Analysis of a "Meta-Trade Study" Interpretation of Decision-making with a Value Proposition for Space Programs

The article of record as published may be found at http://dx.doi.org/10.2514/6.2006-7225Tightening budgets and greater competition for funding are increasing the need to more completely, persuasively, and transparently value and market complex, and often exotic, Space Programs. This is driving an expanding view of what's required in an engineering, economic, and political language of discourse. Words and phrases like holistic, future generations, new frontiers, vision, inspiring, and sustainable are increasingly important to encompass the full range of stakeholders, the full spectrum of societal needs and values, and the vastly differing awareness, sophistication, and priorities among stakeholders. There's a well-known saying in Sales, that "you sell the sizzle, not the steak". This is increasingly necessary to achieve widespread understanding, public buy-in, and sustainability. We consider how the components of a "value proposition" may be mapped to corresponding parts of the final report for a kind of "Meta – Trade Study" with respect to allocation of Society's resources among alternative objectives and programs. We investigate how that viewpoint helps us to understand, quantify and communicate a "Value Proposition for Space". We also point out limitations of this perspective, hence areas that must be extended, and suggest how this may be done

Quantum derivation of K-distributed noise for finite (N)

J. Opt. Soc. Am. A, Volume 5, No. 5, pp. 730-734 (May 1988)Semiclassical derivations of the fluctuations of light beams have relied on limiting procedures in which the average number, (N), of scattering elements, photons, or superposed wave packets approaches infinity. We show that the fluctuations of thermal light having a Bose-Einstein photon distribution and of light with an amplitude distribution based on the modified Bessel functions, Kai, which has been found useful in describing light scattered from or through turbulent media, may be derived with a quantum-mechanical analysis as the superposition of a random number, N, of single-photon eigenstates with finite (N). The analysis also provides the P representation for Kdistributed noise. Generalizations of K noise are proposed. The factor-of-2 increase in the photon-number second factorial moment related to photon clumping in the Hanbury Brown-Twiss effect for thermal (Gaussian) fields is shown to arise generally in these random superposition models, even for non-Gaussian fields.This research was supported in part by a contract from the U.S. Naval Sea Systems Command

Integral identities for random variables

Using a general method for deriving identities for random variables, the author finds a number of new results involving characteristic functions and generating functions. The method is simply to promote a parameter in an integral relation to the status of a random variable and then take expected values of both sides of the equation. Results include formulas for calculating the characteristic functions for sq x, square root of x, 1/x, sq x + x, sq R = sq x + sq y, etc. in terms of integral transforms of the characteristic functions for x and (x,y), etc. Generalizations to higher dimensions can be obtained using the same method. Expressions for inverse/ fractional moments, E(n ), etc. are also presented, demonstrating the methodPrepared for: Commander, Space and Naval Warfare Systems Command Washington, D.C.http://archive.org/details/integralidentiti00rockN0003986WRDJ850NAApproved for public release; distribution is unlimited

Reliability in a random environment

Correlations in the failures of subsystems or components may arise when they share a common, random environment. It is shown that a natural tool for calculating the reliability of such systems is the characteristic functional of the random hazard rate, h(t). Some general results for the reliability of series and parallel systems in terms of the characteristic functional of the hazard rate are derived and applied to a number of models of random environments. The applications include random hazard functions arising from 1) non-fatal shocks of random amplitudes, 2) a Markovian, Gamma-marginal stochastic process, 3) system stress related to unrepaired damage from incoming rounds, and 4) impulsive and accumulated heat stresses from a laser battleThe work reported herein was supported in part by the Space and Naval Warfare Systems Command.http://archive.org/details/reliabilityinran00rockApproved for public release; distribution is unlimited

Calculating the quantum characteristic function and the photon-number generating function in quantum optics

