Mean field strategies induce unrealistic nonlinearities in calcium puffs

Directory of Open Access Journals (Sweden)

Guillermo eSolovey

2011-08-01

Full Text Available Mean field models are often useful approximations to biological systems, but sometimes, they can yield misleading results. In this work, we compare mean field approaches with stochastic models of intracellular calcium release. In particular, we concentrate on calcium signals generated by the concerted opening of several clustered channels (calcium puffs. To this end we simulate calcium puffs numerically and then try to reproduce features of the resulting calcium distribution using mean field models were all the channels open and close simultaneously. We show that an unrealistic nonlinear relationship between the current and the number of open channels is needed to reproduce the simulated puffs. Furthermore, a single channel current which is five times smaller than the one of the stochastic simulations is also needed. Our study sheds light on the importance of the stochastic kinetics of the calcium release channel activity to estimate the release fluxes.

Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model

KAUST Repository

Erban, Radek; Chapman, S. Jonathan; Kevrekidis, Ioannis G.; Vejchodský , Tomá š

2009-01-01

A framework for the analysis of stochastic models of chemical systems for which the deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs, for example

Noisy mean field game model for malware propagation in opportunistic networks

KAUST Repository

Tembine, Hamidou

2012-01-01

In this paper we present analytical mean field techniques that can be used to better understand the behavior of malware propagation in opportunistic large networks. We develop a modeling methodology based on stochastic mean field optimal control that is able to capture many aspects of the problem, especially the impact of the control and heterogeneity of the system on the spreading characteristics of malware. The stochastic large process characterizing the evolution of the total number of infected nodes is examined with a noisy mean field limit and compared to a deterministic one. The stochastic nature of the wireless environment make stochastic approaches more realistic for such types of networks. By introducing control strategies, we show that the fraction of infected nodes can be maintained below some threshold. In contrast to most of the existing results on mean field propagation models which focus on deterministic equations, we show that the mean field limit is stochastic if the second moment of the number of object transitions per time slot is unbounded with the size of the system. This allows us to compare one path of the fraction of infected nodes with the stochastic trajectory of its mean field limit. In order to take into account the heterogeneity of opportunistic networks, the analysis is extended to multiple types of nodes. Our numerical results show that the heterogeneity can help to stabilize the system. We verify the results through simulation showing how to obtain useful approximations in the case of very large systems. © 2012 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering.

Risk-sensitive mean-field games

KAUST Repository

Tembine, Hamidou

2014-04-01

In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a Hamilton -Jacobi- Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics. © 1963-2012 IEEE.

Risk-sensitive mean-field games

KAUST Repository

Tembine, Hamidou; Zhu, Quanyan; Başar, Tamer

2014-01-01

In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a Hamilton -Jacobi- Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics. © 1963-2012 IEEE.

Revisiting the cape cod bacteria injection experiment using a stochastic modeling approach

Science.gov (United States)

Maxwell, R.M.; Welty, C.; Harvey, R.W.

2007-01-01

Bromide and resting-cell bacteria tracer tests conducted in a sandy aquifer at the U.S. Geological Survey Cape Cod site in 1987 were reinterpreted using a three-dimensional stochastic approach. Bacteria transport was coupled to colloid filtration theory through functional dependence of local-scale colloid transport parameters upon hydraulic conductivity and seepage velocity in a stochastic advection - dispersion/attachment - detachment model. Geostatistical information on the hydraulic conductivity (K) field that was unavailable at the time of the original test was utilized as input. Using geostatistical parameters, a groundwater flow and particle-tracking model of conservative solute transport was calibrated to the bromide-tracer breakthrough data. An optimization routine was employed over 100 realizations to adjust the mean and variance ofthe natural-logarithm of hydraulic conductivity (InK) field to achieve best fit of a simulated, average bromide breakthrough curve. A stochastic particle-tracking model for the bacteria was run without adjustments to the local-scale colloid transport parameters. Good predictions of mean bacteria breakthrough were achieved using several approaches for modeling components of the system. Simulations incorporating the recent Tufenkji and Elimelech (Environ. Sci. Technol. 2004, 38, 529-536) correlation equation for estimating single collector efficiency were compared to those using the older Rajagopalan and Tien (AIChE J. 1976, 22, 523-533) model. Both appeared to work equally well at predicting mean bacteria breakthrough using a constant mean bacteria diameter for this set of field conditions. Simulations using a distribution of bacterial cell diameters available from original field notes yielded a slight improvement in the model and data agreement compared to simulations using an average bacterial diameter. The stochastic approach based on estimates of local-scale parameters for the bacteria-transport process reasonably captured

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.

Stochastic approach and fluctuation theorem for charge transport in diodes

Science.gov (United States)

Gu, Jiayin; Gaspard, Pierre

2018-05-01

A stochastic approach for charge transport in diodes is developed in consistency with the laws of electricity, thermodynamics, and microreversibility. In this approach, the electron and hole densities are ruled by diffusion-reaction stochastic partial differential equations and the electric field generated by the charges is determined with the Poisson equation. These equations are discretized in space for the numerical simulations of the mean density profiles, the mean electric potential, and the current-voltage characteristics. Moreover, the full counting statistics of the carrier current and the measured total current including the contribution of the displacement current are investigated. On the basis of local detailed balance, the fluctuation theorem is shown to hold for both currents.

Hybrid approaches for multiple-species stochastic reaction–diffusion models

International Nuclear Information System (INIS)

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen

2015-01-01

Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. - Highlights: • A novel hybrid stochastic/deterministic reaction–diffusion simulation method is given. • Can massively speed up stochastic simulations while preserving stochastic effects. • Can handle multiple reacting species. • Can handle moving boundaries

Hybrid approaches for multiple-species stochastic reaction–diffusion models

Energy Technology Data Exchange (ETDEWEB)

Spill, Fabian, E-mail: fspill@bu.edu [Department of Biomedical Engineering, Boston University, 44 Cummington Street, Boston, MA 02215 (United States); Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Guerrero, Pilar [Department of Mathematics, University College London, Gower Street, London WC1E 6BT (United Kingdom); Alarcon, Tomas [Centre de Recerca Matematica, Campus de Bellaterra, Edifici C, 08193 Bellaterra (Barcelona) (Spain); Departament de Matemàtiques, Universitat Atonòma de Barcelona, 08193 Bellaterra (Barcelona) (Spain); Maini, Philip K. [Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom); Byrne, Helen [Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom); Computational Biology Group, Department of Computer Science, University of Oxford, Oxford OX1 3QD (United Kingdom)

2015-10-15

Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. - Highlights: • A novel hybrid stochastic/deterministic reaction–diffusion simulation method is given. • Can massively speed up stochastic simulations while preserving stochastic effects. • Can handle multiple reacting species. • Can handle moving boundaries.

International Diversification Versus Domestic Diversification: Mean-Variance Portfolio Optimization and Stochastic Dominance Approaches

Directory of Open Access Journals (Sweden)

Fathi Abid

2014-05-01

Full Text Available This paper applies the mean-variance portfolio optimization (PO approach and the stochastic dominance (SD test to examine preferences for international diversification versus domestic diversification from American investors’ viewpoints. Our PO results imply that the domestic diversification strategy dominates the international diversification strategy at a lower risk level and the reverse is true at a higher risk level. Our SD analysis shows that there is no arbitrage opportunity between international and domestic stock markets; domestically diversified portfolios with smaller risk dominate internationally diversified portfolios with larger risk and vice versa; and at the same risk level, there is no difference between the domestically and internationally diversified portfolios. Nonetheless, we cannot find any domestically diversified portfolios that stochastically dominate all internationally diversified portfolios, but we find some internationally diversified portfolios with small risk that dominate all the domestically diversified portfolios.

Stochastic modeling of catalytic processes in nanoporous materials: Beyond mean-field approach

Energy Technology Data Exchange (ETDEWEB)

Garcia, Andres [Iowa State Univ., Ames, IA (United States)

2017-08-05

Transport and reaction in zeolites and other porous materials, such as mesoporous silica particles, has been a focus of interest in recent years. This is in part due to the possibility of anomalous transport effects (e.g. single-file diffusion) and its impact in the reaction yield in catalytic processes. Computational simulations are often used to study these complex nonequilibrium systems. Computer simulations using Molecular Dynamics (MD) techniques are prohibitive, so instead coarse grained one-dimensional models with the aid of Kinetic Monte Carlo (KMC) simulations are used. Both techniques can be computationally expensive, both time and resource wise. These coarse-grained systems can be exactly described by a set of coupled stochastic master equations, that describe the reaction-diffusion kinetics of the system. The equations can be written exactly, however, coupling between the equations and terms within the equations make it impossible to solve them exactly; approximations must be made. One of the most common methods to obtain approximate solutions is to use Mean Field (MF) theory. MF treatments yield reasonable results at high ratios of reaction rate k to hop rate h of the particles, but fail completely at low k=h due to the over-estimation of fluxes of particles within the pore. We develop a method to estimate fluxes and intrapore diffusivity in simple one- dimensional reaction-diffusion models at high and low k=h, where the pores are coupled to an equilibrated three-dimensional fluid. We thus successfully describe analytically these simple reaction-diffusion one-dimensional systems. Extensions to models considering behavior with long range steric interactions and wider pores require determination of multiple boundary conditions. We give a prescription to estimate the required parameters for these simulations. For one dimensional systems, if single-file diffusion is relaxed, additional parameters to describe particle exchange have to be introduced. We use

Hybrid approaches for multiple-species stochastic reaction-diffusion models

Science.gov (United States)

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen

2015-10-01

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

Hybrid approaches for multiple-species stochastic reaction-diffusion models.

KAUST Repository

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K; Byrne, Helen

2015-01-01

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

Hybrid approaches for multiple-species stochastic reaction-diffusion models.

KAUST Repository

Spill, Fabian

2015-10-01

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

Mean Field Games with a Dominating Player

Energy Technology Data Exchange (ETDEWEB)

Bensoussan, A., E-mail: axb046100@utdallas.edu [The University of Texas at Dallas, International Center for Decision and Risk Analysis, Jindal School of Management (United States); Chau, M. H. M., E-mail: michaelchaumanho@gmail.com; Yam, S. C. P., E-mail: scpyam@sta.cuhk.edu.hk [The Chinese University of Hong Kong, Department of Statistics (Hong Kong, People’s Republic of China) (China)

2016-08-15

In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the dominating player. We first provide the general theory and discuss the necessary condition for the optimal controls and equilibrium condition by adopting adjoint equation approach. We then present a special case in the context of linear-quadratic framework, in which a necessary and sufficient condition can be asserted by stochastic maximum principle; we finally establish the sufficient condition that guarantees the unique existence of the equilibrium control. The proof of the convergence result of finite player game to mean field counterpart is provided in Appendix.

A new approach to stochastic transport via the functional Volterra expansion

International Nuclear Information System (INIS)

Ziya Akcasu, A.; Corngold, N.

2005-01-01

In this paper we present a new algorithm (FDA) for the calculation of the mean and the variance of the flux in stochastic transport when the transport equation contains a spatially random parameter θ(r), such as the density of the medium. The approach is based on the renormalized functional Volterra expansion of the flux around its mean. The attractive feature of the approach is that it explicitly displays the functional dependence of the flux on the products of θ(r i ), and hence enables one to take ensemble averages directly to calculate the moments of the flux in terms of the correlation functions of the underlying random process. The renormalized deterministic transport equation for the mean flux has been obtained to the second order in θ(r), and a functional relationship between the variance and the mean flux has been derived to calculate the variance to this order. The feasibility and accuracy of FDA has been demonstrated in the case of stochastic diffusion, using the diffusion equation with a spatially random diffusion coefficient. The connection of FDA with the well-established approximation schemes in the field of stochastic linear differential equations, such as the Bourret approximation, developed by Van Kampen using cumulant expansion, and by Terwiel using projection operator formalism, which has recently been extended to stochastic transport by Corngold. We hope that FDA's potential will be explored numerically in more realistic applications of the stochastic transport. (authors)

A stochastic-field description of finite-size spiking neural networks.

Science.gov (United States)

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.

Renormalization in the stochastic quantization of field theories

International Nuclear Information System (INIS)

Brunelli, J.C.

1991-01-01

In the stochastic quantization scheme of Parisi and Wu the renormalization of the stochastic theory of some models in field theory is studied. Following the path integral approach for stochastic process the 1/N expansion of the non linear sigma model is performed and, using a Ward identity obtained, from a BRS symmetry of the effective action of this formulation. It is shown the renormalizability of the model. Using the Langevin approach for stochastic process the renormalizability of the massive Thirring model is studied showing perturbatively the vanishing of the renormalization group's beta functions at finite fictitious time. (author)

Stochastic spin-one massive field

International Nuclear Information System (INIS)

Lim, S.C.

1984-01-01

Stochastic quantization schemes of Nelson and Parisi and Wu are applied to a spin-one massive field. Unlike the scalar case Nelson's stochastic spin-one massive field cannot be identified with the corresponding euclidean field even if the fourth component of the euclidean coordinate is taken as equal to the real physical time. In the Parisi-Wu quantization scheme the stochastic Proca vector field has a similar property as the scalar field; which has an asymptotically stationary part and a transient part. The large equal-time limit of the expectation values of the stochastic Proca field are equal to the expectation values of the corresponding euclidean field. In the Stueckelberg formalism the Parisi-Wu scheme gives rise to a stochastic vector field which differs from the massless gauge field in that the gauge cannot be fixed by the choice of boundary condition. (orig.)

Linear response in stochastic mean-field theories and the onset of instabilities

International Nuclear Information System (INIS)

Colonna, M.; Chomaz, Ph.

1993-01-01

The small amplitude response of stochastic one-body theories, such as the Boltzmann-Langevin approach is studied. Whereas the two-time correlation function only describes the propagation of fluctuations initially present, the equal-time correlation function is related to the source of stochasticity. For stable systems it yields the Einstein relation, while for unstable systems it determines the growth of the instabilities. These features are illustrated for unstable nuclear matter in two dimensions. (author) 14 refs.; 5 figs

Mean field games for cognitive radio networks

KAUST Repository

Tembine, Hamidou

2012-06-01

In this paper we study mobility effect and power saving in cognitive radio networks using mean field games. We consider two types of users: primary and secondary users. When active, each secondary transmitter-receiver uses carrier sensing and is subject to long-term energy constraint. We formulate the interaction between primary user and large number of secondary users as an hierarchical mean field game. In contrast to the classical large-scale approaches based on stochastic geometry, percolation theory and large random matrices, the proposed mean field framework allows one to describe the evolution of the density distribution and the associated performance metrics using coupled partial differential equations. We provide explicit formulas and algorithmic power management for both primary and secondary users. A complete characterization of the optimal distribution of energy and probability of success is given.

Stochastic quantization of Proca field

International Nuclear Information System (INIS)

Lim, S.C.

1981-03-01

We discuss the complications that arise in the application of Nelson's stochastic quantization scheme to classical Proca field. One consistent way to obtain spin-one massive stochastic field is given. It is found that the result of Guerra et al on the connection between ground state stochastic field and the corresponding Euclidean-Markov field extends to the spin-one case. (author)

Stochastic massless fields I: Integer spin

International Nuclear Information System (INIS)

Lim, S.C.

1981-04-01

Nelson's stochastic quantization scheme is applied to classical massless tensor potential in ''Coulomb'' gauge. The relationship between stochastic potential field in various gauges is discussed using the case of vector potential as an illustration. It is possible to identify the Euclidean tensor potential with the corresponding stochastic field in physical Minkowski space-time. Stochastic quantization of massless fields can also be carried out in terms of field strength tensors. An example of linearized stochastic gravitational field in vacuum is given. (author)

Stochastic-field cavitation model

International Nuclear Information System (INIS)

Dumond, J.; Magagnato, F.; Class, A.

2013-01-01

Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations

Stochastic-field cavitation model

Science.gov (United States)

Dumond, J.; Magagnato, F.; Class, A.

2013-07-01

Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

Mean-field dynamics of a population of stochastic map neurons

Science.gov (United States)

Franović, Igor; Maslennikov, Oleg V.; Bačić, Iva; Nekorkin, Vladimir I.

2017-07-01

We analyze the emergent regimes and the stimulus-response relationship of a population of noisy map neurons by means of a mean-field model, derived within the framework of cumulant approach complemented by the Gaussian closure hypothesis. It is demonstrated that the mean-field model can qualitatively account for stability and bifurcations of the exact system, capturing all the generic forms of collective behavior, including macroscopic excitability, subthreshold oscillations, periodic or chaotic spiking, and chaotic bursting dynamics. Apart from qualitative analogies, we find a substantial quantitative agreement between the exact and the approximate system, as reflected in matching of the parameter domains admitting the different dynamical regimes, as well as the characteristic properties of the associated time series. The effective model is further shown to reproduce with sufficient accuracy the phase response curves of the exact system and the assembly's response to external stimulation of finite amplitude and duration.

Stochastic mean-field theory: Method and application to the disordered Bose-Hubbard model at finite temperature and speckle disorder

International Nuclear Information System (INIS)

Bissbort, Ulf; Hofstetter, Walter; Thomale, Ronny

2010-01-01

We discuss the stochastic mean-field theory (SMFT) method, which is a new approach for describing disordered Bose systems in the thermodynamic limit including localization and dimensional effects. We explicate the method in detail and apply it to the disordered Bose-Hubbard model at finite temperature, with on-site box disorder, as well as experimentally relevant unbounded speckle disorder. We find that disorder-induced condensation and re-entrant behavior at constant filling are only possible at low temperatures, beyond the reach of current experiments [M. Pasienski, D. McKay, M. White, and B. DeMarco, e-print arXiv:0908.1182]. Including off-diagonal hopping disorder as well, we investigate its effect on the phase diagram in addition to pure on-site disorder. To make connection to present experiments on a quantitative level, we also combine SMFT with an LDA approach and obtain the condensate fraction in the presence of an external trapping potential.

On Social Optima of Non-Cooperative Mean Field Games

Energy Technology Data Exchange (ETDEWEB)

Li, Sen; Zhang, Wei; Zhao, Lin; Lian, Jianming; Kalsi, Karanjit

2016-12-12

This paper studies the social optima in noncooperative mean-field games for a large population of agents with heterogeneous stochastic dynamic systems. Each agent seeks to maximize an individual utility functional, and utility functionals of different agents are coupled through a mean field term that depends on the mean of the population states/controls. The paper has the following contributions. First, we derive a set of control strategies for the agents that possess *-Nash equilibrium property, and converge to the mean-field Nash equilibrium as the population size goes to infinity. Second, we study the social optimal in the mean field game. We derive the conditions, termed the socially optimal conditions, under which the *-Nash equilibrium of the mean field game maximizes the social welfare. Third, a primal-dual algorithm is proposed to compute the *-Nash equilibrium of the mean field game. Since the *-Nash equilibrium of the mean field game is socially optimal, we can compute the equilibrium by solving the social welfare maximization problem, which can be addressed by a decentralized primal-dual algorithm. Numerical simulations are presented to demonstrate the effectiveness of the proposed approach.

A Dynamic BI–Orthogonal Field Equation Approach to Efficient Bayesian Inversion

Directory of Open Access Journals (Sweden)

Tagade Piyush M.

2017-06-01

Full Text Available This paper proposes a novel computationally efficient stochastic spectral projection based approach to Bayesian inversion of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on the decomposition of the solution into its mean and a random field using a generic Karhunen-Loève expansion. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spatial dimensions that are spectrally represented using respective orthogonal bases. In particular, the present paper investigates generalized polynomial chaos bases for the stochastic dimension and eigenfunction bases for the spatial dimension. Dynamic orthogonality is used to derive closed-form equations for the time evolution of mean, spatial and the stochastic fields. The resultant system of equations consists of a partial differential equation (PDE that defines the dynamic evolution of the mean, a set of PDEs to define the time evolution of eigenfunction bases, while a set of ordinary differential equations (ODEs define dynamics of the stochastic field. This system of dynamic evolution equations efficiently propagates the prior parametric uncertainty to the system response. The resulting bi-orthogonal expansion of the system response is used to reformulate the Bayesian inference for efficient exploration of the posterior distribution. The efficacy of the proposed method is investigated for calibration of a 2D transient diffusion simulator with an uncertain source location and diffusivity. The computational efficiency of the method is demonstrated against a Monte Carlo method and a generalized polynomial chaos approach.

Diffusion with intrinsic trapping in 2-d incompressible stochastic velocity fields

International Nuclear Information System (INIS)

Vlad, M.; Spineanu, F.; Misguich, J.H.; Vlad, M.; Spineanu, F.; Balescu, R.

1998-10-01

A new statistical approach that applies to the high Kubo number regimes for particle diffusion in stochastic velocity fields is presented. This 2-dimensional model describes the partial trapping of the particles in the stochastic field. the results are close to the numerical simulations and also to the estimations based on percolation theory. (authors)

(Non-) homomorphic approaches to denoise intensity SAR images with non-local means and stochastic distances

Science.gov (United States)

Penna, Pedro A. A.; Mascarenhas, Nelson D. A.

2018-02-01

The development of new methods to denoise images still attract researchers, who seek to combat the noise with the minimal loss of resolution and details, like edges and fine structures. Many algorithms have the goal to remove additive white Gaussian noise (AWGN). However, it is not the only type of noise which interferes in the analysis and interpretation of images. Therefore, it is extremely important to expand the filters capacity to different noise models present in li-terature, for example the multiplicative noise called speckle that is present in synthetic aperture radar (SAR) images. The state-of-the-art algorithms in remote sensing area work with similarity between patches. This paper aims to develop two approaches using the non local means (NLM), developed for AWGN. In our research, we expanded its capacity for intensity SAR ima-ges speckle. The first approach is grounded on the use of stochastic distances based on the G0 distribution without transforming the data to the logarithm domain, like homomorphic transformation. It takes into account the speckle and backscatter to estimate the parameters necessary to compute the stochastic distances on NLM. The second method uses a priori NLM denoising with a homomorphic transformation and applies the inverse Gamma distribution to estimate the parameters that were used into NLM with stochastic distances. The latter method also presents a new alternative to compute the parameters for the G0 distribution. Finally, this work compares and analyzes the synthetic and real results of the proposed methods with some recent filters of the literature.

Uncertainty quantification for mean field games in social interactions

KAUST Repository

Dia, Ben Mansour

2016-01-09

We present an overview of mean field games formulation. A comparative analysis of the optimality for a stochastic McKean-Vlasov process with time-dependent probability is presented. Then we examine mean-field games for social interactions and we show that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize couple (marriage). However , if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. Finally we introduce the Wiener chaos expansion for the construction of solution of stochastic differential equations of Mckean-Vlasov type. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and allow to quantify the uncertainty in the optimality system.

Uncertainty quantification for mean field games in social interactions

KAUST Repository

Dia, Ben Mansour

2016-01-01

We present an overview of mean field games formulation. A comparative analysis of the optimality for a stochastic McKean-Vlasov process with time-dependent probability is presented. Then we examine mean-field games for social interactions and we show that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize couple (marriage). However , if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. Finally we introduce the Wiener chaos expansion for the construction of solution of stochastic differential equations of Mckean-Vlasov type. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and allow to quantify the uncertainty in the optimality system.

Polarization of the vacuum by a stochastic external field

International Nuclear Information System (INIS)

Krive, I.V.; Pastur, L.A.; Rozhavskii, A.S.

1988-01-01

The effect of disorder, realized in the form of a fluctuating extra mass term, on the bosonic vacuum and fermionic vacuum of models of quantum field theory is studied. A method is developed for calculating the mean effective potential in the stochastic external field. For a model of interacting scalar and fermion fields in (3+1)-dimensional space-time it is shown that random fluctuations of the mass lead to an increase of the equilibrium mean scalar field in the system

Market efficiency of oil spot and futures: A mean-variance and stochastic dominance approach

Energy Technology Data Exchange (ETDEWEB)

Lean, Hooi Hooi [Economics Program, School of Social Sciences, Universiti Sains Malaysia (Malaysia); McAleer, Michael [Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam, and, Tinbergen Institute (Netherlands); Wong, Wing-Keung, E-mail: awong@hkbu.edu.h [Department of Economics, Hong Kong Baptist University (Hong Kong)

2010-09-15

This paper examines the market efficiency of oil spot and futures prices by using both mean-variance (MV) and stochastic dominance (SD) approaches. Based on the West Texas Intermediate crude oil data for the sample period 1989-2008, we find no evidence of any MV and SD relationships between oil spot and futures indices. This infers that there is no arbitrage opportunity between these two markets, spot and futures do not dominate one another, investors are indifferent to investing spot or futures, and the spot and futures oil markets are efficient and rational. The empirical findings are robust to each sub-period before and after the crises for different crises, and also to portfolio diversification.

Market efficiency of oil spot and futures. A mean-variance and stochastic dominance approach

Energy Technology Data Exchange (ETDEWEB)

Lean, Hooi Hooi [Economics Program, School of Social Sciences, Universiti Sains Malaysia (Malaysia); McAleer, Michael [Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam (Netherlands); Wong, Wing-Keung [Department of Economics, Hong Kong Baptist University (China); Tinbergen Institute (Netherlands)

2010-09-15

This paper examines the market efficiency of oil spot and futures prices by using both mean-variance (MV) and stochastic dominance (SD) approaches. Based on the West Texas Intermediate crude oil data for the sample period 1989-2008, we find no evidence of any MV and SD relationships between oil spot and futures indices. This infers that there is no arbitrage opportunity between these two markets, spot and futures do not dominate one another, investors are indifferent to investing spot or futures, and the spot and futures oil markets are efficient and rational. The empirical findings are robust to each sub-period before and after the crises for different crises, and also to portfolio diversification. (author)

Market efficiency of oil spot and futures: A mean-variance and stochastic dominance approach

International Nuclear Information System (INIS)

Lean, Hooi Hooi; McAleer, Michael; Wong, Wing-Keung

2010-01-01

This paper examines the market efficiency of oil spot and futures prices by using both mean-variance (MV) and stochastic dominance (SD) approaches. Based on the West Texas Intermediate crude oil data for the sample period 1989-2008, we find no evidence of any MV and SD relationships between oil spot and futures indices. This infers that there is no arbitrage opportunity between these two markets, spot and futures do not dominate one another, investors are indifferent to investing spot or futures, and the spot and futures oil markets are efficient and rational. The empirical findings are robust to each sub-period before and after the crises for different crises, and also to portfolio diversification.

Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource

Energy Technology Data Exchange (ETDEWEB)

Graber, P. Jameson, E-mail: jameson-graber@baylor.edu [Baylor University, Department of Mathematics (United States)

2016-12-15

We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of Riccati equations. In certain cases, the solution to the mean field type control is also the equilibrium strategy for a class of mean field games. We use this fact to study an economic model of production of exhaustible resources.

Stochastic Neural Field Theory and the System-Size Expansion

KAUST Repository

Bressloff, Paul C.

2010-01-01

We analyze a master equation formulation of stochastic neurodynamics for a network of synaptically coupled homogeneous neuronal populations each consisting of N identical neurons. The state of the network is specified by the fraction of active or spiking neurons in each population, and transition rates are chosen so that in the thermodynamic or deterministic limit (N → ∞) we recover standard activity-based or voltage-based rate models. We derive the lowest order corrections to these rate equations for large but finite N using two different approximation schemes, one based on the Van Kampen system-size expansion and the other based on path integral methods. Both methods yield the same series expansion of the moment equations, which at O(1/N) can be truncated to form a closed system of equations for the first-and second-order moments. Taking a continuum limit of the moment equations while keeping the system size N fixed generates a system of integrodifferential equations for the mean and covariance of the corresponding stochastic neural field model. We also show how the path integral approach can be used to study large deviation or rare event statistics underlying escape from the basin of attraction of a stable fixed point of the mean-field dynamics; such an analysis is not possible using the system-size expansion since the latter cannot accurately determine exponentially small transitions. © by SIAM.

Stochastic Fractional Programming Approach to a Mean and Variance Model of a Transportation Problem

Directory of Open Access Journals (Sweden)

V. Charles

2011-01-01

Full Text Available In this paper, we propose a stochastic programming model, which considers a ratio of two nonlinear functions and probabilistic constraints. In the former, only expected model has been proposed without caring variability in the model. On the other hand, in the variance model, the variability played a vital role without concerning its counterpart, namely, the expected model. Further, the expected model optimizes the ratio of two linear cost functions where as variance model optimize the ratio of two non-linear functions, that is, the stochastic nature in the denominator and numerator and considering expectation and variability as well leads to a non-linear fractional program. In this paper, a transportation model with stochastic fractional programming (SFP problem approach is proposed, which strikes the balance between previous models available in the literature.

Linear–Quadratic Mean-Field-Type Games: A Direct Method

Directory of Open Access Journals (Sweden)

Tyrone E. Duncan

2018-02-01

Full Text Available In this work, a multi-person mean-field-type game is formulated and solved that is described by a linear jump-diffusion system of mean-field type and a quadratic cost functional involving the second moments, the square of the expected value of the state, and the control actions of all decision-makers. We propose a direct method to solve the game, team, and bargaining problems. This solution approach does not require solving the Bellman–Kolmogorov equations or backward–forward stochastic differential equations of Pontryagin’s type. The proposed method can be easily implemented by beginners and engineers who are new to the emerging field of mean-field-type game theory. The optimal strategies for decision-makers are shown to be in a state-and-mean-field feedback form. The optimal strategies are given explicitly as a sum of the well-known linear state-feedback strategy for the associated deterministic linear–quadratic game problem and a mean-field feedback term. The equilibrium cost of the decision-makers are explicitly derived using a simple direct method. Moreover, the equilibrium cost is a weighted sum of the initial variance and an integral of a weighted variance of the diffusion and the jump process. Finally, the method is used to compute global optimum strategies as well as saddle point strategies and Nash bargaining solution in state-and-mean-field feedback form.

Stochastic Approaches Within a High Resolution Rapid Refresh Ensemble

Science.gov (United States)

Jankov, I.

2017-12-01

It is well known that global and regional numerical weather prediction (NWP) ensemble systems are under-dispersive, producing unreliable and overconfident ensemble forecasts. Typical approaches to alleviate this problem include the use of multiple dynamic cores, multiple physics suite configurations, or a combination of the two. While these approaches may produce desirable results, they have practical and theoretical deficiencies and are more difficult and costly to maintain. An active area of research that promotes a more unified and sustainable system is the use of stochastic physics. Stochastic approaches include Stochastic Parameter Perturbations (SPP), Stochastic Kinetic Energy Backscatter (SKEB), and Stochastic Perturbation of Physics Tendencies (SPPT). The focus of this study is to assess model performance within a convection-permitting ensemble at 3-km grid spacing across the Contiguous United States (CONUS) using a variety of stochastic approaches. A single physics suite configuration based on the operational High-Resolution Rapid Refresh (HRRR) model was utilized and ensemble members produced by employing stochastic methods. Parameter perturbations (using SPP) for select fields were employed in the Rapid Update Cycle (RUC) land surface model (LSM) and Mellor-Yamada-Nakanishi-Niino (MYNN) Planetary Boundary Layer (PBL) schemes. Within MYNN, SPP was applied to sub-grid cloud fraction, mixing length, roughness length, mass fluxes and Prandtl number. In the RUC LSM, SPP was applied to hydraulic conductivity and tested perturbing soil moisture at initial time. First iterative testing was conducted to assess the initial performance of several configuration settings (e.g. variety of spatial and temporal de-correlation lengths). Upon selection of the most promising candidate configurations using SPP, a 10-day time period was run and more robust statistics were gathered. SKEB and SPPT were included in additional retrospective tests to assess the impact of using

Mean field dynamics of networks of delay-coupled noisy excitable units

Energy Technology Data Exchange (ETDEWEB)

Franović, Igor, E-mail: franovic@ipb.ac.rs [Scientific Computing Laboratory, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade (Serbia); Todorović, Kristina; Burić, Nikola [Department of Physics and Mathematics, Faculty of Pharmacy, University of Belgrade, Vojvode Stepe 450, Belgrade (Serbia); Vasović, Nebojša [Department of Applied Mathematics, Faculty of Mining and Geology, University of Belgrade, PO Box 162, Belgrade (Serbia)

2016-06-08

We use the mean-field approach to analyze the collective dynamics in macroscopic networks of stochastic Fitzhugh-Nagumo units with delayed couplings. The conditions for validity of the two main approximations behind the model, called the Gaussian approximation and the Quasi-independence approximation, are examined. It is shown that the dynamics of the mean-field model may indicate in a self-consistent fashion the parameter domains where the Quasi-independence approximation fails. Apart from a network of globally coupled units, we also consider the paradigmatic setup of two interacting assemblies to demonstrate how our framework may be extended to hierarchical and modular networks. In both cases, the mean-field model can be used to qualitatively analyze the stability of the system, as well as the scenarios for the onset and the suppression of the collective mode. In quantitative terms, the mean-field model is capable of predicting the average oscillation frequency corresponding to the global variables of the exact system.

Improved ensemble-mean forecast skills of ENSO events by a zero-mean stochastic model-error model of an intermediate coupled model

Science.gov (United States)

Zheng, F.; Zhu, J.

2015-12-01

To perform an ensemble-based ENSO probabilistic forecast, the crucial issue is to design a reliable ensemble prediction strategy that should include the major uncertainties of a forecast system. In this study, we developed a new general ensemble perturbation technique to improve the ensemble-mean predictive skill of forecasting ENSO using an intermediate coupled model (ICM). The model uncertainties are first estimated and analyzed from EnKF analysis results through assimilating observed SST. Then, based on the pre-analyzed properties of the model errors, a zero-mean stochastic model-error model is developed to mainly represent the model uncertainties induced by some important physical processes missed in the coupled model (i.e., stochastic atmospheric forcing/MJO, extra-tropical cooling and warming, Indian Ocean Dipole mode, etc.). Each member of an ensemble forecast is perturbed by the stochastic model-error model at each step during the 12-month forecast process, and the stochastical perturbations are added into the modeled physical fields to mimic the presence of these high-frequency stochastic noises and model biases and their effect on the predictability of the coupled system. The impacts of stochastic model-error perturbations on ENSO deterministic predictions are examined by performing two sets of 21-yr retrospective forecast experiments. The two forecast schemes are differentiated by whether they considered the model stochastic perturbations, with both initialized by the ensemble-mean analysis states from EnKF. The comparison results suggest that the stochastic model-error perturbations have significant and positive impacts on improving the ensemble-mean prediction skills during the entire 12-month forecast process. Because the nonlinear feature of the coupled model can induce the nonlinear growth of the added stochastic model errors with model integration, especially through the nonlinear heating mechanism with the vertical advection term of the model, the

Compressible cavitation with stochastic field method

Science.gov (United States)

Class, Andreas; Dumond, Julien

2012-11-01

Non-linear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on Lagrange particles or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic field method solving pdf transport based on Euler fields has been proposed which eliminates the necessity to mix Euler and Lagrange techniques or prescribed pdf assumptions. In the present work, part of the PhD Design and analysis of a Passive Outflow Reducer relying on cavitation, a first application of the stochastic field method to multi-phase flow and in particular to cavitating flow is presented. The application considered is a nozzle subjected to high velocity flow so that sheet cavitation is observed near the nozzle surface in the divergent section. It is demonstrated that the stochastic field formulation captures the wide range of pdf shapes present at different locations. The method is compatible with finite-volume codes where all existing physical models available for Lagrange techniques, presumed pdf or binning methods can be easily extended to the stochastic field formulation.

Front Propagation in Stochastic Neural Fields

KAUST Repository

Bressloff, Paul C.

2012-01-01

We analyze the effects of extrinsic multiplicative noise on front propagation in a scalar neural field with excitatory connections. Using a separation of time scales, we represent the fluctuating front in terms of a diffusive-like displacement (wandering) of the front from its uniformly translating position at long time scales, and fluctuations in the front profile around its instantaneous position at short time scales. One major result of our analysis is a comparison between freely propagating fronts and fronts locked to an externally moving stimulus. We show that the latter are much more robust to noise, since the stochastic wandering of the mean front profile is described by an Ornstein-Uhlenbeck process rather than a Wiener process, so that the variance in front position saturates in the long time limit rather than increasing linearly with time. Finally, we consider a stochastic neural field that supports a pulled front in the deterministic limit, and show that the wandering of such a front is now subdiffusive. © 2012 Society for Industrial and Applied Mathematics.

Diffusive processes in a stochastic magnetic field

International Nuclear Information System (INIS)

Wang, H.; Vlad, M.; Vanden Eijnden, E.; Spineanu, F.; Misguich, J.H.; Balescu, R.

1995-01-01

The statistical representation of a fluctuating (stochastic) magnetic field configuration is studied in detail. The Eulerian correlation functions of the magnetic field are determined, taking into account all geometrical constraints: these objects form a nondiagonal matrix. The Lagrangian correlations, within the reasonable Corrsin approximation, are reduced to a single scalar function, determined by an integral equation. The mean square perpendicular deviation of a geometrical point moving along a perturbed field line is determined by a nonlinear second-order differential equation. The separation of neighboring field lines in a stochastic magnetic field is studied. We find exponentiation lengths of both signs describing, in particular, a decay (on the average) of any initial anisotropy. The vanishing sum of these exponentiation lengths ensures the existence of an invariant which was overlooked in previous works. Next, the separation of a particle's trajectory from the magnetic field line to which it was initially attached is studied by a similar method. Here too an initial phase of exponential separation appears. Assuming the existence of a final diffusive phase, anomalous diffusion coefficients are found for both weakly and strongly collisional limits. The latter is identical to the well known Rechester-Rosenbluth coefficient, which is obtained here by a more quantitative (though not entirely deductive) treatment than in earlier works

Stochastic quantization of gravity and string fields

International Nuclear Information System (INIS)

Rumpf, H.

1986-01-01

The stochastic quantization method of Parisi and Wu is generalized so as to make it applicable to Einstein's theory of gravitation. The generalization is based on the existence of a preferred metric in field configuration space, involves Ito's calculus, and introduces a complex stochastic process adapted to Lorentzian spacetime. It implies formally the path integral measure of DeWitt, a causual Feynman propagator, and a consistent stochastic perturbation theory. The lineraized version of the theory is also obtained from the stochastic quantization of the free string field theory of Siegel and Zwiebach. (Author)

Halo nuclei studied by relativistic mean-field approach

International Nuclear Information System (INIS)

Gmuca, S.

