A fast method to generate collisional excitation cross-sections of highly charged ions in a hot dense matter

A method to compute collisional excitation cross-sections in jj-averaged configuration sets is presented in the framework of plane-wave Born approximation using Dirac–Hartree–Slater wave functions with appropriate low-energy corrections. When averaged into the ls configuration or hydrogenic superconfiguration sets, the results are found to compare with distorted wave calculations well within 30% on average. The cross-sections are averaged into hydrogenic cross-sections and fitted using the Gaunt factor formalism. We present analytic fit coefficients of Gaunt factors for 12 atoms of Z between 5 and 79 for hydrogenic transitions.     

用二维逆Born近似法对杆中圆形缺陷的反演

在三维弹性波散射问题的Born近似解基础上,进一步分析了在纵波入射条件下二维散射问题的Born近似解,对铝质长杆中的椭圆形空穴缺陷的散射场情况进行了对比分析;最后,提出了在低频下识别缺陷几何特征的二维逆Born近似法,并用此法对铝质长杆中的圆形空穴缺陷作了计算机模拟。     

Integration of the boussinesq equations for steady channel and jet flows

The equations of long nonlinear waves in round jets and channels of arbitrary cross section are considered with account for the transverse acceleration of the fluid particles (Boussinesq approximation). In the general case of steady flows, the equations in the form of shallow water equations with the pressure expressed in terms of the variational derivative of the kinetic energy of a thin transverse fluid layer, have three first integrals with three arbitrary constants. Examples of solutions of the equations for solitary capillary-gravitation waves in rectangular and triangular channels are presented and compared with the higher approximations. The shape of the free boundary of the round jet is determined. In the case of outflow from a conical nozzle an analytical dependence of the jet contraction ratio on the conicity angle is obtained. The dependence is in agreement with the experimental data for angles of less than 45°.     

Concerning the description of long nonlinear waves in channels

A method of deriving the equations that describe long nonlinear waves in channels of arbitrary cross section, taking the transverse acceleration of fluid particles into account (the Boussinesq approximation), is proposed. For channels of certain cross sections the equations are written in explicit form. In the case of narrow channels the Boussinesq equations and those of the next approximation are written in explicit form for arbitrary cross sections.     

Generalized Born scattering in anisotropic media

The Born scattering approximation has been widely used in seismology to study scattered waves, and to linearize the propagation problem for inversion. The standard Born theory requires the model be separated into a smooth, reference model and a perturbation. Scattering occurs from the pertubation. In the distorted Born approximation, when the reference model is inhomogeneous, the reference Green's functions are normally not known exactly, but the error in these Green's functions is rarely quantified. In this paper, we generalize Born scattering theory to include the errors in the Green's functions explicitly, and obtain scattering integrals from these errors. For forward modelling, there is no need to separate the model into a reference and perturbation part - approximate Green's functions in the true model can be used to calculate the scattered signals.

The theory is developed for inhomogeneous, anisotropic media. Asymptotic ray theory results are suitable approximate Green's functions for the generalized Born scattering theory. The error terms are simple, easily calculated and included in the scattering integrals. Various applications of generalized Born scattering theory have already appeared in the literature, e.g. quasi-shear ray coupling, and this paper is restricted to an improved and more complete theoretical development. Further applications will appear elsewhere.     

Purely irrotational theories for the viscous effects on the oscillations of drops and bubbles

In this paper, we apply two purely irrotational theories of the motion of a viscous fluid, namely, viscous potential flow (VPF) and the dissipation method to the problem of the decay of waves on the surface of a sphere. We treat the problem of the decay of small disturbances on a viscous drop surrounded by gas of negligible density and viscosity and a bubble immersed in a viscous liquid. The instantaneous velocity field in the viscous liquid is assumed to be irrotational. In VPF, viscosity enters the problem through the viscous normal stress at the free surface. In the dissipation method, viscosity appears in the dissipation integral included in the mechanical energy equation. Comparisons of the eigenvalues from VPF and the dissipation approximation with those from the exact solution of the linearized governing equations are presented. The results show that the viscous irrotational theories exhibit most of the features of the wave dynamics described by the exact solution. In particular, VPF and DM give rise to a viscous correction for the frequency that determines the crossover from oscillatory to monotonically decaying waves. Good to reasonable quantitative agreement with the exact solution is also shown for certain ranges of modes and dimensionless viscosity: For large viscosity and short waves, VPF is a very good approximation to the exact solution. For ‘small’ viscosity and long waves, the dissipation method furnishes the best approximation.     

