Dispersion processes

We study a synchronous dispersion process in which $M$ particles are initially placed at a distinguished origin vertex of a graph $G$. At each time step, at each vertex $v$ occupied by more than one particle at the beginning of this step, each of these particles moves to a neighbour of $v$ chosen independently and uniformly at random. The dispersion process ends once the particles have all stopped moving, i.e. at the first step at which each vertex is occupied by at most one particle. For the complete graph $K_n$ and star graph $S_n$, we show that for any constant $\delta>1$, with high probability, if $M \le n/2(1-\delta)$, then the process finishes in $O(\log n)$ steps, whereas if $M \ge n/2(1+\delta)$, then the process needs $e^{\Omega(n)}$ steps to complete (if ever). We also show that an analogous lazy variant of the process exhibits the same behaviour but for higher thresholds, allowing faster dispersion of more particles. For paths, trees, grids, hypercubes and Cayley graphs of large enough sizes (in terms of $M$) we give bounds on the time to finish and the maximum distance traveled from the origin as a function of the number of particles $M$

Investigation of a lineament expressed in an oblique Apollo 9 photograph

The author has identified the following significant results. A linear topographic feature, referred to as the New York Mountains lineament, was recognized in an oblique Apollo 9 photograph to extend from the Providence Mountains of California to near Lake Mead, Arizona. In subsequent vertical ERTS-1 imagery this feature was found to have vague and indistinct expression. A study was conducted to determine the possible geologic origin(s) of the lineament and to explain its anomalous expression in the Apollo 9 photograph. The results suggest that the apparent expression of the lineament is due to a combination of the oblique view of the Apollo photograph, low sun angle illumination of southeast facing slopes, shadowing of northwest facing slopes, and linear snow line along the southeastern flank of the New York Mountains. No geologic or structural causes for the lineament have been found

Structural lineaments in the southern Sierra Nevada, California

The author has identified the following significant results. Several lineaments observed in ERTS-1 MSS imagery over the southern Sierra Nevada of California have been studied in the field in an attempt to explain their geologic origins and significance. The lineaments are expressed topographically as alignments of linear valleys, elongate ridges, breaks in slope or combinations of these. Natural outcrop exposures along them are characteristically poor. Two lineaments were found to align with foliated metamorphic roof pendants and screens within granitic country rocks. Along other lineaments, the most consistant correlations were found to be alignments of diabase dikes of Cretaceous age, and younger cataclastic shear zones and minor faults. The location of several Pliocene and Pleistocene volcanic centers at or near lineament intersections suggests that the lineaments may represent zones of crustal weakness which have provided conduits for rising magma

Crustal extension and transform faulting in the southern Basin Range Province

The author has identified the following significant results. Field reconnaissance and study of geologic literature guided by analysis of ERTS-1 MSS imagery have led to a hypothesis of tectonic control of Miocene volcanism, plutonism, and related mineralization in part of the Basin Range Province of southern Nevada and northwestern Arizona. The easterly trending right-lateral Las Vegas Shear Zone separates two volcanic provinces believed to represent areas of major east-west crustal extension. One volcanic province is aligned along the Colorado River south of the eastern termination of the Las Vegas Shear Zone; the second province is located north of the western termination of the shear zone in southern Nye County, Nevada. Geochronologic, geophysical, and structural evidence suggests that the Las Vegas Shear Zone may have formed in response to crustal extension in the two volcanic provinces in a manner similar to the formation of a ridge-ridge transform fault, as recognized in ocean floor tectonics

Evidence of a major fault zone along the California-Nevada state line 35 deg 30 min to 36 deg 30 min north latitude

The author has identified the following significant results. Geologic reconnaissance guided by analysis of ERTS-1 and Apollo-9 satellite imagery and intermediate scale photography from X-15 and U-2 aircraft has confirmed the presence of a major fault zone along the California-Nevada state line, between 35 deg 30 min and 36 deg 30 min north latitude. The name Pahrump Fault Zone has been suggested for this feature after the valley in which it is best exposed. Field reconnaissance has indicated the existence of previously unreported faults cutting bedrock along range fronts, and displacing Tertiary and Quaternary basin sediments. Gravity data support the interpretation of regional structural discontinuity along this zone. Individual fault traces within the Pahrump Fault Zone form generally left-stepping en echelon patterns. These fault patterns, the apparent offset of a Laramide age thrust fault, and possible drag folding along a major fault break suggest a component of right lateral displacement. The trend and postulated movement of the Pahrump Fault Zone are similar to the adjacent Las Vegas Shear Zone and Death Valley-Furnace Creek Faults, which are parts of a regional strike slip system in the southern Basin-Range Province

