Phonon spectra and temperature variation of thermodynamic properties of fcc metals via Finnis-Sinclair type many body potentials: Sutton-Chen and improved Sutton-Chen models

Volume(density)-independent pair-potentials cannot describe metallic cohesion adequately as the presence of the free electron gas renders the total energy strongly dependent on the electron density. The embedded atom method (EAM) addresses this issue by replacing part of the total energy with an explicitly density-dependent term called the embedding function. Finnis and Sinclair proposed a model where the embedding function is taken to be proportional to the square root of the electron density. Models of this type are known as Finnis-Sinclair many body potentials. In this work we study a particular parametrization of the Finnis-Sinclair type potential, called the "Sutton-Chen" model, and a later version, called the "Quantum Sutton-Chen" model, to study the phonon spectra and the temperature variation thermodynamic properties of fcc metals. Both models give poor results for thermal expansion, which can be traced to rapid softening of transverse phonon frequencies with increasing lattice parameter. We identify the power law decay of the electron density with distance assumed by the model as the main cause of this behaviour and show that an exponentially decaying form of charge density improves the results significantly. Results for Sutton-Chen and our improved version of Sutton-Chen models are compared for four fcc metals: Cu, Ag, Au and Pt. The calculated properties are the phonon spectra, thermal expansion coefficient, isobaric heat capacity, adiabatic and isothermal bulk moduli, atomic root-mean-square displacement and Gr\"{u}neisen parameter. For the sake of comparison we have also considered two other models where the distance-dependence of the charge density is an exponential multiplied by polynomials. None of these models exhibits the instability against thermal expansion (premature melting) as shown by the Sutton-Chen model. We also present results obtained via pure pair potential models, in order to identify advantages and disadvantages of methods used to obtain the parameters of these potentials.

Certain problems concerning polynomials and transcendental entire functions of exponential type

Soit $\displaystyle P(z):=\sum_{\nu=0}^na_\nu z^{\nu}$ un polynôme de degré $n$ et $\displaystyle M:=\sup_{|z|=1}|P(z)|.$ Sans aucne restriction suplémentaire, on sait que $|P'(z)|\leq Mn$ pour $|z|\leq 1$ (inégalité de Bernstein). Si nous supposons maintenant que les zéros du polynôme $P$ sont à l'extérieur du cercle $|z|=k,$ quelle amélioration peut-on apporter à l'inégalité de Bernstein? Il est déjà connu [{\bf \ref{Mal1}}] que dans le cas où $k\geq 1$ on a $$(*) \qquad |P'(z)|\leq \frac{n}{1+k}M \qquad (|z|\leq 1),$$ qu'en est-il pour le cas où $k < 1$? Quelle est l'inégalité analogue à $(*)$ pour une fonction entière de type exponentiel $\tau ?$ D'autre part, si on suppose que $P$ a tous ses zéros dans $|z|\geq k \, \, (k\geq 1),$ quelle est l'estimation de $|P'(z)|$ sur le cercle unité, en terme des quatre premiers termes de son développement en série entière autour de l'origine. Cette thèse constitue une contribution à la théorie analytique des polynômes à la lumière de ces questions.

Oaxaca-Blinder type counterfactual decomposition methods for duration outcomes

Los métodos disponibles para realizar análisis de descomposición que se pueden aplicar cuando los datos son completamente observados, no son válidos cuando la variable de interés es censurada. Esto puede explicar la escasez de este tipo de ejercicios considerando variables de duración, las cuales se observan usualmente bajo censura. Este documento propone un método del tipo Oaxaca-Blinder para descomponer diferencias en la media en el contexto de datos censurados. La validez de dicho método radica en la identificación y estimación de la distribución conjunta de la variable de duración y un conjunto de covariables. Adicionalmente, se propone un método más general que permite descomponer otros funcionales de interés como la mediana o el coeficiente de Gini, el cual se basa en la especificación de la función de distribución condicional de la variable de duración dado un conjunto de covariables. Con el fin de evaluar el desempeño de dichos métodos, se realizan experimentos tipo Monte Carlo. Finalmente, los métodos propuestos son aplicados para analizar las brechas de género en diferentes características de la duración del desempleo en España, tales como la duración media, la probabilidad de ser desempleado de largo plazo y el coeficiente de Gini. Los resultados obtenidos permiten concluir que los factores diferentes a las características observables, tales como capital humano o estructura del hogar, juegan un papel primordial para explicar dichas brechas.