Wave interaction with multiple articulated floating elastic plates

Flexural gravity wave scattering by multiple articulated floating elastic plates is investigated in the three cases for water of finite depth, infinite depth and shallow water approximation under the assumptions of two-dimensional linearized theory of water waves. The elastic plates are joined through connectors, which act as articulated joints. In the case when two semi-infinite plates are connected through a single articulation, using the symmetric characteristic of the plate geometry and the expansion formulae for wave-structure interaction problem, the velocity potentials are obtained in closed forms in the case of finite and infinite water depths. On the other hand, in the case of shallow water approximation, the continuity of energy and mass flux are used to obtain a system of equations for the determination of the full velocity potentials for wave scattering by multiple articulations. Further, using the results for single articulation and assuming that the articulated joints are wide apart, the wide-spacing approximation method is used to obtain the reflection coefficient for wave scattering due to multiple articulated floating elastic plates. The effects of the stiffness of the connectors, length of the elastic plates and water depth on the propagation of flexural gravity waves are investigated by analysing the reflection coefficient.     

Convective inertia effects in wall-bounded thin film flows

We apply the boundary layer equations to inertial flow in wall bounded films that might be characterized as ‘thin’, say ɛ ≤ 0.1 where ɛ is the ratio of the characteristic lengths, yet to which the lubrication approximation of Reynolds no longer applies. Two particular flow geometries are investigated, nominally parallel plates and nominally inclined plates, both with and without spatially periodic perturbation of the stationary plate. A Galerkin-B spline formulation of the governing equations is employed, and we rely on parametric continuation to obtain solutions at higher values of the Reynolds number. In particular, we are able to demonstrate that the boundary layer equations yield accurate results for a wide range of Reynolds numbers when the aspect ratio is less than 1/10. We also find that in both nominally parallel and nominally inclined geometries the sign of the inertial force correction is determined by the film contour in the neighborhood of the exit, this result might have implications in the design of MEMS devices.     

大延伸非均匀介质中地震波全弹性散射理论Ⅰ--弹性波单次散射理论

所描述的工作聚焦于大延伸非均匀介质中非均匀弹性地震波散射问题的研究.应用Born近似及等效源原理,推出了来自连续横向无界非均匀层的弹性散射波的通解.这一工作是解决大延伸非均匀介质的弹性地震波多次散射问题的基础.在上述通解的基础上,建立了适用于大延伸非均匀介质的全弹性散射理论.该理论可包容小尺度非均匀体、大延伸非均匀介质全弹性波单次弱散射理论及标量波单次弱散射理论,因此可视其为一个更为广义和统一的弱散射理论.     

A unified asymptotic theory of the anelastic approximation in geophysical gases and liquids

An asymptotic theory of the anelastic approximation is developed for fluids having arbitrary equations of state under two assumptions: weak compressibility and small Brunt–Väisälä frequency. We show that both Boussinesq approximation (BA) and anelastic approximation (AA) may be included in a unique quasi-incompressible approximation (QIA) already constructed by Durran for polytropic gases. The only difference between AA and BA is that, in the BA, the equations are with slowly varying coefficients, while in the AA the coefficients are fast varying. Applications are made to atmospheric air and to sea-water.     

Elastodynamic inversion for shape reconstruction and type classification of flaws

Two linearized inverse scattering methods are investigated to reconstruct the shape of flaws in the elastic solid. One is based on the Born approximation and the other is based on the Kirchhoff approximation. The Born inversion is sensitive to the volumetric flaw but not to a crack-like flaw. On the other hand, the Kirchhoff inversion reacts to both boundaries of volumetric and crack-like flaws. The combined use of Born and Kirchhoff inversions leads to the classification method of flaw type. The performance of the proposed classification procedure is demonstrated by the numerical simulations and then by the experimental measurements for the two-dimensional models of flaws. An example for the three-dimensional shape reconstruction is also shown by using the numerically calculated backscattering amplitudes.     

Chaotic Oscillation of Saddle Form Cable-Suspended Roofs under Vertical Excitation Action

The purpose of this paper is to investigate the dynamic behaviour of saddle form cable-suspended roofs under vertical excitation action. The governing equations of this problem are system of nonlinear partial differential and integral equations. We first establish a spectral equation, and then consider a model with one coefficient, i.e., a perturbed Duffing equation. The analytical solution is derived for the Duffing equation. Successive approximation solutions can be obtained in likely way for each time to only one new unknown function of time. Numerical results are given for our analytical solution. By using the Melnikov method, it is shown that the spectral system has chaotic solutions and subharmonic solutions under determined parametric conditions.     

