Asymptotic analysis of a system of algebraic equations arising in dislocation theory

The system of algebraic equations given by\ud \ud $\sum_{j=0, j \neq i}^n sgn(x_i - x_j) / |x_i - x_j|^a = 1, i = 1, 2, \ldots n, x_0 = 0,$\ud \ud appears in dislocation theory in models of dislocation pile-ups. Specifically, the case a = 1 corresponds to the simple situation where n dislocations are piled up against a locked dislocation, while the case a = 3 corresponds to n dislocation dipoles piled up against a locked dipole.\ud \ud We present a general analysis of systems of this type for a > 0 and n large. In the asymptotic limit n -> ∞, it becomes possible to replace the system of discrete equations with a continuum equation for the particle density. For 0 < a < 2, this takes the form of a singular integral equation, while for a > 2 it is a first-order differential equation. The critical case a = 2 requires special treatment but, up to corrections of logarithmic order, it also leads to a differential equation.\ud \ud The continuum approximation is only valid for i not too small nor too close to n. The boundary layers at either end of the pile-up are also analyzed, which requires matching between discrete and continuum approximations to the main problem

An analysis of the Mariner 4 photography of Mars

Crater analysis of Mariner 4 photography of Mar

AE, D ST and their SuperMAG Counterparts : the effect of improved spatial resolution in geomagnetic indices

For decades, geomagnetic indices have been used extensively to parameterize space weather events, as input to various models and as space weather specifications. The auroral electrojet (AE) index and disturbance storm time index (DST) are two such indices that span multiple solar cycles and have been widely studied. The production of improved spatial coverage analogs to AE and DST is now possible using the SuperMAG collaboration of ground‐based magnetometers. SME is an electrojet index that shares methodology with AE. SMR is a ring current index that shares methodology with DST. As the number of magnetometer stations in the SuperMAG network increases over time, so does the spatial resolution of SME and SMR. Our statistical comparison between the established indices and their new SuperMAG counterparts finds that, for large excursions in geomagnetic activity, AE systematically underestimates SME for later cycles. The difference between distributions of recorded AE and SME values for a single solar maximum can be of the same order as changes in activity seen from one solar cycle to the next. We demonstrate that DST and SMR track each other but are subject to an approximate linear shift as a result of the procedure used to map stations to the magnetic equator. We explain the observed differences between AE and SME with the assistance of a simple model, based on the construction methodology of the electrojet indices. We show that in the case of AE and SME, it is not possible to simply translate between the two indices

Analysis of Brownian Dynamics Simulations of Reversible Bimolecular Reactions

A class of Brownian dynamics algorithms for stochastic reaction-diffusion models which include reversible bimolecular reactions is presented and analyzed. The method is a generalization of the $\lambda$--\newrho model for irreversible bimolecular reactions which was introduced in [arXiv:0903.1298]. The formulae relating the experimentally measurable quantities (reaction rate constants and diffusion constants) with the algorithm parameters are derived. The probability of geminate recombination is also investigated.Comment: 16 pages, 13 figures, submitted to SIAM Appl Mat

Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity

The bifurcation of asymmetric superconducting solutions from the normal solution is considered for the one-dimensional Ginzburg--Landau equations by the methods of formal asymptotics. The behavior of the bifurcating branch depends on the parameters d, the size of the superconducting slab, and $\kappa$, the Ginzburg--Landau parameter. The secondary bifurcation in which the asymmetric solution branches reconnect with the symmetric solution branch is studied for values of $(\kappa,d)$ for which it is close to the primary bifurcation from the normal state. These values of $(\kappa,d)$ form a curve in the $\kappa d$-plane, which is determined. At one point on this curve, called the quintuple point, the primary bifurcations switch from being subcritical to supercritical, requiring a separate analysis. The results answer some of the conjectures of [A. Aftalion and W. C. Troy, Phys. D, 132 (1999), pp. 214--232]

Analysis of Brownian dynamics simulations of reversible biomolecular reactions

A class of Brownian dynamics algorithms for stochastic reaction-diffusion models which include reversible bimolecular reactions is presented and analyzed. The method is a generalization of the λ-rho model for irreversible bimolecular reactions which was introduced in [11]. The formulae relating the experimentally measurable quantities (reaction rate constants and diffusion constants) with the algorithm parameters are derived. The probability of geminate recombination is also investigated

Report of the Terrestrial Bodies Science Working Group. Volume 8: The comets

The determination of the nuclear and atmospheric properties of comets, and the interaction of the solar wind with the comet tail are scientific objectives for a mission to one or more comets in the next decade. Recommended priorities for direct cometary exploration are listed