Novel self-assembled morphologies from isotropic interactions

We present results from particle simulations with isotropic medium range interactions in two dimensions. At low temperature novel types of aggregated structures appear. We show that these structures can be explained by spontaneous symmetry breaking in analytic solutions to an adaptation of the spherical spin model. We predict the critical particle number where the symmetry breaking occurs and show that the resulting phase diagram agrees well with results from particle simulations.Comment: 4 pages, 4 figure

On uniformization of Burnside's curve y2=x5−xy^2=x^5-x

Main objects of uniformization of the curve $y^2=x^5-x$ are studied: its Burnside's parametrization, corresponding Schwarz's equation, and accessory parameters. As a result we obtain the first examples of solvable Fuchsian equations on torus and exhibit number-theoretic integer $q$-series for uniformizing functions, relevant modular forms, and analytic series for holomorphic Abelian integrals. A conjecture of Whittaker for hyperelliptic curves and its hypergeometric reducibility are discussed. We also consider the conversion between Burnside's and Whittaker's uniformizations.Comment: Final version. LaTeX, 23 pages, 1 figure. The handbook for elliptic functions has been moved to arXiv:0808.348

The response of the ionospheric peak electron density (NmF2) to solar activity)

The ionospheric peak electron density NmF2, simulated with the Coupled Thermosphere Ionosphere Plasmasphere electrodynamics (CTIPe) model was used to study the ionospheric response to solar flux in years of low (2008) and high (2013) solar activity. The CTIPe NmF2 was compared to the Whole Atmosphere Community Climate Model with Thermosphere and Ionosphere Extension (WACCM-X) and the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) NmF2 in March and July of 2008 and 2013. The comparison shows that the CTIPe NmF2 is lower than the COSMIC andWACCM-X NmF2. Both models successfully reproduce the semi-annual variations seen in the COSMIC observations. Analysis of the 27-day variations of the CTIPe NmF2 shows that the midnight NmF2 deviations are stronger than the midday deviations. In addition, at low solar activity, the 27-day variations of NmF2 are larger in the Southern Hemisphere, while at high solar activity, the 27-day variations of NmF2 are larger at the equator and in the Northern Hemisphere. An ionospheric delay was estimated with CTIPe simulated NmF2 at the 27-day solar rotation period during low and high solar activity. During low (high) solar activity, an ionospheric delay of about 12 (34) hours is predicted indicating an increasing ionospheric delay with solar activity.Die maximale ionosphärische Elektronendichte NmF2, die mit dem Coupled Thermosphere Ionosphere Plasmasphere electrodynamics (CTIPe) Modell simuliert wurde, wurde zur Untersuchung der ionosphärischen Reaktion in Jahren mit geringer (2008) und hoher (2013) Sonnenaktivität verwendet. CTIPe vorhergesagte NmF2 wurde mit derjenigen des Whole Atmosphere Community Climate Model with Thermosphere and Ionosphere Extension (WACCM-X) und Messwerten des Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) im März und Juli der Jahre 2008 und 2013 verglichen. Der Vergleich zeigt, dass NmF2 aus CTIPe geringer ist als das COSMIC gemessene und von WACCM-X simulierte. Beide Modelle reproduzieren erfolgreich die von COSMIC beobachteten halbjährlichen Schwankungen. Die Analyse der 27-tägigen Schwankungen des CTIPe NmF2 zeigt, dass die mitternächtlichen NMF2-Abweichungen stärker sind als diejenigen am Mittag. Außerdem sind bei geringer Sonnenaktivität die 27-Tage-Abweichungen von NmF2 in der Südhemisphäre größer, während bei hoher Sonnenaktivität die 27-Tage-Abweichungen von NmF2 am Äquator und in der Nordhemisphäre größer sind. Die ionosphärische Verzögerung während geringer und hoher Sonnenaktivität wurde für die 27-tägige Sonnenrotation mit CTIPe simuliert. Bei geringer (hoher) Sonnenaktivität wird eine ionosphärische Verzögerung von etwa 12 (34) Stunden beobachtet, was auf eine zunehmende ionosphärische Verzögerung mit zunehmender Sonnenaktivität hinweist

Using force covariance to derive effective stochastic interactions in dissipative particle dynamics

There exist methods for determining effective conservative interactions in coarse grained particle based mesoscopic simulations. The resulting models can be used to capture thermal equilibrium behavior, but in the model system we study do not correctly represent transport properties. In this article we suggest the use of force covariance to determine the full functional form of dissipative and stochastic interactions. We show that a combination of the radial distribution function and a force covariance function can be used to determine all interactions in dissipative particle dynamics. Furthermore we use the method to test if the effective interactions in dissipative particle dynamics (DPD) can be adjusted to produce a force covariance consistent with a projection of a microscopic Lennard-Jones simulation. The results indicate that the DPD ansatz may not be consistent with the underlying microscopic dynamics. We discuss how this result relates to theoretical studies reported in the literature.Comment: 10 pages, 10 figure

A characterization of Dirac morphisms

Relating the Dirac operators on the total space and on the base manifold of a horizontally conformal submersion, we characterize Dirac morphisms, i.e. maps which pull back (local) harmonic spinor fields onto (local) harmonic spinor fields.Comment: 18 pages; restricted to the even-dimensional cas

General relativistic gravitational field of a rigidly rotating disk of dust: Solution in terms of ultraelliptic functions

In a recent paper we presented analytic expressions for the axis potential, the disk metric, and the surface mass density of the global solution to Einstein's field equations describing a rigidly rotating disk of dust. Here we add the complete solution in terms of ultraelliptic functions and quadratures.Comment: 5 pages, published in 1995 [Phys. Rev. Lett. 75 (1995) 3046

Hypercube matrix computation task

A major objective of the Hypercube Matrix Computation effort at the Jet Propulsion Laboratory (JPL) is to investigate the applicability of a parallel computing architecture to the solution of large-scale electromagnetic scattering problems. Three scattering analysis codes are being implemented and assessed on a JPL/California Institute of Technology (Caltech) Mark 3 Hypercube. The codes, which utilize different underlying algorithms, give a means of evaluating the general applicability of this parallel architecture. The three analysis codes being implemented are a frequency domain method of moments code, a time domain finite difference code, and a frequency domain finite elements code. These analysis capabilities are being integrated into an electromagnetics interactive analysis workstation which can serve as a design tool for the construction of antennas and other radiating or scattering structures. The first two years of work on the Hypercube Matrix Computation effort is summarized. It includes both new developments and results as well as work previously reported in the Hypercube Matrix Computation Task: Final Report for 1986 to 1987 (JPL Publication 87-18)