1997-01-01

Density distributions of light neutron-rich nuclei are studied by using the relativistic mean-field approach. The effective interaction which parameterizes the recent Dirac-Brueckner-Hartree-Fock calculations of nuclear matter is used. The results are discussed and compared with the experimental observations with special reference to the neutron halo in the drip-line nuclei. (author)

Dynamic magnetic behavior of the mixed-spin bilayer system in an oscillating field within the mean-field theory

International Nuclear Information System (INIS)

Ertaş, Mehmet; Keskin, Mustafa

2012-01-01

The dynamic magnetic behavior of the mixed Ising bilayer system (σ=2 and S=5/2), with a crystal-field interaction in an oscillating field are studied, within the mean-field approach, by using the Glauber-type stochastic dynamics for both ferromagnetic/ferromagnetic and antiferromagnetic/ferromagnetic interactions. The time variations of average magnetizations and the temperature dependence of the dynamic magnetizations are investigated. The dynamic phase diagrams are presented in the reduced temperature and magnetic field amplitude plane and they exhibit several ordered phases, coexistence phase regions and critical points as well as a re-entrant behavior depending on interaction parameters. -- Highlights: ► Dynamic magnetic behavior of the mixed Ising bilayer system is investigated within the Glauber-type stochastic dynamics. ► The time variations of average magnetizations are studied to find the phases. ► The temperature dependence of the dynamic magnetizations is investigated to obtain the dynamic phase transition points. ► The dynamic phase diagrams are presented and they exhibit several ordered phases, coexistence phase regions and critical points as well as a re-entrant behavior.

Dynamic magnetic behavior of the mixed-spin bilayer system in an oscillating field within the mean-field theory

Energy Technology Data Exchange (ETDEWEB)

Ertaş, Mehmet [Department of Physics, Erciyes University, 38039 Kayseri (Turkey); Keskin, Mustafa, E-mail: keskin@erciyes.edu.tr [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)

2012-07-23

The dynamic magnetic behavior of the mixed Ising bilayer system (σ=2 and S=5/2), with a crystal-field interaction in an oscillating field are studied, within the mean-field approach, by using the Glauber-type stochastic dynamics for both ferromagnetic/ferromagnetic and antiferromagnetic/ferromagnetic interactions. The time variations of average magnetizations and the temperature dependence of the dynamic magnetizations are investigated. The dynamic phase diagrams are presented in the reduced temperature and magnetic field amplitude plane and they exhibit several ordered phases, coexistence phase regions and critical points as well as a re-entrant behavior depending on interaction parameters. -- Highlights: ► Dynamic magnetic behavior of the mixed Ising bilayer system is investigated within the Glauber-type stochastic dynamics. ► The time variations of average magnetizations are studied to find the phases. ► The temperature dependence of the dynamic magnetizations is investigated to obtain the dynamic phase transition points. ► The dynamic phase diagrams are presented and they exhibit several ordered phases, coexistence phase regions and critical points as well as a re-entrant behavior.

Modelling of diesel spray flames under engine-like conditions using an accelerated Eulerian Stochastic Field method

DEFF Research Database (Denmark)

Pang, Kar Mun; Jangi, Mehdi; Bai, Xue-Song

2018-01-01

This paper aims to simulate diesel spray flames across a wide range of engine-like conditions using the Eulerian Stochastic Field probability density function (ESF-PDF) model. The ESF model is coupled with the Chemistry Coordinate Mapping approach to expedite the calculation. A convergence study...... is carried out for a number of stochastic fields at five different conditions, covering both conventional diesel combustion and low-temperature combustion regimes. Ignition delay time, flame lift-off length as well as distributions of temperature and various combustion products are used to evaluate...... the performance of the model. The peak values of these properties generated using thirty-two stochastic fields are found to converge, with a maximum relative difference of 27% as compared to those from a greater number of stochastic fields. The ESF-PDF model with thirty-two stochastic fields performs reasonably...

Stochastic Simulation of Chloride Ingress into Reinforced Concrete Structures by Means of Multi-Dimensional Gaussian Random Fields

DEFF Research Database (Denmark)

Frier, Christian; Sørensen, John Dalsgaard

2005-01-01

For many reinforced concrete structures corrosion of the reinforcement is an important problem since it can result in expensive maintenance and repair actions. Further, a significant reduction of the load-bearing capacity can occur. One mode of corrosion initiation occurs when the chloride content...... is modeled by a 2-dimensional diffusion process by FEM (Finite Element Method) and the diffusion coefficient, surface chloride concentration and reinforcement cover depth are modeled by multidimensional stochastic fields, which are discretized using the EOLE (Expansion Optimum Linear Estimation) approach....... As an example a bridge pier in a marine environment is considered and the results are given in terms of the distribution of the time for initialization of corrosion...

Beyond mean-field approach to heavy-ion reactions around the Coulomb barrier

Directory of Open Access Journals (Sweden)

Ayik Sakir

2011-10-01

Full Text Available Dissipation and fluctuations of one-body observables in heavy-ion reactions around the Coulomb barrier are investigated with a microscopic stochastic mean-field approach. By projecting the stochastic meanfield dynamics on a suitable collective path, transport coefficients associated with the relative distance between colliding nuclei and a fragment mass are extracted. Although microscopic mean-field approach is know to underestimate the variance of fragment mass distribution, the description of the variance is much improved by the stochastic mean-field method. While fluctuations are consistent with the empirical (semiclassical analysis of the experimental data, concerning mean values of macroscopic variables the semiclassical description breaks down below the Coulomb barrier.

The Covariance and Bicovariance of the Stochastic Neutron Field

International Nuclear Information System (INIS)

Perez, R.B.; Mattingly, J.K.; Valentine, T.E.; Mihalczo, J.T.

2000-01-01

On the basis of the general stochastic neutron field theory developed by Munoz-Cobo et al, results on the covariance and bicovariance of the neutron field have been presented. These two statistical quantities are obtained from the counts observed in detectors operating during a period of time (gate length), Δ qc . A classical example is the so called Feynmann Y-function that is defined as the variance to mean ratio of the neutron field. Upon taking the limit of the covariance and bicovariance function for Δ qc r a rrow O , one obtains the two and three detector cross correlation functions respectively. The mathematical structure of the results so obtained have a transparent physical interpretation in terms of the space and delay time overlap between the field-of-view of the detectors. For the first time, an expression has been obtained for the bispectrum function of the stochastic neutron field and for the appropriate weight functions to be used as space-energy-angle correction factors for the one-point kinetics approximation

A spectral k-means approach to bright-field cell image segmentation.

Science.gov (United States)

Bradbury, Laura; Wan, Justin W L

2010-01-01

Automatic segmentation of bright-field cell images is important to cell biologists, but difficult to complete due to the complex nature of the cells in bright-field images (poor contrast, broken halo, missing boundaries). Standard approaches such as level set segmentation and active contours work well for fluorescent images where cells appear as round shape, but become less effective when optical artifacts such as halo exist in bright-field images. In this paper, we present a robust segmentation method which combines the spectral and k-means clustering techniques to locate cells in bright-field images. This approach models an image as a matrix graph and segment different regions of the image by computing the appropriate eigenvectors of the matrix graph and using the k-means algorithm. We illustrate the effectiveness of the method by segmentation results of C2C12 (muscle) cells in bright-field images.

A cavitation model based on Eulerian stochastic fields

Science.gov (United States)

Magagnato, F.; Dumond, J.

2013-12-01

Non-linear phenomena can often be described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and in particular to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. Firstly, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

Optimising stochastic trajectories in exact quantum jump approaches of interacting systems

International Nuclear Information System (INIS)

Lacroix, D.

2004-11-01

The standard methods used to substitute the quantum dynamics of two interacting systems by a quantum jump approach based on the Stochastic Schroedinger Equation (SSE) are described. It turns out that for a given situation, there exists an infinite number of SSE reformulation. This fact is used to propose general strategies to optimise the stochastic paths in order to reduce the statistical fluctuations. In this procedure, called the 'adaptative noise method', a specific SSE is obtained for which the noise depends explicitly on both the initial state and on the properties of the interaction Hamiltonian. It is also shown that this method can be further improved by the introduction of a mean-field dynamics. The different optimisation procedures are illustrated quantitatively in the case of interacting spins. A significant reduction of the statistical fluctuations is obtained. Consequently, a much smaller number of trajectories is needed to accurately reproduce the exact dynamics as compared to the standard SSE method. (author)

Stochastic field theory and finite-temperature supersymmetry

International Nuclear Information System (INIS)

Ghosh, P.; Bandyopadhyay, P.

1988-01-01

The finite-temperature behavior of supersymmetry is considered from the viewpoint of stochastic field theory. To this end, it is considered that Nelson's stochastic mechanics may be generalized to the quantization of a Fermi field when the classical analog of such a field is taken to be a scalar nonlocal field where the internal space is anisotropic in nature such that when quantized this gives rise to two internal helicities corresponding to fermion and antifermion. Stochastic field theory at finite temperature is then formulated from stochastic mechanics which incorporates Brownian motion in the external space as well as in the internal space of a particle. It is shown that when the anisotropy of the internal space is suppressed so that the internal time ξ 0 vanishes and the internal space variables are integrated out one has supersymmetry at finite temperature. This result is true for T = 0, also. However, at this phase equilibrium will be destroyed. Thus for a random process van Hove's result involving quantum mechanical operators, i.e., that when supersymmetry remains unbroken at T = 0 it will also remain unbroken at Tnot =0, occurs. However, this formalism indicates that when at T = 0 broken supersymmetry results, supersymmetry may be restored at a critical temperature T/sub c/

Stochastic Still Water Response Model

DEFF Research Database (Denmark)

Friis-Hansen, Peter; Ditlevsen, Ove Dalager

2002-01-01

In this study a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model is...... out that an important parameter of the stochastic cargo field model is the mean number of containers delivered by each customer.......In this study a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model...... is to establish the stochastic load field conditional on a given draft and trim of the vessel. The model contributes to a realistic modelling of the stochastic load processes to be used in a reliability evaluation of the ship hull. Emphasis is given to container vessels. The formulation of the model for obtaining...

Alfven-wave current drive and magnetic field stochasticity

International Nuclear Information System (INIS)

Litwin, C.; Hegna, C.C.

1993-01-01

Propagating Alfven waves can generate parallel current through an alpha effect. In resistive MHD however, the dynamo field is proportional to resistivity and as such cannot drive significant currents for realistic parameters. In the search for an enhancement of this effect the authors investigate the role of magnetic field stochasticity. They show that the presence of a stochastic magnetic field, either spontaneously generated by instabilities or induced externally, can enhance the alpha effect of the wave. This enhancement is caused by an increased wave dissipation due to both current diffusion and filamentation. For the range of parameters of current drive experiments at Phaedrus-T tokamak, a moderate field stochasticity leads to significant modifications in the loop voltage

Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework

International Nuclear Information System (INIS)

Zhou, X.Y.; Li, D.

2000-01-01

This paper is concerned with a continuous-time mean-variance portfolio selection model that is formulated as a bicriteria optimization problem. The objective is to maximize the expected terminal return and minimize the variance of the terminal wealth. By putting weights on the two criteria one obtains a single objective stochastic control problem which is however not in the standard form due to the variance term involved. It is shown that this nonstandard problem can be 'embedded' into a class of auxiliary stochastic linear-quadratic (LQ) problems. The stochastic LQ control model proves to be an appropriate and effective framework to study the mean-variance problem in light of the recent development on general stochastic LQ problems with indefinite control weighting matrices. This gives rise to the efficient frontier in a closed form for the original portfolio selection problem

Stability analysis of stochastic delayed cellular neural networks by LMI approach

International Nuclear Information System (INIS)

Zhu Wenli; Hu Jin

2006-01-01

Some sufficient mean square exponential stability conditions for a class of stochastic DCNN model are obtained via the LMI approach. These conditions improve and generalize some existing global asymptotic stability conditions for DCNN model

Diffusion of test particles in stochastic magnetic fields for small Kubo numbers

International Nuclear Information System (INIS)

Neuer, Marcus; Spatschek, Karl H.

2006-01-01

Motion of charged particles in a collisional plasma with stochastic magnetic field lines is investigated on the basis of the so-called A-Langevin equation. Compared to the previously used V-Langevin model, here finite Larmor radius effects are taken into account. The A-Langevin equation is solved under the assumption that the Lagrangian correlation function for the magnetic field fluctuations is related to the Eulerian correlation function (in Gaussian form) via the Corrsin approximation. The latter is justified for small Kubo numbers. The velocity correlation function, being averaged with respect to the stochastic variables including collisions, leads to an implicit differential equation for the mean square displacement. From the latter, different transport regimes, including the well-known Rechester-Rosenbluth diffusion coefficient, are derived. Finite Larmor radius contributions show a decrease of the diffusion coefficient compared to the guiding center limit. The case of small (or vanishing) mean fields is also discussed

Nelson's stochastic quantization of free linearized gravitational field and its Markovian structure

International Nuclear Information System (INIS)

Lim, S.C.

1983-05-01

It is shown that by applying Nelson's stochastic quantization scheme to free linearized gravitational field tensor one can associate with the resulting stochastic system a stochastic tensor field which coincides with the ''space'' part of the Riemannian tensor in Euclidean space-time. However, such a stochastic field fails to satisfy the Markov property. Instead, it satisfies the reflection positivity. The Markovian structure of the stochastic fields associated with the electromagnetic field is also discussed. (author)

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.

A constructive mean-field analysis of multi-population neural networks with random synaptic weights and stochastic inputs.

Science.gov (United States)

Faugeras, Olivier; Touboul, Jonathan; Cessac, Bruno

2009-01-01

We deal with the problem of bridging the gap between two scales in neuronal modeling. At the first (microscopic) scale, neurons are considered individually and their behavior described by stochastic differential equations that govern the time variations of their membrane potentials. They are coupled by synaptic connections acting on their resulting activity, a nonlinear function of their membrane potential. At the second (mesoscopic) scale, interacting populations of neurons are described individually by similar equations. The equations describing the dynamical and the stationary mean-field behaviors are considered as functional equations on a set of stochastic processes. Using this new point of view allows us to prove that these equations are well-posed on any finite time interval and to provide a constructive method for effectively computing their unique solution. This method is proved to converge to the unique solution and we characterize its complexity and convergence rate. We also provide partial results for the stationary problem on infinite time intervals. These results shed some new light on such neural mass models as the one of Jansen and Rit (1995): their dynamics appears as a coarse approximation of the much richer dynamics that emerges from our analysis. Our numerical experiments confirm that the framework we propose and the numerical methods we derive from it provide a new and powerful tool for the exploration of neural behaviors at different scales.

Diffusion of test particles in stochastic magnetic fields in the percolative regime

International Nuclear Information System (INIS)

Neuer, Marcus; Spatschek, Karl H.

2006-01-01

For stochastic magnetic flux functions with percolative contours the test particle transport is investigated. The calculations make use of the stochastic Liouville approach. They start from the so-called A-Langevin equations, including stochastic magnetic field components and binary collisions. Using the decorrelation trajectory method, a relation between the Lagrangian velocity correlation function and the Eulerian magnetic field correlation is derived and introduced into the Green-Kubo formalism. Finite Larmor radius effects are included. Interesting results are presented in the percolation regime corresponding to high Kubo numbers. Previous results are found to be limiting cases for small Kubo numbers. For different percolative scenarios the diffusion is analyzed and strong influences of the percolative structures on the transport scaling are found. The finite Larmor radius effects are discussed in detail. Numerical simulations of the A-Langevin equation confirm the semianalytical predictions

Stochastic Thermodynamics: A Dynamical Systems Approach

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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.

Stochastic inflation in phase space: is slow roll a stochastic attractor?

Energy Technology Data Exchange (ETDEWEB)

Grain, Julien [Institut d' Astrophysique Spatiale, UMR8617, CNRS, Univ. Paris Sud, Université Paris-Saclay, Bt. 121, Orsay, F-91405 (France); Vennin, Vincent, E-mail: julien.grain@ias.u-psud.fr, E-mail: vincent.vennin@port.ac.uk [Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth, PO13FX (United Kingdom)

2017-05-01

An appealing feature of inflationary cosmology is the presence of a phase-space attractor, ''slow roll'', which washes out the dependence on initial field velocities. We investigate the robustness of this property under backreaction from quantum fluctuations using the stochastic inflation formalism in the phase-space approach. A Hamiltonian formulation of stochastic inflation is presented, where it is shown that the coarse-graining procedure—where wavelengths smaller than the Hubble radius are integrated out—preserves the canonical structure of free fields. This means that different sets of canonical variables give rise to the same probability distribution which clarifies the literature with respect to this issue. The role played by the quantum-to-classical transition is also analysed and is shown to constrain the coarse-graining scale. In the case of free fields, we find that quantum diffusion is aligned in phase space with the slow-roll direction. This implies that the classical slow-roll attractor is immune to stochastic effects and thus generalises to a stochastic attractor regardless of initial conditions, with a relaxation time at least as short as in the classical system. For non-test fields or for test fields with non-linear self interactions however, quantum diffusion and the classical slow-roll flow are misaligned. We derive a condition on the coarse-graining scale so that observational corrections from this misalignment are negligible at leading order in slow roll.

Non-equilibrium mean-field theories on scale-free networks

International Nuclear Information System (INIS)

Caccioli, Fabio; Dall'Asta, Luca

2009-01-01

Many non-equilibrium processes on scale-free networks present anomalous critical behavior that is not explained by standard mean-field theories. We propose a systematic method to derive stochastic equations for mean-field order parameters that implicitly account for the degree heterogeneity. The method is used to correctly predict the dynamical critical behavior of some binary spin models and reaction–diffusion processes. The validity of our non-equilibrium theory is further supported by showing its relation with the generalized Landau theory of equilibrium critical phenomena on networks

A mean field approach to the Ising chain in a transverse magnetic field

Science.gov (United States)

Osácar, C.; Pacheco, A. F.

2017-07-01

We evaluate a mean field method to describe the properties of the ground state of the Ising chain in a transverse magnetic field. Specifically, a method of the Bethe-Peierls type is used by solving spin blocks with a self-consistency condition at the borders. The computations include the critical point for the phase transition, exponent of magnetisation and energy density. All results are obtained using basic quantum mechanics at an undergraduate level. The advantages and the limitations of the approach are emphasised.

RPA correlations and nuclear densities in relativistic mean field approach

International Nuclear Information System (INIS)

Van Giai, N.; Liang, H.Z.; Meng, J.

2007-02-01

The relativistic mean field approach (RMF) is well known for describing accurately binding energies and nucleon distributions in atomic nuclei throughout the nuclear chart. The random phase approximation (RPA) built on top of the RMF is also a good framework for the study of nuclear excitations. Here, we examine the consequences of long range correlations brought about by the RPA on the neutron and proton densities as given by the RMF approach. (authors)

Mean Square Synchronization of Stochastic Nonlinear Delayed Coupled Complex Networks

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Chengrong Xie

2013-01-01

Full Text Available We investigate the problem of adaptive mean square synchronization for nonlinear delayed coupled complex networks with stochastic perturbation. Based on the LaSalle invariance principle and the properties of the Weiner process, the controller and adaptive laws are designed to ensure achieving stochastic synchronization and topology identification of complex networks. Sufficient conditions are given to ensure the complex networks to be mean square synchronization. Furthermore, numerical simulations are also given to demonstrate the effectiveness of the proposed scheme.

Stochastic approach to microphysics

Energy Technology Data Exchange (ETDEWEB)

Aron, J.C.

1987-01-01

The presently widespread idea of ''vacuum population'', together with the quantum concept of vacuum fluctuations leads to assume a random level below that of matter. This stochastic approach starts by a reminder of the author's previous work, first on the relation of diffusion laws with the foundations of microphysics, and then on hadron spectrum. Following the latter, a random quark model is advanced; it gives to quark pairs properties similar to those of a harmonic oscillator or an elastic string, imagined as an explanation to their asymptotic freedom and their confinement. The stochastic study of such interactions as electron-nucleon, jets in e/sup +/e/sup -/ collisions, or pp -> ..pi../sup 0/ + X, gives form factors closely consistent with experiment. The conclusion is an epistemological comment (complementarity between stochastic and quantum domains, E.P.R. paradox, etc...).

Nonlocal quantum field theory and stochastic quantum mechanics

International Nuclear Information System (INIS)

Namsrai, K.

1986-01-01

This volume presents a systematic development of the implications to both quantum mechanics and quantum field theory of the hypothesis of a stochastic structure of space-time. Some applications to elementary particle physics are also considered. Part 1 is concerned with nonlocal quantum field theory and, among other topics, deals with quantized fields, electromagnetic and weak processes, the Schroedinger equation, and functional methods and their applications. Part 2 presents an introduction to stochastic mechanics and many specific problems of interest are discussed. (Auth.)

Fractional Stochastic Field Theory

Science.gov (United States)

Honkonen, Juha

2018-02-01

Models describing evolution of physical, chemical, biological, social and financial processes are often formulated as differential equations with the understanding that they are large-scale equations for averages of quantities describing intrinsically random processes. Explicit account of randomness may lead to significant changes in the asymptotic behaviour (anomalous scaling) in such models especially in low spatial dimensions, which in many cases may be captured with the use of the renormalization group. Anomalous scaling and memory effects may also be introduced with the use of fractional derivatives and fractional noise. Construction of renormalized stochastic field theory with fractional derivatives and fractional noise in the underlying stochastic differential equations and master equations and the interplay between fluctuation-induced and built-in anomalous scaling behaviour is reviewed and discussed.

A stochastic differential equations approach for the description of helium bubble size distributions in irradiated metals

Energy Technology Data Exchange (ETDEWEB)

Seif, Dariush, E-mail: dariush.seif@iwm-extern.fraunhofer.de [Fraunhofer Institut für Werkstoffmechanik, Freiburg 79108 (Germany); Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095-1597 (United States); Ghoniem, Nasr M. [Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095-1597 (United States)

2014-12-15

A rate theory model based on the theory of nonlinear stochastic differential equations (SDEs) is developed to estimate the time-dependent size distribution of helium bubbles in metals under irradiation. Using approaches derived from Itô’s calculus, rate equations for the first five moments of the size distribution in helium–vacancy space are derived, accounting for the stochastic nature of the atomic processes involved. In the first iteration of the model, the distribution is represented as a bivariate Gaussian distribution. The spread of the distribution about the mean is obtained by white-noise terms in the second-order moments, driven by fluctuations in the general absorption and emission of point defects by bubbles, and fluctuations stemming from collision cascades. This statistical model for the reconstruction of the distribution by its moments is coupled to a previously developed reduced-set, mean-field, rate theory model. As an illustrative case study, the model is applied to a tungsten plasma facing component under irradiation. Our findings highlight the important role of stochastic atomic fluctuations on the evolution of helium–vacancy cluster size distributions. It is found that when the average bubble size is small (at low dpa levels), the relative spread of the distribution is large and average bubble pressures may be very large. As bubbles begin to grow in size, average bubble pressures decrease, and stochastic fluctuations have a lessened effect. The distribution becomes tighter as it evolves in time, corresponding to a more uniform bubble population. The model is formulated in a general way, capable of including point defect drift due to internal temperature and/or stress gradients. These arise during pulsed irradiation, and also during steady irradiation as a result of externally applied or internally generated non-homogeneous stress fields. Discussion is given into how the model can be extended to include full spatial resolution and how the

A stochastic differential equations approach for the description of helium bubble size distributions in irradiated metals

Science.gov (United States)

Seif, Dariush; Ghoniem, Nasr M.

2014-12-01

A rate theory model based on the theory of nonlinear stochastic differential equations (SDEs) is developed to estimate the time-dependent size distribution of helium bubbles in metals under irradiation. Using approaches derived from Itô's calculus, rate equations for the first five moments of the size distribution in helium-vacancy space are derived, accounting for the stochastic nature of the atomic processes involved. In the first iteration of the model, the distribution is represented as a bivariate Gaussian distribution. The spread of the distribution about the mean is obtained by white-noise terms in the second-order moments, driven by fluctuations in the general absorption and emission of point defects by bubbles, and fluctuations stemming from collision cascades. This statistical model for the reconstruction of the distribution by its moments is coupled to a previously developed reduced-set, mean-field, rate theory model. As an illustrative case study, the model is applied to a tungsten plasma facing component under irradiation. Our findings highlight the important role of stochastic atomic fluctuations on the evolution of helium-vacancy cluster size distributions. It is found that when the average bubble size is small (at low dpa levels), the relative spread of the distribution is large and average bubble pressures may be very large. As bubbles begin to grow in size, average bubble pressures decrease, and stochastic fluctuations have a lessened effect. The distribution becomes tighter as it evolves in time, corresponding to a more uniform bubble population. The model is formulated in a general way, capable of including point defect drift due to internal temperature and/or stress gradients. These arise during pulsed irradiation, and also during steady irradiation as a result of externally applied or internally generated non-homogeneous stress fields. Discussion is given into how the model can be extended to include full spatial resolution and how the

A stochastic differential equations approach for the description of helium bubble size distributions in irradiated metals

International Nuclear Information System (INIS)

Seif, Dariush; Ghoniem, Nasr M.

2014-01-01

A rate theory model based on the theory of nonlinear stochastic differential equations (SDEs) is developed to estimate the time-dependent size distribution of helium bubbles in metals under irradiation. Using approaches derived from Itô’s calculus, rate equations for the first five moments of the size distribution in helium–vacancy space are derived, accounting for the stochastic nature of the atomic processes involved. In the first iteration of the model, the distribution is represented as a bivariate Gaussian distribution. The spread of the distribution about the mean is obtained by white-noise terms in the second-order moments, driven by fluctuations in the general absorption and emission of point defects by bubbles, and fluctuations stemming from collision cascades. This statistical model for the reconstruction of the distribution by its moments is coupled to a previously developed reduced-set, mean-field, rate theory model. As an illustrative case study, the model is applied to a tungsten plasma facing component under irradiation. Our findings highlight the important role of stochastic atomic fluctuations on the evolution of helium–vacancy cluster size distributions. It is found that when the average bubble size is small (at low dpa levels), the relative spread of the distribution is large and average bubble pressures may be very large. As bubbles begin to grow in size, average bubble pressures decrease, and stochastic fluctuations have a lessened effect. The distribution becomes tighter as it evolves in time, corresponding to a more uniform bubble population. The model is formulated in a general way, capable of including point defect drift due to internal temperature and/or stress gradients. These arise during pulsed irradiation, and also during steady irradiation as a result of externally applied or internally generated non-homogeneous stress fields. Discussion is given into how the model can be extended to include full spatial resolution and how the

Mean square exponential stability of stochastic delayed Hopfield neural networks

International Nuclear Information System (INIS)

Wan Li; Sun Jianhua

2005-01-01

Stochastic effects to the stability property of Hopfield neural networks (HNN) with discrete and continuously distributed delay are considered. By using the method of variation parameter, inequality technique and stochastic analysis, the sufficient conditions to guarantee the mean square exponential stability of an equilibrium solution are given. Two examples are also given to demonstrate our results

A mean-field approach for an intercarrier interference canceller for OFDM

International Nuclear Information System (INIS)

Sakata, A; Kabashima, Y; Peleg, Y

2012-01-01

The similarity of the mathematical description of random-field spin systems to the orthogonal frequency-division multiplexing (OFDM) scheme for wireless communication is exploited in an intercarrier interference (ICI) canceller used in the demodulation of OFDM. The translational symmetry in the Fourier domain generically concentrates the major contribution of ICI from each subcarrier in the subcarrier’s neighbourhood. This observation in conjunction with the mean-field approach leads to the development of an ICI canceller whose necessary cost of computation scales linearly with respect to the number of subcarriers. It is also shown that the dynamics of the mean-field canceller are well captured by a discrete map of a single macroscopic variable, without taking the spatial and time correlations of estimated variables into account. (paper)

Beyond mean-field approximations for accurate and computationally efficient models of on-lattice chemical kinetics

Science.gov (United States)

Pineda, M.; Stamatakis, M.

2017-07-01

Modeling the kinetics of surface catalyzed reactions is essential for the design of reactors and chemical processes. The majority of microkinetic models employ mean-field approximations, which lead to an approximate description of catalytic kinetics by assuming spatially uncorrelated adsorbates. On the other hand, kinetic Monte Carlo (KMC) methods provide a discrete-space continuous-time stochastic formulation that enables an accurate treatment of spatial correlations in the adlayer, but at a significant computation cost. In this work, we use the so-called cluster mean-field approach to develop higher order approximations that systematically increase the accuracy of kinetic models by treating spatial correlations at a progressively higher level of detail. We further demonstrate our approach on a reduced model for NO oxidation incorporating first nearest-neighbor lateral interactions and construct a sequence of approximations of increasingly higher accuracy, which we compare with KMC and mean-field. The latter is found to perform rather poorly, overestimating the turnover frequency by several orders of magnitude for this system. On the other hand, our approximations, while more computationally intense than the traditional mean-field treatment, still achieve tremendous computational savings compared to KMC simulations, thereby opening the way for employing them in multiscale modeling frameworks.

MEASURING INFLATION THROUGH STOCHASTIC APPROACH TO INDEX NUMBERS FOR PAKISTAN

Directory of Open Access Journals (Sweden)

Zahid Asghar

2010-09-01

Full Text Available This study attempts to estimate the rate of inflation in Pakistan through stochastic approach to index numbers which provides not only point estimate but also confidence interval for the rate of inflation. There are two types of approaches to index number theory namely: the functional economic approaches and the stochastic approach. The attraction of stochastic approach is that it estimates the rate of inflation in which uncertainty and statistical ideas play a major roll of screening index numbers. We have used extended stochastic approach to index numbers for measuring inflation by allowing for the systematic changes in the relative prices. We use CPI data covering the period July 2001--March 2008 for Pakistan.

A Maximum Principle for SDEs of Mean-Field Type

Energy Technology Data Exchange (ETDEWEB)

Andersson, Daniel, E-mail: danieand@math.kth.se; Djehiche, Boualem, E-mail: boualem@math.kth.se [Royal Institute of Technology, Department of Mathematics (Sweden)

2011-06-15

We study the optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state of the process. Moreover the cost functional is also of mean-field type, which makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. Under the assumption of a convex action space a maximum principle of local form is derived, specifying the necessary conditions for optimality. These are also shown to be sufficient under additional assumptions. This maximum principle differs from the classical one, where the adjoint equation is a linear backward SDE, since here the adjoint equation turns out to be a linear mean-field backward SDE. As an illustration, we apply the result to the mean-variance portfolio selection problem.

A Maximum Principle for SDEs of Mean-Field Type

International Nuclear Information System (INIS)

Andersson, Daniel; Djehiche, Boualem

2011-01-01

We study the optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state of the process. Moreover the cost functional is also of mean-field type, which makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. Under the assumption of a convex action space a maximum principle of local form is derived, specifying the necessary conditions for optimality. These are also shown to be sufficient under additional assumptions. This maximum principle differs from the classical one, where the adjoint equation is a linear backward SDE, since here the adjoint equation turns out to be a linear mean-field backward SDE. As an illustration, we apply the result to the mean-variance portfolio selection problem.

Mean-Variance stochastic goal programming for sustainable mutual funds' portfolio selection.

Directory of Open Access Journals (Sweden)

García-Bernabeu, Ana

2015-11-01

Full Text Available Mean-Variance Stochastic Goal Programming models (MV-SGP provide satisficing investment solutions in uncertain contexts. In this work, an MV-SGP model is proposed for portfolio selection which includes goals with regards to traditional and sustainable assets. The proposed approach is based on a two-step procedure. In the first step, sustainability and/or financial screens are applied to a set of assets (mutual funds previously evaluated with TOPSIS to determine the opportunity set. In a second step, satisficing portfolios of assets are obtained using a Goal Programming approach. Two different goals are considered. The first goal reflects only the purely financial side of the target while the second goal is referred to the sustainable side. Aversion to Risk Absolute (ARA coefficients are estimated and incorporated in our investment decision making approach using two different approaches.

Toward Development of a Stochastic Wake Model: Validation Using LES and Turbine Loads

Directory of Open Access Journals (Sweden)

Jae Sang Moon

2017-12-01

Full Text Available Wind turbines within an array do not experience free-stream undisturbed flow fields. Rather, the flow fields on internal turbines are influenced by wakes generated by upwind unit and exhibit different dynamic characteristics relative to the free stream. The International Electrotechnical Commission (IEC standard 61400-1 for the design of wind turbines only considers a deterministic wake model for the design of a wind plant. This study is focused on the development of a stochastic model for waked wind fields. First, high-fidelity physics-based waked wind velocity fields are generated using Large-Eddy Simulation (LES. Stochastic characteristics of these LES waked wind velocity field, including mean and turbulence components, are analyzed. Wake-related mean and turbulence field-related parameters are then estimated for use with a stochastic model, using Multivariate Multiple Linear Regression (MMLR with the LES data. To validate the simulated wind fields based on the stochastic model, wind turbine tower and blade loads are generated using aeroelastic simulation for utility-scale wind turbine models and compared with those based directly on the LES inflow. The study’s overall objective is to offer efficient and validated stochastic approaches that are computationally tractable for assessing the performance and loads of turbines operating in wakes.

Stochastic inflation: Quantum phase-space approach

International Nuclear Information System (INIS)

Habib, S.

1992-01-01

In this paper a quantum-mechanical phase-space picture is constructed for coarse-grained free quantum fields in an inflationary universe. The appropriate stochastic quantum Liouville equation is derived. Explicit solutions for the phase-space quantum distribution function are found for the cases of power-law and exponential expansions. The expectation values of dynamical variables with respect to these solutions are compared to the corresponding cutoff regularized field-theoretic results (we do not restrict ourselves only to left-angle Φ 2 right-angle). Fair agreement is found provided the coarse-graining scale is kept within certain limits. By focusing on the full phase-space distribution function rather than a reduced distribution it is shown that the thermodynamic interpretation of the stochastic formalism faces several difficulties (e.g., there is no fluctuation-dissipation theorem). The coarse graining does not guarantee an automatic classical limit as quantum correlations turn out to be crucial in order to get results consistent with standard quantum field theory. Therefore, the method does not by itself constitute an explanation of the quantum to classical transition in the early Universe. In particular, we argue that the stochastic equations do not lead to decoherence

Mean field approach to nuclear structure

International Nuclear Information System (INIS)

Nazarewicz, W.; Tennessee Univ., Knoxville, TN

1993-01-01

Several examples of mean-field calculations, relevant to the recent and planned low-spin experimental works, are presented. The perspectives for future studies (mainly related to spectroscopy of exotic nuclei) are reviewd

Mean Square Exponential Stability of Stochastic Switched System with Interval Time-Varying Delays

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Manlika Rajchakit

2012-01-01

Full Text Available This paper is concerned with mean square exponential stability of switched stochastic system with interval time-varying delays. The time delay is any continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the mean square exponential stability of switched stochastic system with interval time-varying delays and new delay-dependent sufficient conditions for the mean square exponential stability of the switched stochastic system are first established in terms of LMIs. Numerical example is given to show the effectiveness of the obtained result.

Stochastic quantization

International Nuclear Information System (INIS)

Klauder, J.R.

1983-01-01

The author provides an introductory survey to stochastic quantization in which he outlines this new approach for scalar fields, gauge fields, fermion fields, and condensed matter problems such as electrons in solids and the statistical mechanics of quantum spins. (Auth.)

A Proposed Stochastic Finite Difference Approach Based on Homogenous Chaos Expansion

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O. H. Galal

2013-01-01

Full Text Available This paper proposes a stochastic finite difference approach, based on homogenous chaos expansion (SFDHC. The said approach can handle time dependent nonlinear as well as linear systems with deterministic or stochastic initial and boundary conditions. In this approach, included stochastic parameters are modeled as second-order stochastic processes and are expanded using Karhunen-Loève expansion, while the response function is approximated using homogenous chaos expansion. Galerkin projection is used in converting the original stochastic partial differential equation (PDE into a set of coupled deterministic partial differential equations and then solved using finite difference method. Two well-known equations were used for efficiency validation of the method proposed. First one being the linear diffusion equation with stochastic parameter and the second is the nonlinear Burger's equation with stochastic parameter and stochastic initial and boundary conditions. In both of these examples, the probability distribution function of the response manifested close conformity to the results obtained from Monte Carlo simulation with optimized computational cost.

Approaching complexity by stochastic methods: From biological systems to turbulence

Energy Technology Data Exchange (ETDEWEB)

Friedrich, Rudolf [Institute for Theoretical Physics, University of Muenster, D-48149 Muenster (Germany); Peinke, Joachim [Institute of Physics, Carl von Ossietzky University, D-26111 Oldenburg (Germany); Sahimi, Muhammad [Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, CA 90089-1211 (United States); Reza Rahimi Tabar, M., E-mail: mohammed.r.rahimi.tabar@uni-oldenburg.de [Department of Physics, Sharif University of Technology, Tehran 11155-9161 (Iran, Islamic Republic of); Institute of Physics, Carl von Ossietzky University, D-26111 Oldenburg (Germany); Fachbereich Physik, Universitaet Osnabrueck, Barbarastrasse 7, 49076 Osnabrueck (Germany)

2011-09-15

This review addresses a central question in the field of complex systems: given a fluctuating (in time or space), sequentially measured set of experimental data, how should one analyze the data, assess their underlying trends, and discover the characteristics of the fluctuations that generate the experimental traces? In recent years, significant progress has been made in addressing this question for a class of stochastic processes that can be modeled by Langevin equations, including additive as well as multiplicative fluctuations or noise. Important results have emerged from the analysis of temporal data for such diverse fields as neuroscience, cardiology, finance, economy, surface science, turbulence, seismic time series and epileptic brain dynamics, to name but a few. Furthermore, it has been recognized that a similar approach can be applied to the data that depend on a length scale, such as velocity increments in fully developed turbulent flow, or height increments that characterize rough surfaces. A basic ingredient of the approach to the analysis of fluctuating data is the presence of a Markovian property, which can be detected in real systems above a certain time or length scale. This scale is referred to as the Markov-Einstein (ME) scale, and has turned out to be a useful characteristic of complex systems. We provide a review of the operational methods that have been developed for analyzing stochastic data in time and scale. We address in detail the following issues: (i) reconstruction of stochastic evolution equations from data in terms of the Langevin equations or the corresponding Fokker-Planck equations and (ii) intermittency, cascades, and multiscale correlation functions.

Approaching complexity by stochastic methods: From biological systems to turbulence

International Nuclear Information System (INIS)

Friedrich, Rudolf; Peinke, Joachim; Sahimi, Muhammad; Reza Rahimi Tabar, M.

2011-01-01

This review addresses a central question in the field of complex systems: given a fluctuating (in time or space), sequentially measured set of experimental data, how should one analyze the data, assess their underlying trends, and discover the characteristics of the fluctuations that generate the experimental traces? In recent years, significant progress has been made in addressing this question for a class of stochastic processes that can be modeled by Langevin equations, including additive as well as multiplicative fluctuations or noise. Important results have emerged from the analysis of temporal data for such diverse fields as neuroscience, cardiology, finance, economy, surface science, turbulence, seismic time series and epileptic brain dynamics, to name but a few. Furthermore, it has been recognized that a similar approach can be applied to the data that depend on a length scale, such as velocity increments in fully developed turbulent flow, or height increments that characterize rough surfaces. A basic ingredient of the approach to the analysis of fluctuating data is the presence of a Markovian property, which can be detected in real systems above a certain time or length scale. This scale is referred to as the Markov-Einstein (ME) scale, and has turned out to be a useful characteristic of complex systems. We provide a review of the operational methods that have been developed for analyzing stochastic data in time and scale. We address in detail the following issues: (i) reconstruction of stochastic evolution equations from data in terms of the Langevin equations or the corresponding Fokker-Planck equations and (ii) intermittency, cascades, and multiscale correlation functions.

