Gotowe bibliografie tematyczne / Stochastic Fokker-Planck

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Gotowa bibliografia na temat „Stochastic Fokker-Planck”

Autor: Grafiati

Data publikacji: 14 grudnia 2024

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Artykuły w czasopismach na temat "Stochastic Fokker-Planck"

Liu, Chang, Chuo Chang i Zhe Chang. "Distribution of Return Transition for Bohm-Vigier Stochastic Mechanics in Stock Market". Symmetry 15, nr 7 (17.07.2023): 1431. http://dx.doi.org/10.3390/sym15071431.

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The Bohm-Vigier stochastic model is assumed as a natural generalization of the Black-Scholes model in stock market. The behavioral factor of stock market recognizes as a hidden sector in Bohmian mechanics. A Fokker-Planck equation description for the Bohm-Vigier stochastic model is presented. We find the familiar Boltzmann distribution is a stationary solution of the Fokker-Planck equation for the Bohm-Vigier model. The return transition distribution of stock market, which corresponds with a time-dependent solution of the Fokker-Planck equation, is obtained.

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Coghi, Michele, i Benjamin Gess. "Stochastic nonlinear Fokker–Planck equations". Nonlinear Analysis 187 (październik 2019): 259–78. http://dx.doi.org/10.1016/j.na.2019.05.003.

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Chavanis, Pierre-Henri. "Generalized Stochastic Fokker-Planck Equations". Entropy 17, nr 5 (13.05.2015): 3205–52. http://dx.doi.org/10.3390/e17053205.

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Lin, Y. K., i G. Q. Cai. "Equivalent Stochastic Systems". Journal of Applied Mechanics 55, nr 4 (1.12.1988): 918–22. http://dx.doi.org/10.1115/1.3173742.

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Equivalent stochastic systems are defined as randomly excited dynamical systems whose response vectors in the state space share the same probability distribution. In this paper, the random excitations are restricted to Gaussian white noises; thus, the system responses are Markov vectors, and their probability densities are governed by the associated Fokker-Planck equations. When the associated Fokker-Planck equations are identical, the equivalent stochastic systems must share both the stationary probability distribution and the transient nonstationary probability distribution under identical initial conditions. Such systems are said to be stochastically equivalent in the strict (or strong) sense. A wider class, referred to as the class of equivalent stochastic systems in the wide (or weak) sense, also includes those sharing only the stationary probability distribution but having different Fokker-Planck equations. Given a stochastic system with a known probability distribution, procedures are developed to identify and construct equivalent stochastic systems, both in the strict and in the wide sense.

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KOTELENEZ, PETER M. "A QUASI-LINEAR STOCHASTIC FOKKER–PLANCK EQUATION IN σ-FINITE MEASURES". Stochastics and Dynamics 08, nr 03 (wrzesień 2008): 475–504. http://dx.doi.org/10.1142/s021949370800241x.

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Solutions of quasi-linear stochastic Fokker–Planck equations for the number density of a system of solute particles in suspension are derived. The initial values and the solutions take values in a class of σ-finite Borel measures over Rd where d ≥ 1. The stochastic driving noise is defined by Itô differentials. For the special case of semi-linear stochastic Fokker–Planck equations, the solutions can be represented as solutions of first-order stochastic transport equations driven by Stratonovich differentials.

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Sun, Xu, Xiaofan Li i Yayun Zheng. "Governing equations for probability densities of Marcus stochastic differential equations with Lévy noise". Stochastics and Dynamics 17, nr 05 (23.09.2016): 1750033. http://dx.doi.org/10.1142/s0219493717500332.

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Marcus stochastic differential equations (SDEs) often are appropriate models for stochastic dynamical systems driven by non-Gaussian Lévy processes and have wide applications in engineering and physical sciences. The probability density of the solution to an SDE offers complete statistical information on the underlying stochastic process. Explicit formula for the Fokker–Planck equation, the governing equation for the probability density, is well-known when the SDE is driven by a Brownian motion. In this paper, we address the open question of finding the Fokker–Planck equations for Marcus SDEs in arbitrary dimensions driven by non-Gaussian Lévy processes. The equations are given in a simple form that facilitates theoretical analysis and numerical computation. Several examples are presented to illustrate how the theoretical results can be applied to obtain Fokker–Planck equations for Marcus SDEs driven by Lévy processes.

