STABILITY ANALYSIS FOR NONLINEAR SCHRODINGER EQUATIONS WITH NONLINEAR ABSORBING BOUNDARY CONDITIONS

Local absorbing boundary conditions （LABCs） for nonlinear Schr6dinger equations have been constructed in papers [PRE 78（2008） 026709; and PRE 79 （2009） 046711] using the so-called unified approach. In this paper, we present stability analysis for the reduced problem with LABCs on the bounded computational domain by the energy estimate, and discuss a class of modified versions of LABCs. To prove the stability analysis of the re- duced problem, we turn to the technique of some auxiliary variables which reduces the higher-order derivatives in LABCs into a family of equations with lower-order derivatives. Furthermore, we extend the strategy to the stability analysis of two-dimensional problems by carefully dealing with the LABCs at corners. Numerical examples are given to demon- strate the effectiveness of our boundary conditions and validate the theoretical analysis.

On two-point boundary correlations of the gl(1|1) supersymmetric vertex model

The gl（1｜1） supersymmetric vertex model with domain wall boundary conditions （DWBC） on an N ×N square lattice is considered. We obtain the reduction formulae for the two-point boundary correlation functions of the model.

Wave Propagation in Fluid-Filled Single-Walled Carbon Nanotube Based on the Nonlocal Strain Gradient Theory

A dynamic Timoshenko beam model is established based on the new nonlocal strain gradient theory and slip boundary theory to study the wave propagation behaviors of fluid-filled carbon nanotubes （CNTs） at nanoscale. The nanoscale effects caused by the CNTs and the inner fluid are simulated by the nonlocal strain gradient effect and the slip boundary effect, respectively. The governing equations of motion are derived and resolved to investigate the wave characteristics in detail. The numerical solution shows that the strain gradient effect leads to the stiffness enhancement of CNTs when the nonlocal stress effect causes the decrease in stiffness. The dynamic properties of CNTs are affected by the coupling of these two scale effects. The flow velocity of fluid inside the CNT is increased due to the slip boundary effect, resulting in the promotion of wave propagation in the dynamic system.

Mixed convection boundary layer flow pasta vertical cone embedded in a porous medium subjected to a convective boundary condition

In the present analysis,we study the steady mixed convection boundary layer flowpast a vertical cone embedded in a porous medium subjected to a convective boundarycondition.The governing partial differential equations are reduced to the coupled nonlinearordinary differential equations using a similarity transformation before being solved numeri-cally by a shooting method.Both assisting and opposing flows are considered.The influence ofthe convective heat transfer parameter is analysed and discussed through graphs.Dualsolutions are found to exist for the case of opposing flow.

The effect of induced magnetic field and convective boundary condition on MHD stagnation point flow and heat transfer of upper-convected Maxwell fluid in the presence of nanoparticle past a stretching sheet

The present study examines the effect of induced magnetic field and convectiveboundary condition on magnetohydrodynamic(MHD)stagnation point flow and heat transfer dueto upper-convected Maxwell fluid over a stretching sheet in the presence of nanoparticles.Boundary layer theory is used to simplify the equation of motion,induced magnetic field,energyand concentration which results in four coupled non-linear ordinary differential equations.Thestudy takes into account the effect of Brownian motion and thermophoresis parameters.Thegoverning equations and their associated boundary conditions are initially cast into dimensionlessfonm by similarity variables.The resulting system of equations is then solved numerically usingfourth order Runge-Kutta-Fehlberg method along with shooting technique.The solution for thegoverning equations depends on parameters such as,magnetic,velocity ratio parameter B,Biotnumber Bi,Prandtl number Pr,Lewis number Le,Brownian motion Nb,reciprocal of magnetic Prandtl number A,the thermophoresis parameter Nt,and Maxwell parameter β.The numerical results are obtained for velocity,temperature,induced magnetic field andconcentration profiles as well as skin friction coefficient,the local Nusselt number andSherwood number.The results indicate that the skin friction coefficient,the local Nusseltnumber and Sherwood number decrease with an increase in B and M parameters.Moreover,local Sherwood number-φ'(O)decreases with an increase in convective parameter Bi,but the local Nusselt number-φ'(0)increases with an increase in Bi.The results are displayed both ingraphical and tabular form to illustrate the effect of the governing parameters on thedimensionless velocity,induced magnetic field,temperature and concentration.The numericalresults are compared and found to be in good agreement with the previously published resultson special cases of the problem.