Pseudo-molecular dynamics study of grain boundary segregation

The segregation of bismuth atoms on the [101] tilt copper grain boundaries Σ3 ( ) 70.53°, Σ33 ( ) 58.99°, Σ11 ( ) 50.48° and Σ9 ( ) 38.94° has been studied by pseudo-molecular dynamics using the empiricalN-body potentials. The relationship between bismuth segregation and grain boundary structure has been discussed in detail. The subject supported by the Chinese Academy of Sciences and National Natural Science Foundation of China     

Molecular dynamics study of deformation and fracture of Bi-segregated copper bicrystals

The microprocesses of deformation and fracture of Bi-segregated copper bicrystals Σ33 ( ) 58.99°, Σ11 ( ) 50.48° and Σ9 ( ) 38.94° have been simulated by molecular dynamics in order to study the relationship between the grain boundary embrittlement (GBE) and grain boundary (GB) structure. It is shown that GBE is related to the segregated concentration and distribution of Bi atoms, while Bi segregation is related to the GB structure. Due to their different structures, the bicrystals Σ33, Σ11 and Σ9 show an increasing propensity for Bi segregated concentration. So under the action of external force, Σ33, Σ11 and Σ9 show transgranular ductile, intergranular tearing and intergranular brittle fracture modes, respectively. The subject supported by the Chinese Academy of Sciences and National Natural Science Foundation of China     

The numerical stabilities of multiderivative block method

In [1], a class of multiderivative block methods (MDBM) was studied for the numerical solutions of stiff ordinary differential equations. This paper is aimed at solving the problem proposed in [1] that what conditions should be fulfilled for MDBMs in order to guarantee the A-stabilities. The explicit expressions of the polynomials and in the stability functions are given. Furthermore, we prove . With the aid of symbolic computations and the expressions of diagonal Pade' approximations, we obtained the biggest block size k of the A-stable MDBM for any given l (the order of the highest derivatives used in MDBM, l≥1)     

Effects of couple-stresses on the dispersion of a soluble matter in a pipe flow of blood

Summary An analysis of the effects of couple-stresses on the effective Taylor diffusion coefficient has been carried out with the help of two non-dimensional parameters based on the concentration of suspensions and , a constant associated with the couple-stresses. It is observed that the concentration distribution increases with increasing or The effective Taylor diffusion coefficient falls rapidly with increasing when is negative.

---

Zusammenfassung Der Einfluß der Momentenspannungen auf den effektiven Taylorschen Diffusionskoeffizienten wird untersucht. Dabei treten zwei dimensionslose Parameter and auf: Der erste bezieht sich auf die Suspensionskonzentration, der zweite kennzeichnet die Momentenspannungen. Man findet, daß die Verteilungsgeschwindigkeit mit wachsendem oder zunimmt. Dagegen fällt der Taylorsche Diffusionskoeffizient bei wachsendem stark ab, wenn negativ ist.

---

a Tube radius - C Concentration - C _i Body moment vector - C ₀ Concentration at the axis of the tube - C _m Mean concentration - D Molecular diffusion coefficient - d _ij Symmetric part of velocity gradient - F Function of and characterising effective Taylor diffusion coefficient - f _i Body force vector - H A function of and - K ₂ Integration constant - K ^* Effective Taylor diffusion coefficient - k Radius of gyration of a unit cuboid with its sides normal to the spatial axes - I _n Modified Bessel's function ofnth order - L Length of the tube over which the concentration is spread - M Function ofH and - M _ij Couple stress tensor - P Function of - p Fluid pressure - Q Volume rate of the transport of the solute across a section of the tube - r Radial distance from the axis of the tube - T _ij Stress tensor - t Time coordinate - T _ij ^A Antisymmetric part of the stress tensor - u Relative fluid velocity - Average velocity - v _i Velocity vector - Fluid velocity at any point of the tube - v ₀ ⁿ Velocity of Newtonian fluid at the axis of the tube - _i Vorticity vector - x Axial coordinate - x ₁ Relative axial coordinate - z Non-Dimensional radial coordinate - Density - _ij Symmetric part of the stress tensor - µ Viscosity of the fluid - µ _ij Deviatoric part ofM _ij - , Constants associated with couple-stress With 3 figures     

Optimal cupolas of uniform strength: Spherical M-shells and axisymmetric T-shells

Summary The first part of this paper is concerned with the optimal design of spherical cupolas obeying the von Mises yield condition. Five different load combinations, which all include selfweight, are investigated. The second part of the paper deals with the optimal quadratic meridional shape of cupolas obeying the Tresca yield condition, considering selfweight plus the weight of a non-carrying uniform cover. It is established that at long spans some non-spherical Tresca cupolas are much more economical than spherical ones.

---

Optimale Kuppeln gleicher Festigkeit: Kugelschalen und axialsymmetrische Schalen

Übersicht Im ersten Teil dieser Arbeit wird der optimale Entwurf sphärischer Kuppeln behandelt, wobei die von Misessche Fließbewegung zugrunde gelegt wird. Fünf verschiedene Lastkombinationen werden untersucht. Der zweite Teil befaßt sich mit der optimalen quadratischen Form des Meridians von Kuppeln, die der Fließbedingung von Tresca folgen.

