International Journal of Geometric Methods in Modern Physics

In this paper, a canonical ensemble of fractional harmonic oscillator has been considered. Then by using the $q$-deformed formalism of super-statistic, thermodynamical properties of such an ensemble have been evaluated. The important point in this paper is that because of the existence of the fractional parameter, the partition functions, consequently and the other thermodynamical properties, can be analytically derived. Therefore, these quantities have been evaluated numerically. These quantities have been plotted in terms of temperature when the deformation and the fractional parameter vary. Effects of these parameters on the thermodynamical properties of the canonical ensemble have been discussed in detail.

Catheterization has an imperative rule in heat transfer investigations, which are frequently applied to analyze and deal with the heart transfer studies. Here, the entering of a catheter adjusts the flow of the blood and it affects the hemodynamic status in the artery region. In practical clinical cases, catheters cannot be precisely concentric with the artery. The impartial of this work is to investigate the behavior of a blood streaming characteristics, in the case of injecting the catheter eccentrically all the way through a stenotic overlapping artery. In this paper, we consider the heat transfer within the presence of blood corpuscle which has been characterized by a macroscopic two-phase model (i.e. a suspension of erythrocytes in plasma). The model here considers the blood fluid as a liquid fluid with adjourned particles in the gap bounded by the eccentric cylinder. The inside cylinder is identically rigid demonstrating the movable thin catheter and kept at constant temperature, where the outer cylinder is a taper cylinder demonstrating the artery that has overlapping stenosis and it is cooled and maintained at zero temperature. The coupled differential equations for both fluid (plasma) and particle (erythrocyte) phases have been solved. The expressions for the flow characteristics, namely, the flow rate, the impedance (resistance to flow), the wall shear stress and the temperature distribution, have been derived. The model is very useful in medicine, where the hemodynamic speed is higher for eccentric case than that of concentric one. Also, the temperature distribution and the entropy generation in the state of eccentric position are higher than in the case of the concentric position. A significant increase in the magnitude of the impedance and the wall shear stress occurs for an increase in the hematocrit, C for diseased blood.

Schwinger’s algebra of selective measurements has a natural interpretation in the formalism of groupoids. Its kinematical foundations, as well as the structure of the algebra of observables of the theory, were presented in [F. M. Ciaglia, A. Ibort and G. Marmo, Schwinger’s picture of quantum mechanics I: Groupoids, Int. J. Geom. Meth. Mod. Phys. (2019), arXiv: 1905.12274 [math-ph]. https://doi.org/10.1142/S0219887819501196. F. M. Ciaglia, A. Ibort and G. Marmo, Schwinger’s picture of quantum mechanics II: Algebras and observables, Int. J. Geom. Meth. Mod. Phys. (2019). https://doi.org/10.1142/S0219887819501366]. In this paper, a closer look to the statistical interpretation of the theory is taken and it is found that an interpretation in terms of Sorkin’s quantum measure emerges naturally. It is proven that a suitable class of states of the algebra of virtual transitions of the theory allows to define quantum measures by means of the corresponding decoherence functionals. Quantum measures satisfying a reproducing property are described and a class of states, called factorizable states, possessing the Dirac–Feynman “exponential of the action” form are characterized. Finally, Schwinger’s transformation functions are interpreted similarly as transition amplitudes defined by suitable states. The simple examples of the qubit and the double slit experiment are described in detail, illustrating the main aspects of the theory.

We show the nonpositivity of the Einstein–Hilbert action for conformal flat Riemannian metrics on noncommutative 4-torus. In addition, we prove that this action vanishes only when the metric is constant flat. This recovers an earlier result of Fathizadeh–Khalkhali in the setting of spectral triples on noncommutative 4-torus. We also give a new proof of their result. Furthermore, computations of the gradient flow and the scalar curvature of noncommutative 4-torus are given.

In this paper, we study the quantum dynamics of an electron/hole in a two-dimensional quantum ring within a spherical space. For this geometry, we consider a harmonic confining potential. Suggesting that the quantum ring is affected by the presence of an Aharonov–Bohm flux and a uniform magnetic field, we solve the Schrödinger equation for this problem and obtain exactly the eigenvalues of energy and corresponding eigenfunctions for this nanometric quantum system. Afterwards, we calculate the magnetization and persistent current are calculated, and discuss influence of curvature of space on these values.

