Готові списки джерел за темами / Planar Brownian motion

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Добірка наукової літератури з теми "Planar Brownian motion"

Автор: Grafiati

Опубліковано: 23 вересня 2022

Оновлено: 28 січня 2023

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Статті в журналах з теми "Planar Brownian motion"

Jedidi, Wissem, and Stavros Vakeroudis. "Windings of planar processes, exponential functionals and Asian options." Advances in Applied Probability 50, no. 3 (September 2018): 726–42. http://dx.doi.org/10.1017/apr.2018.33.

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Abstract Motivated by a common mathematical finance topic, we discuss the reciprocal of the exit time from a cone of planar Brownian motion which also corresponds to the exponential functional of Brownian motion in the framework of planar Brownian motion. We prove a conjecture of Vakeroudis and Yor (2012) concerning infinite divisibility properties of this random variable and present a novel simple proof of the result of DeBlassie (1987), (1988) concerning the asymptotic behavior of the distribution of the Bessel clock appearing in the skew-product representation of planar Brownian motion, as t→∞. We use the results of the windings approach in order to obtain results for quantities associated to the pricing of Asian options.

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Davis, Burgess. "Conditioned Brownian motion in planar domains." Duke Mathematical Journal 57, no. 2 (October 1988): 397–421. http://dx.doi.org/10.1215/s0012-7094-88-05718-3.

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Werner, Wendelin, and Gregory F. Lawler. "Intersection Exponents for Planar Brownian Motion." Annals of Probability 27, no. 4 (October 1999): 1601–42. http://dx.doi.org/10.1214/aop/1022677543.

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Lawler, Gregory F., and Wendelin Werner. "Intersection Exponents for Planar Brownian Motion." Annals of Probability 27, no. 4 (October 1999): 1601–42. http://dx.doi.org/10.1214/aop/1022874810.

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Brassesco, Stella. "A Note on Planar Brownian Motion." Annals of Probability 20, no. 3 (July 1992): 1498–503. http://dx.doi.org/10.1214/aop/1176989703.

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Pitman, Jim, and Marc Yor. "Asymptotic Laws of Planar Brownian Motion." Annals of Probability 14, no. 3 (July 1986): 733–79. http://dx.doi.org/10.1214/aop/1176992436.

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Bass, Richard F., and Krzysztof Burdzy. "Conditioned Brownian motion in planar domains." Probability Theory and Related Fields 101, no. 4 (December 1995): 479–93. http://dx.doi.org/10.1007/bf01202781.

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Zhan, Dapeng. "Loop-Erasure of Planar Brownian Motion." Communications in Mathematical Physics 303, no. 3 (March 27, 2011): 709–20. http://dx.doi.org/10.1007/s00220-011-1234-9.

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Pitman, Jim, and Marc Yor. "Further Asymptotic Laws of Planar Brownian Motion." Annals of Probability 17, no. 3 (July 1989): 965–1011. http://dx.doi.org/10.1214/aop/1176991253.

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Klenke, Achim, and Peter Mörters. "Multiple Intersection Exponents for Planar Brownian Motion." Journal of Statistical Physics 136, no. 2 (July 2009): 373–97. http://dx.doi.org/10.1007/s10955-009-9780-7.

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Дисертації з теми "Planar Brownian motion"

Sauzedde, Isao. "Windings of the planar Brownian motion and Green’s formula." Thesis, Sorbonne université, 2021. http://www.theses.fr/2021SORUS437.

