Exact resultants for corner-cut unmixed multivariate polynomial systems using the dixon formulation

Structural conditions on the support of a multivariate polynomial system are developed for which the Dixon-based resultant methods compute exact resultants. For cases when this cannot be done, an upper bound on the degree of the extraneous factor in the projection operator can be determined a priori, thus resulting in quick identification of the extraneous factor in the projection operator. (For the bivariate case, the degree of the extraneous factor in a projection operator can be determined a priori.) The concepts of a corner-cut support and almost corner-cut support of an unmixed polynomial system are introduced. For generic unmixed polynomial systems with corner-cut and almost corner-cut supports, the Dixon based methods can be used to compute their resultants exactly. These structural conditions on supports are based on analyzing how such supports differ from box supports of n-degree systems for which the Dixon formulation is known to compute the resultants exactly. Such an analysis also gives a sharper bound on the complexity of resultant computation using the Dixon formulation in terms of the support and the mixed volume of the Newton polytope of the support. These results are a direct generalization of the authors ’ results on bivariate systems including the results of Zhang and Goldman as well as of Chionh for generic unmixed bivariate polynomial systems with corner-cut supports

Early detection of first-time slope failures using acoustic emission measurements : large-scale physical modelling

Early warning systems for slope instability need to alert users of accelerating slope deformation behaviour to enable safety-critical decisions to be made. This study shows that acoustic emission (AE) monitoring of active waveguides (i.e. a steel tube with a granular backfill surround installed through a slope) can both detect shear surface development and quantify increasing rates of movement during slope failure, thereby providing an early detection of slope instability. A large-scale physical model was designed and built to simulate slope failures on elements of soil, through which full-scale active waveguides were installed. A shear surface develops in each test and the sliding mass accelerates during failure, reaching velocities greater than 300 mm/h and shear deformations of 50 mm. Continuous measurementswere obtained to examine the behaviour of activewaveguides subjected to first-time slope failure dynamics (i.e. development of new shear surfaces and accelerating deformation behaviour). Comparisons with continuous subsurface deformation measurements show that AE detection began during shear surface formation, and AE rates increased proportionally with displacement rates as failure occurred. Empirical AE rate–slope velocity relationships are presented for three granular backfill types, which demonstrate that generic AE rate–slope velocity relationships can be obtained for groups of backfill types; these relationships allow displacement rates to be quantified from measured AE rates to provide early detection of slope instability. © 2017, ICE Publishing. All rights reserved

Computer Science for Continuous Data:Survey, Vision, Theory, and Practice of a Computer Analysis System

Building on George Boole's work, Logic provides a rigorous foundation for the powerful tools in Computer Science that underlie nowadays ubiquitous processing of discrete data, such as strings or graphs. Concerning continuous data, already Alan Turing had applied "his" machines to formalize and study the processing of real numbers: an aspect of his oeuvre that we transform from theory to practice.The present essay surveys the state of the art and envisions the future of Computer Science for continuous data: natively, beyond brute-force discretization, based on and guided by and extending classical discrete Computer Science, as bridge between Pure and Applied Mathematics

