Approximation Methods for Solving the Cauchy Problem

In this paper we give some new results concerning solvability of the 1-dimensional differential equation y′ = f(x, y) with initial conditions. We study the basic theorem due to Picard. First we prove that the existence and uniqueness result remains true if f is a Lipschitz function with respect to the first argument. In the second part we give a contractive method for the proof of Picard theorem. These considerations allow us to develop two new methods for finding an approximation sequence for the solution. Finally, some applications are given.     

Measurements and simulations of particle dispersion in a turbulent flow

A particle imaging technique has been used to collect droplet displacement statistics in a round turbulent jet of air. Droplets are injected on the jet axis, and a laser sheet and position-sensitive photomultiplier tube are used to track their radial displacement and time-of-flight. Dispersion statistics can be computed which are Lagrangian or Eulerian in nature. The experiments have been simulated numerically using a second-order closure scheme for the jet and a stochastic simulation for the particle trajectories. Results are presented for non-vaporizing droplets of sizes from 35 to 160 μm. The simulations have underscored the importance of initial conditions and early droplet displacement history on the droplet trajectory for droplets with large inertia relative to the turbulence. Estimates of initial conditions have been made and their effect on dispersion is quantified.     

Response of line focus acoustic microscope to specimen containing a subsurface crack

A numerical model is presented to calculate V(z) and V(x, z) curves for a line focus acoustic microscope and a specimen containing a subsurface crack. In this model, a Gaussian beam which is tracked through the lens into the coupling fluid and into the specimen, interacts with the crack. The numerical approach is based on the solution of singular integral equations by the boundary element method. The system of singular integral equations follows from the conditions at the interface of the coupling fluid and the specimen and on the faces of the crack. An electromechanical reciprocity relation is used to express the voltage at the terminals of the microscope's transducer in terms of the calculated incident and back-scattered fields. V(z) and V(x, z) curves are presented for various locations and orientations of the crack. The characteristic features of the V(z) and particularly the V(x, z) curves, as they relate to crack configuration, are discussed in some detail.     

Application of heat flow calorimetry to the study of oilwell cements

The majority of previous studies of the hydration of cements using heat flow calorimetry have been carried out isothermally. However, with oilwell cements the slurry is mixed on the surface at ambient temperature and then gradually increases in temperature as it is pumped down the well. A Setaram C-80 calorimeter has been used to simulate the temperature ramp in API oilwell cement test schedules. This approach has enabled cementing reactions to be studied for the first time under conditions approaching those encountered in the field, and has shown that the results obtained from isothermal experiments may be misleading.The permission of the British Petroleum Company PLC to publish this paper is gratefully acknowledged.     

Partially finite convex programming,Part I: Quasi relative interiors and duality theory

We study convex programs that involve the minimization of a convex function over a convex subset of a topological vector space, subject to a finite number of linear inequalities. We develop the notion of the quasi relative interior of a convex set, an extension of the relative interior in finite dimensions. We use this idea in a constraint qualification for a fundamental Fenchel duality result, and then deduce duality results for these problems despite the almost invariable failure of the standard Slater condition. Part II of this work studies applications to more concrete models, whose dual problems are often finite-dimensional and computationally tractable.     

Analysis of plane and axisymmetric flows of incompressible fluids with the stream tube method: Numerical simulation by trust-region optimization algorithm

New concepts for the study of incompressible plane or axisymmetric flows are analysed by the stream tube method. Flows without eddies and pure vortex flows are considered in a transformed domain where the mapped streamlines are rectilinear or circular. The transformation between the physical domain and the computational domain is an unknown of the problem. In order to solve the non-linear set of relevant equations, we present a new algorithm based on a trust region technique which is effective for non-convex optimization problems. Experimental results show that the new algorithm is more robust compared to the Newton-Raphson method.     

CX_2(NO_2)_2(X=H,F,C1)分子旋转势和构型稳定性的ab initio研究

本文用ab initio计算方法,采用STO-3G基组,对二硝基卤代甲烷CH_2(NO_2)_3(1),CF_2(NO_2)_2(2);CCl_2(NO_2)_2(3)等分子作了单点计算,研究其旋转势能.全构型优化研究了五个具有对称性构型的结构和稳定性,并作了理论分析和探讨.     

Averaged topological equations for dispersed two-phase flows

A general relationship between the volume fraction and the specific interfacial area for averaged dispersed two-phase flows is proposed. This relationship, expressed as a basic set of two scalar evolution equations and two vectorial non-uniformity state equations, is an analytical result obtained by a systematic approach using the derivatives of some generalized functions and a local volume-averaging technique. The proposed set of equations was expressed for measurable macroscopic parameters of the system and has the same generality as the averaged transport equations of two-phase flows. By combination of the basic set of equations, called the averaged topological equations (ATEs), second-order ATEs for the volume fraction were found. The second-order ATEs were expressed both by a Lagrangian formulation and by a Eulerian formulation. The importance and physical meaning of the ATEs developed in this study were clarified within the framework of the theory of kinematic waves.     

Effect of distortion in electron impact excitation in Coulomb-projected Born approximation

We have calculated total and differential cross-sections for 1s →ns (n = 2, 3, 4) electron impact excitation of hydrogen and hydrogenic ions at various energies in Coulomb-projected Born approximation. Distortion due to static interactions, target polarization and exchange effects has been incorporated in the initial channel. The present calculations have been compared with other theoretical and experimental results.     

There exist no 2-type surfaces in E 3 which are images under stereographic projection of minimal surfaces in S 3

In this paper we deal with the following particular case of a weaker conjecture by B. Y. Chen: Are there 2-type Willmore surfaces in E ³? In particular we prove that the above question has a negative answer when the surface is the image under stereographic projection of a minimal surface in S ³.