Characteristics of Extreme Auroral Charging Events

The highest level spacecraft charging observed in low Earth orbit (LEO) occurs when spacecraft are exposed to energetic auroral electrons. Since auroral charging has been identified as a mechanism responsible for on-orbit anomalies and even possible satellite failures it is important to consider extreme auroral charging events as design and test environments for spacecraft to be used in high inclination LEO orbits. This paper will report on studies of extreme auroral charging events using data from the SSJ/4 and SSJ/5 precipitating electron and ion sensors on the Defense Meteorology Satellite Program (DMSP) satellites. Early studies of DMSP charging to negative potentials 100 V focused on statistics of the electron environment responsible for charging. Later statistical studies of auroral charging have generally focused on solar cycle dependence of charging behavior and magnitude of the maximum potential and duration of the charging events. We extend these studies to focus on more detailed investigations of extreme charging event characteristics that are required to evaluate potential threats to spacecraft systems. A collection of example auroral charging events is assembled from the DMSP data set using the criteria that "extreme auroral charging" is defined as periods with spacecraft negative potentials 400 V. Specific characteristics to be treated include (but are not limited to) maximum and mean potentials, time history of spacecraft potentials through the events, total charging duration and the time potentials exceed voltage thresholds, frame charging/discharging rates, and information on geographic and geomagnetic latitudes at which the events are observed. Finally, we will comment on the implications of these studies for potential auroral charging risks to the International Space Station

Numeric and symbolic evaluation of the pfaffian of general skew-symmetric matrices

Evaluation of pfaffians arises in a number of physics applications, and for some of them a direct method is preferable to using the determinantal formula. We discuss two methods for the numerical evaluation of pfaffians. The first is tridiagonalization based on Householder transformations. The main advantage of this method is its numerical stability that makes unnecessary the implementation of a pivoting strategy. The second method considered is based on Aitken's block diagonalization formula. It yields to a kind of LU (similar to Cholesky's factorization) decomposition (under congruence) of arbitrary skew-symmetric matrices that is well suited both for the numeric and symbolic evaluations of the pfaffian. Fortran subroutines (FORTRAN 77 and 90) implementing both methods are given. We also provide simple implementations in Python and Mathematica for purpose of testing, or for exploratory studies of methods that make use of pfaffians.Comment: 13 pages, Download links: http://gamma.ft.uam.es/robledo/Downloads.html and http://www.phys.washington.edu/users/bertsch/computer.htm

Microscopic Description of Band Structure at Very Extended Shapes in the A ~ 110 Mass Region

Recent experiments have confirmed the existence of rotational bands in the A \~ 110 mass region with very extended shapes lying between super- and hyper-deformation. Using the projected shell model, we make a first attempt to describe quantitatively such a band structure in 108Cd. Excellent agreement is achieved in the dynamic moment of inertia J(2) calculation. This allows us to suggest the spin values for the energy levels, which are experimentally unknown. It is found that at this large deformation, the sharply down-sloping orbitals in the proton i_{13/2} subshell are responsible for the irregularity in the experimental J(2), and the wave functions of the observed states have a dominant component of two-quasiparticles from these orbitals. Measurement of transition quadrupole moments and g-factors will test these findings, and thus can provide a deeper understanding of the band structure at very extended shapes.Comment: 4 pages, 3 eps figures, final version accepted by Phys. Rev. C as a Rapid Communicatio

Stochastic Models on a Ring and Quadratic Algebras. The Three Species Diffusion Problem

The stationary state of a stochastic process on a ring can be expressed using traces of monomials of an associative algebra defined by quadratic relations. If one considers only exclusion processes one can restrict the type of algebras and obtain recurrence relations for the traces. This is possible only if the rates satisfy certain compatibility conditions. These conditions are derived and the recurrence relations solved giving representations of the algebras.Comment: 12 pages, LaTeX, Sec. 3 extended, submitted to J.Phys.

Spectral structure and decompositions of optical states, and their applications

We discuss the spectral structure and decomposition of multi-photon states. Ordinarily `multi-photon states' and `Fock states' are regarded as synonymous. However, when the spectral degrees of freedom are included this is not the case, and the class of `multi-photon' states is much broader than the class of `Fock' states. We discuss the criteria for a state to be considered a Fock state. We then address the decomposition of general multi-photon states into bases of orthogonal eigenmodes, building on existing multi-mode theory, and introduce an occupation number representation that provides an elegant description of such states that in many situations simplifies calculations. Finally we apply this technique to several example situations, which are highly relevant for state of the art experiments. These include Hong-Ou-Mandel interference, spectral filtering, finite bandwidth photo-detection, homodyne detection and the conditional preparation of Schr\"odinger Kitten and Fock states. Our techniques allow for very simple descriptions of each of these examples.Comment: 12 page

