Asymptotic Behaviour Research Papers - Academia.edu (original) (raw)

New simple and general expressions for the stress intensity factor, compliance and crack mouth opening displacement for three-point bend specimens are computed. Inverse functions giving the crack length as a function of load-point... more

New simple and general expressions for the stress intensity factor, compliance and crack mouth opening displacement for three-point bend specimens are computed. Inverse functions giving the crack length as a function of load-point displacement or crack mouth opening displacement are also included. The expressions are valid for any crack length and for any span-to-depth ratio larger than 2.5. The expressions are checked by comparing them to direct finite element computations and to available expressions by other authors. The accuracy of the new expression is equal to or better than available formulas when compared with finite element computations, and its range of applicability is much larger. Moreover, all the new expressions exhibit the correct asymptotic behaviour for very shallow and very deep cracks.

In this study, the finite element method is used to analyse the behaviour of repaired cracks with bonded composite patches in mode I and mixed mode by computing the stress intensity factors at the crack tip. The effects of the patch size... more

In this study, the finite element method is used to analyse the behaviour of repaired cracks with bonded composite patches in mode I and mixed mode by computing the stress intensity factors at the crack tip. The effects of the patch size and the adhesive properties on the stress intensity factors variation were highlighted. The plot of the stress intensity

Remarkable anisotropic structures have been recently observed in the order parameter Delta_k of the underdoped superconductor Bi-2212. Such findings are strongly suggestive of deviations from a simple d_{x^2 - y^2}-wave picture of high-Tc... more

Remarkable anisotropic structures have been recently observed in the order parameter Delta_k of the underdoped superconductor Bi-2212. Such findings are strongly suggestive of deviations from a simple d_{x^2 - y^2}-wave picture of high-Tc superconductivity, i.e. Delta_k ~ cos (k_x) - cos (k_y). In particular, flatter nodes in Delta_k are observed along the k_x = (+/-) k_y directions in k-space, than within this simple model for a d-wave gap. We argue that nonlinear corrections in the k-dependence of Delta_k near the nodes introduce new energy scales, which would lead to deviations in the predicted power-law asymptotic behaviour of several measurable quantities, at low or intermediate temperatures. We evaluate such deviations, either analytically or numerically, within the interlayer pair-tunneling model, and within yet another phenomenological model for a d-wave order parameter. We find that such deviations are expected to be of different sign in the two cases. Moreover, the doping ...

SUMMARY This paper focuses on the application of orthotropi c plate bending theory to stiffened plating. Schade 's design charts for rectangular plates are extended to the case where t he boundary contour is clamped, which is almost... more

SUMMARY This paper focuses on the application of orthotropi c plate bending theory to stiffened plating. Schade 's design charts for rectangular plates are extended to the case where t he boundary contour is clamped, which is almost tot ally incomplete in the afore mentioned charts. A numerical solution for the clamped orthotropic p late equation is obtained. The Rayleigh-Ritz

In this paper, we apply current geological knowledge on faulting processes to digital processing of Digital Elevation Models (DEM) in order to pinpoint locations of active faults. The analysis is based on semiautomatic interpretation of... more

In this paper, we apply current geological knowledge on faulting processes to digital processing of Digital Elevation Models (DEM) in order to pinpoint locations of active faults. The analysis is based on semiautomatic interpretation of 20- and 60-m DEM and their products (slope, shaded relief). In Northern–Eastern Attica, five normal fault segments were recognized on the 20-m DEM. All faults strike WNW–ESE. The faults are from west to east: Thriassion (THFS), Fili (FIFS), Afidnai (AFFS), Avlon (AVFS), and Pendeli (PEFS) and range in length from 10 to 20 km. All of them show geomorphic evidence for recent activity such as prominent range-front escarpments, V-shaped valleys, triangular facets, and tilted footwall areas. However, escarpment morphometry and footwall geometry reveal systematic differences between the “external” segments (PEFS, THFS, and AVFS) and the “internal” segments (AFFS and FIFS), which may be due to mechanical interaction among segments and/or preexisting topogra...

