Liouville operator resolvent method applied to the hubbard dimer

Summary The problem of two hydrogenlike atomic sites (s-shells only) coupled via a hopping matrix is considered. We employ a new formalism, the Liouville operator resolvent method, to evaluate the single-particle thermodynamic Green’s function for this system. Details of the method are also discussed. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

The mixed finite element method as applied to waveguide diffraction problems

A mixed finite element algorithm for solving the vector problem of diffraction by an inhomogeneity in a waveguide is constructed and implemented. Partial radiation conditions are used to proceed to a bounded domain.     

A scaled boundary node method applied to two-dimensional crack problems

A boundary-type meshless method called the scaled boundary node method(SBNM) is developed to directly evaluate mixed mode stress intensity factors(SIFs) without extra post-processing.The SBNM combines the scaled boundary equations with the moving Kriging(MK) interpolation to retain the dimensionality advantage of the former and the meshless attribute of the latter.As a result,the SBNM requires only a set of scattered nodes on the boundary,and the displacement field is approximated by using the MK interpolation technique,which possesses the δ function property.This makes the developed method efficient and straightforward in imposing the essential boundary conditions,and no special treatment techniques are required.Besides,the SBNM works by weakening the governing differential equations in the circumferential direction and then solving the weakened equations analytically in the radial direction.Therefore,the SBNM permits an accurate representation of the singularities in the radial direction when the scaling center is located at the crack tip.Numerical examples using the SBNM for computing the SIFs are presented.Good agreements with available results in the literature are obtained.     

A new rf plasma oxidation method for the insulating AlOx barrier in magnetic tunneling junctions

An rf remote plasma oxidation technique to form an insulating barrier was carried out to enhance properties of CoFe/AlO_x/CoFe magnetic tunneling junctions. The rf remote plasma method was found to reduce self-bias effect on the barrier during the rf oxidation process and to increase atomic oxygen concentration in a plasma state. Experimentally observed rms roughness of the barrier in our magnetic tunnel junction was decreased from 5 to 1.5 Å. In addition, electrical breakdown voltage and magnetoresistance of our magnetic tunnel junction devices were increased from 0.8 V up to 1.2 V and from 7% up to 30%, respectively.     

Pulse analysis method as applied to one of the problems of micro- and nanooptics

The possibility of applying the pulse method to analyze operation of a multicomponent optical system, i.e., the Fresnel lens, exposed to signals of various shape and duration is shown. In particular, this method makes it possible to study random trains of femto- and attopulses and non-monochromatic radiation. The problem is especially urgent in connection with prospects for application of ultrashort pulses in solving scientific, technical, and technological problems of micro- and nanoelectronics.     

Square lattice calculations for the general dimer and trimer problems using the Kikuchi method

Square lattice models for the general dimer and trimer problems are considered. A secondary lattice for the dimer problem is constructed, and a double square Kikuchi calculation produces an athermal molecular freedom within 2% of the known exact result. With interactions, departures from ideality of mixing entropy and vapour pressure are calculated at different temperatures, and an asymmetrical phase separation occurs at a reduced temperature 0.08. The general trimer problem is considered in a single square Kikuchi calculation. A single interaction is included. The molecular freedom and thermodynamic non-ideality of rigid linear, rigid angled and flexible trimers are compared. In the rigid linear case a phase separation occurs at reduced temperature 0.04. The molecular freedom of rigid linear trimers is calculated using higher Kikuchi approximations, and the result agrees well with previous estimates.     

A multiple flux boundary element method applied to the description of surface water waves

This paper concerns a two dimensional numerical model based on a high-order boundary element method with fully nonlinear free surface boundary conditions. Multiple fluxes are applied as a method of removing the so-called “corner problem”, whereby the direction of the outward normal at geometric discontinuities is ill-defined. In the present method, both fluxes associated with differing directions of the outward normal at a corner are considered, allowing a single node to be placed at that position. This prevents any loss of information at what can be an important part of the boundary, especially if considering simulations of wave reflection and wave run-up. The method is compared to both the double node approach and the use of discontinuous elements and is shown to be a more accurate technique. The success of the method is further demonstrated by its ability to accurately simulate various problems involving wave transmission and wave-structure interactions at domain corners; the results being achieved without the need for filtering, smoothing or re-gridding of any kind.     

The generalized vectorial laws of reflection and refraction applied to the rotation problems in ray optics

This paper deals with the mirror rotation problem and the problem of rotation of refracting surface in ray optics. These two problems of rotation in ray optics have been dealt with on the basis of the generalized vectorial laws of reflection and refraction discovered by the author in 2005. In addition to the development of many interesting physical insights to the aforesaid rotation problems in ray optics, the most remarkable fact that has been discovered in the present study is that the proposition ‘Velocity of light is unattainable’ is not correct. Rather, it is possible to have velocity exceeding the velocity of light - a result not in agreement with the special theory of relativity.     