In geometrothermodynamics (GTD), to study the geometric properties of the equilibrium space, three thermodynamic metrics have been proposed so far. These metrics are obtained by using the condition of Legendre invariance and can be computed explicitly once a thermodynamic potential is specified as fundamental equation. We use the remaining diffeomorphism invariance in the phase and equilibrium spaces to show that the components of the GTD-metrics can be interpreted as the second moment of the fluctuation of a new thermodynamic potential. This result establishes a direct connection between GTD and fluctuation theory. In this way, the diffeomorphism invariance of GTD allows us to introduce new thermodynamic coordinates and new thermodynamic potentials, which are not related by means of Legendre transformations to the fundamental thermodynamic potentials.

Cosmological solutions in the Randall–Sundrum (RS) type II brane-world model including Gauss–Bonnet (GB) term, in the presence of a bulk viscous cosmological fluid are discussed. Transport equations described by Eckart and Israel Stewart are implemented here. Cosmological models admitting emergent universe (EU) of the early universe is explored here in the presence of imperfect fluid described by Eckart theory and Truncated Israel Stewart (TIS) theory and Full Israel Stewart (FIS) theory. We also study the permitted values of the EU model parameters by considering cosmological observational dataset. The stability analysis of the equilibrium points of the dynamical system associated with the evolution in the RS brane including GB term are studied in Eckart theory, TIS theory and FIS theory.

In this study, we analyze the complexity factor that is extended up to the dynamical spherically symmetric non-static case with anisotropic dissipative self-gravitating fluid distribution in context of $f(R)$ theory of gravity. For this evaluation we choose the particular $f(R)$ model that signifies the physical nature of the self-gravitating system. The proposed work discusses not only the complexity factor of the structure of the fluid distribution, but also defines the minimization rate of complexity of the pattern of evolution. Here, first we have applied similar approach for obtaining the structure scalar $Y_{TF}$ of the complexity factor as used for in the static case, and next we have described explicitly the dissipative and non-dissipative cases by assuming the simplest pattern of evolution (homologous condition). It has been found that the system configuration fulfills the vanishing condition of complexity factor and emerging homologously, corresponds to a energy density homogeneity, shearfree and geodesic, isotropic in pressure. Moreover, we define the stability results for the vanishing complexity factor condition. Finally, we would like to mention that these results are satisfying the prior investigation about complexity factor in General Relativity (GR) by setting $\beta =0$.

In this work, we have made an attempt to investigate the dark energy possibility from the thermodynamical point of view. For this purpose, we have studied thermodynamic stability of three popular dark energy models in the framework of an expanding, homogeneous, isotropic and spatially flat FRW Universe filled with dark energy and cold dark matter. The models considered in this work are Chevallier–Polarski–Linder (CPL) model, Generalized Chaplygin Gas (GCG) model and Modified Chaplygin Gas (MCG) model. By considering the cosmic components (dark energy and cold dark matter) as perfect fluid, we have examined the constraints imposed on the total equation of state parameter ($w_T$) of the dark fluid by thermodynamics and found that the phantom nature ($w_T<-1$) is not thermodynamically stable. Our investigation indicates that the dark fluid models (CPL, GCG and MCG) are thermodynamically stable under some restrictions of the parameters of each model.

We consider an elastic medium with a disclination and investigate the topological effects on the interaction of a spinless electron with radial electric fields through the WKB (Wentzel, Kramers, Brillouin) approximation. We show how the centrifugal term of the radial equation must be modified due to the influence of the topological defect in order that the WKB approximation can be valid. Then, we search for bound states solutions from the interaction of a spinless electron with the electric field produced by this linear distribution of electric charges. In addition, we search for bound states solutions from the interaction of a spinless electron with radial electric field produced by uniform electric charge distribution inside a long non-conductor cylinder.

