36,082 research outputs found

### Lavrentiev Phenomenon in Microstructure Theory

A variational problem arising as a model in martensitic phase transformation
including surface energy is studied. It explains the complex,
multi-dimensional pattern of twin branching which is often observed in a
martensitic phase near the austenite interface.
We prove that a Lavrentiev phenomenon can occur
if the domain is a rectangle. We show that this phenomenon
disappears under arbitrarily small shears
of the domain. We also prove that other perturbations of the problem lead to
an extinction of the Lavrentiev phenomenon

### The Complex X-ray Spectrum of the Sefyert 1.5 Source NGC 6860

The X-ray spectrum of the Seyfert 1.5 source NGC 6860 is among the most
complex of the sources detected in the Swift Burst Alert Telescope all-sky
survey. A short XMM-Newton follow-up observation of the source revealed a flat
spectrum both above and below 2 keV. To uncover the complexity of the source,
in this paper we analyze both a 40 ks Suzaku and a 100 ks XMM-Newton
observation of NGC 6860. While the spectral state of the source changed between
the newer observations presented here and the earlier short XMM-Newton spectrum
- showing a higher flux and steeper power law component - the spectrum of NGC
6860 is still complex with clearly detected warm absorption signatures. We find
that a two component warm ionized absorber is present in the soft spectrum,
with column densities of about 10^20 and 10^21 cm$^-2, ionization parameters of
xi = 180 and 45 ergs cm s^-1, and outflow velocities for each component in the
range of 0-300 km s^-1. Additionally, in the hard spectrum we find a broad
(approx 11000 km s^-1) Fe K-alpha emission line, redshifted by approx 2800 km
s^-1.Comment: 35 pages, 9 figures, Accepted to Ap

### Uncovering Local Absorbed Active Galactic Nuclei with Swift and Suzaku

Detection of absorbed active galactic nuclei and their properties remains an
elusive and important problem in understanding the evolution and activation of
black holes. With the very hard X-ray survey conducted by Swift's Burst Alert
Telescope - the first all-sky survey in 30 years - we are beginning to uncover
the characteristics of obscured AGN. The synergy between Suzaku and Swift has
been crucial in pinning down the X-ray properties of newly detected heavily
obscured but bright hard X-ray sources. We review the X-ray and optical
spectroscopic properties of obscured AGN in the local Universe, as detected in
the Swift survey. We discuss the relative distribution of absorbed/unabsorbed
sources, including "hidden" and Compton thick AGN populations. Among the
results from the survey, we find that absorbed AGN are less luminous than
unabsorbed sources. Optical spectra reveal that sources with emission line
ratios indicative of LINERs/H II galaxies/composites are the least luminous
objects in the sample, while optical absorbed and unabsorbed Seyferts have the
same luminosity distributions. Thus, the least luminous sources are likely
accreting in a different mode than the Seyferts.Comment: 8 pages, 5 figures, To appear in the conference proceedings for
"Exploring the X-ray Universe: Suzaku and Beyond", the July 2011 Suzaku
Science Conferenc

Recommended from our members

### Symmetric and Asymmetric Multiple Clusters In a Reaction-Diffusion System

We consider the Gierer-Meinhardt system in
the interval (-1,1) with Neumann boundary
conditions for small diffusion constant
of the activator and finite diffusion
constant of the inhibitor.
A cluster is a combination of several spikes
concentrating at the same point.
In this paper, we rigorously show the existence
of symmetric and asymmetric multiple clusters.
This result is new for systems and seems not
to occur for single equations.
We reduce the problem to the computation of two
matrices which depend on the coefficient of
the inhibitor as well as the number of different clusters and the number of spikes within each
cluster

Recommended from our members

### On the stationary Cahn-Hilliard equation: Interior spike solutions

We study solutions of the stationary Cahn-Hilliard equation in a bounded smooth domain which have a spike in the interior. We show that a large class of interior points (the "nondegenerate peak" points) have the following property: there exist such solutions whose spike lies close to a given nondegenerate peak point. Our construction uses among others the methods of viscosity solution, weak convergence of measures and Liapunov-Schmidt reduction