The second order approximation theory of three dimensional elastic plates and its boundary conditions without using kirchhoff-love assumptions

The first order approximation theory of three dimensional elastic plates and its boundary conditions presented in the previous paper^[1] establishes six differential equations for the solutions of six undetermined functions u_o, u_a, A_(o) and S_(2)a defined in the x, y plane. They can be divided into two groups, each constitutes three equations to calculate u_o, S_(2)a and u_a, A_(o) respectively. Their boundary conditions as well as these equations are derived from the stationary conditions of variations of a functional for this problem based on the generalized variational principle. The solutions given by this theory are close to those given by the classical theory of thin plates as the ratio of thickness h to width a is small. For large ratio, say h/a=0.3 a considerable difference arises between the two theories. It has not been made clear that in what range of the ratio such difference is reasonable to give more precise solutions. In order, to solve this problem, we must study the second order approximation theory. In this paper following the previous one, we shall establish the second order approximation theory by applying the, stationary condition of variations of a functional for this problem based on the generalized variational principle, to derive nine differential equations and the relate boundary conditions, which are used to calculate nine undetermined functions u_o u_a, A_(o), A₍₁₎, S_(2)a and S_(3)a. And the range of the validity of the first order approximation theory can be found out by comparing the second order theory with the first order theory and the classical theory. It should be pointed out here that the equations of, the second order theory can also be divided into two groups to be solved separately, and the procedure of solution is not too complicate to perform as well. Here, we will use the same notations adopted in the previous paper, and not repeat their definitions.     

The structure and asymptotic behaviour of compression waves

In the study of weak solutions to nonlinear hyperbolic partial differential equations both rarefaction waves and compression waves arise. Although the behavior of rarefaction waves is known for all time, the characteristics that determine a compression wave intersect and hence the development of the wave is not easily determined. The purpose of this paper is to study compression waves. As a first step we consider the Cauchy problem for the nonlinear wave equation. We show that if the data outside some finite interval consist of constant states, then after finite time the solution involves the same states as does the solution to the Riemann problem determined by these constant states. This result is then applied to compression waves to obtain information on the shock that arises and on the steady-state solution. The region of interaction is also described. This information is obtained via a constructive procedure.     

Generation of Nonlinear Waves on a Viscoelastic Coating in a Turbulent Boundary Layer

Self–induced excitation of periodic nonlinear waves on a viscoelastic coating interacting with a turbulent boundary layer of an incompressible flow is studied. The response of the flow to multiwave excitation of the coating surface is determined in the approximation of small slopes. A system of equations is obtained for complex amplitudes of multiple harmonics of a slow (divergent) wave resulting from the development of hydroelastic instability on a coating with large losses. It is shown that three–wave resonant relations between the harmonics lead to the development of explosive instability, which is stabilized due to the deformation of the mean (Sover the wave period) shear flow in the boundary layer. Conditions of soft and hard excitation of divergent waves are determined. Based on the calculations performed, qualitative features of excitation of divergent waves in known experiments are explained.     

半空间SH波方程非线性井间双参数反演

以半空间的ＳＨ波方程出发,采用Ｂｏｒｎ迭代法求解半空间弹性介质中密度和剪切模量分布的非线性反演问题。首先,采用矩量法和正则化方法,给出井间反演积分方程的离散形式,然后应用Ｂｒｏｎ迭代法求解非线性反演问题。     

An approximate analysis of thickness-stretch waves in an elastic plate

Two-dimensional equations for coupled extensional and thickness-stretch waves in an elastic plate are simplified by eliminating the extensional displacements in a systematic manner; the result is a single equation governing thickness-stretch motions. A similar reduction is also performed for coupled extensional, thickness-stretch, and symmetric thickness-shear waves. The procedure is similar to that used in the thickness-shear approximation, wherein the flexural displacement is eliminated from the equations for coupled flexural and thickness-shear motions. The resulting equations are used to discuss the energy-trapped vibration of plates in thickness-stretch modes.     

The Effect of Thermal Expansion on Porous Media Convection Part 1: Thermal Expansion Solution

The effect of thermal expansion on porous media convection is investigated by isolating first the solution of thermal expansion in the absence of convection which allows to evaluate the leading order effects that need to be included in the convection problem that is solved later. A relaxation of the Boussinesq approximation is applied and the relevant time scales for the formulated problem are identified from the equations as well as from the derived analytical solutions. Particular attention is paid to the problem of waves propagation in porous media and a significant conceptual difference between the isothermal compression problem in flows in porous media and its non-isothermal counterpart is established. The contrast between these two distinct problems, in terms of the different time scales involved, is evident from the results. While the thermal expansion is identified as a transient phenomenon, its impact on the post-transient solutions is found to be sensitive to the symmetry of the particular temperature initial conditions that are applied.     

On the one-dimensional modeling of camber bending deformations in active anisotropic slender structures

The paper presents a one-dimensional model for anisotropic active slender structures that captures arbitrary cross-sectional deformations. The 1-D geometrically-nonlinear static problem is derived by an asymptotic reduction process from the equations of 3-D electroelasticity. In addition to the conventional (bending–extension–shear–twist) beam strain measures, it includes a Ritz approximation to account for arbitrary deformation shapes of the finite-size cross-sections. As a particular case, closed-form analytical expressions are derived for the linear static equilibrium of a composite thin strip with surface-mounted piezoelectric actuators. This solution is based on a boundary-layer approximation to the static equilibrium equations in regions where Saint-Venant’s principle for elastic bodies cannot be applied and includes camber bending deformations to account for the local bimoments induced by the distributed actuation in a finite-width strip.