Explore the vast range of titles available.

Pulsars are rapidly rotating, highly magnetized neutron stars emitting radiation across the electromagnetic spectrum. Although there are more than 1800 known radio pulsars, until recently only seven were observed to pulse in gamma rays, and these were all discovered at other wavelengths. The Fermi Large Area Telescope (LAT) makes it possible to pinpoint neutron stars through their gamma-ray pulsations. We report the detection of 16 gamma-ray pulsars in blind frequency searches using the LAT. Most of these pulsars are coincident with previously unidentified gamma-ray sources, and many are associated with supernova remnants. Direct detection of gamma-ray pulsars enables studies of emission mechanisms, population statistics, and the energetics of pulsar wind nebulae and supernova remnants.

In comparison with the Cahn–Hilliard equation, the classic Allen-Cahn equation satisfies the maximum bound principle (MBP) but fails to conserve the mass along the time. In this paper, we consider the MBP and corresponding numerical schemes for the modified Allen–Cahn equation, which is formed by introducing a nonlocal Lagrange multiplier term to enforce the mass conservation. We first study sufficient conditions on the nonlinear potentials under which the MBP holds and provide some concrete examples of nonlinear functions. Then we propose first and second order stabilized exponential time differencing schemes for time integration, which are linear schemes and unconditionally preserve the MBP in the time discrete level. Convergence of these schemes is analyzed as well as their energy stability. Various two and three dimensional numerical experiments are also carried out to validate the theoretical results and demonstrate the performance of the proposed schemes.

A modification of the exponential time-differencing fourth-order Runge--Kutta method for solving stiff nonlinear PDEs is presented that solves the problem of numerical instability in the scheme as proposed by Cox and Matthews and generalizes the method to nondiagonal operators. A comparison is made of the performance of this modified exponential time-differencing (ETD) scheme against the competing methods of implicit-explicit differencing, integrating factors, time-splitting, and Fornberg and Driscoll's \"sliders\" for the KdV, Kuramoto--Sivashinsky, Burgers, and Allen--Cahn equations in one space dimension. Implementation of the method is illustrated by short MATLAB programs for two of the equations. It is found that for these applications with fixed time steps, the modified ETD scheme is the best.

This paper introduces an efficient unconditionally stable fourth-order method for solving nonlinear space-fractional reaction-diffusion systems with nonhomogeneous Dirichlet boundary conditions on bounded domains. The proposed method is based on a compact improved matrix transformed technique for fourth-order spatial approximation and exponential time differencing approximation for fourth-order time integration. The main advantage of the improved matrix transfer technique is that it leads to a system of ordinary differential equations with spatial discretization matrix raised to the desired fractional order. The key benefit of the fourth-order exponential integrator is that it can be implemented with essentially the same computational complexity as the backward Euler method by utilizing a partial fraction splitting technique in which it is just required to solve two backward Euler-type well-conditioned linear systems at each time step by computing LU decomposition of spatial discretization matrix once outside the time loop. Linear stability analysis and various numerical experiments are also performed to demonstrate stability and accuracy of the proposed method. Moreover, calculation of local truncation error and an empirical convergence analysis show the fourth-order accuracy of the proposed method.