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Hirpara, Ravish Himmatlal, i Shambhu Nath Sharma. "An Analysis of a Wind Turbine-Generator System in the Presence of Stochasticity and Fokker-Planck Equations". International Journal of System Dynamics Applications 9, nr 1 (styczeń 2020): 18–43. http://dx.doi.org/10.4018/ijsda.2020010102.

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In power systems dynamics and control literature, theoretical and practical aspects of the wind turbine-generator system have received considerable attentions. The evolution equation of the induction machine encompasses a system of three first-order differential equations coupled with two algebraic equations. After accounting for stochasticity in the wind speed, the wind turbine-generator system becomes a stochastic system. That is described by the standard and formal Itô stochastic differential equation. Note that the Itô process is a strong Markov process. The Itô stochasticity of the wind speed is attributed to the Markov modeling of atmospheric turbulence. The article utilizes the Fokker-Planck method, a mathematical stochastic method, to analyse the noise-influenced wind turbine-generator system by doing the following: (i) the authors develop the Fokker-Planck model for the stochastic power system problem considered here; (ii) the Fokker-Planck operator coupled with the Kolmogorov backward operator are exploited to accomplish the noise analysis from the estimation-theoretic viewpoint.

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Annunziato, Mario, i Alfio Borzì. "OPTIMAL CONTROL OF PROBABILITY DENSITY FUNCTIONS OF STOCHASTIC PROCESSES". Mathematical Modelling and Analysis 15, nr 4 (15.11.2010): 393–407. http://dx.doi.org/10.3846/1392-6292.2010.15.393-407.

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A Fokker‐Planck framework for the formulation of an optimal control strategy of stochastic processes is presented. Within this strategy, the control objectives are defined based on the probability density functions of the stochastic processes. The optimal control is obtained as the minimizer of the objective under the constraint given by the Fokker‐Planck model. Representative stochastic processes are considered with different control laws and with the purpose of attaining a final target configuration or tracking a desired trajectory. In this latter case, a receding‐horizon algorithm over a sequence of time windows is implemented.

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ANNUNZIATO, M., i A. BORZI. "FOKKER–PLANCK-BASED CONTROL OF A TWO-LEVEL OPEN QUANTUM SYSTEM". Mathematical Models and Methods in Applied Sciences 23, nr 11 (23.07.2013): 2039–64. http://dx.doi.org/10.1142/s0218202513500255.

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The control of a two-level open quantum system subject to dissipation due to environment interaction is considered. The evolution of this system is governed by a Lindblad master equation which is augmented by a stochastic term to model the effect of time-continuous measurements. In order to control this stochastic master equation model, a Fokker–Planck control framework is investigated. Within this strategy, the control objectives are defined based on the probability density functions of the two-level stochastic process and the controls are computed as minimizers of these objectives subject to the constraints represented by the Fokker–Planck equation. This minimization problem is characterized by an optimality system including the Fokker–Planck equation and its adjoint. This optimality system is approximated by a second-order accurate, stable, conservative and positive-preserving discretization scheme. The implementation of the resulting open-loop controls is realized with a receding-horizon algorithm over a sequence of time windows. Results of numerical experiments demonstrate the effectiveness of the proposed approach.

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RENNER, CHRISTOPH, J. PEINKE i R. FRIEDRICH. "Experimental indications for Markov properties of small-scale turbulence". Journal of Fluid Mechanics 433 (25.04.2001): 383–409. http://dx.doi.org/10.1017/s0022112001003597.