A Comparison of Deterministic and Stochastic Modeling Approaches for Biochemical Reaction Systems: On Fixed Points, Means, and Modes.

Science.gov (United States)

Hahl, Sayuri K; Kremling, Andreas

2016-01-01

In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still

A comparison of the stochastic and machine learning approaches in hydrologic time series forecasting

Science.gov (United States)

Kim, T.; Joo, K.; Seo, J.; Heo, J. H.

2016-12-01

Hydrologic time series forecasting is an essential task in water resources management and it becomes more difficult due to the complexity of runoff process. Traditional stochastic models such as ARIMA family has been used as a standard approach in time series modeling and forecasting of hydrological variables. Due to the nonlinearity in hydrologic time series data, machine learning approaches has been studied with the advantage of discovering relevant features in a nonlinear relation among variables. This study aims to compare the predictability between the traditional stochastic model and the machine learning approach. Seasonal ARIMA model was used as the traditional time series model, and Random Forest model which consists of decision tree and ensemble method using multiple predictor approach was applied as the machine learning approach. In the application, monthly inflow data from 1986 to 2015 of Chungju dam in South Korea were used for modeling and forecasting. In order to evaluate the performances of the used models, one step ahead and multi-step ahead forecasting was applied. Root mean squared error and mean absolute error of two models were compared.

Green's Function and Stress Fields in Stochastic Heterogeneous Continua

Science.gov (United States)

Negi, Vineet

Many engineering materials used today are heterogenous in composition e.g. Composites - Polymer Matrix Composites, Metal Matrix Composites. Even, conventional engineering materials - metals, plastics, alloys etc. - may develop heterogeneities, like inclusions and residual stresses, during the manufacturing process. Moreover, these materials may also have intrinsic heterogeneities at a nanoscale in the form of grain boundaries in metals, crystallinity in amorphous polymers etc. While, the homogenized constitutive models for these materials may be satisfactory at a macroscale, recent studies of phenomena like fatigue failure, void nucleation, size-dependent brittle-ductile transition in polymeric nanofibers reveal a major play of micro/nanoscale physics in these phenomena. At this scale, heterogeneities in a material may no longer be ignored. Thus, this demands a study into the effects of various material heterogeneities. In this work, spatial heterogeneities in two material properties - elastic modulus and yield stress - have been investigated separately. The heterogeneity in the elastic modulus is studied in the context of Green's function. The Stochastic Finite Element method is adopted to get the mean statistics of the Green's function defined on a stochastic heterogeneous 2D infinite space. A study of the elastic-plastic transition in a domain having stochastic heterogenous yield stress was done using Mont-Carlo methods. The statistics for various stress and strain fields during the transition were obtained. Further, the effects of size of the domain and the strain-hardening rate on the stress fields during the heterogeneous elastic-plastic transition were investigated. Finally, a case is made for the role of the heterogenous elastic-plastic transition in damage nucleation and growth.

Differential form representation of stochastic electromagnetic fields

Science.gov (United States)

Haider, Michael; Russer, Johannes A.

2017-09-01

In this work, we revisit the theory of stochastic electromagnetic fields using exterior differential forms. We present a short overview as well as a brief introduction to the application of differential forms in electromagnetic theory. Within the framework of exterior calculus we derive equations for the second order moments, describing stochastic electromagnetic fields. Since the resulting objects are continuous quantities in space, a discretization scheme based on the Method of Moments (MoM) is introduced for numerical treatment. The MoM is applied in such a way, that the notation of exterior calculus is maintained while we still arrive at the same set of algebraic equations as obtained for the case of formulating the theory using the traditional notation of vector calculus. We conclude with an analytic calculation of the radiated electric field of two Hertzian dipole, excited by uncorrelated random currents.

Some stochastic techniques in quantization, new developments in Markov fields and quantum fields

International Nuclear Information System (INIS)

Albeverio, S.; Zegarlinski, B.

1990-01-01

In these lectures we intend to discuss a few recent developments in the area of interactions between quantum fields and Markow fields in which we have been involved. We stress particularly developments involving techniques of stochastic analysis and where mathematical results have been obtained. In sections 1 and 2 we discuss recent developments in the study and applications of the theory of Dirichlet forms in its relations with quantum mechanics and quantum field theory. In our opinion, this theory provides a natural setting for the study of the singular stochastic processes associated with quantum theory. In section 3 we discuss a recent rigorous construction of a convergent simplicial approximation to quantum fields. We look upon these developments as a first step towards a mathematical realization, at least in 2 space-time dimensions, of a convergent 'Regge-calculus', and as first steps to the mathematical control of more general models (like e.g. models involving actions of Chern-Simons type) in the continuum. In Sect. 4 we discuss applications of some stochastic techniques to the study of gauge fields and Higgs fields, mainly in 2 space time dimensions and certain non linear electromagnetic-type fields in 4-space-time dimensions. (orig./HSI)

Stochastic methods in quantum mechanics

CERN Document Server

Gudder, Stanley P

2005-01-01

Practical developments in such fields as optical coherence, communication engineering, and laser technology have developed from the applications of stochastic methods. This introductory survey offers a broad view of some of the most useful stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering. Starting with a history of quantum mechanics, it examines both the quantum logic approach and the operational approach, with explorations of random fields and quantum field theory.The text assumes a basic knowledge of fun

Maximum likelihood approach for several stochastic volatility models

International Nuclear Information System (INIS)

Camprodon, Jordi; Perelló, Josep

2012-01-01

Volatility measures the amplitude of price fluctuations. Despite it being one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method which assumes that price and volatility follow a two-dimensional diffusion process where volatility is the stochastic diffusion coefficient of the log-price dynamics. We apply this method to the simplest versions of the expOU, the OU and the Heston stochastic volatility models and we study their performance in terms of the log-price probability, the volatility probability, and its Mean First-Passage Time. The approach has some predictive power on the future returns amplitude by only knowing the current volatility. The assumed models do not consider long-range volatility autocorrelation and the asymmetric return-volatility cross-correlation but the method still yields very naturally these two important stylized facts. We apply the method to different market indices and with a good performance in all cases. (paper)

A combined stochastic analysis of mean daily temperature and diurnal temperature range

Science.gov (United States)

Sirangelo, B.; Caloiero, T.; Coscarelli, R.; Ferrari, E.

2018-03-01

In this paper, a stochastic model, previously proposed for the maximum daily temperature, has been improved for the combined analysis of mean daily temperature and diurnal temperature range. In particular, the procedure applied to each variable sequentially performs the deseasonalization, by means of truncated Fourier series expansions, and the normalization of the temperature data, with the use of proper transformation functions. Then, a joint stochastic analysis of both the climatic variables has been performed by means of a FARIMA model, taking into account the stochastic dependency between the variables, namely introducing a cross-correlation between the standardized noises. The model has been applied to five daily temperature series of southern Italy. After the application of a Monte Carlo simulation procedure, the return periods of the joint behavior of the mean daily temperature and the diurnal temperature range have been evaluated. Moreover, the annual maxima of the temperature excursions in consecutive days have been analyzed for the synthetic series. The results obtained showed different behaviors probably linked to the distance from the sea and to the latitude of the station.

Stochastic Gravity: Theory and Applications

Directory of Open Access Journals (Sweden)

Hu Bei Lok

2004-01-01

Full Text Available Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field's Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction

Stochastic Funding of a Defined Contribution Pension Plan with Proportional Administrative Costs and Taxation under Mean-Variance Optimization Approach

Directory of Open Access Journals (Sweden)

Charles I Nkeki

2014-11-01

Full Text Available This paper aim at studying a mean-variance portfolio selection problem with stochastic salary, proportional administrative costs and taxation in the accumulation phase of a defined contribution (DC pension scheme. The fund process is subjected to taxation while the contribution of the pension plan member (PPM is tax exempt. It is assumed that the flow of contributions of a PPM are invested into a market that is characterized by a cash account and a stock. The optimal portfolio processes and expected wealth for the PPM are established. The efficient and parabolic frontiers of a PPM portfolios in mean-variance are obtained. It was found that capital market line can be attained when initial fund and the contribution rate are zero. It was also found that the optimal portfolio process involved an inter-temporal hedging term that will offset any shocks to the stochastic salary of the PPM.

Mean-field inference of Hawkes point processes

International Nuclear Information System (INIS)

Bacry, Emmanuel; Gaïffas, Stéphane; Mastromatteo, Iacopo; Muzy, Jean-François

2016-01-01

We propose a fast and efficient estimation method that is able to accurately recover the parameters of a d-dimensional Hawkes point-process from a set of observations. We exploit a mean-field approximation that is valid when the fluctuations of the stochastic intensity are small. We show that this is notably the case in situations when interactions are sufficiently weak, when the dimension of the system is high or when the fluctuations are self-averaging due to the large number of past events they involve. In such a regime the estimation of a Hawkes process can be mapped on a least-squares problem for which we provide an analytic solution. Though this estimator is biased, we show that its precision can be comparable to the one of the maximum likelihood estimator while its computation speed is shown to be improved considerably. We give a theoretical control on the accuracy of our new approach and illustrate its efficiency using synthetic datasets, in order to assess the statistical estimation error of the parameters. (paper)

The stochastic versus the Euclidean approach to quantum fields on a static space-time

International Nuclear Information System (INIS)

De Angelis, G.F.; de Falco, D.

1986-01-01

Equations are presented which modify the definition of the Gaussian field in the Rindler chart in order to make contact with the Wightman state, the Hartle-Hawking state, and the Euclidean field. By taking Ornstein-Uhlenbeck processes the authors have chosen, in the sense of stochastic mechanics, to place precisely the Fulling modes in their harmonic oscillator ground state. In this respect, together with the periodicity of Minkowski space-time, the authors observe that the covariance of the Ornstein-Uhlenbeck process can be obtained by analytical continuation of the Wightman function of the harmonic oscillator at zero temperature

Stochastic approach to the derivation of emission limits for wastewater treatment plants.

Science.gov (United States)

Stransky, D; Kabelkova, I; Bares, V

2009-01-01

Stochastic approach to the derivation of WWTP emission limits meeting probabilistically defined environmental quality standards (EQS) is presented. The stochastic model is based on the mixing equation with input data defined by probability density distributions and solved by Monte Carlo simulations. The approach was tested on a study catchment for total phosphorus (P(tot)). The model assumes input variables independency which was proved for the dry-weather situation. Discharges and P(tot) concentrations both in the study creek and WWTP effluent follow log-normal probability distribution. Variation coefficients of P(tot) concentrations differ considerably along the stream (c(v)=0.415-0.884). The selected value of the variation coefficient (c(v)=0.420) affects the derived mean value (C(mean)=0.13 mg/l) of the P(tot) EQS (C(90)=0.2 mg/l). Even after supposed improvement of water quality upstream of the WWTP to the level of the P(tot) EQS, the WWTP emission limits calculated would be lower than the values of the best available technology (BAT). Thus, minimum dilution ratios for the meaningful application of the combined approach to the derivation of P(tot) emission limits for Czech streams are discussed.

Differential form representation of stochastic electromagnetic fields

Directory of Open Access Journals (Sweden)

M. Haider

2017-09-01

Full Text Available In this work, we revisit the theory of stochastic electromagnetic fields using exterior differential forms. We present a short overview as well as a brief introduction to the application of differential forms in electromagnetic theory. Within the framework of exterior calculus we derive equations for the second order moments, describing stochastic electromagnetic fields. Since the resulting objects are continuous quantities in space, a discretization scheme based on the Method of Moments (MoM is introduced for numerical treatment. The MoM is applied in such a way, that the notation of exterior calculus is maintained while we still arrive at the same set of algebraic equations as obtained for the case of formulating the theory using the traditional notation of vector calculus. We conclude with an analytic calculation of the radiated electric field of two Hertzian dipole, excited by uncorrelated random currents.

Symmetries of stochastic differential equations: A geometric approach

Energy Technology Data Exchange (ETDEWEB)

De Vecchi, Francesco C., E-mail: francesco.devecchi@unimi.it; Ugolini, Stefania, E-mail: stefania.ugolini@unimi.it [Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, Milano (Italy); Morando, Paola, E-mail: paola.morando@unimi.it [DISAA, Università degli Studi di Milano, via Celoria 2, Milano (Italy)

2016-06-15

A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence between an algebra of weak symmetries for a given SDE and an algebra of strong symmetries for a modified SDE is proved under suitable regularity assumptions. This general approach is applied to a stochastic version of a two dimensional symmetric ordinary differential equation and to the case of two dimensional Brownian motion.

A stochastic approach to chemical evolution

International Nuclear Information System (INIS)

Copi, C.J.

1997-01-01

Observations of elemental abundances in the Galaxy have repeatedly shown an intrinsic scatter as a function of time and metallicity. The standard approach to chemical evolution does not attempt to address this scatter in abundances since only the mean evolution is followed. In this work, the scatter is addressed via a stochastic approach to solving chemical evolution models. Three simple chemical evolution scenarios are studied using this stochastic approach: a closed box model, an infall model, and an outflow model. These models are solved for the solar neighborhood in a Monte Carlo fashion. The evolutionary history of one particular region is determined randomly based on the star formation rate and the initial mass function. Following the evolution in an ensemble of such regions leads to the predicted spread in abundances expected, based solely on different evolutionary histories of otherwise identical regions. In this work, 13 isotopes are followed, including the light elements, the CNO elements, a few α-elements, and iron. It is found that the predicted spread in abundances for a 10 5 M circle-dot region is in good agreement with observations for the α-elements. For CN, the agreement is not as good, perhaps indicating the need for more physics input for low-mass stellar evolution. Similarly for the light elements, the predicted scatter is quite small, which is in contradiction to the observations of 3 He in HII regions. The models are tuned for the solar neighborhood so that good agreement with HII regions is not expected. This has important implications for low-mass stellar evolution and on using chemical evolution to determine the primordial light-element abundances in order to test big bang nucleosynthesis. copyright 1997 The American Astronomical Society

Intermittency in multiparticle production analyzed by means of stochastic theories

International Nuclear Information System (INIS)

Bartl, A.; Suzuki, N.

1990-01-01

Intermittency in multiparticle production is described by means of probability distributions derived from pure birth stochastic equations. The UA1, TASSO, NA22 and cosmic ray data are analyzed. 24 refs., 1 fig. (Authors)

Computing Optimal Stochastic Portfolio Execution Strategies: A Parametric Approach Using Simulations

Science.gov (United States)

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).

Diffusion of charged particles in a stochastic magnetic field

International Nuclear Information System (INIS)

Balescu, R.; Misguich, J.H.; Nakach, R.

1992-07-01

The diffusive motion of charged particles in a stochastic magnetic field is investigated systematically in a model in which the statistics of both the collisions and the magnetic field are described by coloured noises characterized, respectively, by a finite correlation time and finite correlation lengths. An analytic solution is obtained for the basic nonlinear differential equation of the model..It describes asymptotically a pure diffusion process, in which the mean square displacement in the perpendicular direction, Γ(t), grows proportionally to time (after a sufficiently long time). The corresponding diffusion coefficient scales like the fourth power of the magnetic fluctuation intensity. The values obtained are in very good agreement with experimental data in reverse-field pinch experiments. The present result contradicts earlier results predicting subdiffusive behaviour: Γ(t) ∼ t 1/2 or Γ(t) ∼ t 1/4 . The relation of these results to ours is discussed in detail

The limits of the mean field

International Nuclear Information System (INIS)

Guerra, E.M. de

2001-01-01

In these talks, we review non relativistic selfconsistent mean field theories, their scope and limitations. We first discuss static and time dependent mean field approaches for particles and quasiparticles, together with applications. We then discuss extensions that go beyond the non-relativistic independent particle limit. On the one hand, we consider extensions concerned with restoration of symmetries and with the treatment of collective modes, particularly by means of quantized ATDHF. On the other hand, we consider extensions concerned with the relativistic dynamics of bound nucleons. We present data on nucleon momentum distributions that show the need for relativistic mean field approach and probe the limits of the mean field concept. Illustrative applications of various methods are presented stressing the role that selfconsistency plays in providing a unifying reliable framework to study all sorts of properties and phenomena. From global properties such as size, mass, lifetime,.., to detailed structure in excitation spectra (high spin, RPA modes,..), as well as charge, magnetization and velocity distributions. (orig.)

Fast and robust estimation of spectro-temporal receptive fields using stochastic approximations.

Science.gov (United States)

Meyer, Arne F; Diepenbrock, Jan-Philipp; Ohl, Frank W; Anemüller, Jörn

2015-05-15

The receptive field (RF) represents the signal preferences of sensory neurons and is the primary analysis method for understanding sensory coding. While it is essential to estimate a neuron's RF, finding numerical solutions to increasingly complex RF models can become computationally intensive, in particular for high-dimensional stimuli or when many neurons are involved. Here we propose an optimization scheme based on stochastic approximations that facilitate this task. The basic idea is to derive solutions on a random subset rather than computing the full solution on the available data set. To test this, we applied different optimization schemes based on stochastic gradient descent (SGD) to both the generalized linear model (GLM) and a recently developed classification-based RF estimation approach. Using simulated and recorded responses, we demonstrate that RF parameter optimization based on state-of-the-art SGD algorithms produces robust estimates of the spectro-temporal receptive field (STRF). Results on recordings from the auditory midbrain demonstrate that stochastic approximations preserve both predictive power and tuning properties of STRFs. A correlation of 0.93 with the STRF derived from the full solution may be obtained in less than 10% of the full solution's estimation time. We also present an on-line algorithm that allows simultaneous monitoring of STRF properties of more than 30 neurons on a single computer. The proposed approach may not only prove helpful for large-scale recordings but also provides a more comprehensive characterization of neural tuning in experiments than standard tuning curves. Copyright © 2015 Elsevier B.V. All rights reserved.

Stochastic TDHF and the Boltzman-Langevin equation

International Nuclear Information System (INIS)

Suraud, E.; Reinhard, P.G.

1991-01-01

Outgoing from a time-dependent theory of correlations, we present a stochastic differential equation for the propagation of ensembles of Slater determinants, called Stochastic Time-Dependent Hartree-Fock (Stochastic TDHF). These ensembles are allowed to develop large fluctuations in the Hartree-Fock mean fields. An alternative stochastic differential equation, the Boltzmann-Langevin equation, can be derived from Stochastic TDHF by averaging over subensembles with small fluctuations

Exact Robust Counterparts of Ambiguous Stochastic Constraints Under Mean and Dispersion Information

NARCIS (Netherlands)

Postek, Krzysztof; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand

2015-01-01

In this paper we consider ambiguous stochastic constraints under partial information consisting of means and dispersion measures of the underlying random parameters. Whereas the past literature used the variance as the dispersion measure, here we use the mean absolute deviation from the mean (MAD).

Stochastic Gravity: Theory and Applications

Directory of Open Access Journals (Sweden)

Hu Bei Lok

2008-05-01

Full Text Available Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein–Langevin equation, which has, in addition, sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued stress-energy bitensor, which describes the fluctuations of quantum-matter fields in curved spacetimes. A new improved criterion for the validity of semiclassical gravity may also be formulated from the viewpoint of this theory. In the first part of this review we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to the correlation functions. The functional approach uses the Feynman–Vernon influence functional and the Schwinger–Keldysh closed-time-path effective action methods. In the second part, we describe three applications of stochastic gravity. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic-gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, using the Einstein–Langevin equation, we discuss the backreaction of Hawking radiation and the behavior of metric fluctuations for both the quasi-equilibrium condition of a black-hole in a box and the fully nonequilibrium condition of an evaporating black hole spacetime. Finally, we briefly discuss the theoretical structure of stochastic gravity in relation to quantum gravity and point out

Endogenous fields enhanced stochastic resonance in a randomly coupled neuronal network

International Nuclear Information System (INIS)

Deng, Bin; Wang, Lin; Wang, Jiang; Wei, Xi-le; Yu, Hai-tao

2014-01-01

Highlights: • We study effects of endogenous fields on stochastic resonance in a neural network. • Stochastic resonance can be notably enhanced by endogenous field feedback. • Endogenous field feedback delay plays a vital role in stochastic resonance. • The parameters of low-passed filter play a subtle role in SR. - Abstract: Endogenous field, evoked by structured neuronal network activity in vivo, is correlated with many vital neuronal processes. In this paper, the effects of endogenous fields on stochastic resonance (SR) in a randomly connected neuronal network are investigated. The network consists of excitatory and inhibitory neurons and the axonal conduction delays between neurons are also considered. Numerical results elucidate that endogenous field feedback results in more rhythmic macroscope activation of the network for proper time delay and feedback coefficient. The response of the network to the weak periodic stimulation can be notably enhanced by endogenous field feedback. Moreover, the endogenous field feedback delay plays a vital role in SR. We reveal that appropriately tuned delays of the feedback can either induce the enhancement of SR, appearing at every integer multiple of the weak input signal’s oscillation period, or the depression of SR, appearing at every integer multiple of half the weak input signal’s oscillation period for the same feedback coefficient. Interestingly, the parameters of low-passed filter which is used in obtaining the endogenous field feedback signal play a subtle role in SR

Stochastic quantization and gauge-fixing of the linearized gravitational field

International Nuclear Information System (INIS)

Hueffel, H.; Rumpf, H.

1984-01-01

Due to the indefiniteness of the Euclidean gravitational action the Parisi-Wu stochastic quantization scheme fails in the case of the gravitational field. Therefore we apply a recently proposed modification of stochastic quantization that works in Minkowski space and preserves all the advantages of the original Parisi-Wu method; in particular no gauge-fixing is required. Additionally stochastic gauge-fixing may be introduced and is also studied in detail. The graviton propagators obtained with and without stochastic gauge-fixing all exhibit a noncausal contribution, but apart from this effect the gauge-invariant quantities are the same as those of standard quantization. (Author)

Interplanetary Alfvenic fluctuations: A stochastic model

International Nuclear Information System (INIS)

Barnes, A.

1981-01-01

The strong alignment of the average directions of minimum magnetic variance and mean magnetic field in interplanetary Alfvenic fluctuations is inconsistent with the usual wave-propagation models. We investigate the concept of minimum variance for nonplanar Alfvenic fluctuations in which the field direction varies stochastically. It is found that the tendency of the minimum variance and mean field directions to be aligned may be purely a consequence of the randomness of the field direction. In particular, a well-defined direction of minimum variance does not imply that the fluctuations are necessarily planar. The fluctuation power spectrum is a power law for frequencies much higher than the inverse of the correlation time. The probability distribution of directions a randomly fluctuating field of constant magnitude is calculated. A new approach for observational studies of interplanetary fluctuations is suggested

Markovian approach: From Ising model to stochastic radiative transfer

International Nuclear Information System (INIS)

Kassianov, E.; Veron, D.

2009-01-01

The origin of the Markovian approach can be traced back to 1906; however, it gained explicit recognition in the last few decades. This overview outlines some important applications of the Markovian approach, which illustrate its immense prestige, respect, and success. These applications include examples in the statistical physics, astronomy, mathematics, computational science and the stochastic transport problem. In particular, the overview highlights important contributions made by Pomraning and Titov to the neutron and radiation transport theory in a stochastic medium with homogeneous statistics. Using simple probabilistic assumptions (Markovian approximation), they have introduced a simplified, but quite realistic, representation of the neutron/radiation transfer through a two-component discrete stochastic mixture. New concepts and methodologies introduced by these two distinguished scientists allow us to generalize the Markovian treatment to the stochastic medium with inhomogeneous statistics and demonstrate its improved predictive performance for the down-welling shortwave fluxes. (authors)

Stable oscillations of a predator-prey probabilistic cellular automaton: a mean-field approach

International Nuclear Information System (INIS)

Tome, Tania; Carvalho, Kelly C de

2007-01-01

We analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator-prey system. The individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired by the processes of the Lotka-Volterra model. Two levels of mean-field approximations are set up. The simple approximation is equivalent to an extended patch model, a simple metapopulation model with patches colonized by prey, patches colonized by predators and empty patches. This approximation is capable of describing the limited available space for species occupancy. The pair approximation is moreover able to describe two types of coexistence of prey and predators: one where population densities are constant in time and another displaying self-sustained time oscillations of the population densities. The oscillations are associated with limit cycles and arise through a Hopf bifurcation. They are stable against changes in the initial conditions and, in this sense, they differ from the Lotka-Volterra cycles which depend on initial conditions. In this respect, the present model is biologically more realistic than the Lotka-Volterra model

Estimation of mean-reverting oil prices: a laboratory approach

International Nuclear Information System (INIS)

Bjerksund, P.; Stensland, G.

1993-12-01

Many economic decision support tools developed for the oil industry are based on the future oil price dynamics being represented by some specified stochastic process. To meet the demand for necessary data, much effort is allocated to parameter estimation based on historical oil price time series. The approach in this paper is to implement a complex future oil market model, and to condense the information from the model to parameter estimates for the future oil price. In particular, we use the Lensberg and Rasmussen stochastic dynamic oil market model to generate a large set of possible future oil price paths. Given the hypothesis that the future oil price is generated by a mean-reverting Ornstein-Uhlenbeck process, we obtain parameter estimates by a maximum likelihood procedure. We find a substantial degree of mean-reversion in the future oil price, which in some of our decision examples leads to an almost negligible value of flexibility. 12 refs., 2 figs., 3 tabs

The extended local gauge invariance and the BRS symmetry in stochastic quantization of gauge fields

International Nuclear Information System (INIS)

Nakazawa, Naohito.

1989-05-01

We investigate the BRS invariance of the first-class constrained systems in the context of the stochastic quantization. For the first-class constrained systems, we construct the nilpotent BRS transformation and the BRS invariant stochastic effective action based on the D+1 dimensional field theoretical formulation of stochastic quantization. By eliminating the multiplier field of the gauge fixing condition and an auxiliary field, it is shown that there exists a truncated BRS transformation which satisfies the nilpotency condition. The truncated BRS invariant stochastic action is also derived. As the examples of the general formulation, we investigate the BRS invariant structure in the massless and massive Yang-Mills fields in stochastic quantization. (author)

Molecules with an induced dipole moment in a stochastic electric field.

Science.gov (United States)

Band, Y B; Ben-Shimol, Y

2013-10-01

The mean-field dynamics of a molecule with an induced dipole moment (e.g., a homonuclear diatomic molecule) in a deterministic and a stochastic (fluctuating) electric field is solved to obtain the decoherence properties of the system. The average (over fluctuations) electric dipole moment and average angular momentum as a function of time for a Gaussian white noise electric field are determined via perturbative and nonperturbative solutions in the fluctuating field. In the perturbative solution, the components of the average electric dipole moment and the average angular momentum along the deterministic electric field direction do not decay to zero, despite fluctuations in all three components of the electric field. This is in contrast to the decay of the average over fluctuations of a magnetic moment in a Gaussian white noise magnetic field. In the nonperturbative solution, the component of the average electric dipole moment and the average angular momentum in the deterministic electric field direction also decay to zero.

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 modelling of conjugate heat transfer in near-wall turbulence

International Nuclear Information System (INIS)

Pozorski, Jacek; Minier, Jean-Pierre

2006-01-01

The paper addresses the conjugate heat transfer in turbulent flows with temperature assumed to be a passive scalar. The Lagrangian approach is applied and the heat transfer is modelled with the use of stochastic particles. The intensity of thermal fluctuations in near-wall turbulence is determined from the scalar probability density function (PDF) with externally provided dynamical statistics. A stochastic model for the temperature field in the wall material is proposed and boundary conditions for stochastic particles at the solid-fluid interface are formulated. The heated channel flow with finite-thickness walls is considered as a validation case. Computation results for the mean temperature profiles and the variance of thermal fluctuations are presented and compared with available DNS data

Stochastic modelling of conjugate heat transfer in near-wall turbulence

Energy Technology Data Exchange (ETDEWEB)

Pozorski, Jacek [Institute of Fluid-Flow Machinery, Polish Academy of Sciences, Fiszera 14, 80952 Gdansk (Poland)]. E-mail: jp@imp.gda.pl; Minier, Jean-Pierre [Research and Development Division, Electricite de France, 6 quai Watier, 78400 Chatou (France)

2006-10-15

The paper addresses the conjugate heat transfer in turbulent flows with temperature assumed to be a passive scalar. The Lagrangian approach is applied and the heat transfer is modelled with the use of stochastic particles. The intensity of thermal fluctuations in near-wall turbulence is determined from the scalar probability density function (PDF) with externally provided dynamical statistics. A stochastic model for the temperature field in the wall material is proposed and boundary conditions for stochastic particles at the solid-fluid interface are formulated. The heated channel flow with finite-thickness walls is considered as a validation case. Computation results for the mean temperature profiles and the variance of thermal fluctuations are presented and compared with available DNS data.

Stochastic Loewner evolution as an approach to conformal field theory

International Nuclear Information System (INIS)

Mueller-Lohmann, Annekathrin

2008-01-01

The main focus on this work lies on the relationship between two-dimensional boundary Conformal Field Theories (BCFTs) and SCHRAMM-LOEWNER Evolutions (SLEs) as motivated by their connection to the scaling limit of Statistical Physics models at criticality. The BCFT approach used for the past 25 years is based on the algebraic formulation of local objects such as fields and their correlations in these models. Introduced in 1999, SLE describes the physical properties from a probabilistic point of view, studying measures on growing curves, i.e. global objects such as cluster interfaces. After a short motivation of the topic, followed by a more detailed introduction to two-dimensional boundary Conformal Field Theory and SCHRAMM-LOEWNER Evolution, we present the results of our original work. We extend the method of obtaining SLE variants for a change of measure of the single SLE to derive the most general BCFT model that can be related to SLE. Moreover, we interpret the change of the measure in the context of physics and Probability Theory. In addition, we discuss the meaning of bulk fields in BCFT as bulk force-points for the SLE variant SLE (κ, vector ρ). Furthermore, we investigate the short-distance expansion of the boundary condition changing fields, creating cluster interfaces that can be described by SLE, with other boundary or bulk fields. Thereby we derive new SLE martingales related to the existence of boundary fields with vanishing descendant on level three. We motivate that the short-distance scaling law of these martingales as adjustment of the measure can be interpreted as the SLE probability of curves coming close to the location of the second field. Finally, we extend the algebraic κ-relation for the allowed variances in multiple SLE, arising due to the commutation requirement of the infinitesimal growth operators, to the joint growth of two SLE traces. The analysis straightforwardly suggests the form of the infinitesimal LOEWNER mapping of joint

Stochastic lattice model of synaptic membrane protein domains.

Science.gov (United States)

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 Collocation Applications in Computational Electromagnetics

Directory of Open Access Journals (Sweden)

Dragan Poljak

2018-01-01

Full Text Available The paper reviews the application of deterministic-stochastic models in some areas of computational electromagnetics. Namely, in certain problems there is an uncertainty in the input data set as some properties of a system are partly or entirely unknown. Thus, a simple stochastic collocation (SC method is used to determine relevant statistics about given responses. The SC approach also provides the assessment of related confidence intervals in the set of calculated numerical results. The expansion of statistical output in terms of mean and variance over a polynomial basis, via SC method, is shown to be robust and efficient approach providing a satisfactory convergence rate. This review paper provides certain computational examples from the previous work by the authors illustrating successful application of SC technique in the areas of ground penetrating radar (GPR, human exposure to electromagnetic fields, and buried lines and grounding systems.

A robust decision-making approach for p-hub median location problems based on two-stage stochastic programming and mean-variance theory : a real case study

NARCIS (Netherlands)

Ahmadi, T.; Karimi, H.; Davoudpour, H.

2015-01-01

The stochastic location-allocation p-hub median problems are related to long-term decisions made in risky situations. Due to the importance of this type of problems in real-world applications, the authors were motivated to propose an approach to obtain more reliable policies in stochastic

Mean square stabilization and mean square exponential stabilization of stochastic BAM neural networks with Markovian jumping parameters

International Nuclear Information System (INIS)

Ye, Zhiyong; Zhang, He; Zhang, Hongyu; Zhang, Hua; Lu, Guichen

2015-01-01

Highlights: •This paper introduces a non-conservative Lyapunov functional. •The achieved results impose non-conservative and can be widely used. •The conditions are easily checked by the Matlab LMI Tool Box. The desired state feedback controller can be well represented by the conditions. -- Abstract: This paper addresses the mean square exponential stabilization problem of stochastic bidirectional associative memory (BAM) neural networks with Markovian jumping parameters and time-varying delays. By establishing a proper Lyapunov–Krasovskii functional and combining with LMIs technique, several sufficient conditions are derived for ensuring exponential stabilization in the mean square sense of such stochastic BAM neural networks. In addition, the achieved results are not difficult to verify for determining the mean square exponential stabilization of delayed BAM neural networks with Markovian jumping parameters and impose less restrictive and less conservative than the ones in previous papers. Finally, numerical results are given to show the effectiveness and applicability of the achieved results

BRS symmetry in stochastic quantization of the gravitational field

International Nuclear Information System (INIS)

Nakazawa, Naohito.

1989-12-01

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 a 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 for gravity (in general, for the first-class constrained systems). The stochastic action of gravity includes explicitly an unique De Witt's type superspace metric which leads to a geometrical interpretation of quantum gravity analogous to nonlinear σ-models. (author)

Virtual-site correlation mean field approach to criticality in spin systems

International Nuclear Information System (INIS)

Sen, Aditi; Sen, Ujjwal

2013-01-01

We propose a virtual-site correlation mean field theory for dealing with interacting many-body systems. It involves a coarse-graining technique that terminates a step before the mean field theory: While mean field theory deals with only single-body physical parameters, the virtual-site correlation mean field theory deals with single- as well as two-body ones, and involves a virtual site for every interaction term in the Hamiltonian. We generalize the theory to a cluster virtual-site correlation mean field, that works with a fundamental unit of the lattice of the many-body system. We apply these methods to interacting Ising spin systems in several lattice geometries and dimensions, and show that the predictions of the onset of criticality of these models are generally much better in the proposed theories as compared to the corresponding ones in mean field theories

Diagrammatic Monte Carlo approach for diagrammatic extensions of dynamical mean-field theory: Convergence analysis of the dual fermion technique

Science.gov (United States)

Gukelberger, Jan; Kozik, Evgeny; Hafermann, Hartmut

2017-07-01

The dual fermion approach provides a formally exact prescription for calculating properties of a correlated electron system in terms of a diagrammatic expansion around dynamical mean-field theory (DMFT). Most practical implementations, however, neglect higher-order interaction vertices beyond two-particle scattering in the dual effective action and further truncate the diagrammatic expansion in the two-particle scattering vertex to a leading-order or ladder-type approximation. In this work, we compute the dual fermion expansion for the two-dimensional Hubbard model including all diagram topologies with two-particle interactions to high orders by means of a stochastic diagrammatic Monte Carlo algorithm. We benchmark the obtained self-energy against numerically exact diagrammatic determinant Monte Carlo simulations to systematically assess convergence of the dual fermion series and the validity of these approximations. We observe that, from high temperatures down to the vicinity of the DMFT Néel transition, the dual fermion series converges very quickly to the exact solution in the whole range of Hubbard interactions considered (4 ≤U /t ≤12 ), implying that contributions from higher-order vertices are small. As the temperature is lowered further, we observe slower series convergence, convergence to incorrect solutions, and ultimately divergence. This happens in a regime where magnetic correlations become significant. We find, however, that the self-consistent particle-hole ladder approximation yields reasonable and often even highly accurate results in this regime.

Quantum noise in the mirror–field system: A field theoretic approach

International Nuclear Information System (INIS)

Hsiang, Jen-Tsung; Wu, Tai-Hung; Lee, Da-Shin; King, Sun-Kun; Wu, Chun-Hsien

2013-01-01

We revisit the quantum noise problem in the mirror–field system by a field-theoretic approach. Here a perfectly reflecting mirror is illuminated by a single-mode coherent state of the massless scalar field. The associated radiation pressure is described by a surface integral of the stress-tensor of the field. The read-out field is measured by a monopole detector, from which the effective distance between the detector and mirror can be obtained. In the slow-motion limit of the mirror, this field-theoretic approach allows to identify various sources of quantum noise that all in all leads to uncertainty of the read-out measurement. In addition to well-known sources from shot noise and radiation pressure fluctuations, a new source of noise is found from field fluctuations modified by the mirror’s displacement. Correlation between different sources of noise can be established in the read-out measurement as the consequence of interference between the incident field and the field reflected off the mirror. In the case of negative correlation, we found that the uncertainty can be lowered than the value predicted by the standard quantum limit. Since the particle-number approach is often used in quantum optics, we compared results obtained by both approaches and examine its validity. We also derive a Langevin equation that describes the stochastic dynamics of the mirror. The underlying fluctuation–dissipation relation is briefly mentioned. Finally we discuss the backreaction induced by the radiation pressure. It will alter the mean displacement of the mirror, but we argue this backreaction can be ignored for a slowly moving mirror. - Highlights: ► The quantum noise problem in the mirror–field system is re-visited by a field-theoretic approach. ► Other than the shot noise and radiation pressure noise, we show there are new sources of noise and correlation between them. ► The noise correlations can be used to suppress the overall quantum noise on the mirror. �

Quantum noise in the mirror-field system: A field theoretic approach

Energy Technology Data Exchange (ETDEWEB)

Hsiang, Jen-Tsung, E-mail: cosmology@gmail.com [Department of Physics, National Dong-Hwa University, Hua-lien, Taiwan, ROC (China); Wu, Tai-Hung [Department of Physics, National Dong-Hwa University, Hua-lien, Taiwan, ROC (China); Lee, Da-Shin, E-mail: dslee@mail.ndhu.edu.tw [Department of Physics, National Dong-Hwa University, Hua-lien, Taiwan, ROC (China); King, Sun-Kun [Institutes of Astronomy and Astrophysics, Academia Sinica, Taipei, Taiwan, ROC (China); Wu, Chun-Hsien [Department of Physics, Soochow University, Taipei, Taiwan, ROC (China)

2013-02-15

We revisit the quantum noise problem in the mirror-field system by a field-theoretic approach. Here a perfectly reflecting mirror is illuminated by a single-mode coherent state of the massless scalar field. The associated radiation pressure is described by a surface integral of the stress-tensor of the field. The read-out field is measured by a monopole detector, from which the effective distance between the detector and mirror can be obtained. In the slow-motion limit of the mirror, this field-theoretic approach allows to identify various sources of quantum noise that all in all leads to uncertainty of the read-out measurement. In addition to well-known sources from shot noise and radiation pressure fluctuations, a new source of noise is found from field fluctuations modified by the mirror's displacement. Correlation between different sources of noise can be established in the read-out measurement as the consequence of interference between the incident field and the field reflected off the mirror. In the case of negative correlation, we found that the uncertainty can be lowered than the value predicted by the standard quantum limit. Since the particle-number approach is often used in quantum optics, we compared results obtained by both approaches and examine its validity. We also derive a Langevin equation that describes the stochastic dynamics of the mirror. The underlying fluctuation-dissipation relation is briefly mentioned. Finally we discuss the backreaction induced by the radiation pressure. It will alter the mean displacement of the mirror, but we argue this backreaction can be ignored for a slowly moving mirror. - Highlights: Black-Right-Pointing-Pointer The quantum noise problem in the mirror-field system is re-visited by a field-theoretic approach. Black-Right-Pointing-Pointer Other than the shot noise and radiation pressure noise, we show there are new sources of noise and correlation between them. Black-Right-Pointing-Pointer The noise

A network of spiking neurons that can represent interval timing: mean field analysis.

