Modeling a waveguide with a nonlinear insert with a quadratic nonlinearity

The scalar problem of the scattering of a wave from a nonlinear insertion lying in the interior of a waveguide is reduced by the incomplete Galerkin method to the boundary value problem for a Hamiltonian system. The cases in which this problem admits a solution in finite terms are indicated. Examples are given to illustrate specific phenomena due to the nonlinearity of the problem.     

Hartree-Fock theory with constrained deformation

We study the variational Hartree-Fock problem with constrained deformation. If the deformation is defined by prescribed expectation values of the conventional multipole moments, we show that a necessary condition for the problem to have physically meaningful solutions is that the multipole operators are negligible outside the nucleus, so that they must be state dependent. In this way, a further non-linearity is introduced into the problem. An alternative formulation is to impose a given shape to the nuclear surface by means of two inequality constraints.     

Hamiltonian systems with constraints: A geometric approach

Hamilton-Dirac equations for a constrained Hamiltonian system are deduced from a variational principle. In the local problem for such systems an algorithm is proposed to obtain the final constraint manifold and the dynamical vector field on it using vector fields on the phase space. The global problem is solved in terms of fiber bundles associated with the problem.     

Contact problem with wear for a foundation with a surface nonuniform coating

The plane contact problem with wear for an elastic foundation with a longitudinally nonuniform (surface nonuniform) coating and a rigid punch with a flat foundation has been solved for the first time. The case of linear wear is considered. The nonuniformity of the coating is described by a rapidly changing function. This strong nonuniformity arises when coatings are deposited using modern additive manufacturing technologies. The problem is reduced to the solution of an integral equation with two different integral operators: a compact self-adjoint positively defined operator with respect to the coordinate and the non-selfadjoint integral Volterra operator with respect to time. The solution is obtained in series using author’s projection method. The efficiency of the proposed approach for constructing a high-accuracy approximate solution to the problem (with only a few expansion terms retained) is demonstrated. A simple engineering formula for estimating the contact stresses under a punch for large values of times is proposed.     

Light transfer problem in turbid media with surface reflectivity

Light transfer problems in turbid media with surface reflectivity satisfying Fresnel's law are formulated. The intensity of light is considered as a sum of collimated and diffuse radiances. The problem with a collimated source and boundary conditions with surface reflectivity is solved in terms of the corresponding source-free problem with simple boundary conditions. In order to solve the source-free problem, two-flux models in the differential and integral forms are obtained. For the differential form, weight functions are introduced in order to force the boundary conditions to be met, while in the integral form the boundary conditions are embedded. The integral form has the advantage over the differential form that it permits one to extend the validity of the model and to consider inhomogeneous media. Numerical results are given for albedos and partial fluxes depending upon the refractive index of the medium. The calculations are performed in both semi-infinite and finite media and are compared with the published calculations.     

Self-induced transparency with the Stark pulse technique

A theory based on the method of the inverse scattering problem is presented describing propagation of an ultrashort light pulse under the condition that resonant interaction with atoms of the medium is initially switched on by an additional Stark pulse. A Hamiltonian form of the Maxwell-Bloch equation is found without redefining the spatiotemporal variables. The method of the inverse scattering problem is based on a special spectral problem. Equations of the Gel’fand-Levitan-Marchenko type and a soliton solution are obtained.     

Stochastic radiative transfer in a finite plane-parallel medium with general boundary conditions

The time-independent radiative transfer problem in a scattering and absorbing planar random medium with general boundary conditions and internal energy source is considered. The medium is assumed to consist of two randomly mixed immiscible fluids, with the mixing statistics described as a two-state homogeneous Markov process. The problem is solved in terms of the solution of the corresponding free-source problem with simple boundary conditions which is solved using Pomraning-Eddington approximation in the deterministic case. A formalism, developed to treat radiative transfer in statistical mixtures, is used to obtain the ensemble-averaged solution. The average partial heat fluxes are calculated in terms of the albedoes of the source-free problem. Results are obtained for isotropic and anisotropic scattering for specular and diffused reflecting boundaries.     

Tokamak equilibria with reversed current density

Observations of nearly zero toroidal current in the central region of tokamaks (the "current hole") raises the question of the existence of toroidal equilibria with very low or reversed current in the core. The solutions of the Grad-Shafranov equilibrium equation with hollow toroidal current density profile including negative current density in the plasma center are investigated. Solutions of the corresponding eigenvalue problem provide simple examples of such equilibrium configurations. More realistic equilibria with toroidal current density reversal are computed using a new equilibrium problem formulation and computational algorithm which do not assume nested magnetic surfaces.     

The albedo problem with Fresnel reflection

The classic albedo problem for a half-space is generalised to include the effect of refraction at the boundary by inclusion of the Fresnel boundary conditions. The problem is solved using the Wiener-Hopf technique with both specular and diffuse reflection. The non-singular Fredholm integral equations that arise for the surface angular distribution are solved numerically and the solutions are illustrated by a number of results in graphical and tabular form. The significant effect of refraction on the albedo and the associated angular distributions is highlighted.     