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We present a stochastic analysis of a data set consisting of 1.25 × 107 samples of the local velocity measured in the turbulent region of a round free jet. We find evidence that the statistics of the longitudinal velocity increment v(r) can be described as a Markov process. This new approach to characterize small-scale turbulence leads to a Fokker–Planck equation for the r-evolution of the probability density function (p.d.f.) of v(r). This equation for p(v, r) is completely determined by two coefficients D1(v, r) and D2(v, r) (drift and diffusion coefficient, respectively). It is shown how these coefficients can be estimated directly from the experimental data without using any assumptions or models for the underlying stochastic process. The solutions of the resulting Fokker–Planck equation are compared with experimentally determined probability density functions. It is shown that the Fokker–Planck equation describes the measured p.d.f.(s) correctly, including intermittency effects. Furthermore, knowledge of the Fokker–Planck equation also allows the joint probability density of N increments on N different scales p(v1, r1, …, vN, rN) to be determined.

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Rozprawy doktorskie na temat "Stochastic Fokker-Planck"

Adesina, Owolabi Abiona. "Statistical Modelling and the Fokker-Planck Equation". Thesis, Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-1177.

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A stochastic process or sometimes called random process is the counterpart to a deterministic process in theory. A stochastic process is a random field, whose domain is a region of space, in other words, a random function whose arguments are drawn from a range of continuously changing values. In this case, Instead of dealing only with one possible 'reality' of how the process might evolve under time (as is the case, for example, for solutions of an ordinary differential equation), in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions. This means that even if the initial condition (or starting point) is known, there are many possibilities the process might go to, but some paths are more probable and others less. However, in discrete time, a stochastic process amounts to a sequence of random variables known as a time series. Over the past decades, the problems of synergetic are concerned with the study of macroscopic quantitative changes of systems belonging to various disciplines such as natural science, physical science and electrical engineering. When such transition from one state to another take place, fluctuations i.e. (random process) may play an important role. Fluctuations in its sense are very common in a large number of fields and nearly every system is subjected to complicated external or internal influences that are often termed noise or fluctuations. Fokker-Planck equation has turned out to provide a powerful tool with which the effects of fluctuation or noise close to transition points can be adequately be treated. For this reason, in this thesis work analytical and numerical methods of solving Fokker-Planck equation, its derivation and some of its applications will be carefully treated. Emphasis will be on both for one variable and N- dimensional cases.

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Guillouzic, Steve. "Fokker-Planck approach to stochastic delay differential equations". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/NQ58279.pdf.

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Noble, Patrick. "Stochastic processes in Astrophysics". Thesis, The University of Sydney, 2013. http://hdl.handle.net/2123/10013.

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This thesis makes two contributions to the solar literature. The first is the development and application of a formal statistical framework for describing short-term (daily) variation in the level of magnetic activity on the Sun. Modelling changes on this time-scale is important because rapid developments of magnetic structures on the sun have important consequences for the space weather experienced on Earth (Committee On The Societal & Economic Impacts Of Severe Space Weather Events, 2008). The second concerns how energetic particles released from the Sun travel through the solar wind. The contribution from this thesis is to resolve a mathematical discrepancy in theoretical models for the transport of charged particles.

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Li, Wuchen. "A study of stochastic differential equations and Fokker-Planck equations with applications". Diss., Georgia Institute of Technology, 2016. http://hdl.handle.net/1853/54999.

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Fokker-Planck equations, along with stochastic differential equations, play vital roles in physics, population modeling, game theory and optimization (finite or infinite dimensional). In this thesis, we study three topics, both theoretically and computationally, centered around them. In part one, we consider the optimal transport for finite discrete states, which are on a finite but arbitrary graph. By defining a discrete 2-Wasserstein metric, we derive Fokker-Planck equations on finite graphs as gradient flows of free energies. By using dynamical viewpoint, we obtain an exponential convergence result to equilibrium. This derivation provides tools for many applications, including numerics for nonlinear partial differential equations and evolutionary game theory. In part two, we introduce a new stochastic differential equation based framework for optimal control with constraints. The framework can efficiently solve several real world problems in differential games and Robotics, including the path-planning problem. In part three, we introduce a new noise model for stochastic oscillators. With this model, we prove global boundedness of trajectories. In addition, we derive a pair of associated Fokker-Planck equations.

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Miserocchi, Andrea. "The Fokker-Planck equation as model for the stochastic gradient descent in deep learning". Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18290/.

