Misorientation dependent thermal condition-solute field cooperative effect on competitive grain growth in the converging case during directional solidification of a nickel-base superalloy

Nowadays,thermal condition and solute field are considered as the potential dominant factors controlling competitive grain growth during directional solidification process.However,the controlling modes and critical conditions of competitive grain growth have been drastically debated over the past two decades.In this work,thermal condition and solute field are combined to study the competitive grain growth in the converging case by experimental observation and numerical simulation of bicrystal samples.We find the competitive grain growth is controlled by the cooperative effect of thermal condition and solute field,and the controlling modes are related to the bicrystal misorientation between favorably and unfavorably oriented grains.When the unfavorably oriented grain is low misoriented,unfavorably oriented grain dominates grain selection,and the competitive grain growth performs as solute field domination.However,with the increase of unfavorably oriented grain’s misorientation,the grain selection converts into favorably oriented grain domination,and the competitive grain growth changes to thermal condition domination.To explain these abnormal transformation phenomena,we propose a misorientation dependent thermal condition-solute field cooperative domination model and identify the critical conditions by a critical misorientation(θ_(cm)).According to dynamic equation of dendrite growth,we calculate the critical misorientationθ;to prove this model.The theoretical calculation results agree well with the experimental results.

Investigation of the solute transportation coupled with heat transfer and fluid flow during twin-roll strip casting process

Mathematical model of solute [C] distribution in twin-roll strip casting process has been setup successfully with Calcosoft for the first time. Simulation result shows that in the center of the molten steel pool between the two rolls there is a vortex flow, which is a solute enriched area. But the highest solute concentration position is at the solidification front of the columnar grain zone near the cooling roll surface. Another solute enriched position is in the back flow above the nip point. Combined with the formation mechanism of microstruoture in final as cast strip, analysis shows that solute enriched area is in the transitional area between columnar and equiaxed grain zone.

An analytical model for local-nonequilibrium solute trapping during rapid solidification

Updated version of local non-equilibrium diffusion model （LNDM） for rapid solidification of binary alloys was considered. The LNDM takes into account deviation from local equilibrium of solute concentration and solute flux fields in bulk liquid. The exact solutions for solute concentration and flux in bulk liquid were obtained using hyperbolic diffusion equations. The results show the transition from diffusion-limited to purely thermally controlled solidification with effective diffusion coefficient →0 and complete solute trapping KLNDM（v）→1 at v→vDb for any kind of solid-liquid interface kinetics. Critical parameter for diffusionless solidification and complete solute trapping is the diffusion speed in bulk liquid vDb. Different models for solute trapping at the interface with different interface kinetic approaches were considered.

Equation of Motion of a Mass Point in Gravitational Field and Classical Tests of Gauge Theory of Gravity

A systematic method is developed to studY the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton＇s second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.

Exact Solution to Spin Squeezing of the Arbitrary-Range Spin Interaction and Transverse Field Model

We investigate spin squeezing effects of trapped ions in an off-resonance optical potential system using the arbitrary range spin spin interaction and transverse field model. The collective spin noises at any time are analyzed exactly. The general expression of spin squeezing factor is presented for arbitrary-range spin interaction. For the nearest-neighbor and next-nearest neighbor spin interaction model, the analytic solutions are reduced from the general expressions. It is shown that the maximum spin squeezing is enhanced for the general arbitrary-range spin interaction compared with the nearest-neighbor interaction model as the long-range interaction with arbitrary sites enforces stronger correlation.

Influence of electric field on the quenched-in vacancy and solute clustering during early stage ageing of Al-Cu alloy

The effects of electric field on the evolution of excess quenched-in vacancy as well as solute clustering in Al-4wt%Cu alloy, and on the vacancy migration and formation enthalpy of pure aluminum were investigated, using positron annihilation lifetime spectroscopy, high-angle annular dark-field scanning transmission electron microscopy, transmission electron microscopy, hardness measurement and four-probe electrical resistivity measurement. The results showed that the electric field improved age hardening response obviously and postponed the decay of excess vacancies for 30rain during the early stage ageing of Al-4wt%Cu alloy. A large number of 2-4nm GP zones with dense distribution were observed after 1 min ageing with an electric field applied. The electric field-assisted-aged sample owned a lower coarsening rate of GP zone, which was about three fifths of that in the aged sample without an electric field, from 1 min to 120 rain ageing. The electric field contributed 8% increase of the vacancy migration enthalpy （0.663 ±0.021 eV） of pure Al, comparing with that （0.611 ±0.023 eV） of pure Al without an electric field. The increase of vacancy migration enthalpy, induced by the electric field, was responsible for the difference on evolution of quenched-in vacancy, rapid solute clustering and age hardening improvement during the early stage ageing of Al-4wt%Cu alloy.

