Understanding the Hamiltonian Function through the Geometry of Partial Legendre Transforms

The relationship between the Hamiltonian and Lagrangean functions in analytical mechanics is a type of duality. The two functions, while distinct, are both descriptive functions encoding the behavior of the same dynamical system. One difference is that the Lagrangean naturally appears as one investigates the fundamental equation of classical dynamics. It is not that way for the Hamiltonian. The Hamiltonian comes after Lagrange's equations have been fully formed, most commonly through a Legendre transform of the Lagrangean function. We revisit the Legendre transform approach and offer a more refined geometrical interpretation than what is commonly shown

Pattern Recognition for a Flight Dynamics Monte Carlo Simulation

The design, analysis, and verification and validation of a spacecraft relies heavily on Monte Carlo simulations. Modern computational techniques are able to generate large amounts of Monte Carlo data but flight dynamics engineers lack the time and resources to analyze it all. The growing amounts of data combined with the diminished available time of engineers motivates the need to automate the analysis process. Pattern recognition algorithms are an innovative way of analyzing flight dynamics data efficiently. They can search large data sets for specific patterns and highlight critical variables so analysts can focus their analysis efforts. This work combines a few tractable pattern recognition algorithms with basic flight dynamics concepts to build a practical analysis tool for Monte Carlo simulations. Current results show that this tool can quickly and automatically identify individual design parameters, and most importantly, specific combinations of parameters that should be avoided in order to prevent specific system failures. The current version uses a kernel density estimation algorithm and a sequential feature selection algorithm combined with a k-nearest neighbor classifier to find and rank important design parameters. This provides an increased level of confidence in the analysis and saves a significant amount of time

Tool for Rapid Analysis of Monte Carlo Simulations

Designing a spacecraft, or any other complex engineering system, requires extensive simulation and analysis work. Oftentimes, the large amounts of simulation data generated are very difficult and time consuming to analyze, with the added risk of overlooking potentially critical problems in the design. The authors have developed a generic data analysis tool that can quickly sort through large data sets and point an analyst to the areas in the data set that cause specific types of failures. The first version of this tool was a serial code and the current version is a parallel code, which has greatly increased the analysis capabilities. This paper describes the new implementation of this analysis tool on a graphical processing unit, and presents analysis results for NASA's Orion Monte Carlo data to demonstrate its capabilities

Tool for Rapid Analysis of Monte Carlo Simulations

Designing a spacecraft, or any other complex engineering system, requires extensive simulation and analysis work. Oftentimes, the large amounts of simulation data generated are very di cult and time consuming to analyze, with the added risk of overlooking potentially critical problems in the design. The authors have developed a generic data analysis tool that can quickly sort through large data sets and point an analyst to the areas in the data set that cause specific types of failures. The Tool for Rapid Analysis of Monte Carlo simulations (TRAM) has been used in recent design and analysis work for the Orion vehicle, greatly decreasing the time it takes to evaluate performance requirements. A previous version of this tool was developed to automatically identify driving design variables in Monte Carlo data sets. This paper describes a new, parallel version, of TRAM implemented on a graphical processing unit, and presents analysis results for NASA's Orion Monte Carlo data to demonstrate its capabilities

Tachyon fields with effects of quantum matter in an Anti-de Sitter Universe

We consider an Anti-de Sitter universe filled by quantum conformal matter with the contribution from the usual tachyon and a perfect fluid. The model represents the combination of a trace-anomaly annihilated and a tachyon driven Anti-de Sitter universe. The influence exerted by the quantum effects and by the tachyon on the AdS space is studied. The radius corresponding to this universe is calculated and the effect of the tachyon potential is discussed, in particular, concerning to the possibility to get an accelerated scale factor for the proposed model (implying an accelerated expansion of the AdS type of universe). Fulfillment of the cosmological energy conditions in the model is also investigatedComment: 14 Latex pages, no figure

Surveillance for Invasive Meningococcal Disease in Children, US–Mexico Border, 2005–20081

We reviewed confirmed cases of pediatric invasive meningococcal disease in Tijuana, Mexico, and San Diego County, California, USA, during 2005–2008. The overall incidence and fatality rate observed in Tijuana were similar to those found in the US, and serogroup distribution suggests that most cases in Tijuana are vaccine preventable

Automated nanoscale absolute accuracy alignment system for transfer printing

The heterogeneous integration of micro- and nanoscale devices with on-chip circuits and waveguide platforms is a key enabling technology, with wide-ranging applications in areas including telecommunications, quantum information processing, and sensing. Pick and place integration with absolute positional accuracy at the nanoscale has been previously demonstrated for single proof-of-principle devices. However, to enable scaling of this technology for realization of multielement systems or high throughput manufacturing, the integration process must be compatible with automation while retaining nanoscale accuracy. In this work, an automated transfer printing process is realized by using a simple optical microscope, computer vision, and high accuracy translational stage system. Automatic alignment using a cross-correlation image processing method demonstrates absolute positional accuracy of transfer with an average offset of <40 nm (3σ < 390 nm) for serial device integration of both thin film silicon membranes and single nanowire devices. Parallel transfer of devices across a 2 × 2 mm 2 area is demonstrated with an average offset of <30 nm (3σ < 705 nm). Rotational accuracy better than 45 mrad is achieved for all device variants. Devices can be selected and placed with high accuracy on a target substrate, both from lithographically defined positions on their native substrate or from a randomly distributed population. These demonstrations pave the way for future scalable manufacturing of heterogeneously integrated chip systems

Algorithms and analysis for underwater vehicle plume tracing.

The goal of this research was to develop and demonstrate cooperative 3-D plume tracing algorithms for miniature autonomous underwater vehicles. Applications for this technology include Lost Asset and Survivor Location Systems (L-SALS) and Ship-in-Port Patrol and Protection (SP3). This research was a joint effort that included Nekton Research, LLC, Sandia National Laboratories, and Texas A&amp;M University. Nekton Research developed the miniature autonomous underwater vehicles while Sandia and Texas A&amp;M developed the 3-D plume tracing algorithms. This report describes the plume tracing algorithm and presents test results from successful underwater testing with pseudo-plume sources