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La discesa stocastica del gradiente (SGD) è alla base degli algoritmi di ottimizzazione di reti di Deep Learning più usati in AI, dal riconoscimento delle immagini all’elaborazione del linguaggio naturale. Questa tesi si propone di descrivere un modello basato sull’equazione di Fokker-Planck della dinamica del SGD. Si introduce la teoria dei processi stocastici, con particolare enfasi sulle equazioni di Langevin e sull’equazione di Fokker-Planck. Si mostra come il SGD minimizzi un funzionale sulla densità di probabilità dei pesi, non dipendente direttamente dalla funzione di costo. Infine si discutono le implicazioni di questa inferenza variazionale ottenuta dal SGD.

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Ющенко, Ольга Володимирівна, Ольга Владимировна Ющенко, Olha Volodymyrivna Yushchenko, Тетяна Іванівна Жиленко, Татьяна Ивановна Жиленко i Tetiana Ivanivna Zhylenko. "Description of the Stochastic Condensation Process under Quasi-Equilibrium Conditions". Thesis, Sumy State University, 2012. http://essuir.sumdu.edu.ua/handle/123456789/34910.

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The system of three differential equations describing the stochastic condensation process under quasiequilibrium equilibrium conditions is constructed taking into account the additive and multiplicative components. The phase diagram of the system states was constructed and analyzed. The domains of the existence of the condensation processes, disassembly of previously deposited material, and the complete evaporation were determined. The distribution density of the concentration of adsorbed atoms was defined. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/34910

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Денисов, Станіслав Іванович, Станислав Иванович Денисов, Stanislav Ivanovych Denysov, V. V. Reva i O. O. Bondar. "Generalized Fokker-Planck Equation for the Nanoparticle Magnetic Moment Driven by Poisson White Noise". Thesis, Sumy State University, 2012. http://essuir.sumdu.edu.ua/handle/123456789/35373.

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We derive the generalized Fokker-Planck equation for the probability density function of the nanoparticle magnetic moment driven by Poisson white noise. Our approach is based on the reduced stochastic Landau-Lifshitz equation in which this noise is included into the effective magnetic field. We take into account that the magnetic moment under the noise action can change its direction instantaneously and show that the generalized equation has an integro-differential form. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/35373

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Li, Yao. "Stochastic perturbation theory and its application to complex biological networks -- a quantification of systematic features of biological networks". Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/49013.

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The primary objective of this thesis is to make a quantitative study of complex biological networks. Our fundamental motivation is to obtain the statistical dependency between modules by injecting external noise. To accomplish this, a deep study of stochastic dynamical systems would be essential. The first chapter is about the stochastic dynamical system theory. The classical estimation of invariant measures of Fokker-Planck equations is improved by the level set method. Further, we develop a discrete Fokker-Planck-type equation to study the discrete stochastic dynamical systems. In the second part, we quantify systematic measures including degeneracy, complexity and robustness. We also provide a series of results on their properties and the connection between them. Then we apply our theory to the JAK-STAT signaling pathway network.

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Vellmer, Sebastian. "Applications of the Fokker-Planck Equation in Computational and Cognitive Neuroscience". Doctoral thesis, Humboldt-Universität zu Berlin, 2020. http://dx.doi.org/10.18452/21597.