Science.gov (United States)

Gavornik, Jeffrey P; Shouval, Harel Z

2011-04-01

Despite the vital importance of our ability to accurately process and encode temporal information, the underlying neural mechanisms are largely unknown. We have previously described a theoretical framework that explains how temporal representations, similar to those reported in the visual cortex, can form in locally recurrent cortical networks as a function of reward modulated synaptic plasticity. This framework allows networks of both linear and spiking neurons to learn the temporal interval between a stimulus and paired reward signal presented during training. Here we use a mean field approach to analyze the dynamics of non-linear stochastic spiking neurons in a network trained to encode specific time intervals. This analysis explains how recurrent excitatory feedback allows a network structure to encode temporal representations.

From stochastic completion fields to tensor voting

NARCIS (Netherlands)

Almsick, van M.A.; Duits, R.; Franken, E.M.; Haar Romenij, ter B.M.; Olsen, O.F.; Florack, L.M.J.; Kuijper, A.

2005-01-01

Several image processing algorithms imitate the lateral interaction of neurons in the visual striate cortex V1 to account for the correlations along contours and lines. Here we focus on two methodologies: tensor voting by Guy and Medioni, and stochastic completion fields by Mumford, Williams and

On Mean-Variance Hedging of Bond Options with Stochastic Risk Premium Factor

NARCIS (Netherlands)

Aihara, ShinIchi; Bagchi, Arunabha; Kumar, Suresh K.

2014-01-01

We consider the mean-variance hedging problem for pricing bond options using the yield curve as the observation. The model considered contains infinite-dimensional noise sources with the stochastically- varying risk premium. Hence our model is incomplete. We consider mean-variance hedging under the

Stochastic approach to equilibrium and nonequilibrium thermodynamics.

Science.gov (United States)

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.

Expansions of general stationary stochastic optical fields: general formalism

International Nuclear Information System (INIS)

Martinez-Herrero, R.; Mejias, P.M.

1985-01-01

A new expansion of a general stationary stochastic optical field is derived. Each term of the series is seen to represent a recently defined new class of optical fields, the so-called spectrally quasi-factorizable fields. Alternative expansion in terms of nonstationary fields that obey the wave equation is also shown. A relationship between temporal and spatial features of stationary free optical fields is discussed

Distribution of particles in stochastic electric fields

International Nuclear Information System (INIS)

Rolland, Paul.

1979-11-01

The distribution of one particle as well as an ensemble of particles submitted to a stochastic electric field obeying different kinds of laws is studied. A particular attention is devoted to the deviation from the gaussian distribution and to the consequences of this effect on diffusion and heating [fr

Probability, Statistics, and Stochastic Processes

CERN Document Server

Olofsson, Peter

2011-01-01

A mathematical and intuitive approach to probability, statistics, and stochastic processes This textbook provides a unique, balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. This text combines a rigorous, calculus-based development of theory with a more intuitive approach that appeals to readers' sense of reason and logic, an approach developed through the author's many years of classroom experience. The text begins with three chapters that d

A polynomial-chaos-expansion-based building block approach for stochastic analysis of photonic circuits

Science.gov (United States)

Waqas, Abi; Melati, Daniele; Manfredi, Paolo; Grassi, Flavia; Melloni, Andrea

2018-02-01

The Building Block (BB) approach has recently emerged in photonic as a suitable strategy for the analysis and design of complex circuits. Each BB can be foundry related and contains a mathematical macro-model of its functionality. As well known, statistical variations in fabrication processes can have a strong effect on their functionality and ultimately affect the yield. In order to predict the statistical behavior of the circuit, proper analysis of the uncertainties effects is crucial. This paper presents a method to build a novel class of Stochastic Process Design Kits for the analysis of photonic circuits. The proposed design kits directly store the information on the stochastic behavior of each building block in the form of a generalized-polynomial-chaos-based augmented macro-model obtained by properly exploiting stochastic collocation and Galerkin methods. Using this approach, we demonstrate that the augmented macro-models of the BBs can be calculated once and stored in a BB (foundry dependent) library and then used for the analysis of any desired circuit. The main advantage of this approach, shown here for the first time in photonics, is that the stochastic moments of an arbitrary photonic circuit can be evaluated by a single simulation only, without the need for repeated simulations. The accuracy and the significant speed-up with respect to the classical Monte Carlo analysis are verified by means of classical photonic circuit example with multiple uncertain variables.

Out-of-equilibrium dynamical mean-field equations for the perceptron model

Science.gov (United States)

Agoritsas, Elisabeth; Biroli, Giulio; Urbani, Pierfrancesco; Zamponi, Francesco

2018-02-01

Perceptrons are the building blocks of many theoretical approaches to a wide range of complex systems, ranging from neural networks and deep learning machines, to constraint satisfaction problems, glasses and ecosystems. Despite their applicability and importance, a detailed study of their Langevin dynamics has never been performed yet. Here we derive the mean-field dynamical equations that describe the continuous random perceptron in the thermodynamic limit, in a very general setting with arbitrary noise and friction kernels, not necessarily related by equilibrium relations. We derive the equations in two ways: via a dynamical cavity method, and via a path-integral approach in its supersymmetric formulation. The end point of both approaches is the reduction of the dynamics of the system to an effective stochastic process for a representative dynamical variable. Because the perceptron is formally very close to a system of interacting particles in a high dimensional space, the methods we develop here can be transferred to the study of liquid and glasses in high dimensions. Potentially interesting applications are thus the study of the glass transition in active matter, the study of the dynamics around the jamming transition, and the calculation of rheological properties in driven systems.

A stochastic aerodynamic model for stationary blades in unsteady 3D wind fields

International Nuclear Information System (INIS)

Fluck, Manuel; Crawford, Curran

2016-01-01

Dynamic loads play an important roll in the design of wind turbines, but establishing the life-time aerodynamic loads (e.g. extreme and fatigue loads) is a computationally expensive task. Conventional (deterministic) methods to analyze long term loads, which rely on the repeated analysis of multiple different wind samples, are usually too expensive to be included in optimization routines. We present a new stochastic approach, which solves the aerodynamic system equations (Lagrangian vortex model) in the stochastic space, and thus arrive directly at a stochastic description of the coupled loads along a turbine blade. This new approach removes the requirement of analyzing multiple different realizations. Instead, long term loads can be extracted from a single stochastic solution, a procedure that is obviously significantly faster. Despite the reduced analysis time, results obtained from the stochastic approach match deterministic result well for a simple test-case (a stationary blade). In future work, the stochastic method will be extended to rotating blades, thus opening up new avenues to include long term loads into turbine optimization. (paper)

A stochastic approach for quantifying immigrant integration: the Spanish test case

Science.gov (United States)

Agliari, Elena; Barra, Adriano; Contucci, Pierluigi; Sandell, Richard; Vernia, Cecilia

2014-10-01

We apply stochastic process theory to the analysis of immigrant integration. Using a unique and detailed data set from Spain, we study the relationship between local immigrant density and two social and two economic immigration quantifiers for the period 1999-2010. As opposed to the classic time-series approach, by letting immigrant density play the role of ‘time’ and the quantifier the role of ‘space,’ it becomes possible to analyse the behavior of the quantifiers by means of continuous time random walks. Two classes of results are then obtained. First, we show that social integration quantifiers evolve following diffusion law, while the evolution of economic quantifiers exhibits ballistic dynamics. Second, we make predictions of best- and worst-case scenarios taking into account large local fluctuations. Our stochastic process approach to integration lends itself to interesting forecasting scenarios which, in the hands of policy makers, have the potential to improve political responses to integration problems. For instance, estimating the standard first-passage time and maximum-span walk reveals local differences in integration performance for different immigration scenarios. Thus, by recognizing the importance of local fluctuations around national means, this research constitutes an important tool to assess the impact of immigration phenomena on municipal budgets and to set up solid multi-ethnic plans at the municipal level as immigration pressures build.

A stochastic approach for quantifying immigrant integration: the Spanish test case

International Nuclear Information System (INIS)

Agliari, Elena; Barra, Adriano; Contucci, Pierluigi; Sandell, Richard; Vernia, Cecilia

2014-01-01

We apply stochastic process theory to the analysis of immigrant integration. Using a unique and detailed data set from Spain, we study the relationship between local immigrant density and two social and two economic immigration quantifiers for the period 1999–2010. As opposed to the classic time-series approach, by letting immigrant density play the role of ‘time’ and the quantifier the role of ‘space,’ it becomes possible to analyse the behavior of the quantifiers by means of continuous time random walks. Two classes of results are then obtained. First, we show that social integration quantifiers evolve following diffusion law, while the evolution of economic quantifiers exhibits ballistic dynamics. Second, we make predictions of best- and worst-case scenarios taking into account large local fluctuations. Our stochastic process approach to integration lends itself to interesting forecasting scenarios which, in the hands of policy makers, have the potential to improve political responses to integration problems. For instance, estimating the standard first-passage time and maximum-span walk reveals local differences in integration performance for different immigration scenarios. Thus, by recognizing the importance of local fluctuations around national means, this research constitutes an important tool to assess the impact of immigration phenomena on municipal budgets and to set up solid multi-ethnic plans at the municipal level as immigration pressures build. (paper)

A stochastic programming approach to manufacturing flow control

OpenAIRE

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...

3D stochastic inversion and joint inversion of potential fields for multi scale parameters

Science.gov (United States)

Shamsipour, Pejman

In this thesis we present the development of new techniques for the interpretation of potential field (gravity and magnetic data), which are the most widespread economic geophysical methods used for oil and mineral exploration. These new techniques help to address the long-standing issue with the interpretation of potential fields, namely the intrinsic non-uniqueness inversion of these types of data. The thesis takes the form of three papers (four including Appendix), which have been published, or soon to be published, in respected international journals. The purpose of the thesis is to introduce new methods based on 3D stochastical approaches for: 1) Inversion of potential field data (magnetic), 2) Multiscale Inversion using surface and borehole data and 3) Joint inversion of geophysical potential field data. We first present a stochastic inversion method based on a geostatistical approach to recover 3D susceptibility models from magnetic data. The aim of applying geostatistics is to provide quantitative descriptions of natural variables distributed in space or in time and space. We evaluate the uncertainty on the parameter model by using geostatistical unconditional simulations. The realizations are post-conditioned by cokriging to observation data. In order to avoid the natural tendency of the estimated structure to lay near the surface, depth weighting is included in the cokriging system. Then, we introduce algorithm for multiscale inversion, the presented algorithm has the capability of inverting data on multiple supports. The method involves four main steps: i. upscaling of borehole parameters (It could be density or susceptibility) to block parameters, ii. selection of block to use as constraints based on a threshold on kriging variance, iii. inversion of observation data with selected block densities as constraints, and iv. downscaling of inverted parameters to small prisms. Two modes of application are presented: estimation and simulation. Finally, a novel

Communication: Electronic and transport properties of molecular junctions under a finite bias: A dual mean field approach

International Nuclear Information System (INIS)

Liu, Shuanglong; Feng, Yuan Ping; Zhang, Chun

2013-01-01

We show that when a molecular junction is under an external bias, its properties cannot be uniquely determined by the total electron density in the same manner as the density functional theory for ground state properties. In order to correctly incorporate bias-induced nonequilibrium effects, we present a dual mean field (DMF) approach. The key idea is that the total electron density together with the density of current-carrying electrons are sufficient to determine the properties of the system. Two mean fields, one for current-carrying electrons and the other one for equilibrium electrons can then be derived. Calculations for a graphene nanoribbon junction show that compared with the commonly used ab initio transport theory, the DMF approach could significantly reduce the electric current at low biases due to the non-equilibrium corrections to the mean field potential in the scattering region

Rapid change of field line connectivity and reconnection in stochastic magnetic fields

International Nuclear Information System (INIS)

Huang, Yi-Min; Bhattacharjee, A.; Boozer, Allen H.

2014-01-01

Magnetic fields without a direction of continuous symmetry have the generic feature that neighboring field lines exponentiate away from each other and become stochastic, and hence the ideal constraint of preserving magnetic field line connectivity becomes exponentially sensitive to small deviations from ideal Ohm's law. The idea of breaking field line connectivity by stochasticity as a mechanism for fast reconnection is tested with numerical simulations based on reduced magnetohydrodynamics equations with a strong guide field line-tied to two perfectly conducting end plates. Starting from an ideally stable force-free equilibrium, the system is allowed to undergo resistive relaxation. Two distinct phases are found in the process of resistive relaxation. During the quasi-static phase, rapid change of field line connectivity and strong induced flow are found in regions of high field line exponentiation. However, although the field line connectivity of individual field lines can change rapidly, the overall pattern of field line mapping appears to deform gradually. From this perspective, field line exponentiation appears to cause enhanced diffusion rather than reconnection. In some cases, resistive quasi-static evolution can cause the ideally stable initial equilibrium to cross a stability threshold, leading to formation of intense current filaments and rapid change of field line mapping into a qualitatively different pattern. It is in this onset phase that the change of field line connectivity is more appropriately designated as magnetic reconnection. Our results show that rapid change of field line connectivity appears to be a necessary, but not a sufficient condition for fast reconnection.

Chemotherapy appointment scheduling under uncertainty using mean-risk stochastic integer programming.

Science.gov (United States)

Alvarado, Michelle; Ntaimo, Lewis

2018-03-01

Oncology clinics are often burdened with scheduling large volumes of cancer patients for chemotherapy treatments under limited resources such as the number of nurses and chairs. These cancer patients require a series of appointments over several weeks or months and the timing of these appointments is critical to the treatment's effectiveness. Additionally, the appointment duration, the acuity levels of each appointment, and the availability of clinic nurses are uncertain. The timing constraints, stochastic parameters, rising treatment costs, and increased demand of outpatient oncology clinic services motivate the need for efficient appointment schedules and clinic operations. In this paper, we develop three mean-risk stochastic integer programming (SIP) models, referred to as SIP-CHEMO, for the problem of scheduling individual chemotherapy patient appointments and resources. These mean-risk models are presented and an algorithm is devised to improve computational speed. Computational results were conducted using a simulation model and results indicate that the risk-averse SIP-CHEMO model with the expected excess mean-risk measure can decrease patient waiting times and nurse overtime when compared to deterministic scheduling algorithms by 42 % and 27 %, respectively.

Stochastic geometry, spatial statistics and random fields models and algorithms

CERN Document Server

2015-01-01

Providing a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, this volume places a special emphasis on fundamental classes of models and algorithms as well as on their applications, for example in materials science, biology and genetics. This book has a strong focus on simulations and includes extensive codes in Matlab and R, which are widely used in the mathematical community. It can be regarded as a continuation of the recent volume 2068 of Lecture Notes in Mathematics, where other issues of stochastic geometry, spatial statistics and random fields were considered, with a focus on asymptotic methods.

Mean-field models and superheavy elements

International Nuclear Information System (INIS)

Reinhard, P.G.; Bender, M.; Maruhn, J.A.; Frankfurt Univ.

2001-03-01

We discuss the performance of two widely used nuclear mean-field models, the relativistic mean-field theory (RMF) and the non-relativistic Skyrme-Hartree-Fock approach (SHF), with particular emphasis on the description of superheavy elements (SHE). We provide a short introduction to the SHF and RMF, the relations between these two approaches and the relations to other nuclear structure models, briefly review the basic properties with respect to normal nuclear observables, and finally present and discuss recent results on the binding properties of SHE computed with a broad selection of SHF and RMF parametrisations. (orig.)

All-loop calculations of total, elastic and single diffractive cross sections in RFT via the stochastic approach

International Nuclear Information System (INIS)

Kolevatov, R. S.; Boreskov, K. G.

2013-01-01

We apply the stochastic approach to the calculation of the Reggeon Field Theory (RFT) elastic amplitude and its single diffractive cut. The results for the total, elastic and single difractive cross sections with account of all Pomeron loops are obtained.

All-loop calculations of total, elastic and single diffractive cross sections in RFT via the stochastic approach

Energy Technology Data Exchange (ETDEWEB)

Kolevatov, R. S. [SUBATECH, Ecole des Mines de Nantes, 4 rue Alfred Kastler, 44307 Nantes Cedex 3 (France); Boreskov, K. G. [Institute of Theoretical and Experimental Physics, 117259, Moscow (Russian Federation)

2013-04-15

We apply the stochastic approach to the calculation of the Reggeon Field Theory (RFT) elastic amplitude and its single diffractive cut. The results for the total, elastic and single difractive cross sections with account of all Pomeron loops are obtained.

Stochastic formulation of quantum field at finite temperature

International Nuclear Information System (INIS)

Lim, S.C.

1989-01-01

This paper reports that, based on an extension of the stochastic quantization method of Nelson, it is possible to obtain finite temperature fields in both the imaginary and real time formalisms which are usually quantized by using the functional integral technique

A philosophical approach to quantum field theory

CERN Document Server

Öttinger, Hans Christian

2015-01-01

This text presents an intuitive and robust mathematical image of fundamental particle physics based on a novel approach to quantum field theory, which is guided by four carefully motivated metaphysical postulates. In particular, the book explores a dissipative approach to quantum field theory, which is illustrated for scalar field theory and quantum electrodynamics, and proposes an attractive explanation of the Planck scale in quantum gravity. Offering a radically new perspective on this topic, the book focuses on the conceptual foundations of quantum field theory and ontological questions. It also suggests a new stochastic simulation technique in quantum field theory which is complementary to existing ones. Encouraging rigor in a field containing many mathematical subtleties and pitfalls this text is a helpful companion for students of physics and philosophers interested in quantum field theory, and it allows readers to gain an intuitive rather than a formal understanding.

Many-Body Mean-Field Equations: Parallel implementation

International Nuclear Information System (INIS)

Vallieres, M.; Umar, S.; Chinn, C.; Strayer, M.

1993-01-01

We describe the implementation of Hartree-Fock Many-Body Mean-Field Equations on a Parallel Intel iPSC/860 hypercube. We first discuss the Nuclear Mean-Field approach in physical terms. Then we describe our parallel implementation of this approach on the Intel iPSC/860 hypercube. We discuss and compare the advantages and disadvantages of the domain partition versus the Hilbert space partition for this problem. We conclude by discussing some timing experiments on various computing platforms

Full particle orbit effects in regular and stochastic magnetic fields

Energy Technology Data Exchange (ETDEWEB)

Ogawa, Shun, E-mail: shun.ogawa@cpt.univ-mrs.fr [Aix Marseille Univ., Univ. Toulon, CNRS, CPT, Marseille (France); CEA, IRFM, F-13108 St. Paul-lez-Durance Cedex (France); Cambon, Benjamin; Leoncini, Xavier; Vittot, Michel [Aix Marseille Univ., Univ. Toulon, CNRS, CPT, Marseille (France); Castillo-Negrete, Diego del [Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6169 (United States); Dif-Pradalier, Guilhem; Garbet, Xavier [CEA, IRFM, F-13108 St. Paul-lez-Durance Cedex (France)

2016-07-15

We present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, the particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. We show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the

Estimation of Motion Vector Fields

DEFF Research Database (Denmark)

Larsen, Rasmus

1993-01-01

This paper presents an approach to the estimation of 2-D motion vector fields from time varying image sequences. We use a piecewise smooth model based on coupled vector/binary Markov random fields. We find the maximum a posteriori solution by simulated annealing. The algorithm generate sample...... fields by means of stochastic relaxation implemented via the Gibbs sampler....

Stochastic parameterizing manifolds and non-Markovian reduced equations stochastic manifolds for nonlinear SPDEs II

CERN Document Server

Chekroun, Mickaël D; Wang, Shouhong

2015-01-01

In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.

Restructuring of workflows to minimise errors via stochastic model checking: An automated evolutionary approach

International Nuclear Information System (INIS)

Herbert, L.T.; Hansen, Z.N.L.

2016-01-01

This paper presents a framework for the automated restructuring of stochastic workflows to reduce the impact of faults. The framework allows for the modelling of workflows by means of a formalised subset of the BPMN workflow language. We extend this modelling formalism to describe faults and incorporate an intention preserving stochastic semantics able to model both probabilistic- and non-deterministic behaviour. Stochastic model checking techniques are employed to generate the state-space of a given workflow. Possible improvements obtained by restructuring are measured by employing the framework's capacity for tracking real-valued quantities associated with states and transitions of the workflow. The space of possible restructurings of a workflow is explored by means of an evolutionary algorithm, where the goals for improvement are defined in terms of optimising quantities, typically employed to model resources, associated with a workflow. The approach is fully automated and only the modelling of the production workflows, potential faults and the expression of the goals require manual input. We present the design of a software tool implementing this framework and explore the practical utility of this approach through an industrial case study in which the risk of production failures and their impact are reduced by restructuring the workflow. - Highlights: • We present a framework which allows for the automated restructuring of workflows. • This framework seeks to minimise the impact of errors on the workflow. • We illustrate a scalable software implementation of this framework. • We explore the practical utility of this approach through an industry case. • The impact of errors can be substantially reduced by restructuring the workflow.

Stochastic quantization of the Kink solution of phi4 field theory

International Nuclear Information System (INIS)

Kates, R.; Rosenblum, A.

1989-01-01

The method of Parisi-Wu Stochastic quantization in quantum field theory is compared to earlier work in classical field equations. The method is applied to solve for the propagator for Phi 4 field theory by perturbing the Kink solution

Gas contract portfolio management: a stochastic programming approach

International Nuclear Information System (INIS)

Haurie, A.; Smeers, Y.; Zaccour, G.

1991-01-01

This paper deals with a stochastic programming model which complements long range market simulation models generating scenarios concerning the evolution of demand and prices for gas in different market segments. Agas company has to negociate contracts with lengths going from one to twenty years. This stochastic model is designed to assess the risk associated with committing the gas production capacity of the company to these market segments. Different approaches are presented to overcome the difficulties associated with the very large size of the resulting optimization problem

Sustainment dynamo reexamined: nonlocal electrical conductivity of plasma in a stochastic magnetic field

International Nuclear Information System (INIS)

Jacobson, A.R.; Moses, R.W.

1984-01-01

The plasma dynamo is both an intriguing and a practical concept. The intrigue derives from attempting to explain naturally occurring and man-made plasmas whose strong field-aligned currents j/sub parallel/ apparently disobey the most naive Ohm's law j/sub parallel/ = sigma/sub parallel/E/sub parallel/. The practical importance derives from the dynamo's role both in formation and in sustainment of reversed-field pinch (RFP) and Spheromak fusion plasmas. We will examine certain features of the documented quasi-steady discharges on ZT-40M, and RFP in apparent need of a sustainment dynamo. We will show that the tail electrons (which carry j/sub parallel/) are probably wandering (along stochastic B Vector-field lines) over much of the minor radius in one mean-free-path

Alternative Approaches to Technical Efficiency Estimation in the Stochastic Frontier Model

OpenAIRE

Acquah, H. de-Graft; Onumah, E. E.

2014-01-01

Estimating the stochastic frontier model and calculating technical efficiency of decision making units are of great importance in applied production economic works. This paper estimates technical efficiency from the stochastic frontier model using Jondrow, and Battese and Coelli approaches. In order to compare alternative methods, simulated data with sample sizes of 60 and 200 are generated from stochastic frontier model commonly applied to agricultural firms. Simulated data is employed to co...

Nonasymptotic mean-field games

KAUST Repository

Tembine, Hamidou

2014-12-01

Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networked systems with few entities. In this paper we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through a dynamic auction with asymmetric valuation distributions.

Nonasymptotic mean-field games

KAUST Repository

Tembine, Hamidou

2014-12-01

Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists of approximating large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networks with few entities. In this paper, we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through various examples including dynamic auction with asymmetric valuation distributions, and spiteful bidders.

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

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.

A penalty guided stochastic fractal search approach for system reliability optimization

International Nuclear Information System (INIS)

Mellal, Mohamed Arezki; Zio, Enrico

2016-01-01

Modern industry requires components and systems with high reliability levels. In this paper, we address the system reliability optimization problem. A penalty guided stochastic fractal search approach is developed for solving reliability allocation, redundancy allocation, and reliability–redundancy allocation problems. Numerical results of ten case studies are presented as benchmark problems for highlighting the superiority of the proposed approach compared to others from literature. - Highlights: • System reliability optimization is investigated. • A penalty guided stochastic fractal search approach is developed. • Results of ten case studies are compared with previously published methods. • Performance of the approach is demonstrated.

Microscopic mean-field boson approach to the shape transition in Sm isotopes

International Nuclear Information System (INIS)

Kuchta, R.

1988-01-01

The phase transition from spherical to deformed shape in Sm 146-156 nuclei is analyzed within the mean-field approximation applied to the Dyson image of the shell-model Hamiltonian. No quasiparticle transformation is involved in the present approach and the Pauli principle in the physical boson subspace is properly taken into account. The low-lying spectra, B(E2; O 1 + →2 + ) probabilities and the corresponding densities of electromagnetic transitions are calculated. The results provide a reasonable explanation of the phase transition in the Sm isotopes. The role of bosons with different multipolarity is investigated and it is found that g-bosons (J=4) cannot be neglected in the transition region. Comparison of the present results with those of other approaches is given as well

Plasma transport in the stochastic fields at the tokamak edge. Final report, February 15, 1993--February 14, 1994

International Nuclear Information System (INIS)

Punjabi, A.

1994-01-01

The purpose of this project is to calculate the contribution of field line diffusion to particle diffusion in the stochastic magnetic field at the tokamak edge. The author uses the approach of quasi magnetic surfaces. If the magnetic field line makes sufficiently large number of toroidal transits before suffering large radial excursion, then the method of quasi magnetic surface is valid for this problem. This method has three components: determination of particle drift trajectories, a model for magnetic field configuration, and determination of field line diffusion

Stochastic gravity: a primer with applications

International Nuclear Information System (INIS)

Hu, B L; Verdaguer, E

2003-01-01

Stochastic semiclassical gravity of the 1990s is a theory naturally evolved from semiclassical gravity of the 1970s and 1980s. It improves on the semiclassical Einstein equation with source given by the expectation value of the stress-energy tensor of quantum matter fields in curved spacetime by incorporating an additional source due to their fluctuations. In stochastic semiclassical gravity the main object of interest is the noise kernel, the vacuum expectation value of the (operator-valued) stress-energy bi-tensor, and the centrepiece is the (semiclassical) Einstein-Langevin equation. We describe this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the energy-momentum tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open system concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise and decoherence. We then describe the applications of stochastic gravity to the backreaction problems in cosmology and black-hole physics. In the first problem, we study the backreaction of conformally coupled quantum fields in a weakly inhomogeneous cosmology. In the second problem, we study the backreaction of a thermal field in the gravitational background of a quasi-static black hole (enclosed in a box) and its fluctuations. These examples serve to illustrate closely the ideas and techniques presented in the first part. This topical review is intended as a first introduction providing readers with some basic ideas and working knowledge. Thus, we place more emphasis here on pedagogy than completeness. (Further discussions of ideas, issues and ongoing research topics can be found

Stochastic gravity: a primer with applications

Energy Technology Data Exchange (ETDEWEB)

Hu, B L [Department of Physics, University of Maryland, College Park, MD 20742-4111 (United States); Verdaguer, E [Departament de Fisica Fonamental and CER en Astrofisica Fisica de Particules i Cosmologia, Universitat de Barcelona, Av. Diagonal 647, 08028 Barcelona (Spain)

2003-03-21

Stochastic semiclassical gravity of the 1990s is a theory naturally evolved from semiclassical gravity of the 1970s and 1980s. It improves on the semiclassical Einstein equation with source given by the expectation value of the stress-energy tensor of quantum matter fields in curved spacetime by incorporating an additional source due to their fluctuations. In stochastic semiclassical gravity the main object of interest is the noise kernel, the vacuum expectation value of the (operator-valued) stress-energy bi-tensor, and the centrepiece is the (semiclassical) Einstein-Langevin equation. We describe this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the energy-momentum tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open system concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise and decoherence. We then describe the applications of stochastic gravity to the backreaction problems in cosmology and black-hole physics. In the first problem, we study the backreaction of conformally coupled quantum fields in a weakly inhomogeneous cosmology. In the second problem, we study the backreaction of a thermal field in the gravitational background of a quasi-static black hole (enclosed in a box) and its fluctuations. These examples serve to illustrate closely the ideas and techniques presented in the first part. This topical review is intended as a first introduction providing readers with some basic ideas and working knowledge. Thus, we place more emphasis here on pedagogy than completeness. (Further discussions of ideas, issues and ongoing research topics can be found

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...

One-and two-dimensional topological charge distributions in stochastic optical fields

CSIR Research Space (South Africa)

Roux, FS

2011-06-01

Full Text Available The presentation on topological charge distributions in stochastic optical fields concludes that by using a combination of speckle fields one can produce inhomogeneous vortex distributions that allow both analytical calculations and numerical...

Merging Belief Propagation and the Mean Field Approximation: A Free Energy Approach

DEFF Research Database (Denmark)

Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro

2013-01-01

We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al. We show that the message passing fixed-point equations obtained with this combination...... correspond to stationary points of a constrained region-based free energy approximation. Moreover, we present a convergent implementation of these message passing fixed-point equations provided that the underlying factor graph fulfills certain technical conditions. In addition, we show how to include hard...

Study of stochastic approaches of the n-bodies problem: application to the nuclear fragmentation

International Nuclear Information System (INIS)

Guarnera, A.

1996-01-01

In the last decade nuclear physics research has found, with the observation of phenomena such as multifragmentation or vaporization, the possibility to get a deeper insight into the nuclear matter phase diagram. For example, a spinodal decomposition scenario has been proposed to explain the multifragmentation: because of the initial compression, the system may enter a region, the spinodal zone, in which the nuclear matter is no longer stable, and so any fluctuation leads to the formation of fragments. This thesis deals with spinodal decomposition within the theoretical framework of stochastic mean filed approaches, in which the one-body density function may experience a stochastic evolution. We have shown that these approaches are able to describe phenomena, such as first order phase transitions, in which fluctuations and many-body correlations plan an important role. In the framework of stochastic mean-filed approaches we have shown that the fragment production by spinodal decomposition is characterized by typical time scales of the order of 100 fm/c and by typical size scales around the Neon mass. We have also shown that these features are robust and that they are not affected significantly by a possible expansion of the system or by the finite size of nuclei. We have proposed as a signature of the spinodal decomposition some typical partition of the largest fragments. The study and the comparison with experimental data, performed for the reactions Xe + Cu at 45 MeV/A and Xe + Sn at 50 MeV/A, have shown a remarkable agreement. Moreover we would like to stress that the theory does not contain any adjustable parameter. These results seem to give a strong indication of the possibility to observe a spinodal decomposition of nuclei. (author)

COMPARISON OF EIGENMODE-BASED AND RANDOM FIELD-BASED IMPERFECTION MODELING FOR THE STOCHASTIC BUCKLING ANALYSIS OF I-SECTION BEAM–COLUMNS

KAUST Repository

STAVREV, A.

2013-03-01

The uncertainty of geometric imperfections in a series of nominally equal I-beams leads to a variability of corresponding buckling loads. Its analysis requires a stochastic imperfection model, which can be derived either by the simple variation of the critical eigenmode with a scalar random variable, or with the help of the more advanced theory of random fields. The present paper first provides a concise review of the two different modeling approaches, covering theoretical background, assumptions and calibration, and illustrates their integration into commercial finite element software to conduct stochastic buckling analyses with the Monte-Carlo method. The stochastic buckling behavior of an example beam is then simulated with both stochastic models, calibrated from corresponding imperfection measurements. The simulation results show that for different load cases, the response statistics of the buckling load obtained with the eigenmode-based and the random field-based models agree very well. A comparison of our simulation results with corresponding Eurocode 3 limit loads indicates that the design standard is very conservative for compression dominated load cases. © 2013 World Scientific Publishing Company.

Modeling flow in fractured medium. Uncertainty analysis with stochastic continuum approach

International Nuclear Information System (INIS)

Niemi, A.

1994-01-01

For modeling groundwater flow in formation-scale fractured media, no general method exists for scaling the highly heterogeneous hydraulic conductivity data to model parameters. The deterministic approach is limited in representing the heterogeneity of a medium and the application of fracture network models has both conceptual and practical limitations as far as site-scale studies are concerned. The study investigates the applicability of stochastic continuum modeling at the scale of data support. No scaling of the field data is involved, and the original variability is preserved throughout the modeling. Contributions of various aspects to the total uncertainty in the modeling prediction can also be determined with this approach. Data from five crystalline rock sites in Finland are analyzed. (107 refs., 63 figs., 7 tabs.)

5th Seminar on Stochastic Processes, Random Fields and Applications

CERN Document Server

Russo, Francesco; Dozzi, Marco

2008-01-01

This volume contains twenty-eight refereed research or review papers presented at the 5th Seminar on Stochastic Processes, Random Fields and Applications, which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, from May 30 to June 3, 2005. The seminar focused mainly on stochastic partial differential equations, random dynamical systems, infinite-dimensional analysis, approximation problems, and financial engineering. The book will be a valuable resource for researchers in stochastic analysis and professionals interested in stochastic methods in finance. Contributors: Y. Asai, J.-P. Aubin, C. Becker, M. Benaïm, H. Bessaih, S. Biagini, S. Bonaccorsi, N. Bouleau, N. Champagnat, G. Da Prato, R. Ferrière, F. Flandoli, P. Guasoni, V.B. Hallulli, D. Khoshnevisan, T. Komorowski, R. Léandre, P. Lescot, H. Lisei, J.A. López-Mimbela, V. Mandrekar, S. Méléard, A. Millet, H. Nagai, A.D. Neate, V. Orlovius, M. Pratelli, N. Privault, O. Raimond, M. Röckner, B. Rüdiger, W.J. Runggaldi...

Influence of stochastic geometric imperfections on the load-carrying behaviour of thin-walled structures using constrained random fields

Science.gov (United States)

Lauterbach, S.; Fina, M.; Wagner, W.

2018-04-01

Since structural engineering requires highly developed and optimized structures, the thickness dependency is one of the most controversially debated topics. This paper deals with stability analysis of lightweight thin structures combined with arbitrary geometrical imperfections. Generally known design guidelines only consider imperfections for simple shapes and loading, whereas for complex structures the lower-bound design philosophy still holds. Herein, uncertainties are considered with an empirical knockdown factor representing a lower bound of existing measurements. To fully understand and predict expected bearable loads, numerical investigations are essential, including geometrical imperfections. These are implemented into a stand-alone program code with a stochastic approach to compute random fields as geometric imperfections that are applied to nodes of the finite element mesh of selected structural examples. The stochastic approach uses the Karhunen-Loève expansion for the random field discretization. For this approach, the so-called correlation length l_c controls the random field in a powerful way. This parameter has a major influence on the buckling shape, and also on the stability load. First, the impact of the correlation length is studied for simple structures. Second, since most structures for engineering devices are more complex and combined structures, these are intensively discussed with the focus on constrained random fields for e.g. flange-web-intersections. Specific constraints for those random fields are pointed out with regard to the finite element model. Further, geometrical imperfections vanish where the structure is supported.

Stochastic Levy Divergence and Maxwell's Equations

Directory of Open Access Journals (Sweden)

B. O. Volkov

2015-01-01

Full Text Available One of the main reasons for interest in the Levy Laplacian and its analogues such as Levy d'Alembertian is a connection of these operators with gauge fields. The theorem proved by Accardi, Gibillisco and Volovich stated that a connection in a bundle over a Euclidean space or over a Minkowski space is a solution of the Yang-Mills equations if and only if the corresponding parallel transport to the connection is a solution of the Laplace equation for the Levy Laplacian or of the d'Alembert equation for the Levy d'Alembertian respectively (see [5, 6]. There are two approaches to define Levy type operators, both of which date back to the original works of Levy [7]. The first is that the Levy Laplacian (or Levy d'Alembertian is defined as an integral functional generated by a special form of the second derivative. This approach is used in the works [5, 6], as well as in the paper [8] of Leandre and Volovich, where stochastic Levy-Laplacian is discussed. Another approach to the Levy Laplacian is defining it as the Cesaro mean of second order derivatives along the family of vectors, which is an orthonormal basis in the Hilbert space. This definition of the Levy Laplacian is used for the description of solutions of the Yang-Mills equations in the paper [10].The present work shows that the definitions of the Levy Laplacian and the Levy d'Alembertian based on Cesaro averaging of the second order directional derivatives can be transferred to the stochastic case. In the article the values of these operators on a stochastic parallel transport associated with a connection (vector potential are found. In this case, unlike the deterministic case and the stochastic case of Levy Laplacian from [8], these values are not equal to zero if the vector potential corresponding to the stochastic parallel transport is a solution of the Maxwell's equations. As a result, two approaches to definition of the Levy Laplacian in the stochastic case give different operators. This

Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach

OpenAIRE

Chenavaz, Régis; Paraschiv, Corina; Turinici, Gabriel

2017-01-01

Dynamic pricing of new products has been extensively studied in monopolistic and oligopolistic markets. But, the optimal control and differential game tools used to investigate the pricing behavior on markets with a finite number of firms are not well-suited to model competitive markets with an infinity of firms. Using a mean-field games approach, this paper examines dynamic pricing policies in competitive markets, where no firm exerts market power. The theoretical setting is based on a diffu...

Stochastic quantum inflation for a canonical scalar field with linear self-interaction potential

Energy Technology Data Exchange (ETDEWEB)

Panotopoulos, Grigoris [CENTRA, Instituto Superior Tecnico, Universidade de Lisboa, Lisboa (Portugal)

2017-10-15

We apply Starobinsky's formalism of stochastic inflation to the case of a massless minimally coupled scalar field with linear self-interaction potential. We solve the corresponding Fokker-Planck equation exactly, and we obtain analytical expressions for the stochastic expectation values. (orig.)

Mean-Square Convergence of Drift-Implicit One-Step Methods for Neutral Stochastic Delay Differential Equations with Jump Diffusion

Directory of Open Access Journals (Sweden)

Lin Hu

2011-01-01

Full Text Available A class of drift-implicit one-step schemes are proposed for the neutral stochastic delay differential equations (NSDDEs driven by Poisson processes. A general framework for mean-square convergence of the methods is provided. It is shown that under certain conditions global error estimates for a method can be inferred from estimates on its local error. The applicability of the mean-square convergence theory is illustrated by the stochastic θ-methods and the balanced implicit methods. It is derived from Theorem 3.1 that the order of the mean-square convergence of both of them for NSDDEs with jumps is 1/2. Numerical experiments illustrate the theoretical results. It is worth noting that the results of mean-square convergence of the stochastic θ-methods and the balanced implicit methods are also new.

A DG approach to the numerical solution of the Stein-Stein stochastic volatility option pricing model

Science.gov (United States)

Hozman, J.; Tichý, T.

