Search results for "boundary"

Displacements approach with external variables only for multi-domain analysis via symmetric BEM

2011

Abstract In the present paper a new displacement method, defined as external variables one, is proposed inside the multidomain symmetric Boundary Element formulation. This method is a natural evolution of the displacement approach with interface variables in the multidomain symmetric BEM analysis. Indeed, the strategy employed has the advantage of considering only the kinematical quantities of the free boundary nodes and the algebraic operators involved show symmetry and very small dimensions. The proposed approach is characterized by strong condensation of the mechanical and kinematical boundary nodes variables of the macro-elements. All the domain quantities, such as tractions and stresse…

Facies stacking and extinctions across the Triassic–Jurassic boundary in a peritidal succession from western Sicily

2017

An uppermost Triassic–lowermost Jurassic carbonate platform succession, which is 430 m thick, in northwestern Sicily is described with the aim to provide new data on the sedimentological and biological variations across the Triassic–Jurassic boundary in peritidal environments. The studied succession belonged to the rimmed carbonate shelf that developed during the upper Triassic along the margins of the Ionian Tethys. The peritidal sediments consist of metre-scale shallowing-upward cycles formed by subtidal, intertidal and supratidal facies. Three main informal units are differentiated along the section on the basis of the variations recorded by the subtidal facies. The lower and middle unit…

Mercury contents and isotope ratios from diverse depositional environments across the Triassic–Jurassic Boundary: Towards a more robust mercury proxy…

2021

Abstract Mercury is gaining prominence as a proxy for large igneous province (LIP) volcanism in the sedimentary record. Despite temporal overlap between some mass extinctions and LIPs, the precise timing of magmatism relative to major ecological and environmental change is difficult to untangle, especially in marine settings. Changes in the relative contents of Hg in sedimentary rocks through time, or ‘Hg anomalies’, can help resolve the timing of LIP activity and marine extinctions. However, major questions remain unanswered about the fidelity of Hg as a proxy for LIP magmatism. In particular, depositional (e.g., redox) and post-depositional (e.g., oxidative weathering) processes can affec…

Extremal length and Hölder continuity of conformal mappings

1986

Reliability analysis of processes with moving cracked material

2015

Abstract The reliability of processes with moving elastic and isotropic material containing initial cracks is considered in terms of fracture. The material is modelled as a moving plate which is simply supported from two of its sides and subjected to homogeneous tension acting in the travelling direction. For tension, two models are studied: (i) tension is constant with respect to time, and (ii) tension varies temporally according to an Ornstein–Uhlenbeck process. Cracks of random length are assumed to occur in the material according to a stochastic counting process. For a general counting process, a representation of the nonfracture probability of the system is obtained that exploits condi…

Determinantal sets, singularities and application to optimal control in medical imagery

2016

International audience; Control theory has recently been involved in the field of nuclear magnetic resonance imagery. The goal is to control the magnetic field optimally in order to improve the contrast between two biological matters on the pictures. Geometric optimal control leads us here to analyze mero-morphic vector fields depending upon physical parameters , and having their singularities defined by a deter-minantal variety. The involved matrix has polynomial entries with respect to both the state variables and the parameters. Taking into account the physical constraints of the problem, one needs to classify, with respect to the parameters, the number of real singularities lying in som…

General framework for testing Poisson-Voronoi assumption for real microstructures

2020

Modeling microstructures is an interesting problem not just in Materials Science but also in Mathematics and Statistics. The most basic model for steel microstructure is the Poisson-Voronoi diagram. It has mathematically attractive properties and it has been used in the approximation of single phase steel microstructures. The aim of this paper is to develop methods that can be used to test whether a real steel microstructure can be approximated by such a model. Therefore, a general framework for testing the Poisson-Voronoi assumption based on images of 2D sections of real metals is set out. Following two different approaches, according to the use or not of periodic boundary conditions, thre…

Acoustic Su-Schrieffer-Heeger lattice: Direct mapping of acoustic waveguides to the Su-Schrieffer-Heeger model

2021

Topological physics strongly relies on prototypical lattice model with particular symmetries. We report here on a theoretical and experimental work on acoustic waveguides that is directly mapped to the one-dimensional Su-Schrieffer-Heeger chiral model. Starting from the continuous two dimensional wave equation we use a combination of monomadal approximation and the condition of equal length tube segments to arrive at the wanted discrete equations. It is shown that open or closed boundary conditions topological leads automatically to the existence of edge modes. We illustrate by graphical construction how the edge modes appear naturally owing to a quarter-wavelength condition and the conserv…

Free boundary methods and non-scattering phenomena

2021

We study a question arising in inverse scattering theory: given a penetrable obstacle, does there exist an incident wave that does not scatter? We show that every penetrable obstacle with real-analytic boundary admits such an incident wave. At zero frequency, we use quadrature domains to show that there are also obstacles with inward cusps having this property. In the converse direction, under a nonvanishing condition for the incident wave, we show that there is a dichotomy for boundary points of any penetrable obstacle having this property: either the boundary is regular, or the complement of the obstacle has to be very thin near the point. These facts are proved by invoking results from t…

Diffusion front capturing schemes for a class of Fokker–Planck equations: Application to the relativistic heat equation

2010

In this research work we introduce and analyze an explicit conservative finite difference scheme to approximate the solution of initial-boundary value problems for a class of limited diffusion Fokker-Planck equations under homogeneous Neumann boundary conditions. We show stability and positivity preserving property under a Courant-Friedrichs-Lewy parabolic time step restriction. We focus on the relativistic heat equation as a model problem of the mentioned limited diffusion Fokker-Planck equations. We analyze its dynamics and observe the presence of a singular flux and an implicit combination of nonlinear effects that include anisotropic diffusion and hyperbolic transport. We present numeri…