that it can be of practical utility as an alternative test for determinism.
Stochastic dynamics of dengue epidemics.
de Souza, David R; Tomé, Tânia; Pinho, Suani T R; Barreto, Florisneide R; de Oliveira, Mário J
2013-01-01
We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, such as dengue, and the threshold of the disease. The coexistence space is composed of two structures representing the human and mosquito populations. The human population follows a susceptible-infected-recovered (SIR) type dynamics and the mosquito population follows a susceptible-infected-susceptible (SIS) type dynamics. The human infection is caused by infected mosquitoes and vice versa, so that the SIS and SIR dynamics are interconnected. We develop a truncation scheme to solve the evolution equations from which we get the threshold of the disease and the reproductive ratio. The threshold of the disease is also obtained by performing numerical simulations. We found that for certain values of the infection rates the spreading of the disease is impossible, for any death rate of infected mosquitoes.
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 temperat......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 control architecture is defined by parsimonious communication requirements that also have a high level data privacy, and it furthermore guarantees a robust and secure local operation. Mathematical models are put forward, and the effectiveness is shown by numerical simulations. A case study of 10000...
The dynamics of stochastic processes
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas
In the present thesis the dynamics of stochastic processes is studied with a special attention to the semimartingale property. This is mainly motivated by the fact that semimartingales provide the class of the processes for which it is possible to define a reasonable stochastic calculus due...... to the Bichteler-Dellacherie Theorem. The semimartingale property of Gaussian processes is characterized in terms of their covariance function, spectral measure and spectral representation. In addition, representation and expansion of filtration results are provided as well. Special attention is given to moving...... average processes, and when the driving process is a Lévy or a chaos process the semimartingale property is characterized in the filtration spanned by the driving process and in the natural filtration when the latter is a Brownian motion. To obtain some of the above results an integrability of seminorm...
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.
Cotter, C J; Gottwald, G A; Holm, D D
2017-09-01
In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.
Symplectic Integrators to Stochastic Hamiltonian Dynamical Systems Derived from Composition Methods
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Tetsuya Misawa
2010-01-01
Full Text Available “Symplectic” schemes for stochastic Hamiltonian dynamical systems are formulated through “composition methods (or operator splitting methods” proposed by Misawa (2001. In the proposed methods, a symplectic map, which is given by the solution of a stochastic Hamiltonian system, is approximated by composition of the stochastic flows derived from simpler Hamiltonian vector fields. The global error orders of the numerical schemes derived from the stochastic composition methods are provided. To examine the superiority of the new schemes, some illustrative numerical simulations on the basis of the proposed schemes are carried out for a stochastic harmonic oscillator system.
Nuclear quantum effects in solids using a colored-noise thermostat.
Ceriotti, Michele; Bussi, Giovanni; Parrinello, Michele
2009-07-17
We present a method, based on a non-Markovian Langevin equation, to include quantum corrections to the classical dynamics of ions in a quasiharmonic system. By properly fitting the correlation function of the noise, one can vary the fluctuations in positions and momenta as a function of the vibrational frequency, and fit them so as to reproduce the quantum-mechanical behavior, with minimal a priori knowledge of the details of the system. We discuss the application of the thermostat to diamond and to ice Ih. We find that results in agreement with path-integral methods can be obtained using only a fraction of the computational effort.
Stochastic dynamic analysis of marine risers considering Gaussian system uncertainties
Ni, Pinghe; Li, Jun; Hao, Hong; Xia, Yong
2018-03-01
This paper performs the stochastic dynamic response analysis of marine risers with material uncertainties, i.e. in the mass density and elastic modulus, by using Stochastic Finite Element Method (SFEM) and model reduction technique. These uncertainties are assumed having Gaussian distributions. The random mass density and elastic modulus are represented by using the Karhunen-Loève (KL) expansion. The Polynomial Chaos (PC) expansion is adopted to represent the vibration response because the covariance of the output is unknown. Model reduction based on the Iterated Improved Reduced System (IIRS) technique is applied to eliminate the PC coefficients of the slave degrees of freedom to reduce the dimension of the stochastic system. Monte Carlo Simulation (MCS) is conducted to obtain the reference response statistics. Two numerical examples are studied in this paper. The response statistics from the proposed approach are compared with those from MCS. It is noted that the computational time is significantly reduced while the accuracy is kept. The results demonstrate the efficiency of the proposed approach for stochastic dynamic response analysis of marine risers.
Age distribution dynamics with stochastic jumps in mortality.
Calabrese, Salvatore; Porporato, Amilcare; Laio, Francesco; D'Odorico, Paolo; Ridolfi, Luca
2017-11-01
While deterministic age distribution models have been extensively studied and applied in various disciplines, little work has been devoted to understanding the role of stochasticity in birth and mortality terms. In this paper, we analyse a stochastic M'Kendrick-von Foerster equation in which jumps in mortality represent intense losses of population due to external events. We present explicit solutions for the probability density functions of the age distribution and the total population and for the temporal dynamics of their moments. We also derive the dynamics of the mean age of the population and its harmonic mean. The framework is then used to calculate the age distribution of salt in the soil root zone, where the accumulation of salt by atmospheric deposition is counteracted by plant uptake and by jump losses due to percolation events.
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...
International Nuclear Information System (INIS)
Perfumo, Cristian; Kofman, Ernesto; Braslavsky, Julio H.; Ward, John K.
2012-01-01
Highlights: ► Characterisation of power response of a population of air conditioners. ► Implementation of demand side management on a group of air conditioners. ► Design of a controller for the power output of a group of air conditioners. ► Quantification of comfort impact of demand side management. - Abstract: Large groups of electrical loads can be controlled as a single entity to reduce their aggregate power demand in the electricity network. This approach, known as load management (LM) or demand response, offers an alternative to the traditional paradigm in the electricity market, where matching supply and demand is achieved solely by regulating how much generation is dispatched. Thermostatically controlled loads (TCLs), such as air conditioners (ACs) and fridges, are particularly suitable for LM, which can be implemented using feedback control techniques to regulate their aggregate power. To achieve high performance, such feedback control techniques require an accurate mathematical model of the TCL aggregate dynamics. Although such models have been developed, they appear too complex to be effectively used in control design. In this paper we develop a mathematical model aimed at the design of a model-based feedback control strategy. The proposed model analytically characterises the aggregate power response of a population of ACs to a simultaneous step change in temperature set points. Based on this model, we then derive, and completely parametrise in terms of the ACs ensemble properties, a reduced-order mathematical model to design an internal-model controller that regulates aggregate power by broadcasting temperature set-point offset changes. The proposed controller achieves high LM performance provided the ACs are equipped with high resolution thermostats. With coarser resolution thermostats, which are typical in present commercial and residential ACs, performance deteriorates significantly. This limitation is overcome by subdividing the population
Measures of thermodynamic irreversibility in deterministic and stochastic dynamics
International Nuclear Information System (INIS)
Ford, Ian J
2015-01-01
It is generally observed that if a dynamical system is sufficiently complex, then as time progresses it will share out energy and other properties amongst its component parts to eliminate any initial imbalances, retaining only fluctuations. This is known as energy dissipation and it is closely associated with the concept of thermodynamic irreversibility, measured by the increase in entropy according to the second law. It is of interest to quantify such behaviour from a dynamical rather than a thermodynamic perspective and to this end stochastic entropy production and the time-integrated dissipation function have been introduced as analogous measures of irreversibility, principally for stochastic and deterministic dynamics, respectively. We seek to compare these measures. First we modify the dissipation function to allow it to measure irreversibility in situations where the initial probability density function (pdf) of the system is asymmetric as well as symmetric in velocity. We propose that it tests for failure of what we call the obversibility of the system, to be contrasted with reversibility, the failure of which is assessed by stochastic entropy production. We note that the essential difference between stochastic entropy production and the time-integrated modified dissipation function lies in the sequence of procedures undertaken in the associated tests of irreversibility. We argue that an assumed symmetry of the initial pdf with respect to velocity inversion (within a framework of deterministic dynamics) can be incompatible with the Past Hypothesis, according to which there should be a statistical distinction between the behaviour of certain properties of an isolated system as it evolves into the far future and the remote past. Imposing symmetry on a velocity distribution is acceptable for many applications of statistical physics, but can introduce difficulties when discussing irreversible behaviour. (paper)
Directory of Open Access Journals (Sweden)
Xiaona Leng
2017-06-01
Full Text Available Abstract This paper proposes a new nonlinear stochastic SIVS epidemic model with double epidemic hypothesis and Lévy jumps. The main purpose of this paper is to investigate the threshold dynamics of the stochastic SIVS epidemic model. By using the technique of a series of stochastic inequalities, we obtain sufficient conditions for the persistence in mean and extinction of the stochastic system and the threshold which governs the extinction and the spread of the epidemic diseases. Finally, this paper describes the results of numerical simulations investigating the dynamical effects of stochastic disturbance. Our results significantly improve and generalize the corresponding results in recent literatures. The developed theoretical methods and stochastic inequalities technique can be used to investigate the high-dimensional nonlinear stochastic differential systems.
Stochastic Relational Presheaves and Dynamic Logic for Contextuality
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Kohei Kishida
2014-12-01
Full Text Available Presheaf models provide a formulation of labelled transition systems that is useful for, among other things, modelling concurrent computation. This paper aims to extend such models further to represent stochastic dynamics such as shown in quantum systems. After reviewing what presheaf models represent and what certain operations on them mean in terms of notions such as internal and external choices, composition of systems, and so on, I will show how to extend those models and ideas by combining them with ideas from other category-theoretic approaches to relational models and to stochastic processes. It turns out that my extension yields a transitional formulation of sheaf-theoretic structures that Abramsky and Brandenburger proposed to characterize non-locality and contextuality. An alternative characterization of contextuality will then be given in terms of a dynamic modal logic of the models I put forward.
Effects of stochastic noise on dynamical decoupling procedures
Energy Technology Data Exchange (ETDEWEB)
Bernad, Jozsef Zsolt; Frydrych, Holger; Alber, Gernot [Institut fuer Angewandte Physik, Technische Universitaet Darmstadt, D-64289 Darmstadt (Germany)
2013-07-01
Dynamical decoupling is a well-established technique to protect quantum systems from unwanted influences of their environment by exercising active control. It has been used experimentally to drastically increase the lifetime of qubit states in various implementations. The efficiency of different dynamical decoupling schemes defines the lifetime. However, errors in control operations always limit this efficiency. We propose a stochastic model as a possible description of imperfect control pulses and discuss the impact of this kind of error on different decoupling schemes. In the limit of continuous control, i.e. if the number of pulses N → ∞, we derive a stochastic differential equation for the evolution of the density operator of the controlled system and its environment. In the context of this modified time evolution we discuss possibilities of protecting qubit states against environmental noise.
Energy Technology Data Exchange (ETDEWEB)
Rejc, Jure; Munih, Marko [University of Ljubljana, Ljubljana (Slovenia)
2017-05-15
A mechanical thermostat is a device that switches heating or cooling appliances on or off based on temperature. For this kind of use, electronic or mechanical switching concepts are applied. During the production of electrical contacts, several irregularities can occur leading to improper switching events of the thermostat electrical contacts. This paper presents a non-obstructive method based on the fact that when the switching event occurs it can be heard and felt by human senses. We performed several laboratory tests with two different methods. The first method includes thermostat switch sound signal analysis during the switching event. The second method is based on sampling of the accelerometer signal during the switching event. The results show that the sound analysis approach has great potential. The approach enables an accurate determination of the switching event even if the sampled signal carries also the switching event of the neighbour thermostat.
Temperature control in molecular dynamic simulations of non-equilibrium processes
International Nuclear Information System (INIS)
Toton, Dawid; Lorenz, Christian D; Rompotis, Nikolaos; Martsinovich, Natalia; Kantorovich, Lev
2010-01-01
Thermostats are often used in various condensed matter problems, e.g. when a biological molecule undergoes a transformation in a solution, a crystal surface is irradiated with energetic particles, a crack propagates in a solid upon applied stress, two surfaces slide with respect to each other, an excited local phonon dissipates its energy into a crystal bulk, and so on. In all of these problems, as well as in many others, there is an energy transfer between different local parts of the entire system kept at a constant temperature. Very often, when modelling such processes using molecular dynamics simulations, thermostatting is done using strictly equilibrium approaches serving to describe the NVT ensemble. In this paper we critically discuss the applicability of such approaches to non-equilibrium problems, including those mentioned above, and stress that the correct temperature control can only be achieved if the method is based on the generalized Langevin equation (GLE). Specifically, we emphasize that a meaningful compromise between computational efficiency and a physically appropriate implementation of the NVT thermostat can be achieved, at least for solid state and surface problems, if the so-called stochastic boundary conditions (SBC), recently derived from the GLE (Kantorovich and Rompotis 2008 Phys. Rev. B 78 094305), are used. For SBC, the Langevin thermostat is only applied to the outer part of the simulated fragment of the entire system which borders the surrounding environment (not considered explicitly) serving as a heat bath. This point is illustrated by comparing the performance of the SBC and some of the equilibrium thermostats in two problems: (i) irradiation of the Si(001) surface with an energetic CaF 2 molecule using an ab initio density functional theory based method, and (ii) the tribology of two amorphous SiO 2 surfaces coated with self-assembled monolayers of methyl-terminated hydrocarbon alkoxylsilane molecules using a classical atomistic
International Nuclear Information System (INIS)
Sabass, Benedikt; Schwarz, Ulrich S
2010-01-01
In migrating cells, retrograde flow of the actin cytoskeleton is related to traction at adhesion sites located at the base of the lamellipodium. The coupling between the moving cytoskeleton and the stationary adhesions is mediated by the continuous association and dissociation of molecular bonds. We introduce a simple model for the competition between the stochastic dynamics of elastic bonds at the moving interface and relaxation within the moving actin cytoskeleton represented by an internal viscous friction coefficient. Using exact stochastic simulations and an analytical mean field theory, we show that the stochastic bond dynamics lead to biphasic friction laws as observed experimentally. At low internal dissipation, stochastic bond dynamics lead to a regime of irregular stick-and-slip motion. High internal dissipation effectively suppresses cooperative effects among bonds and hence stabilizes the adhesion.
Zhang, Wei; Wang, Jun
2018-05-01
A novel nonlinear stochastic interacting price dynamics is proposed and investigated by the bond percolation on Sierpinski gasket fractal-like lattice, aim to make a new approach to reproduce and study the complexity dynamics of real security markets. Fractal-like lattices correspond to finite graphs with vertices and edges, which are similar to fractals, and Sierpinski gasket is a well-known example of fractals. Fractional ordinal array entropy and fractional ordinal array complexity are introduced to analyze the complexity behaviors of financial signals. To deeper comprehend the fluctuation characteristics of the stochastic price evolution, the complexity analysis of random logarithmic returns and volatility are preformed, including power-law distribution, fractional sample entropy and fractional ordinal array complexity. For further verifying the rationality and validity of the developed stochastic price evolution, the actual security market dataset are also studied with the same statistical methods for comparison. The empirical results show that this stochastic price dynamics can reconstruct complexity behaviors of the actual security markets to some extent.
Stochastic Modelling, Analysis, and Simulations of the Solar Cycle Dynamic Process
Turner, Douglas C.; Ladde, Gangaram S.
2018-03-01
Analytical solutions, discretization schemes and simulation results are presented for the time delay deterministic differential equation model of the solar dynamo presented by Wilmot-Smith et al. In addition, this model is extended under stochastic Gaussian white noise parametric fluctuations. The introduction of stochastic fluctuations incorporates variables affecting the dynamo process in the solar interior, estimation error of parameters, and uncertainty of the α-effect mechanism. Simulation results are presented and analyzed to exhibit the effects of stochastic parametric volatility-dependent perturbations. The results generalize and extend the work of Hazra et al. In fact, some of these results exhibit the oscillatory dynamic behavior generated by the stochastic parametric additative perturbations in the absence of time delay. In addition, the simulation results of the modified stochastic models influence the change in behavior of the very recently developed stochastic model of Hazra et al.
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 Erosion of Fractal Structure in Nonlinear Dynamical Systems
Agarwal, S.; Wettlaufer, J. S.
2014-12-01
We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.
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.
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.
A stochastic phase-field model determined from molecular dynamics
von Schwerin, Erik; Szepessy, Anders
2010-01-01
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.
Dynamics and Physiological Roles of Stochastic Firing Patterns Near Bifurcation Points
Jia, Bing; Gu, Huaguang
2017-06-01
Different stochastic neural firing patterns or rhythms that appeared near polarization or depolarization resting states were observed in biological experiments on three nervous systems, and closely matched those simulated near bifurcation points between stable equilibrium point and limit cycle in a theoretical model with noise. The distinct dynamics of spike trains and interspike interval histogram (ISIH) of these stochastic rhythms were identified and found to build a relationship to the coexisting behaviors or fixed firing frequency of four different types of bifurcations. Furthermore, noise evokes coherence resonances near bifurcation points and plays important roles in enhancing information. The stochastic rhythms corresponding to Hopf bifurcation points with fixed firing frequency exhibited stronger coherence degree and a sharper peak in the power spectrum of the spike trains than those corresponding to saddle-node bifurcation points without fixed firing frequency. Moreover, the stochastic firing patterns changed to a depolarization resting state as the extracellular potassium concentration increased for the injured nerve fiber related to pathological pain or static blood pressure level increased for aortic depressor nerve fiber, and firing frequency decreased, which were different from the physiological viewpoint that firing frequency increased with increasing pressure level or potassium concentration. This shows that rhythms or firing patterns can reflect pressure or ion concentration information related to pathological pain information. Our results present the dynamics of stochastic firing patterns near bifurcation points, which are helpful for the identification of both dynamics and physiological roles of complex neural firing patterns or rhythms, and the roles of noise.
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. Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.
Stochastic population dynamics in spatially extended predator-prey systems
Dobramysl, Ulrich; Mobilia, Mauro; Pleimling, Michel; Täuber, Uwe C.
2018-02-01
Spatially extended population dynamics models that incorporate demographic noise serve as case studies for the crucial role of fluctuations and correlations in biological systems. Numerical and analytic tools from non-equilibrium statistical physics capture the stochastic kinetics of these complex interacting many-particle systems beyond rate equation approximations. Including spatial structure and stochastic noise in models for predator-prey competition invalidates the neutral Lotka-Volterra population cycles. Stochastic models yield long-lived erratic oscillations stemming from a resonant amplification mechanism. Spatially extended predator-prey systems display noise-stabilized activity fronts that generate persistent correlations. Fluctuation-induced renormalizations of the oscillation parameters can be analyzed perturbatively via a Doi-Peliti field theory mapping of the master equation; related tools allow detailed characterization of extinction pathways. The critical steady-state and non-equilibrium relaxation dynamics at the predator extinction threshold are governed by the directed percolation universality class. Spatial predation rate variability results in more localized clusters, enhancing both competing species’ population densities. Affixing variable interaction rates to individual particles and allowing for trait inheritance subject to mutations induces fast evolutionary dynamics for the rate distributions. Stochastic spatial variants of three-species competition with ‘rock-paper-scissors’ interactions metaphorically describe cyclic dominance. These models illustrate intimate connections between population dynamics and evolutionary game theory, underscore the role of fluctuations to drive populations toward extinction, and demonstrate how space can support species diversity. Two-dimensional cyclic three-species May-Leonard models are characterized by the emergence of spiraling patterns whose properties are elucidated by a mapping onto a complex
Stochastic population dynamics of a montane ground-dwelling squirrel.
Directory of Open Access Journals (Sweden)
Jeffrey A Hostetler
Full Text Available Understanding the causes and consequences of population fluctuations is a central goal of ecology. We used demographic data from a long-term (1990-2008 study and matrix population models to investigate factors and processes influencing the dynamics and persistence of a golden-mantled ground squirrel (Callospermophilus lateralis population, inhabiting a dynamic subalpine habitat in Colorado, USA. The overall deterministic population growth rate λ was 0.94±SE 0.05 but it varied widely over time, ranging from 0.45±0.09 in 2006 to 1.50±0.12 in 2003, and was below replacement (λ<1 for 9 out of 18 years. The stochastic population growth rate λ(s was 0.92, suggesting a declining population; however, the 95% CI on λ(s included 1.0 (0.52-1.60. Stochastic elasticity analysis showed that survival of adult females, followed by survival of juvenile females and litter size, were potentially the most influential vital rates; analysis of life table response experiments revealed that the same three life history variables made the largest contributions to year-to year changes in λ. Population viability analysis revealed that, when the influences of density dependence and immigration were not considered, the population had a high (close to 1.0 in 50 years probability of extinction. However, probability of extinction declined to as low as zero when density dependence and immigration were considered. Destabilizing effects of stochastic forces were counteracted by regulating effects of density dependence and rescue effects of immigration, which allowed our study population to bounce back from low densities and prevented extinction. These results suggest that dynamics and persistence of our study population are determined synergistically by density-dependence, stochastic forces, and immigration.
A Simulation-Based Dynamic Stochastic Route Choice Model for Evacuation
Directory of Open Access Journals (Sweden)
Xing Zhao
2012-01-01
Full Text Available This paper establishes a dynamic stochastic route choice model for evacuation to simulate the propagation process of traffic flow and estimate the stochastic route choice under evacuation situations. The model contains a lane-group-based cell transmission model (CTM which sets different traffic capacities for links with different turning movements to flow out in an evacuation situation, an actual impedance model which is to obtain the impedance of each route in time units at each time interval and a stochastic route choice model according to the probit-based stochastic user equilibrium. In this model, vehicles loading at each origin at each time interval are assumed to choose an evacuation route under determinate road network, signal design, and OD demand. As a case study, the proposed model is validated on the network nearby Nanjing Olympic Center after the opening ceremony of the 10th National Games of the People's Republic of China. The traffic volumes and clearing time at five exit points of the evacuation zone are calculated by the model to compare with survey data. The results show that this model can appropriately simulate the dynamic route choice and evolution process of the traffic flow on the network in an evacuation situation.
Dynamic Stochastic Superresolution of sparsely observed turbulent systems
International Nuclear Information System (INIS)
Branicki, M.; Majda, A.J.
2013-01-01
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
Convergence of Sample Path Optimal Policies for Stochastic Dynamic Programming
National Research Council Canada - National Science Library
Fu, Michael C; Jin, Xing
2005-01-01
.... These results have practical implications for Monte Carlo simulation-based solution approaches to stochastic dynamic programming problems where it is impractical to extract the explicit transition...
Stochastic Online Learning in Dynamic Networks under Unknown Models
2016-08-02
The key is to develop online learning strategies at each individual node. Specifically, through local information exchange with its neighbors, each...infinitely repeated game with incomplete information and developed a dynamic pricing strategy referred to as Competitive and Cooperative Demand Learning...Stochastic Online Learning in Dynamic Networks under Unknown Models This research aims to develop fundamental theories and practical algorithms for
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
Nonlinear and stochastic dynamics of coherent structures
DEFF Research Database (Denmark)
Rasmussen, Kim
1997-01-01
This Thesis deals with nonlinear and stochastic dynamics in systems which can be described by nonlinear Schrödinger models. Basically three different models are investigated. The first is the continuum nonlinear Schröndinger model in one and two dimensions generalized by a tunable degree of nonli......This Thesis deals with nonlinear and stochastic dynamics in systems which can be described by nonlinear Schrödinger models. Basically three different models are investigated. The first is the continuum nonlinear Schröndinger model in one and two dimensions generalized by a tunable degree...... introduces the nonlinear Schrödinger model in one and two dimensions, discussing the soliton solutions in one dimension and the collapse phenomenon in two dimensions. Also various analytical methods are described. Then a derivation of the nonlinear Schrödinger equation is given, based on a Davydov like...... system described by a tight-binding Hamiltonian and a harmonic lattice coupled b y a deformation-type potential. This derivation results in a two-dimensional nonline ar Schrödinger model, and considering the harmonic lattice to be in thermal contact with a heat bath w e show that the nonlinear...
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...
Extension of Nelson's stochastic quantization to finite temperature using thermo field dynamics
International Nuclear Information System (INIS)
Kobayashi, K.; Yamanaka, Y.
2011-01-01
We present an extension of Nelson's stochastic quantum mechanics to finite temperature. Utilizing the formulation of Thermo Field Dynamics (TFD), we can show that Ito's stochastic equations for tilde and non-tilde particle positions reproduce the TFD-type Schroedinger equation which is equivalent to the Liouville-von Neumann equation. In our formalism, the drift terms in the Ito's stochastic equation have the temperature dependence and the thermal fluctuation is induced through the correlation of the non-tilde and tilde particles. We show that our formalism satisfies the position-momentum uncertainty relation at finite temperature. -- Highlights: → Utilizing TFD, we extend Nelson's stochastic method to finite temperature. → We introduce stochastic equations for tilde and non-tilde particles. → Our stochastic equations can reproduce the TFD-type Schroedinger equation. → Our formalism satisfies the uncertainly relation at finite temperature.
Vindenes, Yngvild; Sæther, Bernt-Erik; Engen, Steinar
2012-12-01
The development of stochastic demography has largely been based on age structured populations, although other types of demographic structure, especially permanent and dynamic heterogeneity, are likely common in natural populations. The combination of stochasticity and demographic structure is a challenge for analyses of population dynamics and extinction risk, because the population structure will fluctuate around the stable structure and the population size shows transient fluctuations. However, by using a diffusion approximation for the total reproductive value, density-independent dynamics of structured populations can be described with only three population parameters: the expected population growth rate, the environmental variance and the demographic variance. These parameters depend on population structure via the state-specific vital rates and transition rates. Once they are found, the diffusion approximation represents a substantial reduction in model complexity. Here, we review and compare the key population parameters across a wide range of demographic structure, from the case of no structure to the most general case of dynamic heterogeneity, and for both discrete and continuous types. We focus on the demographic variance, but also show how environmental stochasticity can be included. This study brings together results from recent models, each considering a specific type of population structure, and places them in a general framework for structured populations. Comparison across different types of demographic structure reveals that the reproductive value is an essential concept for understanding how population structure affects stochastic dynamics and extinction risk. Copyright © 2011 Elsevier Inc. All rights reserved.
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.
Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes
International Nuclear Information System (INIS)
Kumar, Ashutosh; Chatterjee, Sambarta; Nandi, Mintu; Dua, Arti
2016-01-01
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.
Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes
Energy Technology Data Exchange (ETDEWEB)
Kumar, Ashutosh; Chatterjee, Sambarta; Nandi, Mintu; Dua, Arti, E-mail: arti@iitm.ac.in [Department of Chemistry, Indian Institute of Technology, Madras, Chennai 600036 (India)
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.
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.
An Inductive Water Thermostat Using On‐Off Triac Control and Platinum Sensing
DEFF Research Database (Denmark)
Diamond, Joseph M.
1971-01-01
An on‐off thermostat is described using novel means for heating, sensing, and triac control. Heating is performed by sending the water through a coil of silver tubing which forms the short‐circuited secondary winding of a transformer. This arrangement permits extremely good insulation, which...... was essential in the medical application (a dialysis water thermostat) for which it was designed; its quick response also contributes to the excellent regulation achieved with simple on‐off control. Sensing is provided by a very low resistance platinum coil in direct contact with the water, thus providing quick...
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 quasi-gradient based optimization algorithms for dynamic reliability applications
International Nuclear Information System (INIS)
Bourgeois, F.; Labeau, P.E.
2001-01-01
On one hand, PSA results are increasingly used in decision making, system management and optimization of system design. On the other hand, when severe accidental transients are considered, dynamic reliability appears appropriate to account for the complex interaction between the transitions between hardware configurations, the operator behavior and the dynamic evolution of the system. This paper presents an exploratory work in which the estimation of the system unreliability in a dynamic context is coupled with an optimization algorithm to determine the 'best' safety policy. Because some reliability parameters are likely to be distributed, the cost function to be minimized turns out to be a random variable. Stochastic programming techniques are therefore envisioned to determine an optimal strategy. Monte Carlo simulation is used at all stages of the computations, from the estimation of the system unreliability to that of the stochastic quasi-gradient. The optimization algorithm is illustrated on a HNO 3 supply system
Lectures on Dynamics of Stochastic Systems
Klyatskin, Valery I
2010-01-01
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. Models naturally render to statistical description, where random processes and fields express the input parameters and solutions. 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 the system and initial data. This book is a revised a
A Microwave Thermostatic Reactor for Processing Liquid Materials Based on a Heat-Exchanger.
Zhou, Yongqiang; Zhang, Chun; Xie, Tian; Hong, Tao; Zhu, Huacheng; Yang, Yang; Liu, Changjun; Huang, Kama
2017-10-08
Microwaves have been widely used in the treatment of different materials. However, the existing adjustable power thermostatic reactors cannot be used to analyze materials characteristics under microwave effects. In this paper, a microwave thermostatic chemical reactor for processing liquid materials is proposed, by controlling the velocity of coolant based on PLC (programmable logic controller) in different liquid under different constant electric field intensity. A nonpolar coolant (Polydimethylsiloxane), which is completely microwave transparent, is employed to cool the liquid materials. Experiments are performed to measure the liquid temperature using optical fibers, the results show that the precision of temperature control is at the range of ±0.5 °C. Compared with the adjustable power thermostatic control system, the effect of electric field changes on material properties are avoided and it also can be used to detect the properties of liquid materials and special microwave effects.
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...
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 ...
Regular and stochastic particle motion in plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1979-08-01
A Hamiltonian formalism is presented for the study of charged-particle trajectories in the self-consistent field of the particles. The intention is to develop a general approach to plasma dynamics. Transformations of phase-space variables are used to separate out the regular, adiabatic motion from the irregular, stochastic trajectories. Several new techniques are included in this presentation
Stochastic feeding dynamics arise from the need for information and energy.
Scholz, Monika; Dinner, Aaron R; Levine, Erel; Biron, David
2017-08-29
Animals regulate their food intake in response to the available level of food. Recent observations of feeding dynamics in small animals showed feeding patterns of bursts and pauses, but their function is unknown. Here, we present a data-driven decision-theoretical model of feeding in Caenorhabditis elegans Our central assumption is that food intake serves a dual purpose: to gather information about the external food level and to ingest food when the conditions are good. The model recapitulates experimentally observed feeding patterns. It naturally implements trade-offs between speed versus accuracy and exploration versus exploitation in responding to a dynamic environment. We find that the model predicts three distinct regimes in responding to a dynamical environment, with a transition region where animals respond stochastically to periodic signals. This stochastic response accounts for previously unexplained experimental data.
Stochastic Wilson–Cowan models of neuronal network dynamics with memory and delay
International Nuclear Information System (INIS)
Goychuk, Igor; Goychuk, Andriy
2015-01-01
We consider a simple Markovian class of the stochastic Wilson–Cowan type models of neuronal network dynamics, which incorporates stochastic delay caused by the existence of a refractory period of neurons. From the point of view of the dynamics of the individual elements, we are dealing with a network of non-Markovian stochastic two-state oscillators with memory, which are coupled globally in a mean-field fashion. This interrelation of a higher-dimensional Markovian and lower-dimensional non-Markovian dynamics is discussed in its relevance to the general problem of the network dynamics of complex elements possessing memory. The simplest model of this class is provided by a three-state Markovian neuron with one refractory state, which causes firing delay with an exponentially decaying memory within the two-state reduced model. This basic model is used to study critical avalanche dynamics (the noise sustained criticality) in a balanced feedforward network consisting of the excitatory and inhibitory neurons. Such avalanches emerge due to the network size dependent noise (mesoscopic noise). Numerical simulations reveal an intermediate power law in the distribution of avalanche sizes with the critical exponent around −1.16. We show that this power law is robust upon a variation of the refractory time over several orders of magnitude. However, the avalanche time distribution is biexponential. It does not reflect any genuine power law dependence. (paper)
Time step MOTA thermostat simulation
International Nuclear Information System (INIS)
Guthrie, G.L.
1978-09-01
The report details the logic, program layout, and operating procedures for the time-step MOTA (Materials Open Test Assembly) thermostat simulation program known as GYRD. It will enable prospective users to understand the operation of the program, run it, and interpret the results. The time-step simulation analysis was the approach chosen to determine the maximum value gain that could be used to minimize steady temperature offset without risking undamped thermal oscillations. The advantage of the GYRD program is that it directly shows hunting, ringing phenomenon, and similar events. Programs BITT and CYLB are faster, but do not directly show ringing time
Numerical simulation of stochastic point kinetic equation in the dynamical system of nuclear reactor
International Nuclear Information System (INIS)
Saha Ray, S.