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On s'intéresse dans cette thèse à l'enlacement du mouvement Brownien plan autour des points, dans la succession des travaux de Wendelin Werner en particulier. Dans le premier chapitre, on motive cette étude par celle du cas des courbes plus lisses que le mouvement Brownien. On y démontre notamment une formule de Green pour l'intégrale de Young, sans hypothèse de simplicité de la courbe. Dans le chapitre 2, on étudie l'aire de l'ensemble des points autour desquels l'enlacement du mouvement brownien est plus grand que N. On donne, au sens presque sûr et dans les espaces Lp, une estimation asymptotique au second ordre de cette aire lorsque N tend vers l'infini. Le chapitre 3 est dévoué à la preuve d'un résultat qui montre que les points de grands enlacements se répartissent de manière très équilibrée le long de la trajectoire. Dans le chapitre 4, on utilise les résultats des deux précédents chapitres pour énoncer une formule de Green pour le mouvement brownien. On étudie aussi l'enlacement moyen de points répartis aléatoirement dans le plan. On montre que cet enlacement moyen converge en distribution (presque surement pour la trajectoire), non pas vers une constante (qui serait alors l’aire de Lévy) mais vers une variable de Cauchy centrée en l’aire de Lévy. Dans les deux derniers chapitres, on applique les idées des précédents chapitres pour définir et étudier l’aire de Lévy du mouvement Brownien lorsque la mesure d’aire sous-jacente n’est plus la mesure de Lebesgue mais une mesure aléatoire particulièrement irrégulière. On traite le cas du chaos multiplicatif gaussien en particulier, mais la méthode s’applique dans un cadre plus général
We study the windings of the planar Brownian motion around points, following the previous works of Wendelin Werner in particular. In the first chapter, we motivate this study by the one of smoother curves. We prove in particular a Green formula for Young integration, without simplicity assumption for the curve. In the second chapter, we study the area of the set of points around which the Brownian motion winds at least N times. We give an asymptotic estimation for this area, up to the second order, both in the almost sure sense and in the Lp spaces, when N goes to infinity.The third chapter is devoted to the proof of a result which shows that the points with large winding are distributed in a very balanced way along the trajectory. In the fourth chapter, we use the results from the two previous chapters to give a new Green formula for the Brownian motion. We also study the averaged winding around randomly distributed points in the plan. We show that, almost surely for the trajectory, this averaged winding converges in distribution, not toward a constant (which would be the Lévy area), but toward a Cauchy distribution centered at the Lévy area. In the last two chapters, we apply the ideas from the previous chapters to define and study the Lévy area of the Brownian motion, when the underlying area measure is not the Lebesgue measure anymore, but instead a random and highly irregular measure. We deal with the case of the Gaussian multiplicative chaos in particular, but the tools can be used in a much more general framework

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Cortez, Otto. "Brownian Motion and Planar Regions: Constructing Boundaries from h-Functions." Scholarship @ Claremont, 2000. https://scholarship.claremont.edu/hmc_theses/119.

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In this thesis, we study the relationship between the geometric shape of a region in the plane, and certain probabilistic information about the behavior of Brownian particles inside the region. The probabilistic information is contained in the function h(r), called the harmonic measure distribution function. Consider a domain Ω in the plane, and fix a basepoint z0. Imagine lining the boundary of this domain with fly paper and releasing a million fireflies at the basepoint z0. The fireflies wander around inside this domain randomly until they hit a wall and get stuck in the fly paper. What fraction of these fireflies are stuck within a distance r of their starting point z0? The answer is given by evaluating our h-function at this distance; that is, it is given by h(r). In more technical terms, the h-function gives the probability of a Brownian first particle hitting the boundary of the domain Ω within a radius r of the basepoint z0. This function is dependent on the shape of the domain Ω, the location of the basepoint z0, and the radius r. The big question to consider is: How much information does the h-function contain about the shape of the domain’s boundary? It is known that an h-function cannot uniquely determine a domain, but is it possible to construct a domain that generates a given hfunction? This is the question we try to answer. We begin by giving some examples of domains with their h-functions, and then some examples of sequences of converging domains whose corresponding h-functions also converge to the h-function. In a specific case, we prove that artichoke domains converge to the wedge domain, and their h-functions also converge. Using another class of approximating domains, circle domains, we outline a method for constructing bounded domains from possible hfunctions f(r). We prove some results about these domains, and we finish with a possible for a proof of the convergence of the sequence of domains constructed.

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Trefán, György. "Deterministic Brownian Motion." Thesis, University of North Texas, 1993. https://digital.library.unt.edu/ark:/67531/metadc279262/.