Determination of isoclinics in photoelasticity with a fast regularized estimator

The determination of isoclinics from photoelastic fringe patterns is a key problem in photoelasticity. Dealing with this problem, however, is not a simple task when isotropic points are present which is common for most experimental situations. Because of this, few researchers have proposed effective and practical solutions. Visualizing this problem as the problem of the determination of the modulo 2π fringe orientation, in this paper it is proposed an efficient regularized algorithm to solve it. Experimental results show that the proposal is effective and can be used with either monochromatic or white light.     

Passivity analysis for uncertain neural networks with discrete and distributed time-varying delays

In this Letter, the passivity problem of uncertain neural networks with discrete and distributed time-varying delays is investigated. New delay-dependent conditions for this problem are obtained by using a novel Lyapunov functional together with the linear matrix inequality (LMI) approach. Numerical examples are given to show the effectiveness of our theoretical results.     

Reflection analysis for planar surface wave antennas with different tapering profiles

The reflection characteristics of the planar surface wave antennas with different tapering profiles are analyzed by a method which transforms the radiation problem into the transmission problem of the eigen mode in the partially dielectric filled planar waveguide to avoid the difficulty of the field source problem which is met in the traditional analysis. As a result, the analysis procedure is tremendously simplified. The effect of the tapering profile on the reflection property is carefully investigated and extensive numerical results are given to establish useful guidelines for the design of the planar surface wave antennas.     

Radiation transfer for a homogeneous half-space with an internal source

The emergent flux for radiation transfer in a homogeneous half-space with internal source solved in terms of the diffuse reflection problem. An efficient method of analysis which utilizes trial functions based on Cases eigenvalues is developed for solving the problem. Numerical results are given and compared with the previous results.     

Diffuse waves in a random medium layer with rough boundaries

The problem of scattering from a random medium layer with rough boundaries is formulated as an integral equation in which the random fluctuations are represented as a zero-mean random operator. The analysis for the diffuse fields is based on the ladder-approximated Bethe-Salpeter equation. An integral equation for the diffuse intensities thus derived displays the various multiple-scattering processes involved in our problem. Transport equations are also derived and several special cases are considered to illustrate the characteristics of the results and to compare them with those in the literature.     

Two-Level Defect-Correction Method for Steady Navier-Stokes Problem with Friction Boundary Conditions

In this paper, we present two-level defect-correction finite element method for steady Navier-Stokes equations at high Reynolds number with the friction boundary conditions, which results in a variational inequality problem of the second kind. Based on Taylor-Hood element, we solve a variational inequality problem of Navier-Stokes type on the coarse mesh and solve a variational inequality problem of Navier-Stokes type corresponding to Newton linearization on the fine mesh. The error estimates for the velocity in the $H^1$ norm and the pressure in the $L^2$ norm are derived. Finally, the numerical results are provided to confirm our theoretical analysis.     

共轭梯度法求解双曲传热多宗量反问题

提出双曲传热反问题热物性参数和边界条件多宗量联合反演的一般数值求解模式,考虑了非均质和分布参数的影响,时域上采用时域精细算法进行离散,建立了便于敏度分析的有限元正演模型.由最小二乘原理建立反演模型,应用共轭梯度法进行求解.探讨了时间步长和测量误差对反演结果的影响,并进行了数值验证.     

Simulations of MHD flows with moving interfaces

We report on the numerical simulation of a two-fluid magnetohydrodynamics problem arising in the industrial production of aluminium. The motion of the two non-miscible fluids is modeled through the incompressible Navier–Stokes equations coupled with the Maxwell equations. Stabilized finite elements techniques and an arbitrary Lagrangian–Eulerian formulation (for the motion of the interface separating the two fluids) are used in the numerical simulation. With a view to justifying our strategy, details on the numerical analysis of the problem, with a special emphasis on conservation and stability properties and on the surface tension discretization, as well as results on tests cases are provided. Examples of numerical simulations of the industrial case are eventually presented.     

Bethe-Salpeter Equation with Self-Energy Graphs I-Generalized Fredholm Theory,Parameter Imbedding Method

In this paper the classical Fredholm theory is generalized. The conceptions of the generalized fredholm denominator (GFD) and generalized Fredholm numerator (GFN) are defined. A set of parameter imbedding equations for GFD and GFN is deduced. In this way, the eigenvalue problem of the BS equation in ladder approximation with self-energy graphs, and the eigenvalue problem of nonlinear parameter integral equation, are carried over into an initial-value problem of a set of ordinary differential equations.     

外伸梁差分离散系统的模态反问题

研究外伸梁模态的反问题,即由两组位移模态或应变模态及相应的频率构造外伸梁差分离散模型物理参数的方法,讨论反问题解存在的充要条件.提出算法并用算例验证.结果表明,由应变模态构造外伸梁的物理参数比用位移模态构造梁的物理参数精度要高.     

双频光栅轮廓术的研究

在投影栅相位法轮廓检测中,当物体含突变部分时,包裹相位很难准确恢复,对此可用双频变精度技术来解决。如果用两种不同频率光栅分两次进行测量,无疑增加了测量负担,也无法满足实时检测的要求。提出用软件生成两种不同频率成分的复合正弦光栅,用液晶投影仪投影,针对不同物体具体突变部分的情况,可灵活生成各种不同灵敏度的复合光栅。只采一次图像就可以达到以往双频技术中多次采集的效果,该法具有快速和去包裹精度高的特点。最后,进行了实验测试,结果非常满意。