Recommended from our members

### Existence, classification and stability analysis of multiple-peaked solutions for the gierer-meinhardt system in R^1

We consider the Gierer-Meinhardt system in R^1.
where the exponents (p, q, r, s) satisfy
1< \frac{ qr}{(s+1)( p-1)} < \infty, 1 <p < +\infty,
and where \ep<<1, 0<D<\infty, \tau\geq 0,
D and \tau are constants which are independent of \ep.
We give a rigorous and unified approach to show that the existence and stability of N-peaked steady-states can be reduced to computing two
matrices in terms of the coefficients D, N, p, q, r, s. Moreover, it is shown that N-peaked steady-states are generated by exactly two types of peaks, provided their mutual distance is bounded away from zero

### Symmetry of Nodal Solutions for Singularly Perturbed Elliptic Problems on a Ball

In [40], it was shown that the following singularly perturbed Dirichlet problem
\ep^2 \Delta u - u+ |u|^{p-1} u=0, \ \mbox{in} \ \Om,\]
\[ u=0 \ \mbox{on} \ \partial \Om
has a nodal solution u_\ep which has the least energy among all nodal solutions. Moreover, it is shown that u_\ep has exactly one local maximum point P_1^\ep with a positive value
and one local minimum point P_2^\ep with a negative value and, as \ep \to 0,
\varphi (P_1^\ep, P_2^\ep) \to \max_{ (P_1, P_2) \in \Om \times \Om } \varphi (P_1, P_2),
where \varphi (P_1, P_2)= \min (\frac{|P_1-P_2}{2}, d(P_1, \partial \Om), d(P_2, \partial \Om)). The following question naturally arises: where is the {\bf nodal surface} \{ u_\ep (x)=0 \}? In this paper, we give an answer in the case of the unit ball \Om=B_1 (0).
In particular, we show that for \epsilon sufficiently small, P_1^\ep, P_2^\ep and the origin must lie on a line. Without loss of generality, we may assume that this line is the x_1-axis.
Then u_\ep must be even in x_j, j=2, ..., N, and odd in x_1.
As a consequence, we show that \{ u_\ep (x)=0 \} = \{ x \in B_1 (0) | x_1=0 \}. Our proof
is divided into two steps:
first, by using the method of moving planes, we show that P_1^\ep, P_2^\ep and the origin must lie on the x_1-axis and u_\ep must be even in x_j, j=2, ..., N. Then,
using the Liapunov-Schmidt reduction method, we prove
the uniqueness of u_\ep (which implies the odd symmetry of u_\ep in x_1). Similar results are also proved for the problem with Neumann boundary conditions

Recommended from our members

### Existence and stability of multiple spot solutions for the gray-scott model in R^2

We study the Gray-Scott model in a bounded two dimensional domain and establish the existence and stability of {\bf symmetric} and {\bf asymmetric} multiple spotty patterns. The Green's function and its derivatives
together with two nonlocal eigenvalue problems
both play a major role in the analysis.
For symmetric spots, we establish a threshold behavior for stability:
If a certain inequality for the parameters holds
then we get stability, otherwise we get instability of multiple spot solutions.
For asymmetric spots, we show that they can be stable within a narrow parameter range

### Young measures in a nonlocal phase transition problem

A nonlocal variational problem modelling phase transitions is studied
in the framework of Young measures. The existence of global minimisers
among functions
with internal layers on an infinite tube is proved by combining
a weak convergence result for Young measures and the principle of
concentration-compactness. The regularity of such global minimisers is
discussed, and the nonlocal variational problem is also considered on
asymptotic tubes

### Multi-interior-spike solutions for the Cahn-Hilliard equation with arbitrarily many peaks

We study the Cahn-Hilliard equation in a bounded smooth
domain without any symmetry
assumptions. We prove that for any fixed positive integer K there
exist interior $K$--spike solutions
whose peaks have maximal possible distance from the boundary and
from one another. This implies that for any bounded and smooth
domain there
exist interior K-peak solutions.
The central ingredient of our analysis is the novel derivation
and exploitation of a reduction of the energy to finite dimensions
(Lemma 5.5) with variables which are closely related to the location of
the peaks.
We do not assume nondegeneracy of the points of
maximal distance to the boundary but can do with a global condition instead
which in many cases is weaker

- ā¦