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In dieser Arbeit werden mithilfe der Fokker-Planck-Gleichung die Statistiken, vor allem die Leistungsspektren, von Punktprozessen berechnet, die von mehrdimensionalen Integratorneuronen [Engl. integrate-and-fire (IF) neuron], Netzwerken von IF Neuronen und Entscheidungsfindungsmodellen erzeugt werden. Im Gehirn werden Informationen durch Pulszüge von Aktionspotentialen kodiert. IF Neurone mit radikal vereinfachter Erzeugung von Aktionspotentialen haben sich in Studien die auf Pulszeiten fokussiert sind als Standardmodelle etabliert. Eindimensionale IF Modelle können jedoch beobachtetes Pulsverhalten oft nicht beschreiben und müssen dazu erweitert werden. Im erste Teil dieser Arbeit wird eine Theorie zur Berechnung der Pulszugleistungsspektren von stochastischen, multidimensionalen IF Neuronen entwickelt. Ausgehend von der zugehörigen Fokker-Planck-Gleichung werden partiellen Differentialgleichung abgeleitet, deren Lösung sowohl die stationäre Wahrscheinlichkeitsverteilung und Feuerrate, als auch das Pulszugleistungsspektrum beschreibt. Im zweiten Teil wird eine Theorie für große, spärlich verbundene und homogene Netzwerke aus IF Neuronen entwickelt, in der berücksichtigt wird, dass die zeitlichen Korrelationen von Pulszügen selbstkonsistent sind. Neuronale Eingangströme werden durch farbiges Gaußsches Rauschen modelliert, das von einem mehrdimensionalen Ornstein-Uhlenbeck Prozess (OUP) erzeugt wird. Die Koeffizienten des OUP sind vorerst unbekannt und sind als Lösung der Theorie definiert. Um heterogene Netzwerke zu untersuchen, wird eine iterative Methode erweitert. Im dritten Teil wird die Fokker-Planck-Gleichung auf Binärentscheidungen von Diffusionsentscheidungsmodellen [Engl. diffusion-decision models (DDM)] angewendet. Explizite Gleichungen für die Entscheidungszugstatistiken werden für den einfachsten und analytisch lösbaren Fall von der Fokker-Planck-Gleichung hergeleitet. Für nichtliniear Modelle wird die Schwellwertintegrationsmethode erweitert.
This thesis is concerned with the calculation of statistics, in particular the power spectra, of point processes generated by stochastic multidimensional integrate-and-fire (IF) neurons, networks of IF neurons and decision-making models from the corresponding Fokker-Planck equations. In the brain, information is encoded by sequences of action potentials. In studies that focus on spike timing, IF neurons that drastically simplify the spike generation have become the standard model. One-dimensional IF neurons do not suffice to accurately model neural dynamics, however, the extension towards multiple dimensions yields realistic behavior at the price of growing complexity. The first part of this work develops a theory of spike-train power spectra for stochastic, multidimensional IF neurons. From the Fokker-Planck equation, a set of partial differential equations is derived that describes the stationary probability density, the firing rate and the spike-train power spectrum. In the second part of this work, a mean-field theory of large and sparsely connected homogeneous networks of spiking neurons is developed that takes into account the self-consistent temporal correlations of spike trains. Neural input is approximated by colored Gaussian noise generated by a multidimensional Ornstein-Uhlenbeck process of which the coefficients are initially unknown but determined by the self-consistency condition and define the solution of the theory. To explore heterogeneous networks, an iterative scheme is extended to determine the distribution of spectra. In the third part, the Fokker-Planck equation is applied to calculate the statistics of sequences of binary decisions from diffusion-decision models (DDM). For the analytically tractable DDM, the statistics are calculated from the corresponding Fokker-Planck equation. To determine the statistics for nonlinear models, the threshold-integration method is generalized.

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Sjöberg, Paul. "Numerical Methods for Stochastic Modeling of Genes and Proteins". Doctoral thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8293.

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Stochastic models of biochemical reaction networks are used for understanding the properties of molecular regulatory circuits in living cells. The state of the cell is defined by the number of copies of each molecular species in the model. The chemical master equation (CME) governs the time evolution of the the probability density function of the often high-dimensional state space. The CME is approximated by a partial differential equation (PDE), the Fokker-Planck equation and solved numerically. Direct solution of the CME rapidly becomes computationally expensive for increasingly complex biological models, since the state space grows exponentially with the number of dimensions. Adaptive numerical methods can be applied in time and space in the PDE framework, and error estimates of the approximate solutions are derived. A method for splitting the CME operator in order to apply the PDE approximation in a subspace of the state space is also developed. The performance is compared to the most widely spread alternative computational method.

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Książki na temat "Stochastic Fokker-Planck"

Frank, T. D. Nonlinear Fokker-Planck equations: Fundamentals and applications. Berlin: Springer, 2004.

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Grasman, Johan. Asymptotic methods for the Fokker-Planck equation and the exit problem in applications. Berlin: Springer, 1999.

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Chirikjian, Gregory S. Stochastic models, information theory, and lie groups. Boston: Birkhäuser, 2009.

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Fokker-Planck-Kolmogorov equations. Providence, Rhode Island: American Mathematical Society, 2015.