2017-12-01

Stochastic volatility models enable to capture the real world features of the options better than the classical Black-Scholes treatment. Here we focus on pricing of European-style options under the Stein-Stein stochastic volatility model when the option value depends on the time, on the price of the underlying asset and on the volatility as a function of a mean reverting Orstein-Uhlenbeck process. A standard mathematical approach to this model leads to the non-stationary second-order degenerate partial differential equation of two spatial variables completed by the system of boundary and terminal conditions. In order to improve the numerical valuation process for a such pricing equation, we propose a numerical technique based on the discontinuous Galerkin method and the Crank-Nicolson scheme. Finally, reference numerical experiments on real market data illustrate comprehensive empirical findings on options with stochastic volatility.

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology.

Science.gov (United States)

Schaff, James C; Gao, Fei; Li, Ye; Novak, Igor L; Slepchenko, Boris M

2016-12-01

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium 'sparks' as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.

Expansion of a stochastic stationary optical field at a fixed point

International Nuclear Information System (INIS)

Martinez-Herrero, R.; Mejias, P.M.

1984-01-01

An important problem in single and multifold photoelectron statistics is to determine the statistical properties of a totally polarized optical field at some point →r from the photoelectron counts registered by the detector. The solution to this problem may be found in the determination of the statistical properties of an integral over a stochastic process; a complicated and formidable task. This problem can be solved in some cases of interest by expanding the process V(t) (which represents the field at →r) in a set of complete orthonormal deterministic functions, resulting in the so-called Karhunen-Loeve expansion of V(t). Two disadvantages are that the process must be defined over a finite time interval, and that each term of the series does not represent any special optical field. Taking into account these limitations of the expansion, the purpose of this work is to find another alternative expansion of stationary optical fields defined over the infinite time interval, and whose terms represent stochastic fields

Two Numerical Approaches to Stationary Mean-Field Games

KAUST Repository

Almulla, Noha; Ferreira, Rita; Gomes, Diogo A.

2016-01-01

Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.

Two Numerical Approaches to Stationary Mean-Field Games

KAUST Repository

Almulla, Noha

2016-10-04

Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.

Dynamic behaviors of spin-1/2 bilayer system within Glauber-type stochastic dynamics based on the effective-field theory

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

Dynamic behaviors of spin-1/2 bilayer system within Glauber-type stochastic dynamics based on the effective-field theory

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.

Investor preferences for oil spot and futures based on mean-variance and stochastic dominance

NARCIS (Netherlands)

H.H. Lean (Hooi Hooi); M.J. McAleer (Michael); W.-K. Wong (Wing-Keung)

2010-01-01

textabstractThis paper examines investor preferences for oil spot and futures based on mean-variance (MV) and stochastic dominance (SD). The mean-variance criterion cannot distinct the preferences of spot and market whereas SD tests leads to the conclusion that spot dominates futures in the downside

Stationary solutions of linear stochastic delay differential equations: applications to biological systems.

Science.gov (United States)

Frank, T D; Beek, P J

2001-08-01

Recently, Küchler and Mensch [Stochastics Stochastics Rep. 40, 23 (1992)] derived exact stationary probability densities for linear stochastic delay differential equations. This paper presents an alternative derivation of these solutions by means of the Fokker-Planck approach introduced by Guillouzic [Phys. Rev. E 59, 3970 (1999); 61, 4906 (2000)]. Applications of this approach, which is argued to have greater generality, are discussed in the context of stochastic models for population growth and tracking movements.

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)

The Risk-Return Tradeoff and Leverage Effect in a Stochastic Volatility-in-Mean Model

DEFF Research Database (Denmark)

Christensen, Bent Jesper; Posedel, Petra

We study the risk premium and leverage effect in the S&P500 market using the stochastic volatility-in-mean model of Barndor¤-Nielsen & Shephard (2001). The Merton (1973, 1980) equilibrium asset pricing condition linking the conditional mean and conditional variance of discrete time returns is rei...

Stochastic quantization of field theories on the lattice and supersymmetrical models

International Nuclear Information System (INIS)

Aldazabal, Gerardo.

1984-01-01

Several aspects of the stochastic quantization method are considered. Specifically, field theories on the lattice and supersymmetrical models are studied. A non-linear sigma model is studied firstly, and it is shown that it is possible to obtain evolution equations written directly for invariant quantities. These ideas are generalized to obtain Langevin equations for the Wilson loops of non-abelian lattice gauge theories U (N) and SU (N). In order to write these equations, some different ways of introducing the constraints which the fields must satisfy are discussed. It is natural to have a strong coupling expansion in these equations. The correspondence with quantum field theory is established, and it is noticed that at all orders in the perturbation theory, Langevin equations reduce to Schwinger-Dyson equations. From another point of view, stochastic quantization is applied to large N matrix models on the lattice. As a result, a simple and systematic way of building reduced models is found. Referring to stochastic quantization in supersymmetric theories, a simple supersymmetric model is studied. It is shown that it is possible to write an evolution equation for the superfield wich leads to quantum field theory results in equilibrium. As the Langevin equation preserves supersymmetry, the property of dimensional reduction known for the quantum model is shown to be valid at all times. (M.E.L.) [es

Correlations and fluctuations in static and dynamic mean-field approaches

International Nuclear Information System (INIS)

Balian, R.; Veneroni, M.

1991-01-01

Let the state of a many-body system at an initial time be specified, completely or partly; find the expectation values, correlations and fluctuations of single-particle observables at a later time. The characteristic function of these observables is optimized within a general variational scheme. The expansion of the optimal characteristic function provides the same results as the conventional mean-field approaches for the thermodynamic potentials and the expectation values: for fermions the best initial state is then the Hartree-Fock (HF) solution and the evolution is described by the time-dependent Hartree-Fock (TDHF) equation. Two special cases are investigated as preliminary steps. The first case deals with the evaluation of correlations for static problems, where the initial and final times coincide. In the second special case, the exact initial state is assumed to be an independent-particle one. (K.A.) 23 refs.; 1 fig

Simulation of the stochastic wave loads using a physical modeling approach

DEFF Research Database (Denmark)

Liu, W.F.; Sichani, Mahdi Teimouri; Nielsen, Søren R.K.

2013-01-01

In analyzing stochastic dynamic systems, analysis of the system uncertainty due to randomness in the loads plays a crucial role. Typically time series of the stochastic loads are simulated using traditional random phase method. This approach combined with fast Fourier transform algorithm makes...... reliability or its uncertainty. Moreover applicability of the probability density evolution method on engineering problems faces critical difficulties when the system embeds too many random variables. Hence it is useful to devise a method which can make realization of the stochastic load processes with low...

A stochastic phase-field model determined from molecular dynamics

KAUST Repository

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

KAUST Repository

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.

Mean-field approach to evolving spatial networks, with an application to osteocyte network formation

Science.gov (United States)

Taylor-King, Jake P.; Basanta, David; Chapman, S. Jonathan; Porter, Mason A.

2017-07-01

We consider evolving networks in which each node can have various associated properties (a state) in addition to those that arise from network structure. For example, each node can have a spatial location and a velocity, or it can have some more abstract internal property that describes something like a social trait. Edges between nodes are created and destroyed, and new nodes enter the system. We introduce a "local state degree distribution" (LSDD) as the degree distribution at a particular point in state space. We then make a mean-field assumption and thereby derive an integro-partial differential equation that is satisfied by the LSDD. We perform numerical experiments and find good agreement between solutions of the integro-differential equation and the LSDD from stochastic simulations of the full model. To illustrate our theory, we apply it to a simple model for osteocyte network formation within bones, with a view to understanding changes that may take place during cancer. Our results suggest that increased rates of differentiation lead to higher densities of osteocytes, but with a smaller number of dendrites. To help provide biological context, we also include an introduction to osteocytes, the formation of osteocyte networks, and the role of osteocytes in bone metastasis.

On the distribution and mean of received power in stochastic cellular network

OpenAIRE

Cao, Fengming; Ganesh, Ayalvadi; Armour, Simon; Sooriyabandara, Mahesh

2016-01-01

This paper exploits the distribution and mean of received power for cellular network with stochastic network modeling to study the difference between the two cell association criteria, i.e. the strongest received power based cell association and the closest distance based cell association. Consequently we derive the analytical expression of the distribution and the mean of the nth strongest received power and the received power from the nth nearest base station and the derivations have been c...

Application of Stochastic Partial Differential Equations to Reservoir Property Modelling

KAUST Repository

Potsepaev, R.

2010-09-06

Existing algorithms of geostatistics for stochastic modelling of reservoir parameters require a mapping (the \\'uvt-transform\\') into the parametric space and reconstruction of a stratigraphic co-ordinate system. The parametric space can be considered to represent a pre-deformed and pre-faulted depositional environment. Existing approximations of this mapping in many cases cause significant distortions to the correlation distances. In this work we propose a coordinate free approach for modelling stochastic textures through the application of stochastic partial differential equations. By avoiding the construction of a uvt-transform and stratigraphic coordinates, one can generate realizations directly in the physical space in the presence of deformations and faults. In particular the solution of the modified Helmholtz equation driven by Gaussian white noise is a zero mean Gaussian stationary random field with exponential correlation function (in 3-D). This equation can be used to generate realizations in parametric space. In order to sample in physical space we introduce a stochastic elliptic PDE with tensor coefficients, where the tensor is related to correlation anisotropy and its variation is physical space.

Advances in dynamic and mean field games theory, applications, and numerical methods

CERN Document Server

Viscolani, Bruno

2017-01-01

This contributed volume considers recent advances in dynamic games and their applications, based on presentations given at the 17th Symposium of the International Society of Dynamic Games, held July 12-15, 2016, in Urbino, Italy. Written by experts in their respective disciplines, these papers cover various aspects of dynamic game theory including mean-field games, stochastic and pursuit-evasion games, and computational methods for dynamic games. Topics covered include Pedestrian flow in crowded environments Models for climate change negotiations Nash Equilibria for dynamic games involving Volterra integral equations Differential games in healthcare markets Linear-quadratic Gaussian dynamic games Aircraft control in wind shear conditions Advances in Dynamic and Mean-Field Games presents state-of-the-art research in a wide spectrum of areas. As such, it serves as a testament to the continued vitality and growth of the field of dynamic games and their applications. It will be of interest to an interdisciplinar...

An application of information theory to stochastic classical gravitational fields

Science.gov (United States)

Angulo, J.; Angulo, J. C.; Angulo, J. M.

2018-06-01

The objective of this study lies on the incorporation of the concepts developed in the Information Theory (entropy, complexity, etc.) with the aim of quantifying the variation of the uncertainty associated with a stochastic physical system resident in a spatiotemporal region. As an example of application, a relativistic classical gravitational field has been considered, with a stochastic behavior resulting from the effect induced by one or several external perturbation sources. One of the key concepts of the study is the covariance kernel between two points within the chosen region. Using this concept and the appropriate criteria, a methodology is proposed to evaluate the change of uncertainty at a given spatiotemporal point, based on available information and efficiently applying the diverse methods that Information Theory provides. For illustration, a stochastic version of the Einstein equation with an added Gaussian Langevin term is analyzed.

Quantum fields and processes a combinatorial approach

CERN Document Server

Gough, John

2018-01-01

Wick ordering of creation and annihilation operators is of fundamental importance for computing averages and correlations in quantum field theory and, by extension, in the Hudson-Parthasarathy theory of quantum stochastic processes, quantum mechanics, stochastic processes, and probability. This book develops the unified combinatorial framework behind these examples, starting with the simplest mathematically, and working up to the Fock space setting for quantum fields. Emphasizing ideas from combinatorics such as the role of lattice of partitions for multiple stochastic integrals by Wallstrom-Rota and combinatorial species by Joyal, it presents insights coming from quantum probability. It also introduces a 'field calculus' which acts as a succinct alternative to standard Feynman diagrams and formulates quantum field theory (cumulant moments, Dyson-Schwinger equation, tree expansions, 1-particle irreducibility) in this language. Featuring many worked examples, the book is aimed at mathematical physicists, quant...

Quantum fields and processes a combinatorial approach

CERN Document Server

Gough, John

2018-01-01

Wick ordering of creation and annihilation operators is of fundamental importance for computing averages and correlations in quantum field theory and, by extension, in the Hudson–Parthasarathy theory of quantum stochastic processes, quantum mechanics, stochastic processes, and probability. This book develops the unified combinatorial framework behind these examples, starting with the simplest mathematically, and working up to the Fock space setting for quantum fields. Emphasizing ideas from combinatorics such as the role of lattice of partitions for multiple stochastic integrals by Wallstrom–Rota and combinatorial species by Joyal, it presents insights coming from quantum probability. It also introduces a 'field calculus' which acts as a succinct alternative to standard Feynman diagrams and formulates quantum field theory (cumulant moments, Dyson–Schwinger equation, tree expansions, 1-particle irreducibility) in this language. Featuring many worked examples, the book is aimed at mathematical physicists,...

Field Trial Measurements to Validate a Stochastic Aircraft Boarding Model

Directory of Open Access Journals (Sweden)

Michael Schultz

2018-03-01

Full Text Available Efficient boarding procedures have to consider both operational constraints and the individual passenger behavior. In contrast to the aircraft handling processes of fueling, catering and cleaning, the boarding process is more driven by passengers than by airport or airline operators. This paper delivers a comprehensive set of operational data including classification of boarding times, passenger arrival times, times to store hand luggage, and passenger interactions in the aircraft cabin as a reliable basis for calibrating models for aircraft boarding. In this paper, a microscopic approach is used to model the passenger behavior, where the passenger movement is defined as a one-dimensional, stochastic, and time/space discrete transition process. This model is used to compare measurements from field trials of boarding procedures with simulation results and demonstrates a deviation smaller than 5%.

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

Mass dispersions in a time-dependent mean-field approach

International Nuclear Information System (INIS)

Balian, R.; Bonche, P.; Flocard, H.; Veneroni, M.

1984-05-01

Characteristic functions for single-particle (s.p.) observables are evaluated by means of a time-dependent variational principle, which involves a state and an observable as conjugate variables. This provides a mean-field expression for fluctuations of s.p. observables, such as mass dispersions. The result differs from TDHF, it requires only the use of existing codes, and it presents attractive theoretical features. First numerical tests are encouraging. In particular, a calculation for 16 O + 16 O provides a significant increase of the predicted mass dispersion

The Rapid Evaluation of Mean Concentration Fields in Lagrangian Stochastic Modelling Using a Density Kernel Estimator

National Research Council Canada - National Science Library

Shao, Y

2004-01-01

Lagrangian Stochastic (LS) particle models have proven to be a useful computational tool for the description and prediction of dispersion of pollutant releases in complex meteorological situations (e.g...

Stabilization and destabilization effects of the electric field on stochastic precipitate pattern

NARCIS (Netherlands)

Lagzi, István; Izsak, F.

2004-01-01

Stabilization and destabilization effects of an applied electric field on the Liesegang pattern formation in low concentration gradient were studied with numerical model simulations. In the absence of an electric field pattern formation exhibits increasingly stochastic behaviour as the initial

Stochastic resonance a mathematical approach in the small noise limit

CERN Document Server

Herrmann, Samuel; Pavlyukevich, Ilya; Peithmann, Dierk

2013-01-01

Stochastic resonance is a phenomenon arising in a wide spectrum of areas in the sciences ranging from physics through neuroscience to chemistry and biology. This book presents a mathematical approach to stochastic resonance which is based on a large deviations principle (LDP) for randomly perturbed dynamical systems with a weak inhomogeneity given by an exogenous periodicity of small frequency. Resonance, the optimal tuning between period length and noise amplitude, is explained by optimizing the LDP's rate function. The authors show that not all physical measures of tuning quality are robust with respect to dimension reduction. They propose measures of tuning quality based on exponential transition rates explained by large deviations techniques and show that these measures are robust. The book sheds some light on the shortcomings and strengths of different concepts used in the theory and applications of stochastic resonance without attempting to give a comprehensive overview of the many facets of stochastic ...

A stochastic approach to anelastic creep

International Nuclear Information System (INIS)

Venkataraman, G.

1976-01-01

Anelastic creep or the time-dependent yielding or a material subjected to external stresses has been found to be of great importantance in technology in the recent years, particularly in engineering structures including nuclear reactors wherein structural members may be under stress. The physics aspects underlying this phenomenon is dealt with in detail. The basics of time-dependent elasticity, constitutive relation, network models, constitutive equation in the frequency domain and its mearurements, and stochastic approach to creep are discussed. (K.B.)

Comments on the use of stochastic processes in the field of the ionizing radiations

International Nuclear Information System (INIS)

Alvarez Romero, Jose T.

2008-01-01

. Although models exist for the former one with stochastic processes such as birth-death, Poisson, two state or mixed states methods (Tan 1991), the conventional literature in radiobiology does not go beyond traditional target models of the Poisson or exponential type. Such approaches are dealt with by Rossi, Zaider, Goodhead, etc. in microdosimetry and radiobiology. Finally, in radiation protection the dose-effect projection models which back-up the recommendations of ICRP or from BEIR, probability functions, projection of regression time dependent models appear, buy very little, if any, is mentioned about their properties from the point of view of stochastic processes. Summing up, very little has been said about the nature of the stochastic background describing physical, chemical, biological and risk phenomena which are present in the field of ionizing radiations. In short, it would be nice to learn if there are processes such as: Gauss, Markov, branching, birth-death, Weiner, Poisson, stationary state methods or other ones to deal with these questions and further, to clarify the mathematical conditions they satisfy together with their significance and phenomenological consequences. (author)

A stochastic differential equation framework for the turbulent velocity field

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole Eiler; Schmiegel, Jürgen

We discuss a stochastic differential equation, as a modelling framework for the turbulent velocity field, that is capable of capturing basic stylized facts of the statistics of velocity increments. In particular, we focus on the evolution of the probability density of velocity increments...

Stochastic disk dynamo as a model of reversals of the Earth's magnetic field

International Nuclear Information System (INIS)

Ito, H.M.

1988-01-01

A stochastic model is given of a system composed of N similar disk dynamos interacting with one another. The time evolution of the system is governed by a master equation of the class introduced by van Kampen as relevant to stochastic macrosystems. In the model, reversals of the Earth's magnetic field are regarded as large deviations caused by a small random force of O(N/sup -1/2/) from one of the field polarities to the other. Reversal processes are studied by simulation, which shows that the model explains well the activities of the paleomagnetic field inclusive of statistical laws of the reversal sequence and the intensity distribution. Comparison are made between the model and dynamical disk dynamo models

Portfolios dominating indices: Optimization with second-order stochastic dominance constraints vs. minimum and mean variance portfolios

OpenAIRE

Keçeci, Neslihan Fidan; Kuzmenko, Viktor; Uryasev, Stan

2016-01-01

The paper compares portfolio optimization with the Second-Order Stochastic Dominance (SSD) constraints with mean-variance and minimum variance portfolio optimization. As a distribution-free decision rule, stochastic dominance takes into account the entire distribution of return rather than some specific characteristic, such as variance. The paper is focused on practical applications of the portfolio optimization and uses the Portfolio Safeguard (PSG) package, which has precoded modules for op...

Portfolios Dominating Indices: Optimization with Second-Order Stochastic Dominance Constraints vs. Minimum and Mean Variance Portfolios

OpenAIRE

Neslihan Fidan Keçeci; Viktor Kuzmenko; Stan Uryasev

2016-01-01

The paper compares portfolio optimization with the Second-Order Stochastic Dominance (SSD) constraints with mean-variance and minimum variance portfolio optimization. As a distribution-free decision rule, stochastic dominance takes into account the entire distribution of return rather than some specific characteristic, such as variance. The paper is focused on practical applications of the portfolio optimization and uses the Portfolio Safeguard (PSG) package, which has precoded modules for op...

Stochastic growth of localized plasma waves

International Nuclear Information System (INIS)

Robinson, P.A.; Cairns, I.H.

2000-01-01

Full text: Localized bursty plasma waves occur in many natural systems, where they are detected by spacecraft. The large spatiotemporal scales involved imply that beam and other instabilities relax to marginal stability and that mean wave energies are low. Stochastic wave growth occurs when ambient fluctuations perturb the wave-driver interaction, causing fluctuations about marginal stability. This yields regions where growth is enhanced and others where damping is increased; observed bursts are associated with enhanced growth and can occur even when the mean growth rate is negative. In stochastic growth, energy loss from the source is suppressed relative to secular growth, preserving it for much longer times and distances than otherwise possible. Linear stochastic growth can operate at wave levels below thresholds of nonlinear wave-clumping mechanisms such as strong-turbulence modulational instability and is not subject to their coherence and wavelength limits. Growth mechanisms can be distinguished by statistics of the fields, whose strengths are lognormally distributed if stochastically growing, power-law distributed in strong turbulence, and uniformly distributed in log under secular growth. After delineating stochastic growth and strong-turbulence regimes, recent applications of stochastic growth theory (SGT) are described, involving bursty plasma waves and unstable particle distributions in type II and III solar radio sources, foreshock regions upstream of the bow shocks of Earth and planets, and Earth's magnetosheath, auroras, and polar-caps. It is shown that when combined with wave-wave processes, SGT accounts for type II and III solar radio emissions. SGT thus removes longstanding problems in understanding persistent unstable distributions, bursty fields, and radio emissions observed in space

Stochastic dynamics for two biological species and ecological niches

Science.gov (United States)

Ruziska, Flávia M.; Arashiro, Everaldo; Tomé, Tânia

2018-01-01

We consider an ecological system in which two species interact with two niches. To this end we introduce a stochastic model with four states. Our analysis is founded in three approaches: Monte Carlo simulations of the model on a square lattice, mean-field approximation, and birth and death master equation. From this last approach we obtain a description in terms of Langevin equations which show in an explicit way the role of noise in population biology. We focus mainly on the description of time oscillations of the species population and the alternating dominance between them. The model treated here may provide insights on these properties.

Stochastic tools in turbulence

CERN Document Server

Lumey, John L

2012-01-01

Stochastic Tools in Turbulence discusses the available mathematical tools to describe stochastic vector fields to solve problems related to these fields. The book deals with the needs of turbulence in relation to stochastic vector fields, particularly, on three-dimensional aspects, linear problems, and stochastic model building. The text describes probability distributions and densities, including Lebesgue integration, conditional probabilities, conditional expectations, statistical independence, lack of correlation. The book also explains the significance of the moments, the properties of the

Two new algorithms to combine kriging with stochastic modelling

Science.gov (United States)

Venema, Victor; Lindau, Ralf; Varnai, Tamas; Simmer, Clemens

2010-05-01

Two main groups of statistical methods used in the Earth sciences are geostatistics and stochastic modelling. Geostatistical methods, such as various kriging algorithms, aim at estimating the mean value for every point as well as possible. In case of sparse measurements, such fields have less variability at small scales and a narrower distribution as the true field. This can lead to biases if a nonlinear process is simulated driven by such a kriged field. Stochastic modelling aims at reproducing the statistical structure of the data in space and time. One of the stochastic modelling methods, the so-called surrogate data approach, replicates the value distribution and power spectrum of a certain data set. While stochastic methods reproduce the statistical properties of the data, the location of the measurement is not considered. This requires the use of so-called constrained stochastic models. Because radiative transfer through clouds is a highly nonlinear process, it is essential to model the distribution (e.g. of optical depth, extinction, liquid water content or liquid water path) accurately. In addition, the correlations within the cloud field are important, especially because of horizontal photon transport. This explains the success of surrogate cloud fields for use in 3D radiative transfer studies. Up to now, however, we could only achieve good results for the radiative properties averaged over the field, but not for a radiation measurement located at a certain position. Therefore we have developed a new algorithm that combines the accuracy of stochastic (surrogate) modelling with the positioning capabilities of kriging. In this way, we can automatically profit from the large geostatistical literature and software. This algorithm is similar to the standard iterative amplitude adjusted Fourier transform (IAAFT) algorithm, but has an additional iterative step in which the surrogate field is nudged towards the kriged field. The nudging strength is gradually

Stochastic Growth Theory of Spatially-Averaged Distributions of Langmuir Fields in Earth's Foreshock

Science.gov (United States)

Boshuizen, Christopher R.; Cairns, Iver H.; Robinson, P. A.

2001-01-01

Langmuir-like waves in the foreshock of Earth are characteristically bursty and irregular, and are the subject of a number of recent studies. Averaged over the foreshock, it is observed that the probability distribution is power-law P(bar)(log E) in the wave field E with the bar denoting this averaging over position, In this paper it is shown that stochastic growth theory (SGT) can explain a power-law spatially-averaged distributions P(bar)(log E), when the observed power-law variations of the mean and standard deviation of log E with position are combined with the log normal statistics predicted by SGT at each location.

The stochastic system approach for estimating dynamic treatments effect.

Science.gov (United States)

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.

A random walk approach to stochastic neutron transport

International Nuclear Information System (INIS)

Mulatier, Clelia de

2015-01-01

One of the key goals of nuclear reactor physics is to determine the distribution of the neutron population within a reactor core. This population indeed fluctuates due to the stochastic nature of the interactions of the neutrons with the nuclei of the surrounding medium: scattering, emission of neutrons from fission events and capture by nuclear absorption. Due to these physical mechanisms, the stochastic process performed by neutrons is a branching random walk. For most applications, the neutron population considered is very large, and all physical observables related to its behaviour, such as the heat production due to fissions, are well characterised by their average values. Generally, these mean quantities are governed by the classical neutron transport equation, called linear Boltzmann equation. During my PhD, using tools from branching random walks and anomalous diffusion, I have tackled two aspects of neutron transport that cannot be approached by the linear Boltzmann equation. First, thanks to the Feynman-Kac backward formalism, I have characterised the phenomenon of 'neutron clustering' that has been highlighted for low-density configuration of neutrons and results from strong fluctuations in space and time of the neutron population. Then, I focused on several properties of anomalous (non-exponential) transport, that can model neutron transport in strongly heterogeneous and disordered media, such as pebble-bed reactors. One of the novel aspects of this work is that problems are treated in the presence of boundaries. Indeed, even though real systems are finite (confined geometries), most of previously existing results were obtained for infinite systems. (author) [fr

Mean-field approach to unconventional superconductivity

International Nuclear Information System (INIS)

Sacks, William; Mauger, Alain; Noat, Yves

2014-01-01

Highlights: • A model Hamiltonian for unconventional superconductivity (SC) is proposed. • The pseudogap (PG) state is described in terms of pair fluctuations. • SC coherence is restored by a new pair–pair interaction, which counteracts fluctuations. • Given the temperature dependence of the parameters, the SC to PG transition is examined. • The theory fits the ‘peak–dip–hump’ features of cuprate and pnictide excitation spectra. - Abstract: We propose a model that connects the quasiparticle spectral function of high-T c superconductors to the condensation energy. Given the evidence for pair correlations above T c , we consider a coarse-grain Hamiltonian of fluctuating pairs describing the incoherent pseudogap (PG) state, together with a novel pair–pair interaction term that restores long-range superconducting (SC) coherence below T c . A mean-field solution then leads to a self-consistent gap equation containing the new pair–pair coupling. The corresponding spectral function A(k,E) reveals the characteristic peak–dip–hump features of cuprates, now observed on iron pnictides (LiFeAs). The continuous transition from SC to PG states is discussed

Error performance analysis in K-tier uplink cellular networks using a stochastic geometric approach

KAUST Repository

Afify, Laila H.; Elsawy, Hesham; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim

2015-01-01

-in-Distribution approach that utilizes stochastic geometric tools to account for the network geometry in the performance characterization. Different from the other stochastic geometry models adopted in the literature, the developed analysis accounts for important

Stochastic geometry of critical curves, Schramm-Loewner evolutions and conformal field theory

International Nuclear Information System (INIS)

Gruzberg, Ilya A

2006-01-01

Conformally invariant curves that appear at critical points in two-dimensional statistical mechanics systems and their fractal geometry have received a lot of attention in recent years. On the one hand, Schramm (2000 Israel J. Math. 118 221 (Preprint math.PR/9904022)) has invented a new rigorous as well as practical calculational approach to critical curves, based on a beautiful unification of conformal maps and stochastic processes, and by now known as Schramm-Loewner evolution (SLE). On the other hand, Duplantier (2000 Phys. Rev. Lett. 84 1363; Fractal Geometry and Applications: A Jubilee of Benot Mandelbrot: Part 2 (Proc. Symp. Pure Math. vol 72) (Providence, RI: American Mathematical Society) p 365 (Preprint math-ph/0303034)) has applied boundary quantum gravity methods to calculate exact multifractal exponents associated with critical curves. In the first part of this paper, I provide a pedagogical introduction to SLE. I present mathematical facts from the theory of conformal maps and stochastic processes related to SLE. Then I review basic properties of SLE and provide practical derivation of various interesting quantities related to critical curves, including fractal dimensions and crossing probabilities. The second part of the paper is devoted to a way of describing critical curves using boundary conformal field theory (CFT) in the so-called Coulomb gas formalism. This description provides an alternative (to quantum gravity) way of obtaining the multifractal spectrum of critical curves using only traditional methods of CFT based on free bosonic fields

A Decomposition Algorithm for Mean-Variance Economic Model Predictive Control of Stochastic Linear Systems

DEFF Research Database (Denmark)

Sokoler, Leo Emil; Dammann, Bernd; Madsen, Henrik

2014-01-01

This paper presents a decomposition algorithm for solving the optimal control problem (OCP) that arises in Mean-Variance Economic Model Predictive Control of stochastic linear systems. The algorithm applies the alternating direction method of multipliers to a reformulation of the OCP...

Individual based and mean-field modeling of direct aggregation

KAUST Repository

Burger, Martin

2013-10-01

We introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighborhood. In the firstorder model the location of each individual is subject to a density-dependent random walk, while in the second-order model the density-dependent random walk acts on the velocity variable, together with a density-dependent damping term. The main novelty of our models is that we do not assume any explicit aggregative force acting on the individuals; instead, aggregation is obtained exclusively by reducing the individual stochasticity in response to higher perceived density. We formally derive the corresponding mean-field limits, leading to nonlocal degenerate diffusions. Then, we carry out the mathematical analysis of the first-order model, in particular, we prove the existence of weak solutions and show that it allows for measure-valued steady states. We also perform linear stability analysis and identify conditions for pattern formation. Moreover, we discuss the role of the nonlocality for well-posedness of the first-order model. Finally, we present results of numerical simulations for both the first- and second-order model on the individual-based and continuum levels of description. 2012 Elsevier B.V. All rights reserved.

Individual based and mean-field modeling of direct aggregation

KAUST Repository

Burger, Martin; Haskovec, Jan; Wolfram, Marie-Therese

2013-01-01

We introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighborhood. In the firstorder model the location of each individual is subject to a density-dependent random walk, while in the second-order model the density-dependent random walk acts on the velocity variable, together with a density-dependent damping term. The main novelty of our models is that we do not assume any explicit aggregative force acting on the individuals; instead, aggregation is obtained exclusively by reducing the individual stochasticity in response to higher perceived density. We formally derive the corresponding mean-field limits, leading to nonlocal degenerate diffusions. Then, we carry out the mathematical analysis of the first-order model, in particular, we prove the existence of weak solutions and show that it allows for measure-valued steady states. We also perform linear stability analysis and identify conditions for pattern formation. Moreover, we discuss the role of the nonlocality for well-posedness of the first-order model. Finally, we present results of numerical simulations for both the first- and second-order model on the individual-based and continuum levels of description. 2012 Elsevier B.V. All rights reserved.

Electron Acceleration by Stochastic Electric Fields in Thunderstorms: Terrestrial Gamma-Ray Flashes

Science.gov (United States)

Alnussirat, S.; Miller, J. A.; Christian, H. J., Jr.; Fishman, G. J.

2016-12-01

Terrestrial gamma-ray flashes (TGFs) are energetic pulses of photons, which are intense and short, originating in the atmosphere during thunderstorm activity. Despite the number of observations, the production mechanism(s) of TGFs and other energetic particles is not well understood. However, two mechanisms have been suggested as a source of TGFs: (1) the relativistic runaway electron avalanche mechanism (RREA), and (2) the lightning leader mechanism. The RREA can account for the TGF observations, but requires restrictive or unrealistic assumptions. The lightning leader channel is also expected to produce runaway electrons, but through inhomogeneous, small scale, strong electric fields. In this work we use the Boltzmann equation to model the electron acceleration by the lightning leader mechanism, and we derive the gamma-ray spectrum from the electron distribution function. The electric fields at the tip of the leaders are assumed to be stochastic in space and time. Since the physics involved in the lightening leader is not known, we test different cases of the stochastic acceleration agent. From this modeling we hope to investigate the possibility and efficiency of stochastic acceleration in thunderstorm.

Impact of stochastic primordial magnetic fields on the scalar contribution to cosmic microwave background anisotropies

International Nuclear Information System (INIS)

Finelli, Fabio; Paci, Francesco; Paoletti, Daniela

2008-01-01

We study the impact of a stochastic background of primordial magnetic fields on the scalar contribution of cosmic microwave background (CMB) anisotropies and on the matter power spectrum. We give the correct initial conditions for cosmological perturbations and the exact expressions for the energy density and Lorentz force associated to the stochastic background of primordial magnetic fields, given a power-law for their spectra cut at a damping scale. The dependence of the CMB temperature and polarization spectra on the relevant parameters of the primordial magnetic fields is illustrated.

Lateral diffusion of the topological charge density in stochastic optical fields

CSIR Research Space (South Africa)

Roux, FS

2010-01-01

Full Text Available Stochastic (i.e. random and quasi-random) optical fields may contain distributions of optical vortices that are represented by non-uniform topological charge densities. Numerical simulations are used to investigate the evolution under free...

Fat versus Thin Threading Approach on GPUs: Application to Stochastic Simulation of Chemical Reactions

KAUST Repository

Klingbeil, Guido; Erban, Radek; Giles, Mike; Maini, Philip K.

2012-01-01

We explore two different threading approaches on a graphics processing unit (GPU) exploiting two different characteristics of the current GPU architecture. The fat thread approach tries to minimize data access time by relying on shared memory and registers potentially sacrificing parallelism. The thin thread approach maximizes parallelism and tries to hide access latencies. We apply these two approaches to the parallel stochastic simulation of chemical reaction systems using the stochastic simulation algorithm (SSA) by Gillespie [14]. In these cases, the proposed thin thread approach shows comparable performance while eliminating the limitation of the reaction system's size. © 2006 IEEE.

Fat versus Thin Threading Approach on GPUs: Application to Stochastic Simulation of Chemical Reactions

KAUST Repository

Klingbeil, Guido

2012-02-01

We explore two different threading approaches on a graphics processing unit (GPU) exploiting two different characteristics of the current GPU architecture. The fat thread approach tries to minimize data access time by relying on shared memory and registers potentially sacrificing parallelism. The thin thread approach maximizes parallelism and tries to hide access latencies. We apply these two approaches to the parallel stochastic simulation of chemical reaction systems using the stochastic simulation algorithm (SSA) by Gillespie [14]. In these cases, the proposed thin thread approach shows comparable performance while eliminating the limitation of the reaction system\\'s size. © 2006 IEEE.

Kinetic theory of age-structured stochastic birth-death processes

Science.gov (United States)

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.

Mean-Field-Game Model for Botnet Defense in Cyber-Security

Energy Technology Data Exchange (ETDEWEB)

Kolokoltsov, V. N., E-mail: v.kolokoltsov@warwick.ac.uk [University of Warwick, Department of Statistics (United Kingdom); Bensoussan, A. [The University of Texas at Dallas, School of Management (United States)

2016-12-15

We initiate the analysis of the response of computer owners to various offers of defence systems against a cyber-hacker (for instance, a botnet attack), as a stochastic game of a large number of interacting agents. We introduce a simple mean-field game that models their behavior. It takes into account both the random process of the propagation of the infection (controlled by the botner herder) and the decision making process of customers. Its stationary version turns out to be exactly solvable (but not at all trivial) under an additional natural assumption that the execution time of the decisions of the customers (say, switch on or out the defence system) is much faster that the infection rates.

Mean-Field-Game Model for Botnet Defense in Cyber-Security

International Nuclear Information System (INIS)

Kolokoltsov, V. N.; Bensoussan, A.

2016-01-01

We initiate the analysis of the response of computer owners to various offers of defence systems against a cyber-hacker (for instance, a botnet attack), as a stochastic game of a large number of interacting agents. We introduce a simple mean-field game that models their behavior. It takes into account both the random process of the propagation of the infection (controlled by the botner herder) and the decision making process of customers. Its stationary version turns out to be exactly solvable (but not at all trivial) under an additional natural assumption that the execution time of the decisions of the customers (say, switch on or out the defence system) is much faster that the infection rates.

Stochastic Control of Energy Efficient Buildings: A Semidefinite Programming Approach

Energy Technology Data Exchange (ETDEWEB)

Ma, Xiao [ORNL; Dong, Jin [ORNL; Djouadi, Seddik M [ORNL; Nutaro, James J [ORNL; Kuruganti, Teja [ORNL

2015-01-01

The key goal in energy efficient buildings is to reduce energy consumption of Heating, Ventilation, and Air- Conditioning (HVAC) systems while maintaining a comfortable temperature and humidity in the building. This paper proposes a novel stochastic control approach for achieving joint performance and power control of HVAC. We employ a constrained Stochastic Linear Quadratic Control (cSLQC) by minimizing a quadratic cost function with a disturbance assumed to be Gaussian. The problem is formulated to minimize the expected cost subject to a linear constraint and a probabilistic constraint. By using cSLQC, the problem is reduced to a semidefinite optimization problem, where the optimal control can be computed efficiently by Semidefinite programming (SDP). Simulation results are provided to demonstrate the effectiveness and power efficiency by utilizing the proposed control approach.

Electricity price modeling with stochastic time change

International Nuclear Information System (INIS)

Borovkova, Svetlana; Schmeck, Maren Diane

2017-01-01

In this paper, we develop a novel approach to electricity price modeling, based on the powerful technique of stochastic time change. This technique allows us to incorporate the characteristic features of electricity prices (such as seasonal volatility, time varying mean reversion and seasonally occurring price spikes) into the model in an elegant and economically justifiable way. The stochastic time change introduces stochastic as well as deterministic (e.g., seasonal) features in the price process' volatility and in the jump component. We specify the base process as a mean reverting jump diffusion and the time change as an absolutely continuous stochastic process with seasonal component. The activity rate of the stochastic time change can be related to the factors that influence supply and demand. Here we use the temperature as a proxy for the demand and hence, as the driving factor of the stochastic time change, and show that this choice leads to realistic price paths. We derive properties of the resulting price process and develop the model calibration procedure. We calibrate the model to the historical EEX power prices and apply it to generating realistic price paths by Monte Carlo simulations. We show that the simulated price process matches the distributional characteristics of the observed electricity prices in periods of both high and low demand. - Highlights: • We develop a novel approach to electricity price modeling, based on the powerful technique of stochastic time change. • We incorporate the characteristic features of electricity prices, such as seasonal volatility and spikes into the model. • We use the temperature as a proxy for the demand and hence, as the driving factor of the stochastic time change • We derive properties of the resulting price process and develop the model calibration procedure. • We calibrate the model to the historical EEX power prices and apply it to generating realistic price paths.