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The goal of this thesis is to contribute to the ambitious program of the foundation of developing statistical physics using chaos. We build a deterministic model of Brownian motion and provide a microscpoic derivation of the Fokker-Planck equation. Since the Brownian motion of a particle is the result of the competing processes of diffusion and dissipation, we create a model where both diffusion and dissipation originate from the same deterministic mechanism - the deterministic interaction of that particle with its environment. We show that standard diffusion which is the basis of the Fokker-Planck equation rests on the Central Limit Theorem, and, consequently, on the possibility of deriving it from a deterministic process with a quickly decaying correlation function. The sensitive dependence on initial conditions, one of the defining properties of chaos insures this rapid decay. We carefully address the problem of deriving dissipation from the interaction of a particle with a fully deterministic nonlinear bath, that we term the booster. We show that the solution of this problem essentially rests on the linear response of a booster to an external perturbation. This raises a long-standing problem concerned with Kubo's Linear Response Theory and the strong criticism against it by van Kampen. Kubo's theory is based on a perturbation treatment of the Liouville equation, which, in turn, is expected to be totally equivalent to a first-order perturbation treatment of single trajectories. Since the boosters are chaotic, and chaos is essential to generate diffusion, the single trajectories are highly unstable and do not respond linearly to weak external perturbation. We adopt chaotic maps as boosters of a Brownian particle, and therefore address the problem of the response of a chaotic booster to an external perturbation. We notice that a fully chaotic map is characterized by an invariant measure which is a continuous function of the control parameters of the map. Consequently if the external perturbation is made to act on a control parameter of the map, we show that the booster distribution undergoes slight modifications as an effect of the weak external perturbation, thereby leading to a linear response of the mean value of the perturbed variable of the booster. This approach to linear response completely bypasses the criticism of van Kampen. The joint use of these two phenomena, diffusion and friction stemming from the interaction of the Brownian particle with the same booster, makes the microscopic derivation of a Fokker-Planck equation and Brownian motion, possible.

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Yamaki, Tania Patricia Simões. "Solução exata da equação de Kramers para uma partícula Browniana carregada sob ação de campos elétrico e magnético externos e aplicações à hidrotermodinâmica." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/277085.

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Orientadores: Roberto Eugenio Lagos Monaco, Roberto Antonio Clemente
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin
Made available in DSpace on 2018-08-17T17:49:01Z (GMT). No. of bitstreams: 1 Yamaki_TaniaPatriciaSimoes_D.pdf: 15751882 bytes, checksum: 3bccb71a25a31c07f0e3e25ffb074896 (MD5) Previous issue date: 2010
Resumo: Após apresentarmos uma revisão dos principais modelos teóricos para o movimento Browniano, consideramos em particular o caso de uma partícula Browniana carregada sob ação de campos elétrico e magnético. A obtenção de uma solução analítica para este caso, resolvendo a equação de Kramers para a distribuição de probabilidades de uma partícula no espaço de fase, foi sugerida em 1943 por Chandrasekhar, mas até os anos noventa do século passado, o problema foi raramente considerado na literatura. Obtivemos a solução fundamental exata deste problema, e analisamos algumas aplicações. Consideramos uma classe particular de soluções, aquelas com perfil inicial Gaussiano (no espaço de fase), sendo a solução uma convolução de Gaussianas (a solução fundamental ou propagador, e o perfil inicial). Calculamos algumas grandezas hidrodinâmicas e termodinâmicas a partir da expressão exata para a distribuição de probabilidades de uma partícula Browniana, a saber, a densidade de partículas, as densidades de fluxo de partículas, de energia, de fluxo de energia, de entropia e também a temperatura efetiva do gás Browniano, que pode ser obtida a partir das densidades de partícula e energia cinética. Publicamos em 2005 a solução fundamental exata e algumas aplicações no regime assintótico.
Abstract: After presenting a sketch of the several theoretical approaches to the Brownian motion model, we consider a charged Brownian particle under electric and magnetic fields. A path to solve analitically Kramers equation, for the particle distribution probability in phase space, was suggested in 1943 by Chandrasekhar, nevertheless until the nineties of last century, this problem was rarely considered. We present the exact fundamental solution and analyze some applications. We consider a particular class of solutions, namely, with a gaussian initial profile (in phase space), thus the resulting solution is a convolution of gaussians (both the fundamental solution or propagator, and the initial profile). Then we compute some hydrodinamical and thermodynamical densities from the exact expression for the probability distribution of a Brownian particle, for example, particle density, matter ux density, energy density, energy ux density, entropy density, among others, and some derived quantities suchs as the effective temperature of the Brownian gas. In 2005 we published part of these results, namely the fundamental solution and some application on the asymptotic regime
Doutorado
Física Estatistica e Termodinamica
Doutora em Ciências

