Nonequilibrium behavior of the kinetic metamagnetic spin-5/2 Blume–Capel model

The dynamic magnetic behavior of the kinetic metamagnetic spin-5/2 Blume–Capel model is examined, within a mean-field approach, under a time-dependent oscillating magnetic field. To describe the kinetics of the system, Glaubertype stochastic dynamics has been utilized. The mean-field dynamic equations of the model are obtained from the Master equation. Firstly, these dynamic equations are solved to find the phases in the system. Then, the dynamic phase transition temperatures are obtained by investigating the thermal behavior of dynamic sublattice magnetizations. Moreover, from this investigation, the nature of the phase transitions(first- or second-order) is characterized. Finally, the dynamic phase diagrams are plotted in five different planes. It is found that the dynamic phase diagrams contain the paramagnetic(P),antiferromagnetic(AF5/2, AF3/2, AF1/2) phases and five different mixed phases. The phase diagrams also display many dynamic critical points, such as tricritical point, triple point, quadruple point, double critical end point and separating point.     

Coupling p-multigrid to geometric multigrid for discontinuous Galerkin formulations of the convection–diffusion equation

An improved p-multigrid algorithm for discontinuous Galerkin (DG) discretizations of convection–diffusion problems is presented. The general p  -multigrid algorithm for DG discretizations involves a restriction from the p=1$p=1$ to p=0$p=0$ discontinuous polynomial solution spaces. This restriction is problematic and has limited the efficiency of the p  -multigrid method. For purely diffusive problems, Helenbrook and Atkins have demonstrated rapid convergence using a method that restricts from a discontinuous to continuous polynomial solution space at p=1$p=1$. It is shown that this method is not directly applicable to the convection–diffusion (CD) equation because it results in a central-difference discretization for the convective term. To remedy this, ideas from the streamwise upwind Petrov–Galerkin (SUPG) formulation are used to devise a transition from the discontinuous to continuous space at p=1$p=1$ that yields an upwind discretization. The results show that the new method converges rapidly for all Peclet numbers.     

Another representation of the β form of the inhomogeneous Picard-Fuchs equation

In this letter we give another representation of the β form in the inhomogeneous Picard-Fuchs equation for open topological string for some one-parameter Calabi-Yau hypersurfaces in weighted projective spaces. Furthermore, the corresponding domain wall tensions calculated by using these β forms are consistent with the results that appear in literature. The β form is essential for the calculation of the D-brane domain wall tension, and a convenient choice of β forms should simplify the calculation. The freedom of the choice of β forms shows some symmetries in Calabi-Yau space.     

Pfaffianization of the variable-coefficient Kadomtsev-Petviashvili equation＊

This paper constructs more general exact solutions than $N$-soliton solution and Wronskian solution for variable-coefficient Kadomtsev--Petviashvili (KP) equation. By using the Hirota method and Pfaffian technique, it finds the Grammian determinant-type solution for the variable-coefficient KP equation (VCKP), the Wronski-type Pfaffian solution and the Gram-type Pfaffian solutions for the Pfaffianized VCKP equation.     

Thermal transport property of Ge34 and d-Ge investigated by molecular dynamics and the Slack’s equation

In this study,we evaluate the values of lattice thermal conductivity κ L of type II Ge clathrate (Ge 34) and diamond phase Ge crystal (d-Ge) with the equilibrium molecular dynamics (EMD) method and the Slack's equation.The key parameters of the Slack's equation are derived from the thermodynamic properties obtained from the lattice dynamics (LD) calculations.The empirical Tersoff's potential is used in both EMD and LD simulations.The thermal conductivities of d-Ge calculated by both methods are in accordance with the experimental values.The predictions of the Slack's equation are consistent with the EMD results above 250 K for both Ge34 and d-Ge.In a temperature range of 200-1000 K,the κ L value of d-Ge is about several times larger than that of Ge 34.     

Exact solutions of stochastic fractional Korteweg de–Vries equation with conformable derivatives

We deal with the Wick-type stochastic fractional Korteweg de–Vries(KdV) equation with conformable derivatives.With the aid of the Exp-function method, white noise theory, and Hermite transform, we produce a novel set of exact soliton and periodic wave solutions to the fractional KdV equation with conformable derivatives. With the help of inverse Hermite transform, we get stochastic soliton and periodic wave solutions of the Wick-type stochastic fractional KdV equation with conformable derivatives. Eventually, by an application example, we show how the stochastic solutions can be given as Brownian motion functional solutions.     

