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111.
J. D. Gunton 《Journal of statistical physics》1984,34(5-6):1019-1037
A review is given of recent developments involving the dynamics of random interfaces formed in the evolution of metastable and unstable systems. Topics which are discussed include interface growth and nonequilibrium dynamical scaling. The possibility of there being dynamical universality classes in first-order phase transitions is also discussed. There are a large number of systems of experimental interest which include binary alloys, binary fluids, and polymer mixtures. Other systems studied by computer simulation include the kinetic Ising, Potts, andZ
N
models.Work supported by NSF grant No. DMR-8013700. 相似文献
112.
Alfredo De Rossi Gaetano Assanto Stefano Trillo William E. Torruellas 《Optics Communications》1998,150(1-6):390-398
We have identified a family of (2+1)D spatial solitary waves which can stably propagate in bulk media in the presence of coexisting diffraction, self-focusing Kerr and quadratic nonlinearities. In a conspicuous range of excitation conditions close to the stationary solutions, the emerging wavepackets are immune to the detrimental occurrence of filamentation and collapse, typical of pure Kerr media. The presence of a second-order contribution to the cubic nonlinear response is, therefore, able to prevent optical damage in applications relying on self-guidance. We show that the cross-phase modulation plays an important effect on stability. Our estimate shows that the effects of the cubic susceptibility cannot be neglected below a certain beam size in realistic crystals (e.g. KTP or similar). 相似文献
113.
114.
Ramachandramurty Ponnapalli 《Journal of multivariate analysis》1975,5(2):278-281
Optimality of estimators of a vector parameter in terms of the probability of the estimators being contained in suitable region(s) around the parameter point is defined. Conditions under which optimal estimators in the usual senses are also optimal in the above sense are investigated. 相似文献
115.
116.
Rice [J. Mech. Phys. Solids 26 (1978) 61] proposes a refined Griffith criterion,
at any local crack front, where G is the Irwin's energy release rate, γ is the surface free energy and
is the rate of crack advance. The refined version implies that the entropy production inequality should holds locally rather than globally from the thermodynamic point of view. Within the irreversible thermodynamic framework developed by Rice [J. Mech. Phys. Solids 19 (1971) 433; Constitutive Equations in Plasticity, 1975, p. 23], it is revealed in this paper that the entropy production inequality holds for each internal variable if its rate is a homogeneous function in its conjugate force. It is further shown that widely-used power laws for crack growth are just certain homogeneous kinetic rate laws, so it is concluded that the power laws directly lead to the refined Griffith criterion. 相似文献
117.
A pair of kinematical conservation laws (KCL) in a ray coordinatesystem (,t) are the basic equations governing the evolutionof a moving curve in two space dimensions. We first study elementarywave solutions and then the Riemann problem for KCL when themetric g, associated with the coordinate designating differentrays, is an arbitrary function of the velocity of propagationm of the moving curve. We assume that m>1 (m is appropriatelynormalized), for which the system of KCL becomes hyperbolic.We interpret the images of the elementary wave solutions inthe (,t)-plane to the (x,y)-plane as elementary shapes of themoving curve (or a nonlinear wavefront when interpreted in aphysical system) and then describe their geometrical properties.Solutions of the Riemann problem with different initial datagive the shapes of the nonlinear wavefront with different combinationsof elementary shapes. Finally, we study all possible interactionsof elementary shapes. 相似文献
118.
Zaqueu Coelho 《Transactions of the American Mathematical Society》2004,356(11):4427-4445
For a minimal circle homeomorphism we study convergence in law of rescaled hitting time point process of an interval of length 0$">. Although the point process in the natural time scale never converges in law, we study all possible limits under a subsequence. The new feature is the fact that, for rotation numbers of unbounded type, there is a sequence going to zero exhibiting coexistence of two non-trivial asymptotic limit point processes depending on the choice of time scales used when rescaling the point process. The phenomenon of loss of tightness of the first hitting time distribution is an indication of this coexistence behaviour. Moreover, tightness occurs if and only if the rotation number is of bounded type. Therefore tightness of time distributions is an intrinsic property of badly approximable irrational rotation numbers.
119.
Shinji Fukuhara Noriko Yui 《Transactions of the American Mathematical Society》2004,356(10):4237-4254
We introduce an elliptic analogue of the Apostol sums, which we call elliptic Apostol sums. These sums are defined by means of certain elliptic functions with a complex parameter having positive imaginary part. When , these elliptic Apostol sums represent the well-known Apostol generalized Dedekind sums. Also these elliptic Apostol sums are modular forms in the variable . We obtain a reciprocity law for these sums, which gives rise to new relations between certain modular forms (of one variable).
120.
MiaoLI QuanZHENG 《数学学报(英文版)》2004,20(5):821-828
Let T = (T(t))t≥0 be a bounded C-regularized semigroup generated by A on a Banach space X and R(C) be dense in X. We show that if there is a dense subspace Y of X such that for every x ∈ Y, σu(A, Cx), the set of all points λ ∈ iR to which (λ - A)^-1 Cx can not be extended holomorphically, is at most countable and σr(A) N iR = Ф, then T is stable. A stability result for the case of R(C) being non-dense is also given. Our results generalize the work on the stability of strongly continuous senfigroups. 相似文献