Comparison Of Finite-Difference And Analytic Microwave Calculation Methods

1996 ◽  
Vol 430 ◽  
Author(s):  
F. I. Friedlander ◽  
H. W. Jackson ◽  
M. Barmatz ◽  
P. Wagner
Keyword(s):  
Finite Difference ◽  
Numerical Evaluation ◽  
Normal Modes ◽  
Materials Processing ◽  
Calculation Methods ◽  
Power Absorption ◽  
Microwave Cavities ◽  
Analytic Expressions ◽  
Lossy Dielectric ◽  
Electromagnetic Solver

AbstractNormal modes and power absorption distributions in microwave cavities containing lossy dielectric samples were calculated for problems of interest in materials processing. The calculations were performed both using a commercially available finite-difference electromagnetic solver and by numerical evaluation of exact analytic expressions. Results obtained by the two methods applied to identical physical situations were compared. Our studies validate the accuracy of the finite-difference electromagnetic solver. Relative advantages of the analytic and finitedifference methods are discussed.

scholarly journals Pentagon functions for scattering of five massless particles

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
D. Chicherin ◽  
V. Sotnikov
Keyword(s):  
Phase Space ◽  
Numerical Evaluation ◽  
Public Library ◽  
Basis Set ◽  
Particle Scattering ◽  
Minimal Basis ◽  
Feynman Integrals ◽  
Analytic Expressions ◽  
Transcendental Functions ◽  
Branch Cuts

Abstract We complete the analytic calculation of the full set of two-loop Feynman integrals required for computation of massless five-particle scattering amplitudes. We employ the method of canonical differential equations to construct a minimal basis set of transcendental functions, pentagon functions, which is sufficient to express all planar and nonplanar massless five-point two-loop Feynman integrals in the whole physical phase space. We find analytic expressions for pentagon functions which are manifestly free of unphysical branch cuts. We present a public library for numerical evaluation of pentagon functions suitable for immediate phenomenological applications.

Transient Temperature Distributions in a Cylinder Heated by Microwaves

1996 ◽  
Vol 430 ◽  
Author(s):  
H. W. Jackson ◽  
M. Barmatz ◽  
P. Wagner
Keyword(s):  
Numerical Solutions ◽  
Single Mode ◽  
Dielectric Constants ◽  
Microwave Cavity ◽  
Transient Temperature ◽  
Hybrid Heating ◽  
Fine Mesh ◽  
Temperature Distributions ◽  
Analytic Expressions ◽  
Lossy Dielectric

AbstractTransient temperature distributions were calculated for a lossy dielectric cylinder coaxially aligned in a cylindrical microwave cavity excited in a single mode. Results were obtained for sample sizes that range from fibers to large cylinders. Realistic values for temperature dependent complex dielectric constants and thermophysical properties of the samples were used. Losses in cavity walls were taken into account as were realistic thermal emissivities at all surfaces. For a fine mesh of points in time, normal mode properties and microwave power absorption profiles were evaluated using analytic expressions. Those expressions correspond to exact solutions of Maxwell's equations within the framework of a cylindrical shell model. Heating produced by the microwave absorption was included in self-consistent numerical solutions of thermal equations. In this model, both direct microwave heating and radiant heating of the sample (hybrid heating) were studied by including a lossy dielectric tube surrounding the sample. Calculated results are discussed within the context of two parametric studies. One is concerned with relative merits of microwave and hybrid heating of fibers, rods, and larger cylinders. The other is concerned with thermal runaway.

Measurements and Calculations of the Isothermal Flow in Axisymmetric Models of Combustor Geometries

1980 ◽  
Vol 22 (3) ◽  
pp. 119-124 ◽  
Author(s):  
A. Green ◽  
J. H. Whitelaw
Keyword(s):  
Finite Difference ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Laser Doppler Anemometry ◽  
Isothermal Flow ◽  
Navier Stokes ◽  
Calculation Methods ◽  
Navier Stokes Equations ◽  
Annular Jet ◽  
Grid Nodes