A new operator derivation of the relation giving the photon-number generating function, G (y), in terms of the quantum characteristic function, C(s,5*), is presented. The inverse problem is then solved, calculating C( s.s*) directly from G ( y). Because G ( y) contains less phase information than C(s,s*), we can either assume that the field has a completely random phase (e.g., a stationary field) or be content with calculating the phase average of C(s,s*). We then derive an expression giving G ( r> for the superposition of two arbitrary, independent fields in terms of the individual G (y)'s for each (stationary) field. A number of examples illustrate the methods, including a determination of the quantum characteristic function for a field with K-distributed amplitude fluctuations.Approved for public release; distribution is unlimited

Dynamical analysis of random, quantum interference of light

The well-known photon correlations of thermal light are now understood to result from the ran­dom superposition of independently emitted photons from spontaneous emission. Through random interference the number of photons evolves as a Bose-Einstein distribution rather than the Poisson distribution as one might expect for independent emissions of classical particles. By identifying terms in the density-matrix (p) equation for a linear amplifier, those terms giving rise to spontaneous emission were earlier distinguished from those causing amplification and absorption. We investi­gate the role of interference in the evolution of the photon statistics by further identifying terms in the equation for p. solely responsible for quantum interference phenomena. The effects of this random interference on the photon factorial moments are quantified, even for those cases where the final field statistics are not Bose-Einstein. From our analysis we conclude that stimulated emission should be viewed as analogous to time-reversed absorption, rather than either a cascade process or pure constructive interference.Work supported in part by the U.S. Naval Sea Systems CommandApproved for public release; distribution is unlimited

Laser beam-quality/aperture-shape scaling relation

Applied Optics, Volume 25, No. 9, pp. 1394-1397 (1 May 1986)This work was supported by a contract from the U.S. Army TRADOC Operations Research Activity, White Sands Missile Range, NM

Integral Identities for Random Variables

The article of record as published may be found at http://dx.doi.org/10.1080/00031305.1988.10475526Using a general method for deriving identities for random variables, we find a number of new results involving characteristic functions and generating functions. The method is simply to promote a parameter in an integral relation to the status of a random variable and then take expected values of both sides of the equation. Results include formulas for calculating the characteristic functions for x 2, √x, 1/x, x 2 + x, R 2 = x 2 + y 2, and so forth in terms of integral transforms of the characteristic functions for x and (x, y), and so forth. Generalizations to higher dimensions can be obtained using the same method. Expressions for inverse/fractional moments, E{n!}, and so forth are also presented, demonstrating the method

Laser propagation code study

A number of laser propagation codes have been assessed as to their suitability for modeling Army High Energy Laser (HEL) weapons used in an anti- sensor mode. We identify a number of areas in which systems analysis HEL codes are deficient. Most notably, available HEL scaling law codes model the laser aperture as circular, possibly with a fixed (e.g. 10%) obscuration. However, most HELs have rectangular apertures with up to 30% obscuration. We present a beam-quality/aperture shape scaling relation which can be useful when applying these codes to realistic designs for HELs. Originator supplied keywords: High energy lasers; Laser propagation; Beam quality; Diffraction; Laser aperture; Pupil function; Thermal bloomingUS Army Tradoc, Operations Research Activityhttp://archive.org/details/laserpropagation00rockMLPR# TRASANA 5029N

A Relativistic Mass Tensor with Geometric Interpretation

We derive a relativistic mass tensor (dyadic or matrix) whose origin and properties have a direct geometric interpretation in terms of projection operators related to the particle's world line and local inertial frame in Minkowski space, yet whose eigenvalues are simply the longitudinal (m1 ) and the transverse (m1 ) mass. Writing the noncovariant equations of motion (EOM) for a point particle in terms of this mass tensor bridges the gap between the compact but sterile form of the Lorentz covariant EOM and the usual ("unwieldy") noncovariant EOM in which m1 and m1 appear. General expressions for 3- and 4-space mass (inverse mass) tensors are presented in terms of the system Lagrangian (Hamiltonian).Federick A. Hauck Physics Research Fund