Stagnation point flow and heat transfer over a non-linearly moving flat plate in a parallel free stream with slip

An analysis is presented for the steady boundary layer flow and heat transfer of a viscous and incompressible fluid in the stagnation point towards a non-linearly moving flat plate in a parallel free stream with a partial slip velocity. The governing partial differential equations are converted into nonlinear ordinary differential equations by a similarity transformation, which are then solved numerically using the function bvp4c from Matlab for different values of the governing parameters. Dual (upper and lower branch) solutions are found to exist for certain parameters. Particular attention is given to deriving numerical results for the critical/turning points which determine the range of existence of the dual solutions. A stability analysis has been also performed to show that the upper branch solutions are stable and physically realizable, while the lower branch solutions are not stable and, therefore, not physically possible.     

Abundant bursting patterns of a fractional-order Morris–Lecar neuron model

In this paper, a fractional-order Morris–Lecar (M–L) neuron model with fast-slow variables is firstly proposed. The fractional-order M–L model is a generalization of the integer-order M–L model with fast-slow variables, where the fractional-order derivative is used to characterize the memory effect and power law of membranes. Then the bursting patterns of the new model are investigated by using the bifurcation theory of fast-slow dynamical systems. Numerical simulation shows that the new model exhibits some bursting patterns that appear in some common neuron models with properly chosen parameters but do not exist in the corresponding integer-order M–L model. Further, on the basis of a comparison of the nonlinear dynamics between the fractional-order M–L model and the integer-order M–L model, we show that the fractional-order derivative can activate the slow potassium ion channel faster and play an important role to modulate the firing activity of the new model.     

Integrability and soliton-like solutions for the coupled higher-order nonlinear Schrödinger equations with variable coefficients in inhomogeneous optical fibers

Under investigation in this paper are the coupled higher-order nonlinear Schrödinger equations with variable coefficients, which represent the propagation of femtosecond soliton pulses comprising of two fields with the left and right polarization in the inhomogeneous optical fiber media. Infinitely-many conservation laws are obtained based on the Lax pair. Via the Hirota method and symbolic computation, bilinear forms, bilinear Bäcklund transformations, one- and two-soliton-like solutions are also derived. With different coefficients, bell-shaped, periodic-changing, quadratic-varying, exponential-decreasing and exponential-increasing soliton-like profiles are seen, to describe the propagation and interactions of the femtosecond soliton pulses. Head-on and overtaking elastic interactions are shown, which are decided by the directions of the velocities. We also get the bound states with periodic attraction and repulsion between two solitons.     

Dynamical and statistical properties of a rotating oval billiard

Some dynamical and statistical properties of a time-dependent rotating oval billiard are studied. We considered cases with (i) positive and (ii) negative curvature for the boundary. For (i) we show the system does not present unlimited energy growth. For case (ii) however the average velocity for an ensemble of noninteracting particles grows as a power law with acceleration exponent well defined. Finally, we show for both cases that after introducing time-dependent perturbation, the mixed structure of the phase space observed for static case is recovered by making a suitable transformation in the angular position of the particle.     

Analysis of diffusion process in fractured reservoirs using fractional derivative approach

The fractal geometry is used to model of a naturally fractured reservoir and the concept of fractional derivative is applied to the diffusion equation to incorporate the history of fluid flow in naturally fractured reservoirs. The resulting fractally fractional diffusion (FFD) equation is solved analytically in the Laplace space for three outer boundary conditions. The analytical solutions are used to analyze the response of a naturally fractured reservoir considering the anomalous behavior of oil production. Several synthetic examples are provided to illustrate the methodology proposed in this work and to explain the diffusion process in fractally fractured systems.     

Numerical solutions of boundary value problems for variable coefficient generalized KdV equations using Lie symmetries

The exhaustive group classification of a class of variable coefficient generalized KdV equations is presented, which completes and enhances results existing in the literature. Lie symmetries are used for solving an initial and boundary value problem for certain subclasses of the above class. Namely, the found Lie symmetries are applied in order to reduce the initial and boundary value problem for the generalized KdV equations (which are PDEs) to an initial value problem for nonlinear third-order ODEs. The latter problem is solved numerically using the finite difference method. Numerical solutions are computed and the vast parameter space is studied.     

Lie symmetry analysis of electron–electromagnetic wave interaction under condition of the anomalous Doppler effect

Lie symmetry analysis is applied for a problem of interaction of electron cyclotron oscillators with a slow electromagnetic wave under condition of the anomalous Doppler effect. This analysis reveals scaling invariance of the system and existence of self-similar solutions which describe amplification of a short electromagnetic pulse with its subsequent compression. The results of theoretical analysis are confirmed by numerical simulations.     

Tensor force effect on single-proton energy levels of oxygen isotopes

In the framework of the Hartree-Fock approach the proton spin-orbital splittings of the 1p orbits and the shell gaps in the oxygen isotopes are investigated with the interactions SLy5+T,SLy5+Tw,SGII+Te1,SGII+Te2,SGII+Te3 and many sets of the TIJ interactions.All of the interactions are the Skyrme interactions and contain a tensor component(tensor force).It is shown that the evolution of the single-proton levels for the oxygen isotopes is sensitive to a parameterβTwhich is associated with the tensor force strength of the Skyrme interactions.To understand this phenomenon,we systematically analyze the dependence of the spin-orbit splittings and shell gaps on the parameterβTin terms of the spin-orbit potential and the corresponding wave function.We find that the Skyrme interactions can be classified into two groups:(a)T21,T32,T43,T54,SLy5+T,SLy5+Tw,SGII+Te1 and SGII+Te2,which can roughly reproduce the experimental shell gaps of the oxygen isotopes;(b)T1J and SGII+Te3,which can not reproduce the experimental shell gaps.     

辫子T-范畴的构造

本文首先引入了一类新的范畴_AYD_G^H, 这个范畴是一簇范畴{_AYD^H(α,β)}_(α,β)∈G的非交并, 获得了范畴{_AYD^H(α,β)}_(α,β)∈G是一个辫子T-范畴当且仅当(A,H,Q)是一个G-偶结构, 推广了2005年Panaite和Staic的主要结论. 最后, 当H是有限维时, 构造了一个拟三角T-余代数{A#H^*(α,β)}_(α,β)∈G, 它的表示范畴与{_AYD^H(α,β)}_(α,β)∈G是同构的.