We propose two linearly implicit energy-preserving schemes for the complex modified Korteweg–de Vries equation, based on the invariant energy quadratization method. First, a new variable is introduced and a new Hamiltonian system is constructed for this equation. Then the Fourier pseudospectral method is used for the space discretization and the Crank–Nicolson leap-frog schemes for the time discretization. The proposed schemes are linearly implicit, which is only needed to solve a linear system at each time step. The fully discrete schemes can be shown to conserve both mass and energy in the discrete setting. Some numerical examples are also presented to validate the effectiveness of the proposed schemes.

The aim of this work is to develop a calculation model based on the method of characteristics making it possible to study the effect of the stagnation pressure of the combustion chamber on the 2D and axisymmetric minimum length nozzle design giving a uniform and parallel flow at the exit section. The model is based on the use of the real gas approach. The co-volume and the intermolecular interaction effect are taken into account by the use of the Berthelot state equation. The effect of molecular vibration is considered in our model to evaluate the behaviour of gas at a high temperature. In this case, the stagnation pressure and the stagnation temperature are important parameters in our model. The resolution of the algebraic equations is done by the finite difference corrector predictor algorithm. The validation of the results is controlled by the convergence of the critical section ratios calculated numerically as obtained by the theory. The mass and the thrust are evaluated to improve the efficiency of the nozzle. The comparison is made with the high temperature and perfect gas models. The application is made for air.

For the observed 18 pairs of double neutron star (DNS) systems, we find that DNS mass distribution is very narrow and its mean value (about 1.34 solar mass) is less than the mean of all measured pulsars of about 1.4 solar mass. To interpret the special DNS mass characteristics, we analyze the DNS formation process, via the phases of HMXBs, by investigating the evolution of massive binary stars. Moreover, in DNSs, two classes of NSs are taken into account, formed by supernova (SN) and electron capture (EC), respectively, and generally the NS mass by SN is bigger than that by EC. Quantitatively, with various initial conditions of binary stars, the observed special DNS distribution can be satisfactorily explained.

In this paper, we propose a new energy-preserving scheme and a new momentum-preserving scheme for the modified regularized long wave equation. The proposed schemes are designed by using the discrete variational derivative method and the finite volume element method. For comparison, we also propose a finite volume element scheme. The conservation properties of the proposed schemes are analyzed and we find that the energy-preserving scheme can precisely conserve the discrete total mass and total energy, the momentum-preserving scheme can precisely conserve the discrete total mass and total momentum, while the finite volume element scheme merely conserve the discrete total mass. We also analyze their linear stability property using the Von Neumann theory and find that the proposed schemes are unconditionally linear stable. Finally, we present some numerical examples to illustrate the effectiveness of the proposed schemes.

This essay is inspired by an intriguing late sixteenth-century Catholic liturgical object, the Bosworth Hall burse. It commemorates a vision of the crucified Christ seen by the missionary priest (and later martyr) John Payne in Douai in 1575, which apparently dispelled a moment of doubt about the real presence in the consecrated eucharist. The incident is situated in the context of the heated Catholic and Protestant controversies about the doctrine of transubstantiation in post-Reformation England and against the backdrop of similar medieval miracles designed to counter disbelief, including the Mass of St Gregory and the miracle of Bolsena of 1263. The essay illuminates the persistence and transformation of anxieties about the sacred in the sixteenth century, considers the part they played in private and public crises of faith, and explores the mechanisms by which they were resolved. It also investigates how the memory of Payne's miraculous vision was crystallized in a material object.

We have collected the parameter of 38 neutron stars (NSs) in binary systems with spin periods and measured masses. By adopting the Boot-strap method, we reproduced the procedure of mass calculated for each system separately, to determine the truly mass distribution of the NS that obtained from observation. We also applied the Monte-Carlo simulation and introduce the characteristic spin period 20 ms, in order to distinguish between millisecond pulsars (MSPs) and less recycled pulsars. The mass distributions of MSPs and the less recycled pulsars could be fitted by a Gaussian function as 1.45±0.42 M⊙ and 1.31±0.17 M⊙ (with 1σ) respectively. As such, the MSP masses are heavier than those in less recycled systems by factor of ~ 0.13M⊙, since the accretion effect during the recycling process.

About 0.2 solar mass is absorbed by the millisecond pulsar (MSP) at the binary accretion phase, while the polar magnetic field of MSP is diluted to a magnitude of order 108.5 Gauss, which is proportionally related to the mass accretion rate. It is found that the minimum magnetic field of MSP can be as low as 107 Gauss if the accretion rate of the binary system reaches its the minimum value of 1015 g/s. This bottom field has nothing to do with the MSP initial field. Some questions on MPSs are proposed and answered.

The orbital angular momenta OAM (J) of detached binaries (including both cool and hot binaries) were estimated and nine subgroups were formed according to their OAM (J) distribution. The mean kinematical ages of all subgroups have been estimated by using their space velocity distributions and, thus, the age dependent variations of the mean OAM (J), orbital period (P), and total mass (M) of all subgroups were investigated. It was discovered that: i) The orbital period of detached binaries with radiative components decrease very slowly during the main sequence (MS) evolution. It is interesting that the large amount of mass loss is almost balanced by the OAM loss, and not much change in the orbital periods is observed. ii) The nuclear evolution of radiative components beyond the MS initiates the increase of the periods until the components have convective upper layers, i.e. until they become later than F5 IV, and the system becomes a cool binary with sub-giant or giant components. iii) The large co-rotating distance of the magnetically-driven wind in cool binaries (CAB) carries out a large amount of OAM and then the periods of such binaries decrease significantly, and the orbits shrink until another effect such as mass transfer dominates the period changes.