The buffer property in resonance systems of non-linear hyperbolic equations

Abstract

This paper presents a systematic study of the effects of reversals of current polarity on 1 Ω standard resistors. A selection of 1 Ω standards were measured on a dc cryogenic current comparator bridge and also on an ac current comparator bridge operating at 1 Hz. We find that the apparent 4 terminal resistance depends strongly on the dc reversal rate, in one case showing a variation of more than 0.1 μΩ/Ω for cycle times between 10 s and 1000 s. Even in the best cases, effects of at least 0.01 μΩ/Ω are present. Furthermore, the assumption that the apparent resistance value converges to a limiting value for long waiting times after reversal is not always upheld, making it difficult to quote a simple dc value. Existing models of Peltier heating at wire junctions do not completely explain our observations. The problems presented have been the limiting factor for 1 Ω measurements as part of a recent on-site comparison of quantum Hall effect resistance standards.

Инвариантные Торы Одного Класса Нелинейных Эволюционных Уравнений

“…Создан же он был только в 80-е годы Ю. С. Колесовым сначала для параболических уравнений с малыми коэффициентами диффузии [5]- [8], а затем перенесен на аналогичный класс волновых уравнений [9]- [14]. Дальнейшее развитие методов работ [5]- [8] применительно к гиперболическим уравнениям отражено в монографиях [15]- [17] и обзорных статьях [18]- [20].…”