Classification and fault detection methods for fuel cell monitoring and quality control

In this paper, various types of fault detection methods for fuel cells are compared. For example, those that use a model based approach or a data driven approach or a combination of the two. The potential advantages and drawbacks of each method are discussed and comparisons between methods are made. In particular, classification algorithms are investigated, which separate a data set into classes or clusters based on some prior knowledge or measure of similarity. In particular, the application of classification methods to vectors of reconstructed currents by magnetic tomography or to vectors of magnetic field measurements directly is explored. Bases are simulated using the finite integration technique (FIT) and regularization techniques are employed to overcome ill-posedness. Fisher's linear discriminant is used to illustrate these concepts. Numerical experiments show that the ill-posedness of the magnetic tomography problem is a part of the classification problem on magnetic field measurements as well. This is independent of the particular working mode of the cell but influenced by the type of faulty behavior that is studied. The numerical results demonstrate the ill-posedness by the exponential decay behavior of the singular values for three examples of fault classes.

A Wiener-Hopf type factorization for the exponential functional of Levy processes

For a Lévy process ξ=(ξt)t≥0 drifting to −∞, we define the so-called exponential functional as follows: Formula Under mild conditions on ξ, we show that the following factorization of exponential functionals: Formula holds, where × stands for the product of independent random variables, H− is the descending ladder height process of ξ and Y is a spectrally positive Lévy process with a negative mean constructed from its ascending ladder height process. As a by-product, we generate an integral or power series representation for the law of Iξ for a large class of Lévy processes with two-sided jumps and also derive some new distributional properties. The proof of our main result relies on a fine Markovian study of a class of generalized Ornstein–Uhlenbeck processes, which is itself of independent interest. We use and refine an alternative approach of studying the stationary measure of a Markov process which avoids some technicalities and difficulties that appear in the classical method of employing the generator of the dual Markov process.

Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version

We consider the two-dimensional Helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft obstacle. Our discretisation relies on the Trefftz-discontinuous Galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. We prove exponential convergence of the discrete solution in terms of number of unknowns.

Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation

An equation of Monge-Ampère type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport generates meshes that keep the same connectivity as the original mesh, making them suitable for r-adaptive simulations, in which the equations of motion can be solved in a moving frame of reference in order to avoid mapping the solution between old and new meshes and to avoid load balancing problems on parallel computers. The semi-implicit solution of the Monge-Ampère type equation involves a new linearisation of the Hessian term, and exponential maps are used to map from old to new meshes on the sphere. The determinant of the Hessian is evaluated as the change in volume between old and new mesh cells, rather than using numerical approximations to the gradients. OT meshes are generated to compare with centroidal Voronoi tesselations on the sphere and are found to have advantages and disadvantages; OT equidistribution is more accurate, the number of iterations to convergence is independent of the mesh size, face skewness is reduced and the connectivity does not change. However anisotropy is higher and the OT meshes are non-orthogonal. It is shown that optimal transport on the sphere leads to meshes that do not tangle. However, tangling can be introduced by numerical errors in calculating the gradient of the mesh potential. Methods for alleviating this problem are explored. Finally, OT meshes are generated using observed precipitation as a monitor function, in order to demonstrate the potential power of the technique.

NORDSIECK FORMS OF STIFFLY-STABLE ADAMS-TYPE CYCLIC METHODS THAT ARE INSENSITIVE TO STEP-SIZE CHANGES

In this paper we determine a matrix S and a vector l for stiffly-stable Adams-type cyclic methods that are insensitive to step size changes by using the definition of equivalent methods, (see, e.g. [l]), in the Nordsieck notation. The elements S and l, written in a parametric form, permit us to represent in Nordsieck form the methods that were constructed in [7] and the new methods that satisfy the above properties.

