Influence Of Free Surface Curvature Of A Liquid Layer On The Critical Marangoni Convection

The Pearson instability was suggested to discuss the onset of Marangoni convection in a liquid layer of large Prandtl number under an applied temperature difference perpendicular to the free surface in the microgravity environment. In this case, the temperature distribution on the curved free surface is nonuniform, and the thermocapillary convection is induced and coupled with the Marangoni convection. In the present paper the effect of volume ratio of the liquid layer on the critical Marangoni convection and the corresponding spatial variation of the convection structure in zero-gravity condition were numerically investigated by two-dimensional model. (C) 2008 Elsevier Ltd. All rights reserved.

Radius of curvature measurements for laser beams: A simple method

A simple method for measuring the radius of curvature of laser beams is introduced. It has been developed to estimate the astigmatic aberration of a diode laser. Compared with the interferornetry, this method is convenient and straightforward. (c) 2005 Elsevier GmbH. All rights reserved.

Curvature Correction of FWHM in the X-Ray Rocking Curve of Bent Heteroepitaxial Films

A method for accurate determination of the curvature radius of semiconductor thin films is proposed. The curvature-induced broadening of the x-ray rocking curve (XRC) of a heteroepitaxially grown layer can be determined if the dependence of the full width at half maximum (FWHM) of XRC is measured as a function of the width of incident x-ray beam. It is found that the curvature radii of two GaN films grown on a sapphire wafer are different when they are grown under similar MOCVD conditions but have different values of layer thickness. At the same time, the dislocation-induced broadening of XRC and thus the dislocation density of the epitaxial film can be well calculated after the curvature correction.

Crossing the phantom divide in brane cosmology with curvature corrections and brane-bulk energy transfer

We consider the Randall-Sundrum brane-world model with bulk-brane energy transfer where the Einstein-Hilbert action is modified by curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. It is remarkable that these curvature terms will not change the dynamics of the brane universe at low energy. Parameterizing the energy transfer and taking the dark radiation term into account, we find that the phantom divide of the equation of state of effective dark energy could be crossed, without the need of any new dark energy components. Fitting the two most reliable and robust SNIa datasets, the 182 Gold dataset and the Supernova Legacy Survey (SNLS), our model indeed has a small tendency of phantom divide crossing for the Gold dataset, but not for the SNLS dataset. Furthermore, combining the recent detection of the SDSS baryon acoustic oscillations peak (BAO) with lower matter density parameter prior, we find that the SNLS dataset also mildly favors phantom divide crossing.

Strain gradient theory with couple stress for crystalline solids

A new phenomenological strain gradient theory for crystalline solid is proposed. It fits within the framework of general couple stress theory and involves a single material length scale Ics. In the present theory three rotational degrees of freedom omega (i) are introduced, which denote part of the material angular displacement theta (i) and are induced accompanying the plastic deformation. omega (i) has no direct dependence upon u(i) while theta = (1 /2) curl u. The strain energy density omega is assumed to consist of two parts: one is a function of the strain tensor epsilon (ij) and the curvature tensor chi (ij), where chi (ij) = omega (i,j); the other is a function of the relative rotation tensor alpha (ij). alpha (ij) = e(ijk) (omega (k) - theta (k)) plays the role of elastic rotation reason The anti-symmetric part of Cauchy stress tau (ij) is only the function of alpha (ij) and alpha (ij) has no effect on the symmetric part of Cauchy stress sigma (ij) and the couple stress m(ij). A minimum potential principle is developed for the strain gradient deformation theory. In the limit of vanishing l(cs), it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in detail. For simplicity, the elastic relation between the anti-symmetric part of Cauchy stress tau (ij), and alpha (ij) is established and only one elastic constant exists between the two tensors. Combining the same hardening law as that used in previously by other groups, the present theory is used to investigate two typical examples, i.e., thin metallic wire torsion and ultra-thin metallic beam bend, the analytical results agree well with the experiment results. While considering the, stretching gradient, a new hardening law is presented and used to analyze the two typical problems. The flow theory version of the present theory is also given.

Applicability Range of Stoneys Formula and Modified Formulas for a Film/Substrate Bilayer

In addition to the layer thickness and effective Young’s modulus, the impact of the kinematic assumptions, interfacial condition, in-plane force, boundary conditions, and structure dimensions on the curvature of a film/substrate bilayer is examined. Different models for the analysis of the bilayer curvature are compared. It is demonstrated in our model that the assumption of a uniform curvature is valid only if there is no in-plane force. The effects of boundary conditions and structure dimensions, which are not-fully-included in previous models are shown to be significant. Three different approaches for deriving the curvature of a film/substrate bilayer are presented, compared, and analyzed. A more comprehensive study of the conditions regarding the applicability of Stoney’s formula and modified formulas is presented.