2012-01-01
Highlights: ► In this paper stochastic neutron point kinetic equations have been analyzed. ► Euler–Maruyama method and Strong Taylor 1.5 order method have been discussed. ► These methods are applied for the solution of stochastic point kinetic equations. ► Comparison between the results of these methods and others are presented in tables. ► Graphs for neutron and precursor sample paths are also presented. -- Abstract: In the present paper, the numerical approximation methods, applied to efficiently calculate the solution for stochastic point kinetic equations () in nuclear reactor dynamics, are investigated. A system of Itô stochastic differential equations has been analyzed to model the neutron density and the delayed neutron precursors in a point nuclear reactor. The resulting system of Itô stochastic differential equations are solved over each time-step size. The methods are verified by considering different initial conditions, experimental data and over constant reactivities. The computational results indicate that the methods are simple and suitable for solving stochastic point kinetic equations. In this article, a numerical investigation is made in order to observe the random oscillations in neutron and precursor population dynamics in subcritical and critical reactors.
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
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.
Analytical vs. Simulation Solution Techniques for Pulse Problems in Non-linear Stochastic Dynamics
DEFF Research Database (Denmark)
Iwankiewicz, R.; Nielsen, Søren R. K.
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-numerical tec......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...
Sharp asymptotics for stochastic dynamics with parallel updating rule
Nardi, F.R.; Spitoni, C.
2012-01-01
In this paper we study the metastability problem for a stochastic dynamics with a parallel updating rule; in particular we consider a finite volume Probabilistic Cellular Automaton (PCA) in a small external field at low temperature regime. We are interested in the nucleation of the system, i.e., the
Sharp Asymptotics for Stochastic Dynamics with Parallel Updating Rule
Nardi, F.R.; Spitoni, C.
2012-01-01
In this paper we study the metastability problem for a stochastic dynamics with a parallel updating rule; in particular we consider a finite volume Probabilistic Cellular Automaton (PCA) in a small external field at low temperature regime. We are interested in the nucleation of the system, i.e.,
International Nuclear Information System (INIS)
Ertaş, Mehmet; Kantar, Ersin; Keskin, Mustafa
2014-01-01
The dynamic phase transitions (DPTs) and dynamic phase diagrams of the kinetic spin-1/2 bilayer system in the presence of a time-dependent oscillating external magnetic field are studied by using Glauber-type stochastic dynamics based on the effective-field theory with correlations for the ferromagnetic/ferromagnetic (FM/FM), antiferromagnetic/ferromagnetic (AFM/FM) and antiferromagnetic/antiferromagnetic (AFM/AFM) interactions. The time variations of average magnetizations and the temperature dependence of the dynamic magnetizations are investigated. The dynamic phase diagrams for the amplitude of the oscillating field versus temperature were presented. The results are compared with the results of the same system within Glauber-type stochastic dynamics based on the mean-field theory. - Highlights: • The Ising bilayer system is investigated within the Glauber dynamics based on EFT. • The time variations of average order parameters to find phases are studied. • The dynamic phase diagrams are found for the different interaction parameters. • The system displays the critical points as well as a re-entrant behavior
Energy Technology Data Exchange (ETDEWEB)
Ertaş, Mehmet; Kantar, Ersin, E-mail: ersinkantar@erciyes.edu.tr; Keskin, Mustafa
2014-05-01
The dynamic phase transitions (DPTs) and dynamic phase diagrams of the kinetic spin-1/2 bilayer system in the presence of a time-dependent oscillating external magnetic field are studied by using Glauber-type stochastic dynamics based on the effective-field theory with correlations for the ferromagnetic/ferromagnetic (FM/FM), antiferromagnetic/ferromagnetic (AFM/FM) and antiferromagnetic/antiferromagnetic (AFM/AFM) interactions. The time variations of average magnetizations and the temperature dependence of the dynamic magnetizations are investigated. The dynamic phase diagrams for the amplitude of the oscillating field versus temperature were presented. The results are compared with the results of the same system within Glauber-type stochastic dynamics based on the mean-field theory. - Highlights: • The Ising bilayer system is investigated within the Glauber dynamics based on EFT. • The time variations of average order parameters to find phases are studied. • The dynamic phase diagrams are found for the different interaction parameters. • The system displays the critical points as well as a re-entrant behavior.
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.
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.
Sharp asymptotics for stochastic dynamics with parallel updating rule
Nardi, F.R.; Spitoni, C.
2012-01-01
In this paper we study the metastability problem for a stochastic dynamics with a parallel updating rule; in particular we consider a ¿nite volume Probabilistic Cellular Automaton (PCA) in a small external ¿eld at low temperature regime. We are interested in the nucleation of the system, i.e., the
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.
Darmon, David
2018-03-01
In the absence of mechanistic or phenomenological models of real-world systems, data-driven models become necessary. The discovery of various embedding theorems in the 1980s and 1990s motivated a powerful set of tools for analyzing deterministic dynamical systems via delay-coordinate embeddings of observations of their component states. However, in many branches of science, the condition of operational determinism is not satisfied, and stochastic models must be brought to bear. For such stochastic models, the tool set developed for delay-coordinate embedding is no longer appropriate, and a new toolkit must be developed. We present an information-theoretic criterion, the negative log-predictive likelihood, for selecting the embedding dimension for a predictively optimal data-driven model of a stochastic dynamical system. We develop a nonparametric estimator for the negative log-predictive likelihood and compare its performance to a recently proposed criterion based on active information storage. Finally, we show how the output of the model selection procedure can be used to compare candidate predictors for a stochastic system to an information-theoretic lower bound.
End users heat energy savings using thermostat regulation valves radiators, v. 16(64)
International Nuclear Information System (INIS)
Jakimovska, Emilija Misheva; Potsev, Eftim
2008-01-01
Billing the used heat energy offers the opportunity to motivate end users to use the heat energy rationally and to save the energy. Installing the thermostat valves on the radiators it is possible frequently to regulate the room temperature and to use the heat gains, obtaining comfortable climate in the apartments and saving the energy. Thermostat valves give the possibility to use the heat energy rationally and save the energy, and these way and users can regulate the heat energy consumption according to their own level of thermal comfort. (Author)
End users heat energy savings using thermostat regulation valves radiators, v. 16(63)
International Nuclear Information System (INIS)
Jakimovska, Emilija Misheva; Potsev, Eftim
2008-01-01
Billing the used heat energy offers the opportunity to motivate end users to use the heat energy rationally and to save the energy. Installing the thermostat valves on the radiators it is possible frequently to regulate the room temperature and to use the heat gains, obtaining comfortable climate in the apartments and saving the energy. Thermostat valves give the possibility to use the heat energy rationally and save the energy, and these way and users can regulate the heat energy consumption according to their own level of thermal comfort. (Author)
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 evolution of the Universe: A possible dynamical process ...
Indian Academy of Sciences (India)
C Sivakumar
2017-12-11
Dec 11, 2017 ... https://doi.org/10.1007/s12043-017-1491-z. Stochastic evolution of the Universe: A possible dynamical process leading to fractal structures. C SIVAKUMAR. Department of Physics, Maharaja's College, Ernakulam 682 011, India. E-mail: thrisivc@yahoo.com. MS received 6 July 2016; revised 26 June 2017; ...
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.
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
Stochastic Dynamics through Hierarchically Embedded Markov Chains.
Vasconcelos, Vítor V; Santos, Fernando P; Santos, Francisco C; Pacheco, Jorge M
2017-02-03
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.
International Nuclear Information System (INIS)
Wu, Wei; Wang, Jin
2014-01-01
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 an aggregation in birth-and-death stochastic dynamics
Finkelshtein, Dmitri; Kondratiev, Yuri; Kutoviy, Oleksandr; Zhizhina, Elena
2014-06-01
We consider birth-and-death stochastic dynamics of particle systems with attractive interaction. The heuristic generator of the dynamics has a constant birth rate and density-dependent decreasing death rate. The corresponding statistical dynamics is constructed. Using the Vlasov-type scaling we derive the limiting mesoscopic evolution and prove that this evolution propagates chaos. We study a nonlinear non-local kinetic equation for the first correlation function (density of population). The existence of uniformly bounded solutions as well as solutions growing inside of a bounded domain and expanding in the space are shown. These solutions describe two regimes in the mesoscopic system: regulation and aggregation.
On an aggregation in birth-and-death stochastic dynamics
International Nuclear Information System (INIS)
Finkelshtein, Dmitri; Kondratiev, Yuri; Kutoviy, Oleksandr; Zhizhina, Elena
2014-01-01
We consider birth-and-death stochastic dynamics of particle systems with attractive interaction. The heuristic generator of the dynamics has a constant birth rate and density-dependent decreasing death rate. The corresponding statistical dynamics is constructed. Using the Vlasov-type scaling we derive the limiting mesoscopic evolution and prove that this evolution propagates chaos. We study a nonlinear non-local kinetic equation for the first correlation function (density of population). The existence of uniformly bounded solutions as well as solutions growing inside of a bounded domain and expanding in the space are shown. These solutions describe two regimes in the mesoscopic system: regulation and aggregation. (paper)
Stochastic Simulation of Cardiac Ventricular Myocyte Calcium Dynamics and Waves
Tuan, Hoang-Trong Minh; Williams, George S. B.; Chikando, Aristide C.; Sobie, Eric A.; Lederer, W. Jonathan; Jafri, M. Saleet
2011-01-01
A three dimensional model of calcium dynamics in the rat ventricular myocyte was developed to study the mechanism of calcium homeostasis and pathological calcium dynamics during calcium overload. The model contains 20,000 calcium release units (CRUs) each containing 49 ryanodine receptors. The model simulates calcium sparks with a realistic spontaneous calcium spark rate. It suggests that in addition to the calcium spark-based leak, there is an invisible calcium leak caused by the stochastic ...
Stochastic dynamic stiffness of surface footing for offshore wind turbines
DEFF Research Database (Denmark)
Vahdatirad, Mohammadjavad; Andersen, Lars Vabbersgaard; Ibsen, Lars Bo
2014-01-01
Highlights •This study concerns the stochastic dynamic stiffness of foundations for large offshore wind turbines. •A simple model of wind turbine structure with equivalent coupled springs at the base is utilized. •The level of uncertainties is quantified through a sensitivity analysis. •Estimation...
The global dynamics for a stochastic SIS epidemic model with isolation
Chen, Yiliang; Wen, Buyu; Teng, Zhidong
2018-02-01
In this paper, we investigate the dynamical behavior for a stochastic SIS epidemic model with isolation which is as an important strategy for the elimination of infectious diseases. It is assumed that the stochastic effects manifest themselves mainly as fluctuation in the transmission coefficient, the death rate and the proportional coefficient of the isolation of infective. It is shown that the extinction and persistence in the mean of the model are determined by a threshold value R0S . That is, if R0S 1, then the disease is stochastic persistent in the means with probability one. Furthermore, the existence of a unique stationary distribution is discussed, and the sufficient conditions are established by using the Lyapunov function method. Finally, some numerical examples are carried out to confirm the analytical results.
Optimal Stochastic Control Problem for General Linear Dynamical Systems in Neuroscience
Directory of Open Access Journals (Sweden)
Yan Chen
2017-01-01
Full Text Available This paper considers a d-dimensional stochastic optimization problem in neuroscience. Suppose the arm’s movement trajectory is modeled by high-order linear stochastic differential dynamic system in d-dimensional space, the optimal trajectory, velocity, and variance are explicitly obtained by using stochastic control method, which allows us to analytically establish exact relationships between various quantities. Moreover, the optimal trajectory is almost a straight line for a reaching movement; the optimal velocity bell-shaped and the optimal variance are consistent with the experimental Fitts law; that is, the longer the time of a reaching movement, the higher the accuracy of arriving at the target position, and the results can be directly applied to designing a reaching movement performed by a robotic arm in a more general environment.
Patterns of Stochastic Behavior in Dynamically Unstable High-Dimensional Biochemical Networks
Directory of Open Access Journals (Sweden)
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.
A Dynamic Momentum Compaction Factor Lattice for Improvements to Stochastic Cooling in Storage Rings
Energy Technology Data Exchange (ETDEWEB)
Olivieri, David Nicholas [Massachusetts U., Amherst
1996-01-01
A dynamic momentum compaction factor, also referred to as a dynamic $\\Delta \\gamma \\tau$, lattice for the FNAL Antiproton Source Debuncher Storage Ring is studied, both theoretically and experimentally, for the purpose of improving stochastic precooling, and hence, improving the global antiproton production and stacking performance. A dynamic $\\Delta \\gamma \\tau$ lattice is proposed due to the competing requirements inherent within the Debuncher storage ring upon $\\gamma \\tau$· Specifically, the Debuncher storage ring performs two disparate functions, $(i)$ accepting and debunching a large number of $\\overline{p}$s/pulse at the outset of the production cycle, which would perform ideally with a large value of $\\gamma\\tau$, and $(ii)$ subsequently employing stochastic cooling throughout the remainder of the $\\overline{p}$ production cycle for improved transfer and stacking efficiency into the Accumulator, for which a small value $\\gamma \\tau$ is ideal in order to reduce the diffusive heating caused by the mixing factor. In the initial design of the Debuncher optical lattice, an intermediate value of $\\gamma \\tau$ was chosen as a compromise between the two functional requirements. The goal of the thesis is to improve stochastic precooling by changing $\\gamma \\tau$ between two desired values during each p production cycle. In particular, the dynamic $\\Delta \\gamma \\tau$ lattice accomplishes a reduction in $\\gamma \\tau$, and hence the mixing factor, through an uniform increase to the dispersion throughout the arc sections of the storage ring. Experimental measurements of cooling rates and system performance parameters, with the implementation of the dynamic $\\Delta \\gamma \\tau$ lattice, are in agreement with theoretical predictions based upon a detailed integration of the stochastic cooling Fokker Planck equations. Based upon the consistency between theory and experiment, predictions of cooling rates are presented for future operational
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
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).
Threshold Dynamics in Stochastic SIRS Epidemic Models with Nonlinear Incidence and Vaccination
Directory of Open Access Journals (Sweden)
Lei Wang
2017-01-01
Full Text Available 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.
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...
International Nuclear Information System (INIS)
Jiang, Shixiao W; Lu, Haihao; Zhou, Douglas; Cai, David
2016-01-01
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. (paper)
Wang, Ting; Plecháč, Petr
2017-12-01
Stochastic reaction networks that exhibit bistable behavior are common in systems biology, materials science, and catalysis. Sampling of stationary distributions is crucial for understanding and characterizing the long-time dynamics of bistable stochastic dynamical systems. However, simulations are often hindered by the insufficient sampling of rare transitions between the two metastable regions. In this paper, we apply the parallel replica method for a continuous time Markov chain in order to improve sampling of the stationary distribution in bistable stochastic reaction networks. The proposed method uses parallel computing to accelerate the sampling of rare transitions. Furthermore, it can be combined with the path-space information bounds for parametric sensitivity analysis. With the proposed methodology, we study three bistable biological networks: the Schlögl model, the genetic switch network, and the enzymatic futile cycle network. We demonstrate the algorithmic speedup achieved in these numerical benchmarks. More significant acceleration is expected when multi-core or graphics processing unit computer architectures and programming tools such as CUDA are employed.
Wang, Ting; Plecháč, Petr
2017-12-21
Stochastic reaction networks that exhibit bistable behavior are common in systems biology, materials science, and catalysis. Sampling of stationary distributions is crucial for understanding and characterizing the long-time dynamics of bistable stochastic dynamical systems. However, simulations are often hindered by the insufficient sampling of rare transitions between the two metastable regions. In this paper, we apply the parallel replica method for a continuous time Markov chain in order to improve sampling of the stationary distribution in bistable stochastic reaction networks. The proposed method uses parallel computing to accelerate the sampling of rare transitions. Furthermore, it can be combined with the path-space information bounds for parametric sensitivity analysis. With the proposed methodology, we study three bistable biological networks: the Schlögl model, the genetic switch network, and the enzymatic futile cycle network. We demonstrate the algorithmic speedup achieved in these numerical benchmarks. More significant acceleration is expected when multi-core or graphics processing unit computer architectures and programming tools such as CUDA are employed.
Bashkirtseva, Irina; Ryashko, Lev; Ryazanova, Tatyana
2018-01-01
A problem of mathematical modeling of complex stochastic processes in macroeconomics is discussed. For the description of dynamics of income and capital stock, the well-known Kaldor model of business cycles is used as a basic example. The aim of the paper is to give an overview of the variety of stochastic phenomena which occur in Kaldor model forced by additive and parametric random noise. We study a generation of small- and large-amplitude stochastic oscillations, and their mixed-mode intermittency. To analyze these phenomena, we suggest a constructive approach combining the study of the peculiarities of deterministic phase portrait, and stochastic sensitivity of attractors. We show how parametric noise can stabilize the unstable equilibrium and transform dynamics of Kaldor system from order to chaos.
Dynamics of the stochastic low concentration trimolecular oscillatory chemical system with jumps
Wei, Yongchang; Yang, Qigui
2018-06-01
This paper is devoted to discern long time dynamics through the stochastic low concentration trimolecular oscillatory chemical system with jumps. By Lyapunov technique, this system is proved to have a unique global positive solution, and the asymptotic stability in mean square of such model is further established. Moreover, the existence of random attractor and Lyapunov exponents are obtained for the stochastic homeomorphism flow generated by the corresponding global positive solution. And some numerical simulations are given to illustrate the presented results.
Liu, Xiangdong; Li, Qingze; Pan, Jianxin
2018-06-01
Modern medical studies show that chemotherapy can help most cancer patients, especially for those diagnosed early, to stabilize their disease conditions from months to years, which means the population of tumor cells remained nearly unchanged in quite a long time after fighting against immune system and drugs. In order to better understand the dynamics of tumor-immune responses under chemotherapy, deterministic and stochastic differential equation models are constructed to characterize the dynamical change of tumor cells and immune cells in this paper. The basic dynamical properties, such as boundedness, existence and stability of equilibrium points, are investigated in the deterministic model. Extended stochastic models include stochastic differential equations (SDEs) model and continuous-time Markov chain (CTMC) model, which accounts for the variability in cellular reproduction, growth and death, interspecific competitions, and immune response to chemotherapy. The CTMC model is harnessed to estimate the extinction probability of tumor cells. Numerical simulations are performed, which confirms the obtained theoretical results.
International Nuclear Information System (INIS)
Zhu, Zhi-Wen; Zhang, Qing-Xin; Xu, Jia
2014-01-01
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
Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics.
Chen, Minghan; Li, Fei; Wang, Shuo; Cao, Young
2017-03-14
Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity. In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method. Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.
International Nuclear Information System (INIS)
Sutrisno; Widowati; Solikhin
2016-01-01
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. (paper)
On the stochastic dynamics of disordered spin models
International Nuclear Information System (INIS)
Semerjian, G.; Montanari, A.; Cugliandolo, L.F.
2003-09-01
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in equilibrium with a thermal bath. We propose a fluctuation principle that allows us to derive fluctuation-dissipation relations for many-time correlations and linear responses. We also speculate on how these features will be modified in systems evolving slowly out of equilibrium, as finite-dimensional or dilute spin-glasses. Secondly, we present a formalism that allows one to derive a series of approximated equations that determine the dynamics of disordered spin models on random (hyper) graphs. (author)
International Nuclear Information System (INIS)
Volchenkov, D.
2009-01-01
Stochastic counterparts of nonlinear dynamics are studied by means of nonperturbative functional methods developed in the framework of quantum field theory (QFT). In particular, we discuss fully developed turbulence, including leading corrections on possible compressibility of fluids, transport through porous media, theory of waterspouts and tsunami waves, stochastic magnetohydrodynamics, turbulent transport in crossed fields, self-organized criticality, and dynamics of accelerated wrinkled flame fronts advancing in a wide canal. This report would be of interest to the broad auditorium of physicists and applied mathematicians, with a background in nonperturbative QFT methods or nonlinear dynamical systems, having an interest in both methodological developments and interdisciplinary applications. (author)
Energy Technology Data Exchange (ETDEWEB)
Volchenkov, D. [Bielefeld Univ., Center of Excellence Cognitive Interaction Technology (CITEC) (Germany)
2009-03-15
Stochastic counterparts of nonlinear dynamics are studied by means of nonperturbative functional methods developed in the framework of quantum field theory (QFT). In particular, we discuss fully developed turbulence, including leading corrections on possible compressibility of fluids, transport through porous media, theory of waterspouts and tsunami waves, stochastic magnetohydrodynamics, turbulent transport in crossed fields, self-organized criticality, and dynamics of accelerated wrinkled flame fronts advancing in a wide canal. This report would be of interest to the broad auditorium of physicists and applied mathematicians, with a background in nonperturbative QFT methods or nonlinear dynamical systems, having an interest in both methodological developments and interdisciplinary applications. (author)
Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics
Bressloff, Paul C.
2010-01-01
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
DEFF Research Database (Denmark)
Moura, Scott; Ruiz, Victor; Bendtsen, Jan Dimon
2013-01-01
This paper focuses on developing a partial differential equation (PDE)-based model and parameter identification scheme for heterogeneous populations of thermostatically controlled loads (TCLs). First, a coupled two-state hyperbolic PDE model for homogenous TCL populations is derived. This model i...
Comparison of stochastic resonance in static and dynamical nonlinearities
International Nuclear Information System (INIS)
Ma, Yumei; Duan, Fabing
2014-01-01
We compare the stochastic resonance (SR) effects in parallel arrays of static and dynamical nonlinearities via the measure of output signal-to-noise ratio (SNR). For a received noisy periodic signal, parallel arrays of both static and dynamical nonlinearities can enhance the output SNR by optimizing the internal noise level. The static nonlinearity is easily implementable, while the dynamical nonlinearity has more parameters to be tuned, at the risk of not exploiting the beneficial role of internal noise components. It is of interest to note that, for an input signal buried in the external Laplacian noise, we show that the dynamical nonlinearity is superior to the static nonlinearity in obtaining a better output SNR. This characteristic is assumed to be closely associated with the kurtosis of noise distribution. - Highlights: • Comparison of SR effects in arrays of both static and dynamical nonlinearities. • Static nonlinearity is easily implementable for the SNR enhancement. • Dynamical nonlinearity yields a better output SNR for external Laplacian noise
Kemper, A; Nishino, T; Schadschneider, A; Zittartz, J
2003-01-01
We develop a new variant of the recently introduced stochastic transfer matrix DMRG which we call stochastic light-cone corner-transfer-matrix DMRG (LCTMRG). It is a numerical method to compute dynamic properties of one-dimensional stochastic processes. As suggested by its name, the LCTMRG is a modification of the corner-transfer-matrix DMRG, adjusted by an additional causality argument. As an example, two reaction-diffusion models, the diffusion-annihilation process and the branch-fusion process are studied and compared with exact data and Monte Carlo simulations to estimate the capability and accuracy of the new method. The number of possible Trotter steps of more than 10 sup 5 shows a considerable improvement on the old stochastic TMRG algorithm.
A Volterra series approach to the approximation of stochastic nonlinear dynamics
Wouw, van de N.; Nijmeijer, H.; Campen, van D.H.
2002-01-01
A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. Herein, the output of the nonlinear system isapproximated by a finite-order Volterra series. The original nonlinear system is replaced by a bilinear system in order to determine the kernels of this
Nonlinear and Stochastic Dynamics in the Heart
Qu, Zhilin; Hu, Gang; Garfinkel, Alan; Weiss, James N.
2014-01-01
In a normal human life span, the heart beats about 2 to 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. PMID:25267872
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.
Nonlinear and stochastic dynamics in the heart
International Nuclear Information System (INIS)
Qu, Zhilin; Hu, Gang; Garfinkel, Alan; Weiss, James N.
2014-01-01
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 population dynamics of a montane ground-dwelling squirrel.
Hostetler, Jeffrey A; Kneip, Eva; Van Vuren, Dirk H; Oli, Madan K
2012-01-01
Understanding the causes and consequences of population fluctuations is a central goal of ecology. We used demographic data from a long-term (1990-2008) study and matrix population models to investigate factors and processes influencing the dynamics and persistence of a golden-mantled ground squirrel (Callospermophilus lateralis) population, inhabiting a dynamic subalpine habitat in Colorado, USA. The overall deterministic population growth rate λ was 0.94±SE 0.05 but it varied widely over time, ranging from 0.45±0.09 in 2006 to 1.50±0.12 in 2003, and was below replacement (λbounce back from low densities and prevented extinction. These results suggest that dynamics and persistence of our study population are determined synergistically by density-dependence, stochastic forces, and immigration.
Effects of stochastic time-delayed feedback on a dynamical system modeling a chemical oscillator
González Ochoa, Héctor O.; Perales, Gualberto Solís; Epstein, Irving R.; Femat, Ricardo
2018-05-01
We examine how stochastic time-delayed negative feedback affects the dynamical behavior of a model oscillatory reaction. We apply constant and stochastic time-delayed negative feedbacks to a point Field-Körös-Noyes photosensitive oscillator and compare their effects. Negative feedback is applied in the form of simulated inhibitory electromagnetic radiation with an intensity proportional to the concentration of oxidized light-sensitive catalyst in the oscillator. We first characterize the system under nondelayed inhibitory feedback; then we explore and compare the effects of constant (deterministic) versus stochastic time-delayed feedback. We find that the oscillatory amplitude, frequency, and waveform are essentially preserved when low-dispersion stochastic delayed feedback is used, whereas small but measurable changes appear when a large dispersion is applied.
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
Dynamic-stochastic modeling of snow cover formation on the European territory of Russia
A. N. Gelfan; V. M. Moreido
2014-01-01
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 ...
Nuclear quantum effects in ab initio dynamics: Theory and experiments for lithium imide
Ceriotti, Michele; Miceli, Giacomo; Pietropaolo, Antonino; Colognesi, Daniele; Nale, Angeloclaudio; Catti, Michele; Bernasconi, Marco; Parrinello, Michele
2010-11-01
Owing to their small mass, hydrogen atoms exhibit strong quantum behavior even at room temperature. Including these effects in first-principles calculations is challenging because of the huge computational effort required by conventional techniques. Here we present the first ab initio application of a recently developed stochastic scheme, which allows to approximate nuclear quantum effects inexpensively. The proton momentum distribution of lithium imide, a material of interest for hydrogen storage, was experimentally measured by inelastic neutron-scattering experiments and compared with the outcome of quantum thermostatted ab initio dynamics. We obtain favorable agreement between theory and experiments for this purely quantum-mechanical property, thereby demonstrating that it is possible to improve the modeling of complex hydrogen-containing materials without additional computational effort.
Lippert, Ross A.; Predescu, Cristian; Ierardi, Douglas J.; Mackenzie, Kenneth M.; Eastwood, Michael P.; Dror, Ron O.; Shaw, David E.
2013-10-01
In molecular dynamics simulations, control over temperature and pressure is typically achieved by augmenting the original system with additional dynamical variables to create a thermostat and a barostat, respectively. These variables generally evolve on timescales much longer than those of particle motion, but typical integrator implementations update the additional variables along with the particle positions and momenta at each time step. We present a framework that replaces the traditional integration procedure with separate barostat, thermostat, and Newtonian particle motion updates, allowing thermostat and barostat updates to be applied infrequently. Such infrequent updates provide a particularly substantial performance advantage for simulations parallelized across many computer processors, because thermostat and barostat updates typically require communication among all processors. Infrequent updates can also improve accuracy by alleviating certain sources of error associated with limited-precision arithmetic. In addition, separating the barostat, thermostat, and particle motion update steps reduces certain truncation errors, bringing the time-average pressure closer to its target value. Finally, this framework, which we have implemented on both general-purpose and special-purpose hardware, reduces software complexity and improves software modularity.
Modeling and stochastic analysis of dynamic mechanisms of the perception
Pisarchik, A.; Bashkirtseva, I.; Ryashko, L.
2017-10-01
Modern studies in physiology and cognitive neuroscience consider a noise as an important constructive factor of the brain functionality. Under the adequate noise, the brain can rapidly access different ordered states, and provide decision-making by preventing deadlocks. Bistable dynamic models are often used for the study of the underlying mechanisms of the visual perception. In the present paper, we consider a bistable energy model subject to both additive and parametric noise. Using the catastrophe theory formalism and stochastic sensitivity functions technique, we analyze a response of the equilibria to noise, and study noise-induced transitions between equilibria. We demonstrate and analyse the effect of hysteresis squeezing when the intensity of noise is increased. Stochastic bifurcations connected with the suppression of oscillations by parametric noises are discussed.
International Nuclear Information System (INIS)
Luhur, M.R.
2014-01-01
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. (author)
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
Extended Plefka expansion for stochastic dynamics
International Nuclear Information System (INIS)
Bravi, B; Sollich, P; Opper, M
2016-01-01
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. (paper)
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.
Dynamic electricity pricing for electric vehicles using stochastic programming
International Nuclear Information System (INIS)
Soares, João; Ghazvini, Mohammad Ali Fotouhi; Borges, Nuno; Vale, Zita
2017-01-01
Electric Vehicles (EVs) are an important source of uncertainty, due to their variable demand, departure time and location. In smart grids, the electricity demand can be controlled via Demand Response (DR) programs. Smart charging and vehicle-to-grid seem highly promising methods for EVs control. However, high capital costs remain a barrier to implementation. Meanwhile, incentive and price-based schemes that do not require high level of control can be implemented to influence the EVs' demand. Having effective tools to deal with the increasing level of uncertainty is increasingly important for players, such as energy aggregators. This paper formulates a stochastic model for day-ahead energy resource scheduling, integrated with the dynamic electricity pricing for EVs, to address the challenges brought by the demand and renewable sources uncertainty. The two-stage stochastic programming approach is used to obtain the optimal electricity pricing for EVs. A realistic case study projected for 2030 is presented based on Zaragoza network. The results demonstrate that it is more effective than the deterministic model and that the optimal pricing is preferable. This study indicates that adequate DR schemes like the proposed one are promising to increase the customers' satisfaction in addition to improve the profitability of the energy aggregation business. - Highlights: • A stochastic model for energy scheduling tackling several uncertainty sources. • A two-stage stochastic programming is used to tackle the developed model. • Optimal EV electricity pricing seems to improve the profits. • The propose results suggest to increase the customers' satisfaction.
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...
Thermostatic system of sensor in NIR spectrometer based on PID control
Wang, Zhihong; Qiao, Liwei; Ji, Xufei
2016-11-01
Aiming at the shortcomings of the primary sensor thermostatic control system in the near infrared (NIR) spectrometer, a novel thermostatic control system based on proportional-integral-derivative (PID) control technology was developed to improve the detection precision of the NIR spectrometer. There were five parts including bridge amplifier circuit, analog-digital conversion (ADC) circuit, microcontroller, digital-analog conversion (DAC) circuit and drive circuit in the system. The five parts formed a closed-loop control system based on PID algorithm that was used to control the error between the temperature calculated by the sampling data of ADC and the designed temperature to ensure the stability of the spectrometer's sensor. The experimental results show that, when the operating temperature of sensor is -11°, compared with the original system, the temperature control precision of the new control system is improved from ±0.64° to ±0.04° and the spectrum signal to noise ratio (SNR) is improved from 4891 to 5967.
Wijaya Sunu, Putu; Made Rasta, I.; Anakottapary, Daud Simon; Made Suarta, I.; Cipta Santosa, I. D. M.
2018-01-01
The aims of this study to compares the performance characteristics of a water chiller air conditioning simulation equipped with thermostatic expansion valve (TEV) with those of a capillary tube. Water chiller system filled with the same charge of refrigerant. Comparative analyses were performed based on coefficient of performance (COP) and performance parameter of the refrigeration system, carried out at medium cooling load level with the ambient temperature of 29-31°C, constant compressor speed and fixed chilled water volume flowrate at 15 lpm. It was shown that the TEV system showed better energy consumption compared to that of capillary tube. From the coefficient of performance perspective, the thermostatic expansion valve system showed higher COP (± 21.4%) compared to that of capillary tube system.
