Capillary instability in nanowire geometries

The vapor-liquid-solid (VLS) mechanism has been applied extensively as a framework for growing single-crystal semiconductor nanowires for applications spanning optoelectronic, sensor and energy-related technologies. Recent experiments have demonstrated that subtle changes in VLS growth conditions produce a diversity of nanowire morphologies, and result in intricate kinked structures that may yield novel properties. These observations have motivated modeling studies that have linked kinking phenomena to processes at the triple line between vapor, liquid and solid phases that cause spontaneous "tilting" of the growth direction. Here we present atomistic simulations and theoretical analyses that reveal a tilting instability that is intrinsic to nanowire geometries, even in the absence of pronounced anisotropies in solid-liquid interface properties. The analysis produces a very simple conclusion: the transition between axisymmetric and tilted triple lines is shown to occur when the triple line geometry satisfies Young's force-balance condition. The intrinsic nature of the instability may have broad implications for the design of experimental strategies for controlled growth of crystalline nanowires with complex geometries.Comment: 10 pages, 5 figure

Fields in Nonaffine Bundles. I. The general bitensorially covariant differentiation procedure

The standard covariant differentiation procedure for fields in vector bundles is generalised so as to be applicable to fields in general nonaffine bundles in which the fibres may have an arbitrary nonlinear structure. In addition to the usual requirement that the base space should be flat or endowed with its own linear connection, and that there should be an ordinary gauge connection on the bundle, it is necessary to require also that there should be an intrinsic, bundle-group invariant connection on the fibre space. The procedure is based on the use of an appropriate primary-field (i.e. section) independent connector that is constructed in terms of the natural fibre-tangent-vector realisation of the gauge connection. The application to gauged harmonic mappings will be described in a following article.Comment: 17 page Latex file with some minor misprint corrections and added color for article originally published in black and whit

An empirical analysis of the distribution of overshoots in a stationary Gaussian stochastic process

The frequency distribution of overshoots in a stationary Gaussian stochastic process is analyzed. The primary processes involved in this analysis are computer simulation and statistical estimation. Computer simulation is used to simulate stationary Gaussian stochastic processes that have selected autocorrelation functions. An analysis of the simulation results reveals a frequency distribution for overshoots with a functional dependence on the mean and variance of the process. Statistical estimation is then used to estimate the mean and variance of a process. It is shown that for an autocorrelation function, the mean and the variance for the number of overshoots, a frequency distribution for overshoots can be estimated

Chaotic string-capture by black hole

We consider a macroscopic charge-current carrying (cosmic) string in the background of a Schwarzschild black hole. The string is taken to be circular and is allowed to oscillate and to propagate in the direction perpendicular to its plane (that is parallel to the equatorial plane of the black hole). Nurmerical investigations indicate that the system is non-integrable, but the interaction with the gravitational field of the black hole anyway gives rise to various qualitatively simple processes like "adiabatic capture" and "string transmutation".Comment: 13 pages Latex + 3 figures (not included), Nordita 93/55

Probability models for the variation in the number of thunderstorm hits per day

Negative binomial distribution as new probability model for representing thunderstorm hit variation per day at Cape Kenned

Mass of Rotating Black Holes in Gauged Supergravities

The masses of several recently-constructed rotating black holes in gauged supergravities, including the general such solution in minimal gauged supergravity in five dimensions, have until now been calculated only by integrating the first law of thermodynamics. In some respects it is more satisfactory to have a calculation of the mass that is based directly upon the integration of a conserved quantity derived from a symmetry principal. In this paper, we evaluate the masses for the newly-discovered rotating black holes using the conformal definition of Ashtekar, Magnon and Das (AMD), and show that the results agree with the earlier thermodynamic calculations. We also consider the Abbott-Deser (AD) approach, and show that this yields an identical answer for the mass of the general rotating black hole in five-dimensional minimal gauged supergravity. In other cases we encounter discrepancies when applying the AD procedure. We attribute these to ambiguities or pathologies of the chosen decomposition into background AdS metric plus deviations when scalar fields are present. The AMD approach, involving no decomposition into background plus deviation, is not subject to such complications. Finally, we also calculate the Euclidean action for the five-dimensional solution in minimal gauged supergravity, showing that it is consistent with the quantum statistical relation.Comment: Typos corrected and references update

B-R Colors of Globular Clusters in NGC 6166 (A2199)

We have analysed new R-band photometry of globular clusters in NGC 6166, the cD galaxy in the cooling flow cluster A2199. In combination with the earlier B photometry of Pritchet \& Harris (1990), we obtain B$-$R colours for $\sim$ 40 globular clusters in NGC 6166. The mean B$-$R is 1.26 $\pm$ 0.11, corresponding to a mean [Fe/H] = $-$1 $\pm$ 0.4. Given that NGC 6166 is one of the most luminous cD galaxies studied to date, our result implies significant scatter in the relationship between mean cluster [Fe/H] and parent galaxy luminosity. We obtain a globular cluster specific frequency of S$_N$ $\sim$ 9, with a possible range between 5 and 18. This value is inconsistent with the value of S$_N$ $\leq$ 4 determined earlier by Pritchet \& Harris (1990) from B-band photometry, and we discuss possible reasons for the discrepancy. Finally, we reassess whether or not cooling flows are an important mechanism for forming globular clusters in gE/cD galaxies.Comment: 8 pages, uuencoded, gzipped tar file with latex file, 6 figures (Fig 1 omitted because of size), and mn.sty file. Figures will be embedded into the postscript file. Accepted (March 1996) for publication in MNRA

Dynamics of cosmic strings and springs; a covariant formulation

A general family of charge-current carrying cosmic string models is investigated. In the special case of circular configurations in arbitrary axially symmetric gravitational and electromagnetic backgrounds the dynamics is determined by simple point particle Hamiltonians. A certain "duality" transformation relates our results to previous ones, obtained by Carter et. al., for an infinitely long open stationary string in an arbitrary stationary background.Comment: 11 pages, Latex, Nordita preprint 93/28