On the approximation of local efflux/influx bed discharge in the shallow water equations based on a wave propagation algorithm

In cities, flood waves may propagate over street surfaces below which lie complicated pipe networks used for storm drainage and sewage. The flood and pipe flows can interact at connections between the underground pipes and the street surface. The present paper examines this interaction, using the shallow water equations to model the flood wave hydrodynamics. Sources and sinks in the mass conservation equation are used to model the pipe inflow and outflow conditions at bed connections. We consider the problem reduced to one dimension. The shallow water equations are solved using a Godunov‐type wave propagation scheme. Wave speeds are modified in the wave propagation algorithm to enable flows to be simulated over nearly dry beds and dry states. First, the model is used to simulate vertical flows through finite gaps in the bed. Next, the interaction of the vertical flows with a dam break flow is considered for both dry and wet beds. An efflux number, En, is defined based on the vertical efflux velocity and the gap length. Comparisons are made with numerical predictions from STAR‐CD, a commercial Navier–Stokes solver that models the free‐surface motions, and a parameter study is undertaken to investigate the effect of the one‐dimensional approximation of the present model, for a range of non‐dimensional efflux numbers. It is found that the shallow flow model gives sensible predictions at all time provided En<0.5, and for long durations for En>0.5. Dam break flow over an underground connecting pipe is also considered. Copyright © 2010 John Wiley & Sons, Ltd.     

Photolithographic Route to the Fabrication of Micro/Nanowires of III–V Semiconductors

Nano/microwires of semiconducting materials (e.g., GaAs and InP) with triangular cross‐sections can be fabricated by “top–down” approaches that combine lithography of high‐quality bulk wafers (using either traditional photolithography or phase‐shift optical lithography) with anisotropic chemical etching. This method gives good control over the lateral dimensions, lengths, and morphologies of free‐standing wires. The behaviors of many different resist layers and etching chemistries are presented. It is shown how wire arrays with highly ordered alignments can be transfer printed onto plastic substrates. This “top–down” approach provides a simple, effective, and versatile way of generating high‐quality single‐crystalline wires of various compound semiconductors. The resultant wires and wire arrays have potential applications in electronics, optics, optoelectronics, and sensing.     

Analysis of flow between a wafer and pad during CMP processes

In this paper, we summarize the development of a numerical model for the chemical mechanical planarization (CMP) process and experimentally investigate the effects of pad conditioning on slurry transport and mixing. A simplified two-dimensional numerical model of slurry flow beneath a stationary wafer was developed to determine the pressure and shear stress beneath a wafer. The initial results indicate that in the hydrodynamic regime a positive upward pressure is exerted on the wafer. We also examined three cases to study pad effects on slurry transport; polishing with an Embossed Politex pad, an unconditioned IC1000 pad, and a conditioned IC1000 pad. Cab-O-Sperse SC1 slurry was used in a 1:1.5 dilution with water. Mixing data show that conditioning has a negligible effect on the rate of slurry entrainment and mixing; however, conditioning has a large effect on the thickness of the slurry layer between the wafer and pad. Conditioning was found to increase the slurry thickness by a factor of two. In addition the gradients in slurry age beneath the wafer were compared among the three cases. The IC1000 pads supported a gradient in the inner third of the wafer only, while the Embossed Politex pad showed a linear gradient across the wafer implying it retains pockets of unmixed slurry in the embossed topography.     

On the stability of linear repetitive processes described by a delay-difference equation

This paper considers linear repetitive processes which are a distinct class of two-dimensional linear systems of both physical and systems theoretic interest. Their essential unique feature is a series of sweeps, termed passes, through a set of dynamics defined over a finite and fixed duration known as the pass length. The result can be oscillations in the output sequence of pass profiles which increase in amplitude in the pass-to-pass direction. This cannot be controlled by existing techniques and instead control must be based on a suitably defined stability theory. In the literature to date, the development of such a theory has been attempted from two different starting points, and in this paper, we critically compare these for dynamics defined by a delay-difference equation.     

Photorefractive polarization couplers in elliptical core fibres

Photorefractive polarization couplers written internally in germanium-doped elliptical core fibers at 488, 514, and 532 nm are reported. Complete power transfer between the orthogonal polarization modes of the fiber was achieved for couplers written at 514 and 488 nm, respectively. It is shown that the couplers are nonuniform in length because of the high photoinduced attenuation and also due to two-photon absorption. Polarization coupling of higher order modes is also demonstrated at shorter wavelengths where their polarization beat lengths match the polarization beat length of the fundamental mode at which the coupler was written.<>     

Temperature compensation of total power radiometers

This paper describes a new technique to compensate output variations of total power radiometers due to physical temperature changes of the instrument. This technique performs the correction without the addition of expensive microwave hardware required in Dicke switching or many other widely used methods. A characterization period, over which the input antenna temperature is known, indicates the appropriate output adjustment needed for a change in physical temperature of the radiometer. The method effectively corrects the output in an example radiometer system built with inexpensive commercially available parts. For a 30-K variation in physical temperature, the measured data shows an improvement from 60-K peak-to-peak error to 6.9 K with an average absolute error of 1.1 K.     

The Kinematics of the Planar Motion of Ideal Fiber-Reinforced Fluids: An Integrable Reduction and Bäcklund Transformation

We establish that the kinematic constraints on the steady planar motion of an ideal fiber-reinforced fluid can be consolidated in a single third-order nonlinear equation. Remarkably, this equation admits a solitonic reduction related to the classical sine-Gordon equation. The kinematic conditions in this case admit a novel duality property and a Bäcklund transformation.     

An immersed finite element space and its approximation capability

This article discusses an immersed finite element (IFE) space introduced for solving a second‐order elliptic boundary value problem with discontinuous coefficients (interface problem). The IFE space is nonconforming and its partition can be independent of the interface. The error estimates for the interpolation of a function in the usual Sobolev space indicate that this IFE space has an approximation capability similar to that of the standard conforming linear finite element space based on body‐fit partitions. Numerical examples of the related finite element method based on this IFE space are provided. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 338–367, 2004