Deflections and Curvatures of a Film–Substrate Structure with the Presence of Gradient Stress in MEMS Applications

The close form solutions of deflections and curvatures for a film–substrate composite structure with the presence of gradient stress are derived. With the definition of more precise kinematic assumption, the effect of axial loading due to residual gradient stress is incorporated in the governing equation. The curvature of film–substrate with the presence of gradient stress is shown to be nonuniform when the axial loading is nonzero. When the axial loading is zero, the curvature expressions of some structures derived in this paper recover the previous ones which assume the uniform curvature. Because residual gradient stress results in both moment and axial loading inside the film–substrate composite structure, measuring both the deflection and curvature is proposed as a safe way to uniquely determine the residual stress state inside a film–substrate composite structure with the presence of gradient stress.

An Effective Method of Determining the Residual Stress Gradients in a Micro-Cantilever

A method of determining the micro-cantilever residual stress gradients by studying its deflection and curvature is presented. The stress gradients contribute to both axial load and bending moment, which, in prebuckling regime, cause the structural stiffness change and curving up/down, respectively. As the axial load corresponds to the even polynomial terms of stress gradients and bending moment corresponds to the odd polynomial terms, the deflection itself is not enough to determine the axial load and bending moment. Curvature together with the deflection can uniquely determine these two parameters. Both linear analysis and nonlinear analysis of micro-cantilever deflection under axial load and bending moment are presented. Because of the stiffening effect due to the nonlinearity of (large) deformation, the difference between linear and nonlinear analyses enlarges as the micro-cantilever deflection increases. The model developed in this paper determines the resultant axial load and bending moment due to the stress gradients. Under proper assumptions, the stress gradients profile is obtained through the resultant axial load and bending moment.

考虑压头尖端曲率的弹塑性材料硬度的解答形式

结合近年来发表的对金属材料采用球形压头的微压痕实验结果及Johnson对应原理，讨论了在传统弹塑性理论下锥形压头在计及压头顶端曲率半径影响时硬度的解答形式。进而得出结论：压头尖端曲率半径不是引起尺度效应的根源，相反，它全使尺度效应减弱。

A New Deformation Theory with Strain Gradient Effects

A new phenomenological deformation theory with strain gradient effects is proposed. This theory, which belongs to nonlinear elasticity, fits within the framework of general couple stress theory and involves a single material length scale l. In the present theory three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom u(i). omega(i) has no direct dependence upon ui and is called the micro-rotation, i.e. the material rotation theta(i) plus the particle relative rotation. The strain energy density is assumed to only be a function of the strain tensor and the overall curvature tensor, which results in symmetric Cauchy stresses. Minimum potential principle is developed for the strain gradient deformation theory version. In the limit of vanishing 1, it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in details. Comparisons between the present theory and the theory proposed by Shizawa and Zbib (Shizawa, K., Zbib, H.M., 1999. A thermodynamical theory gradient elastoplasticity with dislocation density Censor: fundamentals. Int. J. Plast. 15, 899) are given. With the same hardening law as Fleck et al. (Fleck, N.A., Muller, G.H., Ashby, M.F., Hutchinson, JW., 1994 Strain gradient plasticity: theory and experiment. Acta Metall. Mater 42, 475), the new strain gradient deformation theory is used to investigate two typical examples, i.e. thin metallic wire torsion and ultra-thin metallic beam bend. The results are compared with those given by Fleck et al, 1994 and Stolken and Evans (Stolken, J.S., Evans, A.G., 1998. A microbend test method for measuring the plasticity length scale. Acta Mater. 46, 5109). In addition, it is explained for a unit cell that the overall curvature tensor produced by the overall rotation vector is the work conjugate of the overall couple stress tensor. (C) 2002 Elsevier Science Ltd. All rights reserved.

Tolman Effect On Fluid Dynamics In Carbon Nanotubes

The numerical solutions of or(R) given by two different methods (Samsonov et al., 2003; and Lu et al., 2005) are compared with the result that they are coincident closely (the difference is within 4%). We conclude that it is necessary to consider the Tolman correction in the calculation of fluid dynamics in carbon nanotubes. Although our conclusion is the same as that of Prylutskyy et al. (2005), the sign of our Tolman correction is opposite to theirs, and the difference can be attributed to the errors appeared in the paper of Prylutskyy et al.

Single Curved Fiber Sedimentation Under Gravity

Dynamics of single curved fiber sedimentation under gravity are simulated by using the lattice Boltzmann method. The results of migration and rotation of the curved fiber at different Reynolds numbers are reported. The results show that the rotation and migration processes are sensitive to the curvature of the fiber. (c) 2007 Elsevier Ltd. All rights reserved.