The Experts below are selected from a list of 249 Experts worldwide ranked by ideXlab platform
G Lozano - One of the best experts on this subject based on the ideXlab platform.
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magnetization dynamics path integral formalism for the Stochastic landau lifshitz gilbert Equation
Journal of Statistical Mechanics: Theory and Experiment, 2014Co-Authors: Camille Aron, Daniel G Barci, Leticia F Cugliandolo, Zochil Gonzalez Arenas, G LozanoAbstract:We construct a path-integral representation of the generating functional for the dissipative dynamics of a classical magnetic moment as described by the Stochastic generalization of the Landau?Lifshitz?Gilbert Equation?proposed by Brown (1963 Phys. Rev. 130 1677), with the possible addition of spin-torque terms. In the process of constructing this functional in the Cartesian coordinate system, we critically revisit this Stochastic Equation. We present it in a form that accommodates for any discretization scheme thanks to the inclusion of a drift term. The generalized Equation?ensures the conservation of the magnetization modulus and the approach to the Gibbs?Boltzmann equilibrium in the absence of non-potential and time-dependent forces. The drift term vanishes only if the mid-point Stratonovich prescription is used. We?next reset the problem in the more natural spherical coordinate system. We show that the noise transforms non-trivially to spherical coordinates acquiring a non-vanishing mean value in this coordinate system, a fact that has been often overlooked in the literature. We next construct the generating functional formalism in this system of coordinates for any discretization prescription. The functional formalism in Cartesian or spherical coordinates should serve as a starting point to study different aspects of the out-of-equilibrium dynamics of magnets. Extensions to colored noise, micro-magnetism and disordered problems are straightforward.
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magnetization dynamics path integral formalism for the Stochastic landau lifshitz gilbert Equation
arXiv: Statistical Mechanics, 2014Co-Authors: Camille Aron, Daniel G Barci, Leticia F Cugliandolo, Zochil Gonzalez Arenas, G LozanoAbstract:We construct a path-integral representation of the generating functional for the dissipative dynamics of a classical magnetic moment as described by the Stochastic generalization of the Landau-Lifshitz-Gilbert Equation proposed by Brown, with the possible addition of spin-torque terms. In the process of constructing this functional in the Cartesian coordinate system, we critically revisit this Stochastic Equation. We present it in a form that accommodates for any discretization scheme thanks to the inclusion of a drift term. The generalized Equation ensures the conservation of the magnetization modulus and the approach to the Gibbs-Boltzmann equilibrium in the absence of non-potential and time-dependent forces. The drift term vanishes only if the mid-point Stratonovich prescription is used. We next reset the problem in the more natural spherical coordinate system. We show that the noise transforms non-trivially to spherical coordinates acquiring a non-vanishing mean value in this coordinate system, a fact that has been often overlooked in the literature. We next construct the generating functional formalism in this system of coordinates for any discretization prescription. The functional formalism in Cartesian or spherical coordinates should serve as a starting point to study different aspects of the out-of-equilibrium dynamics of magnets. Extensions to colored noise, micro-magnetism and disordered problems are straightforward.
Camille Aron - One of the best experts on this subject based on the ideXlab platform.
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magnetization dynamics path integral formalism for the Stochastic landau lifshitz gilbert Equation
Journal of Statistical Mechanics: Theory and Experiment, 2014Co-Authors: Camille Aron, Daniel G Barci, Leticia F Cugliandolo, Zochil Gonzalez Arenas, G LozanoAbstract:We construct a path-integral representation of the generating functional for the dissipative dynamics of a classical magnetic moment as described by the Stochastic generalization of the Landau?Lifshitz?Gilbert Equation?proposed by Brown (1963 Phys. Rev. 130 1677), with the possible addition of spin-torque terms. In the process of constructing this functional in the Cartesian coordinate system, we critically revisit this Stochastic Equation. We present it in a form that accommodates for any discretization scheme thanks to the inclusion of a drift term. The generalized Equation?ensures the conservation of the magnetization modulus and the approach to the Gibbs?Boltzmann equilibrium in the absence of non-potential and time-dependent forces. The drift term vanishes only if the mid-point Stratonovich prescription is used. We?next reset the problem in the more natural spherical coordinate system. We show that the noise transforms non-trivially to spherical coordinates acquiring a non-vanishing mean value in this coordinate system, a fact that has been often overlooked in the literature. We next construct the generating functional formalism in this system of coordinates for any discretization prescription. The functional formalism in Cartesian or spherical coordinates should serve as a starting point to study different aspects of the out-of-equilibrium dynamics of magnets. Extensions to colored noise, micro-magnetism and disordered problems are straightforward.