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.
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
Information Dynamics of a Nonlinear Stochastic Nanopore System
Directory of Open Access Journals (Sweden)
Claire Gilpin
2018-03-01
Full Text Available Nanopores have become a subject of interest in the scientific community due to their potential uses in nanometer-scale laboratory and research applications, including infectious disease diagnostics and DNA sequencing. Additionally, they display behavioral similarity to molecular and cellular scale physiological processes. Recent advances in information theory have made it possible to probe the information dynamics of nonlinear stochastic dynamical systems, such as autonomously fluctuating nanopore systems, which has enhanced our understanding of the physical systems they model. We present the results of local (LER and specific entropy rate (SER computations from a simulation study of an autonomously fluctuating nanopore system. We learn that both metrics show increases that correspond to fluctuations in the nanopore current, indicating fundamental changes in information generation surrounding these fluctuations.
Path integral methods for the dynamics of stochastic and disordered systems
International Nuclear Information System (INIS)
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 of the perturbative, i.e. diagrammatic, approach to dynamics and how this formalism can be used for studying soft spin models. We review the supersymmetric formulation of the Langevin dynamics of these models and discuss the physical implications of the supersymmetry. We also describe the key steps involved 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. (topical review)
Markov stochasticity coordinates
International Nuclear Information System (INIS)
Eliazar, Iddo
2017-01-01
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
Markov stochasticity coordinates
Energy Technology Data Exchange (ETDEWEB)
Eliazar, Iddo, E-mail: iddo.eliazar@intel.com
2017-01-15
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
Dynamic asset allocation for bank under stochastic interest rates.
Chakroun, Fatma; Abid, Fathi
2014-01-01
This paper considers the optimal asset allocation strategy for bank with stochastic interest rates when there are three types of asset: Bank account, loans and securities. The asset allocation problem is to maximize the expected utility from terminal wealth of a bank's shareholders over a finite time horizon. As a consequence, we apply a dynamic programming principle to solve the Hamilton-Jacobi-Bellman (HJB) equation explicitly in the case of the CRRA utility function. A case study is given ...
Stochastic dynamics of a delayed bistable system with multiplicative noise
Energy Technology Data Exchange (ETDEWEB)
Dung, Nguyen Tien, E-mail: dung-nguyentien10@yahoo.com, E-mail: dungnt@fpt.edu.vn [Department of Mathematics, FPT University, No 8 Ton That Thuyet, My Dinh, Tu Liem, Hanoi (Viet Nam)
2014-05-15
In this paper we investigate the properties of a delayed bistable system under the effect of multiplicative noise. We first prove the existence and uniqueness of the positive solution and show that its moments are uniformly bounded. Then, we study stochastic dynamics of the solution in long time, the lower and upper bounds for the paths and an estimate for the average value are provided.
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...
Who Is Afraid of Liquidity Risk? : Dynamic Portfolio Choice with Stochastic Illiquidity
Driessen, Joost; Xing, R.
Recent 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 opportunity set. We
Portfolio Optimization with Stochastic Dividends and Stochastic Volatility
Varga, Katherine Yvonne
2015-01-01
We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…
Spreading dynamics on complex networks: a general stochastic approach.
Noël, Pierre-André; Allard, Antoine; Hébert-Dufresne, Laurent; Marceau, Vincent; Dubé, Louis J
2014-12-01
Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible and susceptible-infectious-removed dynamics (e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions.
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
Fine tuning classical and quantum molecular dynamics using a generalized Langevin equation
Rossi, Mariana; Kapil, Venkat; Ceriotti, Michele
2018-03-01
Generalized Langevin Equation (GLE) thermostats have been used very effectively as a tool to manipulate and optimize the sampling of thermodynamic ensembles and the associated static properties. Here we show that a similar, exquisite level of control can be achieved for the dynamical properties computed from thermostatted trajectories. We develop quantitative measures of the disturbance induced by the GLE to the Hamiltonian dynamics of a harmonic oscillator, and show that these analytical results accurately predict the behavior of strongly anharmonic systems. We also show that it is possible to correct, to a significant extent, the effects of the GLE term onto the corresponding microcanonical dynamics, which puts on more solid grounds the use of non-equilibrium Langevin dynamics to approximate quantum nuclear effects and could help improve the prediction of dynamical quantities from techniques that use a Langevin term to stabilize dynamics. Finally we address the use of thermostats in the context of approximate path-integral-based models of quantum nuclear dynamics. We demonstrate that a custom-tailored GLE can alleviate some of the artifacts associated with these techniques, improving the quality of results for the modeling of vibrational dynamics of molecules, liquids, and solids.
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.
International Nuclear Information System (INIS)
Yan-Mei, Kang; Yao-Lin, Jiang
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 sub diffusion exponent inhibits the stochastic resonance (SR), while for larger driving frequency the decrease of sub diffusion 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
Spatial effect on stochastic dynamics of bistable evolutionary games
International Nuclear Information System (INIS)
So, Kohaku H Z; Ohtsuki, Hisashi; Kato, Takeo
2014-01-01
We consider the lifetimes of metastable states in bistable evolutionary games (coordination games), and examine how they are affected by spatial structure. A semiclassical approximation based on a path integral method is applied to stochastic evolutionary game dynamics with and without spatial structure, and the lifetimes of the metastable states are evaluated. It is shown that the population dependence of the lifetimes is qualitatively different in these two models. Our result indicates that spatial structure can accelerate the transitions between metastable states. (paper)
Nonperturbative stochastic dynamics driven by strongly correlated colored noise
Jing, Jun; Li, Rui; You, J. Q.; Yu, Ting
2015-02-01
We propose a quantum model consisting of two remote qubits interacting with two correlated colored noises and establish an exact stochastic Schrödinger equation for this open quantum system. It is shown that the quantum dynamics of the qubit system is profoundly modulated by the mutual correlation between baths and the bath memory capability through dissipation and fluctuation. We report a physical effect on generating inner correlation and entanglement of two distant qubits arising from the strong bath-bath correlation.
Automated planning through abstractions in dynamic and stochastic environments
Martínez Muñoz, Moisés
2016-01-01
Mención Internacional en el título de doctor Generating sequences of actions - plans - for an automatic system, like a robot, using Automated Planning is particularly diflicult in stochastic and/or dynamic environments. These plans are composed of actions whose execution, in certain scenarios, might fail, which in tum prevents the execution of the rest of the actions in the plan. Also, in some environments, plans must he generated fast, hoth at the start of the execution and after every ex...
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.
Viñuelas, José; Kaneko, Gaël; Coulon, Antoine; Vallin, Elodie; Morin, Valérie; Mejia-Pous, Camila; Kupiec, Jean-Jacques; Beslon, Guillaume; Gandrillon, Olivier
2013-02-25
A number of studies have established that stochasticity in gene expression may play an important role in many biological phenomena. This therefore calls for further investigations to identify the molecular mechanisms at stake, in order to understand and manipulate cell-to-cell variability. In this work, we explored the role played by chromatin dynamics in the regulation of stochastic gene expression in higher eukaryotic cells. For this purpose, we generated isogenic chicken-cell populations expressing a fluorescent reporter integrated in one copy per clone. Although the clones differed only in the genetic locus at which the reporter was inserted, they showed markedly different fluorescence distributions, revealing different levels of stochastic gene expression. Use of chromatin-modifying agents showed that direct manipulation of chromatin dynamics had a marked effect on the extent of stochastic gene expression. To better understand the molecular mechanism involved in these phenomena, we fitted these data to a two-state model describing the opening/closing process of the chromatin. We found that the differences between clones seemed to be due mainly to the duration of the closed state, and that the agents we used mainly seem to act on the opening probability. In this study, we report biological experiments combined with computational modeling, highlighting the importance of chromatin dynamics in stochastic gene expression. This work sheds a new light on the mechanisms of gene expression in higher eukaryotic cells, and argues in favor of relatively slow dynamics with long (hours to days) periods of quiet state.
Sharp asymptotics for stochastic dynamics with parallel updating rule with self-interaction
Bovier, A.; Nardi, F.R.; Spitoni, C.
2011-01-01
In this paper we study metastability for a stochastic dynamics with a parallel updating rule in particular for a probabilistic cellular automata. The problem is addressed in the Freidlin Wentzel regime, i.e., finite volume, small magnetic field, and in the limit when temperature tends to zero. We
Quantization of dynamical systems and stochastic control theory
International Nuclear Information System (INIS)
Guerra, F.; Morato, L.M.
1982-09-01
In the general framework of stochastic control theory we introduce a suitable form of stochastic action associated to the controlled process. Then a variational principle gives all main features of Nelson's stochastic mechanics. In particular we derive the expression of the current velocity field as the gradient of the phase action. Moreover the stochastic corrections to the Hamilton-Jacobi equation are in agreement with the quantum mechanical form of the Madelung fluid (equivalent to the Schroedinger equation). Therefore stochastic control theory can provide a very simple model simulating quantum mechanical behavior
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.
International Nuclear Information System (INIS)
Sun, Zhi-Yuan; Gao, Yi-Tian; Yu, Xin; Liu, Ying
2013-01-01
We respectively investigate breakup and switching of the Manakov-typed bound vector solitons (BVSs) induced by two types of stochastic perturbations: the homogenous and nonhomogenous. Symmetry-recovering is discovered for the asymmetrical homogenous case, while soliton switching is found to relate with the perturbation amplitude and soliton coherence. Simulations show that soliton switching in the circularly-polarized light system is much weaker than that in the Manakov and linearly-polarized systems. In addition, the homogenous perturbations can enhance the soliton switching in both of the Manakov and non-integrable (linearly- and circularly-polarized) systems. Our results might be helpful in interpreting dynamics of the BVSs with stochastic noises in nonlinear optics or with stochastic quantum fluctuations in Bose–Einstein condensates.
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.
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 ...
Parallel Stochastic discrete event simulation of calcium dynamics in neuron.
Ishlam Patoary, Mohammad Nazrul; Tropper, Carl; McDougal, Robert A; Zhongwei, Lin; Lytton, William W
2017-09-26
The intra-cellular calcium signaling pathways of a neuron depends on both biochemical reactions and diffusions. Some quasi-isolated compartments (e.g. spines) are so small and calcium concentrations are so low that one extra molecule diffusing in by chance can make a nontrivial difference in its concentration (percentage-wise). These rare events can affect dynamics discretely in such way that they cannot be evaluated by a deterministic simulation. Stochastic models of such a system provide a more detailed understanding of these systems than existing deterministic models because they capture their behavior at a molecular level. Our research focuses on the development of a high performance parallel discrete event simulation environment, Neuron Time Warp (NTW), which is intended for use in the parallel simulation of stochastic reaction-diffusion systems such as intra-calcium signaling. NTW is integrated with NEURON, a simulator which is widely used within the neuroscience community. We simulate two models, a calcium buffer and a calcium wave model. The calcium buffer model is employed in order to verify the correctness and performance of NTW by comparing it to a serial deterministic simulation in NEURON. We also derived a discrete event calcium wave model from a deterministic model using the stochastic IP3R structure.
Peltier battery thermostat for semiconductor detectors
International Nuclear Information System (INIS)
Caini, V.
1980-01-01
The description is given of a Peltier battery cooling thermostat for semiconductor detectors, whose sensing element is the detector itself. A signal proportional to the leakage current is amplified and compared with a chosen reference voltage. The difference, amplified and sensed, regulates the cooling current to the Peltier battery. Special mechanical devices speed up measurement-taking. The leakage current proved to be reducible to as little as 1/1000 of that at ambient temperature and the stabilization obtained is between +-5 nA (although between +-1 nA is also feasible). Hence it is possible to use very high load resistance preamplifiers to reduce noise and to improve stability and pulse height resolution in α spectroscopy, even with a detector unsuitable for work at very low temperatures. Other applications can be foreseen. (orig.)
Langevin Dynamics with Spatial Correlations as a Model for Electron-Phonon Coupling
Tamm, A.; Caro, M.; Caro, A.; Samolyuk, G.; Klintenberg, M.; Correa, A. A.
2018-05-01
Stochastic Langevin dynamics has been traditionally used as a tool to describe nonequilibrium processes. When utilized in systems with collective modes, traditional Langevin dynamics relaxes all modes indiscriminately, regardless of their wavelength. We propose a generalization of Langevin dynamics that can capture a differential coupling between collective modes and the bath, by introducing spatial correlations in the random forces. This allows modeling the electronic subsystem in a metal as a generalized Langevin bath endowed with a concept of locality, greatly improving the capabilities of the two-temperature model. The specific form proposed here for the spatial correlations produces a physical wave-vector and polarization dependency of the relaxation produced by the electron-phonon coupling in a solid. We show that the resulting model can be used for describing the path to equilibration of ions and electrons and also as a thermostat to sample the equilibrium canonical ensemble. By extension, the family of models presented here can be applied in general to any dense system, solids, alloys, and dense plasmas. As an example, we apply the model to study the nonequilibrium dynamics of an electron-ion two-temperature Ni crystal.
The stochastic dynamics of intermittent porescale particle motion
Dentz, Marco; Morales, Veronica; Puyguiraud, Alexandre; Gouze, Philippe; Willmann, Matthias; Holzner, Markus
2017-04-01
Numerical and experimental data for porescale particle dynamics show intermittent patterns in Lagrangian velocities and accelerations, which manifest in long time intervals of low and short durations of high velocities [1, 2]. This phenomenon is due to the spatial persistence of particle velocities on characteristic heterogeneity length scales. In order to systematically quantify these behaviors and extract the stochastic dynamics of particle motion, we focus on the analysis of Lagrangian velocities sampled equidistantly along trajectories [3]. This method removes the intermittency observed under isochrone sampling. The space-Lagrangian velocity series can be quantified by a Markov process that is continuous in distance along streamline. It is fully parameterized in terms of the flux-weighted Eulerian velocity PDF and the characteristic pore-length. The resulting stochastic particle motion describes a continuous time random walk (CTRW). This approach allows for the process based interpretation of experimental and numerical porescale velocity, acceleration and displacement data. It provides a framework for the characterization and upscaling of particle transport and dispersion from the pore to the Darcy-scale based on the medium geometry and Eulerian flow attributes. [1] P. De Anna, T. Le Borgne, M. Dentz, A.M. Tartakovsky, D. Bolster, and P. Davy, "Flow intermittency, dispersion, and correlated continuous time random walks in porous media," Phys. Rev. Lett. 110, 184502 (2013). [2] M. Holzner, V. L. Morales, M. Willmann, and M. Dentz, "Intermittent Lagrangian velocities and accelerations in three- dimensional porous medium flow," Phys. Rev. E 92, 013015 (2015). [3] M. Dentz, P. K. Kang, A. Comolli, T. Le Borgne, and D. R. Lester, "Continuous time random walks for the evolution of Lagrangian velocities," Phys. Rev. Fluids (2016).
Gottwald, G.A.; Crommelin, D.T.; Franzke, C.L.E.; Franzke, C.L.E.; O'Kane, T.J.
2017-01-01
In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations contain a Markov term, a memory term and a term suggestive of
DEFF Research Database (Denmark)
Davidsen, Claus; Liu, Suxia; Mo, Xinguo
2014-01-01
. 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...
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...... that shows how the p-safe initial set is computed numerically....
How to remove the spurious resonances from ring polymer molecular dynamics
Energy Technology Data Exchange (ETDEWEB)
Rossi, Mariana; Manolopoulos, David E. [Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ (United Kingdom); Ceriotti, Michele [Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne (Switzerland)
2014-06-21
Two of the most successful methods that are presently available for simulating the quantum dynamics of condensed phase systems are centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD). Despite their conceptual differences, practical implementations of these methods differ in just two respects: the choice of the Parrinello-Rahman mass matrix and whether or not a thermostat is applied to the internal modes of the ring polymer during the dynamics. Here, we explore a method which is halfway between the two approximations: we keep the path integral bead masses equal to the physical particle masses but attach a Langevin thermostat to the internal modes of the ring polymer during the dynamics. We justify this by showing analytically that the inclusion of an internal mode thermostat does not affect any of the established features of RPMD: thermostatted RPMD is equally valid with respect to everything that has actually been proven about the method as RPMD itself. In particular, because of the choice of bead masses, the resulting method is still optimum in the short-time limit, and the transition state approximation to its reaction rate theory remains closely related to the semiclassical instanton approximation in the deep quantum tunneling regime. In effect, there is a continuous family of methods with these properties, parameterised by the strength of the Langevin friction. Here, we explore numerically how the approximation to quantum dynamics depends on this friction, with a particular emphasis on vibrational spectroscopy. We find that a broad range of frictions approaching optimal damping give similar results, and that these results are immune to both the resonance problem of RPMD and the curvature problem of CMD.
How to remove the spurious resonances from ring polymer molecular dynamics
International Nuclear Information System (INIS)
Rossi, Mariana; Manolopoulos, David E.; Ceriotti, Michele
2014-01-01
Two of the most successful methods that are presently available for simulating the quantum dynamics of condensed phase systems are centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD). Despite their conceptual differences, practical implementations of these methods differ in just two respects: the choice of the Parrinello-Rahman mass matrix and whether or not a thermostat is applied to the internal modes of the ring polymer during the dynamics. Here, we explore a method which is halfway between the two approximations: we keep the path integral bead masses equal to the physical particle masses but attach a Langevin thermostat to the internal modes of the ring polymer during the dynamics. We justify this by showing analytically that the inclusion of an internal mode thermostat does not affect any of the established features of RPMD: thermostatted RPMD is equally valid with respect to everything that has actually been proven about the method as RPMD itself. In particular, because of the choice of bead masses, the resulting method is still optimum in the short-time limit, and the transition state approximation to its reaction rate theory remains closely related to the semiclassical instanton approximation in the deep quantum tunneling regime. In effect, there is a continuous family of methods with these properties, parameterised by the strength of the Langevin friction. Here, we explore numerically how the approximation to quantum dynamics depends on this friction, with a particular emphasis on vibrational spectroscopy. We find that a broad range of frictions approaching optimal damping give similar results, and that these results are immune to both the resonance problem of RPMD and the curvature problem of CMD
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.
Stochastic Analysis : A Series of Lectures
Dozzi, Marco; Flandoli, Franco; Russo, Francesco
2015-01-01
This book presents in thirteen refereed survey articles an overview of modern activity in stochastic analysis, written by leading international experts. The topics addressed include stochastic fluid dynamics and regularization by noise of deterministic dynamical systems; stochastic partial differential equations driven by Gaussian or Lévy noise, including the relationship between parabolic equations and particle systems, and wave equations in a geometric framework; Malliavin calculus and applications to stochastic numerics; stochastic integration in Banach spaces; porous media-type equations; stochastic deformations of classical mechanics and Feynman integrals and stochastic differential equations with reflection. The articles are based on short courses given at the Centre Interfacultaire Bernoulli of the Ecole Polytechnique Fédérale de Lausanne, Switzerland, from January to June 2012. They offer a valuable resource not only for specialists, but also for other researchers and Ph.D. students in the fields o...
Non-ergodicity of Nosé–Hoover dynamics
International Nuclear Information System (INIS)
Legoll, Frédéric; Luskin, Mitchell; Moeckel, Richard
2009-01-01
The Nosé–Hoover dynamics is a deterministic method that is commonly used to sample the canonical Gibbs measure. This dynamics extends the physical Hamiltonian dynamics by the addition of a 'thermostat' variable, which is coupled nonlinearly with the physical variables. The accuracy of the method depends on the dynamics being ergodic. Numerical experiments have been published earlier that are consistent with non-ergodicity of the dynamics for some model problems. The authors recently proved the non-ergodicity of the Nosé–Hoover dynamics for the one-dimensional harmonic oscillator. In this paper, this result is extended to non-harmonic one-dimensional systems. We also show that, for some multidimensional systems, the averaged dynamics for the limit of infinite thermostat 'mass' has many invariants, thus giving theoretical support for either non-ergodicity or slow ergodization. Numerical experiments for a two-dimensional central force problem and the one-dimensional pendulum problem give evidence for non-ergodicity
Dynamical Behaviors of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Delays
Directory of Open Access Journals (Sweden)
Li Wan
2012-01-01
Full Text Available This paper investigates dynamical behaviors of stochastic Cohen-Grossberg neural network with delays and reaction diffusion. By employing Lyapunov method, Poincaré inequality and matrix technique, some sufficient criteria on ultimate boundedness, weak attractor, and asymptotic stability are obtained. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.
Threshold Dynamics of a Stochastic SIR Model with Vertical Transmission and Vaccination
Miao, Anqi; Zhang, Jian; Zhang, Tongqian; Pradeep, B. G. Sampath Aruna
2017-01-01
A stochastic SIR model with vertical transmission and vaccination is proposed and investigated in this paper. The threshold dynamics are explored when the noise is small. The conditions for the extinction or persistence of infectious diseases are deduced. Our results show that large noise can lead to the extinction of infectious diseases which is conducive to epidemic diseases control.
A stochastic differential equation analysis of cerebrospinal fluid dynamics.
Raman, Kalyan
2011-01-18
Clinical measurements of intracranial pressure (ICP) over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data. The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE) that accommodates the fluctuations in ICP. The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise. Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.
Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows
International Nuclear Information System (INIS)
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.
Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost
International Nuclear Information System (INIS)
Bokanowski, Olivier; Picarelli, Athena; Zidani, Hasnaa
2015-01-01
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
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.
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
Multivariate moment closure techniques for stochastic kinetic models
International Nuclear Information System (INIS)
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.
2015-01-01
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs
Multivariate moment closure techniques for stochastic kinetic models
Energy Technology Data Exchange (ETDEWEB)
Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H., E-mail: m.stumpf@imperial.ac.uk [Department of Life Sciences, Centre for Integrative Systems Biology and Bioinformatics, Imperial College London, London SW7 2AZ (United Kingdom)
2015-09-07
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Yu, Qian; Fang, Debin; Zhang, Xiaoling; Jin, Chen; Ren, Qiyu
2016-06-27
Stochasticity plays an important role in the evolutionary dynamic of cyclic dominance within a finite population. To investigate the stochastic evolution process of the behaviour of bounded rational individuals, we model the Rock-Scissors-Paper (RSP) game as a finite, state dependent Quasi Birth and Death (QBD) process. We assume that bounded rational players can adjust their strategies by imitating the successful strategy according to the payoffs of the last round of the game, and then analyse the limiting distribution of the QBD process for the game stochastic evolutionary dynamic. The numerical experiments results are exhibited as pseudo colour ternary heat maps. Comparisons of these diagrams shows that the convergence property of long run equilibrium of the RSP game in populations depends on population size and the parameter of the payoff matrix and noise factor. The long run equilibrium is asymptotically stable, neutrally stable and unstable respectively according to the normalised parameters in the payoff matrix. Moreover, the results show that the distribution probability becomes more concentrated with a larger population size. This indicates that increasing the population size also increases the convergence speed of the stochastic evolution process while simultaneously reducing the influence of the noise factor.
DEFF Research Database (Denmark)
Langmaack, Lasse Nicolai; Knudsen, Hans-Jørgen Høgaard
2006-01-01
The bulb of a thermostatic expansion valve (TXV) is basically a temperature-pressure converter. It senses the temperature at the outlet of the evaporator, and the substance in the bulb (charge) generates the corresponding saturation pressure inside the bulb. The aim of the work presented in this ...
Control for large scale demand response of thermostatic loads
DEFF Research Database (Denmark)
Totu, Luminita Cristiana; Leth, John; Wisniewski, Rafal
2013-01-01
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......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...
Stochastic dynamics of genetic broadcasting networks
Potoyan, Davit A.; Wolynes, Peter G.
2017-11-01
The complex genetic programs of eukaryotic cells are often regulated by key transcription factors occupying or clearing out of a large number of genomic locations. Orchestrating the residence times of these factors is therefore important for the well organized functioning of a large network. The classic models of genetic switches sidestep this timing issue by assuming the binding of transcription factors to be governed entirely by thermodynamic protein-DNA affinities. Here we show that relying on passive thermodynamics and random release times can lead to a "time-scale crisis" for master genes that broadcast their signals to a large number of binding sites. We demonstrate that this time-scale crisis for clearance in a large broadcasting network can be resolved by actively regulating residence times through molecular stripping. We illustrate these ideas by studying a model of the stochastic dynamics of the genetic network of the central eukaryotic master regulator NFκ B which broadcasts its signals to many downstream genes that regulate immune response, apoptosis, etc.
P.A.N. Bosman (Peter); J.A. La Poutré (Han); D. Thierens (Dirk)
2007-01-01
htmlabstractThe focus of this paper is on how to design evolutionary algorithms (EAs) for solving stochastic dynamic optimization problems online, i.e. as time goes by. For a proper design, the EA must not only be capable of tracking shifting optima, it must also take into account the future
DEFF Research Database (Denmark)
Vrettos, Evangelos; Ziras, Charalampos; Andersson, Goran
2016-01-01
in the controller to account for thermostat resolution limitations, and finally, we modify the control design to account for refrigerator door openings. Extensive simulations with actual frequency signal data and with different aggregation sizes, load characteristics, and control parameters, demonstrate......Due to increasing shares of renewable energy sources, more frequency reserves are required to maintain power system stability. In this paper, we present a decentralized control scheme that allows a large aggregation of refrigerators to provide Primary Frequency Control (PFC) reserves to the grid...... based on local frequency measurements and without communication. The control is based on stochastic switching of refrigerators depending on the frequency deviation. We develop methods to account for typical lockout constraints of compressors and increased power consumption during the startup phase...
Fundamentals of stochastic nature sciences
Klyatskin, Valery I
2017-01-01
This book addresses the processes of stochastic structure formation in two-dimensional geophysical fluid dynamics based on statistical analysis of Gaussian random fields, as well as stochastic structure formation in dynamic systems with parametric excitation of positive random fields f(r,t) described by partial differential equations. Further, the book considers two examples of stochastic structure formation in dynamic systems with parametric excitation in the presence of Gaussian pumping. In dynamic systems with parametric excitation in space and time, this type of structure formation either happens – or doesn’t! However, if it occurs in space, then this almost always happens (exponentially quickly) in individual realizations with a unit probability. In the case considered, clustering of the field f(r,t) of any nature is a general feature of dynamic fields, and one may claim that structure formation is the Law of Nature for arbitrary random fields of such type. The study clarifies the conditions under wh...
Threshold Dynamics of a Stochastic SIR Model with Vertical Transmission and Vaccination
Directory of Open Access Journals (Sweden)
Anqi Miao
2017-01-01
Full Text Available A stochastic SIR model with vertical transmission and vaccination is proposed and investigated in this paper. The threshold dynamics are explored when the noise is small. The conditions for the extinction or persistence of infectious diseases are deduced. Our results show that large noise can lead to the extinction of infectious diseases which is conducive to epidemic diseases control.
Buesing, Lars; Bill, Johannes; Nessler, Bernhard; Maass, Wolfgang
2011-11-01
The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution, both for the case of discrete and continuous time. This provides a step towards closing the gap between abstract functional models of cortical computation and more detailed models of networks of spiking neurons.
On the precision of quasi steady state assumptions in stochastic dynamics
Agarwal, Animesh; Adams, Rhys; Castellani, Gastone C.; Shouval, Harel Z.
2012-07-01
Many biochemical networks have complex multidimensional dynamics and there is a long history of methods that have been used for dimensionality reduction for such reaction networks. Usually a deterministic mass action approach is used; however, in small volumes, there are significant fluctuations from the mean which the mass action approach cannot capture. In such cases stochastic simulation methods should be used. In this paper, we evaluate the applicability of one such dimensionality reduction method, the quasi-steady state approximation (QSSA) [L. Menten and M. Michaelis, "Die kinetik der invertinwirkung," Biochem. Z 49, 333369 (1913)] for dimensionality reduction in case of stochastic dynamics. First, the applicability of QSSA approach is evaluated for a canonical system of enzyme reactions. Application of QSSA to such a reaction system in a deterministic setting leads to Michaelis-Menten reduced kinetics which can be used to derive the equilibrium concentrations of the reaction species. In the case of stochastic simulations, however, the steady state is characterized by fluctuations around the mean equilibrium concentration. Our analysis shows that a QSSA based approach for dimensionality reduction captures well the mean of the distribution as obtained from a full dimensional simulation but fails to accurately capture the distribution around that mean. Moreover, the QSSA approximation is not unique. We have then extended the analysis to a simple bistable biochemical network model proposed to account for the stability of synaptic efficacies; the substrate of learning and memory [J. E. Lisman, "A mechanism of memory storage insensitive to molecular turnover: A bistable autophosphorylating kinase," Proc. Natl. Acad. Sci. U.S.A. 82, 3055-3057 (1985)], 10.1073/pnas.82.9.3055. Our analysis shows that a QSSA based dimensionality reduction method results in errors as big as two orders of magnitude in predicting the residence times in the two stable states.
A stochastic differential equation analysis of cerebrospinal fluid dynamics
Directory of Open Access Journals (Sweden)
Raman Kalyan
2011-01-01
Full Text Available Abstract Background Clinical measurements of intracranial pressure (ICP over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data. Methods The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE that accommodates the fluctuations in ICP. Results The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise. Conclusions Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.
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)
Ahn, Byung-Cheon [Department of Building Equipment System Engineering, Kyungwon University, Seongnam City (Korea); Song, Jae-Yeob [Graduate School, Building Equipment System Engineering, Kyungwon University, Seongnam City (Korea)
2010-04-15
Computer simulations and experiments are carried out to research the control characteristics and heating performances for a radiant slab heating system with automatic thermostatic valves in residential apartments. An electrical equivalent R-C circuit is applied to analyze the unsteady heat transfer in the house. In addition, the radiant heat transfer between slabs, ceilings and walls in the room is evaluated by enclosure analysis method. Results of heating performance and control characteristics were determined from control methods such as automatic thermostatic valves, room air temperature-sensing method, water-temperature-sensing method, proportional control method, and On-Off control method. (author)
Variance decomposition in stochastic simulators.
Le Maître, O P; Knio, O M; Moraes, A
2015-06-28
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Variance decomposition in stochastic simulators
Le Maître, O. P.; Knio, O. M.; Moraes, A.
2015-06-01
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Variance decomposition in stochastic simulators
Energy Technology Data Exchange (ETDEWEB)
Le Maître, O. P., E-mail: olm@limsi.fr [LIMSI-CNRS, UPR 3251, Orsay (France); Knio, O. M., E-mail: knio@duke.edu [Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708 (United States); Moraes, A., E-mail: alvaro.moraesgutierrez@kaust.edu.sa [King Abdullah University of Science and Technology, Thuwal (Saudi Arabia)
2015-06-28
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Variance decomposition in stochastic simulators
Le Maî tre, O. P.; Knio, O. M.; Moraes, Alvaro
2015-01-01
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Dissipative particle dynamics: Effects of thermostating schemes on nano-colloid electrophoresis
Hassanzadeh Afrouzi, Hamid; Moshfegh, Abouzar; Farhadi, Mousa; Sedighi, Kurosh
2018-05-01
A novel fully explicit approach using dissipative particle dynamics (DPD) method is introduced in the present study to model the electrophoretic transport of nano-colloids in an electrolyte solution. Slater type charge smearing function included in 3D Ewald summation method is employed to treat electrostatic interaction. Performance of various thermostats are challenged to control the system temperature and study the dynamic response of colloidal electrophoretic mobility under practical ranges of external electric field (0 . 072 relationships respectively with electric field and colloidal repulsion; although they each respectively behave direct and inverse trends with salt concentration under various thermostats. Nosé-Hoover-Lowe-Andersen and Lowe-Andersen thermostats are found to function more effectively under high electric fields (E > 0 . 145[v/nm ]) while thermal equilibrium is maintained. Reasonable agreements are achieved by benchmarking the system radial distribution function with available EW3D modellings, as well as comparing reduced mobility against conventional Smoluchowski and Hückel theories, and numerical solution of Poisson-Boltzmann equation.