Distance-based formulations for the position analysis of kinematic chains

This thesis addresses the kinematic analysis of mechanisms, in particular, the position analysis of kinematic chains, or linkages, that is, mechanisms with rigid bodies (links) interconnected by kinematic pairs (joints). This problem, of completely geometrical nature, consists in finding the feasible assembly modes that a kinematic chain can adopt. An assembly mode is a possible relative transformation between the links of a kinematic chain. When an assignment of positions and orientations is made for all links with respect to a given reference frame, an assembly mode is called a configuration. The methods reported in the literature for solving the position analysis of kinematic chains can be classified as graphical, analytical, or numerical. The graphical approaches are mostly geometrical and designed to solve particular problems. The analytical and numerical methods deal, in general, with kinematic chains of any topology and translate the original geometric problem into a system of kinematic analysis of all the Assur kinematic chains resulting from replacing some of its revolute joints by slider joints. Thus, it is concluded that the polynomials of all fully-parallel planar robots can be derived directly from that of the widely known 3-RPR robot. In addition to these results, this thesis also presents an efficient procedure, based on distance and oriented area constraints, and geometrical arguments, to trace coupler curves of pin-jointed Gr¨ubler kinematic chains. All these techniques and results together are contributions to theoretical kinematics of mechanisms, robot kinematics, and distance plane geometry. equations that defines the location of each link based, mainly, on independent loop equations. In the analytical approaches, the system of kinematic equations is reduced to a polynomial, known as the characteristic polynomial of the linkage, using different elimination methods —e.g., Gr¨obner bases or resultant techniques. In the numerical approaches, the system of kinematic equations is solved using, for instance, polynomial continuation or interval-based procedures. In any case, the use of independent loop equations to solve the position analysis of kinematic chains, almost a standard in kinematics of mechanisms, has seldom been questioned despite the resulting system of kinematic equations becomes quite involved even for simple linkages. Moreover, stating the position analysis of kinematic chains directly in terms of poses, with or without using independent loop equations, introduces two major disadvantages: arbitrary reference frames has to be included, and all formulas involve translations and rotations simultaneously. This thesis departs from this standard approach by, instead of directly computing Cartesian locations, expressing the original position problem as a system of distance-based constraints that are then solved using analytical and numerical procedures adapted to their particularities. In favor of developing the basics and theory of the proposed approach, this thesis focuses on the study of the most fundamental planar kinematic chains, namely, Baranov trusses, Assur kinematic chains, and pin-jointed Gr¨ubler kinematic chains. The results obtained have shown that the novel developed techniques are promising tools for the position analysis of kinematic chains and related problems. For example, using these techniques, the characteristic polynomials of most of the cataloged Baranov trusses can be obtained without relying on variable eliminations or trigonometric substitutions and using no other tools than elementary algebra. An outcome in clear contrast with the complex variable eliminations require when independent loop equations are used to tackle the problem. The impact of the above result is actually greater because it is shown that the characteristic polynomial of a Baranov truss, derived using the proposed distance-based techniques, contains all the necessary and sufficient information for solving the positionEsta tesis aborda el problema de análisis de posición de cadenas cinemáticas, mecanismos con cuerpos rígidos (enlaces) interconectados por pares cinemáticos (articulaciones). Este problema, de naturaleza geométrica, consiste en encontrar los modos de ensamblaje factibles que una cadena cinemática puede adoptar. Un modo de ensamblaje es una transformación relativa posible entre los enlaces de una cadena cinemática. Los métodos reportados en la literatura para la solución del análisis de posición de cadenas cinemáticas se pueden clasificar como gráficos, analíticos o numéricos. Los enfoques gráficos son geométricos y se diseñan para resolver problemas particulares. Los métodos analíticos y numéricos tratan con cadenas cinemáticas de cualquier topología y traducen el problema geométrico original en un sistema de ecuaciones cinemáticas que define la ubicación de cada enlace, basado generalmente en ecuaciones de bucle independientes. En los enfoques analíticos, el sistema de ecuaciones cinemáticas se reduce a un polinomio, conocido como el polinomio característico de la cadena cinemática, utilizando diferentes métodos de eliminación. En los métodos numéricos, el sistema se resuelve utilizando, por ejemplo, la continuación polinomial o procedimientos basados en intervalos. En cualquier caso, el uso de ecuaciones de bucle independientes, un estándar en cinemática de mecanismos, rara vez ha sido cuestionado a pesar de que el sistema resultante de ecuaciones es bastante complicado, incluso para cadenas simples. Por otra parte, establecer el análisis de la posición de cadenas cinemáticas directamente en términos de poses, con o sin el uso de ecuaciones de bucle independientes, presenta dos inconvenientes: sistemas de referencia arbitrarios deben ser introducidos, y todas las fórmulas implican traslaciones y rotaciones de forma simultánea. Esta tesis se aparta de este enfoque estándar expresando el problema de posición original como un sistema de restricciones basadas en distancias, en lugar de directamente calcular posiciones cartesianas. Estas restricciones son posteriormente resueltas con procedimientos analíticos y numéricos adaptados a sus particularidades. Con el propósito de desarrollar los conceptos básicos y la teoría del enfoque propuesto, esta tesis se centra en el estudio de las cadenas cinemáticas planas más fundamentales, a saber, estructuras de Baranov, cadenas cinemáticas de Assur, y cadenas cinemáticas de Grübler. Los resultados obtenidos han demostrado que las técnicas desarrolladas son herramientas prometedoras para el análisis de posición de cadenas cinemáticas y problemas relacionados. Por ejemplo, usando dichas técnicas, los polinomios característicos de la mayoría de las estructuras de Baranov catalogadas se puede obtener sin realizar eliminaciones de variables o sustituciones trigonométricas, y utilizando solo álgebra elemental. Un resultado en claro contraste con las complejas eliminaciones de variables que se requieren cuando se utilizan ecuaciones de bucle independientes. El impacto del resultado anterior es mayor porque se demuestra que el polinomio característico de una estructura de Baranov, derivado con las técnicas propuestas, contiene toda la información necesaria y suficiente para resolver el análisis de posición de las cadenas cinemáticas de Assur que resultan de la sustitución de algunas de sus articulaciones de revolución por articulaciones prismáticas. De esta forma, se concluye que los polinomios de todos los robots planares totalmente paralelos se pueden derivar directamente del polinomio característico del conocido robot 3-RPR. Adicionalmente, se presenta un procedimiento eficaz, basado en restricciones de distancias y áreas orientadas, y argumentos geométricos, para trazar curvas de acoplador de cadenas cinemáticas de Grübler. En conjunto, todas estas técnicas y resultados constituyen contribuciones a la cinemática teórica de mecanismos, la cinemática de robots, y la geometría plana de distancias. Barcelona 13

The effect of temperature upon the growth and metabolism of aeromonas hydrophila and lactobacillus plantarum in pure and mixed culture

