Search results for "integral"
showing 10 items of 902 documents
Note on the super-extended Moyal formalism and its BBGKY hierarchy
2017
We consider the path integral associated to the Moyal formalism for quantum mechanics extended to contain higher differential forms by means of Grassmann odd fields. After revisiting some properties of the functional integral associated to the (super-extended) Moyal formalism, we give a convenient functional derivation of the BBGKY hierarchy in this framework. In this case the distribution functions depend also on the Grassmann odd fields.
Structural quantities of quasi-two-dimensional fluids
2014
Quasi-two-dimensional fluids can be generated by confining a fluid between two parallel walls with narrow separation. Such fluids exhibit an inhomogeneous structure perpendicular to the walls due to the loss of translational symmetry. Taking the transversal degrees of freedom as a perturbation to an appropriate 2D reference fluid we provide a systematic expansion of the $m$-particle density for arbitrary $m$. To leading order in the slit width this density factorizes into the densities of the transversal and lateral degrees of freedom. Explicit expressions for the next-to-leading order terms are elaborated analytically quantifying the onset of inhomogeneity. The case $m=1$ yields the densit…
Geometric efficiency for a parallel-surface source and detector system with at least one axisymmetric surface
2007
Abstract An exact and numerically friendly method is given to calculate the geometric efficiency G of a planar radiation source and cosine detector system. Either the source or the detector, but not necessarily both, must have axial symmetry. For two non-coaxial disks the results are in exact agreement with a recent generalization of Ruby's formula for G. Detailed formulas and sample numerical results are given for a disk combined with rectangles and triangles. A disk and a general polygon can be solved by dividing the polygon into triangles. The method can also be applied to electrical inductance calculations and a solution recently given for the inductance of circular and elliptic loops c…
Differential Geometry of Curves and Surfaces
2001
The goal of this article is to present the relation between some differential formulas, like the Gauss integral for a link, or the integral of the Gaussian curvature on a surface, and topological invariants like the linking number or the Euler characteristic.
Accurate consideration of metal losses at waveguide junctions using admittance and impedance integral equation formulations
2005
[1] At higher frequencies, metal loss effects in passive waveguide components become more pronounced and hazardous. In this paper, we propose two integral equation techniques, based on the generalized admittance and impedance matrices, for the accurate consideration of losses in the metal walls of waveguide junctions. Both techniques have been evaluated in terms of accuracy and numerical efficiency, and conclusions are drawn regarding the best properties of the admittance parameter formulation. Finally, combining such technique with a classical perturbative method for considering propagation losses, we have successfully predicted all loss effects in two real waveguide filters used for comme…
A Monte Carlo investigation of the dosimetric characteristics of the CSM11 137Cs source from CIS
2000
The purpose of this study is to calculate basic dosimetry data for a CSM11 low dose rate 137Cs source in water. This source is widely used in afterloadable dome cylinders designed to homogeneously irradiate the vaginal cuff alone or additional areas of the vagina in hysterectomized patients. In this study, the Monte Carlo simulation code GEANT, incorporating in detail source geometry, is used to investigate the dosimetric characteristics of the source. The calculated data were analyzed using a fitting procedure that is described in detail. Absolute dose rate distributions in water were calculated around this source and are presented as conventional 2D Cartesian lookup tables (classically al…
Solving the Cut-Off Wave Numbers in Partially filled Rectangular Waveguides with Ferrite by the Cauchy Integral Method
2005
The modal analysis of the off-centered rectangular waveguide loaded with a vertical slab of ferrite material, biased in the y-direction by a DC magnetic field, leads to the resolution of a transcendent equation whose infinite solutions are the TE/sub m0/ cutoff wave numbers in the guide. The method based on the Cauchy integral (Delvest L.M. and Lyness, J.N., 1967) is becoming very popular for solving such equations. This powerful method is described for solving the propagation constant in a partially ferrite filled waveguide. The method is used to calculate the propagation constant of the fundamental TE mode for some configurations used in the literature about ferrites. Results obtained in …
Magnetoelectric effects in superconductors due to spin-orbit scattering : Nonlinear σ-model description
2021
We suggest a generalization of the nonlinear σ model for diffusive superconducting systems to account for magnetoelectric effects due to spin-orbit scattering. In the leading orders of spin-orbit strength and gradient expansion, it includes two additional terms responsible for the spin-Hall effect and the spin-current swapping. First, assuming a delta-correlated disorder, we derive the terms from the Keldysh path integral representation of the generating functional. Then we argue phenomenologically that they exhaust all invariants allowed in the effective action to the leading order in the spin-orbit coupling (SOC). Finally, the results are confirmed by a direct derivation of the saddle-poi…
Forces Between Thin Coils With Parallel Axes Using Bessel Functions
2013
A method based on Bessel functions is presented for calculating the forces between combinations of thin coils with parallel axes. The coaxial case is solved in closed form in terms of elliptic integrals, whereas for the noncoaxial case the force components are expressed both as integrals of Bessel functions and as integrals of complete elliptic integrals. The results for the coaxial case have been compared with calculations in the literature with excellent agreement. The numerical results presented for the noncoaxial have been cross-checked by comparing the two methods. These methods can also be applied to current loops, disk coils, thick noncoaxial cylindrical coils, and various combinatio…