MacKenzie, K; Bishop, S C
2001-08-01
A stochastic model describing disease transmission dynamics for a microparasitic infection in a structured domestic animal population is developed and applied to hypothetical epidemics on a pig farm. Rational decision making regarding appropriate control strategies for infectious diseases in domestic livestock requires an understanding of the disease dynamics and risk profiles for different groups of animals. This is best achieved by means of stochastic epidemic models. Methodologies are presented for 1) estimating the probability of an epidemic, given the presence of an infected animal, whether this epidemic is major (requires intervention) or minor (dies out without intervention), and how the location of the infected animal on the farm influences the epidemic probabilities; 2) estimating the basic reproductive ratio, R0 (i.e., the expected number of secondary cases on the introduction of a single infected animal) and the variability of the estimate of this parameter; and 3) estimating the total proportion of animals infected during an epidemic and the total proportion infected at any point in time. The model can be used for assessing impact of altering farm structure on disease dynamics, as well as disease control strategies, including altering farm structure, vaccination, culling, and genetic selection.
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.
Energy Technology Data Exchange (ETDEWEB)
Kaczmarczyk, S [School of Applied Sciences, University of Northampton, St. George' s Avenue, Northampton NN2 6JD (United Kingdom); Iwankiewicz, R [Institute of Mechanics and Ocean Engineering, Hamburg University of Technology, Eissendorfer Strasse 42 D-21073, Hamburg (Germany); Terumichi, Y, E-mail: stefan.kaczmarczyk@northampton.ac.u [Faculty of Science and Technology, Sophia University, 7-1 KIOI-CHO, CHIYODAKU, Tokyo, 102-8554 Japan (Japan)
2009-08-01
Moving slender elastic elements such as ropes, cables and belts are pivotal components of vertical transportation systems such as traction elevators. Their lengths vary within the host building structure during the elevator operation which results in the change of the mass and stiffness characteristics of the system. The structure of modern high-rise buildings is flexible and when subjected to loads due to strong winds and earthquakes it vibrates at low frequencies. The inertial load induced by the building motion excites the flexible components of the elevator system. The compensating ropes due to their lower tension are particularly affected and undergo large dynamic deformations. The paper focuses on the presentation of the non-stationary model of a building-compensating rope system and on the analysis to predict its dynamic response. The excitation mechanism is represented by a harmonic process and the results of computer simulations to predict transient resonance response are presented. The analysis of the simulation results leads to recommendations concerning the selection of the weight of the compensation assembly to minimize the effects of an adverse dynamic response of the system. The scenario when the excitation is represented as a narrow-band stochastic process with the state vector governed by stochastic equations is then discussed and the stochastic differential equations governing the second-order statistical moments of the state vector are developed.
International Nuclear Information System (INIS)
Babykina, Génia; Brînzei, Nicolae; Aubry, Jean-François; Deleuze, Gilles
2016-01-01
The paper proposes a modeling framework to support Monte Carlo simulations of the behavior of a complex industrial system. The aim is to analyze the system dependability in the presence of random events, described by any type of probability distributions. Continuous dynamic evolutions of physical parameters are taken into account by a system of differential equations. Dynamic reliability is chosen as theoretical framework. Based on finite state automata theory, the formal model is built by parallel composition of elementary sub-models using a bottom-up approach. Considerations of a stochastic nature lead to a model called the Stochastic Hybrid Automaton. The Scilab/Scicos open source environment is used for implementation. The case study is carried out on an example of a steam generator of a nuclear power plant. The behavior of the system is studied by exploring its trajectories. Possible system trajectories are analyzed both empirically, using the results of Monte Carlo simulations, and analytically, using the formal system model. The obtained results are show to be relevant. The Stochastic Hybrid Automaton appears to be a suitable tool to address the dynamic reliability problem and to model real systems of high complexity; the bottom-up design provides precision and coherency of the system model. - Highlights: • A part of a nuclear power plant is modeled in the context of dynamic reliability. • Stochastic Hybrid Automaton is used as an input model for Monte Carlo simulations. • The model is formally built using a bottom-up approach. • The behavior of the system is analyzed empirically and analytically. • A formally built SHA shows to be a suitable tool to approach dynamic reliability.
Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons
Guillermo Gallego; Garrett van Ryzin
1994-01-01
In many industries, managers face the problem of selling a given stock of items by a deadline. We investigate the problem of dynamically pricing such inventories when demand is price sensitive and stochastic and the firm's objective is to maximize expected revenues. Examples that fit this framework include retailers selling fashion and seasonal goods and the travel and leisure industry, which markets space such as seats on airline flights, cabins on vacation cruises, and rooms in hotels that ...
Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems
Antown, Fadi; Dragičević, Davor; Froyland, Gary
2018-03-01
The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.
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
Noise-sustained fluctuations in stochastic dynamics with a delay.
D'Odorico, Paolo; Laio, Francesco; Ridolfi, Luca
2012-04-01
Delayed responses to external drivers are ubiquitous in environmental, social, and biological processes. Delays may induce oscillations, Hopf bifurcations, and instabilities in deterministic systems even in the absence of nonlinearities. Despite recent advances in the study of delayed stochastic differential equations, the interaction of random drivers with delays remains poorly understood. In particular, it is unclear whether noise-induced behaviors may emerge from these interactions. Here we show that noise may enhance and sustain transient periodic oscillations inherent to deterministic delayed systems. We investigate the conditions conducive to the emergence and disappearance of these dynamics in a linear system in the presence of both additive and multiplicative noise.
Barthel, Thomas; De Bacco, Caterina; Franz, Silvio
2018-01-01
We introduce and apply an efficient method for the precise simulation of stochastic dynamical processes on locally treelike graphs. Networks with cycles are treated in the framework of the cavity method. Such models correspond, for example, to spin-glass systems, Boolean networks, neural networks, or other technological, biological, and social networks. Building upon ideas from quantum many-body theory, our approach is based on a matrix product approximation of the so-called edge messages—conditional probabilities of vertex variable trajectories. Computation costs and accuracy can be tuned by controlling the matrix dimensions of the matrix product edge messages (MPEM) in truncations. In contrast to Monte Carlo simulations, the algorithm has a better error scaling and works for both single instances as well as the thermodynamic limit. We employ it to examine prototypical nonequilibrium Glauber dynamics in the kinetic Ising model. Because of the absence of cancellation effects, observables with small expectation values can be evaluated accurately, allowing for the study of decay processes and temporal correlations.
Momentum Maps and Stochastic Clebsch Action Principles
Cruzeiro, Ana Bela; Holm, Darryl D.; Ratiu, Tudor S.
2018-01-01
We derive stochastic differential equations whose solutions follow the flow of a stochastic nonlinear Lie algebra operation on a configuration manifold. For this purpose, we develop a stochastic Clebsch action principle, in which the noise couples to the phase space variables through a momentum map. This special coupling simplifies the structure of the resulting stochastic Hamilton equations for the momentum map. In particular, these stochastic Hamilton equations collectivize for Hamiltonians that depend only on the momentum map variable. The Stratonovich equations are derived from the Clebsch variational principle and then converted into Itô form. In comparing the Stratonovich and Itô forms of the stochastic dynamical equations governing the components of the momentum map, we find that the Itô contraction term turns out to be a double Poisson bracket. Finally, we present the stochastic Hamiltonian formulation of the collectivized momentum map dynamics and derive the corresponding Kolmogorov forward and backward equations.
Construction and Start-up of a Large-Volume Thermostat for Dielectric-Constant Gas Thermometry
Merlone, A.; Moro, F.; Zandt, T.; Gaiser, C.; Fellmuth, B.
2010-07-01
A liquid-bath thermostat with a volume of about 800 L was designed to provide a suitable thermal environment for a dielectric-constant gas thermometer (DCGT) in the range from the triple point of mercury to the melting point of gallium. In the article, results obtained with the unique, huge thermostat without the DCGT measuring chamber are reported to demonstrate the capability of controlling the temperature of very large systems at a metrological level. First tests showed that the bath together with its temperature controller provide a temperature variation of less than ±0.5mK peak-to-peak. This temperature instability could be maintained over a period of several days. In the central working volume (diameter—500mm, height—650mm), in which the vacuum chamber containing the measuring system of the DCGT will be placed later, the temperature inhomogeneity has been demonstrated to be also well below 1mK.
Tarim, S.A.; Ozen, U.; Dogru, M.K.; Rossi, R.
2011-01-01
We provide an efficient computational approach to solve the mixed integer programming (MIP) model developed by Tarim and Kingsman [8] for solving a stochastic lot-sizing problem with service level constraints under the static–dynamic uncertainty strategy. The effectiveness of the proposed method
The stochastic system approach for estimating dynamic treatments effect.
Commenges, Daniel; Gégout-Petit, Anne
2015-10-01
The problem of assessing the effect of a treatment on a marker in observational studies raises the difficulty that attribution of the treatment may depend on the observed marker values. As an example, we focus on the analysis of the effect of a HAART on CD4 counts, where attribution of the treatment may depend on the observed marker values. This problem has been treated using marginal structural models relying on the counterfactual/potential response formalism. Another approach to causality is based on dynamical models, and causal influence has been formalized in the framework of the Doob-Meyer decomposition of stochastic processes. Causal inference however needs assumptions that we detail in this paper and we call this approach to causality the "stochastic system" approach. First we treat this problem in discrete time, then in continuous time. This approach allows incorporating biological knowledge naturally. When working in continuous time, the mechanistic approach involves distinguishing the model for the system and the model for the observations. Indeed, biological systems live in continuous time, and mechanisms can be expressed in the form of a system of differential equations, while observations are taken at discrete times. Inference in mechanistic models is challenging, particularly from a numerical point of view, but these models can yield much richer and reliable results.
Patrick C. Tobin; Ottar N. Bjornstad
2005-01-01
Natural enemy-victim systems may exhibit a range of dynamic space-time patterns. We used a theoretical framework to study spatiotemporal structuring in a transient natural enemy-victim system subject to differential rates of dispersal, stochastic forcing, and nonlinear dynamics. Highly mobile natural enemies that attacked less mobile victims were locally spatially...
International Nuclear Information System (INIS)
Vega G, J.D.
1994-01-01
In this work, metallic coatings of nickel was made over carbon steel using two different electrolytic solutions: The Watts's bath and the nickel sulfamate bath, using a pulse variable current. The method use was the traditional method, its means a thermostatic cell and one movable anode, which is a few know technique nowadays, it allow realize depositions away from any laboratory or special workshop, it has the advantage to be a portable dispositive. At last of all the electro depositions the coatings quality was valuable by them physical properties like: adhesion, hardness, wrinkled and thickness. The best results was obtain by the Nickel sulfamate bath and movable anode, less in the thickness, which has higher on the thermostatic cell. The variable current was obtain by a Pulse Generator and a Cathodic galvanometer. (Author)
Energy Technology Data Exchange (ETDEWEB)
Velickovic, Lj; Petrovic, M [Boris Kidric Institute of nuclear sciences Vinca, Belgrade (Yugoslavia)
1968-12-15
Stochastic reactor oscillator and cross correlation method were used for determining reactor dynamics characteristics. Experimental equipment, fast reactor oscillator (BOR-1) was activated by random pulses from the GBS-16 generator. Tape recorder AMPEX-SF-300 and data acquisition tool registered reactor response to perturbations having different frequencies. Reactor response and activation signals were cross correlated by digital computer for different positions of stochastic oscillator and ionization chamber.
Demand Response of Thermostatic Loads by Optimized Switching-Fraction Broadcast
DEFF Research Database (Denmark)
Totu, Luminita Cristiana; Wisniewski, Rafal
2014-01-01
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 the problem of managing large populations of thermostat-based devices with on/off operation. The objective is to enable demand...... Method is used to spatially discretize these equations. Next, a broadcast strategy with two switching-fraction signals is proposed for actuating the population. This is applied in an open-loop scenario for tracking a power reference by running an optimization with a multilinear objective....
International Nuclear Information System (INIS)
Dybiec, Bartłomiej; Gudowska-Nowak, Ewa
2009-01-01
A standard approach to analysis of noise-induced effects in stochastic dynamics assumes a Gaussian character of the noise term describing interaction of the analyzed system with its complex surroundings. An additional assumption about the existence of timescale separation between the dynamics of the measured observable and the typical timescale of the noise allows external fluctuations to be modeled as temporally uncorrelated and therefore white. However, in many natural phenomena the assumptions concerning the above mentioned properties of 'Gaussianity' and 'whiteness' of the noise can be violated. In this context, in contrast to the spatiotemporal coupling characterizing general forms of non-Markovian or semi-Markovian Lévy walks, so called Lévy flights correspond to the class of Markov processes which can still be interpreted as white, but distributed according to a more general, infinitely divisible, stable and non-Gaussian law. Lévy noise-driven non-equilibrium systems are known to manifest interesting physical properties and have been addressed in various scenarios of physical transport exhibiting a superdiffusive behavior. Here we present a brief overview of our recent investigations aimed at understanding features of stochastic dynamics under the influence of Lévy white noise perturbations. We find that the archetypal phenomena of noise-induced ordering are robust and can be detected also in systems driven by memoryless, non-Gaussian, heavy-tailed fluctuations with infinite variance
Demand Response on domestic thermostatically controlled loads
DEFF Research Database (Denmark)
Lakshmanan, Venkatachalam
. For a safe and reliable operation of electric power systems, the balance between electricity generation and consumption has to be maintained. The conventional fossil fuel based power generation achieves this balance by adjusting the generation to follow the consumption. In the electric power system......Electricity has become an inevitable part of human life in present day world. In the past two centuries, the electric power system has undergone a lot of changes. Due to the awareness about the adverse impact of the fossil fuels, the power industry is adopting green and sustainable energy sources....... 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...
International Nuclear Information System (INIS)
Do, Duy Minh; Gao, Wei; Song, Chongmin; Tangaramvong, Sawekchai
2014-01-01
This paper presents the non-deterministic dynamic analysis and reliability assessment of structures with uncertain-but-bounded parameters under stochastic process excitations. Random ground acceleration from earthquake motion is adopted to illustrate the stochastic process force. The exact change ranges of natural frequencies, random vibration displacement and stress responses of structures are investigated under the interval analysis framework. Formulations for structural reliability are developed considering the safe boundary and structural random vibration responses as interval parameters. An improved particle swarm optimization algorithm, namely randomised lower sequence initialized high-order nonlinear particle swarm optimization algorithm, is employed to capture the better bounds of structural dynamic characteristics, random vibration responses and reliability. Three numerical examples are used to demonstrate the presented method for interval random vibration analysis and reliability assessment of structures. The accuracy of the results obtained by the presented method is verified by the randomised Quasi-Monte Carlo simulation method (QMCSM) and direct Monte Carlo simulation method (MCSM). - Highlights: • Interval uncertainty is introduced into structural random vibration responses. • Interval dynamic reliability assessments of structures are implemented. • Boundaries of structural dynamic response and reliability are achieved
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.
Stochastic Ocean Predictions with Dynamically-Orthogonal Primitive Equations
Subramani, D. N.; Haley, P., Jr.; Lermusiaux, P. F. J.
2017-12-01
The coastal ocean is a prime example of multiscale nonlinear fluid dynamics. Ocean fields in such regions are complex and intermittent with unstationary heterogeneous statistics. Due to the limited measurements, there are multiple sources of uncertainties, including the initial conditions, boundary conditions, forcing, parameters, and even the model parameterizations and equations themselves. For efficient and rigorous quantification and prediction of these uncertainities, the stochastic Dynamically Orthogonal (DO) PDEs for a primitive equation ocean modeling system with a nonlinear free-surface are derived and numerical schemes for their space-time integration are obtained. Detailed numerical studies with idealized-to-realistic regional ocean dynamics are completed. These include consistency checks for the numerical schemes and comparisons with ensemble realizations. As an illustrative example, we simulate the 4-d multiscale uncertainty in the Middle Atlantic/New York Bight region during the months of Jan to Mar 2017. To provide intitial conditions for the uncertainty subspace, uncertainties in the region were objectively analyzed using historical data. The DO primitive equations were subsequently integrated in space and time. The probability distribution function (pdf) of the ocean fields is compared to in-situ, remote sensing, and opportunity data collected during the coincident POSYDON experiment. Results show that our probabilistic predictions had skill and are 3- to 4- orders of magnitude faster than classic ensemble schemes.
Stochastic differential equations for quantum dynamics of spin-boson networks
International Nuclear Information System (INIS)
Mandt, Stephan; Sadri, Darius; Houck, Andrew A; Türeci, Hakan E
2015-01-01
A popular approach in quantum optics is to map a master equation to a stochastic differential equation, where quantum effects manifest themselves through noise terms. We generalize this approach based on the positive-P representation to systems involving spin, in particular networks or lattices of interacting spins and bosons. We test our approach on a driven dimer of spins and photons, compare it to the master equation, and predict a novel dynamic phase transition in this system. Our numerical approach has scaling advantages over existing methods, but typically requires regularization in terms of drive and dissipation. (paper)
Energy Technology Data Exchange (ETDEWEB)
Chorošajev, Vladimir [Department of Theoretical Physics, Faculty of Physics, Vilnius University, Sauletekio 9-III, 10222 Vilnius (Lithuania); Gelzinis, Andrius; Valkunas, Leonas [Department of Theoretical Physics, Faculty of Physics, Vilnius University, Sauletekio 9-III, 10222 Vilnius (Lithuania); Department of Molecular Compound Physics, Center for Physical Sciences and Technology, Sauletekio 3, 10222 Vilnius (Lithuania); Abramavicius, Darius, E-mail: darius.abramavicius@ff.vu.lt [Department of Theoretical Physics, Faculty of Physics, Vilnius University, Sauletekio 9-III, 10222 Vilnius (Lithuania)
2016-12-20
Highlights: • The Davydov ansatze can be used for finite temperature simulations with an extension. • The accuracy is high if the system is strongly coupled to the environmental phonons. • The approach can simulate time-resolved fluorescence spectra. - Abstract: 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.
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...
DEFF Research Database (Denmark)
Huang, Lina; Zhang, Zhe; Andersen, Michael A. E.
2014-01-01
In radiator thermostat applications, DEAP (Dielectric Electro Active Polymer) actuator tends to be a good candidate to replace the conventional self-actuating or step motor based actuator due to its intrinsic advantages. The capacitive property and high voltage (HV) driving demand of DEAP actuator...
Stabilizing simulations of complex stochastic representations for quantum dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Perret, C; Petersen, W P, E-mail: wpp@math.ethz.ch [Seminar for Applied Mathematics, ETH, Zurich (Switzerland)
2011-03-04
Path integral representations of quantum dynamics can often be formulated as stochastic differential equations (SDEs). In a series of papers, Corney and Drummond (2004 Phys. Rev. Lett. 93 260401), Deuar and Drummond (2001 Comput. Phys. Commun. 142 442-5), Drummond and Gardnier (1980 J. Phys. A: Math. Gen. 13 2353-68), Gardiner and Zoller (2004 Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer Series in Synergetics) 3rd edn (Berlin: Springer)) and Gilchrist et al (1997 Phys. Rev. A 55 3014-32) and their collaborators have derived SDEs from coherent states representations for density matrices. Computationally, these SDEs are attractive because they seem simple to simulate. They can be quite unstable, however. In this paper, we consider some of the instabilities and propose a few remedies. Particularly, because the variances of the simulated paths typically grow exponentially, the processes become de-localized in relatively short times. Hence, the issues of boundary conditions and stable integration methods become important. We use the Bose-Einstein Hamiltonian as an example. Our results reveal that it is possible to significantly extend integration times and show the periodic structure of certain functionals.
Renormalization group equations in the stochastic quantization scheme
International Nuclear Information System (INIS)
Pugnetti, S.
1987-01-01
We show that there exists a remarkable link between the stochastic quantization and the theory of critical phenomena and dynamical statistical systems. In the stochastic quantization of a field theory, the stochastic Green functions coverge to the quantum ones when the frictious time goes to infinity. We therefore use the typical techniques of the Renormalization Group equations developed in the framework of critical phenomena to discuss some features of the convergence of the stochastic theory. We are also able, in this way, to compute some dynamical critical exponents and give new numerical valuations for them. (orig.)
Design and Modelling of Thermostatically Controlled Loads as Frequency Controlled Reserve
DEFF Research Database (Denmark)
Xu, Zhao; Østergaard, Jacob; Togeby, Mikael
2007-01-01
Using demand as frequency controlled reserve (DFR) is beneficial to power systems in many aspects. To study the impacts of this technology on power system operation, control logics and simulation models of relevant loads should be carefully developed. Two advanced control logics for using demand...... frequency, is developed. The developed simulation model is able to represent a variety of aggregated thermostatically controlled loads, such as heaters or refrigerators. Uncertainties including customer behaviours and ambient temperature variation are also modelled. Preliminary simulation results...
Theory on the Coupled Stochastic Dynamics of Transcription and Splice-Site Recognition
Murugan, Rajamanickam; Kreiman, Gabriel
2012-01-01
Eukaryotic genes are typically split into exons that need to be spliced together to form the mature mRNA. The splicing process depends on the dynamics and interactions among transcription by the RNA polymerase II complex (RNAPII) and the spliceosomal complex consisting of multiple small nuclear ribonucleo proteins (snRNPs). Here we propose a biophysically plausible initial theory of splicing that aims to explain the effects of the stochastic dynamics of snRNPs on the splicing patterns of eukaryotic genes. We consider two different ways to model the dynamics of snRNPs: pure three-dimensional diffusion and a combination of three- and one-dimensional diffusion along the emerging pre-mRNA. Our theoretical analysis shows that there exists an optimum position of the splice sites on the growing pre-mRNA at which the time required for snRNPs to find the 5′ donor site is minimized. The minimization of the overall search time is achieved mainly via the increase in non-specific interactions between the snRNPs and the growing pre-mRNA. The theory further predicts that there exists an optimum transcript length that maximizes the probabilities for exons to interact with the snRNPs. We evaluate these theoretical predictions by considering human and mouse exon microarray data as well as RNAseq data from multiple different tissues. We observe that there is a broad optimum position of splice sites on the growing pre-mRNA and an optimum transcript length, which are roughly consistent with the theoretical predictions. The theoretical and experimental analyses suggest that there is a strong interaction between the dynamics of RNAPII and the stochastic nature of snRNP search for 5′ donor splicing sites. PMID:23133354
Theory on the coupled stochastic dynamics of transcription and splice-site recognition.
Directory of Open Access Journals (Sweden)
Rajamanickam Murugan
Full Text Available Eukaryotic genes are typically split into exons that need to be spliced together to form the mature mRNA. The splicing process depends on the dynamics and interactions among transcription by the RNA polymerase II complex (RNAPII and the spliceosomal complex consisting of multiple small nuclear ribonucleo proteins (snRNPs. Here we propose a biophysically plausible initial theory of splicing that aims to explain the effects of the stochastic dynamics of snRNPs on the splicing patterns of eukaryotic genes. We consider two different ways to model the dynamics of snRNPs: pure three-dimensional diffusion and a combination of three- and one-dimensional diffusion along the emerging pre-mRNA. Our theoretical analysis shows that there exists an optimum position of the splice sites on the growing pre-mRNA at which the time required for snRNPs to find the 5' donor site is minimized. The minimization of the overall search time is achieved mainly via the increase in non-specific interactions between the snRNPs and the growing pre-mRNA. The theory further predicts that there exists an optimum transcript length that maximizes the probabilities for exons to interact with the snRNPs. We evaluate these theoretical predictions by considering human and mouse exon microarray data as well as RNAseq data from multiple different tissues. We observe that there is a broad optimum position of splice sites on the growing pre-mRNA and an optimum transcript length, which are roughly consistent with the theoretical predictions. The theoretical and experimental analyses suggest that there is a strong interaction between the dynamics of RNAPII and the stochastic nature of snRNP search for 5' donor splicing sites.
A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds
Hagos, Samson; Feng, Zhe; Plant, Robert S.; Houze, Robert A.; Xiao, Heng
2018-02-01
A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii) the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. In addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.
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...
Inverse stochastic-dynamic models for high-resolution Greenland ice core records
DEFF Research Database (Denmark)
Boers, Niklas; Chekroun, Mickael D.; Liu, Honghu
2017-01-01
as statistical properties such as probability density functions, waiting times and power spectra, with no need for any external forcing. The crucial ingredients for capturing these properties are (i) high-resolution training data, (ii) cubic drift terms, (iii) nonlinear coupling terms between the 18O and dust......Proxy records from Greenland ice cores have been studied for several decades, yet many open questions remain regarding the climate variability encoded therein. Here, we use a Bayesian framework for inferring inverse, stochastic-dynamic models from 18O and dust records of unprecedented, subdecadal...
Directory of Open Access Journals (Sweden)
Rathinasamy Sakthivel
2018-01-01
Full Text Available The problem of robust nonfragile synchronization is investigated in this paper for a class of complex dynamical networks subject to semi-Markov jumping outer coupling, time-varying coupling delay, randomly occurring gain variation, and stochastic noise over a desired finite-time interval. In particular, the network topology is assumed to follow a semi-Markov process such that it may switch from one to another at different instants. In this paper, the random gain variation is represented by a stochastic variable that is assumed to satisfy the Bernoulli distribution with white sequences. Based on these hypotheses and the Lyapunov-Krasovskii stability theory, a new finite-time stochastic synchronization criterion is established for the considered network in terms of linear matrix inequalities. Moreover, the control design parameters that guarantee the required criterion are computed by solving a set of linear matrix inequality constraints. An illustrative example is finally given to show the effectiveness and advantages of the developed analytical results.
GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations II: Dynamics and stochastic simulations
Antoine, Xavier; Duboscq, Romain
2015-08-01
GPELab is a free Matlab toolbox for modeling and numerically solving large classes of systems of Gross-Pitaevskii equations that arise in the physics of Bose-Einstein condensates. The aim of this second paper, which follows (Antoine and Duboscq, 2014), is to first present the various pseudospectral schemes available in GPELab for computing the deterministic and stochastic nonlinear dynamics of Gross-Pitaevskii equations (Antoine, et al., 2013). Next, the corresponding GPELab functions are explained in detail. Finally, some numerical examples are provided to show how the code works for the complex dynamics of BEC problems.
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 social contagions (σ >1 ).
Development of modular thermostatic vapour-cooled current leads for cryogenic service
International Nuclear Information System (INIS)
Blessing, H.; Lebrun, P.
1983-01-01
Cryogenic current leads cooled by helium vapour have been developed, built and tested. Their construction, based on standard electrolytic copper braids crimped at the ends, is such as to provide flexible cold terminations and make possible a modular design. The warm terminations combine electrical insulation, leak-tightness and integrated thermostatic valves controlling lead temperature and avoiding thermal run-away or ice build-up. After giving a detailed description of their construction, this report presents results of performance and reliability tests made on prototype units. (orig.)
Homogenization of the stochastic Navier–Stokes equation with a stochastic slip boundary condition
Bessaih, Hakima
2015-11-02
The two-dimensional Navier–Stokes equation in a perforated domain with a dynamical slip boundary condition is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the holes. We consider a scaling (ᵋ for the viscosity and 1 for the density) that will lead to a time-dependent limit problem. However, the noncritical scaling (ᵋ, β > 1) is considered in front of the nonlinear term. The homogenized system in the limit is obtained as a Darcy’s law with memory with two permeabilities and an extra term that is due to the stochastic perturbation on the boundary of the holes. The nonhomogeneity on the boundary contains a stochastic part that yields in the limit an additional term in the Darcy’s law. We use the two-scale convergence method after extending the solution with 0 inside the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. Due to the stochastic integral, the pressure that appears in the variational formulation does not have enough regularity in time. This fact made us rely only on the variational formulation for the passage to the limit on the solution. We obtain a variational formulation for the limit that is solution of a Stokes system with two pressures. This two-scale limit gives rise to three cell problems, two of them give the permeabilities while the third one gives an extra term in the Darcy’s law due to the stochastic perturbation on the boundary of the holes.
Achieving control and synchronization merely through a stochastically adaptive feedback coupling
Lin, Wei; Chen, Xin; Zhou, Shijie
2017-07-01
Techniques of deterministically adaptive feedback couplings have been successfully and extensively applied to realize control or/and synchronization in chaotic dynamical systems and even in complex dynamical networks. In this article, a technique of stochastically adaptive feedback coupling is novelly proposed to not only realize control in chaotic dynamical systems but also achieve synchronization in unidirectionally coupled systems. Compared with those deterministically adaptive couplings, the proposed stochastic technique interestingly shows some advantages from a physical viewpoint of time and energy consumptions. More significantly, the usefulness of the proposed stochastic technique is analytically validated by the theory of stochastic processes. It is anticipated that the proposed stochastic technique will be widely used in achieving system control and network synchronization.
Joost van Hoof; P.W.J.J. van der Wielen; E. van der Blom; O.W.W. Nuijten; L. Hornstra
2014-01-01
Legislation in the Netherlands requires routine analysis of drinking water samples for cultivable Legionella species from high-priority installations. A field study was conducted to investigate the presence of Legionella species in thermostatic shower mixer taps. Water samples and the interior of
Stochastic lattice model of synaptic membrane protein domains.
Li, Yiwei; Kahraman, Osman; Haselwandter, Christoph A
2017-05-01
Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.
Stochastic ferromagnetism analysis and numerics
Brzezniak, Zdzislaw; Neklyudov, Mikhail; Prohl, Andreas
2013-01-01
This monograph examines magnetization dynamics at elevated temperatures which can be described by the stochastic Landau-Lifshitz-Gilbert equation (SLLG). Comparative computational studies with the stochastic model are included. Constructive tools such as e.g. finite element methods are used to derive the theoretical results, which are then used for computational studies.
Stochasticity and transport in Hamiltonian systems
International Nuclear Information System (INIS)
MacKay, R.S.; Meiss, J.D.; Percival, I.C.
1983-08-01
The theory of transport in nonlinear dynamics is developed in terms of leaky barriers which remain when invariant tori are destroyed. We describe the organization of stochastic motion by these barriers and give an explanation of long-time correlations in the stochastic regime
Directory of Open Access Journals (Sweden)
Junhai Ma
2017-01-01
Full Text Available Apart from the price fluctuation, the retailers’ service level becomes another key factor that affects the market demand. This paper depicts a modified price and demand game model based on the stochastic demand and the retailer’s service level which influences the market demand decided by customers’ preference, while the market demand is stochastic in this model. We explore how the price adjustment speed affects the stability of the supply chain system with respect to service level and stochastic demand. The dynamic behavior of the system is researched by simulation and the stability domain and the bifurcation phenomenon are shown clearly. The largest Lyapunov exponent and the chaotic attractor are also given to confirm the chaotic characteristic of the system. The simulation results indicate that relatively small price adjustment speed may maintain the system at stable state. With the price adjustment speed gradually increasing, the price system gets unstable and finally becomes chaotic. This chaotic phenomenon will perturb the product market and this phenomenon should be controlled to keep the system stay in the stable region. So the chaos control is done and the chaos can be controlled completely. The conclusion makes significant contribution to the system referring to the price fluctuation based on the service level and stochastic demand.
Energy Technology Data Exchange (ETDEWEB)
Anon.
2008-04-15
Fifty percent of all installed thermostat valves are assumed to be lacking in energy efficiency, according to the ''Optimus'' research report. Industry has reacted to this by developing a ThermostatCheck, which can be accessed in the internet by builder-owners and fitters. (orig.)
Tuckwell, H C; Toubiana, L; Vibert, J F
2000-05-01
We extend a previous dynamical viral network model to include stochastic effects. The dynamical equations for the viral and immune effector densities within a host population of size n are bilinear, and the noise is white, additive, and Gaussian. The individuals are connected with an n x n transmission matrix, with terms which decay exponentially with distance. In a single individual, for the range of noise parameters considered, it is found that increasing the amplitude of the noise tends to decrease the maximum mean virion level, and slightly accelerate its attainment. Two different spatial dynamical models are employed to ascertain the effects of environmental stochasticity on viral spread. In the first model transmission is unrestricted and there is no threshold within individuals. This model has the advantage that it can be analyzed using a Fokker-Planck approach. The noise is found both to synchronize and uniformize the trajectories of the viral levels across the population of infected individuals, and thus to promote the epidemic spread of the virus. Quantitative measures of the speed of spread and overall amplitude of the epidemic are obtained as functions of the noise and virulence parameters. The mean amplitude increases steadily without threshold effects for a fixed value of the virulence as the noise amplitude sigma is increased, and there is no evidence of a stochastic resonance. However, the speed of transmission, both with respect to its mean and variance, undergoes rapid increases as sigma changes by relatively small amounts. In the second, more realistic, model, there is a threshold for infection and an upper limit to the transmission rate. There may be no spread of infection at all in the absence of noise. With increasing noise level and a low threshold, the mean maximum virion level grows quickly and shows a broad-based stochastic resonance effect. When the threshold within individuals is increased, the mean population virion level increases only
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.