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Bruna, Maria. "Excluded-volume effects in stochastic models of diffusion." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:020c2d3e-5fef-478c-9861-553cd310daf5.

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Stochastic models describing how interacting individuals give rise to collective behaviour have become a widely used tool across disciplines—ranging from biology to physics to social sciences. Continuum population-level models based on partial differential equations for the population density can be a very useful tool (when, for large systems, particle-based models become computationally intractable), but the challenge is to predict the correct macroscopic description of the key attributes at the particle level (such as interactions between individuals and evolution rules). In this thesis we consider the simple class of models consisting of diffusive particles with short-range interactions. It is relevant to many applications, such as colloidal systems and granular gases, and also for more complex systems such as diffusion through ion channels, biological cell populations and animal swarms. To derive the macroscopic model of such systems, previous studies have used ad hoc closure approximations, often generating errors. Instead, we provide a new systematic method based on matched asymptotic expansions to establish the link between the individual- and the population-level models. We begin by deriving the population-level model of a system of identical Brownian hard spheres. The result is a nonlinear diffusion equation for the one-particle density function with excluded-volume effects enhancing the overall collective diffusion rate. We then expand this core problem in several directions. First, for a system with two types of particles (two species) we obtain a nonlinear cross-diffusion model. This model captures both alternative notions of diffusion, the collective diffusion and the self-diffusion, and can be used to study diffusion through obstacles. Second, we study the diffusion of finite-size particles through confined domains such as a narrow channel or a Hele–Shaw cell. In this case the macroscopic model depends on a confinement parameter and interpolates between severe confinement (e.g., a single- file diffusion in the narrow channel case) and an unconfined situation. Finally, the analysis for diffusive soft spheres, particles with soft-core repulsive potentials, yields an interaction-dependent non-linear term in the diffusion equation.

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Flegg, Mark Bruce. "Theoretical investigation of mechanisms of formation and interaction of nanoparticles." Thesis, Queensland University of Technology, 2010. https://eprints.qut.edu.au/31843/1/Mark_Flegg_Thesis.pdf.

