Illustrating Dynamical Symmetries in Classical Mechanics: The Laplace-Runge-Lenz Vector Revisited

The inverse square force law admits a conserved vector that lies in the plane of motion. This vector has been associated with the names of Laplace, Runge, and Lenz, among others. Many workers have explored aspects of the symmetry and degeneracy associated with this vector and with analogous dynamical symmetris. We define a conserved dynamical variable $\alpha$ that characterizes the orientation of the orbit in two-dimensional configuration space for the Kepler problem and an analogous variable $\beta$ for the isotropic harmonics oscillator. This orbit orientation variable is canonically conjugate to the angular momentum component normal to the plane of motion. We explore the canoncial one-parameter group of transformations generated by $\alpha (\beta).$ Because we have an obvious pair of conserved canonically conjugate variables, it is desirable to us them as a coordinate-momentum pair. In terms of these phase space coordinates, the form of the Hamiltonian is nearly trivial because neither member of the pair can occur explicitly in the Hamiltonian. From these considerations we gain a simple picture of the dynamics in phase space. The procedure we use is in the spirit of the Hamilton-Jacobi method.Comment: 15 pages, 1 figure, to be published in American Journal of Physic

Bayesian Cointegrated Vector Autoregression models incorporating Alpha-stable noise for inter-day price movements via Approximate Bayesian Computation

We consider a statistical model for pairs of traded assets, based on a Cointegrated Vector Auto Regression (CVAR) Model. We extend standard CVAR models to incorporate estimation of model parameters in the presence of price series level shifts which are not accurately modeled in the standard Gaussian error correction model (ECM) framework. This involves developing a novel matrix variate Bayesian CVAR mixture model comprised of Gaussian errors intra-day and Alpha-stable errors inter-day in the ECM framework. To achieve this we derive a novel conjugate posterior model for the Scaled Mixtures of Normals (SMiN CVAR) representation of Alpha-stable inter-day innovations. These results are generalized to asymmetric models for the innovation noise at inter-day boundaries allowing for skewed Alpha-stable models. Our proposed model and sampling methodology is general, incorporating the current literature on Gaussian models as a special subclass and also allowing for price series level shifts either at random estimated time points or known a priori time points. We focus analysis on regularly observed non-Gaussian level shifts that can have significant effect on estimation performance in statistical models failing to account for such level shifts, such as at the close and open of markets. We compare the estimation accuracy of our model and estimation approach to standard frequentist and Bayesian procedures for CVAR models when non-Gaussian price series level shifts are present in the individual series, such as inter-day boundaries. We fit a bi-variate Alpha-stable model to the inter-day jumps and model the effect of such jumps on estimation of matrix-variate CVAR model parameters using the likelihood based Johansen procedure and a Bayesian estimation. We illustrate our model and the corresponding estimation procedures we develop on both synthetic and actual data.Comment: 30 page

Three-fold way to extinction in populations of cyclically competing species

Species extinction occurs regularly and unavoidably in ecological systems. The time scales for extinction can broadly vary and inform on the ecosystem's stability. We study the spatio-temporal extinction dynamics of a paradigmatic population model where three species exhibit cyclic competition. The cyclic dynamics reflects the non-equilibrium nature of the species interactions. While previous work focusses on the coarsening process as a mechanism that drives the system to extinction, we found that unexpectedly the dynamics to extinction is much richer. We observed three different types of dynamics. In addition to coarsening, in the evolutionary relevant limit of large times, oscillating traveling waves and heteroclinic orbits play a dominant role. The weight of the different processes depends on the degree of mixing and the system size. By analytical arguments and extensive numerical simulations we provide the full characteristics of scenarios leading to extinction in one of the most surprising models of ecology

On a Spinner dolphin, Stenella longirostris (Gray) washed ashore at Mandapam, Gulf of Mannar

A dead dolphin was washed ashore at C.M.F.R.I. jetty along Gulf of Mannar coast on 19-7-200

Activation of defense enzymes in arecanut (Areca catechu L.) seedlings upon inoculation with biocontrol agents

The effect of soil application of three biocontrol agents viz., Pseudomonas fluorescens, Bacillus subtilis and Trichoderma viride on arecanut seedlings were studied with respect to the induction, dynamics and persistence of activity of the defense enzymes viz., peroxidase, poly phenol oxidase, phenyl alanine ammonia lyase, catalase and chitinase. Results showed that the biocontrol agents differed in their ability to activate different enzymes and sustain their persistence in the seedlings

A Comparision of Three Phase 27 Level Inverter Scheme under No Load and Multiple Load Conditions

Multilevel inverters have been used in the industrial as well as the drive applications. Here three phase system of the 27 level inverter scheme with and without loads have been presented by combining the three single phase inverters of various and asymmetrical voltage ranges. Here capacitors, batteries may be used for multiple dc sources in order to achieve high voltage output. It is shown that by implementing the single phase model in the three phase system the harmonic content is lowered even in the loaded conditions than compared to the single phase system. The proposed method can be validated and simulation is carried out with the help of MATLAB/Simulink software

The Effect of Thin Film Adhesives on Mode I Interlaminar Fracture Toughness in Carbon Fiber Composites with Shape Memory Alloy Inserts

Shape Memory Alloy (SMA) was placed within Polymer Matrix Composite (PMC) panels alongside film adhesives to examine bonding. Double cantilever beam (DCB) testing was performed using ASTM D5528. C-scanning was performed before testing, modal acoustic emissions (MAE) were monitored during testing, and microscopy performed post-test. Data was analyzed using modified beam theory (MBT), compliance calibration (CC) and modified compliance calibration (MCC) methods. Fracture toughness for control specimens was higher than previously reported due to fiber-bridging. Specimens with SMAs and adhesives stabilized crack propagation. Results revealed SMA-bridging; a phenomenon mimicking fiber-bridging which increased the load and fracture toughness of SMA specimens