Algebraic Bethe ansatz for the Zamolodchikov–Fateev and Izergin–Korepin models with open boundary conditions

We have considered the Zamolodchikov–Fateev and the Izergin–Korepin models with diagonal reflection boundaries. In each case the eigenspectrum of the transfer matrix is determined by application of the algebraic Bethe ansatz.     

Asymptotic Bethe ansatz for the Sutherland–Römer model with open boundary conditions

By constructing the reflection spin-Dunkl operators, the integrable Sutherland–Römer model (SRM) with open boundary condition is established, which describes a one-dimensional, two-component, quantum many-particle system in which like particles interact with a pair potential g(g+1)/sinh²(r), while unlike particles interact with a pair potential −g(g+1)/cosh²(r). By solving the Schrödinger equation and using the properties of the hypergeometric functions and gamma functions, the two-particle scattering matrix and the reflection matrix are obtained in the framework of the asymptotic Bethe ansatz method. The Bethe ansatz equations of the system are obtained. The Hamiltonians of SRM with some other open boundary conditions are expressed explicitly. Our method can be generalized, as a example, to the boundary Calogero–Sutherland model which is also constructed by the reflection spin-Dunkl operators.     

Pattern formation in a predator–prey model with spatial effect

In this paper, spatial dynamics in the Beddington–DeAngelis predator–prey model with self-diffusion and cross-diffusion is investigated. We analyze the linear stability and obtain the condition of Turing instability of this model. Moreover, we deduce the amplitude equations and determine the stability of different patterns. Numerical simulations show that this system exhibits complex dynamical behaviors. In the Turing space, we find three types of typical patterns. One is the coexistence of hexagon patterns and stripe patterns. The other two are hexagon patterns of different types. The obtained results well enrich the finding in predator–prey models with Beddington–DeAngelis functional response.     

Isgur–Wise function in a QCD-inspired potential model with WKB approximation

We use Wentzel–Kramers–Brillouin (WKB) approximation for calculating the slope and curvature of Isgur–Wise function in a QCD-inspired potential model. This work is an extension of the approximation methods to the QCD-inspired potential model. The approach hints at an effective range of distance for calculating the slope and curvature of Isgur–Wise function. Comparison is also made with those of Dalgarno method and variationally improved perturbation theory (VIPT) as well as other models to show the advantages of using WKB approximation.     

Adsorption thermodynamics of a lattice–gas model with non-additive lateral interactions

In the present paper, we study the adsorption thermodynamics of a lattice–gas model with non-additive interactions between adsorbed particles. We have assumed that the energy which links a certain atom with any of its nearest neighbors strongly depends on the state of occupancy in the first coordination sphere of that adatom. By means of Monte Carlo simulations in the grand canonical ensemble the adsorption isotherms, isothermal susceptibility (or equivalently the mean square density fluctuations of adparticles), and isosteric heat of adsorption were calculated and their striking behavior was analyzed and discussed in terms of the low temperature phases formed in the system.     

Moment stability for a predator–prey model with parametric dichotomous noises

In this paper,we investigate the solution moment stability for a Harrison-type predator–prey model with parametric dichotomous noises.Using the Shapiro–Loginov formula,the equations for the first-order and second-order moments are obtained and the corresponding stable conditions are given.It is found that the solution moment stability depends on the noise intensity and correlation time of noise.The first-order and second-order moments become unstable with the decrease of correlation time.That is,the dichotomous noise can improve the solution moment stability with respect to Gaussian white noise.Finally,some numerical results are presented to verify the theoretical analyses.     

Analytical study of Cattaneo–Christov heat flux model for a boundary layer flow of Oldroyd-B fluid

We investigate the Cattaneo–Christov heat flux model for a two-dimensional laminar boundary layer flow of an incompressible Oldroyd-B fluid over a linearly stretching sheet. Mathematical formulation of the boundary layer problems is given. The nonlinear partial differential equations are converted into the ordinary differential equations using similarity transformations. The dimensionless velocity and temperature profiles are obtained through optimal homotopy analysis method(OHAM). The influences of the physical parameters on the velocity and the temperature are pointed out. The results show that the temperature and the thermal boundary layer thickness are smaller in the Cattaneo–Christov heat flux model than those in the Fourier's law of heat conduction.     

Validation of a lattice Boltzmann model for gas–solid reactions with experiments

A lattice Boltzmann method is used to model gas–solid reactions where the composition of both the gas and solid phase changes with time, while the boundary between phases remains fixed. The flow of the bulk gas phase is treated using a multiple relaxation time MRT D3Q19 model; the dilute reactant is treated as a passive scalar using a single relaxation time BGK D3Q7 model with distinct inter- and intraparticle diffusivities. A first-order reaction is incorporated by modifying the method of Sullivan et al. [13] to include the conversion of a solid reactant. The detailed computational model is able to capture the multiscale physics encountered in reactor systems. Specifically, the model reproduced steady state analytical solutions for the reaction of a porous catalyst sphere (pore scale) and empirical solutions for mass transfer to the surface of a sphere at Re = 10 (particle scale). Excellent quantitative agreement between the model and experiments for the transient reduction of a single, porous sphere of Fe₂O₃ to Fe₃O₄ in CO at 1023 K and 10⁵ Pa is demonstrated. Model solutions for the reduction of a packed bed of Fe₂O₃ (reactor scale) at identical conditions approached those of experiments after 25 s, but required prohibitively long processor times. The presented lattice Boltzmann model resolved successfully mass transport at the pore, particle and reactor scales and highlights the relevance of LB methods for modelling convection, diffusion and reaction physics.     

