An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation

In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional. For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.Comment: This paper has been accepted for publication in SCIENCE CHINA Mathematic

Radio-to-TeV Phase-resolved Emission from the Crab Pulsar: The Annular Gap Model

In the framework of the three-dimensional (3D) annular gap model with reasonable parameters (the magnetic inclination angle \alpha = 45 deg and the view angle \zeta = 63 deg), we first use the latest hight energy data to self-consistently calculate radio, X-ray, gamma-ray and TeV (MAGIC and VERITAS) light curves, phase-averaged spectrum and phase-resolved spectra for the Crab pulsar. It is found that the acceleration electric field and potential in the annular gap and core gap are huge enough in the several tens of neutron star radii. The pulsed emission of radio, X-ray, gamma-ray and TeV are mainly generated from the emission of primary particles or secondary particles with different emission mechanisms in the nearly similar region of the annular gap located in the only one magnetic pole, which leads to the nearly "phase-aligned" multi-wavelength light curves. The emission of peak 1 (P1) and peak 2 (P2) is originated from the annular gap region near the null charge surface, while the emission of bridge is mainly originated from the core gap region. The phase-averaged spectrum and phase-resolved spectra of the Crab pulsar from soft X-ray to TeV band are produced by four components: synchrotron radiation from CR-induced and ICS-induced pairs dominates the X-ray band to soft gamma-ray band (100 eV to 10 MeV); curvature radiation and synchrotron radiation from the primary particles mainly contribute to gamma-ray band (10 MeV to \sim 20 GeV); ICS from the pairs significantly contributes to the TeV gamma-ray band (\sim 20 GeV to 400 GeV). The multi-wavelength pulsed emission from the Crab pulsar has been well modeled with the annular gap and core gap model. To distinguish our single magnetic pole model from two-pole models, the convincing values of the magnetic inclination angle and the viewing angle will play a key role.Comment: 12 pages, 7 figures, 3 tables; published in ApJ on March 12. Due to the character limitation, the abstract here has been adopted a shortened versio

A convenient basis for the Izergin-Korepin model

We propose a convenient orthogonal basis of the Hilbert space for the Izergin-Korepin model (or the quantum spin chain associated with the $A^{(2)}_{2}$ algebra). It is shown that the monodromy-matrix elements acting on the basis take relatively simple forms (c.f. acting on the original basis ), which is quite similar as that in the so-called F-basis for the quantum spin chains associated with $A$-type (super)algebras. As an application, we present the recursive expressions of Bethe states in the basis for the Izergin-Korepin model.Comment: 24 pages, no figure

Abrasive Wear of Geometrical Surface Structures of Scapharca Subcrenata and Burnt-end Ark Against Soil

Scapharca subcrenata(Arca subcrenala Lischke）and Burnt-end Ark (Arca inflata Reeve) were selected as the research object. The abrasive wear experiments of three types of surface structures against soil were performed in the abrasive tester. These surface structures include the Scapharca subcrenata node rib pattern shell, Scapharca subcrenata rib pattern shell and Burnt-end Ark. The test results showed that the wear-resistant function of the surface structures of the Scapharca subcrenata node rib pattern shell and the Burnt-end Ark shell was better than that of the surface structure of the Scapharca subcrenata rib pattern shell when the relative sliding velocity was 2.41m/s. When abrasive size was range from 0.380mm to 0.830mm, the wear loss of these three types of surface structures were increased with the relative sliding velocity increasing.Keywords: Scapharca subcrenata; Burnt-end Ark; geometrical surface structure; abrasive wear; wear resistanc