Search results for "Boundary"
showing 10 items of 1626 documents
Pointwise Hardy inequalities and uniformly fat sets
2008
We prove that it is equivalent for domain in R n \mathbb {R}^n to admit the pointwise p p -Hardy inequality, have uniformly p p -fat complement, or satisfy a uniform inner boundary density condition.
Numerical simulations of air pollutant dispersion in a stratified planetary boundary layer
1978
Abstract A numerical model is described for computing pollutant concentration distributions downwind from a source. It is based on the three-dimensional dispersion equation governing the time-dependent advective and diffusive transport of air pollutants and is solved numerically by a mixed Lagrangian-Eulerian finite-difference scheme. The model includes the vertical wind shear, the turning of the actual wind, and vertical variations of the vertical eddy diffusivity. In this paper the model is used to simulate the pollutant dispersion process in a stratified planetary boundary layer. The vertical profiles of horizontal mean wind and vertical eddy diffusivities are calculated numerically from…
An infinite-horizon model of dynamic membership of international environmental agreements
2007
Abstract Much of the literature on international environmental agreements (IEAs) uses static models, although most important transboundary pollution problems involve stock pollutants. The few papers that study IEAs using models of stock pollutants do not allow for the possibility that membership of the IEA may change endogenously over time. In this paper we analyse a simple infinite-horizon version of the static model of self-enforcing IEAs, in which damage costs increase with the stock of pollution, and countries decide each period whether to join an IEA. Using a quadratic approximation of the value function of the representative country we show that there exists a steady-state stock of po…
THE MATHEMATICAL MODELING OF METALS CONTENT IN PEAT
2015
Metals deposition in peat can aid to evaluate impact of atmospheric or wastewaters pollution and thus can be a good indicator of recent and historical changes in the pollution loading. For peat using in agriculture, industrial, heat production etc. knowledge of peat metals content is important. Experimental determination of metals in peat is very long and expensive work. Using experimental data the mathematical model for calculation of concentrations of metals in different points for different layers is developed. The values of the metals (Ca, Mg, Fe, Sr, Cu, Zn, Mn, Pb, Cr, Ni, Se, Co, Cd, V, Mo) concentrations in different layers in peat taken from Knavu peat bog from four sites are deter…
A multiscale approach to polycrystalline materials damage and failure
2015
A two-scale three-dimensional approach for degradation and failure in polycrystalline materials is presented. The method involves the component level and the grain scale. The damageinduced softening at the macroscale is modelled employing an initial stress boundary element approach. The microscopic degradation is explicitly modelled associating Representative Volume Elements (RVEs) to relevant points of the macro continuum and employing a cohesive-frictional 3D grain-boundary formulation to simulate intergranular degradation and failure in the Voronoi morphology. Macro-strains are downscaled as RVEs' periodic boundary conditions, while overall macro-stresses are obtained upscaling the micro…
Porosity effects on elastic properties of polycrystalline materials: a three-dimensional grain boundary formulation
2013
Polycrystalline materials are widely used in many technological applications of engineering interest. They constitute an important class of heterogeneous materials, and the investigation of the link between their macro and micro properties, main task of the micromechanics [1], is of relevant technological concern. The internal structure of a polycrystalline material is determined by the size and the shape of the grains, by their crystallographic orientation and by different type of defects within them. In this sense, the presence of internal voids, pores, is important to take into account in the determination of the polycrystalline aggregate properties. Porosity exists in almost all materia…
Polycrystalline materials with pores: effective properties through a boundary element homogenization scheme
2014
In this study, the influence of porosity on the elastic effective properties of polycrystalline materials is investigated using a formulation built on a boundary integral representation of the elastic problem for the grains, which are modeled as 3D linearly elastic orthotropic domains with arbitrary spatial orientation. The artificial polycrystalline morphology is represented using 3D Voronoi tessellations. The formulation is expressed in terms of intergranular fields, namely displacements and tractions that play an important role in polycrystalline micromechanics. The continuity of the aggregate is enforced through suitable intergranular conditions. The effective material properties are ob…
A cohesive boundary element approach to material degradation in three-dimensional polycrystalline aggregates
2013
A new three-dimensional grain-level formulation for intergranular degradation and failure in polycrystalline materials is presented. The polycrystalline microstructure is represented as a Voronoi tessellation and the boundary element method is used to express the elastic problem for each crystal of the aggregate. The continuity of the aggregate is enforced through suitable conditions at the intergranular interfaces. The grain-boundary model takes into account the onset and evolution of damage by means of an irreversible linear cohesive law, able to address mixed-mode failure conditions. Upon interface failure, a non-linear frictional contact analysis is introduced for addressing the contact…
A three-dimensional boundary element model for the analysis of polycrystalline materials at the microscale
2012
A three-dimensional multi-domain anisotropic boundary element formulation is presented for the analysis of polycrystalline microstructures. The formulation is naturally expressed in terms of intergranular displacements and tractions that play an important role in polycrystalline micromechanics, micro-damage and micro-cracking. The artificial morphology is generated by Hardcore Voronoi tessellation, which embodies the main statistical features of polycrystalline microstructures. Each crystal is modeled as an anisotropic elastic region and the integrity of the aggregate is restored by enforcing interface continuity and equilibrium between contiguous grains. The developed technique has been ap…
A Microstructural Model for Micro-Cracking in Piezoceramics
2018
Piezoelectric ceramics are employed in several applications for their capability to couple mechanical and electrical fields, which can be advantageously exploited for the implementation of smart functionalities. The electromechanical coupling, which can be employed for fast accurate micro-positioning devices, makes such materials suitable for application in micro electromechanical systems (MEMS). However, due to their brittleness, piezoceramics can develop damage leading to initiation of micro-cracks, affecting the performance of the material in general and the micro-devices in particular. For such reasons, the development of accurate and robust numerical tools is an important asset for the…