Local symmetries in gauge theories in a finite-dimensional setting

It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group bundles and, more generally, of Lie groupoids and their actions on fiber bundles. This applies not only to local symmetries, which lie at the heart of gauge theories, but is already true even for global symmetries when one allows for fields that are sections of bundles with (possibly) non-trivial topology or, even when these are topologically trivial, in the absence of a preferred trivialization. (C) 2012 Elsevier B.V. All rights reserved.

Ultrastructural features of the myotendinous junction of the sternomastoid muscle in Wistar rats: from newborn to aging

The myotendinous junction (MTJ) is a major area for transmitting force from the skeletal muscle system and acts in joint position and stabilization. This study aimed to use transmission electron microscopy to describe the ultrastructural features of the MTJ of the sternomastoid muscle in Wistar rats from newborn to formation during adulthood and possible changes with aging. Ultrastructural features of the MTJ from the newborn group revealed pattern during development with interactions between muscle cells and extracellular matrix elements with thin folds in the sarcolemma and high cellular activity evidenced through numerous oval mitochondria groupings. The adult group had classical morphological features of the MTJ, with folds in the sarcolemma forming long projections called finger-like processes and sarcoplasmic invaginations. Sarcomeres were aligned in series, showing mitochondria near the Z line in groupings between collagen fiber bundles. The old group had altered finger-like processes, thickened in both levels of sarcoplasmic invaginations and in central connections with the lateral junctions. We conclude that the MTJ undergoes intense activity from newborn to its formation during adulthood. With increasing age, changes to the MTJ were observed in the shapes of the invaginations and finger-like processes due to hypoactivity, potentially compromising force transmission and joint stability. Microsc. Res. Tech. 75:12921296, 2012. (C) 2012 Wiley Periodicals, Inc.

Design of laminated piezocomposite shell transducers with arbitrary fiber orientation using topology optimization approach

Sensor and actuator based on laminated piezocomposite shells have shown increasing demand in the field of smart structures. The distribution of piezoelectric material within material layers affects the performance of these structures; therefore, its amount, shape, size, placement, and polarization should be simultaneously considered in an optimization problem. In addition, previous works suggest the concept of laminated piezocomposite structure that includes fiber-reinforced composite layer can increase the performance of these piezoelectric transducers; however, the design optimization of these devices has not been fully explored yet. Thus, this work aims the development of a methodology using topology optimization techniques for static design of laminated piezocomposite shell structures by considering the optimization of piezoelectric material and polarization distributions together with the optimization of the fiber angle of the composite orthotropic layers, which is free to assume different values along the same composite layer. The finite element model is based on the laminated piezoelectric shell theory, using the degenerate three-dimensional solid approach and first-order shell theory kinematics that accounts for the transverse shear deformation and rotary inertia effects. The topology optimization formulation is implemented by combining the piezoelectric material with penalization and polarization model and the discrete material optimization, where the design variables describe the amount of piezoelectric material and polarization sign at each finite element, with the fiber angles, respectively. Three different objective functions are formulated for the design of actuators, sensors, and energy harvesters. Results of laminated piezocomposite shell transducers are presented to illustrate the method. Copyright (C) 2012 John Wiley & Sons, Ltd.