Riccati-parameter solutions of nonlinear second-order ODEs

It has been proven by Rosu and Cornejo-Perez in 2005 that for some nonlinear second-order ODEs it is a very simple task to find one particular solution once the nonlinear equation is factorized with the use of two first-order differential operators. Here, it is shown that an interesting class of parametric solutions is easy to obtain if the proposed factorization has a particular form, which happily turns out to be the case in many problems of physical interest. The method that we exemplify with a few explicitly solved cases consists in using the general solution of the Riccati equation, which contributes with one parameter to this class of parametric solutions. For these nonlinear cases, the Riccati parameter serves as a `growth' parameter from the trivial null solution up to the particular solution found through the factorization procedureComment: 5 pages, 3 figures, change of title and more tex

Painlev\'e Analysis, Prelle-Singer Approach, Symmetries and Integrability of Damped H\'enon-Heiles System

We consider a modified damped version of H\'enon-Heiles system and investigate its integrability. By extending the Painlev\'e analysis of ordinary differential equations we find that the modified H\'enon-Heiles system possesses the Painlev\'e property for three distinct parametric restrictions. For each of the identified cases, we construct two independent integrals of motion using the well known Prelle-Singer method. We then derive a set of nontrivial non-point symmetries for each of the identified integrable cases of the modified H\'enon-Heiles system. We infer that the modified H\'enon-Heiles system is integrable for three distinct parametric restrictions. Exact solutions are given explicitly for two integrable cases.Comment: Accepted for publication in Journal of Mathematical Physic

Exact solutions of coupled Li\'enard-type nonlinear systems using factorization technique

General solutions of nonlinear ordinary differential equations (ODEs) are in general difficult to find although powerful integrability techniques exist in the literature for this purpose. It has been shown that in some scalar cases particular solutions may be found with little effort if it is possible to factorize the equation in terms of first order differential operators. In our present study we use this factorization technique to address the problem of finding solutions of a system of general two-coupled Li\'enard type nonlinear differential equations. We describe a generic algorithm to identify specific classes of Li\'enard type systems for which solutions may be found. We demonstrate this method by identifying a class of two-coupled equations for which the particular solution can be found by solving a Bernoulli equation. This class of equations include coupled generalization of the modified Emden equation. We further deduce the general solution of a class of coupled ordinary differential equations using the factorization procedure discussed in this manuscript.Comment: Accepted for publication in J. Math. Phy

Current oscillations in a metallic ring threaded by a time-dependent magnetic flux

We study a mesoscopic metallic ring threaded by a magnetic flux which varies linearly in time PhiM(t)=Phi t with a formalism based in Baym-Kadanoff-Keldysh non-equilibrium Green functions. We propose a method to calculate the Green functions in real space and we consider an experimental setup to investigate the dynamics of the ring by recourse to a transport experiment. This consists in a single lead connecting the ring to a particle reservoir. We show that different dynamical regimes are attained depending on the ratio hbar Phi/Phi0 W, being Phi0=h c/e and W, the bandwidth of the ring. For moderate lengths of the ring, a stationary regime is achieved for hbar Phi/Phi0 >W. In the opposite case with hbar Phi/Phi0 < W, the effect of Bloch oscillations driven by the induced electric field manifests itself in the transport properties of the system. In particular, we show that in this time-dependent regime a tunneling current oscillating in time with a period tau=2piPhi0/Phi can be measured in the lead. We also analyze the resistive effect introduced by inelastic scattering due to the coupling to the external reservoir.Comment: 17 pages, 13 figure

On the complete integrability of a nonlinear oscillator from group theoretical perspective

In this paper, we investigate the integrability aspects of a physically important nonlinear oscillator which lacks sufficient number of Lie point symmetries but can be integrated by quadrature. We explore the hidden symmetry, construct a second integral and derive the general solution of this oscillator by employing the recently introduced $\lambda$-symmetry approach and thereby establish the complete integrability of this nonlinear oscillator equation from a group theoretical perspective.Comment: 15 page

