Remote sensing of tropospheric turbulence using GPS radio occultation

Radio occultation (RO) measurements are sensitive to the small-scale irregularities in the atmosphere. In this study, we present a new technique to estimate tropospheric turbulence strength (namely, scintillation index) by analyzing RO amplitude fluctuations in impact parameter domain. GPS RO observations from the COSMIC (Constellation Observing System for Meteorology, Ionosphere, and Climate) satellites enabled us to calculate global maps of scintillation measures, revealing the seasonal, latitudinal, and longitudinal characteristics of the turbulent troposphere. Such information are both difficult and expensive to obtain especially over the oceans. To verify our approach, simulation experiments using the multiple phase screen (MPS) method were conducted. The results show that scintillation indices inferred from the MPS simulations are in good agreement with scintillation measures estimated from COSMIC observations

Faster Processing for Inverting GPS Occultation Data

A document outlines a computational method that can be incorporated into two prior methods used to invert Global Positioning System (GPS) occultation data [signal data acquired by a low-Earth-orbiting satellite as either this or the GPS satellite rises above or falls below the horizon] to obtain information on altitude-dependent properties of the atmosphere. The two prior inversion methods, known as back propagation and canonical transform, are computationally expensive because for each occultation, they involve numerical evaluation of a large number of diffraction-like spatial integrals. The present method involves an angular-spectrum-based phase-extrapolation approximation in which each data point is associated with a plane-wave component that propagates in a unique direction from the orbit of the receiving satellite to intersect a straight line tangent to the orbit at a nearby point. This approximation enables the use of fast Fourier transforms (FFTs), which apply only to data collected along a straight-line trajectory. The computation of the diffraction-like integrals in the angular-spectrum domain by use of FFTs takes only seconds, whereas previously, it took minutes

Tidal Excitation of Modes in Binary Systems with Applications to Binary Pulsars

We consider the tidal excitation of modes in a binary system of arbitrary eccentricity. For a circular orbit, the modes generally undergo forced oscillation with a period equal to the orbital period ($T$). For an eccentric orbit, the amplitude of each tidally excited mode can be written approximately as the sum of an oscillatory term that varies sinusoidally with the mode frequency and a `static' term that follows the time dependence of the tidal forcing function. The oscillatory term falls off exponentially with increasing \b (defined as the ratio of the periastron passage time to the mode period), whereas the `static' term is independent of \b. For small \b modes (\b \approx 1), the two terms are comparable, and the magnitude of the mode amplitude is nearly constant over the orbit. For large \b modes (\b \gta a few), the oscillatory term is very small compared to the `static' term, in which case the mode amplitude, like the tidal force, varies as the distance cubed. For main sequence stars, $p$, $f$, and low order $g$-modes generally have large \b and hence small amplitudes of oscillation. High overtone $g$-modes, however, have small overlap with the tidal forcing function. Thus, we expect an intermediate overtone $g$-mode with \b \sim 1 to have the largest oscillation amplitude. The dependence on mode damping and the stellar rotation rate is considered, as well as the effects of orbital evolution. We apply our work to the two binary pulsar system: PSR J0045-7319 and PSR B1259-63.Comment: 28 pages of uuencoded compressed postscript. 9 postscript figures available by anonymous ftp from ftp://brmha.mit.edu/ To be published in ApJ

Plastic Strain Ratio and Texture Coefficients in Orthotropic Sheets of Cubic Metals

Since first demonstrated by Stickels and Mould [1], there has been ample evidence that some elastic and plastic anisotropic parameters of cold-rolled and annealed steel sheets are correlated. These correlations suggest that some formability parameters of steel sheets (e.g., the average (plastic) strain ratio r¯ , the planar anisotropy Δr, etc.), which are usually determined by destructive tests, could possibly be inferred from nondestructive measurements of elastic anisotropic parameters. Indeed, much work has been done lately in exploring the possibility of on-line determination of r-value of steel sheets by ultrasonic techniques. [2–5]

On the Validity of the Classical Apsidal Motion Formula for Tidal Distortion

We check the validity of the widely used classical apsidal motion formula as a function of orbital parameters, stellar structure, and stellar rotation rate by comparing dynamical calculations of the periastron advance with the static tidal formula. We find that the classical formula gives very accurate results when the periods of the low order quadrupole g, f and p modes are smaller than the periastron passage time by a factor of about 7 or more. However, when this condition is not satisfied, the difference between the classical formula and the exact result can be quite large, and even periastron recession can result. The largest difference arises when one of the low order modes of the star is nearly resonant with an integer multiple of the orbital frequency minus twice the rotation rate of the star. The resonance of higher order g-modes (number of radial nodes \gta 4) with the orbit is very unlikely to cause significant deviation from the classical result because of their weak coupling to the tidal force and thus their small contribution to the apsidal motion. Resonances involving rotational modes of the star are also unlikely to make much contribution to the apsidal motion because of their small overlap with the tidal force, even though they have periods comparable to the periastron passage time. We apply our work to two famous binary systems (AS Cam and DI Her) which show abnormally small apsidal motion, and conclude that dynamical effects are unimportant for these systems, i.e. the static tide assumption is an excellent approximation.Comment: paper is in uuencoded, compressed post-script file: 6 post-script figures available via anonymous ftp at ftp://brmha.mit.edu/papers/ftp

