Structural efficiency variation with the problem size in some bending problems = Variación del rendimiento estructural con el tamaño del problema en algunos casos de flexión simple

Existe normalmente el propósito de obtener la mejor solución posible cuando se plantea un problema estructural, entendiendo como mejor la solución que cumpliendo los requisitos estructurales, de uso, etc., tiene un coste físico menor. En una primera aproximación se puede representar el coste físico por medio del peso propio de la estructura, lo que permite plantear la búsqueda de la mejor solución como la de menor peso. Desde un punto de vista práctico, la obtención de buenas soluciones—es decir, soluciones cuyo coste sea solo ligeramente mayor que el de la mejor solución— es una tarea tan importante como la obtención de óptimos absolutos, algo en general difícilmente abordable. Para disponer de una medida de la eficiencia que haga posible la comparación entre soluciones se propone la siguiente definición de rendimiento estructural: la razón entre la carga útil que hay que soportar y la carga total que hay que contabilizar (la suma de la carga útil y el peso propio). La forma estructural puede considerarse compuesta por cuatro conceptos, que junto con el material, definen una estructura: tamaño, esquema, proporción, y grueso.Galileo (1638) propuso la existencia de un tamaño insuperable para cada problema estructural— el tamaño para el que el peso propio agota una estructura para un esquema y proporción dados—. Dicho tamaño, o alcance estructural, será distinto para cada material utilizado; la única información necesaria del material para su determinación es la razón entre su resistencia y su peso especifico, una magnitud a la que denominamos alcance del material. En estructuras de tamaño muy pequeño en relación con su alcance estructural la anterior definición de rendimiento es inútil. En este caso —estructuras de “talla nula” en las que el peso propio es despreciable frente a la carga útil— se propone como medida del coste la magnitud adimensional que denominamos número de Michell, que se deriva de la “cantidad” introducida por A. G. M. Michell en su artículo seminal de 1904, desarrollado a partir de un lema de J. C. Maxwell de 1870. A finales del siglo pasado, R. Aroca combino las teorías de Galileo y de Maxwell y Michell, proponiendo una regla de diseño de fácil aplicación (regla GA), que permite la estimación del alcance y del rendimiento de una forma estructural. En el presente trabajo se estudia la eficiencia de estructuras trianguladas en problemas estructurales de flexión, teniendo en cuenta la influencia del tamaño. Por un lado, en el caso de estructuras de tamaño nulo se exploran esquemas cercanos al optimo mediante diversos métodos de minoración, con el objetivo de obtener formas cuyo coste (medido con su numero deMichell) sea muy próximo al del optimo absoluto pero obteniendo una reducción importante de su complejidad. Por otro lado, se presenta un método para determinar el alcance estructural de estructuras trianguladas (teniendo en cuenta el efecto local de las flexiones en los elementos de dichas estructuras), comparando su resultado con el obtenido al aplicar la regla GA, mostrando las condiciones en las que es de aplicación. Por último se identifican las líneas de investigación futura: la medida de la complejidad; la contabilidad del coste de las cimentaciones y la extensión de los métodos de minoración cuando se tiene en cuenta el peso propio. ABSTRACT When a structural problem is posed, the intention is usually to obtain the best solution, understanding this as the solution that fulfilling the different requirements: structural, use, etc., has the lowest physical cost. In a first approximation, the physical cost can be represented by the self-weight of the structure; this allows to consider the search of the best solution as the one with the lowest self-weight. But, from a practical point of view, obtaining good solutions—i.e. solutions with higher although comparable physical cost than the optimum— can be as important as finding the optimal ones, because this is, generally, a not affordable task. In order to have a measure of the efficiency that allows the comparison between different solutions, a definition of structural efficiency is proposed: the ratio between the useful load and the total load —i.e. the useful load plus the self-weight resulting of the structural sizing—. The structural form can be considered to be formed by four concepts, which together with its material, completely define a particular structure. These are: Size, Schema, Slenderness or Proportion, and Thickness. Galileo (1638) postulated the existence of an insurmountable size for structural problems—the size for which a structure with a given schema and a given slenderness, is only able to resist its self-weight—. Such size, or structural scope will be different for every different used material; the only needed information about the material to determine such size is the ratio between its allowable stress and its specific weight: a characteristic length that we name material structural scope. The definition of efficiency given above is not useful for structures that have a small size in comparison with the insurmountable size. In this case—structures with null size, inwhich the self-weight is negligible in comparisonwith the useful load—we use as measure of the cost the dimensionless magnitude that we call Michell’s number, an amount derived from the “quantity” introduced by A. G. M. Michell in his seminal article published in 1904, developed out of a result from J. C.Maxwell of 1870. R. Aroca joined the theories of Galileo and the theories of Maxwell and Michell, obtaining some design rules of direct application (that we denominate “GA rule”), that allow the estimation of the structural scope and the efficiency of a structural schema. In this work the efficiency of truss-like structures resolving bending problems is studied, taking into consideration the influence of the size. On the one hand, in the case of structures with null size, near-optimal layouts are explored using several minimization methods, in order to obtain forms with cost near to the absolute optimum but with a significant reduction of the complexity. On the other hand, a method for the determination of the insurmountable size for truss-like structures is shown, having into account local bending effects. The results are checked with the GA rule, showing the conditions in which it is applicable. Finally, some directions for future research are proposed: the measure of the complexity, the cost of foundations and the extension of optimization methods having into account the self-weight.