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Krylov, Nicolai V., Michael Rockner, Vladimir I. Bogachev i Stanislav V. Shaposhnikov. Fokker-Planck-Kolmogorov Equations. American Mathematical Society, 2015.

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Nonlinear Fokker-Planck equations: Fundamentals and applications. Berlin: Springer, 2005.

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Pavliotis, Grigorios A. Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations. Springer, 2014.

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Pavliotis, Grigorios A. Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations. Springer, 2016.

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Pavliotis, Grigorios A. Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations. Springer London, Limited, 2014.

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McClintock, P. V. E., i Frank Moss. Noise in Nonlinear Dynamical Systems Vol. 1: Theory of Continuous Fokker-Planck Systems. Cambridge University Press, 2007.

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Części książek na temat "Stochastic Fokker-Planck"

Loos, Sarah A. M. "Fokker-Planck Equations". W Stochastic Systems with Time Delay, 77–86. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-80771-9_3.

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Loos, Sarah A. M. "Infinite Fokker-Planck Hierarchy". W Stochastic Systems with Time Delay, 121–36. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-80771-9_5.

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Rodean, Howard C. "The Fokker-Planck Equation". W Stochastic Lagrangian Models of Turbulent Diffusion, 19–24. Boston, MA: American Meteorological Society, 1996. http://dx.doi.org/10.1007/978-1-935704-11-9_5.

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Qian, Hong, i Hao Ge. "Stochastic Processes, Fokker-Planck Equation". W Encyclopedia of Systems Biology, 2000–2004. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_279.

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Bogachev, Vladimir I. "Stationary Fokker–Planck–Kolmogorov Equations". W Stochastic Partial Differential Equations and Related Fields, 3–24. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74929-7_1.

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Da Prato, Giuseppe. "Fokker–Planck Equations in Hilbert Spaces". W Stochastic Partial Differential Equations and Related Fields, 101–29. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74929-7_5.

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Möhl, Dieter. "The Distribution Function and Fokker-Planck Equations". W Stochastic Cooling of Particle Beams, 91–104. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-34979-9_7.

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Carmichael, Howard J. "Fokker—Planck Equations and Stochastic Differential Equations". W Statistical Methods in Quantum Optics 1, 147–93. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-662-03875-8_5.

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Shaposhnikov, Stanislav V. "Nonlinear Fokker–Planck–Kolmogorov Equations for Measures". W Stochastic Partial Differential Equations and Related Fields, 367–79. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74929-7_24.

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Yoshida, T., i S. Yanagita. "A Stochastic Simulation Method for Fokker-Planck Equations". W Numerical Astrophysics, 399–400. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4780-4_121.

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Streszczenia konferencji na temat "Stochastic Fokker-Planck"

Metzler, Ralf. "From the Langevin equation to the fractional Fokker–Planck equation". W Stochastic and chaotic dynamics in the lakes. AIP, 2000. http://dx.doi.org/10.1063/1.1302409.

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Holliday, G. S., i Surendra Singh. "Second harmonic generation in the positive P-representation". W OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1987. http://dx.doi.org/10.1364/oam.1987.wr6.

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Equation of motion for the density operator of the field in the process of second harmonic generation is converted into a Fokker-Planck equation by using the positive P-representation of the density operator. This Fokker-Planck equation is replaced by a set of four coupled stochastic differential equations using the Ito interpretation. The statistics of the light field are studied by numerically solving these stochastic equations. For long interaction times substantial antibunching and squeezing are possible in principle.

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Allison, A. "Stochastic Resonance, Brownian Ratchets and the Fokker-Planck Equation". W UNSOLVED PROBLEMS OF NOISE AND FLUCTUATIONS: UPoN 2002: Third International Conference on Unsolved Problems of Noise and Fluctuations in Physics, Biology, and High Technology. AIP, 2003. http://dx.doi.org/10.1063/1.1584877.

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Wedig, Walter V., i Utz von Wagner. "Stochastic Car Vibrations With Strong Nonlinearities". W ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21605.

