Inflation with f(R,ϕ)f(R,\phi) in Jordan frame

We consider an $f(R)$ action that is non-minimally coupled to a massive scalar field. The model closely resembles scalar-tensor theory and by conformal transformation can be transformed to Einstein frame. To avoid the ambiguity of the frame dependence, we obtain an exact analytical solution in Jordan frame and show that the model leads to a period of accelerated expansion with an exit. Further, we compute the scalar and tensor power spectrum for the model and compare them with observations.Comment: 10 pages, 3 figure

Exact inflationary solutions in exponential gravity

We consider a modified gravity model of the form $f(R,\phi)=R e^{h(\phi)R}$, where the strong gravity corrections are taken to all orders and $\phi$ is a self-interacting massless scalar field. We show that the conformal transformation of this model to Einstein frame leads to non-canonical kinetic term and negates the advantage of the Einstein frame. We obtain exact solutions for the background in the Jordan frame without performing conformal transformations and show that the model leads to inflation with exit. We obtain scalar and tensor power-spectrum in Jordan frame and show that the model leads to red-tilt. We discuss the implications of the same in the light of cosmological observations.Comment: 17 pages, 4 figures, 2 table

Large scale flow around turbulent spots

Numerical simulations of a model of plane Couette flow focusing on its in-plane spatio-temporal properties are used to study the dynamics of turbulent spots.Comment: 16 pages, 6 figure

Hyper-Rayleigh scattering in centrosymmetric systems

Hyper-Rayleigh scattering (HRS) is an incoherent mechanism for optical second harmonic generation. The frequency-doubled light that emerges from this mechanism is not emitted in a laser-like manner, in the forward direction; it is scattered in all directions. The underlying theory for this effect involves terms that are quadratic in the incident field and involves an even-order optical susceptibility (for a molecule, its associated hyperpolarizability). In consequence, HRS is often regarded as formally forbidden in centrosymmetric media. However, for the fundamental three-photon interaction, theory based on the standard electric dipole approximation, representable as E13, does not account for all experimental observations. The relevant results emerge upon extending the theory to include E12M1 and E12E2 contributions, incorporating one magnetic dipolar or electric quadrupolar interaction, respectively, to a consistent level of multipolar expansion. Both additional interactions require the deployment of higher orders in the multipole expansion, with the E12E2 interaction analogous in rank and parity to a four-wave susceptibility. To elicit the correct form of response from fluid or disordered media invites a tensor representation which does not oversimplify the molecular components, yet which can produce results to facilitate the interpretation of experimental observations. The detailed derivation in this work leads to results which are summarized for the following: perpendicular detection of polarization components both parallel and perpendicular to the pump radiation, leading to distinct polarization ratio results, as well as a reversal ratio for forward scattered circular polarizations. The results provide a route to handling data with direct physical interpretation, to enable the more sophisticated design of molecules with sought nonlinear optical properties

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Development of a Friction Rig and Experimental Results

The development of a friction rig, which is integrated into a milling machine for testing the frictional characteristics of various types of materials and specimen shapes are described. This is followed by the experimental technique used to measure the friction coefficient for different experimental conditions. The results obtained indicate the frictional coefficient obtained changes with the specimen type, contact area and lubrication condition. The results obtained are also compared to available published results. The discussions and conclusions related to the development and experimental results are finally presented

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