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21.
Piotr Garbaczewski 《Journal of statistical physics》2006,123(2):315-355
We analyze the functioning of Gibbs-type entropy functionals in the time domain, with emphasis on Shannon and Kullback-Leibler entropies of time-dependent continuous probability distributions. The Shannon entropy validity is extended to probability distributions inferred from L
2(R
n
) quantum wave packets. In contrast to the von Neumann entropy which simply vanishes on pure states, the differential entropy quantifies the degree of probability (de)localization and its time development. The associated dynamics of the Fisher information functional quantifies nontrivial power transfer processes in the mean, both in dissipative and quantum mechanical cases.
PACS NUMBERS: 05.45.+b, 02.50.-r, 03.65.Ta, 03.67.-a 相似文献
22.
对于非定常输运问题提出了一种基于香农熵的自动调整样本数策略。将每一计算步的总样本数划分为若干批并逐步模拟每批中的粒子, 可以在每批粒子模拟结束后通过计算得到该时间步幸存粒子属性分布对应的香农熵值。采用在线收敛性诊断方法, 一旦通过香农熵值序列判断对应的幸存粒子属性分布已经收敛, 则可以提前结束本时间步的计算。对一个空间一维非定常输运模型的计算结果表明, 该策略可以显著减少每一计算步的实际样本数且保持最终的结果基本不变, 从而减少了计算时间, 提高了计算效率。 相似文献
23.
The present study aims to derive an analytical model on bed-load layer thickness in an open channel turbulent flow carrying sediments. Determination of the thickness of the bed-load layer is of utmost importance in the study of bed-load transport as it is required to determine the bed-load transport rate, as well as in the study of suspended load transport as it acts as reference level for the particles in suspension. Apart from the several deterministic approaches available in the literature, the work adopts probabilistic approach based on entropy theory to determine the bed-load layer thickness. The concept of entropy theory developed by Shannon is used and the method of Lagrange multipliers is employed for the maximization of entropy function to find the least biased probability distribution. To calculate the Lagrange multipliers, present in the probabilistic model of dimensionless bed-load layer thickness, two different methodologies are presented. The model of bed-load layer thickness is a function of dimensionless shear stress and also depends on three other parameters which are found to be functions of specific gravity of sediment particle and dimensionless particle diameter from a non-linear regression analysis. The proposed model is validated with wide sets of experimental data available in literature and a good agreement is achieved. Apart from comparison with data, the model is also compared with existing deterministic model and computation of relative percentage error proves the better efficiency of the present model. 相似文献
24.
In the mid-1980s an equivalence was established between the simple closed geodesics on the Riemann surfaces obtained as quotients of the upper half plane H by any of the following subgroups of the modular group (1) : , (3), and 3. An axis of a hyperbolic element of (1) projects to a simple closed geodesic on one of these surfaces if and only if it does so on the other two.This equivalence was used to obtain a variety of Diophantine and geometric results. In subsequent related investigations, the role of (1) was assumed by the Hecke triangle group Gq for q 3. (For q = 3, we have (1) = G3.) These works employed the analog of 3, denoted q.In the context of the Gq, the present paper gives the analog of , which we denote q. As in the case q = 3, we have [q:q] = 2. A rather full discussion of geometry of q\ H is given. In particular, we demonstrate that the equivalence of simple closed geodesics on q\ H and q\ H does not hold for q 7.As of this writing, we have not been able to obtain an appropriate analog of (3). 相似文献
25.
Differential FBG sensor for temperature-compensated high-pressure (or displacement) measurement 总被引:2,自引:0,他引:2
A differential fiber Bragg grating (FBG) sensor with a free active element bulk-modulus for high-pressure (or displacement) measurement is presented. Based on the differential measurement method and an isosceles triangle cantilever structure, problems of cross-sensitivity and chirped signal in FBG sensor are improved both theoretically and experimentally. Preliminary experiments indicate that temperature-compensated measurement results agree well with the theoretical analysis. Displacement measurement sensitivity is 1.75 pm/μm, and the estimated pressure measurement resolution can reach 0.27 MPa in case the wavelength shift measurement resolution is 0.01 nm. 相似文献
26.
《Physics letters. A》2019,383(17):2028-2032
We find that the simple coupling of network growth to the position of a random walker on the network generates a traveling wave in the probability distribution of nodes visited by the walker. We argue that the entropy of this probability distribution is bounded as the network size tends to infinity. This means that the growth of a space coupled to a random walker situated in it constrains its dynamics to a set of typical random walker trajectories, and walker trajectories inside the growing space are compressible. 相似文献
27.
研究了杨辉三角中的D av id星恒等式,给出了n阶星恒等式的定义,证明了n(n 3)阶星恒等式的存在性,并且给出了构造n阶星恒等式的方法. 相似文献
28.
We continue our study [S. Smale, D.X. Zhou, Shannon sampling and function reconstruction from point values, Bull. Amer. Math. Soc. 41 (2004) 279–305] of Shannon sampling and function reconstruction. In this paper, the error analysis is improved. Then we show how our approach can be applied to learning theory: a functional analysis framework is presented; dimension independent probability estimates are given not only for the error in the L2 spaces, but also for the error in the reproducing kernel Hilbert space where the learning algorithm is performed. Covering number arguments are replaced by estimates of integral operators. 相似文献
29.
The exponential functional of simple, symmetric random walks with negative
drift is an infinite polynomial Y = 1 + ξ1 + ξ1ξ2 + ξ1ξ2ξ3 + ⋯ of independent
and identically distributed non-negative random variables. It has moments that are
rational functions of the variables μ
k
= E(ξ
k
) < 1 with universal coefficients. It
turns out that such a coefficient is equal to the number of permutations with descent
set defined by the multiindex of the coefficient. A recursion enumerates all numbers
of permutations with given descent sets in the form of a Pascal-type triangle.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
30.