High-power laser beam shaping by inseparable two-dimensional binary-phase gratings for surface modification of stamping dies

For surface modification of stamping dies, an inseparable two-dimensional binary-phase gratings is introduced to implement the wavefront transformation of high-power laser beams. The design and fabrication of the gratings are described in detail. Two-dimensional even sampling encoding scheme is adopted to overcome the limitations of conventional Dammann grating in the design of two-dimensional output patterns. High diffractive efficiency (>70%) can be achieved through the transformation of the Gaussian laser beam into several kinds of two-dimensional arrays in focal plan. The application of the binary-phase gratings in the laser surface modification of ductile iron is investigated, and the results show that the hardness and the wear resistance of the sample surface were improved significantly by using the binary-phase gratings. (C) 2008 Elsevier Ltd. All rights reserved.

Impact of carrier stiffness and microtopology on two-dimensional kinetics of P-selectin and P-selectin glycoprotein ligand-1 (PSGL-1) interactions

Mechanics and surface microtopology of the molecular carrier influence cell adhesion, but the mechanisms underlying these effects are not well understood. We used a micropipette adhesion frequency assay to quantify how the carrier stiffness and microtopology affected two-dimensional kinetics of interacting adhesion molecules on two apposing surfaces. Interactions of P-selectin with P-selectin glycoprotein ligand-1 (PSGL-1) were used to demonstrate such effects by presenting the molecules on three carrier systems: human red blood cells (RBCs), human promyelocytic leukemia HL-60 cells, and polystyrene beads. Stiffening the carrier alone or in cooperation with roughing the surface lowered the two-dimensional affinity of interacting molecules by reducing the forward rate but not the reverse rate, whereas softening the carrier and roughing the surface had opposing effects in affecting two-dimensional kinetics. In contrast, the soluble antibody bound with similar three-dimensional affinity to surface-anchored P-selectin or PSGL-1 constructs regardless of carrier stiffness and microtopology. These results demonstrate that the carrier stiffness and microtopology of a receptor influences its rate of encountering and binding a surface ligand but does not subsequently affect the stability of binding. This provides new insights into understanding the rolling and tethering mechanism of leukocytes onto endothelium in both physiological and pathological processes.

Numerical simulation of coherent structure in two-dimensional compressible mixing layers

The coherent structure in two-dimensional mixing layers is simulated numerically with the compressible Navier-Stokes equations. The Navier-Stokes equations are discretized with high-order accurate upwind compact schemes. The process of development of flow structure is presented: loss of stability, development of Kelvin-Helmholtz instability, rolling up and pairing. The time and space development of the plane mixing layer and influence of the compressibility are investigated.

Two-dimensional simulation of inductive plasma sources with self-consistent power deposition

A time averaged two-dimensional fluid model including an electromagnetic module with self-consistent power deposition was developed to simulate the transport of a low pressure radio frequency inductively coupled plasma source. Comparsions with experiment and previous simulation results show, that the fluid model is feasible in a certain range of gas pressure. In addition, the effects of gas pressure and power input have been discussed.

Thermophoretic deposition of particles onto cold surfaces of bodies in two-dimensional and axisymmetric flows

The problem of thermophoretic deposition of small particles onto cold surfaces is studied in two-dimensional and axisymmetric flow fields. The particle concentration equation is solved numerically together with the momentum and energy equations in the laminar boundary layer with variable density effect included. It is shown explicitly to what extent the particle concentration and deposition rate at the wall are influenced by the density variation effect for external flow past bodies. The general numerical procedure is given for two-dimensional and axisymmetric cases and is illustrated with examples of thermophoretic deposition of particles in flows past a cold cylinder and a sphere.

Characteristics of a CW HF chemical-laser calculated from a simplified two-dimensional model

A two-dimensional simplified model of an HF chemical laser is introduced. Using an implicit finite difference scheme, the solution of two adjacent parallel streams with diffusion mixing and chemical reaction is generated. A contour of mixing and reaction boundary is obtained without presupposition. The distribution of the HF(v) concentrations, gas temperature and the optical small signal gain (alpha sub V, J) on the flowing plane (X, Y) are presented. Compared with the solution solved directly from a set of Navier-Stokes equations, the results of these two methods agree with each other qualitatively. The influences of the different velocity, temperature (T sub 0) and composition of the two streams on the small signal gain after the nozzle exit are investigated. It is interesting that for larger J with a fixed v, the peaks of alpha sub v-T sub 0 profiles move towards higher T sub 0. The computing method is simple and only a short computing time is needed.

Nonequilibrium statistical mechanics of two-dimensional turbulence

The vorticity dynamics of two-dimensional turbulence are investigated analytically, applying the method of Qian (1983). The vorticity equation and its Fourier transform are presented; a set of modal parameters and a modal dynamic equation are derived; and the corresponding Liouville equation for the probability distribution in phase space is solved using a Langevin/Fokker-Planck approach to obtain integral equations for the enstrophy and for the dynamic damping coefficient eta. The equilibrium spectrum for inviscid flow is found to be a stationary solution of the enstrophy equation, and the inertial-range spectrum is determined by introducing a localization factor in the two integral equations and evaluating the localized versions numerically.