Neutrino mixing and masses in a left–right model with mirror fermions

In the framework of a left–right model containing mirror fermions with gauge group SU(3) _C ⊗SU(2) _L ⊗SU(2) _R ⊗U(1) _Y′, we estimate the neutrino masses, which are found to be consistent with their experimental bounds and hierarchy. We evaluate the decay rates of the Lepton Flavor Violation (LFV) processes μ→eγ, τ→μγ and τ→eγ. We obtain upper limits for the flavor-changing branching ratios in agreement with their present experimental bounds. We also estimate the decay rates of heavy Majorana neutrinos in the channels N→W ^± l ^∓, N→Zν _l and N→Hν _l , which are roughly equal for large values of the heavy neutrino mass. Starting from the most general Majorana neutrino mass matrix, the smallness of active neutrino masses turns out from the interplay of the hierarchy of the involved scales and the double application of seesaw mechanism. An appropriate parameterization on the structure of the neutrino mass matrix imposing a symmetric mixing of electron neutrino with muon and tau neutrinos leads to tri-bimaximal mixing matrix for light neutrinos.     

Topological self-dual configurations in a Maxwell–Higgs model with a CPT-odd and Lorentz-violating nonminimal coupling

We have studied the existence of topological self-dual configurations in a nonminimal CPT-odd and Lorentz-violating (LV) Maxwell–Higgs model, where the LV interaction is introduced by modifying the minimal covariant derivative. The Bogomol’nyi–Prasad–Sommerfield formalism has been implemented, revealing that the scalar self-interaction implying self-dual equations contains a derivative coupling. The CPT-odd self-dual equations describe electrically neutral configurations with finite total energy proportional to the total magnetic flux, which differ from the charged solutions of other CPT-odd and LV models previously studied. In particular, we have investigated the axially symmetrical self-dual vortex solutions altered by the LV parameter. For large distances, the profiles possess general behavior similar to the vortices of Abrikosov–Nielsen–Olesen. However, within the vortex core, the profiles of the magnetic field and energy can differ substantially from ones of the Maxwell–Higgs model depending if the LV parameter is negative or positive.     

Flame capturing with an advection–reaction–diffusion model

We conduct several verification tests of the advection–reaction–diffusion flame-capturing model, developed by Khokhlov in 1995 for subsonic nuclear burning fronts in supernova simulations. We find that energy conservation is satisfied, but there is systematic error in the computed flame speed due to thermal expansion, which was neglected in the original model. We decouple the model from the full system, determine the necessary corrections for thermal expansion, and then demonstrate that these corrections produce the correct flame speed. The flame-capturing model is an alternative to other popular interface tracking techniques, and might be useful for applications beyond astrophysics.     

Boson–boson pure-dephasing model with non-Markovian properties

In this paper, we discuss the mechanism of pure-dephasing process with a newly proposed boson–boson model, namely, a bosonic field coupled to another bosonic bath in thermal equilibrium. Our model is fully solvable and can reproduce the pure-dephasing process which is usually described by the well-known spin–boson model, therefore offering a new perspective to understanding decoherence processes in open quantum systems of high dimension. We also show that this model admits a generically non-Markovian dynamics with respect to various different non-Markovian characterizations, i.e., the criteria based on divisibility, quantum regression formula and Wigner function, respectively. The criterion based on Wigner function is firstly proposed in this paper. For the case that the particle number of the pure-dephasing system is constrained to be 0 or 1, we analytically prove its equivalence to the criteria based on trace distance and divisibility.     

Chiral Thirring–Wess model with Faddeevian regularization

Replacing vector type of interaction of the Thirring–Wess model by the chiral type a new model is presented which is termed here as chiral Thirring–Wess model. Ambiguity parameters of regularization are so chosen that the model falls into the Faddeevian class. The resulting Faddeevian class of model in general does not possess Lorentz invariance. However we can exploit the arbitrariness admissible in the ambiguity parameters to relate the quantum mechanically generated ambiguity parameters with the classical parameter involved in the masslike term of the gauge field which helps to maintain physical Lorentz invariance instead of the absence of manifestly Lorentz covariance of the model. The phase space structure and the theoretical spectrum of this class of model have been determined through Dirac’s method of quantization of constraint system.     

Plasmonic wave propagation along a magnetized plasmon–dielectric boundary

The emphasis of this paper is on investigation of the TM/TE depolarization along a magnetized surface. In this regard, initially, the wave equation with appropriate boundary conditions is solved for the propagation constant of the wave along the interface. Next, in order to investigate the electromagnetic field TM/TE depolarization along a linear magnetoplasmon–dielectric interface, coupled partial differential equations are derived for the amplitudes of the TE and TM polarized fields along the surface. These equations are then solved using the Fourier transform and 4th order Runge–Kutta methods and the envelopes of the electric field are obtained. The dependency of the propagation constants of the slow and fast modes on the frequency and magnitude of DC magnetic bias field is investigated. A discussion of TE mode deflection is also provided.     

Acoustic-wave reflection from a gas−droplet–mixture boundary

The problem on acoustic-wave reflection from the boundary of a gas?droplet mixture is considered. For the interface between the pure gas and the gas?droplet mixture at a wave inclined incidence, a nonmonotonic dependence of the reflectance on the volume content of droplets is established. The values of the critical wave-incidence angle and the volume content of inclusions at which the reflectance vanishes are found and illustrated. The possibility of occurrence of the lowest reflectance in dependence on the frequency of perturbations in a certain interval of the wave-incidence angle related mainly to the difference in the densities of the gas-droplet mixture and the pure gas is shown.