Irrelevant Interactions without Composite Operators - A Remark on the Universality of Second Order Phase Transitions

We study the critical behaviour of symmetric $\phi^4_4$ theory including irrelevant terms of the form $\phi^{4+2n}/\Lambda_0^{2n}$ in the bare action, where $\Lambda_0$ is the UV cutoff (corresponding e.g. to the inverse lattice spacing for a spin system). The main technical tool is renormalization theory based on the flow equations of the renormalization group which permits to establish the required convergence statements in generality and rigour. As a consequence the effect of irrelevant terms on the critical behaviour may be studied to any order without using renormalization theory for composite operators. This is a technical simplification and seems preferable from the physical point of view. In this short note we restrict for simplicity to the symmetry class of the Ising model, i.e. one component $\phi^4_4$ theory. The method is general, however.Comment: 13 page

Coolant side heat transfer with rotation. Task 3 report: Application of computational fluid dynamics

An experimental and analytical program was conducted to investigate heat transfer and pressure losses in rotating multipass passages with configurations and dimensions typical of modern turbine blades. The objective of this program is the development and verification of improved analysis methods that will form the basis for a design system that will produce turbine components with improved durability. As part of this overall program, a technique is developed for computational fluid dynamics. The specific objectives were to: select a baseline CFD computer code, assess the limitations of the baseline code, modify the baseline code for rotational effects, verify the modified code against benchmark experiments in the literature, and to identify shortcomings in the code as revealed by the verification. The Pratt and Whitney 3D-TEACH CFD code was selected as the vehicle for this program. The code was modified to account for rotating internal flows, and these modifications were evaluated for flow characteristics of those expected in the application. Results can make a useful contribution to blade internal cooling

Estimation of time delay by coherence analysis

Using coherence analysis (which is an extensively used method to study the correlations in frequency domain, between two simultaneously measured signals) we estimate the time delay between two signals. This method is suitable for time delay estimation of narrow band coherence signals for which the conventional methods cannot be reliably applied. We show by analysing coupled R\"ossler attractors with a known delay, that the method yields satisfactory results. Then, we apply this method to human pathologic tremor. The delay between simultaneously measured traces of Electroencephalogram (EEG) and Electromyogram (EMG) data of subjects with essential hand tremor is calculated. We find that there is a delay of 11-27 milli-seconds ($ms$) between the tremor correlated parts (cortex) of the brain (EEG) and the trembling hand (EMG) which is in agreement with the experimentally observed delay value of 15 $ms$ for the cortico-muscular conduction time. By surrogate analysis we calculate error-bars of the estimated delay.Comment: 21 pages, 8 figures, elstart.cls file included. Accepted for publication in Physica