Singularity-free space-time

We show that the solution published in the paper by Senovilla [Phys. Rev. Lett. 64, 2219 (1990)] is geodesically complete and singularity-free. We also prove that the solution satisfies the stronger energy and causality conditions, such as global hyperbolicity, the strong energy condition, causal symmetry, and causal stability. A detailed discussion about which assumptions in the singularity theorems are not satisfied is performed, and we show explicitly that the solution is in accordance with those theorems. A brief discussion of the results is given.

Singularity-Free Fully-Isotropic Translational Parallel Manipulators

Parallel mechanisms show desirable characteristics such as a large payload to robot weight ratio, considerable stiffness, low inertia and high dynamic performances. In particular, parallel manipulators with fewer than six degrees of freedom have recently attracted researchers’ attention, as their employ may prove valuable in those applications in which a higher mobility is uncalled-for. The attention of this dissertation is focused on translational parallel manipulators (TPMs), that is on parallel manipulators whose output link (platform) is provided with a pure translational motion with respect to the frame. The first part deals with the general problem of the topological synthesis and classification of TPMs, that is it identifies the architectures that TPM legs must possess for the platform to be able to freely translate in space without altering its orientation. The second part studies both constraint and direct singularities of TPMs. In particular, special families of fully-isotropic mechanisms are identified. Such manipulators exhibit outstanding properties, as they are free from singularities and show a constant orthogonal Jacobian matrix throughout their workspace. As a consequence, both the direct and the inverse position problems are linear and the kinematic analysis proves straightforward.

Frustration and anomalous behavior in the Bell-Lavis model of liquid water

We have reconsidered the Bell-Lavis model of liquid water and investigated its relation to its isotropic version, the antiferromagnetic Blume-Emery-Griffiths model on the triangular lattice. Our study was carried out by means of an exact solution on the sequential Husimi cactus. We show that the ground states of both models share the same topology and that fluid phases (gas and low- and high-density liquids) can be mapped onto magnetic phases (paramagnetic, antiferromagnetic, and dense paramagnetic, respectively). Both models present liquid-liquid coexistence and several thermodynamic anomalies. This result suggests that anisotropy introduced through orientational variables play no specific role in producing the density anomaly, in agreement with a similar conclusion discussed previously following results for continuous soft core,models. We propose that the presence of liquid anomalies may be related to energetic frustration, a feature common to both models.

Topological analysis of singularity loci for serial and parallel manipulators

Singularities of robot manipulators have been intensely studied in the last decades by researchers of many fields. Serial singularities produce some local loss of dexterity of the manipulator, therefore it might be desirable to search for singularityfree trajectories in the jointspace. On the other hand, parallel singularities are very dangerous for parallel manipulators, for they may provoke the local loss of platform control, and jeopardize the structural integrity of links or actuators. It is therefore utterly important to avoid parallel singularities, while operating a parallel machine. Furthermore, there might be some configurations of a parallel manipulators that are allowed by the constraints, but nevertheless are unreachable by any feasible path. The present work proposes a numerical procedure based upon Morse theory, an important branch of differential topology. Such procedure counts and identify the singularity-free regions that are cut by the singularity locus out of the configuration space, and the disjoint regions composing the configuration space of a parallel manipulator. Moreover, given any two configurations of a manipulator, a feasible or a singularity-free path connecting them can always be found, or it can be proved that none exists. Examples of applications to 3R and 6R serial manipulators, to 3UPS and 3UPU parallel wrists, to 3UPU parallel translational manipulators, and to 3RRR planar manipulators are reported in the work.

General clas of inhomogeneous perfect-fluid solutions

We present a general class of solutions to Einstein's field equations with two spacelike commuting Killing vectors by assuming the separation of variables of the metric components. The solutions can be interpreted as inhomogeneous cosmological models. We show that the singularity structure of the solutions varies depending on the different particular choices of the parameters and metric functions. There exist solutions with a universal big-bang singularity, solutions with timelike singularities in the Weyl tensor only, solutions with singularities in both the Ricci and the Weyl tensors, and also singularity-free solutions. We prove that the singularity-free solutions have a well-defined cylindrical symmetry and that they are generalizations of other singularity-free solutions obtained recently.