Application of the homogenization techniques to the determination of the effective flexure constants of plate structural systems

A Mindlin plate with periodically distributed ribs patterns is analyzed by using homogenization techniques based on asymptotic expansion methods. The stiffness matrix of the homogenized plate is found to be dependent on the geometrical characteristics of the periodical cell, i.e. its skewness, plan shape, thickness variation etc. and on the plate material elastic constants. The computation of this plate stiffness matrix is carried out by averaging over the cell domain some solutions of different periodical boundary value problems. These boundary value problems are defined in variational form by linear first order differential operators on the cell domain and the boundary conditions of the variational equation correspond to a periodic structural problem. The elements of the stiffness matrix of homogenized plate are obtained by linear combinations of the averaged solution functions of the above mentioned boundary value problems. Finally, an illustrative example of application of this homogenization technique to hollowed plates and plate structures with ribs patterns regularly arranged over its area is shown. The possibility of using in the profesional practice the present procedure to the actual analysis of floors of typical buildings is also emphasized.

High throughput determination of sequence-function relationships in protein and RNA

Thesis (Ph.D.)--University of Washington, 2016-06

About the determination of key of a musical excerpt

Knowledge of the key of a musical passage is a pre-requisite for all the analyses that require functional labelling. In the past, people from either a musical or AI background have tended to solve the problem by means of implementing a computerized version of musical analysis. Previous attempts are discussed and then attention is focused on a non-analytical solution first reported by J.A.Gabura. A practical way to carry it out is discussed as well as its limitations in relation to examples. References are made to the MusicXML format as needed. © Springer-Verlag Berlin Heidelberg 2006.

An investigation of the factor-analytic approach to the determination of abilities involved in psychomotor learning

This research began with an attempt to solve a practical problem, namely, the prediction of the rate at which an operator will learn a task. From a review of the literature, communications with researchers in this area and the study of psychomotor learning in factories it was concluded that a more fundamental approach was required which included the development of a task taxonomy. This latter objective had been researched for over twenty years by E. A. Fleishman and his approach was adopted. Three studies were carried out to develop and extend Fleishman's approach to the industrial area. However, the results of these studies were not in accord with FIeishman's conclusions and suggested that a critical re-assessment was required of the arguments, methods and procedures used by Fleishman and his co-workers. It was concluded that Fleishman's findings were to some extent an artifact of the approximate methods and procedures which he used in the original factor analyses and that using the more modern computerised factor analytic methods a reliable ability taxonomy could be developed to describe the abilities involved in the learning of psychomotor tasks. The implications for a changing-task or changing-subject model were drawn and it was concluded that a changing task and subject model needs to be developed.

On the numerical solution of a Cauchy problem for the Laplace equation via a direct integral equation approach

We investigate the problem of determining the stationary temperature field on an inclusion from given Cauchy data on an accessible exterior boundary. On this accessible part the temperature (or the heat flux) is known, and, additionally, on a portion of this exterior boundary the heat flux (or temperature) is also given. We propose a direct boundary integral approach in combination with Tikhonov regularization for the stable determination of the temperature and flux on the inclusion. To determine these quantities on the inclusion, boundary integral equations are derived using Green’s functions, and properties of these equations are shown in an L2-setting. An effective way of discretizing these boundary integral equations based on the Nystr¨om method and trigonometric approximations, is outlined. Numerical examples are included, both with exact and noisy data, showing that accurate approximations can be obtained with small computational effort, and the accuracy is increasing with the length of the portion of the boundary where the additionally data is given.

Determination of a spacewise dependent heat source

This paper investigates the inverse problem of determining a spacewise dependent heat source in the parabolic heat equation using the usual conditions of the direct problem and information from a supplementary temperature measurement at a given single instant of time. The spacewise dependent temperature measurement ensures that the inverse problem has a unique solution, but this solution is unstable, hence the problem is ill-posed. For this inverse problem, we propose an iterative algorithm based on a sequence of well-posed direct problems which are solved at each iteration step using the boundary element method (BEM). The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for various typical benchmark test examples which have the input measured data perturbed by increasing amounts of random noise.