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magnetization dynamics path integral formalism for the Stochastic landau lifshitz gilbert Equation
arXiv: Statistical Mechanics, 2014Co-Authors: Camille Aron, Daniel G Barci, Leticia F Cugliandolo, Zochil Gonzalez Arenas, G LozanoAbstract:We construct a path-integral representation of the generating functional for the dissipative dynamics of a classical magnetic moment as described by the Stochastic generalization of the Landau-Lifshitz-Gilbert Equation proposed by Brown, with the possible addition of spin-torque terms. In the process of constructing this functional in the Cartesian coordinate system, we critically revisit this Stochastic Equation. We present it in a form that accommodates for any discretization scheme thanks to the inclusion of a drift term. The generalized Equation ensures the conservation of the magnetization modulus and the approach to the Gibbs-Boltzmann equilibrium in the absence of non-potential and time-dependent forces. The drift term vanishes only if the mid-point Stratonovich prescription is used. We next reset the problem in the more natural spherical coordinate system. We show that the noise transforms non-trivially to spherical coordinates acquiring a non-vanishing mean value in this coordinate system, a fact that has been often overlooked in the literature. We next construct the generating functional formalism in this system of coordinates for any discretization prescription. The functional formalism in Cartesian or spherical coordinates should serve as a starting point to study different aspects of the out-of-equilibrium dynamics of magnets. Extensions to colored noise, micro-magnetism and disordered problems are straightforward.
Georgiy Bobashev - One of the best experts on this subject based on the ideXlab platform.
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controlling pandemic flu the value of international air travel restrictions
PLOS ONE, 2007Co-Authors: Joshua M Epstein, Robert Morris, Diane K. Wagener, Feng Yu, Michael D Goedecke, Georgiy BobashevAbstract:Background: Planning for a possible influenza pandemic is an extremely high priority, as social and economic effects of an unmitigated pandemic would be devastating. Mathematical models can be used to explore different scenarios and provide insight into potential costs, benefits, and effectiveness of prevention and control strategies under consideration. Methods and Findings: A Stochastic, Equation-based epidemic model is used to study global transmission of pandemic flu, including the effects of travel restrictions and vaccination. Economic costs of intervention are also considered. The distribution of First Passage Times (FPT) to the United States and the numbers of infected persons in metropolitan areas worldwide are studied assuming various times and locations of the initial outbreak. International air travel restrictions alone provide a small delay in FPT to the U.S. When other containment measures are applied at the source in conjunction with travel restrictions, delays could be much longer. If in addition, control measures are instituted worldwide, there is a significant reduction in cases worldwide and specifically in the U.S. However, if travel restrictions are not combined with other measures, local epidemic severity may increase, because restriction-induced delays can push local outbreaks into high epidemic season. The per annum cost to the U.S. economy of international and major domestic air passenger travel restrictions is minimal: on the order of 0.8 % of Gross National Product. Conclusions: International air travel restrictions may provide a small but important delay in the spread of a pandemic, especially if other disease control measures are implemented during the afforded time. However, if other measures are not instituted, delays may worsen regional epidemics by pushing the outbreak into high epidemic season. This important interaction between policy and seasonality is only evident with a global-scale model. Since the benefit of travel restrictions can be substantial while their costs are minimal, their dismissal as an aid in dealing with a global pandemic seems premature.
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controlling pandemic flu the value of international air travel restrictions
PLOS ONE, 2007Co-Authors: Joshua M Epstein, Diane K. Wagener, Michael D Goedecke, Robert J Morris, Georgiy BobashevAbstract:Background Planning for a possible influenza pandemic is an extremely high priority, as social and economic effects of an unmitigated pandemic would be devastating. Mathematical models can be used to explore different scenarios and provide insight into potential costs, benefits, and effectiveness of prevention and control strategies under consideration. Methods and Findings A Stochastic, Equation-based epidemic model is used to study global transmission of pandemic flu, including the effects of travel restrictions and vaccination. Economic costs of intervention are also considered. The distribution of First Passage Times (FPT) to the United States and the numbers of infected persons in metropolitan areas worldwide are studied assuming various times and locations of the initial outbreak. International air travel restrictions alone provide a small delay in FPT to the U.S. When other containment measures are applied at the source in conjunction with travel restrictions, delays could be much longer. If in addition, control measures are instituted worldwide, there is a significant reduction in cases worldwide and specifically in the U.S. However, if travel restrictions are not combined with other measures, local epidemic severity may increase, because restriction-induced delays can push local outbreaks into high epidemic season. The per annum cost to the U.S. economy of international and major domestic air passenger travel restrictions is minimal: on the order of 0.8% of Gross National Product. Conclusions International air travel restrictions may provide a small but important delay in the spread of a pandemic, especially if other disease control measures are implemented during the afforded time. However, if other measures are not instituted, delays may worsen regional epidemics by pushing the outbreak into high epidemic season. This important interaction between policy and seasonality is only evident with a global-scale model. Since the benefit of travel restrictions can be substantial while their costs are minimal, dismissal of travel restrictions as an aid in dealing with a global pandemic seems premature.
Joshua M Epstein - One of the best experts on this subject based on the ideXlab platform.