This paper deals with the study of the effect of Maxwell’s nonlinear electrodynamics (NLED) in the framework of Dvali–Gabadadze–Porrati (DGP) brane gravity for Friedmann–Robertson–Walker (FRW) Universe. Recently, the Hawking temperature and Bekenstein entropy have been modified for the validity of the thermodynamical laws at the event horizon. In this context, we test the validity of the generalized second law of thermodynamics (GSLT) at the apparent and event horizons. Here, the entropy of the horizon has been extracted for the following two cases: (i) by assuming the first law of thermodynamics (ii) by using modified entropy-area relation. In the case of apparent horizon, we consider the usual Hawking temperature. On the other hand, in the case of event horizon, we consider the modified Hawking temperature. Next, we discuss the geometrical parameters (deceleration, statefinder parameters and $Om$ diagnostic) to explore the expansion of the accelerating Universe. From the general expression of GSLT, we find that for the apparent horizon, the GSLT always holds for any choice of model parameters in both the branches of the DGP model. However, the null energy condition must satisfy for the plausibility of GSLT at the event horizon. Finally, we use the recent observational data from Stern datasets, Baryon Acoustic Oscillations (BAO), Cosmic Microwave Background (CMB) and Type Ia Supernovae (SNIa) observations to hold down the model parameters. Our analysis reveals that the DGP braneworld is free from classical instability issues and also cannot be ruled out by present thermodynamical and observational constraints.

This paper explores the physical attributes of a static axial source that induce complexity within the fluid in the background of self-interacting Brans–Dicke theory. Bel’s approach is used to split the Riemann tensor and construct structure scalars that involve physical features of the fluid in the presence of scalar field. Using the evolution equations derived from Bianchi identities as well as structure scalars, five complexity factors are identified which include constraints on the scalar field. Finally, the conditions of vanishing complexity are used to present solutions for an anisotropic inhomogeneous spheroid. It is concluded that scalar field is an additional source of complexity.

Confining the traveling trajectory of a tachyon to the two-dimensional Lorentzian space forms, we describe the trajectory as a spacelike front in these Lorentzian space forms. Introducing the differential geometry of singular curves in Lorentzian space forms, that is, the hyperbolic space and de Sitter space, and applying the Legendrian duality theorems, we establish the moving frame along the front, whereby the definitions of the evolutes of spacelike fronts in Lorentzian space forms are presented and the geometric properties of these evolutes are investigated in detail. It is shown that these evolutes can be interpreted as wavefronts under the viewpoint of Legendrian singularity theory.

Work reported in this study demonstrates the reconstruction schemes for the $f(G)$ gravity in the framework of bulk viscosity and holographic background evolution by considering the universe filled by the viscous fluid that is just special class of more general fluids as described in Nojiri and Odintsov [Inhomogeneous equation of state of the universe: Phantom era, future singularity, and crossing the phantom barrier, Phys. Rev. D 72 (2005) 023003]. The bulk viscous pressure has been considered as $\mathrm{\Pi }=-3H\xi$, with $\xi ={\xi }_0+{\xi }_{1}H+{\xi }_2(Ḣ+H^2)$. Considering the scale factor in power law form and taking holographic dark energy (HDE) with density ${\rho }_{\mathrm{\Lambda }}=3c^3{M}_p^2{L}^{-2}$ and generalized extended holographic dark energy (EGHRDE) with density ${\rho }_{\mathrm{\Lambda }}=3c^2(\alpha Ḣ+\beta H^2)$, a specific case of Nojiri–Odintsov holographic DE ([Unifying phantom inflation with late-time acceleration: Scalar phantom–non-phantom transition model and generalized holographic dark energy, Gen. Relativ. Gravit. 38 (2006) 1285]) we have derived solutions for $f(G)$ and the subsequent effective equation of state parameters have been found to behave like quintom irrespective of the choice of $c^2$. Finally, considering $f(G)$ as quintessence scalar field we have explored the possibility of quasi-exponential expansion and warm inflation.

