Noether symmetries of LRS Bianchi type-I spacetime in f(ℛ,φ,χ) gravity

This paper investigates the Noether symmetry approach in modified [Formula: see text] theory of gravity, where [Formula: see text] is the Ricci scalar, [Formula: see text] is a scalar field and [Formula: see text] is the kinetic energy term. For this purpose, we consider Locally Rotationally Symmetric (LRS) Bianchi Type-I spacetimes. The cosmological solutions are developed through Noether symmetry approach. The determining equations are computed in the context of a point-like Lagrangian for [Formula: see text] gravity. In particular, three different cases are taken into account for the LRS Bianchi Type-I spacetimes. Some important conserved quantities for the Lagrangian in this modified theory of gravity are worked out through the determining equations. In this scenario, the graphical behavior of energy density, pressure component and equation of state parameter are reported and analyzed with the help of first integrals of motion. The negative trends of the strong energy conditions actually suggest that the said theory supports expanding Universe with dark energy.

Some aspects of modified theory of gravity in Palatini formalism unveiled

Under conformal transformation, [Formula: see text] theory of gravity in Palatini formalism leads to a Brans–Dicke type of scalar-tensor equivalent theory with a wrong sign in the effective kinetic energy term. This means that the effective scalar acts as the dark energy and so late-time cosmic acceleration in the matter-dominated era is accountable. However, we unveil some aspects of Palatini formalism, which reveals the fact that the formalism is not suitable to explain the cosmological evolution of the early universe with [Formula: see text] gravity alone. Additionally, it is noticed that some authors, in an attempt to explore Noether symmetry of the theory changed the sign of the kinetic term and hence obtained the wrong answer. Here, we make the correction and unmask a very interesting aspect of symmetry analysis. Mathematical inequivalence between Jordan’s and Einstein’s frame in Palatini [Formula: see text] theory has also been revealed.

Dynamical system analysis for DBI dark energy interacting with dark matter

A dynamical system analysis related to Dirac–Born–Infeld (DBI) cosmological model has been investigated in this present work. For spatially flat FRW spacetime, the Einstein field equation for DBI scenario has been used to study the dynamics of DBI dark energy interacting with dark matter. The DBI dark energy model is considered as a scalar field with a nonstandard kinetic energy term. An interaction between the DBI dark energy and dark matter is considered through a phenomenological interaction between DBI scalar field and the dark matter fluid. The field equations are reduced to an autonomous dynamical system by a suitable redefinition of the basic variables. The potential of the DBI scalar field is assumed to be exponential. Finally, critical points are determined, their nature have been analyzed and corresponding cosmological scenario has been discussed.

Low temperature specific heat anomaly in electron doped R2-xCexCuO4 superconductors

The electron doped rare earth copper oxide superconductors R 2-x Ce x CuO 4 exhibit anomalous heavy fermion behavior at low temperature with large Sommerfeld specific heat coefficient which is different from the conventional heavy fermion systems. The system is described by a model Hamiltonian consisting of staggered magnetic field in the two sub-lattices of the copper sites in presence of hybridization between the localized 4f electrons of Nd atom and the conduction electrons as well as the f-electron kinetic energy term. The Hamiltonian is solved by Zubarev's Green's function technique and the sub-lattice magnetization is calculated and solved self-consistently. The entropy and specific heat are calculated from the free energy of the system. The temperature dependent entropy and specific heat are numerically evaluated by successive differentiations of sub-lattice magnetization and temperature dependent entropy. It is observed that when the position of the f-level of Nd atom is of the order of hybridization strength, the sub-lattice magnetization is destroyed drastically at lower temperatures. As a result, the specific heat exhibits a large enhancement at low temperatures suggesting the enhancement of the electron density of states and the effective mass of the itinerant electrons exhibiting the heavy fermion character. Similarly, the specific heat shows anomalously sharp jump near the Néel temperature.

Comparative assesment of steady-state pipeline gas flow models / Analiza porównawcza modeli przepływu gazu w rurociągu w stanach ustalonych

One-dimensional, non-isothermal flow of gas in a straight pipe has been considered to predict pressure and temperature profiles along the horizontal pipeline under steady-state conditions. Selected analytical models for the simplified calculation of these profiles are evaluated on the basis of the numerical solution of the accurate model, which incorporates the convective term in the momentum equation and the kinetic energy term in the energy equation, while treating the enthalpy as a function of pressure and temperature. For closure of the system of the conservation equations, the GERG 2004 equation of state was chosen. In order to present the discrepancies introduced by the models, the results of the numerical and analytical solutions are compared with the field data. The results show that in the case of the high pressure gas transmission system, the effects of the convective term in the momentum equation and the kinetic energy term in the energy equation are negligible for pipeline pressure and temperature calculation accuracies. It also indicates that real gas effects play an important role in the temperature distribution along the pipeline and cannot be neglected from the calculation when approximate analytical equations are used.

Design and Validation of a Probe for Spatially and Temporally Resolved Measurements of Vorticity and Strain Rates in Compressible Turbulence Interactions

A custom-made hot-wire vorticity probe was designed and developed capable of measuring the time-dependent highly fluctuating three dimensional velocity and vorticity vectors, and associated total temperature, in non-isothermal and inhomogeneous flows with reasonable spatial and temporal resolution. These measurements allowed computation of the vorticity stretching/tilting terms, vorticity generation through dilatation terms, full dissipation rate of the kinetic energy term and full rate-of-strain tensor. The probe has been validated experimentally in low-speed boundary layers and used in the CCNY Shock Tube Research Facility, where interactions of planar expansion waves or shock waves with homogeneous and isotropic turbulence have been investigated at several Reynolds numbers.

STATEFINDER PARAMETERS FOR QUINTOM DARK ENERGY MODEL

We perform in this paper a statefinder diagnostic to a dark energy model with two scalar fields, called "quintom," where one of the scalar fields has a canonical kinetic energy term and the other has a negative one. Several kinds of potentials are discussed. Our results show that the statefinder diagnostic can differentiate quintom model with other dark energy models.