Integrable boundary conditions for the B_2 model

New integrable B_2 model with off-diagonal boundary reflections is proposed. The general solutions of the reflection matrix for the B_2 model are obtained by using the fusion technique. Wefind that the reflection matrix has 7 free boundary parameters, which are used to describe the degree of freedom of boundary couplings, without breaking the integrability of the system. The new quantization conditions will induce the novel structure of the energy spectrum and the boundary states. The corresponding boundary effects can be studied based on the results in this paper. Meanwhile, the reflection matrix of high rank models associated with Bnalgebra can also be obtained by using the method suggested in this paper.     

Multiple rogue wave and solitary solutions for the generalized BK equation via Hirota bilinear and SIVP schemes arising in fluid mechanics

The multiple lump solutions method is employed for the purpose of obtaining multiple soliton solutions for the generalized Bogoyavlensky-Konopelchenko(BK) equation. The solutions obtained contain first-order, second-order, and third-order wave solutions. At the critical point,the second-order derivative and Hessian matrix for only one point is investigated, and the lump solution has one maximum value. He's semi-inverse variational principle(SIVP) is also used for the generalized BK equation. Three major cases are studied, based on two different ansatzes using the SIVP. The physical phenomena of the multiple soliton solutions thus obtained are then analyzed and demonstrated in the figures below, using a selection of suitable parameter values.This method should prove extremely useful for further studies of attractive physical phenomena in the fields of heat transfer, fluid dynamics, etc.     

Vertex correction and conductivity in 2D Dirac-like systems with non-conserving spin disorder

We determine the classical diffusion of two dimensional Dirac-like quasiparticles, in the presence of conserving spin disorder (scattering off electric impurities) and non-conserving spin disorder (scattering off magnetic impurities). We use the Kubo formula for the conductivity tensor and employ diagrammatic perturbation theory to calculate the vertex correction and the renormalisation of the current operator for both electric and magnetic scattering. Scattering off electric impurities is isotropic and the current operator renormalised to two times the bare current operator irrespective of the direction of the dynamics, as usual for Dirac-like fermions. For magnetic scattering the renormalisation of the current operator depends on the direction of the dynamics and on the polarisation of the magnetic impurities, making the system anisotropic. We calculate the anisotropic magnetoresistance (AMR) and analyse it as a function of the ratio of the strength of the electric to the magnetic scattering potentials, for short range Gaussian correlation.     

Coordinate transformation and construction of finite element mesh in a diverted tokamak geometry

A coordinate transformation technique between straight magnetic field line coordinate system (Ψ, θ) and Cartesian coordinate system (R, Z) is presented employing a Solov'ev solution of the Grad-Shafranov equation. Employing the equilibrium solution, the poloidal magnetic flux Ψ(R, Z) of a diverted tokamak, magnetic field line equation is solved computationally to find curves of constant poloidal angle θ, which provides us with explicit relations R = R(Ψ, θ) and Z = Z(Ψ, θ). Correspondingly, conversion from one coordinate to the other along particle trajectories in the vicinity of separatrix is demonstrated. Based on the magnetic structure, a finite element mesh is generated in a diverted tokamak geometry to solve Poisson's equation.     

基于激光雷达的垂直能见度反演算法及其误差评估

针对大气垂直方向上消光系数分布不均匀难以用传统方法直接测量垂直能见度的问题,提出了一种基于激光雷达探测垂直能见度的计算方法。根据大气辐射传输基本原理,借助于辐射传输方程,推导出了垂直能见度的计算公式;然后利用激光雷达原理方程和Klett算法反演出大气垂直方向上的消光系数分布,基于此提出了垂直能见度的迭代算法。最后,利用灰色模型GM(1,1)和批统计算法,对激光雷达反演得到的后向散射系数进行了评估,给出了误差置信区间为(0.760±0.339)×10^-4(srad·km)^-1。结果表明,该方法是一种特别有效的计算垂直能见度的方法,符合探测的基本需求,且误差小精度高。     