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controlling pandemic flu the value of international air travel restrictions
PLOS ONE, 2007Co-Authors: Joshua M Epstein, Robert Morris, Diane K. Wagener, Feng Yu, Michael D Goedecke, Georgiy BobashevAbstract:Background: Planning for a possible influenza pandemic is an extremely high priority, as social and economic effects of an unmitigated pandemic would be devastating. Mathematical models can be used to explore different scenarios and provide insight into potential costs, benefits, and effectiveness of prevention and control strategies under consideration. Methods and Findings: A Stochastic, Equation-based epidemic model is used to study global transmission of pandemic flu, including the effects of travel restrictions and vaccination. Economic costs of intervention are also considered. The distribution of First Passage Times (FPT) to the United States and the numbers of infected persons in metropolitan areas worldwide are studied assuming various times and locations of the initial outbreak. International air travel restrictions alone provide a small delay in FPT to the U.S. When other containment measures are applied at the source in conjunction with travel restrictions, delays could be much longer. If in addition, control measures are instituted worldwide, there is a significant reduction in cases worldwide and specifically in the U.S. However, if travel restrictions are not combined with other measures, local epidemic severity may increase, because restriction-induced delays can push local outbreaks into high epidemic season. The per annum cost to the U.S. economy of international and major domestic air passenger travel restrictions is minimal: on the order of 0.8 % of Gross National Product. Conclusions: International air travel restrictions may provide a small but important delay in the spread of a pandemic, especially if other disease control measures are implemented during the afforded time. However, if other measures are not instituted, delays may worsen regional epidemics by pushing the outbreak into high epidemic season. This important interaction between policy and seasonality is only evident with a global-scale model. Since the benefit of travel restrictions can be substantial while their costs are minimal, their dismissal as an aid in dealing with a global pandemic seems premature.
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controlling pandemic flu the value of international air travel restrictions
PLOS ONE, 2007Co-Authors: Joshua M Epstein, Diane K. Wagener, Michael D Goedecke, Robert J Morris, Georgiy BobashevAbstract:Background Planning for a possible influenza pandemic is an extremely high priority, as social and economic effects of an unmitigated pandemic would be devastating. Mathematical models can be used to explore different scenarios and provide insight into potential costs, benefits, and effectiveness of prevention and control strategies under consideration. Methods and Findings A Stochastic, Equation-based epidemic model is used to study global transmission of pandemic flu, including the effects of travel restrictions and vaccination. Economic costs of intervention are also considered. The distribution of First Passage Times (FPT) to the United States and the numbers of infected persons in metropolitan areas worldwide are studied assuming various times and locations of the initial outbreak. International air travel restrictions alone provide a small delay in FPT to the U.S. When other containment measures are applied at the source in conjunction with travel restrictions, delays could be much longer. If in addition, control measures are instituted worldwide, there is a significant reduction in cases worldwide and specifically in the U.S. However, if travel restrictions are not combined with other measures, local epidemic severity may increase, because restriction-induced delays can push local outbreaks into high epidemic season. The per annum cost to the U.S. economy of international and major domestic air passenger travel restrictions is minimal: on the order of 0.8% of Gross National Product. Conclusions International air travel restrictions may provide a small but important delay in the spread of a pandemic, especially if other disease control measures are implemented during the afforded time. However, if other measures are not instituted, delays may worsen regional epidemics by pushing the outbreak into high epidemic season. This important interaction between policy and seasonality is only evident with a global-scale model. Since the benefit of travel restrictions can be substantial while their costs are minimal, dismissal of travel restrictions as an aid in dealing with a global pandemic seems premature.
Thomas G. Kurtz - One of the best experts on this subject based on the ideXlab platform.
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Continuous Time Markov Chain Models for Chemical Reaction Networks
Design and Analysis of Biomolecular Circuits, 2011Co-Authors: David F Anderson, Thomas G. KurtzAbstract:A reaction network is a chemical system involving multiple reactions and chemical species. The simplest Stochastic models of such networks treat the system as a continuous time Markov chain with the state being the number of molecules of each species and with reactions modeled as possible transitions of the chain. This chapter is devoted to the mathematical study of such Stochastic models. We begin by developing much of the mathematical machinery we need to describe the Stochastic models we are most interested in. We show how one can represent counting processes of the type we need in terms of Poisson processes. This random time-change representation gives a Stochastic Equation for continuous-time Markov chain models. We include a discussion on the relationship between this Stochastic Equation and the corresponding martingale problem and Kolmogorov forward (master) Equation. Next, we exploit the representation of the Stochastic Equation for chemical reaction networks and, under what we will refer to as the classical scaling, show how to derive the deterministic law of mass action from the Markov chain model. We also review the diffusion, or Langevin, approximation, include a discussion of first order reaction networks, and present a large class of networks, those that are weakly reversible and have a deficiency of zero, that induce product-form stationary distributions. Finally, we discuss models in which the numbers of molecules and/or the reaction rate constants of the system vary over several orders of magnitude. We show that one consequence of this wide variation in scales is that different subsystems may evolve on different time scales and this time-scale variation can be exploited to identify reduced models that capture the behavior of parts of the system. We will discuss systematic ways of identifying the different time scales and deriving the reduced models.
