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11.
Mark A. Pinsky 《Journal of statistical physics》1975,13(3):189-196
For the linearized Boltzmann equation with finite cross section, the solution is represented as an integral over the paths of a Markov jump process. The integral is only shown to converge conditionally, where the limiting process is defined by an increasing sequence of stopping times. The notion of local martingale plays an important role. A number of related kinetic models are also mentioned.Supported by NSF Grant GP 28576. 相似文献
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Ross G. Pinsky 《Random Structures and Algorithms》2006,29(3):277-295
Let the random variable Zn,k denote the number of increasing subsequences of length k in a random permutation from Sn, the symmetric group of permutations of {1,…,n}. We show that Var(Z) = o((EZ)2) as n → ∞ if and only if . In particular then, the weak law of large numbers holds for Z if ; that is, We also show the following approximation result for the uniform measure Un on Sn. Define the probability measure μ on Sn by where U denotes the uniform measure on the subset of permutations that contain the increasing subsequence {x1,x2,…,x}. Then the weak law of large numbers holds for Z if and only if where ∣∣˙∣∣ denotes the total variation norm. In particular then, (*) holds if . In order to evaluate the asymptotic behavior of the second moment, we need to analyze occupation times of certain conditioned two‐dimensional random walks. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006 相似文献
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A nonlinear, macroscopic multi-phasic model for describing the interactions between solid, fluid, and ionic species in porous materials is presented. Governing equations are derived based on the nonlinear theories of solid mechanics, linear flow theory of Newtonian fluids, and theory of irreversible thermodynamics for the transport of ions and ionic solutions. The model shows that the transport coupling between ions and ionic solution exists only when the porous material has a membrane-like feature, which could be inside the material or on the material boundaries. Otherwise, the coupling occurs only between the solid and fluid phases and the transport of ionic species will have no effect on the macroscopic stresses, strains and displacements of the porous material. As an application of the present multi-phasic model, a numerical example of the human cornea under the shock of NaCl hypertonic solution applied to its endothelial surface is presented. This is a typical example of how ionic transport induces swelling in biological tissues. The results obtained from the present multi-phasic model demonstrate that the mechanical properties of the tissue have an important influence on the swelling of the cornea. Without taking into account this influence, the predicted swelling may be exaggerated. 相似文献
15.
Nonlinear Dynamics - Estimation of the degree of stability and the bounds of solutions to nonautonomous nonlinear systems present major concerns in numerous applied problems. Yet, current... 相似文献
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We consider a diffusion process on D⊂Rd, which upon hitting ∂D, is redistributed in D according to a probability measure depending continuously on its exit point. We prove that the distribution of the process converges exponentially fast to its unique invariant distribution and characterize the exponent as the spectral gap for a differential operator that serves as the generator of the process on a suitable function space. 相似文献
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Mark A. Pinsky 《Proceedings of the American Mathematical Society》2004,132(6):1729-1737
We state and prove sufficient conditions for the absolute integrability of the inverse of the continuum wavelet kernel.
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Volume of a small Extrinsic Ball in a Submanifold 总被引:1,自引:0,他引:1
For a submanifold Mp R, we determine a two-term asymptoticformula for vol (Mp B(x)) for x Mp as 0. The second termis a quadratic curvature invariant of the second fundamentalform of the imbedding. Imbedded spheres are characterized amongcompact hypersurfaces by this term. 相似文献
20.
Ross G. Pinsky 《Random Structures and Algorithms》2015,46(2):362-390
Consider a permutation σ ∈ Sn as a deck of cards numbered from 1 to n and laid out in a row, where σj denotes the number of the card that is in the j‐th position from the left. We study some probabilistic and combinatorial aspects of the shuffle on Sn defined by removing and then randomly reinserting each of the n cards once, with the removal and reinsertion being performed according to the original left to right order of the cards. The novelty here in this nonstandard shuffle is that every card is removed and reinserted exactly once. The bias that remains turns out to be quite strong and possesses some surprising features. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 362–390, 2015 相似文献