Man-computer role in space navigation and guidance Final report

Man computer roles and hardware requirements for navigation and guidance in deep space manned mission

Man-computer roles in space navigation and guidance, phase I

Estimated man-machine requirement computations for space navigation and guidanc

Bound States of the Klein-Gordon Equation for Woods-Saxon Potential With Position Dependent Mass

The effective mass Klein-Gordon equation in one dimension for the Woods-Saxon potential is solved by using the Nikiforov-Uvarov method. Energy eigenvalues and the corresponding eigenfunctions are computed. Results are also given for the constant mass case.Comment: 13 page

Global shallow water magnetohydrodynamic waves in the solar tachocline

We derive analytical solutions and dispersion relations of global magnetic Poincar\'e (magneto-gravity) and magnetic Rossby waves in the approximation of shallow water magnetohydrodynamics. The solutions are obtained in a rotating spherical coordinate system for strongly and weakly stable stratification separately in the presence of toroidal magnetic field. In both cases magnetic Rossby waves split into fast and slow magnetic Rossby modes. In the case of strongly stable stratification (valid in the radiative part of the tachocline) all waves are slightly affected by the layer thickness and the toroidal magnetic field, while in the case of weakly stable stratification (valid in the upper overshoot layer of the tachocline) magnetic Poincar\'e and fast magnetic Rossby waves are found to be concentrated near the solar equator, leading to equatorially trapped waves. However, slow magnetic Rossby waves tend to concentrate near the poles, leading to polar trapped waves. The frequencies of all waves are smaller in the upper weakly stable stratification region than in the lower strongly stable stratification one

Self-force on a scalar charge in radial infall from rest using the Hadamard-WKB expansion

We present an analytic method based on the Hadamard-WKB expansion to calculate the self-force for a particle with scalar charge that undergoes radial infall in a Schwarzschild spacetime after being held at rest until a time t = 0. Our result is valid in the case of short duration from the start. It is possible to use the Hadamard-WKB expansion in this case because the value of the integral of the retarded Green's function over the particle's entire past trajectory can be expressed in terms of two integrals over the time period that the particle has been falling. This analytic result is expected to be useful as a check for numerical prescriptions including those involving mode sum regularization and for any other analytical approximations to self-force calculations.Comment: 22 pages, 2 figures, Physical Review D version along with the corrections given in the erratu

Diffusive transport in networks built of containers and tubes

We developed analytical and numerical methods to study a transport of non-interacting particles in large networks consisting of M d-dimensional containers C_1,...,C_M with radii R_i linked together by tubes of length l_{ij} and radii a_{ij} where i,j=1,2,...,M. Tubes may join directly with each other forming junctions. It is possible that some links are absent. Instead of solving the diffusion equation for the full problem we formulated an approach that is computationally more efficient. We derived a set of rate equations that govern the time dependence of the number of particles in each container N_1(t),N_2(t),...,N_M(t). In such a way the complicated transport problem is reduced to a set of M first order integro-differential equations in time, which can be solved efficiently by the algorithm presented here. The workings of the method have been demonstrated on a couple of examples: networks involving three, four and seven containers, and one network with a three-point junction. Already simple networks with relatively few containers exhibit interesting transport behavior. For example, we showed that it is possible to adjust the geometry of the networks so that the particle concentration varies in time in a wave-like manner. Such behavior deviates from simple exponential growth and decay occurring in the two container system.Comment: 21 pages, 18 figures, REVTEX4; new figure added, reduced emphasis on graph theory, additional discussion added (computational cost, one dimensional tubes

Higher-order Continuum Approximation for Rarefied Gases

The Hilbert-Chapman-Enskog expansion of the kinetic equations in mean flight times is believed to be asymptotic rather than convergent. It is therefore inadvisable to use lower order results to simplify the current approximation as is done in the traditional Chapman-Enskog procedure, since that is an iterative method. By avoiding such recycling of lower order results, one obtains macroscopic equations that are asymptotically equivalent to the ones found in the Chapman-Enskog approach. The new equations contain higher order terms that are discarded in the Chapman-Enskog method. These make a significant impact on the results for such problems as ultrasound propagation. In this paper, it is shown that these results turn out well with relatively little complication when the expansions are carried to second order in the mean free time, for the example of the relaxation or BGK model of kinetic theory.Comment: 20 pages, 2 figures, RevTeX 4 macro

Suppressing Diffusion-Mediated Exciton Annihilation in 2D Semiconductors Using the Dielectric Environment

Atomically thin semiconductors such as monolayer MoS2 and WS2 exhibit nonlinear exciton-exciton annihilation at notably low excitation densities (below ~10 excitons/um2 in MoS2). Here, we show that the density threshold at which annihilation occurs can be tuned by changing the underlying substrate. When the supporting substrate is changed from SiO2 to Al2O3 or SrTiO3, the rate constant for second-order exciton-exciton annihilation, k_XX [cm2/s], is reduced by one or two orders of magnitude, respectively. Using transient photoluminescence microscopy, we measure the effective room-temperature exciton diffusion coefficient in chemical-treated MoS2 to be D = 0.06 +/- 0.01 cm2/s, corresponding to a diffusion length of LD = 350 nm for an exciton lifetime of {\tau} = 20 ns, which is independent of the substrate. These results, together with numerical simulations, suggest that the effective exciton-exciton annihilation radius monotonically decreases with increasing refractive index of the underlying substrate. Exciton-exciton annihilation limits the overall efficiency of 2D semiconductor devices operating at high exciton densities; the ability to tune these interactions via the dielectric environment is an important step toward more efficient optoelectronic technologies featuring atomically thin materials

Amplitude Modulation and Relaxation-Oscillation of Counterpropagating Rolls within a Broken-Symmetry Laser-Induced Electroconvection Strip

We report a liquid-crystal pattern-formation experiment in which we break the lateral (translational) symmetry of a nematic medium with a laser-induced thermal gradient. The work is motivated by an improved measurement (reported here) of the temperature dependence of the electroconvection threshold voltage in planar-nematic 4-methoxybenzylidene-4-butylaniline (MBBA). In contrast with other broken-symmetry-pattern studies that report a uniform drift, we observe a strip of counterpropagating rolls that collide at a sink point, and a strong temporally periodic amplitude modulation within a width of 3-4 rolls about the sink point. The time dependence of the amplitude at a fixed position is periodic but displays a nonsinusoidal relaxation-oscillation profile. After reporting experimental results based on spacetime contours and wavenumber profiles, along with a measurement of the change in the drift frequency with applied voltage at a fixed control parameter, we propose some potential guidelines for a theoretical model based on saddle-point solutions for Eckhaus-unstable states and coupled complex Ginzburg-Landau equations. Published in PRE 73, 036317 (2006).Comment: Published in Physical Review E in March 200