Artisan procedures to generate uniform tilings

This paper try to prove how artisans c ould discover all uniform tilings and very interesting others us ing artisanal combinatorial pro cedures without having to use mathematical procedures out of their reac h. Plane Geometry started up his way through History by means of fundamental drawing tools: ruler and co mpass. Artisans used same tools to carry out their orna mental patterns but at some point they began to work manually using physical representations of fi gures or tiles previously drawing by means of ruler and compass. That is an important step for craftsman because this way provides tools that let him come in the world of symmetry opera tions and empirical knowledge of symmetry groups. Artisans started up to pr oduce little wooden, ceramic or clay tiles and began to experiment with them by means of joining pieces whether edge to edge or vertex to vertex in that way so it can c over the plane without gaps. Economy in making floor or ceramic tiles could be most important reason to develop these procedures. This empiric way to develop tilings led not only to discover all uniform tilings but later discovering of aperiodic tilings.

Time-multiscale methods for the simulation of slow transport problems in atomistic systems

En esta tesis presentamos una teoría adaptada a la simulación de fenómenos lentos de transporte en sistemas atomísticos. En primer lugar, desarrollamos el marco teórico para modelizar colectividades estadísticas de equilibrio. A continuación, lo adaptamos para construir modelos de colectividades estadísticas fuera de equilibrio. Esta teoría reposa sobre los principios de la mecánica estadística, en particular el principio de máxima entropía de Jaynes, utilizado tanto para sistemas en equilibrio como fuera de equilibrio, y la teoría de las aproximaciones del campo medio. Expresamos matemáticamente el problema como un principio variacional en el que maximizamos una entropía libre, en lugar de una energía libre. La formulación propuesta permite definir equivalentes atomísticos de variables macroscópicas como la temperatura y la fracción molar. De esta forma podemos considerar campos macroscópicos no uniformes. Completamos el marco teórico con reglas de cuadratura de Monte Carlo, gracias a las cuales obtenemos modelos computables. A continuación, desarrollamos el conjunto completo de ecuaciones que gobiernan procesos de transporte. Deducimos la desigualdad de disipación entrópica a partir de fuerzas y flujos termodinámicos discretos. Esta desigualdad nos permite identificar la estructura que deben cumplir los potenciales cinéticos discretos. Dichos potenciales acoplan las tasas de variación en el tiempo de las variables microscópicas con las fuerzas correspondientes. Estos potenciales cinéticos deben ser completados con una relación fenomenológica, del tipo definido por la teoría de Onsanger. Por último, aportamos validaciones numéricas. Con ellas ilustramos la capacidad de la teoría presentada para simular propiedades de equilibrio y segregación superficial en aleaciones metálicas. Primero, simulamos propiedades termodinámicas de equilibrio en el sistema atomístico. A continuación evaluamos la habilidad del modelo para reproducir procesos de transporte en sistemas complejos que duran tiempos largos con respecto a los tiempos característicos a escala atómica. ABSTRACT In this work, we formulate a theory to address simulations of slow time transport effects in atomic systems. We first develop this theoretical framework in the context of equilibrium of atomic ensembles, based on statistical mechanics. We then adapt it to model ensembles away from equilibrium. The theory stands on Jaynes' maximum entropy principle, valid for the treatment of both, systems in equilibrium and away from equilibrium and on meanfield approximation theory. It is expressed in the entropy formulation as a variational principle. We interpret atomistic equivalents of macroscopic variables such as the temperature and the molar fractions, wich are not required to be uniform, but can vary from particle to particle. We complement this theory with Monte Carlo summation rules for further approximation. In addition, we provide a framework for studying transport processes with the full set of equations driving the evolution of the system. We first derive a dissipation inequality for the entropic production involving discrete thermodynamic forces and fluxes. This discrete dissipation inequality identifies the adequate structure for discrete kinetic potentials which couple the microscopic field rates to the corresponding driving forces. Those kinetic potentials must finally be expressed as a phenomenological rule of the Onsanger Type. We present several validation cases, illustrating equilibrium properties and surface segregation of metallic alloys. We first assess the ability of a simple meanfield model to reproduce thermodynamic equilibrium properties in systems with atomic resolution. Then, we evaluate the ability of the model to reproduce a long-term transport process in complex systems.

