Near-encounter geometry generation

Generation of near encounter spacecraft-target planet celestial geometry using two body trajectory computerized simulatio

The origin of the grooves on Phobos

Various theories for the long, linear depressions on the surface of Phobos are reviewed. Imagery from Viking Orbiters is used to map the surface distribution of the grooves, study their morphology, and date them by means of the density of superimposed impact craters. Data is presented which tends to support the hypothesis that the deep-seated fracturing was caused by a large, nearly catastrophic cratering event. It is suggested that the grooves were produced during the creation of the Stickney crater, rather than as the result of tidal stresses induced by Mars or by drag forces during the hypothetical capture of the satellite by Mars

Phobos: Photometry and origin of dark markings on crater floors

High resolution photographs of Phobos taken during close flybys of Viking Orbiter 1 reveal many dark patches on the floors of several craters. The apparently dark material is only prominent at large phase angles. Analysis of the photometric properties indicates that the dark patches represent areas of unusually rough textures whose reflectance near zero phase is similar to that of the mean surface (approximately 6 percent in the visible), but whose phase curve is much steeper. The contrast of such areas is less than 10 percent zero phase but approaches 100 percent near phase angles of 90 degrees. It is proposed that these intricately textured deposits represent patches of vesticular impact melt

Mariner Mars 1971 optical navigation demonstration

The feasibility of using a combination of spacecraft-based optical data and earth-based Doppler data to perform near-real-time approach navigation was demonstrated by the Mariner Mars 71 Project. The important findings, conclusions, and recommendations are documented. A summary along with publications and papers giving additional details on the objectives of the demonstration are provided. Instrument calibration and performance as well as navigation and science results are reported

Minimum spanning trees on random networks

We show that the geometry of minimum spanning trees (MST) on random graphs is universal. Due to this geometric universality, we are able to characterise the energy of MST using a scaling distribution ($P(\epsilon)$) found using uniform disorder. We show that the MST energy for other disorder distributions is simply related to $P(\epsilon)$. We discuss the relationship to invasion percolation (IP), to the directed polymer in a random media (DPRM) and the implications for the broader issue of universality in disordered systems.Comment: 4 pages, 3 figure

Combinatorial models of rigidity and renormalization

We first introduce the percolation problems associated with the graph theoretical concepts of $(k,l)$-sparsity, and make contact with the physical concepts of ordinary and rigidity percolation. We then devise a renormalization transformation for $(k,l)$-percolation problems, and investigate its domain of validity. In particular, we show that it allows an exact solution of $(k,l)$-percolation problems on hierarchical graphs, for $k\leq l<2k$. We introduce and solve by renormalization such a model, which has the interesting feature of showing both ordinary percolation and rigidity percolation phase transitions, depending on the values of the parameters.Comment: 22 pages, 6 figure

Random manifolds in non-linear resistor networks: Applications to varistors and superconductors

We show that current localization in polycrystalline varistors occurs on paths which are, usually, in the universality class of the directed polymer in a random medium. We also show that in ceramic superconductors, voltage localizes on a surface which maps to an Ising domain wall. The emergence of these manifolds is explained and their structure is illustrated using direct solution of non-linear resistor networks

Ground state non-universality in the random field Ising model

Two attractive and often used ideas, namely universality and the concept of a zero temperature fixed point, are violated in the infinite-range random-field Ising model. In the ground state we show that the exponents can depend continuously on the disorder and so are non-universal. However, we also show that at finite temperature the thermal order parameter exponent one half is restored so that temperature is a relevant variable. The broader implications of these results are discussed.Comment: 4 pages 2 figures, corrected prefactors caused by a missing factor of two in Eq. 2., added a paragraph in conclusions for clarit

Structural Properties of Self-Attracting Walks

Self-attracting walks (SATW) with attractive interaction u > 0 display a swelling-collapse transition at a critical u_{\mathrm{c}} for dimensions d >= 2, analogous to the \Theta transition of polymers. We are interested in the structure of the clusters generated by SATW below u_{\mathrm{c}} (swollen walk), above u_{\mathrm{c}} (collapsed walk), and at u_{\mathrm{c}}, which can be characterized by the fractal dimensions of the clusters d_{\mathrm{f}} and their interface d_{\mathrm{I}}. Using scaling arguments and Monte Carlo simulations, we find that for u<u_{\mathrm{c}}, the structures are in the universality class of clusters generated by simple random walks. For u>u_{\mathrm{c}}, the clusters are compact, i.e. d_{\mathrm{f}}=d and d_{\mathrm{I}}=d-1. At u_{\mathrm{c}}, the SATW is in a new universality class. The clusters are compact in both d=2 and d=3, but their interface is fractal: d_{\mathrm{I}}=1.50\pm0.01 and 2.73\pm0.03 in d=2 and d=3, respectively. In d=1, where the walk is collapsed for all u and no swelling-collapse transition exists, we derive analytical expressions for the average number of visited sites and the mean time to visit S sites.Comment: 15 pages, 8 postscript figures, submitted to Phys. Rev.

Susceptibility and Percolation in 2D Random Field Ising Magnets

The ground state structure of the two-dimensional random field Ising magnet is studied using exact numerical calculations. First we show that the ferromagnetism, which exists for small system sizes, vanishes with a large excitation at a random field strength dependent length scale. This {\it break-up length scale} $L_b$ scales exponentially with the squared random field, $\exp(A/\Delta^2)$. By adding an external field $H$ we then study the susceptibility in the ground state. If $L>L_b$, domains melt continuously and the magnetization has a smooth behavior, independent of system size, and the susceptibility decays as $L^{-2}$. We define a random field strength dependent critical external field value $\pm H_c(\Delta)$, for the up and down spins to form a percolation type of spanning cluster. The percolation transition is in the standard short-range correlated percolation universality class. The mass of the spanning cluster increases with decreasing $\Delta$ and the critical external field approaches zero for vanishing random field strength, implying the critical field scaling (for Gaussian disorder) $H_c \sim (\Delta -\Delta_c)^\delta$, where $\Delta_c = 1.65 \pm 0.05$ and $\delta=2.05\pm 0.10$. Below $\Delta_c$ the systems should percolate even when H=0. This implies that even for H=0 above $L_b$ the domains can be fractal at low random fields, such that the largest domain spans the system at low random field strength values and its mass has the fractal dimension of standard percolation $D_f = 91/48$. The structure of the spanning clusters is studied by defining {\it red clusters}, in analogy to the ``red sites'' of ordinary site-percolation. The size of red clusters defines an extra length scale, independent of $L$.Comment: 17 pages, 28 figures, accepted for publication in Phys. Rev.