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Academic literature on the topic 'Glimm approximations'

Author: Grafiati

Published: 14 March 2023

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Journal articles on the topic "Glimm approximations"

1

Hoff, David, and Joel Smoller. "Error bounds for Glimm difference approximations for scalar conservation laws." Transactions of the American Mathematical Society 289, no. 2 (February 1, 1985): 611. http://dx.doi.org/10.1090/s0002-9947-1985-0784006-5.

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Kutsenko, Anton A. "Classification of Integrodifferential C∗-Algebras." Symmetry 13, no. 10 (October 9, 2021): 1900. http://dx.doi.org/10.3390/sym13101900.

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The infinite product of matrices with integer entries, known as a modified Glimm–Bratteli symbol n, is a new, sufficiently simple, and very powerful tool for the characterization of approximately finite-dimensional (AF) algebras. This symbol provides a convenient algebraic representation of the Bratteli diagram for AF algebras in the same way as was previously performed by J. Glimm for more simple uniformly hyperfinite (UHF) algebras. We apply this symbol to characterize integrodifferential algebras. The integrodifferential algebra FN,M is the C∗-algebra generated by the following operators acting on L2([0,1)N→CM): (1) operators of multiplication by bounded matrix-valued functions, (2) finite-difference operators, and (3) integral operators. Most of the operators and their approximations studying in physics belong to these algebras. We give a complete characterization of FN,M. In particular, we show that FN,M does not depend on M, but depends on N. At the same time, it is known that differential algebras HN,M, generated by the operators (1) and (2) only, do not depend on both dimensions N and M; they are all ∗-isomorphic to the universal UHF algebra. We explicitly compute the Glimm–Bratteli symbols (for HN,M, it was already computed earlier) which completely characterize the corresponding AF algebras. This symbol n is an infinite product of matrices with nonnegative integer entries. Roughly speaking, all the symmetries appearing in the approximation of complex infinite-dimensional integrodifferential and differential algebras by finite-dimensional ones are coded by a product of integer matrices.

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TSIKKOU, CHARIS. "SHARPER TOTAL VARIATION BOUNDS FOR THE P-SYSTEM OF FLUID DYNAMICS." Journal of Hyperbolic Differential Equations 08, no. 02 (June 2011): 173–232. http://dx.doi.org/10.1142/s0219891611002391.

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For the p-system of fluid dynamics and under the assumption that the initial data have small oscillation but not necessarily small total variation, we reproduce the so-called Glimm–Lax estimates with greater accuracy. Our approach recovers the results known for smooth flux functions, and is based on the theory of generalized characteristics and Dafermos' technique of polygonal approximations.

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4

Ye, Xiao Ping, and Long Wei Lin. "Error Bounds for Glimm Difference Approximations for Scalar Conservation Laws Without Convexity." Acta Mathematica Sinica, English Series 22, no. 4 (March 23, 2006): 1271–82. http://dx.doi.org/10.1007/s10114-005-0713-3.

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Bianchini, Stefano, and Stefano Modena. "On a quadratic functional for scalar conservation laws." Journal of Hyperbolic Differential Equations 11, no. 02 (June 2014): 355–435. http://dx.doi.org/10.1142/s0219891614500118.

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We prove a quadratic interaction estimate for approximate solutions to scalar conservation laws obtained by the wavefront tracking approximation or the Glimm scheme. This quadratic estimate has been used in the literature to prove the convergence rate of the Glimm scheme. The proof is based on the introduction of a quadratic functional 𝔔(t), decreasing at every interaction, and such that its total variation in time is bounded. Differently from other interaction potentials present in the literature, the form of this functional is the natural extension of the original Glimm functional, and coincides with it in the genuinely nonlinear case.

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Berman, Mark, and T. Rolf Turner. "Approximating Point Process Likelihoods with GLIM." Applied Statistics 41, no. 1 (1992): 31. http://dx.doi.org/10.2307/2347614.

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Berman, M., and T. R. Turner. "Approximating point process likelihoods with GLIM." Insurance: Mathematics and Economics 13, no. 2 (November 1993): 147. http://dx.doi.org/10.1016/0167-6687(93)90845-g.