---

List of Symbols a_k, b_k, c_k, A_k, B_k, C_k coefficients used in series solutions - A, B constants in the nondimensional equation of the meridional curve - normal component of the load per unit area of the middle surface - meridional and circumferential forces per unit width - radial pressure per unit area of the middle surface, - skin weight per unit area of the middle surface, - vertical external load per unit horizontal area, - base radius, - R radius of convergence - s - cupola thickness, - u, w subsidiary functions for quadratic cupolas - vertical component of the load per unit area of middle surface - resultant vertical force on a cupola segment - structural weight of cupola, - combined weight of cupola and skin, - distance from the axis of rotation, - vertical distance from the shell apex, - z auxiliary variable in series solutions - specific weight of structural material of cupola - radius of the middle surface, - uniaxial yield stress - meridional stress, - circumferential stress, - _a, _b, _c, _d, _e subsidiary variables used in evaluating the meridional stress - auxiliary function used in series solutions This paper constitutes the third part of a study of shell optimization which was initiated and planned by the late Prof. W. Prager     

Unsteady flow in an annulus between two concentric rotating spheres

An analysis is presented for the unsteady laminar flow of an incompressible Newtonian fluid in an annulus between two concentric spheres rotating about a common axis of symmetry. A solution of the Navier-Stokes equations is obtained by employing an iterative technique. The solution is valid for small values of Reynolds numbers and acceleration parameters of the spheres. In applying the results of this analysis to a rotationally accelerating sphere, a virtual moment of intertia is introduced to account for the local inertia of the fluid.Nomenclature R _i radius of the inner sphere - R _o radius of the outer sphere - radial coordinate - r dimensionless radial coordinate, - meridional coordinate - azimuthal coordinate - time - t dimensionless time, - Re _i instantaneous Reynolds number of the inner sphere, _i R _k ² / - Re _o instantaneous Reynolds number of the outer sphere, _o R _o ² / - radial velocity component - V _r dimensionless radial velocity component, - meridional velocity component - V dimensionless meridional velocity component, - azimuthal velocity component - V dimensionless azimuthal velocity component, - viscous torque - T dimensionless viscous torque, - viscous torque at surface of inner sphere - T _i dimensionless viscous torque at surface of inner sphere, - viscous torque at surface of outer sphere - T _o dimensionless viscous torque at surface of outer sphere, - externally applied torque on inner sphere - T _p,i dimensionless applied torque on inner sphere, - moment of inertia of inner sphere - Z _i dimensionless moment of inertia of inner sphere, - virtual moment of inertia of inner sphere - Z _i,v dimensionless virtual moment of inertia of inner sphere, - virtual moment of inertia of outer sphere - _i instantaneous angular velocity of the inner sphere - _o instantaneous angular velocity of the outer sphere - density of fluid - viscosity of fluid - kinematic viscosity of fluid,/ - radius ratio,R _i/R _o - swirl function, - dimensionless swirl function, - stream function - dimensionless stream function, - _i acceleration parameter for the inner sphere, - _o acceleration parameter for the outer sphere, - shear stress - _r dimensionless shear stress,      

Solution for plane strain forward and backward extrusions with a fractional reductionR=0.5 by the integartion depending on a parameter

A parameter t is introduced to boundary slip line of rigid regions for plane strain and indirect extrusions with a fractional reduction R=0.5. Integration by substitution has been used along the boundary slip line in order to obtain the extrusion pressure. By the integration depending on a parameter, the following results are obtained, and die pressure is 5.14k for backward extrusion; and pad average pressure is 2.57k for forward extrusion. All the results from this method are the same as those of the conventional solution.     

Transient response of a finite crack in an orthotropic strip under the in-plane shear impact

The transient response of a central crack in an orthotropic strip under the in-plane shear impact loading is studied by using the dual integral equation method proposed by Copson and Sih. The general formula for the shear stress intensity factor near the crack tip is derived. Numerical results of with in various cases are obtained by solving the second kind Fredholm integral equation and by performing the inverse Laplace transform.     

Some characteristics of low-speed streaks under sheared air-water interfaces

The characteristics of low-speed fluid streaks occurring under sheared air-water interfaces were examined by means of hydrogen bubble visualization technique. A critical shear condition under which the streaky structure first appears was determined to beu _τ≈0.19 cm/s. The mean spanwise streak spacing increases with distance from the water surface owing to merging and bursting processes, and a linear relationship describing variation of non-dimensional spacing versusy ⁺ was found essentially independent of shear stress on the interface. Values of , however, are remarkably smaller than their counterparts in the near-wall region of turbulent boundary layers. Though low-speed streaks occur randomly in time and space, the streak spacing exhibits a lognormal probability distribution behavior. A tentative explanation concerning the formation of streaky structure is suggested, and the fact that takes rather smaller values than that in wall turbulence is briefly discussed. The project supported by the National Natural Science Foundation of China (19672070)     

Theoretical mean wave resistance of precursor solition generation in two-layer flow

A new concept of pseudo mean wave resistance is introduced to find theoretical mean wave resistances of the precursor soliton generation in two-layer flow over a localized topography at near-resonance in this paper. The pseudo mean wave resistance of the precursor soliton generation of two-layer flow is determined in terms of the AfKdV equation. From the theoretical results it is shown that the theoretical mean wave resistance is equal to the pseudo mean wave resistance times 1/m ₁, wherem ₁ is the coefficient of the fKdV equation. From the regional distribution of the energy of the precursor soliton generation at the resonant points, it is shown that ratios of the theoretical mean wave resistance and regional mean energy to the total mean energy are invariant constants, i.e. : (−1/2):1:1, in which and are the mean energy of the generating regions of the precursor solitons, of the depression and of the trailing, wavetrain at the resonant points respectively, and <D> are the total energy of the system and the theoretical mean wave resistance at the resonant points. A prediction of the theoretical mean wave resistance flow over the semicircular topography is carried out in terms of the theoretical results of the present paper. The comparison shows that the theoretical mean wave resistance is in good agreement with the numerical calculation. The project supported by the Foundation of The State Education Commission “The Dynamics of Upper Ocean” and the Grants of The Physical Oceanography Laboratory of Ocean University of Qingdao