Ricci Symmetries of Static Space-Times with Maximal Symmetric Transverse Spaces

In the paper [M. Akbar and R.G. Cai, Commun. Theor. Phys. 45 （2006） 95], a complete classification is provided with at least one component of the vector field V is zero. In this paper, I consider the vector field V with all non-zero components and the static space times with maximal symmetric transverse spaces are classified according to their Ricci collineations. These are investigated for non-degenerate Ricci tensor det R ≠0. It turns out that the only collineations admitted by these spaces can be ten, seven, six or four. It also covers our previous results as a spacial case. Some new metrics admitting proper Ricci collineations are also investigated.

Ricci Collineations of Static Space Times with Maximal Symmetric Transverse Spaces

A complete classification of static space times with maximal symmetric transverse spaces is provided, according to their Ricci collineations. The classification is made when one component of Ricci collineation vector field V is non-zero （cases 1 - 4）, two components of V are non-zero （cases 5 - 10）, and three components of V are non-zero （cases 11 - 14）, respectlvily. Both non-degenerate （detRab ≠ 0） as well as the degenerate （det Rab = 0） cases are discussed and some new metrics are found.

STRESS RATE INTEGRAL EQUATIONS OF ELASTOPLASTICITY

The stress rate integral equations of elastoplasticity are deduced based on Ref. [1] by consistent methods. The point at which the stresses and/or displacements are calculated can be in the body or on the boundary, and in the plastic region or elastic one. The existence of the principal value integral in the plastic region is demonstrated strictly, and the theoretical basis is presented for the paticular solution method by unit initial stress fields. In the present method, programming is easy and general, and the numerical results are excellent.

Exact solution for the rotational flow of a generalized second grade fluid in a circular cylinder

This paper deals with the rotational flow of a generalized second grade fluid, within a circular cylinder, due to a torsional shear stress. The fractional calculus approach in the constitutive relationship model of a second grade fluid is introduced. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms to satisfy all imposed initial and boundary conditions. The solutions corresponding to second grade fluids as well as those for Newtonian fluids are obtained as limiting cases of our general solutions. The influence of the fractional coefficient on the velocity of the fluid is also analyzed by graphical illustrations.

A rapid compensation method for launch data of long-range rockets under influence of the Earth＇s disturbing gravity field

Regarding the rapid compensation of the influence of the Earth＇ s disturbing gravity field upon trajectory calculation,the key point lies in how to derive the analytical solutions to the partial derivatives of the state of burnout point with respect to the launch data.In view of this,this paper mainly expounds on two issues：one is based on the approximate analytical solution to the motion equation for the vacuum flight section of a long-range rocket,deriving the analytical solutions to the partial derivatives of the state of burnout point with respect to the changing rate of the finalstage pitch program;the other is based on the initial positioning and orientation error propagation mechanism,proposing the analytical calculation formula for the partial derivatives of the state of burnout point with respect to the launch azimuth.The calculation results of correction data are simulated and verified under different circumstances.The simulation results are as follows：（1） the accuracy of approximation between the analytical solutions and the results attained via the difference method is higher than 90%,and the ratio of calculation time between them is lower than 0.2%,thus demonstrating the accuracy of calculation of data corrections and advantages in calculation speed;（2） after the analytical solutions are compensated,the longitudinal landing deviation of the rocket is less than 20 m and the lateral landing deviation of the rocket is less than 10 m,demonstrating that the corrected data can meet the requirements for the hit accuracy of a long-range rocket.

Solvability of Parabolic Anderson Equation with Fractional Gaussian Noise

This paper provides necessary as well as sufficient conditions on the Hurst parameters so that the continuous time parabolic Anderson model ∂u/∂t=1/2△+u˙W on[0,∞)×R^(d) with d≥1 has a unique randomfield solution,where W(t,x)is a fractional Brownian sheet on[0,∞)×Rd and formally ˙W=∂d+1/∂t+∂x_(1)…∂x_(d)=W(t,x).When the noise W(t,x) is white in time,our condition is both necessary and sufficient when the initial data u(0,x)is bounded between two positive constants.When the noise is fractional in time with Hurst parameter H_(0)>1/2,our sufficient condition,which improves the known results in the literature,is different from the necessary one.