Search results for "Boundary"
showing 10 items of 1626 documents
Double precision errors in the logistic map: statistical study and dynamical interpretation.
2007
The nature of the round-off errors that occur in the usual double precision computation of the logistic map is studied in detail. Different iterative regimes from the whole panoply of behaviors exhibited in the bifurcation diagram are examined, histograms of errors in trajectories given, and for the case of fully developed chaos an explicit formula is found. It is shown that the statistics of the largest double precision error as a function of the map parameter is characterized by jumps whose location is determined by certain boundary crossings in the bifurcation diagram. Both jumps and locations seem to present geometric convergence characterized by the two first Feigenbaum constants. Even…
Trial Methods for Nonlinear Bernoulli Problem
1997
In this article we consider a free boundary problem which is related to formation of waves on a fluid surface (for example the ship waves). We study the possibility to construct ‘trial’ methods where one solves a sequence of standard flow problems formulated in different geometries that converge to the final free boundary. Furthermore, we use the shape optimization techniques to analyse the convergence of the fixed point iteration near a fixed point. For stream function case we conclude that the fast convergence can be obtained by using non-standard boundary conditions and we present numerical results to confirm the analysis.
Application of the 3-D boundary element method to delaminated composite structures
2013
A three-dimensional boundary element model for anisotropic solids is presented to study the fracture mechanics behavior of delaminated composite structures. The multi-domain technique is implemented to model the layered configurations and the cracks occurring at bi-material interface. The Modified Crack Closure Integral technique is implemented to characterize the fracture mechanics behavior of delaminations in terms of the total energy release rate and mode mix phase angles. Validating analyses, performed on different delaminated configurations, have shown the effectiveness of the proposed approach. Moreover, some original results are presented to investigate the effects of the stacking se…
Critical end point behaviour in a binary fluid mixture
1997
We consider the liquid-gas phase boundary in a binary fluid mixture near its critical end point. Using general scaling arguments we show that the diameter of the liquid-gas coexistence curve exhibits singular behaviour as the critical end point is approached. This prediction is tested by means of extensive Monte-Carlo simulations of a symmetrical Lennard-Jones binary mixture within the grand canonical ensemble. The simulation results show clear evidence for the proposed singularity, as well as confirming a previously predicted singularity in the coexistence chemical potential [Fisher and Upton, Phys. Rev. Lett. 65, 2402 (1990)]. The results suggest that the observed singularities, particula…
Finite Size Effects in Thin Film Simulations
2003
Phase transitions in thin films are discussed, with an emphasis on Ising-type systems (liquid-gas transition in slit-like pores, unmixing transition in thin films, orderdisorder transitions on thin magnetic films, etc.) The typical simulation geometry then is a L xL x D system, where at the low confining L x L surfaces appropriate boundary “fields” are applied, while in the lateral directions periodic boundary conditions are used. In the z-direction normal to the film, the order parameter always is inhomogeneous, due to the boundary “fields” at the confining surfaces. When one varies the temperature T from the region of the bulk disordered phase to a temperature below the critical temperatu…
Phase separation versus wetting: A mean field theory for symmetrical polymer mixtures confined between selectively attractive walls
1996
Partially compatible symmetrical (N A # N B = N) binary mixtures of linear flexible polymers (A, B) are considered in the presence of two equivalent walls a distance D apart, assuming that both walls preferentially adsorb the same component. Using a Flory-Huggins type mean field approach analogous to previous work studying wetting phenomena in the semi-infinite version of this model, where D → ∞, it is shown that a single phase transition occurs in this thin film geometry, namely a phase separation between an A-rich and a B-rich phase (both phases include the bulk of the film). The coexistence curve is shifted to smaller values of the inverse Flory-Huggins parameter x -1 with decreasing D, …
Analysis of the Characteristics in the Meudon Constrained Evolution Scheme
2007
A first analysis of the characteristics associated with the evolving modes in the constraint evolution scheme proposed by the Meudon group in 2004 is presented. The system is written in a first-order hyperbolic form and a so-called generalized Dirac gauge is considered. Applications to inner boundary conditions in an excised approach to black hole evolutions are discussed.
A double mean field equation related to a curvature prescription problem
2019
We study a double mean field-type PDE related to a prescribed curvature problem on compacts surfaces with boundary. We provide a general blow-up analysis, then a Moser-Trudinger inequality, which gives energy-minimizing solutions for some range of parameters. Finally, we provide existence of min-max solutions for a wider range of parameters, which is dense in the plane if $��$ is not simply connected.
Wave propagation in 1D elastic solids in presence of long-range central interactions
2011
Abstract In this paper wave propagation in non-local elastic solids is examined in the framework of the mechanically based non-local elasticity theory established by the author in previous papers. It is shown that such a model coincides with the well-known Kroner–Eringen integral model of non-local elasticity in unbounded domains. The appeal of the proposed model is that the mechanical boundary conditions may easily be imposed because the applied pressure at the boundaries of the solid must be equilibrated by the Cauchy stress. In fact, the long-range forces between different volume elements are modelled, in the body domain, as central body forces applied to the interacting elements. It is …
Stress fields by the symmetric Galerkin boundary element method
2004
The paper examines the stress state of a body with the discretized boundary embedded in the infinite domain subjected to layered or double-layered actions, such as forces and displacement discontinuities on the boundary, and to internal actions, such as body forces and thermic variations, in the ambit of the symmetric Galerkin boundary element method (SGBEM). The stress distributions due to internal actions (body forces and thermic variations) were computed by transforming the volume integrals into boundary integrals. The aim of the paper is to show the tension state in Ω∞ as a response to all the actions acting in Ω when this analysis concerns the crossing of the discretized boundary, thu…