New interaction solutions of the Kadomtsev–Petviashvili equation

The residual symmetry relating to the truncated Painlev′e expansion of the Kadomtsev–Petviashvili(KP) equation is nonlocal, which is localized in this paper by introducing multiple new dependent variables. By using the standard Lie group approach, new symmetry reduction solutions for the KP equation are obtained based on the general form of Lie point symmetry for the prolonged system. In this way, the interaction solutions between solitons and background waves are obtained, which are hard to find by other traditional methods.     

Physical design of FEL injector based on the performance-enhanced EC-ITC RF gun

To meet the requirements of high performance THz-FEL (Free Electron Laser), a compact scheme of FEL injector was proposed. A thermionic cathode was chosen to emit electrons instead of a photo-cathode with its complex structure and high cost. The effective bunch charge was improved to ～200 pC by adopting an enhanced EC-ITC (External Cathode Independently Tunable Cells) RF gun to extract micro-bunches; back bombardment effects were almost eliminated as well. Constant gradient accelerator structures were designed to improve energy to ～14 MeV, while the focusing system was applied for emittance suppressing and bunch state maintenance. The physical design and beam dynamics of the key components for the FEL injector were analyzed. Furthermore, start-to-end simulations with multi-pulses were performed using homemade MATLAB and Parmela. The results show that continual high brightness electron bunches with a low energy spread and emittance could be obtained stably.     

A certain critical two-soliton solution of the nonlinear Schroedinger equation

An exact two-soliton solution of the nonlinear Schroedinger equation is derived by using the Hirota direct approach. This solution describes such a critical process that two still solitons separated infinitely approach and then pass through each other and keep straight on infinitely.     

Some new exact solutions of Jacobian elliptic function about the generalized Boussinesq equation and Boussinesq-Burgers equation

By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions.     

Solving the initial condition of the string relaxation equation of the string model for glass transition:part-Ⅱ

The string model for the glass transition can quantitatively describe the universal α-relaxation in glassformers. The string relaxation equation (SRE) of the model simplifies the well-known Debye and Rouse--Zimm relaxation equations at high and low enough temperatures, respectively. However, its initial condition, necessary to the further model predictions of glassy dynamics, has not been solved. In this paper, the general initial condition of the SRE for stochastically spatially configurative strings is solved exactly based on the obtained special initial condition of the SRE for straight strings in a previous paper (J. L. Zhang et al. 2010 Chin. Phys. B 19, 056403).     

The Hugoniot equation of state of the fluid He+D2 mixtures

The fluid variational theory and effective one-component model have been used to calculate the Hugoniot equation of state (EOS) of fluid He, D2, and He+D2 mixtures with different He:D2 compositions under high pressures and temperatures. An examination of the confidence of above computation is performed by comparing experiment and calculation, in which the similar calculation procedure used for He+D2 is adopted, of He and D2 each, since no experimental data are available to conduct this kind of comparison. Good agreement in both comparisons is found. This fact may be looked as if an indirect positive verification of calculation procedure used here at least in the pressure and temperature domain covered by the experimental data of He and D2 used for comparison, numerically nearly up to 35 GPa and 105K.     

Dynamic behaviour of the icosahedral Al——Pd——Mn quasicrystal with a Griffith crack

The dynamic response of an icosahedral Al--Pd--Mn quasicrystal with a Griffith crack to impact loading is investigated in this paper. The elastohydrodynamic model for the wave propagation and diffusion together with their interaction is adopted. Numerical results of stress, displacement and dynamic stress intensity factors are obtained by using the finite difference method. The effects of wave propagation, diffusion and phonon--phason coupling on the quasicrystal in the dynamic process are discussed in detail, where the phason dynamics is explored particularly.     

Some dynamical property of the Tsallis distribution from a Fokker-Planck equation

This paper studies the possible dynamical property of the Tsallis distribution from a Fokker--Planck equation. For the Langevin dynamical system with an {arbitrary} potential function, Markovian friction and Gaussian white noise, it shows that the current form of Tsallis distribution cannot describe any nonequilibrium dynamics of the system, and it only stands for a simple isothermal situation of the system governed by a potential field. So the form of Tsallis distribution and many existing applications using the Tsallis distribution need to be reconsidered.     

Evolution property of soliton solutions for the Whitham－Broer－Kaup equation and variant Boussinesq equation

Using the standard Painlevé analysis approach, the (1+1)-dimensional Whitham－Broer－Kaup (WBK) and variant Boussinesq equations are solved. Some significant and exact solutions are given. We investigate the behaviour of the interactions between the multi-soliton-kink-type solution for the WBK equation and the multi-solitonic solutions and find the interactions are not elastic. The fission of solutions for the WBK equation and the fusions of those for the variant Boussinesq equation may occur after their interactions.     

