Bubble Nucleation of Spatial Vector Fields

We study domain-walls and bubble nucleation in a non-relativistic vector field theory with different longitudinal and transverse speeds of sound. We describe analytical and numerical methods to calculate the orientation dependent domain-wall tension, $\sigma(\theta)$. We then use this tension to calculate the critical bubble shape. The longitudinally oriented domain-wall tends to be the heaviest, and sometime suffers an instability. It can spontaneously break into zigzag segments. In this case, the critical bubble develops kinks, and its energy, and therefore the tunneling rate, scales with the sound speeds very differently than what would be expected for a smooth bubble.Comment: version 4, correction in the citation

Autonomous attitude using potential function method under control input saturation

The potential function method has been used extensively in nonlinear control for the development of feedback laws which result in global asymptotic stability for a certain prescribed operating point of the closed-loop system. It is a variation of the Lyapunov direct method in the sense that here the Lyapunov function, also called potential function, is constructed in such a way that the undesired points of the system state space are avoided. The method has been considered for the space applications where the systems involved are usually composed of the cascaded subsystems of kinematics and dynamics and the kinematic states are mapped onto an appropriate potential function which is augmented for the overall system by the use of the method of integrator backstepping. The conventional backstepping controls, however, may result in an excessive control effort that may be beyond the saturation bound of the actuators. The present paper, while remaining within the framework of conventional backstepping control design, proposes analytical formulation for the control torque bound being a function of the tracking error and the control gains. The said formulation can be used to tune to the control gains to bound the control torque to a prescribed saturation bound of the control actuators

Space processing of chalcogenide glass

The manner in which the weightless, containerless nature of in-space processing can be successfully utilized to improve the quality of infrared transmitting chalcogenide glasses is determined. The technique of space processing chalcogenide glass was developed, and the process and equipment necessary to do so was defined. Earthbound processing experiments with As2S3 and G28Sb12Se60 glasses were experimented with. Incorporated into these experiments is the use of an acoustic levitation device

Geometric Phase, Bundle Classification, and Group Representation

The line bundles which arise in the holonomy interpretations of the geometric phase display curious similarities to those encountered in the statement of the Borel-Weil-Bott theorem of the representation theory. The remarkable relation of the geometric phase to the classification of complex line bundles provides the necessary tools for establishing the relevance of the Borel-Weil-Bott theorem to Berry's adiabatic phase. This enables one to define a set of topological charges for arbitrary compact connected semisimple dynamical Lie groups. In this paper, the problem of the determination of the parameter space of the Hamiltonian is also addressed. A simple topological argument is presented to indicate the relation between the Riemannian structure on the parameter space and Berry's connection. The results about the fibre bundles and group theory are used to introduce a procedure to reduce the problem of the non-adiabatic (geometric) phase to Berry's adiabatic phase for cranked Hamiltonians. Finally, the possible relevance of the topological charges of the geometric phase to those of the non-abelian monopoles is pointed out.Comment: 30 pages (LaTeX); UT-CR-12-9