Two-point Green's function is measured on the manifolds of a 2-dimensional quantum gravity. The recursive sampling technique is used to generate the triangulations, lattice sizes being up to hundred thousand trian...
Two-point Green's function is measured on the manifolds of a 2-dimensional quantum gravity. The recursive sampling technique is used to generate the triangulations, lattice sizes being up to hundred thousand triangles. The grid Laplacian was inverted by means of the algebraic multi-grid solver. The free field model of the Quantum Gravity assumes the Gaussian behavior of Liouville field and curvature. We measured histograms as well as six momenta of these fields. Our results support the Gaussian assumption.
In this article we present a new formulation for coupling spectral element discretizations to finite difference and finite element discretizations addressing flow problems in very complicated geometries. A general ite...
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This article reviews the application of various notions from the theory of dynamical systems to the analysis of numerical approximation of initial value problems over long-time intervals. Standard error estimates comp...
We characterize the behavior of solutions to systems of boundary integral equations associated with Laplace transmission problems in composite media consisting of regions with polygonal boundaries. In particular we co...
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Wavelet transforms and machine learning tools can be used to assist art experts in the stylistic analysis of paintings. A dual-tree complex wavelet transform, Hidden Markov Tree modeling and Random Forest classifiers ...
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This IMA Volume in mathematics and its Applications MULTIDIMENSIONAL HYPERBOLIC PROBLEMS AND COMPUTATIONS is based on the proceedings of a workshop which was an integral part ofthe 1988-89 IMA program on NONLINEAR WAV...
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ISBN:
(数字)9781461391210
ISBN:
(纸本)9781461391234
This IMA Volume in mathematics and its Applications MULTIDIMENSIONAL HYPERBOLIC PROBLEMS AND COMPUTATIONS is based on the proceedings of a workshop which was an integral part ofthe 1988-89 IMA program on NONLINEAR WAVES. We are grateful to the Scientific Commit tee: James Glimm, Daniel Joseph, Barbara Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for planning and implementing an exciting and stimulating year-long program. We especially thank the Work shop Organizers, Andrew Majda and James Glimm, for bringing together many of the major figures in a variety of research fields connected with multidimensional hyperbolic problems. A vner Friedman Willard Miller PREFACE A primary goal of the IMA workshop on Multidimensional Hyperbolic Problems and Computations from April 3-14, 1989 was to emphasize the interdisciplinary nature of contemporary research in this field involving the combination of ideas from the theory of nonlinear partial differential equations, asymptotic methods, numerical computation, and experiments. The twenty-six papers in this volume span a wide cross-section of this research including some papers on the kinetic theory of gases and vortex sheets for incompressible flow in addition to many papers on systems of hyperbolic conservation laws. This volume includes several papers on asymptotic methods such as nonlinear geometric optics, a number of articles applying numerical algorithms such as higher order Godunov methods and front tracking to physical problems along with comparison to experimental data, and also several interesting papers on the rigorous mathematical theory of shock waves.
As an important model in quantum semiconductor devices, the SchrSdinger-Poisson equations have generated widespread interests in both analysis and numerical simulations in recent years. In this paper, we present Gauss...
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As an important model in quantum semiconductor devices, the SchrSdinger-Poisson equations have generated widespread interests in both analysis and numerical simulations in recent years. In this paper, we present Gaussian beam methods for the numerical simulation of the one-dimensional Schrodinger-Poisson equations. The Gaussian beam methods for high frequency waves outperform the geometrical optics method in that the former are accurate even around caustics. The purposes of the paper are first to develop the Gaussian beam methods, based on our previous methods for the linear SchrSdinger equation, for the Schrodinger-Poisson equations, and then check their validity for this weakly-nonlinear system.
Unsupervised methods for dimensionality reduction of neural activity and behavior have provided unprecedented insights into the underpinnings of neural information processing. One popular approach involves the recurre...
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We present an algorithm generating a collection of fat arcs which bound the zero set of a given bivariate polynomial in Bernstein-Bezier representation. We demonstrate the performance of the algorithm (in particular t...
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ISBN:
(纸本)9783642116193
We present an algorithm generating a collection of fat arcs which bound the zero set of a given bivariate polynomial in Bernstein-Bezier representation. We demonstrate the performance of the algorithm (in particular the convergence rate) and we apply the results to the computation of intersection curves between implicitly defined algebraic surfaces and rational parametric surfaces.
The Ising model is stimulated on the manifolds of 2-dimensional quantum gravity, which are represented by fixed random triangulations (so-called quenched Ising model). Unlike the case of the Ising model on a dynamical...
The Ising model is stimulated on the manifolds of 2-dimensional quantum gravity, which are represented by fixed random triangulations (so-called quenched Ising model). Unlike the case of the Ising model on a dynamical random triangulation, there is no analytical prediction for the quenched case, since these manifolds do not have internal Hausdorff dimension and the problem cannot be formulated in matrix model language. The recursive sampling technique is used to generate the triangulations, lattice sizes being up to ten thousand triangles. The Metropolis algorithm was used for the spin update in order to obtain the initial estimation of the Curie point. After that we used the Wolff cluster algorithm in the critical region. We observed a second order phase transition, similar to that for the Ising model on a regular 2-dimensional lattice, and measured the critical exponents.
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