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81.
We investigate the small ball problem for d-dimensional fractional Brownian sheets by functional analytic methods. For this reason we show that integration operators of Riemann–Liouville and Weyl type are very close in the sense of their approximation properties, i.e., the Kolmogorov and entropy numbers of their difference tend to zero exponentially. This allows us to carry over properties of the Weyl operator to the Riemann–Liouville one, leading to sharp small ball estimates for some fractional Brownian sheets. In particular, we extend Talagrand's estimate for the 2-dimensional Brownian sheet to the fractional case. When passing from dimension 1 to dimension d2, we use a quite general estimate for the Kolmogorov numbers of the tensor products of linear operators. 相似文献
82.
Vahedi Tafreshi H. Piseri P. Barborini E. Benedek G. Milani P. 《Journal of nanoparticle research》2002,4(6):511-524
We describe a simulation of the nanoparticle trajectories in a pulsed cluster beam source. Clusters, formed by condensation of atomic vapor in a helium bath, and considered here as rigid spheres having a diameter of 1.5nm, were tracked during their travel inside the source cavity, an aerodynamic lens, and a cylindrical nozzle. Steady state supersonic laminar flow of helium is considered in an axi-symmetric geometry aiming to simulate, within some limitations, the conditions under which cluster formation takes place in a pulsed microplasma cluster source. In spite of the unsteady nature of the pulsed source, the time scale characterizing particle motion in the flow field is significantly smaller than the characteristic time constant for the evolution of gas pressure in the source. For this reason, a steady simulation can shed some light on the understanding of processes governing nanoparticle motion in a pulsed vaporization source. The extent to which the Brownian diffusion can affect the particle extraction from the source is investigated. Simulations have shown that the Brownian motion perturbs the clusters from the trajectories dictated by the carrier gas and increases the rate of cluster deposition on the source internal walls. However, it does not hinder the aerodynamic focalization produced by the lens even in nano-size cluster regime. This result is qualitatively confirmed by experiment. 相似文献
83.
Frequency-sensitive stochastic resonance in periodically forced and globally coupled systems 总被引:1,自引:0,他引:1
J. Xiao G. Hu H. Liu Y. Zhang 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,5(1):133-138
A model of globally coupled bistable systems consisting of two kinds of sites, subject to periodic driving and spatially uncorrelated
stochastic force, is investigated. The extended system models the competing process of activators and suppressers. Analytical
computations for linear response of the system to the external periodic forcing is carried out. Noise-induced Hopf bifurcation
is revealed, and stochastic resonance, sensitively depending on the frequency of the external forcing, is predicted under
the Hopf bifurcation condition. Numerical simulations agree with the analytical predictions satisfactorily.
Received: 5 September 1997 / Revised: 13 May 1998 /
Accepted: 18 May 1998 相似文献
84.
An analysis is made of the effects on the diffusion of Brownian particles whose Knudsen number is large compared to unity, of nonuniformities in the host gas. As examples, in one type of nonuniformity of the host gas, the Chapman-Enskog velocity distribution function for the gas molecules is used; in the other, the host gas is a free-molecule Couette flow. In both cases, a new force on the Brownian particles appears. Two techniques are used (extending Kramers' method and utilizing the Chapman-Enskog method) to transform the new Fokker-Planck equation into generalized Smoluchowski and convective diffusion equations. In these equations, the diffusion coefficient appears as a second-order tensor. Thus, it is demonstrated that Brownian diffusion in a nonuniform gas is anisotropic.The work of Slinn was financially supported in part by Battelle Memorial Institute and in part by U.S. Atomic Energy Commission Contract AT(45-1)-1830. The work of Shen was supported in part by U.S. Air Force Office of Scientific Research Contract 49(638)-1346. 相似文献
85.
Two models are given of branching transport processes that converge to branching Brownian motion starting with one initial particle. The martingale problem method is used. 相似文献
86.
Pilot-Wave Theory and Financial Option Pricing 总被引:1,自引:0,他引:1
This paper tries to argue why pilot-wave theory could be of use in financial economics. We introduce the notion of information
wave. We consider a stochastic guidance equation and part of the drift term of that equation makes reference to the phase
of the wave. In order to embed information in financial option pricing we could use such a drift. We also briefly argue how
we could embed information in the pricing kernel of the option price.
PACS: 03, 89.65.Gh. 相似文献
87.
Relativistic Brownian Motion and Gravity as an Eikonal Approximation to a Quantum Evolution Equation
We solve the problem of formulating Brownian motion in a relativistically covariant framework in 3+1 dimensions. We obtain
covariant Fokker–Planck equations with (for the isotropic case) a differential operator of invariant d’Alembert form. Treating
the spacelike and timelike fluctuations separately in order to maintain the covariance property, we show that it is essential
to take into account the analytic continuation of “unphysical” fluctuations. 相似文献
88.
For two types of stochastic particle systems in we show non-explosion in finite time by proving that their respective generators are L1(μ)-unique, where μ is their respective invariant (in these cases even symmetrizing) measure. We also prove the much harder L2(μ)-uniqueness in both models. 相似文献
89.
The Brownian loop soup 总被引:6,自引:0,他引:6
Gregory F.?Lawler Wendelin?WernerEmail author 《Probability Theory and Related Fields》2004,128(4):565-588
We define a natural conformally invariant measure on unrooted Brownian loops in the plane and study some of its properties. We relate this measure to a measure on loops rooted at a boundary point of a domain and show how this relation gives a way to chronologically add Brownian loops to simple curves in the plane.Cornell University; Research supported in part by the National Science FoundationUniversité Paris-Sud and IUFMathematics Subject Classification (2000):60J65, 81T40 相似文献
90.
A new and general approach is proposed to analyze the dynamics of a colloidal particle interacting with a nearby wall. This
analysis can be used to determine the acting forces even when the system is non-stationary. As an illustration, we use total
internal reflection microscopy to investigate the forces acting on a polystyrene sulfate latex particle as it is receding
from a charged glass surface.
Received 10 October 2002 Published online: 16 April 2003
RID="a"
ID="a"Present address: Department of Polymer Physics, BASF Aktiengesellschaft, 67056 Ludwigshafen, Germany
RID="b"
ID="b"Present address: Arryx. Inc., Chicago, IL 60601, USA 相似文献