In this paper we study the asymptotic behaviour of the Laplace equation in a periodically perforated domain of R n , where we assume that the period is ε and the size of the holes is of the same order of greatness. An homogeneous... more

In this paper we study the asymptotic behaviour of the Laplace equation in a periodically perforated domain of R n , where we assume that the period is ε and the size of the holes is of the same order of greatness. An homogeneous Dirichlet condition is given on the whole exterior boundary of the domain and on a flat portion of diameter $ \varepsilon ^{ \frac{n}{n-2}} $ if $ n>2 $ ( $ \exp (-\varepsilon ^{-2}) $ , if n=2) of the boundary of every hole, while we take an homogeneous Neumann condition elsewhere.

In the present work, Galton-Watson branching critical processes with only one type of par- ticle are studied, in the case that second moments are infinite. The probability generating functions which have a Slack type (17) with index a � 2... more

In the present work, Galton-Watson branching critical processes with only one type of par- ticle are studied, in the case that second moments are infinite. The probability generating functions which have a Slack type (17) with index a � 2 (0,1) are studied. Limiting theo- rems are presented and demonstrated where the asymptotic behaviour of joint distributions are studied of

This work considers the Keller-Segel system of parabolic-parabolic type in {R}^{n} for n >= 2. We prove existence results in a new framework and with initial data in N_{r,\lambda,\infty}^{-\beta}\times\dot{B}_{\infty,\infty}^{0} . This... more

This work considers the Keller-Segel system of parabolic-parabolic type in {R}^{n} for n >= 2. We prove existence results in a new framework and with initial data in N_{r,\lambda,\infty}^{-\beta}\times\dot{B}_{\infty,\infty}^{0} . This initial data class is larger than the previous ones, e.g., Kozono-Sugiyama (2008 Indiana Univ. Math. J. 57 1467-500) and Biler (1998 Adv. Math. Sci. Appl. 8 715-43), and covers physical cases of initial aggregation at points (Diracs) and on filaments. Self-similar solutions are obtained for initial data with the correct homogeneity and a certain value of parameter γ. We also show an asymptotic behaviour result, which provides a basin of attraction around each self-similar solution.

Let H1;H2;:::;Hk+1 be a sequence of k + 1 nite, undirected, simple graphs. The (mul- ticolored) Ramsey number r(H1;H2;:::;Hk+1) is the minimum integer r such that in every edge-coloring of the complete graph on r vertices by k + 1 colors,... more

Let H1;H2;:::;Hk+1 be a sequence of k + 1 nite, undirected, simple graphs. The (mul- ticolored) Ramsey number r(H1;H2;:::;Hk+1) is the minimum integer r such that in every edge-coloring of the complete graph on r vertices by k + 1 colors, there is a monochromatic copy of Hi in color i for some 1 i k + 1. We describe a general technique that supplies tight lower bounds for several numbers r(H1;H2;:::;Hk+1) when k 2, and the last graph Hk+1 is the complete graph Km on m vertices. This technique enables us to determine the asymptotic behaviour of these numbers, up to a polylogarithmic factor, in various cases. In particular we show that r(K3;K3;Km) = ( m3poly logm), thus solving (in a strong form) a conjecture of Erd} os and S os raised in 1979. Another special case of our result implies that r(C4;C4;Km) = ( m2poly logm) and that r(C4;C4;C4;Km) = ( m2= log 2 m). The proofs combine combinatorial and probabilistic arguments with spectral techniques and certain esti- mates of character sums.

The problems considered in the present paper have their roots in two different cultures. The 'true' (or myopic) self-avoiding walk model (TSAW) was introduced in the physics literature by Amit, Parisi and Peliti. This is a nearest... more