Automated Problem Domain Cognition Process in Information Systems Design

An automated cognitive approach for the design of Information Systems is presented. It is supposed to be used at the very beginning of the design process, between the stages of requirements determination and analysis, including the stage of analysis. In the context of the approach used either UML or ERD notations may be used for model representation. The approach provides the opportunity of using natural language text documents as a source of knowledge for automated problem domain model generation. It also simplifies the process of modelling by assisting the human user during the whole period of working upon the model (using UML or ERD notations).

Heterogeneous labour and the determination of value

Heterogeneity of labour and its implications for the Marxian theory of value has been one of the most controversial issues in the literature of the Marxist political economy. The adoption of Marx's conjecture about a uniform rate of surplus value leads to a simultaneous determination of the values of common and labour commodities of different types and the uniform rate of surplus value. Determination of these variables can be formally represented as a parametric cigenvalue problem. Morishima's and Bródy's earlier results are analysed and given new interpretations in the light of the suggested procedure. The main questions are addressed in a more general context too. The analysis is extended to the problem of segmented labour market, as well.

(Table 2) Age determination of Aegean Sea sediments

The modern Aegean Sea is an important source of deep water for the eastern Mediterranean. Its contribution to deep water ventilation is known to fluctuate in response to climatic variation on a decadal timescale. This study uses marine micropalaeontological and stable isotope data to investigate longer-term variability during the late glacial and Holocene, in particular that associated with the deposition of the early Holocene dysoxic/anoxic sapropel S1. Concentrating on the onset of sapropel-forming conditions, we identify the start of 'seasonal' stratification and highlight a lag in d18O response of the planktonic foraminifer N. pachyderma to termination T1b as identified in the d18O record of G. ruber. By use of a simple model we determine that this offset cannot be a function of bioturbation effects. The lag is of the order of 1 kyr and suggests that isolation of intermediate/deep water preceded the start of sapropel formation by up to 1.5 kyr. Using this discovery, we propose an explanation for the major unresolved problem in sapropel studies, namely, the source of nutrient supply required for export productivity to reach levels needed for sustained sapropel deposition. We suggest that nutrients had been accumulating in a stagnant basin for 1-1.5 kyr and that these accumulated resources were utilized during the deposition of S1. In addition, we provide a first quantitative estimate of the diffusive (1/e) mixing timescale for the eastern Mediterranean in its "stratified" sapropel mode, which is of the order of 450 years.

Distribution network reconfiguration validation with uncertain loads - network configuration determination and application

Automatic load transfer (ALT) on the 11 kV network is the process by which circuit breakers on the network are switched to form open points in order to feed load from different primary substations. Some of the potential benefits that may be gained from dynamically using ALT include maximising utilisation of existing assets, voltage regulation and reduced losses. One of the key issues, that has yet to be properly addressed in published research, is how to validate that the modelled benefits really exist. On an 11 kV distribution network where the load is continually changing and the load on each distribution substation is unlikely to be monitored - reduction in losses from moving the normally open point is particularly difficult to prove. This study proposes a method to overcome this problem and uses measured primary feeder data from two parts of the Western Power Distribution 11 kV Network under different configurations. The process of choosing the different configurations is based on a heuristic modelling method of locating minimum voltages to help reduce losses.

Determination of Biomolecular Interdomain Motions using Nuclear Magnetic Resonance

Biological macromolecules can rearrange interdomain orientations when binding to various partners. Interdomain dynamics serve as a molecular mechanism to guide the transitions between orientations. However, our understanding of interdomain dynamics is limited because a useful description of interdomain motions requires an estimate of the probabilities of interdomain conformations, increasing complexity of the problem.

Staphylococcal protein A (SpA) has five tandem protein-binding domains and four interdomain linkers. The domains enable Staphylococcus aureus to evade the host immune system by binding to multiple host proteins including antibodies. Here, I present a study of the interdomain motions of two adjacent domains in SpA. NMR spin relaxation experiments identified a 6-residue flexible interdomain linker and interdomain motions. To quantify the anisotropy of the distribution of interdomain orientations, we measured residual dipolar couplings (RDCs) from the two domains with multiple alignments. The N-terminal domain was directly aligned by a lanthanide ion and not influenced by interdomain motions, so it acted as a reference frame to achieve motional decoupling. We also applied {\it de novo} methods to extract spatial dynamic information from RDCs and represent interdomain motions as a continuous distribution on the 3D rotational space. Significant anisotropy was observed in the distribution, indicating the motion populates some interdomain orientations more than others. Statistical thermodynamic analysis of the observed orientational distribution suggests that it is among the energetically most favorable orientational distributions for binding to antibodies. Thus, the affinity is enhanced by a pre-posed distribution of interdomain orientations while maintaining the flexibility required for function.

