A two-dimensional finite element model of front surface current flow in cells under non-uniform, concentrated illumination

A two-dimensional finite element model of current flow in the front surface of a PV cell is presented. In order to validate this model we perform an experimental test. Later, particular attention is paid to the effects of non-uniform illumination in the finger direction which is typical in a linear concentrator system. Fill factor, open circuit voltage and efficiency are shown to decrease with increasing degree of non-uniform illumination. It is shown that these detrimental effects can be mitigated significantly by reoptimization of the number of front surface metallization fingers to suit the degree of non-uniformity. The behavior of current flow in the front surface of a cell operating at open circuit voltage under non-uniform illumination is discussed in detail.

One dimensional exciton luminescence induced by extended defects in nonpolar (Al,Ga)N/GaN quantum wells

In this study, we present the optical properties of nonpolar GaN/(Al,Ga)N single quantum wells (QWs) grown on either a- or m-plane GaN templates for Al contents set below 15%. In order to reduce the density of extended defects, the templates have been processed using the epitaxial lateral overgrowth technique. As expected for polarization-free heterostructures, the larger the QW width for a given Al content, the narrower the QW emission line. In structures with an Al content set to 5 or 10%, we also observe emission from excitons bound to the intersection of I1-type basal plane stacking faults (BSFs) with the QW. Similarly to what is seen in bulk material, the temperature dependence of BSF-bound QW exciton luminescence reveals intra-BSF localization. A qualitative model evidences the large spatial extension of the wavefunction of these BSF-bound QW excitons, making them extremely sensitive to potential fluctuations located in and away from BSF. Finally, polarization-dependent measurements show a strong emission anisotropy for BSF-bound QW excitons, which is related to their one-dimensional character and that confirms that the intersection between a BSF and a GaN/(Al,Ga)N QW can be described as a quantum wire.

Dynamic analysis of road vehicle-bridge systems under turbulent wind by means of Finite Element Models

When an automobile passes over a bridge dynamic effects are produced in vehicle and structure. In addition, the bridge itself moves when exposed to the wind inducing dynamic effects on the vehicle that have to be considered. The main objective of this work is to understand the influence of the different parameters concerning the vehicle, the bridge, the road roughness or the wind in the comfort and safety of the vehicles when crossing bridges. Non linear finite element models are used for structures and multibody dynamic models are employed for vehicles. The interaction between the vehicle and the bridge is considered by contact methods. Road roughness is described by the power spectral density (PSD) proposed by the ISO 8608. To consider that the profiles under right and left wheels are different but not independent, the hypotheses of homogeneity and isotropy are assumed. To generate the wind velocity history along the road the Sandia method is employed. The global problem is solved by means of the finite element method. First the methodology for modelling the interaction is verified in a benchmark. Following, the case of a vehicle running along a rigid road and subjected to the action of the turbulent wind is analyzed and the road roughness is incorporated in a following step. Finally the flexibility of the bridge is added to the model by making the vehicle run over the structure. The application of this methodology will allow to understand the influence of the different parameters in the comfort and safety of road vehicles crossing wind exposed bridges. Those results will help to recommend measures to make the traffic over bridges more reliable without affecting the structural integrity of the viaduct

A Three-Dimensional B.I.E.M. Program

The program PECET (Boundary Element Program in Three-Dimensional Elasticity) is presented in this paper. This program, written in FORTRAN V and implemen ted on a UNIVAC 1100,has more than 10,000 sentences and 96 routines and has a lot of capabilities which will be explained in more detail. The object of the program is the analysis of 3-D piecewise heterogeneous elastic domains, using a subregionalization process and 3-D parabolic isopara, metric boundary elements. The program uses special data base management which will be described below, and the modularity followed to write it gives a great flexibility to the package. The Method of Analysis includes an adaptive integration process, an original treatment of boundary conditions, a complete treatment of body forces, the utilization of a Modified Conjugate Gradient Method of solution and an original process of storage which makes it possible to save a lot of memory.

A method for revealing phase space structures of general time dependent dynamical systems

In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as Lagrangian descriptors. These quantities are based on the integration, for a finite time, along trajectories of an intrinsic bounded, positive geometrical and/or physical property of the trajectory itself. We discuss a general methodology for constructing Lagrangian descriptors, and we discuss a “heuristic argument” that explains why this method is successful for revealing geometrical structures in the phase space of a dynamical system. We support this argument by explicit calculations on a benchmark problem having a hyperbolic fixed point with stable and unstable manifolds that are known analytically. Several other benchmark examples are considered that allow us the assess the performance of Lagrangian descriptors in revealing invariant tori and regions of shear. Throughout the paper “side-by-side” comparisons of the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field (“time averages”) are carried out and discussed. In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. We also perform computations for an explicitly three dimensional, aperiodically time-dependent vector field and an aperiodically time dependent vector field defined as a data set. Comparisons with FTLEs and time averages for these examples are also carried out, with similar conclusions as for the benchmark examples.

