Fundamental Radar Properties: Hidden Variables in Spacetime

A derivation of the properties of pulsed radiative imaging systems is presented with examples drawn from conventional, synthetic aperture, and interferometric radar. A geometric construction of the space and time components of a radar observation yields a simple underlying structural equivalence between many of the properties of radar, including resolution, range ambiguity, azimuth aliasing, signal strength, speckle, layover, Doppler shifts, obliquity and slant range resolution, finite antenna size, atmospheric delays, and beam and pulse limited configurations. The same simple structure is shown to account for many interferometric properties of radar - height resolution, image decorrelation, surface velocity detection, and surface deformation measurement. What emerges is a simple, unified description of the complex phenomena of radar observations. The formulation comes from fundamental physical concepts in relativistic field theory, of which the essential elements are presented. In the terminology of physics, radar properties are projections of hidden variables - curved worldlines from a broken symmetry in Minkowski spacetime - onto a time-serial receiver.Comment: 24 pages, 18 figures Accepted JOSA-

Semidirect Product Groups, Vacuum Alignment and Tribimaximal Neutrino Mixing

The neutrino oscillation data are in very good agreement with the tribimaximal mixing pattern: \sin^2\theta_{23}=1/2, \sin^2\theta_{12}=1/3, and \sin^2\theta_{13}=0. Attempts to generate this pattern based on finite family symmetry groups typically assume that the family symmetry is broken to different subgroups in the charged lepton and the neutrino mass matrices. This leads to a technical problem, where the cross-couplings between the Higgs fields responsible for the two symmetry breaking chains force their vacuum expectation values to align, upsetting the desired breaking pattern. Here, we present a class of models based on the semidirect product group (S_3)^4 \rtimes A_4, where the lepton families belong to representations which are not faithful. In effect, the Higgs sector knows about the full symmetry while the lepton sector knows only about the A_4 factor group. This can solve the alignment problem without altering the desired properties of the family symmetry. Inclusion of quarks into the framework is straightforward, and leads to small and arbitrary CKM mixing angles. Supersymmetry is not essential for our proposal, but the model presented is easily supersymmetrized, in which case the same family symmetry solves the SUSY flavor problem.Comment: Typos fixed, 26 pages in LaTe

Multiple Avalanches Across the Metal-Insulator Transition of Vanadium Oxide Nano-scaled Junctions

The metal insulator transition of nano-scaled $VO_2$ devices is drastically different from the smooth transport curves generally reported. The temperature driven transition occurs through a series of resistance jumps ranging over 2 decades in amplitude, indicating that the transition is caused by avalanches. We find a power law distribution of the jump amplitudes, demonstrating an inherent property of the $VO_2$ films. We report a surprising relation between jump amplitude and device size. A percolation model captures the general transport behavior, but cannot account for the statistical behavior.Comment: 4 papers and 4 figures submitted to PR

Method for detecting surface motions and mapping small terrestrial or planetary surface deformations with synthetic aperture radar

A technique based on synthetic aperture radar (SAR) interferometry is used to measure very small (1 cm or less) surface deformations with good resolution (10 m) over large areas (50 km). It can be used for accurate measurements of many geophysical phenomena, including swelling and buckling in fault zones, residual, vertical and lateral displacements from seismic events, and prevolcanic swelling. Two SAR images are made of a scene by two spaced antennas and a difference interferogram of the scene is made. After unwrapping phases of pixels of the difference interferogram, surface motion or deformation changes of the surface are observed. A second interferogram of the same scene is made from a different pair of images, at least one of which is made after some elapsed time. The second interferogram is then compared with the first interferogram to detect changes in line of sight position of pixels. By resolving line of sight observations into their vector components in other sets of interferograms along at least one other direction, lateral motions may be recovered in their entirety. Since in general, the SAR images are made from flight tracks that are separated, it is not possible to distinguish surface changes from the parallax caused by topography. However, a third image may be used to remove the topography and leave only the surface changes

The Makeenko-Migdal equation for Yang-Mills theory on compact surfaces

We prove the Makeenko-Migdal equation for two-dimensional Euclidean Yang-Mills theory on an arbitrary compact surface, possibly with boundary. In particular, we show that two of the proofs given by the first, third, and fourth authors for the plane case extend essentially without change to compact surfaces.Comment: Final version, minor typographical corrections. To appear in Comm. Math. Phy

Computational Methods for Parameter Estimation in Climate Models

Intensive computational methods have been used by Earth scientists in a wide range of problems in data inversion and uncertainty quantification such as earthquake epicenter location and climate projections. To quantify the uncertainties resulting from a range of plausible model configurations it is necessary to estimate a multidimensional probability distribution. The computational cost of estimating these distributions for geoscience applications is impractical using traditional methods such as Metropolis/Gibbs algorithms as simulation costs limit the number of experiments that can be obtained reasonably. Several alternate sampling strategies have been proposed that could improve on the sampling efficiency including Multiple Very Fast Simulated Annealing (MVFSA) and Adaptive Metropolis algorithms. The performance of these proposed sampling strategies are evaluated with a surrogate climate model that is able to approximate the noise and response behavior of a realistic atmospheric general circulation model (AGCM). The surrogate model is fast enough that its evaluation can be embedded in these Monte Carlo algorithms. We show that adaptive methods can be superior to MVFSA to approximate the known posterior distribution with fewer forward evaluations. However the adaptive methods can also be limited by inadequate sample mixing. The Single Component and Delayed Rejection Adaptive Metropolis algorithms were found to resolve these limitations, although challenges remain to approximating multi-modal distributions. The results show that these advanced methods of statistical inference can provide practical solutions to the climate model calibration problem and challenges in quantifying climate projection uncertainties. The computational methods would also be useful to problems outside climate prediction, particularly those where sampling is limited by availability of computational resources.National Science Foundation OCE-0415251CONACyT-Mexico 159764Institute for Geophysic