Structural motifs of biomolecules.

Biomolecular structures are assemblies of emergent anisotropic building modules such as uniaxial helices or biaxial strands. We provide an approach to understanding a marginally compact phase of matter that is occupied by proteins and DNA. This phase, which is in some respects analogous to the liquid crystal phase for chain molecules, stabilizes a range of shapes that can be obtained by sequence-independent interactions occurring intra- and intermolecularly between polymeric molecules. We present a singularity-free self-interaction for a tube in the continuum limit and show that this results in the tube being positioned in the marginally compact phase. Our work provides a unified framework for understanding the building blocks of biomolecules.

Flexible multibody dynamics and intelligent control of a hydraulically driven hybrid redundant robot machine

The assembly and maintenance of the International Thermonuclear Experimental Reactor (ITER) vacuum vessel (VV) is highly challenging since the tasks performed by the robot involve welding, material handling, and machine cutting from inside the VV. The VV is made of stainless steel, which has poor machinability and tends to work harden very rapidly, and all the machining operations need to be carried out from inside of the ITER VV. A general industrial robot cannot be used due to its poor stiffness in the heavy duty machining process, and this will cause many problems, such as poor surface quality, tool damage, low accuracy. Therefore, one of the most suitable options should be a light weight mobile robot which is able to move around inside of the VV and perform different machining tasks by replacing different cutting tools. Reducing the mass of the robot manipulators offers many advantages: reduced material costs, reduced power consumption, the possibility of using smaller actuators, and a higher payload-to-robot weight ratio. Offsetting these advantages, the lighter weight robot is more flexible, which makes it more difficult to control. To achieve good machining surface quality, the tracking of the end effector must be accurate, and an accurate model for a more flexible robot must be constructed. This thesis studies the dynamics and control of a 10 degree-of-freedom (DOF) redundant hybrid robot (4-DOF serial mechanism and 6-DOF 6-UPS hexapod parallel mechanisms) hydraulically driven with flexible rods under the influence of machining forces. Firstly, the flexibility of the bodies is described using the floating frame of reference method (FFRF). A finite element model (FEM) provided the Craig-Bampton (CB) modes needed for the FFRF. A dynamic model of the system of six closed loop mechanisms was assembled using the constrained Lagrange equations and the Lagrange multiplier method. Subsequently, the reaction forces between the parallel and serial parts were used to study the dynamics of the serial robot. A PID control based on position predictions was implemented independently to control the hydraulic cylinders of the robot. Secondly, in machining, to achieve greater end effector trajectory tracking accuracy for surface quality, a robust control of the actuators for the flexible link has to be deduced. This thesis investigates the intelligent control of a hydraulically driven parallel robot part based on the dynamic model and two schemes of intelligent control for a hydraulically driven parallel mechanism based on the dynamic model: (1) a fuzzy-PID self-tuning controller composed of the conventional PID control and with fuzzy logic, and (2) adaptive neuro-fuzzy inference system-PID (ANFIS-PID) self-tuning of the gains of the PID controller, which are implemented independently to control each hydraulic cylinder of the parallel mechanism based on rod length predictions. The serial component of the hybrid robot can be analyzed using the equilibrium of reaction forces at the universal joint connections of the hexa-element. To achieve precise positional control of the end effector for maximum precision machining, the hydraulic cylinder should be controlled to hold the hexa-element. Thirdly, a finite element approach of multibody systems using the Special Euclidean group SE(3) framework is presented for a parallel mechanism with flexible piston rods under the influence of machining forces. The flexibility of the bodies is described using the nonlinear interpolation method with an exponential map. The equations of motion take the form of a differential algebraic equation on a Lie group, which is solved using a Lie group time integration scheme. The method relies on the local description of motions, so that it provides a singularity-free formulation, and no parameterization of the nodal variables needs to be introduced. The flexible slider constraint is formulated using a Lie group and used for modeling a flexible rod sliding inside a cylinder. The dynamic model of the system of six closed loop mechanisms was assembled using Hamilton’s principle and the Lagrange multiplier method. A linearized hydraulic control system based on rod length predictions was implemented independently to control the hydraulic cylinders. Consequently, the results of the simulations demonstrating the behavior of the robot machine are presented for each case study. In conclusion, this thesis studies the dynamic analysis of a special hybrid (serialparallel) robot for the above-mentioned special task involving the ITER and investigates different control algorithms that can significantly improve machining performance. These analyses and results provide valuable insight into the design and control of the parallel robot with flexible rods.