An Analysis of the Statistics of the Hubble Space Telescope Kuiper Belt Object Search

We calculate statistical limits to the detection of Kuiper belt objects in the Hubble Space Telescope (HST) data of Cochran et al., in which they report the discovery of a population of Halley-sized objects in Pluto-like orbits. Detection of a population of faint objects in these data is limited by the number of false objects that appear owing only to random noise; the number of real objects must exceed the uncertainty in the number of these false objects for the population to be observable. We determine the number of false objects expected owing to random noise in the data of Cochran et al. by measuring the pixel-to-pixel noise level in the raw HST data and propagating this noise through the detection method employed by Cochran et al. We find that the uncertainty in the number of false objects exceeds by 2 orders of magnitude the reported number of objects detected by Cochran et al. The detection of such a population of Halley-sized Kuiper belt objects with these data is therefore not possible

A reconnaissance space sensing investigation of crustal structure for a strip from the eastern Sierra Nevada to the Colorado Plateau

There are no author-identified significant results in this report. Research progress in applications of ERTS-1 MSS imagery in study of Basin-Range tectonics is summarized. Field reconnaissance of ERTS-1 image anomalies has resulted in recognition of previously unreported fault zones and regional structural control of volcanic and plutonic activity. NIMBUS, Apollo 9, X-15, U-2, and SLAR imagery are discussed with specific applications, and methods of image enhancement and analysis employed in the research are summarized. Areas studied and methods employed in geologic field work are outlined

Noise driven dynamic phase transition in a a one dimensional Ising-like model

The dynamical evolution of a recently introduced one dimensional model in \cite{biswas-sen} (henceforth referred to as model I), has been made stochastic by introducing a parameter $\beta$ such that $\beta =0$ corresponds to the Ising model and $\beta \to \infty$ to the original model I. The equilibrium behaviour for any value of $\beta$ is identical: a homogeneous state. We argue, from the behaviour of the dynamical exponent $z$,that for any $\beta \neq 0$, the system belongs to the dynamical class of model I indicating a dynamic phase transition at $\beta = 0$. On the other hand, the persistence probabilities in a system of $L$ spins saturate at a value $P_{sat}(\beta, L) = (\beta/L)^{\alpha}f(\beta)$, where $\alpha$ remains constant for all $\beta \neq 0$ supporting the existence of the dynamic phase transition at $\beta =0$. The scaling function $f(\beta)$ shows a crossover behaviour with $f(\beta) = \rm{constant}$ for $\beta <<1$ and $f(\beta) \propto \beta^{-\alpha}$ for $\beta >>1$.Comment: 4 pages, 5 figures, accepted version in Physical Review

The contact process in heterogeneous and weakly-disordered systems

The critical behavior of the contact process (CP) in heterogeneous periodic and weakly-disordered environments is investigated using the supercritical series expansion and Monte Carlo (MC) simulations. Phase-separation lines and critical exponents $\beta$ (from series expansion) and $\eta$ (from MC simulations) are calculated. A general analytical expression for the locus of critical points is suggested for the weak-disorder limit and confirmed by the series expansion analysis and the MC simulations. Our results for the critical exponents show that the CP in heterogeneous environments remains in the directed percolation (DP) universality class, while for environments with quenched disorder, the data are compatible with the scenario of continuously changing critical exponents.Comment: 5 pages, 3 figure

A Fredholm Determinant Representation in ASEP

In previous work the authors found integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice. The dynamics are uniquely determined once the initial state is specified. In this note we restrict our attention to the case of step initial condition with particles at the positive integers, and consider the distribution function for the m'th particle from the left. In the previous work an infinite series of multiple integrals was derived for this distribution. In this note we show that the series can be summed to give a single integral whose integrand involves a Fredholm determinant. We use this determinant representation to derive (non-rigorously, at this writing) a scaling limit.Comment: 12 Pages. Version 3 includes a scaling conjectur