Exponential stability for a plate equation with p-Laplacian and memory terms

This paper is concerned with the energy decay for a class of plate equations with memory and lower order perturbation of p-Laplacian type, utt+?2u-?pu+?0tg(t-s)?u(s)ds-?ut+f(u)=0inOXR+, with simply supported boundary condition, where O is a bounded domain of RN, g?>?0 is a memory kernel that decays exponentially and f(u) is a nonlinear perturbation. This kind of problem without the memory term models elastoplastic flows.

Finite element methods for the Stokes system based on a Zienkiewicz type N-simplex

Hermite interpolation is increasingly showing to be a powerful numerical solution tool, as applied to different kinds of second order boundary value problems. In this work we present two Hermite finite element methods to solve viscous incompressible flows problems, in both two- and three-dimension space. In the two-dimensional case we use the Zienkiewicz triangle to represent the velocity field, and in the three-dimensional case an extension of this element to tetrahedra, still called a Zienkiewicz element. Taking as a model the Stokes system, the pressure is approximated with continuous functions, either piecewise linear or piecewise quadratic, according to the version of the Zienkiewicz element in use, that is, with either incomplete or complete cubics. The methods employ both the standard Galerkin or the Petrov–Galerkin formulation first proposed in Hughes et al. (1986) [18], based on the addition of a balance of force term. A priori error analyses point to optimal convergence rates for the PG approach, and for the Galerkin formulation too, at least in some particular cases. From the point of view of both accuracy and the global number of degrees of freedom, the new methods are shown to have a favorable cost-benefit ratio, as compared to velocity Lagrange finite elements of the same order, especially if the Galerkin approach is employed.

Comparison of three strip-type tests and two laboratory methods for salivary buffering analysis

This study evaluated the correlation between three strip-type, colorimetric tests and two laboratory methods with respect to the analysis of salivary buffering. The strip-type tests were saliva-check buffer, Dentobuff strip and CRT(®) Buffer test. The laboratory methods included Ericsson's laboratory method and a monotone acid/base titration to create a reference scale for the salivary titratable acidity. Additionally, defined buffer solutions were prepared and tested to simulate the carbonate, phosphate and protein buffer systems of saliva. The correlation between the methods was analysed by the Spearman's rank test. Disagreement was detected between buffering capacity values obtained with three strip-type tests that was more pronounced in case of saliva samples with medium and low buffering capacities. All strip-type tests were able to assign the hydrogencarbonate, di-hydrogenphosphate and 0.1% protein buffer solutions to the correct buffer categories. However, at 0.6% total protein concentrations, none of the test systems worked accurately. Improvements are necessary for strip-type tests because of certain disagreement with the Ericsson's laboratory method and dependence on the protein content of saliva.

Comparing remote sensing and ground-based methods of quantifying cover type and carbon storage in an urban forest

Understanding the canopy cover of an urban environment leads to better estimates of carbon storage and more informed management decisions by urban foresters. The most commonly used method for assessing urban forest cover type extent is ground surveys, which can be both timeconsuming and expensive. The analysis of aerial photos is an alternative method that is faster, cheaper, and can cover a larger number of sites, but may be less accurate. The objectives of this paper were (1) to compare three methods of cover type assessment for Los Angeles, CA: handdelineation of aerial photos in ArcMap, supervised classification of aerial photos in ERDAS Imagine, and ground-collected data using the Urban Forest Effects (UFORE) model protocol; (2) to determine how well remote sensing methods estimate carbon storage as predicted by the UFORE model; and (3) to explore the influence of tree diameter and tree density on carbon storage estimates. Four major cover types (bare ground, fine vegetation, coarse vegetation, and impervious surfaces) were determined from 348 plots (0.039 ha each) randomly stratified according to land-use. Hand-delineation was better than supervised classification at predicting ground-based measurements of cover type and UFORE model-predicted carbon storage. Most error in supervised classification resulted from shadow, which was interpreted as unknown cover type. Neither tree diameter or tree density per plot significantly affected the relationship between carbon storage and canopy cover. The efficiency of remote sensing rather than in situ data collection allows urban forest managers the ability to quickly assess a city and plan accordingly while also preserving their often-limited budget.