A stochastic MILP energy planning model incorporating power market dynamics
International Nuclear Information System (INIS)
Koltsaklis, Nikolaos E.; Nazos, Konstantinos
2017-01-01
Highlights: •Stochastic MILP model for the optimal energy planning of a power system. •Power market dynamics (offers/bids) are incorporated in the proposed model. •Monte Carlo method for capturing the uncertainty of some key parameters. •Analytical supply cost composition per power producer and activity. •Clean dark and spark spreads are calculated for each power unit. -- Abstract: This paper presents an optimization-based methodological approach to address the problem of the optimal planning of a power system at an annual level in competitive and uncertain power markets. More specifically, a stochastic mixed integer linear programming model (MILP) has been developed, combining advanced optimization techniques with Monte Carlo method in order to deal with uncertainty issues. The main focus of the proposed framework is the dynamic formulation of the strategy followed by all market participants in volatile market conditions, as well as detailed economic assessment of the power system’s operation. The applicability of the proposed approach has been tested on a real case study of the interconnected Greek power system, quantifying in detail all the relevant technical and economic aspects of the system’s operation. The proposed work identifies in the form of probability distributions the optimal power generation mix, electricity trade at a regional level, carbon footprint, as well as detailed total supply cost composition, according to the assumed market structure. The paper demonstrates that the proposed optimization approach is able to provide important insights into the appropriate energy strategies designed by market participants, as well as on the strategic long-term decisions to be made by investors and/or policy makers at a national and/or regional level, underscoring potential risks and providing appropriate price signals on critical energy projects under real market operating conditions.
International Nuclear Information System (INIS)
Zhu, Zhiwen; Zhang, Qingxin; Xu, Jia
2014-01-01
Stochastic bifurcation and fractal and chaos control of a giant magnetostrictive film–shape memory alloy (GMF–SMA) composite cantilever plate subjected to in-plane harmonic and stochastic excitation were studied. Van der Pol items were improved to interpret the hysteretic phenomena of both GMF and SMA, and the nonlinear dynamic model of a GMF–SMA composite cantilever plate subjected to in-plane harmonic and stochastic excitation was developed. The probability density function of the dynamic response of the system was obtained, and the conditions of stochastic Hopf bifurcation were analyzed. The conditions of noise-induced chaotic response were obtained in the stochastic Melnikov integral method, and the fractal boundary of the safe basin of the system was provided. Finally, the chaos control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that stochastic Hopf bifurcation and chaos appear in the parameter variation process. The boundary of the safe basin of the system has fractal characteristics, and its area decreases when the noise intensifies. The system reliability was improved through stochastic optimal control, and the safe basin area of the system increased
Stochastic Effects; Application in Nuclear Physics
International Nuclear Information System (INIS)
Mazonka, O.
2000-04-01
Stochastic effects in nuclear physics refer to the study of the dynamics of nuclear systems evolving under stochastic equations of motion. In this dissertation we restrict our attention to classical scattering models. We begin with introduction of the model of nuclear dynamics and deterministic equations of evolution. We apply a Langevin approach - an additional property of the model, which reflect the statistical nature of low energy nuclear behaviour. We than concentrate our attention on the problem of calculating tails of distribution functions, which actually is the problem of calculating probabilities of rare outcomes. Two general strategies are proposed. Result and discussion follow. Finally in the appendix we consider stochastic effects in nonequilibrium systems. A few exactly solvable models are presented. For one model we show explicitly that stochastic behaviour in a microscopic description can lead to ordered collective effects on the macroscopic scale. Two others are solved to confirm the predictions of the fluctuation theorem. (author)
Hirakawa, Teruo; Suzuki, Teppei; Bowler, David R; Miyazaki, Tsuyoshi
2017-10-11
We discuss the development and implementation of a constant temperature (NVT) molecular dynamics scheme that combines the Nosé-Hoover chain thermostat with the extended Lagrangian Born-Oppenheimer molecular dynamics (BOMD) scheme, using a linear scaling density functional theory (DFT) approach. An integration scheme for this canonical-ensemble extended Lagrangian BOMD is developed and discussed in the context of the Liouville operator formulation. Linear scaling DFT canonical-ensemble extended Lagrangian BOMD simulations are tested on bulk silicon and silicon carbide systems to evaluate our integration scheme. The results show that the conserved quantity remains stable with no systematic drift even in the presence of the thermostat.
Stochasticity in the Josephson map
International Nuclear Information System (INIS)
Nomura, Y.; Ichikawa, Y.H.; Filippov, A.T.
1996-04-01
The Josephson map describes nonlinear dynamics of systems characterized by standard map with the uniform external bias superposed. The intricate structures of the phase space portrait of the Josephson map are examined on the basis of the tangent map associated with the Josephson map. Numerical observation of the stochastic diffusion in the Josephson map is examined in comparison with the renormalized diffusion coefficient calculated by the method of characteristic function. The global stochasticity of the Josephson map occurs at the values of far smaller stochastic parameter than the case of the standard map. (author)
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
Stochasticity and determinism in models of hematopoiesis.
Kimmel, Marek
2014-01-01
This chapter represents a novel view of modeling in hematopoiesis, synthesizing both deterministic and stochastic approaches. Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis. New types of models are on the horizon. These models attempt to account for distributed environments such as hematopoietic niches and their impact on dynamics. Mixed effects of such structures and chance events are largely unknown and constitute both a challenge and promise for modeling. Our discussion is presented under the separate headings of deterministic and stochastic modeling; however, the connections between both are frequently mentioned. Four case studies are included to elucidate important examples. We also include a primer of deterministic and stochastic dynamics for the reader's use.
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.
The stochastic goodwill problem
Marinelli, Carlo
2003-01-01
Stochastic control problems related to optimal advertising under uncertainty are considered. In particular, we determine the optimal strategies for the problem of maximizing the utility of goodwill at launch time and minimizing the disutility of a stream of advertising costs that extends until the launch time for some classes of stochastic perturbations of the classical Nerlove-Arrow dynamics. We also consider some generalizations such as problems with constrained budget and with discretionar...
Stochastic Dynamics of a Time-Delayed Ecosystem Driven by Poisson White Noise Excitation
Directory of Open Access Journals (Sweden)
Wantao Jia
2018-02-01
Full Text Available We investigate the stochastic dynamics of a prey-predator type ecosystem with time delay and the discrete random environmental fluctuations. In this model, the delay effect is represented by a time delay parameter and the effect of the environmental randomness is modeled as Poisson white noise. The stochastic averaging method and the perturbation method are applied to calculate the approximate stationary probability density functions for both predator and prey populations. The influences of system parameters and the Poisson white noises are investigated in detail based on the approximate stationary probability density functions. It is found that, increasing time delay parameter as well as the mean arrival rate and the variance of the amplitude of the Poisson white noise will enhance the fluctuations of the prey and predator population. While the larger value of self-competition parameter will reduce the fluctuation of the system. Furthermore, the results from Monte Carlo simulation are also obtained to show the effectiveness of the results from averaging method.
Raso , L.; Malaterre , P.O.; Bader , J.C.
2017-01-01
International audience; This article presents an innovative streamflow process model for use in reservoir operational rule design in stochastic dual dynamic programming (SDDP). Model features, which can be applied independently, are (1) a multiplicative process model for the forward phase and its linearized version for the backward phase; and (2) a nonuniform time-step length that is inversely proportional to seasonal variability. The advantages are (1) guaranteeing positive streamflow values...
Exact solutions to chaotic and stochastic systems
González, J. A.; Reyes, L. I.; Guerrero, L. E.
2001-03-01
We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems.
Sharma, Pankaj; Jain, Ajai
2014-12-01
Stochastic dynamic job shop scheduling problem with consideration of sequence-dependent setup times are among the most difficult classes of scheduling problems. This paper assesses the performance of nine dispatching rules in such shop from makespan, mean flow time, maximum flow time, mean tardiness, maximum tardiness, number of tardy jobs, total setups and mean setup time performance measures viewpoint. A discrete event simulation model of a stochastic dynamic job shop manufacturing system is developed for investigation purpose. Nine dispatching rules identified from literature are incorporated in the simulation model. The simulation experiments are conducted under due date tightness factor of 3, shop utilization percentage of 90% and setup times less than processing times. Results indicate that shortest setup time (SIMSET) rule provides the best performance for mean flow time and number of tardy jobs measures. The job with similar setup and modified earliest due date (JMEDD) rule provides the best performance for makespan, maximum flow time, mean tardiness, maximum tardiness, total setups and mean setup time measures.
Stochastic Reachability Analysis of Hybrid Systems
Bujorianu, Luminita Manuela
2012-01-01
Stochastic reachability analysis (SRA) is a method of analyzing the behavior of control systems which mix discrete and continuous dynamics. For probabilistic discrete systems it has been shown to be a practical verification method but for stochastic hybrid systems it can be rather more. As a verification technique SRA can assess the safety and performance of, for example, autonomous systems, robot and aircraft path planning and multi-agent coordination but it can also be used for the adaptive control of such systems. Stochastic Reachability Analysis of Hybrid Systems is a self-contained and accessible introduction to this novel topic in the analysis and development of stochastic hybrid systems. Beginning with the relevant aspects of Markov models and introducing stochastic hybrid systems, the book then moves on to coverage of reachability analysis for stochastic hybrid systems. Following this build up, the core of the text first formally defines the concept of reachability in the stochastic framework and then...
The sequence relay selection strategy based on stochastic dynamic programming
Zhu, Rui; Chen, Xihao; Huang, Yangchao
2017-07-01
Relay-assisted (RA) network with relay node selection is a kind of effective method to improve the channel capacity and convergence performance. However, most of the existing researches about the relay selection did not consider the statically channel state information and the selection cost. This shortage limited the performance and application of RA network in practical scenarios. In order to overcome this drawback, a sequence relay selection strategy (SRSS) was proposed. And the performance upper bound of SRSS was also analyzed in this paper. Furthermore, in order to make SRSS more practical, a novel threshold determination algorithm based on the stochastic dynamic program (SDP) was given to work with SRSS. Numerical results are also presented to exhibit the performance of SRSS with SDP.
Coron, Camille
2016-01-01
We are interested in the long-time behavior of a diploid population with sexual reproduction and randomly varying population size, characterized by its genotype composition at one bi-allelic locus. The population is modeled by a 3-dimensional birth-and-death process with competition, weak cooperation and Mendelian reproduction. This stochastic process is indexed by a scaling parameter K that goes to infinity, following a large population assumption. When the individual birth and natural death rates are of order K, the sequence of stochastic processes indexed by K converges toward a new slow-fast dynamics with variable population size. We indeed prove the convergence toward 0 of a fast variable giving the deviation of the population from quasi Hardy-Weinberg equilibrium, while the sequence of slow variables giving the respective numbers of occurrences of each allele converges toward a 2-dimensional diffusion process that reaches (0,0) almost surely in finite time. The population size and the proportion of a given allele converge toward a Wright-Fisher diffusion with stochastically varying population size and diploid selection. We insist on differences between haploid and diploid populations due to population size stochastic variability. Using a non trivial change of variables, we study the absorption of this diffusion and its long time behavior conditioned on non-extinction. In particular we prove that this diffusion starting from any non-trivial state and conditioned on not hitting (0,0) admits a unique quasi-stationary distribution. We give numerical approximations of this quasi-stationary behavior in three biologically relevant cases: neutrality, overdominance, and separate niches.
A Stochastic Fractional Dynamics Model of Rainfall Statistics
Kundu, Prasun; Travis, James
2013-04-01
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 designed to faithfully reflect the scale dependence and 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. The main restriction is the assumption that the statistics of the precipitation field is spatially homogeneous and isotropic and stationary in time. 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 the radar data. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well without any further adjustment. Some data sets containing periods of non-stationary behavior that involves occasional anomalously correlated rain events, present a challenge for the model.
Burger, Eric M.; Moura, Scott J.
2015-01-01
A fundamental requirement of the electric power system is to maintain a continuous and instantaneous balance between generation and load. The intermittency and uncertainty introduced by renewable energy generation requires the expansion of ancillary power system services to maintain such a balance. In this paper, we examine the potential of thermostatically controlled loads (TCLs), such as refrigerators and electric water heaters, to provide generation following services in real-time energy m...
Inverse stochastic-dynamic models for high-resolution Greenland ice core records
Boers, Niklas; Chekroun, Mickael D.; Liu, Honghu; Kondrashov, Dmitri; Rousseau, Denis-Didier; Svensson, Anders; Bigler, Matthias; Ghil, Michael
2017-12-01
Proxy records from Greenland ice cores have been studied for several decades, yet many open questions remain regarding the climate variability encoded therein. Here, we use a Bayesian framework for inferring inverse, stochastic-dynamic models from δ18O and dust records of unprecedented, subdecadal temporal resolution. The records stem from the North Greenland Ice Core Project (NGRIP), and we focus on the time interval 59-22 ka b2k. Our model reproduces the dynamical characteristics of both the δ18O and dust proxy records, including the millennial-scale Dansgaard-Oeschger variability, as well as statistical properties such as probability density functions, waiting times and power spectra, with no need for any external forcing. The crucial ingredients for capturing these properties are (i) high-resolution training data, (ii) cubic drift terms, (iii) nonlinear coupling terms between the δ18O and dust time series, and (iv) non-Markovian contributions that represent short-term memory effects.
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.
Directory of Open Access Journals (Sweden)
A. Elhassanein
2014-06-01
Full Text Available This paper introduced a stochastic discretized version of the modified Leslie-Gower predator-prey model with Michaelis-Menten type prey harvesting. The dynamical behavior of the proposed model was investigated. The existence and stability of the equilibria of the skeleton were studied. Numerical simulations were employed to show the model's complex dynamics by means of the largest Lyapunov exponents, bifurcations, time series diagrams and phase portraits. The effects of noise intensity on its dynamics and the intermittency phenomenon were also discussed via simulation.
International Nuclear Information System (INIS)
Sinitsyn, Nikolai A.; Kundu, Soumya; Backhaus, Scott
2013-01-01
Highlights: ► Algorithms to produce useful load response from a heterogeneous group of TCLs. ► Generation of sharp power pulses without initiating any unwanted oscillation. ► Open-loop methods, not requiring any detailed system modeling. ► One-way, utility-to-consumer, communication. ► Potential use in secondary frequency regulation, generation-load balancing, etc. - Abstract: We explore methods to use thermostatically controlled loads (TCLs), such as water heaters and air conditioners, to provide ancillary services by assisting in balancing generation and load. We show that by adding simple imbedded instructions and a small amount of memory to temperature controllers of TCLs, it is possible to design open-loop control algorithms capable of creating short-term pulses of demand response without unwanted power oscillations associated with temporary synchronization of the TCL dynamics. By moving a small amount of intelligence to each of the end point TCL devices, we are able to leverage our knowledge of the time dynamics of TCLs to shape the demand response pulses for different power system applications. A significant benefit of our open-loop method is the reduction from two-way to one-way broadcast communication which also eliminates many basic consumer privacy issues. In this work, we focus on developing the algorithms to generate a set of fundamental pulse shapes that can subsequently be used to create demand response with arbitrary profiles. Demand response control methods, such as the one developed here, open the door to fast, nonperturbative control of large aggregations of TCLs
Stochastic fractional differential equations: Modeling, method and analysis
International Nuclear Information System (INIS)
Pedjeu, Jean-C.; Ladde, Gangaram S.
2012-01-01
By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model described by a system of multi-time scale stochastic differential equations is formulated. The classical Picard–Lindelöf successive approximations scheme is applied to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this leads to the problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations of Itô–Doob type. Finally, to illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are outlined.
Some Remarks on Stochastic Versions of the Ramsey Growth Model
Czech Academy of Sciences Publication Activity Database
Sladký, Karel
2012-01-01
Roč. 19, č. 29 (2012), s. 139-152 ISSN 1212-074X R&D Projects: GA ČR GAP402/10/1610; GA ČR GAP402/10/0956; GA ČR GAP402/11/0150 Institutional support: RVO:67985556 Keywords : Economic dynamics * Ramsey growth model with disturbance * stochastic dynamic programming * multistage stochastic programs Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2013/E/sladky-some remarks on stochastic versions of the ramsey growth model.pdf
Modeling and Properties of Nonlinear Stochastic Dynamical System of Continuous Culture
Wang, Lei; Feng, Enmin; Ye, Jianxiong; Xiu, Zhilong
The stochastic counterpart to the deterministic description of continuous fermentation with ordinary differential equation is investigated in the process of glycerol bio-dissimilation to 1,3-propanediol by Klebsiella pneumoniae. We briefly discuss the continuous fermentation process driven by three-dimensional Brownian motion and Lipschitz coefficients, which is suitable for the factual fermentation. Subsequently, we study the existence and uniqueness of solutions for the stochastic system as well as the boundedness of the Two-order Moment and the Markov property of the solution. Finally stochastic simulation is carried out under the Stochastic Euler-Maruyama method.
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.
Stochastic resonance and coherence resonance in groundwater-dependent plant ecosystems.
Borgogno, Fabio; D'Odorico, Paolo; Laio, Francesco; Ridolfi, Luca
2012-01-21
Several studies have shown that non-linear deterministic dynamical systems forced by external random components can give rise to unexpectedly regular temporal behaviors. Stochastic resonance and coherence resonance, the two best known processes of this type, have been studied in a number of physical and chemical systems. Here, we explore their possible occurrence in the dynamics of groundwater-dependent plant ecosystems. To this end, we develop two eco-hydrological models, which allow us to demonstrate that stochastic and coherence resonance may emerge in the dynamics of phreatophyte vegetation, depending on their deterministic properties and the intensity of external stochastic drivers. Copyright © 2011 Elsevier Ltd. All rights reserved.
DEFF Research Database (Denmark)
Lakshmanan, Venkatachalam; Marinelli, Mattia; Kosek, Anna M.
2017-01-01
This paper investigates the usability of thermostat controlled domestic appliances for load shift in LV distribution grids. The proposed method uses refrigerators for the demonstration of adaptive load prediction to estimate its flexibility and perform scheduling based on load threshold limit. Tw...
The intrinsic stochasticity of near-integrable Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Krlin, L [Ceskoslovenska Akademie Ved, Prague (Czechoslovakia). Ustav Fyziky Plazmatu
1989-09-01
Under certain conditions, the dynamics of near-integrable Hamiltonian systems appears to be stochastic. This stochasticity (intrinsic stochasticity, or deterministic chaos) is closely related to the Kolmogorov-Arnold-Moser (KAM) theorem of the stability of near-integrable multiperiodic Hamiltonian systems. The effect of the intrinsic stochasticity attracts still growing attention both in theory and in various applications in contemporary physics. The paper discusses the relation of the intrinsic stochasticity to the modern ergodic theory and to the KAM theorem, and describes some numerical experiments on related astrophysical and high-temperature plasma problems. Some open questions are mentioned in conclusion. (author).
Thermal response of a Fermi-Pasta-Ulam chain with Andersen thermostats
D'Ambrosio, Federico; Baiesi, Marco
2017-11-01
The linear response to temperature variations is well characterised for equilibrium systems but a similar theory is not available, for example, for inertial heat conducting systems, whose paradigm is the Fermi-Pasta-Ulam (FPU) model driven by two different boundary temperatures. For models of inertial systems out of equilibrium, including relaxing systems, we show that Andersen thermostats are a natural tool for studying the thermal response. We derive a fluctuation-response relation that allows to predict thermal expansion coefficients or the heat capacitance in nonequilibrium regimes. Simulations of the FPU chain of oscillators suggest that estimates of susceptibilities obtained with our relation are better than those obtained via a small perturbation.
Stochastic volatility and stochastic leverage
DEFF Research Database (Denmark)
Veraart, Almut; Veraart, Luitgard A. M.
This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic...... treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility...... models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new...
Stochastic Wake Modelling Based on POD Analysis
Directory of Open Access Journals (Sweden)
David Bastine
2018-03-01
Full Text Available In this work, large eddy simulation data is analysed to investigate a new stochastic modeling approach for the wake of a wind turbine. The data is generated by the large eddy simulation (LES model PALM combined with an actuator disk with rotation representing the turbine. After applying a proper orthogonal decomposition (POD, three different stochastic models for the weighting coefficients of the POD modes are deduced resulting in three different wake models. Their performance is investigated mainly on the basis of aeroelastic simulations of a wind turbine in the wake. Three different load cases and their statistical characteristics are compared for the original LES, truncated PODs and the stochastic wake models including different numbers of POD modes. It is shown that approximately six POD modes are enough to capture the load dynamics on large temporal scales. Modeling the weighting coefficients as independent stochastic processes leads to similar load characteristics as in the case of the truncated POD. To complete this simplified wake description, we show evidence that the small-scale dynamics can be captured by adding to our model a homogeneous turbulent field. In this way, we present a procedure to derive stochastic wake models from costly computational fluid dynamics (CFD calculations or elaborated experimental investigations. These numerically efficient models provide the added value of possible long-term studies. Depending on the aspects of interest, different minimalized models may be obtained.
International Nuclear Information System (INIS)
Tung Wenwen; Qi Yan; Gao, J.B.; Cao Yinhe; Billings, Lora
2005-01-01
In recent years it has been increasingly recognized that noise and determinism may have comparable but different influences on population dynamics. However, no simple analysis methods have been introduced into ecology which can readily characterize those impacts. In this paper, we study a population model with strong periodicity and both with and without noise. The noise-free model generates both quasi-periodic and chaotic dynamics for certain parameter values. Due to the strong periodicity, however, the generated chaotic dynamics have not been satisfactorily described. The dynamics becomes even more complicated when there is noise. Characterizing the chaotic and stochastic dynamics in this model thus represents a challenging problem. Here we show how the chaotic dynamics can be readily characterized by the direct dynamical test for deterministic chaos developed by [Gao JB, Zheng ZM. Europhys. Lett. 1994;25:485] and how the influence of noise on quasi-periodic motions can be characterized as asymmetric diffusions wandering along the quasi-periodic orbit. It is hoped that the introduced methods will be useful in studying other population models as well as population time series obtained both in field and laboratory experiments
Trip-oriented stochastic optimal energy management strategy for plug-in hybrid electric bus
International Nuclear Information System (INIS)
Du, Yongchang; Zhao, Yue; Wang, Qinpu; Zhang, Yuanbo; Xia, Huaicheng
2016-01-01
A trip-oriented stochastic optimal energy management strategy for plug-in hybrid electric bus is presented in this paper, which includes the offline stochastic dynamic programming part and the online implementation part performed by equivalent consumption minimization strategy. In the offline part, historical driving cycles of the fixed route are divided into segments according to the position of bus stops, and then a segment-based stochastic driving condition model based on Markov chain is built. With the segment-based stochastic model obtained, the control set for real-time implemented equivalent consumption minimization strategy can be achieved by solving the offline stochastic dynamic programming problem. Results of stochastic dynamic programming are converted into a 3-dimensional lookup table of parameters for online implemented equivalent consumption minimization strategy. The proposed strategy is verified by both simulation and hardware-in-loop test of real-world driving cycle on an urban bus route. Simulation results show that the proposed method outperforms both the well-tuned equivalent consumption minimization strategy and the rule-based strategy in terms of fuel economy, and even proved to be close to the optimal result obtained by dynamic programming. Furthermore, the practical application potential of the proposed control method was proved by hardware-in-loop test. - Highlights: • A stochastic problem was formed based on a stochastic segment-based driving condition model. • Offline stochastic dynamic programming was employed to solve the stochastic problem. • The instant power split decision was made by the online equivalent consumption minimization strategy. • Good performance in fuel economy of the proposed method was verified by simulation results. • Practical application potential of the proposed method was verified by the hardware-in-loop test results.
Sheng, Li; Wang, Zidong; Zou, Lei; Alsaadi, Fuad E
2017-10-01
In this paper, the event-based finite-horizon H ∞ state estimation problem is investigated for a class of discrete time-varying stochastic dynamical networks with state- and disturbance-dependent noises [also called (x,v) -dependent noises]. An event-triggered scheme is proposed to decrease the frequency of the data transmission between the sensors and the estimator, where the signal is transmitted only when certain conditions are satisfied. The purpose of the problem addressed is to design a time-varying state estimator in order to estimate the network states through available output measurements. By employing the completing-the-square technique and the stochastic analysis approach, sufficient conditions are established to ensure that the error dynamics of the state estimation satisfies a prescribed H ∞ performance constraint over a finite horizon. The desired estimator parameters can be designed via solving coupled backward recursive Riccati difference equations. Finally, a numerical example is exploited to demonstrate the effectiveness of the developed state estimation scheme.
Stochastic approach to equilibrium and nonequilibrium thermodynamics.
Tomé, Tânia; de Oliveira, Mário J
2015-04-01
We develop the stochastic approach to thermodynamics based on stochastic dynamics, which can be discrete (master equation) and continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of entropy itself and the second the definition of entropy production rate, which is non-negative and vanishes in thermodynamic equilibrium. Based on these assumptions, we study interacting systems with many degrees of freedom in equilibrium or out of thermodynamic equilibrium and how the macroscopic laws are derived from the stochastic dynamics. These studies include the quasiequilibrium processes; the convexity of the equilibrium surface; the monotonic time behavior of thermodynamic potentials, including entropy; the bilinear form of the entropy production rate; the Onsager coefficients and reciprocal relations; and the nonequilibrium steady states of chemical reactions.
On the stochastic approach to marine population dynamics
Directory of Open Access Journals (Sweden)
Eduardo Ferrandis
2007-03-01
Full Text Available The purpose of this article is to deepen and structure the statistical basis of marine population dynamics. The starting point is the correspondence between the concepts of mortality, survival and lifetime distribution. This is the kernel of the possibilities that survival analysis techniques offer to marine population dynamics. A rigorous definition of survival and mortality based on their properties and their probabilistic versions is briefly presented. Some well established models for lifetime distribution, which generalise the usual simple exponential distribution, might be used with their corresponding survivals and mortalities. A critical review of some published models is also made, including original models proposed in the way opened by Caddy (1991 and Sparholt (1990, which allow for a continuously decreasing natural mortality. Considering these elements, the pure death process dealt with in the literature is used as a theoretical basis for the evolution of a marine cohort. The elaboration of this process is based on Chiang´s study of the probability distribution of the life table (Chiang, 1960 and provides specific structured models for stock evolution as a Markovian process. These models may introduce new ideas in the line of thinking developed by Gudmundsson (1987 and Sampson (1990 in order to model the evolution of a marine cohort by stochastic processes. The suitable approximation of these processes by means of Gaussian processes may allow theoretical and computational multivariate Gaussian analysis to be applied to the probabilistic treatment of fisheries issues. As a consequence, the necessary catch equation appears as a stochastic integral with respect to the mentioned Markovian process of the stock. The solution of this equation is available when the mortalities are proportional, hence the use of the proportional hazards model (Cox, 1959. The assumption of these proportional mortalities leads naturally to the construction of a
DEFF Research Database (Denmark)
Ghoreishi, Maryam
2018-01-01
Many models within the field of optimal dynamic pricing and lot-sizing models for deteriorating items assume everything is deterministic and develop a differential equation as the core of analysis. Two prominent examples are the papers by Rajan et al. (Manag Sci 38:240–262, 1992) and Abad (Manag......, we will try to expose the model by Abad (1996) and Rajan et al. (1992) to stochastic inputs; however, designing these stochastic inputs such that they as closely as possible are aligned with the assumptions of those papers. We do our investigation through a numerical test where we test the robustness...... of the numerical results reported in Rajan et al. (1992) and Abad (1996) in a simulation model. Our numerical results seem to confirm that the results stated in these papers are indeed robust when being imposed to stochastic inputs....
Dynamic analysis of stochastic bidirectional associative memory neural networks with delays
International Nuclear Information System (INIS)
Zhao Hongyong; Ding Nan
2007-01-01
In this paper, stochastic bidirectional associative memory neural networks model with delays is considered. By constructing Lyapunov functionals, and using stochastic analysis method and inequality technique, we give some sufficient criteria ensuring almost sure exponential stability, pth exponential stability and mean value exponential stability. The obtained criteria can be used as theoretic guidance to stabilize neural networks in practical applications when stochastic noise is taken into consideration
Tong, Shaocheng; Wang, Tong; Li, Yongming; Zhang, Huaguang
2014-06-01
This paper discusses the problem of adaptive neural network output feedback control for a class of stochastic nonlinear strict-feedback systems. The concerned systems have certain characteristics, such as unknown nonlinear uncertainties, unknown dead-zones, unmodeled dynamics and without the direct measurements of state variables. In this paper, the neural networks (NNs) are employed to approximate the unknown nonlinear uncertainties, and then by representing the dead-zone as a time-varying system with a bounded disturbance. An NN state observer is designed to estimate the unmeasured states. Based on both backstepping design technique and a stochastic small-gain theorem, a robust adaptive NN output feedback control scheme is developed. It is proved that all the variables involved in the closed-loop system are input-state-practically stable in probability, and also have robustness to the unmodeled dynamics. Meanwhile, the observer errors and the output of the system can be regulated to a small neighborhood of the origin by selecting appropriate design parameters. Simulation examples are also provided to illustrate the effectiveness of the proposed approach.
Weather Derivatives and Stochastic Modelling of Temperature
Directory of Open Access Journals (Sweden)
Fred Espen Benth
2011-01-01
Full Text Available We propose a continuous-time autoregressive model for the temperature dynamics with volatility being the product of a seasonal function and a stochastic process. We use the Barndorff-Nielsen and Shephard model for the stochastic volatility. The proposed temperature dynamics is flexible enough to model temperature data accurately, and at the same time being analytically tractable. Futures prices for commonly traded contracts at the Chicago Mercantile Exchange on indices like cooling- and heating-degree days and cumulative average temperatures are computed, as well as option prices on them.
Pesin’s entropy formula for stochastic flows of diffeomorphisms
Institute of Scientific and Technical Information of China (English)
刘培东
1996-01-01
Pesin’s entropy formula relating entropy and Lyapunov exponents within the context of random dynamical systems generated by (discrete or continuous) stochastic flows of diffeomorphisms (including solution flows of stochastic differential equations on manifolds) is proved.
Phenomenology of stochastic exponential growth
Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya
2017-06-01
Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.
Directory of Open Access Journals (Sweden)
Wenying Yue
2014-01-01
Full Text Available Cloud computing has come to be a significant commercial infrastructure offering utility-oriented IT services to users worldwide. However, data centers hosting cloud applications consume huge amounts of energy, leading to high operational cost and greenhouse gas emission. Therefore, green cloud computing solutions are needed not only to achieve high level service performance but also to minimize energy consumption. This paper studies the dynamic placement of virtual machines (VMs with deterministic and stochastic demands. In order to ensure a quick response to VM requests and improve the energy efficiency, a two-phase optimization strategy has been proposed, in which VMs are deployed in runtime and consolidated into servers periodically. Based on an improved multidimensional space partition model, a modified energy efficient algorithm with balanced resource utilization (MEAGLE and a live migration algorithm based on the basic set (LMABBS are, respectively, developed for each phase. Experimental results have shown that under different VMs’ stochastic demand variations, MEAGLE guarantees the availability of stochastic resources with a defined probability and reduces the number of required servers by 2.49% to 20.40% compared with the benchmark algorithms. Also, the difference between the LMABBS solution and Gurobi solution is fairly small, but LMABBS significantly excels in computational efficiency.
