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11.
We consider the asymptotic dynamics of the Einstein-Maxwell field equations for the class of non-tilted Bianchi cosmologies with a barotropic perfect fluid and a pure homogeneous source-free magnetic field, with emphasis on models of Bianchi type VII0, which have not been previously studied. Using the orthonormal frame formalism and Hubble-normalized variables, we show that, as is the case for the previously studied class A magnetic Bianchi models, the magnetic Bianchi VII0 cosmologies also exhibit an oscillatory approach to the initial singularity. However, in contrast to the other magnetic Bianchi models, we rigorously establish that typical magnetic Bianchi VII0 cosmologies exhibit the phenomena of asymptotic self-similarity breaking and Weyl curvature dominance in the late-time regime. 相似文献
12.
Atsushi Wada Hiroyuki Ohminato Takashi Yonemura Yoko Miyamoto Mitsuo Takeda 《Optical Review》2005,12(6):451-455
Seidel comatic aberration is an important cause of deformation for a Laguerre--Gaussian (LG) beam. In addition, mono-axial
comatic aberration, whose phase modulation depends only on one transverse coordinate, is also an important cause of beam deformation.
Deformation of an LG beam by such aberrations is analyzed through numerical simulation based on the angular spectrum method.
It is also shown that for holographically generated LG beams quadratic spatial variation of grating pitch can produce seidel
and mono-axial comatic aberrations. An example of an experimentally generated LG beam with mono-axial comatic aberration is
reported. 相似文献
13.
GAO Xing-Ru 《理论物理通讯》2006,46(11)
In this paper, we propose a modified traffic model in which a single car moves through a sequence of traffic lights controlled by a step function instead of a sine function. In contrast to the previous work [Phys. Rev. E 70 (2004)016107], we have investigated in detail the dependence of the behavior on four parameters, ω, α, η, and a1, and given three kinds of bifurcation diagrams, which show three kinds of complex behaviors. We have found that in this model there are chaotic and complex periodic motions, as well as special singularities. We have also analyzed the characteristic of the complex period motion and the essential feature of the singularity. 相似文献
14.
15.
We study the collapse process of a homogeneous perfect fluid (in FLRW background) with a barotropic equation of state in Brans–Dicke (BD) theory in the presence of phase space deformation effects. Such a deformation is introduced as a particular type of non-commutativity between phase space coordinates. For the commutative case, it has been shown in the literature (Scheel, 1995), that the dust collapse in BD theory leads to the formation of a spacetime singularity which is covered by an event horizon. In comparison to general relativity (GR), the authors concluded that the final state of black holes in BD theory is identical to the GR case but differs from GR during the dynamical evolution of the collapse process. However, the presence of non-commutative effects influences the dynamics of the collapse scenario and consequently a non-singular evolution is developed in the sense that a bounce emerges at a minimum radius, after which an expanding phase begins. Such a behavior is observed for positive values of the BD coupling parameter. For large positive values of the BD coupling parameter, when non-commutative effects are present, the dynamics of collapse process differs from the GR case. Finally, we show that for negative values of the BD coupling parameter, the singularity is replaced by an oscillatory bounce occurring at a finite time, with the frequency of oscillation and amplitude being damped at late times. 相似文献
16.
17.
G. A. Mezincescu 《Journal of statistical physics》1987,49(5-6):1181-1190
UsingX-bounding (lower bounds by Laplacians with mixed boundary conditions and discrete analogs), we obtain the Lifschitz exponent at the bottom of the spectrum for random operators of typeH
=T+V
, withT a (periodic) generator of a positivity-preserving semigroup, extending results by Kirsch and Simon. 相似文献
18.
Explorations and Expectations of Equidistribution Adaptations for Nonlinear Quenching Problems 下载免费PDF全文
Finite difference computations that involve spatial adaptation commonly employ an
equidistribution principle. In these cases, a new mesh is constructed such that a
given monitor function is equidistributed in some sense. Typical choices of the
monitor function involve the solution or one of its many derivatives. This straightforward
concept has proven to be extremely effective and practical. However, selections of core
monitoring functions are often challenging
and crucial to the computational success. This paper concerns six different
designs of the monitoring function that targets a highly nonlinear partial
differential equation that exhibits both quenching-type and degeneracy singularities.
While the first four monitoring strategies are within the so-called
primitive regime, the rest belong to a later category of the
modified type, which requires the priori knowledge of certain
important quenching solution characteristics. Simulated examples are given
to illustrate our study and conclusions. 相似文献
19.
The elastic analysis of a mode II Griffith crack penetrating through a decagonal quasi-crystal along the periodic axis is made within the context of the continuum theory. By using a general solution obtained previously, the problem in the case of uniform shear stress at infinity is solved, and the analytical expressions for the entire stress field disturbed by an internal crack are derived in an explicit form. The asymptotic fields of the displacement and stress around a crack tip in both phonon and phason fields indicate that the stresses near a crack tip exhibit the square-root singularity. The formula for evaluating the energy release rate is also given. If imposing that the phason field is absent, the well-known results of a mode II crack in a conventional material are recovered from the present results. 相似文献
20.
幂硬化介质中平面应力动态裂纹的尖端弹塑性场 总被引:1,自引:0,他引:1
本文采用塑性动力学方程,对幂硬化介质中平面应力动态裂纹尖端场进行了渐近分析,其结果表明:在裂纹尖端附近,应力具有的奇异性,应变具有的奇异性,其中A是一个与塑性区尺寸有关的常数因子,r是离开裂纹尖端的距离,n为硬化指数,文中给出了尖端场的控制参量D,它依赖于马赫数;并且给出了各物理量的角函数。 相似文献