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8

Chou, Shih-Wei, John M. Hong, Bo-Chih Huang, and Reyna Quita. "Global bounded variation solutions describing Fanno–Rayleigh fluid flows in nozzles." Mathematical Models and Methods in Applied Sciences 28, no. 06 (May 21, 2018): 1135–69. http://dx.doi.org/10.1142/s0218202518500306.

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In this paper, we investigate the initial-boundary value problem of compressible Euler equations including friction and heating that model the transonic Fanno–Rayleigh flows through symmetric variable area nozzles. In particular, the case of contracting nozzles is considered. A new version of a generalized Glimm scheme (GGS) is presented for establishing the global existence of entropy solutions with bounded variation. Modified Riemann and boundary Riemann solutions are applied to design this GGS, which is constructed using the contraction matrices acting on the homogeneous Riemann (or boundary-Riemann) solutions. The extended Glimm–Goodman’s type of wave interaction estimates are investigated to determine the stability of the scheme and the positivity of gas velocity that results in the existence of the weak solution. The limit of approximation solutions serves as an entropy solution. Moreover, a quantitative relation between the shape of the nozzle, friction, and heat is proposed for the global existence result in the contracting nozzle. Numerical simulations of the contraction-expansion and expansion-contraction nozzles are presented to validate the scheme.

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Abgrall, Remi, and Harish Kumar. "Numerical Approximation of a Compressible Multiphase System." Communications in Computational Physics 15, no. 5 (May 2014): 1237–65. http://dx.doi.org/10.4208/cicp.110313.230913a.

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AbstractThe numerical simulation of non conservative system is a difficult challenge for two reasons at least. The first one is that it is not possible to derive jump relations directly from conservation principles, so that in general, if the model description is non ambiguous for smooth solutions, this is no longer the case for discontinuous solutions. From the numerical view point, this leads to the following situation: if a scheme is stable, its limit for mesh convergence will depend on its dissipative structure. This is well known since at least [1]. In this paper we are interested in the “dual” problem: given a system in non conservative form and consistent jump relations, how can we construct a numerical scheme that will, for mesh convergence, provide limit solutions that are the exact solution of the problem. In order to investigate this problem, we consider a multiphase flow model for which jump relations are known. Our scheme is an hybridation of Glimm scheme and Roe scheme.

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10

Hong, John Meng-Kai, and Reyna Marsya Quita. "Approximation of generalized Riemann solutions to compressible Euler-Poisson equations of isothermal flows in spherically symmetric space-times." Tamkang Journal of Mathematics 48, no. 1 (March 30, 2017): 73–94. http://dx.doi.org/10.5556/j.tkjm.48.2017.2274.

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In this paper, we consider the compressible Euler-Poisson system in spherically symmetric space-times. This system, which describes the conservation of mass and momentum of physical quantity with attracting gravitational potential, can be written as a $3\times 3$ mixed-system of partial differential systems or a $2\times 2$ hyperbolic system of balance laws with $global$ source. We show that, by the equation for the conservation of mass, Euler-Poisson equations can be transformed into a standard $3\times 3$ hyperbolic system of balance laws with $local$ source. The generalized approximate solutions to the Riemann problem of Euler-Poisson equations, which is the building block of generalized Glimm scheme for solving initial-boundary value problems, are provided as the superposition of Lax's type weak solutions of the associated homogeneous conservation laws and the perturbation terms solved by the linearized hyperbolic system with coefficients depending on such Lax solutions.

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Dissertations / Theses on the topic "Glimm approximations"

1

Chang, Sheng-Mao. "A Stationary Stochastic Approximation Algorithm for Estimation in the GLMM." NCSU, 2007. http://www.lib.ncsu.edu/theses/available/etd-05172007-164438/unrestricted/etd.pdf.

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Book chapters on the topic "Glimm approximations"

1

Seeber, G. U. H. "Saddlepoint Approximations for Generalized Linear Models: A Gentle Introduction." In Advances in GLIM and Statistical Modelling, 195–200. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-2952-0_30.

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Conference papers on the topic "Glimm approximations"

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Handayani, Dian, Khairil Anwar Notodiputro, Kusman Sadik, and Anang Kurnia. "A comparative study of approximation methods for maximum likelihood estimation in generalized linear mixed models (GLMM)." In STATISTICS AND ITS APPLICATIONS: Proceedings of the 2nd International Conference on Applied Statistics (ICAS II), 2016. Author(s), 2017. http://dx.doi.org/10.1063/1.4979449.

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