Evaluation of EM-wave propagation in fully three-dimensional atmospheric refractive index distributions

We present a novel numerical method, based on high-frequency localization, for evaluation of electromagnetic-wave propagation through atmospheres exhibiting fully three-dimensional (height, range and cross-range) refractive index variations. This methodology, which is based on localization of Rytov-integration domains to small tubes around geometrical optics paths, can accurately solve three-dimensional propagation problems in orders-of-magnitude shorter computing times than other algorithms available presently. For example, the proposed approach can accurately produce solutions for propagation of ≈20 cm GPS signals across hundreds of kilometers of realistic, three-dimensional atmospheres in computing times on the order of 1 hour in a present-day single-processor workstation, a task for which other algorithms would require, in such single-processor computers, computing times on the order of several months

Higher-order solutions to non-Markovian quantum dynamics via hierarchical functional derivative

Solving realistic quantum systems coupled to an environment is a challenging task. Here we develop a hierarchical functional derivative (HFD) approach for efficiently solving the non-Markovian quantum trajectories of an open quantum system embedded in a bosonic bath. An explicit expression for arbitrary order HFD equation is derived systematically. Moreover, it is found that for an analytically solvable model, this hierarchical equation naturally terminates at a given order and thus becomes exactly solvable. This HFD approach provides a systematic method to study the non-Markovian quantum dynamics of an open system coupled to a bosonic environment.Comment: 5 pages, 2 figure

Electromagnetic wave scattering by discrete random media with remote sensing applications

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2001.Includes bibliographical references (p. 171-182).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.The scattering of electromagnetic waves in medium with randomly distributed discrete scatterers is studied. Analytical and numerical solutions to several problems with implications for the active and passive remote sensing of the Earth environment are obtained. The quasi-magnetostatic (QMS) solution for a conducting and permeable spheroid under arbitrary excitation is presented. The spheroid is surrounded by a weakly conducting background medium. The magnetic field inside the spheroid satisfies the vector wave equation, while the magnetic field outside can be expressed as the gradient of the Laplace solution. We solve this problem exactly using the separation of variables method in spheroidal coordinates by expanding the internal field in terms of vector spheroidal wavefunctions. The exact formulation works well for low to moderate frequencies; however, the solution breaks down at high frequency due to numerical difficulty in computing the spheroidal wavefunctions. To circumvent this difficulty, an approximate theory known as the small penetration-depth approximation (SPA) is developed. The SPA relates the internal field in terms of the external field by making use of the fact that at high frequency, the external field can only penetrate slightly into a thin skin layer below the surface of the spheroid. For spheroids with general permeability, the SPA works well at high frequency and complements the exact formulation. However, for high permeability, the SPA is found to give accurate broadband results. By neglecting mutual interactions, the QMS frequency response from a collection of conducting and permeable spheroids is also studied.(cont.) In a dense medium, the failure to properly take into account of multiple scattering effects could lead to significant errors. This has been demonstrated in the past from extensive theoretical, numerical, and experimental studies of electromagnetic wave scattering by densely packed dielectric spheres. Here, electromagnetic wave scattering by dense packed dielectric spheroids is studied both numerically through Monte Carlo simulations and analytically through the quasi-crystalline approximation (QCA) and QCA with coherent potential (QCA-CP). We assume that the spheroids are electrically small so that single-particle scattering is simple. In the numerical simulations, the Metropolis shuffling method is used to generate realizations of configurations for non-interpenetrable spheroids. The multiple scattering problem is formulated with the volume integral equation and solved using the method of moments with electrostatic basis functions. General expressions for the self-interaction elements are obtained using the low-frequency expansion of the dyadic Green's function, and radiative correction terms are included. Results of scattering coefficient, absorption coefficient, and scattering matrix for spheroids in random and aligned orientation configurations are presented. It is shown that independent scattering approximation can give grossly incorrect results when the fractional volume of the spheroids is appreciable.(cont.) In the analytical approach, only spheroids in the aligned configuration are solved. Low-frequency QCA and QCA-CP solutions are obtained for the average Green's function and the effective permittivity tensor. For QCA-CP, the low-frequency expansion of the uniaxial dyadic Green's function is required. The real parts of the effective permittivities from QCA and QCA-CP are compared with the Maxwell-Garnett mixing formula. ...by Chi On Ao.Ph.D

Dynamical invariants in non-Markovian quantum state diffusion equation

We find dynamical invariants for open quantum systems described by the non-Markovian quantum state diffusion (QSD) equation. In stark contrast to closed systems where the dynamical invariant can be identical to the system density operator, these dynamical invariants no longer share the equation of motion for the density operator. Moreover, the invariants obtained with from bi-orthonormal basis can be used to render an exact solution to the QSD equation and the corresponding non-Markovian dynamics without using master equations or numerical simulations. Significantly we show that we can apply these dynamic invariants to reverse-engineering a Hamiltonian that is capable of driving the system to the target state, providing a novel way to design control strategy for open quantum systems.Comment: 6 pages, 2 figure