3 resultados para summation

em Universidad Politécnica de Madrid


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Analyzing residential architecture in Spain today signifies tackling a complex, apparently fragmentary situation, one that makes comment or criticism quite difficult. In the last few years authority over housing and city planning has been transferred to the regions,1 and each has developed its own framework of laws, its own regulations and requirements, and has shaped urban and regional development on the basis of its own criteria. In parallel, schools of architecture have multiplied, reaching many of the zones previously regarded as ?peripheral.? It is easy to understand how the old administrative centrality has given way to a more pluralistic situation closer to the specific problems of each city and region. As a result cultural differences have been accentuated, even compromising the possibility of speaking of an ?architecture Spanish? or reducing it to a mere summation or mosaic of local circumstances. Part of the debate of recent years has been focused on underlining these differences. This essay takes the opposite approach. The premise from which it starts out is that analysis of the phenomenon of ?residential architecture in Spain? makes it possible to acknowledge the survival of a cultural unity that explains the present and the recent past and that does not conflict with the diversity of local experiences.

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In this paper we present the tests on a structure designed to be a gymnasium, which has natural frequencies within that range. In these tests the gym slab was instrumented with acceleration sensors and different people jumped on a force plate installed on the floor. The test results have been compared with predictions based on the two existing load modelling alternatives (Sim and SCI Guide) and two new methodologies for modelling jumping loads has been proposed. The results of the force plate trials were analysed in an attempt to better characterize the profile of the jump force and determine how best to approximate it. In the first proposed methodology the study is carried out in the frequency domain using an average power spectral density of the jumps. In the second proposed methodology, the jump force is decomposed into the summation of one peak with a large period and a number of peaks with smaller periods. Utilizing a similar model to that of the Sim model, the approximation will still be comprised of the summation of two quadratic cosine functions.

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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.