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In this thesis an investigation into theoretical models for formation and interaction of nanoparticles is presented. The work presented includes a literature review of current models followed by a series of five chapters of original research. This thesis has been submitted in partial fulfilment of the requirements for the degree of doctor of philosophy by publication and therefore each of the five chapters consist of a peer-reviewed journal article. The thesis is then concluded with a discussion of what has been achieved during the PhD candidature, the potential applications for this research and ways in which the research could be extended in the future. In this thesis we explore stochastic models pertaining to the interaction and evolution mechanisms of nanoparticles. In particular, we explore in depth the stochastic evaporation of molecules due to thermal activation and its ultimate effect on nanoparticles sizes and concentrations. Secondly, we analyse the thermal vibrations of nanoparticles suspended in a fluid and subject to standing oscillating drag forces (as would occur in a standing sound wave) and finally on lattice surfaces in the presence of high heat gradients. We have described in this thesis a number of new models for the description of multicompartment networks joined by a multiple, stochastically evaporating, links. The primary motivation for this work is in the description of thermal fragmentation in which multiple molecules holding parts of a carbonaceous nanoparticle may evaporate. Ultimately, these models predict the rate at which the network or aggregate fragments into smaller networks/aggregates and with what aggregate size distribution. The models are highly analytic and describe the fragmentation of a link holding multiple bonds using Markov processes that best describe different physical situations and these processes have been analysed using a number of mathematical methods. The fragmentation of the network/aggregate is then predicted using combinatorial arguments. Whilst there is some scepticism in the scientific community pertaining to the proposed mechanism of thermal fragmentation,we have presented compelling evidence in this thesis supporting the currently proposed mechanism and shown that our models can accurately match experimental results. This was achieved using a realistic simulation of the fragmentation of the fractal carbonaceous aggregate structure using our models. Furthermore, in this thesis a method of manipulation using acoustic standing waves is investigated. In our investigation we analysed the effect of frequency and particle size on the ability for the particle to be manipulated by means of a standing acoustic wave. In our results, we report the existence of a critical frequency for a particular particle size. This frequency is inversely proportional to the Stokes time of the particle in the fluid. We also find that for large frequencies the subtle Brownian motion of even larger particles plays a significant role in the efficacy of the manipulation. This is due to the decreasing size of the boundary layer between acoustic nodes. Our model utilises a multiple time scale approach to calculating the long term effects of the standing acoustic field on the particles that are interacting with the sound. These effects are then combined with the effects of Brownian motion in order to obtain a complete mathematical description of the particle dynamics in such acoustic fields. Finally, in this thesis, we develop a numerical routine for the description of "thermal tweezers". Currently, the technique of thermal tweezers is predominantly theoretical however there has been a handful of successful experiments which demonstrate the effect it practise. Thermal tweezers is the name given to the way in which particles can be easily manipulated on a lattice surface by careful selection of a heat distribution over the surface. Typically, the theoretical simulations of the effect can be rather time consuming with supercomputer facilities processing data over days or even weeks. Our alternative numerical method for the simulation of particle distributions pertaining to the thermal tweezers effect use the Fokker-Planck equation to derive a quick numerical method for the calculation of the effective diffusion constant as a result of the lattice and the temperature. We then use this diffusion constant and solve the diffusion equation numerically using the finite volume method. This saves the algorithm from calculating many individual particle trajectories since it is describes the flow of the probability distribution of particles in a continuous manner. The alternative method that is outlined in this thesis can produce a larger quantity of accurate results on a household PC in a matter of hours which is much better than was previously achieveable.

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HUANG, FANG-GUO, and 黃芳國. "The sets containing points of multiplicity c of planar brownian motion." Thesis, 1989. http://ndltd.ncl.edu.tw/handle/83165117657231954209.

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Blaschke, Johannes Paul. "Entropic Motors." Doctoral thesis, 2014. http://hdl.handle.net/11858/00-1735-0000-0022-5E50-C.

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Книги з теми "Planar Brownian motion"

Guionnet, Alice. Free probability. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0003.

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Free probability was introduced by D. Voiculescu as a theory of noncommutative random variables (similar to integration theory) equipped with a notion of freeness very similar to independence. In fact, it is possible in this framework to define the natural ‘free’ counterpart of the central limit theorem, Gaussian distribution, Brownian motion, stochastic differential calculus, entropy, etc. It also appears as the natural setup for studying large random matrices as their size goes to infinity and hence is central in the study of random matrices as their size go to infinity. In this chapter the free probability framework is introduced, and it is shown how it naturally shows up in the random matrices asymptotics via the so-called ‘asymptotic freeness’. The connection with combinatorics and the enumeration of planar maps, including loop models, are discussed.

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Seth, Raghav, and George E. Smith. Brownian Motion and Molecular Reality. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780190098025.001.0001.

