10,511 research outputs found
Heat content and inradius for regions with a Brownian boundary
In this paper we consider , Brownian motion of time length , in -dimensional Euclidean space and on the -dimensional
torus . We compute the expectation of (i) the heat content at time
of for fixed and in the
limit , when is kept at temperature 1 for all and has initial temperature 0, and (ii)
the inradius of for in the
limit .Comment: 13 page
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
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 with Dirichlet boundary conditions, and show that an abundance of
isospectral deformations do not preserve the heat content.Comment: 18 page
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
The Approximating Hamiltonian Method for the Imperfect Boson Gas
The pressure for the Imperfect (Mean Field) Boson gas can be derived in
several ways. The aim of the present note is to provide a new method based on
the Approximating Hamiltonian argument which is extremely simple and very
general.Comment: 7 page
Estimates for Dirichlet Eigenfunctions
Estimates for the Dirichlet eigenfunctions near the boundary of an open, bounded set in euclidean space are obtained. It is assumed that the boundary satisfies a uniform capacitary density conditio
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 R^m and on the m-dimensional torus T^m. We compute the expectation of (i) the heat content at time t of R^m \ \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 R^m \ \beta [0, s] has initial temperature 0, and (ii) the inradius of T^m \ \beta [0, s] for m = 2,3,… in the limit s \rightarrow \infty. Key words and phrases. Laplacian, Brownian motion, Wiener sausage, heat content, inradius, spectrum
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