Krylov implicit integration factor discontinuous Galerkin methods on sparse grids for high dimensional reaction-diffusion equations

Computational costs of numerically solving multidimensional partial differential equations (PDEs) increase significantly when the spatial dimensions of the PDEs are high, due to large number of spatial grid points. For multidimensional reaction-diffusion equations, stiffness of the system provides additional challenges for achieving efficient numerical simulations. In this paper, we propose a class of Krylov implicit integration factor (IIF) discontinuous Galerkin (DG) methods on sparse grids to solve reaction-diffusion equations on high spatial dimensions. The key ingredient of spatial DG discretization is the multiwavelet bases on nested sparse grids, which can significantly reduce the numbers of degrees of freedom. To deal with the stiffness of the DG spatial operator in discretizing reaction-diffusion equations, we apply the efficient IIF time discretization methods, which are a class of exponential integrators. Krylov subspace approximations are used to evaluate the large size matrix exponentials resulting from IIF schemes for solving PDEs on high spatial dimensions. Stability and error analysis for the semi-discrete scheme are performed. Numerical examples of both scalar equations and systems in two and three spatial dimensions are provided to demonstrate the accuracy and efficiency of the methods. The stiffness of the reaction-diffusion equations is resolved well and large time step size computations are obtained

Search for serendipitous TNO occultation in X-rays

To study the population properties of small, remote objects beyond Neptune's orbit in the outer solar system, of kilometer size or smaller, serendipitous occultation search is so far the only way. For hectometer-sized Trans-Neptunian Objects (TNOs), optical shadows actually disappear because of diffraction. Observations at shorter wave lengths are needed. Here we report the effort of TNO occultation search in X-rays using RXTE/PCA data of Sco X-1 taken from June 2007 to October 2011. No definite TNO occultation events were found in the 334 ks data. We investigate the detection efficiency dependence on the TNO size to better define the sensible size range of our approach and suggest upper limits to the TNO size distribution in the size range from 30 m to 300 m. A list of X-ray sources suitable for future larger facilities to observe is proposed.Comment: Accepted to publish in MNRA

Potential Application of the CRISPR/Cas9 System against Herpesvirus Infections.

The CRISPR/Cas9 system has been applied in the genome editing and disruption of latent infections for herpesviruses such as the herpes simplex virus, Epstein⁻Barr virus, cytomegalovirus, and Kaposi's sarcoma-associated herpesvirus. CRISPR/Cas9-directed mutagenesis can introduce similar types of mutations to the viral genome as can bacterial artificial chromosome recombination engineering, which maintains and reconstitutes the viral genome successfully. The cleavage mediated by CRISPR/Cas9 enables the manipulation of disease-associated viral strains with unprecedented efficiency and precision. Additionally, current therapies for herpesvirus productive and latent infections are limited in efficacy and cannot eradicate viruses. CRISPR/Cas9 is potentially adapted for antiviral treatment by specifically targeting viral genomes during latent infections. This review, which focuses on recently published progress, suggests that the CRISPR/Cas9 system is not only a useful tool for basic virology research, but also a promising strategy for the control and prevention of herpesvirus latent infections