A three-parameter shooting method as applied to a problem in combustion theory

The two-step reaction A + X → 2X, 2X + M → 2P + M is considered, with high activation energy Arrhenius kinetics in the first step and zero activation energy in the second. A model of an assumed thin flame layer is shown to have a solution, using a three parameter shooting method and topological degree theory.     

Variational multiscale element free Galerkin method for the water wave problems

A new numerical method, which is based on the coupling between variational multiscale method and meshfree methods, is developed for the water wave problems, in which the free surface capturing technique is used to capture the position of the free surface. The proposed method takes full advantage of meshfree methods, therefore, no mesh generation and mesh reconstruction are involved. Meanwhile, due to that the proposed method belongs to meshfree methods, thus it is suitable for the highly deformed free surface flow problems. Finally, two water wave problems are solved and the results have also been analyzed. The numerical results show that the proposed method can indeed obtain accurate numerical results for the water wave problems, which does not refer to the choice of a proper stabilization parameter.     

A control method applied to mixed traffic flow for the coupled-map car-following model

In light of previous work [Phys. Rev. E 60 4000 （1999）], a modified coupled-map car-following model is proposed by considering the headways of two successive vehicles in front of a considered vehicle described by the optimal velocity function. The non-jam conditions are given on the basis of control theory. Through simulation, we find that our model can exhibit a better effect as p = 0.65, which is a parameter in the optimal velocity function. The control scheme, which was proposed by Zhao and Gao, is introduced into the modified model and the feedback gain range is determined. In addition, a modified control method is applied to a mixed traffic system that consists of two types of vehicle. The range of gains is also obtained by theoretical analysis. Comparisons between our method and that of Zhao and Gao are carried out, and the corresponding numerical simulation results demonstrate that the temporal behavior of traffic flow obtained using our method is better than that proposed by Zhao and Gao in mixed traffic systems.     

A weighting window applied to the digital image correlation method

In the digital image correlation method, two steps are used to calculate the displacements of tested images. The first step is to locate the integer-pixel displacement, and the next one is to compute the sub-pixel displacement based on the first step. The benefit from the computation method for the integer-pixel displacement is that its results directly affect the displacement accuracy of each point in tested images. In this paper, a new method is developed to calculate the displacement fields between two images taken before and after deformation of an object. A new correlation function with a weighting factor related to the position of each point in the image is taken into account. The analysis and experimental results confirm the validity of the new method. In addition, the calculation results from our method have more accuracy than that of the traditional one.     

用扭摆验证转动惯量平行轴定理的新方法

提出利用扭摆验证转动惯量平行轴定理的两种简单易行的新方法,并通过实验证明了该方法的可行性.     

A relaxation method for large eigenvalue problems,with an application to flow stability analysis

Linear stability analysis of fluid flows usually involves the numerical solution of large eigenvalue problems. We present a spectral transformation allowing the computation of the least stable eigenmodes in a prescribed frequency range, based on the filtering of the linearized equations of motion. This “shift-relax” method has the advantage of low memory requirements and is therefore suitable for large two- or three-dimensional problems. For demonstration purposes, this new method is applied to compute eigenmodes of a compressible jet.     

A meshless method for the nonlinear generalized regularized long wave equation

This paper presents a meshless method for the nonlinear generalized regularized long wave(GRLW) equation based on the moving least-squares approximation.The nonlinear discrete scheme of the GRLW equation is obtained and is solved using the iteration method.A theorem on the convergence of the iterative process is presented and proved using theorems of the infinity norm.Compared with numerical methods based on mesh,the meshless method for the GRLW equation only requires the scattered nodes instead of meshing the domain of the problem.Some examples,such as the propagation of single soliton and the interaction of two solitary waves,are given to show the effectiveness of the meshless method.     

A holographic method for the determination of all linear electrooptic coefficients applied to Ce-doped strontium-barium-niobate

Using c- and a-cut plates of strontium-barium-niobate doped with 0.66 mol.% cerium all nonzero components of the linear electrooptic tensor r₁₃, r₄₂, r₃₃ including the sign are determined from angular dependence of the two-beam coupling coefficient Γ using transmission and reflection geometry of holographic recording. We found: r₁₃=56 pm/V, r₄₂=38 pm/V, and r₃₃=333 pm/V. In addition we calculated the effective trap density N_eff to be 2.2×10¹⁷ cm^-3. The advantages of this method as well as the values obtained are discussed. Received: 19 November 1998 / Revised version: 15 January 1999 / Published online: 7 April 1999