Statische Felder und stationäre Ströme

Wendt, Georg

doi:10.1007/978-3-642-45895-8_1

Cited by 5 publications

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Suppose we have N identical line charges, equally spaced around a circle. This electrostatic problem is discussed on page 290 of [3], page 1235 of [4] and in §44 of [5], for example. Suppose the circle is centred at the origin and has radius b.…”

Section: (B) Ring Of Electrostatic Line Chargesmentioning

confidence: 99%

On acoustic and electric Faraday cages

Martin

2014

Proc. R. Soc. A.

View full text Add to dashboard Cite

Two-dimensional problems involving many identical small circles are considered; the circles are the cross sections of parallel wires, modelling a cage or a grating. Both electrostatic and acoustic fields are considered. The main emphasis is on periodic configurations of N circles distributed evenly around a large circle (a ring). Foldy's theory is used for acoustic problems and then adapted for electrostatic problems. In both cases, circulant matrices are encountered: the fields can be calculated explicitly. Then, the limit N → ∞ is studied. A connection between the N-circle problem and the limiting problem (fields exterior to the ring) is established, using known results on the convergence of a defective form of the trapezoidal rule, defective in that endpoint contributions are ignored, because the integrand has logarithmic singularities at those points. This shows that the solution of the limiting problem is approached very slowly, as N −1 log N as N → ∞.

show abstract

Section: (B) Ring Of Electrostatic Line Chargesmentioning

confidence: 99%

On acoustic and electric Faraday cages

Martin

2014

Proc. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…3 .1. Fixed Configurations of N Scatterers '1'he static limits for two parallel circular cylinder, a grating of N parallel cylinders, two parallel coplaner strips, and two spheres, are conveniently found in Wendt's [1958] recent review article. He has many references to the recent literature, and a bibliography of texts going back to Maxwell's.…”

Section: Surveymentioning

confidence: 99%

URSI National Committee Report: Commission 6. Radio Waves and Circuits. Part 1. Information Theory and Coding

Eliáš¹

1960

J. RES. NATL. BUR. STAN. SECT. D. RAD. PROP.

View full text Add to dashboard Cite

Since 1957, there has been considerable progress i n the theo ry of coding messages for transmission over noisy channels. There have been three main directions of advance. First, there has been work on the foundation s of the theory. During this time American mathematicians interested in probability have shown a serious interest in informat ion theory, since Feinstein's work (now available in book form) [Feinstein, 1958al and since the interest shown by Kolmogorov and Khinchin. Second, a great deal of work has been done on error-correcting block codes for noisy binary channels. This work has involved a good deal of modern a lgebra, and so me mathematical algebraists have been joining the communications research workers in attacking these problems. T h ird , there has been cont inu ing investigation of procedures in which input messages are coded and decoded sequ entially rather t han in long blocks. This work and the work on binar y block codes both have significant practical implications for electrical communications.

show abstract