Recent observers have shown that an anisotropy cosmic expansion may exist. In this work, we study the effects of low anisotropy with Bianchi type I model using the current observational data, which includes the supernova Legacy Survey (SNLS) sample of 238 SN events ($0.15<z<1.1$) and 1048 Pantheon sample confirmed type Ia supernova (SNIa) covering the redshift range $0.01<z<2.3$. Assuming an anisotropic universe, we use the two parametrizations of the dark energy equation-of-state, such as the $w(z)=w_0+w_{1}z$ (PA) and $w(z)=w_0+w_1\frac{z}{1+z}$ (PB), and then we fit the SNIa light-curve parameters and free cosmological parameters, simultaneously employing maximum likelihood estimation method. When combining the Baryon Acoustic Oscillations (BAO) and the observational Hubble data (OHD) measurements with the SNLS SN sample, we find ${\mathrm{\Omega }}_m=0.258\pm 0.019$, ${\mathrm{\Omega }}_{\sigma }=(-1.19\pm 1.97)\times 10^{-3}$, $w_0=-1.19\pm 0.122$, and $w_1=0.4499\pm 0.59$ for the PA model and ${\mathrm{\Omega }}_m=0.259\pm 0.021$, ${\mathrm{\Omega }}_{\sigma }=(-6.25\pm 7.08)\times 10^{-4}$, $w_0=-1.2\pm 0.186$, and $w_1=0.63\pm 1.17$ for the PB model. When combining also Pantheon data, we obtain ${\mathrm{\Omega }}_m=0.269\pm 0.018$, ${\mathrm{\Omega }}_{\sigma }=(-4.33\pm 5.45)\times 10^{-3}$, $w_0=-1.124\pm 0.061$, and $w_1=0.733\pm 0.42$ for the PA model and ${\mathrm{\Omega }}_m=0.267\pm 0.0197$, ${\mathrm{\Omega }}_{\sigma }=(-16.88\pm 8.64)\times 10^{-4}$, $w_0=-1.17\pm 0.084$, and $w_1=1.098\pm 0.55$ for the PB model. The analysis shows that by considering the anisotropy effects, it leads to more best-fit parameters in $w_0{w}_1$CDM model with the current observational data.

In 2000, Dvali et al. [4-D gravity on a brane in 5-D Minkowski space, Phys. Lett. B 485 (2000) 208–214] proposed a new braneworld model named as DGP model, having two branches with $(𝜖=\pm 1)$. Former one $(𝜖=+1)$ known as accelerating branch, which explains accelerating phase of the Universe without adding cosmological constant or Dark energy (DE), whereas later one $(𝜖=-1)$ represents the decelerating branch. Here, we have investigated the behavior of Generalized Ghost Dark Energy (GGDE) under the decelerating branch of DGP model. We have studied the importance of GGDE model to explain the current phase of the Universe. To check the validity of the present model, we study the behavior of different cosmological parameters such as Hubble parameter, equation of state (EoS) parameter and deceleration parameter with respect to scale factor. Then, we have analyzed the ${\omega }_D-\acute{{\omega }_D}$ to confirm no freezing region of this study and point out thawing region. Furthermore, we have checked the gradient of stability by calculating the squared sound speed. Then, we extend our study to check the viability of this model under investigation through the analysis of statefinder diagnosis parameters for the present cosmological setup.

In this paper, we study null helices, Cartan slant helices and two special developable surfaces associated to them in Lorentz–Minkowski 3-space. We give a method using a special plane curve to construct a null helix. We also define the null tangential Darboux developable of a null Cartan curve, and we give a classification of singularities of it. Moreover, we study the relationship between null helices (or Cartan slant helices) with the developable surfaces of them.

Motivated by the hindrance of defining metric tensors compatible with the underlying spinor structure, other than the ones obtained via a conformal transformation, we study how some geometric objects are affected by the action of a disformal transformation in the closest scenario possible: the disformal transformation in the direction of a null-like vector field. Subsequently, we analyze symmetry properties such as mutual geodesics and mutual Killing vectors, generalized Weyl transformations that leave the disformal relation invariant, and introduce the concept of disformal Killing vector fields. In most cases, we use the Schwarzschild metric, in the Kerr–Schild formulation, to verify our calculations and results. We also revisit the disformal operator using a Newman–Penrose basis to show that, in the null-like case, this operator is not diagonalizable.