A new class of cosmological models in f (R, T ) modified theories of gravity proposed by Harko et al. (2011), has been investigated for a specific choice of f (R, T ) = f1(R) + f2(T ) by considering time dependent deceleration parameter. The concept of time dependent deceleration parameter (DP) with some proper assumptions yield the average scale factor a(t) = sinh 1 n (αt), where n and α are positive constants. For 0 < n ≤ 1, this generates a class of accelerating models while for n > 1, the models of universe exhibit phase transition from early decelerating phase to present accelerating phase which is in good agreement with the results from recent astrophysical observations. Our intention is to reconstruct f (R, T ) models inspired by this special law for the deceleration parameter in connection with the theories of modified gravity. In the present study we consider the cosmological constant Λ as a function of the trace of the stress energymomentum-tensor, and dub such a model "Λ(T ) gravity" where we have specified a certain form of Λ(T ). Such models may display better uniformity with the cosmological observations. The statefinder diagnostic pair {r, s} parameter has been embraced to characterize different phases of the universe. We also discuss the physical consequences of the derived models.
The present paper is concerned with the investigation of disturbances in a homogeneous, isotropic, generalized thermo-viscoelastic diffusion material with voids under the influence of magnetic field. The formulation is applied to the generalized thermoelasticity theory under the Lord–Shulman and the classical dynamical coupled theories. The analytical expressions for the physical quantities are obtained in the physical domain by using the normal mode analysis. These expressions are calculated numerically for a specific material and explained graphically. Comparisons are made with the results predicted by the Lord–Shulman and the coupled theories in the presence and absence of the magnetic field and diffusion.
Purpose
The purpose of this paper is to study the effect of rotation and gravity on a homogeneous, isotropic, and generalized thermo-viscoelastic material with voids. The problem is studied in the context of the coupled theory, Lord-Shulman theory with one relaxation time, and Green-Lindsay theory with two relaxation times.
Design/methodology/approach
The analytical method used was the normal mode analysis technique.
Findings
Numerical results for the physical quantities were analyzed and presented graphically. The graphical results indicated that the effects of rotation and gravity were observable physical effects on the thermo-viscoelastic material with voids. Comparisons were made between the results obtained in the absence and presence of rotation and gravity.
Originality/value
In the present work, the authors investigated the effect of rotation and gravity on thermo-viscoelastic medium with voids. Comparisons were also made between the three theories in the absence and the presence of rotation and gravity. Such problems are very important in many dynamical systems.
The article investigates the residual stresses arising in a thermoelastic cylinder as a result of layer-by-layer deposition of material on its lateral surface. Residual stresses are defined as the limiting values of internal stresses developing during the technological process. Internal stresses are caused by incompatible deformations that accumulate in the body as a result of joining parts with different temperatures. For the analysis of internal stresses, an analytical solution of the axisymmetric quasi-static problem of thermoelasticity for a layer-by-layer growing cylinder is constructed. It is shown that the distribution of residual stresses dependson the scenario of the surfacing process. In this case, the supply of additional heat to the growing body can significantly reduce the unevenness of the temperature fields and reduce the intensity of residual stresses. The most effective is uneven heating, which can be realized, for example, by the action of an alternating current with a tunable excitation frequency. This is illustrated by the calculations performed using the constructedanalytical solution.
In this paper, we have constructed a flat Friedmann-Robertson-Walker (FRW) cosmological model in f ðR; TÞ gravity. The solution of Friedmann equations has been obtained assuming the quadratic equation of state p ¼ αρ þ βρ 2 , where α and β are parameters. The model describes an accelerating universe with positive energy density, negative pressure and negative cosmological constant. The behaviour of the deceleration parameter shows that the universe accelerates after an epoch of deceleration in a good agreement with recent observations. The nonconventional scenario for an accelerating universe with negative cosmological constant has been discussed.
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