Business cycles, long waves, and company langevity in Birmingham area metal industries 1780-1980

This doctoral thesis originates from an observational incongruence between the perennial aims and aspirations of economic endeavour and actually recorded outcomes, which frequently seem contrary to those intended and of a recurrent, cyclical type. The research hypothesizes parallel movement between unstable business environments through time, as expressed by periodically fluctuating levels of economic activity, and the precipitation rates of industrial production companies. A major problem arose from the need to provide theoretical and empirical cohesion from the conflicting, partial and fragmented interpretations of several hundred historians and economists, without which the research question would remain unanswerable. An attempt to discover a master cycle, or superimposition theorem, failed, but was replaced by minute analysis of both the concept of cycles and their underlying data-bases. A novel technique of congregational analysis emerged, resulting in an integrated matrix of numerical history. Two centuries of industrial revolution history in England and Wales was then explored and recomposed for the first time in a single account of change, thereby providing a factual basis for the matrix. The accompanying history of the Birmingham area provided the context of research into the failure rates and longevities of firms in the city's staple metal industries. Sample specific results are obtained for company longevities in the Birmingham area. Some novel presentational forms are deployed for results of a postal questionnaire to surviving firms. Practical demonstration of the new index of national economic activity (INEA) in relation to company insolvencies leads to conclusions and suggestions for further applications of research into the tempo of change, substantial Appendices support the thesis and provide a compendium of information covering immediately contiguous domains.

Interaction of Kelvin waves and nonlocality of energy transfer in superfluids

We argue that the physics of interacting Kelvin Waves (KWs) is highly nontrivial and cannot be understood on the basis of pure dimensional reasoning. A consistent theory of KW turbulence in superfluids should be based upon explicit knowledge of their interactions. To achieve this, we present a detailed calculation and comprehensive analysis of the interaction coefficients for KW turbuelence, thereby, resolving previous mistakes stemming from unaccounted contributions. As a first application of this analysis, we derive a local nonlinear (partial differential) equation. This equation is much simpler for analysis and numerical simulations of KWs than the Biot-Savart equation, and in contrast to the completely integrable local induction approximation (in which the energy exchange between KWs is absent), describes the nonlinear dynamics of KWs. Second, we show that the previously suggested Kozik-Svistunov energy spectrum for KWs, which has often been used in the analysis of experimental and numerical data in superfluid turbulence, is irrelevant, because it is based upon an erroneous assumption of the locality of the energy transfer through scales. Moreover, we demonstrate the weak nonlocality of the inverse cascade spectrum with a constant particle-number flux and find resulting logarithmic corrections to this spectrum.