Multiple fields in stochastic inflation
Energy Technology Data Exchange (ETDEWEB)
Assadullahi, Hooshyar [Institute of Cosmology & Gravitation, University of Portsmouth,Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX (United Kingdom); Firouzjahi, Hassan [School of Astronomy, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Noorbala, Mahdiyar [Department of Physics, University of Tehran,P.O. Box 14395-547, Tehran (Iran, Islamic Republic of); School of Astronomy, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Vennin, Vincent; Wands, David [Institute of Cosmology & Gravitation, University of Portsmouth,Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX (United Kingdom)
2016-06-24
Stochastic effects in multi-field inflationary scenarios are investigated. A hierarchy of diffusion equations is derived, the solutions of which yield moments of the numbers of inflationary e-folds. Solving the resulting partial differential equations in multi-dimensional field space is more challenging than the single-field case. A few tractable examples are discussed, which show that the number of fields is, in general, a critical parameter. When more than two fields are present for instance, the probability to explore arbitrarily large-field regions of the potential, otherwise inaccessible to single-field dynamics, becomes non-zero. In some configurations, this gives rise to an infinite mean number of e-folds, regardless of the initial conditions. Another difference with respect to single-field scenarios is that multi-field stochastic effects can be large even at sub-Planckian energy. This opens interesting new possibilities for probing quantum effects in inflationary dynamics, since the moments of the numbers of e-folds can be used to calculate the distribution of primordial density perturbations in the stochastic-δN formalism.
Collective, stochastic and nonequilibrium behavior of highly excited hadronic matter
Energy Technology Data Exchange (ETDEWEB)
Carruthers, P [Los Alamos National Lab., NM (USA). Theoretical Div.
1984-04-23
We discuss selected problems concerning the dynamics and stochastic behavior of highly excited matter, particularly the QCD plasma. For the latter we consider the equation of state, kinetics, quasiparticles, flow properties and possible chaos and turbulence. The promise of phase space distribution functions for covariant transport and kinetic theory is stressed. The possibility and implications of a stochastic bag are spelled out. A simplified space-time model of hadronic collisions is pursued, with applications to A-A collisions and other matters. The domain wall between hadronic and plasma phase is of potential importance: its thickness and relation to surface tension is noticed. Finally, we review the recently developed stochastic cell model of multiparticle distributions and KNO scaling. This topic leads to the notion that fractional dimensions are involved in a rather general dynamical context. We speculate that various scaling phenomena are independent of the full dynamical structure, depending only on a general stochastic framework having to do with simple maps and strange attractors. 42 refs.
Helbing, Dirk; Schönhof, Martin; Kern, Daniel
2002-06-01
The coordinated and efficient distribution of limited resources by individual decisions is a fundamental, unsolved problem. When individuals compete for road capacities, time, space, money, goods, etc, they normally make decisions based on aggregate rather than complete information, such as TV news or stock market indices. In related experiments, we have observed a volatile decision dynamics and far-from-optimal payoff distributions. We have also identified methods of information presentation that can considerably improve the overall performance of the system. In order to determine optimal strategies of decision guidance by means of user-specific recommendations, a stochastic behavioural description is developed. These strategies manage to increase the adaptibility to changing conditions and to reduce the deviation from the time-dependent user equilibrium, thereby enhancing the average and individual payoffs. Hence, our guidance strategies can increase the performance of all users by reducing overreaction and stabilizing the decision dynamics. These results are highly significant for predicting decision behaviour, for reaching optimal behavioural distributions by decision support systems and for information service providers. One of the promising fields of application is traffic optimization.
High-energy hadron dynamics based on a stochastic-field multieikonal theory
International Nuclear Information System (INIS)
Arnold, R.C.
1977-01-01
Multieikonal theory, using a stochastic-field representation for collective long-range rapidity correlations, is developed and applied to the calculation of Regge-pole parameters, high-transverse-momentum enhancements, and fluctuation patterns in rapidity densities. If a short-range-order model, such as the one-dimensional planar bootstrap, with only leading t-channel meson poles, is utilized as input to the multieikonal method, the pole spectrum is modified in three ways: promotion and renormalization of leading trajectories (suggesting an effective Pomeron above unity at intermediate energies), and a proliferation of dynamical secondary trajectories, reminiscent of dual models. When transverse dimensions are included, the collective effects produce a growth with energy of large-P/sub T/ inclusive cross sections. Typical-event rapidity distributions, at energies of a few TeV, can be estimated by suitable approximations; the fluctuations give rise to ''domain'' patterns, which have the appearance of clusters separated by rapidity gaps. The relations between this approach to strong-interaction dynamics and a possible unification of weak, electromagnetic, and strong interactions are outlined
Kinetic theory of age-structured stochastic birth-death processes
Greenman, Chris D.; Chou, Tom
2016-01-01
Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.
A stochastic modeling of recurrent measles epidemic | Kassem ...
African Journals Online (AJOL)
A simple stochastic mathematical model is developed and investigated for the dynamics of measles epidemic. The model, which is a multi-dimensional diffusion process, includes susceptible individuals, latent (exposed), infected and removed individuals. Stochastic effects are assumed to arise in the process of infection of ...
International Nuclear Information System (INIS)
Hasegawa, Keita; Komiyama, Ryoichi; Fujii, Yasumasa
2016-01-01
The paper presents an economic rationality analysis of power generation mix by stochastic dynamic programming considering fuel price uncertainties and supply disruption risks such as import disruption and nuclear power plant shutdown risk. The situation revolving around Japan's energy security adopted the past statistics, it cannot be applied to a quantitative analysis of future uncertainties. Further objective and quantitative evaluation methods are required in order to analyze Japan's energy system and make it more resilient in sight of long time scale. In this paper, the authors firstly develop the cost minimization model considering oil and natural gas price respectively by stochastic dynamic programming. Then, the authors show several premises of model and an example of result with related to crude oil stockpile, liquefied natural gas stockpile and nuclear power plant capacity. (author)
Stochastic quantization and topological theories
International Nuclear Information System (INIS)
Fainberg, V.Y.; Subbotin, A.V.; Kuznetsov, A.N.
1992-01-01
In the last two years topological quantum field theories (TQFT) have attached much attention. This paper reports that from the very beginning it was realized that due to a peculiar BRST-like symmetry these models admitted so-called Nicolai mapping: the Nicolai variables, in terms of which actions of the theories become gaussian, are nothing but (anti-) selfduality conditions or their generalizations. This fact became a starting point in the quest of possible stochastic interpretation to topological field theories. The reasons behind were quite simple and included, in particular, the well-known relations between stochastic processes and supersymmetry. The main goal would have been achieved, if it were possible to construct stochastic processes governed by Langevin or Fokker-Planck equations in a real Euclidean time leading to TQFT's path integrals (equivalently: to reformulate TQFTs as non-equilibrium phase dynamics of stochastic processes). Further on, if it would appear that these processes correspond to the stochastic quantization of theories of some definite kind, one could expect (d + 1)-dimensional TQFTs to share some common properties with d-dimensional ones
Stochastic quantization of Einstein gravity
International Nuclear Information System (INIS)
Rumpf, H.
1986-01-01
We determine a one-parameter family of covariant Langevin equations for the metric tensor of general relativity corresponding to DeWitt's one-parameter family of supermetrics. The stochastic source term in these equations can be expressed in terms of a Gaussian white noise upon the introduction of a stochastic tetrad field. The only physically acceptable resolution of a mathematical ambiguity in the ansatz for the source term is the adoption of Ito's calculus. By taking the formal equilibrium limit of the stochastic metric a one-parameter family of covariant path-integral measures for general relativity is obtained. There is a unique parameter value, distinguished by any one of the following three properties: (i) the metric is harmonic with respect to the supermetric, (ii) the path-integral measure is that of DeWitt, (iii) the supermetric governs the linearized Einstein dynamics. Moreover the Feynman propagator corresponding to this parameter is causal. Finally we show that a consistent stochastic perturbation theory gives rise to a new type of diagram containing ''stochastic vertices.''
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...... a modified economic MPC based on linear parameter-varying model. In particular, we provide an exact transformation from a standard economic MPC formulation to a linear program. We assume that the variables influencing the model parameters are known (predictable) for the prediction horizon of the controller...
Analysis of dynamic regimes in stochastically forced Kaldor model
International Nuclear Information System (INIS)
Bashkirtseva, Irina; Ryazanova, Tatyana; Ryashko, Lev
2015-01-01
We consider the business cycle Kaldor model forced by random noise. Detailed parametric analysis of deterministic system is carried out and zones of coexisting stable equilibrium and stable limit cycle are found. Noise-induced transitions between these attractors are studied using stochastic sensitivity function technique and confidence domains method. Critical values of noise intensity corresponding to noise-induced transitions “equilibrium → cycle” and “cycle → equilibrium” are estimated. Dominants in combined stochastic regimes are discussed.
Threshold Dynamics of a Stochastic Chemostat Model with Two Nutrients and One Microorganism
Directory of Open Access Journals (Sweden)
Jian Zhang
2017-01-01
Full Text Available A new stochastic chemostat model with two substitutable nutrients and one microorganism is proposed and investigated. Firstly, for the corresponding deterministic model, the threshold for extinction and permanence of the microorganism is obtained by analyzing the stability of the equilibria. Then, for the stochastic model, the threshold of the stochastic chemostat for extinction and permanence of the microorganism is explored. Difference of the threshold of the deterministic model and the stochastic model shows that a large stochastic disturbance can affect the persistence of the microorganism and is harmful to the cultivation of the microorganism. To illustrate this phenomenon, we give some computer simulations with different intensity of stochastic noise disturbance.
风力发电高塔系统风致随机动力响应分析%Stochastic dynamic analysis of wind turbine systems under wind loads
Institute of Scientific and Technical Information of China (English)
贺广零; 李杰
2011-01-01
Wind energy development is an effective way to solve problems such as energy shortage and environmental pollution, so it is very useful to accurately compute the stochastic dynamic response of wind turbine systems under wind loads. Firstly< a new method termed as generalized probability density evolution method (GPDEM) is presented in the paper. The GPDEM has been proved to be of high accuracy and efficiency in most kinds of stochastic analysis of dynamical systems. Associated with the physical model of stochastic wind field and the integrated finite element model consisting of the rotor, the nacelle. The tower and the foundation, it is very hopeful to apply the GPDEM in stochastic dynamic analysis of wind turbine systems. Then, a 1. 25 MW wind turbine system subject to wind loads is investigated in detail, and the dynamic responses and the stochastic ones are also compared. The results demonstrate that the randomness of wind velocities places a great influence on the stochastic dynamic analysis of wind turbine systems.%介绍了一种高精度且高效的随机动力系统分析方法-广义概率密度演化方法.基于广义概率密度演化方法,结合随机脉动风场物理模型和“桨叶-机舱-塔体-基础”一体化有限元模型,分别对1.25 MW风力发电高钢塔和钢筋混凝土风力发电高塔进行了风致随机动力响应分析,并将分析结果同确定性动力响应分析结果进行比较.研究表明,随机性对风力发电高塔系统结构风致动力响应分析的影响非常显著.
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.
Brasseur, Pierre; Candille, Guillem; Bouttier, Pierre-Antoine; Brankart, Jean-Michel; Verron, Jacques
2015-04-01
The objective of this study is to explicitly simulate and quantify the uncertainty related to sea-level anomalies diagnosed from eddy-resolving ocean circulation models, in order to develop advanced methods suitable for addressing along-track altimetric data assimilation into such models. This work is carried out jointly with the MyOcean and SANGOMA (Stochastic Assimilation for the Next Generation Ocean Model Applications) consortium, funded by EU under the GMES umbrella over the 2012-2015 period. In this framework, a realistic circulation model of the North Atlantic ocean at 1/4° resolution (NATL025 configuration) has been adapted to include effects of unresolved scales on the dynamics. This is achieved by introducing stochastic perturbations of the equation of state to represent the associated model uncertainty. Assimilation experiments are designed using altimetric data from past and on-going missions (Jason-2 and Saral/AltiKA experiments, and Cryosat-2 for fully independent altimetric validation) to better control the Gulf Stream circulation, especially the frontal regions which are predominantly affected by the non-resolved dynamical scales. An ensemble based on such stochastic perturbations is then produced and evaluated -through the probabilistic criteria: the reliability and the resolution- using the model equivalent of along-track altimetric observations. These three elements (stochastic parameterization, ensemble simulation and 4D observation operator) are used together to perform optimal 4D analysis of along-track altimetry over 10-day assimilation windows. In this presentation, the results show that the free ensemble -before starting the assimilation process- well reproduces the climatological variability over the Gulf Stream area: the system is then pretty reliable but no informative (null probabilistic resolution). Updating the free ensemble with altimetric data leads to a better reliability and to an improvement of the information (resolution
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...
International Nuclear Information System (INIS)
Lu, Yunfan; Wang, Jun; Niu, Hongli
2015-01-01
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
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.
International Nuclear Information System (INIS)
Ren Xiaoan; Wu Wenquan; Xanthis, Leonidas S.
2011-01-01
Highlights: → New approach for stochastic computations based on polynomial chaos. → Development of dynamically adaptive wavelet multiscale solver using space refinement. → Accurate capture of steep gradients and multiscale features in stochastic problems. → All scales of each random mode are captured on independent grids. → Numerical examples demonstrate the need for different space resolutions per mode. - Abstract: In stochastic computations, or uncertainty quantification methods, the spectral approach based on the polynomial chaos expansion in random space leads to a coupled system of deterministic equations for the coefficients of the expansion. The size of this system increases drastically when the number of independent random variables and/or order of polynomial chaos expansions increases. This is invariably the case for large scale simulations and/or problems involving steep gradients and other multiscale features; such features are variously reflected on each solution component or random/uncertainty mode requiring the development of adaptive methods for their accurate resolution. In this paper we propose a new approach for treating such problems based on a dynamically adaptive wavelet methodology involving space-refinement on physical space that allows all scales of each solution component to be refined independently of the rest. We exemplify this using the convection-diffusion model with random input data and present three numerical examples demonstrating the salient features of the proposed method. Thus we establish a new, elegant and flexible approach for stochastic problems with steep gradients and multiscale features based on polynomial chaos expansions.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Xiaodong, E-mail: xiaodong.zhang@beg.utexas.edu [Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas at Austin, Austin, TX 78713 (United States); Huang, Gordon [Institute of Energy, Environment and Sustainable Communities, University of Regina, Regina, Saskatchewan S4S 0A2 (Canada)
2013-02-15
Highlights: ► A dynamic stochastic possibilistic multiobjective programming model is developed. ► Greenhouse gas emission control is considered. ► Three planning scenarios are analyzed and compared. ► Optimal decision schemes under three scenarios and different p{sub i} levels are obtained. ► Tradeoffs between economics and environment are reflected. -- Abstract: Greenhouse gas (GHG) emissions from municipal solid waste (MSW) management facilities have become a serious environmental issue. In MSW management, not only economic objectives but also environmental objectives should be considered simultaneously. In this study, a dynamic stochastic possibilistic multiobjective programming (DSPMP) model is developed for supporting MSW management and associated GHG emission control. The DSPMP model improves upon the existing waste management optimization methods through incorporation of fuzzy possibilistic programming and chance-constrained programming into a general mixed-integer multiobjective linear programming (MOP) framework where various uncertainties expressed as fuzzy possibility distributions and probability distributions can be effectively reflected. Two conflicting objectives are integrally considered, including minimization of total system cost and minimization of total GHG emissions from waste management facilities. Three planning scenarios are analyzed and compared, representing different preferences of the decision makers for economic development and environmental-impact (i.e. GHG-emission) issues in integrated MSW management. Optimal decision schemes under three scenarios and different p{sub i} levels (representing the probability that the constraints would be violated) are generated for planning waste flow allocation and facility capacity expansions as well as GHG emission control. The results indicate that economic and environmental tradeoffs can be effectively reflected through the proposed DSPMP model. The generated decision variables can help
Constant-pH molecular dynamics using stochastic titration
Baptista, António M.; Teixeira, Vitor H.; Soares, Cláudio M.
2002-09-01
A new method is proposed for performing constant-pH molecular dynamics (MD) simulations, that is, MD simulations where pH is one of the external thermodynamic parameters, like the temperature or the pressure. The protonation state of each titrable site in the solute is allowed to change during a molecular mechanics (MM) MD simulation, the new states being obtained from a combination of continuum electrostatics (CE) calculations and Monte Carlo (MC) simulation of protonation equilibrium. The coupling between the MM/MD and CE/MC algorithms is done in a way that ensures a proper Markov chain, sampling from the intended semigrand canonical distribution. This stochastic titration method is applied to succinic acid, aimed at illustrating the method and examining the choice of its adjustable parameters. The complete titration of succinic acid, using constant-pH MD simulations at different pH values, gives a clear picture of the coupling between the trans/gauche isomerization and the protonation process, making it possible to reconcile some apparently contradictory results of previous studies. The present constant-pH MD method is shown to require a moderate increase of computational cost when compared to the usual MD method.
Fiore, Andrew M.; Swan, James W.
2018-01-01
equations of motion leads to a stochastic differential algebraic equation (SDAE) of index 1, which is integrated forward in time using a mid-point integration scheme that implicitly produces stochastic displacements consistent with the fluctuation-dissipation theorem for the constrained system. Calculations for hard sphere dispersions are illustrated and used to explore the performance of the algorithm. An open source, high-performance implementation on graphics processing units capable of dynamic simulations of millions of particles and integrated with the software package HOOMD-blue is used for benchmarking and made freely available in the supplementary material (ftp://ftp.aip.org/epaps/journ_chem_phys/E-JCPSA6-148-012805)
Solving Langevin equation with the stochastic algebraically correlated noise
International Nuclear Information System (INIS)
Ploszajczak, M.; Srokowski, T.
1996-01-01
Long time tail in the velocity and force autocorrelation function has been found recently in the molecular dynamics simulations of the peripheral collisions of ions. Simulation of those slowly decaying correlations in the stochastic transport theory requires the development of new methods of generating stochastic force of arbitrarily long correlation times. The Markovian process and the multidimensional Kangaroo process which permit describing various algebraic correlated stochastic processes are proposed. (author)
A stochastic approach to multi-gene expression dynamics
International Nuclear Information System (INIS)
Ochiai, T.; Nacher, J.C.; Akutsu, T.
2005-01-01
In the last years, tens of thousands gene expression profiles for cells of several organisms have been monitored. Gene expression is a complex transcriptional process where mRNA molecules are translated into proteins, which control most of the cell functions. In this process, the correlation among genes is crucial to determine the specific functions of genes. Here, we propose a novel multi-dimensional stochastic approach to deal with the gene correlation phenomena. Interestingly, our stochastic framework suggests that the study of the gene correlation requires only one theoretical assumption-Markov property-and the experimental transition probability, which characterizes the gene correlation system. Finally, a gene expression experiment is proposed for future applications of the model
International Nuclear Information System (INIS)
Buonomano, Annamaria; Calise, Francesco; Ferruzzi, Gabriele; Palombo, Adolfo
2014-01-01
This paper investigates several actions for the energy refurbishment of some buildings of the University Hospital Federico II of Naples. The analysis focuses on a specific lot of 4 buildings, representative of the whole district hospital. For those structures, sustainable energy savings actions are investigated. They regard the installation of: i) roofs thermal insulation; ii) a substation climatic 3-way valve; iii) radiators thermostatic valves; iv) AHU (air handling unit) time-programmable regulation. This paper aims at presenting an investigation methodology, useful for designers and other stakeholders involved in hospital energy refurbishments, based on an integrated approach which combines dynamic energy performance simulations and experimental campaigns. In order to measure all the simulations' missing input parameters, a suitable experimental analysis, including measurements of temperature, humidity, flow rate and density of construction materials, is performed. A thermographic investigation is also performed for investigating the building envelope performance. This analysis showed that significant savings can be achieved especially by adopting radiators thermostatic valves and AHU regulations. Coherently, the installation of a 3-way valve in the substation does not determine significant additional savings when radiators thermostatic valves are already installed. For high-rise buildings, roofs insulation returns only marginal reductions of space heating and cooling demands. - Highlights: • Energy saving measures applied to the largest hospital of South Italy are analyzed. • A new approach combining dynamic simulations and measurements is implemented. • Thermography, temperature and flow measurements are performed. • High savings are achieved by adopting thermostatic valves and AHU control systems. • The simplest energy saving actions resulted to be the most profitable ones
On Nash Equilibria in Stochastic Games
2003-10-01
Traditionally automata theory and veri cation has considered zero sum or strictly competitive versions of stochastic games . In these games there are two players...zero- sum discrete-time stochastic dynamic games . SIAM J. Control and Optimization, 19(5):617{634, 1981. 18. R.J. Lipton, E . Markakis, and A. Mehta...Playing large games using simple strate- gies. In EC 03: Electronic Commerce, pages 36{41. ACM Press, 2003. 19. A. Maitra and W. Sudderth. Finitely
A stochastic model of enzyme kinetics
Stefanini, Marianne; Newman, Timothy; McKane, Alan
2003-10-01
Enzyme kinetics is generally modeled by deterministic rate equations, and in the simplest case leads to the well-known Michaelis-Menten equation. It is plausible that stochastic effects will play an important role at low enzyme concentrations. We have addressed this by constructing a simple stochastic model which can be exactly solved in the steady-state. Throughout a wide range of parameter values Michaelis-Menten dynamics is replaced by a new and simple theoretical result.
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
Fractional noise destroys or induces a stochastic bifurcation
Energy Technology Data Exchange (ETDEWEB)
Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Sciences, South China University of Technology, Guangzhou 510640 (China); Zeng, Caibin, E-mail: zeng.cb@mail.scut.edu.cn [School of Sciences, South China University of Technology, Guangzhou 510640 (China); School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640 (China); Wang, Cong, E-mail: wangcong@scut.edu.cn [School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640 (China)
2013-12-15
Little seems to be known about the stochastic bifurcation phenomena of non-Markovian systems. Our intention in this paper is to understand such complex dynamics by a simple system, namely, the Black-Scholes model driven by a mixed fractional Brownian motion. The most interesting finding is that the multiplicative fractional noise not only destroys but also induces a stochastic bifurcation under some suitable conditions. So it opens a possible way to explore the theory of stochastic bifurcation in the non-Markovian framework.
QUANTUM STOCHASTIC PROCESSES: BOSON AND FERMION BROWNIAN MOTION
Directory of Open Access Journals (Sweden)
A.E.Kobryn
2003-01-01
Full Text Available Dynamics of quantum systems which are stochastically perturbed by linear coupling to the reservoir can be studied in terms of quantum stochastic differential equations (for example, quantum stochastic Liouville equation and quantum Langevin equation. In order to work it out one needs to define the quantum Brownian motion. As far as only its boson version has been known until recently, in the present paper we present the definition which makes it possible to consider the fermion Brownian motion as well.
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
Quantum Oscillator in the Thermostat as a Model in the Thermodynamics of Open Quantum Systems
Sukhanov, Aleksander
2005-01-01
The quantum oscillator in the thermostat is considered as the model of an open quantum system. Our analysis will be heavily founded on the use of the Schroedinger generalized uncertainties relations (SUR). Our first aim is to demonstrate that for the quantum oscillator the state of thermal equilibrium belongs to the correlated coherent states (CCS), which imply the saturation of SUR at any temperature. The obtained results open the perspective for the search of some statistical theory, which ...
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.
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.
Overview of Existing and Future Residential Use Cases for Connected Thermostats
Energy Technology Data Exchange (ETDEWEB)
Rotondo, Julia [Energetics Inc., Washington, DC (United States); Johnson, Robert [Energetics Inc., Washington, DC (United States); Gonzalez, Nancy [Energetics Inc., Washington, DC (United States); Waranowski, Alexandra [Energetics Inc., Washington, DC (United States); Badger, Chris [Vermont Energy Investment Corporation, Burlington, VT (United States); Lange, Nick [Vermont Energy Investment Corporation, Burlington, VT (United States); Goldman, Ethan [Vermont Energy Investment Corporation, Burlington, VT (United States); Foster, Rebecca [Vermont Energy Investment Corporation, Burlington, VT (United States)
2017-03-01
This paper is intended to help inform future technology deployment opportunities for connected thermostats (CTs), based on investigation and review of the U.S. residential housing and CT markets, as well as existing, emerging, and future use cases for CT hardware and CT-generated data. The CT market has experienced tremendous growth over the last 5 years—both in terms of the number of units sold and the number of firms offering competing products—and can be characterized by its rapid pace of technological innovation. Despite many assuming CTs would become powerful tools for increasing comfort while saving energy, there remains a great deal of uncertainty about the actual energy and cost savings that are likely to be realized from deployment of CTs, particularly under different conditions.
Energy Technology Data Exchange (ETDEWEB)
2016-02-01
Modern, energy-efficient homes conforming to the Zero Energy Ready Home standard face the challenge of meeting high customer expectations for comfort. Traditional heating, ventilation, and air conditioning (HVAC) sizing and control strategies may be insufficient to adequately condition each zone due to unique load patterns in each room caused by a number of factors. These factors include solar heat gains, occupant-related gains, and gains associated with appliances and electronics. Because of shrinking shell loads, these intermittent factors are having an increasingly significant impact on the thermal load in each zone. Consequently, occupant comfort can be compromised. To evaluate the impact of climate and house geometry, as well as HVAC system and control strategies on comfort conditions, IBACOS analyzed the results of 99 TRNSYS multiple-zone simulations. The results of this analysis indicate that for simple-geometry and single-story plans, a single zone and thermostat can adequately condition the entire house. Demanding house geometry and houses with multiple stories require the consideration of multiple thermostats and multiple zones.
Stochastic population dynamics under resource constraints
Energy Technology Data Exchange (ETDEWEB)
Gavane, Ajinkya S., E-mail: ajinkyagavane@gmail.com; Nigam, Rahul, E-mail: rahul.nigam@hyderabad.bits-pilani.ac.in [BITS Pilani Hyderabad Campus, Shameerpet, Hyd - 500078 (India)
2016-06-02
This paper investigates the population growth of a certain species in which every generation reproduces thrice over a period of predefined time, under certain constraints of resources needed for survival of population. We study the survival period of a species by randomizing the reproduction probabilities within a window at same predefined ages and the resources are being produced by the working force of the population at a variable rate. This randomness in the reproduction rate makes the population growth stochastic in nature and one cannot predict the exact form of evolution. Hence we study the growth by running simulations for such a population and taking an ensemble averaged over 500 to 5000 such simulations as per the need. While the population reproduces in a stochastic manner, we have implemented a constraint on the amount of resources available for the population. This is important to make the simulations more realistic. The rate of resource production then is tuned to find the rate which suits the survival of the species. We also compute the mean life time of the species corresponding to different resource production rate. Study for these outcomes in the parameter space defined by the reproduction probabilities and rate of resource production is carried out.
A microscopic derivation of stochastic differential equations
International Nuclear Information System (INIS)
Arimitsu, Toshihico
1996-01-01
With the help of the formulation of Non-Equilibrium Thermo Field Dynamics, a unified canonical operator formalism is constructed for the quantum stochastic differential equations. In the course of its construction, it is found that there are at least two formulations, i.e. one is non-hermitian and the other is hermitian. Having settled which framework should be satisfied by the quantum stochastic differential equations, a microscopic derivation is performed for these stochastic differential equations by extending the projector methods. This investigation may open a new field for quantum systems in order to understand the deeper meaning of dissipation
100 years after Smoluchowski: stochastic processes in cell biology
International Nuclear Information System (INIS)
Holcman, D; Schuss, Z
2017-01-01
100 years after Smoluchowski introduced his approach to stochastic processes, they are now at the basis of mathematical and physical modeling in cellular biology: they are used for example to analyse and to extract features from a large number (tens of thousands) of single molecular trajectories or to study the diffusive motion of molecules, proteins or receptors. Stochastic modeling is a new step in large data analysis that serves extracting cell biology concepts. We review here Smoluchowski’s approach to stochastic processes and provide several applications for coarse-graining diffusion, studying polymer models for understanding nuclear organization and finally, we discuss the stochastic jump dynamics of telomeres across cell division and stochastic gene regulation. (topical review)
Temperature specification in atomistic molecular dynamics and its impact on simulation efficacy
Ocaya, R. O.; Terblans, J. J.
2017-10-01
Temperature is a vital thermodynamical function for physical systems. Knowledge of system temperature permits assessment of system ergodicity, entropy, system state and stability. Rapid theoretical and computational developments in the fields of condensed matter physics, chemistry, material science, molecular biology, nanotechnology and others necessitate clarity in the temperature specification. Temperature-based materials simulations, both standalone and distributed computing, are projected to grow in prominence over diverse research fields. In this article we discuss the apparent variability of temperature modeling formalisms used currently in atomistic molecular dynamics simulations, with respect to system energetics,dynamics and structural evolution. Commercial simulation programs, which by nature are heuristic, do not openly discuss this fundamental question. We address temperature specification in the context of atomistic molecular dynamics. We define a thermostat at 400K relative to a heat bath at 300K firstly using a modified ab-initio Newtonian method, and secondly using a Monte-Carlo method. The thermostatic vacancy formation and cohesion energies, equilibrium lattice constant for FCC copper is then calculated. Finally we compare and contrast the results.
Extinction in neutrally stable stochastic Lotka-Volterra models
Dobrinevski, Alexander; Frey, Erwin
2012-05-01
Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. Here, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: It destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.
Nano-colloid electrophoretic transport: Fully explicit modelling via dissipative particle dynamics
Hassanzadeh Afrouzi, Hamid; Farhadi, Mousa; Sedighi, Kurosh; Moshfegh, Abouzar
2018-02-01
In present study, a novel fully explicit approach using dissipative particle dynamics (DPD) method is introduced for modelling electrophoretic transport of nano-colloids in an electrolyte solution. Slater type charge smearing function included in 3D Ewald summation method is employed to treat electrostatic interaction. Moreover, capability of different thermostats are challenged to control the system temperature and study the dynamic response of colloidal electrophoretic mobility under practical ranges of external electric field in nano scale application (0.072 600 in DPD units regardless of electric field intensity. Nosé-Hoover-Lowe-Andersen and Lowe-Andersen thermostats are found to function more effectively under high electric fields (E > 0.145 [ v / nm ]) while thermal equilibrium is maintained. Reasonable agreements are achieved by benchmarking the radial distribution function with available electrolyte structure modellings, as well as comparing reduced mobility against conventional Smoluchowski and Hückel theories, and numerical solution of Poisson-Boltzmann equation.
A Molecular Dynamics Approach for Nucleation-Growth of Cryogenic Cavitation
Tsuda, Shin-ichi; Komatsu, Taiga; Takagi, Shu; Matsumoto, Yoichiro
2011-01-01
The growth of cavitation bubble nuclei in a metastable state in liquid argon, as one of cryogenic fluids, was investigated using a Molecular Dynamics (MD) simulation with a Nosé-Hoover chain thermostat. We observed rapid growth of bubble nuclei with weak inter-bubble interaction in the early stage, while observed a competing coarsening that looks like Ostwald ripening in the late stage and its growth exponent n became 0.51. We compared the present MD result with that in an adiabatic simulation (Energy-constant MD without any thermostats), and the influence of the field temperature was discussed. Also, we compared the present MD results with a coarsening theory for droplets, and discussed the characteristics of the coarsening mechanism of bubble nuclei. Copyright © 2011 by ASME.
How the Invisible Hand is Supposed to Adjust the Natural Thermostat: A Guide for the Perplexed
Storm, Servaas
2016-01-01
Mainstream climate economics takes global warming seriously, but perplexingly concludes that the optimal economic policy is to almost do nothing about it. This conclusion can be traced to just a few “normative” assumptions, over which there exists fundamental disagreement amongst economists. This paper explores two axes of this disagreement. The first axis (“market vs. regulation”) measures faith in the invisible hand to adjust the natural thermostat. The second axis expresses differences in ...
THE GROSSER ALETSCHGLETSCHER DYNAMICS: FROM A “MINIMAL MODEL” TO A STOCHASTIC EQUATION
Directory of Open Access Journals (Sweden)
Alexander V. Kislov
2016-01-01
Full Text Available Mountain glaciers manifest oscillations at different time-scales. Apart from synchronous reaction to lasting changes, there is asynchronism between climatic forcing and observed anomalies of the glaciers. Based on general theories on the laws of temporal dynamics relating to massive inertial objects, the observed interannual changes of glacier length could result from the accumulation of small anomalies in the heat/water fluxes. Despite the fact that the original model of the dynamics of mountain glaciers is deterministically based on the physical law of conservation of water mass, the model of length change is interpreted as stochastic; from this perspective, it is the Langevin equation that incorporates the action of temperature anomalies and precipitation like random white noise. The process is analogous to Brownian motion. Under these conditions, the Grosser Aletschgletscher (selected as an example is represented by a system undergoing a random walk. It was shown that the possible range of variability covers the observed interval of length fluctuations.
