Relativistic Elastic Differential Cross Sections for Equal Mass Nuclei

The effects of relativistic kinematics are studied for nuclear collisions of equal mass nuclei. It is found that the relativistic and non-relativistic elastic scattering amplitudes are nearly indistinguishable, and, hence, the relativistic and non-relativistic differential cross sections become indistinguishable. These results are explained by analyzing the Lippmann-Schwinger equation with the first order optical potential that was employed in the calculatio

Weak energy condition violation and superluminal travel

Recent solutions to the Einstein Field Equations involving negative energy densities, i.e., matter violating the weak-energy-condition, have been obtained, namely traversable wormholes, the Alcubierre warp drive and the Krasnikov tube. These solutions are related to superluminal travel, although locally the speed of light is not surpassed. It is difficult to define faster-than-light travel in generic space-times, and one can construct metrics which apparently allow superluminal travel, but are in fact flat Minkowski space-times. Therefore, to avoid these difficulties it is important to provide an appropriate definition of superluminal travel.Comment: 15 pages, 3 figures, LaTeX2e, Springer style files -included. Contribution to the Proceedings of the Spanish Relativity Meeting-2001 (Madrid, September 2001

Parameter scaling in the decoherent quantum-classical transition for chaotic systems

The quantum to classical transition has been shown to depend on a number of parameters. Key among these are a scale length for the action, $\hbar$, a measure of the coupling between a system and its environment, $D$, and, for chaotic systems, the classical Lyapunov exponent, $\lambda$. We propose computing a measure, reflecting the proximity of quantum and classical evolutions, as a multivariate function of $(\hbar,\lambda,D)$ and searching for transformations that collapse this hyper-surface into a function of a composite parameter $\zeta = \hbar^{\alpha}\lambda^{\beta}D^{\gamma}$. We report results for the quantum Cat Map, showing extremely accurate scaling behavior over a wide range of parameters and suggest that, in general, the technique may be effective in constructing universality classes in this transition.Comment: Submitte

Robust designs for Poisson regression models

We consider the problem of how to construct robust designs for Poisson regression models. An analytical expression is derived for robust designs for first-order Poisson regression models where uncertainty exists in the prior parameter estimates. Given certain constraints in the methodology, it may be necessary to extend the robust designs for implementation in practical experiments. With these extensions, our methodology constructs designs which perform similarly, in terms of estimation, to current techniques, and offers the solution in a more timely manner. We further apply this analytic result to cases where uncertainty exists in the linear predictor. The application of this methodology to practical design problems such as screening experiments is explored. Given the minimal prior knowledge that is usually available when conducting such experiments, it is recommended to derive designs robust across a variety of systems. However, incorporating such uncertainty into the design process can be a computationally intense exercise. Hence, our analytic approach is explored as an alternative

Quantum Inequalities and Singular Energy Densities

There has been much recent work on quantum inequalities to constrain negative energy. These are uncertainty principle-type restrictions on the magnitude and duration of negative energy densities or fluxes. We consider several examples of apparent failures of the quantum inequalities, which involve passage of an observer through regions where the negative energy density becomes singular. We argue that this type of situation requires one to formulate quantum inequalities using sampling functions with compact support. We discuss such inequalities, and argue that they remain valid even in the presence of singular energy densities.Comment: 18 pages, LaTex, 2 figures, uses eps

Exponential Divergence and Long Time Relaxation in Chaotic Quantum Dynamics

Phase space representations of the dynamics of the quantal and classical cat map are used to explore quantum--classical correspondence in a K-system: as $\hbar \to 0$, the classical chaotic behavior is shown to emerge smoothly and exactly. The quantum dynamics near the classical limit displays both exponential separation of adjacent distributions and long time relaxation, two characteristic features of classical chaotic motion.Comment: 10 pages, ReVTeX, to appear in Phys. Rev. Lett. 13 figures NOT included. Available either as LARGE (uuencoded gzipped) postscript files or hard-copies from [email protected]

Optical and X-ray Observations of the Afterglow to XRF030723

The X-ray-flash XRF030723 was detected by the HETE satellite and rapidly disseminated, allowing for an optical transient to be detected ~1 day after the burst. We discuss observations in the optical with Magellan, which confirmed the fade of the optical transient. In a 2-epoch ToO observation with Chandra, we discovered a fading X-ray source spatially coincident with the optical transient. We present spectral fits to the X-ray data. We also discuss the possibility that the source underwent a rebrightening in the X-rays, as was observed in the optical. We find that the significance of a possible rebrightening is very low (~1 sigma).Comment: 4 pages, 2 figures, to appear in Santa Fe GRB Conference Proceedings, 200

The Importance of Human Motion for Simulation Testing of GNSS

Human motion is generally considered benign to the performance of global navigation satellite system (GNSS) and other positioning sensors. This study proves that this is not the case, even for typical human behaviour involving GNSS user equipment, e.g. in smartphones. Using recorded human motion, it is shown that phase-lock loops (PLLs) in GNSS receivers are sensitive to jerk dynamics induced by user motion, resulting in carrier cycle slips. To test the effects of human dynamics on GNSS carrier tracking, real human motion profiles were captured. These profiles comprised typical types of movements using a mobile phone, e.g. holding, answering and texting, different types of activities, e.g. walking or jogging, as well as different phone locations on the human body, e.g. in a hand, pocket, backpack and on an arm band. The data were captured outdoors using an Xsens MTi-G MEMS (Micro-Electronic Mechanical Systems) Inertial Measurement Unit (IMU) aided by a Global Positioning System (GPS) receiver with a 100Hz output rate. Then the captured motion (MoCap) was processed and input into a simulated PLL in Matlab with different tracking loop bandwidths (BL_CA) and carrier power-to-noise density ratios (C/N0). The results show that pedestrian gestures and type of activity, e.g. walking or jogging, affect the performance of the simulated PLL more adversely than the location of the phone on the human body. Also, to track pedestrian motion encompassing these gestures, activities and receiver locations, a minimum of 15Hz tracking bandwidth is required. Consequently, receiver manufacturers should exercise caution before reducing tracking bandwidths to compensate for the reduction in C/N0 resulting from GNSS antenna design, human body masking and the effects of buildings, trees and other environmental features. This paper also proposes and describes a pedestrian motion model (PMM) that simulates the GNSS antenna trajectory in 3D, when it is held by or attached to a pedestrian. The PMM will be validated using real MoCap scenarios and will enable Spirent to increase their product offering in the area of simulation-based testing of positioning sensors for pedestrian applications by generating human motion profiles which affect realistically the performance of GNSS user equipment