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Abstract High dimensional probability density functions of nonlinear dynamical systems are calculated by solutions of Fokker-Planck equations. First approximations are derived via the solutions of the associated linear system and the analytical results of the expected values. These first approximations are utilized as weighting functions for the construction of generalized orthogonal polynomials. The Fokker-Planck equation is expanded into these polynomials and solved by a Galerkin method. As an example, a simple model of a quarter car with nonlinear damping subjected to white or coloured noise excitation is considered. The damping characteristic is piecewisely linear and highly non-symmetrical. The excitation is generated by the roughness of the road surface on which the car is driving with constant velocity. The main result is a non-vanishing mean value of the vertical car vibrations. Monte-Carlo simulations and analytical results are applied for comparison and tests.

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Wang, Yan. "Simulating Drift-Diffusion Processes With Generalized Interval Probability". W ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70699.

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The Fokker-Planck equation is widely used to describe the time evolution of stochastic systems in drift-diffusion processes. Yet, it does not differentiate two types of uncertainties: aleatory uncertainty that is inherent randomness and epistemic uncertainty due to lack of perfect knowledge. In this paper, a generalized Fokker-Planck equation based on a new generalized interval probability theory is proposed to describe drift-diffusion processes under both uncertainties, where epistemic uncertainty is modeled by the generalized interval while the aleatory one is by the probability measure. A path integral approach is developed to numerically solve the generalized Fokker-Planck equation. The resulted interval-valued probability density functions rigorously bound the real-valued ones computed from the classical path integral method. The new approach is demonstrated by numerical examples.

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Claussen, Jens Christian. "Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations". W Stochastic Models in Biological Sciences. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc80-0-1.

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Kumar, Mrinal, Suman Chakravorty i John Junkins. "Computational Nonlinear Stochastic Control Based on the Fokker-Planck-Kolmogorov Equation". W AIAA Guidance, Navigation and Control Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2008. http://dx.doi.org/10.2514/6.2008-6477.

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Horowicz, R. J., i L. A. Lugiato. "Noise Effects In Optical Bistability". W Instabilities and Dynamics of Lasers and Nonlinear Optical Systems. Washington, D.C.: Optica Publishing Group, 1985. http://dx.doi.org/10.1364/idlnos.1985.wd2.

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We formulate a running wave, singlemode model for purely dispersive optical bistability, which incorporates amplitude and frequency fluctuations in the incident field, cavity length fluctuations, thermal noise in the radiation field and in the material (1). This model is given by a set of three Langevin-type equations for the real and the imaginary part of the slowly-varying electric field, and for the material variable. In the white noise limit, it is equivalent to a Fokker-Planck equation in three variables. Even if our model can describe also a Kerr medium or a two-level system in a suitable range of parameters, we are mainly interested in the case of miniaturized all–optical bistable devices which utilize semiconductor dispersive media. In this situation, we can adiabatically eliminate the field variables and therefore reduce the problem to a single stochastic differential equation in one variable, which contains several terms of additive and multiplicative noise. We find that noise in the imaginary part of the slowly varying electric field does not contribute to this equation. In the white, -noise case, our stochastic equation is equivalent to a Fokker-Planck equation in one variable, whereas in the case of colored noise we obtain a onedimensional Fokker-Planck equation only in the limit of short correlation times.

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Kikuchi, T., S. Kawata i T. Katayama. "Numerical solver with cip method for Fokker Planck equation of stochastic cooling". W 2007 IEEE Particle Accelerator Conference (PAC). IEEE, 2007. http://dx.doi.org/10.1109/pac.2007.4440417.

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Das, Shreepriya, Haris Vikalo i Arjang Hassibi. "Stochastic modeling of reaction kinetics in biosensors using the Fokker Planck equation". W 2009 IEEE International Workshop on Genomic Signal Processing and Statistics (GENSIPS). IEEE, 2009. http://dx.doi.org/10.1109/gensips.2009.5174363.

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Raporty organizacyjne na temat "Stochastic Fokker-Planck"

Marriner, John. Simulations of Transverse Stochastic Cooling Using the Fokker-Planck Equation. Office of Scientific and Technical Information (OSTI), marzec 1998. http://dx.doi.org/10.2172/1985058.