A combined stochastic programming and optimal control approach to personal finance and pensions
DEFF Research Database (Denmark)
Konicz, Agnieszka Karolina; Pisinger, David; Rasmussen, Kourosh Marjani
2015-01-01
The paper presents a model that combines a dynamic programming (stochastic optimal control) approach and a multi-stage stochastic linear programming approach (SLP), integrated into one SLP formulation. Stochastic optimal control produces an optimal policy that is easy to understand and implement....
Stochastic Control - External Models
DEFF Research Database (Denmark)
Poulsen, Niels Kjølstad
2005-01-01
This note is devoted to control of stochastic systems described in discrete time. We are concerned with external descriptions or transfer function model, where we have a dynamic model for the input output relation only (i.e.. no direct internal information). The methods are based on LTI systems...
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.
On the theory of stochastic dynamics of magnetically confined plasma
Energy Technology Data Exchange (ETDEWEB)
El-Sharif, R.N.; El-Atoy, N.S. [Plasma and Nuclear Fusion Dept., N.R.C, Atomic Energy Authority, Cairo (Egypt)]|[Physics Dept., Girls Colleges, KSA (Saudi Arabia)
2004-07-01
This work is devoted to a study of the motion of plasma electrons in a system of two fields, a magnetic field along z-axis and wave-packet field, which propagates in the x-z plane. The strongest interaction between plasma electrons and both fields is due to their resonance with these fields. The motion of plasma electrons become stochastic when a set of resonance overlapping. Conditions for stochasticity are obtained. (orig.)
On the theory of stochastic dynamics of magnetically confined plasma
International Nuclear Information System (INIS)
El-Sharif, R.N.; El-Atoy, N.S.
2004-01-01
This work is devoted to a study of the motion of plasma electrons in a system of two fields, a magnetic field along z-axis and wave-packet field, which propagates in the x-z plane. The strongest interaction between plasma electrons and both fields is due to their resonance with these fields. The motion of plasma electrons become stochastic when a set of resonance overlapping. Conditions for stochasticity are obtained. (orig.)
Overview of Existing and Future Residential Use Cases for Connected Thermostats
Energy Technology Data Exchange (ETDEWEB)
Rotondo, Julia [Energetics Inc., Washington, DC (United States); Johnson, Robert [Energetics Inc., Washington, DC (United States); Gonzales, Nancy [Energetics Inc., Washington, DC (United States); Waranowski, Alexandra [Energetics Inc., Washington, DC (United States); Badger, Chris [Vermont Energy Investment Corp., Burlington, VT (United States); Lange, Nack [Vermont Energy Investment Corp., Burlington, VT (United States); Goldman, Ethan [Vermont Energy Investment Corp., Burlington, VT (United States); Foster, Rebecca [Vermont Energy Investment Corp., Burlington, VT (United States)
2016-12-01
This paper is intended to help inform future technology deployment opportunities for connected thermostats (CTs), based on investigation and review of the U.S. residential housing and CT markets, as well as existing, emerging, and future use cases for CT hardware and CT-generated data. The CT market has experienced tremendous growth over the last five years — both in terms of the number of units sold and the number of firms offering competing products — and can be characterized by its rapid pace of technological innovation. Despite many assuming CTs would become powerful tools for increasing comfort while saving energy, there remains a great deal of uncertainty about the actual energy and cost savings that are likely to be realized from deployment of CTs, particularly under different conditions.
Problems of Mathematical Finance by Stochastic Control Methods
Stettner, Łukasz
The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.
Stochastic goal-oriented error estimation with memory
Ackmann, Jan; Marotzke, Jochem; Korn, Peter
2017-11-01
We propose a stochastic dual-weighted error estimator for the viscous shallow-water equation with boundaries. For this purpose, previous work on memory-less stochastic dual-weighted error estimation is extended by incorporating memory effects. The memory is introduced by describing the local truncation error as a sum of time-correlated random variables. The random variables itself represent the temporal fluctuations in local truncation errors and are estimated from high-resolution information at near-initial times. The resulting error estimator is evaluated experimentally in two classical ocean-type experiments, the Munk gyre and the flow around an island. In these experiments, the stochastic process is adapted locally to the respective dynamical flow regime. Our stochastic dual-weighted error estimator is shown to provide meaningful error bounds for a range of physically relevant goals. We prove, as well as show numerically, that our approach can be interpreted as a linearized stochastic-physics ensemble.
A stochastic fractional dynamics model of space-time variability of rain
Kundu, Prasun K.; Travis, James E.
2013-09-01
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, which 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 time scales. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and on the Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to fit the second moment statistics of radar data at the smaller spatiotemporal scales. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well at these scales without any further adjustment.
Dynamic Behaviour of a Population of Controlled-by-price Demand Side Resources
DEFF Research Database (Denmark)
Sossan, Fabrizio; Han, Xue; Bindner, Henrik W.
2014-01-01
It is described that controlling or shedding by price the power consumption of a population of thermostatic loads introduces in the aggregate consumption dynamic effects th at cannot be disregarded if electrical flexible demand is meant to supply power system services. It is shown that inducing...
Stochastic modelling of turbulence
DEFF Research Database (Denmark)
Sørensen, Emil Hedevang Lohse
previously been shown to be closely connected to the energy dissipation. The incorporation of the small scale dynamics into the spatial model opens the door to a fully fledged stochastic model of turbulence. Concerning the interaction of wind and wind turbine, a new method is proposed to extract wind turbine...
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.
Stochastic Averaging and Stochastic Extremum Seeking
Liu, Shu-Jun
2012-01-01
Stochastic Averaging and Stochastic Extremum Seeking develops methods of mathematical analysis inspired by the interest in reverse engineering and analysis of bacterial convergence by chemotaxis and to apply similar stochastic optimization techniques in other environments. The first half of the text presents significant advances in stochastic averaging theory, necessitated by the fact that existing theorems are restricted to systems with linear growth, globally exponentially stable average models, vanishing stochastic perturbations, and prevent analysis over infinite time horizon. The second half of the text introduces stochastic extremum seeking algorithms for model-free optimization of systems in real time using stochastic perturbations for estimation of their gradients. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms...
Stochastic Eulerian Lagrangian methods for fluid-structure interactions with thermal fluctuations
International Nuclear Information System (INIS)
Atzberger, Paul J.
2011-01-01
We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for operators coupling these descriptions. Stochastic driving fields for the formalism are derived using principles from statistical mechanics. The stochastic differential equations of the formalism are found to exhibit significant stiffness in some physical regimes. To cope with this issue, we derive reduced stochastic differential equations for several physical regimes. We also present stochastic numerical methods for each regime to approximate the fluid-structure dynamics and to generate efficiently the required stochastic driving fields. To validate the methodology in each regime, we perform analysis of the invariant probability distribution of the stochastic dynamics of the fluid-structure formalism. We compare this analysis with results from statistical mechanics. To further demonstrate the applicability of the methodology, we perform computational studies for spherical particles having translational and rotational degrees of freedom. We compare these studies with results from fluid mechanics. The presented approach provides for fluid-structure systems a set of rather general computational methods for treating consistently structure mechanics, hydrodynamic coupling, and thermal fluctuations.
American options under stochastic volatility
Chockalingam, A.; Muthuraman, K.
2011-01-01
The problem of pricing an American option written on an underlying asset with constant price volatility has been studied extensively in literature. Real-world data, however, demonstrate that volatility is not constant, and stochastic volatility models are used to account for dynamic volatility
Stochastic processes in mechanical engineering
Brouwers, J.J.H.
2006-01-01
Stochastic or random vibrations occur in a variety of applications of mechanicalengineering. Examples are: the dynamics of a vehicle on an irregular roadsurface; the variation in time of thermodynamic variables in municipal wasteincinerators due to fluctuations in heating value of the waste; the
Stochastic space-time and quantum theory
International Nuclear Information System (INIS)
Frederick, C.
1976-01-01
Much of quantum mechanics may be derived if one adopts a very strong form of Mach's principle such that in the absence of mass, space-time becomes not flat, but stochastic. This is manifested in the metric tensor which is considered to be a collection of stochastic variables. The stochastic-metric assumption is sufficient to generate the spread of the wave packet in empty space. If one further notes that all observations of dynamical variables in the laboratory frame are contravariant components of tensors, and if one assumes that a Lagrangian can be constructed, then one can obtain an explanation of conjugate variables and also a derivation of the uncertainty principle. Finally the superposition of stochastic metrics and the identification of root -g in the four-dimensional invariant volume element root -g dV as the indicator of relative probability yields the phenomenon of interference as will be described for the two-slit experiment
International Nuclear Information System (INIS)
Gutierrez, Rafael M.; Useche, Gina M.; Buitrago, Elias
2007-01-01
We present a procedure developed to detect stochastic and deterministic information contained in empirical time series, useful to characterize and make models of different aspects of complex phenomena represented by such data. This procedure is applied to a seismological time series to obtain new information to study and understand geological phenomena. We use concepts and methods from nonlinear dynamics and maximum entropy. The mentioned method allows an optimal analysis of the available information
Stochastic bifurcation in a model of love with colored noise
Yue, Xiaokui; Dai, Honghua; Yuan, Jianping
2015-07-01
In this paper, we wish to examine the stochastic bifurcation induced by multiplicative Gaussian colored noise in a dynamical model of love where the random factor is used to describe the complexity and unpredictability of psychological systems. First, the dynamics in deterministic love-triangle model are considered briefly including equilibrium points and their stability, chaotic behaviors and chaotic attractors. Then, the influences of Gaussian colored noise with different parameters are explored such as the phase plots, top Lyapunov exponents, stationary probability density function (PDF) and stochastic bifurcation. The stochastic P-bifurcation through a qualitative change of the stationary PDF will be observed and bifurcation diagram on parameter plane of correlation time and noise intensity is presented to find the bifurcation behaviors in detail. Finally, the top Lyapunov exponent is computed to determine the D-bifurcation when the noise intensity achieves to a critical value. By comparison, we find there is no connection between two kinds of stochastic bifurcation.
van der Ham, Wim; Klein, Michel; Tabatabaei, Seyed Amin; Thilakarathne, Dilhan; Treur, Jan
Smart thermostats can play an important role in achieving more economic energy usage in domestic situations. This paper focuses on the energy used for natural gas-based heating, and monitoring of gas usages versus indoor and outdoor temperatures over time. Two methods are presented that enable the
Higher-order stochastic differential equations and the positive Wigner function
Drummond, P. D.
2017-12-01
General higher-order stochastic processes that correspond to any diffusion-type tensor of higher than second order are obtained. The relationship of multivariate higher-order stochastic differential equations with tensor decomposition theory and tensor rank is explained. Techniques for generating the requisite complex higher-order noise are proved to exist either using polar coordinates and γ distributions, or from products of Gaussian variates. This method is shown to allow the calculation of the dynamics of the Wigner function, after it is extended to a complex phase space. The results are illustrated physically through dynamical calculations of the positive Wigner distribution for three-mode parametric downconversion, widely used in quantum optics. The approach eliminates paradoxes arising from truncation of the higher derivative terms in Wigner function time evolution. Anomalous results of negative populations and vacuum scattering found in truncated Wigner quantum simulations in quantum optics and Bose-Einstein condensate dynamics are shown not to occur with this type of stochastic theory.
Collective, stochastic and nonequilibrium behavior of highly excited hadronic matter
International Nuclear Information System (INIS)
Carruthers, P.
1983-01-01
We discuss selected problems concerning the dynamic and stochasticc behavior of highly excited matter, particularly the QCD plasma. For the latter we consider the equation of state, kinetics, quasiparticles, flow properties and possible chaos and turbulence. The promise of phase space distribution functions for covariant transport and kinetic theory is stressed. The possibility and implications of a stochastic bag are spelled out. A simplified space-time model of hadronic collisions is pursued, with applications to A-A collisions and other matters. The domain wall between hadronic and plasma phase is of potential importance: its thickness and relation to surface tension are noticed. Finally we reviewed the recently developed stochastic cell model of multiparticle distributions and KNO scaling. This topic leads to the notion that fractal dimensions are involved in a rather general dynamical context. We speculate that various scaling phenomena are independent of the full dynamical structure, depending only on a general stochastic framework having to do with simple maps and strange attractors. 42 references
Stochastic and Chaotic Relaxation Oscillations
Grasman, J.; Roerdink, J.B.T.M.
1988-01-01
For relaxation oscillators stochastic and chaotic dynamics are investigated. The effect of random perturbations upon the period is computed. For an extended system with additional state variables chaotic behavior can be expected. As an example, the Van der Pol oscillator is changed into a
Mellin Transform Method for European Option Pricing with Hull-White Stochastic Interest Rate
Directory of Open Access Journals (Sweden)
Ji-Hun Yoon
2014-01-01
Full Text Available Even though interest rates fluctuate randomly in the marketplace, many option-pricing models do not fully consider their stochastic nature owing to their generally limited impact on option prices. However, stochastic dynamics in stochastic interest rates may have a significant impact on option prices as we take account of issues of maturity, hedging, or stochastic volatility. In this paper, we derive a closed form solution for European options in Black-Scholes model with stochastic interest rate using Mellin transform techniques.
A stochastic SIRS epidemic model with infectious force under intervention strategies
Cai, Yongli; Kang, Yun; Banerjee, Malay; Wang, Weiming
2015-12-01
In this paper, we extend a classical SIRS epidemic model with the infectious forces under intervention strategies from a deterministic framework to a stochastic differential equation (SDE) one through introducing random fluctuations. The value of our study lies in two aspects. Mathematically, by using the Markov semigroups theory, we prove that the reproduction number R0S can be used to govern the stochastic dynamics of SDE model. If R0S 1, under mild extra conditions, it has an endemic stationary distribution which leads to the stochastical persistence of the disease. Epidemiologically, we find that random fluctuations can suppress disease outbreak, which can provide us some useful control strategies to regulate disease dynamics.
Lima, L. S.; Miranda, L. L. B.
2018-01-01
We have used the Itô's stochastic differential equation for the double well with additive white noise as a mathematical model for price dynamics of the financial market. We have presented a model which allows us to test within the same framework the comparative explanatory power of rational agents versus irrational agents, with respect to the facts of financial markets. We have obtained the mean price in terms of the β parameter that represents the force of the randomness term of the model.
Distributed Consensus of Stochastic Delayed Multi-agent Systems Under Asynchronous Switching.
Wu, Xiaotai; Tang, Yang; Cao, Jinde; Zhang, Wenbing
2016-08-01
In this paper, the distributed exponential consensus of stochastic delayed multi-agent systems with nonlinear dynamics is investigated under asynchronous switching. The asynchronous switching considered here is to account for the time of identifying the active modes of multi-agent systems. After receipt of confirmation of mode's switching, the matched controller can be applied, which means that the switching time of the matched controller in each node usually lags behind that of system switching. In order to handle the coexistence of switched signals and stochastic disturbances, a comparison principle of stochastic switched delayed systems is first proved. By means of this extended comparison principle, several easy to verified conditions for the existence of an asynchronously switched distributed controller are derived such that stochastic delayed multi-agent systems with asynchronous switching and nonlinear dynamics can achieve global exponential consensus. Two examples are given to illustrate the effectiveness of the proposed method.
Asymptotic analysis for functional stochastic differential equations
Bao, Jianhai; Yuan, Chenggui
2016-01-01
This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity. This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes.
Multiscale Hy3S: Hybrid stochastic simulation for supercomputers
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Kaznessis Yiannis N
2006-02-01
Full Text Available Abstract Background Stochastic simulation has become a useful tool to both study natural biological systems and design new synthetic ones. By capturing the intrinsic molecular fluctuations of "small" systems, these simulations produce a more accurate picture of single cell dynamics, including interesting phenomena missed by deterministic methods, such as noise-induced oscillations and transitions between stable states. However, the computational cost of the original stochastic simulation algorithm can be high, motivating the use of hybrid stochastic methods. Hybrid stochastic methods partition the system into multiple subsets and describe each subset as a different representation, such as a jump Markov, Poisson, continuous Markov, or deterministic process. By applying valid approximations and self-consistently merging disparate descriptions, a method can be considerably faster, while retaining accuracy. In this paper, we describe Hy3S, a collection of multiscale simulation programs. Results Building on our previous work on developing novel hybrid stochastic algorithms, we have created the Hy3S software package to enable scientists and engineers to both study and design extremely large well-mixed biological systems with many thousands of reactions and chemical species. We have added adaptive stochastic numerical integrators to permit the robust simulation of dynamically stiff biological systems. In addition, Hy3S has many useful features, including embarrassingly parallelized simulations with MPI; special discrete events, such as transcriptional and translation elongation and cell division; mid-simulation perturbations in both the number of molecules of species and reaction kinetic parameters; combinatorial variation of both initial conditions and kinetic parameters to enable sensitivity analysis; use of NetCDF optimized binary format to quickly read and write large datasets; and a simple graphical user interface, written in Matlab, to help users
Måren, Inger Elisabeth; Kapfer, Jutta; Aarrestad, Per Arild; Grytnes, John-Arvid; Vandvik, Vigdis
2018-01-01
Successional dynamics in plant community assembly may result from both deterministic and stochastic ecological processes. The relative importance of different ecological processes is expected to vary over the successional sequence, between different plant functional groups, and with the disturbance levels and land-use management regimes of the successional systems. We evaluate the relative importance of stochastic and deterministic processes in bryophyte and vascular plant community assembly after fire in grazed and ungrazed anthropogenic coastal heathlands in Northern Europe. A replicated series of post-fire successions (n = 12) were initiated under grazed and ungrazed conditions, and vegetation data were recorded in permanent plots over 13 years. We used redundancy analysis (RDA) to test for deterministic successional patterns in species composition repeated across the replicate successional series and analyses of co-occurrence to evaluate to what extent species respond synchronously along the successional gradient. Change in species co-occurrences over succession indicates stochastic successional dynamics at the species level (i.e., species equivalence), whereas constancy in co-occurrence indicates deterministic dynamics (successional niche differentiation). The RDA shows high and deterministic vascular plant community compositional change, especially early in succession. Co-occurrence analyses indicate stochastic species-level dynamics the first two years, which then give way to more deterministic replacements. Grazed and ungrazed successions are similar, but the early stage stochasticity is higher in ungrazed areas. Bryophyte communities in ungrazed successions resemble vascular plant communities. In contrast, bryophytes in grazed successions showed consistently high stochasticity and low determinism in both community composition and species co-occurrence. In conclusion, stochastic and individualistic species responses early in succession give way to more
Quantum noise and stochastic reduction
International Nuclear Information System (INIS)
Brody, Dorje C; Hughston, Lane P
2006-01-01
In standard nonrelativistic quantum mechanics the expectation of the energy is a conserved quantity. It is possible to extend the dynamical law associated with the evolution of a quantum state consistently to include a nonlinear stochastic component, while respecting the conservation law. According to the dynamics thus obtained, referred to as the energy-based stochastic Schroedinger equation, an arbitrary initial state collapses spontaneously to one of the energy eigenstates, thus describing the phenomenon of quantum state reduction. In this paper, two such models are investigated: one that achieves state reduction in infinite time and the other in finite time. The properties of the associated energy expectation process and the energy variance process are worked out in detail. By use of a novel application of a nonlinear filtering method, closed-form solutions-algebraic in character and involving no integration-are obtained of both these models. In each case, the solution is expressed in terms of a random variable representing the terminal energy of the system and an independent noise process. With these solutions at hand it is possible to simulate explicitly the dynamics of the quantum states of complicated physical systems
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...
Stochastic Modeling of Past Volcanic Crises
Woo, Gordon
2018-01-01
The statistical foundation of disaster risk analysis is past experience. From a scientific perspective, history is just one realization of what might have happened, given the randomness and chaotic dynamics of Nature. Stochastic analysis of the past is an exploratory exercise in counterfactual history, considering alternative possible scenarios. In particular, the dynamic perturbations that might have transitioned a volcano from an unrest to an eruptive state need to be considered. The stochastic modeling of past volcanic crises leads to estimates of eruption probability that can illuminate historical volcanic crisis decisions. It can also inform future economic risk management decisions in regions where there has been some volcanic unrest, but no actual eruption for at least hundreds of years. Furthermore, the availability of a library of past eruption probabilities would provide benchmark support for estimates of eruption probability in future volcanic crises.
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.
Mean, covariance, and effective dimension of stochastic distributed delay dynamics
René, Alexandre; Longtin, André
2017-11-01
Dynamical models are often required to incorporate both delays and noise. However, the inherently infinite-dimensional nature of delay equations makes formal solutions to stochastic delay differential equations (SDDEs) challenging. Here, we present an approach, similar in spirit to the analysis of functional differential equations, but based on finite-dimensional matrix operators. This results in a method for obtaining both transient and stationary solutions that is directly amenable to computation, and applicable to first order differential systems with either discrete or distributed delays. With fewer assumptions on the system's parameters than other current solution methods and no need to be near a bifurcation, we decompose the solution to a linear SDDE with arbitrary distributed delays into natural modes, in effect the eigenfunctions of the differential operator, and show that relatively few modes can suffice to approximate the probability density of solutions. Thus, we are led to conclude that noise makes these SDDEs effectively low dimensional, which opens the possibility of practical definitions of probability densities over their solution space.
Stochastic Dynamics of Clay Translocation and Formation of Argillic Horizons
Calabrese, S.; Richter, D. D., Jr.; Porporato, A. M.
2017-12-01
The formation of argillic horizons in vertical soil profiles is mainly attributed to lessivage, namely the transport of clay from an upper E horizon to a deeper illuviated horizon. Because of the long timescales involved in this phenomenon, quantitative modeling is useful to explore the role of clay lessivage on soil formation and sub-surface clay accumulation. The limitations of detailed models of colloidal transport to short timescales make it necessary to resort to simple models. Here, we present a parsimonious model of clay transport in which lessivage is interpreted stochastically. Clay particles approach the soil surface at a speed equal to the erosion rate and are intermittently transported to deeper soil layers when percolation events occur or removed by erosion. Along with the evolution of clay particles trajectories, the model predicts the vertical clay profile, the depth of the B horizon, and the mean time to erosion. Dimensional analysis reveals the two dimensionless parameters governing the dynamics, leading to a new classification of soil types based on erosion rates and intensity of lessivage.
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.
Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows
Gay-Balmaz, François; Holm, Darryl D.
2018-01-01
Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.
Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows
Gay-Balmaz, François; Holm, Darryl D.
2018-06-01
Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.
Directory of Open Access Journals (Sweden)
Wenlei Bai
2017-12-01
Full Text Available The deterministic methods generally used to solve DC optimal power flow (OPF do not fully capture the uncertainty information in wind power, and thus their solutions could be suboptimal. However, the stochastic dynamic AC OPF problem can be used to find an optimal solution by fully capturing the uncertainty information of wind power. That uncertainty information of future wind power can be well represented by the short-term future wind power scenarios that are forecasted using the generalized dynamic factor model (GDFM—a novel multivariate statistical wind power forecasting model. Furthermore, the GDFM can accurately represent the spatial and temporal correlations among wind farms through the multivariate stochastic process. Fully capturing the uncertainty information in the spatially and temporally correlated GDFM scenarios can lead to a better AC OPF solution under a high penetration level of wind power. Since the GDFM is a factor analysis based model, the computational time can also be reduced. In order to further reduce the computational time, a modified artificial bee colony (ABC algorithm is used to solve the AC OPF problem based on the GDFM forecasting scenarios. Using the modified ABC algorithm based on the GDFM forecasting scenarios has resulted in better AC OPF’ solutions on an IEEE 118-bus system at every hour for 24 h.
Stochastic synchronization in finite size spiking networks
Doiron, Brent; Rinzel, John; Reyes, Alex
2006-09-01
We study a stochastic synchronization of spiking activity in feedforward networks of integrate-and-fire model neurons. A stochastic mean field analysis shows that synchronization occurs only when the network size is sufficiently small. This gives evidence that the dynamics, and hence processing, of finite size populations can be drastically different from that observed in the infinite size limit. Our results agree with experimentally observed synchrony in cortical networks, and further strengthen the link between synchrony and propagation in cortical systems.
International Nuclear Information System (INIS)
Ghirardi, G.C.; Pearle, P.
1991-02-01
The problem of getting a relativistic generalization of the CSL dynamical reduction model, which has been presented in part I, is discussed. In so doing we have the opportunity to introduce the idea of a stochastically invariant theory. The theoretical model we present, that satisfies this kind of invariance requirement, offers us the possibility to reconsider, from a new point of view, some conceptually relevant issues such as nonlocality, the legitimacy of attributing elements of physical reality to physical systems and the problem of establishing causal relations between physical events. (author). Refs, 3 figs
Stochastic electromagnetic radiation of complex sources
Naus, H.W.L.
2007-01-01
The emission of electromagnetic radiation by localized complex electric charge and current distributions is studied. A statistical formalism in terms of general dynamical multipole fields is developed. The appearing coefficients are treated as stochastic variables. Hereby as much as possible a
Energy Technology Data Exchange (ETDEWEB)
Homem-de-Mello, Tito [University of Illinois at Chicago, Department of Mechanical and Industrial Engineering, Chicago, IL (United States); Matos, Vitor L. de; Finardi, Erlon C. [Universidade Federal de Santa Catarina, LabPlan - Laboratorio de Planejamento de Sistemas de Energia Eletrica, Florianopolis (Brazil)
2011-03-15
The long-term hydrothermal scheduling is one of the most important problems to be solved in the power systems area. This problem aims to obtain an optimal policy, under water (energy) resources uncertainty, for hydro and thermal plants over a multi-annual planning horizon. It is natural to model the problem as a multi-stage stochastic program, a class of models for which algorithms have been developed. The original stochastic process is represented by a finite scenario tree and, because of the large number of stages, a sampling-based method such as the Stochastic Dual Dynamic Programming (SDDP) algorithm is required. The purpose of this paper is two-fold. Firstly, we study the application of two alternative sampling strategies to the standard Monte Carlo - namely, Latin hypercube sampling and randomized quasi-Monte Carlo - for the generation of scenario trees, as well as for the sampling of scenarios that is part of the SDDP algorithm. Secondly, we discuss the formulation of stopping criteria for the optimization algorithm in terms of statistical hypothesis tests, which allows us to propose an alternative criterion that is more robust than that originally proposed for the SDDP. We test these ideas on a problem associated with the whole Brazilian power system, with a three-year planning horizon. (orig.)
Stochastic three-wave interaction in flaring solar loops
Vlahos, L.; Sharma, R. R.; Papadopoulos, K.
1983-01-01
A model is proposed for the dynamic structure of high-frequency microwave bursts. The dynamic component is attributed to beams of precipitating electrons which generate electrostatic waves in the upper hybrid branch. Coherent upconversion of the electrostatic waves to electromagnetic waves produces an intrinsically stochastic emission component which is superposed on the gyrosynchrotron continuum generated by stably trapped electron fluxes. The role of the density and temperature of the ambient plasma in the wave growth and the transition of the three wave upconversion to stochastic, despite the stationarity of the energy source, are discussed in detail. The model appears to reproduce the observational features for reasonable parameters of the solar flare plasma.
Stochastic three-wave interaction in flaring solar loops
International Nuclear Information System (INIS)
Vlahos, L.; Sharma, R.R.; Papadopoulos, K.
1983-01-01
We propose a model for the dynamic structure of high-frequency microwave bursts. The dynamic component is attributed to beams of precipitating electrons which generate electrostatic waves in the upper hybrid branch. Coherent upconversion of the electrostatic waves to electromagnetic waves produces an intrinsically stochastic emission component which is superposed on the gyrosynchrotron continuum generated by stably trapped electron fluxes. The role of the density and temperature of the ambient plasma in the wave growth and the transition of the three wave upconversion to stochastic, despite the stationarity of the energy source are discussed in detail. The model appears to reproduce the observational features for reasonable parameters of the solar flare plasma
A stochastic programming approach to manufacturing flow control
Haurie, Alain; Moresino, Francesco
2012-01-01
This paper proposes and tests an approximation of the solution of a class of piecewise deterministic control problems, typically used in the modeling of manufacturing flow processes. This approximation uses a stochastic programming approach on a suitably discretized and sampled system. The method proceeds through two stages: (i) the Hamilton-Jacobi-Bellman (HJB) dynamic programming equations for the finite horizon continuous time stochastic control problem are discretized over a set of sample...
A stochastic analysis for a phytoplankton-zooplankton model
International Nuclear Information System (INIS)
Ge, G; Wang, H-L; Xu, J
2008-01-01
A simple phytoplankton-zooplankton nonlinear dynamical model was proposed to study the coexistence of all the species and a Hopf bifurcation was observed. In order to study the effect of environmental robustness on this system, we have stochastically perturbed the system with respect to white noise around its positive interior equilibrium. We have observed that the system remains stochastically stable around the positive equilibrium for same parametric values in the deterministic situation
Simons, S.L.; Bartelings, H.; Hamon, K.G.; Kempf, A.J.; Doring, R.; Temming, A.
2014-01-01
There is growing interest in bioeconomic models as tools for understanding pathways of fishery behaviour in order to assess the impact of alternative policies on natural resources. A model system is presented that combines stochastic age-structured population dynamics with complex fisheries
DEFF Research Database (Denmark)
Mosekilde, Erik
Through a significant number of detailed and realistic examples this book illustrates how the insights gained over the past couple of decades in the fields of nonlinear dynamics and chaos theory can be applied in practice. Aomng the topics considered are microbiological reaction systems, ecological...... food-web systems, nephron pressure and flow regulation, pulsatile secretion of hormones, thermostatically controlled radiator systems, post-stall maneuvering of aircrafts, transfer electron devices for microwave generation, economic long waves, human decision making behavior, and pattern formation...... in chemical reaction-diffusion systems....
Manipulating potential wells in Logical Stochastic Resonance to obtain XOR logic
International Nuclear Information System (INIS)
Storni, Remo; Ando, Hiroyasu; Aihara, Kazuyuki; Murali, K.; Sinha, Sudeshna
2012-01-01
Logical Stochastic Resonance (LSR) is the application of Stochastic Resonance to logic computation, namely the phenomenon where a nonlinear system driven by weak signals representing logic inputs, under optimal noise, can yield logic outputs. We extend the existing results, obtained in the context of bistable systems, to multi-stable dynamical systems, allowing us to obtain XOR logic, in addition to the AND (NAND) and OR (NOR) logic observed in earlier studies. This strategy widens the scope of LSR from the application point of view, as XOR forms the basis of ubiquitous bit-by-bit addition, and conceptually, showing the ability to yield non-monotonic input–output logic associations. -- Highlights: ► We generalize Logical Stochastic Resonance from bistable to multi-stable systems. ► We propose a tristable dynamical system formed of piecewise linear functions. ► The system can correctly reproduce XOR logic behavior using the LSR principle. ► The system yields different logic behavior without the need to change the dynamics.