Remote sensing and GIS in coral reef environment: An overview

Indian Coast line particularly Tamil Nadu, Andaman and Nicobar islands, Lakshadweep island and Gulf of Kachchh are characterized by mangroves, coral reefs, sea grass ,and seaweeds. The need for better monitoring and mapping of these resources has ' increased dramatically in recent yearn. The main aim of this paper is to review the potential of high resolution satellites used for coral reef ecosystem. Recent studies have warranted the usefulness of GIs for better planning and management practices of Coral conservation

Elastofibroma Dorsi: An Uncommon Benign Pseudotumour

Elastofibroma dorsi is an uncommon benign soft tissue pseudotumour usually located at the lower pole of the scapula, deep to serratus anterior, and often attached to the periosteum of the ribs, presenting with long history of swelling and occasionally pain and discomfort. This lesion is usually seen in patients over the age of 50 years and is not uncommonly mistaken as a malignant tumour because of its size and location deep to the periscapular muscles. Review of the orthopaedic oncology database of 17 500 patients revealed that there were 15 patients with elastofibroma dorsi. There were 12 males and 3 females, mean age at diagnosis of 68.4 years range 51–79 years. The diagnosis was confirmed by MRI in 3 patients, excision biopsy in 3 patients, trucut biopsy in 8 patients and open biopsy in 1 patient. Eight patients had excision of the lesion which was symptomatic. There have been no recurrences. We highlight the clinical and radiological presentation of elastofibroma dorsi to increase awareness of its existence and management

PP-waves, Israel's Matching conditions, Brane-world scenarios and BPS states in gravity

The matching between two 4-dimensional PP-waves is discussed by using Israel's matching conditions. Physical consequences on the dynamics of (cosmic) strings are analyzed. The extension to space-time of arbitrary dimension is discussed and some interesting features related to the brane world scenario, BPS states in gravity and Dirac-like quantization conditions are briefly described.Comment: 16 pages, no figures. Accepted for pubblication on Classical and Quantum Gravit

Observations on the recruitment of the Scleractinian coral in the Gulf of Mannar, India

Techniques to enhance natural recruitment in the restoration of coral reefs are being developed in many reef areas around the World. The Indian reefs, which were subjected to widescale destruction in the past due to several factors, natural as well as anthropogenic, also demand the understanding of coral recruitment patterns as the first step to evolve restorative measures. This study reports coral recruitment patterns at a reef location in Gulf of Mannar along southeast coast of India. Though the results of this study are preliminary, subsequent observations are recommended for a complete understanding on species-wise behavioural patterns and seasonal role in recruitment

Temporal Experiment for Storms and Tropical Systems Technology Demonstration (TEMPEST-D) Mission: Enabling Time-Resolved Cloud and Precipitation Observations from 6U-Class Satellite Constellations

The Temporal Experiment for Storms and Tropical Systems Technology Demonstration (TEMPEST-D) mission is to demonstrate the capability of 6U-Class satellite constellations to perform repeat-pass radiometry to measure clouds and precipitation with high temporal resolution on a global basis. The TEMPEST mission concept is to improve understanding of clouds and precipitation by providing critical information on their time evolution in different climatic regimes. Measuring at five frequencies from 89 to 182 GHz, TEMPEST-D millimeter-wave radiometers are capable of penetrating into the cloud to observe changes as precipitation begins or ice accumulates inside the storm. The TEMPEST-D flight model radiometer instrument has been completed, passed functional testing, vibration testing and self-compatibility testing with the XB1 spacecraft bus. The next steps for the TEMPEST-D millimeter-wave radiometer are thermal vacuum testing and antenna pattern measurements. The complete TEMPEST-D flight system will be delivered to NanoRacks for launch integration in the autumn of 2017, in preparation for launch to the ISS in the second quarter of 2018, with deployment shortly thereafter into a nominal orbit at 400-km altitude and 51.6° inclination