The problems considered in the present paper have their roots in two different cultures. The 'true' (or myopic) self-avoiding walk model (TSAW) was introduced in the physics literature by Amit, Parisi and Peliti. This is a nearest neighbor non-Markovian random walk in Z^d which prefers to jump to those neighbors which were less visited in the past. The self-repelling Brownian polymer model (SRBP), initiated in the probabilistic literature by Durrett and Rogers (independently of the physics community), is the continuous space-time counterpart: a diffusion in R^d pushed by the negative gradient of the (mollified) occupation time measure of the process. In both cases, similar long memory effects are caused by a pathwise self-repellency of the trajectories due to a push by the negative gradient of (softened) local time. We investigate the asymptotic behaviour of TSAW and SRBP in the non-recurrent dimensions. First, we identify a natural stationary (in time) and ergodic distribution of the environment (the local time profile) as seen from the moving particle. The main results are diffusive limits. In the case of TSAW, for a wide class of self-interaction functions, we establish diffusive lower and upper bounds for the displacement and for a particular, more restricted class of interactions, we prove full CLT for the finite dimensional distributions of the displacement. In the case of SRBP, we prove full CLT without restrictions on the interaction functions. These results settle part of the conjectures, based on non-rigorous renormalization group arguments (equally 'valid' for the TSAW and SRBP cases). The proof of the CLT follows the non-reversible version of Kipnis-Varadhan theory. On the way to the proof, we slightly weaken the so-called graded sector condition.

Wang & Wells ["J. Amer. Statist. Assoc." 95 (2000) 62] describe a non-parametric approach for checking whether the dependence structure of a random sample of censored bivariate data is appropriately modelled by a given family of... more

Wang & Wells ["J. Amer. Statist. Assoc." 95 (2000) 62] describe a non-parametric approach for checking whether the dependence structure of a random sample of censored bivariate data is appropriately modelled by a given family of Archimedean copulas. Their procedure is based on a truncated version of the Kendall process introduced by Genest & Rivest ["J. Amer. Statist. Assoc." 88 (1993) 1034] and later studied by Barbe "et al". ["J. Multivariate Anal." 58 (1996) 197]. Although Wang & Wells (2000) determine the asymptotic behaviour of their truncated process, their model selection method is based exclusively on the observed value of its "L"-super-2-norm. This paper shows how to compute asymptotic "p"-values for various goodness-of-fit test statistics based on a non-truncated version of Kendall's process. Conditions for weak convergence are met in the most common copula models, whether Archimedean or not. The empirical beh...

In this lectures various methods which give a possibility to extend an area of applicability of perturbation series and hence to omit their local character are analysed. While applying asymptotic methods as a rule the following situation... more

In this lectures various methods which give a possibility to extend an area of applicability of perturbation series and hence to omit their local character are analysed. While applying asymptotic methods as a rule the following situation appears: the existence of asymptotics for verightarrow0\ve\rightarrow 0verightarrow0 implies an existence of the asymptotics for verightarrowinfty\ve\rightarrow\inftyverightarrowinfty. Therefore, the idea to construct one function valid for the whole parameter interval for ve\veve is very attractive. The construction of asymptotically equivalent functions possessing a known asymptotic behaviour for verightarrow0\ve\rightarrow 0verightarrow0 and verightarrowinfty\ve\rightarrow \inftyverightarrowinfty will be discussed. Using summation and interpolation procedures we focus on continuous models derived from a discrete micro-structure. Various continualization procedures that take the non-local interaction between variables of the discrete media into account are analysed.

We consider a 2D Schroedinger operator H0 with constant magnetic field, on a strip of finite width. The spectrum of H0 is absolutely continuous, and contains a discrete set of thresholds. We perturb H0 by an electric potential V which... more

We consider a 2D Schroedinger operator H0 with constant magnetic field, on a strip of finite width. The spectrum of H0 is absolutely continuous, and contains a discrete set of thresholds. We perturb H0 by an electric potential V which decays in a suitable sense at infinity, and study the spectral properties of the perturbed operator H = H0 + V . First, we establish a Mourre estimate, and as a corollary prove that the singular continuous spectrum of H is empty, and any compact subset of the complement of the threshold set may contain at most a finite set of eigenvalues of H, each of them having a finite multiplicity. Next, we introduce the Krein spectral shift function (SSF) for the operator pair (H,H0). We show that this SSF is bounded on any compact subset of the complement of the threshold set, and is continuous away from the threshold set and the eigenvalues of H. The main results of the article concern the asymptotic behaviour of the SSF at the thresholds, which is described in ...