Browsing by Author "Zhang, C"

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    Dynamic Properties of Coupled Maps
    (2010) Zhang, C; Zheng, H
    Dynamic properties are investigated in the coupled system of three maps with symmetric nearest neighbor coupling and periodic boundary conditions. The dynamics of the system is controlled by certain coupling parameters. We show that, for some values of the parameters, the system exhibits nontrivial collective behavior, such as multiple bifurcations, and chaos. We give computer simulations to support the theoretical predictions.
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    Homogenization for chemical vapor infiltration process
    (Communications in Mathematical Sciences, 2017-01-01) Zhang, C; Bai, Y; Xu, S; Yue, X
    Multi-scale modeling and numerical simulations of the isothermal chemical vapor infiltration (CVI) process for the fabrication of carbon fiber reinforced silicon carbide (C/SiC) composites were presented in [Bai, Yue and Zeng, Commun. Comput. Phys., 7(3):597-612, 2010]. The homogenization theory, which played a fundamental role in the multi-scale algorithm, will be rigorously established in this paper. The governing system, which is a multi-scale reaction-diffusion equation, is different in the two stages of CVI process, so we will consider the homogenization for the two stages respectively. One of the main features is that the reaction only occurs on the surface of fiber, so it behaves as a singular surface source. The other feature is that in the second stage of the process when the micro pores inside the fiber bundles are all closed, the diffusion only occurs in the macro pores between fiber bundles and we face up with a problem in a locally periodic perforated domain.
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    HOMOGENIZATION OF A DISCRETE NETWORK MODEL FOR CHEMICAL VAPOR INFILTRATION PROCESS
    (COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2021) Xiao, C; Xu, S; Yuex, X; Zhang, C; Zhang, C
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    Homogenization: In mathematics or physics?
    (Discrete and Continuous Dynamical Systems - Series S, 2016-10-01) Xu, S; Yue, X; Zhang, C
    In mathematics, homogenization theory considers the limitations of the sequences of the problems and their solutions when a parameter tends to zero. This parameter is regarded as the ratio of the characteristic size between the micro scale and macro scale. So what is considered is a sequence of problems in axed domain while the characteristic size in micro scale tends to zero. But in the real physics or engineering situations, the micro scale of a medium isxed and can not be changed. In the process of homogenization, it is the size in macro scale which becomes larger and larger and tends to innity. We observe that the homogenization in physics is not equivalent to the homogenization in mathematics up to some simple rescaling. With some direct error estimates, we explain in what sense we can accept the homogenized problem as the limitation of the original real physical problems. As a byproduct, we present some results on the mathematical homogenization of some problems with source term being only weakly compacted in H1, while in standard homogenization theory, the source term is assumed to be at least compacted in H1. A real example is also given to show the validation of our observation and results.
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    Role of mesons in the electromagnetic form factors of the nucleon
    (Physical Review C - Nuclear Physics, 2010-11-30) Crawford, C; Akdogan, T; Alarcon, R; Bertozzi, W; Booth, E; Botto, T; Calarco, JR; Clasie, B; de Grush, A; Donnelly, TW; Dow, K; Farkhondeh, M; Fatemi, R; Filoti, O; Franklin, W; Gao, H; Geis, E; Gilad, S; Hasell, D; Karpius, P; Kohl, M; Kolster, H; Lee, T; Lomon, E; Maschinot, A; Matthews, J; McIlhany, K; Meitanis, N; Milner, R; Rapaport, J; Redwine, R; Seely, J; Shinozaki, A; Sindile, A; Širca, S; Six, E; Smith, T; Tonguc, B; Tschalaer, C; Tsentalovich, E; Turchinetz, W; Xiao, Y; Xu, W; Zhang, C; Zhou, Z; Ziskin, V; Zwart, T
    The roles played by mesons in the electromagnetic form factors of the nucleon are explored using as a basis a model containing vector mesons with coupling to the continuum together with the asymptotic Q2 behavior of perturbative QCD. Specifically, the vector dominance model (GKex) developed by E. L. Lomon is employed, as it is known to be very successful in representing the existing high-quality data published to date. An analysis is made of the experimental uncertainties present when the differences between the GKex model and the data are expanded in orthonormal basis functions. A main motivation for the present study is to provide insight into how the various ingredients in this model yield the measured behavior, including discussions of when dipole form factors are to be expected or not, of which mesons are the major contributors, for instance, at low Q2 or large distances, and of what effects are predicted from coupling to the continuum. Such insights are first discussed in momentum space, followed by an analysis of how different and potentially useful information emerges when both the experimental and theoretical electric form factors are Fourier transformed to coordinate space. While these Fourier transforms should not be interpreted as "charge distributions," nevertheless the roles played by the various mesons, especially those which are dominant at large or small distance scales, can be explored via such experiment-theory comparisons. © 2010 The American Physical Society.