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Kumar, Manish, i Subramanian Ramakrishnan. Modeling and Analysis of Stochastic Dynamics and Emergent Phenomena in Swarm Robotic Systems Using the Fokker-Planck Formalism. Fort Belvoir, VA: Defense Technical Information Center, październik 2010. http://dx.doi.org/10.21236/ada547014.

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Yu, D., i S. Chakravorty. A Multi-Resolution Approach to the Fokker-Planck-Kolmogorov Equation with Application to Stochastic Nonlinear Filtering and Optimal Design. Fort Belvoir, VA: Defense Technical Information Center, grudzień 2012. http://dx.doi.org/10.21236/ada582272.

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Snyder, Victor A., Dani Or, Amos Hadas i S. Assouline. Characterization of Post-Tillage Soil Fragmentation and Rejoining Affecting Soil Pore Space Evolution and Transport Properties. United States Department of Agriculture, kwiecień 2002. http://dx.doi.org/10.32747/2002.7580670.bard.

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Tillage modifies soil structure, altering conditions for plant growth and transport processes through the soil. However, the resulting loose structure is unstable and susceptible to collapse due to aggregate fragmentation during wetting and drying cycles, and coalescense of moist aggregates by internal capillary forces and external compactive stresses. Presently, limited understanding of these complex processes often leads to consideration of the soil plow layer as a static porous medium. With the purpose of filling some of this knowledge gap, the objectives of this Project were to: 1) Identify and quantify the major factors causing breakdown of primary soil fragments produced by tillage into smaller secondary fragments; 2) Identify and quantify the. physical processes involved in the coalescence of primary and secondary fragments and surfaces of weakness; 3) Measure temporal changes in pore-size distributions and hydraulic properties of reconstructed aggregate beds as a function of specified initial conditions and wetting/drying events; and 4) Construct a process-based model of post-tillage changes in soil structural and hydraulic properties of the plow layer and validate it against field experiments. A dynamic theory of capillary-driven plastic deformation of adjoining aggregates was developed, where instantaneous rate of change in geometry of aggregates and inter-aggregate pores was related to current geometry of the solid-gas-liquid system and measured soil rheological functions. The theory and supporting data showed that consolidation of aggregate beds is largely an event-driven process, restricted to a fairly narrow range of soil water contents where capillary suction is great enough to generate coalescence but where soil mechanical strength is still low enough to allow plastic deforn1ation of aggregates. The theory was also used to explain effects of transient external loading on compaction of aggregate beds. A stochastic forInalism was developed for modeling soil pore space evolution, based on the Fokker Planck equation (FPE). Analytical solutions for the FPE were developed, with parameters which can be measured empirically or related to the mechanistic aggregate deformation model. Pre-existing results from field experiments were used to illustrate how the FPE formalism can be applied to field data. Fragmentation of soil clods after tillage was observed to be an event-driven (as opposed to continuous) process that occurred only during wetting, and only as clods approached the saturation point. The major mechanism of fragmentation of large aggregates seemed to be differential soil swelling behind the wetting front. Aggregate "explosion" due to air entrapment seemed limited to small aggregates wetted simultaneously over their entire surface. Breakdown of large aggregates from 11 clay soils during successive wetting and drying cycles produced fragment size distributions which differed primarily by a scale factor l (essentially equivalent to the Van Bavel mean weight diameter), so that evolution of fragment size distributions could be modeled in terms of changes in l. For a given number of wetting and drying cycles, l decreased systematically with increasing plasticity index. When air-dry soil clods were slightly weakened by a single wetting event, and then allowed to "age" for six weeks at constant high water content, drop-shatter resistance in aged relative to non-aged clods was found to increase in proportion to plasticity index. This seemed consistent with the rheological model, which predicts faster plastic coalescence around small voids and sharp cracks (with resulting soil strengthening) in soils with low resistance to plastic yield and flow. A new theory of crack growth in "idealized" elastoplastic materials was formulated, with potential application to soil fracture phenomena. The theory was preliminarily (and successfully) tested using carbon steel, a ductile material which closely approximates ideal elastoplastic behavior, and for which the necessary fracture data existed in the literature.

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