Tempêtes. Composition audiovisuelle.

La version intégrale de cette thèse est disponible uniquement pour consultation individuelle à la Bibliothèque de musique de l’Université de Montréal (www.bib.umontreal.ca/MU ).

Colombia y el transpacific partnership agreement

Colombia, a partir de 1990, inicia un plan de gobierno enfocado en la apertura económica, con estrategias que propugnaban por un cambio en el modelo económico a través de políticas como la reducción de aranceles a las importaciones y otra serie de medidas proteccionistas, flexibilización laboral, la reducción del papel del Estado para darle protagonismo al sector privado y procesos de privatización de empresas públicas En este entorno internacional se ha adquirido conciencia de que, en un mundo globalizado y cada vez más interdependiente, no puede haber espacio para “aventuras solitarias de Estados soberanos”, lo que justifica la proliferación de organizaciones multilaterales en América Latina y el Caribe en la última década. Recientemente Colombia ha mostrado su interés en entrar a formar parte de un bloque económico de gran relevancia a nivel internacional: el "Transpacific Partnership Agreement" (TPP); tratado integrado por: Canadá, Estados Unidos, México, Perú, Chile, Japón, Vietnam, Malasia, Singapur, Brunei, Australia y Nueva Zelanda, representando el 35% del PIB mundial y el 11% de la población. El presente trabajo pretende presentar una visión objetiva del TPP, generando el espacio para la libre interpretación de sus beneficios o perjuicios. Para ello, se analiza el estado actual del TPP con sus principales indicadores, su desempeño en los últimos años y las relaciones diplomáticas y los flujos comerciales entre Colombia y los países miembros del mismo.

The gambin model provides a superior fit to species abundance distributions with a single free parameter : evidence, implementation and interpretation

The species abundance distribution (SAD) has been a central focus of community ecology for over fifty years, and is currently the subject of widespread renewed interest. The gambin model has recently been proposed as a model that provides a superior fit to commonly preferred SAD models. It has also been argued that the model's single parameter (α) presents a potentially informative ecological diversity metric, because it summarises the shape of the SAD in a single number. Despite this potential, few empirical tests of the model have been undertaken, perhaps because the necessary methods and software for fitting the model have not existed. Here, we derive a maximum likelihood method to fit the model, and use it to undertake a comprehensive comparative analysis of the fit of the gambin model. The functions and computational code to fit the model are incorporated in a newly developed free-to-download R package (gambin). We test the gambin model using a variety of datasets and compare the fit of the gambin model to fits obtained using the Poisson lognormal, logseries and zero-sum multinomial distributions. We found that gambin almost universally provided a better fit to the data and that the fit was consistent for a variety of sample grain sizes. We demonstrate how α can be used to differentiate intelligibly between community structures of Azorean arthropods sampled in different land use types. We conclude that gambin presents a flexible model capable of fitting a wide variety of observed SAD data, while providing a useful index of SAD form in its single fitted parameter. As such, gambin has wide potential applicability in the study of SADs, and ecology more generally.

Body composition interpretation. Contributions of the fat-free mass index and the body fat mass index.

OBJECTIVE: Low and high body mass index (BMI) values have been shown to increase health risks and mortality and result in variations in fat-free mass (FFM) and body fat mass (BF). Currently, there are no published ranges for a fat-free mass index (FFMI; kg/m(2)), a body fat mass index (BFMI; kg/m(2)), and percentage of body fat (%BF). The purpose of this population study was to determine predicted FFMI and BFMI values in subjects with low, normal, overweight, and obese BMI. METHODS: FFM and BF were determined in 2986 healthy white men and 2649 white women, age 15 to 98 y, by a previously validated 50-kHz bioelectrical impedance analysis equation. FFMI, BFMI, and %BF were calculated. RESULTS: FFMI values were 16.7 to 19.8 kg/m(2) for men and 14.6 to 16.8 kg/m(2) for women within the normal BMI ranges. BFMI values were 1.8 to 5.2 kg/m(2) for men and 3.9 to 8.2 kg/m(2) for women within the normal BMI ranges. BFMI values were 8.3 and 11.8 kg/m(2) in men and women, respectively, for obese BMI (>30 kg/m(2)). Normal ranges for %BF were 13.4 to 21.7 and 24.6 to 33.2 for men and women, respectively. CONCLUSION: BMI alone cannot provide information about the respective contribution of FFM or fat mass to body weight. This study presents FFMI and BFMI values that correspond to low, normal, overweight, and obese BMIs. FFMI and BFMI provide information about body compartments, regardless of height.