Mean-variance portfolio selection for defined-contribution pension funds with stochastic salary.

Science.gov (United States)

Zhang, Chubing

2014-01-01

This paper focuses on a continuous-time dynamic mean-variance portfolio selection problem of defined-contribution pension funds with stochastic salary, whose risk comes from both financial market and nonfinancial market. By constructing a special Riccati equation as a continuous (actually a viscosity) solution to the HJB equation, we obtain an explicit closed form solution for the optimal investment portfolio as well as the efficient frontier.

Mean-Variance Portfolio Selection for Defined-Contribution Pension Funds with Stochastic Salary

OpenAIRE

Chubing Zhang

2014-01-01

This paper focuses on a continuous-time dynamic mean-variance portfolio selection problem of defined-contribution pension funds with stochastic salary, whose risk comes from both financial market and nonfinancial market. By constructing a special Riccati equation as a continuous (actually a viscosity) solution to the HJB equation, we obtain an explicit closed form solution for the optimal investment portfolio as well as the efficient frontier.

Application of Stochastic Unsaturated Flow Theory, Numerical Simulations, and Comparisons to Field Observations

DEFF Research Database (Denmark)

Jensen, Karsten Høgh; Mantoglou, Aristotelis

1992-01-01

unsaturated flow equation representing the mean system behavior is solved using a finite difference numerical solution technique. The effective parameters are evaluated from the stochastic theory formulas before entering them into the numerical solution for each iteration. The stochastic model is applied...... seems to offer a rational framework for modeling large-scale unsaturated flow and estimating areal averages of soil-hydrological processes in spatially variable soils....

Diagram of collisional regimes for particle diffusion in a stochastic magnetic field

International Nuclear Information System (INIS)

Misguich, J.H.; Balescu, R.

1995-01-01

This document deals with static stochastic fields, where magnetic lines experience exponential separation and magnetic diffusion. It more particularly focuses on the diffusivity of collisional particles in such a fields and presents a general graph which describes most regimes of collisional and weakly collisional diffusion for guiding centers in a time-independent magnetic field. (TEC). 9 refs., 1 fig., 2 tabs

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.

Portfolios Dominating Indices: Optimization with Second-Order Stochastic Dominance Constraints vs. Minimum and Mean Variance Portfolios

Directory of Open Access Journals (Sweden)

Neslihan Fidan Keçeci

2016-10-01

Full Text Available The paper compares portfolio optimization with the Second-Order Stochastic Dominance (SSD constraints with mean-variance and minimum variance portfolio optimization. As a distribution-free decision rule, stochastic dominance takes into account the entire distribution of return rather than some specific characteristic, such as variance. The paper is focused on practical applications of the portfolio optimization and uses the Portfolio Safeguard (PSG package, which has precoded modules for optimization with SSD constraints, mean-variance and minimum variance portfolio optimization. We have done in-sample and out-of-sample simulations for portfolios of stocks from the Dow Jones, S&P 100 and DAX indices. The considered portfolios’ SSD dominate the Dow Jones, S&P 100 and DAX indices. Simulation demonstrated a superior performance of portfolios with SD constraints, versus mean-variance and minimum variance portfolios.

An Approach to Stochastic Peridynamic Theory.

Energy Technology Data Exchange (ETDEWEB)

Demmie, Paul N.

2018-04-01

In many material systems, man-made or natural, we have an incomplete knowledge of geometric or material properties, which leads to uncertainty in predicting their performance under dynamic loading. Given the uncertainty and a high degree of spatial variability in properties of materials subjected to impact, a stochastic theory of continuum mechanics would be useful for modeling dynamic response of such systems. Peridynamic theory is such a theory. It is formulated as an integro- differential equation that does not employ spatial derivatives, and provides for a consistent formulation of both deformation and failure of materials. We discuss an approach to stochastic peridynamic theory and illustrate the formulation with examples of impact loading of geological materials with uncorrelated or correlated material properties. We examine wave propagation and damage to the material. The most salient feature is the absence of spallation, referred to as disorder toughness, which generalizes similar results from earlier quasi-static damage mechanics. Acknowledgements This research was made possible by the support from DTRA grant HDTRA1-08-10-BRCWM. I thank Dr. Martin Ostoja-Starzewski for introducing me to the mechanics of random materials and collaborating with me throughout and after this DTRA project.

Stochastic Boolean networks: An efficient approach to modeling gene regulatory networks

Directory of Open Access Journals (Sweden)

Liang Jinghang

2012-08-01

network inferred from a T cell immune response dataset. An SBN can also implement the function of an asynchronous PBN and is potentially useful in a hybrid approach in combination with a continuous or single-molecule level stochastic model. Conclusions Stochastic Boolean networks (SBNs are proposed as an efficient approach to modelling gene regulatory networks (GRNs. The SBN approach is able to recover biologically-proven regulatory behaviours, such as the oscillatory dynamics of the p53-Mdm2 network and the dynamic attractors in a T cell immune response network. The proposed approach can further predict the network dynamics when the genes are under perturbation, thus providing biologically meaningful insights for a better understanding of the dynamics of GRNs. The algorithms and methods described in this paper have been implemented in Matlab packages, which are attached as Additional files.

Large-deviation principles, stochastic effective actions, path entropies, and the structure and meaning of thermodynamic descriptions

International Nuclear Information System (INIS)

Smith, Eric

2011-01-01

The meaning of thermodynamic descriptions is found in large-deviations scaling (Ellis 1985 Entropy, Large Deviations, and Statistical Mechanics (New York: Springer); Touchette 2009 Phys. Rep. 478 1-69) of the probabilities for fluctuations of averaged quantities. The central function expressing large-deviations scaling is the entropy, which is the basis both for fluctuation theorems and for characterizing the thermodynamic interactions of systems. Freidlin-Wentzell theory (Freidlin and Wentzell 1998 Random Perturbations in Dynamical Systems 2nd edn (New York: Springer)) provides a quite general formulation of large-deviations scaling for non-equilibrium stochastic processes, through a remarkable representation in terms of a Hamiltonian dynamical system. A number of related methods now exist to construct the Freidlin-Wentzell Hamiltonian for many kinds of stochastic processes; one method due to Doi (1976 J. Phys. A: Math. Gen. 9 1465-78; 1976 J. Phys. A: Math. Gen. 9 1479) and Peliti (1985 J. Physique 46 1469; 1986 J. Phys. A: Math. Gen. 19 L365, appropriate to integer counting statistics, is widely used in reaction-diffusion theory. Using these tools together with a path-entropy method due to Jaynes (1980 Annu. Rev. Phys. Chem. 31 579-601), this review shows how to construct entropy functions that both express large-deviations scaling of fluctuations, and describe system-environment interactions, for discrete stochastic processes either at or away from equilibrium. A collection of variational methods familiar within quantum field theory, but less commonly applied to the Doi-Peliti construction, is used to define a 'stochastic effective action', which is the large-deviations rate function for arbitrary non-equilibrium paths. We show how common principles of entropy maximization, applied to different ensembles of states or of histories, lead to different entropy functions and different sets of thermodynamic state variables. Yet the relations among all these levels of

Electron transport in the stochastic fields of RFP ZT-40M

International Nuclear Information System (INIS)

Punjabi, A.; Verma, A.; Kim, Myung-Hee; Boozer, A.

1991-01-01

In this paper, we use our newly developed Monte Carlo Method to study the transport of electrons in stochastic magnetic fields of the device RFP ZT4OM. The results of this calculation will be compared with the Rechester-Rosenbluth scaling

Stochastic growth of localized plasma waves

International Nuclear Information System (INIS)

Robinson, P.A.; Cairns, Iver H.

2001-01-01

Localized bursty plasma waves are detected by spacecraft in many space plasmas. The large spatiotemporal scales involved imply that beam and other instabilities relax to marginal stability and that mean wave energies are low. Stochastic wave growth occurs when ambient fluctuations perturb the system, causing fluctuations about marginal stability. This yields regions where growth is enhanced and others where damping is increased; bursts are associated with enhanced growth and can occur even when the mean growth rate is negative. In stochastic growth, energy loss from the source is suppressed relative to secular growth, preserving it far longer than otherwise possible. Linear stochastic growth can operate at wave levels below thresholds of nonlinear wave-clumping mechanisms such as strong-turbulence modulational instability and is not subject to their coherence and wavelength limits. These mechanisms can be distinguished by statistics of the fields, whose strengths are lognormally distributed if stochastically growing and power-law distributed in strong turbulence. Recent applications of stochastic growth theory (SGT) are described, involving bursty plasma waves and unstable particle distributions in type III solar radio sources, the Earth's foreshock, magnetosheath, and polar cap regions. It is shown that when combined with wave-wave processes, SGT also accounts for associated radio emissions

A two-stage stochastic programming approach for operating multi-energy systems

DEFF Research Database (Denmark)

Zeng, Qing; Fang, Jiakun; Chen, Zhe

2017-01-01

This paper provides a two-stage stochastic programming approach for joint operating multi-energy systems under uncertainty. Simulation is carried out in a test system to demonstrate the feasibility and efficiency of the proposed approach. The test energy system includes a gas subsystem with a gas...

Simple Planar Truss (Linear, Nonlinear and Stochastic Approach

Directory of Open Access Journals (Sweden)

Frydrýšek Karel

2016-11-01

Full Text Available This article deals with a simple planar and statically determinate pin-connected truss. It demonstrates the processes and methods of derivations and solutions according to 1st and 2nd order theories. The article applies linear and nonlinear approaches and their simplifications via a Maclaurin series. Programming connected with the stochastic Simulation-Based Reliability Method (i.e. the direct Monte Carlo approach is used to conduct a probabilistic reliability assessment (i.e. a calculation of the probability that plastic deformation will occur in members of the truss.

A Stochastic Approach for Blurred Image Restoration and Optical Flow Computation on Field Image Sequence

Institute of Scientific and Technical Information of China (English)

高文; 陈熙霖

1997-01-01

The blur in target images caused by camera vibration due to robot motion or hand shaking and by object(s) moving in the background scene is different to deal with in the computer vision system.In this paper,the authors study the relation model between motion and blur in the case of object motion existing in video image sequence,and work on a practical computation algorithm for both motion analysis and blut image restoration.Combining the general optical flow and stochastic process,the paper presents and approach by which the motion velocity can be calculated from blurred images.On the other hand,the blurred image can also be restored using the obtained motion information.For solving a problem with small motion limitation on the general optical flow computation,a multiresolution optical flow algoritm based on MAP estimation is proposed. For restoring the blurred image ,an iteration algorithm and the obtained motion velocity are used.The experiment shows that the proposed approach for both motion velocity computation and blurred image restoration works well.

Mean-Variance Portfolio Selection for Defined-Contribution Pension Funds with Stochastic Salary

Directory of Open Access Journals (Sweden)

Chubing Zhang

2014-01-01

Full Text Available This paper focuses on a continuous-time dynamic mean-variance portfolio selection problem of defined-contribution pension funds with stochastic salary, whose risk comes from both financial market and nonfinancial market. By constructing a special Riccati equation as a continuous (actually a viscosity solution to the HJB equation, we obtain an explicit closed form solution for the optimal investment portfolio as well as the efficient frontier.

Mean-Variance Portfolio Selection for Defined-Contribution Pension Funds with Stochastic Salary

Science.gov (United States)

Zhang, Chubing

2014-01-01

This paper focuses on a continuous-time dynamic mean-variance portfolio selection problem of defined-contribution pension funds with stochastic salary, whose risk comes from both financial market and nonfinancial market. By constructing a special Riccati equation as a continuous (actually a viscosity) solution to the HJB equation, we obtain an explicit closed form solution for the optimal investment portfolio as well as the efficient frontier. PMID:24782667

Recursive stochastic effects in valley hybrid inflation

Science.gov (United States)

Levasseur, Laurence Perreault; Vennin, Vincent; Brandenberger, Robert

2013-10-01

Hybrid inflation is a two-field model where inflation ends because of a tachyonic instability, the duration of which is determined by stochastic effects and has important observational implications. Making use of the recursive approach to the stochastic formalism presented in [L. P. Levasseur, preceding article, Phys. Rev. D 88, 083537 (2013)], these effects are consistently computed. Through an analysis of backreaction, this method is shown to converge in the valley but points toward an (expected) instability in the waterfall. It is further shown that the quasistationarity of the auxiliary field distribution breaks down in the case of a short-lived waterfall. We find that the typical dispersion of the waterfall field at the critical point is then diminished, thus increasing the duration of the waterfall phase and jeopardizing the possibility of a short transition. Finally, we find that stochastic effects worsen the blue tilt of the curvature perturbations by an O(1) factor when compared with the usual slow-roll contribution.

Stochastic quantization and gravity

International Nuclear Information System (INIS)

Rumpf, H.

1984-01-01

We give a preliminary account of the application of stochastic quantization to the gravitational field. We start in Section I from Nelson's formulation of quantum mechanics as Newtonian stochastic mechanics and only then introduce the Parisi-Wu stochastic quantization scheme on which all the later discussion will be based. In Section II we present a generalization of the scheme that is applicable to fields in physical (i.e. Lorentzian) space-time and treat the free linearized gravitational field in this manner. The most remarkable result of this is the noncausal propagation of conformal gravitons. Moreover the concept of stochastic gauge-fixing is introduced and a complete discussion of all the covariant gauges is given. A special symmetry relating two classes of covariant gauges is exhibited. Finally Section III contains some preliminary remarks on full nonlinear gravity. In particular we argue that in contrast to gauge fields the stochastic gravitational field cannot be transformed to a Gaussian process. (Author)

Stochastic Turing Patterns: Analysis of Compartment-Based Approaches

KAUST Repository

Cao, Yang; Erban, Radek

2014-01-01

© 2014, Society for Mathematical Biology. Turing patterns can be observed in reaction-diffusion systems where chemical species have different diffusion constants. In recent years, several studies investigated the effects of noise on Turing patterns and showed that the parameter regimes, for which stochastic Turing patterns are observed, can be larger than the parameter regimes predicted by deterministic models, which are written in terms of partial differential equations (PDEs) for species concentrations. A common stochastic reaction-diffusion approach is written in terms of compartment-based (lattice-based) models, where the domain of interest is divided into artificial compartments and the number of molecules in each compartment is simulated. In this paper, the dependence of stochastic Turing patterns on the compartment size is investigated. It has previously been shown (for relatively simpler systems) that a modeler should not choose compartment sizes which are too small or too large, and that the optimal compartment size depends on the diffusion constant. Taking these results into account, we propose and study a compartment-based model of Turing patterns where each chemical species is described using a different set of compartments. It is shown that the parameter regions where spatial patterns form are different from the regions obtained by classical deterministic PDE-based models, but they are also different from the results obtained for the stochastic reaction-diffusion models which use a single set of compartments for all chemical species. In particular, it is argued that some previously reported results on the effect of noise on Turing patterns in biological systems need to be reinterpreted.

Stochastic Turing Patterns: Analysis of Compartment-Based Approaches

KAUST Repository

Cao, Yang

2014-11-25

© 2014, Society for Mathematical Biology. Turing patterns can be observed in reaction-diffusion systems where chemical species have different diffusion constants. In recent years, several studies investigated the effects of noise on Turing patterns and showed that the parameter regimes, for which stochastic Turing patterns are observed, can be larger than the parameter regimes predicted by deterministic models, which are written in terms of partial differential equations (PDEs) for species concentrations. A common stochastic reaction-diffusion approach is written in terms of compartment-based (lattice-based) models, where the domain of interest is divided into artificial compartments and the number of molecules in each compartment is simulated. In this paper, the dependence of stochastic Turing patterns on the compartment size is investigated. It has previously been shown (for relatively simpler systems) that a modeler should not choose compartment sizes which are too small or too large, and that the optimal compartment size depends on the diffusion constant. Taking these results into account, we propose and study a compartment-based model of Turing patterns where each chemical species is described using a different set of compartments. It is shown that the parameter regions where spatial patterns form are different from the regions obtained by classical deterministic PDE-based models, but they are also different from the results obtained for the stochastic reaction-diffusion models which use a single set of compartments for all chemical species. In particular, it is argued that some previously reported results on the effect of noise on Turing patterns in biological systems need to be reinterpreted.

Mean field instabilities in dissipative heavy ion collisions

International Nuclear Information System (INIS)

Colonna, M.; Guarnera, A.; Istituto Nazionale di Fisica Nucleare, Bologna; Catania Univ.; Di Torro, M.; Catania Univ.

1995-01-01

We discuss new reaction mechanisms that may occur in semi-peripheral heavy ion collisions at intermediate energies. In particular we focus on the dynamics of the overlapping zone, showing the development of neck instabilities, coupled with the possibility of an increasing amount amount of dynamical fluctuations. In a very selected beam energy range between 40 and 70 MeV/u we observe an important interplay between stochastic nucleon exchange and the random nature of nucleon-nucleon collisions. Expected consequences are intermediate mass fragment emissions from the neck region and large variances in the projectile-like and target-like observables. The crucial importance of a time matching between the growth of mean field instabilities and the separation of the interacting system is stressed. Some hints towards the observation of relatively large instability effects in deep inelastic collisions at lower energy are finally suggested. (authors). 29 refs., 5 figs., 2 tabs

Fictive impurity approach to dynamical mean field theory

Energy Technology Data Exchange (ETDEWEB)

Fuhrmann, A.

2006-10-15

A new extension of the dynamical mean-field theory was investigated in the regime of large Coulomb repulsion. A number of physical quantities such as single-particle density of states, spin-spin correlation, internal energy and Neel temperature, were computed for a two-dimensional Hubbard model at half-filling. The numerical data were compared to our analytical results as well as to the results computed using the dynamical cluster approximation. In the second part of this work we consider a two-plane Hubbard model. The transport properties of the bilayer were investigated and the phase diagram was obtained. (orig.)

Fictive impurity approach to dynamical mean field theory

International Nuclear Information System (INIS)

Fuhrmann, A.

2006-10-01

A new extension of the dynamical mean-field theory was investigated in the regime of large Coulomb repulsion. A number of physical quantities such as single-particle density of states, spin-spin correlation, internal energy and Neel temperature, were computed for a two-dimensional Hubbard model at half-filling. The numerical data were compared to our analytical results as well as to the results computed using the dynamical cluster approximation. In the second part of this work we consider a two-plane Hubbard model. The transport properties of the bilayer were investigated and the phase diagram was obtained. (orig.)

A Constructive Sharp Approach to Functional Quantization of Stochastic Processes

OpenAIRE

Junglen, Stefan; Luschgy, Harald

2010-01-01

We present a constructive approach to the functional quantization problem of stochastic processes, with an emphasis on Gaussian processes. The approach is constructive, since we reduce the infinite-dimensional functional quantization problem to a finite-dimensional quantization problem that can be solved numerically. Our approach achieves the sharp rate of the minimal quantization error and can be used to quantize the path space for Gaussian processes and also, for example, Lévy processes.

Cluster Mean-Field Approach to the Steady-State Phase Diagram of Dissipative Spin Systems

Directory of Open Access Journals (Sweden)

Jiasen Jin

2016-07-01

Full Text Available We show that short-range correlations have a dramatic impact on the steady-state phase diagram of quantum driven-dissipative systems. This effect, never observed in equilibrium, follows from the fact that ordering in the steady state is of dynamical origin, and is established only at very long times, whereas in thermodynamic equilibrium it arises from the properties of the (free energy. To this end, by combining the cluster methods extensively used in equilibrium phase transitions to quantum trajectories and tensor-network techniques, we extend them to nonequilibrium phase transitions in dissipative many-body systems. We analyze in detail a model of spin-1/2 on a lattice interacting through an XYZ Hamiltonian, each of them coupled to an independent environment that induces incoherent spin flips. In the steady-state phase diagram derived from our cluster approach, the location of the phase boundaries and even its topology radically change, introducing reentrance of the paramagnetic phase as compared to the single-site mean field where correlations are neglected. Furthermore, a stability analysis of the cluster mean field indicates a susceptibility towards a possible incommensurate ordering, not present if short-range correlations are ignored.

Mean field games

KAUST Repository

Gomes, Diogo A.

2014-01-06

In this talk we will report on new results concerning the existence of smooth solutions for time dependent mean-field games. This new result is established through a combination of various tools including several a-priori estimates for time-dependent mean-field games combined with new techniques for the regularity of Hamilton-Jacobi equations.

Mean field games

KAUST Repository

Gomes, Diogo A.

2014-01-01

In this talk we will report on new results concerning the existence of smooth solutions for time dependent mean-field games. This new result is established through a combination of various tools including several a-priori estimates for time-dependent mean-field games combined with new techniques for the regularity of Hamilton-Jacobi equations.

Electron transport in the stochastic fields of the reversed-field pinch

International Nuclear Information System (INIS)

Kim, M.-H.; Punjabi, A.

1996-01-01

We employ the Monte Carlo method for the calculation of anomalous transport developed by Punjabi and Boozer to calculate the particle diffusion coefficient for electrons in the stochastic magnetic fields of the reversed-field pinch (RFP). In the Monte Carlo calculations represented here, the transport mechanism is the loss of magnetic surfaces due to resistive perturbations. The equilibrium magnetic fields are represented by the Bessel function model for the RFP. The diffusion coefficient D is calculated as a function of a, the amplitude of the perturbation. We see three regimes as the amplitude of the tearing modes is increased: the Rechester-Rosenbluth regime where D scales as a 2 ; the anomalous regime where D scales more rapidly than a 2 ; and the Mynick-Krommes regime where D scales more slowly than a 2 . Inclusion of the effects of loop voltage on the particle drift orbits in the RFP does not affect the intervals in the amplitude a where these regimes operate. (Author)

Stochastic kinetics of photoinduced phase transitions in spin-crossover solids

Science.gov (United States)

Gudyma, Iurii; Maksymov, Artur; Dimian, Mihai

2013-10-01

We study the stochastic macroscopic kinetics of photoinduced phase transitions in spin-crossover compounds assisted by white and colored Ornstein-Uhlenbeck noise. By using a phenomenological master equation obtained in the mean-field approach, the phase diagram is constructed based on the associated Lyapunov function. The stochastic behavior is then analyzed in the Langevin framework and the corresponding Fokker-Planck equations. Both additive and multiplicative and white and colored types of noise are considered and the stationary probability densities are found along with the noise-assisted light induced hysteretic loops. By using the Kramers formalism, we also focus our attention on the escape time problem in these noise perturbed systems. A detailed study of the relative escape time dependence on various noise characteristics is performed and the main features are compared for different types of noise.

Thermal behavior of dynamic magnetizations, hysteresis loop areas and correlations of a cylindrical Ising nanotube in an oscillating magnetic field within the effective-field theory and the Glauber-type stochastic dynamics approach

International Nuclear Information System (INIS)

Deviren, Bayram; Keskin, Mustafa

2012-01-01

The dynamical aspects of a cylindrical Ising nanotube in the presence of a time-varying magnetic field are investigated within the effective-field theory with correlations and Glauber-type stochastic approach. Temperature dependence of the dynamic magnetizations, dynamic total magnetization, hysteresis loop areas and correlations are investigated in order to characterize the nature of dynamic transitions as well as to obtain the dynamic phase transition temperatures and compensation behaviors. Some characteristic phenomena are found depending on the ratio of the physical parameters in the surface shell and core, i.e., five different types of compensation behaviors in the Néel classification nomenclature exist in the system. -- Highlights: ► Kinetic cylindrical Ising nanotube is investigated using the effective-field theory. ► The dynamic magnetizations, hysteresis loop areas and correlations are calculated. ► The effects of the exchange interactions have been studied in detail. ► Five different types of compensation behaviors have been found. ► Some characteristic phenomena are found depending on ratio of physical parameters.

Thermal behavior of dynamic magnetizations, hysteresis loop areas and correlations of a cylindrical Ising nanotube in an oscillating magnetic field within the effective-field theory and the Glauber-type stochastic dynamics approach

Energy Technology Data Exchange (ETDEWEB)

Deviren, Bayram, E-mail: bayram.deviren@nevsehir.edu.tr [Department of Physics, Nevsehir University, 50300 Nevsehir (Turkey); Keskin, Mustafa [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)

2012-02-20

The dynamical aspects of a cylindrical Ising nanotube in the presence of a time-varying magnetic field are investigated within the effective-field theory with correlations and Glauber-type stochastic approach. Temperature dependence of the dynamic magnetizations, dynamic total magnetization, hysteresis loop areas and correlations are investigated in order to characterize the nature of dynamic transitions as well as to obtain the dynamic phase transition temperatures and compensation behaviors. Some characteristic phenomena are found depending on the ratio of the physical parameters in the surface shell and core, i.e., five different types of compensation behaviors in the Néel classification nomenclature exist in the system. -- Highlights: ► Kinetic cylindrical Ising nanotube is investigated using the effective-field theory. ► The dynamic magnetizations, hysteresis loop areas and correlations are calculated. ► The effects of the exchange interactions have been studied in detail. ► Five different types of compensation behaviors have been found. ► Some characteristic phenomena are found depending on ratio of physical parameters.

On a stochastic process associated to non-abelian gauge fields

International Nuclear Information System (INIS)

Vilela Mendes, R.

1989-01-01

A stochastic process is constructed from a ground state measure that generalizes to non-abelian fields the ground state of abelian (free) gauge fields without fermions. Using a latticized version one shows how the process leads to a well-defined quantum theory in the Schroedinger representation. An analysis of the qualitative behaviour of the theory seems to imply a quasi-free behaviour at short distances and a maximally disordered field strength configuration for the low-momentum component of the ground state. Scaling relations for the mass gap are inferred from the theory of small random perturbations of dynamical systems. (orig.)

Numerical computation of the transport matrix in toroidal plasma with a stochastic magnetic field

Science.gov (United States)

Zhu, Siqiang; Chen, Dunqiang; Dai, Zongliang; Wang, Shaojie

2018-04-01

A new numerical method, based on integrating along the full orbit of guiding centers, to compute the transport matrix is realized. The method is successfully applied to compute the phase-space diffusion tensor of passing electrons in a tokamak with a stochastic magnetic field. The new method also computes the Lagrangian correlation function, which can be used to evaluate the Lagrangian correlation time and the turbulence correlation length. For the case of the stochastic magnetic field, we find that the order of magnitude of the parallel correlation length can be estimated by qR0, as expected previously.

Development of mean field theories in nuclear physics and in desordered media

International Nuclear Information System (INIS)

Orland, Henri.

1981-04-01

This work, in two parts, deals with the development of mean field theories in nuclear physics (nuclei in balance and collisions of heavy ions) as well as in disordered media. In the first part, two different ways of tackling the problem of developments around mean field theories are explained. Possessing an approach wave function for the system, the natural idea for including the correlations is to develop the exact wave function of the system around the mean field wave function. The first two chapters show two different ways of dealing with this problem: the perturbative approach - Hartree-Fock equations with two body collisions and functional methods. In the second part: mean field theory for spin glasses. The problem for spin glasses is to construct a physically acceptable mean field theory. The importance of this problem in statistical mechanics is linked to the fact that the mean field theory provides a qualitative description of the low temperature phase and is the starting point needed for using more sophisticated methods (renormalization group). Two approaches to this problem are presented, one based on the Sherrington-Kirkpatrick model and the other based on a model of spins with purely local disorder and competitive interaction between the spins [fr

Explicit calibration and simulation of stochastic fields by low-order ARMA processes

DEFF Research Database (Denmark)

Krenk, Steen

2011-01-01

A simple framework for autoregressive simulation of stochastic fields is presented. The autoregressive format leads to a simple exponential correlation structure in the time-dimension. In the case of scalar processes a more detailed correlation structure can be obtained by adding memory...... to the process via an extension to autoregressive moving average (ARMA) processes. The ARMA format incorporates a more detailed correlation structure by including previous values of the simulated process. Alternatively, a more detailed correlation structure can be obtained by including additional 'state......-space' variables in the simulation. For a scalar process this would imply an increase of the dimension of the process to be simulated. In the case of a stochastic field the correlation in the time-dimension is represented, although indirectly, in the simultaneous spatial correlation. The model with the shortest...

Stochastic price modeling of high volatility, mean-reverting, spike-prone commodities: The Australian wholesale spot electricity market

International Nuclear Information System (INIS)

Higgs, Helen; Worthington, Andrew

2008-01-01

It is commonly known that wholesale spot electricity markets exhibit high price volatility, strong mean-reversion and frequent extreme price spikes. This paper employs a basic stochastic model, a mean-reverting model and a regime-switching model to capture these features in the Australian national electricity market (NEM), comprising the interconnected markets of New South Wales, Queensland, South Australia and Victoria. Daily spot prices from 1 January 1999 to 31 December 2004 are employed. The results show that the regime-switching model outperforms the basic stochastic and mean-reverting models. Electricity prices are also found to exhibit stronger mean-reversion after a price spike than in the normal period, and price volatility is more than fourteen times higher in spike periods than in normal periods. The probability of a spike on any given day ranges between 5.16% in NSW and 9.44% in Victoria

Continuous strong Markov processes in dimension one a stochastic calculus approach

CERN Document Server

Assing, Sigurd

1998-01-01

The book presents an in-depth study of arbitrary one-dimensional continuous strong Markov processes using methods of stochastic calculus. Departing from the classical approaches, a unified investigation of regular as well as arbitrary non-regular diffusions is provided. A general construction method for such processes, based on a generalization of the concept of a perfect additive functional, is developed. The intrinsic decomposition of a continuous strong Markov semimartingale is discovered. The book also investigates relations to stochastic differential equations and fundamental examples of irregular diffusions.

Simple stochastic simulation.

Science.gov (United States)

Schilstra, Maria J; Martin, Stephen R

2009-01-01

Stochastic simulations may be used to describe changes with time of a reaction system in a way that explicitly accounts for the fact that molecules show a significant degree of randomness in their dynamic behavior. The stochastic approach is almost invariably used when small numbers of molecules or molecular assemblies are involved because this randomness leads to significant deviations from the predictions of the conventional deterministic (or continuous) approach to the simulation of biochemical kinetics. Advances in computational methods over the three decades that have elapsed since the publication of Daniel Gillespie's seminal paper in 1977 (J. Phys. Chem. 81, 2340-2361) have allowed researchers to produce highly sophisticated models of complex biological systems. However, these models are frequently highly specific for the particular application and their description often involves mathematical treatments inaccessible to the nonspecialist. For anyone completely new to the field to apply such techniques in their own work might seem at first sight to be a rather intimidating prospect. However, the fundamental principles underlying the approach are in essence rather simple, and the aim of this article is to provide an entry point to the field for a newcomer. It focuses mainly on these general principles, both kinetic and computational, which tend to be not particularly well covered in specialist literature, and shows that interesting information may even be obtained using very simple operations in a conventional spreadsheet.

Lateral phase drift of the topological charge density in stochastic optical fields

CSIR Research Space (South Africa)

Roux, FS

2012-03-01

Full Text Available The statistical distributions of optical vortices or topological charge in stochastic optical fields can be inhomogeneous in both transverse directions. Such two-dimensional inhomogeneous vortex or topological charge distributions evolve in a...

Stochastic synchronization in finite size spiking networks

Science.gov (United States)

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.

Analytic equation of state for FCC C60 solid based on analytic mean-field potential approach

International Nuclear Information System (INIS)

Sun Jiuxun

2006-01-01

The analytic mean-field approach (AMFP) was applied to the FCC C60 solid. For the intermolecular forces the Girifalco potential has been utilized. The analytic expressions for the Helmholtz free energy, internal energy and equation of state have been derived. The numerical results of thermodynamic quantities are compared with the molecular dynamic (MD) simulations and the unsymmetrized self-consistent field approach (CUSF) in the literature. It is shown that our AMFP results are in good agreement with the MD data both at low and high temperatures. The results of CUSF are in accordance with the AMFP at low temperature, but at high temperature the difference becomes prominent. Especially the AMFP predicted that the FCC C60 solid is stable upto 2202 K, the spinodal temperature, in good agreement with 2320 K from the MD simulation. However, the CUST just gives 1916 K, a temperature evidently lower than the MD data. The AMFP qualifies as a useful approach that can reasonably consider the anharmonic effects at high temperature

Stochastic approaches for time series forecasting of boron: a case study of Western Turkey.

Science.gov (United States)

Durdu, Omer Faruk

2010-10-01

In the present study, a seasonal and non-seasonal prediction of boron concentrations time series data for the period of 1996-2004 from Büyük Menderes river in western Turkey are addressed by means of linear stochastic models. The methodology presented here is to develop adequate linear stochastic models known as autoregressive integrated moving average (ARIMA) and multiplicative seasonal autoregressive integrated moving average (SARIMA) to predict boron content in the Büyük Menderes catchment. Initially, the Box-Whisker plots and Kendall's tau test are used to identify the trends during the study period. The measurements locations do not show significant overall trend in boron concentrations, though marginal increasing and decreasing trends are observed for certain periods at some locations. ARIMA modeling approach involves the following three steps: model identification, parameter estimation, and diagnostic checking. In the model identification step, considering the autocorrelation function (ACF) and partial autocorrelation function (PACF) results of boron data series, different ARIMA models are identified. The model gives the minimum Akaike information criterion (AIC) is selected as the best-fit model. The parameter estimation step indicates that the estimated model parameters are significantly different from zero. The diagnostic check step is applied to the residuals of the selected ARIMA models and the results indicate that the residuals are independent, normally distributed, and homoscadastic. For the model validation purposes, the predicted results using the best ARIMA models are compared to the observed data. The predicted data show reasonably good agreement with the actual data. The comparison of the mean and variance of 3-year (2002-2004) observed data vs predicted data from the selected best models show that the boron model from ARIMA modeling approaches could be used in a safe manner since the predicted values from these models preserve the basic

Backward-stochastic-differential-equation approach to modeling of gene expression.

Science.gov (United States)

Shamarova, Evelina; Chertovskih, Roman; Ramos, Alexandre F; Aguiar, Paulo

2017-03-01

In this article, we introduce a backward method to model stochastic gene expression and protein-level dynamics. The protein amount is regarded as a diffusion process and is described by a backward stochastic differential equation (BSDE). Unlike many other SDE techniques proposed in the literature, the BSDE method is backward in time; that is, instead of initial conditions it requires the specification of end-point ("final") conditions, in addition to the model parametrization. To validate our approach we employ Gillespie's stochastic simulation algorithm (SSA) to generate (forward) benchmark data, according to predefined gene network models. Numerical simulations show that the BSDE method is able to correctly infer the protein-level distributions that preceded a known final condition, obtained originally from the forward SSA. This makes the BSDE method a powerful systems biology tool for time-reversed simulations, allowing, for example, the assessment of the biological conditions (e.g., protein concentrations) that preceded an experimentally measured event of interest (e.g., mitosis, apoptosis, etc.).

On a mean field game optimal control approach modeling fast exit scenarios in human crowds

KAUST Repository

Burger, Martin; Di Francesco, Marco; Markowich, Peter A.; Wolfram, Marie Therese

2013-01-01

The understanding of fast exit and evacuation situations in crowd motion research has received a lot of scientific interest in the last decades. Security issues in larger facilities, like shopping malls, sports centers, or festivals necessitate a better understanding of the major driving forces in crowd dynamics. In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. The model is formulated in the framework of mean field games and based on a parabolic optimal control problem. We consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position and velocity, the overall density of people, and the time to exit. This microscopic setup leads in a mean-field formulation to a nonlinear macroscopic optimal control problem, which raises challenging questions for the analysis and numerical simulations.We discuss different aspects of the mathematical modeling and illustrate them with various computational results. ©2013 IEEE.

On a mean field game optimal control approach modeling fast exit scenarios in human crowds

KAUST Repository

Burger, Martin

2013-12-01

The understanding of fast exit and evacuation situations in crowd motion research has received a lot of scientific interest in the last decades. Security issues in larger facilities, like shopping malls, sports centers, or festivals necessitate a better understanding of the major driving forces in crowd dynamics. In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. The model is formulated in the framework of mean field games and based on a parabolic optimal control problem. We consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position and velocity, the overall density of people, and the time to exit. This microscopic setup leads in a mean-field formulation to a nonlinear macroscopic optimal control problem, which raises challenging questions for the analysis and numerical simulations.We discuss different aspects of the mathematical modeling and illustrate them with various computational results. ©2013 IEEE.

Mean-field approximation for spacing distribution functions in classical systems

Science.gov (United States)

González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.

2012-01-01

We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p(n)(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.

Exponential mean-square stability of two classes of theta Milstein methods for stochastic delay differential equations

Science.gov (United States)

Rouz, Omid Farkhondeh; Ahmadian, Davood; Milev, Mariyan

2017-12-01

This paper establishes exponential mean square stability of two classes of theta Milstein methods, namely split-step theta Milstein (SSTM) method and stochastic theta Milstein (STM) method, for stochastic differential delay equations (SDDEs). We consider the SDDEs problem under a coupled monotone condition on drift and diffusion coefficients, as well as a necessary linear growth condition on the last term of theta Milstein method. It is proved that the SSTM method with θ ∈ [0, ½] can recover the exponential mean square stability of the exact solution with some restrictive conditions on stepsize, but for θ ∈ (½, 1], we proved that the stability results hold for any stepsize. Then, based on the stability results of SSTM method, we examine the exponential mean square stability of the STM method and obtain the similar stability results to that of the SSTM method. In the numerical section the figures show thevalidity of our claims.

Condition monitoring with Mean field independent components analysis

DEFF Research Database (Denmark)

Pontoppidan, Niels Henrik; Sigurdsson, Sigurdur; Larsen, Jan

2005-01-01

We discuss condition monitoring based on mean field independent components analysis of acoustic emission energy signals. Within this framework it is possible to formulate a generative model that explains the sources, their mixing and also the noise statistics of the observed signals. By using...... a novelty approach we may detect unseen faulty signals as indeed faulty with high precision, even though the model learns only from normal signals. This is done by evaluating the likelihood that the model generated the signals and adapting a simple threshold for decision. Acoustic emission energy signals...... from a large diesel engine is used to demonstrate this approach. The results show that mean field independent components analysis gives a better detection of fault compared to principal components analysis, while at the same time selecting a more compact model...

Stochastic equations theory and applications in acoustics, hydrodynamics, magnetohydrodynamics, and radiophysics

CERN Document Server

Klyatskin, Valery I

2015-01-01

This monograph set presents a consistent and self-contained framework of stochastic dynamic systems with maximal possible completeness. Volume 1 presents the basic concepts, exact results, and asymptotic approximations of the theory of stochastic equations on the basis of the developed functional approach. This approach offers a possibility of both obtaining exact solutions to stochastic problems for a number of models of fluctuating parameters and constructing various asymptotic buildings. Ideas of statistical topography are used to discuss general issues of generating coherent structures from chaos with probability one, i.e., almost in every individual realization of random parameters. The general theory is illustrated with certain problems and applications of stochastic mathematical physics in various fields such as mechanics, hydrodynamics, magnetohydrodynamics, acoustics, optics, and radiophysics.  

arXiv Stochastic locality and master-field simulations of very large lattices

CERN Document Server

Lüscher, Martin

2018-01-01

In lattice QCD and other field theories with a mass gap, the field variables in distant regions of a physically large lattice are only weakly correlated. Accurate stochastic estimates of the expectation values of local observables may therefore be obtained from a single representative field. Such master-field simulations potentially allow very large lattices to be simulated, but require various conceptual and technical issues to be addressed. In this talk, an introduction to the subject is provided and some encouraging results of master-field simulations of the SU(3) gauge theory are reported.

