Download or read book Competing Brownian Particles written by Andrey Sarantsev and published by . This book was released on 2015 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consider a finite system of N Brownian particles on the real line. Rank them from bottom to top: the (currently) lowest particle has rank 1, the second lowest has rank 2, etc., up to the top particle, which has rank N. The particle which has (currently) rank k moves as a Brownian motion with drift coefficient gk and diffusion coefficient [sigma]k^2. When two or more particles collide, they might exchange ranks; in this case, they exchange drift and diffusion coefficients. This model is called a system of competing Brownian particles. It was introduced in Banner, Fernholz, Karatzas (2005) for the purpose of financial modeling. Since then, it attracted a considerable amount of attention. We can also consider infinite systems of competing Brownian particles (with the lowest particle but no highest particle, that is, with ranks ranging from 1 to infinity). For both finite and infinite systems, the gap process is formed by the spacings (gaps) between adjacent particles. It is (N-1)-dimensional for a finite system with N particles and infinite-dimensional for an infinite system. We say that a triple collision has occurred if three or more particles occupy the same position at the same time. In this thesis, we prove several new results about these systems. In particular, we establish convergence results for the gap process of infinite systems, building on the work of Pal, Pitman (2008); and we find a necessary and sufficient condition for a.s. absence of triple collisions, continuing the research from Ichiba, Karatzas, Shkolnikov (2013).

Download or read book Chains of Interacting Brownian Particles Under Strain written by Michael John Allman and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Probability and Stochastic Processes written by Siva Athreya and published by Springer Nature. This book was released on with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Convection and Diffusion of Brownian Particles Within Porous Systems written by Dermot Mary Malone and published by . This book was released on 1977 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Active Brownian Particles Moving in Complex Environments written by Narinder Narinder and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Deposition and Reentrainment of Brownian Particles Under Unfavorable Chemical Conditions written by Melinda Walker Hahn and published by . This book was released on 1995 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Long Time Diffusion of Interacting Brownian Particles written by and published by . This book was released on 1980 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Collective Phenomena in Active Brownian Particles with Feedback Controlled Interaction Rules written by Tobias Doyle Bäuerle and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the long time diffusion of interacting brownian particles written by Friedrich Grüner and published by . This book was released on 1980 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Stochastic Behavior of Brownian Particles in Potential Wells as Observed with Optical Traps written by Ross Paul Brody and published by . This book was released on 2008 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Computer Simulations of Active Brownian Particles written by Jonathan Tammo Siebert and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Brownian Particles Interacting with a Newtonian Barrier written by Clayton Barnes and published by . This book was released on 2018 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we pioneer the use of Skorohod maps in establishing the hydrodynamic behavior of an interacting particle system. This technique has the benefit of using stochastic methods to show both existence and uniqueness of the resulting PDE with free boundary condition. In 2001, Frank Knight constructed a stochastic process modeling the one dimensional interaction of two particles, one being Newtonian in the sense that it obeys Newton's laws of motion, and the other particle being Brownian. In the first chapter we construct a multi-particle analog, using Skorohod map estimates in proving a propagation of chaos and characterizing the hydrodynamic limit as the solution to a PDE with free boundary condition. The resulting PDE is similar to the solution of the Stefan problem. As mentioned, both existence and uniqueness of the PDE are done using stochastic methods; the uniqueness is done using a novel, and new, coupling method. In the second chapter, we give a strong approximation of Brownian motion with inert drift. We also determine the distribution of the maximum of the Newtonian particle via its Laplace transform. In the third chapter, we consider a random walker on the nonnegative lattice, moving in continuous time, whose transition rate is a linear function of the time the walker spends at the origin. In this way the walker is a jump process with a stochastic and adapted intensity. When Brownian scaling is introduced, such a process converges to Brownian motion with inert drift. This solves a conjecture of Burdzy and White in 2008. This convergence result is used to show two Brownian motions separated by an inert particle has a product stationary distribution on its state space where the velocity of the inert particle is Gaussian. This process of two Brownian motions separated by an inert particle was studied by White, in 2007, where the demonstration of existence for the process contains a nontrivial gap that we complete.

Download or read book Kinetics of Brownian Particles Driven Through Periodic Potential Energy Landscapes written by Pamela T. Korda and published by . This book was released on 2002 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Complex Motion and Structure Formation of Active Brownian Particles written by and published by . This book was released on 1998 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book State dependent Diffusion of Brownian Particles Near a Boundary Wall written by Mpumelelo Matse and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brownian motion refers to the erratic random movement of microscopic particles suspended in a fluid. In a simple fluid, Brownian motion exhibits two key properties: the mean-squared displacement (MSD) increases linearly with time (the proportionality constant is the diffusivity D) and the displacement distribution is Gaussian. Although a linear MSD was initially assumed to always imply Gaussian displacements, recent experiments show that non-Gaussian displacements can coexist with a linear MSD in complex environments. Chubynsky et al. [PRL 113, 098302, 2014] have argued that such behavior arises when D has temporal and/or spatial fluctuations that are convolved together and form a non-Gaussian distribution. Experiments to date have been in complex settings where direct measurements of D(x, t) have not been possible. Here, we report experiments on a simple system where D(x, t) is known: the Brownian motion of a colloidal sphere near a boundary wall. By choosing the particle size carefully, we ensure that the bead explores a wide range of D. We observe a linear MSD curve and non-Gaussian displacements for vertical motion and directly confirm the proposed mechanism of Chubynsky et al. for such "diffusing diffusivity."

Download or read book A Mode Coupling Theory for Brownian Particles in Homogeneous Steady Shear Flow written by Matthias Fuchs and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Light Scattering from Interacting Brownian Particles written by Dennis Gregory Neal and published by . This book was released on 1981 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: