arXiv subjects

J. A. Morgan

Publications and source records attributed to J. A. Morgan.

10 recordsLinked to original sources

arXiv2013

Interception in differential pursuit/evasion games

A qualitative criterion for a pursuer to intercept a target in a class of differential games is obtained in terms of \emph{future cones}: Topological cones that contain all attainable trajectories of target or interceptor originating from an initial position. An interception solution exists after some initial time iff the future cone of the target lies within the future cone of the interceptor. The solution may be regarded as a kind of Nash equillibrium. This result is applied to two examples: 1. The game of Two Cars: The future cone condition is shown to be equivalent to conditions for interception obtained by Cockayne. \cite{ref2} 2. Satellite warfare: The future cone for a spacecraft or direct-ascent antisatellite weapon (ASAT) maneuvering in a central gravitational field is obtained and is shown to equal that for a spacecraft which maneuvers solely by means of a single velocity change at the cone vertex. The latter result is illustrated with an analysis of the January 2007 interception of the FengYun-1C spacecraft.

math.OC↗

arXiv2010

Comparison of Bayesian Land Surface Temperature algorithm performance with Terra MODIS observations

An approach to land surface temperature (LST) estimation that relies upon Bayesian inference has been tested against multiband infrared radiometric imagery from the Terra MODIS instrument. Bayesian LST estimators are shown to reproduce standard MODIS product LST values starting from a parsimoniously chosen (hence, uninformative) range of prior band emissivity knowledge. Two estimation methods have been tested. The first is the iterative contraction mapping of joint expectation values for LST and surface emissivity described in a previous paper. In the second method, the Bayesian algorithm is reformulated as a Maximum \emph{A-Posteriori} (MAP) search for the maximum joint \emph{a-posteriori} probability for LST, given observed sensor aperture radiances and \emph{a-priori} probabilities for LST and emissivity. Two MODIS data granules each for daytime and nighttime were used for the comparison. The granules were chosen to be largely cloud-free, with limited vertical relief in those portions of the granules for which the sensor zenith angle $| ZA | < 30^{\circ}$. Level 1B radiances were used to obtain LST estimates for comparison with the Level 2 MODIS LST product. The Bayesian LST estimators accurately reproduce standard MODIS product LST values. In particular, the mean discrepancy for the MAP retrievals is $| < ΔT > | < 0.3 K$, and its standard deviation does not exceed $1 K$. The $\pm 68 %$ confidence intervals for individual LST estimates associated with assumed uncertainty in surface emissivity are of order $0.8 K$. The Appendix presents a proof of convergence of the iterative contraction mapping algorithm.

physics.data-an↗

arXiv2007

Visual Observability of the Cassiopeia A Supernova

It is generally believed that the explosion which gave birth to the Cassiopeia A supernova remmant resulted from core collapse of a hydrogen-deficient star. A progenitor that has lost all its hydrogen envelope and part of its helium envelope would lead to an explosion with the optical properties of a Type Ic supernova. There is evidence, if not general agreement, that Flamsteed observed the Cas A supernova as a sixth magnitude object in August, 1680. If an explosion with a typical SNIc light curve at the position and distance of Cas A attained maximum luminosity during the winter of 1679-1680, it would at that time have been poorly situated for visual observation, as its upper culmination would have taken place during daylight, while in August, between 170-200 days after peak luminosity, it would have been a sixth magnitude star.

astro-ph↗

arXiv2007

Demonstration of the spin-statistics connection in elementary quantum mechanics

A simple demonstration of the spin-statistics connection is presented. The effect of exchange and space inversion operators on two-particle states is reviewed. The connection follows directly from successive application of these operations to the two-particle wave function for identical particles in an s-state, evaluated at spatial coordinates $\pm x$, but at equal time, \emph{i.e.}, at spacelike interval.

physics.gen-ph↗

arXiv2006

The spin-statistics connection in classical field theory

The spin-statistics connection is obtained for a simple formulation of a classical field theory containing even and odd Grassmann variables. To that end, the construction of irreducible canonical realizations of the rotation group corresponding to general causal fields is reviewed. The connection is obtained by imposing local commutativity on the fields and exploiting the parity operation to exchange spatial coordinates in the scalar product of classical field evaluated at one spatial location with the same field evaluated at a distinct location. The spin-statistics connection for irreducible canonical realizations of the Poincaré group of spin $j$ is obtained in the form: Classical fields and their conjugate momenta satisfy fundamental field-theoretic Poisson bracket relations for 2$j$ even, and fundamental Poisson antibracket relations for 2$j$ odd

physics.class-ph↗

arXiv2005

A Bayesian Estimator for Linear Calibration Error Effects in Thermal Remote Sensing

The Bayesian Land Surface Temperature estimator previously developed has been extended to include the effects of imperfectly known gain and offset calibration errors. It is possible to treat both gain and offset as nuisance parameters and, by integrating over an uninformative range for their magnitudes, eliminate the dependence of surface temperature and emissivity estimates upon the exact calibration error.

physics.data-an↗

arXiv2004

Bayesian Estimation for Land Surface Temperature Retrieval: The Nuisance of Emissivities

An approach to the remote sensing of land surface temperature is developed using the methods of Bayesian inference. The starting point is the maximum entropy estimate for the posterior distribution of radiance in multiple bands. In order to convert this quantity to an estimator for surface temperature and emissivity with Bayes' theorem, it is necessary to obtain the joint prior probability for surface temperature and emissivity, given available prior knowledge. The requirement that any pair of distinct observers be able to relate their descriptions of radiance under arbitrary Lorentz transformations uniquely determines the prior probability. Perhaps surprisingly, surface temperature acts as a scale parameter, while emissivity acts as a location parameter, giving the prior probability P(T,emissivity|K)=const./T dT d(emissivity). Given this result, it is a simple matter to construct estimators for surface temperature and emssivity. Monte Carlo simulations of land surface temeprature retrieval in selected MODIS bands are presented as examples of the utility of the approach.

physics.data-an↗

arXiv2004

Parity and the Spin-Statistics Connection

The spin-statistics connection is obtained in a simple and elementary way for general causal fields by using the parity operation to exchange spatial coordinates in the scalar product of a locally commuting field operator, evaluated at position x, with the same field operator evaluated at -x, at equal times.

physics.ed-ph↗

arXiv2004

Spin and Statistics in Classical Mechanics

The spin-statistics conection is obtained for classical point particles. The connection holds within pseudomechanics, a theory of particle motion that extends classical physics to include anticommuting Grassmann variables, and which exhibits classical analogs of both spin and statistics. Classical realizations of Lie groups can be constructed in a canonical formalism generalized to include Grassmann variables. The theory of irreducible canonical realizations of the Poincare group is developed in this framework, with particular emphasis on the rotation subgroup. The behavior of irreducible realizations under time inversion and charge conjugation is obtained. The requirement that the Lagrangian retain its form under the cominbed operation CT leads directly to the spin-statistics connection, by an adaptation of Schwinger's 1951 proof to irreducible canonical realizations of the Poincare group of spin j: Generalized spin coordinates and momenta satisfy fundamental Poisson bracket relations for 2j=even, and fundamental Poisson antibracket relations for 2j=odd.

physics.class-ph↗

arXiv1998

Neutrino Propulsion for Interstellar Spacecraft

An exotic spacecraft propulsion technology is described which exploits parity violation in weak interactions. Anisotropic neutrino emission from a polarized assembly of weakly interacting particles converts rest mass directly to spacecraft impulse.

physics.gen-ph↗