Early resistance change and stress/electromigration evolution in near bamboo interconnects

A complete description for early resistance change and mechanical stress evolution in near-bamboo interconnects, related to the electromigration, is given in this paper. The proposed model, for the first time, combines the stress/vacancy concentration evolution with the early resistance change of the Al line with a near-bamboo microstructure, which has been proven to be a fast technique for prediction of the MTF of a line compared to the conventional (accelerated) stres

Resolvent Estimates in L^p for the Stokes Operator in Lipschitz Domains

We establish the $L^p$ resolvent estimates for the Stokes operator in Lipschitz domains in $R^d$, $d\ge 3$ for $|\frac{1}{p}-1/2|< \frac{1}{2d} +\epsilon$. The result, in particular, implies that the Stokes operator in a three-dimensional Lipschitz domain generates a bounded analytic semigroup in $L^p$ for (3/2)-\varep < p< 3+\epsilon. This gives an affirmative answer to a conjecture of M. Taylor.Comment: 28 page. Minor revision was made regarding the definition of the Stokes operator in Lipschitz domain

The mixed problem for the Laplacian in Lipschitz domains

We consider the mixed boundary value problem or Zaremba's problem for the Laplacian in a bounded Lipschitz domain in R^n. We specify Dirichlet data on part of the boundary and Neumann data on the remainder of the boundary. We assume that the boundary between the sets where we specify Dirichlet and Neumann data is a Lipschitz surface. We require that the Neumann data is in L^p and the Dirichlet data is in the Sobolev space of functions having one derivative in L^p for some p near 1. Under these conditions, there is a unique solution to the mixed problem with the non-tangential maximal function of the gradient of the solution in L^p of the boundary. We also obtain results with data from Hardy spaces when p=1.Comment: Version 5 includes a correction to one step of the main proof. Since the paper appeared long ago, this submission includes the complete paper, followed by a short section that gives the correction to one step in the proo

Discrete exterior calculus (DEC) for the surface Navier-Stokes equation

We consider a numerical approach for the incompressible surface Navier-Stokes equation. The approach is based on the covariant form and uses discrete exterior calculus (DEC) in space and a semi-implicit discretization in time. The discretization is described in detail and related to finite difference schemes on staggered grids in flat space for which we demonstrate second order convergence. We compare computational results with a vorticity-stream function approach for surfaces with genus 0 and demonstrate the interplay between topology, geometry and flow properties. Our discretization also allows to handle harmonic vector fields, which we demonstrate on a torus.Comment: 21 pages, 9 figure

Finite Element Convergence for the Joule Heating Problem with Mixed Boundary Conditions

We prove strong convergence of conforming finite element approximations to the stationary Joule heating problem with mixed boundary conditions on Lipschitz domains in three spatial dimensions. We show optimal global regularity estimates on creased domains and prove a priori and a posteriori bounds for shape regular meshes.Comment: Keywords: Joule heating problem, thermistors, a posteriori error analysis, a priori error analysis, finite element metho

A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

Spectral bounds for the Neumann-Poincaré operator on planar domains with corners

The boundary double layer potential, or the Neumann-Poincaré operator, is studied on the Sobolev space of order 1/2 along the boundary, coinciding with the space of charges giving rise to double layer potentials with finite energy in the whole space. Poincaré’s program of studying the spectrum of the boundary double layer potential is developed in complete generality on closed Lipschitz hypersurfaces in euclidean space. Furthermore, the Neumann-Poincaré operator is realized as a singular integral transform bearing similarities to the Beurling-Ahlfors transform in 2 dimensions. As an application, in the case of planar curves with corners, bounds for the spectrum of the Neumann-Poincaré operator are derived from recent results in quasi-conformal mapping theory

The transmission problem on a three-dimensional wedge

We consider the transmission problem for the Laplace equation on an infinite three-dimensional wedge, determining the complex parameters for which the problem is well-posed, and characterizing the infinite multiplicity nature of the spectrum. This is carried out in two formulations leading to rather different spectral pictures. One formulation is in terms of square integrable boundary data, the other is in terms of finite energy solutions. We use the layer potential method, which requires the harmonic analysis of a non-commutative non-unimodular group associated with the wedge

Comparison of Urban Climate Change Adaptation Plans in Selected European Cities from a Legal and Spatial Perspective

Publisher Copyright: © 2024 by the authors.The aim of this paper is to identify and compare the key institutional features of urban climate change adaptation plans in three geographically, systemically, and climatically distinct European countries (Greece, Spain, and Poland). The paper concentrates on the tool indicated and confirms the circumstances and potential outcomes of its usage in the selected countries. A case study of a particular city was chosen in each country and the applicability of the climate change adaptation plan there was confirmed. Analysis was also performed on the plans’ legal aspect, connection to national-level strategic planning, and spatial planning. The research questions formulated and addressed are as follows: how do urban climate change adaptation plans in the selected countries define key climate challenges? Is the content of the municipal climate change adaptation plans consistent with the content of the diagnosis of climate challenges at the supra-local level and in the scientific discussion? How are climate change adaptation plans translated into the implementation sphere? Τhe example of Spain and Greece confirms that plans can combine general climate change adaptation objectives with specific (evasive) guidelines for urban policies, while the example of Poland shows that the content of climate change adaptation plans can often be too vague and difficult to further integrate into urban policies. The research results obtained are relevant from the perspective of comparing institutional responses to climate challenges. The research proposes possible methods for making such comparisons.publishersversionpublishe

Low potency toxins reveal dense interaction networks in metabolism

Background The chemicals of metabolism are constructed of a small set of atoms and bonds. This may be because chemical structures outside the chemical space in which life operates are incompatible with biochemistry, or because mechanisms to make or utilize such excluded structures has not evolved. In this paper I address the extent to which biochemistry is restricted to a small fraction of the chemical space of possible chemicals, a restricted subset that I call Biochemical Space. I explore evidence that this restriction is at least in part due to selection again specific structures, and suggest a mechanism by which this occurs. Results Chemicals that contain structures that our outside Biochemical Space (UnBiological groups) are more likely to be toxic to a wide range of organisms, even though they have no specifically toxic groups and no obvious mechanism of toxicity. This correlation of UnBiological with toxicity is stronger for low potency (millimolar) toxins. I relate this to the observation that most chemicals interact with many biological structures at low millimolar toxicity. I hypothesise that life has to select its components not only to have a specific set of functions but also to avoid interactions with all the other components of life that might degrade their function. Conclusions The chemistry of life has to form a dense, self-consistent network of chemical structures, and cannot easily be arbitrarily extended. The toxicity of arbitrary chemicals is a reflection of the disruption to that network occasioned by trying to insert a chemical into it without also selecting all the other components to tolerate that chemical. This suggests new ways to test for the toxicity of chemicals, and that engineering organisms to make high concentrations of materials such as chemical precursors or fuels may require more substantial engineering than just of the synthetic pathways involved