Gravitational actions upon a tether in a non-uniform gravity field with arbitrary number of zonal harmonics

We develop general closed-form expressions for the mutual gravitational potential, resultant and torque acting upon a rigid tethered system moving in a non-uniform gravity field produced by an attracting body with revolution symmetry, such that an arbitrary number of zonal harmonics is considered. The final expressions are series expansion in two small parameters related to the reference radius of the primary and the length of the tether, respectively, each of which are scaled by the mutual distance between their centers of mass. A few numerical experiments are performed to study the convergence behavior of the final expressions, and conclude that for high precision applications it might be necessary to take into account additional perturbation terms, which come from the mutual Two-Body interaction.

Optimal Piecewise Linear Function Approximation for GPU-based Applications

Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind of functions often implies a very high computational cost, unacceptable in real-time applications. To alleviate this problem, functions are commonly approximated by simpler piecewise-polynomial representations. Following this idea, we propose a novel, efficient, and practical technique to evaluate complex and continuous functions using a nearly optimal design of two types of piecewise linear approximations in the case of a large budget of evaluation subintervals. To this end, we develop a thorough error analysis that yields asymptotically tight bounds to accurately quantify the approximation performance of both representations. It provides an improvement upon previous error estimates and allows the user to control the trade-off between the approximation error and the number of evaluation subintervals. To guarantee real-time operation, the method is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), where it outperforms previous alternative approaches by exploiting the fixed-function interpolation routines present in their texture units. The proposed technique is a perfect match for any application requiring the evaluation of continuous functions, we have measured in detail its quality and efficiency on several functions, and, in particular, the Gaussian function because it is extensively used in many areas of computer vision and cybernetics, and it is expensive to evaluate.

Dust effects on PV array performance: in-field observations with non-uniform patterns

This paper presents the impact of non-homogeneous deposits of dust on the performance of a PV array. The observations have been made in a 2-MW PV park in the southeast region of Spain. The results are that inhomogeneous dust leads to more significant consequences than the mere short-circuit current reduction resulting from transmittance losses. In particular, when the affected PV modules are part of a string together with other cleaned (or less dusty) ones, operation voltage losses arise. These voltage losses can be several times larger than the short-circuit ones, leading to power losses that can be much larger than what measurements suggest when the PV modules are considered separately. Significant hot-spot phenomena can also arise leading to cells exhibiting temperature differences of more than 20 degrees and thus representing a threat to the PV modules' lifetime.

XRD analysis of InGaN uniform layers grown on Si (111) without any buffer layers and on Sapphire

The International Workshop on Nitride Semiconductors (IWN) is a biennial academic conference in the field of group III nitride research. The IWN and the International Conference on Nitride Semiconductors (ICNS) are held in alternating years and cover similar subject areas.

Artisan procedures to generate uniform tilings

This paper try to prove how artisans c ould discover all uniform tilings and very interesting others us ing artisanal combinatorial pro cedures without having to use mathematical procedures out of their reac h. Plane Geometry started up his way through History by means of fundamental drawing tools: ruler and co mpass. Artisans used same tools to carry out their orna mental patterns but at some point they began to work manually using physical representations of fi gures or tiles previously drawing by means of ruler and compass. That is an important step for craftsman because this way provides tools that let him come in the world of symmetry opera tions and empirical knowledge of symmetry groups. Artisans started up to pr oduce little wooden, ceramic or clay tiles and began to experiment with them by means of joining pieces whether edge to edge or vertex to vertex in that way so it can c over the plane without gaps. Economy in making floor or ceramic tiles could be most important reason to develop these procedures. This empiric way to develop tilings led not only to discover all uniform tilings but later discovering of aperiodic tilings.

The segmental approximation in multijunction solar cells

The segmental approach has been considered to analyze dark and light I-V curves. The photovoltaic (PV) dependence of the open-circuit voltage (Voc), the maximum power point voltage (Vm), the efficiency (?) on the photogenerated current (Jg), or on the sunlight concentration ratio (X), are analyzed, as well as other photovoltaic characteristics of multijunction solar cells. The characteristics being analyzed are split into monoexponential (linear in the semilogarithmic scale) portions, each of which is characterized by a definite value of the ideality factor A and preexponential current J0. The monoexponentiality ensures advantages, since at many steps of the analysis, one can use the analytical dependences instead of numerical methods. In this work, an experimental procedure for obtaining the necessary parameters has been proposed, and an analysis of GaInP/GaInAs/Ge triple-junction solar cell characteristics has been carried out. It has been shown that up to the sunlight concentration ratios, at which the efficiency maximum is achieved, the results of calculation of dark and light I-V curves by the segmental method fit well with the experimental data. An important consequence of this work is the feasibility of acquiring the resistanceless dark and light I-V curves, which can be used for obtaining the I-V curves characterizing the losses in the transport part of a solar cell.

