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81.
On the Path of a Quasi-static Crack in Mode III 总被引:1,自引:0,他引:1
A method for finding the path of a quasi-static crack growing in a brittle body is presented. The propagation process is modelled by a sequence of discrete steps optimizing the elastic energy released. An explicit relationship between the optimal growing direction and the parameters defining the local elastic field around the tip is obtained for an anti-plane field. This allows to describe a simple algorithm to compute the crack path.
Mathematics Subject Classifications (2000) 74R05, 74B05, 74G70.Gerardo E. Oleaga: Supported by EU-Project Front Singularities University of Leipzig and the Max Planck Institute MIS. Partial support was also provided by the Spanish DGES project BFM2000-0605. 相似文献
82.
83.
We consider the following system of discrete equations
. Criteria for the existence of three constant-sign solutions of the system will be developed. To illustrate the generality of the results obtained, we include applications to several well-known boundary value problems. Parallel results are also established for a system on {0,1,...}
. 相似文献
84.
Gamaliel?BléEmail author Víctor?Castellanos Manuel?J.?Falconi 《Bulletin of the Brazilian Mathematical Society》2003,34(2):333-345
In this paper we consider a system whose state
x changes to (x) if a perturbation occurs at the time
t, for
. Moreover, the state
x changes to the new state
(x) at time
t, for
. It is assumed that the
number of perturbations in an interval (0,
t) is a Poisson process. Here
and are measurable maps from a measure space
into itself. We give
conditions for the existence of a stationary distribution of the
system when the maps and commute, and we prove that any
stationary distribution is an invariant measure of these
maps. 相似文献
85.
Salt-mediated electrostatics interactions play an essential role in biomolecular structures and dynamics. Because macromolecular systems modeled at atomic resolution contain thousands of solute atoms, the electrostatic computations constitute an expensive part of the force and energy calculations. Implicit solvent models are one way to simplify the model and associated calculations, but they are generally used in combination with standard atomic models for the solute. To approximate electrostatics interactions in models on the polymer level (e.g., supercoiled DNA) that are simulated over long times (e.g., milliseconds) using Brownian dynamics, Beard and Schlick have developed the DiSCO (Discrete Surface Charge Optimization) algorithm. DiSCO represents a macromolecular complex by a few hundred discrete charges on a surface enclosing the system modeled by the Debye-Hückel (screened Coulombic) approximation to the Poisson-Boltzmann equation, and treats the salt solution as continuum solvation. DiSCO can represent the nucleosome core particle (>12,000 atoms), for example, by 353 discrete surface charges distributed on the surfaces of a large disk for the nucleosome core particle and a slender cylinder for the histone tail; the charges are optimized with respect to the Poisson-Boltzmann solution for the electric field, yielding a approximately 5.5% residual. Because regular surfaces enclosing macromolecules are not sufficiently general and may be suboptimal for certain systems, we develop a general method to construct irregular models tailored to the geometry of macromolecules. We also compare charge optimization based on both the electric field and electrostatic potential refinement. Results indicate that irregular surfaces can lead to a more accurate approximation (lower residuals), and the refinement in terms of the electric field is more robust. We also show that surface smoothing for irregular models is important, that the charge optimization (by the TNPACK minimizer) is efficient and does not depend on the initial assigned values, and that the residual is acceptable when the distance to the model surface is close to, or larger than, the Debye length. We illustrate applications of DiSCO's model-building procedure to chromatin folding and supercoiled DNA bound to Hin and Fis proteins. DiSCO is generally applicable to other interesting macromolecular systems for which mesoscale models are appropriate, to yield a resolution between the all-atom representative and the polymer level. 相似文献
86.
This paper examines the complexity of global verification for MAX-SAT, MAX-k-SAT (for k3), Vertex Cover, and Traveling Salesman Problem. These results are obtained by adaptations of the transformations that prove such problems to be NP-complete. The class of problems PGS is defined to be those discrete optimization problems for which there exists a polynomial time algorithm such that given any solution , either a solution can be found with a better objective function value or it can be concluded that no such solution exists and is a global optimum. This paper demonstrates that if any one of MAX-SAT, MAX-k-SAT (for k3), Vertex Cover, or Traveling Salesman Problem are in PGS, then P=NP. 相似文献
87.
In this paper, theoretical results are described on the maximum norm stability and accuracy of finite difference discretizations of parabolic equations on overset nonmatching space-time grids. We consider parabolic equations containing a linear reaction term on a space-time domain which is decomposed into an overlapping collection of cylindrical subregions of the form , for . Each of the space-time domains are assumed to be independently grided (in parallel) according to the local geometry and space-time regularity of the solution, yielding space-time grids with mesh parameters and . In particular, the different space-time grids need not match on the regions of overlap, and the time steps can differ from one grid to the next. We discretize the parabolic equation on each local grid by employing an explicit or implicit -scheme in time and a finite difference scheme in space satisfying a discrete maximum principle. The local discretizations are coupled together, without the use of Lagrange multipliers, by requiring the boundary values on each space-time grid to match a suitable interpolation of the solution on adjacent grids. The resulting global discretization yields a large system of coupled equations which can be solved by a parallel Schwarz iterative procedure requiring some communication between adjacent subregions. Our analysis employs a contraction mapping argument.
Applications of the results are briefly indicated for reaction-diffusion equations with contractive terms and heterogeneous hyperbolic-parabolic approximations of parabolic equations.
88.
E. V. Troitsky 《Proceedings of the American Mathematical Society》2003,131(11):3411-3422
We address the problem of interrelations between the properties of an action of a discrete group on a compact Hausdorff space and the algebraic and analytical properties of the module of all continuous functions over the algebra of invariant continuous functions . The present paper is a continuation of our joint paper with M. Frank and V. Manuilov. Here we prove some statements inverse to the ones obtained in that paper: we deduce properties of actions from properties of modules. In particular, it is proved that if for a uniformly continuous action the module is finitely generated projective over , then the cardinality of orbits of the action is finite and fixed. Sufficient conditions for existence of natural conditional expectations are obtained.
89.
Robert L. Benedetto 《Compositio Mathematica》2000,122(3):281-298
In this paper we study dynamics on the Fatou set of a rational function
. Using a notion of components of the Fatou set defined by Benedetto, we state and prove an analogue of Sullivan's No Wandering Domains Theorem for p-adic rational functions which have no wild recurrent Julia critical points. 相似文献
90.
B. B. Bhattacharyya X. Li M. Pensky G. D. Richardson 《Annals of the Institute of Statistical Mathematics》2000,52(1):71-83
The limiting distribution of the normalized periodogram ordinate is used to test for unit roots in the first-order autoregressive model st= s-1,t+s,t-1- s-1,t-1+st. Moreover, for the sequence
n
= e
c/n
,
n
= e
d/n
of local Pitman-type alternatives, the limiting distribution of the normalized periodogram ordinate is shown to be a linear combination of two independent chi-square random variables whose coefficients depend on c and d. This result is used to tabulate the asymptotic power of a test for various values of c and d. A comparison is made between the periodogram test and a spatial domain test. 相似文献