Construction and Simulation of Composite Measures and Condensation Model for Designing Probabilistic Computational Applications

The probabilistic algorithms are widely applied in designing computational applications such as distributed systems and probabilistic databases, to determine distributed consensus in the presence of random failures of nodes or networks. In distributed computing, symmetry breaking is performed by employing probabilistic algorithms. In general, probabilistic symmetry breaking without any bias is preferred. Thus, the designing of randomized and probabilistic algorithms requires modeling of associated probability spaces to generate control-inputs. It is required that discrete measures in such spaces are computable and tractable in nature. This paper proposes the construction of composite discrete measures in real as well as complex metric spaces. The measures are constructed on different varieties of continuous smooth curves having distinctive non-linear profiles. The compositions of discrete measures consider arbitrary functions within metric spaces. The measures are constructed on 1-D interval and 2-D surfaces and, the corresponding probability metric product is defined. The associated sigma algebraic properties are formulated. The condensation measure of the uniform contraction map is constructed as axioms. The computational evaluations of the proposed composite set of measures are presented.

Estimation of Weld Induced Residual Stresses of Thick Welded Sections Using Numerical Welding Simulation

Welding processes are quite complex in nature as they involve the interaction of multiple physical phenomena. The thermal history developed during the process causes the material to undergo complex phase transformations. Non-uniform contraction and expansion of heat affected, softer, areas constrained by cooler, harder, areas of the material induce residual stresses and the weldment undergoes permanent deformation. When thick sections are welded, the formation of phases and the distribution of residual stresses are even more complex. These could lead to failure of the welded components during service. For the design of pressure vessel applications understanding the phase formation and residual stress distribution in thick weldments is critical. Numerical simulation was used to understand the influence of multiple variables on the residual stresses induced by a welding process The challenges involved in performing welding simulation of thick sections are described. Furthermore numerical and experimental results are compared and discussed.

CHARACTERIZING THE DEPOLARIZING QUANTUM CHANNEL IN TERMS OF RIEMANNIAN GEOMETRY

We explore the conceptual usefulness of Riemannian geometric tools induced by the statistical concept of distinguishability in quantifying the effect of a depolarizing channel on quantum states. Specifically, we compare the geometries of the interior of undeformed and deformed Bloch spheres related to density operators on a two-dimensional Hilbert space. We show that randomization emerges geometrically through a smaller infinitesimal quantum line element on the deformed Bloch sphere while the uniform contraction manifests itself via a deformed set of geodesics where the spacial components of the deformed four-Bloch vector are simply the contracted versions of the undeformed Bloch vector components.

Low-Level Thermodynamic, Kinematic, and Reflectivity Fields of Hurricane Guillermo (1997) during Rapid Intensification

From 0600 UTC 2 August to 1200 UTC 3 August Hurricane Guillermo (1997) deepened by 54 hPa over the eastern North Pacific Ocean, easily exceeding the thresholds that define rapid intensification (RI). The NOAA WP-3Ds observed a portion of this RI with similar two-aircraft missions on consecutive days. The aircraft jettisoned 70 successful global positioning system (GPS) dropwindsondes (or GPS sondes), which reveal how conditions in the lower troposphere on the octant to quadrant scale evolved within 250 km of the eye. Reflectivity fields demonstrate that the deepening is correlated with a spiraling in of the northern eyewall that reduces the eye diameter by 10 km. This behavior contrasts the more uniform contraction witnessed during eyewall replacement cycles. Mixing between the lower eye and eyewall, as detailed by other investigators, appears to have triggered the reduction in the eye diameter. After RI the eyewall remains asymmetrical with the tallest echo tops and heaviest rain rates located on the east or trailing side of the hurricane and to the left of the deep-layer shear vector. Net latent heat release within 60 km of the circulation center increases 21% from 2 to 3 August and is matched by a 30% increase in the inflow below 2 km at the 100-km radius. The GPS sondes, combined with aircraft in situ data for the eyewall region, reveal that the tropical cyclone (TC) establishes an annulus adjacent to and under the eyewall where the tangential wind component and equivalent potential temperature increase substantially. The radial extent of this annulus is constrained by the rainbands that remain robust throughout RI. The results support the argument that RI is controlled by processes within 100 km of the circulation center, and in particular within the eyewall.