Physical interpretation of the spectral radiative signature in the transition zone between cloud-free and cloudy regions

One-second-resolution zenith radiance measure- ments from the Atmospheric Radiation Measurement pro- gram’s new shortwave spectrometer (SWS) provide a unique opportunity to analyze the transition zone between cloudy and cloud-free air, which has considerable bearing on the aerosol indirect effect. In the transition zone, we find a re- markable linear relationship between the sum and difference of radiances at 870 and 1640 nm wavelengths. The intercept of the relationship is determined primarily by aerosol prop- erties, and the slope by cloud properties. We then show that this linearity can be predicted from simple theoretical con- siderations and furthermore that it supports the hypothesis of inhomogeneous mixing, whereby optical depth increases as a cloud is approached but the effective drop size remains un- changed.

Free expanding cloud of cold atoms as an atomic standard: Ramsey fringes contrast

A compact frequency standard based on an expanding cold (133)CS cloud is under development in our laboratory. In a first experiment, Cs cold atoms were prepared by a magneto-optical trap in a vapor cell, and a microwave antenna was used to transmit the radiation for the clock transition. The signal obtained from fluorescence of the expanding cold atoms cloud is used to lock a microwave chain. In this way the overall system stability is evaluated. A theoretical model based on a two-level system interacting with the two microwave pulses enables interpretation for the observed features, especially the poor Ramsey fringes contrast. (C) 2008 Optical Society of America.

Isotropic singularities in shear-free perfect fluid cosmologies

We investigate barotropic perfect fluid cosmologies which admit an isotropic singularity. From the General Vorticity Result of Scott, it is known that these cosmologies must be irrotational. In this paper we prove, using two different methods, that if we make the additional assumption that the perfect fluid is shear-free, then the fluid flow must be geodesic. This then implies that the only shear-free, barotropic, perfect fluid cosmologies which admit an isotropic singularity are the FRW models.

Exploring through cover - the integrated interpretation of high resolution aeromagnetic, airborne electromagnetic and ground gravity data from the Grant's Patch area, Eastern Goldfields Province, Archaean Yigarn Craton Part B; Gravity inversion as a

The cost and risk associated with mineral exploration in Australia increases significantly as companies move into deeper regolith-covered terrain. The ability to map the bedrock and the depth of weathering within an area has the potential to decrease this risk and increase the effectiveness of exploration programs. This paper is the second in a trilogy concerning the Grant's Patch area of the Eastern Goldfields. The recent development of the VPmg potential field inversion program in conjunction with the acquisition of high-resolution gravity data over an area with extensive drilling provided an opportunity to evaluate three-dimensional gravity inversion as a bedrock and regolith mapping tool. An apparent density model of the study area was constructed, with the ground represented as adjoining 200 m by 200 m vertical rectangular prisms. During inversion VPmg incrementally adjusted the density of each prism until the free-air gravity response of the model replicated the observed data. For the Grant's Patch study area, this image of the apparent density values proved easier to interpret than the Bouguer gravity image. A regolith layer was introduced into the model and realistic fresh-rock densities assigned to each basement prism according to its interpreted lithology. With the basement and regolith densities fixed, the VPmg inversion algorithm adjusted the depth to fresh basement until the misfit between the calculated and observed gravity response was minimised. The resulting geometry of the bedrock/regolith contact largely replicated the base of weathering indicated by drilling with predicted depth of weathering values from gravity inversion typically within 15% of those logged during RAB and RC drilling.