基于Retinex理论与概率非局部均值的红外图像增强方法

针对传统红外图像增强算法中细节模糊及过度增强的问题,提出了一种基于Retinex理论与概率非局部均值相结合的红外图像增强方法.首先通过单尺度Retinex方法调整图像中过暗与过亮部分的灰度级;然后利用概率非局部均值对图像进行分解处理得到基本层与细节层,对基本层采用直方图均衡化拉伸对比度,对细节层采用非线性函数进行增强;最后,将不同层次的结果融合得到对比度与细节增强的红外图像.用该方法对多组不同场景的红外图像进行仿真实验,并将其与多种增强方法进行主、客观对比分析,结果表明所提方法在红外图像的细节及对比度增强方面都获得了更好的效果.     

Soliton molecules and the CRE method in the extended mKdV equation

The soliton molecules of the(1+1)-dimensional extended modified Korteweg–de Vries(mKdV)system are obtained by a new resonance condition, which is called velocity resonance. One soliton molecule and interaction between a soliton molecule and one-soliton are displayed by selecting suitable parameters. The soliton molecules including the bright and bright soliton, the dark and bright soliton, and the dark and dark soliton are exhibited in figures 1–3, respectively.Meanwhile, the nonlocal symmetry of the extended mKdV equation is derived by the truncated Painlevé method. The consistent Riccati expansion(CRE) method is applied to the extended mKdV equation. It demonstrates that the extended mKdV equation is a CRE solvable system. A nonauto-B?cklund theorem and interaction between one-soliton and cnoidal waves are generated by the CRE method.     

A discontinuous Galerkin method for Stokes equation by divergence-free patch reconstruction

A discontinuous Galerkin method by patch reconstruction is proposed for Stokes flows. A locally divergence-free reconstruction space is employed as the approximation space, and the interior penalty method is adopted which imposes the normal component penalty terms to cancel out the pressure term. Consequently, the Stokes equation can be solved as an elliptic system instead of a saddle-point problem due to such weak form. The number of degree of freedoms of our method is the same as the number of elements in the mesh for different order of accuracy. The error estimations of the proposed method are given in a classical style, which are then verified by some numerical examples.     

Solvent Effects in the Homogeneous Catalytic Reduction of Propionaldehyde with Aluminium Isopropoxide Catalyst: New Insights from PFG NMR and NMR Relaxation Studies

Solvent effects in homogeneous catalysis are known to affect catalytic activity. Whilst these effects are often described using qualitative features, such as Kamlet-Taft parameters, experimental tools able to quantify and reveal in more depth such effects have remained unexplored. In this work, PFG NMR diffusion and T₁ relaxation measurements have been carried out to probe solvent effects in the homogeneous catalytic reduction of propionaldehyde to 1-propanol in the presence of aluminium isopropoxide catalyst. Using data on diffusion coefficients it was possible to estimate trends in aggregation of different solvents. The results show that solvents with a high hydrogen-bond accepting ability, such as ethers, tend to form larger aggregates, which slow down the molecular dynamics of aldehyde molecules, as also suggested by T₁ measurements, and preventing their access to the catalytic sites, which results in the observed decrease of catalytic activity. Conversely, weakly interacting solvents, such as alkanes, do not lead to the formation of such aggregates, hence allowing easy access of the aldehyde molecules to the catalytic sites, resulting in higher catalytic activity. The work reported here is a clear example on how combining traditional catalyst screening in homogeneous catalysis with NMR diffusion and relaxation time measurements can lead to new physico-chemical insights into such systems by providing data able to quantify aggregation phenomena and molecular dynamics.     

Implementation of a separate fluid-neutral energy equation in SOLPS-ITER and its impact on the validity range of advanced fluid-neutral models

In plasma edge transport codes for nuclear fusion devices, fluid-neutral models offer an interesting alternative to the currently used kinetic Monte Carlo simulations, especially for cases of high ion-neutral collisionality. In this paper, we elaborate a separate neutral energy equation in the state-of-the-art SOLPS-ITER code suite, which previously assumed perfect ion-neutral temperature equilibration. Furthermore, we study the coupled plasma-neutral solutions for a range of divertor operating regimes, proving the validity of these fluid-neutral models for high-recycling and detached regimes.