Reel Notes

https://orc.library.atu.edu/atu_reel390/1002/thumbnail.jp

A feynman path integral representation for elastic wave scattering by anisotropic weakly perturbations

We write a space-time Feynman path integral representation for scattered elastic wave fields from a weakly compact supported anisotropic non-homogeneity.Replacement by a new version where We (I!) propose a new tomographic inversion methodology based solely in the wave sampling of the Ray paths through Monte Carlo path integral sampling Holding thus great potentiality for Navy's advanced Sonar detection .Comment: 8 page

An electromyographic evaluation of dual role breathing and upper body muscles in response to front crawl swimming

The upper body trunk musculature is key in supporting breathing, propulsion, and stabilization during front crawl swimming. The aim of this study was to determine if the latissimus dorsi, pectoralis major, and serratus anterior contributed to the development of inspiratory muscle fatigue observed following front crawl swimming. Fourteen trained swimmers completed a 200-m front crawl swim at 90% of race pace. Maximal inspiratory and expiratory mouth pressures (PImax and PEmax) were assessed before (baseline) and after each swim, and electromyography was recorded from the three muscles. Post-swim PImax fell by 11% (P < 0.001, d = 0.57) and the median frequency (MDF: a measure of fatigue) of the latissimus dorsi, pectoralis major, and serratus anterior fell to 90% (P = 0.001, d = 1.57), 87% (P = 0.001, r = −0.60) and 89% (P = 0.018, d = 1.04) of baseline, respectively. The fall in serratus anterior MDF was correlated with breathing frequency (r = 0.675, P = 0.008) and stroke rate (r = 0.639, P = 0.014). The results suggest that the occurrence of inspiratory muscle fatigue was partly caused by fatigue of these muscles, and that breathing frequency and stroke rate particularly affect the serratus anterior

Modelling the structure of star clusters with fractional Brownian motion

The degree of fractal substructure in molecular clouds can be quantified by comparing them with Fractional Brownian Motion (FBM) surfaces or volumes. These fields are self-similar over all length scales and characterised by a drift exponent $H$, which describes the structural roughness. Given that the structure of molecular clouds and the initial structure of star clusters are almost certainly linked, it would be advantageous to also apply this analysis to clusters. Currently, the structure of star clusters is often quantified by applying $\mathcal{Q}$ analysis. $\mathcal{Q}$ values from observed targets are interpreted by comparing them with those from artificial clusters. These are typically generated using a Box-Fractal (BF) or Radial Density Profile (RDP) model. We present a single cluster model, based on FBM, as an alternative to these models. Here, the structure is parameterised by $H$, and the standard deviation of the log-surface/volume density $\sigma$. The FBM model is able to reproduce both centrally concentrated and substructured clusters, and is able to provide a much better match to observations than the BF model. We show that $\mathcal{Q}$ analysis is unable to estimate FBM parameters. Therefore, we develop and train a machine learning algorithm which can estimate values of $H$ and $\sigma$, with uncertainties. This provides us with a powerful method for quantifying the structure of star clusters in terms which relate to the structure of molecular clouds. We use the algorithm to estimate the $H$ and $\sigma$ for several young star clusters, some of which have no measurable BF or RDP analogue.Comment: 11 Pages, accepted by MNRA

Mechanical Systems: Symmetry and Reduction

Reduction theory is concerned with mechanical systems with symmetries. It constructs a lower dimensional reduced space in which associated conservation laws are taken out and symmetries are \factored out" and studies the relation between the dynamics of the given system with the dynamics on the reduced space. This subject is important in many areas, such as stability of relative equilibria, geometric phases and integrable systems

Characterising lognormal fractional-Brownian-motion density fields with a Convolutional Neural Network

In attempting to quantify statistically the density structure of the interstellar medium, astronomers have considered a variety of fractal models. Here we argue that, to properly characterise a fractal model, one needs to define precisely the algorithm used to generate the density field, and to specify -- at least -- three parameters: one parameter constrains the spatial structure of the field; one parameter constrains the density contrast between structures on different scales; and one parameter constrains the dynamic range of spatial scales over which self-similarity is expected (either due to physical considerations, or due to the limitations of the observational or numerical technique generating the input data). A realistic fractal field must also be noisy and non-periodic. We illustrate this with the exponentiated fractional Brownian motion (xfBm) algorithm, which is popular because it delivers an approximately lognormal density field, and for which the three parameters are, respectively, the power spectrum exponent, $\beta$, the exponentiating factor, ${\cal S}$, and the dynamic range, ${\cal R}$. We then explore and compare two approaches that might be used to estimate these parameters: Machine Learning and the established $\Delta$-Variance procedure. We show that for $2\leq\beta \leq 4$ and $0\leq{\cal S}\leq 3$, a suitably trained Convolutional Neural Network is able to estimate objectively both $\beta$ (with root-mean-square error $\epsilon_{_\beta}\sim 0.12$) and ${\cal S}$ (with $\epsilon_{_{\cal S}}\sim 0.29$). $\;\Delta$-variance is also able to estimate $\beta$, albeit with a somewhat larger error ($\epsilon_{_\beta}\sim 0.17$) and with some human intervention, but is not able to estimate ${\cal S}$

Voltera's Solution of the Wave Equation as Applied to Three-Dimensional Supersonic Airfoil Problems

A surface integral is developed which yields solutions of the linearized partial differential equation for supersonic flow. These solutions satisfy boundary conditions arising in wing theory. Particular applications of this general method are made, using acceleration potentials, to flat surfaces and to uniformly loaded lifting surfaces. Rectangular and trapezoidal plan forms are considered along with triangular forms adaptable to swept-forward and swept-back wings. The case of the triangular plan form in sideslip is also included. Emphasis is placed on the systematic application of the method to the lifting surfaces considered and on the possibility of further application