Multi-variable special polynomials using an operator ordering method

Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.     

An Intuitive Electric-field Contribution Decomposition Model for Chemical Processes and Its Applications on Diels-Alder Reactions

External electric field(EEF) has shown its advantages in tuning chemical reaction as an efficient and feasible-to-control tool. In this paper, we explored the mechanisms of three EEF-regulated Diels-Alder reactions including two traditional-DA reactions to form two C-C single bonds and a hetero-DA reaction to form both a C-C and a C-O bond, respectively, and introduced an EEF contribution decomposition(ECD) model to understand how the EEF coupled with the intrinsic nuclear and electronic redistributions so as to affect chemical reaction. The ECD model, by decomposing the overall EEF effects into geometry re-equilibrium and static induction parts, can give a clear and quantitative picture of a physical quantity change upon EEF, as demonstrated on relative energies, activation barriers, charge distribution and dipole moments. The ECD analyses will shed light on the effective tuning of chemical reactions by the electric field.     

Jordan–Cattaneo waves: Analogues of compressible flow

We review work of Jordan on a hyperbolic variant of the Fisher–KPP equation, where a shock solution is found and the amplitude is calculated exactly. The Jordan procedure is extended to a hyperbolic variant of the Chafee–Infante equation. Extension of Jordan’s ideas to a model for traffic flow are also mentioned. We also examine a diffusive susceptible–infected (SI) model, and generalizations of diffusive Lotka–Volterra equations, including a Lotka–Volterra–Bass competition model with diffusion. For all cases we show how a Jordan–Cattaneo wave may be analysed and we indicate how to find the wavespeeds and the amplitudes. Finally we present details of a fully nonlinear analysis of acceleration waves in a Cattaneo–Christov poroacoustic model.     

Investigation on the effect of density ratio on the convergence behavior of partitioned method for fluid–structure interaction simulation

In order to investigate the effect of density ratio of fluid and solid on the convergence behavior of partitioned FSI algorithm, three strong-coupling partitioned algorithms (fixed-point method with a constant under-relaxation parameter, Aitken’s method and Quasi-Newton inverse least squares (QN-ILS) method) have been considered in the context of finite element method. We have employed the incompressible Navier–Stokes equations for a Newtonian fluid domain and the total Lagrangian formulation for a non-linear motion of solid domain. Linear-elastic (hyper-elastic) model has been employed for solid material with small (large) deformation. A pulsatile inlet-flow interacting with a 2D circular channel of linear-elastic material and a pressure wave propagation in a 3D flexible vessel have been simulated. Both linear-elastic and hyper-elastic (Mooney–Rivlin) models have been adopted for the 3D flexible vessel. From the present numerical experiments, we have found that QN-ILS outperforms the others leading to a robust convergence regardless of the density ratio for both linear-elastic and hyper-elastic models. On the other hand, the performances of the fixed-point method with a constant under-relaxation parameter and the Aitken’s method depend strongly on the density ratio, relaxation parameter selected for coupling iteration, and degree of deformation. Although the QN-ILS of this work is still slower than a monolithic method for serial computation, it has an advantage of easier parallelization due to the modularity of the partitioned FSI algorithm.     

Aeroelastic analysis of cantilever plates using Peters’ aerodynamic model,and the influence of choosing beam or plate theories as the structural model

In this paper, the aeroelastic analyses of a rectangular cantilever plate of varying aspect ratio is presented. The classical plate theory has been selected as the structural model. The main point that distinguishes this study from previously reported research is employing Peters’ theory to model aerodynamic effect which is not straightforward. The Peters’ aerodynamic model was originally developed to provide lift and moment, which is only applicable to the structural model based on the beam theories. In this study, using the basic concept of the Peters’ aerodynamic model in addition to utilizing the Fourier series, the pressure distribution is derived, which makes Peters’ model applicable to structural models based on plate theory. This combination provides a much simpler state–space aeroelastic model for plates in comparison to the prevalent panel methods, which could lead to a significant reduction in computational time. In addition, the aeroelastic response of the plate with respect to changes in the structural model from the beam theory to the plate theory is evaluated. By using data from an experiment carried out at Duke University, the theoretical results are evaluated. Furthermore, the differences in structural models obtained from the plate and beam theories can be divided into two distinct parts, which are responsible for differences in bending and torsional behaviors of the structure, separately. This approach enables us to measure the effects of differences of each behavior separately, which could provide with a new insight into the problem. It has been determined that the flutter speeds obtained from the beam and plate aeroelastic models are little affected by the difference in bending behavior, but rather is mainly caused by the difference in torsional frequencies.     

Measured and Predicted Solubility Phase Diagrams of Quaternary Systems LiBr-NaBr-MgBr2-H2O and LiBr-KBr-MgBr2-H2O at 298.15 K

The stable phase equilibria of quaternary systems LiBr-NaBr-MgBr₂-H₂O and LiBr-KBr-MgBr₂-H₂O at 298.15 K were studied by both experimental measurement(isothermal solution saturation method) and theoretical prediction(Pitzer model). The solubilities of the saturated solution have been determined experimentally and two stable phase diagrams and relevant water diagrams of the two quaternary systems were obtained. Results show that quaternary system LiBr-NaBr-MgBr₂-H₂O is hydrate II type as NaBr and NaBr·2H₂O coexistence. Its phase diagram consists of only one invariant point, four univariant curves, and five crystallization fields. The quaternary system LiBr-KBr-MgBr₂-H₂O is a complex type as the double salt KBr·MgBr₂·6H₂O formed. In addition to this double salt, the three single salts LiBr·2H₂O, KBr and MgBr₂·6H₂O also crystallize. In this paper, the solubilities of phase equilibria in above quaternary systems were also calculated by the Pitzer's electrolyte solution model. All the needed parameters can be obtained from the literature or be fitted by experimental data. On the Basis of the experimental and calculated results, the phase diagram of the quaternary system was plotted for comparison. It shows that the calculation results are consistent with the experimental ones.     

Bogdanov-Takens Bifurcation in a Host-parasitoid Model

In this paper, we study a host-parasitoid model with Holling II Functional response, where we focus on a special case: the carrying capacity K2 for parasitoids is equal to a critical value r 1η. It is shown that the model can undergo Bogdanov-Takens bifurcation. The approximate expressions for saddle-node, Homoclinic and Hopf bifurcation curves are calculated. Numerical simulations, including bifurcation diagrams and corresponding phase portraits, are also given to illustrate the theoretical results.