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Legend has it that Jean Perrin’s experiments on Brownian motion between 1905 and 1913 “put a definite end to the long struggle regarding the real existence of molecules.” Close examination of these experiments, however, shows how little access they gained to the molecular realm. They did succeed in determining mean kinetic energies of particles in Brownian motion, but the values for molecular magnitudes Perrin inferred from them simply presupposed that those energies match the mean kinetic energies of molecules in the surrounding fluid. This presupposition became increasingly suspect between 1908 and 1913 as distinctly different values for these magnitudes were obtained from alpha-particle emissions (by Rutherford et al.), from ionization (by Millikan), and from Planck’s blackbody radiation equation. This monograph explains how Perrin’s measurements of the kinetic energies in Brownian motion were nevertheless exemplars of theory-mediated measurement—the practice of inferring values for inaccessible quantities from values of accessible proxies via theoretical relationships between them. Moreover, though Planck in 1900 had proposed turning to complementary theory-mediated measurements of interlinked molecular magnitudes as a source of evidence, it was Perrin more than anyone else who championed this approach. The concerted efforts of Rutherford, Millikan, Planck, Perrin, and their colleagues during the years in question led to evidence of this form becoming central to microphysics. The analysis here of how this came about replaces an untenable legend with an account that is not only tenable, but far more instructive about what the evidence did and did not show.

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Succi, Sauro. Stochastic Particle Dynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0009.

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Dense fluids and liquids molecules are in constant interaction; hence, they do not fit into the Boltzmann’s picture of a clearcut separation between free-streaming and collisional interactions. Since the interactions are soft and do not involve large scattering angles, an effective way of describing dense fluids is to formulate stochastic models of particle motion, as pioneered by Einstein’s theory of Brownian motion and later extended by Paul Langevin. Besides its practical value for the study of the kinetic theory of dense fluids, Brownian motion bears a central place in the historical development of kinetic theory. Among others, it provided conclusive evidence in favor of the atomistic theory of matter. This chapter introduces the basic notions of stochastic dynamics and its connection with other important kinetic equations, primarily the Fokker–Planck equation, which bear a complementary role to the Boltzmann equation in the kinetic theory of dense fluids.

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Milonni, Peter W. An Introduction to Quantum Optics and Quantum Fluctuations. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780199215614.001.0001.

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This book is an introduction to quantum optics for students who have studied electromagnetism and quantum mechanics at an advanced undergraduate or graduate level. It provides detailed expositions of theory with emphasis on general physical principles. Foundational topics in classical and quantum electrodynamics, including the semiclassical theory of atom-field interactions, the quantization of the electromagnetic field in dispersive and dissipative media, uncertainty relations, and spontaneous emission, are addressed in the first half of the book. The second half begins with a chapter on the Jaynes-Cummings model, dressed states, and some distinctly quantum-mechanical features of atom-field interactions, and includes discussion of entanglement, the no-cloning theorem, von Neumann’s proof concerning hidden variable theories, Bell’s theorem, and tests of Bell inequalities. The last two chapters focus on quantum fluctuations and fluctuation-dissipation relations, beginning with Brownian motion, the Fokker-Planck equation, and classical and quantum Langevin equations. Detailed calculations are presented for the laser linewidth, spontaneous emission noise, photon statistics of linear amplifiers and attenuators, and other phenomena. Van der Waals interactions, Casimir forces, the Lifshitz theory of molecular forces between macroscopic media, and the many-body theory of such forces based on dyadic Green functions are analyzed from the perspective of Langevin noise, vacuum field fluctuations, and zero-point energy. There are numerous historical sidelights throughout the book, and approximately seventy exercises.

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Частини книг з теми "Planar Brownian motion"

Le Gall, Jean-François. "Some properties of planar brownian motion." In Lecture Notes in Mathematics, 111–229. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0084700.

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Le Gall, J. F., and S. James Taylor. "The Packing Measure of Planar Brownian Motion." In Seminar on Stochastic Processes, 1986, 139–47. Boston, MA: Birkhäuser Boston, 1987. http://dx.doi.org/10.1007/978-1-4684-6751-2_9.

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Yor, Marc. "From Planar Brownian Windings to Asian Options." In Exponential Functionals of Brownian Motion and Related Processes, 123–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56634-9_8.

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Werner, Wendelin. "Critical Exponents, Conformal Invariance and Planar Brownian Motion." In European Congress of Mathematics, 87–103. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8266-8_8.

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Brossard, Jean, Michel Émery, and Christophe Leuridan. "Skew-Product Decomposition of Planar Brownian Motion and Complementability." In Lecture Notes in Mathematics, 377–94. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11970-0_15.