Determination of the stellar reaction rate for 12C（α,γ）16O： using a new expression with the reaction mechanism

The astrophysical reaction rate of 12C(α, γ)16O plays a key role in massive star evolution. However, this reaction rate and its uncertainties have not been well determined yet, especially at T9=0.2. The existing results even disagree with each other to a certain extent. In this paper, the E1, E2 and total (E1+E2) 12C(α, γ)16O reaction rates are calculated in the temperature range from T9=0.3 to 2 according to all the available cross section data. A new analytic expression of the 12 C(α, γ)16 O reaction rate is brought forward based on the reaction mechanism. In this expression, each part embodies the underlying physics of the reaction. Unlike previous works, some physical parameters are chosen from experimental results directly, instead of all the parameters obtained from fitting. These parameters in the new expression, with their 3σ fit errors, are obtained from fit to our calculated reaction rate from T9=0.3 to 2. Using the fit results, the analytic expression of 12C(α, γ)16O reaction rate is extrapolated down to T9=0.05 based on the underlying physics. The 12C(α, γ)16 O reaction rate at T9=0.2 is (8.78 ± 1.52) × 1015 cm3s-1mol-1. Some comparisons and discussions about our new 12 C(α, γ)16 O reaction rate are presented, and the contributions of the reaction rate correspond to the different part of reaction mechanism are given. The agreements of the reaction rate below T9=2 between our results and previous works indicate that our results are reliable, and they could be included in the astrophysical reaction rate network. Furthermore, we believe our method to investigate the 12C(α, γ)16O reaction rate is reasonable, and this method can also be employed to study the reaction rate of other astrophysical reactions. Finally, a new constraint of the supernovae production factor of some isotopes are illustrated according to our 12C(α, γ)16O reaction rates.     

An approximate solution of the DKP equation under the Hulthén vector potential

Using the analytical NU technique as well as an acceptable physical approximation to the centrifugal term, the bound-state solutions of the Duffin-Kemmer-Petiau equation are obtained for arbitrary quantum numbers. The solutions appear in terms of the Jacobi Polynomials. Various explanatory figures and tables are included to complete the study.     

Global dynamical analysis of vibrational manifolds of HOCl and HOBr under anharmonicity and Fermi resonance:the dynamical potential approach

The vibrational dynamics of HOCl and HOBr between bending and OCl/OBr stretching coordinates with anharmonicity and Fermi coupling is studied with the classical dynamical potential approach. The quantal vibrational dynamics is mostly mapped out by the classical nonlinear variables such as fixed points, except for the state energies, which are quantized. This approach is global in the sense that the focus is on a set of levels instead of individual ones. The dynamics of HOBr is demonstrated to be less complicated. The localized modes along the OCl/OBr stretching coordinates are also shown to have O-Br bonds more prone to dissociation.     

Structural transition dynamics of the formation of warm dense gold: From an atomic scale view

With the highly optimized embedded-atom-method(EAM)potential and electron-phonon coupling factor obtained from experimental data,the dynamics of the formation of warm dense gold and the nuclear response of gold foils upon intense laser excitation were investigated using two-temperature molecular dynamics simulations.Considering laser energy densities ranging from 0.18 to 1.17 MJ/kg,we provide a microscopic picture of the formation of warm dense gold.A threshold(0.19 MJ/kg)for the laser energy density was determined,identifying two different melting mechanisms.For an energy density below 0.19 MJ/kg,the melting of the foil is controlled by the propagation of melt fronts from external surfaces,which results in heterogeneous melting on the time scale of hundreds of picoseconds.For an energy density above 0.19 MJ/kg,homogeneous nucleation and growth of liquid regions inside the foil play the leading role,and homogeneous melting occurs with several picoseconds.Compared with previous simulations and experimental measurements,the evaluated different threshold value indicates that the improvement in the electron heat capacity for the two-temperature model by including the kinetic information of electrons may predict better laser-matter interactions under such extreme non-equilibrium conditions.     

Solution of the Schrödinger equation for a particular form of Morse potential using the Laplace transform

In this paper, we have solved the Schrdinger equation for a particular kind of Morse potential and find its normalized eigenfunctions and eigenvalues, exactly. Our work is based on the Laplace transform technique which reduces the second-order differential equation to a first-order.