The protocol described above can be applied to other biological systems in general. Protein molecule calmodulin and RNA molecule trans-activation response element (TAR) also have intensive interdomain motions with relative small intradomain dynamics. Their interdomain motions were studied using our method based on published RDC data. Our results were consistent with literature results in general. The differences could be due to previous studies' use of physical models, which contain assumptions about potential energy and thus introduced non-experimental information into the interpretations.

On Provable Algorithms for Determination of Continuous Protein Interdomain Motions from Residual Dipolar Couplings

Dynamics of biomolecules over various spatial and time scales are essential for biological functions such as molecular recognition, catalysis and signaling. However, reconstruction of biomolecular dynamics from experimental observables requires the determination of a conformational probability distribution. Unfortunately, these distributions cannot be fully constrained by the limited information from experiments, making the problem an ill-posed one in the terminology of Hadamard. The ill-posed nature of the problem comes from the fact that it has no unique solution. Multiple or even an infinite number of solutions may exist. To avoid the ill-posed nature, the problem needs to be regularized by making assumptions, which inevitably introduce biases into the result.

Here, I present two continuous probability density function approaches to solve an important inverse problem called the RDC trigonometric moment problem. By focusing on interdomain orientations we reduced the problem to determination of a distribution on the 3D rotational space from residual dipolar couplings (RDCs). We derived an analytical equation that relates alignment tensors of adjacent domains, which serves as the foundation of the two methods. In the first approach, the ill-posed nature of the problem was avoided by introducing a continuous distribution model, which enjoys a smoothness assumption. To find the optimal solution for the distribution, we also designed an efficient branch-and-bound algorithm that exploits the mathematical structure of the analytical solutions. The algorithm is guaranteed to find the distribution that best satisfies the analytical relationship. We observed good performance of the method when tested under various levels of experimental noise and when applied to two protein systems. The second approach avoids the use of any model by employing maximum entropy principles. This 'model-free' approach delivers the least biased result which presents our state of knowledge. In this approach, the solution is an exponential function of Lagrange multipliers. To determine the multipliers, a convex objective function is constructed. Consequently, the maximum entropy solution can be found easily by gradient descent methods. Both algorithms can be applied to biomolecular RDC data in general, including data from RNA and DNA molecules.

Quantitative Analysis and Determination of Microcystin in water by Capillary Electrophoresis Mass Spectrometry

The presence of harmful algal blooms (HAB) is a growing concern in aquatic environments. Among HAB organisms, cyanobacteria are of special concern because they have been reported worldwide to cause environmental and human health problem through contamination of drinking water. Although several analytical approaches have been applied to monitoring cyanobacteria toxins, conventional methods are costly and time-consuming so that analyses take weeks for field sampling and subsequent lab analysis. Capillary electrophoresis (CE) becomes a particularly suitable analytical separation method that can couple very small samples and rapid separations to a wide range of selective and sensitive detection techniques. This paper demonstrates a method for rapid separation and identification of four microcystin variants commonly found in aquatic environments. CE coupled to UV and electrospray ionization time-of-flight mass spectrometry (ESI-TOF) procedures were developed. All four analytes were separated within 6 minutes. The ESI-TOF experiment provides accurate molecular information, which further identifies analytes.

A framework for experimental determination of localised vertical pedestrian forces on full-scale structures using wireless attitude and heading reference systems

A major weakness among loading models for pedestrians walking on flexible structures proposed in recent years is the various uncorroborated assumptions made in their development. This applies to spatio-temporal characteristics of pedestrian loading and the nature of multi-object interactions. To alleviate this problem, a framework for the determination of localised pedestrian forces on full-scale structures is presented using a wireless attitude and heading reference systems (AHRS). An AHRS comprises a triad of tri-axial accelerometers, gyroscopes and magnetometers managed by a dedicated data processing unit, allowing motion in three-dimensional space to be reconstructed. A pedestrian loading model based on a single point inertial measurement from an AHRS is derived and shown to perform well against benchmark data collected on an instrumented treadmill. Unlike other models, the current model does not take any predefined form nor does it require any extrapolations as to the timing and amplitude of pedestrian loading. In order to assess correctly the influence of the moving pedestrian on behaviour of a structure, an algorithm for tracking the point of application of pedestrian force is developed based on data from a single AHRS attached to a foot. A set of controlled walking tests with a single pedestrian is conducted on a real footbridge for validation purposes. A remarkably good match between the measured and simulated bridge response is found, indeed confirming applicability of the proposed framework.