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Dynkin, E. B. "Functionals associated with self-intersections of the planar Brownian motion." In Séminaire de Probabilités XX 1984/85, 553–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0075741.

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Rosen, Jay. "A renormalized local time for multiple intersections of planar brownian motion." In Séminaire de Probabilités XX 1984/85, 515–31. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0075738.

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Bertoin, Jean, and Wendelin Werner. "Asymptotic windings of planar Brownian motion revisited via the Ornstein-Uhlenbeck process." In Lecture Notes in Mathematics, 138–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0073842.

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Shi, Z. "Liminf behaviours of the windings and Lévy's stochastic areas of planar Brownian motion." In Lecture Notes in Mathematics, 122–37. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0073841.

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Le Gall, Jean-François. "Exponential moments for the renormalized self-intersection local time of planar brownian motion." In Lecture Notes in Mathematics, 172–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0073845.

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Тези доповідей конференцій з теми "Planar Brownian motion"

Zhou, Yu, and Gregory S. Chirikjian. "Nonholonomic Motion Planning Using Diffusion of Workspace Density Functions." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-42916.

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Анотація:

This paper introduces a trajectory planning algorithm for nonholonomic mobile robots which operate in an environment with obstacles. An important feature of our approach is that the planning domain is the workspace of the mobile robot rather than its configuration space. The basic idea is to imagine the robot being subjected to Brownian motion forcing, and to generate evolving probability density functions (PDF) that describe all attainable positions and orientations of the robot at a given value of time. By planning a path that optimizes the value of this PDF at each instant in time, we generate a feasible trajectory. The PDF of robot pose can be constructed by solving the corresponding Fokker-Planck equation using the Fourier transform for SE(N). A closed-form approximation of the resulting time-dependent PDF is then used to plan a trajectory based on the observation that the evolution of this “workspace density” is a diffusion process. Examples are provided to illustrate the algorithm.

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Vuillerme, Nicolas, Nicolas Pinsault, Olivier Chenu, Anthony Fleury, Yohan Payan, and Jacques Demongeot. "The Effects of a Plantar Pressure-Based, Tongue-Placed Tactile Biofeedback System on the Regulation of the Centre of Foot Pressure Displacements During Upright Quiet Standing: A Fractional Brownian Motion Analysis." In 2008 International Conference on Complex, Intelligent and Software Intensive Systems. IEEE, 2008. http://dx.doi.org/10.1109/cisis.2008.32.

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Lin, Xiaohui, Chibin Zhang, Changbao Wang, Wenquan Chu, and Zhaomin Wang. "A Two-Phase Model for Analysis of Blood Flow and Rheological Properties in the Elastic Microvessel." In ASME 2016 14th International Conference on Nanochannels, Microchannels, and Minichannels collocated with the ASME 2016 Heat Transfer Summer Conference and the ASME 2016 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/icnmm2016-8103.

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The blood in microvascular is seemed as a two-phase flow system composed of plasma and red blood cells (RBCs). Based on hydrodynamic continuity equation, Navier-Stokes equation, Fokker-Planck equation, generalized Reynolds equation and elasticity equation, a two-phase flow transport model of blood in elastic microvascular is proposed. The continuous medium assumption of RBCs is abandoned. The impact of the elastic deformation of the vessel wall, the interaction effect between RBCs, the Brownian motion effect of RBCs and the viscous resistance effect between RBCs and plasma on blood transport are considered. Model does not introduce any phenolmeno-logical parameter, compared with the previous phenolmeno-logical model, this model is more comprehensive in theory. The results show that, the plasma velocity distribution is cork-shaped, which is apparently different with the parabolic shape of the single-phase flow model. The reason of taper angle phenomenon and RBCs “Center focus” phenomenon are also analyzed. When the blood vessel radius is in the order of microns, blood apparent viscosity’s Fahraeus-Lindqvist effect and inverse Fahraeus-Lindqvist effect will occur, the maximum of wall shear stress will appear in the minimum of diameter, the variations of blood apparent viscosity with consider of RBCs volume fraction and shear rate calculated by the model are in good agreement with the experimental values.

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