Measurements with laser-Doppler anemometry and calculations with finite-difference solutions of the time-averaged Navier-Stokes equations and a two-equation turbulence model, have been obtained for the turbulent isothermal flow in an axisymmetric geometry related to gas-turbine combustors. The results quantify the flow patterns in the arrangement and demonstrate the extent to which they can be represented by calculation. The discrepancies between measured and calculated results are shown to depend more on the distribution of grid nodes than on the turbulence model. Even with a distribution of nodes which is considered to be near optimum, differences between measurement and calculation exist and are particularly significant in the regions of steep velocity gradient immediately downstream of the incoming annular jet. The general trends are, however, correctly represented, and the calculation method has been used to determine the influence of the width of the annulus and of the jet gap. The results provide information of relevance to the development of calculation methods for real combustors, and this is discussed.

scholarly journals Leading-color two-loop QCD corrections for three-jet production at hadron colliders

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
S. Abreu ◽  
F. Febres Cordero ◽  
H. Ita ◽  
B. Page ◽  
V. Sotnikov
Keyword(s):  
Numerical Evaluation ◽  
Physical Region ◽  
Leading Order ◽  
Hadron Colliders ◽  
Generating Set ◽  
Jet Production ◽  
Analytic Expressions ◽  
Small Set ◽  
Complete Set ◽  
Euclidean Region

Abstract We present the complete set of leading-color two-loop contributions required to obtain next-to-next-to-leading-order (NNLO) QCD corrections to three-jet production at hadron colliders. We obtain analytic expressions for a generating set of finite remainders, valid in the physical region for three-jet production. The analytic continuation of the known Euclidean-region results is determined from a small set of numerical evaluations of the amplitudes. We obtain analytic expressions that are suitable for phenomenological applications and we present a C++ library for their efficient and stable numerical evaluation.

scholarly journals Lindelöf Representations and (Non-)Holonomic Sequences

10.37236/275 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Philippe Flajolet ◽  
Stefan Gerhold ◽  
Bruno Salvy
Keyword(s):  
Finite Difference ◽  
Generating Functions ◽  
Complex Analysis ◽  
Integral Representations ◽  
Asymptotic Estimates ◽  
Linear Recurrences ◽  
Polynomial Coefficients ◽  
Difference Sequences ◽  
Analytic Expressions ◽  
Linear Differential

Various sequences that possess explicit analytic expressions can be analysed asymptotically through integral representations due to Lindelöf, which belong to an attractive but somewhat neglected chapter of complex analysis. One of the outcomes of such analyses concerns the non-existence of linear recurrences with polynomial coefficients annihilating these sequences, and, accordingly, the non-existence of linear differential equations with polynomial coefficients annihilating their generating functions. In particular, the corresponding generating functions are transcendental. Asymptotic estimates of certain finite difference sequences come out as a byproduct of the Lindelöf approach.

scholarly journals Nonlinear Modeling of Cables with Flexural Stiffness

2008 ◽  
Vol 2008 ◽  
pp. 1-21 ◽  
Author(s):  
Walter Lacarbonara ◽  
Arnaud Pacitti
Keyword(s):  
Finite Difference ◽  
Nonlinear Modeling ◽  
Continuation Method ◽  
Normal Modes ◽  
Bending Moment ◽  
Flexural Stiffness ◽  
Weak Formulation ◽  
Static Responses ◽  
Quasistatic Regime ◽  
Extensible Cables

A geometrically exact formulation of cables suffering axis stretching and flexural curvature is presented. The dynamical formulation is based on nonlinearly viscoelastic constitutive laws for the tension and bending moment with the additional constitutive nonlinearity accounting for the no-compression condition. A continuation method, combined with a mixed finite-difference spatial discretization, is then employed to path-follow the static responses of cables subject to forces or support displacements. These computations, conducted in the quasistatic regime, are based on cables with linearly elastic material behaviors, whereas the nonlinearity is in the geometric stiffness terms and the no-compression behavior. The finite-difference results have been confirmed employing a weak formulation based on quadratic Lagrangian finite elements. The influence of the flexural stiffness on the nonlinear static responses is assessed comparing the results with those obtained for purely extensible cables. The properties of the frequencies of the linear normal modes of cables with flexural stiffness are also investigated and compared with those of purely extensible cables.

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