Mean-Variance Analysis in a Multiperiod Setting

OpenAIRE

Frauendorfer, Karl; Siede, Heiko

1997-01-01

Similar to the classical Markowitz approach it is possible to apply a mean-variance criterion to a multiperiod setting to obtain efficient portfolios. To represent the stochastic dynamic characteristics necessary for modelling returns a process of asset returns is discretized with respect to time and space and summarized in a scenario tree. The resulting optimization problem is solved by means of stochastic multistage programming. The optimal solutions show equivalent structural properties as...

Mean-field learning for satisfactory solutions

KAUST Repository

Tembine, Hamidou

2013-12-01

One of the fundamental challenges in distributed interactive systems is to design efficient, accurate, and fair solutions. In such systems, a satisfactory solution is an innovative approach that aims to provide all players with a satisfactory payoff anytime and anywhere. In this paper we study fully distributed learning schemes for satisfactory solutions in games with continuous action space. Considering games where the payoff function depends only on own-action and an aggregate term, we show that the complexity of learning systems can be significantly reduced, leading to the so-called mean-field learning. We provide sufficient conditions for convergence to a satisfactory solution and we give explicit convergence time bounds. Then, several acceleration techniques are used in order to improve the convergence rate. We illustrate numerically the proposed mean-field learning schemes for quality-of-service management in communication networks. © 2013 IEEE.

Rapidity-density patterns for events in a stochastic-field multiparticle theory

International Nuclear Information System (INIS)

Arnold, R.C.

1976-02-01

Typical-event rapidity distributions expected at energies of a few TeV are calculated in a stochastic-field multiparticle production theory. Short range rapidity correlations with characteristics of a Van der Waals fluid give rise to ''domain'' patterns in rapidity density, which have the appearance of clusters separated by rapidity gaps

Response spectrum analysis of a stochastic seismic model

International Nuclear Information System (INIS)

Kimura, Koji; Sakata, Masaru; Takemoto, Shinichiro.

1990-01-01

The stochastic response spectrum approach is presented for predicting the dynamic behavior of structures to earthquake excitation expressed by a random process, one of whose sample functions can be regarded as a recorded strong-motion earthquake accelerogram. The approach consists of modeling recorded ground motion by a random process and the root-mean-square response (rms) analysis of a single-degree-of-freedom system by using the moment equations method. The stochastic response spectrum is obtained as a plot of the maximum rms response versus the natural period of the system and is compared with the conventional response spectrum. (author)

An Improved Asymptotic Sampling Approach For Stochastic Finite Element Stiffness of a Laterally Loaded Monopile

DEFF Research Database (Denmark)

Vahdatirad, Mohammadjavad; Bayat, Mehdi; Andersen, Lars Vabbersgaard

2012-01-01

In this study a stochastic approach is conducted to obtain the horizontal and rotational stiffness of an offshore monopile foundation. A nonlinear stochastic p-y curve is integrated into a finite element scheme for calculation of the monopile response in over-consolidated clay having spatial...

An Augmented Incomplete Factorization Approach for Computing the Schur Complement in Stochastic Optimization

KAUST Repository

Petra, Cosmin G.; Schenk, Olaf; Lubin, Miles; Gä ertner, Klaus

2014-01-01

We present a scalable approach and implementation for solving stochastic optimization problems on high-performance computers. In this work we revisit the sparse linear algebra computations of the parallel solver PIPS with the goal of improving the shared-memory performance and decreasing the time to solution. These computations consist of solving sparse linear systems with multiple sparse right-hand sides and are needed in our Schur-complement decomposition approach to compute the contribution of each scenario to the Schur matrix. Our novel approach uses an incomplete augmented factorization implemented within the PARDISO linear solver and an outer BiCGStab iteration to efficiently absorb pivot perturbations occurring during factorization. This approach is capable of both efficiently using the cores inside a computational node and exploiting sparsity of the right-hand sides. We report on the performance of the approach on highperformance computers when solving stochastic unit commitment problems of unprecedented size (billions of variables and constraints) that arise in the optimization and control of electrical power grids. Our numerical experiments suggest that supercomputers can be efficiently used to solve power grid stochastic optimization problems with thousands of scenarios under the strict "real-time" requirements of power grid operators. To our knowledge, this has not been possible prior to the present work. © 2014 Society for Industrial and Applied Mathematics.

Plasma transport in stochastic magnetic fields. III. Kinetics of test-particle diffusion

International Nuclear Information System (INIS)

Krommes, J.A.; Oberman, C.; Kleva, R.G.

1982-07-01

A discussion is given of test particle transport in the presence of specified stochastic magnetic fields, with particular emphasis on the collisional limit. Certain paradoxes and inconsistencies in the literature regarding the form of the scaling laws are resolved by carefully distinguishing a number of physically distinct correlation lengths, and thus by identifying several collisional subregimes. The common procedure of averaging the conventional fluid equations over the statistics of a random field is shown to fail in some important cases because of breakdown of the Chapman-Enskog ordering in the presence of a stochastic field component with short autocorrelation length. A modified perturbation theory is introduced which leads to a Kubo-like formula valid in all collisionality regimes. The direct-interaction approximation is shown to fail in the interesting limit in which the orbit exponentiation length L/sub K/ appears explicitly. A higher order renormalized kinetic theory in which L/sub K/ appears naturally is discussed and used to rederive more systematically the results of the heuristic scaling arguments

Scalar field dark matter in hybrid approach

NARCIS (Netherlands)

Friedrich, Pavel; Prokopec, Tomislav

2017-01-01

We develop a hybrid formalism suitable for modeling scalar field dark matter, in which the phase-space distribution associated to the real scalar field is modeled by statistical equal-time two-point functions and gravity is treated by two stochastic gravitational fields in the longitudinal gauge (in

Stochastic quantisation: theme and variation

International Nuclear Information System (INIS)

Klauder, J.R.; Kyoto Univ.

1987-01-01

The paper on stochastic quantisation is a contribution to the book commemorating the sixtieth birthday of E.S. Fradkin. Stochastic quantisation reformulates Euclidean quantum field theory in the language of Langevin equations. The generalised free field is discussed from the viewpoint of stochastic quantisation. An artificial family of highly singular model theories wherein the space-time derivatives are dropped altogether is also examined. Finally a modified form of stochastic quantisation is considered. (U.K.)

Stationary stochastic processes theory and applications

CERN Document Server

Lindgren, Georg

2012-01-01

Some Probability and Process BackgroundSample space, sample function, and observablesRandom variables and stochastic processesStationary processes and fieldsGaussian processesFour historical landmarksSample Function PropertiesQuadratic mean propertiesSample function continuityDerivatives, tangents, and other characteristicsStochastic integrationAn ergodic resultExercisesSpectral RepresentationsComplex-valued stochastic processesBochner's theorem and the spectral distributionSpectral representation of a stationary processGaussian processesStationary counting processesExercisesLinear Filters - General PropertiesLinear time invariant filtersLinear filters and differential equationsWhite noise in linear systemsLong range dependence, non-integrable spectra, and unstable systemsThe ARMA-familyLinear Filters - Special TopicsThe Hilbert transform and the envelopeThe sampling theoremKarhunen-Loève expansionClassical Ergodic Theory and MixingThe basic ergodic theorem in L2Stationarity and transformationsThe ergodic th...

Stochasticity Modeling in Memristors

KAUST Repository

Naous, Rawan

2015-10-26

Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.

Stochasticity Modeling in Memristors

KAUST Repository

Naous, Rawan; Al-Shedivat, Maruan; Salama, Khaled N.

2015-01-01

Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.

Background field method for nonlinear σ-model in stochastic quantization

International Nuclear Information System (INIS)

Nakazawa, Naohito; Ennyu, Daiji

1988-01-01

We formulate the background field method for the nonlinear σ-model in stochastic quantization. We demonstrate a one-loop calculation for a two-dimensional non-linear σ-model on a general riemannian manifold based on our formulation. The formulation is consistent with the known results in ordinary quantization. As a simple application, we also analyse the multiplicative renormalization of the O(N) nonlinear σ-model. (orig.)

Stochastic description of supersymmetric fields with values in a manifold

International Nuclear Information System (INIS)

Hoba, Z.

1986-01-01

This paper discusses the mathematical problem of the imaginary time quantum mechanics of a particle moving in Euclidean space as considered from the theory of diffusion processes. The diffusion process is defined by a stochastic equation; the equation describes the diffusion process as a time evolution of a Brownian particle in a force field. The paper considers a Brownian particle on a Riemannian manifold

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth

Science.gov (United States)

de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

2017-12-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of

A Pumping Algorithm for Ergodic Stochastic Mean Payoff Games with Perfect Information

Science.gov (United States)

Boros, Endre; Elbassioni, Khaled; Gurvich, Vladimir; Makino, Kazuhisa

In this paper, we consider two-person zero-sum stochastic mean payoff games with perfect information, or BWR-games, given by a digraph G = (V = V B ∪ V W ∪ V R , E), with local rewards r: E to { R}, and three types of vertices: black V B , white V W , and random V R . The game is played by two players, White and Black: When the play is at a white (black) vertex v, White (Black) selects an outgoing arc (v,u). When the play is at a random vertex v, a vertex u is picked with the given probability p(v,u). In all cases, Black pays White the value r(v,u). The play continues forever, and White aims to maximize (Black aims to minimize) the limiting mean (that is, average) payoff. It was recently shown in [7] that BWR-games are polynomially equivalent with the classical Gillette games, which include many well-known subclasses, such as cyclic games, simple stochastic games (SSG's), stochastic parity games, and Markov decision processes. In this paper, we give a new algorithm for solving BWR-games in the ergodic case, that is when the optimal values do not depend on the initial position. Our algorithm solves a BWR-game by reducing it, using a potential transformation, to a canonical form in which the optimal strategies of both players and the value for every initial position are obvious, since a locally optimal move in it is optimal in the whole game. We show that this algorithm is pseudo-polynomial when the number of random nodes is constant. We also provide an almost matching lower bound on its running time, and show that this bound holds for a wider class of algorithms. Let us add that the general (non-ergodic) case is at least as hard as SSG's, for which no pseudo-polynomial algorithm is known.

Stochastic approaches to inflation model building

International Nuclear Information System (INIS)

Ramirez, Erandy; Liddle, Andrew R.

2005-01-01

While inflation gives an appealing explanation of observed cosmological data, there are a wide range of different inflation models, providing differing predictions for the initial perturbations. Typically models are motivated either by fundamental physics considerations or by simplicity. An alternative is to generate large numbers of models via a random generation process, such as the flow equations approach. The flow equations approach is known to predict a definite structure to the observational predictions. In this paper, we first demonstrate a more efficient implementation of the flow equations exploiting an analytic solution found by Liddle (2003). We then consider alternative stochastic methods of generating large numbers of inflation models, with the aim of testing whether the structures generated by the flow equations are robust. We find that while typically there remains some concentration of points in the observable plane under the different methods, there is significant variation in the predictions amongst the methods considered

A constrained approach to multiscale stochastic simulation of chemically reacting systems

KAUST Repository

Cotter, Simon L.

2011-01-01

Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper, we introduce a multiscale methodology suitable to address this problem, assuming that the evolution of the slow species in the system is well approximated by a Langevin process. It is based on the conditional stochastic simulation algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the constrained multiscale algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Fokker-Planck equation approximation, we can in turn approximate average switching times in stochastic chemical systems. © 2011 American Institute of Physics.

Rapid core field variations during the satellite era: Investigations using stochastic process based field models

DEFF Research Database (Denmark)

Finlay, Chris; Olsen, Nils; Gillet, Nicolas

We present a new ensemble of time-dependent magnetic field models constructed from satellite and observatory data spanning 1997-2013 that are compatible with prior information concerning the temporal spectrum of core field variations. These models allow sharper field changes compared to tradition...... physical hypotheses can be tested by asking questions of the entire ensemble of core field models, rather than by interpreting any single model.......We present a new ensemble of time-dependent magnetic field models constructed from satellite and observatory data spanning 1997-2013 that are compatible with prior information concerning the temporal spectrum of core field variations. These models allow sharper field changes compared to traditional...... regularization methods based on minimizing the square of second or third time derivative. We invert satellite and observatory data directly by adopting the external field and crustal field modelling framework of the CHAOS model, but apply the stochastic process method of Gillet et al. (2013) to the core field...

Stochastic behaviour of particle orbits in field reversed geometries

International Nuclear Information System (INIS)

Finn, J.M.

1979-01-01

Studies of stochastic or ergodic behaviour of beam particle orbits in axisymmetric systems with field reversal produced by ion rings or by neutral injection are presented. In the former case a large class of orbits is ergodic, whereas in the latter most are integrable. Effects of ergodic behaviour on particle confinement, equilibrium, magnetic compression, and stability are discussed. The modification, due to ergodic orbits of the stability criterion for low frequency (ω << ωsub(ci)) resonant instabilities is presented. (author)

Multiagent model and mean field theory of complex auction dynamics

Science.gov (United States)

Chen, Qinghua; Huang, Zi-Gang; Wang, Yougui; Lai, Ying-Cheng

2015-09-01

Recent years have witnessed a growing interest in analyzing a variety of socio-economic phenomena using methods from statistical and nonlinear physics. We study a class of complex systems arising from economics, the lowest unique bid auction (LUBA) systems, which is a recently emerged class of online auction game systems. Through analyzing large, empirical data sets of LUBA, we identify a general feature of the bid price distribution: an inverted J-shaped function with exponential decay in the large bid price region. To account for the distribution, we propose a multi-agent model in which each agent bids stochastically in the field of winner’s attractiveness, and develop a theoretical framework to obtain analytic solutions of the model based on mean field analysis. The theory produces bid-price distributions that are in excellent agreement with those from the real data. Our model and theory capture the essential features of human behaviors in the competitive environment as exemplified by LUBA, and may provide significant quantitative insights into complex socio-economic phenomena.

Multiagent model and mean field theory of complex auction dynamics

International Nuclear Information System (INIS)

Chen, Qinghua; Wang, Yougui; Huang, Zi-Gang; Lai, Ying-Cheng

2015-01-01

Recent years have witnessed a growing interest in analyzing a variety of socio-economic phenomena using methods from statistical and nonlinear physics. We study a class of complex systems arising from economics, the lowest unique bid auction (LUBA) systems, which is a recently emerged class of online auction game systems. Through analyzing large, empirical data sets of LUBA, we identify a general feature of the bid price distribution: an inverted J-shaped function with exponential decay in the large bid price region. To account for the distribution, we propose a multi-agent model in which each agent bids stochastically in the field of winner’s attractiveness, and develop a theoretical framework to obtain analytic solutions of the model based on mean field analysis. The theory produces bid-price distributions that are in excellent agreement with those from the real data. Our model and theory capture the essential features of human behaviors in the competitive environment as exemplified by LUBA, and may provide significant quantitative insights into complex socio-economic phenomena. (paper)

Mean-field lattice trees

NARCIS (Netherlands)

Borgs, C.; Chayes, J.T.; Hofstad, van der R.W.; Slade, G.

1999-01-01

We introduce a mean-field model of lattice trees based on embeddings into d of abstract trees having a critical Poisson offspring distribution. This model provides a combinatorial interpretation for the self-consistent mean-field model introduced previously by Derbez and Slade [9], and provides an

Stochastic quantization of topological field theory: generalized Langevin equation with memory kernel

International Nuclear Information System (INIS)

Menezes, G.; Svaiter, N.F.

2006-04-01

We use the method of stochastic quantization in a topological field theory defined in an Euclidean space, assuming a Langevin equation with a memory kernel. We show that our procedure for the Abelian Chern-Simons theory converges regardless of the nature of the Chern-Simons coefficient. (author)

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth

International Nuclear Information System (INIS)

Cruz, Roberto de la; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

2017-01-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction–diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction–diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge

Critical study of the dispersive n- 90Zr mean field by means of a new variational method

Science.gov (United States)

Mahaux, C.; Sartor, R.

1994-02-01

A new variational method is developed for the construction of the dispersive nucleon-nucleus mean field at negative and positive energies. Like the variational moment approach that we had previously proposed, the new method only uses phenomenological optical-model potentials as input. It is simpler and more flexible than the previous approach. It is applied to a critical investigation of the n- 90Zr mean field between -25 and +25 MeV. This system is of particular interest because conflicting results had recently been obtained by two different groups. While the imaginary parts of the phenomenological optical-model potentials provided by these two groups are similar, their real parts are quite different. Nevertheless, we demonstrate that these two sets of phenomenological optical-model potentials are both compatible with the dispersion relation which connects the real and imaginary parts of the mean field. Previous hints to the contrary, by one of the two other groups, are shown to be due to unjustified approximations. A striking outcome of the present study is that it is important to explicitly introduce volume absorption in the dispersion relation, although volume absorption is negligible in the energy domain investigated here. Because of the existence of two sets of phenomenological optical-model potentials, our variational method yields two dispersive mean fields whose real parts are quite different at small or negative energies. No preference for one of the two dispersive mean fields can be expressed on purely empirical grounds since they both yield fair agreement with the experimental cross sections as well as with the observed energies of the bound single-particle states. However, we argue that one of these two mean fields is physically more meaningful, because the radial shape of its Hartree-Fock type component is independent of energy, as expected on theoretical grounds. This preferred mean field is very close to the one which had been obtained by the Ohio

Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach

Science.gov (United States)

Aguilo, Miguel A.; Warner, James E.

2017-01-01

This work presents a stochastic reduced order modeling strategy for the quantification and propagation of uncertainties in topology optimization. Uncertainty aware optimization problems can be computationally complex due to the substantial number of model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity is greatly magnified if a high-fidelity, physics-based numerical model is used for the topology optimization calculations. Stochastic reduced order model (SROM) methods are applied here to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections. A generic SROM framework that transforms the uncertainty aware, stochastic topology optimization problem into a deterministic optimization problem that relies only on independent calls to a deterministic numerical model is presented. This approach facilitates the use of existing optimization and modeling tools to accurately solve the uncertainty aware topology optimization problems in a fraction of the computational demand required by Monte Carlo methods. Finally, an example in structural topology optimization is presented to demonstrate the effectiveness of the proposed uncertainty aware structural topology optimization approach.

Mean field approximation versus exact treatment of collisions in few-body systems

International Nuclear Information System (INIS)

Lemm, J.; Weiguny, A.; Giraud, B.G.

1990-01-01

A variational principle for calculating matrix elements of the full resolvent operator for a many-body system is studied. Its mean field approximation results in non-linear equations of Hartree (-Fock) type, with initial and final channel wave functions as driving terms. The mean field equations will in general have many solutions whereas the exact problem being linear, has a unique solution. In a schematic model with separable forces the mean field equations are analytically soluble, and for the exact problem the resulting integral equations are solved numerically. Comparing exact and mean field results over a wide range of system parameters, the mean field approach proves to be a very reliable approximation, which is not plagued by the notorious problem of defining asymptotic channels in the time-dependent mean field method. (orig.)

Modelling airborne gravity data by means of adapted Space-Wise approach

Science.gov (United States)

Sampietro, Daniele; Capponi, Martina; Hamdi Mansi, Ahmed; Gatti, Andrea

2017-04-01

Regional gravity field modelling by means of remove - restore procedure is nowadays widely applied to predict grids of gravity anomalies (Bouguer, free-air, isostatic, etc.) in gravimetric geoid determination as well as in exploration geophysics. Considering this last application, due to the required accuracy and resolution, airborne gravity observations are generally adopted. However due to the relatively high acquisition velocity, presence of atmospheric turbulence, aircraft vibration, instrumental drift, etc. airborne data are contaminated by a very high observation error. For this reason, a proper procedure to filter the raw observations both in the low and high frequency should be applied to recover valuable information. In this work, a procedure to predict a grid or a set of filtered along track gravity anomalies, by merging GGM and airborne dataset, is presented. The proposed algorithm, like the Space-Wise approach developed by Politecnico di Milano in the framework of GOCE data analysis, is based on a combination of along track Wiener filter and Least Squares Collocation adjustment and properly considers the different altitudes of the gravity observations. Among the main differences with respect to the satellite application of the Space-Wise approach there is the fact that, while in processing GOCE data the stochastic characteristics of the observation error can be considered a-priori well known, in airborne gravimetry, due to the complex environment in which the observations are acquired, these characteristics are unknown and should be retrieved from the dataset itself. Some innovative theoretical aspects focusing in particular on the theoretical covariance modelling are presented too. In the end, the goodness of the procedure is evaluated by means of a test on real data recovering the gravitational signal with a predicted accuracy of about 0.25 mGal.

Stochastic calculus of protein filament formation under spatial confinement

Science.gov (United States)

Michaels, Thomas C. T.; Dear, Alexander J.; Knowles, Tuomas P. J.

2018-05-01

The growth of filamentous aggregates from precursor proteins is a process of central importance to both normal and aberrant biology, for instance as the driver of devastating human disorders such as Alzheimer's and Parkinson's diseases. The conventional theoretical framework for describing this class of phenomena in bulk is based upon the mean-field limit of the law of mass action, which implicitly assumes deterministic dynamics. However, protein filament formation processes under spatial confinement, such as in microdroplets or in the cellular environment, show intrinsic variability due to the molecular noise associated with small-volume effects. To account for this effect, in this paper we introduce a stochastic differential equation approach for investigating protein filament formation processes under spatial confinement. Using this framework, we study the statistical properties of stochastic aggregation curves, as well as the distribution of reaction lag-times. Moreover, we establish the gradual breakdown of the correlation between lag-time and normalized growth rate under spatial confinement. Our results establish the key role of spatial confinement in determining the onset of stochasticity in protein filament formation and offer a formalism for studying protein aggregation kinetics in small volumes in terms of the kinetic parameters describing the aggregation dynamics in bulk.

Non-local correlations within dynamical mean field theory

Energy Technology Data Exchange (ETDEWEB)

Li, Gang

2009-03-15

The contributions from the non-local fluctuations to the dynamical mean field theory (DMFT) were studied using the recently proposed dual fermion approach. Straight forward cluster extensions of DMFT need the solution of a small cluster, where all the short-range correlations are fully taken into account. All the correlations beyond the cluster scope are treated in the mean-field level. In the dual fermion method, only a single impurity problem needs to be solved. Both the short and long-range correlations could be considered on equal footing in this method. The weak-coupling nature of the dual fermion ensures the validity of the finite order diagram expansion. The one and two particle Green's functions calculated from the dual fermion approach agree well with the Quantum Monte Carlo solutions, and the computation time is considerably less than with the latter method. The access of the long-range order allows us to investigate the collective behavior of the electron system, e.g. spin wave excitations. (orig.)

Non-local correlations within dynamical mean field theory

International Nuclear Information System (INIS)

Li, Gang

2009-03-01

The contributions from the non-local fluctuations to the dynamical mean field theory (DMFT) were studied using the recently proposed dual fermion approach. Straight forward cluster extensions of DMFT need the solution of a small cluster, where all the short-range correlations are fully taken into account. All the correlations beyond the cluster scope are treated in the mean-field level. In the dual fermion method, only a single impurity problem needs to be solved. Both the short and long-range correlations could be considered on equal footing in this method. The weak-coupling nature of the dual fermion ensures the validity of the finite order diagram expansion. The one and two particle Green's functions calculated from the dual fermion approach agree well with the Quantum Monte Carlo solutions, and the computation time is considerably less than with the latter method. The access of the long-range order allows us to investigate the collective behavior of the electron system, e.g. spin wave excitations. (orig.)

Mean-Field Games for Marriage

Science.gov (United States)

Bauso, Dario; Dia, Ben Mansour; Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul

2014-01-01

This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple’s network on their feeling states and their well-being. PMID:24804835

Mean-field games for marriage.

Directory of Open Access Journals (Sweden)

Dario Bauso

Full Text Available This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple's network on their feeling states and their well-being.

Energy-Efficient FPGA-Based Parallel Quasi-Stochastic Computing

Directory of Open Access Journals (Sweden)

Ramu Seva

2017-11-01

Full Text Available The high performance of FPGA (Field Programmable Gate Array in image processing applications is justified by its flexible reconfigurability, its inherent parallel nature and the availability of a large amount of internal memories. Lately, the Stochastic Computing (SC paradigm has been found to be significantly advantageous in certain application domains including image processing because of its lower hardware complexity and power consumption. However, its viability is deemed to be limited due to its serial bitstream processing and excessive run-time requirement for convergence. To address these issues, a novel approach is proposed in this work where an energy-efficient implementation of SC is accomplished by introducing fast-converging Quasi-Stochastic Number Generators (QSNGs and parallel stochastic bitstream processing, which are well suited to leverage FPGA’s reconfigurability and abundant internal memory resources. The proposed approach has been tested on the Virtex-4 FPGA, and results have been compared with the serial and parallel implementations of conventional stochastic computation using the well-known SC edge detection and multiplication circuits. Results prove that by using this approach, execution time, as well as the power consumption are decreased by a factor of 3.5 and 4.5 for the edge detection circuit and multiplication circuit, respectively.

Asymptotic problems for stochastic partial differential equations

Science.gov (United States)

Salins, Michael

Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.

Stochastic Reconstruction and Interpolation of Precipitation Fields Using Combined Information of Commercial Microwave Links and Rain Gauges

Science.gov (United States)

Haese, B.; Hörning, S.; Chwala, C.; Bárdossy, A.; Schalge, B.; Kunstmann, H.

2017-12-01

For the reconstruction and interpolation of precipitation fields, we present the application of a stochastic approach called Random Mixing. Generated fields are based on a data set consisting of rain gauge observations and path-averaged rain rates estimated using Commercial Microwave Link (CML) derived information. Precipitation fields are received as linear combination of unconditional spatial random fields, where the spatial dependence structure is described by copulas. The weights of the linear combination are optimized such that the observations and the spatial structure of the precipitation observations are reproduced. The innovation of the approach is that this strategy enables the simulation of ensembles of precipitation fields of any size. Each ensemble member is in concordance with the observed path-averaged CML derived rain rates and additionally reflects the observed rainfall variability along the CML paths. The ensemble spread allows additionally an estimation of the uncertainty of the reconstructed precipitation fields. The method is demonstrated both for a synthetic data set and a real-world data set in South Germany. While the synthetic example allows an evaluation against a known reference, the second example demonstrates the applicability for real-world observations. Generated precipitation fields of both examples reproduce the spatial precipitation pattern in good quality. A performance evaluation of Random Mixing compared to Ordinary Kriging demonstrates an improvement of the reconstruction of the observed spatial variability. Random Mixing is concluded to be a beneficial new approach for the provision of precipitation fields and ensembles of them, in particular when different measurement types are combined.

Instantaneous stochastic perturbation theory

International Nuclear Information System (INIS)

Lüscher, Martin

2015-01-01

A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.

Elitism and Stochastic Dominance

OpenAIRE

Bazen, Stephen; Moyes, Patrick

2011-01-01

Stochastic dominance has typically been used with a special emphasis on risk and inequality reduction something captured by the concavity of the utility function in the expected utility model. We claim that the applicability of the stochastic dominance approach goes far beyond risk and inequality measurement provided suitable adpations be made. We apply in the paper the stochastic dominance approach to the measurment of elitism which may be considered the opposite of egalitarianism. While the...

Mean-field games for marriage

KAUST Repository

Bauso, Dario

2014-05-07

This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple\\'s network on their feeling states and their well-being. © 2014 Bauso et al.

Mean-field games for marriage

KAUST Repository

Bauso, Dario; Dia, Ben Mansour; Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul

2014-01-01

This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple's network on their feeling states and their well-being. © 2014 Bauso et al.

Benchmarking the stochastic time-dependent variational approach for excitation dynamics in molecular aggregates

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.

Estimation of Parameters in Mean-Reverting Stochastic Systems

Directory of Open Access Journals (Sweden)

Tianhai Tian

2014-01-01

Full Text Available Stochastic differential equation (SDE is a very important mathematical tool to describe complex systems in which noise plays an important role. SDE models have been widely used to study the dynamic properties of various nonlinear systems in biology, engineering, finance, and economics, as well as physical sciences. Since a SDE can generate unlimited numbers of trajectories, it is difficult to estimate model parameters based on experimental observations which may represent only one trajectory of the stochastic model. Although substantial research efforts have been made to develop effective methods, it is still a challenge to infer unknown parameters in SDE models from observations that may have large variations. Using an interest rate model as a test problem, in this work we use the Bayesian inference and Markov Chain Monte Carlo method to estimate unknown parameters in SDE models.

Lumping of degree-based mean-field and pair-approximation equations for multistate contact processes

Science.gov (United States)

Kyriakopoulos, Charalampos; Grossmann, Gerrit; Wolf, Verena; Bortolussi, Luca

2018-01-01

Contact processes form a large and highly interesting class of dynamic processes on networks, including epidemic and information-spreading networks. While devising stochastic models of such processes is relatively easy, analyzing them is very challenging from a computational point of view, particularly for large networks appearing in real applications. One strategy to reduce the complexity of their analysis is to rely on approximations, often in terms of a set of differential equations capturing the evolution of a random node, distinguishing nodes with different topological contexts (i.e., different degrees of different neighborhoods), such as degree-based mean-field (DBMF), approximate-master-equation (AME), or pair-approximation (PA) approaches. The number of differential equations so obtained is typically proportional to the maximum degree kmax of the network, which is much smaller than the size of the master equation of the underlying stochastic model, yet numerically solving these equations can still be problematic for large kmax. In this paper, we consider AME and PA, extended to cope with multiple local states, and we provide an aggregation procedure that clusters together nodes having similar degrees, treating those in the same cluster as indistinguishable, thus reducing the number of equations while preserving an accurate description of global observables of interest. We also provide an automatic way to build such equations and to identify a small number of degree clusters that give accurate results. The method is tested on several case studies, where it shows a high level of compression and a reduction of computational time of several orders of magnitude for large networks, with minimal loss in accuracy.

Market Efficiency of Oil Spot and Futures: A Stochastic Dominance Approach

NARCIS (Netherlands)

H.H. Lean (Hooi Hooi); M.J. McAleer (Michael); W.-K. Wong (Wing-Keung)

2010-01-01

textabstractThis paper examines the market efficiency of oil spot and futures prices by using a stochastic dominance (SD) approach. As there is no evidence of an SD relationship between oil spot and futures, we conclude that there is no arbitrage opportunity between these two markets, and that both

Mean Field Theory, Ginzburg Criterion, and Marginal Dimensionality of Phase-Transitions

DEFF Research Database (Denmark)

Als-Nielsen, Jens Aage; Birgenau, R. J.

1977-01-01

By applying a real space version of the Ginzburg criterion, the role of fluctuations and thence the self‐consistency of mean field theory are assessed in a simple fashion for a variety of phase transitions. It is shown that in using this approach the concept of ’’marginal dimensionality’’ emerges...... in a natural way. For example, it is shown that for many homogeneous structural transformations the marginal dimensionality is two, so that mean field theory will be valid for real three‐dimensional systems. It is suggested that this simple self‐consistent approach to Landau theory should be incorporated...

Merging Belief Propagation and the Mean Field Approximation

DEFF Research Database (Denmark)

Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro

2010-01-01

We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al., which allows to use the same objective function (Kullback-Leibler divergence......) as a starting point. In this method message passing fixed point equations (which correspond to the update rules in a message passing algorithm) are then obtained by imposing different region-based approximations and constraints on the mean field and belief propagation parts of the corresponding factor graph....... Our results can be applied, for example, to algorithms that perform joint channel estimation and decoding in iterative receivers. This is demonstrated in a simple example....

Nuclear collective vibrations in extended mean-field theory

Energy Technology Data Exchange (ETDEWEB)

Lacroix, D. [Lab. de Physique Corpusculaire/ ENSICAEN, 14 - Caen (France); Ayik, S. [Tennessee Technological Univ., Cookeville, TN (United States); Chomaz, Ph. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France)

2003-07-01

The extended mean-field theory, which includes both the incoherent dissipation mechanism due to nucleon-nucleon collisions and the coherent dissipation mechanism due to coupling to low-lying surface vibrations, is briefly reviewed. Expressions of the strength functions for the collective excitations are presented in the small amplitude limit of this approach. This fully microscopic theory is applied by employing effective Skyrme forces to various giant resonance excitations at zero and finite temperature. The theory is able to describe the gross properties of giant resonance excitations, the fragmentation of the strength distributions as well as their fine structure. At finite temperature, the success and limitations of this extended mean-field description are discussed. (authors)

Multi-Period Natural Gas Market Modeling. Applications, Stochastic Extensions and Solution Approaches

International Nuclear Information System (INIS)

Egging, R.G.

2010-11-01

This dissertation develops deterministic and stochastic multi-period mixed complementarity problems (MCP) for the global natural gas market, as well as solution approaches for large-scale stochastic MCP. The deterministic model is unique in the combination of the level of detail of the actors in the natural gas markets and the transport options, the detailed regional and global coverage, the multi-period approach with endogenous capacity expansions for transportation and storage infrastructure, the seasonal variation in demand and the representation of market power according to Nash-Cournot theory. The model is applied to several scenarios for the natural gas market that cover the formation of a cartel by the members of the Gas Exporting Countries Forum, a low availability of unconventional gas in the United States, and cost reductions in long-distance gas transportation. The results provide insights in how different regions are affected by various developments, in terms of production, consumption, traded volumes, prices and profits of market participants. The stochastic MCP is developed and applied to a global natural gas market problem with four scenarios for a time horizon until 2050 with nineteen regions and containing 78,768 variables. The scenarios vary in the possibility of a gas market cartel formation and varying depletion rates of gas reserves in the major gas importing regions. Outcomes for hedging decisions of market participants show some significant shifts in the timing and location of infrastructure investments, thereby affecting local market situations. A first application of Benders decomposition (BD) is presented to solve a large-scale stochastic MCP for the global gas market with many hundreds of first-stage capacity expansion variables and market players exerting various levels of market power. The largest problem solved successfully using BD contained 47,373 variables of which 763 first-stage variables, however using BD did not result in

The interpolation method of stochastic functions and the stochastic variational principle

International Nuclear Information System (INIS)

Liu Xianbin; Chen Qiu

1993-01-01

-order stochastic finite element equations are not very reasonable. On the other hand, Galerkin Method is hopeful, along with the method, the projection principle had been advanced to solve the stochastic operator equations. In Galerkin Method, by means of projecting the stochastic solution functions into the subspace of the solution function space, the treatment of the stochasticity of the structural physical properties and the loads is reasonable. However, the construction or the selection of the subspace of the solution function space which is a Hilbert Space of stochastic functions is difficult, and furthermore it is short of a reasonable rule to measure whether the approximation of the subspace to the solution function space is fine or not. In stochastic finite element method, the discretization of stochastic functions in space and time shows a very importance, so far, the discrete patterns consist of Local Average Theory, Interpolation Method and Orthogonal Expansion Method. Although the Local Average Theory has already been a success in the stationary random fields, it is not suitable for the non-stationary ones as well. For the general stochastic functions, whether it is stationary or not, interpolation method is available. In the present paper, the authors have shown that the error between the true solution function and its approximation, its projection in the subspace, depends continuously on the errors between the stochastic functions and their interpolation functions, the latter rely continuously on the scales of the discrete elements; so a conclusion can be obtained that the Interpolation method of stochastic functions is convergent. That is to say that the approximation solution functions would limit to the true solution functions when the scales of the discrete elements goes smaller and smaller. Using the Interpolation method, a basis of subspace of the solution function space is constructed in this paper, and by means of combining the projection principle and

Perturbative approach to non-Markovian stochastic Schroedinger equations

International Nuclear Information System (INIS)

Gambetta, Jay; Wiseman, H.M.

2002-01-01

In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian stochastic Schroedinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are presented for a classically driven two-level atom immersed in an environment with a simple memory function. It is observed that as the order of the perturbation is increased the numerical results for the ensemble average state ρ red (t) approach the exact reduced state found via Imamog-barlu ' s enlarged system method [Phys. Rev. A 50, 3650 (1994)

Stochastic description of heterogeneities of permeability within groundwater flow models

International Nuclear Information System (INIS)

Cacas, M.C.; Lachassagne, P.; Ledoux, E.; Marsily, G. de

1991-01-01

In order to model radionuclide migration in the geosphere realistically at the field scale, the hydrogeologist needs to be able to simulate groundwater flow in heterogeneous media. Heterogeneity of the medium can be described using a stochastic approach, that affects the way in which a flow model is formulated. In this paper, we discuss the problems that we have encountered in modelling both continuous and fractured media. The stochastic approach leads to a methodology that enables local measurements of permeability to be integrated into a model which gives a good prediction of groundwater flow on a regional scale. 5 Figs.; 8 Refs

Magnetic moments in present relativistic nuclear theories: a mean-field problem

International Nuclear Information System (INIS)

Desplanques, B.

1986-07-01

We show that the magnetic moments of LS closed shell nuclei plus or minus one nucleon derived from non-relativistic Hartree-Fock mean-fields are as bad as those obtained in relativistic approaches of nuclear structure. Deviations with respect to more complete results in both cases are ascribed to the mean-field approximation which neglects some degrees of freedom in the nucleus description. 18 refs

Dynamic-Programming Approaches to Single- and Multi-Stage Stochastic Knapsack Problems for Portfolio Optimization

National Research Council Canada - National Science Library

Khoo, Wai

1999-01-01

.... These problems model stochastic portfolio optimization problems (SPOPs) which assume deterministic unit weight, and normally distributed unit return with known mean and variance for each item type...

Extended Deterministic Mean-Field Games

KAUST Repository

Gomes, Diogo A.

2016-04-21

In this paper, we consider mean-field games where the interaction of each player with the mean field takes into account not only the states of the players but also their collective behavior. To do so, we develop a random variable framework that is particularly convenient for these problems. We prove an existence result for extended mean-field games and establish uniqueness conditions. In the last section, we consider the Master Equation and discuss properties of its solutions.

Extended Deterministic Mean-Field Games

KAUST Repository

Gomes, Diogo A.; Voskanyan, Vardan K.

2016-01-01

In this paper, we consider mean-field games where the interaction of each player with the mean field takes into account not only the states of the players but also their collective behavior. To do so, we develop a random variable framework that is particularly convenient for these problems. We prove an existence result for extended mean-field games and establish uniqueness conditions. In the last section, we consider the Master Equation and discuss properties of its solutions.

Modelling of diesel spray flame under engine-like conditions using an accelerated eulerian stochastic fields method: A convergence study of the number of stochastic fields

OpenAIRE

Pang, Kar Mun; Jangi, Mehdi; Bai, X.-S.; Schramm, Jesper; Walther, Jens Honore

2016-01-01

The use of transported Probability Density Function(PDF) methods allows a single model to compute the autoignition, premixed mode and diffusion flame of diesel combustion under engine-like conditions [1,2]. The Lagrangian particle based transported PDF models have been validated across a wide range of conditions [2,3]. Alternatively, the transported PDF model can also be formulated in the Eulerian framework[4]. The Eulerian PDF is commonly known as the Eulerian Stochastic Fields (ESF) model. ...

