Space-time extensions II

The global extendibility of smooth causal geodesically incomplete spacetimes is investigated. Denote by $\gamma$ one of the incomplete non-extendible causal geodesics of a causal geodesically incomplete spacetime $(M,g_{ab})$. First, it is shown that it is always possible to select a synchronised family of causal geodesics $\Gamma$ and an open neighbourhood $\mathcal{U}$ of a final segment of $\gamma$ in $M$ such that $\mathcal{U}$ is comprised by members of $\Gamma$, and suitable local coordinates can be defined everywhere on $\mathcal{U}$ provided that $\gamma$ does not terminate either on a tidal force tensor singularity or on a topological singularity. It is also shown that if, in addition, the spacetime, $(M,g_{ab})$, is globally hyperbolic, and the components of the curvature tensor, and its covariant derivatives up to order $k-1$ are bounded on $\mathcal{U}$, and also the line integrals of the components of the $k^{th}$-order covariant derivatives are finite along the members of $\Gamma$---where all the components are meant to be registered with respect to a synchronised frame field on $\mathcal{U}$---then there exists a $C^{k-}$ extension $\Phi: (M,g_{ab}) \rightarrow (\widehat{M},\widehat{g}_{ab})$ so that for each $\bar\gamma\in\Gamma$, which is inextendible in $(M,g_{ab})$, the image, $\Phi\circ\bar\gamma$, is extendible in $(\widehat{M},\widehat{g}_{ab})$. Finally, it is also proved that whenever $\gamma$ does terminate on a topological singularity $(M,g_{ab})$ cannot be generic.Comment: 42 pages, no figures, small changes to match the published versio

\u3ci\u3eSteganoderma\u3c/i\u3e Stafford, 1904 (Digenea: Zoogonidae: Lepidophyllinae) from Two Species of Rockfishes from Deep Waters off Oregon Including a New Species and an Updated Key to Species of This Genus

Steganoderma eamiqtrema n. sp. and a single unidentified specimen of Steganoderma Stafford, 1904 (Zoogonidae: Lepidophyllinae) obtained from the intestine of the greenstriped rockfish, Sebastes elongatus Ayres, 1859, and the flag rockfish, Sebastes rubrivinctus (Jordan and Gilbert, 1880) (Scorpaeniformes: Sebastidae), collected from 190–200 m depths off Oregon, USA, are described. The new species is distinguished from its seven other congeners by a diagnostic combination of morphological features including an elongate oval to spindle-shaped body, a clavate to comma-shaped cirrus pouch located in the forebody and hindbody, a bipartite seminal vesicle, a bifurcal or just post-bifurcal genital pore, a larger ventral than oral sucker, and a smooth testes and ovary with a relatively small distance between them. We present an updated key to the eight species now in Steganoderma and provide a list of parasites known from Se. elongatus and Se. rubrivinctus. The discovery of S. eamiqtrema in Se. elongatus represents the second species of zoogonid known from this host, and the finding of Steganoderma sp. in Se. rubrivinctus represents the first report of a digenean from this host species. A detailed discussion also is given of the type species, S. formosum Stafford, 1904, and questions are raised as to whether this species has a worldwide distribution and infects such a wide variety of fish hosts. We present evidence including variation we observed in redescriptions of the type species, query the implausible idea that there could be gene flow between conspecific helminths geographically separated in the North Atlantic and North Pacific Oceans over such a vast geological period, and offer the possibility that some prior reports of S. formosum may, indeed, be S. eamiqtrema; all of which suggests S. formosum sensu lato may be part of a species complex and not the same worldwide species. Steganoderma is represented in the deep sea by S. eamiqtrema, S. formosum, and Steganoderma sp., and limited speculation is given as to the host specificity of this genus and life history strategies of the new species in deeper waters. Finally, molecular studies of species of Steganoderma are sorely needed (i.e., there is no DNA sequence data currently available in GenBank for any species of this genus), and we suspect that with further molecular, morphological, and life history work, this genus will be taxonomically divided up

Dynamic Scaling of Width Distribution in Edwards--Wilkinson Type Models of Interface Dynamics

Edwards--Wilkinson type models are studied in 1+1 dimensions and the time-dependent distribution, P_L(w^2,t), of the square of the width of an interface, w^2, is calculated for systems of size L. We find that, using a flat interface as an initial condition, P_L(w^2,t) can be calculated exactly and it obeys scaling in the form _\infty P_L(w^2,t) = Phi(w^2 / _\infty, t/L^2) where _\infty is the stationary value of w^2. For more complicated initial states, scaling is observed only in the large- time limit and the scaling function depends on the initial amplitude of the longest wavelength mode. The short-time limit is also interesting since P_L(w^2,t) is found to closely approximate the log-normal distribution. These results are confirmed by Monte Carlo simulations on a `roof-top' model of surface evolution.Comment: 5 pages, latex, 3 ps figures in a separate files, submitted to Phys.Rev.

Formation of Liesegang patterns: Simulations using a kinetic Ising model

A kinetic Ising model description of Liesegang phenomena is studied using Monte Carlo simulations. The model takes into account thermal fluctuations, contains noise in the chemical reactions, and its control parameters are experimentally accessible. We find that noisy, irregular precipitation takes place in dimension d=2 while, depending on the values of the control parameters, either irregular patterns or precipitation bands satisfying the regular spacing law emerge in d=3.Comment: 7 pages, 8 ps figures, RevTe

What does a strongly excited 't Hooft-Polyakov magnetic monopole do?

The time evolution of strongly exited SU(2) Bogomolny-Prasad-Sommerfield (BPS) magnetic monopoles in Minkowski spacetime is investigated by means of numerical simulations based on the technique of conformal compactification and on the use of hyperboloidal initial value problem. It is found that an initially static monopole does not radiate the entire energy of the exciting pulse toward future null infinity. Rather, a long-lasting quasi-stable `breathing state' develops in the central region and certain expanding shell structures -- built up by very high frequency oscillations -- are formed in the far away region.Comment: 4 pages, 6 figure

Reaction-diffusion fronts with inhomogeneous initial conditions

Properties of reaction zones resulting from A+B -> C type reaction-diffusion processes are investigated by analytical and numerical methods. The reagents A and B are separated initially and, in addition, there is an initial macroscopic inhomogeneity in the distribution of the B species. For simple two-dimensional geometries, exact analytical results are presented for the time-evolution of the geometric shape of the front. We also show using cellular automata simulations that the fluctuations can be neglected both in the shape and in the width of the front.Comment: 11 pages, 3 figures, submitted to J. Phys.