The thermal and mechanical structure of a two-dimensional plume in the earths mantle

On the condition that the distribution of velocity and temperature at the mid-plane of a mantle plume has been obtained (pages 213–218, this issue), the problem of determining the lateral structure of the plume at a given depth is reduced to solving an eigenvalue problem of a set of ordinary differential equations with five unknown functions, with an eigenvalue being related to the thermal thickness of the plume at this depth. The lateral profiles of upward velocity, temperature and viscosity in the plume and the thickness of the plume at various depths are calculated for two sets of Newtonian rheological parameters. The calculations show that the precondition for the existence of the plume, δT/L 1 (L = the height of the plume, δT = lateral distance from the mid-plane), can be satisfied, except for the starting region of the plume or near the base of the lithosphere. At the lateral distance, δT, the upward velocity decreases to 0.1 – 50% of its maximum value at different depths. It is believed that this model may provide an approach for a quantitative description of the detailed structure of a mantle plume.

One-dimensional improvement and two-dimensional and 3-dimensional treatments for stable oscillation condition, mode structure and power output in high-speed-flow lasers

For high-speed-flow lasers, the one-dimensional and first-order approximate treatment in[1] under approximation of geometrical optics is improved still within the scope of approx-imation of geometrical optics. The strict accurate results are obtained, and what is more,two- and three-dimensional treatments are done. Thus for two- and three-dimensional cases, thestable oscillation condition, the formulae of power output and analytical expression of modesunder approximation of geometrical optics (in terms of gain function) are derived. Accord-ing to the present theory, one-and two-dimensional calculations for the typical case of Gerry'sexperiment are presented. All the results coincide well with the experiment and are better thanthe results obtained in [1].In addition, the applicable scope of Lee's stable oscillation condition given by [1] is ex-panded; the condition for the approximation of gcometrical optics to be applied to mode con-structure in optical cavity is obtained for the first time and the difference between thiscondition and that for free space is also pointed out in the present work.

Adhesive behavior of two-dimensional power-law graded materials

In this paper, we investigate the adhesive contact between a rigid cylinder of radius R and a graded elastic half-space with a Young's modulus varying with depth according to a power-law, E = E-0(y/c(0))(k) (0 < k < 1), while the Poisson's ratio v remains constant. The results show that, for a given value of ratio R/C-0, a critical value of k exists at which the pull-off force attains a maximum; for a fixed value of k, the larger the ratio R/c(0), the larger the pull-off force is. For Gibson materials (i.e., k = 1 and v = 0.5), closed-form analytical solutions can be obtained for the critical contact half-width at pull-off and pull-off force. We further discuss the perfect stick case with both externally normal and tangential loads.

An extension of the two dimensional JKR theory to the case with a large contact width

In the Hertz and JKR theories, parabolic assumptions for the rounded profiles of the sphere or cylinder are adopted under the condition that the contact radius (width) should be very small compared to the radius of the sphere or cylinder. However, a large contact radius (width) is often found in experiments even under a zero external loading. We aim at extending the plane strain JKR theory to the case with a large contact width. The relation between the external loading and the contact width is given. Solutions for the Hertz, JKR and rounded-profile cases are compared and analyzed. It is found that when the ratio of a/R is approximately larger than about 0.4, the parabolic assumptions in the Hertz and JKR theories are no longer valid and the exact rounded profile function should be used.

Two-dimensional Vortex-induced Vibrations of Submerged Floating Tunnel Tethers

A vortex-induced vibration (VIV) model is presented for predicting the nonlinear dynamic response of submerged floating tunnel (SFT) tethers which are subjected to wave, current and tunnel oscillatory displacements at their upper end in horizontal and vertical directions. A nonlinear fluid force formula is introduced in this model, and the effect of the nonlinearity of tether is investigated. First, the tunnel is stationary and the tether vibrates due to the vortices shedding. The calculated results show that the cross-flow amplitude of VIV decreases compared with the linear model. However the in-line amplitude of VIV increases. Next, the periodical oscillation of tunnel is considered. The oscillation caused by wave forces plays the roles of parametric exciter and forcing exciter to the VIV of tether. The time history of displacement of the tether mid-span is obtained by the proposed model. It is shown that the in-line amplitude increases obviously and the corresponding frequency is changed. The cross-flow amplitude exhibits a periodic behavior.

Ballistic Electron Transport In Hybrid Ferromagnet/Two-Dimensional Electron Gas Sandwich Nanostructure: Spin Polarization And Magnetoresistance Effect

We have theoretically investigated ballistic electron transport through a combination of magnetic-electric barrier based on a vertical ferromagnet/two-dimensional electron gas/ferromagnet sandwich structure, which can be experimentally realized by depositing asymmetric metallic magnetic stripes both on top and bottom of modulation-doped semiconductor heterostructures. Our numerical results have confirmed the existence of finite spin polarization even though only antisymmetric stray field B-z is considered. By switching the relative magnetization of ferromagnetic layers, the device in discussion shows evident magnetoconductance. In particular, both spin polarization and magnetoconductance can be efficiently enhanced by proper electrostatic barrier up to the optimal value relying on the specific magnetic-electric modulation. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3041477]

Fabrication of two-dimensional periodic nanostructures by two-beam interference of femtosecond pulses

Two-dimensional periodic nanostructures on ZnO crystal surface were fabricated by two-beam interference of 790 nm femtosecond laser. The long period is, as usually reported, determined by the interference pattern of two laser beams. Surprisingly, there is another short periodic nanostructures with periods of 220-270 nm embedding in the long periodic structures. We studied the periods, orientation, and the evolution of the short periodic nanostructures, and found them analogous to the self-organized nanostructures induced by single fs laser beam. (C) 2008 Optical Society of America.