A new coupled model for alloy solidification

A new coupled model in the binary alloy solidification has been developed. The model is based on the cellular automaton (CA) technique to calculate the evolution of the interface governed by temperature, solute diffusion and Gibbs-Thomson effect. The diffusion equation of temperature with the release of latent heat on the solid/liquid (S/L) interface is valid in the entire domain. The temperature diffusion without the release of latent heat and solute diffusion are solved in the entire domain. In the interface cells, the     

Dynamics of a coupled atmosphere–ocean model

We consider a coupled atmosphere–ocean model, which involves hydrodynamics, thermodynamics and nonautonomous interaction at the air–sea interface. First, we show that the coupled atmosphere–ocean system is stable under the external fluctuation in the atmospheric energy balance relation. Then, we estimate the atmospheric temperature feedback in terms of the freshwater flux, heat flux and the external fluctuation at the air–sea interface, as well as the earth's longwave radiation coefficient and the shortwave solar radiation profile. Finally, we prove that the coupled atmosphere–ocean system has time-periodic, quasiperiodic and almost periodic motions, whenever the external fluctuation in the atmospheric energy balance relation is time-periodic, quasiperiodic and almost periodic, respectively.     

Synchronization of boundary coupled Hindmarsh–Rose neuron network

In this work, we present a new mathematical model of a boundary coupled neuron network described by the partly diffusive Hindmarsh–Rose equations. We prove the global absorbing property of the solution semiflow and then the main result on the asymptotic synchronization of this neuron network at a uniform exponential rate provided that the boundary coupling strength and the stimulating signal exceed a quantified threshold in terms of the parameters.     

An Eulerian–Lagrangian method for coupled parabolic-hyperbolic equations

We present an Eulerian–Lagrangian method for the numerical solution of coupled parabolic-hyperbolic equations. The method combines advantages of the modified method of characteristics to accurately solve the hyperbolic equations with an Eulerian method to discretize the parabolic equations. The Runge–Kutta Chebyshev scheme is used for the time integration. The implementation of the proposed method differs from its Eulerian counterpart in the fact that it is applied during each time step, along the characteristic curves rather than in the time direction. The focus is on constructing explicit schemes with a large stability region to solve coupled radiation hydrodynamics models. Numerical results are presented for two test examples in coupled convection-radiation and conduction–radiation problems.     

Bound states for a coupled Schrödinger system

We consider the existence of bound states for the coupled elliptic system

The existence of Silnikov''''s orbits in one coupled Duffing equation

The existence of Silnikov's orbits in one coupled Duffing equation is discussed by using the fiber structure of invariant manifold and high-dimensional Melnikov's method. Example and numerical simulation results are also given to demonstrate the theoretical analysis.     

A coupled phase-field – Cahn-Hilliard model for lower bainitic transformation

The lower bainitic transformation is highly dependent on carbon diffusion. Bainite consists of bainitic ferrite, residual austenite and carbides. The numerical modeling of the interaction between these phases and the carbon is extremely demanding. The goal of this work is to describe the formation of carbides in lower bainite. To model the evolution of a bainitic sheaf a phase-field model is coupled with a Cahn-Hilliard equation simulating the diffusion. The system of equations is solved using the finite element method. Numerical examples show the growth of the ferrite and the following uphill diffusion within this phase. At accumulation points of carbon, carbides are precipitated. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Conversion of a rhotrix to a ‘coupled matrix’

In this note, a method of converting a rhotrix to a special form of matrix termed a ‘coupled matrix’ is proposed. The special matrix can be used to solve various problems involving n?×?n and (n?–?1)?×?(n?–?1) matrices simultaneously.     

Conservation laws for a complexly coupled KdV system,coupled Burgers’ system and Drinfeld–Sokolov–Wilson system via multiplier approach

The multiplier approach (variational derivative method) is used to derive the conservation laws for some nonlinear systems of partial differential equations. Firstly, the multipliers (characteristics) are computed and then conserved vectors are obtained for the each multiplier. Examples of the third-order complexly coupled KdV system, second-order coupled Burgers’ system and third-order Drinfeld–Sokolov–Wilson system are considered. For all three systems the local conservation laws are established by utilizing the multiplier approach.     

Hirota bilinearization of coupled higher-order nonlinear Schrödinger equation

In this paper, we present the Hirota bilinearization of the coupled Sasa–Satsuma equation. The procedure employed here generates a more general solution than the one reported earlier. We also discuss the soliton solutions of the equation and show that the solutions found earlier are only special cases of the solution discussed here.     

Pfaffian solution for coupled discrete nonlinear Schrödinger equation

The Pfaffian solution for the coupled discrete nonlinear Schrödinger equation is studied by using the direct method of soliton theory. The bilinear form of the equation contains a new Pfaffian identity. The Pfaffian representation of Toeplitz determinant is also derived.     

New numerical methods for the coupled nonlinear Schrödinger equations

In this paper, three numerical schemes with high accuracy for the coupled Schrodinger equations are studied. The conserwtive properties of the schemes are obtained and the plane wave solution is analysised. The split step Runge-Kutta scheme is conditionally stable by linearized analyzed. The split step compact scheme and the split step spectral method are unconditionally stable. The trunction error of the schemes are discussed. The fusion of two solitions colliding with different β is shown in the figures. The numerical experments demonstrate that our algorithms are effective and reliable.     

On–off intermittency and coherent bursting in stochastically-driven coupled maps

On–off intermittency is a phase space mechanism for bursting in dynamical systems. Here we recall how the simple example of a logistic map with a time-dependent control parameter, considered as a dynamical variable of the system, gives rise to bursting or on–off behavior. We show that, for a given realization of the driver, a stochastically driven logistic map in the on–off intermittent regime always converges to the same temporal dynamics, independently of initial conditions. In that sense, the map is not chaotic. We then explore the behavior of two coupled on–off logistic maps, each driven by a separate random process, and show that, for a wide range of coupling strengths, bursting becomes at least partially coherent. The bursting coherence has a smooth dependence on the coupling parameter and no sharp transition from coherence to incoherence is detected. In the system of two coupled on–off maps studied here, coherent bursting is rooted in the behavior during off phases when the mapped coordinates take on extremely small values.