The effects of temperature upon the growth and metabolism of pure and mixed populations of Aeromonas hydrophila and Lactobacillus p/an/Qrum were studied. Initially a medium was developed to provide unbiased support for both organisms. The effect of temperature upon lag phase, growth rate, and final population level between pure and mixed culture was investigated. Temperature effects were only found to be significant when comparing the final population levels of Lb. p/anlDrum between pure and mixed culture. The lactobacilli exhibited a bomofermentative to heterofermentative switch between pure and mixed culture. This was probably due to substrate competition from the aeromonad population in mixed culture The metabolism of Aer. hydrophi!a has not been well described in the literature, compared to that of the lactobacilli. Due to the simplicity of the growth medium it was possible to determine the substrates relatively easily, although quantification required amino acid analysis. It was found that the organism utilized amino acids as primary substrates, switching to available carbohydrate as the population moved from growth to stationary phase. The principal product was found to be urea. During the stationary phase of population development it was interesting to note that the pH of the medium increased to well above the starting point of around S.S. This was principally due to de-amination of the urea product. Growth temperature above recognized optimum (28°C) was found to affect the metabolic profile of this organism, leading to low final pH levels. 4 The pattern of temperature effect upon the metabolism of Lb. plantarum as expressed by growth yields showed a similar pattern to the final population levels. The ratio of lactate formed : dextrose utilized was reversed at the 100e point. Growth of Lb. plantarum was not detected at the soe point. A new third order polynomial model was developed to describe the tag phase of bacterial cultures across a temperature range. The new model was compared with two others from the literature. The new model was chosen based upon statistical results. The pattern exhibited by final population levels at the different temperatures showed • similar point of inflection to that expressed by the polynomiallag phase model. The growth rate was modeled with the Schoolfield model which was proven to be the closest estimate of the three models tested. The theory ofhomeoviscous adaptation was used to explain the behavior patterns observed

The Bernstein basis in set-theoretic geometric modelling

SIGLEAvailable from British Library Document Supply Centre-DSC:DXN037062 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Polynomial continuation in the design of deployable structures

Polynomial continuation, a branch of numerical continuation, has been applied to several primary problems in kinematic geometry. The objective of the research presented in this document was to explore the possible extensions of the application of polynomial continuation, especially in the field of deployable structure design. The power of polynomial continuation as a design tool lies in its ability to find all solutions of a system of polynomial equations (even positive dimensional solution sets). A linkage design problem posed in polynomial form can be made to yield every possible feasible outcome, many of which may never otherwise have been found. Methods of polynomial continuation based design are illustrated here by way of various examples. In particular, the types of deployable structures which form planar rings, or frames, in their deployed configurations are used as design cases. Polynomial continuation is shown to be a powerful component of an equation-based design process. A polyhedral homotopy method, particularly suited to solving problems in kinematics, was synthesised from several researchers’ published continuation techniques, and augmented with modern, freely available mathematical computing algorithms. Special adaptations were made in the areas of level-k subface identification, lifting value balancing, and path-following. Techniques of forming closure/compatibility equations by direct use of symmetry, or by use of transfer matrices to enforce loop closure, were developed as appropriate for each example. The geometry of a plane symmetric (rectangular) 6R foldable frame was examined and classified in terms of Denavit-Hartenberg Parameters. Its design parameters were then grouped into feasible and non-feasible regions, before continuation was used as a design tool; generating the design parameters required to build a foldable frame which meets certain configurational specifications. iv Two further deployable ring/frame classes were then used as design cases: (a) rings which form (planar) regular polygons when deployed, and (b) rings which are doubly plane symmetric and planar when deployed. The governing equations used in the continuation design process are based on symmetry compatibility and transfer matrices respectively. Finally, the 6, 7 and 8-link versions of N-loops were subjected to a witness set analysis, illustrating the way in which continuation can reveal the nature of the mobility of an unknown linkage. Key features of the results are that polynomial continuation was able to provide complete sets of feasible options to a number of practical design problems, and also to reveal the nature of the mobility of a real overconstrained linkage

Elasto-multi-body dynamics of internal combustion engines with thin-shell elastohydrodynamic journal bearings

This thesis describes problems associated with noise and vibration concern in internal combustion engines as the result of a growing trend in the development of modern vehicular engines with high power to light weight ratios. There are a plethora of vibration concerns. These are owed to the increasing combustion forces in lean burn engines and the progressive use of materials of durable, but light-weight construction. The latter has come about as a result of a need to reduce the inertial imbalances. These features have resulted in achieving fuel efficiency. Although the primary aims in high output power and structural integrity have been largely achieved, these have culminated in an assortment of sources of noise and vibration, chiefly among them those associated with signature output of the combustion process. For the common four stroke engines, the contributory sources are at half-engine order multiples, referred to as engine "roughness". A holistic approach is to incorporate reduced engine roughness contributions as an integral part of engine design and development. The aim of this thesis is to create a methodology for fundamental design evaluation and analysis of engine dynamics, which comprises rigid body inertial dynamics of engine assembly, the elasto-dynamics of flexible and compliant components and applied and reactive forces in such a complex assembly. [Continues.