A unified approach to stochastic integration on the real line

DEFF Research Database (Denmark)

Basse-O'Connor, Andreas; Graversen, Svend-Erik; Pedersen, Jan

Stochastic integration on the predictable σ-field with respect to σ-finite L0-valued measures, also known as formal semimartingales, is studied. In particular, the triplet of such measures is introduced and used to characterize the set of integrable processes. Special attention is given to Lévy...... processes indexed by the real line. Surprisingly, many of the basic properties break down in this situation compared to the usual R+ case....

Intimate Partner Violence: A Stochastic Model.

Science.gov (United States)

Guidi, Elisa; Meringolo, Patrizia; Guazzini, Andrea; Bagnoli, Franco

2017-01-01

Intimate partner violence (IPV) has been a well-studied problem in the past psychological literature, especially through its classical methodology such as qualitative, quantitative and mixed methods. This article introduces two basic stochastic models as an alternative approach to simulate the short and long-term dynamics of a couple at risk of IPV. In both models, the members of the couple may assume a finite number of states, updating them in a probabilistic way at discrete time steps. After defining the transition probabilities, we first analyze the evolution of the couple in isolation and then we consider the case in which the individuals modify their behavior depending on the perceived violence from other couples in their environment or based on the perceived informal social support. While high perceived violence in other couples may converge toward the own presence of IPV by means a gender-specific transmission, the gender differences fade-out in the case of received informal social support. Despite the simplicity of the two stochastic models, they generate results which compare well with past experimental studies about IPV and they give important practical implications for prevention intervention in this field. Copyright: © 2016 by Fabrizio Serra editore, Pisa · Roma.

Backward stochastic differential equations from linear to fully nonlinear theory

CERN Document Server

Zhang, Jianfeng

2017-01-01

This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.

Time independent mean-field theory

International Nuclear Information System (INIS)

Negele, J.W.

1980-02-01

The physical and theoretical motivations for the time-dependent mean-field theory are presented, and the successes and limitations of the time-dependent Hartree-Fock initial-vaue problem are reviewed. New theoretical developments are described in the treatment of two-body correlations and the formulation of a quantum mean-field theory of large-amplitude collective motion and tunneling decay. Finally, the mean-field theory is used to obtain new insights into the phenomenon of pion condensation in finite nuclei. 18 figures

Whole-field visual motion drives swimming in larval zebrafish via a stochastic process.

Science.gov (United States)

Portugues, Ruben; Haesemeyer, Martin; Blum, Mirella L; Engert, Florian

2015-05-01

Caudo-rostral whole-field visual motion elicits forward locomotion in many organisms, including larval zebrafish. Here, we investigate the dependence on the latency to initiate this forward swimming as a function of the speed of the visual motion. We show that latency is highly dependent on speed for slow speeds (1.5 s, which is much longer than neuronal transduction processes. What mechanisms underlie these long latencies? We propose two alternative, biologically inspired models that could account for this latency to initiate swimming: an integrate and fire model, which is history dependent, and a stochastic Poisson model, which has no history dependence. We use these models to predict the behavior of larvae when presented with whole-field motion of varying speed and find that the stochastic process shows better agreement with the experimental data. Finally, we discuss possible neuronal implementations of these models. © 2015. Published by The Company of Biologists Ltd.

Functional differential equation approach to the large N expansion and mean field perturbation theory

International Nuclear Information System (INIS)

Bender, C.M.; Cooper, F.

1985-01-01

An apparent difference between formulating mean field perturbation theory for lambdaphi 4 field theory via path integrals or via functional differential equations when there are external sources present is shown not to exist when mean field theory is considered as the N = 1 limit of the 0(N)lambdaphi 4 field theory. A simply method is given for determining the 1/N expansion for the Green's functions in the presence of external sources by directly solving the functional differential equations order by order in 1/N. The 1/N expansion for the effective action GAMMA(phi,chi) is obtained by directly integrating the functional differential equations for the fields phi and chi (equivalent1/2lambda/Nphi/sub α/phi/sup α/-μ 2 ) in the presence of two external sources j = -deltaGAMMA/deltaphi, S = -deltaGAMMA/deltachi

Stochastic processes and quantum theory

International Nuclear Information System (INIS)

Klauder, J.R.

1975-01-01

The author analyses a variety of stochastic processes, namely real time diffusion phenomena, which are analogues of imaginary time quantum theory and convariant imaginary time quantum field theory. He elaborates some standard properties involving probability measures and stochastic variables and considers a simple class of examples. Finally he develops the fact that certain stochastic theories actually exhibit divergences that simulate those of covariant quantum field theory and presents examples of both renormaizable and unrenormalizable behavior. (V.J.C.)

The field theory approach to percolation processes

International Nuclear Information System (INIS)

Janssen, Hans-Karl; Taeuber, Uwe C.

2005-01-01

We review the field theory approach to percolation processes. Specifically, we focus on the so-called simple and general epidemic processes that display continuous non-equilibrium active to absorbing state phase transitions whose asymptotic features are governed, respectively, by the directed (DP) and dynamic isotropic percolation (dIP) universality classes. We discuss the construction of a field theory representation for these Markovian stochastic processes based on fundamental phenomenological considerations, as well as from a specific microscopic reaction-diffusion model realization. Subsequently we explain how dynamic renormalization group (RG) methods can be applied to obtain the universal properties near the critical point in an expansion about the upper critical dimensions d c = 4 (DP) and 6 (dIP). We provide a detailed overview of results for critical exponents, scaling functions, crossover phenomena, finite-size scaling, and also briefly comment on the influence of long-range spreading, the presence of a boundary, multispecies generalizations, coupling of the order parameter to other conserved modes, and quenched disorder

Functional stochastic differential equations: mathematical theory of nonlinear parabolic systems with applications in field theory and statistical mechanics

International Nuclear Information System (INIS)

Doering, C.R.

1985-01-01

Applications of nonlinear parabolic stochastic differential equations with additive colored noise in equilibrium and nonequilibrium statistical mechanics and quantum field theory are developed in detail, providing a new unified mathematical approach to many problems. The existence and uniqueness of solutions to these equations is established, and some of the properties of the solutions are investigated. In particular, asymptotic expansions for the correlation functions of the solutions are introduced and compared to rigorous nonperturbative bounds on the moments. It is found that the perturbative analysis is in qualitative disagreement with the exact result in models corresponding to cut-off self-interacting nonperturbatively renormalizable scalar quantum field theories. For these theories the nonlinearities cannot be considered as perturbations of the linearized theory

Stochastic resonance and vibrational resonance in an excitable system: The golden mean barrier

International Nuclear Information System (INIS)

Stan, Cristina; Cristescu, C.P.; Alexandroaei, D.; Agop, M.

2009-01-01

We report on stochastic resonance and vibrational resonance in an electric charge double layer configuration as usually found in electrical discharges, biological cell membranes, chemical systems and nanostructures. The experiment and numerical computation show the existence of a barrier expressible in terms of the golden mean above which the two phenomena do not take place. We consider this as new evidence for the importance of the golden mean criticality in the oscillatory dynamics, in agreement with El Naschie's E-infinity theory. In our experiment, the dynamics of a charge double layer generated in the inter-anode space of a twin electrical discharge is investigated under noise-harmonic and harmonic-harmonic perturbations. In the first case, a Gaussian noise can enhance the response of the system to a weak injected periodic signal, a clear mark of stochastic resonance. In the second case, similar enhancement can appear if the noise is replaced by a harmonic perturbation with a frequency much higher than the frequency of the weak oscillation. The amplitude of the low frequency oscillation shows a maximum versus the amplitude of the high frequency perturbation demonstrating vibrational resonance. In order to model these dynamics, we derived an excitable system by modifying a biased van der Pol oscillator. The computational study considers the behaviour of this system under the same types of perturbation as in the experimental investigations and is found to give consistent results in both situations.

Recent advances in ambit stochastics with a view towards tempo-spatial stochastic volatility/intermittency

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole E.; Benth, Fred Espen; Veraart, Almut

Ambit stochastics is the name for the theory and applications of ambit fields and ambit processes and constitutes a new research area in stochastics for tempo-spatial phenomena. This paper gives an overview of the main findings in ambit stochastics up to date and establishes new results on genera...

SU-F-T-182: A Stochastic Approach to Daily QA Tolerances On Spot Properties for Proton Pencil Beam Scanning

International Nuclear Information System (INIS)

St James, S; Bloch, C; Saini, J

2016-01-01

Purpose: Proton pencil beam scanning is used clinically across the United States. There are no current guidelines on tolerances for daily QA specific to pencil beam scanning, specifically related to the individual spot properties (spot width). Using a stochastic method to determine tolerances has the potential to optimize tolerances on individual spots and decrease the number of false positive failures in daily QA. Individual and global spot tolerances were evaluated. Methods: As part of daily QA for proton pencil beam scanning, a field of 16 spots (corresponding to 8 energies) is measured using an array of ion chambers (Matrixx, IBA). Each individual spot is fit to two Gaussian functions (x,y). The spot width (σ) in × and y are recorded (32 parameters). Results from the daily QA were retrospectively analyzed for 100 days of data. The deviations of the spot widths were histogrammed and fit to a Gaussian function. The stochastic spot tolerance was taken to be the mean ± 3σ. Using these results, tolerances were developed and tested against known deviations in spot width. Results: The individual spot tolerances derived with the stochastic method decreased in 30/32 instances. Using the previous tolerances (± 20% width), the daily QA would have detected 0/20 days of the deviation. Using a tolerance of any 6 spots failing the stochastic tolerance, 18/20 days of the deviation would have been detected. Conclusion: Using a stochastic method we have been able to decrease daily tolerances on the spot widths for 30/32 spot widths measured. The stochastic tolerances can lead to detection of deviations that previously would have been picked up on monthly QA and missed by daily QA. This method could be easily extended for evaluation of other QA parameters in proton spot scanning.

A stochastic approach to the derivation of exemption and clearance levels

International Nuclear Information System (INIS)

Deckert, A.

1997-01-01

Deciding what clearance levels are appropriate for a particular waste stream inherently involves a number of uncertainties. Some of these uncertainties can be quantified using stochastic modeling techniques, which can aid the process of decision making. In this presentation the German approach to dealing with the uncertainties involved in setting clearance levels is addressed. (author)

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

Shapes and dynamics from the time-dependent mean field

International Nuclear Information System (INIS)

Stevenson, P.D.; Goddard, P.M.; Rios, A.

2015-01-01

Explaining observed properties in terms of underlying shape degrees of freedom is a well-established prism with which to understand atomic nuclei. Self-consistent mean-field models provide one tool to understand nuclear shapes, and their link to other nuclear properties and observables. We present examples of how the time-dependent extension of the mean-field approach can be used in particular to shed light on nuclear shape properties, particularly looking at the giant resonances built on deformed nuclear ground states, and at dynamics in highly-deformed fission isomers. Example calculations are shown of 28 Si in the first case, and 240 Pu in the latter case

Internal additive noise effects in stochastic resonance using organic field effect transistor

Energy Technology Data Exchange (ETDEWEB)

Suzuki, Yoshiharu; Asakawa, Naoki [Division of Molecular Science, Graduate School of Science and Technology, Gunma University, 1-5-1 Tenjin-cho, Kiryu, Gunma 376-8515 (Japan); Matsubara, Kiyohiko [KOOROGI LLC, 6-1585-1-B Sakaino-cho, Kiryu, Gunma 376-0002 (Japan)

2016-08-29

Stochastic resonance phenomenon was observed in organic field effect transistor using poly(3-hexylthiophene), which enhances performance of signal transmission with application of noise. The enhancement of correlation coefficient between the input and output signals was low, and the variation of correlation coefficient was not remarkable with respect to the intensity of external noise, which was due to the existence of internal additive noise following the nonlinear threshold response. In other words, internal additive noise plays a positive role on the capability of approximately constant signal transmission regardless of noise intensity, which can be said “homeostatic” behavior or “noise robustness” against external noise. Furthermore, internal additive noise causes emergence of the stochastic resonance effect even on the threshold unit without internal additive noise on which the correlation coefficient usually decreases monotonically.

Relativistic mean-field mass models

Energy Technology Data Exchange (ETDEWEB)

Pena-Arteaga, D.; Goriely, S.; Chamel, N. [Universite Libre de Bruxelles, Institut d' Astronomie et d' Astrophysique, CP-226, Brussels (Belgium)

2016-10-15

We present a new effort to develop viable mass models within the relativistic mean-field approach with density-dependent meson couplings, separable pairing and microscopic estimations for the translational and rotational correction energies. Two interactions, DD-MEB1 and DD-MEB2, are fitted to essentially all experimental masses, and also to charge radii and infinite nuclear matter properties as determined by microscopic models using realistic interactions. While DD-MEB1 includes the σ, ω and ρ meson fields, DD-MEB2 also considers the δ meson. Both mass models describe the 2353 experimental masses with a root mean square deviation of about 1.1 MeV and the 882 measured charge radii with a root mean square deviation of 0.029 fm. In addition, we show that the Pb isotopic shifts and moments of inertia are rather well reproduced, and the equation of state in pure neutron matter as well as symmetric nuclear matter are in relatively good agreement with existing realistic calculations. Both models predict a maximum neutron-star mass of more than 2.6 solar masses, and thus are able to accommodate the heaviest neutron stars observed so far. However, the new Lagrangians, like all previously determined RMF models, present the drawback of being characterized by a low effective mass, which leads to strong shell effects due to the strong coupling between the spin-orbit splitting and the effective mass. Complete mass tables have been generated and a comparison with other mass models is presented. (orig.)

The application of mean field theory to image motion estimation.

Science.gov (United States)

Zhang, J; Hanauer, G G

1995-01-01

Previously, Markov random field (MRF) model-based techniques have been proposed for image motion estimation. Since motion estimation is usually an ill-posed problem, various constraints are needed to obtain a unique and stable solution. The main advantage of the MRF approach is its capacity to incorporate such constraints, for instance, motion continuity within an object and motion discontinuity at the boundaries between objects. In the MRF approach, motion estimation is often formulated as an optimization problem, and two frequently used optimization methods are simulated annealing (SA) and iterative-conditional mode (ICM). Although the SA is theoretically optimal in the sense of finding the global optimum, it usually takes many iterations to converge. The ICM, on the other hand, converges quickly, but its results are often unsatisfactory due to its "hard decision" nature. Previously, the authors have applied the mean field theory to image segmentation and image restoration problems. It provides results nearly as good as SA but with much faster convergence. The present paper shows how the mean field theory can be applied to MRF model-based motion estimation. This approach is demonstrated on both synthetic and real-world images, where it produced good motion estimates.

Existence of optimal controls for systems governed by mean-field ...

African Journals Online (AJOL)

In this paper, we study the existence of an optimal control for systems, governed by stochastic dierential equations of mean-eld type. For non linear systems, we prove the existence of an optimal relaxed control, by using tightness techniques and Skorokhod selection theorem. The optimal control is a measure valued process ...

Stochastic electron dynamics due to drift waves in a sheared magnetic field and other drift motion problems

International Nuclear Information System (INIS)

Robertson, J.A.

1986-12-01

Electron motion in a single electrostatic wave in a sheared magnetic field is shown to become stochastic in the presence of a second wave at an amplitude well below that obtained from the overlapping pendulum resonance approximation. The enhanced stochasticity occurs for low parallel velocity electrons for which the parallel trapping motion from eE/sub parallel//m interacts strongly with the E x B trapping motion due to the presence of magnetic shear. The guiding-center equations for single particle electron orbits in given fields are investigated using both analytical and numerical techniques. The model assumes a slab magnetic field geometry with shear and two electrostatic plane waves propagating at an angle with respect to each other. Collisions and the self-consistent effect of the electron motion upon the fields are ignored. The guiding-center motion in an inertial reference frame moving in phase with the two waves is given by a two degree-of-freedom, autonomous Hamiltonian system. The single wave particle motion may be reduced to a two parameter family of one degree-of-freedom Hamiltonians which bifurcate from a pendulum phase space to a topology with three chains of elliptic and hyperbolic fixed points separated in radius about the mode-rational surface. In the presence of a perturbing wave with a different helicity, electrons in the small parallel velocity regime become stochastic at an amplitude scaling as the fourth root of the wave potential. The results obtained for stochastic motion apply directly to the problem of electron diffusion in drift waves occurring in toroidal fusion confinement devices. The effect of an adiabatically changing radial electric field upon guiding-center orbits in tokamaks is also investigated. This perturbation causes a radial polarization drift of trapped particle tokamak orbits

Multi-period natural gas market modeling Applications, stochastic extensions and solution approaches

Science.gov (United States)

Egging, Rudolf Gerardus

This dissertation develops deterministic and stochastic multi-period mixed complementarity problems (MCP) for the global natural gas market, as well as solution approaches for large-scale stochastic MCP. The deterministic model is unique in the combination of the level of detail of the actors in the natural gas markets and the transport options, the detailed regional and global coverage, the multi-period approach with endogenous capacity expansions for transportation and storage infrastructure, the seasonal variation in demand and the representation of market power according to Nash-Cournot theory. The model is applied to several scenarios for the natural gas market that cover the formation of a cartel by the members of the Gas Exporting Countries Forum, a low availability of unconventional gas in the United States, and cost reductions in long-distance gas transportation. 1 The results provide insights in how different regions are affected by various developments, in terms of production, consumption, traded volumes, prices and profits of market participants. The stochastic MCP is developed and applied to a global natural gas market problem with four scenarios for a time horizon until 2050 with nineteen regions and containing 78,768 variables. The scenarios vary in the possibility of a gas market cartel formation and varying depletion rates of gas reserves in the major gas importing regions. Outcomes for hedging decisions of market participants show some significant shifts in the timing and location of infrastructure investments, thereby affecting local market situations. A first application of Benders decomposition (BD) is presented to solve a large-scale stochastic MCP for the global gas market with many hundreds of first-stage capacity expansion variables and market players exerting various levels of market power. The largest problem solved successfully using BD contained 47,373 variables of which 763 first-stage variables, however using BD did not result in

Dependence of synchronization transitions on mean field approach in two-way coupled neural system

Science.gov (United States)

Shi, J. C.; Luo, M.; Huang, C. S.

2018-03-01

This work investigates the synchronization transitions in two-way coupled neural system by mean field approach. Results show that, there exists a critical noise intensity for the synchronization transitions, i.e., above (or below) the critical noise intensity, the synchronization transitions are decreased (or hardly change) with increasing the noise intensity. Meanwhile, the heterogeneity effect plays a negative role for the synchronization transitions, and above critical coupling strength, the heterogeneity effect on synchronization transitions can be negligible. Furthermore, when an external signal is introduced into the coupled system, the novel frequency-induced and amplitude-induced synchronization transitions are found, and there exist an optimal frequency and an optimal amplitude of external signal which makes the system to display the best synchronization transitions. In particular, it is observed that the synchronization transitions can not be further affected above critical frequency of external signal.

Mean-field approximations of fixation time distributions of evolutionary game dynamics on graphs

Science.gov (United States)

Ying, Li-Min; Zhou, Jie; Tang, Ming; Guan, Shu-Guang; Zou, Yong

2018-02-01

The mean fixation time is often not accurate for describing the timescales of fixation probabilities of evolutionary games taking place on complex networks. We simulate the game dynamics on top of complex network topologies and approximate the fixation time distributions using a mean-field approach. We assume that there are two absorbing states. Numerically, we show that the mean fixation time is sufficient in characterizing the evolutionary timescales when network structures are close to the well-mixing condition. In contrast, the mean fixation time shows large inaccuracies when networks become sparse. The approximation accuracy is determined by the network structure, and hence by the suitability of the mean-field approach. The numerical results show good agreement with the theoretical predictions.

A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances

International Nuclear Information System (INIS)

Wang Yao; Wang Zidong; Liang Jinling

2008-01-01

In this Letter, the synchronization problem is investigated for a class of stochastic complex networks with time delays. By utilizing a new Lyapunov functional form based on the idea of 'delay fractioning', we employ the stochastic analysis techniques and the properties of Kronecker product to establish delay-dependent synchronization criteria that guarantee the globally asymptotically mean-square synchronization of the addressed delayed networks with stochastic disturbances. These sufficient conditions, which are formulated in terms of linear matrix inequalities (LMIs), can be solved efficiently by the LMI toolbox in Matlab. The main results are proved to be much less conservative and the conservatism could be reduced further as the number of delay fractioning gets bigger. A simulation example is exploited to demonstrate the advantage and applicability of the proposed result

Stochastic Finite Elements in Reliability-Based Structural Optimization

DEFF Research Database (Denmark)

Sørensen, John Dalsgaard; Engelund, S.

Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...

Electron heat transport in stochastic magnetic layer

International Nuclear Information System (INIS)

Becoulet, M.; Ghendrih, Ph.; Capes, H.; Grosman, A.

1999-06-01

Progress in the theoretical understanding of the local behaviour of the temperature field in ergodic layer was done in the framework of quasi-linear approach but this quasi-linear theory was not complete since the resonant modes coupling (due to stochasticity) was neglected. The stochastic properties of the magnetic field in the ergodic zone are now taken into account by a non-linear coupling of the temperature modes. The three-dimension heat transfer modelling in the ergodic-divertor configuration is performed by quasi-linear (ERGOT1) and non-linear (ERGOT2) numerical codes. The formalism and theoretical basis of both codes are presented. The most important effect that can be simulated with non-linear code is the averaged temperature profile flattening that occurs in the ergodic zone and the barrier creation that appears near the separatrix during divertor operation. (A.C.)

Calculation of large scale relative permeabilities from stochastic properties of the permeability field and fluid properties

Energy Technology Data Exchange (ETDEWEB)

Lenormand, R.; Thiele, M.R. [Institut Francais du Petrole, Rueil Malmaison (France)

1997-08-01

The paper describes the method and presents preliminary results for the calculation of homogenized relative permeabilities using stochastic properties of the permeability field. In heterogeneous media, the spreading of an injected fluid is mainly sue to the permeability heterogeneity and viscosity fingering. At large scale, when the heterogeneous medium is replaced by a homogeneous one, we need to introduce a homogenized (or pseudo) relative permeability to obtain the same spreading. Generally, is derived by using fine-grid numerical simulations (Kyte and Berry). However, this operation is time consuming and cannot be performed for all the meshes of the reservoir. We propose an alternate method which uses the information given by the stochastic properties of the field without any numerical simulation. The method is based on recent developments on homogenized transport equations (the {open_quotes}MHD{close_quotes} equation, Lenormand SPE 30797). The MHD equation accounts for the three basic mechanisms of spreading of the injected fluid: (1) Dispersive spreading due to small scale randomness, characterized by a macrodispersion coefficient D. (2) Convective spreading due to large scale heterogeneities (layers) characterized by a heterogeneity factor H. (3) Viscous fingering characterized by an apparent viscosity ration M. In the paper, we first derive the parameters D and H as functions of variance and correlation length of the permeability field. The results are shown to be in good agreement with fine-grid simulations. The are then derived a function of D, H and M. The main result is that this approach lead to a time dependent . Finally, the calculated are compared to the values derived by history matching using fine-grid numerical simulations.

Stochastic diffusion of dust grains by the interplanetary magnetic field

International Nuclear Information System (INIS)

Hassan, M.H.A.; Wallis, M.K.

1983-10-01

The effects of the sectored Interplanetary Magnetic Field on charged dust grains orbiting around the sun under radiation pressure and Poynting-Robertson drag forces are examined for initially circular and non-inclined orbits. The distribution function of the charged grains satisfies a Fokker-Planck equation in which the sectored field is taken as a source of stochastic impulses. By adopting the integrals of the impulse-free motion as variable parameters, the Fokker-Planck equation can be properly treated as a diffusion equation. Analytic solutions of the resulting diffusion equation show that dust grains injected near the ecliptic plane are scattered strongly to high helio-latitudes. The scattering is more pronounced for small grains injected at large distances from the Sun. (author)

Stochastic Watershed Models for Risk Based Decision Making

Science.gov (United States)

Vogel, R. M.

2017-12-01

Over half a century ago, the Harvard Water Program introduced the field of operational or synthetic hydrology providing stochastic streamflow models (SSMs), which could generate ensembles of synthetic streamflow traces useful for hydrologic risk management. The application of SSMs, based on streamflow observations alone, revolutionized water resources planning activities, yet has fallen out of favor due, in part, to their inability to account for the now nearly ubiquitous anthropogenic influences on streamflow. This commentary advances the modern equivalent of SSMs, termed `stochastic watershed models' (SWMs) useful as input to nearly all modern risk based water resource decision making approaches. SWMs are deterministic watershed models implemented using stochastic meteorological series, model parameters and model errors, to generate ensembles of streamflow traces that represent the variability in possible future streamflows. SWMs combine deterministic watershed models, which are ideally suited to accounting for anthropogenic influences, with recent developments in uncertainty analysis and principles of stochastic simulation

Pedestrian Flow in the Mean Field Limit

KAUST Repository

Haji Ali, Abdul Lateef

2012-11-01

We study the mean-field limit of a particle-based system modeling the behavior of many indistinguishable pedestrians as their number increases. The base model is a modified version of Helbing\\'s social force model. In the mean-field limit, the time-dependent density of two-dimensional pedestrians satisfies a four-dimensional integro-differential Fokker-Planck equation. To approximate the solution of the Fokker-Planck equation we use a time-splitting approach and solve the diffusion part using a Crank-Nicholson method. The advection part is solved using a Lax-Wendroff-Leveque method or an upwind Backward Euler method depending on the advection speed. Moreover, we use multilevel Monte Carlo to estimate observables from the particle-based system. We discuss these numerical methods, and present numerical results showing the convergence of observables that were calculated using the particle-based model as the number of pedestrians increases to those calculated using the probability density function satisfying the Fokker-Planck equation.

Synthetic Sediments and Stochastic Groundwater Hydrology

Science.gov (United States)

Wilson, J. L.

2002-12-01

For over twenty years the groundwater community has pursued the somewhat elusive goal of describing the effects of aquifer heterogeneity on subsurface flow and chemical transport. While small perturbation stochastic moment methods have significantly advanced theoretical understanding, why is it that stochastic applications use instead simulations of flow and transport through multiple realizations of synthetic geology? Allan Gutjahr was a principle proponent of the Fast Fourier Transform method for the synthetic generation of aquifer properties and recently explored new, more geologically sound, synthetic methods based on multi-scale Markov random fields. Focusing on sedimentary aquifers, how has the state-of-the-art of synthetic generation changed and what new developments can be expected, for example, to deal with issues like conceptual model uncertainty, the differences between measurement and modeling scales, and subgrid scale variability? What will it take to get stochastic methods, whether based on moments, multiple realizations, or some other approach, into widespread application?

Collective enhancement of inclusive cross sections at large transverse momentum in stochastic-field multiparticle theory

International Nuclear Information System (INIS)

Arnold, R.C.

1976-01-01

A stochastic-field calculus, previously discussed in connection with Regge intercepts and instability questions, is applied to inclusive cross sections, and is shown to predict a growth with energy of large-P/perpendicular/ to inclusives

Structural factoring approach for analyzing stochastic networks

Science.gov (United States)

Hayhurst, Kelly J.; Shier, Douglas R.

1991-01-01

The problem of finding the distribution of the shortest path length through a stochastic network is investigated. A general algorithm for determining the exact distribution of the shortest path length is developed based on the concept of conditional factoring, in which a directed, stochastic network is decomposed into an equivalent set of smaller, generally less complex subnetworks. Several network constructs are identified and exploited to reduce significantly the computational effort required to solve a network problem relative to complete enumeration. This algorithm can be applied to two important classes of stochastic path problems: determining the critical path distribution for acyclic networks and the exact two-terminal reliability for probabilistic networks. Computational experience with the algorithm was encouraging and allowed the exact solution of networks that have been previously analyzed only by approximation techniques.

Relativistic mean field calculations in neutron-rich nuclei

Energy Technology Data Exchange (ETDEWEB)

Gangopadhyay, G.; Bhattacharya, Madhubrata [Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700 009 (India); Roy, Subinit [Saha Institute of Nuclear Physics, Block AF, Sector 1, Kolkata- 700 064 (India)

2014-08-14

Relativistic mean field calculations have been employed to study neutron rich nuclei. The Lagrange's equations have been solved in the co-ordinate space. The effect of the continuum has been effectively taken into account through the method of resonant continuum. It is found that BCS approximation performs as well as a more involved Relativistic Continuum Hartree Bogoliubov approach. Calculations reveal the possibility of modification of magic numbers in neutron rich nuclei. Calculation for low energy proton scattering cross sections shows that the present approach reproduces the density in very light neutron rich nuclei.

Optimal Integration of Intermittent Renewables: A System LCOE Stochastic Approach

Directory of Open Access Journals (Sweden)

Carlo Lucheroni

2018-03-01

Full Text Available We propose a system level approach to value the impact on costs of the integration of intermittent renewable generation in a power system, based on expected breakeven cost and breakeven cost risk. To do this, we carefully reconsider the definition of Levelized Cost of Electricity (LCOE when extended to non-dispatchable generation, by examining extra costs and gains originated by the costly management of random power injections. We are thus lead to define a ‘system LCOE’ as a system dependent LCOE that takes properly into account intermittent generation. In order to include breakeven cost risk we further extend this deterministic approach to a stochastic setting, by introducing a ‘stochastic system LCOE’. This extension allows us to discuss the optimal integration of intermittent renewables from a broad, system level point of view. This paper thus aims to provide power producers and policy makers with a new methodological scheme, still based on the LCOE but which updates this valuation technique to current energy system configurations characterized by a large share of non-dispatchable production. Quantifying and optimizing the impact of intermittent renewables integration on power system costs, risk and CO 2 emissions, the proposed methodology can be used as powerful tool of analysis for assessing environmental and energy policies.

Dynamical chaos of nonabelian gauge fields

Energy Technology Data Exchange (ETDEWEB)

Matinyan, S G

1985-01-01

A special class of the Yang - Mills field-the spatially homogeneous fields (Yan - Mills classical mechanics)-having no analog in the linear abelian electrodynamics is studied. Both the computer and analytical approaches show that such fields possess dynamical stochasticity, this allowing one to claim that the Yang - Mills classical equations without external sources represent a non-integrable system. The Higgs mechanism eliminates this stochasticity: at some expectation value of scalar field, a phase transition of disorder-order (confinement-deconfinement) type takes plce. The system with external sources behaves apparently analogously. A relation of the discovered stochasticity with the dimensional reduction mechanism in the macroscopic systems as well as with colour confinement is considered. It is shown that the presence of the random (Gaussian) currents in vacuum leads to confinement of fields generated by those currents. Attention is paid to the possible manifestation of the revealed stochasticity of the classical non-abelian gauge fields in the multiple hadrnoproduction processes which apparently reflect the universal stochastic regularities typical of the systems of quite different nature.

Dynamical chaos of nonabelian gauge fields

International Nuclear Information System (INIS)

Matinyan, S.G.

1985-01-01

A special class of the Yang - Mills field-the spatially homogeneous fields (Yan - Mills classical mechanics)-having no analog in the linear abelian electrodynamics is studied. Both the computer and analytical approaches show that such fields possess dynamical stochasticity, this allowing one to claim that the Yang - Mills classical equations without external sources represent a non-integrable system. The Higgs mechanism eliminates this stochasticity: at some expectation value of scalar field, a phase transition of disorder-order (confinement-deconfinement) type takes plce. The system with external sources behaves apparently analogously. A relation of the discovered stochasticity with the dimensional reduction mechanism in the macroscopic systems as well as with colour confinement is considered. It is shown that the presence of the random (Gaussian) currents in vacuum leads to confinement of fields generated by those currents. Attention is paid to the possible manifestation of the revealed stochasticity of the classical non-abelian gauge fields in the multiple hadrnoproduction processes which apparently reflect the universal stochastic regularities typical of the systems of quite different nature

Modelling and application of stochastic processes

CERN Document Server

1986-01-01

The subject of modelling and application of stochastic processes is too vast to be exhausted in a single volume. In this book, attention is focused on a small subset of this vast subject. The primary emphasis is on realization and approximation of stochastic systems. Recently there has been considerable interest in the stochastic realization problem, and hence, an attempt has been made here to collect in one place some of the more recent approaches and algorithms for solving the stochastic realiza­ tion problem. Various different approaches for realizing linear minimum-phase systems, linear nonminimum-phase systems, and bilinear systems are presented. These approaches range from time-domain methods to spectral-domain methods. An overview of the chapter contents briefly describes these approaches. Also, in most of these chapters special attention is given to the problem of developing numerically ef­ ficient algorithms for obtaining reduced-order (approximate) stochastic realizations. On the application side,...

Stochastic Discount Factor Approach to International Risk-Sharing:A Robustness Check of the Bilateral Setting

NARCIS (Netherlands)

Hadzi-Vaskov, M.; Kool, C.J.M.

2007-01-01

This paper presents a robustness check of the stochastic discount factor approach to international (bilateral) risk-sharing given in Brandt, Cochrane, and Santa-Clara (2006). We demonstrate two main inherent limitations of the bilateral SDF approach to international risk-sharing. First, the discount

Autonomously responsive pumping by a bacterial flagellar forest: A mean-field approach

Science.gov (United States)

Martindale, James D.; Fu, Henry C.

2017-09-01

This study is motivated by a microfluidic device that imparts a magnetic torque on an array of bacterial flagella. Bacterial flagella can transform their helical geometry autonomously in response to properties of the background fluid, which provides an intriguing mechanism allowing their use as an engineered element for the regulation or transport of chemicals in microscale applications. The synchronization of flagellar phase has been widely studied in biological contexts, but here we examine the synchronization of flagellar tilt, which is necessary for effective pumping. We first examine the effects of helical geometry and tilt on the pumping flows generated by a single rotating flagellum. Next, we explore a mean-field model for an array of helical flagella to understand how collective tilt arises and influences pumping. The mean-field methodology allows us to take into account possible phase differences through a time-averaging procedure and to model an infinite array of flagella. We find array separation distances, magnetic field strengths, and rotation frequencies that produce nontrivial self-consistent pumping solutions. For individual flagella, pumping is reversed when helicity or rotation is reversed; in contrast, when collective effects are included, self-consistent tilted pumping solutions become untilted nonpumping solutions when helicity or rotation is reversed.

Stochastic control of inertial sea wave energy converter.

Science.gov (United States)

Raffero, Mattia; Martini, Michele; Passione, Biagio; Mattiazzo, Giuliana; Giorcelli, Ermanno; Bracco, Giovanni

2015-01-01

The ISWEC (inertial sea wave energy converter) is presented, its control problems are stated, and an optimal control strategy is introduced. As the aim of the device is energy conversion, the mean absorbed power by ISWEC is calculated for a plane 2D irregular sea state. The response of the WEC (wave energy converter) is driven by the sea-surface elevation, which is modeled by a stationary and homogeneous zero mean Gaussian stochastic process. System equations are linearized thus simplifying the numerical model of the device. The resulting response is obtained as the output of the coupled mechanic-hydrodynamic model of the device. A stochastic suboptimal controller, derived from optimal control theory, is defined and applied to ISWEC. Results of this approach have been compared with the ones obtained with a linear spring-damper controller, highlighting the capability to obtain a higher value of mean extracted power despite higher power peaks.

Stochastic optimal control, forward-backward stochastic differential equations and the Schroedinger equation

Energy Technology Data Exchange (ETDEWEB)

Paul, Wolfgang; Koeppe, Jeanette [Institut fuer Physik, Martin Luther Universitaet, 06099 Halle (Germany); Grecksch, Wilfried [Institut fuer Mathematik, Martin Luther Universitaet, 06099 Halle (Germany)

2016-07-01

The standard approach to solve a non-relativistic quantum problem is through analytical or numerical solution of the Schroedinger equation. We show a way to go around it. This way is based on the derivation of the Schroedinger equation from conservative diffusion processes and the establishment of (several) stochastic variational principles leading to the Schroedinger equation under the assumption of a kinematics described by Nelson's diffusion processes. Mathematically, the variational principle can be considered as a stochastic optimal control problem linked to the forward-backward stochastic differential equations of Nelson's stochastic mechanics. The Hamilton-Jacobi-Bellmann equation of this control problem is the Schroedinger equation. We present the mathematical background and how to turn it into a numerical scheme for analyzing a quantum system without using the Schroedinger equation and exemplify the approach for a simple 1d problem.

Conservative diffusions: a constructive approach to Nelson's stochastic mechanics

International Nuclear Information System (INIS)

Carlen, E.A.

1984-01-01

In Nelson's stochastic mechanics, quantum phenomena are described in terms of diffusions instead of wave functions; this thesis is a study of that description. Concern here is with the possibility of describing, as opposed to explaining, quantum phenomena in terms of diffusions. In this direction, the following questions arise: ''Do the diffusion of stochastic mechanics - which are formally given by stochastic differential equations with extremely singular coefficients - really exist.'' Given that they exist, one can ask, ''Do these diffusions have physically reasonable paths to study the behavior of physical systems.'' These are the questions treated in this thesis. In Chapter 1, stochastic mechanics and diffusion theory are reviewed, using the Guerra-Morato variational principle to establish the connection with the Schroedinger equation. Chapter II settles the first of the questions raised above. Using PDE methods, the diffusions of stochastic mechanics are constructed. The result is sufficiently general to be of independent mathematical interest. In Chapter III, potential scattering in stochastic mechanics is treated and direct probabilistic methods of studying quantum scattering problems are discussed. The results provide a solid YES in answer to the second question raised above

Mean-field magnetohydrodynamics and dynamo theory

CERN Document Server

Krause, F

2013-01-01

Mean-Field Magnetohydrodynamics and Dynamo Theory provides a systematic introduction to mean-field magnetohydrodynamics and the dynamo theory, along with the results achieved. Topics covered include turbulence and large-scale structures; general properties of the turbulent electromotive force; homogeneity, isotropy, and mirror symmetry of turbulent fields; and turbulent electromotive force in the case of non-vanishing mean flow. The turbulent electromotive force in the case of rotational mean motion is also considered. This book is comprised of 17 chapters and opens with an overview of the gen

From complex to simple: interdisciplinary stochastic models

International Nuclear Information System (INIS)

Mazilu, D A; Zamora, G; Mazilu, I

2012-01-01

We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions for certain physical quantities, such as the time dependence of the length of the microtubules, and diffusion coefficients. The second one is a stochastic adsorption model with applications in surface deposition, epidemics and voter systems. We introduce the ‘empty interval method’ and show sample calculations for the time-dependent particle density. These models can serve as an introduction to the field of non-equilibrium statistical physics, and can also be used as a pedagogical tool to exemplify standard statistical physics concepts, such as random walks or the kinetic approach of the master equation. (paper)

Continuous Time Finite State Mean Field Games

International Nuclear Information System (INIS)

Gomes, Diogo A.; Mohr, Joana; Souza, Rafael Rigão

2013-01-01

In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games