Heat content and inradius for regions with a Brownian boundary

In this paper we consider $\beta[0; s]$, Brownian motion of time length $s > 0$, in $m$-dimensional Euclidean space $\mathbb R^m$ and on the $m$-dimensional torus $\mathbb T^m$. We compute the expectation of (i) the heat content at time $t$ of $\mathbb R^m\setminus \beta[0; s]$ for fixed $s$ and $m = 2,3$ in the limit $t \downarrow 0$, when $\beta[0; s]$ is kept at temperature 1 for all $t > 0$ and $\mathbb R^m\setminus \beta[0; s]$ has initial temperature 0, and (ii) the inradius of $\mathbb R^m\setminus \beta[0; s]$ for $m = 2,3,\cdots$ in the limit $s \rightarrow \infty$.Comment: 13 page

New and known Criconematoidea (Nemata) form forests in South African with a redescription of Mesocriconema teres (Raski, 1952) Loof & De Grisse, 1989

Les femelles de #Mesocriconema neli sp. n. sont caractérisées par : 95 à 113 anneaux retorses, lisses ; deux anneaux labiaux ; présence de plaques labiales, de quatre lobes submédians et de quatre lobes supplémentaires ; premier anneau labial indenté ou fendu ; vagin non sigmoïde ; vulve "ouverte" ; stylet long de 65 à 79 um. #Ogma ornatum sp. n. est caractérisé par (femelles) : un seul anneau labial de diamètre supérieur à celui des deux premiers anneaux du corps ; 50 à 52 anneaux retorses ornés chacun de plages comportant des projections contiguës, alternant avec des plages nues, formant ainsi des rangées longitudinales, les projections étant simples ou divisées, plus longues à la partie postérieure du corps et comportant de petites protubérances ; cuticule pourvue de petits tubercules ; les juvéniles montrent un seul anneau labial de même diamètre que le premier anneau du corps, 57 à 66 anneaux retorses comportant huit rangées d'écailles pourvues de filaments foliacés, une cuticule pourvue de tubercules. #Trophotylenchulus obscurus (Colbran, 1961) Cohn & Kaplan, 1983 est signalé et figuré. Des données sont fournies sur #Criconema duplicivestitum (Andrassy, 1963) Luc & Raski, 1985. #Criconemella jessiensis Van den Berg, 1992 est renommé #Mesocriconema jessiense (Van den Berg, 1992) n. comb. #Mesocriconema teres$ (Raski, 1952) Loof & de Grisse, 1989 est redécrit. (Résumé d'auteur

A Simultaneous Optical and X-ray Variability Study of the Orion Nebula Cluster. II. A Common Origin in Magnetic Activity

We present a statistical analysis of simultaneous optical and X-ray light curves, spanning 600 ks, for 814 pre-main-sequence (PMS) stars in the Orion Nebula Cluster. The aim of this study is to establish the relationship, if any, between the sites of optical and X-ray variability, and thereby to elucidate the origins of X-ray production in PMS stars. In a previous paper we showed that optical and X-ray variability in PMS stars are very rarely time-correlated. Here, using time-averaged variability indicators to examine the joint occurrences of optical and X-ray variability, we confirm that the two forms of variability are not directly causally related. However, a strong and highly statistically significant correlation is found between optical variability and X-ray luminosity. As this correlation is found to be independent of accretion activity, we argue that X-ray production in PMS stars must instead be intimately connected with the presence and strength of optically variable, magnetically active surface regions (i.e. spots) on these stars. Moreover, because X-ray variability and optical variability are rarely time-correlated, we conclude that the sites of X-ray production are not exclusively co-spatial with these regions. We argue that solar-analog coronae, heated by topologically complex fields, can explain these findings.Comment: To appear in the Astrophysical Journal. 33 pages, 3 figure

Sharpness versus robustness of the percolation transition in 2D contact processes

We study versions of the contact process with three states, and with infections occurring at a rate depending on the overall infection density. Motivated by a model described in [17] for vegetation patterns in arid landscapes, we focus on percolation under invariant measures of such processes. We prove that the percolation transition is sharp (for one of our models this requires a reasonable assumption). This is shown to contradict a form of 'robust critical behaviour' with power law cluster size distribution for a range of parameter values, as suggested in [17].Comment: 31 pages, to appear in Stochastic Processes and their Application

Thruster Allocation for Dynamical Positioning

Positioning a vessel at a fixed position in deep water is of great importance when working offshore. In recent years a Dynamical Positioning (DP) system was developed at Marin [2]. After the measurement of the current position and external forces (like waves, wind etc.), each thruster of the vessel is actively controlled to hold the desired location. In this paper we focus on the allocation process to determine the settings for each thruster that results in the minimal total power and thus fuel consumption. The mathematical formulation of this situation leads to a nonlinear optimization problem with equality and inequality constraints, which can be solved by applying Lagrange multipliers. We give three approaches: first of all, the full problem was solved using the MATLAB fmincon routine with the solution from the linearised problem as a starting point. This implementation, with robust handling of the situations where the thrusters are overloaded, lead to promising results: an average reduction in fuel consumption of approximately two percent. However, further analysis proved useful. A second approach changes the set of variables and so reduces the number of equations. The third and last approach solves the Lagrange equations with an iterative method on the linearized Lagrange problem

The strength of countable saturation

We determine the proof-theoretic strength of the principle of countable saturation in the context of the systems for nonstandard arithmetic introduced in our earlier work.Comment: Corrected typos in Lemma 3.4 and the final paragraph of the conclusio

Isospectrality and heat content

We present examples of isospectral operators that do not have the same heat content. Several of these examples are planar polygons that are isospectral for the Laplace operator with Dirichlet boundary conditions. These include examples with infinitely many components. Other planar examples have mixed Dirichlet and Neumann boundary conditions. We also consider Schr\"{o}dinger operators acting in $L^2[0,1]$ with Dirichlet boundary conditions, and show that an abundance of isospectral deformations do not preserve the heat content.Comment: 18 page