We give a closed form for the correlation functions of ensembles of a class of asymmetric real matrices in terms of the Pfaffian
of an antisymmetric matrix formed from a 2 × 2 matrix kernel associated to the ensemble. We apply this result to the real
Ginibre ensemble and compute the bulk and edge scaling limits of its correlation functions as the size of the matrices becomes
large. 相似文献
In this paper we further develop the Method of Nearby Problems (MNP) for generating exact solutions to realistic partial differential equations by extending it to two dimensions. We provide an extensive discussion of the 2D spline fitting approach which provides Ck continuity (continuity of the solution value and its first k derivatives) along spline boundaries and is readily extendable to higher dimensions. A detailed one-dimensional example is given to outline the general concepts, then the two-dimensional spline fitting approach is applied to two problems: heat conduction with a distributed source term and the viscous, incompressible flow in a lid-driven cavity with both a constant lid velocity and a regularized lid velocity (which removes the strong corner singularities). The spline fitting approach results in very small spline fitting errors for the heat conduction problem and the regularized driven cavity, whereas the fitting errors in the standard lid-driven cavity case are somewhat larger due to the singular behaviour of the pressure near the driven lid. The MNP approach is used successfully as a discretization error estimator for the driven cavity cases, outperforming Richardson extrapolation which requires two grid levels. However, MNP has difficulties with the simpler heat conduction case due to the discretization errors having the same magnitude as the spline fitting errors. 相似文献
Solving the frequency equation and plotting the dispersion curves in problems of wave propagation in cylinders and plates, particularly when the material is anisotropic, are complicated tasks. The traditional numerical methods are usually based on determination of the zeros of the frequency equation by using an iterative find-root algorithm. In this paper, an alternative method is proposed which extracts the solution of the frequency equation in the form of dispersion curves from the three-dimensional illustration of the frequency equation. For this purpose, a three-dimensional representation of the real roots of the frequency equation is first plotted. The dispersion curves, which are the numerical solutions of the frequency equation, are then obtained by a suitable cut in the velocity-frequency plane. The advantages of this method include simplicity, high speed, low possibility of numerical error, and presentation of the results in a graphical form that promotes ease of interpretation. This method is not directly applicable to problems which incorporate high damping or leaky waves. However, if the damping is not very high, it could be a good estimate of the true dispersion curves. 相似文献
Guest‐love‐ometer : The equilibrium inside–outside atropisomeric ratio of ortho‐substituted phenyl cavitands shows a strong solvent dependence. The competition between the ortho‐substituent and the solvent guest for the bowl cavity leads to a sensitive system for the measurement of relative guest binding affinities.
The objective of this article is to present a sharp result to determine when the cut locus for a class of metrics on a two-sphere of revolution is reduced to a single branch. This work is motivated by optimal control problems in space and quantum dynamics and gives global optimal results in orbital transfer and for Lindblad equations in quantum control. 相似文献
The title compound, [Fe(C10H8N2)3](ClO4)2, is isomorphous with the ZnII and RuII analogues. A twofold axis passes through the metal atom and the midpoint of the C—C bond joining the two pyridine rings of one of the bipyridyl ligands. 相似文献
gsa =3.0×10-18 cm2 and σesa=1.4×10-19 cm2 at 1064 nm, and σgsa=7.2×10-18 cm2 and σesa=7.4×10-19 cm2 at 1342 nm. Q-switched operation was demonstrated at 1064 nm and 1342 nm from a Nd:YVO4 microchip laser, producing pulses as short as 9.3 ns at 1342 nm with peak powers of 350 W.
Received: 17 March 1998/Revised version: 8 June 1998 相似文献