Shock Profiles for the Asymmetric Simple Exclusion Process in One Dimension

The asymmetric simple exclusion process (ASEP) on a one-dimensional lattice is a system of particles which jump at rates $p$ and $1-p$ (here $p>1/2$) to adjacent empty sites on their right and left respectively. The system is described on suitable macroscopic spatial and temporal scales by the inviscid Burgers' equation; the latter has shock solutions with a discontinuous jump from left density $\rho_-$ to right density $\rho_+$, $\rho_-<\rho_+$, which travel with velocity $(2p-1)(1-\rho_+-\rho_-)$. In the microscopic system we may track the shock position by introducing a second class particle, which is attracted to and travels with the shock. In this paper we obtain the time invariant measure for this shock solution in the ASEP, as seen from such a particle. The mean density at lattice site $n$, measured from this particle, approaches $\rho_{\pm}$ at an exponential rate as $n\to\pm\infty$, with a characteristic length which becomes independent of $p$ when $p/(1-p)>\sqrt{\rho_+(1-\rho_-)/\rho_-(1-\rho_+)}$. For a special value of the asymmetry, given by $p/(1-p)=\rho_+(1-\rho_-)/\rho_-(1-\rho_+)$, the measure is Bernoulli, with density $\rho_-$ on the left and $\rho_+$ on the right. In the weakly asymmetric limit, $2p-1\to0$, the microscopic width of the shock diverges as $(2p-1)^{-1}$. The stationary measure is then essentially a superposition of Bernoulli measures, corresponding to a convolution of a density profile described by the viscous Burgers equation with a well-defined distribution for the location of the second class particle.Comment: 34 pages, LaTeX, 2 figures are included in the LaTeX file. Email: [email protected], [email protected], [email protected]

Extremal-point Densities of Interface Fluctuations

We introduce and investigate the stochastic dynamics of the density of local extrema (minima and maxima) of non-equilibrium surface fluctuations. We give a number of exact, analytic results for interface fluctuations described by linear Langevin equations, and for on-lattice, solid-on-solid surface growth models. We show that in spite of the non-universal character of the quantities studied, their behavior against the variation of the microscopic length scales can present generic features, characteristic to the macroscopic observables of the system. The quantities investigated here present us with tools that give an entirely un-orthodox approach to the dynamics of surface morphologies: a statistical analysis from the short wavelength end of the Fourier decomposition spectrum. In addition to surface growth applications, our results can be used to solve the asymptotic scalability problem of massively parallel algorithms for discrete event simulations, which are extensively used in Monte-Carlo type simulations on parallel architectures.Comment: 30 pages, 5 ps figure

Local Density Approximation for proton-neutron pairing correlations. I. Formalism

In the present study we generalize the self-consistent Hartree-Fock-Bogoliubov (HFB) theory formulated in the coordinate space to the case which incorporates an arbitrary mixing between protons and neutrons in the particle-hole (p-h) and particle-particle (p-p or pairing) channels. We define the HFB density matrices, discuss their spin-isospin structure, and construct the most general energy density functional that is quadratic in local densities. The consequences of the local gauge invariance are discussed and the particular case of the Skyrme energy density functional is studied. By varying the total energy with respect to the density matrices the self-consistent one-body HFB Hamiltonian is obtained and the structure of the resulting mean fields is shown. The consequences of the time-reversal symmetry, charge invariance, and proton-neutron symmetry are summarized. The complete list of expressions required to calculate total energy is presented.Comment: 22 RevTeX page

Statistical Theory for the Kardar-Parisi-Zhang Equation in 1+1 Dimension

The Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimension dynamically develops sharply connected valley structures within which the height derivative {\it is not} continuous. There are two different regimes before and after creation of the sharp valleys. We develop a statistical theory for the KPZ equation in 1+1 dimension driven with a random forcing which is white in time and Gaussian correlated in space. A master equation is derived for the joint probability density function of height difference and height gradient $P(h-\bar h,\partial_{x}h,t)$ when the forcing correlation length is much smaller than the system size and much bigger than the typical sharp valley width. In the time scales before the creation of the sharp valleys we find the exact generating function of $h-\bar h$ and $\partial_x h$. Then we express the time scale when the sharp valleys develop, in terms of the forcing characteristics. In the stationary state, when the sharp valleys are fully developed, finite size corrections to the scaling laws of the structure functions $<(h-\bar h)^n (\partial_x h)^m>$ are also obtained.Comment: 50 Pages, 5 figure