Calculating standard captured γ spectra of formation elements

Multi-element gamma-ray spectrum logging requires standard spectra of individual elements for its interpretation.Since the standard element spectra are usually derived using Monte Carlo simulation of either a pure element or its oxide,we synthesized the standard neutron captured γ spectra（as would be observed using a NaI（Tl） detector） of elements H,Si,Ca and Fe from each element and its oxide.To compare the standard spectra from the elements and oxides,we operated three simulations of sandstone,limestone and mixed formation of sandstone and limestone each with ten different porosities,and used the two kinds of standard spectra to analyze the mixed spectra modeled from sandstone and limestone formations.The results show that the standard element spectra from oxides have more prominent energy peaks than the standard spectra from pure elements.The calculated formation element contents are close to the theoretical values when the standard element spectra from oxides are used to analyze the formation mixed spectra.Therefore,the formation element standard spectra should be calculated from oxide models in the analysis of neutron captured γ spectra by logging tools.

FINITE ELEMENT ANALYSIS FOR CHIP FORMATION IN HIGH SPEED TURNING OPERATIONS BY ARBITRARY LAGRANGIAN EULERIAN METHOD

A two-dimensional finite element （FE） model for the high speed turning operations when orthogonally machining AISI H13 tool steel at 49HRC using poly crystalline cubic boron nitride （PCBN） is described. An arbitrary Lagrangian Eulerian （ALE） method has been adopted which does not need any chip separation criteria as opposed to the traditional Lagrangian approach. Through FE simulations temperature and stresses distributions are presented that could be helpful in predicting tool life and improving process parameters. The results show that high temperatures are generated along the tool rake face as compared to the shear zone temperatures due to high thermal conductivity of PCBN tools.

Solution set on the natural satellite formation orbits under first-order earth's non-spherical perturbation

Using the reference orbital element approach, the precise governing equations for the relative motion of formation flight are formulated. A number of ideal formations with respect to an elliptic orbit can be designed based on the relative motion analysis from the equations. The features of the oscillating reference orbital elements are studied by using the perturbation theory. The changes in the relative orbit under perturbation are divided into three categories, termed scale enlargement, drift and distortion respectively. By properly choosing the initial mean orbital elements for the leader and follower satellites, the deviations from originally regular formation orbit caused by the perturbation can be suppressed. Thereby the natural formation is set up. It behaves either like non-disturbed or need little control to maintain. The presented reference orbital element approach highlights the kinematics properties of the relative motion and is convenient to incorporate the results of perturbation analysis on orbital elements. This method of formation design has advantages over other methods in seeking natural formation and in initializing formation.

CONVERGENCE OF SIMPLIFIED AND STABILIZED MIXED ELEMENT FORMATS BASED ON BUBBLE FUNCTION FOR THE STOKES PROBLEM

Two simplifled and stabilized mixed element formats for the Stokes problem are derived by bubble function, and their convergence, i.e., error analysis, are proved. These formats can save more freedom degrees than other usual formats.

Reduced-order proper orthogonal decomposition extrapolating finite volume element format for two-dimensional hyperbolic equations

This paper is concerned with establishing a reduced-order extrapolating fi- nite volume element （FVE） format based on proper orthogonal decomposition （POD） for two-dimensional （2D） hyperbolic equations. For this purpose, a semi discrete variational format relative time and a fully discrete FVE format for the 2D hyperbolic equations are built, and a set of snapshots from the very few FVE solutions are extracted on the first very short time interval. Then, the POD basis from the snapshots is formulated, and the reduced-order POD extrapolating FVE format containing very few degrees of freedom but holding sufficiently high accuracy is built. Next, the error estimates of the reduced-order solutions and the algorithm procedure for solving the reduced-order for- mat are furnished. Finally, a numerical example is shown to confirm the correctness of theoretical conclusions. This means that the format is efficient and feasible to solve the 2D hyperbolic equations.

Elliptical formation control based on relative orbit elements

A new set of relative orbit elements（ROEs）is used to derive a new elliptical formation flying model.In-plane and out-of-plane motions can be completely decoupled,which benefts elliptical formation design.The inverse transformation of the state transition matrix is derived to study the relative orbit control strategy.Impulsive feedback control laws are developed for both in-plane and out-of-plane relative motions.Control of in-plane and out-of-plane relative motions can be completely decoupled using the ROE-based feedback control law.A tangential impulsive control method is proposed to study the relationship of fuel consumption and maneuvering positions.An optimal analytical along-track impulsive control strategy is then derived.Different typical orbit maneuvers,including formation establishment,reconfguration,long-distance maneuvers,and formation keeping,are taken as examples to demonstrate the performance of the proposed control laws.The effects of relative measurement errors are also considered to validate the high accuracy of the proposed control method.