Determination of the crystal-melt interface kinetic coefficient from molecular dynamics simulations
International Nuclear Information System (INIS)
Monk, J; Mendelev, M I; Yang, Y; Asta, M; Hoyt, J J; Sun, D Y
2010-01-01
The generation and dissipation of latent heat at the moving solid–liquid boundary during non-equilibrium molecular dynamics (MD) simulations of crystallization can lead to significant underestimations of the interface mobility. In this work we examine the heat flow problem in detail for an embedded atom description of pure Ni and offer strategies to obtain an accurate value of the kinetic coefficient, μ. For free-solidification simulations in which the entire system is thermostated using a Nose–Hoover or velocity rescaling algorithm a non-uniform temperature profile is observed and a peak in the temperature is found at the interface position. It is shown that if the actual interface temperature, rather than the thermostat set point temperature, is used to compute the kinetic coefficient then μ is approximately a factor of 2 larger than previous estimates. In addition, we introduce a layered thermostat method in which several sub-regions, aligned normal to the crystallization direction, are indepently thermostated to a desired undercooling. We show that as the number of thermostats increases (i.e., as the width of each independently thermostated layer decreases) the kinetic coefficient converges to a value consistent with that obtained using a single thermostat and the calculated interface temperature. Also, the kinetic coefficient was determined from an analysis of the equilibrium fluctuations of the solid–liquid interface position. We demonstrate that the kinetic coefficient obtained from the relaxation times of the fluctuation spectrum is equivalent to the two values obtained from free-solidification simulations provided a simple correction is made for the contribution of heat flow controlled interface motion. Finally, a one-dimensional phase field model that captures the effect of thermostats has been developed. The mesoscale model reproduces qualitatively the results from MD simulations and thus allows for an a priori estimate of the accuracy of a
Directory of Open Access Journals (Sweden)
Xueling Jiang
2014-01-01
Full Text Available The problem of adaptive asymptotical synchronization is discussed for the stochastic complex dynamical networks with time-delay and Markovian switching. By applying the stochastic analysis approach and the M-matrix method for stochastic complex networks, several sufficient conditions to ensure adaptive asymptotical synchronization for stochastic complex networks are derived. Through the adaptive feedback control techniques, some suitable parameters update laws are obtained. Simulation result is provided to substantiate the effectiveness and characteristics of the proposed approach.
BRS invariant stochastic quantization of Einstein gravity
International Nuclear Information System (INIS)
Nakazawa, Naohito.
1989-11-01
We study stochastic quantization of gravity in terms of a BRS invariant canonical operator formalism. By introducing artificially canonical momentum variables for the original field variables, a canonical formulation of stochastic quantization is proposed in the sense that the Fokker-Planck hamiltonian is the generator of the fictitious time translation. Then we show that there exists a nilpotent BRS symmetry in an enlarged phase space of the first-class constrained systems. The phase space is spanned by the dynamical variables, their canonical conjugate momentum variables, Faddeev-Popov ghost and anti-ghost. We apply the general BRS invariant formulation to stochastic quantization of gravity which is described as a second-class constrained system in terms of a pair of Langevin equations coupled with white noises. It is shown that the stochastic action of gravity includes explicitly the De Witt's type superspace metric which leads to a geometrical interpretation of quantum gravity analogous to nonlinear σ-models. (author)
Evolutionary stability concepts in a stochastic environment
Zheng, Xiu-Deng; Li, Cong; Lessard, Sabin; Tao, Yi
2017-09-01
Over the past 30 years, evolutionary game theory and the concept of an evolutionarily stable strategy have been not only extensively developed and successfully applied to explain the evolution of animal behaviors, but also widely used in economics and social sciences. Nonetheless, the stochastic dynamical properties of evolutionary games in randomly fluctuating environments are still unclear. In this study, we investigate conditions for stochastic local stability of fixation states and constant interior equilibria in a two-phenotype model with random payoffs following pairwise interactions. Based on this model, we develop the concepts of stochastic evolutionary stability (SES) and stochastic convergence stability (SCS). We show that the condition for a pure strategy to be SES and SCS is more stringent than in a constant environment, while the condition for a constant mixed strategy to be SES is less stringent than the condition to be SCS, which is less stringent than the condition in a constant environment.
Willigenburg, van L.G.; Koning, de W.L.
2013-01-01
Two different descriptions are used in the literature to formulate the optimal dynamic output feedback control problem for linear dynamical systems with white stochastic parameters and quadratic criteria, called the optimal compensation problem. One describes the matrix valued white stochastic
Optimization of stochastic discrete systems and control on complex networks computational networks
Lozovanu, Dmitrii
2014-01-01
This book presents the latest findings on stochastic dynamic programming models and on solving optimal control problems in networks. It includes the authors' new findings on determining the optimal solution of discrete optimal control problems in networks and on solving game variants of Markov decision problems in the context of computational networks. First, the book studies the finite state space of Markov processes and reviews the existing methods and algorithms for determining the main characteristics in Markov chains, before proposing new approaches based on dynamic programming and combinatorial methods. Chapter two is dedicated to infinite horizon stochastic discrete optimal control models and Markov decision problems with average and expected total discounted optimization criteria, while Chapter three develops a special game-theoretical approach to Markov decision processes and stochastic discrete optimal control problems. In closing, the book's final chapter is devoted to finite horizon stochastic con...
Stabilization Strategies of Supply Networks with Stochastic Switched Topology
Directory of Open Access Journals (Sweden)
Shukai Li
2013-01-01
Full Text Available In this paper, a dynamical supply networks model with stochastic switched topology is presented, in which the stochastic switched topology is dependent on a continuous time Markov process. The goal is to design the state-feedback control strategies to stabilize the dynamical supply networks. Based on Lyapunov stability theory, sufficient conditions for the existence of state feedback control strategies are given in terms of matrix inequalities, which ensure the robust stability of the supply networks at the stationary states and a prescribed H∞ disturbance attenuation level with respect to the uncertain demand. A numerical example is given to illustrate the effectiveness of the proposed method.
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.
Hughes, Samantha Jane; Cabral, João Alexandre; Bastos, Rita; Cortes, Rui; Vicente, Joana; Eitelberg, David; Yu, Huirong; Honrado, João; Santos, Mário
2016-01-01
This method development paper outlines an integrative stochastic dynamic methodology (StDM) framework to anticipate land use (LU) change effects on the ecological status of monitored and non-monitored lotic surface waters under the Water Framework Directive (WFD). Tested in the Alto Minho River
Probabilistic DHP adaptive critic for nonlinear stochastic control systems.
Herzallah, Randa
2013-06-01
Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Káarnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained. Copyright © 2013 Elsevier Ltd. All rights reserved.
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.
Stochastic resonance: noise-enhanced order
International Nuclear Information System (INIS)
Anishchenko, Vadim S; Neiman, Arkady B; Moss, F; Shimansky-Geier, L
1999-01-01
Stochastic resonance (SR) provides a glaring example of a noise-induced transition in a nonlinear system driven by an information signal and noise simultaneously. In the regime of SR some characteristics of the information signal (amplification factor, signal-to-noise ratio, the degrees of coherence and of order, etc.) at the output of the system are significantly improved at a certain optimal noise level. SR is realized only in nonlinear systems for which a noise-intensity-controlled characteristic time becomes available. In the present review the physical mechanism and methods of theoretical description of SR are briefly discussed. SR features determined by the structure of the information signal, noise statistics and properties of particular systems with SR are studied. A nontrivial phenomenon of stochastic synchronization defined as locking of the instantaneous phase and switching frequency of a bistable system by external periodic force is analyzed in detail. Stochastic synchronization is explored in single and coupled bistable oscillators, including ensembles. The effects of SR and stochastic synchronization of ensembles of stochastic resonators are studied both with and without coupling between the elements. SR is considered in dynamical and nondynamical (threshold) systems. The SR effect is analyzed from the viewpoint of information and entropy characteristics of the signal, which determine the degree of order or self-organization in the system. Applications of the SR concept to explaining the results of a series of biological experiments are discussed. (reviews of topical problems)
Stochastic resonance: noise-enhanced order
Energy Technology Data Exchange (ETDEWEB)
Anishchenko, Vadim S; Neiman, Arkady B [N.G. Chernyshevskii Saratov State University, Saratov (Russian Federation); Moss, F [Department of Physics and Astronomy, University of Missouri at St. Louis (United States); Shimansky-Geier, L [Humboldt University at Berlin (Germany)
1999-01-31
Stochastic resonance (SR) provides a glaring example of a noise-induced transition in a nonlinear system driven by an information signal and noise simultaneously. In the regime of SR some characteristics of the information signal (amplification factor, signal-to-noise ratio, the degrees of coherence and of order, etc.) at the output of the system are significantly improved at a certain optimal noise level. SR is realized only in nonlinear systems for which a noise-intensity-controlled characteristic time becomes available. In the present review the physical mechanism and methods of theoretical description of SR are briefly discussed. SR features determined by the structure of the information signal, noise statistics and properties of particular systems with SR are studied. A nontrivial phenomenon of stochastic synchronization defined as locking of the instantaneous phase and switching frequency of a bistable system by external periodic force is analyzed in detail. Stochastic synchronization is explored in single and coupled bistable oscillators, including ensembles. The effects of SR and stochastic synchronization of ensembles of stochastic resonators are studied both with and without coupling between the elements. SR is considered in dynamical and nondynamical (threshold) systems. The SR effect is analyzed from the viewpoint of information and entropy characteristics of the signal, which determine the degree of order or self-organization in the system. Applications of the SR concept to explaining the results of a series of biological experiments are discussed. (reviews of topical problems)
Path probability of stochastic motion: A functional approach
Hattori, Masayuki; Abe, Sumiyoshi
2016-06-01
The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a tube/band, the center of which is stipulated by a given path, is analytically evaluated in a way analogous to continuous measurements in quantum mechanics. Then, the formalism developed here is applied to the stochastic dynamics of stock price in finance.
Directory of Open Access Journals (Sweden)
K. Hacıefendioğlu
2012-04-01
Full Text Available The deconvolution effect of the near-fault earthquake ground motions on the stochastic dynamic response of tunnel-soil deposit interaction systems are investigated by using the finite element method. Two different earthquake input mechanisms are used to consider the deconvolution effects in the analyses: the standard rigid-base input and the deconvolved-base-rock input model. The Bolu tunnel in Turkey is chosen as a numerical example. As near-fault ground motions, 1999 Kocaeli earthquake ground motion is selected. The interface finite elements are used between tunnel and soil deposit. The mean of maximum values of quasi-static, dynamic and total responses obtained from the two input models are compared with each other.
Stochastic dynamical models for ecological regime shifts
DEFF Research Database (Denmark)
Møller, Jan Kloppenborg; Carstensen, Jacob; Madsen, Henrik
the physical and biological knowledge of the system, and nonlinearities introduced here can generate regime shifts or enhance the probability of regime shifts in the case of stochastic models, typically characterized by a threshold value for the known driver. A simple model for light competition between...... definition and stability of regimes become less subtle. Ecological regime shifts and their modeling must be viewed in a probabilistic manner, particularly if such model results are to be used in ecosystem management....
A stochastic-field description of finite-size spiking neural networks.
Dumont, Grégory; Payeur, Alexandre; Longtin, André
2017-08-01
Neural network dynamics are governed by the interaction of spiking neurons. Stochastic aspects of single-neuron dynamics propagate up to the network level and shape the dynamical and informational properties of the population. Mean-field models of population activity disregard the finite-size stochastic fluctuations of network dynamics and thus offer a deterministic description of the system. Here, we derive a stochastic partial differential equation (SPDE) describing the temporal evolution of the finite-size refractory density, which represents the proportion of neurons in a given refractory state at any given time. The population activity-the density of active neurons per unit time-is easily extracted from this refractory density. The SPDE includes finite-size effects through a two-dimensional Gaussian white noise that acts both in time and along the refractory dimension. For an infinite number of neurons the standard mean-field theory is recovered. A discretization of the SPDE along its characteristic curves allows direct simulations of the activity of large but finite spiking networks; this constitutes the main advantage of our approach. Linearizing the SPDE with respect to the deterministic asynchronous state allows the theoretical investigation of finite-size activity fluctuations. In particular, analytical expressions for the power spectrum and autocorrelation of activity fluctuations are obtained. Moreover, our approach can be adapted to incorporate multiple interacting populations and quasi-renewal single-neuron dynamics.
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.
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.
DEFF Research Database (Denmark)
Duun-Henriksen, Anne Katrine; Schmidt, S.; Nørgaard, K.
2013-01-01
extension incorporating exercise effects on insulin and glucose dynamics. Our model is constructed as a stochastic state space model consisting of a set of stochastic differential equations (SDEs). In a stochastic state space model, the residual error is split into random measurement error...
Fractional diffusion equation with distributed-order material derivative. Stochastic foundations
International Nuclear Information System (INIS)
Magdziarz, M; Teuerle, M
2017-01-01
In this paper, we present the stochastic foundations of fractional dynamics driven by the fractional material derivative of distributed-order type. Before stating our main result, we present the stochastic scenario which underlies the dynamics given by the fractional material derivative. Then we introduce the Lévy walk process of distributed-order type to establish our main result, which is the scaling limit of the considered process. It appears that the probability density function of the scaling limit process fulfills, in a weak sense, the fractional diffusion equation with the material derivative of distributed-order type. (paper)
Predicting Footbridge Response using Stochastic Load Models
DEFF Research Database (Denmark)
Pedersen, Lars; Frier, Christian
2013-01-01
Walking parameters such as step frequency, pedestrian mass, dynamic load factor, etc. are basically stochastic, although it is quite common to adapt deterministic models for these parameters. The present paper considers a stochastic approach to modeling the action of pedestrians, but when doing so...... decisions need to be made in terms of statistical distributions of walking parameters and in terms of the parameters describing the statistical distributions. The paper explores how sensitive computations of bridge response are to some of the decisions to be made in this respect. This is useful...
Computing Optimal Stochastic Portfolio Execution Strategies: A Parametric Approach Using Simulations
Moazeni, Somayeh; Coleman, Thomas F.; Li, Yuying
2010-09-01
Computing optimal stochastic portfolio execution strategies under appropriate risk consideration presents great computational challenge. We investigate a parametric approach for computing optimal stochastic strategies using Monte Carlo simulations. This approach allows reduction in computational complexity by computing coefficients for a parametric representation of a stochastic dynamic strategy based on static optimization. Using this technique, constraints can be similarly handled using appropriate penalty functions. We illustrate the proposed approach to minimize the expected execution cost and Conditional Value-at-Risk (CVaR).
Computational stochastic model of ions implantation
Energy Technology Data Exchange (ETDEWEB)
Zmievskaya, Galina I., E-mail: zmi@gmail.ru; Bondareva, Anna L., E-mail: bal310775@yandex.ru [M.V. Keldysh Institute of Applied Mathematics RAS, 4,Miusskaya sq., 125047 Moscow (Russian Federation); Levchenko, Tatiana V., E-mail: tatlevchenko@mail.ru [VNII Geosystem Russian Federal Center, Varshavskoye roadway, 8, Moscow (Russian Federation); Maino, Giuseppe, E-mail: giuseppe.maino@enea.it [Scuola di Lettere e BeniCulturali, University di Bologna, sede di Ravenna, via Mariani 5, 48100 Ravenna (Italy)
2015-03-10
Implantation flux ions into crystal leads to phase transition /PT/ 1-st kind. Damaging lattice is associated with processes clustering vacancies and gaseous bubbles as well their brownian motion. System of stochastic differential equations /SDEs/ Ito for evolution stochastic dynamical variables corresponds to the superposition Wiener processes. The kinetic equations in partial derivatives /KE/, Kolmogorov-Feller and Einstein-Smolukhovskii, were formulated for nucleation into lattice of weakly soluble gases. According theory, coefficients of stochastic and kinetic equations uniquely related. Radiation stimulated phase transition are characterized by kinetic distribution functions /DFs/ of implanted clusters versus their sizes and depth of gas penetration into lattice. Macroscopic parameters of kinetics such as the porosity and stress calculated in thin layers metal/dielectric due to Xe{sup ++} irradiation are attracted as example. Predictions of porosity, important for validation accumulation stresses in surfaces, can be applied at restoring of objects the cultural heritage.
Collective stochastic coherence in recurrent neuronal networks
Sancristóbal, Belén; Rebollo, Beatriz; Boada, Pol; Sanchez-Vives, Maria V.; Garcia-Ojalvo, Jordi
2016-09-01
Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can show substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level coexists with regular oscillations at the global level is still unclear. Here we show that a combination of stochastic recurrence-based initiation with deterministic refractoriness in an excitable network can reconcile these two features, leading to maximum collective coherence for an intermediate noise level. We report this behaviour in the slow oscillation regime exhibited by a cerebral cortex network under dynamical conditions resembling slow-wave sleep and anaesthesia. Computational analysis of a biologically realistic network model reveals that an intermediate level of background noise leads to quasi-regular dynamics. We verify this prediction experimentally in cortical slices subject to varying amounts of extracellular potassium, which modulates neuronal excitability and thus synaptic noise. The model also predicts that this effectively regular state should exhibit noise-induced memory of the spatial propagation profile of the collective oscillations, which is also verified experimentally. Taken together, these results allow us to construe the high regularity observed experimentally in the brain as an instance of collective stochastic coherence.
System Entropy Measurement of Stochastic Partial Differential Systems
Directory of Open Access Journals (Sweden)
Bor-Sen Chen
2016-03-01
Full Text Available System entropy describes the dispersal of a system’s energy and is an indication of the disorder of a physical system. Several system entropy measurement methods have been developed for dynamic systems. However, most real physical systems are always modeled using stochastic partial differential dynamic equations in the spatio-temporal domain. No efficient method currently exists that can calculate the system entropy of stochastic partial differential systems (SPDSs in consideration of the effects of intrinsic random fluctuation and compartment diffusion. In this study, a novel indirect measurement method is proposed for calculating of system entropy of SPDSs using a Hamilton–Jacobi integral inequality (HJII-constrained optimization method. In other words, we solve a nonlinear HJII-constrained optimization problem for measuring the system entropy of nonlinear stochastic partial differential systems (NSPDSs. To simplify the system entropy measurement of NSPDSs, the global linearization technique and finite difference scheme were employed to approximate the nonlinear stochastic spatial state space system. This allows the nonlinear HJII-constrained optimization problem for the system entropy measurement to be transformed to an equivalent linear matrix inequalities (LMIs-constrained optimization problem, which can be easily solved using the MATLAB LMI-toolbox (MATLAB R2014a, version 8.3. Finally, several examples are presented to illustrate the system entropy measurement of SPDSs.
A stochastic-programming approach to integrated asset and liability ...
African Journals Online (AJOL)
This increase in complexity has provided an impetus for the investigation into integrated asset- and liability-management frameworks that could realistically address dynamic portfolio allocation in a risk-controlled way. In this paper the authors propose a multi-stage dynamic stochastic-programming model for the integrated ...
Erdal, Jørgen Sørgård
2017-01-01
This master thesis develops a stochastic optimisation software for household grid-connected batteries combined with PV-systems. The objective of the optimisation is to operate the battery system in order to minimise the costs of the consumer, and it was implemented in MATLAB using a self-written stochastic dynamic programming algorithm. Load was considered as a stochastic variable and modelled as a Markov Chain. Transition probabilities between time steps were calculated using historic load p...
A concise course on stochastic partial differential equations
Prévôt, Claudia
2007-01-01
These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. To keep the technicalities minimal we confine ourselves to the case where the noise term is given by a stochastic integral w.r.t. a cylindrical Wiener process.But all results can be easily generalized to SPDE with more general noises such as, for instance, stochastic integral w.r.t. a continuous local martingale. There are basically three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material, such as definitions and results from the theory of Hilbert spaces, are included in appendices.
Drift-Implicit Multi-Level Monte Carlo Tau-Leap Methods for Stochastic Reaction Networks
Ben Hammouda, Chiheb
2015-01-01
-space and deterministic ones. These stochastic models constitute the theory of stochastic reaction networks (SRNs). Furthermore, in some cases, the dynamics of fast and slow time scales can be well separated and this is characterized by what is called sti
Gerhard, Felipe; Deger, Moritz; Truccolo, Wilson
2017-02-01
Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of the expected conditional intensity function (CIF) for general PP-GLMs. Specifically, in nonlinear Hawkes PP-GLMs, the CIF is expressed as a function of the previous spike history and exogenous inputs. We use a mean-field quasi-renewal (QR) approximation that decomposes spike history effects into the contribution of the last spike and an average of the CIF over all spike histories prior to the last spike. Fixed points for stationary rates are derived as self-consistent solutions of integral equations. Bifurcation analysis and the number of fixed points predict that the original models can show stable, divergent, and metastable (fragile) dynamics. For fragile models, fluctuations of the single-neuron dynamics predict expected divergence times after which rates approach unphysiologically high values. This metric can be used to estimate the probability of rates to remain physiological for given time periods, e.g., for simulation purposes. We demonstrate the use of the stability framework using simulated single-neuron examples and neurophysiological recordings. Finally, we show how to adapt PP-GLM estimation procedures to guarantee model stability. Overall, our results provide a
International Nuclear Information System (INIS)
Rougé, Charles; Mathias, Jean-Denis; Deffuant, Guillaume
2014-01-01
The goal of this paper is twofold: (1) to show that time-variant reliability and a branch of control theory called stochastic viability address similar problems with different points of view, and (2) to demonstrate the relevance of concepts and methods from stochastic viability in reliability problems. On the one hand, reliability aims at evaluating the probability of failure of a system subjected to uncertainty and stochasticity. On the other hand, viability aims at maintaining a controlled dynamical system within a survival set. When the dynamical system is stochastic, this work shows that a viability problem belongs to a specific class of design and maintenance problems in time-variant reliability. Dynamic programming, which is used for solving Markovian stochastic viability problems, then yields the set of design states for which there exists a maintenance strategy which guarantees reliability with a confidence level β for a given period of time T. Besides, it leads to a straightforward computation of the date of the first outcrossing, informing on when the system is most likely to fail. We illustrate this approach with a simple example of population dynamics, including a case where load increases with time. - Highlights: • Time-variant reliability tools cannot devise complex maintenance strategies. • Stochastic viability is a control theory that computes a probability of failure. • Some design and maintenance problems are stochastic viability problems. • Used in viability, dynamic programming can find reliable maintenance actions. • Confronting reliability and control theories such as viability is promising
Antisymmetrized molecular dynamics of wave packets with stochastic incorporation of Vlasov equation
International Nuclear Information System (INIS)
Ono, Akira; Horiuchi, Hisashi.
1996-01-01
The first purpose of this report is to present an extended AMD model which can generally describe such minor branching processes by removing the restriction on the one-body distribution function. This is done not by generalizing the wave packets to arbitrary single-particle wave functions but by representing the diffused and/or deformed wave packet as an ensemble of Gaussian wave packets. In other words, stochastic displacements are given to the wave packets in phase space so that the ensemble-average of the time evolution of the one-body distribution function is essentially equivalent to the solution of Vlasov equation which does not have any restriction on the shape of wave packets. This new model is called AMD-V. Although AMD-V is equivalent to Vlasov equation in the instantaneous time evolution of the one-body distribution function for an AMD wave function, AMD-V describes the branching into channels and the fluctuation of the mean field which are caused by the spreading or the splitting of the single-particle wave function. The second purpose of this report is to show the drastic effect of this new stochastic process of wave packet splitting on the dynamics of heavy ion collisions, especially in the fragmentation mechanism. We take the 40 Ca + 40 Ca system at the incident energy 35 MeV/nucleon. It will be shown that the reproduction of data by the AMD-V calculation is surprisingly good. We will see that the effect of the wave packet diffusion is crucially important to remove the spurious binary feature of the AMD calculation and to enable the multi-fragment final state. (J.P.N.)
Quantum dynamical time evolutions as stochastic flows on phase space
International Nuclear Information System (INIS)
Combe, P.; Rodriguez, R.; Guerra, F.; Sirigue, M.; Sirigue-Collin, M.
1984-01-01
We are mainly interested in describing the time development of the Wigner functions by means of stochastic processes. In the second section we recall the main properties of the Wigner functions as well as those of their Fourier transform. In the next one we derive the evolution equation of these functions for a class of Hamiltonians and we give a probabilistic expression for the solution of these equations by means of a stochastic flow in phase space which reminds of the classical flows. In the last section we remark that the previously defined flow can be extended to the bounded continuous functions on phase space and that this flow conserves the cone generated by the Wigner functions. (orig./HSI)
Effects of demographic stochasticity on biological community assembly on evolutionary time scales
Murase, Yohsuke; Shimada, Takashi; Ito, Nobuyasu; Rikvold, Per Arne
2010-01-01
We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic communities show little dependence on the stochastic population fluctuations, predator-prey models show strong dependence on the stochasticity, indicating the relevance of the finiteness of the populations. For a predator-prey model, the noise causes drastic decreases in diversity and total population size. The communities that emerge under influence of the noise consist of species strongly coupled with each other and have stronger linear stability around the fixed-point populations than the corresponding noiseless model. The dynamics on evolutionary time scales for the predator-prey model are also altered by the noise. Approximate 1/f fluctuations are observed with noise, while 1/ f2 fluctuations are found for the model without demographic noise. © 2010 The American Physical Society.
Effects of demographic stochasticity on biological community assembly on evolutionary time scales
Murase, Yohsuke
2010-04-13
We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic communities show little dependence on the stochastic population fluctuations, predator-prey models show strong dependence on the stochasticity, indicating the relevance of the finiteness of the populations. For a predator-prey model, the noise causes drastic decreases in diversity and total population size. The communities that emerge under influence of the noise consist of species strongly coupled with each other and have stronger linear stability around the fixed-point populations than the corresponding noiseless model. The dynamics on evolutionary time scales for the predator-prey model are also altered by the noise. Approximate 1/f fluctuations are observed with noise, while 1/ f2 fluctuations are found for the model without demographic noise. © 2010 The American Physical Society.
Energy Technology Data Exchange (ETDEWEB)
Van Kessel, L.B.M.
2003-06-11
with the on-line calorific value sensor from chapter 2 and a validated dynamic model of the process is available, the theory from stochastic processes can be applied to MSWC. This new application field of stochastics is discussed in chapter 4. The results obtained in chapter 2 will be used in this analysis. Also new linear transfer functions for thermal processes will be given and applied to MSWC. Finally, applications of the new developed tools will be discussed. As already mentioned, the validation experiments lead to the conclusion that the dynamics of the combustion process can change when the primary air temperature changes. This was a new result, which has never been reported in literature before. For that reason during the research it was decided to start an extensive study into the influence of the primary air temperature on the combustion process. This has been performed by using laboratory experiments. In chapter 5 the results from this search will be presented. The existing theory for combustion of solid fuels is extended with a qualitative as well as a quantitative description of the influence of primary preheating. The new theory is used to explain observations from real plants and the results from system identification. Furthermore, the value of laboratory experiments to simulate the real combustion process on a grate is discussed.
Stochastic mixed-mode oscillations in a three-species predator-prey model
Sadhu, Susmita; Kuehn, Christian
2018-03-01
The effect of demographic stochasticity, in the form of Gaussian white noise, in a predator-prey model with one fast and two slow variables is studied. We derive the stochastic differential equations (SDEs) from a discrete model. For suitable parameter values, the deterministic drift part of the model admits a folded node singularity and exhibits a singular Hopf bifurcation. We focus on the parameter regime near the Hopf bifurcation, where small amplitude oscillations exist as stable dynamics in the absence of noise. In this regime, the stochastic model admits noise-driven mixed-mode oscillations (MMOs), which capture the intermediate dynamics between two cycles of population outbreaks. We perform numerical simulations to calculate the distribution of the random number of small oscillations between successive spikes for varying noise intensities and distance to the Hopf bifurcation. We also study the effect of noise on a suitable Poincaré map. Finally, we prove that the stochastic model can be transformed into a normal form near the folded node, which can be linked to recent results on the interplay between deterministic and stochastic small amplitude oscillations. The normal form can also be used to study the parameter influence on the noise level near folded singularities.
Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness
Hervé, Loïc
2001-01-01
This book shows how techniques from the perturbation theory of operators, applied to a quasi-compact positive kernel, may be used to obtain limit theorems for Markov chains or to describe stochastic properties of dynamical systems. A general framework for this method is given and then applied to treat several specific cases. An essential element of this work is the description of the peripheral spectra of a quasi-compact Markov kernel and of its Fourier-Laplace perturbations. This is first done in the ergodic but non-mixing case. This work is extended by the second author to the non-ergodic case. The only prerequisites for this book are a knowledge of the basic techniques of probability theory and of notions of elementary functional analysis.
A fuzzy-stochastic power system planning model: Reflection of dual objectives and dual uncertainties
International Nuclear Information System (INIS)
Zhang, X.Y.; Huang, G.H.; Zhu, H.; Li, Y.P.
2017-01-01
In this study, a fuzzy stochastic dynamic fractional programming (FSDFP) method is proposed for supporting sustainable management of electric power system (EPS) under dual uncertainties. As an improvement upon the mixed-integer linear fractional programming, FSDFP can not only tackle multi-objective issues effectively without setting weights, but also can deal with uncertain parameters which have both stochastic and fuzzy characteristics. Thus, the developed method can help provide valuable information for supporting capacity-expansion planning and in-depth policy analysis of EPS management problems. For demonstrating these advantages, FSDFP has been applied to a case study of a typical regional EPS planning, where the decision makers have to deal with conflicts between economic development that maximizes the system profit and environmental protection that minimizes the carbon dioxide emissions. The obtained results can be analyzed to generate several decision alternatives, and can then help decision makers make suitable decisions under different input scenarios. Furthermore, comparisons of the solution from FSDFP method with that from fuzzy stochastic dynamic linear programming, linear fractional programming and dynamic stochastic fractional programming methods are undertaken. The contrastive analysis reveals that FSDFP is a more effective approach that can better characterize the complexities and uncertainties of real EPS management problems. - Highlights: • A fuzzy stochastic dynamic fractional programming (FSDFP) method is proposed. • FSDFP can address multiple conflicting objectives without setting weights. • FSDFP can reflect dual uncertainties with both stochastic and fuzzy characteristics. • Some reasonable solutions for a case of power system sustainable planning are generated. • Comparisons of the solutions from FSDFP with other optimization methods are undertaken.
International Conference on Modern Problems of Stochastic Analysis and Statistics
2017-01-01
This book brings together the latest findings in the area of stochastic analysis and statistics. The individual chapters cover a wide range of topics from limit theorems, Markov processes, nonparametric methods, acturial science, population dynamics, and many others. The volume is dedicated to Valentin Konakov, head of the International Laboratory of Stochastic Analysis and its Applications on the occasion of his 70th birthday. Contributions were prepared by the participants of the international conference of the international conference “Modern problems of stochastic analysis and statistics”, held at the Higher School of Economics in Moscow from May 29 - June 2, 2016. It offers a valuable reference resource for researchers and graduate students interested in modern stochastics.
Stochastic analysis of a novel nonautonomous periodic SIRI epidemic system with random disturbances
Zhang, Weiwei; Meng, Xinzhu
2018-02-01
In this paper, a new stochastic nonautonomous SIRI epidemic model is formulated. Given that the incidence rates of diseases may change with the environment, we propose a novel type of transmission function. The main aim of this paper is to obtain the thresholds of the stochastic SIRI epidemic model. To this end, we investigate the dynamics of the stochastic system and establish the conditions for extinction and persistence in mean of the disease by constructing some suitable Lyapunov functions and using stochastic analysis technique. Furthermore, we show that the stochastic system has at least one nontrivial positive periodic solution. Finally, numerical simulations are introduced to illustrate our results.
International Nuclear Information System (INIS)
Nambu, Yohsuke; Takashima, Toshihide; Inagaki, Akiya
2015-01-01
This paper examines the effects of connecting multiplexing shunt circuits composed of inductors and resistors to piezoelectric transducers so as to improve the robustness of a piezoelectric vibration absorber (PVA). PVAs are well known to be effective at suppressing the vibration of an adaptive structure; their weakness is low robustness to changes in the dynamic parameters of the system, including the main structure and the absorber. In the application to space structures, the temperature-dependency of capacitance of piezoelectric ceramics is the factor that causes performance reduction. To improve robustness to the temperature-dependency of the capacitance, this paper proposes a multiple-PVA system that is composed of distributed piezoelectric transducers and several shunt circuits. The optimization problems that determine both the frequencies and the damping ratios of the PVAs are multi-objective problems, which are solved using a real-coded genetic algorithm in this paper. A clamped aluminum beam with four groups of piezoelectric ceramics attached was considered in simulations and experiments. Numerical simulations revealed that the PVA systems designed using the proposed method had tolerance to changes in the capacitances. Furthermore, experiments using a thermostatic bath were conducted to reveal the effectiveness and robustness of the PVA systems. The maximum peaks of the transfer functions of the beam with the open circuit, the single-PVA system, the double-PVA system, and the quadruple-PVA system at 20 °C were 14.3 dB, −6.91 dB, −7.47 dB, and −8.51 dB, respectively. The experimental results also showed that the multiple-PVA system is more robust than a single PVA in a variable temperature environment from −10 °C to 50 °C. In conclusion, the use of multiple PVAs results in an effective, robust vibration control method for adaptive structures. (paper)