Two-dimensional mesh optimization in the finite element method

The solution to the problem of finding the optimum mesh design in the finite element method with the restriction of a given number of degrees of freedom, is an interesting problem, particularly in the applications method. At present, the usual procedures introduce new degrees of freedom (remeshing) in a given mesh in order to obtain a more adequate one, from the point of view of the calculation results (errors uniformity). However, from the solution of the optimum mesh problem with a specific number of degrees of freedom some useful recommendations and criteria for the mesh construction may be drawn. For 1-D problems, namely for the simple truss and beam elements, analytical solutions have been found and they are given in this paper. For the more complex 2-D problems (plane stress and plane strain) numerical methods to obtain the optimum mesh, based on optimization procedures have to be used. The objective function, used in the minimization process, has been the total potential energy. Some examples are presented. Finally some conclusions and hints about the possible new developments of these techniques are also given.

Fundamental finite key limits for information reconciliation in quantum key distribution

The security of quantum key distribution protocols is guaranteed by the laws of quantum mechanics. However, a precise analysis of the security properties requires tools from both classical cryptography and information theory. Here, we employ recent results in non-asymptotic classical information theory to show that information reconciliation imposes fundamental limitations on the amount of secret key that can be extracted in the finite key regime. In particular, we find that an often used approximation for the information leakage during one-way information reconciliation is flawed and we propose an improved estimate.

Finite Element Model of the Innovation Diffusion: An Application to Photovoltaic Systems

This paper presents a Finite Element Model, which has been used for forecasting the diffusion of innovations in time and space. Unlike conventional models used in diffusion literature, the model considers the spatial heterogeneity. The implementation steps of the model are explained by applying it to the case of diffusion of photovoltaic systems in a local region in southern Germany. The applied model is based on a parabolic partial differential equation that describes the diffusion ratio of photovoltaic systems in a given region over time. The results of the application show that the Finite Element Model constitutes a powerful tool to better understand the diffusion of an innovation as a simultaneous space-time process. For future research, model limitations and possible extensions are also discussed.

Two-dimensional isostatic meshes in the finite element method

In a Finite Element (FE) analysis of elastic solids several items are usually considered, namely, type and shape of the elements, number of nodes per element, node positions, FE mesh, total number of degrees of freedom (dot) among others. In this paper a method to improve a given FE mesh used for a particular analysis is described. For the improvement criterion different objective functions have been chosen (Total potential energy and Average quadratic error) and the number of nodes and dof's of the new mesh remain constant and equal to the initial FE mesh. In order to find the mesh producing the minimum of the selected objective function the steepest descent gradient technique has been applied as optimization algorithm. However this efficient technique has the drawback that demands a large computation power. Extensive application of this methodology to different 2-D elasticity problems leads to the conclusion that isometric isostatic meshes (ii-meshes) produce better results than the standard reasonably initial regular meshes used in practice. This conclusion seems to be independent on the objective function used for comparison. These ii-meshes are obtained by placing FE nodes along the isostatic lines, i.e. curves tangent at each point to the principal direction lines of the elastic problem to be solved and they should be regularly spaced in order to build regular elements. That means ii-meshes are usually obtained by iteration, i.e. with the initial FE mesh the elastic analysis is carried out. By using the obtained results of this analysis the net of isostatic lines can be drawn and in a first trial an ii-mesh can be built. This first ii-mesh can be improved, if it necessary, by analyzing again the problem and generate after the FE analysis the new and improved ii-mesh. Typically, after two first tentative ii-meshes it is sufficient to produce good FE results from the elastic analysis. Several example of this procedure are presented.

Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

On representations of finite type

Representations of the (infinite) canonical anticommutation relations and the associated operator algebra, the fermion algebra, are studied. A “coupling constant” (in (0,1]) is defined for primary states of “finite type” of that algebra. Primary, faithful states of finite type with arbitrary coupling are constructed and classified. Their physical significance for quantum thermodynamical systems at high temperatures is discussed. The scope of this study is broadened to include a large class of operator algebras sharing some of the structural properties of the fermion algebra.

Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat

A microcanonical finite-size ansatz in terms of quantities measurable in a finite lattice allows extending phenomenological renormalization the so-called quotients method to the microcanonical ensemble. The ansatz is tested numerically in two models where the canonical specific heat diverges at criticality, thus implying Fisher renormalization of the critical exponents: the three-dimensional ferromagnetic Ising model and the two-dimensional four-state Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows simulating systems as large as L = 1024 Potts or L= 128 (Ising). The quotients method provides accurate determinations of the anomalous dimension, η, and of the (Fisher-renormalized) thermal ν exponent. While in the Ising model the numerical agreement with our theoretical expectations is very good, in the Potts case, we need to carefully incorporate logarithmic corrections to the microcanonical ansatz in order to rationalize our data.

Phase transition in the three dimensional Heisenberg spin glass: Finite-size scaling analysis

We have investigated the phase transition in the Heisenberg spin glass using massive numerical simulations to study very large sizes, 483. A finite-size scaling analysis indicates that the data are compatible with the most economical scenario: a common transition temperature for spins and chiralities.

Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model

We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation including additive white noise and Gilbert damping. Using a collective variable theory with no adjustable parameters we derive an equation of motion for the vortices with stochastic forces which are shown to represent white noise with an effective diffusion constant linearly dependent on temperature. We solve these stochastic equations of motion by means of a Green's function formalism and obtain the mean vortex trajectory and its variance. We find a non-standard time dependence for the variance of the components perpendicular to the driving force. We compare the analytical results with Langevin dynamics simulations and find a good agreement up to temperatures of the order of 25% of the Kosterlitz-Thouless transition temperature. Finally, we discuss the reasons why our approach is not appropriate for higher temperatures as well as the discreteness effects observed in the numerical simulations.