A search for energy-dependence of the Kes 73/1E 1841-045 morphology in GeV

While the Kes 73/1E 1841-045 system had been confirmed as an extended GeV source, whether its morphology depends on the photon energy or not deserves our further investigation. Adopting data collected by Fermi Large Area Telescope (LAT) again, we look into the extensions of this source in three energy bands individually: 0.3-1 GeV, 1-3 GeV and 3-200 GeV. We find that the 0.3-1 GeV morphology is point-like and is quite different from those in the other two bands, although we cannot robustly reject a unified morphology for the whole LAT band.Comment: Approved for publication in PoS as a proceeding of the 7th International Fermi Symposium (IFS2017

Family Control and the Rent-Seeking Society

The small number of very large family-controlled corporate groups in many countries combined with their long continuity of control and ability to act discretely give these organizations a comparative advantage in political rent-seeking. This advantage is a key part of a self-reinforcing system whereby oligarchic family corporate control, political rent seeking, and low general levels of trust combine to stymie growth.http://deepblue.lib.umich.edu/bitstream/2027.42/39971/3/wp585.pd

Fermi Large Area Telescope Observations of the Fast-dimming Crab Nebula in 60-600 MeV

Context: The Crab pulsar and its nebula are the origin of relativistic electrons which can be observed through their synchrotron and inverse Compton emission. The transition between synchrotron-dominated and inverse-Compton-dominated emissions takes place at $\approx 10^9$ eV. Aims: The short-term (weeks to months) flux variability of the synchrotron emission from the most energetic electrons is investigated with data from ten years of observations with the Fermi Large Area Telescope (LAT) in the energy range from 60 MeV to 600 MeV. Methods: The off-pulse light-curve has been reconstructed from phase-resolved data. The corresponding histogram of flux measurements is used to identify distributions of flux-states and the statistical significance of a lower-flux component is estimated with dedicated simulations of mock light-curves. The energy spectra for different flux states are reconstructed. Results: We confirm the presence of flaring-states which follow a log-normal flux distribution. Additionally, we discover a low-flux state where the flux drops to as low as 18.4% of the intermediate-state average flux and stays there for several weeks. The transition time is observed to be as short as 2 days. The energy spectrum during the low-flux state resembles the extrapolation of the inverse-Compton spectrum measured at energies beyond several GeV energy, implying that the high-energy part of the synchrotron emission is dramatically depressed. Conclusions: The low-flux state found here and the transition time of at most 10 days indicate that the bulk ($>75$%) of the synchrotron emission above $10^8$ eV originates in a compact volume with apparent angular size of $\theta\approx0.4" t_\mathrm{var}/(5 \mathrm{d})$. We tentatively infer that the so-called inner knot feature is the origin of the bulk of the $\gamma$-ray emission.Comment: Accepted by A&A on 05.05.2020; Original version submitted on 19.09.201

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{${\epsilon}^2\Delta u -u+u^p =0$ in $\Omega$}\\ \mbox{$u>0$ in $\Omega$ and $\frac{\partial u}{\partial \nu}=0$ on $\partial \Omega$}, \end{array} \right. \end{equation*} where $\Omega$ is a bounded domain in ${\mathbf{R}}^N$ with smooth boundary $\partial \Omega$, $\epsilon>0$ is a small constant and $1< p<\left(\frac{N+2}{N-2}\right)_+$. Associated with the above problem is the energy functional $J_{\epsilon}$ 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 $u\in H^1(\Omega)$, where $F(u)=\int_{0}^{u}s^p ds$. Ni and Takagi (\cite{nt1}, \cite{nt2}) proved that for a single boundary spike solution $u_{\epsilon}$, 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 $I[w]$ is the energy of the ground state, $c_1 >0$ is a generic constant, $P_{\epsilon}$ is the unique local maximum point of $u_{\epsilon}$ and $H(P_{\epsilon})$ is the boundary mean curvature function at $P_{\epsilon}\in \partial \Omega$. Later, Wei and Winter (\cite{ww3}, \cite{ww4}) improved the result and obtained a higher-order expansion of $J_{\epsilon}[u_{\epsilon}]$: \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 $c_2$ and $c_3>0$ are generic constants and $R(P_\epsilon)$ is the scalar curvature at $P_\epsilon$. However, if $N=2$, 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 $2 \leq p <+\infty$. Without loss of generality, we may assume that the boundary near P\in\partial\Om is represented by the graph $\{ x_2 = \rho_{P} (x_1) \}$. Then we have the following higher order expansion of $J_\epsilon[u_\epsilon]:$ \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, $P(t)=A_1 t+A_2 t^2+A_3 t^3$ is a polynomial, $c_1$, $c_2$, $c_3$ and $A_1$, $A_2$,$A_3$ are generic real constants and S(P_\epsilon)= \rho_{P_\ep}^{(4)} (0). In particular $c_3<0$. Some applications of this expansion are given

Self-Organization of Balanced Nodes in Random Networks with Transportation Bandwidths

We apply statistical physics to study the task of resource allocation in random networks with limited bandwidths along the transportation links. The mean-field approach is applicable when the connectivity is sufficiently high. It allows us to derive the resource shortage of a node as a well-defined function of its capacity. For networks with uniformly high connectivity, an efficient profile of the allocated resources is obtained, which exhibits features similar to the Maxwell construction. These results have good agreements with simulations, where nodes self-organize to balance their shortages, forming extensive clusters of nodes interconnected by unsaturated links. The deviations from the mean-field analyses show that nodes are likely to be rich in the locality of gifted neighbors. In scale-free networks, hubs make sacrifice for enhanced balancing of nodes with low connectivity.Comment: 7 pages, 8 figure