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911.
912.
Michael Voit 《Studies in Applied Mathematics》2023,151(4):1230-1281
One-dimensional interacting particle models of Calogero–Moser–Sutherland type with N particles can be regarded as diffusion processes on suitable subsets of like Weyl chambers and alcoves with second-order differential operators as generators of the transition semigroups, where these operators are singular on the boundaries of the state spaces. The most relevant examples are multivariate Bessel processes and Heckman–Opdam processes in a compact and noncompact setting where in all cases, these processes are related to special functions associated with root systems. More precisely, the transition probabilities can be described with the aid of multivariate Bessel functions, Jack and Heckman–Opdam Jacobi polynomials, and Heckman–Opdam hypergeometric functions, respectively. These models, in particular, form dynamic eigenvalue evolutions of the classical random matrix models like β-Hermite, β- Laguerre, and β-Jacobi, that is, MANOVA, ensembles. In particular, Dyson's Brownian motions and multivariate Jacobi processes are included. In all cases, the processes depend on so-called coupling parameters. We review several freezing limit theorems for these diffusions where, for fixed N, one or several of the coupling parameters tend to ∞. In many cases, the limits will be N-dimensional normal distributions and, in the process case, Gauss processes. However, in some cases, normal distributions on half spaces and distributions related to some other ensembles appear as limits. In all cases, the limits are connected with the zeros of the classical one-dimensional orthogonal polynomials of order N. 相似文献
913.
Frontiers of Physics - Nonreciprocal microwave devices, in which the transmission of waves is non-symmetric between two ports, are indispensable for the manipulation of information processing and... 相似文献
914.
Junyang Sui Ruiyang Dong Siyuan Liao Zeyuan Zhao Yubo Wang Hai-Feng Zhang 《Annalen der Physik》2023,535(3):2200509
In this paper, a Janus metastructure (JMS) is proposed that can act both as a logic gate and detect multiple physical quantities. By adjusting the incident angle of electromagnetic waves, arranging the dielectrics asymmetrically, and using the anisotropy of the plasma, the Janus function can be obtained, which gives the metastructure a multiscale property. Sharp transmission peak (TP) is generated by located defect mode resonance. The AND logic gate on the positive and negative scales can be realized by judging the TP value. By locking the point frequency of the TP, the refractive index, magnetic field strength, incident angle, and plasma density can be detected simultaneously on the two scales in the GHz range, which is rarely studied. Good sensing performances are also owned, and the corresponding optimal sensitivities are 0.095 (2πc/d)/RIU, 9.42 × 10−3 (2πc/d)/T, 1.48 × 10−3 (2πc/d)/°, and 0.035 (2πc/d) m3/1019, respectively. Compared with the traditional sensors, the proposed JMS equipped with two scales not only can realize the logic gate but also measure multiple physical quantities, which has a certain application potential. 相似文献
915.
Yutaka Tanaka 《Macromolecular Symposia》2003,200(1):265-270
Dynamic viscoelasticity was observed for polyacrylonitrile solution in dimethylacetamide in the process of sol-gel transition. The gel was prepared by the freezing and thawing method, i.e., the solution was frozen at −50°C and then kept at 25°C so as to undergo gelation. The longer the freezing time, the shorter was the gelation time. Also the higher the concentration, the shorter the gelation time. The strength of the network, S and critical exponent n at the transition point were evaluated. The S value increased with increasing concentration and was constant in value in spite of the variation of freezing time when the concentration of the solution was constant. 相似文献