Reply to the comment on 'Validity of certain soft photon amplitudes'

We respond to the accompanying Comment on our paper, 'Validity of certain soft photon amplitudes'. While we hope the discussion here clarifies the issues, we have found nothing which leads to a change in the original conclusions of our paper.Comment: 6 pages, Latex, uses ReVTeX, now publishe

Comment on ``Validity of certain soft-photon amplitudes''

The criteria suggested by Welsh and Fearing (nucl-th/9606040) to judge the validity of certain soft-photon amplitudes are examined. We comment on aspects of their analysis which lead to incorrect conclusions about published amplitudes and point out important criteria which were omitted from their analysis.Comment: 6 pages plus 1 postscript figure, Revte

An efficient method for solving the steady Euler equations

An efficient numerical procedure for solving a set of nonlinear partial differential equations is given, specifically for the steady Euler equations. Solutions of the equations were obtained by Newton's linearization procedure, commonly used to solve the roots of nonlinear algebraic equations. In application of the same procedure for solving a set of differential equations we give a theorem showing that a quadratic convergence rate can be achieved. While the domain of quadratic convergence depends on the problems studied and is unknown a priori, we show that firstand second-order derivatives of flux vectors determine whether the condition for quadratic convergence is satisfied. The first derivatives enter as an implicit operator for yielding new iterates and the second derivatives indicates smoothness of the flows considered. Consequently flows involving shocks are expected to require larger number of iterations. First-order upwind discretization in conjunction with the Steger-Warming flux-vector splitting is employed on the implicit operator and a diagonal dominant matrix results. However the explicit operator is represented by first- and seond-order upwind differencings, using both Steger-Warming's and van Leer's splittings. We discuss treatment of boundary conditions and solution procedures for solving the resulting block matrix system. With a set of test problems for one- and two-dimensional flows, we show detailed study as to the efficiency, accuracy, and convergence of the present method

Evaluating foam heterogeneity

New analytical tool is available to calculate the degree of foam heterogeneity based on the measurement of gas diffusivity values. Diffusion characteristics of plastic foam are described by a system of differential equations based on conventional diffusion theory. This approach saves research and computation time in studying mass or heat diffusion problems

Interaction between a normal shock wave and a turbulent boundary layer at high transonic speeds. Part 2: Wall shear stress

An analysis is presented of the flow in the two inner layers, the Reynolds stress sublayer and the wall layer. Included is the calculation of the shear stress at the wall in the interaction region. The limit processes considered are those used for an inviscid flow

Navier-Stokes analysis of transonic cascade flow

A new kind of C-type grid is proposed, this grid is non-periodic on the wake and allows minimum skewness for cascades with high turning and large camber. Reynolds-averaged Navier-Stokes equations are solved on this type of grid using a finite volume discretization and a full multigrid method which uses Runge-Kutta stepping as the driving scheme. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. A detailed numerical study is proposed for a highly loaded transonic blade. A grid independence analysis is presented in terms of pressure distribution, exit flow angles, and loss coefficient. Comparison with experiments clearly demonstrates the capability of the proposed procedure

Multigrid calculation of three-dimensional viscous cascade flows

A 3-D code for viscous cascade flow prediction was developed. The space discretization uses a cell-centered scheme with eigenvalue scaling to weigh the artificial dissipation terms. Computational efficiency of a four stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full multigrid method. The Baldwin-Lomax eddy viscosity model is used for turbulence closure. A zonal, nonperiodic grid is used to minimize mesh distortion in and downstream of the throat region. Applications are presented for an annular vane with and without end wall contouring, and for a large scale linear cascade. The calculation is validated by comparing with experiments and by studying grid dependency

A 0.8 V T Network-Based 2.6 GHz Downconverter RFIC

A 2.6 GHz downconverter RFIC is designed and implemented using a 0.18 μm CMOS standard process. An important goal of the design is to achieve the high linearity that is required in WiMAX systems with a low supply voltage. A passive T phase-shift network is used as an RF input stage in a Gilbert cell to reduce supply voltage. A single supply voltage of 0.8 V is used with a power consumption of 5.87 mW. The T network-based downconverter achieves a conversion gain (CG) of 5 dB, a single-sideband noise figure (NF) of 16.16 dB, an RF-to-IF isolation of greater than 20 dB, and an input-referred third-order intercept point (IIP3) of 1 dBm when the LO power of -13 dBm is applied

Migration of giant planets in planetesimal discs

Planets orbiting a planetesimal circumstellar disc can migrate inward from their initial positions because of dynamical friction between planets and planetesimals. The migration rate depends on the disc mass and on its time evolution. Planets that are embedded in long-lived planetesimal discs, having total mass of $10^{-4}-0.01 M_{\odot}$, can migrate inward a large distance and can survive only if the inner disc is truncated or because of tidal interaction with the star. In this case the semi-major axis, a, of the planetary orbit is less than 0.1 AU. Orbits with larger $a$ are obtained for smaller value of the disc mass or for a rapid evolution (depletion) of the disc. This model may explain several of the orbital features of the giant planets that were discovered in last years orbiting nearby stars as well as the metallicity enhancement found in several stars associated with short-period planets.Comment: 21 pages; 6 encapsulated figures. Accepted by MNRA

Interaction between a normal shock wave and a turbulent boundary layer at high transonic speeds. Part 1: Pressure distribution. Part 2: Wall shear stress. Part 3: Simplified formulas for the prediction of surface pressures and skin friction

An asymptotic description is derived for the interaction between a shock wave and a turbulent boundary layer in transonic flow, for a particular limiting case. The dimensionless difference between the external flow velocity and critical sound speed is taken to be much smaller than one, but large in comparison with the dimensionless friction velocity. The basic results are derived for a flat plate, and corrections for longitudinal wall curvature and for flow in a circular pipe are also shown. Solutions are given for the wall pressure distribution and the shape of the shock wave. Solutions for the wall shear stress are obtained, and a criterion for incipient separation is derived. Simplified solutions for both the wall pressure and skin friction distributions in the interaction region are given. These results are presented in a form suitable for use in computer programs