A stochastic approximation algorithm with Markov chain Monte-Carlo method for incomplete data estimation problems

We propose a general procedure for solving incomplete data estimation problems. The procedure can be used to find the maximum likelihood estimate or to solve estimating equations in difficult cases such as estimation with the censored or truncated regression model, the nonlinear structural measurement error model, and the random effects model. The procedure is based on the general principle of stochastic approximation and the Markov chain Monte-Carlo method. Applying the theory on adaptive algorithms, we derive conditions under which the proposed procedure converges. Simulation studies also indicate that the proposed procedure consistently converges to the maximum likelihood estimate for the structural measurement error logistic regression model.

Approximation algorithms

Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models that capture 106 separate “yes” or “no” decisions to be made. Although one could, in principle, try all 2106 possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past 6 years, there has been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees; this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science.

Motor learning by field approximation.

We investigated how human subjects adapt to forces perturbing the motion of their ams. We found that this kind of learning is based on the capacity of the central nervous system (CNS) to predict and therefore to cancel externally applied perturbing forces. Our experimental results indicate: (i) that the ability of the CNS to compensate for the perturbing forces is restricted to those spatial locations where the perturbations have been experienced by the moving arm. The subjects also are able to compensate for forces experienced at neighboring workspace locations. However, adaptation decays smoothly and quickly with distance from the locations where disturbances had been sensed by the moving limb. (ii) Our experiments also how that the CNS builds an internal model of the external perturbing forces in intrinsic (muscles and / or joints) coordinates.

On paracompactness, completeness and boundedness in uniform spaces

Recently two new types of completeness in metric spaces, called Bourbaki-completeness and cofinal Bourbaki-completeness, have been introduced in [7]. The purpose of this note is to analyze these completeness properties in the general context of uniform spaces. More precisely, we are interested in how they are related with uniform paracompactness properties, as well as with some kind of uniform boundedness.

Influence of a uniform current on collective magnetization dynamics in a ferromagnetic metal

We discuss the influence of a uniform current j⃗ on the magnetization dynamics of a ferromagnetic metal. We find that the magnon energy ε(q⃗) has a current-induced contribution proportional to q⃗⋅J→, where J→ is the spin current, and predict that collective dynamics will be more strongly damped at finite j⃗. We obtain similar results for models with and without local moment participation in the magnetic order. For transition metal ferromagnets, we estimate that the uniform magnetic state will be destabilized for j≳109A cm-2. We discuss the relationship of this effect to the spin-torque effects that alter magnetization dynamics in inhomogeneous magnetic systems.

Logic-Based Outer Approximation for the Design of Discrete-Continuous Dynamic Systems with Implicit Discontinuities

We address the optimization of discrete-continuous dynamic optimization problems using a disjunctive multistage modeling framework, with implicit discontinuities, which increases the problem complexity since the number of continuous phases and discrete events is not known a-priori. After setting a fixed alternative sequence of modes, we convert the infinite-dimensional continuous mixed-logic dynamic (MLDO) problem into a finite dimensional discretized GDP problem by orthogonal collocation on finite elements. We use the Logic-based Outer Approximation algorithm to fully exploit the structure of the GDP representation of the problem. This modelling framework is illustrated with an optimization problem with implicit discontinuities (diver problem).

Logic-Based Outer-Approximation Algorithm for Solving Discrete-Continuous Dynamic Optimization Problems

We present an extension of the logic outer-approximation algorithm for dealing with disjunctive discrete-continuous optimal control problems whose dynamic behavior is modeled in terms of differential-algebraic equations. Although the proposed algorithm can be applied to a wide variety of discrete-continuous optimal control problems, we are mainly interested in problems where disjunctions are also present. Disjunctions are included to take into account only certain parts of the underlying model which become relevant under some processing conditions. By doing so the numerical robustness of the optimization algorithm improves since those parts of the model that are not active are discarded leading to a reduced size problem and avoiding potential model singularities. We test the proposed algorithm using three examples of different complex dynamic behavior. In all the case studies the number of iterations and the computational effort required to obtain the optimal solutions is modest and the solutions are relatively easy to find.