68,321 research outputs found
Diverse Temporal Properties of GRB Afterglow
The detection of delayed X-ray, optical and radio emission, "afterglow",
associated with -ray bursts (GRBs) is consistent with fireball models,
where the emission are produced by relativistic expanding blast wave, driven by
expanding fireball at cosmogical distances. The emission mechanisms of GRB
afterglow have been discussed by many authors and synchrotron radiation is
believed to be the main mechanism. The observations show that the optical light
curves of two observed gamma-ray bursts, GRB970228 and GRB GRB970508, can be
described by a simple power law, which seems to support the synchrotron
radiation explanation. However, here we shall show that under some
circumstances, the inverse Compton scattering (ICS) may play an important role
in emission spectrum and this may influence the temporal properties of GRB
afterglow. We expect that the light curves of GRB afterglow may consist of
multi-components, which depends on the fireball parameters.Comment: Latex, no figures, minor correctio
A framework for modelling kinematic measurements in gravity field applications
To assess the resolution of the local gravity field from kinematic measurements, a state model for motion in the gravity field of the earth is formulated. The resulting set of equations can accommodate gravity gradients, specific force, acceleration, velocity and position as input data and can take into account approximation errors as well as sensor errors
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A Higher-Order Energy Expansion to Two-Dimensional Singularly Neumann Problems
Of concern is the
following singularly perturbed semilinear elliptic problem
\begin{equation*}
\left\{ \begin{array}{c}
\mbox{ in }\\
\mbox{ in and on },
\end{array}
\right.
\end{equation*}
where is a bounded domain in with smooth
boundary , is a small constant and
. Associated with the
above problem is the energy functional defined by
\begin{equation*}
J_{\epsilon}[u]:=\int_{\Omega}\left(\frac{\epsilon^2}{2}{|\nabla
u|}^2 +\frac{1}{2}u^2 -F(u)\right)dx
\end{equation*}
for , where .
Ni and Takagi (\cite{nt1}, \cite{nt2}) proved that for a single
boundary spike solution , the following asymptotic
expansion holds:
\begin{equation*}
(1) \ \ \ \ \ \ \ \ J_{\epsilon}[u_{\epsilon}]=\epsilon^{N}
\left[\frac{1}{2}I[w]-c_1 \epsilon
H(P_{\epsilon})+o(\epsilon)\right],
\end{equation*}
where is the energy of the ground state, is a
generic constant, is the unique local maximum point
of and is the boundary mean
curvature function at . Later,
Wei and Winter (\cite{ww3}, \cite{ww4}) improved the result and
obtained a higher-order expansion of :
\begin{equation*}
(2) \ \ \ \ \ \ J_{\epsilon}[u_{\epsilon}]=\epsilon^{N}
\left[\frac{1}{2}I[\omega]-c_{1} \epsilon
H(P_{\epsilon})+\epsilon^2 [c_2(H(P_\epsilon))^2 +c_{3}
R(P_\epsilon)]+o(\epsilon^2)\right],
\end{equation*}
where and are generic constants and
is the scalar curvature at . However, if , the
scalar curvature is always zero. The expansion (2) is no longer sufficient to distinguish spike locations with same mean curvature.
In this paper, we consider
this case and assume that . Without loss of generality, we may assume that the
boundary near P\in\partial\Om is represented by the graph . Then we have the following higher order expansion of
\begin{equation*}
(3) \ \ \ \ \ J_\epsilon [u_\epsilon]
=\epsilon^N \left[\frac{1}{2}I[w]-c_1
\epsilon H({P_\epsilon})+c_2 \epsilon^2(H({P_\epsilon}))^2 ]
+\epsilon^3
[P(H({P_\epsilon}))+c_3S({P_\epsilon})]+o(\epsilon^3)\right],
\end{equation*}
where H(P_\ep)= \rho_{P_\ep}^{''} (0) is the curvature, is a polynomial,
, , and , , are generic real
constants and S(P_\epsilon)= \rho_{P_\ep}^{(4)} (0). In
particular . Some applications of this expansion are given
Performance Analysis of a Dual-Hop Cooperative Relay Network with Co-Channel Interference
This paper analyzes the performance of a dual-hop amplify-and-forward (AF) cooperative relay network in the presence of direct link between the source and destination and multiple co-channel interferences (CCIs) at the relay. Specifically, we derive the new analytical expressions for the moment generating function (MGF) of the output signal-to-interference-plus-noise ratio (SINR) and the average symbol error rate (ASER) of the relay network. Computer simulations are given to confirm the validity of the analytical results and show the effects of direct link and interference on the considered AF relay network
Is GRO J1744-28 a Strange Star?
The unusal hard x-ray burster GRO J1744-28 recently discovered by the Compton
Gamma-ray Observatory (GRO) can be modeled as a strange star with a dipolar
magnetic field Gauss. When the accreted mass of the star exceeds
some critical mass, its crust may break, resulting in conversion of the
accreted matter into strange matter and release of energy. Subsequently, a
fireball may form and expand relativistically outward. The expanding fireball
may interact with the surrounding interstellar medium, causing its kinetic
energy to be radiated in shock waves, producing a burst of x-ray radiation. The
burst energy, duration, interval and spectrum derived from such a model are
consistent with the observations of GRO J1744-28.Comment: Latex, has been published in SCIENCE, Vol. 280, 40
The topological glass in ring polymers
We study the dynamics of concentrated, long, semi-flexible, unknotted and unlinked ring polymers embedded in a gel by Monte Carlo simulation of a coarse-grained model. This involves the ansatz that the rings compactify into a duplex structure where they can be modelled as linear polymers. The classical polymer glass transition involves a rapid loss of microscopic freedom within the polymer molecule as the temperature is reduced toward Tg. Here we are interested in temperatures well above Tg where the polymers retain high microscopic mobility. We analyse the slowing of stress relaxation originating from inter-ring penetrations (threadings). For long polymers an extended network of quasi-topological penetrations forms. The longest relaxation time appears to depend exponentially on the ring polymer contour length, reminiscent of the usual exponential slowing (e.g., with temperature) in classical glasses. Finally, we discuss how this represents a universality class for glassy dynamics
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